National Bureau ot Standards AUG 81972

MSI
Solid State Chemistry

Proceedings of the 5th Materials Research

Symposium sponsored by the Institute for

Materials Research, National Bureau of

Standards, October 18-21, 1971 held at Gaithersburg,

Maryland

Edited by

Robert S. Roth and Samuel J. Schneider, Jr.

Institute for Materials Research

OxS> National Bureau of Standards

U.S. DEPARTMENT OF COMMERCE, Peter G. Peterson, Secretary

NATIONAL BUREAU OF STANDARDS, Lawrence M. Kushner, Acting Director

Issued July 1972
Library of Congress Catalog Card Number: 72-600031

National Bureau of Standards Special Publication 364

Nat. Bur. Stand. (U.S.), Spec. Publ. 364, 799 pages (July 1972)

Issued July 1972

For sale hy the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 (Order by SD Catalog No. C 13.10:364). Price $7.50. Stock Number 0303-1007
GENERAL ABSTRACT

This book presents the proceedings of the 5th Materials Research SymposiiJin on "Solid State Chemistry" held at the National Bureau of Standards, Gaithersburg , Maryland

on October 18-21, 1971. The symposium was sponsored by the Institute for Materials Research,

NBS. The purpose of the conference was to explore the realm of new inorganic crystalline

materials emphasizing crystal chemical and structural aspects, providing a forum for

discussion of new research problems and techniques . A total of 56 invited and contributed

papers were presented. In addition, the symposium included three unscheduled talks and an open discussion period consisting of four impromptu lectures on very current subjects

dealing with nonstoichiometry . The proceedings are divided into four main groupings, I Oxides, II Bromides, Carbides, Silicides, and Related Materials, III Chalcogenides and IV Open Discussion and Nonstoichiometry. An edited version is given on the floor discussion

following each paper.

Key Words: Chalcogenides; crystallographic shear; electron optical lattice images;'

lone pair geometry; nonstoichiometry; oxides; refractory hard metals;

Solid State Chemistry.

i i i

FOREWORD

Progress of modern technology requires a cooperative and intensive effort on the part

of academic, industrial, and government scientists to provide fundamental data on the

properties of materials. Effective dissemination of these data are essential for maximum

impact on technology and the Institute for Materials Research, through its regularly

scheduled symposia, strives to assure the availability of this basic information. These

symposia provide an ideal platform for discussion of current research problems and for a free exchange of ideas and thoughts.

The 5th Materials Research Symposium has as its subject. Solid State Chemistry, a seemingly broad and all encompassing field. Research in this area, however, is materials

oriented rather than along traditional disciplines, and chemists, ceramists, metallurgists,

and crystallographers alike, are intimately involved. The field of Solid State Chemistry

primarily is concerned with the structures, chemical properties, reactivities, and general

chemical character of solids per se, and consequently an overlap of disciplines is required

for significant research. Only in the past ten years or so has Solid State Chemistry as an entity come to the forefront. The Institute for Materials Research, through the Inorganic

Materials Division, organized the symposium to bring together world wide experts and in

doing so, hopes to stimulate further growth in this promising new field.

The National Bureau of Standards is pleased to present the Proceedings of the Symposium

on Solid State Chemistry. Publication of this text expresses our appreciation to the

participants and to all those who contributed to make this a successful conference.

J. B. WACHTMAN, JR. Chief, Inorganic Materials Division

J. D. HOFFMAN

Director, Institute for Materials Research

PREFACE

The purpose of this conference was to explore the realm of new inorganic materials,

emphasizing crystal-chemical and structural aspects, thus providing a forum for discussion

of new research problems and techniques.

The conference was concerned with all aspects of research on the chemical behavior

of crystalline inorganic substances in the solid state. Investigations of the reaction

mechanisms and products and characterization of the solid state were covered, including

crystalline materials produced by chemical reactions between solid-solid and between

solid-liquid and solid-gas phases.

The symposium dealt in particular with those "novel" materials which have not yet been

well characterized as to crystal chemical and other properties, such as melting points,

crystal structure and eauilibrium relations. Studies of synthesis and characterizations

were highlighted. Although emphasis was on the experimental approach, discussion was

included on theoretical aspects as well.

Of primary interest to the conference were fundamental studies on oxides and other

chalcogenides as well as borides, carbides, nitrides, silicides and similar materials.

Specifically excluded from the symposium subject matter were halides and ductile metals and

alloys although mixed materials like oxyhalides were discussed. Papers were primarily on current research although the invited papers also included some reviews.

The proceedings of the conference are presented in an order very similar, though not

exactly the same, as was followed for the presentations. The book is divided on the basis

of material types into three parts: I Oxides, II Borides, Carbides, Silicides and Related

Materials, and III Chalcogenides.

Some very stimulating talks were provided by a group of distinguished foreign

participants. The opening invited lecture by Sten Andersson of the Lund Institute of

Technology, Sweden on "The Structural Chemistry of Some Solid Trivalent Antimony Compounds"

generated considerable discussion throughout the meeting. The paper dealt with lone pair

geometry and the crystallographic location in solids of the 5S electrons, especially those

of antimony. Andersson 's work was complimented by the contributed paper of J. Galy of CNRS

Bordeaux, Prance, who discussed similar aspects in relation to tellurium +IV oxides.

Throughout the entire symposium reference constantly was made to the late David Wadsley

(CSIRO) and his contributions to the science of Solid State Chemistry. The invited papers

of Sten Andersson, John Allpress, CSIRO, Australia and J. S. Anderson, Oxford University,

England, as well as numerous contributed papers paid tribute to Wadsley by highlighting

scientific research which was either a direct or indirect outgrowth of his pioneering work.

With the death of David Wadsely, we in solid state chemistry have truly lost a great leader.

Nevertheless, Wadsley 's work in the field of geometrical structural crystallography is being

carried forward by many scientists who were personally motivated by him.

The lattice image electron microscope techniques discussed by J. G. Allpress and by

J. S. Anderson and many others at the conference have contributed greatly to our knowledge

of the mechanism of structural accommodation of variable valence states in crystalline

solids. One of the most exciting new results shown at the conference was the presentation

for the first time of high resolution lattice image photographs which seem to actually show

the spaces between atoms. These photographs, illustrated in the papers by J. G. Allpress

and J. S. Anderson, are truly spectacular. Still another outgrowth of the lattice image

technique is the important new concept of "swinging shear planes." (See open Discussion

Session, L. Bursill, also frontispiece) . The symposium fittingly concluded with an "Open

Discussion Section" on "Nonstoichiometry" . This session was organized around four impromptu

lectures by L. Bursill, University of Western Australia; E. Kostiner, Cornell University;

D. J. M. Bevan , Flinders University, South Australia; and L. Eyring, Arizona State

University. Several very informative and stimulating discussions were generated and their

essence is reproduced in the final section.

vii
The editors of this book would like to thank their co-members of the program committee;

Drs. H. s. Bennett, T. D. Coyle, H. P. R. Frederikse , J. L. Torgesen, H. T. Yolken , and

J. B. Wachtman, Jr.; R. T. Cook, R. B. Johnson, R. F. Martin, and Mrs. S. R. Torrence of the

arrangements and finance committee; and Mrs. S. J. Schneider and Mrs. H. T. Yolken of the

ladies' program committee. Additional thanks go to the session chairmen: W. L. Roth,

General Electric; B. Hyde, University of Western Australia; R. Ward, University of Connecticut;

B. Post, Polytechnical Institute of Brooklyn; D. J. M. Bevan, Flinders University, South

Australia; H. Young, Princeton University; and F. Holtzberg, IBM, and all of the speakers

and participants of the symposium who together made the whole meeting a very worthwhile

occasion for all concerned. Special thanks are due to Mrs. Mary Clevinger who handled the

organization of this volume including retyping of the manuscripts and reproduction of the

figures and tables, and to her assistants.

R. S. Roth

S. J. Schneider

Drs. Les Bursill and Bruce Hyde, Australia (foreground) authors of the

concept of "swinging shear planes" discuss this revolutionary theory

with Drs. Jean Galy, France, and Sten Andersson, Sweden (background).

In the improvised model, golf balls represent Ti+^ ions, ping-pong

balls are Cr+^ ions and aluminum cans are 0"^ ions.

viii
WELCOME

Lewis M. Brans comb

Director, National Bureau of Standards

It is my pleasure to welcome you this morning to the National Bureau of Standards for

the 5th Materials Research Symposium. We are pleased to join many of our colleagues in universities and industry in a symposium dealing with an area of research of considerable

interest to NBS that gets at a cross section of technical problems of unconventional

dimension. Also gratifying is the attendance of a substantial number of very distinguished

scientists from laboratories in other countries. I think the participation of our guests

from overseas will add much to the distinction and to the pleasure of our meeting together.

We are personally grateful to those who have traveled long distances to be with us.

The title of the conference, "Solid State Chemistry," and its subtitle, "Novel High

Temperature Materials," suggest the sweep of the subject matter from very basic questions

to a more practical interest in some of the new materials technologies on which future

industrial progress may depend. As I have already noted, we have a very productive blend

of academic, industrial, and government people. Perhaps that's not worthy to comment on because it is no novelty to most of you to have your professional interests expressed in

forms that involve such a mixture. However, I would like to make a quick comment on this

subject. I feel that, in this country anyway, there is a very widespread and piiblicly

expressed sense of lack of confidence in the country's basic research enterprise and its

value to the society. There is also a lack of understanding and perhaps again, a lack of

confidence in the technical strength of our industrial life. You now see both of these

views expressed simultaneously, particularly in the latter case, in connection with the

balance of payments and other economic questions. Many people propose various cures for

these economic ills which either are of a type designed to say, "all our basic research

hasn't been very useful; let's re-channel the funds and do applied research and development," or on the other hand, they may take the attitude that industry hasn't been very

imaginative in its research, and that the Government should somehow pay for or do the

research that the industries should have been doing all along.

We at the National Bureau of Standards find ourselves often in a minority in these

policy arguments. We insist that there is a very, very important common ground of scientific

research that has the characteristic of being very sophisticated and intellectually compelling; work that can challenge the best of our bright young students in the universities

and at the same time is of direct importance to the industrial scene. Industrial organizations can best take advantage of the materials potential that they see without the

necessity of either graduate students or Government scientists engaging in new materials

development, and work of that character which is not appropriate to the academic or the

Government scene.

In my vi^w, the emphasis in this conference on the fundamental questions of the characterization of the properties and the behavior of high temperature materials of broad general

interest is a splendid example of that common ground; one of great scientific interest and

one of important utility to those who wish to exploit this knowledge. I share with you

my thought that there is encouragement for this kind of work, not just here at NBS, but in

both industries and universities. On this basis rests the true proper meeting ground of

basic and applied science and technology. Thank you very much. I hope you have a very

good meeting.

ix
WELCOME

E. Horowitz

Deputy Director, Institute for Materials Research

The 5th Materials Research Symposium sponsored by the NBS Institute for Materials

Research will deal with the chemical behavior of crystalline inorganic substances in the

solid state. As in the past, the Materials Research Symposium is intended to provide

a platform for scientific discussion and exchange of ideas. This time it will be related

to new research, new techniques in solid state chemistry, particularly subjects related

to novel high temperature compounds. Dr. Robert S. Roth, the general chairman, and his

symposium committee have worked very hard to put together a very interesting program. We

are especially pleased to note that participants from fourteen countries are in attendance

today, and that at the first morning's session alone, there will be a number of distinguished

speakers from abroad. I was interested in looking over the program to note several words

that appeared in the text which rang very close to my own feelings —words like synthesis,

reaction mechanisms, chemical properties, characterization and new techniques. I promised

that I would not be long; I would like, however, to give a brief summary of activities for

the Institute for Materials Research (below) . Important here are standard reference

materials, well-characterized pure materials that the NBS provides to industry and the

academic community to calibrate instruments and maintain quality control. Closer to your

own interests are research materials which involve both the preparation and purification

of special materials. Other important activities include the measurement of properties

of materials, compilation of physical and chemical data, the development of improved

methods of measurement dealing both with instrumentation and procedures, the analysis

and characterization of materials, and finally the composition and structure of inorganic

materials

.

To all our guests from overseas and the United States, I want to welcome you to the

Bureau of Standards and to the Institute for Materials Research.

Thank you.

INSTITUTE FOR MATERIALS RESEARCH

Major Areas of Activity

° STANDARD REFERENCE MATERIALS

° RESEARCH MATERIALS

- Preparation

- Purification

° MEASUREMENT OF PROPERTIES OF MATERIALS

- Physical Data

- Chemical Data

° DEVELOPMENT OF IMPROVED METHODS OF MEASUREMENT

- Instrumentation

- Procedures

° ANALYSIS AND CHARACTERIZATION OF MATERIALS

- Composition

- Structure

° TECHNICAL AND ADVISORY SERVICES

- other Government Agencies

- State Governments

- Industry

- Standards Bodies

X
CONTENTS

Foreword v Preface vii

Welcome

L. M. Branscomb TX E, Horowitz X

I. OXIDES

THE STEREOCHEMISTRY OF THE INERT PAIR IN SOME SOLID OXIDES OR OXIDE

FLUORIDES OF Sb^^, Bi3+ AND Pb^"^ (invited Paper) 3

o S. Andersson and A. Astrom

THE SINGLE CRYSTAL X-RAY STRUCTURE DETERMINATION OF SOME ALKALI

METAL MOLYBDATES AND NIOBATES 15

B. M. Gatehouse, D. J. Lloyd, and B. K. Miskin

THE CRYSTAL CHEMISTRY OF SOME NEW MIXED OXIDES OF TELLURIUM +IV 29

J. Galy

CRYSTAL STRUCTURE AND PHYSICAL PROPERTIES OF A TRICLINIC SODIUM

TUNGSTEN OXIDE 41

H. F. Franzen, H. R. Shanks, and B. H. W. S. deJong

ELECTROCHEMICAL PREPARATION AND CHARACTERIZATION OF ALKALI METAL

TUNGSTEN BRONZES, M^WOj 51

M. S. Whittingham and R. A. Huggins

SOME ASPECTS OF THE INVESTIGATION OF INTERGROWTH PHASES IN Nb205-

RICH SYSTEMS 63

R. Gruehn

THE APPLICATION OF ELECTRON OPTICAL TECHNIQUES TO HIGH TEMPERATURE

MATERIALS (invited Paper) 87

J. G. Allpress

APPLICATION OF INFRARED AND RAMAN SPECTROSCOPY TO THE CHARACTERIZATION

OF ORDER-DISORDER IN HIGH TEMPERATURE OXIDES 113

W. B. White and V. G. Keramidas

A STUDY OF V2O3 BY PHOTOELECTRON SPECTROSCOPY 127

J. M. Honig, H. E. Weaver, and R. D. Board

OBSERVATIONS IN THE ELECTRON MICROSCOPE OF LATTICE PLANES AND MIGRATION

OF SILVER IN BETA ALUMINA 129

W. L. Roth

BETA ALUMINA - PRELUDE TO A REVOLUTION IN SOLID STATE ELECTROCHEMISTRY 139

M. S. Whittingham and R. A. Huggins

EXPERIMENTAL STUDY ON THE lONICITY IN THE TiO PHASE. AN APPLICATION OF

THE NEW METHOD OF DETERMINING THE STRUCTURE FACTOR BY HIGH VOLTAGE

ELECTRON DIFFRACTION 155

D. Watanabe and 0. Terasaki

xi

/
THE STRUCTURE AND INTERGROWTH OF THE POLYMORPHIC FORMS OF Zr02-16Nb205 165

N. C. Stephenson, J. P. Beale, and D. C. Craig

SUPERSTRUCTURE OF THE ORTHORHOMBIC Nb205-6Zr02 TYPE PHASE(S) IN THE

Nb205-Zr02 AND Ta205-Zr02 SYSTEMS . = 183

R, S. Roth, J. L. Waring, W. S. Brower, and H. S. Parker

PHYSICAL AND GEOMETRICAL PRINCIPLES OF CRYSTALLOGRAPHI C SHEAR IN RUTILE 197

L. A. Bursill, B. G. Hyde, and M. O'Keeffe

STRUCTURES AND CHEMICAL BOND PROBLEMS IN VANADIUM OXIDES (invited Paper) 205

p. Hagenmuller

PREPARATION AND STRUCTURE OF A PYROCHLORE AND PEROVSKITE IN THE BiRh03^^ SYSTEM 219

J. M. Longo, P. M. Raccah, J. A. Kafalas, and J. W. Pierce

PRECIOUS METAL PYROCHLORES 227

A. W. Sleight and R. J. Bouchard

PHASES IN THE SYSTEMS Ba0-Ni0-0-C02 AND BaO-CoO-0-C02 233

T. Negas and R. S. Roth

PREPARATION OF SrFexMni -xOs.y AND CaFexMni 03.^ CRYSTALS AND SOME

OF THEIR PROPERTIES 265

E. Banks, O. Berkooz, and T. Nakagawa

LaxSri_xRu03: A NEW PEROVSKITE SERIES 275

R. J. Bouchard and J. F. Weiher

HIGH PRESSURE SYNTHESIS AND CRYSTAL STRUCTURE OF COBALT SESQUIOXIDE

AND ITS LOW-SPIN ^ HIGH-SPIN TRANSITION 285

M. Marezio, P. D. Dernier, J. Chenavas, and J.-C. Joubert

INFLUENCE OF MADELUNG ENERGY AND COVALENCY ON THE STRUCTURE OF

A+B5+03 COMPOUNDS 287

J. A. Kafalas

DEFECTS IN OXIDES (invited Paper) 295

J. S. Anderson

OXYGEN DISSOCIATION PRESSURES AND PHASE BEHAVIOR IN THE TRANSPLUTONIUM

OXIDES 319

T. D, Chikalla and R. P. Turcotte

BINARY SOLID SOLUTIONS OF Pa02 AND OTHER ACTINIDE DIOXIDES AND THEIR

EXCHANGE EQUILIBRIA WITH MOLTEN SALT REACTOR FLUORIDES 331

C. E. Bamberger, R. G. Ross, and C. F. Baes, Jr.

GROWTH AND X-RAY STUDIES OF SINGLE CRYSTALS OF HIGHER OXIDES OF

PRASEODYMIUM AND TERBIUM 343

M. Z. Lowenstein, L. Kihlborg, K. H. Lau, J. M. Haschke, and

L. Eyring

xi i
DEFECTS AND MASS TRANSPORT IN REDUCED Ce02 SINGLE CRYSTALS 353

Y. Ban and A. S. Nowick

ANION CENTERED COORDINATION POLYHEDRA AND RELATED PHYSICAL PROPERTIES

IN RARE EARTH DXIDES AND OXYSALTS 367

p. E. Caro

PLASMA-SYNTHESIZED SUBSTOICHIOMETRIC SCANDIUM OXIDE 385

J. E. Young, Jr. and M. J. Sienko

CRYSTAL CHEMISTRY AND COMPOUND FORMATION IN THE SYSTEMS RARE EARTH

SESQUIOXIDE-WO3 397

G. J. McCarthy, R. D. Fischer, G. G. Johnson, Jr. and C. E. Gooden

PREPARATION OF OXIDES AND RELATED COMPOUNDS BY CHEMICAL TRANSPORT

(Invited Paper) 413

H. Schafer

PRECISION PARAMETERS OF THE FERROELECTRIC RARE EARTH MOLYBDATES Ln2(Mo04)3 437

L. H. Brixner, P. E. Bierstedt, A. W. Sleight, and M. S. Licis

STRUCTURAL AND PHASE RELATIONSHIPS AMONG TRIVALENT TUNGSTATES AND

MOLYBDATES 445

K. Nassau and J. W. Shiever

CRYSTAL CHEMISTRY OF TETRAHEDRALLY-COORDINATED OXIDES: Li3P04 DERIVATIVES 457

A. R. West and F. P. Glasser

ON THE SOLIDIFICATION TEMPERATURE AND THE NONSTOICHIOMETRY OF COBALTOUS

OXIDE IN AN OXIDIZING ATMOSPHERE 471

J. P. Coutures and M. Foex

THE SYSTEM FeO-Si02-Ti02 AT HIGH TEMPERATURES AND HIGH PRESSURES 483

E. Woermann and A. Lamprecht

II. BORIDES, CARBIDES, SILICIDES, AND RELATED MATERIALS

CARBIDES AND SILICIDES (invited Paper) 487

H. Nowotny, H. Boiler, and G. Zwilling

INVESTIGATIONS IN THE TERNARY SYSTEM BORON - CARBON - SILICON 505

E. Gugel, R. Kieffer, G. Leimer, and P. Ettmayer

VALENCE BONDING IN SOME REFRACTORY TRANSITION METAL COMPOUNDS WITH

HIGH COORDINATION 515

F. L. Carter

CRYSTAL CHEMISTRY OF REFRACTORY CARBIDES 561 A , L . Bowman

A SIMPLE MODEL FOR THE STABILITY OF TRANSITION METAL CARBIDES 567

R. G. Lye

ORDERING EFFECTS IN NbC AND TaC 583

J. D. Venables and M. H. Meyerhoff

xi i i
THE CdP2-Ge SYSTEM AND THE GROWTH OF CRYSTALS OF CdGeP2 591

E. Buehler and J. H. Wernick

HIGH BORON CONTENT RARE-EARTH BORIDES 597

K. E. Spear and G. I. Solovyev

PREPARATION AND CHARACTERIZATION OF BORON SUBOXIDE 605

D. R. Petrak, R. Ruh, and B. F. Goosey

TERNARY TRANSITION METAL SILICIDES AND GERMANIDES: ORDERING AND

METAL-METAL BONDING IN Ni 2ln-RELATED PHASES 613

V. Johnson and W. Jeitschko

III, CHALCOGENIDES

STRUCTURAL TRANSITIONS OF SOME TRANSITION-METAL CHALCOGENIDES 625

F. Jellinek

SOLID SOLUBILITY IN THE FACE CENTERED CUBIC GdxSei _x SYSTEM 637

F. Holtzberg, D. C. Cronemeyer, T. R. McGuire, and S. von Molnar

TERNARY CHALCOGENIDES OF LIGHT RARE EARTH ELEMENTS WITH TRANSITION

ELEMENTS 645

G. Collin, H. D. Nguyen, O. Gorochov, M. Guittard, P. Laruelle,

and J. Flahaut

CRYSTAL CHEMISTRY OF METAL-RICH REFRACTORY SULFIDES 651

H. Chen and H. F. Franzen

MIXED CATION DISULFIDES OF TITANIUM, VANADIUM, AND CHROMIUM 663

L. E. Conroy and K. R. Pisharody

CRYSTAL GROWTH AND PROPERTIES OF SOME I-III-VI2 COMPOUNDS 671

H. M. Kasper

CRYSTAL CHEMISTRY AND MAGNETIC PROPERTIES OF PHASES IN THE Ba-Fe-S(Se)

SYSTEMS 681

H. Steinfink, H. Hong, and I. Grey

STUDY OF SULFOSPINELS 695

R. E. Tressler and V. S. Stubican

PHASE CHANGES IN Cu2S AS A FUNCTION OF TEMPERATURE 703

W. R. Cook, Jr.

PREPARATION AND PROPERTIES OF THE SYSTEMS CuFeS2_x AND Cu^ .^Fe] +xS2_y 713

R. L. Adams, P. Russo, R. J. Arnott, and A. Wold

LASER RAMAN SPECTRA OF POLYCRYSTALLINE ZnS AND ZOxCdi^S SOLID

SOLUTIONS 721

J. Shamir and S. Larach

NOVEL METHOD FOR THE SYNTHESIS OF RARE EARTH CHALCOGENIDES 723

C. Paparoditis and R. Suryanarayanan

xi V
IV. OPEN DISCUSSION

SUBJECT: NONSTOICHIOMETRY

ORDERING AND CLUSTERING OF DEFECTS

EQUILIBRIUM VS NON-EQUILIBRIUM

THE TITANIUM AND TITANIUM-CHROMIUM OXIDE SYSTEMS AND SWINGING SHEAR

PLANES 727

L. A. Bursill

A DEFECT CLUSTER IN MAGNESIUM FLUOROGERMANATE 745

E . Kostiner

THE ORTHORHOMBIC PHASES IN THE SYSTEM YTTRIUM-OXYGEN-FLUORINE 749

D. J. M. Bevan

PHASE REACTIONS NOT EXHIBITED ON THE USUAL PHASE DIAGRAM 761

L. Eyring

V. PARTICIPANTS 765

VI. AUTHOR INDEX 775

VII. SUBJECT INDEX 777

XV

\

I. OXIDES

465-504 O - 72 - 2

National Bureau of Standards Special Publication 354, Solid State Chemistry, Proceedings

of 5th Materials Research Symposixam, issued July 1972.

THE STEREOCHEMISTRY OF THE INERT PAIR IN SOME SOLID OXIDES OR

OXIDE FLUORIDES OF Sb3+, Bi3+ AND Pb2+

o Sten Andersson and Anders Astrom

Division of Inorganic Chemistry 2, Chemical Centre, Lund

Box 540, S-220 07, Lund 7, Sweden

Geometrically it is shown that the inert electron pair in some solid oxides or oxide

fluorides requires space comparable with that of an anion. If the lone pairs are located on certain sites in a lattice, nets consisting of lone pairs and anions are obtained which

correspond to hexagonal, or cubic closest packing of atoms. Other more complex nets,

comparable with those in alloy structures, are also found. The lone pairs are thus found in

positions which are normally occupied by anions. Using this observation, direct structural

relationships with the transition metal compounds can be shown to exist.

Key words: Antimony oxides; antimony oxide fluorides; bismuth oxide fluorides; lead

oxides; lone pairs.

1. INTRODUCTION

In the type of compounds to be discussed here, there are three or four anions bonded to the cation, all to one side. They can be arranged in such a way that the lone pair in the

equatorial plane completes a trigonal bi-pyramidal configuration. In another way the lone

pair is at the apex of a tetragonal pyramid. Finally, in the third way, the lone pair

completes a tetrahedron. These arrangements of electron pairs have been predicted by

Gillespie and Nyholm [10] ^ . The distortions of the various polyhedra that occur are explained by the valence shell electron pair repulsion theory of Gillespie and Nyholm. A stereochemically active lone pair is larger than a bonding pair and takes up more room on the

surface of an atom. The bonding pairs are therefore squeezed together and the angles between them greatly reduced.

Crystallographic constants and references for the various compounds to be discussed

here are given in table 1.

In order to denote that a compound A^B contains stereochemically active lone pairs,

we will often add to the chemical formula, Aj^ByE^, where E stands for lone pair, and z for the number of lone pairs per formula unit.

2. VOLUME OF LONE PAIRS

In table 2 the volumes in A^ per anion are compared for SbOF, 3-Sb20it and some transition metal oxides. For Ti02 (rutile) , which has an approximately hexagonally close packed

arrangement of oxygens, the volume is 15.6 A^ , which is a typical value. For both BaTi03

and BaNi03 the oxygen volume is rather high, and comparable with that of the antimony compounds. However, it is well known that in both of these compounds, the barium atom enters

the close packed layers of oxygens, formally substituting for an oxygen, giving the layers

the composition Ba03. Thus, if barium is treated as an anion in the calculations, the volume

per close packed atom is greatly reduced (column II in table 2), and becomes comparable with

the oxygen volume for Ti02. Regarded in this way, BaTi03 is a cubic close packed structure.

Figures in brackets indicate the literature references at the end of this paper.

3
Table 1

Compounds Unit Cell a b c Spacegroup Reference

Yellow PbO (E) orthorhombic 5.489 A. 115 5.891 Vhma [1] Red PbO (E) tetragonal 3. 975 5.023 VA/nmm [2] BiOF (E) 3. 7469 6. 226 VA/nmm [3]

PbsOtj (E2) 8. 80 6. 56 PA/mbc [4] L-SbOF (E) orthorhombi c 8. 873 4. 099 5 . 483 Pnma [5] M-SbOF (E) 11.618 5.616 12 . 281 Pica [6]

e-SbjOit (E) monoclinic 12.060 4.834 5.383 104. 58 C 2/c [7] B-Nb205 12.73 4.88 5.56 105.1 C 2/c* [8] a-Pb02 orthorhombic 4.947 5.951 5.497 Pien [9]

* Transformed into standard drystallographic setting.

Table 2

I {A3) II (a3)

anion (+E)

packing

L-SbOF (E) 24. 9 16.6 Complex

M-SbOF (E) 25.

1

16.7 Complex

3-Sb204 (E) 19.0 15.2 h. c.p. SbF3 (E) 22. 3 16. 8 Complex

BaNi0 3 21. 8 16. 3 h. c.p. BaTi0 3 21.4 16.0 c. c.p. Ti02 (rutile) 15.6 15.6 h. c.p. Yellow PbO (E) 38. 8 19.4 h. c.p. a-Pb02 20. 2 20.2 h. c.p.

In Column I volume in per anion is given; in

Column II lone paris or barium atoms are included

formally as anions in the corresponding calculations.

and BaNi03 hexagonally close packed. From table 2 we see that if the lone pairs are included in the calculations as anions, we obtain volumes for the Sb3+ compounds which are comparable with those of Ti02 , BaTi03 and BaNi03

.

It is important to note that the oxygen and the lone pairs in yellow PbO occupy almost

the same volume as the oxygens in a-Pb02 , as shown in table 2. The two unit cells are almost

identical (if the axes in table 1 are interchanged) and we will point out below that a very

close structural relationship between the two oxides exists. The same is true for e-Sb20it (E) and B-Nb205; the two structures are almost identical, as also will be discussed below.

3. DISCUSSION OF STRUCTURES

We will now show with a number of structures that the lone pair is stereochemically

active as an anion of the size of F~ or and also that it takes a position in a structure

equivalent to such anions.

4
3.1. YELLOW PbO

In figure 1 the structure of yellow PbO is projected along the ib-axis. The structure

consists of PhOi^ polyhedra, joined by edges and corners along b, and by corners in the ac

plane. The oxygen positions within each separate PbO sheet are in almost ideal hexagonal

closest packing as demonstrated in' the left part of figure 2. These sheets are far apart,

and if the structure is imagined to be compressed ^ c, (fig. 2, right part) an oxygen net is

obtained which is hexagonally close packed in three dimensions. (Such an AB structure, con- taining cations with five coordination is not known, but only small shifts of the lead atoms

are required to move them into tetrahedral positions, and then the wurtzite structure is

obtained.) Alternatively, there is formally space enough between the sheets for an extra

identical sheet. If this is inserted the structure becomes hexagonally close packed. If the

lone pairs are placed in these positions, they complete a trigonal bipyramidal polyhedron a- round Pb^"*", as required by the Gillespie-Nyholm theory (Cf fig. 3) . With this position of a lone pair, the distance between its center and the Pb^"*" cation becomes approximately one A. In the structures described in this article, this distance is used when the lone pairs are located in order to construct OE (oxygen-lone pair) or OFE (oxygen-fluorine-lone pair) nets.

The very regular hexagonally close packed OE net for yellow PbO is given in figure 4.

The structure of yellow PbO (E) should thus be compared with AB2 structures, and only

small shifts of the Pb^ ions are required to obtain a structure of the a-Pb02 type. We

pointed out above that the volumes of the unit cells of a-Pb02 and PbO(E) (table 1) are very

close in size, and it is tempting to carry out the mental experiment of oxidizing yellow PbO

dijrectly to oi-Pb02 or 6-Pb02 , under pressure, with the mechanism that oxygen enters the structure of PbO, captures the lone pairs and takes their positions as 0^~. Simultaneously, Pb^"*" is oxidized to Pb'*"'', and is also pushed into octahedral position by the oxygen. The new structure can then be of rutile or a-Pb02 type. A very simple mechanism for the transformation a-Pb02 % 3-Pb02 has been given [11]. The main part of the structure stays intact. The reverse of this mechanism might be true for the thermal decomposition of Pb02 to yellow PbO,

which occurs at elevated temperatures

.

I ^

C

Fig. 1. The structure of yellow PbO. The

heavier and lighter polyhedra are b/2 apart , as are the Pb-atoms

,

marked with filled and open circles.

All atoms are on y = 0 or §

.

5
.0 ,0

o o o o

Fig. 2. Oxygen positions in yellow PbO. The structure is compressed

by c/2 in the right part of the figure.

Yellow PbO(E)

Fig. 3. Yellow PbO with the lone pairs located.

Heavier and lighter pairs on y = 0 or-g.

6
q >

o

4 '% d

• d' •

o

y(?//ow PbO

Fig. 4. The hexagonally close packed OE net in

yellow PbO.

3.2. RED PbO

In figure 5 the red, tetragonal form of PbO is projected along an a-axis. Each square

pyramid has a lone pair at the apex, and in this way the oxygens and the lone pairs form a somewhat distorted cubic close packed arrangement. Again it is easy to see a path for the

Pb^"*" cations to move into the octahedra formed by the OE net. The AB2 structure formed is

simple and esthetically attractive, but no compound has been reported to have this particular

structure

.

3.3. ^-Sh^^

The structure of g-Sb204 (E) , given in projection along h in figure 6, is another example

in which oxygens and lone pairs form a hexagonally close packed net. This kind of projection

is useful for describing many common structure types, and especially for predicting new ones;

it has been described in more detail in reference 12. Octahedra in the structure of 3-Sb20Lf,

containing Sb^"*", form sheets by sharing corners in the he plane. SbO^ polyhedra, of the same kind as in yellow PbO, form chains in the c-direction by edge-sharing. The structure is

then built up by corner-sharing of the sheets and the SbOi^ chains.

In table 1 it is shown that the B-NbaOs and 3-Sb2 04 structures have the same space group,

and very nearly the same unit cell dimensions. The structures are indeed very similar (fig.

6 a and h) ; the lone pairs in 3-Sb20i| are in the same positions as certain oxygens in

B-Nb205 , the other oxygens and SB^ and half the Nb^"*" are in the same positions in the two

structures. The only difference is in the Sb^"*" positions. However, if they are shifted into neighboring octahedral sites, they do correspond to the rest of the Nb^ in the B-Nb205

structure. B-Nb205 is the high pressure, high temperature form of all the known Nb205 modifications [13]. In its structure the oxygens are hexagonally close packed, and it is easily

related to the common structural types of rutile and PdF3 [12].

7

;
5^

/?(?c/ PbOiE)

Fig. 5. Tetragonal PbO. The heavier and lighter

polyhedra and lone pairs are b/2 apart, as are the Pb-atoms , marked with filled and

open circles. All atoms and lone pairs on

Y

= 0 or |,

Fig. 6 a. The structure of g-Sb20t^ somewhat idealized. The rhombohedral

shaped figures are the SbOi^ polyhedra in projection with lone

pairs pointing upwards (filled or open circles) or downwards

(dotted circles). The Sb^"*" ions are above or below the lone

pairs. Small circles are oxygens, larger circles are lone

pairs. The SbO^ polyhedra form chains which are joined to the

octahedral Sb^"*" sheets by corner sharing.

b. The structure of B-Nb205. Note that the oxygens and half the

Nb atoms in B-Nb205 are in the same positions as the oxygens,

Sb^+ and lone pairs in g-Sb20i^.

8
3.4. TETRAGONAL BiOF

The tetragonal BiOF is projected along an a-axis in figure 7. In the BiOi^ polyhedra,

the lone pairs complete square pyramids. The same metal oxygen lone pair layer is present

in this structure as in the structure of red PbO. But in BiOF these layers are pushed further apart by the entrance of fluorine ions. The arrangement of anions and lone pairs are no longer close packed. In figure 8 the OFF net is drawn, and the two different polyhedra

that can be found are line-shadowed. One is an octahedron, while the other is a bi-capped

cube with 10 vertices. This net is very similar to that of Si atoms in MoSi2 or the net of

A£ atoms in the alloy OsAS,2 [14,15]. Again the lone pair is equivalent to an anion in its

stereochemical activity.

3.5. TETRAGONAL Pb^O^

The tetragonal structure of Pb30^(E2) is shown in figure 9, projected along the c-axis.

As seen in figure 9, the net formed by the oxygens is the same as that formed by the Al atoms

in the CUAI2 structure type. The Pb^"*" ions are coordinated by three oxygens, and the lone

pairs complete a tetrahedron. The oxygens in Pb3 0i| form square antiprisms, which by sharing

faces form tunnels along c. Inside these tunnels the Pb^"*" ions are situated, and the lone

pairs approach the Cu positions in CUAI2 . Due to the positions of the Pb^"*" ions in Pb30i|,

its c^axis is doubled compared with the c-axis of CUAI2 . The square antiprisms are joined

by edges in the ab plane so that octahedral positions for Pb^"*" ions are created, and these

octahedra share edges in the c-direction. Due to the arrangements of the lone pairs, the

square antiprisms are rather flat compared to those in CuA£2

•

9
OFE net in BiOF(E)

Fig. 8. The OFE net of BiOF, the same projection as in figure 7.

Fig. 9. The structures of Pb304 and Ci:iAl2/ projected along the

c-axis. In Pb30[^ the oxygens (large filled and open

circles) are on z = 0, ^, -g, and ^, lead atoms (small

circles) are on 0 or ^ . The line-shadowed polyhedron

represents two octahedra, superimposed in this projection,

containing Pb^"*". In CUAI2, open and filled circles are Al atoms on 0 or e , double circles are two Cu atoms

superimposed on \ and f

.

10
3.6. L-SbOF AND M-SbOF

Different forms of SbOF were made by heating mixtures of SbF3 and Sb203 in the molar

ratio 1:1 in sealed gold or platinum capsules, at temperatures in the range 150-450 °C [5].

The structures of two of them, L-SbOF and M-SbOF, have been determined [5,6]. L-SbOF, projected in figure 10 down the i-axis, consists of SbOi^ polyhedra, with the lone pairs com- pleting trigonal bypyramids. Such octahedra edge-share to form endless chains in the bdirection. If alternate chains are translated, ^ c, and the structure is allowed to shrink

along a so that the chains can join up by edge sharing, the structure of yellow PbO is formed.

In figure 11 the packing of two identical OFE nets of L-SbOF is given, at z=0 and z = . The lone pairs are geometrically equivalent to anions; the packing is complex like in alloys,

and the net, described in figure 11 is also the same as that of the Rh-atoms in one section

of the crystal structure of Rh5Ge3 [16]

.

The structure of M-SbOF is more difficult to describe. A polyhedral drawing in projection down the b-axis is shown in figure 12. ShOn polyhedra of the same kind as in

L-SbOF join by edges and corners to form a layer structure. Anions and lone pairs can be

approximated to be b/2 apart, and in figure 13 it is shown that the packing again is complex.

The pentagonal antiprism is often fo\ind in complex alloy structures. The lone pairs and

anions in M-SbOF are arranged so that they can be described as forming the 10 vertices of

a somewhat distorted antiprism shown in figure 13. In the right part of the figure a regular antiprism is drawn, for comparison.

L-SbOF (E)

Fig. 10. The structure of L-SbOF projected down

the jb-axis . The heavier and lighter

polyhedra and lone pairs are b/2 apart,

as are the Sb-atoms, marked with filled

and open circles. All atoms are on y = 0 or |.

n
c

m-SbOF

Fig. 12. The structure of M-SbOF. SbO[+ polyhedra

of the same kind as in L-SbOF join by corner- and edge-sharing to form SbOF layers.

12
M- SbOF (E)

Fig. 13. Distorted antiprisms of anions and lone pairs found in

M-SbOF. Heavily or lightly drawn anions and lone pairs

are approximately b/2 apart. The tail-shaped figures

are lone pairs, parallel to the plane of the paper.

Circles with crosses inside are lone pairs pointing

downwards, circles with dots inside are lone pairs

pointing upwards . The remaining circles are oxygen

or fluorine. A regular antiprism is drawn in the

right part of the figure.

4. ACKNOWLEDGMENTS

We would like to thank Professor Bengt Aurivillius for valuable discussions. This

investigation forms a part of a research program sponsored by the Swedish Natural Science

Research Council.

5. REFERENCES

[I] Kay, M.J., Acta Cryst. 14_, 80 (1961).

[2] Leciejewicz, J., Acta Cryst. 14, 1304 (1961).

[3] Aurivillius, B. , Acta Chem. Scand. 18, 1823 (1964).

[4] Fayek, M.K. , and Leciejewicz, J., A. Anorg. Allgem. Chem. 336 , 104 (1965).

[5] Astrom, A., and Andersson, S., Acta Chem. Scand. 2_5, 1519 (1971).

[6] Astrom, A., to be published.

[7] Skapski, A.C. , and Rogers, D. , Chem. Communication 23_, 611 (1965).

[8] Laves, F. , Fetter, W. , and Wulf, H. , Naturwissenschaft, 51^, 633 (1964).

[9] Zaslavskii, A.I., and Tolkachev, S.S., Zh. Fiz. Khim. , 26_, 743 (1952).

[10] Gillespie, R.J. , and Nyholm, R.S., Quart. Rev. 1^, 339 (1957).

[II] Andersson, S., and Galy, J., Bull. Soc. Chim. France 1065- (1969).

[12] Andersson, S., and Galy, J., J. of Solid State Chemistry 576 (1970).

[13] Wadsley, A.D. , and Andersson, S., in Perspectives in Structural Chemistry, Vol. 1,

John Wiley and Sons, Inc., New York, 1970.

[14] Edshammar, L-E. , X-Ray Studies on Binary Alloys of Aluminium with Platinum Metals.

Dissertation, SUPERB-tryck , Stockholm, 1969.

[15] Edshammar, L-E., Acta Chem. Scand. 19^, 871 (1965).

[16] Bhan, S., and Schubert, K. , Z. Metallk 51, 327 (1960).

13

/
DISCUSSION

J. B. Goodenough : Some years ago, I think you are familiar with the work, Sten, we at

" Lincoln Laboratory were considering the def ect-pyrochlore stiructures containing lead. It appeared that we transferred the lone-pair electrons into an anion vacancy in that particular

structure. So my question is, have you tried, or is it feasible to do, some electron-density

distribution studies to see whether these electrons, which you describe as electron lone pairs,

are still attached to the parent antimony 3+ ion? Or is it possible that they have really been contributed, or donated, from the antimony to a site that has a positive potential as a result of the crystalline fields? Have they really been donated to the empty space in the

structure?

S. Andersson : You have to pick a light element for such studies. I think with arsenic,

for example, arsenic 3+, it would be possible with very accurate data. However, what you need

is to derive new form factors, non-spherical, just the sort that Barrie Dawson has developed

in Melbourne. That has some very advanced mathematics involved, but it should be possible.

It is not enough just to make a difference Fourier synthesis, you have to go back to the

origin of scattering because you have a non-spherical arrangement.

Note added in proof : There is no donation from the antimony of the lone pair. The distance, according to this geometry, between the lone pair and the metal nucleus is always, in

these structures, between 1.0 - 1.20 A.

E . Banks : The experimental problem here might be solvable by a combination of x-ray and

neutron diffraction techniques because one of your difficulties is that the center of electron

density is different from the nuclear center. Phil Coppens has done that at Brookhaven. He

is continuing at Buffalo on some organic compounds, and he does get, with difference maps,

evidence of bonding electron density and this is the sort of thing that we are looking for.

J> M. Honig : I was wondering, in view of the fact that you have these lone electron

pairs so close together, whether this endows these compounds with any unusual mechanical and

electrical properties? Is this known?

S . Andersson • This is a very interesting point. I think it should involve some interesting

properties, but as far as I know nothing has been done.

i F. Jellinek : This is just a remark to the last question. There have been several examples : of ferroelectricity in antimony 3+ compounds, SbIS , and related compounds, Sb2S3, and so on. j Probably this f erroelectricity is related to the non-spherical character of the antimony 3+ ion f in these compounds.

14
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

THE SINGLE CRYSTAL X-RAY STRUCTURE DETERMINATION OF SOME

ALKALI METAL MOLYBDATES AND NIOBATES

B. M. Gatehouse, D. J. Lloyd and B. K. Miskin

Chemistry Department

Monash University

Clayton, Victoria, Australia 3168

Crystal structures have been determined for the compounds "Rb3Nb5i+Oitt6 , " "RbNb309 " Na MogOiy, K^Mog0i7 (x approximately 0.8 and 1.0 respectively) and Li2Mo40i3 (low temperature

form). Preliminary results are communicated for the compounds Li^MogOiy (x <_ 1.0) and

Li2MoLt0i3 (high temperature form).

For "Rb3Nb5i+Oi 1^6 " unusual structure occurs where niobium-oxygen octahedra are grouped forming four, five, six and seven-sided tunnels through the structure, with the

hexagonal tunnels partly filled with rubidium atoms. The unbalanced electrostatic charge is

discussed in terms of the possible presence of fluoride, or fractional occupancy of oxygen

sites

.

Unusual features are discussed for the M^ogO^y structures (M"'' = Li, Na, K) in terms of

the presence or absence of Mo-Og octahedra or Mo-Oit tetrahedra in the structure. It appears

that the lithium analogue will have a somewhat different structure in spite of similarity

in unit cell dimensions.

The ordering of lithium-oxygen octahedra in planes in Li2Moi|Oi3 is pointed out in an accurate structure determination of this compound, which is basically a cubic close-packed

oxygen lattice with Li and Mo occupying octahedral sites. Systematically absent oxygen

atoms result in the presence of pairs of strings of cube octahedral holes in the structure.

Key words: Alkali metal; bronze; heptagonal holes; hexagonal tungsten bronze; lattice

image; molybdate; molybdenum; niobate; niobium; oxide; single crystal; tetramolybdate

;

x-ray structure determination.

This paper sets out some current research on the structures of a number of compounds

,

and for convenience these will be described in three parts, the formulae of the compounds

discussed will be used as headings for each part.

Thus 1. "Rb3Nb5i+Oittg " and "RbNb309 " 2. LijjMogOiy, NaxMog0i7, and K^MogO^y

3. Li2MottOi3 (low temperature form) .

1. "Rb3Nb540^4g" and "RbNbgOg"

1.1. INTRODUCTION

A study by Reisman and Holtzberg [1]^ in 1960 of equilibria in the system Rb20:Nb205

indicated the existence of eight intermediate compounds; the compositions of these are listed in table 1 together with the results of a recent examination [2] of some of these, in

which unit cell dimensions and crystal systems were given. Samples obtained from Reisman and

Figures in brackets indicate the literature references at the end of this paper.

15
Table 1

Compositions (Expressed as Ratio Rb20:Nb20 5) and

Unit Cell Dimensions Previously Reported

[1] [2] [2] Crystal

a b c p System

2 : 15 1:13 20.17 3. 83 20. 75 123. 5° monoclinic

1 : 4 1:4 26. 55 3. 85 tetragonal

4 :11 1:3 7.45 7.66 hexagonal

1 : z D : 11 "7 /I O 14. 92 106.4° monoclinic

2 : 3 4:7 6. 42 7.68 38.55 orthorhombic

1 :l"

4 : 3 not examined, as highly hygroscopic materials

4 :1

Holtzberg by the late Dr. A. D. Wadsley were subsequently passed on to one of us (B.M.G.)

Two compounds from these samples have been examined so far, a third is currently being

studied.

1.2. "Rb.Nb^ .0^ 3 54 146

1.2. a. EXPERIMENTAL

A clear tetragonal, acicular crystal selected from the 12:88 mol percent Rb20:Nb205

sample had the unit cell dimensions, a = 27.69, c = 3.98 A. Absent reflections were hOO

(or OkO) , h (or k) = 2n + 1 indicating space group P42i2 or P42im^ At this stage the

composition was thought to be RbNbyOis with z = 8, dc = 4.46 g-cm ^, compared with dm = 4.59

g.cm ^ [1]. The doubt concerning composition arose because microscopic examination of the

bulk material using polarizing optics showed that there are several phases present, one in

particular being the tetragonal phase reported here. One other isotropic phase was noted

but not identified to date.

Data was collected using the integrating equi-inclination Weissenberg technique and

796 observed reflections out of a total of 1327 were estimated visually in the usual manner

from the hkO-2 levels. A very small crystal of approximate dimensions 0.02 x 0.02 x 0.2 mm

was used. The linear absorption coefficient for cuKa radiation, which was used, is 450

cm . No absorption correction was applied.

1.2.b. STRUCTURE SOLUTION

Following a niimber of unsuccessful attempts to solve the structure by conventional

Patterson methods, a solution was obtained in projection (hkO) using the direct methods

suite (GSR, LSAMl, LSAM2) of programs of the York-Louvain group kindly supplied by Dr. P. Main of the University of York. The E-map, calculated for this centrosymmetric projection

using 193 phased E-values greater than 1.30, contained major maxima corresponding to all

metal atom positions together with minor maxima which were subsequently confirmed to be

oxygen atom positions.

The niobium atoms are all located in the xyO plane with rubidium in the xyl/2 plane.

Following several cycDes of full matrix least squares refinement varying the metal

parameters, the oxygen atoms were located in a difference Fourier synthesis calculated

using the three-dimensional data. It was clear at this stage that the rubidium site was partially occupied, and the following adjustment of this occupancy on the basis of

difference syntheses (three rubidium atoms distributed over four sites) , together with

16
refinement of atomic positional and isotropic thermal parameters the conventional R factor

was 11.5% (observed data only, 17.0% for all data). No attempt has been made to vary

oxygen or niobium occupancy or to use anisotropic thermal parameters. Individual scales

were adjusted for each level in the final stages of the refinement as reported here.

The structure is illustrated in figure 1 (not idealized) and consists of a framework

of niobium - oxygen octahedra and pentagonal bipyramidal groups, with rubidium atoms

located in hexagonal tunnels formed by the grouping of octahedra. The arrangement of

octahedra around an unoccupied heptagonal tunnel is the most notable feature of this

structure. The only evidence for any scattering matter in this tunnel was a small peak in

the difference Fourier synthesis (approximately 1/3 to 1/4 of an oxygen atom) situated at

z = 1/2 near one side of the tunnel, slightly off-center.

Selected interatomic distances are listed in table 2, from which it may be seen that

Nb - 0 distances in the octahedra range from 1.80 to 2.16 A and in the pentagonal bipyramidal units from 1.99 to 2.21 A. The Rb - 0 distances range from 3.36 to 3.91 A in the

hexagonal tunnels. The numbering scheme used is given in figure 2.

I.2.C. DISCUSSION

The chemical formula determined by counting the atoms in the unit cell is "Rb3Nb540i4g"

which represents an electrical unbalance of nineteen negative charges. This proved to be

rather disturbing and several possibilities for accounting for this unbalance are being

considered.

First, it should be noted that these samples were prepared prior to the observation by

Andersson and Astrdm [3] that some spectroscopically pure Nb205 preparations contain

appreciable amounts of fluoride ion. A formula can be deduced which is electrically

neutral by postulating the formula Rb3Nb5i+0i27Fi g » i-e. 19 fluoride ions in place of a like number of oxygen. This represents approximately 4.7% fluoride in the rubidium compound,

and about 2.8% fluoride in the starting Nb205 preparation. Andersson and Astrom [3] observed

an approximately 2% weight loss from the Nb205 sample they studied.

A sample of the r\ibidium compound was submitted for microanalysis which proved

unprofitable as attempts to get it into solution by fusion with sodium peroxide were unsuccessful. At present this compound is being examined by the I.E.E. or Induced Electron

Emission technique by Professor R. D. Brown and Dr. A. Buckley of this department.

a

b

Fig. 1. Structure of "Rb3Nb5t^Omg" .

465-504 0-72-3 17
Table 2

Selected Interatomic Distances (in Angstrom Units in "Rb3Nb5t^02 t^g"

)

Nbl - 019 2.03 (4x) Nb6 - 013 2.07 (2x)

- 022 1.99 (2x) - 014 1.94

- 016 1.97

Nb2 - 012 1.96 (2x) - 027 2.00 (2x)

- 021 1.94 (2x)

- 023 1.99 (2x) Nb7 - 010 1.96

- 015 1.88

- 016 2.16

- 017 1.93

Nb3 - 017 2.16 - 028 1.99 (2x)

- 018 2.07

- 019 1.88

- 020 2.04

- 029 2.00 (2x) Nb8 - 010 2.02

- Oil 2.01

- 013 2.21

- 014 2.13

- 016 2.17

Nb5 - Oil 2.02 - 025 1.99 (2x)

012 1.95

014 2.12

015 1.93

026 1.99 (2x)

Rb - 018 3. 36 - 023 3. 87

- 019 3.37 - 024 3.60

- 021 3.49 - 029 3.91

- 022 3.67

18
Second, in spite of the use of integrated photographic data it was not felt that a reliable refinement of oxygen occupancy was possible. At present this seems to be the most

practical explanation available. Perhaps some of the niobium atoms are five coordinate or

even tetrahedral in parts of the structure, although no evidence of this was apparent in

the difference Fourier syntheses. Data will be collected shortly using a Picker fourcircle diff ractometer from which a more complete analysis should be possible.

A preliminary examination of this compound by Dr. J. Allpress using the lattice imaging

technique has shown the presence of anti phase boundaries probably arising as a result of a change in the ordering of the three rubidium atoms over four possible sites.

1.3. "RbNb^Og"

1.3. a. EXPERIMENTAL

o This compound crystallizes as minute hexagonal plates, a = 7.39, c = 3.89 A, space

group P6/mmm (z = 1) . For convenience the data was examined in the orthorhombic space

group Cmmm, a = 13.038, b = 7.502, c = 3.89 A. Absences were hkH for h + k = 2n + 1 indicating space group Cmmm (z = 2)

.

A total of 130 reflections were measured visually from the hkO - 2 levels collected

using the integrating Weissenberg technique with CuKa radiation.

1.3.b. STRUCTURE SOLUTION AND DISCUSSION

It was noted from the unit cell dimensions and confirmed from the Patterson synthesis

that this structure would be very similar to that of the hexagonal tungsten bronzes (fig. 3). The principal difference was that the c axis of "RbNbsOg" is half that reported for the

hexagonal tungsten bronzes. For example, Rbo.27W03 has dimensions [4], a = 7.39, c = 7.54 A. Iyer and Smith [2] reported a compound with unit cell dimensions a=7.45 c=7 66a formula RbNbsOg (z = 2) , space group P6322. • o a.

Fig. 3. Hexagonal tungsten bronze structure.

The s-tricapped trigonal prismatic

site is marked by •.

^By courtesy of Dr. A. McL. Mathieson and Dr. W. Denne of the C.S.I.R.O. Division of Chemical Physics

.

19
The structure refined smoothly with both metal and oxygen atoms in the model to an R factor of 14.0%. The formula at this stage corresponded to RbNb309 (cf 3 x Rbo.27W03),

obviously two negative charges i n excess. The fact that both this compound and "Rb3Nb5i|0 jt^g" are almost colorless suggests that all the niobium is Nb^"*"; any reduction would enhance the

charge unbalance. It was noted that the 9 coordinate site, marked • in figure 3, showed

evidence in the difference Fourier synthesis of containing a small amount of scattering

matter (approximately 3/5 of an oxygen atom) . The interatomic distances from the center

of this hole to neighboring oxygen atoms are approximately 2.2 A to oxygen in the xyO plane,

and approximately 2.50 k to oxygens in the xyl/2 plane. These distances are too short for

Rb-0 (3.3 to 3.8 A in this compound) and although a little long for Nb - 0, it appears

quite feasible for a fraction of Nb^+ to be in this site, a symmetrically tricapped trigonal

prism. Possibly the best known example of this coordination is the ion Nd(0H2)9 in

Nd (OH2) 9 (BrOs) 3 reported by Helmholtz [5]. With a 0.2 occupancy of this two-fold site the

formula becomes RbNb3^[t09 (RbsNbiyOi^s) . The possibility of fluoride contamination is

considered unlikely in connection with this compoxind, and therefore for Rb3Nb5itOii^5 also,

as RbNb307F2 would require about 7% of fluoride.

Selected interatomic distances are given in table 3.

2.1. INTRODUCTION

Stephenson [6] partly solved the structure of the sodium compound using data collected

from a twinned crystal which had been prepared by melt electrolysis and characterized

by Wold, Kunnmann, Arnott and Ferretti [7]; however, the structure presented here accounts

for features not readily explained by Stephenson's model.

2.2. EXPERIMENTAL AND STRUCTURE SOLUTION

The lithixjm, sodium and potassium molybdenum oxide bronzes of composition Lij^MogO^y,

NaxMogOiy, and K^MogO^y (where x <_ 1.0, 0.8, and 1.0 approximately, respectively) were prepared as untwinned crystals by heating the respective alkali metal hydride with an excess

of M0O3 in open Pythagoras furnaceware over a gas flame. The loose matrix left after

reaction was extracted with ammonia solution and the crystals collected. The crystals of the

sodium and potassium compounds exhibited a pronounced cleavage plane which was not observed

for the lithium compound.

Crystal data for all three compounds is set out in table 4, together with the means by

which the data were collected. Two sets of unit cell dimensions are reported for the

sodium compound to illustrate the degree of variation that is found with these compounds; a variation which can presumably be correlated with the variable alkali metal content. The

presence of an Re03 sub-cell was noted in the Weissenberg photographs, and can be seen in

figure 4 for the sodium compound where this is compared with the less obvious sub-cell for

the lithium compound.

2. Li^MogO^^, Na^Mog0^7. and K^MogO

Table 3

Interatomic Distances in "RbNb30g" in Angstrom Units

Rb - 0 3. 33 3.75

(6x)

(6x)

Nb - 0 1.94

1.95

1.98

(2x)

(2x)

(2x)

Octahedra

Nb - 0 2.16

2.52

(3x)

(6x)

s -tricapped

trigonal prims

20
Table 4

Crystal Data for the Lithium, sodium and Potassium Bronzes

Li^MogOiy

Monoclinic, space group P2i or P2i/n,

rV' (a)

9.482, b = 5.521, c = 12.737, 3 = 90.59=^ Total number

of reflections 1757, with 742 observed.

Picker four circle dif f ractometer

.

MoKa radiation.

Naj^oeOiy Crystal 1. a = 9.524, b = 5.519, c = 12.975,

6 = 90.03°.

Crystal 2. a = 9.578, b = 5.517, c = 12.992, 6 = 90.11'

Monoclinic, space group C2, Cm or C2/j^. Total number

of reflections 1123, with 861 observed.

Picker four circle diff ractometer

.

MoKct radiation.

KxMogOiy a = 9.60, b = 5.54, c = 13.66, g = 90.1°.

Monoclinic, space group C2 , Cm or C2/^. Total number

of reflections 604, with 277 observed. Weissenberg

multiple film technique. CuKa radiation.

Unit cell dimensions corrected for film shrinkage.

(a) Courtesy of Dr. A. McL. Mathieson and Dr. W. A. Denne,

C.S.I.R.O. Division of Chemical Physics.

L.,r%,o„ - hoi

•"+

Fig. 4. Intensity weighted reciprocal lattice

zero levels for LixMoeOiy and NaxMoeOiy.

21
The structures of the sodium and potassium compounds, which were reported as being

isotypic by Reau [8], were solved by conventional Patterson methods, and refined by full

matrix least squares and Fourier techniques to conventional R values of 7.8% and 8.2%

respectively, for isotropic models.

2.3. DISCUSSION

The structure consists basically of Re03 type slabs of corner-shared molybdenum - oxygen

octahedra perpendicular to the c-axis , with molybdenum atoms in tetrahedral coordination

to oxygen at the surfaces of these slabs. The slabs are weakly held together by sodium

(or potassium) ions in distorted cube octahedral sites along the plane at z = 1/2 as shown

in figure 5 which illustrates the structure of the sodium compound. In the potassium

compound the slabs of Re03 type octahedra are pushed further apart to accommodate the

larger potassium ions. The planes at z = 1/2 correspond to the pronounced cleavage planes

noted above.

There is evidence, found in difference Fourier syntheses principally, that in small

areas of the crystal of the sodium compound some of the molybdenum tetrahedra near the

z = 1/2 plane are replaced by molybdenum octahedra thus extending and cross-linking the

Re03 slabs by corner-sharing of octahedra. It is interesting to note that the potassium

compound refined smoothly to an R of 8.2% on the basis of film data, compared with the

present R of 7.8% from dif f ractometer data for the sodium compound. It is suggested [9] that this may result from the fact that the potassium site is almost fully occupied

resulting in all of the molybdenum at the surface of the slabs being in tetrahedral

coordination. The lower sodium content in the sodium bronze suggests that less molybdenum

is tetrahedrally coordinated compared with the potassium compound, with more octahedra

cross-linking the slabs probably in a disordered manner throughout the crystal. The sodium

coordination is nearly regular cube octahedral when this cross-linking is present. The

sodium site is about 80% occupied in Na^MogOiy and the potassium site about 100% occupied in

In comparison with Stephenson's model the localization of the sodium or potassium ions

in the z = 1/2 plane, and the reported composition Nag.gMogOiy (which is realized if the

tetrahedral sites are fully occupied) are more readily explained on the basis of the model

described here.

K^Mo60i7.

C

a

Fig. 5. An 010 projection of part of the structure

of Nao^9Mo60i7 represented as MoOg octahedra,

M0O4 tetrahedra, and sodium atoms. Heavy

lines represent species at y = 0 , 1, lighter

ones represent those at y = 1/2

.

22
Selected interatomic distances and angles are given in table 5.

In spite of the trend in the uhit cell dimensions from the potassium to the sodium and

the lithium compound, and the fact that we have not yet been able to solve the structure

of the lithiiom compound, it is apparent that there are going to be significant differences

between the structure of the lithium compound and the other two. Crystals of the lithium

compound do not have the pronounced cleavage shown by the other crystals, suggesting that

the sites occupied by sodium and potassium are too large for lithium, and a different

structure exists. The Patterson syntheses are different in features attributable to Mo - 0 vectors, and some peaks are in such positions that Mo - 0 and 0-0 distances both need to be very short if the structure is centrosymmetric. A solution to this structure is being

sought in the non-centrosymmetric space group {P2i) using both Patterson and direct methods.

The same preliminary metal atom structure has been found using both methods, but we have

not been able to proceed further at this stage.

A preliminary report of the structure of the sodium compound was published recently

[10].

I 3. Li2Mo^0^2

3.1. INTRODUCTION

As part of a general study of alkali metal molybdates, which was briefly summarized

in the introduction to a recent report [11] on the structure of the compound K2Mol^Oi3, we present here a preliminary account of the single crystal structure determination of the low

temperature form of lithium tetramolybdate . Following the commencement of this work, samples

of both the low temperature and a high temperature modification were obtained from Dr. R. S. Roth of the National Bureau of Standards, Washington, D. C. [12].

3.2. EXPERIMENTAL

A suitable single crystal of Li2Mo40i3 was obtained from a slowly cooled melt of Li2C03

and M0O3 in the ratio 1:4. The crystals were plate-like, very pale green in color and

possessed a cleavage plane.

Table 5

Selected Bond Lengths and Angles in NaxMogOjy and KxMogO^y.

Mo - O (tetrahedra) A

0 - Mo - O degrees

(tetrahedra)

Mo - O (octahedra 1) A

Mo - O (octahedra 2) K

NaxMogOiy KxMoeOi7

1 X 1.74 1 X 6.2

2 X 1.77 2 X 1. 77

1 X 1. 78 1 X 1.76

2 X 108.6 2 X 108.

3 X 109.8 1 X 106.

1 X 110.3 2 X 112.

1 X 108.

1 X 1.87 1 X 1.84

2 X 1.77 2 X 1.86

2 X 2.04 2 X 1.99

1 X 2.02 1 X 1.95

Av. 1.92 K Av. 1.92

2 X 1.75 2 X 1.78

1 X 1. 77 1 X 1.86

1 X 2.08 2 X 2.08

2 X 2.09 1 X 2.08

Av. 1.92 k Av. 1.94

/
o Crystal data: Li2Mo[tOi3, triclinic, a = 8.225, b = 8.578, c = 11.450 A, a = 95.95°,

e = 109.25°, Y = 96.03°. Space group PI, Cu Ka radiation A = 1.5405 X was used. U = 750.17

A ^, dm = 4.1 - 0.1 g.cm ^ and dc = 4.02 g-cm ^ for z = 3. A total of 2600 reflections, of

which the 1813 observed reflections were used to solve the structure , were collected using

a Picker FACSl four-circle automatic diffractometer (by courtesy of Dr. G. B. Robertson of

the Research School of Chemistry, Australian National University)

.

3.3, STRUCTURE SOLUTION

The structure was solved by the method outlined earlier for triclinic compounds [13]

.

Following the location of all molybdenum atoms, refinement of positional parameters by full

matrix least squares techniques resulted in a conventional R factor of 16.6%. All oxygen

atoms were found in the subsequent difference Fourier synthesis, and refinement of all

positional parameters (R = 9.6%) led to the unambiguous location of the lithium atoms in

the next difference synthesis. Refinement of positional and isotropic thermal parameters

has given R = 3.9% at present.

3.4. STRUCTURE DESCRIPTION AND DISCUSSION

The structure consists essentially of a cubic close packed array of oxygen atoms, some oxygen atoms being absent in a systematic manner, with Li and^Mo atoms occupying octahedral

sites. It is interesting to note that the ionic radius of Li (0.74 A) is the same as the

covalent radius of Mo^"'" [14]. Figure 6, a view perpendicular to the close packed oxygen

layers, shows the layer of (idealized) octahedra which is repeated by edge- and corner- sharing to form the three-dimensional framework of the structure. Every third layer

consists of Li octahedra only, making the sequence of layers of octahedra in this direction,

Mo - Mo - Li - Mo - Mo - Li . The layer sequence can be seen in figure 7, as can the

positions of the oxygens which are absent from the ccp arrangement (marked with *) . These

absences result in the formation of strings of face-shared (square face) c\ibe-octahedral

holes. These strings are in pairs through the structure as a result of additional facesharing of the same type between adjacent cube-octahedral holes.

Figure 8 shows an alternative view of the structure from which the relationship to the

K2M04O13 structure and the structures of other complex molybdates can be more easily seen

[11] . In this view, the lithium - oxygen and molybdenum - oxygen octahedra are edgeand corner-shared to form a sheet. This sheet is repeated by edge-sharing to form a double

layer as shown in the figure. These double layers are then linked by corner-sharing through

a single sheet resulting in a double layer - single layer - double layer sequence reminiscent

of the -S-D-S-D- sequence of Andersson and Wads ley [15]

.

Fig. 6. The basic layer of octahedra in

Li2MoitOi3 with c.c.p. layers of

oxygen in the plane of the paper.

24
Fig. 7. View of 'Li2^°k'^13 structure

illustrating the packing together

of the layers shown in figure 6.

Fig, 8. An alternative view of the structure from

which the relationship to K^yioi^Oi^ and

other complex molybdates can be seen.

The octahedra are considerably distorted from ideal symmetry, in particular for Mo (6) which shows a distortion towards a square-pyramidal coordination. It can be seen from

table 6, in which ranges of interatomic distances are listed, that the Mo - Li edge-shared

distance is shorter than the Mo - Mo and Li - Li edge-shared distance. Similarly the Mo - Li comer-shared distance is less than the Mo - Mo corner-shared distance. It may be

concluded from these observations that the lithium ions are acting to draw the layers of

molybdenum octahedra towards one another.

The structures of Li2Moi+Oi3 (high temperature form) and of CS2M04O13 are currently

being examined in this laboratory. The former compound is triclinic (a = 8.22, b = 8.63,

c - 11.51 A, a = 111.4°, 6 = 94.6*, y = 96.2°) and from the unit cell dimensions and the

distribution of intensities observed on Weissenberg films is expected to have a very

similar structure to that of the low temperature form.

4. ACKNOWLEDGEMENTS

One of us (B.M.G.) is grateful to the organizers of the 5th Materials Research

Symposium, and to the Overseas Travel Grants Committee of Monash University for the

opportunity of presenting this work at the Symposium. Two of us (D.J.L. and B.K.M.) are grateful for the award of a Monash Graduate Studentship and a Commonwealth Post-graduate

Studentship respectively. This work forms part of a project (No. C65/15891) supported

by the Australian Research Grants Committee.

25

/
Table 6

Selected Interatomic Distances in Li2Moi40i3

t n 1 \ -L 1 u J. . O / / 0 ? A oc tahedira

Mo (2) - 0 1.673 - 2,.495

Mo (3) - 0 1.695 - 2,.379

Mo (4) - 0 1.678 - 2.. 389 Average

Mo - 0 1.985

Mo (5) - 0 1.694 - 2,.475

Mo (6) - 0 1.685 - 2,.640

Each Octahedron Has Two Short, Two Medium and Two Long Mo - 0 Distances

Li (1) - 0 1 .924 - 2..562 octahedra

Li (2) - 0 1 .953 - 2,.573 Average

Li (3) - 0 1 .924 - 2,.464

Li - 0 2.162

Mo - Mo edge-shared (10) 3.,239 - 3 ..574 (Av. 3..378)

Mo - Mo corner- shared (7) 3,.733 - 4,. 307 (Av. 3,.978)

Mo - Li edge-shared (5) 3,.130 - 3..335 (Av. 3..218)

Mo - Li corner-shared (13) 3,.532 - 3,.934 (Av. 3..673)

Li - Li edge-shared (4) 3,.359 - 3..549 (Av. 3..445)

5. REFERENCES

[I] Reisman, A., and Holtzberg, F., J. Phys. Chem. , 64_, 748 (1960).

[2] Iyer, P. N. , and Smith, A. J., Acta Cryst. , B27 , 731 (1971).

[3] Andersson, S., and Astrom, A., Acta Chem. Scand., 18_, 2233 (1964).

[4] Magneli, A., Acta Chem. Scand., 7_, 315 (1953).

[5] Helmholtz, L. , J.A.C.S., 61, 1544 (1939).

[6] Stephenson, N. C. , Acta Cryst., 20, 59 (1966).

[7] Wold, A., Kunnmann, W., Arnott, R. J., and Perretti, A., Inorg. Chem., 3_' ' ^45

(1964).

[8] Reau, Jean-Maurice, Thesis, University of Bordeaux, (1970).

[9] Lloyd, D. J., Ph.D. Thesis, Monash University, (1971).

[10] Gatehouse, B. M. , and Lloyd, D. J., Chem. Comm., 13 (1971).

[II] Gatehouse, B. M. , and Leverett, P., J. Chem. Soc . , [A], 2107 (1971).

[12] Roth, R. S., Private Communication, August 1970.

[13] Gatehouse, B. M. , and Leverett, P., J. Solid State Chem., 1_, 484 (1970).

[14] Shannon, R. D. , and Prewitt, C. T., Acta Cryst., B25 , 925 (1969).

[15] Andersson, S., and Wadsley, A. D., Acta Cryst., 15_, 201 (1962).

26
DISCUSSION

E. Banks: Your structure for the pseudohexagonal bronze phase with atoms in the trigonal prism vacancies is reminiscent of some work we did a few years ago in putting lithium

into potassium hexagonal tungsten bronze and I am glad to see someone else has been able to do it. I wanted to comment further on this point though. Have you considered the possibility that you have only, say half as many, or some fraction of that many, niobiums in those

sites with the remaining electron excess being compensated by fluoride in place of oxygen as you had in the other niobi\im compound?

B. M. Gatehouse : I have certainly considered this, Professor Banks, but I think that

unitl I can get a successful analysis of fluoride in these materials ....

E . Banks : Have you tried the electron microprobe?

B. M. Gatehouse : Yes, I think we have one in Australia, probably BHP, the steel people.

We are certainly going to get someone to look at these niobates using that technique.

N. C. Stephenson : These problems you have with charge imbalance are very similar to the ones we had with a sodium niobate. We had dif fractometer data and were able to refine

on population parameters and we found that the residual electron densities in those tunnels

were in fact atoms. In fact, one of the very small electron peaks of about six electrons

turned out to be one-eighth of a niobium atom which was in square-fold coordination, and

this could very well be what you have in your seven-sided tunnels. We also found that we

had a domain structure where we had a slip along the b-axis, and you consider that to be

due to an anti-phase boundry. Now I noticed that your little insert into the host matrix

was related to the host matrix by a two-fold axis. We consider that these slips are due to anti-polar ferroelectric domains. You also said that the domain boundary had finite width

and I would think that in an anti-phase boundary you wouldn't have a finite width boundary,

but you might expect a definite boundary width in a ferroelectric domain. One other thing,

if you are substituting oxygen ions with fluorine ions to account for your charge imbalance,

what sort of a correlation do you get between your observed and calculated densities?

B. M. Gatehouse : There are four or five questions there. I don't think I've got time

to adequately answer them all at the moment, but I'll do so later on. The one thing I would

like is to get diffractometer data on this compound. Our dif fractometer arrives in March

next year. Perhaps you could help me out.

T. Negas : For that first rubidium niobium oxide you perhaps made fluorine the culprit.

What is the possibility of hydroxyl?

B. M. Gatehouse : This is indeed a possibility. The material was prepared, I think,

at 1350 °C. I would probably have to consult either Dr. Andersson or Dr. Holtzberg on that

point, but it is indeed a possibility.

S. Andersson : There is a simple way to decide here if you have fluorine or not. You

can make the compound, can't you. You can buy pure Nb205 these days and you mix it with RbF

or with Rb20(RbNb03) in a sealed platinum tube. Two experiments and you will see.

B. M. Gatehouse : Thank you Sten. Yes, we certainly will be trying this. As you can imagine this was rather a recent solution and I am going back to do these experiments.

27

/

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposi.um, issued July 1972.

THE CRYSTAL CHEMISTRY OF SOME NEW MIXED OXIDES OF TELLURIUM +IV

Jean Galy

National Center of Scientific Research Laboratory

of Inorganic and Structural Chemistry

University of Bordeaux I 33 Talence, France

The structural chemistry of some new mixed oxides between Te02 and some transition

metal oxides is discussed.

A new structural type MTe303 has been found in the Te02 - MO2 systems (M = Ti, Zr, Hf

and Sn) . The structure of TiTe303 determined by x-ray single crystal analysis is cubic,

space group Ia3 with a = 10.956 A. The relationships with the fluorite structure type have

been established. ZrTe303 as well as fourteen new compounds with the general formula

A,B,Te308 (A = Sc, Cr , Fe, Ga, Rh, In, Hi and B = Nb, Ta) are isostructural with TiTe303.

In the system Te02 - VO2 the phase TeVOij has been prepared in two different crystalline

forms, which we designate a and g here. A reversible polymorphic trans fonnation occurs at

650 °C a J B. Both phases crystallize in the monoclinic system. The a-TeVOt^ crystals are black and the 3-TeVOi^ crystals green; a melt of TeVO^ gives a black glass by quenching. In

a-TeVOi^ the coordination number of vanadium and tellurium is 6 and 3, in g-TeVOt^ the C.N.

is 5 and 4.

The crystal structure of NaVTe05 (KVTeOs, RbVTeOs and AgVTeOs are isostructural) exhibits

isolated chains with (VTe05)J^~ formula surrounded by sodium atoms.

Finally, relationship between the structure of a- and 3- TeVOi^ and other "lone pair"

structures such as a-Sb20i^ or SbNbOi^, 3-Sb204 and Pb30t^ is discussed, and comparison with

such simple structures as a-Pb02 , Re03, PdF3 and Ti02 rutile also made.

Key words: Crystal structure; "lone pair" structures; tellurites; tellurium dioxide;

tellurium hypovanadate; titanium tellurite.

1. INTRODUCTION

Tellurium differs from the other elements of the 6th group of the periodic table by its

ability to fom mixed oxides with other elements. Such compounds have typical ionic crystal

structures when tellurium is in the oxidation state six (+VI) or four (+IV) . Tellurium +IV

is characterized by an electronic configuration [Kr] 4d^'^5s^; the pair of s electrons shows

a reluctance or inability to act as bonding electrons and this fact will be illustrated by

the non-symmetric coordination polyhedra, which occur in the crystal structures of the

tellurium +IV compounds.

2. Te02 ^

Tellurium dioxide exists in nature as the minerals tellurite and paratellurite with two

different crystal structures.

Tellurite crystallizes in the orthorhombic system; the crystal structure has been re- ported by Beyer, Sahl and Zeman [1]^ and Beyer [2]. The cell dimensions and the space group

1~

Figures in brackets indicate the literature references at the end of this paper.

29
are given in table 1.

The other modification of Te02 , paratellurite , crystallizes in the tetragonal system;

the crystal structure has been refined by Leciejewicz [3] using neutron diffraction (data are given in table 1)

.

The tellurium oxide Te02 used in our experiments was prepared by the thermal decomposition

of orthotelluric acid:

HgTeOg, > Te02 + 3H2O + %02

The synthetic Te02 has the paratellurite crystal structure.

Table 1

Oxide System Space Parameters Literatu^re

group

Te02 orthorhombic P b c a a = 12 035 A Beyer, Sahl and

b 5. 464 A Zemann (1965) [1] (tellurite) c = 5. 607 k Beyer (1957) [2]

Te02 tetragonal P4l2i2 4, 796

0A

0 LeciGjswxcz (1961) [3] or Q 7

,

525

(parate lluri te

)

P4o2i

2

TiTesOe cubic Ia3 a = 10. 956 Galy and Meunier (1969) [5 SnTeaOg " " a = 11. 144 A Meunier and Galy (1971) [7 HfTeaOe " " a = 11. 291 I ZrTesOs " " a = 11. 308 A

Ga.Te.TegOg a 10. 956

0A Meunier, Galy and

Ga, TaKTegOg a 10. 955

0A Hagenmuller (1970) [16]

Cr.Nb^TesOg a 11. 007

0A Cr.Ta^TegOg a 11. 012

Rh.Nb^TesOg a 11. 014

0A RhiTa,Te30g a 11. 018

0A Fe.Nb.TesOg a 11. 027 %

Fe.Ta.TejOg a 11. 036 K Sc^Nb^TejOg a 11. 136

Sc.Ta. TegOg a 11

.

150

In^Nb^TegOg a 11. 169

In.Ta.TegOg a 11. 185

0A Bi.Nb^TesOg a 11. 275

Bi^Ta^TegOg a 11. 289

a-TeVOi+ monoclinic P2i/c a 5. 099 Meunier, Darriet

b 4. 934 K and Galy (1971) [15]

(black) c 12. 672 K

e 105 .85°

3-TeVOit monoclinic P2i/c a 4. 379

0A

b 13. 502

(green) c 5. 446 A

6 91. 72°

30
Table 1 (continued)

NaVTeOs monoclinic P2i/c a = 5.891 A Darriet, Guillaume

b = 11.389 A Wilhelmi, Galy (1971) [9] c

0 C DOT S

DP

KVTeOs II II a = 6.393 A

b = 11,608 A

c Qp C £ D • oO D i\ 0p J. U D • KJzJ

RbVTeOs II II a = 6.700 ^

- b = 11.833 A

c

O C Q /I C 7\ D . y fiD Pi QP

AgVTeOs II II a = 5.877 A

V-, C = 6.817 A

e = 102.63°

LiVTeOs orthorhombic P2i2i2i a 9.509 A Darriet, Guillaume

b 8.353 A Galy (1970) [19] c 5.285 A

3. TELLURIUM +IV COORDINATION

Tellurium +IV shows two types of coordination towards oxygen, both one-sided.

The fourfold coordination is the most common; in this case the coordination polyhedron

of the tellurium atom can be described as a trigonal bipyramid with one corner of the

equatorial triangle unoccupied, or, as a distorted square pyramid with Te at the apex (fig.

la). Such coordination occurs in several minerals like tellurite [2], paratellurite [3],

spiroffite (Mn, Zn) Te^Og [4] , "cliffordite" UTesOg [5] and the synthetic compounds,

Zn2Te308 [6], TiTesOg [7] g-TeVOi^ [8] and NaVTeOg [9].

a b

Fig. 1. a) Fourfold coordination of Te +IV.

b) Threefold coordination of Te +IV.

31
Threefold coordination is characterized by a trigonal pyramid with Te at the apex (fig.

lb). Such Te03 pyramids have been found in minerals like teineite CuTe03'2H20 [10], the

"unnamed hexagonal tellurite" [11] , the denningite (Mn, Ca, Zn)Te205 [12] , rodalquilarite

[13] and also in the synthetic compounds ZnTe03 [14] and a-TeVOi^ [15] ,

4. DESCRIPTION OF STRUCTURES

4.1. MTe,0„ PHASES (M = Ti, Sn, Hf, Zr)

3 8 The structure type of the MTe30g phases where M is titanium, tin, hafnium or zirconium

has been determined from x-ray single crystal analysis [17]

.

TiTe308 crystallizes in the cubic system, space group Ia3 (table 1) . The structure has

been deduced from a cubic face centered subcell (Ca - atoms in CaF2) of a' = a>piTe 0 /2 parameter, in which titanium and tellurium atoms occupy ordered positions (fig. 2) . ^

The structure is built up of TiOg octahedra and TeO^ polyhedra sharing corners to form

a threedimensional network. In figures 3 and 4 sections of the structure are given. In figure 3 there are TiOg octahedra mixed with TeO^ polyhedra, while in figure 4 there are only

TeOi^ polyhedra. The structure of TiTe308 can be related to the CaF2 structure type. If

X

Fig. 2. The ordered f. c. c. subcell of cations

in TiTe308 (a' = a/2)

.

Fig. 3. Sequence of Ti and Te polyhedra in a plane at Z = 0 and 1/2.

32
j Fig. 4, Sequence of Te polyhedra in a

' plane at Z = 1/4 and 3/4.

anions (large open circles) move in the directions demonstrated by arrows into the filled

circles in figures 5 and 6, the TiOg octahedron and TeOi+ polyhedron are obtained from the

fluorine positions in CaF2 structure.

4.2. A,B,Te^O„ = A SERIES OF COMPOUNDS WITH THE TiTe^O„ STRUCTURE TYPE

is is 3 8 3 8 Fourteen compounds with the general formula A^B^Te308 where A = Sc, Cr, Fe, Ga,

Rh, In, Bi and B = Nb and Ta, have been prepared by solxd state reaction [16]

.

AoOq + B2O5 + 12Te02 4 A B TesOs

X-ray powder pattern analysis show that these phases are isostructural with TiTe30g. A and

B atoms are disordered in the octahedral titanium sites.

465-504 0 - 72 -4
4.3. TeVO , = A TELLURIUM AND VANADIUM +IV OXIDE PHASE

4

TeVOtt has been synthesized by direct solid state reaction between the vanadium and tellurium dioxides VO2 and Te02 , at 600 °C [8,15]. D.T.A. measurements show a reversible polymorphic transformation at 650° + 10 °C. Crystals of both phases, designed a- and g-, have

been prepared using transport reaction with tellurium tetrachloride TeCli^ . The ct-TeVOt, crystals are black and g-TeVOi^ crystals green. The two crystalline forms of TeVOt^ crystallize

in the monoclinic system

a-TeVOi^ Z e-TeVOi^

650 °C

{black) (green)

monoclinic monoclinic

A melt of TeVOii gives a black glass upon quenching.

4. 3. a. a-TeVO^ STRUCTURE

Projection of the a-TeVOj^ structure on the a c plane is given in figure 7. The structure consists of isolated chains of VOg octahedra sharing edges and running parallel to the

b-axis (fig. 8) ; these chains are joined to Te03 polyhedra by corner sharing.

Tellurium has a threefold coordination in the form of a trigonal pyramid with Te at the

apex

.

4.3.b. 6-TeVO^ STRUCTURE

A projection on the (100) plane of the g-TeVO^ structure is given in figure 9 (data in

table 1). This figure shows the general scheme of the structure, which consists of very

distorted octahedra sharing corners to foinn puckered sheets parallel to (010) . These sheets

are linked by tellurium atoms.

In fact, the VOg octahedra are so distorted along the b-axis that it is more reasonable

to consider a fivefold coordination for the vanadium +IV.

The VO5 polyhedron can be described as a square pyramid of oxygens with the V in the

center. The 6th oxygen is at 2.77 A from the vanadium; this appears in the (100) projection

(fig. 10)

.

34
Tellurium has a fourfold coordination; pairs of TeOi^ groups are connected by common

edges to form Te205 units. The lone pair repulses two extra oxygen in the equatorial plane

(0-Te-O) at more than 2.50 A; its influence seems to be marked by the displacement of the

6th oxygen of the VOg octahedron.

o This fact gives a [VOi+]j^ layer elongated in the direction of the a-axis, a = 4.379 A

instead of . 3.80

This structure shows resemblances with the triclinic BiNbOtt phase [17] and the fluoride

BaZnFit [18] .

4.4. MVTeOj PHASES - (M = Li , Na , K , Rb , Ag)

Yellow crystalline MVTeOs compounds have been prepared by heating intimate mixtures of

metavanadates MVO3 and tellurium dioxide Te02 [19] .

MVO3 + Te02 »- MVTe05

LiVTeOs crystallizes in the orthorhombic system (table 1) ; the structure determination is in

progress. When M is the sodium, potassium, rubidium or silver they are all isostructurals

and crystallize in the monoclinic system (table 1) [19,9].

The (100) projection of the structure is given in figure 11.

Vanadium atoms occupy the center of an oxygen tetrahedron; tellurium with a fourfold

coordination form Te206 iinits as in B-TeVOt^

.

Two Te206 units are linked together by two independent VO4 tetrahedra (fig. 12) . In

this way, isolated chains with (VTeOs)!^" formula are built; they are parallel to the [110]

direction. The sodium atoms surround these chains and assume the rigidity of the network.

5. STRUCTURAL RELATIONSHIPS

Our aim now is to show some relationships between these new tellurium compounds and

some "lone pair" compounds of antimony Sb +III and lead Pb +11 with simple structures.

In the first paragraph structural relations between the TiTe30g structure type and calcium fluorite have been established.

35
Fig. 11. (100) projection of NaVTeO

® O o Te • V

Fig. 12, (VTeOs)^^" chains in NaVTeOs

crystal structure.

If we consider now the low temperature form of the tellurium vanadium oxide, a-TeVOij

,

relationship with the a-Pb02 structure type can be developed. Idealized drav;ings of both

structures are given in figures 13 and 14. In both structures similar chains of MOg octahedra sharing edges are found. In a-Pb02 these chains share corners; in a-TeVOt^ isolated

chains of octahedra have identical orientation, the tellurium atoms just play a joining roleAn identical phenomenon is illustrated in the g-TeVO^ structure where the {VOi^) ^ layers

can be derived from the Re03 structure type if it is cut in the way indicated by the arrows

(fig. 15). Tellurium atoms are inserted between the layers.

36
.A. o o o o

Q \ o o o

O 0 \ ..DO To O

o o V o O

(x-TeVO^

Fig. 13. Idealized a-TeVOi^ structure.

(X- PbO<

Fig. 14, Idealized a-PbO? structure.

OTe'

ReO.

m

-Qm\

m

Fig. 15. Idealized g-TeVOt^ and its relation with the Re03

structure type.

In both the crystallographic forms of TeVOi^ the structural principles are the same:

1. A sxjb-array built around the transition element by the oxygens and deriving from simple

structure like the a-Pb02 and Re0 3 types. 2. Tellurium is inserted in these sub-arrays and

do not disturb their orientation.

Some similar examples can be provided in other lone pair compounds. a-Sb204 and the

isostructural compound SbNbOtt exhibit layers of (SbOi+)3n- or (NbOi^)^^- (fig. 16) [20]; the

antimony +III, which is characterized by a lone pair like the tellurium +IV, is inserted be

tween the layers. These are directly derived from the PdF3 structure if sections are made

in the direction indicated by the arrows (fig. 17) . The 3-Sb20^ structure is built on the

same principle (fig. 18).

Pb30i^ constitutes another interesting example. The structure of Pb30t^ consists of isolated infinite chains of Pb'*'*'Og octahedra sharing edges (fig. 19) [21] ; Pb2+ ions with a threefold coordination give the stability to the network. Here again, if we geometrically

pack together the (PbOi|)J^"~ chains by corner sharing, the rutile structure is obtained (fig

20) . The chains in Pb304 have exactly the same orientation as in rutile.

37
o<-Sb20^

Fig. 16. Idealized a-Sb20it or SbNbO^^ structure.

t^^P PHF

Fig. 17. Idealized PdPo structure.

/

A

o o

o

yS-5b20^

Fig. 18. Idealized Q-ShzOi^ structure.

4+ c;.N. Pb^*_^ 6 / / /

Pb'

2+

3 O

Pb30^

Fig. 19, Idealized Vh-^Ou, structure.

Ruti'leN \

Fig. 20. Rutile structure.

38
In conclusion, these investigations on the crystal chemistry of some new mixed oxides

of tellurium +IV have given some new interesting compounds; we have pointed out the ability

of this element characterized by a lone pair to give structures with three-, two- or one- dimensional networks. Some physical measurements could be done, for example on the single

and isolated chains (VOt^)^^"*" and such information should then be compared with the physical

properties of vanadium +IV compounds

.

The chemistry and structural chemistry of the elements like Ge^"*", Sn^"*", Sb^"^, Te^"^,

Xe^+, T1+, Pb^"^, Bi^"^ constitutes an important field of investigation.

The lone pair plays an important role in the structure formation of mixed compounds of

these elements. We expect from the study of its influence on the structures and the coordination polyhedra, that results of great importance can be obtained to further our knowledge

of the chemical bond.

6. REFERENCES

[I] Beyer, H., Sahl, K. and Zemann, J., Naturwiss, 52_, 155 (1965).

[2] Beyer, H., Z. Kristollogr. , 124, 228 (1965).

[3] Leciejewicz, J., Z. Kristallogr . , 116 , 345 (1961).

[4] Mandarine, J. A., Williams, S. J. and Mitchell, R. S., Mineral. Soc. Am. Spec. Paper,

1, 305 (1963) . [5] Galy, J. and Meunier, G. , ActaCryst., B27 , 608 (1971).

[6] Hanke, K. , Naturwiss., 52, 273 (1966).

[7] Meunier, G. and Galy, J., Acta Cryst. , B27 , 602 (1971).

[8] Meunier, G., Darriet, J. and Galy, J., to be published.

[9] Darriet, J., Guillaume, G., Wilhelmi, K. A. and Galy, J. Acta Chem. Scand. , in print.

[10] Zemann, A. and Zemann, J., Acta Cryst., 15_' ^^8 (1962).

[II] Matzat, E. Tschermaks Mineralog. Petrogr. Mitt., 12_, 108 (1967).

[12] Walitzi, E. M. , Tschermaks Mineralog. Petrog. Mitt., 10, 241 (1965).

[13] Dusausoy, Y. and Protas , J., C. R. Acad. Sc., 266C , 91 (1968).

[14] Hanke K. , Naturwiss., 54, 199 (1967).

[15] Meunier, G. , Darriet, J. and Galy, J., to be published.

[16] Meunier, G. , Galy, J. and Hagenmuller, P., C. R. Acad. Sc., 270C , 1987 (1970).

[17] Keve, E. T. and Skapski, A. C., Chem. Commun. , 281 (1967).

[18] Schnering, H. G. and Bleckmann, P., Naturwiss., _55, 342 (1968).

[19] Darriet, J., Guillaume, G. and Galy, J., C. R. Acad. Sc., 269C , 23 (1970)

[20] Skapski, A. C. and Rogers, D., Chem. Commun., 611 (1965).

[21] Fayek, M. K. and Leciejewicz, J., Report 499/11, Institute of Nuclear Research, Warsaw,

Poland (1964)

.

DISCUSSION

N. C. Stephenson : You mentioned a repulsion of one of the oxygens by the lone pair

electrons. Is it possible by looking at these types of distortions in these structures to determine roughly the size, the volume of these lone pair electrons and whether they vary

from cation to cation?

J . Gal

y

: You mean if it is possible to find exactly where is the center of the lone

pair? I think in these compounds they do not fit in networks so nicely as in the compounds

Dr. Andersson told us about in the first talk. However, in TiTe308 for example, I think it

is possible perhaps because in TiTe308 you have two extra oxygens, which complete the central plane of the octahedra around tellurixam with this oxygen around 2.9A. In the structure

of TeV0i4 for example, you have also two extra oxygens at around 2.7, 2.8A. I think it could

be possible to localize the importance of the lone pair. Perhaps, Dr. Andersson has an idea

S. Andersson : On the airplane coming down here we did calculate oxygen volumes for

your compounds

.

J. Galy : They fit in your model.

S. Andersson : They do, yes. So you can see that the volume is the same as for the

anion. But the packing and the nets here are more complicated. We are working with them.

39

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

CRYSTAL STRUCTURE AND PHYSICAL PROPERTIES OF A

TRICLINIC SODIUM TUNGSTEN OXIDE*

H. F. Franzen, H. R. Shanks, and B. H. W. S. deJong

t Institute of Atomic Research and Departments of Chemistry and Physics

Iowa State University, Ames, Iowa 50010

A triclinic sodium tungstate was prepared by the method of electrolysis of molten

mixtures of Na2W0i^ and WO 3 which has been used extensively in the preparation of sodium tungsten bronzes. The electrical resistivities and Seebeck coefficients of several samples were

measured and are reported. A single crystal x-ray diffraction study yielded the tungsten

atom positions. A structure is suggested which is consistent with the tungsten positions

and the electrical properties. The suggested stiochiometry is NagWii^Oi+S. In the suggested

structure the tungsten atoms are coordinated by distorted octahedra of oxygen atoms in all

cases but one, in which case the tungsten is coordinated by a trigonal-bipyramid of oxygen

atoms. The octahedra share corners in planes in a fashion similar to that found in the

hexagonal bronze, and the sodium atoms are located in the resulting hexagonal holes.

Key words: Resistivity; Seebeck coefficient; sodium tungstate; structure.

1. INTRODUCTION

Large single crystals of sodium tungsten bronzes {Na^O^) have been routinely prepared

by fused salt electrolysis [1] '

. The stoichiometry of the crystals has been shown to be

determined by the temperature and composition of the melt, and a variety of structures has

been prepared in the Ames Laboratory. During the process of growing tetragonal sodium tungsten bronze crystals with x-values near 0.30 we obtained on a number of occasions crystals

with apparent hexagonal symmetry. After additional investigation it was found that these

crystals grow at or just above the melting point of the solution (fig. 1) . When the temperature of the melt is increased 10 or 15 °C above the melting point the expected tetragonal bronze crystals are obtained. A photograph of a cluster of the triclinic crystals is

shown in figure 2.

This paper is a report on the characterization of this material by crystallographic

and electrical measurements.

2. EXPERIMENTAL

2.1. ANALYTICAL

The composition of the crystals was determined by neutron activation analysis. The

sodium and tungsten concentrations were determined by the method reported by Reuland and

Voigt [2] and the oxygen concentration was obtained by fast neutron activation analysis

making use of the T(d,n) reaction. The results for five different samples are listed in

table 1. On the basis of these results the compound was initially assigned the formula

Nag .33 WO3 although the data indicated a somewhat higher oxygen content.

Work was performed in the Ames Laboratory of the U.S. Atomic Energy Commission. Contribution

No, 3126.

1

'

' Figures in brackets indicate the literature references at the end of this paper.

41
Fig. 2. Crystals prepared by electrolysis.

Table 1

Crystal Composition from Neutron Activation Analysis

Sample No. Wt % W ± a Wt 5 Na + a Wt % 0 ± a

1 76.09 ± 0.74 3.49 ± 0.04 19.9 ± 0.7

2 75.86 ± 0.81 3.14 ± 0.09 19.8 ± 0.3

3 76.81 ± 3.74 3.10 ± 0.13 19.7 ± 0.1

4 74.58 ± 1.15 3.33 ± 0.07 19.9 ± 0.3

5 77.42 ± 1.78 3.28 ± 0.06 20.0 ± 0.7

NaeWii+Oi+s (calc) 75.00 4,.02 20.98

Nao-33W03 (calc) 76.76 3.20 20.04

42
2.2. CRYSTALLOGRAPHIC

The sample was examined microscopically. The crystal habit was platy, with more or less well formed hexagonal plates forming aggregates with the plates joined by their flat

surfaces. No optical twins were observed under a polarizing microscope. The aggregates

were dark blue, however thin plates were transparent with a light green color. A fragment

with the dimensions 30 pm x 53 ym x 73 ym was selected from a crushed portion of the sample,

and this fragment was examined by the methods of single crystal x-ray diffraction.

Zero and first level Weissenberg patterns with the a axis as the rotation axis and a precession pattern with the b axis parallel to the x-ray beam were obtained. Single crystal

x-ray diffraction data were collected using an automated Hilger-Watts dif fractometer which is

described elsewhere [3] . The data were collected using MoKa radiation filtered by zirconium.

Integrated intensities were measured for all reflections with 0^30°. A total of 2506 re- flections with intensities greater than four times their estimated standard deviations was obtained

.

To obtain data for the refinement of the lattice parameters the 9 angles of 12 strong

reflections were measured each 4 times to ± 0.01°. The 12 average values were used for a least squares refinement of the lattice parameters.

The Weissenberg and precession patterns showed that none of the arbitrarily chosen axes were symmetry axes. The lattice parameters obtained by a least squares refinement of the

diffraction angles indexed on the basis of the arbitrary axes are: a = 18.474 A, b = 12.577

A, c = 7.300 A, a = 29.94°, g = 85.43°, y = 84.34°. The corresponding conventional reduced

cell was found to have the parameters: a = 7.287 A, b = 18.474 A, c = 7.235 A, a = 95.22°,

3 = 119.64°, Y = 89.40°. The density of the sample was determined using a pycnometer and was found to be 6.536 g'cm"^. Assuming the composition reported above there are 13.9 formula

units per unit cell.

The diffraction intensities were corrected for Lorentz and polarization effects and for

adsorption. The transmission factor coefficients were obtained using a computer program by

Busing and Levy [4]. A Howells, Phillips and Rogers plot [5] gave a strong indication that

the structure has a center of symmetry and a Wilson plot [6] yielded an overall temperature

factor of 0.44 . The tungsten positions were determined both by the interpretation of the

Patterson map and, later, by the direct method using Sayre's [7] relation. The two sets of

tungsten positions were in complete agreement. The positions were refined by least squares

refinement [8] to yield a conventional R factor of 18%. The resulting tungsten positions

are given in table 2

.

Table 2

Tungsten Atom Positions

Atom ji y z

Wl 0.250(2) 0,0944 (6) 0.014(2)

W2 0.759 C2) 0.1291(6) 0.030(2)

W3 0.743(2) 0.0979(7) 0.512 (2) W4 0.269 (2) 0.3137 (6) 0.093 (2) W5 0.291 (2) 0.3194 (6) 0.619(2)

W6 0.776 (2) 0.3159(6) 0.584 (2) W7 0.175 (2) 0.4735 (6) 0.331(2)

(a) Uncertainties in the last place are given in parentheses

43
Attempts to fxirther refine the structure and locate the oxygen and sodiim\ positions by

Fourier techniques were unsuccessful. Difference Fourier syntheses did not provide definite

locations for the light atoms, nor did least squares refinement of the structure obtained by

positioning the oxygen atoms by analogy with other tungsten-oxide and tungsten-bronze structures, as discussed in a later section. A crystal 6, counter 26 scan measuring the intensity

at e intervals of 0.01° over several of the diffraction peaks revealed two principal maxima

separated by 0.06° independent of 6.

It was concluded that the sample chosen for the collection of intensity data was not

suitable for a precise structure determination, and that the data obtained were not suitable

for the positioning of the light atoms and refinement of the structure. Attempts to isolate

smaller fragments suitable for the collection of data for a refinement were not successful.

It was concluded that the electrolytically deposited samples consist of aggregates of plate

shaped crystals with variations of alignment, and that the smallest samples that were selected (ca. 10 pm in the dimension perpendicular to the plates) consisted of such aggregates. The failure to obtain a suitable single crystal from the available samples of the

material resulted in the termination of the x-ray crystallographic study at the point of the

determination of the tungsten positions and a rough overall temperature factor, as described

above

.

2.3. ELECTRICAL

Electrical resistivity measurements were made on the a-b plane on four samples in the

temperature range between 77 and 300 K. The resistivity decreased exponentially with increasing temperature in all the samples as shown in figure 3. The activation energy as determined from the slope of the plot Inp versus 10 ^/T was found to vary from one sample to another. The Seebeck coefficients were also measured for three of the four samples (fig. 4)

.

The Seebeck coefficient of sample 4 increased rapidly near 77 K which indicates a possible

large phonon drag effect. Electrical resistivities, activation energies, and Seebeck coefficients at 77 and 300 K are given in table 3.

The Hall effect was measured at 300 K on an additional sample with the use of an a.c. method. A value of -1.4 x 10"^ cm^/coulomb was obtained. The sample had an electrical re- sistivity of 0.4 1^ - cm. If one assumes that the Hall coefficient R = 1/ne then the number

of electrons n, is 4 x lO^'^/cm^ and the Hall mobility is 3.5 x 10~2cm2/volt sec.

7 SAMPLE I O SAMPLE 2

O /

10'.-20 2 4 6

1000/. 8 10 12 14 T(K)

Fig. 3. Resistivities as functions of temperature.

44
„ -250

-300

-350

7 SAMPLE I O SAMPLE 2 X SAMPLE 4

100 200 TEMPERATURE (°K) 300

Fig. 4. Seebeck coefficients as functions of

temperature

.

Table 3

Electrical Resistivity, Activation Energy and Seebeck Coefficient for NagW^Oits

Sample p (fi-m) 300 K

p (J2-m) 77 K

Eg (ev) S (mV/K)

300 K

S (mV/K) 77 K

0.47

0.19

1.5 X 10

2.5 X 10"

-2

100

10

23

0.14

0.06

0.04 - 0.07

0.06

-253

-260

-241 -365

3. DISCUSSION

Figure 5 shows a vertical projection of the tungsten atoms within ±0.32 K of 2.05 A above the z = 0 plane onto that plane. The tungsten atoms in this region are considered to

constitute the "first layer" in a structure which consists, to a first approximation, of

five layers in a nearly hexagonal cell. The Slater [9] radius for tungsten of 1.35 A was

used in constructing the figure.

The tungsten atoms in the first layer are positioned relative to each other in a fashion similar to that found in the hexagonal bronze structure e.g. the hexagonal bronze

KO.27WO3 with a = 7.40 A [10]. This similarity leads to the suggestion that the tungsten

atoms Wl, W2 and W3 are separated by oxygen atoms at positions about 0.9 A from the triangle

connecting centers and midway between the centers, as are the tungsten atoms in the hexagonal bronzes. The W-W distances, given in table 4, are in good agreement with this

suggestion.

The second layer consists of tungsten atoms within ±0.045 A of 5.825 A above the z = 0 plane and is shown in projection in figure 6. The tungsten atoms in the second layer are.

45
a = 7.287A FIRST LAYER

Fig. 5. Tungsten positions in the first layer.

Table 4

Tungsten- tungsten Distances

Atoms Distances (A)

W1-W2 3.71

W2-W3 3.67

W1-W3 3.65

W4-W5 3.70

W5-W5 3.68

W4-W6 3.62

W7-W7 4.17

W1-W4 4.09

W3-W6 4.01

W6-W7 3.89

W5-W7 3.52

W4-W7 3.47

W1-W2 4.17

46
SECOND LAYER

Fig. 6. Tungsten positions in the second layer.

as in the case of the first layer, structurally similar to the layers in the hexagonal

bronzes. W4 , W5 and W6 are separated by distances in the range 3.62 - 3.70 A (the distances

are given in table 4) which are again consistent with the suggestion that there are oxygen

atoms located midway between the tungsten atom centers.

The position of the second layer relative to the first layer is shown in projection in

figure 7. In this figure it can be seen that the two nearly hexagonal layers are located

such that W2 in the first layer is below a hexagonal hole in the second layer, and W5 in the

second layer is above a hexagonal hole in the first layer. Furthermore, W4 in the second

layer is nearly vertically above Wl in the first layer, as is also the case of W6 relative

to W3. The Wl - W4 distance is 4.09 A and the W3- W6 distance is 4.01 A, again leading to the suggestion of W-O-W separations.

Fig. 7. The first and second layers in projection.

47
The third layer is shown in projection in figure 8 and the cominon projection of the

second and third layers is shown in figure 9. The distances from the W7 atoms in the third

layer to atoms in the second layer are 3.47 A, 3.52 A and 3.89 X, again indicating W-O-W

interactions

.

The remaining two layers in the structure are related to the first and second layers by

the centers of symmetry. The first layer is located relative to the fifth layer in the same way that the first is located relative to the second, and the W-W distance between layers is

4.09 A, again suggesting a W-O-W distance.

In sxmmary, the suggested structure consists of groups of four layers with roughly the

structure found in the layers of the hexagonal bronzes, but with the layers arranged so that

the hexagonal holes are not in vertical alignment, and a fifth, new type of layer linking

the groups of four layers. The fifth layer contains tungsten atoms which are apparently

linked to two tungsten atoms via oxygen atoms in one adjacent plane and to a third tungsten

(again via an oxygen) in the plane adjacent in the opposite direction. The coordination of

the tungsten atoms in the third layer is completed, it is suggested, by oxygen atoms com- pleting the trigonal bipyramids. One oxygen is located at the center of symmetry at z,s,z

yielding pairs of corner sharing trigonal bipyramids (the W7-W7 distance is 4.19). It seems

THIRD LAYER

Fig. 8. Tungsten positions in the third layer.

Fig. 9. The second and third layers in projection.

48
reasonable to suggest that the tungsten atoms located above or below the hexagonal holes in

the adjacent layers complete coordination octahedra with oxygen atoms which project into the

holes. The W/0 ratio in the proposed structure is 14/45 = 0.311, which is in good agreement

with the analytical results.

The occurence of oxygen atoms in excess of the 0:W = 3:1 stoichiometry suggests an interpretation for the observed electrical properties of the solid. Namely, rather than

being a bronze, the solid is a tungstate with the formula NaeWi 1+0^5. The six sodium atoms

per unit cell would then fit very nicely into the holes in the layers , and complete the

coordinations of the oxygen atoms surrounding the holes.

Conduction is by electrons in this material since for all samples the Seebeck coefficient was found to be negative. The decrease in electrical resistivity in all samples with

increasing temperature implies an activation energy. This activation energy may be associated with some impurity donor level just below the conduction band but, since different

samples exhibit different activation energies, more than one donor level must exist.

An alternate explanation for the observed electronic properties is polaron type conduction similar to that proposed for doped NiO by Ksendzov et al . [11]. In this case, the

changes in the slope of the Inp versus 1000/T curves are associated with the changes in the

impurity concentrations. However, one can then not assume that the Hall coefficient measures the carrier concentration nor can the Hall mobility be calculated directly.

In either case the electrical properties of the material are not similar to the bronzes

but do support crystallographic findings that it is a tungstate compound.

4. ACKNOWLEDGEMENT

The authors would like to thank A. Voigt's group for the neutron activation analysis

work on this material.

5. REFERENCES

[I] Shanks, H. R. , J. Cryst. Growth (to be piiblished) . [2] Reuland, R. J., and Voigt, A. F., Anal. Chem. 35_, 1253 (1963).

[3] Dahm, D. J., Benson, J. E., Nimrod, D. M. , Fitzwater, D. R. , and Jacobson, R. A.,

USAEC Report IS-1701 (1967)

.

[4] Busing, W. , and Levy, H., Acta Cryst. 10_, 180 (1957).

[5] Howells, E. R., Phillips, D. C, and Rogers, D., Acta Cryst. 3, 210 (1950).

[6] Wilson, A. J. C, Mature, 150 , 152 (1942).

[7] Sayre, D., Acta Cryst. 6, 60 (1953).

[8] Busing, W. R. , Martin, K. 0., and Levy, H. A., USAEC Report ORNL-TM-305 (1962).

[9] Slater, J. C, Chem. Phys. £1, 3199 (1964).

[10] Magneli, A., Acta Chem. Scand. 7_, 315 (1953).

[II] Ksendzov, Ya. M. , Ansel'm, L. N., Vasil'era, L. L., and Latyshera, V. M., Soviet

Physics - Solid State, 5_, 116 (1963) .

DISCUSSION

S. Andersson : The last thing you said, if you take out sodium, then you have too much

oxygen, don't you?

H. F. Franzen: Yes, that's correct.

S. Andersson: Tungsten is only hexavalent in this phase isn't it?

H. F. Franzen: Yes, I would say that, and that does present some problems. I don't

know how to rationalize the composition results but this (NagWi^O^s) is my preferred stoichiometry. Actually, if pressed, I would suggest that there is some trouble with the neutron

activation analyses

.

49

465-504 O - 72 - 5
M. J. Sienko : Your problems in reproducing the activation energy may actually reflect

an anisotropy in the electrical conductivity. Did you try to orient the crystals for the

conductivity measurements? .

;

H. F. Franzen : They were necessarily oriented. The conductivities were measured by the

four probe method and the only dimension suitable for that measurement was the flat plate direction. Oh, orientation within the plane, no, no attempt was made to do that.

B. M. Gatehouse : You didn't comment on the possible stereochemistry of the sodium site, or did I miss that?

H. F. Franzen : You mean the configuration of the oxygen atoms around the sodium sites?

The resultant configuration in the bronze layers is a hexagonal ring of oxygen atoms, an oxygen atom above and an oxygen atom below. The configuration in the trigonal bi-pyramidal layer

is a pretty severe distortion of that although elongated somewhat. Of course we can't give

an accurate estimate of the distortion because the oxygens have been positioned only by conjecture and we don't have refined parameters for the oxygen positions.

E. Banks: Have you considered the possibility that the electrical measurements may

actually be measurements of a composite in which you have a bronze phase interleaved with

some tungsten 5"^ tungstate? This would easily account for the kind of variability that has

been observed. What you would really be measuring would be a contact resistance which is

variable with all sorts of things.

H. F. Franzen : No

.

J. H. Perlstein : I would like to agree with Dr. Banks. I would think that your statement that the material is probably not a single crystal would agree with your electrical

conductivity measurements of showing a semiconductor type of behavior. I am also a little

confused about your statement that the material is insulating, yet you report conductivities

that seem to be extremely high, almost as high as some bronzes that have conductivities of

10 to 100 inverse ohm centimeters.

H. F. Franzen : Well, if I said that it was insulating then I made a slip of the tongue.

What I meant was relative to the metallic bronzes. There is present an activation energy

for the conductivity. The conductivity is down by a couple of orders of magnitude from the

related bronzes in the same composition region. No, I don't claim that it is an insulator,

but it is far more to that side than are the metallic bronzes.

J. H. Perlstein : Okay, then it seems very plausible that until you can get some single

crystals from this phase, that to conclude that the ground state is insulating is open to question. It is possible that the material really is metallic, and that the semi-conducting

behavior is due to the grain boundaries that might be present in the material.

50
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

ELECTROCHEMICAL PREPARATION AND CHARACTERIZATION

OF ALKALI METAL TUNGSTEN BRONZES, M^WO^

M. S. Whittingham and R. A. Huggins

Department of Materials Science and Engineering

Stanford University

Stanford, California 94305

When a current is passed through two inert electrodes immersed in a molten solution

(-750 °C) of alkali metal tungstate, M2WO4 , and tungsten oxide, WO3, oxygen is liberated

at the anode and a crystal of tungsten bronze, Mj^WOs, where 0<x<l , formed at the cathode.

The potential difference between the electrodes is related to the oxygen concentration

gradient across the cell. Thus, if the electrical potential difference across the cell,

rather than the current or current density, is kept constant, crystals with a fixed oxygen

activity and hence composition (stoichiometry ) will be grown. Measurements of the decomposition potential of melts of M2WO4 and WO3 of different composition, and of the oxygen

activity in tungsten bronzes allows a type of phase diagram relating oxygen activity to the

alkali metal/tungsten ratio in both liquid and solid phases to be constructed. Using this

thermodynamic approach, it is possible to rule out certain suggested reaction intermediates

in the electrolytic process and to explain both the overlapping stoichiometric ranges of some phases and the effects of reacting electrodes on the decomposition potential.

Key words: Crystal growth; electrolysis; nonstoichiometry ; reaction mechanisms;

thermodynamics; tungsten bronze.

1. INTRODUCTION

The tungsten bronzes are nonstoichiometric compounds of general formula M^W03 where M

is usually a monovalent cation and x is in the range 0 to 1 . These materials have been the

subject of a number of reviews in recent years [1-3]^, and so their general properties will

not be repeated here. They are of much interest particularly because of their exceptionally

wide stoichiometry ranges, which are most marked for the case of sodium where x may vary all

the way from zero to unity.

The sodium tungsten bronzes were first prepared by the electrolysis of molten mixtures

of sodium tungstate and tungsten trioxide over a century ago by Scheibler [4J . In this

method a tungsten bronze is formed at the cathode, and oxygen is generated at the anode;

both electrodes are usually platinum wire. Since that time bronzes, with sodium replaced

by Li, K, Rb, Cs, TJl, Cu , Ag and the rare earth metals have been formed by this technique.

Although voltages and currents as high as 6 volts and 5 amps (with "current densities" as high as 60 amp/cm^) [5,6] have been used, more typical values are 1-1.5 volts, and 10-20 ma. The effect of these very different electrical parameters on the nature of the bronze product

formed has not previously been considered, and frequently even details of the preparative

procedures are omitted. Apart from the recent work of Fleischmann [7] , who made a study of

the electrodeposition of the bronzes to elucidate the species present in solution, there has

been no serious attempt made to understand the processes occurring during the decomposition

of these melts to form tungsten bronzes.

Figures in brackets indicate the literature references at the end of this paper.

51
Although discovered originally by Wohler [9] in 1824, there is still today no published

thermodynamic data on any tungsten bronze system. It is the purpose of this paper to discuss

the thermodynamic aspects of the processes occurring during the electrolytic decomposition - of tungsten melts to form sodium and potassium tungsten bronzes.

2. EXPERIMENTAL ASPECTS

2.1. MATERIALS AND APPARATUS

Sodium tungstate, potassium tungstate , and tungsten trioxide of reagent grade were obtained from Alfa Inorganics and Research Inorganic Chemicals . All were dried by heating

at 500 °C, and checked for purity of phase by x-ray analysis.

The electrolyte cell arrangement consisted of a Coors 3 Gooch crucible set inside a Coors lA crucible, and is shown in figure 1. This setup keeps the oxygen liberated at the

anode away from the bronze formed at the cathode. The electrodes were usually pure platinum

or gold; whereas the platinum anode was found to be attacked, no reaction appeared to occur

with gold. No inert atmosphere was used, as it has been shown here and previously [7] that

the presence of oxygen in the atmosphere has no measurable influence upon the current-potential relationships obtained.

2.2. PROCEDURE

Before any current-potential relationships were measured, a current of 10 ma was passed

through the cell overnight so that the cathode was first covered with bronze. The potential

across the cell was then measured as a function of the current flowing, for currents from

5 to 40 ma and over about a 150 °C temperature range above the melting point. At least

twenty readings were taken at each temperature, either manually or by means of a Digital

Equipment Corporation Lab 8 computer system; a linear relationship was found, and the decomposition potential, Eq, was then calculated by means of a least squares analysis on the

computer. To insure maximvmi linearity only potential values obtained for currents in excess

of 15 ma were considered. The shape of the curves obtained is shown in figure 2.

In addition, the open circuit voltage, OCV, was determined in a number of cases. If

potentials less than the OCV were applied, the current flowed in the opposite direction,

causing bronze to be dissolved from the cathode. As this caused poor reproducibility in the

current-voltage curves, a current rather than a voltage source was used so that the voltage

could never fall below the OCV value.

The phases formed at the cathode were characterized by x-ray analysis, using a Picker

x-ray diff ractometer with a solid state detector and CuKa radiation, as well as by crystal

form and color.

Ptan cathode

Melt of M2WO4 and WOjAt cathode: M-^^O^ formed

At anode ; liberated

Fig. 1. Cell system for the electrolytic

growth of the tungsten bronzes.

X

^

52
a:

OCV Eo POTENTIAL (volts)

Fig. 2. Typical current-potential relationship, using platinum electrodes.

3. RESULTS

3.1. DECOMPOSITION POTENTIAL

The decomposition potential, Eq, is plotted as a function of the bath composition at

750 °C for the sodium and potassium systems in figures 3 and 4 respectively. It was found

that gold electrodes gave values of Eq about 10 mV higher than those obtained with platinum

electrodes. As the error in these measurements is also about 10 mV, no differentiation will

be made here between the two sets of results. It is to be noted that the slopes of the Eqcomposition curves change at the phase boundaries.

The shape of the crystals prepared in this reaction was determined by the crystal

structure. Thus those with the hexagonal crystal structure were formed as rods of hexagonal

cross-section, up to 1 cm on an edge, and the tetragonal as rods of square or rectangular

cross-section. The latter could be grown readily as rather thin needles, but in order to form material of large cross-section (up to 0.7 cm) it was found necessary to use a seed

crystal and to mechanically prevent growth along the rod axis. The phase with the cubic

perovskite structure grew as cubes in melts of high sodium content but as dodecahedrons at

Fig. 3. Decomposition potential, E , versus melt composition for sodium system.

53
750 °C

~

Third tetragonal! hexagonal

PHASE 1 AND/OR

1 TETRAGONAL

-

^"—^t- ~ ° \ ~

~

- ~

-

\, HEXAGONAL

"

\

° \

1 1 1 I 1

- 500 E

300 40 45 50 55 60 MELT COMPOSITION % WO3

Fig. 4. Decomposition potential, E^, versus melt composition for potassium system.

the low sodium content end of this phase. The third phase in the potassium system did not

have a well defined crystal form, and was of unknown composition. Attempts to interpret the

x-ray data have not been successful to date. However, this phase is of interest because its

color, blue, indicates that it has fewer free electrons [10] than the purple tetragonal

structure and about the same number as the hexagonal, blue, phase despite being formed from

baths of highest potassium content.

A number of different electrodes were used in a bath of composition 46%W03 : 54%Na2WOi| ; in every case the anode and cathode were of identical material. The results of these experiments are shown in figure 5.

02 0 4 06 0 8 10 12 -APPLIED POTENTIAL in VOLTS

Fig. 5. Current-applied potential curves for

46% WO3: 54% Na2W0i+ at 750 °C using

various electrode materials

.

54
3.2. OPEN CIRCUIT VOLTAGE

The open circuit voltage was measured on a number of cells after bronze had been

deposited at the cathode. These values are plotted in figure 6 as a function of the bath

composition for both the sodium and potassium systems.

A zirconia solid electrolyte tube was used as the cathode in one experiment, 42.3%W03:

57 . 7%Na2WOi4. , so as to measure the oxygen activity; the setup is shown in figure 7. The

potential across this tube was found at 750 °C to be 0.87 V compared to a cell OCV of 0.90 V

This difference of 30 mV is due to the difference in oxygen partial pressure between that at the anode (1 atmosphere) and that on the inside of the zirconia tube (0.2 atmospheres). The

potential drop across the zirconia electrolyte was also measured as a function of the potential applied to the cell. It was found to increase by less than 2% for a change of the

latter from open circuit to 4 V. The results are shown in figure 8.

X-VALUE IN SODIUM TUNGSTEN BRONZE 0 8 07 06 05 04 03 02

30 40 50 60

MOLE % WO,

Fig. 6. Open circuit voltage, OCV, measurements.

(Potentials relative to oxygen electrode

at 1 atmosphere O2) . X OCV on cell;

zirconia cathode potential; O powder

preparation zirconia potential

.

Fig. 7. Zirconia tube cathode cell assembly.

55
-0 5

< -025

42 3 % WOj

57.7 % Na,WO^ 750 °C

0 -I -2 -3 -4 CELL APPLIED POTENTIAL (volts)

Fig. 8. Zirconia t\abe potential versus cell

potential, (Potentials relative to oxygen electrode at 1 atmosphere O2)

.

The potential drop across a zirconia tube was also measured during the solid-state

reaction [1 , 11] :

x/2 Na2W0i+ + • WO3 + X/6W ^ Na^WOs. (1)

These results are included in figure 6 as a function of the x value.

4. DISCUSSION

The values of decomposition potential obtained here are in reasonable agreement with

those of Fleischmann, et al. [7,8]. In addition, they and Sienko [12] also observed a sharp

decrease in Eq when a tungsten or tungsten bronze anode was used rather than a noble metal.

The sodium bronze system was found to obey the approximate empirical relationship [7,8]

m (bronze) a; 1/2 m(melt) (2) where m = (atoms of metal) / (atoms of metal + molecules of WO3) , suggested for the sodium and

copper systems. However, this relationship clearly does not hold for the potassium system,

as the hexagonal phase may be formed at compositions exceeding 50%WO3 where m is unity, yet

the maximiim possible value of x in this phase is 0.33, thus the maximum value of m in this

bronze is 0.25.

In the electrolytic preparation of the tungsten bronzes, the melt composition is being

depleted in oxygen forming the lower oxygen content bronze at the cathode with evolution of

oxygen at the anode. The decomposition potential is a direct measure of the energy required

for this reaction. Thus it is possible to calculate the free energy of the reaction, AG,

using the expression, AG = -4 EqF (per mole of oxygen) where F is Faraday's constant. These

values are given in figures 3 and 4. Following the method of Johnson [13] the most probable

electrode reactions can be deduced. For the sake of simplicity it will be assumed that the

only tungstate specie present is M2WO14, the tungsten oxides between WO3 and WO2 will be

ignored, and in the initial analysis that the bath has a composition of M2WO^«W03 ,i.e.

,

M2W2O7

.

The anode reaction is then:

W2O72- = 2WO3 + 2e~ + 1/2 O2. (3)

56
The possible cathode reactions are:

W2O72- + xe~ = WOi^^" + W03^~ (4)

2W207^~ + 2e~ = awo^^" + WO2 (5)

4Vl20y^~ + 6e~ = 7WOi^2~ + W (6)

+ e~ = M. (7) These give four possible overall reactions: —2(2+x) 4 4 M2W2O7 = 4WO3 + — M2W0i^ + — Mj^W03 + O2 (8)

6M2W2O7 = 4WO3 + 6M2WO4 + 2WO2 + O2 (9) ~14 14 M2W2O7 = ~ M2W0lj + WO3 + 2/3 W + O2 (10)

2M2W2O7 = 4WO3 + 4M + 02. (11)

The measured free energy of reaction corresponds to one of the above. However, because

of the sparcity of thermodynamic data for the tungstates, it is not possible in this case to

calculate the theoretical decomposition potentials.

There is, however, one further piece of information that gives more insight into the

most probable reaction; that is the open circuit voltage, OCV. As the OCV measured on the

cell was the same as that measured by the zirconia tube cathode, it must be a measure of the

oxygen concentration change across the cell. This OCV can be related to the oxygen partial

pressures at the cathode and anode by the Nernst expression:

RT / OCV = — in (P02 cathode /pg anode). (12)

At 750 °C, and for a 1 atmosphere pressure of oxygen at the anode this reduces to

OCV = 0.0507 log-|^Q (oxygen partial pressure at cathode). (13)

These values of cathodic oxygen pressure are given in figure 6. If any of the species in

Eqs (8-11) are oxidized at these partial pressures then they cannot exist in the melt. The

oxygen pressures at which oxidation of WO2 , W [14] , K, and Na [15] will take place at 750 °C are given in table 1. Thus, at the electrical potentials and compositions considered here

there is no possibility of the presence of either sodiim or potassium in an unoxidized state.

WO2 and W also can only be formed over a limited melt composition range, and indeed there have

been no reports of their formation from either sodium or potassium melts at this temperature

and at the applied voltages used, < 1.5V. However, we have made single crystals of the dioxide from a lithium tungstate- tungsten trioxide bath under these conditions. The suggestion

proferred by Sienko and Mazumber [16] that the metal M might be a primary cathode product, or

WO2 a primary anode product, and that these species reduce the melt to form the bronze, is

thus not possible, (the oxygen activity at the anode is 1 atmosphere when oxygen gas is being

evolved, and thus there is no possibility of reduced species in the anode region) . In addition, as figure 6 shows, the oxygen activity at the cathode is -the same as that of the sodium

tungsten bronzes, measured in an independent reaction.

Equation (8), the most likely reaction, can be rewritten in a more general form to cover

any melt composition:

2

^

(,2+xy, ^

) (M2WOi+-yW03) , = 2(l+y)W03 + —44M2WO4 + — M^WOs + O2. (14)

57
Table 1

Oxidation Pressures for Metal Species at 750 °C.

Specie - loq Pn

2 -OCV

(atmospheres) (volts)

WO 2 18. 8 0.95

W 20. 3 1.03

K 24.0 1.22

Na 28.5 1.45

The results of figure 5 can now be readily explained in terms of the change in free energy

of the reaction. For platinum or gold electrodes the oxygen is liberated at the anode and

the free energy change is that for equation (14). In the case of nickel, the anode rapidly

becomes covered with a protective layer of oxide and behavior typical of an inert metal is

observed. The different slope for the nickel is due to the increased electrical resistance

of the system due to this protective oxide layer. The slope of the current-applied potential

curve is simply due to the resistive load between the electrodes. For tungsten electrodes,

oxygen is not evolved at the anode, but instead tungstic oxide is formed, so that the free

energy of reaction in this case will be reduced by the free energy of formation of WO3 , which

is equivalent to about 1 volt of applied potential. Thus, the decomposition potential

observed in this case is almost zero. This is a slight over-simplification as the tungsten

oxide formed will be dissolved by the melt, with an associated free energy change. For the

bronze electrodes, no free energy change is expected as the bronze is simply being dissolved

from one electrode and deposited at the other.

Equation (14) can be simplified still further to give

2 (•^^)MoWOi, -yWOa = 2 { '^~^~^^

) Momu + - M WO3 + Oo. (15) xy xy ^^xx-^

This expression does not represent the reaction for which the free ^ergy is known but merely

indicates the stoichiometry of the reaction. It is clear from this, however, that as the

bronze is grown, the bath becomes enriched in the alkali metal, which will cause the decomposition potential to increase with time. This has been observed to occur in both the sodium

and potassium systems. It is important to recognize that this may cause a change in the x- value of the growing bronze with time; in cases where the homogeneity of the bronze formed

is of importance, it will thus be necessary to use a large volume of melt so as to minimize

any possible composition changes . It should be pointed out that in the case of the hexagonal

and tetragonal I phases, the mobility of the M ions within the solid is probably high enough

to prevent the maintenance of any appreciable concentration gradient within the crystal as a result of changes in the bath composition. This is probably not the case, however, for the

cubic sodium tungsten bronzes.

From figures 3, 4, and 6 it can be clearly seen that the decomposition potential is

directly related to the oxygen activity at the cathode. As the oxygen activity is a function

of the bronze composition it may be possible by varying the applied potential to change the

stoichiometiry and even the structure of the phase formed at the cathode. These possibilities

may be seen by consideration of figures 9 and 10, in which both the melt and the resultant

bronze compositions are plotted as a function of the decomposition potential. These figures

are analogous to the familiar temperature-composition phase diagrams, but here the electric

potential rather than the temperature is the variable. It is quite common to saturate a solution by lowering the temperature, causing precipitation of a solid phase, and this is

readily describable in terms of a conventional temperature-composition phase diagram in which

the compositions of both the solid precipitating phase and the liquid are given by a horizontal isothermal tie-line joining the liquidus and solidus lines. In the present case.

58
however, saturation is accomplished by lowering the oxygen activity, rather than the tempei

ture. Nevertheless, one can draw an analogous potential-composition phase diagram, and

represent the compositions of the liquid and product phases at any specified potential by means of a horizontal isopotential tie-line.

To cause crystal growth at the cathode, it is necessary to exceed the decomposition

potential, so as to cross the liquidus line. This excess potential is used primarily to overcome the resistive drop across the cell but part may be used to further decrease the

oxygen activity at the cathode. Figure 8 shows the effect of the applied potential on the

cathodic oxygen activity. An increase of about 14 mV in the potential across the zirconia

tube was observed in increasing the cell applied potential from open circuit to 4 volts.

This corresponds to a change in the x value of the bronze of less than 0.02. However, the

effects of a long term high voltage were not determined. The effect of the cell potential

is much more important for compositions close to phase boundaries. Figures 9 and 10 show

METAL MOLE FRACTION (-rr^^r-)

0 0 2 0 4 0 6

-06

1 1 1

1

1 750°C

-07

y MOLTEN

-0 8 \ SOLUTION

-0 9

-1 0 TET TET

-1 1

II I

-L2

-1 3

1

1 1 1 1 00 010 0 25 0 50 0 75 10 X-VALUE IN TUNGSTEN BRONZE

Fig. 9. Oxygen activity - composition diagram

for sodium system.

METAL MOLE FRACTION (-j^"^)

01 0.2 03 04 05 06

15 25 33 4 5 6 10 X-VALUE IN TUNGSTEN BRONZE

Fig. 10. Oxygen activity - composition

diagram for potassium system.

59
that if the melt composition is at the edge of the tetragonal I phase in the sodium system

or the hexagonal phase in the potassium system, the application of a slightly greater

potential could readily lead to the formation of a different phase, cubic in the former

case, and tetragonal in the latter. That this does, in fact, occur is shown in figure 4. If potentials above the dashed line, in the hexagonal composition range, were used, the

tetragonal, the hexagonal, or both phases were formed. However, if the potential was kept

below this line only the hexagonal phase was found. Thus, it is important to carefully

control the potential drop across the cell in the growth process in order to obtain homogeneous material of a single phase.

The linearity of the sodium curve in figure 6 indicates that there is very little

thermodynamic driving force for interconversion of the cubic and tetragonal I bronze phases.

As the crystal structures are very different, so that interconversion requires complete re- arrangement of the WOg octahedra, it is not surprising that the cubic phase is sometimes

found at low x values [17] more typical of the tetragonal I structure [18]

.

5. CONCLUSIONS

By a consideration of the thermodynamic aspects of the electrolytic growth of the

tungsten bronzes, it has been possible to rationalize both the structures and compositions

of the products formed, as well as the composition dependence of the decomposition potential.

In addition, this approach provides insight into the conditions necessary for the growth

of homogeneous products of desired composition and phase.

6. ACKNOWLEDGEMENT

We should like to thank the Advanced Research Projects Agency (through its IDL Program)

and the National Science Foundation for support of this program; also Professor Ephraim

Banks for providing a copy of C. Fleischmann ' s thesis, and G, Giir and J. Ross for help in

the experimental part of this work.

7. REFERENCES

[I] Dickens, P. G. and Whittingham, M. S., Quart. Rev. 22_, 30 (1968).

[2] Banks, E. and Wold, A., in Preparative Inorganic Reactions (W. L. Jolly, Ed.) 4_, 237 (1968).

[3] Hagenmuller, P., in Progress in Solid State Chemistry (H. Reiss, Ed.) 5_, 71 (1971).

[4] Scheibler, C, J. Prakt. Chem. 83_, 273 (1861).

[5] Conroy, L. E. and Sienko, M. J., J. Amer. Chem. Soc. 74_, 3520 (1952).

[6] Utsumi, S. and Fujieda, S., Bull. Chem. Soc. Japan 42, 1714 (1970).

[7] Fleischmann, C. W. , PhD Dissertation, Polytechnic Institute of Brooklyn, June 1970.

[8] Banks, E. , Fleischmann, C. W. , and Meites, L. , J. Solid State Chem. 1, 372 (1970).

[9] Wohler, F. , Ann. Physik 2_, 345 (1824).

[10] Dickens, P. G. , Quilliam, R. M. P., and Whittingham, M. S. , Mat. Res. Bull. 3_' ^41

(1968).

[II] Dickens, P. G. and l-Jhittingham , M. S., Trans. Faraday Soc. 61_, 1226 (1965).

[12] Sienko, M. J., J. Amer. Chem. Soc. 81, 5556 (1959).

[13] Johnson, K. E., in Proc. 3rd Int. Symp. High Temp. Mat., California, 1967.

Butterworths (1969)

.

[14] Rizzo, F. E. , Bidwell, L. R. , and Frank, D. F. , Trans. Met. Soc. AIME 239 , 1901 (1967).

[15] Swalin, R. A., Thermodynamics of Solids, John Wiley and Son (1962).

[16] Sienko, M. J. and Mazumber , B. R. , J. Amer. Chem. Soc. 82_, 3508 (1960).

[17] McNeill, W. and Conroy, L. E. , J. Chem. Phys. 36_, 87 (1962).

[18] Ribnick, A. S.,-Post, B. , and Banks, E., in Nonstoichiometric Compounds (R. Ward,

Ed.) Amer. Chem. Soc. Advances in Chemistry Series 39_, 246 (1963).

60
DISCUSSION

E. Kostiner : Just a point of information. We were using sodixom tungstate melt a few

years ago to grow transition metal oxides by anodic electrolysis. I believe we were at the

eutectic in the sodium tungstate-tungsten trioxide system using essentially the same potentials as used for bronze growth. We found the formation of sponge tungsten on the cathode.

E . Banks : Bronzes also.

E. Kostiner : And bronzes, but there was sponge tungsten formed on the cathode. This

of course, may be a function of the transition metals present in the system.

A? . S . Whi t tingham : In order to form tungsten at the cathode you must exceed about 1.4

volts across that cell. Otherwise, it's just not possible to form it, unless you were using

a tungsten or some other reacting metal anode, thereby lowering the oxygen activity at that

electrode. This would make a lot of difference. (This value of 1.4 volts is about 350 mV

higher than the OCV, shown in Table 1 for tungsten formation, and the excess is used to overcome the decomposition potential and to provide a reasonable current flow.)

E. Kostiner : Well, perhaps we were then, but we were using platinum electrodes. I don't think, we were above one and a half volts.

M. S. Whittingham : It's about 1.4 volts where you would expect tungsten may be formed.

P. Hagenmuller : You raise a question in my mind. You fix your potential having a con- stant d-electron density, but I believe it can be due to two reasons. The first one, you

have a constant sodium rate, but the second one is you are also able to have an oxygen-tungsten ratio below three. So, in fact you have two composition parameters which can be influenced by your potential. Is it true?

M. S. Whittingham : Yes, we have made one major assumption in all this and it is that

the tungsten to oxygen ratio is fixed and we are in fact at the moment doing measurements to determine whether this tungsten-oxygen ratio can change and if so, by how much.

R . Ward : It might be of interest to mention that some years ago one of our students

was trying to make a mixed tungsten-molybdenum bronze by electrolytic reduction. The product

he got was a black crystalline hexagonal looking plate, very similar to the ones described in

the previous paper. They were also very poor conductors and they were multiply twinned. One

could see the striations on the faces. We never did get any idea of what the structure was. The composition was somewhere around about sodium .25 with about a tenth of molybdenum in

there as a maximum and nine-tenths tiingsten. And these were produced using platinum electrodes. Later on, in further investigations, the student found that you get these just at higher temperatures without any electrodes at all. I don't know what the composition was, but they were very black and they were non-conductors. We thought we had a lower oxidation

state of molybdenum present just as the higher temperatures can get sometimes, but we could

get them without any source of reduction.

M. S. Whittingham : This is similarly observed in the vanadium system. One can, in

fact, form sodium-vanadium bronzes without any electrolytic reduction-^. The oxygen has just

evolved by itself. In other words, the oxygen partial pressure is in excess of that in one atmosphere of air^ and this may be similar to what you have observed.

D. J. Lloyd : If I may just add to that, and it's also relevant to the previous paper,

you can readily determine whether you have a mixed crystal phase of bronze and an unreduced

phase by a simple solvent extraction type process, say with ammonia solution. This will

normally remove the unreduced phase leaving behind the bronze, if you choose your conditions

carefully.

M. S. Whittingham, unpublished results.

V. L. Volkov, A. A. Fotiev, and A. D. Neuimin, Russ. J. Phys. Chem. 44, 1163 (1970X

61
M. S. Whittin^ham: Yes, you can do that with the perovskite phases, but you certainly

have to worry that if you treat the hexagonal phase or even possibly the tetragonal phase with an aqueous medium of any sort you may start removing ions from them. This is very

clearly shown by changes in superconductivity if you heat these materials in aqueous media^

'J. P. Remeika, T. H. Geballe, B. T. Matthias, A. S. Cooper, G. W. Hull, and E. M. Kelly,

Phys. Letters 24A , 565 (1967)

.

[C. N. King, Stanford University, unpublished results.

'D. Vanles, Cornell University, unpublished results.

62
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

SOME ASPECTS OF THE INVESTIGATION OF INTERGROWTH PHASES

IN Nb205-RICH SYSTEMS

Reginald Gruehn

Justus Liebig University

Institute of Inorganic and Analytical Chemistry II

63 Giessen, West Germany

Numerous Nb205-rich compounds with complicated compositions could be prepared as mono- phasic samples. The preparative and analytical work in this field was supplemented by x-ray

investigations using the Guinier technique. In addition to 5 phases (Nbii02 7, Nb2 50g2>

Nb28O70' Nb3i077F, Nb3ij08[+F2) whose structures are known from investigations by Wadsley,

Andersson, and Norin, we found 4 "hybrid" phases also called intergrowth-phases . The building principle of the hybrid phases Nb02.464' Nb02.i+83/ Nb (OfF) 2 . 51 0 ' ^^1*^ Nb(0,F) 2, 523 is a combination of building elements of both neighbor phases e.g. Nb02 tt8 3 combines component

rows of the Nb25062~structure and the Nb2 8O70 "Structure in a ratio 1:1.

It is of special interest that the phases Nb25052f ^^zs'^lO i Nb3i077F, and Nb3Lf08ttF2 have small but exactly reproducible ranges of homogeneity. The fundamental reason for this

deviation from the ideal composition is still unknown. It may be that the deviation from

the ideal composition is due to the special properties of the building elements. According

to this the non-ideal composition of a hybrid phase may be derived from the non-ideal com- position of both neighbor phases e.g. the actual composition Nb02 i+ss+O 00 1 °f the hybrid

phase may be calculated from the actual limits of the phases Nb2 50g2 "(2.478 0/Nb) and

Nb28O70 (2.489 0/Nb) . A hybrid phase with the ideal composition 2.491 0/Nb (Nb250g2+Nb2 807o

)

is nonexisting.

In addition to the combination of compositions of neighbor phases there may be relationship between the stabilities of the basic structures and the resulting hybrid phases.

Key words: Analysis; hybrid phase; intergrowth phase; niobium pentoxide; preparation;

ranges of homogeneity; stability; systems.

1 . INTRODUCTION

More than 10 years ago the author began in the group of Harald Schafer in Miinster

(Westfalia) with the preparative and analytical investigation of Nb205-rich systems. The

main interest was given to results that were inconsistent with the picture of distinct

narrow phases with separated structures. Thus in 1963 Gruehn and Schafer [1]-^ reported a new phase (Ti,Nb)02 1+33 with a composition^'^ not to be described by one of Wadsley 's structural related series Me3n08n-3 [2] and Me3n+i08n-2 • Later on the identification

of (Ti,Nb)02 483' °f '^he isomorphous phase Nb02,i|83 °f Nb02 .464 [4]^ as intergrowthor hybrid^ phases became possible, since a new phase W2Nb26W2077 in the Nb205-W03 system

could be prepared and since its composition could be interpreted as a combination of the

T~

^Figures in brackets indicate the literature references at the end of this paper.

^In reference fl] the composition (Ti ,Nb) O2 . 482 was published.

For the system of notation see tables 2 through 6. ^In reference [2] the composition Nb02.4eo published.

The notation "hybrid phase" proposed by S. Andersson might be preferable.

63
neighbor phases WNbi2033 + WNbittW20i|i^ [5]. From these samples single crystals were selected

and used by Andersson, Mumme, and Wadsley [6] for the first complete crystal structure

determination of an intergrowth or hybrid structure.

To characterize the subsequent development the parallel work, done by two groups with

different methods, may be mentioned. In Munster "simple" hybrid phases which combine

neighboring structures in the 1:1 ratio were prepared as monophase samples and investigated

by chemical analysis. In this way 4 hybrid phases (1:1) were found [7,8] one at a time

intermediate to two known members of the series Me3j^+i (0,F) 3j^_2 (n = 7,8,9,10,11). In Melbourne, Wadsley introduced electron optical methods as a powerful means of structure

investigation [9] . Continuing this work Allpress observed more complicated hybrids e.g.

with a 1:2 ratio of the building elements, Wadsley defects and microdomains of new related

phases [10,11,12]. From these structural results also new important aspects arise for

further preparative work.

2. METHODS FOR PREPAI^TIVE AND ANALYTICAL INVESTIGATION

2.1. PRINCIPLE PROCEDURE

The main interest was turned to the Nb205-rich part of the systems Nb02 - Nb205,

Ti02 - Nb205, Nb205 - WO3, and Nb205 - Nb02F. Additional experiments were performed in the

systems MgO - Nb205, AI2O3 - Nb205, 63203 - Nb205, Fe203 - Nb205, Ge02 - Nb205, WO2 - Nb205-

WO3, Nb02 - Nb205 - WO3, and Nb205 - WO3 - Nb02F. The detection of hybrid phases mostly

required a very subtle technique of investigation because the differences of composition

between phases were very small. A sensitive x-ray method was necessary because of the

structural similarity of these phases. Our criterion for a single phase region was that a sample could be prepared as a monophase substance. Accordingly, in two phase regions only

two phases should exist. Therefore we needed methods to prepare samples near to equilibrium

conditions (paragraph 2.2). The monophase character of a substance was established with

the sensitive Guinier method (paragraph 2.3). Because monophase samples could be prepared,

special chemical methods could be applied for an analysis (paragraph 2.4)

.

2.2. PREPARATIVE METHODS

Methods , suitable for the investigation of oxide systems and for the preparation of

monophase samples, are compiled in table 1. From top to bottom of the table the mobility

of the components increases. In the same direction the chance to approach equilibrium

conditions i.e. defined final states increases.

Table 1

Preparative Methods Used for the Investigation of Nb205 - Rich Systems

Method (a) Temperature

°C

Additional Component (s) of the Investigated

System

Figure

1 heating of the mechanically mixed components (b)

noo

1400

Ti02 Dsl ; AI2O3 03,16] ; Fe^Og U^,^62 ; 00203

[13,16] / MgO D3,16]

1000

1100

2 heating of mixed

precipitations (b)

1100

-1400

64
Table 1 - continued

Method (a) Temperature

°C

Additional Component (s) of the Investigated

System

Figure

3 heating of solid solutions (Ti,Nb)02 with

spontaneous oxidation

of the lower oxidation

states (b)

1200

-1400 TiO^ D^J

4 isothermal heating of

"fnhlfi'f*^ ifUU^^ UO IV nif^ 111^ pO nnn 1 1 U i 1 JL1 pnUX1 miIIIX^v— tures) in sealed tubes;

checking of weight (b^c)

1100

-1420

Nb02 D3J ; WO3 H ; WO2+WO3 / NbOo+WO„ L5J7n

1 a

5 isothermal heating of

mechanical mixtures

in sealed platinum tubes

(c,d)

1200

-1350

1 1 00

-1300

WO3 [JTJ ; Ge02 \J72

UhO^F LB J 7] ; W03+Nb02F LI 7]]

lb

6 pmn 1 1 nT"fi'h ion cit niriKiiim

oxides with gaseous mixtures of H^O/H^ (c)

1 100

1300

"Nibo " ri3~i

[UJ

cf

D8J

7 chemical transport reactions in quartz tubes

under extrem temperature

conditions (d)

1200

-1350

Nb02 O3] ; Ti02 D^J / AI2O3 QSJ ; Fe203 [iSj ; Zr02D7]

Ic

8 chemical transport reactions in sealed platinum

tubes (d)

1100

-1300

Nb02F L8J7j Id

9 chemical transport reac-

"hiring ii*^inn n waII *=»<^'l"n.— blished temperature gradient (d)

600

— 1 1 \J\J Nb02 L1/7J3J9J / Ti02 D3j / AI2O3 D3J

Fe203 [:20J

1 e

(a) for specific details see paragraph 2.2.

(b) heating in air or in O2 . No significant participation of a vapor phase

reaction.

(c) transport of one component by reaction with the vapor phase (vaporization

of WO3; transport of oxygen as H2O)

.

(d) transport of all components by chemical transport reactions.

465-504 0-72-6

65

;
2. 2. a. METHOD 1

This extremely simple way of a solid state reaction often did not yield well defined

products, a fact, proved by the presence of three or more phases in samples belonging to a two phase region. If the composition of neighboring phases differed only slightly a complete

reaction was unobtainable, even when the samples were heated at extremely high temperatures or after melting. Therefore monophase samples of the hybrid phase (Ti,Nb)02 433 were not

obtained in this way, even when prolonged heating with repeated intermediate grinding was performed. The formation of only a small amount of this phase mixed with neighboring phases

indicates that (Ti,Nb) O2. 493 might be stable under these conditions of heating. The incompleteness of the reaction probably is due to the insufficient rate of diffusion of the

components

.

2.2.b. METHOD 2 [1,13]

Exactly weighed amounts of Nb205 and Ti02 (or Zr02) were dissolved in a molten mixture

of (NH4)2SOt| and H2S0t^. After the reaction was finished the oxides were precipitated by

diluting and adding of NH3. The resulting mixture of hydrated oxides was carefully dehydrated at 600 - 800 °C and annealed at the reaction temperature (table 1) . With this method

we could prepare monophase samples of phases that could not be obtained with method 1 because like Ti2Nbio029 (itionoclinic) and (Zr,Nb)02 1461+ [17] they form in a limited range of

temperature. The main advantage of this method is the possibility to prepare phases with

small differences in composition.

2.2.C. METHOD 3 [13]

Tablets of the mechanically mixed components Ti02 and Nb205 (in a known ratio) were

reduced with weighed amount of Nb-foil in sealed tubes at 1250 °C (fig. la) . In this

way homogenous samples consisting of (Ti,Nb)02 solid solutions (Guinier method) were

obtained. In a second step (Ti2yNbi_2y) O2 0 heated in air or in O2 and thereby

spontaneously oxidized. Like method 2 the oxidation of solid solutions provides for a close

contact of the components in the resulting (Ti2yNbi_2y)02 . 5-y . Method 3 is limited to the

systems (Me,Nb)Ox (x>2.0) which are adjacent to solid solutions with the composition

(Me, Nb) 02^0

•

2.2.d. METHOD 4 [5,13]

Tablets of the mechanically mixed components Nb205 + WO3, Nb205 + Nb02 + WO3, and

Nb205 + WO2 + WO3 were isothermally heated in sealed quartz tubes (fig. la) . Before sealing

the tubes were filled with air or O2 (for experiments with Nb205 + WO3) or evacuated in all

other cases. The weight of the tablets was checked before heating and after the experiment

was finished. In this way vaporization of WO 3 could be noticed. In experiments with

Nb205 + WO3 a loss of oxygen was effectively suppressed by the O2 content of the quartz

tube

.

2.2.e. METHOD 5 [8,13]

Isothermal heating of the mixed components Nb205 + Nb02F, Nb205 + Nb02F + WO 3, and

Nb205 + Ge02 was performed in sealed platinum tubes. A loss of oxygen was suppressed by

partly filling the tubes with air or O2. After sealing the platinum tubes were inserted

into quartz tubes which remained filled with air (1 atm at room temperature) when sealed.

At reaction temperature this filling of air exerts a pressure of 3 - 4 atm and prevents

the platinum ttibes from bursting (fig. lb) .

2.2.f. METHOD 6 [14]

In the Nb02 - Nb20 5 system NbO^ phases can be prepared from niobium oxides having

higher (0/Nb>x) or lower (0/Nb<x) oxygen content by equilibrating them with well defined

H2O - H2 mixtures at high temperature. For details of the equipment see [18].

66
50-60 mm 50 -60 mm

T2-T}~W0°C

WO -130mm

0 15 -20mm

Fig. 1. Heating of samples in closed vessels (a) isothermal heating

in a sealed quartz t\ibe (method 4) ; (b) isothermal heating

in a sealed platinum tube enclosed in a sealed quartz tube

(method 5) ; (c) heating in a temperature gradient using a sealed quartz tube (method 7) ; (d) heating in a temperature

gradient using a sealed platinum tube enclosed in a sealed

quartz tube (method 8) . in figures a through d the sealed

quartz tubes are reinforced by surrounding open quartz tubes

.

During an experiment the filled tubes were placed in platinum

boats, (e) chemical transport in a well defined temperature

gradient (method 9) using sealed quartz tubes.

2.2.g. METHOD 7 [13]

Small quartz tubes surrounded by a belt tube (fig. Ic, cf. method 4) made it possible

to use closed quartz vessels for chemical transport reactions at temperatures of 1200 - 1250 °C. For the principle see method 9. The temperature gradient in method 7 is less well

established, of course, than in method 9.

It is favorable to use the inert compound NbsOyCl to introduce the transporting agent

NbOCl3/NbCl5 (eq (2)) into small t\abes with a low volume [7]. At higher temperature NbsOyCl

mainly decomposes as described by equation (1)

.

SNbsOyCl^g = 4Nb205^g + NbOCls^g (1)

The additional Nb205 formed after equation (1) may be taken into account by the starting

weight of the other components.

By this method it became possible to prepare crystals of Nb02.i+53, Nb02.it64' ^^'^ Ti2Nbio02 9 (orthorhombic ) which were not obtainable by method 9.

2.2.h. METHOD 8 [8,13]

Using a temperature gradient and sealed platinum tubes it was also possible to study

transport reactions with niobium oxide fluorides. By this way larger crystals may be

obtained than with method 5. Both methods are similar in equipment (fig. Id).

I

67
2.2.i. METHOD 9 [15]

The method of chemical transport was a particularly suitable one for the preparation of

well crystallized samples of the Nb02 - Nb205 system and for numerous ternary phases con- taining niobium. The deposition of substances by means of a well established temperature

gradient (e.g. T2 - T^ = 100°) can be carried out in sealed quartz tubes of sufficient

length (e.g. 1 = 100 mm; v = 25 cm^) . They can be used at temperatures up to T2 = 1100 °C. Experiments at higher temperatures required smaller tubes (v = 1 - 2 cm^) cf. method 7.

Nb205 is transported along a temperature gradient to the less hot zone at T^ by endothermic reactions as described by equations (2) or (3)

.

Nb205,s + 3NbCl5^g = 5NbOCl3^g _ (2)

Nb205,s + 6HC1 = 2NbOCl3^g + 3H20^g (3)

The ratio 0/Nb in the solid is controlled by the composition of the vapor phase. In the

presence of chlorine (P(Cl2) = 1 atm, 20 °C) the niobium in the solid is in its maximum

oxidation state. Other possible 0/Nb values may be established by using a CO2 - CO mixture

("buffering of the vapor phase") ^. Lower 0/Nb ratios are also obtainable if in reactions,

described in equations (2) and (3) , chlorine is replaced by bromine or iodine [19]

.

Ternary oxides e.g. Ti2Nbio029 can be transported in a temperature gradient if a re- action for the transport of Nb205 (eqs (2) or (3)) and also a similar parallel reaction for

the transport of the other component cf. for Ti02 (eqs (4) or (5)) exists.

Ti02^s + 2NbCl5^g = TiCli^ g

+ 2NbOCl3^g (4)

Ti02,s+ 4HC1 = TiCl^^g + 2H20^g (5)

The composition of the solid deposited at T^ is given by the ratio Nb/Ti and depends

on the ratio Q of the partial pressures P(Nb0Cl3) and P(TiCl4) in the vapor phase and on the

temperature.

The rate of chemical transport for both oxides is only sufficient^ if Q has no extreme

value. This statement shows that chemical transport of ternary oxides is only possible if

the transport reactions for both components (eqs (2) and (4) or (3) and (5) ) do not combine

to a reaction (eq (6) ) the equilibrium of which is shifted extremely to one side [17] . This can be demonstrated for a system Me02 - Nb205 with the simplified equation (6)

.

2Nb205^s + 3MeCltt^g = 4NbOCl3^g + 3Me02 , s (6)

If according to equation (6) MeCl4 disappears from the gas phase the chemical transport of

Me02 comes to a standstill. Similarly Nb205 cannot be transported if Nb0Cl3 disappears. For

an accurate discussion of the position of equilibrium of equation (6) the free enthalpy of

formation of the ternary oxides (and of possibly existing complex molecules in the vapor

phase) has to be taken into account.

For Me = Ti a calculation of the equilibrium (eq (6) ) is in accordance with the observation that chemical transport takes place for ternary titanium niobium oxides. The solid

in the zone with the higher temperature T2 showed a small increase in the Ti02 content.

This is in agreement with the sign of AH°j^ for this reaction.

2.3. X-RAY WORK

In all cases the x-ray investigation was performed with a Jagodzinsky powder camera equipped with one chamber. The circumference of 360 mm and the CuKaj radiation used perSee H. Schafer's paper at this meeting.

7 For further conditions necessary for chemical transport see [15]

.

68
mitted a high resolution. For instance the small amount of 1% of the additional phase Nb02 was still detectable in Nb02.i4i7. The sensitivity was decreased with increasing similarity

of the diagrams. In samples of Nb02,tt83 °f the neighboring phases Nb02.478 or Nb02.tt89 were detectable. In this case the accuracy with regard to the gross composition was 0.001

0/Nb which is still high.

Samples which proved to be monophasic by x-rays may, within the limits of ±0.001 0/Nb

,

in special cases contain up to 1/5 of the neighboring phase. This may possibly explain why

neighboring phases could be detected in these samples with electron optics [11]

.

In all cases the samples were quenched and Guinier diagrams were taken at room temperature .

2.4. ANALYTICAL WORK

For the identification and relation of phases the gross composition 0/Nb (O/EMe = 0/E

(Me + Nb (V) ) in ternary systems) of these phases is of main interest. Generally a reaction

Q was started with components the ratio of which was accurately determined by weighing. A chemical analysis was not performed provided no volatilization occurred or the possibility

of a loss of substance could be excluded by check of weight. In all other cases the com- position was determined by chemical analysis.

For investigation of the region 2.417 - 2.500 O/Nb of the Nb02 - Nb205 system a special

micro analytical method [21] was available. The method is based on the principle that the

Nb (IV) portion of the NbOx oxides reacts with a molten KOH - KBr mixture to form niobate (V) and hydrogen. The amount of hydrogen evolved is measured. The v;eight of the analyzed samples

amounts to 6 - 12 mg. The accuracy depends on the amount of hydrogen. Its limits are 2.420±0.003; 2.460±0.002; 2.490±0.001 0/Nb.

The composition of samples of the systems Ti02 - Nb205, Nb205 - WO3 or Nb205 - Nb02F

is given by the content of Ti, W or F, if the metals are completely in their maximum state

of oxydation. The absence of lower oxidation states [e.g. Nb(IV), Ti(III)] in these cases

was established with the micro method [21]

.

In samples of the system Ti02 - Nb205 the portion of Ti was determined and thereby also

the composition 0/Z (Ti + Nb) [13] . The samples were melted with K2S2O7 and siibsequently

dissolved with a solution of oxalic acid. Then chromotropic acid was added and the resulting

color was compared with the color of similarly prepared standard solutions of titanium. The

accuracy depends on the content of titanium and may be gathered from the following resulting

formulas: (Ti ,Nb) O2 . i+2±0 . 0 0 3

'• (Ti ,Nb) O2 ^ it60 +0 . 0 0 2 ? (Ti ,Nb) ^ tt9 + 0 . 0 0 1 0/E (Ti+Nb) .

For the Nb205 - Nb02F system a micro method for determination of low fluorine contents

was developed [17] . In a closed system a mixture of the sample with K2S2O7 is melted. HF

is distilled off and absorbed in NaOH. The photometric determination of fluorine is performed by the method of Belcher [22]^,

3. RESULTS

3.1. GENERAL ASPECTS

An investigation of hybrid phases necessarily requires an investigation of neighboring

phases with closely related structures, particularly phases with simpler basic structures.

Observations were collected in tables 2 to 6 with the phases arranged according to structural

relationships

.

According to their building principle (paragraph 3.2) each ideal structure has a definite

gross composition O/E Me (or (0,F)/Z Me, respectively). Therefore it is particularly interesting to see that the observed 0/E Me of a structurally well defined phase often disagrees

8 The starting materials were of highest purity if available. As to the problem of additional

contamination of substances in the course of an experiment see [13,14].

9 The experiments were performed by G. Kopke

.

69
II

II

II

II

II

II

II

II "O II ^—

II11

II 0)

II to

II I? II

II Q.

CD II I-t II o

II •H '—1

II

D II C 11 o\ 1 o II

11 In -H II 1 Q II -t-> • T3 II U M- D 11 o O co

•H

+>auI

0) -aho

CD 4-> c E

D.E O O —(

-q"

</) o c u 14- o

•H

(/I (D +j O -C o

+J

u

CL o o -C D. c -p 01 o •H ^^ E 3 a a -H U to 0) u o O'

CO

CM

<DUD

-MO

CN

CO

Csl

CO

CO

CM

11 -Y 11 U (U II CO o N 11 X

•H II CO

U) II

COCO

D II

II 3 II CM

II

O in 11 O II 01 M- 11 o co - E -H 0) O 4-1 C3- -H D >N

tf) -P -(-> >^ O ^

CNJ o c '—s

J3Uo ou

C^lc

CMo I j

so I—I ofx —~- CN > II > :z oo

cS

CO

CM

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cm"

Li.

0) u.Do

Cs! CM Xc / X

CO

Csi

Cseg

CJ

CsU

CM

O o ^

Csl 4-' r— U

0) o

Cs

CsJ Os • CM' ^ O E

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.— -C s IH J3 O

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(Uu

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(C eg

rH ^

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g

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on

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(D1

4J Z +J

C ro 0)

:ab: rH t3 o\° 0 •H 0 >i in g m

64

see ^ 0

U) 4-1 te 4H H <D

11

U CO ft TI

ices

>, 3 X M rH >,

(1) (0 cn X) 0 C <N ^ 0) C B 0 m

0) 0 rl

n

ref

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u • ^ r-H to

0)

X X! >i

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m 0 2 rH

0) „ (N 03

a in Lo -HC

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u rH 0 x; (C (0 - C

ft c J- -rl x; 0 H 0 0 •H H - X!

cr> 4J rH Z

11 •rl Csl W Tl w 0 m m T! Ti QJ t£) 01 ft 0 as rH rtJ rH

ftH ft

4J Q)

U

0) 0 (3 -H s w s D4 W H

W

ITJ XI

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70
oco

•H

+> •H-o

-aoco

•H

+>aoIcH

Q. S E O O r-to

•HO

O

O -C

-C +>

D.O -C c +> O -H E 5

<1> "O

0)co

•HouooM

Q. o

(1) o co E -H

©

(U -t-> O.

-P o w -P •+-> o ^ m<N Oi I-l o o

J3 -D

Q. >

CM O «• o

a.I

CM

j3 in

D.

CM Oo•

CO I I Q.

CO

.CO.

cm"

in oCM omo

CM o II .—1

•H II 0)

a -P II o •H 0) M •H U) II E O II

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(1)

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to

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71
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(1) c ^ • +J 0

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72
-7 II o II

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0) C 0) II u ' N •H E II M hQ. II s =. C>l E O >^ II O-. r— ' O II f—

u

m II K O M fx ^ s ^—

s

O c II CO CO 00 o U- O II so so M3

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y '"I- (0 0) -(-> II o ^ o II > > > - •> > > -C -P Vh II 1—

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II o II -44

CO II

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73
in

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0) 4JOc

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74
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75
with the ideal composition corresponding to a perfect occupied lattice. In these cases either ranges of homogeneity exist or narrow phases with noticeable deviations of composition

from ideal structures (paragraph 3.4).

It may be derived from experimental results up to what extent the replacement of a Me

cation or of 0 by F is tolerated by each type of the compounds without change in the 0/Z Me

ratio. This derived result is compared with the type of the observed hybrid structure (paragraph 3,3) and discussed from the aspects of stability (paragraph 3.5).

3.2. BUILDING PRINCIPLE

The structures most of which were solved by Wadsley and Andersson [43] can be characterized by building elements, which are "blocks" of different sizes that look like sections

of a Re03 lattice. The blocks consist of octahedra having corners in common and also sharing

edges when connecting blocks.

Structures with the same type of connection may be described as members of a structural

related series (e.g. Me3n08n-3; Me3n+i08n+i ) • Members of a series differ in the width of the

building elements (blocks) which in one direction is described by the value of n. Within a series the width of blocks in a second direction, perpendicular to the first one, is constant.

In the third direction which generally coincides with the b axis of the structures the width

of the blocks is not limited. In figure 2 a typical section of a block structure is depicted.

3.3. TYPES OF HYBRID PHASES

The principle of hybrid structures is a combination of the building elements (blocks)

of two simpler '•'^ structures resulting in new more complicated sequences [6] . Since the

blocks are clearly distinguished by their width and their connection with neighboring blocks

they represent the basic elements of this type of structures. Therefore one might consider

that they transmit some properties e.g. the actual composition and the stability of a lattice

from the basic structure to a hybrid phase (paragraph 3.5). A transition of properties in

this assumed way might be most effective if the original surrounding ("sphere of coordination")

of the blocks is transmitted unchanged to the new hybrid structure. In accordance with

results of Allpress [10,11] two types of hybrid structures exist which can be distinguished

by the extent of change of the surrounding of the blocks.

3. 3. a. TYPE 1

The surrounding of the blocks remains unchanged (fig. 3) if both basic structures con- sist of identically connected blocks, i.e. if a hybrid structure is built up from different

members of the same series.

Examples of this type:

Mettn+lOim ; Mei 3033 + MeiyOtttt = MesgOyy (table 6) . -

Me3n+l08n+l ; MeiQOgs + Mei3033 = "Me2305g" (table 6) .

^^ssn+l^Sn-Z ' between two neighboring members (n = 7,8,9,10,11)

exists one 1:1 hybrid phase (table 5). For

additional hybrid phases see table 6 [11]

.

Me3^0gn-3 ; within this series ordered hybrids are not yet

known (except for orthorhombic Mei2029?

paragraph 3.5.b).

10 The most simple structures containing only one type of blocks are called "basic structures"

in this paper.

76
(Me.Nb^)^O (monod)

Fig. 2. Idealized drawing illustrating the principle of

block structures. The picture shows a section

of the structure of monoclinic (Me,Nb) 12O29

(cf. table 2) projected parallel to the crystallographic b axis. In the lower part of the

figure each square represents an Me - 0 octahedron

viewed down a body diagonal. The lighter and

darker squares are centered on parallel planes

half a body diagonal apart. For the connection

of octahedra see paragraph 3.2. The blocks are

3 octahedra x 4 octahedra in size. In the upper

part of the drawing each block is represented by

a rectangle which joins the metal atoms of the comers of a block. This highly idealized model

is also used in figures 3 to 5.

77
Fig. 3. Combination of building elements leading to a hybrid

structure of type 1. Rows of blocks of the basic

structures AA and BB combine to the resulting hybrid

phase with the sequence ABAB. The blocks are represented by rectangles; the atoms in tetrahedral coor- dination by circles, (a) 3x4 blocks arranged as in - WNbi2033' 4x4 blocks arranged as in WNb^ 4W204i^ ; (c) hybrid phase W2Nb2gW2077 containing rows of 3x4

and 4x4 blocks; (d and e) the surrounding of blocks

remains unchanged with respect to 4/4 tetrahedral

positions per block.

3.3.b. TYPE 2

The surrounding of the blocks is a changed one in the hybrid phase with respect to the

basic structure, if these basic structures are members of different series that differ in

the manner by which the blocks are connected.

Type 2a is characterized by a ^r^ibination of blocks identical in size (fig. 4). Planes

in which connection of the blocks occurs remain only partially unchanged (E,F in fig, 4) compared to each one of the basic structures. The resulting different surrounding of the

blocks is shown in figure 4f.

Examples are all phases of the series Me3n+i08n-2 with n even, which can be built up

by the basic structures Me3n08n-3 snd Me3n+iOgn+i with equal values of n. For additional

hybrid phases see table 5.

Type 2b differs from type 2a by having blocks of different size {fig. 5) . The surrounding

of the blocks and the planes in which connection occurs are totally changed in the hybrid

structure when compared with the basic structures. The resulting type of surrounding with

2/4 tetrahedral positions per block corresponding to a sequence 1:1 is given in figure 5f,g.

More complicated sequences lead to blocks surrounded by 1/4 or 3/4 tetrahedral positions

[10] .

Examples of a sequence 1:1 are the phases of the series Me3n+i08n-2 with n odd, which

result from the basic structures already mentioned with type 2a if the value of n in

Me3n08n-3 exceeds the one in Me3n+i08n+i by 1. For additional examples of more complicated

sequences see table 6.

78
E

F

E

F

C ' 1°|

1

1 l-F

c

/4

/4

'F

Fig. 4, Combination of building elementd leading to a hybrid structure

of type 2a. Rows of blocks of the basic structures AA (series

Mssn+iOsn+l^ and CC (series Me3n03n-3) combine to the resulting

hybrid phase of the series Me 3^+103^-2 = even) . The blocks

are represented by rectangles, the atoms in tetrahedral coordination by circles, (a) 3x4 blocks surrounded by atoms in tetrahedral positions as in WNbi2033; (ti) 3x4 blocks arranged as in

Nb;^2029' hybrid phase Nb2 50g2 i^i which the rows A and C can no longer be distinguished, because the surrounding of each

block has changed. Only shear planes E,F of the basic structures

remain unchanged; (d and e) blocks with unchanged surroundings of

4/4 tetrahedral positions per block respectively without tetrahedral positions; (f) surrounding of blocks of the hybrid phase

with the sequence 1:1 resulting in 2/4 tetrahedral positions per

block.

79
Fig. 5. Combination of building elements leading to a hybrid structure

of type 2b. Rows of blocks of the basic structures AA (series

Me3n+i03n+i) and DD (series Me3i^ (0,F) 3^-3) combine to the

resulting hybrid phase of the series Me3n+i (0,F) 3n-2 (n = odd).

The blocks are represented by rectangles, the atoms in tetrahedral

coordination by circles, (a) 3x4 blocks surrounded by atoms in

tetrahedral positions as in WNbi2033; (b) 3x5 blocks as in

MgNbiLj035F2; (c) hybrid phase Nb2807o (H-Nb205) formed by com- bination of rows G and H, not by combination of A and D. In this case shear planes were changed completely, (d and e) blocks with

unchanged surrounding corresponding to the basic structures; (f

and g) surrounding of the blocks in the hybrid phase with a sequence

1:1 resulting in 2/4 tetrahedral positions per block.

3.4. DEVIATION OF CHEMICAL COMPOSITION FROM IDEAL STRUCTURAL VALUES

3. 4. a. RANGES OF HOMOGENEITY

It seems to be characteristic of some types of compounds to exist monophasic in a certain range of gross composition 0/Z Me. In these cases no measurable change in the lattice constants depending on a variation of the chemical composition was detectable. The

accurate determination of the limits of a range of homogeneity is based on the sensitivity

of the determination of neighbor phases by the Guinier method-^ ^

. Explanation for the existence

of these deviations from ideal structures, based on structural arguments, are not consistent

at the moment. Explanations by microdomains of neighbor phases or Wadsley defects proved to

be insufficient as shown by electron optical investigations [44].

A comparison of the results of investigation (table 2 to 6) shows that ranges of homogeneity are especially realized with certain types of structures if equilibrium conditions

are considered. -^^

These ranges of homogeneity must be clearly distinguished from solid solutions resulting

from the substitution of a cation or an anion but leaving the ratio (0,F)/i:Me unchanged

In these cases changes in the lattice constants were observed.

12 Additional metastable ranges of homogeneity are especially observed at lower temperature

[13] .

80
No Stable ranges of homogeneity could be detected for basic structures of the series

Me3j^08n-3-

Among the basic structures of the series Mes^+iOsn+i and related structures (Mei+n+lOi in

Mssn+iOii+n-l ) only one phase (WNbi2033) is known to have a range of homogeneity (table 2).

Hybrid phases of type 1 e.g. ^2^'^2&'^2'^17 (table 6), Nb02,L|82f Nb (0 ,F) 2. 510 ' and

Nb(0,F)2.52 3 (table 5) have no detectable ranges of homogeneity^ .

Well known hybrids of type 2 are phases of the series Me3n+i08n-2- this case each

phase (n = 8,9,10,11) has a range of homogeneity with the exception of Nb2205Lt (n = 7) , cf

.

table 5 and figure 6. It is of special interest, that among these phases Nb2 5O52 (2 . 467 - 2.478 0/Nb) and Nb2807o (H-Nb205; 2.489 - 2.50 0/Nb) have the largest ranges of homogeneity.

Both structures contain the basic element Mei303 3 that by itself has a range of homogeneity

of 2.516 - 2.538 = 0.022 0/Z Me. Therefore one may consider, that the element Mei3033

transmits a portion of its properties corresponding to =

' 0/Me to both hybrid phases

.

Ranges of homogeneity calculated in this way (in brackets) agree well with the observed ones:

Nb25062 (2.469 - 2.480 0/Nb),

NbasOyo (2.490 - 2.500 0/Nb).

A corresponding relation concerning the phases Nb3x077F (2,515 - 2.519 (0,F)/Nb) and

Nb3i^0gitF2 (2.527 - 2. 532 (F,0)/Nb) which have smaller ranges of homogeneity can not be discussed because accurate knowledge of ranges of homogeneity have not been established for

the basic structures MgNbii4035F2 and WNbisOi+gF3.4.b. NARROW PHASES WITH DEVIATIONS OF COMPOSITION

Phases with a sharp composition determined by chemical analysis, but differing from the

ideal composition derived from structural conditions, mainly belong to the hybrid phases of

type 1 (tables 5 and 6). According to paragraph 3.4. a. these phases have no ranges of

homogeneity under equilibrium conditions.

Because the structures of hybrid phases of type 1 are combinations of the building

elements of neighbor phases, their composition should result from the combination of the

compositions of the building elements. These ideal compositions according to their ideal

structures could be observed for only two phases (eqs (7) and (8) )

.

WNbi2033 (2. 538 0/Z Me) + WNbi4W204tt (2.589 O/l Me) A W2Nb25W2077 (2. 567 O/l Me; ideal)^'* (7)

Nb3i077F (2. 517 X/Nb) + Nb3408itF2 (2.529 X/Nb) ^ Nb(0,F) 2 . 523 (Nbg 5O1 g 1^ 3 ; ideal) (8)

For equation (7) the actual limits of the neighboring phases are identical with the

ideal compositions. For equation (8) the actual limits of both neighboring phases deviate

from the ideal composition. For the actual limits of the neighboring phases see equation

(9). As shown, the actual composition of the hybrid phase Nb(0,F)2.523 ^ay result from the

actual limits of the neighboring phases (eq (9) ) as well as from their ideal compositions

(eq (8)).

Nb3i077F (2.519 X/Nb) + Nb3408i+F2 (2. 527 X/Nb) A Nb (O ,F) 2 . 52-3 (actual) O)'

The observed range of homogeneity of the hybrid phase Nb02.i+6i+ '^^'^ possibly be metastable

[7]. .

'

For additional specifications see tables 5 and 6.

81

465-504 O - 72 - 7
The actual composition of the following hybrid phases (see fig. 6) can only be explained

by a combination of the actual phase limits of both neighbor phases. The relationships with

respect to the phases Nb (O ,F) 2 . 5 1 o ? Nb02 i+83' ^^'^ Nb02.U6'4 recognizable from equations

10 through 16.

Nb2807o(2.50 O/Nb)^^ + NbsjOyyF (2.517 X/Nb) A Nb(O,F)2.508 (NbggOi 47F ; ideal) ^ (10)

Nb28O70 (2.504 X/Nb)^^ + Nbs 1O77 (2 . 515 X/Nb) A Nb(0,F)2.5io (actual) (11)

Nb2 506 2 (2.480 0/Nb) + Nb2 8O70 (2 . 50 0/Nb) ^ ^ A Nb02 . 49 1 (Nb530i32; ideal) (12)

Nb25062 (2.478 0/Nb) + Nb2807o (2 .489 0/Nb) ^ ^ A Nb02 . 4 8

3 (actual) (13)

Nb22054 (2. 4545 0/Nb) + Nb2 5O52 (2 . 480 0/Nb) A Nb02 . 458 (^^470115; ideal) ' (14)

Nb2205i+ (2. 453 0/Nb) + Nb2 5O52 (2. 472 0/Nb) A Nb02.46i+ (actual; method 6) (15)

Nb2205tt (2. 453 0/Nb) + Nb2 5052 (2 . 467 0/Nb) A NbO2.460 (actual; method 7) (16)

The chemically determined values of the actual composition e.g. 2.483 0/E Me were obtained

from samples prepared in a different way, or prepared by substituting Ti for Nb(IV). Therefore the resulting values are representative for the phases and consequently the differences

in composition cannot be explained by microdomains consisting of neighbor phases [11]

.

Additional hybrid phases known from the electron optical investigations of Allpress

[10,11] so far have not been prepared in a monophasic state. Therefore the real chemical

composition is still unknown.

ideal structures

Nb (O.F).

8/) -2

experiments at I200-I300°C

NbO-

'2Al: NI3O2 NbO

(2.508) (2S23)

Nbjfyf Nb^O^Fj

asi6) (2.529)

* i1

1

S ^=2 2 In! In fi? io lo IJI 2

N . *lNbjOyF

I I I I I

(OF)lNb ^ ^Nb02F

Fig. 6. Section of the systems Nb02 - Nb205 and Nb205 - Nb02F.

Compositions derived from chemical analysis (lower part

of the figure) and from ideal structures (upper part) are given for the systems in a high temperature region,

in which all known members (n = 7 - 11) of the series

Nb3n+i (0,F) 3j^_2 and the corresponding 1:1 hybrid phases

exist.

1 5 As modification H-Nb205.

82
Additional phases having a composition which deviates from the ideal one are GeNbisOi+y

(table 3) and the hybrid phase PNb22057.5 (table 6), GeNb^gO^y with the ideal structure

(Me,Nb) 10O25 has a deficiency of oxygen of the same order of magnitude (0.022 0/Z Me) as WNbi2033 (paragraph 3. 4. a). This value may be compared with the deviation of the actual

composition PNb22057 5 from the ideal formula "PNb22058"' Y^t these actual compositions

cannot be explained by structural considerations.

3.5. STABILITY

According to numerous observations the experimental results gained at higher temperatures

(table 2 through 6) may be near to equilibrium conditions of a thermodynamically stable system.

This was mainly confirmed by the measurement of equilibrium conditions in the system Nb02 - Nb205 at 1300 °C [14] . Values measured in this investigation made it possible to develop a model of the relations [13] between the stability of these phases and the size of the blocks

in these structures'^. It must be mentioned that according to this, the stability of a phase

can be considered only in relation to the neighboring phases.

The numerous results of experiments in which one component of a typical compound was replaced in several different ways, suggested that it might be possible to compare qualitatively the stabilities of those compounds (represented by definite structures) with regard

to different systems. That means, the situations in a region between two limiting types of

structures realized in different investigated systems {e.g. between (Me, Nb) ^2^29 ^'^^ H-Nb205)

may be comparable. The extent to which a structure tolerates the replacement of Me or of O

by F may be a rough criterion for the stability of the structure in this region. A supplementary indication of the stability may be the extent of the temperature region in which a structure is stable.

3. 5. a. BASIC STRUCTURES

With respect to the basic structures Mesj^ (0 ,F) gn-3 and Mesn+i (0 ,F) 8n-2 members with

3x4 blocks (tables 2 and 3) may be most stable. The structure types (Me, Nb) 12^29 ^nd

(Me,Nb) 1 3O33 , being stable in an extended range of temperature' , tolerate different Me

cations. Within the series Mesn (0 ,F) gn-S and Mes^+i (0 ,F) gn+l the stability decreases with

an increasing value of n. Phases with n = 5, such as MgNbi4035F2 and WNb^ sOi+qF (MoNb^ 5O1+ qF) , only show an insignificant tolerance for the replacement of Me, and phases with n = 6

(e. g., NbigOi+s) are non existent. Related basic structures Meifn+lOjin and Mesj^+i Oj 14^-! tolerate a certain replacement of the Me particles but their ranges of existence decrease

with increasing block size and are shifted to higher temperatures [5]

.

3.5.b. HYBRID STRUCTURES OF TYPE 1

Hybrid phases of type 1 are closely related to their neighbor phases (paragraph 3.3)

.

In addition to relations concerning the compositions (paragraph 3.4.b.) they show

relationships concerning the stabilities of the neighbor phases. According to this, a hybrid of type 1 could only be observed if both building elements of the hybrid phase were realized by neighbor phases of the same system (tables 5 and 6)'^. These relationships

between the 1:1 hybrids and the series Mesn+i (0 ,F ) 8n-2 (Me = Nb(v)) are shown in figure 6.

According to the assumed relation of stability the hybrid Nb02.i+6i+ ^as only observed

in the Nb02 - Nb205 system in which also the phase Nb2205i+ exists as one building element.

Though an analogous (Zr ,Nb) 22O51+ is non existent, the observation of the phase (Zr ,Nb) O2 .i+eit does not disagree with this conception, bacause (Zr ,Nb) O2 .1+61+ very probably is metastable

[17].

^^This model and the considerations following do not take into account the distortion of

octahedra in the actual structures.

^^The transformation of the monoclinic form of (Me,Nb)i2029 into the orthorhombic form

was neglected.

1 8 The existence of PNb22057.5 seems to be an exception to this.

83
It is of special interest that the 1:1 hybrid phases observed so far could only be

obtained at temperatures higher than needed to prepare the basic structures [13] . It may

be possible that the stability of hybrid phases is enhanced by a small increase of entropy-^

with respect to the simpler basic structures. If this is correct it may be understandable

why hybrid phases, with the phases WNbigWi+Oss and WNbigWyOgg as building elements, could not

be observed. Since these (basic) phases are only stable in a region of high temperature,

the resulting hybrid phases may be unstable because their range of existence can be expected

to be above their melting points. It also fits into this picture that monclinic Mei2'-'29' the only phase existing in an especially low temperature region, shows a transformation into

its own hybrid^'' which is the orthorhombic form of Mei2'-'29' other monoclinic phases

which already exist in a region of high temperature obviously do not show a transformation

to orthorhombic modifications because the temperatures required would be above their melting

points. According to that, more complicated sequences should not be stable if the 1:1 hybrid

phases only exist at higher temperature.

3.5.C. HYBRID STRUCTURES OF TYPE 2

Hybrid phases of type 2 show less clear relationships of stability with respect to the

basic structures.

Basic structures of the series Me3n08n-3 ^rif^ Mesn+iOsn+l combine to hybrids (1:1)

represented by the series Me3j^+i Ogn-a • the following these 1:1 hybrids are tabulated

according to decreasing stability.

(Me,Nb)250g2 with the building elements (Me,Nb)i9029 and (Me,Nb)i3033 exists, like its

basic stiructures, in a wide range of temperature and with a considerable variability of

composition with respect to the Me cations.

Nb28O70 (H-Nb205) allowed no replacement of Nb without changing the 0/E Me ratio {cf

.

table 5 (i) ) ; the Nb3i077F structure is only stable in the fluoride system. Both have

extended ranges of existance with respect to temperature.

The members Nb2205tt and Nb3[|08i|F2 limiting the series Me3n+l (0 ,F) Qn-2 (fig- 6), tolerate

no replacement of Me. Their range of stability is limited to a small region at high

temperature. It is remarkable that these phases are stable though they contain blocks of

the non existing structures "NbiQ025" and "NbigOtts" (tables 2 and 3).

4. SCOPE OF FURTHER INVESTIGATION

with the aid of electron optical methods combined with subtle methods of preparation

and chemical analysis it may be possible to perform chemical investigations of hybrid

phases, such as TiNb3g09 7, which have more complicated sequences than 1:1. Furthermore

it may be possible to determine ranges of homogeneity, suspected for hybrid phases like

WNb26058 because of a comparison^^ with the related phases Nb25062 and Nb28O70 • With

respect to this, it is important to know whether the thermodynamic stability of the phases

decreases with increasing complexity of sequences in these structures. This question

should be solved in further investigations. In addition to this the thermodynamic concept

of a phase must be reconsidered if the sequences become extremely complicated. Metastable

regions of homogeneity not mentioned in this paper (c. f., [13]), should also be investigated

with the new methods.

19 In principle the existence of block structures is favored at high temperatures because

of the increase in entropy [13,17].

20 The orthorhombic form may be described as a hybrid consisting of component rows of the

monoclinic form [11]

.

21 A calculation according to paragraph 3. 4. a. leads to a range of homogeneity of 2.502 - 2.518 0/E Me for WNb26058.

84
5. ACKNOWLEDGEMENTS

The author thanks Professor Harald Schafer for his stimulating interest and for

continuous support during a long time of cooperation in the institute at Munster. He also

thanks D. Bergner, M. Gorbing, G. Kopke , W. Mertin, M. Trenkel, and E. Vogel for their

cooperation. The author is obliged to the Landesamt flir Forschung, Dlisseldorf and to the

Verband der Chemischen Industrie - Fonds der Chemischen Industrie - for their support.

6. REFERENCES

[1] Gruehn, R. , and Schafer, H., Naturwissenschaften , 50^, 642 (1963).

[2] Wadsley, A. D. , Acta Cryst. , lj4, 664 (1961).

[3] Roth, R. S., and Wadsley, A. D. , Acta Cryst., 1_8, 724 (1965).

[4] Schafer, H., Gruehn, R. , Schulte, F. , and Mertin, W., Bull. Soc. Chim. France, 1965 , 1161.

[5] Gruehn, Monatshefte Chemie, 96_, 1789 (1965) . [6] Andersson, S., Mumme, W. G., and Wadsley, A. D., Acta Cryst., 22^, 802 (1966).

[7] Gruehn, R. , and Norin, R. , Z. anorg. u. allgem. Chem., 367 , 209 (1969).

[8] Gruehn, R. , Naturwissenschaften , 54_, 645 (1967).

[9] Allpress, J. G. , Sanders, J. V., and Wadsley, A. D. , Phys . Stat. Sol., 25_, 541 (1968).

[10] Allpress, J. G., and Wadsley, A. D. , J. Solid State Chem., 28 (1969).

[11] Allpress, J. G., J. Solid State Chem., 1, 66 (1969).

[12] Allpress, J. G., J. Solid State Chem., 2, 78 (1970).

[13] Gruehn, R. , Habilitationsschrift, Munster 1968.

[14] Schafer, H., Bergner, D. , and Gruehn, R. , Z. anorg. u. allgem. Chem., 365 , 31 (1969).

[15] Schafer, H., Chemical Transport Reactions, Academic Press, N. Y. , London 1964.

[16] Gruehn, R. , and Schafer, H. , J. Less-Common Metals [Amsterdam] 10_, 152 (1966) . [17] Gruehn, R. , unpublished work.

[18] Bergner, D., Ph.D. Thesis, Munster 1966.

[19] Schafer, H. , and Huesker, M. , Z. anorg. u. allg. Chem., 317 , 321 (1962).

[20] Gruehn, R. , and Brunner, H., unpublished work.

[21] Gruehn, R. , Z. analyt. Chem., 221 , 146 (1966).

[22] Quentin, K.-E. and Rosopulo, A,, Z. analyt. Chem. 241, 241 (1968).

[23] Lundberg, M. , J. Solid State Chem., 1, 463 (1970).

[24] Gruehn, R. , Mertin, W. , and Schafer, H. , J. Solid State Chem., 2^, 425 (1970).

[25] Eror, N. G. and Smyth, D. M. , in The Chemistry of Extended Defects in Non-Metallic

Solids", North-Holland Publ. Comp. , 1970.

[26] Waring, J. L., and Roth, R. S., J. Res., NBS , 69A , (phys. and chem.) No. 2, 119 (1965).

[27] The phases were identified through samples from Professor Dr. F. P. Emmenegger, c.f.,

Emmenegger, F. P., and Petermann, A., J. of Crystal Growth, 2_, 33 (1968).

[28] Norin, R. , and Arbin, C. G., unpublished work.

[29] Norin, R. , and Dahlen, B., Acta Chem. Scand. , 23_, 1826 (1969).

[30] Burdese, A., Bolera, M. L. , and Rolando, P., Atti Accad. Sci. Torino I, CI, Sci.

fisiche, mat., natur., 99, 565 (1964/65).

[31] Roth, R. S., Wadsley, A. D. , and Andersson, S., Acta Cryst., 18, 643 (1965).

[32] Roth, R. S., and Wadsley, A. D. , Acta Cryst., 19, 42 (1965).

[33] Mertin, W. , Diplomarbeit, Munster 1964.

[34] Waring, J. L., and Roth, R. S., Acta Cryst., 17_, 455 (1964).

[35] Levin, E. M. , and Roth, R. S., J. Solid State Chem., 2_, 250 (1970).

[36] Andersson, S. , Z. anorg. u. allg. Chem,, 366, 96 (1969).

[37] Norin, R. , Acta chem. Scand., 23_, 1210-1214 (1969).

[38] Gatehouse, B. M. , and Wadsley, A. D. , Acta Cryst., 17_, 1545 (1964).

[39] Sstrom, A., Acta chem. Scand., 20_, 969 (1966).

[40] Norin, R. , Carlsson, M. , and Elgquist, B., Acta. chem. Scand., 2£' 2892 (1966).

[41] Gruehn, R. , and Norin, R. , Z. anorg. u. allgem. Chem., 355 , 176 (1967).

[42] Norin, R. , private communication.

[43] Wadsley, A. D. , and Andersson, S., in Perspectives in Structural Chemistry , (Dunitz,

J. D., and Ibers, J. A., eds.). Vol. Ill, Wiley, New York 1969.

[44] Allpress, J. G., and Roth, R. S., J. Solid State Chem., 3, 209 (1971).

85
DISCUSSION

J. G. Allpress : I would just like to make the comment that in the circumstances where

you have a series of very closely related phases, perhaps the Guinier techniques are not sufficiently sensitive as a means of determining phase boundaries. One really has to look at the

samples at the unit cell level using an electron microscope in order to tell whether one has

randomly distributed Wadsley defects which will contribute to the change in stoichiometry

.

R . Gruehn : Yes, that is a very important point. I had not mentioned it because the time was too short. For the investigation of this field in the future, it is very important to use

the methods you have used in this field. However, I think the compositions of the mono-phasic

state can be determined by Guinier investigations with a deviation of only one in the third

place for phases with small differences in composition. The two phase regions are very small

in this case and there is a detection limit of ~0.001 in the oxygen to metal ratio (O/M=0.001)

The uncertainty of 0.001 in the 0/M ratio may correspond to a content of 20 percent of a very

closely related neighbor phase. This must be the reason why you find regions of neighbor

phases in a sample that was homogeneous on x-ray photographs. I think for the investigation

of the differences in the present work this is a sufficient accuracy but I hope, in the future, we will also investigate this field with the electron optic technique.

B . Cox : Would you like to speculate on what fraction of the composition range of these

compounds is due to extended defects of the type that John Allpress looks at, which presumably

don't contribute to the high temperature electrical conductivity, and what fraction is due to point defects which would contribute to the high temperature electrical conductivity of these

compounds

.

R. Gruehn : We do not know exactly the reasons for these ranges, but I think it is important to know that these ranges of homogeneity are observed also in phases without electric

conductivites . You can have a range of homogeneity_^f rom 0/M 2.500 to 2.489 in the ^ystem with

niobium 4 as well as in the system with titanium 4 . In the_^system with niobium 4 we have

electrical conductivity, increasing with increasing niobium 4 content; but in the other system we have no electrical conductivity and it has exactly the same range. It may be that

there are defects within the blocks or additional matter, metal, and oxygen within the blocks.

I have spoken with Sten Andersson on this point. Some years ago, we considered that there may

be additional metal in the tetrahedral holes. You have seen these holes on the drawings pictured with circles. If these deviations are due to additional metal in tetrahedral positions

they could not be transmitted from one phase to the other, in the way mentioned in my paper,

because the surrounding of the block is not the same in the hybrid as in the original phase.

I think there must be defects within the blocks.

86
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

THE APPLICATION OF ELECTRON OPTICAL TECHNIQUES

TO HIGH TEMPERATURE MATERIALS

John G. Allpress

Commonwealth Scientific and Industrial Research Organization

Division of Tribophysics

Melbourne, Australia

Careful studies of phase equilibria in many high temperature systems have revealed

unexpectedly complex structural relationships, which are frequently very difficult to un- ravel by means of conventional x-ray techniques. The purpose of this contribution is to indicate how and why the electron microscope can be used to advantage in these circumstances. The value of the technique will be demonstrated by referring to the following

recent applications in the field of the structural chemistry of oxides: (1) The determination of unit cell data for microcrystalline samples of alkali metal rare earth titanates,

using electron diffraction. These materials have orthorhombic superlattices of the perovskite

structure; (2) The use of dark field microscopy to study the precipitation of the ferrimagnetic spinel LiFesOs from a nonstoichiometric matrix of a-LiFe02 . The morphology of the

precipitate depends critically upon prior thermal treatment; (3) The direct observation of

crystallographic shear planes in W03_jj (x<0.05) and W03.yNb205 (y=0.03-0.09) . The results

show how changes of composition are accommodated in these systems, and provide clues as to

the mode of formation and diffusion of crystallographic shear defects; (4) The study of

regions of 'solid solution' in the system Ti02-Nb205 (>50 mol % Nb205), by lattice imaging.

Variations in composition are accommodated by coherent intergrowth, at the unit cell level,

of thin slabs of several parent phases; and (5) The study of phases in the system W03-Nb205

which have structures related to that of tetragonal tungsten bronze. Several different

superlattices are possible, and lattice images provide direct evidence for order-disorder,

microdomain formation, and intergrowth with material having a much simpler cubic structure.

Key words: Crystal structure; crystallographic shear planes; electron diffraction;

electron microscopy; lattice images; lithium ferrites; lithium lutetium titanate;

niobium-titanium oxides; niobium-tungsten oxides; tungsten oxides; Wadsley defects.

1 . INTRODUCTION

Of all the techniques available to the solid state chemist, x-ray diffraction is un- doubtedly the most important. Even when structural information is not the primary aim of a particular investigation, x-ray methods are almost universally used to establish the identity and purity of a phase, before proceeding to any study of its properties. However, it

frequently happens that for one reason or another, the structural results obtained by x-ray

diffraction procedures may be incomplete or inconclusive, and other methods of approach

must be sought. Some common instances where this situation arises are as follows: (a) The crystallite size of the material is too small for the application of single crystal

x-ray methods. In these circ\imstances , it is often difficult or impossible to determine

the unit cell dimensions and symmetry unambiguously from x-ray powder data, (b) The

material is disordered in some way, which may or may not be indicated by the x-ray data.

Even when disorder is suspected, its nature and extent may be impossible to determine with

certainty.

87
These and other similar problems occur quite frequently in high temperature solid

state chemistry. The purpose of this paper is to show how and why electron optical techniques can be used to advantage in conjunction with x-ray diffraction procedures for tackling them.

2. ELECTRON AND X-RAY DIFFRACTION

Although the diffraction of electrons is basically similar to that of x-rays, important

differences arise as a consequence of differences in the properties of the two radiations.

In what follows, the properties of 100 kV electrons will be compared with those of Cu Ka

X-radiation.

2.1. WAVELENGTH

o Electron wavelengths A=0.04 A (X-0.004 nm) are about one fortieth of those of x-rays

X=:1.5 A (X=:0.15 nm) . It follows from Bragg's Law that the scattering angles 6 are very

small, and the simple formula A = 2dG , where d is the interplanar spacing, is a good approximation .

A second very important consequence of the shorter wavelengths is demonstrated by the

Ewald construction, illustrated in figure 1. The array of dots represents a two-dimensional

section through a reciprocal lattice, with origin O. The direction of an incident beam of

radiation is indicated by the dashed line, and the vector kQ , terminating at 0, is of length

1/A for x-rays. Any reciprocal lattice point hkl which falls on the surface of the sphere

of radius 1/A, centred on the dashed line and passing through 0, represents a set of planes

for which Bragg's Law is satisfied. In the section shown in figure 1, the circle (in two

dimensions) for x-rays, centred at A, passes through only one point (encircled) , in addition

to the origin. However, for electrons, 1/A is forty times larger, and an arc BOC of the

corresponding circle is shown. It cuts up to four points on either side of the origin.

Thus, in general, for any one angle of incidence, a much larger number of Bragg reflections will be excited by electrons than by x-rays. In the particular case when the beam is

incident down a zone axis, an extended area of a reciprocal lattice section may be excited

at one time. Figure 2 shows electron diffraction patterns from a crystal of high temperature (H-) Nb205, which has a large unit cell. In (a) , the electron beam is incident down

the b axis, and (b) , (c) and (d) were recorded after tilting the crystal about the c* axis

by 1°, 4°, and 24° respectively. The appearance of these patterns can be explained readily

using diagrams, similar to figure 1, by altering the angle of incidence of the radiation.

In figure 2d, the arcs which do not include the central beam of the pattern contain upper

layer reflections of the type hll and hll

.

I

Fig. 1. The Ewald construction. The array of dots

represents a section through a reciprocal

lattice, with origin 0. k^ is a vector in

the incident beam direction, of magnitude

1/X . The circle is a section through the

Ewald sphere appropriate for x-rays, and the arc BOC is part of the section for lOOkV

electrons. Points which lie on the circle

(or arc) represent planes for which Bragg's

Law is satisfied.

88
Fig. 2. Electron diffraction patterns from a fragment of H-Nb^O^.

(a) (010) reciprocal lattice section. (b-d) after tilting

away from (010) about c* , through the angles shown.

Other factors also contribute to the ease with which simultaneous excitation of many

Bragg reflections occurs in electron diffraction. In particular, the reciprocal lattice

spots are extended in the direction of the incident radiation,^ because the specimens are necessarily very thin in this direction. Secondly, the samples may be sufficiently buckled

over the illuminated area to allow additional reflections to satisfy the Bragg condition.

The overall result of the difference in wavelength is therefore that using electrons,

extended sections of the reciprocal lattice can be easily recorded from a stationary

crystal. The equivalent data are obtainable with x-rays only by using a moving crystal

technique, or by employing white radiation. The geometry of electron diffraction patterns

is exceedingly simple, and corresponds closely to that obtained by the x-ray precession

method.

89
2.2. SCATTERING FACTORS

The interaction of electrons with atoms is about 1000 times greater than that of

x-rays. For this reason, a large proportion of electron radiation incident on a thin

crystal is diffracted; the diffraction pattern can be observed visually on a fluorescent

screen and recorded in a few seconds on a photographic emulsion. Adjustments to the

orientations of a crystal can therefore be made while watching the diffraction pattern,

and zone axis orientations such as figure 2a indicates can be obtained quickly and easily.

The facility with which very thin crystals can be examined, combined with the ability to select individual crystals or parts of crystals as small as 10"-^ "^cm^ in cross section,

makes it a straightforward matter to record reciprocal lattice sections from 'single

crystals' which may be only 10" ^^cm^ in volume.

The high scattering factors for electrons have other less favourable consequences.

The limitations on specimen thickness are severe - about 200 nm is the maximum for most

materials. This immediately raises the problem of sample preparation. Thin foils are perhaps the most ideal form of specimen, but apart from metals and a few other materials

which cleave readily, they are not easily prepared. Thinning by ion bombardment shows

promise in this respect [1]-^. The simplest method of obtaining thin samples is by grinding,

dispersing the resulting fine powder on carbon-coated specimen grids and searching in the

electron microscope for thin fracture fragments. Most inorganic materials are brittle, and can be ground without introducing deformation, but the possibility of observing artefacts

which are a consequence of the method of specimen preparation must always be taken into

account.

Multiple scattering of diffracted beams is a serious problem for samples thicker than

10 nm or even less. Diffracted electrons are themselves subject to further diffraction as they traverse the crystal, and the intensity of emergent beams frequently bears no relation

to values expected for single or kinematic scattering. For example, figure 3 shows the

results of computations of the variation of intensity of some OOi beams with thickness, for

a perfect crystal of TiNb2i+052 [2] . For each beam, there is a thickness at which the

intensity drops to zero, and this thickness is known as the extinction distance. Clearly,

these extinction distances vary widely for different beams, and any attempt to interpret

electron diffraction intensities must take these effects into account. This requires the

application of n-beam dynamical theory [3]

.

Thickness in nm

Fig. 3. Computed electron diffraction intensities for some 00?, beams from TiNb240g2' showing that

the variation with thickness is non-linear,

and changes drastically for different beams.

Figures in brackets indicate the literature references at the end of this paper.

90
The modification of diffraction intensities by multiple scattering extends to reflections which are formally forbidden by space group symmetry. Very frequently, these forbidden reflections can be excited with appreciable intensity in electron diffraction, and the

effect is illustrated in figure 4, which shows several patterns from a fragment of LiLuTi205

[4]. Figure 4b was recorded after tilting the fragment about its c axis by ca. 48° from its

position in figure 4a. Figure 4b contains OOJl spots for %i'2n (arrowed) , which are absent in

figure 3a, and forbidden by the space group, Pbcm. This is a consequence of multiple scattering, which can operate to produce intensity at forbidden spots in figure 3b, but not in

figure 3a. The appearance of forbidden spots can usually be predicted, and correct symmetry

information can be derived, provided that a sufficient number of reciprocal lattice sections

are examined.

Finally, a large proportion of the electron radiation incident on a crystal is scattered inelastically , and the energy lost to the crystal appears as heat. It is possible to

melt refractory materials such as Nb205 in the electron beam, but provided thin crystals

and moderate beam intensities are used, the heating effect can be controlled. Nevertheless,

it is not easy to examine heat-sensitive materials such as hydrates , or crystals which

undergo transformations at temperatures below about 600 K, unless special cooled sample

stages are employed.

2.3. CHARGE

The fact that the electron beam carries a charge, in contrast to x-rays, means that

magnified images can be obtained, using magnetic focussing. This fact lies at the basis of

electron microscopy. It allows the direct observation of very small fragments or selected

areas, and correlation with the electron diffraction pattern of the same area. Specific

features in a diffraction pattern can be investigated by dark-field imaging, using selected

diffracted beams. A great deal of information on the nature of defects can be obtained by

recording their images at a number of different but known orientations. These techniques

have been largely developed and refined for application to metals [5] , but their use for

the study of non-metallic materials is equally appropriate and rewarding [5,7].

Finally, the examination of samples at high magnifications is in principle capable of

yielding structural information at the unit cell level. This technique of lattice imaging

has been used for specifying resolution, and some spectacular results have been achieved -

Fig, 4. Electron diffraction patterns from a fragment of LiLuTi205. (a). (010)

reciprocal lattice section. (b). (110) section, obtained by tilting the

fragment about c by 48°. In this orientation, multiple scattering

produces strong reflections in the forbidden positions 0A:0, k / 2n

(arrowed). The rings in the patterns -come from a thin deposit of

aluminium, and are used as a calibration.

91
spacings down to 0.088 nm have been resolved using metal foil samples [8] . Much of this

work requires special skill and equipment, but for materials with large unit cells, useful

results can be obtained relatively easily, using instruments with more moderate resolution

capabilities; say 0.5 - 1 nm. The underlying principle, as stated by Cowley and Moodie [9]

,

is that for very thin specimens which can be regarded as phase gratings, the contrast in the

slightly underfocussed image is a representation of the charge distribution within the object.

This distribution need not be periodic, and it is therefore possible to examine disordered

materials and obtain direct information about their structure.

In the following sections, we shall examine some applications of electron microscopy

to high temperature oxides, which illustrate the advantages of the technique as indicated

by the foregoing discussion.

3. THE STRUCTURE OF ALKALI METAL RARE EARTH TITANATES, MRTi20g [4]

A series of powder samples of MRTi20g (M = Li, Na; R = Y, La, Nd - Lu) was prepared and

examined by x-ray diffraction. The powder data showed obvious similarities to data from

perovskites, but the patterns from the lithium compounds could not be indexed with certainty.

We therefore obtained 'single crystal' electron diffraction patterns from minute fragments

at several different orientations (e.g. fig. 4). A thin layer (ca. 2 nm) of aluminum was evaporated on to the specimen grids in order to provide an internal standard for the determination of interplanar spacings. LiLuTi205 was studied in detail, and its space group

(Pbcm) and approximate unit cell dimensions were obtained from these patterns. The x-ray

data were then indexed, and accurate unit cell dimensions were derived. The compound is

orthorhombic, with a = 5.175, b = 5.409, c = 15.007 A. The limited amount of x-ray powder

intensity data were used to test several possible structural models, all based on a perovskite subcell. It was quickly established that the octahedral sites were occupied by

titanium, and that lithium and lutetiim shared the twelve-co-ordinate sites in an ordered

manner. Refinement of this model is at present being attempted, in order to determine the

distortions from the ideal arrangement.

The sodium compounds proved to orthorhombic, with a-jb-5.4 A, c~7 .6 A, space group Pbnm.

They are isostructural with the rare earth orthoferrites [10] , and an analysis of the x-ray

powder intensity data showed that the sodium and rare earth cations share the twelve-coordinate sites randomly. Electron diffraction patterns from these phases (which were prepared by solid state reaction at about 1300 K) gave a completely false impression of pseudocubic symmetry, with a — 7.6 A, as a consequence of twinning on a very fine scale. When the

samples were sintered for several hours at 1470 K, the twinned domains became large enough

to be readily distinguished by dark field microscopy. For example, figure 5a shows an electron diffraction pattern from a fragment of sintered NaEuTi205. On its own, it indicates a square unit mesh with a dimension of about 7.6 A. However, by selecting the

reflections circled in this pattern, and using them to obtain dark field images (see sec.

4) , the micrographs in figure 5b and 5c respectively, were obtained. They show that the

circled diffracted beams come from different parts of the same fragment. By selecting these

parts separately and recording their diffraction patterns, it was established that the

pattern in figure 5a is a composite one, in which two (110) sections, rotated 90° with

respect to each other, and a third (001) section, of the true orthorhombic reciprocal lattice are superimposed. Within each part of the fragment which is imaged in figures 5b, c, there are boundaries separating regions of similar contrast. We believe that these are probably anti-phase boundaries (see sec. 7) and are currently investigating their origin.

4. PRECIPITATION OF LiFe^Og FROM NON-STOICHIOMETRIC a-LiFe02 [11]

a-LiFe02 has the cubic rocksalt structure with lithium and iron sharing the cation

sites [12] . Electron diffraction patterns from this material (fig. 6a) show distinctive

patterns of diffuse scattering, indicative of short range order of the cations. At temperatures below about 840 K, ordering of the cations takes place, and the diffuse intensity is

replaced by additional sharp reflections from one or other of several tetragonal modifications [2] . When a-LiFe02 is heated at temperatures above about 1250 K for prolonged periods, it

loses lithium, and when quenched in air, extra spots appear in the diffraction patterns

(e.g. fig. 6b) . The origin of these spots was established by the technique of dark field

microscopy - images were recorded with the objective aperture centered on one of the extra

92
Fig. 5. (a). Electron diffraction pattern from a twinned

fragment of NaEuTi20g . (b-c). Dark field images

from the same fragment, using the reflections identified in (a) . A white dashed line marks the

boundary between the two regions of the fragment

from which these two reflections were diffracted.

spots, and all others, including the central beam, were excluded. Bright areas in these

dark field images correspond to regions which diffract into the position selected by the

objective aperture. Thus, in figure 6c, the star-shaped particles embedded in the matrix

of a-LiFe02 are responsible for the extra spots in figure 6b. When the same sample was annealed at 870 K, octahedral particles were obtained, which have square projections when

viewed down <001> (fig. 6d) , and by rapid quenching from 1300 K into water, a homogeneous

material giving patterns without extra spots (i.e. similar to fig. 6a) was obtained. We were able to identify the particles as LiFe508, a ferrimagnetic spinel having a lattice

parameter almost exactly twice that of a-LiFe02 [13] . The anion lattices of the rocksalt

and spinel structures are identical, hence the particles are coherent with the matrix, and

are accommodated with negligible strain.

The lithium deficiency caused by heating a-LiFe02 at 1300 K can be retained by rapid

quenching, but slower rates of cooling result in the precipitation of LiFe508. The morphology of the precipitate is a function of the rate of cooling, and in addition to the shapes

in figure 6, filamentary dendritic growths have been observed.

Intergrowth of the rocksalt and spinel structures has also been observed in thin flakes

grown from borate fluxes [14] . During an attempt to grow larger crystals of a-LiFe02 by

this method [15] , we obtained dendrites which were apparently non-stoichiometric . Some of

these contained extensive regions of LiFesOs in association with a-LiFe02, as illustrated by

the bright field image in figure 7. The featureless region marked P is a-LiFe02, and the

dark region S, which contains numerous domain boundaries (e.g. D) and holes (H) is ordered

LiFesOg. The interface between the two phases is very well defined, and lies on {ill}

planes

.

93
Fig. 6. (a). (001) electron diffraction pattern from a-LiFe02, showing diffuse

scattering in addition to sharp Bragg reflections. (b) . (001) pattern

from a-LiFe02 / after heating at 1270 K for 65 hours. Note the extra

reflections as compared with (a). (c-d) . Dark field images, using the

reflection circled in (b) , from samples quenched in air from 1270 K (c)

,

and annealed at 870 K (d) . The star-shaped and square images come from

precipitates of LiFe503.

Fig. 7. Bright field image from a dendritic fragment,

showing intergrowth of a-LiFe02 (P) with ordered

LiFe^Og (S) . Domain boundaries (D) are present

in the LiFe^Og. The boundary between the region

P and a hole in the fragment (H) is marked by a dashed line.

94
This investigation illustrates the value of selected area diffraction and dark field

microscopy as means of identifying the source of unexpected features in diffraction patterns.

Systems which exhibit order-disorder phenomena, such as TiO^ [16] afford many opportunities

for the application of these techniques.

5. CRYSTALLOGRAPH I C SHEAR IN m^_^ [17-19]

In a series of careful x-ray studies, Magneli et al. [20] have shown that a family of

phases, closely related to Re03 but slightly deficient in oxygen, contain 'recurrent dislocations' or ' crystallographic shear (CS) planes' [21]. In these phases, the regular

arrangement of corner-shared octahedra characteristic of cubic Re03 (fig. 8a) is interrupted

periodically by parallel regions where octahedra share edges (arrowed in fig. 8b, c) . This

reduces the overall oxygen/metal ratio, and is an important means of accommodating non-stoichiometry in Re03-related systems. The idealized structure of ordered W20O58 [22] is shown

in figure 8b. In this case, the CS planes lie parallel to (310) (R = Re03-type parent

structure). In the series {Mo ,VI) j-^O^-^-i > represented in figure 8c by the member n = 8 [20],

the CS planes are parallel to (210) j^. The composition of any particular phase is a function

of the direction and spacing of the CS planes, and Magneli [20] has indicated how the unit

cell dimensions and structures of any hypothetical ordered compound of this type, containing

CS planes parallel to {nilO}p^ can be predicted with reasonable accuracy.

In most of these phases, the periodicity of the CS planes is large (>2 nm) (>20 A) , and

spacings of this magnitude are very readily resolved in the electron microscope. In addition, it seemed probable that an ordered arrangement of CS planes might be the exception

rather than the rule, since the interaction between planes spaced so far apart is likely to be small. While indications of disorder have been obtained from x-ray studies, electron

microscopy should allow the arrangement of CS planes to be observed directly. We have therefore made an electron optical study of W03_x (x<0.05) [17,18] and W03.yNb205 (y=0. 03=0 . 09)

[19] , since both these systems were reported to contain phases of this type.

Fig. 8. Idealized models of (a) ReO^ , (b) W20O58,

and (c) MOg02 3. Each square represents an octahedron of oxygen atoms surrounding a central metal atom, viewed down a bodydiagonal. The corner oxygen atoms are shared

between neighboring octahedra. In the crystallographic shear planes- (arrowed) the octahedra

share edges rather than corners. The subscript

R refers to the ReO^-type subcell.

95

/
Figure 9 shows some results typical of WOs.^. The electron diffraction patterns (a, c) contain a square array of strong spots, characteristic of the Re03-type parent lattice. In addition, there are lines of spots (a) or streaks (c) lying parallel to (310) and (210)

respectively. The corresponding images (b, d) contain dark lines_, more or less regularly

arranged in (b) , but randomly spaced in (d) , lying parallel to [130]r and [120]j^ respectively. We believe that these dark lines correspond to the CS planes, and it has been shown

[17,18,23] that their direction and spacing is consistent with the known compositions of the

samples, x~0 .05 (a, b) and x = 0.006 (c, d) , if it is assumed that they have structures

analogous to those in figure 8.

In W03.yNb205, [19], the situation is more complex. As the Nb205 content increases,

the direction of the CS planes changes from <120>j^ (at y = 0.03) through <140>j^ (y=0.06) to

<010>j^ (^0.09) , while the spacing of the planes tends to remain relatively constant in the

region 5-7 nm. Using Magneli's data [20], it has been possible to postulate idealized

structures whose lattice parameters and compositions agree with the observed results. In the case of Nb205-llW03, in which the CS planes lie parallel to (010) r. Roth and Waring 's x-ray powder data [24] were successfully indexed using parameters derived from electron

diffraction patterns.

In principle, it is possible to cover the whole range of compositions represented in

these studies by a single series of phases, with CS planes parallel to a specific direction

(say (210) j^) , and varying only in spacing. In practice, a variety of directions is observed, and there is an increasing amount of evidence that a narrow range of spacings is

preferred over others, for any particular system. The present results confirm similar

observations on Ti02_x [25-27] that as the composition tends towards that of the parent

structure, the plane of crystallographic shear tends towards that which has the least effect

on the stoichiometry . These planes are {210} for ReOs-type systems, and {132} for rutile

[27] . Possible reasons for a preferred spacing of CS planes have been discussed recently

by Bursill and Hyde [28]

.

Fig. 9. Electron diffraction patterns and lattice images from (a-b) WO2 90 and (c-d) W02.99i+. The axes and directions refer to the Re03-type

subcell of the structure. The black lines in (b) and (d) correspond

to crystallographic shear planes, whose average spacing is about

2.5 nm in (b) and about 25 nm in (d)

.

96
The micrographs in figure 9 show dark lines which are straight, but this is by no means always true. Several examples, which appear to indicate much greater departures

from equilibrium, are shown in figure 10. In these fragments, the black lines indicate the

presence of CS surfaces rather than planes. Most of them are clearly non-planar, and some terminate abruptly within the fragments, presumably at dislocations. Observations of this

kind immediately raise questions about the formation and ordering of CS planes , and there is now a considerable amount of evidence which can be used to discuss various models for these

processes [21,29]. At this stage, it seems clear that a dislocation model [18] is appropriate for describing the formation of CS surfaces, and that their subsequent movements,

including their straightening into planes in specific directions involves a sequence of

diffusive movements of particular ions over short distances [19] . In cases where the formation of CS planes is associated with the presence of a foreign ion (e.g. doping of WO3

with Nb205) , long-range migration of the new species must accompany the movement of the CS

surfaces

.

While the application of electron optical techniques in this area has been very re- warding, most of the work has been qualitative, and there is a great need for carefully

designed experiments to be carried out under conditions selected to yield results which

will enable the proposed models to be tested more specifically.

6. STRUCTURES IN THE SYSTEM Nb205.xTi02

6.1. THE Nb^O^-BASED FAMILY OF STRUCTURES

Until quite recently, it was generally thought that Nb205 could take up very large

amounts of Ti02 (and other oxides, such as WO3) into solid solution [30]. However, the

meticulous x-ray work of A. D. Wadsley and his collaborators [31] has led to the recognition of a large number of phases in these 'solid solution' regions, including four in the

system Nb205 - Ti02 (<50 mol % of Ti02) . A fifth was discovered by Gruehn and Norin [32]

.

These phases all contain elements of the Re03-type structure, which are joined to one another along CS planes in two directions. They are therefore more complex than the WO3-

based Magneli phases which we have discussed in section 5. Idealized drawings of some of

their structures are shown in figure 11. In all cases, the intersecting sets of CS planes

(arrowed) subdivide the structures into blocks or columns, each of which has the Re0 3- type of structure. The blocks are joined by sharing octahedral edges, and the structures

differ only in the sizes of the blocks, and the structures of their corner junctions.

yNb^Og (y = 0,07) . The Fig. 10. Non-planar CS surfaces in (a) WO2 gg and (b) WO3

straight portions of the dark lines (CS planes) lie along <130> in (a) and [010]^ in (b) . R

465-504 O - 72 - 8 97
Figure 11a shows the structure of monoclinic Ti2Nb]^Q029 [33] , in which the blocks are 4 octahedra wide by 3 long, and the corner junctions contain edge-shared octahedra, marked X. A second structure, containing blocks of the same size, but with the corner junctions

occupied by metal atoms in tetrahedral co-ordination (circles) is shown in figure lib. This

structure is adopted by WNbi2033 [34], one of a family of eight phases in the closely re- lated system, Nb205-W03 [31] . The structure of TiNb2i+Og2 [35] (fig. 10c) may be regarded as an ordered intergrowth of these two simpler structures. All of the blocks are 4 x 3 in

size, but only half the junctions are of the type marked X in figure 11a, the remainder

contain metal atoms in tetrahedral co-ordination, represented by black dots. Figure lid

shows the structure of the most stable {H-) form of Nb205 [36] , which is even more complex.

Not only does it contain corner junctions of the two types but it is built from blocks of

two sizes - 4 X 3 (dark) and 5x3 (light) . It can be regarded as an intergrowth of the

structure shown in figure lib with another, which is analogous to that in figure 11a, but

containing 5x3 blocks rather than 4x3. The composition of the latter would be M15O37,

and this structure is adopted by the phase MgNbiLj0 3 5F2 [37] .

In all these phases, the CS planes can be observed in the electron microscope [38-44],

either separately or simultaneously, depending upon the orientation of the fragment being

examined. For example, figure 12 shows images obtained from fragments of TiNb2i4052 [41].

The images (a) and (b) were recorded from fragments oriented so that the CS planes parallel

to a and c respectively (fig. 11c) were parallel to the incident electron beam. They show

a series of dark lines, which are alternately wide and narrow in (a) but have constant

thickness in (b) . These differences can be attributed to the fact that in the structure

(fig. 11c) , the CS planes parallel to a contain corner junctions which are either of the

type X, or O but those parallel to c are indistinguishable.

a i 1 I c \ \ \

Fig. 11. Idealized models of (a) orthorhombic Ti2Nb^Q02 9,

(b) WNb 0 , (c) TiNb2^0 , (d) H-Nb^O^. The

light and dark octahedra lie at different levels

in the structure, half a unit cell apart down the

short (0.38 nm) b axis. The CS planes, where the

component ReO^-type blocks of octahedra are joined

by sharing edges , are marked by arrows . Blocks at any one level are either joined together by edgesharing (e.g. at x) or separated by metal atoms

in tetrahedral co-ordination (circles)

.

98
Fig. 12. Lattice images from fragments of TiNb2t^Og2 recorded at several different

orientations: (a) 00 £ reflections only contribute to the image, (b) hOO reflections only contribute to the image, (c) hOl reflections contribute - electron beam incident parallel to the b axis. Interruptions to

the regular pattern in (b) and (c) are due to the presence of Wadsley

defects - slabs of H-Nb^O^ (b) and Ti2Nb|Q029 (c) coherently intergrown

in the matrix of TiNb2[+052-

When both sets of CS planes are parallel to the incident electron beam, the orientation

is exactly that of the projection shown in figure 11c, and two-dimensional images, such as figure 12c, are obtained. These images contain dark dots rather than lines, and the ar- rangement and spacing of these dots over most of the field is exactly the same as that of

the tetrahedral sites in the structure. This correlation has been found to hold for all

the phases in this family which have been examined by lattice imaging [42]

.

6.2. WADSLEY DEFECTS

The application of the technique of lattice imaging has greatly increased our understanding of structural relationships in NbaOs-based systems. All the phases in this family

may contain Wadsley defects - coherent intergrowths , often only half a unit cell wide, of one mentoer of the family in a matrix of another. For example, figure 12b contains several

fringe spacings of 1.7 nm amongst a majority of 1.5 nm. The latter are typical of CS planes

parallel to c in TiNb24062. "hich have a periodically of 1.49 nm. The 1.7 nm spacing is

characteristic of CS planes parallel to a in H-NfazOg (fig. lid), and it is easy to show that

a 1.68 nm slab of this structure (marked D in fig. lid) , bounded by CS planes, can fit

coherently into the structure of TiNb24052- Similarly, figure 12c contains mteruptions to the regular arrangement of dark dots along the lines marked F. These are caused by the

presence of additional slabs of the Ti2Nbio029 structure. We have already noted that

TiNbouOe? can be regarded as an intergrowth of the structures shown m figures 11a and lib,

hence it is not surprising that extra slabs of Ti2Nbio029 can be incorporated readily.

The Wadsley defects in figures 12b and 12c have opposite effects on the composition.

If we increase the departure from the ideal composition by deliberately adding either Nb205

or Ti02, the number of Wadsley defects may increase, and new ordered arrangements may appear.

99
Figure 13a shows a one-dimensional lattice image from a fragment of nominal composition

Ti02 • 26Nb205 , oriented to reveal the CS planes parallel to c, as in figure lib. The additional niobium content has greatly increased the niomber of slabs typical of H-Nh20c^, with

spacings of 1.7 nm. In the region marked X, these slabs form an ordered sequence with the narrower slabs of TiNb2Lf052- This intergrowth of the structures shown in figures 11c and

lid has also been recognized by x-ray diffraction [32] , and it may be regarded as a distinct

phase of composition TiNb520i32 [41].

More complex defects are found in samples which have been quenched from temperatures

in the neighbourhood of the melting point [43] . It is often possible to make a detailed

analysis of the contrast in two-dimensional images, and to propose models for these defects

which fit coherently into the structure of the surrounding matrix. Figure 13b shows such

an image from a quenched fragment Ti02-7Nb205. Several domains labelled Y show contrast

typical of TiNb2itOg2, but in other areas, vertical lines of dark dots, which correspond to

CS planes containing metal atoms in tetrahedral co-ordination, are more widely spaced. This

ik^XXXZZ^^l'^Z'^'i:

t ^^XxxXZ^''X:Z'X:tf.

^^'-X^lx^XZ'.Z'^'XCZ' jZZ,'*''^-^X'Z"^ 'Z,Z*

-'XXXZZ^^^X

f--^tX-:zz*^^XZ:z ^^^^Z^ZZZ*"^^X:z

tXZT'^^XZZir^^

. lOnm .

^XXXZX'^XX: :zXXXzZ' ^-X: r- ^

' ^'^XZXXz^ , Z'^'*^XZZ'j^'^rZ^'^ -^XZXZZ^- ^XZ'^^^XtZ'^'XyZ'

tN 1-^ Y

^XXX%Z^'-X-/ZrXlX.

xxz ^xx^i^xS;^^

M TN —>H V H

' — -w ^

Fig. 13. (a) Lattice image from a sample of Ti02 • 26Nb205 , using hOO reflections.

Fringes of width 1.5 and 1.7 nm correspond to slabs of TiNb2i+Og2 and

H-Nb20 5 respectively. In the region X, these slabs form an ordered

sequence, and an intergrowth structure, TiNb520i32 can be recognized,

(b) Two-dimensional lattice image from a fragment of Ti02-7Nb205,

using hOl reflections. Domains of TiNb2i+062 (Y) and TisNbsi+Ogi (V) can be identified by their patterns of dark dots, which correspond

to the arrangement of tetrahedral metal atoms. The Wadsley defects

marked N are slabs of 4 x 4 blocks. A number of more complex defects

(arrowed) produce displacements in the lines of dark dots.

100
is due to the insertion of extra slabs of Ti2Nbio029' whose presence alters the composition

in the required direction, i.e. towards Ti02-7Nb205. The area V may be regarded as an ordered microdomain of Ti3Nb3[+09i [41]. Several slabs, labelled N, differ from all the

others in the field, and their width suggests that they contain 4x4 blocks of octahedra.

It is easy to show that a slab of blocks of this size, otherwise identical to the slabs of

4x3 blocks of Ti2NbiQ029, can intergrow readily with the latter. They can be regarded as component slabs of the structure of the W-form of Nb205 [45] . By counting the numbers of

slabs of each composition across the field along the top of figure 13b, one arrives at an overall stoichiometry of Ti02 (6.9Nb205) , in good agreement with the nominal value.

In the bottom half of figure 13b, a number of the lines of dark dots suffer displacements, some of which are marked by arrows. These displacements have only been observed in

quenched samples, and they appear to involve the insertion of a single block which differs

in size from the remainder. Satisfactory models of these defects, in which a3x3or5x3

block occurs amongst slabs of 4 x 3 blocks have been proposed [43]

.

6.3. HIGH RESOLUTION IMAGES

Striking confirmation of these defect structures has recently been obtained by Dr. Sumio lijima, using a high resolution instrument at the Arizona State University. Several

micrographs of fragments which were taken from the same sample of Ti02'7Nb205 as we have

been using, are reproduced in figures 14 and 15, with his permission. The resolution of

these lattice images is of the order of 0.3 nm (3.0 K) , and it has been demonstrated [46]

that there is a 1:1 correspondence between the white dots in the images and the tunnels

between corner-shared octahedra in the structures. Idealized models of the areas outlined

in figures 14 and 15 are shown below the images. The groups of six white dots, corresponding to the six tunnels in each 4x3 block of octahedra, are easily seen, and it is very

easy to characterize the Wadsley defect labelled N in figure 14 as a slab of 4 x 4 blocks,

similar to those labelled N in figure 13b. Similarly, several single 3x3 blocks can be seen (arrowed) in figure 15 and their presence confirms the model proposed previously for

displacements of the kind which are arrowed in figure 13b.

The examination of these and other materials at high resolution obviously offers the

possibility of solving complex structures directly. Micrographs of the quality and re- solution evident in figures 14 and 15 should at least provide sufficient information to enable reliable trial structures and approximate atomic positions to be derived, which could

subsequently be refined using x-ray intensity data. In addition, the technique yields

detailed information about the structure of defects, which cannot be obtained by other

methods

.

6.4. 'SOLID SOLUTION' NON-STOICHIOMETRY

It is now quite clear that composition regions in many Nb205-based systems , which were

once referred to as 'solid solutions' are in fact occupied by series of closely related

phases, which can form intergrowths at the unit cell level. The presence of Wadsley defects

provides a means for accommodating very small discrepancies in composition, and it is

tempting to conclude that regions of true solid solution, i.e. random distributions of point

defects, may not exist in these systems. However, positive evidence for a departure from

stoichiometry which is not accompanied by Wadsley defects has been found in WO3 •yNb205 , for

y = 6 - 8 [47] .

Crystals of W03'8Nb205, when prepared from the component oxides by heating for short

times (2-5 hours at 1700 K) , contained Wadsley defects due to the intergrowth of //-Nb205

(fig. lid) with a matrix of WNbi2033 (fig. lib) . On further annealing, these defects were

entirely removed, leaving a homogeneous material, whose lattice images (at ca. 0.8 nm

resolution) and electron diffraction patterns were indistinguishable from those of WNb22033.

Thus it appears that the composition region W0 3.yNb205, y = 6 - 8 may be a true solid

solution. The ideal composition of this phase is M13O33, but W03'8Nb205 corresponds to

'^IS.OsObS °- -^13032 88' Because the structure contains potential sites for interstitial

atoms (e.g. in the tunnels between the octahedra) , an excess of metal (0.4% of the total

cations in W03.8Nb205), accommodated interstitially in some random manner, may explain this

region of homogeneity

.

101
Fig. 14. (a) High resolution two-dimensional lattice image from a fragment of Ti02-7Nb205 (courtesy S. lijima) . (b) Idealized model of the area m

outlined m (a) showing the intergrowth of a slab of 4 x 4 blocks (N) the matrix of 4 x 3 blocks . Note the correspondence between the white dots m (a) and the projections of tunnels between octahedra within the blocks in (b) ,

102
(a) High resolution two-dimensional lattice image from a fragment

Ti02-7Nb205, showing several displacements of the kind which are arrowed in figure 13b. (Courtesy S. lijima) . The displacements

are associated with the presence of isolated 3x3 blocks (arrowed)

in the matrix of 4 x 3 blocks. (b) Idealized model of the area outlined in (a) . The CS planes which contain tetrahedral metal

atoms are marked. They suffer a displacement at the points where

3x3 blocks (arrowed) occur.

103
In any event, it seems clear that Wadsley defects are the major source of variable

compositions in the systems we have been discussing, and that any contribution from ran- domly distributed point defects is probably limited to levels which are found more generally

in numerous other inorganic materials.

7. STRUCTURES IN THE SYSTEM W03.xNb20g (x = 0.2 - 0.35)

Apart from the Magneli phases (x<0.09, see sec. 5) and the block structures of the type

discussed in section 6 (x>1.125) there is a series of compounds containing 20 - 50 mol % of

Nb205 in which corner-shared octahedra are still the principal structural units, but they are arranged in a more complex manner than in ReO^. One of these is WNb208 (x = 1.0) which

is structurally related to LiNbgOjsF [48], and the remaining four (x=0. 25-0.6) have the

tetragonal bronze host lattice [24] . The arrangement of octahedra in this structure is

o o shown in figure 16a. The unit cell is tetragonal, with a = 12.5 A, c ~ 3.8. A, and contains

txmnels which may be occupied by additional ions. In the W03'Nb205 system, a proportion of

the pentagonal tunnels are filled by metal and oxygen ions, the metal being in pentagonal

bipyramid co-ordination. The number of filled tunnels depends on the composition, and

several ordered and disordered phases have been identified [24] . Figure 16b shows the

structure of WgNbgOi^y, in which one third of the pentagonal tunnels are filled in an ordered

way, and the superlattice is consequently orthorhombic , with a = 37.5, b ~ 12.5, c ~ 3.8 A

[49] .

A preliminary electron optical study of several of these phases has yielded interesting

results , which have thrown further light on some of the questions raised by previous x-ray

studies

.

7.1. DOMAINS IN WgNbgO^^

Craig and Stephenson, in a recent x-ray study of WgNbsO^y [50], were unable to distinguish unequivocally between two possible structures: (a) an orthorhombic 3x1 superlattice

of the tetragonal subcell similar to figure 16b, but twinned about the [130] aixs (arrowed),

(b) a pseudotetragonal 3x3 superlattice of the same subcell. Figure 17 shows some typical

electron optical results, from minute fragments of this phase. The diffraction pattern (a) is a {hko) reciprocal lattice section down the short 3.8 K axis, and contains a square array

of strong reflections due to the tetragonal subcell. Each of the major axes of this subcell appears to be trebled, but the complete absence of reflections within the squares

defined by the subcell reflections immediately suggests some form of twinning, because there

is no space group which requires that this combination of reflections be forbidden. This

conclusion is confirmed directly by the lattice image in figure 17b, which was recorded at an orientation a few degrees away from that of the diffraction pattern in (a) . The image

shows that the fragment contains domains, in which fringes with a spacing of 3.7 nm occur

in mutually perpendicular directions. The domains labelled A are twinned with respect to

those labelled B, and there is a tendency for the twin boundaries to lie on (310) planes of

Fig. 16. (a) The arrangement of corner-shared octahedra

in the tetragonal tungsten bronze structure.

Elements of thip structure which closely reseinble

that of Re03 are circled. The corners of the

tetragonal unit cell are marked. (b) The structure of WgNbgOi^y, which is a superlattice containing

three unit cells of the type shown in (a) . Four of

the twelve pentagonal tunnels in the orthorhombic

unit cell are occupied by metal and oxygen ions.

104
Fig. 17. (a) (001) electron diffraction pattern from a twinned fragment of

WgNbgOi+y. (b) Lattice image from a similar fragment, showing

two perpendicular orientations of the 3.75 ran superlattice

spacing, in the areas of A and B, separated by twin boiindaries,

e.g. at D. Out-of-phase boundaries, such as E, cause a displacement of the superlattice fringes of one third of a unit

cell. (c) Lattice image of the area outlined in (b) , after

tilting slightly to reveal the 1.25 nm subcell fringes. The

sublattice is continuous across both the twin boundary D and

the out-of-phase boundary E, but the superimposed 3.75 nm periodically in A suffers a displacement of one subcell unit

across E.

the orthorhombic superlattice (or 110 planes of the tetragonal siobcell) , e.g. at D. Another

type of domain boundary, labelled E, is associated with a displacement of the superlattice

fringes by about one third of a unit cell.

Further information on these boundaries can be obtained from figure 17c, which is a one-dimensional image showing the same area as is outlined in (b) , but recorded after

tilting the fragment until only reflections from the systematic set parallel to X* in the

figure 17a were operating. These reflections are of the type hOO for the regions A, and

0^0 for the twinned areas B. In B , the fringes are 1.25 nm apart, corresponding to the

periodicity of the structure along the b axis. On the other side of the twin boundary (T)

,

this pattern is modified by the superposition of the 3.75 nm periodicity along the a axis

of the superlattice. Nevertheless, the 1.25 nm fringes can still be seen in this area, and it is clear that they are continuous across the domain boundary E, while the superlattice periodicity is displaced by one siibcell unit.

105
The occurrence of domain boundaries in this material is readily explained in terms of

variations in the occupancy of pentagonal tunnels in an otherwise continuous tetragonal

bronze- type host lattice. The unit cell in figure 16b contains twelve pentagonal tunnels,

but only four of these are occupied. In this situation, there is every possibility that

the filled tunnels in different regions of the same crystal may be either twinned or 'out of phase' with respect to each other. The presence of boundaries similar to those in

figure 17, at the interface between these regions, is an inevitable consequence of this

freedom of choice of tunnels to be occupied. A model of a twin boundary and an out-of-phase

boundary in WgNbsOi^y is shown in figure 18. Each square represents one tetragonal subcell

of the structure, and the full and open circles correspond to occupied and empty pentagonal

tunnels respectively. The orthorhombic superlattice is heavily outlined, and its displacement by one subcell along the out-of-phase boundary is obvious.

Because the pentagonal tunnels are relatively widely separated (>0.6 nm) , interactions

between occupied tunnels and hence domain boundary energies are probably very small. For

this reason, the microdomain structure which is evident in figure 17, while it undoubtedly

represents a metastable condition, probably persists even after long annealing. This

accounts for the fact that untwinned crystals large enough for x-ray studies have not been

found [49,50].

7.2. D0^4AINS AND INTERGROWTH IN 2lJh ^0 IVIO

Stephenson [51] attempted to study the phase W7Nb40 3i [24] using x-rays, but he was unable to select suitable crystals for this purpose. Nevertheless, he predicted that

several structures were likely, all of which contained 4 tetragonal subcell units, to give

a superlattice with a=ii=25A, c~3.8A. This unit cell contains sixteen pentagonal

tunnels, and the correct composition is achieved by filling four of these with metal and

oxygen atoms. There are four different possible arrangements of these filled tunnels, hence

the opportunities for domain formation are even greater than for WgNbsOi+y. This is illustrated by the lattice image in figure 19a, in which a square array of white dots, 2.5 nm

on a side, corresponding to the projection of the unit cell on (001) , is interrupted by

out-of-phase boundaries of several different types.

Fig. 18. Model of twin and out-of-phase boundaries in

WgNbgOi|7. Each square represents a tetragonal

bronze- type subcell, and the open and filled

circles correspond to empty and occupied

pentagonal tunnels respectively. The orthorhombic unit cells of the superlattice are heavily outlined.

106
In many cases, the domain structure is not fully developed, and lattice images show

ordered regions separated from each other by areas in which only the square projection of

the tetragonal subcell, 1.25 nm on a side, is visible. Figures 19b and c illustrate this

situation, which probably corresponds to an early stage in the ordering process. Electron

diffraction patterns from fragments which give images similar to figure 19c contain sharp

subcell reflections surrounded by diffuse scattering due to short range order. This con- firms the supposition that the structure consists of a continuous host lattice in which the

filling of pentagonal tunnels is random, except in isolated patches where a few unit cells

of the 2.5 X 2.5 nm ordered structure occurs.

The contrast within the ordered domains varies considerably, even in the same fragment,

as figure 19 shows. These differences are a consequence of the fact that the micrographs

were recorded at slightly different orientations, and they do not necessarily represent real

differences in the structure of individual domains.

A few fragments contained domains of a much simpler structure, in which lattice fringes were not resolved at 0.8 nm resolution. An example of this intergrowth is shown in figure

20a, in which the region C, which is free of detailed contrast, is embedded in a matrix of

tetragonal bronze-type structure, similar to figure 19b. An attempt was made to characterize the region C by selected area electron diffraction. The technique is difficult to

Fig. 19. Lattice images from fragments with compositions near 2Nb205'7W03.

(a). Ordered domains of WyNbt+Osj , separated by out-of-phase boundaries of several different types. (b). Small ordered domains of ~' WyNbi+Osi, separated by disordered regions where only the 1.25 nm host lattice fringes are visible. (c). Short-range order - groups

of a few unit cells of the 2.5 x 2.5 nm supers tructvire of WyNbi+Oai are scattered in a matrix where the host lattice is continuous,

but the pentagonal tunnels are filled randomly.

107
Fig. 20. (a) . Two-dimensional lattice image showing intergrowth between a tetragonal

bronze host lattice (containing domains of ordered W7NbLj03;^), and a simpler

cubic or pseudo cubic structure C, C' in which no lattice fringes are visible.

The defect S may be a CS plane. (b) . Sketch of (001) electron diffraction

pattern showing the relationship between reflections from the tetragonal

bronze host lattice (dots) and the two orientations of the cubic intergrowth,

C (open circles) and C (squares).

T08
apply to such small areas, but nevertheless, evidence for a cubic or pseudocubic unit cell

with a = 0.38 nm was obtained. Two orientations of this cell were observed; they probably

apply to adjacent regions such as C and C, which are separated by zig-zag boundaries.

Both these orientations bear specific relationships to the tetragonal bronze subcell, as shown by the diagrammatic sketch of the electron diffraction patterns in figure 20b.

The most likely structure for the region C is the Re0 3-type structure (fig. 8a) or some variant of this, such as the cubic tungsten bronze structure [52]. Elements of this

simple 'chess-board' arrangement of octahedra can be recognized in the tetragonal bronze

structure, and they are circled in figure 16a. These groups of four corner-shared octahedra, centred on the corners and centre of the tetragonal unit cell, lie in two orientations, which are the same as those of the regions C and C in figure 20a, as indicated by

the orientation relationship in figure 20b. It therefore seems possible that a Re03-type

structure can be coherently interfaced with the tetragonal bronze structure, and that this

is the explanation for observations such as figure 20a.

Models of the interface between the two structures, and of the zig-zag boundary between the two orientations C and C of Re0 3-type material, are shown in figures 21a and b

respectively. Some of the octahedra in the vicinity of the boundaries may be distorted

excessively, but in general, the models give a satisfactory explanation to what appeared

at first sight to be a most unlikely type of intergrowth. No attempt has been made to explain a number of other features which appear in the region C of figure 20a. However,

it is possible that the extended defect marked S may be a crystallographic shear plane.

Micrographs such as this clearly contain an enormous amount of structural information about

structures and structural relationships which cannot be obtained by other means.

Fig. 21. Models of proposed structures for interfaces between (a) the tetragonal bronze

structure (lower) and a Re03-type lattice (upper) and (b) two orientations

of the Re03-type lattice, separated by a zig-zag boundary of the kind seen between the regions C and C in figure 20a. The orientation of these diagrams

is consistent with figure 20, and the axes are labelled in the same way as those

in figure 20b.

109
8. CONCLUSION

The examples cited in sections 3-7 are sufficient to indicate that the electron microscope has considerable potential as a tool for structural investigations on high temperature

materials. They do not cover the whole range of possible applications by any means; in

particular, the field of dislocation structures has been omitted entirely. This area is an extension of the voluminous work on metals which is very thoroughly documented (5,6).

Perhaps the most interesting new results have been obtained by lattice imaging, and

this technique undoubtedly has a bright future. It is clear that the structures we have

studied by this method have been favorable ones, because of the presence of a very short

projection axis (0.38 nm) and minimal overlap of atoms down this axis. However, using the

improved resolution provided by many modern electron microscopes, it should be possible to handle many other types of structure successfully. Concurrent with experimental studies of

this kind, there is a need for theoretical investigations of the relationship between lattice image contrast and structure. It cannot be assumed that this relationship will always

be as direct and as obvious as is indicated by the results on Nb205-related phases, e.g.

figures 14, 15.

Finally, there are many opportunities for the study of reactions in and between solids

in situ, using a high-temperature specimen stage. For example, the formation and migration

of CS planes in W03_jj could probably be studied by this means. A few qualitative obseirvations have already been made [18] using the heating effect of the incident electron beam,

but meaningful kinetic data might be obtainable with better temperature control provided by

a hot stage.

9. ACKNOWLEDGEMENTS

I am indebted to Dr. J. V. Sanders for his continued interest and encouragement, and

to Prof. J. M. Cowley and Dr. Sumio lijima for permission to reproduce figures 14a and 15a.

10. REFERENCES

[I] Hirthe, W. M. , Melville, A. T., and Wackman, P. H. , Rev. Sci. Inst. 38_, 223 (1967).

[2] O'Keefe, M. A., unpublished results, CSIRO.

[3] Cowley, J. M. , in Progress in Materials Science (B. Chalmers and W. Hume-Rothery ,

' eds . ) , Pergamon Press, Vol. 13, No. 6(1957).

[4] Li, C. , Reid, A. F. , and Allpress , J. G. , to be published.

[5] Hirsch, P. B. , Howie, A., Nicholson, R. B. , Pashley, D. W. , and Whelan, M. J.,

Electron Microscopy of Thin Crystals , Butterworths (London) 1965.

[6] Amelinekx, S. , The Direct Observation of Dislocations , Academic Press (New York) 1964.

[7] See, for example, papers in The Chemistry of Extended Defects in Non-Metallic Solids

(L. Eyring and M. O'Keefe, eds.) North Holland, 1970.

[8] Yada, K. and Hibi, T. , J. Electron Microscopy 18_, 266 (1969).

[9] Cowley, J. M. and Moodie, A. F. , Proc. Phys . Soc. 76, 382 (1960).

[10] Marezio, M. , Remeika, J. P., and Dernier, P. D. , Acta Cryst. B26, 2008 (1970).

[II] Allpress, J. G., J. Mat. Sci. 6, 313 (1971).

[12] Posnjak, E. and Barth, T. , Phys. Rev. 38.' 2234 (1931).

[13] Hoffmann, A., Naturwiss 26_, 431 (1938).

[14] Allpress, J. G. and O'Keefe, M. A., unpublished results.

[15] Anderson, J. C. and Schieber, M. , J. Phys. Chem. 67, 1838 (1963).

[16] Watanabe, D. , Terasaki, O. , Jostsons , A., and Castles, J. R. , in ref. 7, p. 238.

[17] Allpress, J. G. and Gado , P., Crystal Lattice Defects 1_, 311 (1970).

[18] Allpress, J. G. , Tilley, R. J. D. , and Sienko , M. J., J. Solid State Chem. 3_, 440 (1971).

[19] Allpress, J. G. , J. Solid State Chem., in press.

[20] Magneli, A., Acta Cryst. 6, 495 (1953).

[21] Andersson, S. and Wadsley, A. D., Nature 211 , 581 (1966).

[22] Magneli, A., Arkiv. Kemi. 1_, 513 (1950).

[23] Tilley, R. J. D. , Mat. Res. Bull. 5_, 813 (1970).

[24] Roth, R. S. and Waring, J. L. , J. Res. NBS 70A , 281 (1966).

[25] Bursill, L. A., Hyde, B. G. , Terasaki, O, , and Watanabe, D. , Phil. Mag. 2£, 347 (1969).

[26] Anderson, J. S. and Tilley, R. J. D. , J. Solid State Chem. 2_, 472 (1970).

[27] Bursill, L. A., Hyde, B. G. , and Philp, D. K. , Phil. Mag. 23_' 1501 (1971).

110
[28] Bursill, L. A. and Hyde, B. G. , Phil. Mag. 23_, 3 (1971).

[29] Anderson, J. S. and Hyde, B. G. , J. Phys. Chem, Solids 28_, 1393 (1967).

[30] Goldschmidt, H. J., Interstitial Alloys, p. 419-421, Butterworths (London) 1967.

[31] Wadsley, A. D. and Andersson, S. , in Perspectives in Structural Chemistry (J. D. Dunitz and J. A. Ibers, eds . ) Wiley (New York) Vol. 3, 1970.

[32] Gruehn, R. and Norin, R. , Z. Anorg. Allgem. Chem. 355 , 176 (1967).

[33] Wadsley, A. D. , Acta Cryst. 14, 664 (1961).

[34] Roth, R. S. and Wadsley, A. D.,Acta Cryst. 1£, 32 (1965).

[35] Roth, R. S. and Wadsley, A. D. , Acta Cryst. 18_, 724 (1965).

[36] Gatehouse, B. M. and Wadsley, A. D. , Acta Cryst. 17, 1545 (1964).

[37] Lundberg, M. , J. Solid State Chem. 1^, 463 (1970).

[38] Allpress, J. G. , Sanders, J. V., and Wadsley, A. D. , Phys. Stat. Sol. 25^, 541 (1968).

[39] Allpress, J. G. , Sanders, J. V., and Wadsley, A. D. , Acta Cryst. B25 , 1156 (1969).

[40] Allpress, J. G. and Wadsley, A. D. , J. Solid State Chem. _1, 28 (1969).

[41] Allpress, J. G. , J. Solid State Chem. 1_, 66 (1969).

[42] Allpress, J. G. , Mat. Res. Bull. 4_, 707 (1969).

[43] Allpress, J. G. , J. Solid State Chem. 2_, 78 (1970).

[44] Allpress, J. G. and Roth, R.S. , J. Solid State Chem, 2_, 366 (1970).

[45] Andersson, S., Z. Anorg. Allgem. Chem. 351 , 106 (1967).

[46] lijima, S., J. Appl. Phys., in press.

[47] Allpress, J. G. and Roth, R.S. , J. Solid State Chem. 209 (1971).

[48] Lundberg, M. , Acta Chem. Scand. 19_, 2274 (1965).

[49] Sleight, A. W. , Acta Chem. Scand. 20, 1102 (1966).

[50] Craig, D. C. and Stephenson, N. C. , Acta Cryst. B25 , 2071 (1969).

[51] Stephenson, N. C. , Acta Cryst. B24 , 637 (1968).

[52] Wadsley, A. D. , in Non-Stoichiometric Compounds (L. Mandelcorn, ed.) Academic Press

(New York) 1964.

m

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

APPLICATION OF INFRARED AND RAMAN SPECTROSCOPY TO THE

CHARACTERIZATION OF ORDER-DISORDER IN HIGH TEMPERATURE OXIDES

William B. White and Vassilis G. Keramidas

Materials Research Laboratory

The Pennsylvania State University

University Park, Pennsylvania 16802

The vibrational spectra of oxides are remarkably sensitive to ordering effects and are

a useful characterization tool. Cation ordering can be classified into: (a) preferential

distribution of non-equivalent cations onto non-equivalent sites with no change in space

group symmetry or unit cell size, (b) preferential distribution onto equivalent sites with

decrease in space group symmetry only, (c) building of superstructures with same symmetry

as parent structure, (d) both (b) and (c) combined. Experimental Raman spectra of various

stiructures are compared with these schemes. Ordering of type (a) produces only frequency

shifts with no change in spectral pattern and is exemplified by normal-inverse ordering

in spinels. Ordering of type (b) produces additional bands due to selection rule

relaxation and is exemplified by ilmenite, LiNbOs, and NisTeOg orderings on corundum and by

spinels with 1:1 ordering on tetrahedral sites. Ordering of type (c) produces a multiplicity

of bands as is illustrated by the trirutile structure. Ordering of type (d) produces very

complex spectra. Examples include: P3cl ordering on corundum, 1:1 ordering on rocksalt

and the Ruddlesden-Popper superstructures. Raman spectra are sharp but intensities are highly variable. Simple ordering schemes are easy to discern, but complex schemes produce

spectra difficult to interpret.

Key words: Corundum structure; order-disorder; Raman spectra; rocksalt structure;

rutile structure; spinel structure.

1. INTRODUCTION

It was proposed several years ago [1] ^ that the infrared spectra of solids are exceptionally sensitive to cation ordering. Although the theory is simple to apply, the

actual measurement of the ir spectra of many types of structures is difficult if only

powder or ceramic specimens are available. Long-range polarization forces in structures

such as cojrundum and perovskite cause a large separation of the transverse and longitudinal

optic modes. As a result, the ir spectra are very broad and represent some composite of

specular reflectivity and Frohlich-type surface modes rather than the transverse optic modes.

Furthermore, the broadening of the bands obscures splittings and multiplicites of bands that

may occur because of ordering.

In this paper we examine the Raman spectra of various classes of compounds with

ordering schemes derived from the rocksalt, rutile, corundum, perovskite, and spinel

structures. The objective is to test the extent to which the ordering arrangement affects

the Raman spectrum. Corresponding infrared spectra are drawn from the literature as needed.

2. EXPERIMENTAL

The ilmenite phases ZnTi03, MnTi03, and MgTiOs were synthesized by dry-firing

appropriate mixtures of Ti02 with the carbonates of the other cation at 1200 °C in air.

Figures in brackets indicate the literature references at the end of this paper.

113

465-504 O - 72 - 9

/
MgSb205 and ZnSb206 were prepared by heating pressed pellets of the oxides at 950 °C for

48 hours. Phase identification and purity were checked by x-ray diffraction. The complex

niobates were synthesized according to the method of Bertaut et al . [2]. The strontium

titanates were obtained from a previous phase equilibrium study [3]

.

Raman spectra were measured on pressed pellets or sintered chips of pure compounds

using a Spex Ramalog spectrometer with an Ar"*" laser source. Since internal scattering of

powders destroys the depolarization effects, no information on the polarization dependence

of the materials was obtained.

3. INFLUENCE OF ORDER ON VIBRATIONAL SPECTRA

Consider first what is meant by order. We begin with a parent structure with a certain set of equivalent cation sites. In the case of the rocksalt, rutile, and corundum

structures there is only one equivalent set of cations. There are two kinds of sites in

the spinel and perovskite structures. If we substitute some different kind of cation into

a one-cation-sublattice structure in such a way that the substitution takes place at

random positions in the structure, there is no change in symmetry. Because of the random

substitution, all sites remain equivalent under the various symmetry operations of the

space group, the space group remains the same, and the unit cell size does not change.

This corresponds to the disordered structure and has the highest symmetry. In contrast,

if the foreign cation is substituted in a regular way, say in alternate sites in the cation

sublattice, symmetry operations that would exchange non-equivalent cations are lost. The

space group symmetry may be lowered, the cell size enlarged, or both.

The number of zone-center phonon modes active in the infrared or Raman spectrum is

determined by the factor group symmetry of the structure and by the population of the

primitive unit cell. If an ordered arrangement of cations lowers the factor group symmetry,

in general, there will be a change in the number of modes in both the infrared and Raman

spectra caused by a relaxation of selection rules. An enlargement of the primitive cell,

without a change in space group symmetry will cause an increase in the number of allowed

modes usually by some multiplicity factor. A summary of the possible situations is given

in table 1.

Table 1

Types of Cation Order

Ordering Scheme Change in

Symmetry

Spectral

Behavior

Examples

Cation ordering on non- equivalent sites

Same cell size

Same space group

No new bands

Shift in frequency

Normal-Inverse order in

spinels

Cation ordering on equivalent sites

Same cell size

Derivative space

group

New bands superimposed on parent

spectrum

1:1 order on tetrahedral

sites in spinel. Ilmenite

ordering on corundum

Larger cell

Lower symmetry

New spectrum with

many more bands

Octahedral site ordering

on spinel. 1:1 ordering

on rocksalt. 1:3 ordering

on corundum

Cation ordering with

superstructure

Superstructure

cell

Same space group

Parent spectrum

develops multiplicity of lines

Trirutile ordering

Superstructure

cell

Lower space group

Complex spectrum

may not be directly

related to parent

Ruddlesden-Popper phases

1:2 ordering on corundum

114
There is also an effect of the long-range coupling fields in the structure. The

polarization field splits the infrared active modes into a transverse and longitudinal

component, a splitting that is not accounted for by the factor group analysis. The

magnitude of separation between similar motions of vibration is also controlled by the

effectiveness of coupling. If, for example, the tetrahedral sites in spinel contain two kinds of weakly coupled cations , the spectrum may exhibit molecular-like bands of both

tetrahedra in spite of factor group predictions of a single average spectrum. Even if

internal coupling is reasonably strong, as unit cells become large due to superstructure,

it may be impossible to resolve the full predicted number of frequencies because of the

large number of overlapping bands.

4. RESULTS AND DISCUSSION

4.1. STRUCTURES ORDERING ON NON-EQUIVALENT SITES

The best known example of ordering between non-equivalent sites is the normal-inverse

ordering in spinels. Normal spinel has a cation distribution (A2)^"''B-'-^X^ and an inverse

spinel has the distribution {AB)^^A^^X^ . Many real spinels have a mixed cation distribution

(A2_xBx)^"'" (Bi_jjAjj) '^Xi^ . Throughout this series of substitutions there is no change of space

group or unit cell size. It was shown [4] by factor group analysis that the expected modes

of spinel are:

r = Aig(R) + Eg(R) + Tig + 3T2g(R) + 2A2u + 2E^ + 4Tiu{ir) + 2T2u

Four bands are expected in the infrared and five bands in the Raman for a normal spinel.

Many infrared studies show that only the expected four bands appear in the infrared spectrum

of either normal or inverse spinels . As predicted by simple symmetry arguments , the

spectrum does not change with changing cation distribution. Of course frequency shifts occur because the average mass on particular cation sites and the average force constants

for the bonds change with changing cation distribution. New data (DeAngelis, Keramidas

,

and White, to be published) show that the same is true in the Raman effect. Five bands

are predicted and only five are observed for a wide variety of oxide spinels with normal,

inverse, and mixed cation distributions.

The same would be expected for any other structure in which cations are substituting

in an ordered way on distinct crystallographic sites. For example, olivine, Mg2Si0t+

,

has two cation positions M(I) and M(II). An ordered substitution of iron onto one site

in preference to the other would be revealed in the electronic spectrum or the Mossbauer

spectrum, both of which are mainly sensitive to nearest neighbor environment only, but the

ordering should manifest itself in the ir and Raman spectra merely by a frequency shift in

the lattice modes. No new bands should appear.

4.2. ORDERING WITH LOWER SPACE GROUP SYMMETRY

There are many examples of structures in which cation ordering lowers the space group

symmetry without changing the size of the unit cell. We shall examine two, 1:1 ordering

an tetrahedral sites in spinel and several orderings on corundum.

A 1:1 ordering of the tetrahedral cations in the spinel structure lowers the space

group

0^'^(Fd3m) T,^(F43m)

h d

The face-centered cubic cell is retained with nearly the same cell parameter but the point

symmetry is lowered. The ir spectral consequences as given by the factor group analysis of

[4] are:

115
Spinel 1:1 ordered

V3 tetrahedral stretch

Vt^ tetrahedral defomation

4T

lu

Octahedral stretch - Antiphase motion of

tetrahedra

I AXi+ asymm. stretch

' BXlj asymm. stretch

AXlj bend

I BXtt bend

Octahedral stretch

Antiphase motion

Octahedral deformation

7T,

The description of vibrational motion assumes a quasi-molecular behavior from the isolated

spinel tetrahedron and the notation vj , etc., is the standard usage given by Herzberg [5] The Raman spectrum of the ordered spinel is expected to exhibit 15 bands in contrast to 5 in

the disordered form.

ig

Spinel

Vi Symmetric stretch

V2 Symmetric bend

1:1 ordered

AXlj sym. stretch

BXi+ sym. stretch

Translatory mode

AXi+ sym. bend

BXi+ sym. bend

Translatory mode

V3 Asymmetric strecth

2g ^ Asymmetric bend

Translatory mode

!AX assym. stretch

BXtt asymm. stretch

iAXt^ asymm. bend

BXi4 asymm. bend

Three translatory

modes (same as ir)

The group theoretical consequence of the ordering is the removal of the center of

symmetry. Two effects can be seen in the spectra. The first is the loss of the mutual

exclusion rule, so that all infrared modes also become active in the Raman spectra. The

second is a relaxation of selection rules that permits certain modes forbidden in both ir

and Raman to become active in the ordered structure. Important among these are the

vibrations of the two tetrahedra of the primitive spinel cell. There are two sets of

tetrahedral (quasi-molecular) modes in spinel, differing in frequency by the factor group

splitting. In the ordered form, both sets of tetrahedral modes appear in both the ir and

in the Raman as indicated. If no coupling between tetrahedra were operative, we would

expect to see a superposition of spectra with frequencies close to those of the free parent

tetrahedra.

Measured ir and Raman spectra [6] show a more complex situation. The infrared spectra

show the expected seven bands, but the frequencies of those assigned to tetrahedral modes

are not as expected from the de-coupled tetrahedra. Likewise the intensity of one member

of the pair is very strong, while the intensity of the other is very weak. It was concluded

that coupling forces still act to mix the pairs of tetrahedral vibrations (which is permitted

116
by symmetry, since all modes have T2 symmetry) . The expected large number of Raman modes

appears and can be assigned, but no easy correlation with the parent spinel is apparent in

the spectra.

We turn now to cation ordering in the corundum structure. Introduction of two distinct

cations into the corundum structure can produce a variety of cation ordering schemes depending

on how the atoms are arranged in the cation layers. These have been simmarized by Newnham and

Meagher [7]. The pertinent crystallographic data are given in table 2. The ilmenite and

LiNb03 ordering schemes reduce the space group symmetry, but the size and contents of the

unit cell do not change. The ordering arrangement of Mg4Nb209 destroys the rhombohedral

centering of the cell. In this case the factor group symmetry remains the same, but the

system contains thrice as many degrees of freedom as the primitive cell. The NisTeOg

structure, on the other hand, preserves the rhombohedral centering and thus the primitive

cell contains the same number of atoms as the parent corundum.

Factor group analyses for the vibrational modes of these structures are listed in

table 3. Seven Raman bands are expected in the completely disordered corundum structure [8]

.

This number increases to 10 in the ilmenite structure and to 13 in the LiNbOs structure.

The increase in number of modes arises simply from the relaxation of selection rules in the

lower symmetry ordered structures. In the case of ilmenite, the 3 inactive modes of

corundum are grouped with the Raman active Ag representation in C3j_ symmetry. The loss of

the center of symmetry in the LiNb03 structure combined the ir and Raman active sets into

single representations. In both cases the final result can be obtained by a simple descent

of symmetry argument, since both ordered space groups are subgroups of the space group of

corundum.

Raman spectra of three ilmenite structure compounds, ZnTi03, MnTi03, and MgTi03 are shown in figure 1. The spectra of ZnTiOs and MgTi03 are sharp and well defined, while the

spectrum of MnTi03 is surprisingly weak. The spectrum of ZnTi03 contains 16 lines and the

spectrum of MgTi03 contains 13 lines in contrast to the 10 predicted by factor group analysis.

The positions of these lines are compared with the vibrational levels of AI2O3 [8] and

LiNb0 3 [9] in figure 2. Since Aj and E species of the LiNb03 ordering are both ir and Raman

active, the comparison with the infrared data should be valid. It can be seen that the three

highest frequencies correlate with the three highest frequency modes of corundum and also

with LiNb0 3. The lower frequency group of lines do not show an obvious relationship to

those of corundum. The effect of ordering in this case, then, is the appearance of many

low-frequency modes corresponding to lattice vibrations forbidden in the corundum structure.

We do not see any pairs of characteristic frequencies that might be associated with Mg-0 and

Ti-0 or Zn-0 and Ti-0 stretching motions. These remain strongly coupled in the ordered

structure and the three high-frequency bands that do occur have exact analogs in the higher

symmetry corundum structure.

The bands in excess of those permitted by the factor group analysis of ilmenite pose a problem. Since ilmenite is centrosymmetric , the longitudinal modes should not appear in

the Raman spectrum. Perhaps the easy way out is to assign the weaker bands to multi-phonon

processes, although there is really no good evidence for this or criteria for making the

selection.

Table 2

Cation Ordering Schemes Based on Corundum Structure

Space Group R3c R3 R3c P3cl R3

3d C2. ^3i c63v ^3

Structure Type

Z (Hexagonal Cell)

Corundum

6

Ilmenite

6

LiNbOs

6

Mni+Nb20g

2

Ni3Te06

3

117
Table 3

Factor Group Analyses for Corundum-Related Structures

^3d

Number of Modes Selection

Rules

C3i

Number Selection

AI2O3 (a) Mni+Nb209

0 -L ModesRu le s

Alg 2 7 Raman Aq 5 Raman

A2g 3 8 Inactive Eg 5 Raman

Eg 5 15 Raman Au 4 IR(E 1 C)

Alu 2 7 Inactive E,, •^u 4 IR (Ej_C)

A2u 2 7 IR (E 1 1 C)

Eu 4 14 ir(e]_c) C3v(b)

Ai 4 Raman + IR

A2 c Inactive

(a) Porto and Krishnan [8] E 9 Raman + IR

(b) Axe and O'Kane [91 C3

A 10 Raman + IR

E 10 Raman + IR

1

D Li

FfteOUEWCT (cm-'l

Fig. 1. Raman spectra of ilmenite

structure compounds

.

118
100

Fig. 2. Correlation of vibrational

frequencies between corundum

(R3c) , ilmenite (R3) , and

LiNb03 (R3c) . Corundum data

are from reference [8] , and

LiNb03 data are from reference

[9] .

The Ni3Te05 structure is of similar sort, except that it represents a 1:3 ordering

instead of a 1:1 ordering in the cation stacking sequence. The factor group analysis of

table 3 predicts a total of 20 modes active in both ir and Raman. The Raman spectrum of

Ni3Te05 shown in figure 3 exhibits only 10 lines, exactly half the predicted number. The

symmetry here is so low that all vibrational modes are permitted and much of the detail is

not resolved.

4.3. ORDERINGS WITH SUPERSTRUCTURE CELL AND SAME SYMMETRY

The trirutile structure is a rare example in which a 3-fold increase in the size of the

unit cell is obtained by stacking three rutile cells along the c-axis . The space group

remains D^j^ (P42/mnm) , the distribution of atoms over the equipoints remains the same, but

the total number of degrees of freedom is tripled. A factor group analysis of rutile [10]

yields

:

r = Aig(R) + A2g + Big(R) + B2g(R) + Eg (R) + A2u(ir) + 2Bi^ + 3Eu(ir)

Four modes are active in the infrared and four in the Raman. A tripled unit cell with no change in syimrietry or site population would simply triple the number of modes appearing

in each irreducible representation. We would expect 12 Raman active modes in the trirutile

structure but might question whether these would all be distinct, since the individual

segments of the enlarged cell might be poorly coupled.

119
900 800 700 600 500 400 300 200 100 F='REOUENCY (cm-')

Fig. 3. Raman spectrum of Ni3Te05, a 1:3 (R3)

ordering on corundum.

Raman spectra of two trirutile ordered compounds, ZnSb20 5 and MgSbaOe , are shown in

figure 4. Spectra of these colorless compounds, unlike the ilmenites, are almost identical

except for small frequency shifts. The predicted 12 frequencies are observed in the zinc

compound and 11 frequencies are observed in the magnesium compound. Direct comparison

suggests that the 326 cm~-^ band of MgSb206 may represent two modes which exactly overlap.

The bands, however, are not clumped in readily discernible groups of three. Porto et al.

[10] show that the Ajg mode of a variety of rutile structures is quite intense, while the

higher frequency B2g mode is weak. Using this as a guide, the following association of

the bands can be made:

TiO^ (rutile) ZnSb20B MgSb20fi (trirutile)

810

615

481

744

668

537

The 447 cm~^ Eg band and the 143 cm"''' B^g band of rutile must be represented by the six weak

lines in the 200 to 400 cm"-'' region, but -there is no clear-cut criterion for separating

them. These spectra show quite clearly the strong coupling that must exist in the ordered

trirutile structure. Without coupling we would have expected a strong line at frequencies

higher than that of TiOo associated with an Sb-0 vibration and two rather closely spaced

lines m the 500 to 600 cm"'^ region due to the Zn-0 or Mg-0 vibrations. What we observe

are three strong lines about evenly spaced and with the highest frequency component close

to the Aig mode of Ti02. Likewise, the B^g set of modes is spread over a wide frequency

range so that there is complete overlap with the A^g set. Although static trirutile is

very similar to rutile, the dynamics of the structure strongly reflect the ordering.

814

B2g 826 cm~^ 606

412

785

Aig 612 cm~^ 657

526

120
1 I I I 1 I I 900 800 700 600 500 400 300 200 100 FREQUENCY (cm-'l

Fig. 4. Raman spectra of ZnSb20g and MgSb20g with the

trirutile (P42/ninm) structure.

4.4. ORDERINGS WITH CHANGE OF BOTH SYMMETRY AND UNIT CELL

When the ordered structure requires both a lower space group and a larger unit cell,

the spectra become quite complicated and the relationship to the parent structure becomes

hard to discern. We consider here orderings on rocksalt and on corundum.

All of the corundum-related structures are based on a hexagonal unit cell containing

18 oxygens. All except MnL|Nb2 09 have rhombohedral centering which introduces a 3-fold

redundancy in the calculation of vibrational modes and reduces the effective motion of that

of a primitive cell containing 6 oxygens. The MnLjNb2 09 cell is primitive, and the vibrations

of the 18-oxygen cell must be considered. The ordering scheme of MgL,Nb20g requires a superstructure cell which has the same factor group as corundum but requires a different

space group. There are 3 times as many degrees of freedom in the primitive cell, but

because of the different space group symmetry, these are distributed differently among the

irreducible representations of D^,^. Had there been no change in space group symmetry (the case of the trirutile structure) each mode of corundum would have been tripled.

Raman spectra for three compounds with the superstructure cell are shown in figure 5. Twenty-two lines are predicted by factor group analysis. Fifteen are observed in Nii^Nb209,

24 in Mg4Nb20g, and only 7 in Coi+Nb2 09 . The problem here seems quite clearly to be the

color of the cobalt and nickel compounds which reduces the intensity of the Raman scattering.

The highest frequency peaks should be assigned to stretching motions of the NbO

octahedra. The frequencies are unusually high. Nb^"*" will have a higher force constant

than Al^"*" but is much heavier. In contrast, the highest frequency mode in LiNb03 is at

657 cm"'^ about the expected value for face-sharing octahedra. Since the MgitNb209 space

group is centrosymmetric, the longitudinal modes are not allowed in the Raman spectrum.

Likewise, the mode-tripling relationship observed in the spectra of trirutile superstructure

is not observed. The resemblance to corundum is completery lost, and this places a limitation

on the complexity of structural ordering that can be investigated by Raman spectroscopy.

121
J

•

Nl,Nk,0,

s

C.,Nk,0,

0.

1000 900 800 700 600 SCO 400 300 200 100 FREOUEMCT (c»-i)

Fig. 5. Raman spectra of compounds with

1:2 (PScl) ordering on corundum.

The rocksalt structure, Oj^-^, Fm3m contains only one AX forumla unit in the primitive

unit cell and has a single infrared active T^^ vibrational mode. There are no one-phonon

Raman modes. Compounds of the formula ABX2 may exhibit a 1:1 ordering on the rocksalt

structure which reduces the space group symmetry to D^^ I4i/amd with four formula units in

the body-centered cell. Thus the cation ordering produces a lower symmetry, a distortion

of the symmetry from cubic to tetragonal, and an enlarged unit cell. A previously published

factor group analysis [11] shows:

r = Aig{R) + 2Big(R) + B2g(R) + 4Eg(R) + 2A2u{ir) + + 3Eu(ir)

Examined of the infrared spectra [11] shows that the predicted five ir modes are indeed

observed, but the bands are broad and indistinct as is typical of powder infrared spectra - of highly polar compounds

.

Raman spectra of four compounds with a 1:1 ordering on the rocksalt structure are shown in figure 6. The spectrum of YLiFe02 is weak, because the compound is strongly

colored. Spectra of the other three compounds exhibit more than the predicted 8 Raman bands

as did the ilmenite structures. The intense band at low frequencies seems unusually sharp,

and one might ascribe it to a fluorescence line, except that the frequency is different in

Liln02, and further, the line appears in YLiFe02 which should not be fluorescent. The

original spectra of the two rare earth compounds were cluttered with fluorescence lines.

Only lines which appeared with both 488 and 514.5 nm excitation were included in figure 6.

Although strong resemblances can been seen, the relative intensities are surprisingly

different for compounds that are structurally similar. The band near 500 cm~-^ is most

intense in LiEr02 with the second strongest band near 400 cm"-^. The two are comparably

intense in LiLu02, and in Liln02 the 380 cm"-' band is far stronger than the 502 cm"-' band.

122
T T 1 1 1 1 1

1 I 7'-LlF»0j

H—I

1

i—I 1—I

1 1

^

-I 1 1 1—I 1—I 1 1—I1000 900 800 700 600 500 400 300 200 fOO FREQUENCY (em"')

Fig. 6. Raman spectra of compounds with

1:1 (I4i/amd) ordering on rocksalt structure.

The effect of the ordering is to produce strong bands in the Raman spectrum where none are permitted in the disordered structure. In this particular situation the Raman spectrum would

be a sensitive tool for the detection of ordering in rocksalt structure mixed oxides.

4.5. ORDERING BASED ON SUPERSTRUCTURE STACKING

Sr2Ti0it, Sr3Ti207 , and Sri^Ti30io are examples of the Ruddlesden-Popper type of superstructures [3,12,13]. Sr2Ti0i| has the tetragonal K2NiF4 structure which can be constructed

from a perovskite block and a rocksalt block stacked along the c-axis. The other two

compounds can be written SrO-2SrTi0 3 and SrO-3SrTi0 3 and are thus seen to be the same type

of stacking with two and three perovskite blocks respectively. The space group is D^^,

I4/mmm for all three compounds. The a- axis is '^-3.90 A for all compounds, while the c-axis

increases from 13.71 to 20.3 to 28.1 as the number of perovskite blocks increases from one

to three.

A factor group analysis for the Ruddlesden-Popper phases is given in table 4. Four

Raman modes are expected for Sr2Ti04 , 10 for Sr3Ti207, and 14 for Sr4Ti30io- Raman spectra

are shown in figure 7. Of greatest interest are the strong bands in the range of 500 - 700

cm"-^. A single band at 579 cm"-^ appears in Sr2Ti0it , two bands appear in Sr3Ti207, and three

in SritTi30io- The A^g modes should be the most intense and should correspond to a symmetric

stretch of the oxygen lattice corresponding in a first approximation ot the TiOg octahedra.

It must be remembered that the basic perovskite block has no first order Raman spectrum

(3Ti^ + T2u] and neither does rocksalt [T^^ only] . In Di^-^ symmetry, T^^ -> E^ + A^ and

T2U Eu + B2u- The single perovskite block in Sr2Ti0it accounts very nicely for the predicted

infrared active 4Eu + 3A2u modes. As the number of perovskite blocks is increased the

number of ungerade modes no longer accounts for all degrees of freedom. It is apparent

123
"1

1 1 1 1 1 r

\ I -r I I I I I 1 1

1100 1000 900 800 700 600 500 400 300 200 100 FREQUENCY (cm"')

Fig. 7. Raman spectra of the RuddlesdenPopper phases with l4/ininm symmetry.

Table 4

Factor Group Analyses for the Ruddlesden-Popper Phases

Di+h Acoustic Vibrational Modes Selection

Modes Sr2Ti0i| Sr3Ti207 SritTigOio Rules

Alg 2 4 6 Raman

A2g 0 0 0 Big 0 1 1 Raman

B2g 0 0 0 Eg 2 5 7 Raman

Alu 0 0 0 A2u z 3 5 7 Ir, E 1 |c

Blu 0 0 0 B2U 1 1 2 Inactive

Eu (x,y) 4 6 9 Ir, e|_C

124
that a stacking superstructure, although the space group is preserved, does not yield a simple

multiplicity of bands. The new bands that appear in the Raman have no counterparts in the

parent structures.

5. CONCLUSIONS

The overall conclusions reached from the study of order-disorder may be summarized:

1. Vibrational spectroscopy is an exceptionally sensitive tool for the detection of

ordering. We were able to detect ordering in some spinels where no evidence for it occurred

in the x-ray patterns.

2. In general, ir spectra are easier to interpret than Raman spectra. Intensities

in particular are more predictable. Raman intensities tend to be very variable, even between very similar compounds.

3. Specific crystallographic models can be tested if the unit cell is not too large.

Spectra of very large cells show evidence for ordering, but all predicted detail is

generally not resolved.

4. Although ordering seems a rather mild effect cjrystallographically , it produces

dramatic changes in the dynamics of the unit cell. Spectra of ordered structures frequently

bear no resemblance to the spectra of the parent. Atoms or molecules that are equivalent

in the disordered structure may be non-equivalent in the ordered structure but are still

strongly coupled.

This work was supported by the Air Force Materials Laboratory, Wright Patterson Air

Force Base, under Contract F33615-69-C-1105

.

6. REFERENCES

[I] White, W. B., Mat. Res. Bull., 2_' 381 (1967).

[2] Bertaut, E. F., Corliss, L. , Forrat, F., Aleonard, R. , and Pauthenet, R. , J. Phys. Chem.

Solids, 21_, 234 (1961) . [3] McCarthy, G. J., White, W. B., and Roy, R. , J. Amer. Ceram. Soc . , 52_, 463 (1969).

[4] White, W. B. and DeAngelis, B. A., Spectrochim. Acta, 23A, 485 (1967).

[5] Herzberg, G., Ir and Raman Spectra of Polyatomic Molecules, (Van Nostrand, New York,

1945)

.

[6] DeAngelis, B. A., Keramidas, V. G., and White, W. B., J. Solid State Chem., 3_, 358

(1971)

.

[7] Newnham, R. E. and Meagher, E. P., Mat. Res. Bull., 2_, 549 (1967).

[8] Porto, S. P. S., Krishnan, R. S., J. Chem, Phys., 47, 1009 (1967).

[9] Axe, J. D. and O'Kane, D. F., Appl. Phys. Lett., 9_, 58 (1966).

[10] Porto, S. P. S., Fleury, P. A., and Damen, T. C, Phys. Rev., 154, 522 (1967).

[II] Moore, R. K. and White, W. B. , J. Amer. Ceram. Soc, 53_, 679 (1970).

[12] Ruddlesden, S. N. and Popper, P., Acta Cryst., 10^, 538 (1957).

[13] Ruddlesden, S. N. and Popper, P., Acta Cryst., 1_1, 54 (1958).

DISCUSSION

J. Shamir : l would like to ask if the spectra you presented are from single crystals.

I would like to add that we have just recently studied a polycrystalline solid solution of

zinc and cadium sulfide and found that the frequency of the LO phonon shifts linearly with

the composition of zinc sulfide and cadium sulfide. Now my question is have you observed

it only in single crystals or in polycrystals as well?

W. B. White : The data that I have shown you here are all on polycrystalline, pressed

powder materials. However, they are single phases, not solid solutions. If you do look at

solid solutions either by single crystal measurement or by powders you run into this one mode or two mode behavior phenomenon which has been observed in rock salt and sphalerite

structures pretty commonly.

125

/
W . R. Cook : I note on your slide on lithium iron oxide that the Raman lines were ex- tremely weak in comparison with virtually everything else you showed. Does this mean that

the compound is only partly ordered?

W. B. White : No, I'm afraid that what it means in this case is that lithium iron oxide

is very strongly colored and with scattering from a blue line of the ionized argon laser it

just absorbs like the devil.

126
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

A STUDY OF VoO, BY PHOTOELECTRON SPECTROSCOPY*''"

J. M. Honig

Department of Chemistry

Purdue University

West Lafayette, Indiana 47907

H. E. Weaver and R. D. Board

Scientific Instr\iments Division

Hewlett Packard Company

Palo Alto, California 94304

The occupied energy states of single crystal and polycrystalline V2O3 have been studied

by x-ray photoelectron spectroscopy both above and below the metallic-antiferromagnetic

insulator (M-AFI) transition. All of the elemental Vanadium and Oxygen states in the range

20 to 640 ev below the Fermi level were also encountered in V2O3. In addition, a valence

band with structure was observed in the range 0 to 10 ev. In the metallic phase this band

was intersected by the Fermi level; below the transition temperature the topmost portion of

the band was no longer observable, and may have disappeared under increased noise. Under the

experimental conditions involving a resolution of 0.3 to 0.5 ev, a search was made for the

presence of localized states in the energy spectrum of the insulating phase at 77 K. No such

states were encountered; unless they were masked by the residual valence band approximately

4 ev in width it must be concluded that the transition does not involve a change from a localized to an itinerant electron regime.

Key words: Metallic-insulator transition; photoelectron spectroscopy; V2O3.

* Supported in part by the National Science Foundation under Grant GP 8302 to Purdue Univ.

As this is a post-deadline paper only a brief abstract is presented here.

127

I

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

OBSERVATIONS IN THE ELECTRON MICROSCOPE OF LATTICE PLANES AND

MIGRATION OF SILVER IN BETA ALUMINA

W. L. Roth

General Electric Corporate Research and Development

Schenectady, New York 12301

Beta alumina is the commonly accepted name for a sodiiun aluminate of variable composition and structure with "ideal" formula NaAljiOiy. There is considerable interest in beta

alumina and its isomorphs because the monovalent ions diffuse rapidly at temperatures of

300 °C and below. Crystal structure and density studies of the sodium and silver isomorphs

have shown the compound is non-stoichiometric and contains approximately 25% excess sodi\am or silver. All of the monovalent ions lie in basal planes at z=l/4 and 3/4. The planes are

o separated by 11 A and ion conduction takes place by two dimensional diffusion in these planes.

The conducting planes have been resolved in the electron microscope and their identity

established by electron diffraction. High resolution photographs show lattice bending and

rotation

.

When relatively thick crystals of silver beta alumina are observed in the electron

microscope, worm-like filaments or whiskers about 50 A in diameter exude from the edge of

the crystal. The filaments were shown by electron diffraction to be silver. The filaments

are produced by diffusion of Ag"*" ions down channels in the conducting planes to neutralize

the negative charge of absorbed electrons.

Key words: Beta alumina; electron microscope; lattice images; migration of silver;

silver whiskers.

1 . INTRODUCTION

Motivated by the discovery of solids with exceptionally high ionic conductivity, there

has been renewed interest in the structure of beta alumina and some of its isomorphs. Beta

alumina is a member of a small class of unique materials, called super ionic conductors [1]^

that exhibit extremely large ionic dif fusivities at temperatures which are low with respect

to their melting points. For example, the self diffusion constants for sodium and silver

ions in beta alumina [2] are given by D{Na+) = 2.4 x lO"'* exp (-3810/RT) and D(Ag+) = 1.65 x 10"^ exp (-4050/RT) cm^sec"-^, corresponding to room temperature dif fusivities of D (Na+) = 4.0 X 10~^ and D(Ag+) = 1.7 x 10"'' cm^sec"-'- . A particularly important property of the structure is the extreme anisotropy of the diffusion. Movement of ions occurs by two dimensional

flow in widely separated planes which are perpendicular to the hexagonal axis of the crystal

and there is virtually no diffusion between the planes. X-ray diffraction has provided con- siderable insight into the structure at the atomic level, the gtoichiometry , crystal structure, and paths the conducting ions follow in migrating through the crystal [3,4].

Beta alumina is an unfortunate misnomer commonly used to refer to the refractory sodium

aluminate with hexagonal crystal structure which has composition about Na20'llAl203 to Na20 •9AI2O3 . The general features of the atomic arrangement was originally solved by Bragg

et al. [5] and Beevers and Ross [6] , and the structure has been refined with modern methods

by Felsche [7] and Peters et al. [3] . The crystal is composed of spinel-like blocks which

consist of four close packed layers of oxygen atoms with al\m:iinum atoms distributed among the

'Figures in brackets indicate literature references at the end of this paper.

129

465-504 O - 72 - 10
octahedral and tetrahedral interstices. The blocks are bound together by planes of loosely

packed Na+ and ions. The binding between the spinel-like layers is weak, resulting in

easy cleavage of the crystals parallel to the basal planes. The sodium may be replaced by

other monovalent ions of appropriate size [2] and the structures of the K+ [6] Ag+ [4,8]

and H3O+ [9] derivatives have been shown to be isomorphous with beta alumina.

Beta alumina is non-stoichiometric and crystals usually contain about 15-25% Na+ in ex- cess of the "ideal" formula NaAl^j^Oiy [2,4]. The precise mechanism of charge compensation

has not been established and it is not definitely known whether the positive charge due to the excess monovalent cations is neutralized by aluminum vacancies, interstitial oxygens,

or bound electrons.

The present paper describes electron microscope observations on sodium and silver beta

alumina that were undertaken to provide information on a different scale relevant to the

structure and movement of ions through the crystal. Crystals of the sodium and silver isomorphs have been studied in the electron microscope. The lattice planes responsible for

conduction in sodium beta alumina have been resolved and the migration and reduction of Ag"*" to Ag by electrons has been observed.

2. IDENTIFICATION OF CONDUCTING PLANES IN SODIUM BETA ALUMINA

Crystals of beta alumina (Monofrax H, Carborundum Company) were gently crushed and

scattered on a carbon substrate for examination. Electron microscope observations were made

with an updated Sieman's Elmiscope 1, and a Philips EM 300 operated at 100 kV. The observation of lattice fringes due to the conducting planes requires the beam strike the planes at

the Bragg angle which for 100 kV electrons is near grazing incidence. The desired orientation is perpendicular to the easy cleavage plane and it was necessary to seek out fragments

that had fallen with their c-axis roughly parallel to the plane of the supporting grid.

Suitable fragments were identified by scanning the field and observing the diffraction patterns on a fluorescent screen. The c-axis was easily recognized by the close spacing of

O reflections corresponding to the large c^ = 22.6 A lattice parameter. After an appropriate

fragment was selected, the orientation was sometimes extended to two dimensions by rotation

of the crystal about the c-axis.

Figure 1 is an electron micrograph taken at 100,000 magnification of a beta alumina

fragment. The long edge is parallel to the hexagonal axis and the fragment appears to be

made up of bands about 0. ly wide which are parallel to (00.1) planes. The arc-like segments

near the lower fracture edge which appear to intersect the crystal surface at an angle to the cleavage planes are probably deformation structures produced when the crystal was crushed.

The diffraction pattern (fig. 2) shows the fragment consisted of two principal crystals.

The major individual is oriented with the a*c* plane perpendicular to the electron beam and

the c-axis of the second is tilted about 8° with respect to the first. The observed lattice

parameters were found to be ao = 5.46 A and Cq = 23.8 A, in reasonable agreement with more

accurate values, = 5.594 and c^ = 22.603 A, measured with x-rays and bulk crystals. The

diffraction spots contain considerable substructure indicative of twinning or lattice bending

and rotation. The substructure is probably related to the bands in figure 1 and the fragment appears to be composed of lamellae about O.ly thick. The intense pattern shows reflections of the form h-k = 3n,J!. = 2n + 1 which are not allowed by the space group P63/mmc. The

reflections are absent in the weaker pattern which indicates they are due to dynamic or multiple scattering effects in the thick crystal.

Figure 3 is an electron micrograph taken at magnification 500,000 from a thin wedge

near the edge of the same crystal. The region is marked with an X in figure 1. Relatively

perfect lattice fringes approximately perpendicular to the c-axis of the fragment are re- solved. The fringe separation obtained by direct measurement on the electron micrograph

plate is 22 A, equal to the Cq parameter of beta alumina. The fringes are tilted about 8° with respect to the edge of the dense (absorbing) crystal, approximately the angle between

the c-axes of the individuals in figure 2. The fringes were obtained by insertion of a 50p

objective aperture which isolated the (000) and several low order {OOZ) reflections. The

angular correlation of fringes and diffraction pattern was established after correcting for

130
Fig. 1. Beta alumina magnified 100,000X. The

region marked with an X is shown at higher magnification in figure 3.

Fig. 2. Electron diffraction pattern of

beta alumina crystal shown in

figure 1.
rotation of the image by the magnetic field of the lens. The orientation and spacing identify the lattice fringes V7ith the conducting planes in beta alumina. The fringe separation

corresponds to (00.1) planes. Adjacent conducting planes are only 11 A apart and the double

fringe separation is probably due to inclusion of the forbidden (00.1) reflection. The 11 ^ separation corresponding to the (00.2) planes was resolved in the patterns to be described

next.

Figures 4, 5, 6 are high resolution electron micrographs taken by V.A. Phillips and

J. A. Hugo with the Philips EM 300 microscope, axial illumination, and SOp or 50y diameter

objective apertures. Lattice fringes separated by 11 A, equal to the separation of the adjacent conducting planes in beta alumina, are clearly resolved in figure 4. The intensity

reversals along the fringes are attributable to electron optical effects caused by the crystal thickness tapering toward the edge.

The micrograph in figure 5 taken at magnification of 570,000 shows a cross grating pattern of 11.4 K fringes inclined at about 68° to a set of 4.5 K fringes. The wide fringes

correspond to the (00.2) planes (d=11.3 A) and the fine fringes to (10-2) planes (d=4.45 K)

.

The computed angle between (00.2) and 10.2) planes is 67°15', in agreement with the observed

angle. Marked bending of the (00. 2) lattice planes which is a consequence of the weak bonding between spinel blocks is visible in the lower position of the crystal.

o Figure 6 shows a well developed set of 4.8 A fringes traversing a broad expanse of

O nearly perfect crystal except for mottled patches about 25-50 A wide. The lattice fringes

pass continuously through the patches and the similar structure at the edge of the crystal

indicates the mottled appearance may arise from microcleavages in the surface. An alternative interpretation, which is highly speculative based on the limited information at hand,

is the regions may be the B- and D-domains that have been suggested to account for the non- stoichiometry of beta alumina [4]

.

Fig. 4. Lattice fringes corresponding to Fig. 5. Beta alumina cross grating pattern.

(00.2) planes in beta alumina. wide fringes are (00.2) planes

The fringe separation is about (d=11.3A) and fine fringes are

"L-L (10.2) planes (d=4.45A) . Note

curvature of the (00.2) planes.

132
Fig. 6. Lattice fringes corresponding to (10.0)

o planes in beta alumina (d=4.84A).

3. REDUCTION OF Ag+ IN SILVER BETA ALUMINA BY ELECTRONS

The sodium in beta alumina crystals was replaced with silver by exchanging in molten

silver nitrate as described by Yao and Kummer [2] . Crystals were crushed and examined with

the electron microscope in similar fashion to beta alumina. The phenomena to be described

were observed in thick crystals that were opaque to the electron beam. Thin crystal fragments that were highly transparent to electrons appeared to behave in more normal fashion.

Figure 7 is a diffraction pattern obtained from a silver beta alumina crystal which

had been only slightly exposed to the electron beam. The electron micrograph of the same crystal (fig. 8) shows opaque regions, roughly globular or disc-like in shape, with sizes

ranging from about 50 to 300 A. Similar opaque regions observed in other fragments had a worm-like appearance. A set of weak, diffuse rings were generally superimposed on the sharp

reciprocal lattice of the silver beta alumina. The d-values calculated from the diffuse

rings agreed with the first four reflections of metallic silver. The most probable interpretation of these observations is that some of the Ag"^ ions in silver beta alumina were

reduced in the electron beam to form metallic silver.

Attempts to observe the precipitation of silver by working with weak beams focused near

the edge of crystals resulted in the formation of whisker-like filaments which started at

the edge and grew outward in worm-like fashion (fig. 9) . Electron diffraction confirmed

their identity as crystalline silver (fig. 10) . The filaments were about 50-100 A in diameter and had relatively uniform cross section. Initially the filaments grew straight and

parallel to each other, and parallel to the crystal surface. Figure 11 is enlarged to show

a banded substructure in the filaments which may be the result of deformation or twinning.

The evident interpretation of these observations is that metallic silver is formed by

reduction of Ag"*" by electrons incident on the silver beta alumina. Several processes are involved in the growth of the globs and whiskers.

133
Fig. 7. [110] zone of silver beta alumina. Fig. 8. Electron micrograph of silver beta

alumina crystal corresponding to diffraction pattern in figure 7.

Pig. 9. Silver whiskers growing from silver

beta alumina.

Fig. 10. Diffraction pattern of whiskers.

134
Fig. 11. Enlargement showing detail in whiskers

growing from silver beta alumina.

1. The absorption of electrons generates heat and the temperature rise increases the

rate of diffusion of Ag . The effect is more pronounced in thick crystals which absorb a larger number of electrons.

2. When the beam is directly incident on a thick crystal, Ag"*^ ions are attracted and

diffuse toward the negative charge where they are reduced to atomic silver. The rounded

edges of the silver globs suggest high temperatures may be attained in small local regions.

3. The heating is less severe when the electron beam is incident at the edge of the

fragment. The Ag ions are attracted to the negative charge at the crystal edge where they

are reduced to atomic silver. The movement of Ag down the crystal channels is probably

enhanced by collapse of the beta alumina structure into a-Al203 behind the advancing front

of silver. When the accumulation of silver at the edge exceeds that required to form a nu- cleus of critical size [10] , a crystal nucleates and grows in whisker-fashion as it continues

to be fed from the interior of the beta alumina crystal. As the filam.ent extends farther

from the surface, elastic strains due to thermal and electrical gradients at the edge of the

crystal increase and ultimately are relieved by kinking.

The proposed mechanism of whisker growth is associated with the very high mobility of

the Ag+ ions and resembles the growth of whiskers on silver iodide [11] . The observed whisker cross section indicates the critical size of the silver nucleus is about 50 A, which

agrees with 100 K found by Price et al. [12] for silver whiskers electrolytically grown from

AgN03 . According to the suggested mechanism, the crystals in the whisker should be relatively perfect, in agreement with the sharp reflections making up the Debye Sherrer rings in

figure 10. The sharpness of this pattern contrasts with the diffuse rings obtained from the

globular precipitate inside beta alumina crystals.

135

/
4. REDUCTION OF Na"^ IN SODIUM BETA ALUMINA BY ELECTRONS

The reduction of Na"*" to metallic sodium in beta alumina crystals was not observed in

the electron microscope but there is reason to believe that the reaction may occur. Electron

microprobe experiments with sodium beta alumina crystals have shown a gradual increase with

time of the intensity of NaKa x-rays when the electron beam remained focused on a single re- gion. This is believed to be due to an increase in the concentration of sodium by diffusion

of Na+ toward the electrons. If the beam continues to be focused on the same point, the

crystal decomposes and the NaKa x-ray intensity decreases. This is probably due to the sublimation of sodium and a concomitant collapse of the structure into a-Al203

.

5. SUMMARY

1. Lattice fringes due to the conducting planes in beta alumina have been resolved in

the electron microscope. Direct measurement of the separation of the conducting planes

agrees with that obtained by x-ray diffraction.

2. Reduction of Ag"^ to atomic silver occurs when thick crystals of silver beta alumina

are observed in the electron microscope. If the beam strikes the beta alumina directly,

o globs or worm-like clusters of metallic silver, about 50 A in diameter, precipitate within

the crystal. If the beam impinges near the edge, Ag"*" ions diffuse toward the beam and are

O reduced to metallic silver to form filament-like whiskers approximately 50 A m diameter.

3. Evidence is presented that Na"*" is also reduced to atomic sodium by electrons

incident on beta aliomina.

6. ACKNOWLEDGEMENTS

The cooperation of E.F. Koch in obtaining the electron diffraction and electron microscope patterns of sodium and silver beta alumina is gratefully acknowledged. I am grateful

to R.B. Bolon for microprobe observations and to V.A. Phillips and J, A. Hugo for the high

resolution electron micrographs.

7. REFERENCES

[I] Rice, M. J., and Roth, W. L. , J. Solid State Chem. , 4_, 294 (1972).

[2] Yao, Y. Y., and Kummer, J. T. , J. Inorg. Nucl . Chem., 29, 2453 (1967).

[3] Peters, C. R. , Bettman, M. , Moore, J. W. , and Click, M. D. , Acta Cryst. , B27 , 1826

(1971)

.

[4] Roth, W. L., J. Solid State Chem., 4_, 60 (1972).

[5] Bragg, W. L. , Gottfried, C, and West, J., Z. Krist., 255 (1931).

[6] Beevers, C.A., and Ross, M.A.S., Z. Krist., 97, 59 (1937).

[7] Felsche, J., Naturwissen. , 54, 612 (1967).

[8] Whittingham, M.S., and Huggins, R.A. , J. Chem. Phys. , 54, 414 (1971).

[9] Kato, K. , Ph.D. Thesis, University of Hamburg, (1968).

[10] See, for example, Nabarro , F.R.N. , and Jackson, P.J., in Growth and Perfection of

Crystals, Ed. by Doremus, R.H. , Roberts, B.W. , and Turnbull , D., Proceedings of International Conference on Crystal Growth, held at Cooperstown, N. Y., Aug. 27-29(1958),

publ. by John Wiley & Sons, Inc., New York (1958).

[II] Berry, C.R. , J. Opt. Soc. Amer., 40, 615 (1950).

[12] Price, P.B., Vermilyea, D.A. , and Webb, M.B., Acta Metallurgica, 6, 524 (1958).

DISCUSSION

N. C. Stephenson : By looking at the growth of these whiskers, is it possible to tell

whether the movement of the silver atoms on the planes are coordinated, whether they move with respect to other atoms, or just have individual paths?

W. L. Roth: No, except the whiskers seem to have a periodic spacing so that one feels one is seeing the consequences of silver atoms moving down channels. Of course, we do not

see the structure at the atomic level since the whiskers are 50 to 100 angstroms in diameter.

N. C. Stephenson: Are they all coming out at the same rate?

136
W. L. Roth: They are all roughly coming out at the same rate, but I do not know to what

extent the intensity of the field is constant at the edge of the crystal.

B. Cox: This is a comment which was originally intended for John Allpress, but I think

it's just as appropriate here. This is to insert a note of caution into the interpretation

of lattice fringe images when one is interpreting detail on the scale where the dynamical

theory of electron diffraction is breaking down. I would also like to point out the situation

in the imaging of lattice fringes in metals for the study of dislocations where, in a given

area of the sample imaged using two symmetrical but opposite reflections, the actual number

of terminating fringes or dislocations which appear in the same area, can vary from image to image^. I don't think we can go into the reasons for this here, but I would just like to point out that things like wavy fringes are not direct images of the lattice. They are still

an interference phenomenon, to use a simplification in terms.

W. L. Roth: I agree completely. However, I should have pointed out the reason for

showing the first set of fringes was because I had direct evidence that we were looking at the 001 fringes. We correlated the orientation of the diffraction pattern precisely with the

orientation of the fringes by measuring the rotation of the image in the microscope. We know

that we are looking at diffraction effects from the 00 2. planes. Our aperture was such that

we probably included other reflections so that I agree some of the detail may not represent

real images of the lattice.

J. G. Allpress : I agree with that last comment of Brian Cox. In fact, it is very important. The actual conditions under which you take the pictures are very important, the

conditions of focus and so on, the orientation, and the crystal thickness. We really have

to do a lot of quite heavy calculations in order to prove that we are seeing structures

directly in the particular case that we are interested in. However, I think we've got to take each case on its own merits, we can't make generalizations about this technique.

B. Post : In the first place I agree with Dr. Cox about the caution that has to be exer- cised in interpreting these fringes. I think you are familiar with Pendelosung fringes which

are seen with x-rays and with electrons . There is no reason why you shouldn ' t see them in some of these cases. But what I wanted to ask was a very simple question, really. Why does

silver always act as the anomalous metal, not always, but why does silver always act as the

ionic conductor as the material that causes shorting out in semiconductors and so on? Have

you any thoughts on that matter?

W. L. Roth : Well, it may not be that anomalous. For example, consider the beta alumina

structure. One can substitute lithium, sodium, potassium, ammonia or silver ions, and the

base structure, the matrix, changes very little. The diffusion and conduction of silver ions

in beta alumina are similar. The activation energies are within a third of a kilocalorie of

each other and there is very little difference between them. Silver is a small ion which fits

well in open structures. If lithi\jm ions are substituted for silver or sodium, there is a larger activation energy for diffusion because the lithium is too small. The opposite is true

for potassium because it is too large. There also may be some effects due to the polarizing

power of the silver ion.

B. M. Gatehouse : You seem to stress that the silver was growing out from the surface

for 500 angstroms or maybe more along what may possibly be channels. However, I thought I could see one there that seemed to be turning and coming back or was that some odd effect in

the photograph?

W. L. Roth : You should understand one is looking at a dynamic process in the microscope

and must decide at a given instant to take a photograph. The whiskers start out initially

parallel and grow to perhaps three or four times their diameter in length. Then they may

deform in a complex way. There probably are intense fields and temperature gradients in the

vicinity of the surface. The incident electrons introduce surface charges which result in

deformation and the whiskers kink and take off in a new direction. I don't know whether the

whiskers are twinned, but the electron diffraction patterns, the Debye-Scherrer rings, are made up of individual reflections which are quite sharp. Each of the 100 to 200 angstroms

silver elements in the unkinked region of a whisker seems to be a fairly perfect crystal.

^D. J. H. Cockayne, J. R. Parsons and C. W. Hoelke, Phil. Mag., 24_, 130 (1971).

137

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

BETA ALUMINA - PRELUDE TO A REVOLUTION IN SOLID STATE ELECTROCHEMISTRY

M. S. Whittingham and R. A. Huggins

Department of Materials Science and Engineering

Stanford University

Stanford, California 94305

For almost two decades solid state electrochemical techniques have been used to study

the thermodynamic and transport properties of a number of materials. However, these studies

have been restricted essentially to systems utilizing electrolytes containing mobile silver

or copper ions at low temperatures, and oxygen ions at high temperatures.

Transport measurements have been made on single crystals of beta alumina, which has the

nominal formula MAJ^i^Oiy where M is usually a monovalent cation, to test its suitability as a solid electrolyte. In this and related structures, the monovalent cation can be extremely

mobile. By use of a group of novel non-polarizing solid electrodes, which are fully reversible to the monovalent cation, it has been possible to study the ionic conductivity of a series of beta alminas containing alkali metals as well as thallium over a wide temperature

range. The electronic conductivity of silver beta alumina has also been determined by use of

the Wagner asymmetric polarization technique over wide ranges of temperature and oxygen partial pressure.

The results of these studies clearly indicate that the beta alumina family shows excellent promise for use as solid electrolytes, exhibiting high values of ionic conductivity and

a very low electronic transference niunber. These properties were exhibited over extremely

wide ranges of temperature, -150 °C to +820 °C, and oxygen partial pressure, lO"^** to 1 atra. The use of beta alumina opens up many new opportunities in solid state electrochemistry,

particularly in the study of materials containing monovalent cations.

Key words: Beta alumina; diffusion; electrochemical cell; electrochemical transducer;

ionic conductivity; mass transport; solid electrolyte.

1. INTRODUCTION

There has recently been a great deal of interest in a material called "beta alumina"

,

whose nominal formula is HAinOiy , in which M represents a cation, normally monovalent. This

interest has arisen primarily because of the possibility of using materials of this phase, or more probably a related phase called "3" alumina", whose nominal formula is MA£50g, as solid

electrolytes in new types of batteries. This interest arose as a result of the important

pioneering work at the Ford Motor Company [1,2]^ which not only focused attention upon the

unusual physical properties of this type of material, but also. [3] showed that it was possible

to take a rather revolutionary approach to the battery problem, using liquid electrodes and a solid electrolyte; this is, of course, just the inverse of traditional battery designs, and

leads to some very distinct advantages.

Interest in the practical application of these materials and concepts has spread rather

widely, and research is under way in a number of laboratories at the present time. In addition, serious battery development efforts have been undertaken by several companies in the

United States, as well as others in England and Japan. At the present time the commerical

Figures in bracXets indicate the literature references at the end of this paper.

139
interest seems to be focused upon the use of configurations involving a liquid sodium anode,

a solid 3 or 3" alumina electrolyte and a liquid sulfide cathode. Although there are surely

various alternative approaches, it now appears that such a cell is expected to be a serious

contender for widespread application as high energy density and power density secondary cells.

One can find reviews of various new battery possibilities in a number of places [4-14]

,

and it is not our intent to discuss this matter here other than to point out that the theoretically limiting value of energy density for a sodium-sulfur cell operating at 300 °C is

about 1030 watt hours per kilogram [3] , whereas the familiar lead-lead oxide cell typically

gives 5 to 30 watt hours per kilogram at room temperature.

This paper will not discuss the possibility of the use of the beta aluminas as battery

or fuel cell components. Instead, attention will be focused upon the potential use of these

and related materials for a wide range of other purposes, primarily as experimental tools for

the measurement of thermodynamic and kinetic data. We shall see that their unusual properties

open up a very wide vista for the use of solid electrolytes as electrochemical transducers in

a great variety of scientific as well as engineering applications.

2. ELECTROCHEMICAL TRANSDUCERS

2.1. INTRODUCTION

Although there had previously been a few papers in which solid electrolytes had been used

for thermodynamic studies [15] , attention was drawn to the broad possibility of using such

ionically conducting solids as electrochemical transducers for a niimber of purposes in an important paper by Carl Wagner in 1953 [16] , in which he used silver iodide in a simple solid

state cell configuration to measure a nvmiber of properties of silver sulfide. A few years

later, a pair of papers by Kiukkola and Wagner [17,18] expanded this horizon considerably by

pointing out a variety of possible applications, as well as indicating several other ionically

conducting solids which could be used as solid electrolytes. In addition to discussing the

extension of this type of work by the use of other simple binary salts, they pointed out that

cubic oxides with the fluorite structure, such as calcium-doped zirconium dioxide, could be

used in a similar manner at temperatures in the range 750 to 1150 °C. Since that time, there

have been a number of laboratories who have pursued these ideas, as well as extending them,

and one can find reviews of much of this work in several places [15, 19-21],

Before mentioning some of these areas of application and pointing out the implications

of beta alumina and related materials to them, we shall very briefly review a few elementary

concepts for those who are not familiar with this particular field.

If two neighboring regions within a solid are in thermodynamic equilibrium with each

other under isothermal conditions, the concentrations of all species (including all defects)

in both regions will be time-independent. This means that there must be no net forces present

in such a system which tend to cause the transport of either mass or charge from one microscopic region to the other.

Let us focus our attention upon this question of forces acting upon species. We know

that in general one can express the force acting on any species i as

Fi = - grad Ui

where U-j^ is the total potential energy or thermodynamic potential of species i at a given location. The requirement for equilibrium, then, is that the gradient in Uj^ must be equal to zero for all species

.

There are several different kinds of potential that can contribute toward the total thermodynamic potential of a particular species in a solid. Here we will restrict ourselves to the discussion of only two, the chemical potential, (or partial molar free energy) y^, and

the electrostatic potential, Zj^F<^ ((}> is the local value of the electrostatic macropotential

,

whereas Zj_F is the electrostatic charge carried per mole of i) . The sum of these two is known

as the electrochemical potential, rii / so we can write

rij_ = Mj^ + Zj^F(j) (2)

140
For simple one-dimensional transport, the flux density of a species i can be written as

= CjL Vj^ {J^ = no ./cxa^sec) (3)

where Cj_ is the concentration (no./cm^) and is the average velocity of the species i (cm/

sec) relative to a stationairy observer. The absolute mobility B is defined as the velocity

per unit force,

B . =

1

(4)

Note that this is a different quantity from the electrical mobility u, which is defined as the velocity per unit electrostatic field, or

V.

u. = . (5)

d X We find that although these two different "mobilities" have different dimensions, they are related by

u. = z. q B. , (6) 1 11

where q is the electronic charge. If there are two gradients present, a chemical gradient and

an electrostatic gradient, we can write the force acting upon a particle of species i as

dn. dy. F . = - - —- = -[- —- + z a ^1

1 N dx dx i^ dx

1 i .1 ^i . d^,

where N is Avogadro's number. These equations can be combined to get a general expression for

the flux density,

J. = - C. B. q i^] . (8)

1 iiNdx i dx

It is obvious from this expression that xinder equilibrium conditions, when the particle

and charge flux are both zero, one could have a chemical gradient that is just balanced by an electrostatic gradient.

1_ 1 _ _ d (j) N d x i d X

(9)

If one deals with a material in which the transference number for ionic species is close to unity, essentially all the charge transport is by means of ions, and such an equilibrium situation can exist and, in fact, be used to transduce between chemical and electrical quantities.

This simple case is illustrated schematically in figure 1. In that figure, a difference in

the chemical potential of species i is assumed to exist upon the two sides of a solid that is an ionic conductor for species i. Integrating eq. (9) between the two interfaces, we find that

- yj""" = - z^ F E, (10)

where E is the electric potential difference between the electrodes placed at the two interfaces. By substitution of the general relation between chemical potential and activity

141
=y.°+RT£na. 1 1 (11)

it can be rewritten as

E = - ^

(a^ /a") , (12)

i

which is the familiar Nernst equation.

It is obvious from these simple considerations that if one has a situation in which no current passes through the ionic conductor, that is, if the forces causing transport of the

ions are exactly balanced, a measurement of the open circuit electric potential difference

between the two interfaces is a direct measure of the difference in chemical potential or activity in the pertinent species at those locations. If some care is taken, one can play

this game both ways and use a chemical potential difference to generate an electrical voltage, or an electric potential difference to generate a difference in chemical activity.

In addition, if no charge-generating or charge-consuming reaction takes place at the

interfaces, one can obtain a direct measurement of the ionic transport tlirough the electrolyte

by evaluation of the electronic current through the electrode circuit. As will be mentioned

shortly, this allows the use of this type of system for measurements of mass transport and

related matters.

2.2. RANGE OF APPLICATIONS

Although most of the earlier applications of solid electrolytes as electrochemical transducers involved their being employed in emf cells to measure free energy changes of various

reactions, recent work has extended over quite a range of different applications. Some of

these are listed in table 1.

3. PRACTICAL CONSIDERATIONS

Although this appears quite simple, there are several practical considerations that must

be given attention. These include the magnitude of the ionic conductivity of the transducer

phase under the conditions (e.g., temperature and chemical environment) in which it is to be

used. In a static situation, this conductivity must be high enough that equilibrium can be

established within a reasonable period of time. This typically means that one must have a conductance value of about 10~''^ohm~-^ or greater. Furthermore, if the transducer phase is to be used for transport measurements, or under conditions in which transport is expected to occur within it, its conductivity must be considerably greater, so that the electric potential

difference across it (the IR drop) does not seriously interfere with the operation of the cell.

Under these conditions, it is generally considered necessary that the conductance be equal to

10"'* ohm" or greater.

PHASE I

I Ml

IONIC CONDUCTOR

FOR SPECIES L

PHASE n

n

'/y /////// /////

Fig. 1. Schematic representation of simple electrochemical cell with solid electrolyte.

142
Table 1

Examples of the Application of Solid State Electrochemical Techniques

Static Emf Measurements

Free energy of formation of binary and ternary compounds

Free energy changes accompanying various cell reactions

Thermodyniimics of binary phases

Determination of limits of stoichiometry of compounds

Phase diagram determination

Thermodynamics of phase transformations

Effective mass of electrons or holes in semiconductors

Solubility of gases in liquids

Time-dependent Emf Measurements

Phase boundary migration kinetics

Supersaturation required for nucleation within and upon solids and liquids

Combinations of Emf and Current Measurements

Diffusion in liquid and solid metals and mixed conductors

Transport of both ionic and electronic species across phase boundaries

Kinetics of condensation and vaporization processes

Oxidation and reduction reactions on solid surfaces

Tharmodynamics of gaseous species

Studies of the mechanism of catalysis

Ionic and electronic partial conductivities in mixed conductors

Structure of electrode-electrolyte interfaces

Technological Applications

Batteries

Fuel cells

Thermoelectric devices

Memory elements

Solute valence control in semiconductors and ionic solids

Purification of liquids and gases

Measurement and control of gas compositions

Another important consideration is the assumption made in the simple discussion of the

Nernst equation that the only charge-carrying mobile species is the ionic species in question.

Obviously, if the transducing phase is also an electronic conductor, electronic transport will

seriously interfere with, if not completely nullify, the electric potential difference generated by the difference in chemical potentials at the two interfaces. This is obviously a matter of real concern. For, instead of needing to know just the ionic conductivity, one must also know the value of the electronic conductivity or the ratio of electronic conductivity

to total conductivity (the transference nimiber for electronic species, tg) . The influence of

a small but significant electronic transference nimber results in a measured open circuit

potential, Ej^, for a simple cell of the type illustrated in figure 1, given by [17,22,23]

As a rule of thumb, it is normally considered that the electronic transference number

should be less than 10"^ throughout the usable range in order for a solid electrolyte to be

useful as an electrochemical transducer under static conditions. Since the electronic transference number typically varies with the stoichiometry, the thermodynamic range over which an

I

(13)

1

143
electrolyte is useful can thus be quite severely restricted.

Another important matter is the thermodynamic stability of the transducer phase with

respect to reactions with chemical species present at its interfaces. As a first approximation, if a solid electrolyte MX is in contact with species N, it is necessary that the displacement reaction

MX + N NX + M, (14)

not proceed in the forward direction. Another way of saying this is that it is normally nec- essary that the element N be more noble than the element M.

4. PROPERTIES OF SOME SOLID STATE ELECTROCHEMICAL TRANSDUCERS

4.1. MAGNITUDE OF THE IONIC CONDUCTIVITY

As we have mentioned, it is important that electrochemical transducers have relatively

large values of ionic conductivity. Typical values for such materials are indicated in fig- ure 2, which also shows conductivity data for several other common ionic solids as a function

of temperature. It is clear that the conductivity of ionic conductors can /ary over an im- mense range. Materials which are useful as solid electrochemical transducers must have good

values of conductivity in the temperature range in which they are to be used. Thus, it is

quite obvious, for example, that the fluorite structure oxides will not be very useful below

about 600 °C. On the other hand, it is clear that there are several materials which have

large ionic conductivities at unusually low values of temperature. These are of two general

types, materials which are closely related to the body-centered cubic a Agl structure, in

which silver is typically the mobile ion, and the beta aluminas. An important aspect of the

latter case is that there are several choices for the mobile cation.

One of the difficulties encountered in the evaluation of the ionic transport in these

unusually good ionic conductors (for which the term "super ionic conductors" was coined by

Rice and Roth [24]) is the avoidance of polarization effects at measuring electrodes. It is common practice to use ac conductivity techniques to evaluate ionic motion in ionic conductors.

If polarization occurs at the electrodes, the conductivity appears to be frequency dependent

and the normal procedure is to increase the frequency until it is in a range at which this

frequency dependence disappears. This is not a great difficulty in the case of the traditional ionic conductors such as the alkali halides, but it becomes a very severe problem with

solids in which the conductivity is high. Even frequencies of the order of 10^ Hz are often

not high enough to avoid polarization effects in the beta aluminas [25]

.

An alternate approach to this problem is to use reversible electrodes. If this is properly done, the frequency dependence is eliminated. It has been shown [26] that with proper

care it is possible to use solid elemental Ag as a reversible electrode to get reliable values

of the ionic conductivity of the silver ion in beta alumina from 800 °C all the way down to room temperature.

1000 500 300 200 100 25 0 -25 -50 "C

Fig. 2. Conductivity data for various ionic conductors.

144
Another more novel approach was the demonstration [27] that a mixed conductor, in which

the important ion has a high diffusion coefficient, can also be used as a nonpolarizing electrode in connection with materials such as the beta aluminas. By use of this technique, it was possible to measure the conductivity of the sodium ion in sodium beta alumina from 820 °C all the way down to -150 °C.

By use of this nonpolarizing electrode technique, reliable data on the ionic conductivity

of single crystals of several of the beta aluminas have now been obtained over a wide temperature range. These are illustrated in figures 3-6 for silver, sodiiun, potassium and thallium

ions. Also included in those figures are data obtained by the Ford research group by means

of radiotracer [1,2,28] and the dielectric loss [2] techniques. Allowing for correlation

effects, it is seen that the results obtained by the conductivity and radiotracer methods co- incide very well in all cases. The dielectric loss data also give good agreement in the so- dium and potassium cases, and moderate agreement in the silver case, but deviate by about a factor of ten for thallium beta alumina. It appears that the absolute values of the conductivity obtained by these various techniques agree better than one might expect from just con- sideration of the activation energy values determined separately over relatively small

temperature spans [2]

,

Conductivity measurements have also been made on a single crystal sample of beta alumina

containing lithium. In this case, electrodes of a cubic lithium tungsten bronze were used,

rather than the tetragonal or hexagonal bronze phases used with the others. This was necessary as the small lithium ion is only found in the cubic phase. Although we were thus apparently able to avoid a frequency dependence in the conductivity, indicating reversible electrodes, more scatter was present in the data in this case. In addition, the conductivity

data seem to fall along two different straight lines when plotted in the normal way to determine the temperature dependence. This is clearly evident in figure 7. Although the conductivity and tracer diffusion data lie comfortably close to one another above 180 "C, it is not

obvious that the low temperature conductivity measurements and the dielectric loss experiment

are evaluating the same physical process. As a further complication, it was found that an- nealing the sample above 800 °C caused a marked drop in the low temperature conductivity.

Fig. 3. Conductivity, tracer diffusion, and dielectric

loss data for silver beta alumina.

145

465-504 O - 72 - 11
Fig. 4. Conductivity, tracer diffusion, and dielectric

loss data for sodium beta alumina.

Fig. 5. Conductivity, tracer diffusion, and dielectric

loss data for potassium beta alumina.

146
800 300 100 0 -50 -100 °C

~~1 1 1 1 1 1—

Fig. 6. Conductivity, tracer diffusion, and dielectric

loss data for thallium beta alumina.

Fig. 7. Conductivity, tracer diffusion, and dielectric

loss data for lithium beta alumina.

147
There is evidently more to do before we should feel that we understand what is happening in

lithium beta alumina. One possibility that should certainly be given consideration is that

at high temperatures a direct interstitial jump mechanism is becoming important, rather than

transport being dominated by the interstitialcy mechanism that seems to prevail [26] in the

other beta aluminas

.

These conductivity data are compiled in table 2, assuming an Arrhenius relation of the

form

= (a^/T)exp(-H/RT) . (15)

Also included are values of the apparent correlation factor, f, the ratio of the radiotracer

diffusion coefficient to the diffusion coefficient obtained from the ionic conductivity data,

calculated for temperatures at the center of the tracer data. It is seen that the correspondence to the theoretical value [26] for the interstitially diffusion mechanism in this structure, 0.599, is quite good.

Some measurements have also been made upon samples of the phase 3" alumina. It has been

reported [29] that both sodium and potassium ions have greater conductivities in this phase

than in the beta alumina structure. This appears to be true for both single crystals and

dense sintered polycrystalline bodies

.

Using the reversible solid electrode technique, we have done a few experiments on hot

pressed polycrystalline samples of the 3" phase. The results are indicated in figure 8,

along with data from the Ford laboratory [29] . Also shown (dotted line) is the conductivity

of single crystal sodium beta alumina [27] . Above 315 "C the polycrystalline data are essentially frequency-independent and evidently lie upon a straight line parallel to the single

crystal beta alumina data. At lower temperatures, a frequency dependence appears and there

is a deviation from linearity. Preliminary measurements [30] using the complex admittance

method [31] gave essentially the same value of conductivity at room temperature, as also indicated on figure 8. A plot of these data on the complex admittance plane is shown in figure 9

.

4.2. ELECTRONIC CONDUCTIVITY

It was pointed out earlier that a desirable electrochemical transducer should have an electronic transference number less than 10 . Measurements have been made of the electronic

component of the total conductivity of silver beta alumina [26] by use of the Wagner asymmetric polarization technique [23,32-34] from 555 to 790 °C over a wide range of oxygen partial

pressure. Below about 750 °C changes in oxygen partial pressure did not appear to influence

the electronic conductivity beyond normal experimental scatter. It was not possible to extend

these measurements to lower temperatures because of prohibitively long times required for

Table 2

Summary of Data on Ionic Conductivity in Single Crystal Beta Aluminas

Ion Temp. Range a Activation Conductivity Correlation

° ,_) Energy at 25 °C Factor, f °C (ohm-cm , ^ , -, , , s -1 kJ/mole (ohm-cm)

Ag 25 - 800

Na -150 - 820

K -70 - 820

TZ -20 - 800

Li 180 - 800

Li -100 - 180

1.6 X 103 16.5

2.4 X 10^ 15.8

1.5 X 103 28.4

6.8 X 10^ 34.3

9.7 X 10^ 35.8

5.4 X 10^ 18.0

6.7 X 10"3 0.61

1.4 X 10~2 0.61

6.5 X 10~5

2.2 X 10-6 0.58

1.3 X lO"'*

148
Fig. 8. Conductivity data for single crystal and polycrystalline sodium B" alumina. Also shown

(dotted line) are values for single crystal

sodium beta alumina, and measurement made by

complex admittance method.

Fig. 9. Admittance plot for polycrystalline 6" alumina

at 25 °C.

equilibration (presxamably due to very slow electron diffusion) . From these results and total

conductivity values one can compute the electronic transference nimiber tg over this temperature range. Figure 10 shows the variation of the electronic transference number for single

crystalline silver beta alumina with temperature. It is obvious that an extrapolation of

these data to lower temperatures indicates that the beta alumina phase should have an ex- tremely low electronic conductivity at temperatures at which its high ionic conductivity makes

it a very interesting electrochemical transducer.

149
800 700 600 500 °C

0.9 1.0 I.I 1.2 1.3 lOOO/T "K"'

Fig. 10. Temperature dependence of the electronic

transference number, silver beta alumina.

4.3. RANGE OF APPLICABILITY

It was pointed out earlier that the range of thermodynamic conditions over which a solid

electrolyte can be beneficially used can be limited by two general types of problems , the appearance of an appreciable component of electronic conduction, or what might be referred to

as chemical instability with respect to interaction with adjacent phases or structural changes

such as phase transformations.

Information concerning the thermodynamic conditions under which solid electrolytes are usable and have sufficiently low values of electronic transference numbers has been compiled

by Patterson [35,36], as an extension of an approach initiated by Schmalzried [37,38]. Such

information is included in figure 11 for beta alumina and several of the common solid electrolytes. As pointed out by Patterson, reliable information of this type is only available for

a relatively few materials. These fall into two general groups, the fluorite structure oxides,

which are good conductors for oxygen ions and are generally useful only above about 700 °C,

and a group of halides , primarily the silver and copper families. These halides have low

melting points and tend to be relatively unstable, reactive and hard to handle. They are only useful under limited conditions between about 150 and 450 °C. Thus the roster of available solid electrolytes that can be used as electrochemical transducers has been quite limited

until recently. Essentially only three ions could be considered, silver, copper and oxygen,

and each of these over only limited temperature and thermodynamic ranges.

Two important changes have occurred in the solid electrolyte business in the last few

years. A group of ternary silver salts, generally related to the a Agl structure, have been

discovered, and the beta aluminas have appeared. This first group includes materials such

as Ag3SI and RbAgi^Is that have very high values of ionic conductivity to remarkably low temperatures. They have attracted a lot of attention as possible battery components, and a good

review of much of this work has recently been presented by Owens [9]

.

Although these materials have impressive values of ionic conductivity at low temperatures, one should not have too much enthusiasm concerning their potential use as electrochemical transducers because all present members of this group are only good conductors for

150
Fig. 11. Electrolytic conduction domains for several common solid electrolytes and beta alumina.

one ion, silver. Also, they tend to have relatively poor thermodynamic stability. As an example of this latter point, the material Ag3SI is apparently not sufficiently ionic (tg > 0.01) in contact with iodine at 25 °C to be very usable as a solid electrolyte. Also, their

general structural instability is indicated by the fact that a number of them undergo phase

transformations at quite low temperatures. Some examples of this are shown in table 3.

In contrast to these limitations, the stability and scope of apparent applicability of

the beta alxominas is very impressive. This phase is essentially an oxide ceramic with a rigid structural skeleton. It is mechanically very stable, melting incongruently at about

2000 °C [39] . We shall not discuss the available information concerning either its structure

or its various other properties here, however, as such information, as well as discussions of

possible transport mechanisms, can be found in a number of other olaces [24-27, 29, 39-43].

The chemical stability of the beta alumina phase is also very impressive. This phase is

apparently stable at temperatures in the vicinity of 300 °C and lower in contact with the

alkali metals. This is equivalent to being in equilibrium with extremely low oxygen partial

pressures

.

We should hasten to point out, of course, that we are not talking about true equilibrium

in this respect but practical noninteraction, or if you will, "selective equilibrium". In materials like beta alumina, the oxide structural skeleton is apparently stable enough that

one can treat it as an inert matrix or framework within which the M cations can readily move

about in response to various forces and achieve their own version of equilibrium.

Experiments upon silver beta alumina [26] between 600 and 800 °C showed that there was

no apparent influence of oxygen partial pressure in the range from 0.2 to 10~^^ atm. upon the

ionic conductivity of this phase. The indications [26] that the beta alumina phase has unu- sually low electronic conductivity and its apparent lack of oxygen pressure dependence below

about 750 °C also show the broad range of its applicability.

Perhaps the most important feature of the beta aliaminas is the fact that this phase can act as a transducer for a whole new set of ions for which no satisfactory transducer was previously available. Instead of being able to work with just silver, copper, and oxygen, the

151
Table 3

Examples of Solid Ionic Conductors that have

Phase Transformations at Relatively Low Temperatures [9,44]

Material Transition Temperature

CuBr 470, 420 °C

Cul 400 °C

AgjSI 235 "C Agl 144 °C

CU2Hgl4 67 °C

Ag2Hgl4 50 °C

[CsHsNHjAgsIg 50 °C

KAgt^Is -136 °C

RbAg,+ l5 -155 °C

solid state electrochemistry community now has a much wider range of available species with

which to deal. Although well defined transport measurements have only been made on beta aluminas containing silver, sodium, potassium, and thallium, it has been demonstrated that this

phase can also contain Rb"*" , Cu+, Li"*", NHi^+, In"*", N0+, Ga"*", amd H3O+ ions [29], and it is rea- sonable to expect it to be usable as a transducer for some, if not all of those as well. The

ability to exchange one type of cation for another by equilibration techniques [1] or in some cases by electrochemical pumping [25] , adds a new degree of freedom to the materials synthesis problem.

5. SOME APPLICATIONS

Although, as mentioned already, most of the work that has been done by the use of solid

electrolytes as electrochemical transducers has involved either oxide, copper- or silver-containing systems, one begins to see the use of the beta alumina family for such purposes. For

example, Belton and Morzenti [45] reported the use of sodium beta alumina for thermodynamic

studies of liquid sodium-lead alloys, and Gupta and Tischer [46] employed this phase for

measurements of the sodium-sulfur system. Likewise, Hsueh and Bennion [47] have used this

material to make emf measurements of the sodium activity in liquid sodium-mercury alloys at

30 °C.

Measurements in our laboratoiry have indicated that single crystal potassium beta alumina

can be used as a transducer to evaluate the difference in potassium activity between two

solids. In this case, a difference in potassium activity of 300 mV was found at 500 °C between two samples (x values of 0.2 and 0.33) of potassium tungsten bronze, whose nominal formula is K^WOs. These bronzes, which are mixed conductors, as mentioned earlier, were prepared

by electrolytic growth from molten salts, as described elsewhere [48]. In addition to being

the first use of beta alumina for electrochemical measurements upon solids, this is the first

time that successful thermochemical measurements have been made on a tungsten bronze. Previous attempts [49,50] have been unsuccessful, and it was assumed that some kind of alkali

ion-deficient surface layer was an inevitable structural feature of these phases.

6. SUMMARY

In this paper we have endeavored to indicate that the beta alumina phase represents a new departure in solid electrolytes. Enough information is now available about its inherent

ionic conductivity, electronic transference number, and thermodynamic stability to make it

reasonable to expect that it and related materials can be used in a wide variety of scientific

and perhaps engineering applications as an electrochemical transducer for a group of important

species not heretofore measurable and controllable.

Beta alumina and similar rigid framework materials also represent a major change in an- other sense. Heretofore, all useful solid electrolytes were expected to attain thermodynamic

equilibrium with their environment. In these materials, however, the mobility of one constit152
uent within the structure is so much greater than that of the others that it is quite realistic to think in terms of selective equilibrium for only certain species within an essentially inert crystalline environment. This has many potential advantages, not the least of

which involves mechanical properties.

A further unusual and particularly useful characteristic of this class of materials is

the ability that they afford for the synthesis of different solid electrolytes themselves.

The technique of ion exchange within solids means that one can think in terms of preparing a material, or perhaps even a device, with one composition, and by use of ion exchange methods,

convert it to something else in situ.

Because of these factors, we contend that beta alumina truly represents a first step

across a vast new frontier.

7. ACKNOWLEDGEMENT

Work in this area at Stanford has been supported by the Office of Naval Research, the

Environmental Protection Agency, and the Advanced Research Projects Agency (through Stanford's

Center for Materials Research)

.

8. REFERENCES

[I] Yao, Y. F. Y. and Kummer, J. T., J. Inorg. Nucl. Chem. 29_, 2453 (1967).

[2] Radzilowski, R. H., Yao, Y. F. and Kummer, J. T., J. Appl. Phys. 40_, 4716 (1969).

[3] Weber, N. and Kummer, J. T. , Proc. Ann. Power Sources Conf. 22^, 37 (1967).

[4] Foley, R. T. , J. Electrochem. Soc. 116 , 161 (1969).

[5] Hull, M. N., Energy Conversion 1£, 215 (1970).

[6] Mrgudich, J. N., "Solid Electrolyte Batteries," Encyclopedia of Electrochemistry

,

Reinhold, New York, p. 84 (1964).

[7] Takahashi, T., Denki Kagaku, 36_, 402 (1968).

[8] Takahashi, T. , Denki Kagaku, 36_, 481 (1968).

[9] Owens, B. B. , Advances in Electrochemistry and Electrochemical Engineering 8_, 1 (1971).

[10] Cairns, E. J. and Shimotake, H., Science 164, 1347 (1969).

[II] Jasinski , R. , High Energy Batteries, Plenum Press (1967).

[12] U. S. Department of Commerce Report, "The Automobile and Air Pollution," (1967).

[13] Sudworth, J. L. and Dugdale , I., Power Sources 2_» 547 (1968).

[14] Sudworth, J. L. and Hames , M. D., Power Sources 4_, 1 (1970).

[15] Schmalzried, H., Thermodynamics and Atomic Transport in Solids, Int. Atomic Energy

Agency, Vienna (1965)

.

[16] Wagner, C, J. Chem. Phys. 21_, 1819 (1953).

[17] Kiukkola, K. and Wagner, C, J. Electrochem. Soc. 104 , 308 (1957).

[18] Kiukkola, K. and Wagner, C, J. Electrochem. Soc. 104 , 379 (1957).

[19] Wagner, C, Advances in Electrochemistry and Electrochemical Enginering, 4_, 1 (1966).

[20] Raleigh, D. O., Prog, in Solid State Chem. 3_' 83 (1967).

[21] Alcock, C. B. , ed. , Electromotive Force Measurements in High-Temperature Systems, Inst. of Mining and Metallurgy, London (1958)

.

[22] Wagner, C. , Z. physik. Chem. B21 , 25 (1933).

[23] Wagner, C, Proc. Int. Comm. Electrochem. Thermo. Kinetics (CITCE) 7_, 361 (1957).

[24] Rice, M. J. and Roth, W. L., "Ionic Transport in Super Ionic Conductors," to be published

in J. Solid State Chem. (1972) . [25] Whittingham, M. S., Helliwell, R. W. and Huggins , R. A., U. S. Government Res. and Devel

.

Rept. 69_, 158 (1969) . [26] Whittingham, M. S. and Huggins, R. A., J. Electrochem. Soc. 118 , 1 (1971).

[27] Whittingham, M. S. and Huggins, R. A., J. Chem. Phys. 54_, 414 (1971).

[28] Kummer, J. T., personal communication.

[29] Kummer, J. T., "6 Alumina Electrolytes," to be published in Progress in Solid State

Chemistry, 7_' (1972) . [30] Nakagawa, Y. , unpublished work at Stanford (1971).

[31] Bauerle, J. E., J. Phys. Chem. Solids 30.' 2657 (1969).

[32] Wagner, C, Z. Elektrochem. 60, 4 (1956).

[33] Wagner, J. B. and Wagner, C, J. Chem. Phys. 26_, 1597 (1957).

[34] Patterson, J. W. , Bogren, E. C. and Rapp, R. A., J. Electrochem. Soc. 114 , 752 (1967).

153
135] Patterson, J. W. , in The Physics of Electronic Ceramics, ed. by L. L. Hench and D. B. Dove, Marcel Dekker, Inc., New York (1971).

[36] Patterson, J. W. , J. Electrochem. Soc. 118 , 1033 (1971).

[37] Schmalzried, H. , Z, Elektrochem. 66_, 572 (1962).

[38] Schmalzried, H., Z. physik. Chem. N.F. 38, 87 (1963).

[39] DeVries, R. C. and Roth, W. L. , J. Am. Ceram. Soc. 52_, 364 (1969).

[40] Demott, D. S. and Hancock, P., Proc. British Ceramic Soc. 19_, 193 (1971).

[41] Roth, W. L., "Stoichiometry and Structure of the Super Ionic Conductor Silver BetaAlumina," General Electric Report No. 71-C-132 (1971).

[42] Sato, H. and Kikuchi , R. , J. Chem. Phys . 56, 677 (1971).

[43] Bettman, M. and Peters, C. R. , J. Phys. Chem. 73_, 1774 (1969).

[44] Geller, S. and Owens, B. B., "Silver Ion Site-Distribution, Structure and Conductivity

of the Solid Electrolyte Pyridinixim Hexaiodopentaargentate , [C5H5NH] Agslg , Between -30

and 125 °C," to be published.

[45] Belton, G. R. and Morzenti, P. T., j. Metals 22_, No. 12, 26A (1970).

[46] Gupta, N. K, and Tischer, R. P., J, Electrochem. Soc. 117 , 125C (1970).

[47] Hsueh, L. and Bennion, D. N., J. Electrochem. Soc. 118 , 1128 (1971).

[48] Whittingham, M. S. and Huggins , R. A. , "Electrochemical Preparation and Characterization of Alkali Tungsten Bronzes, MjjW03," to be published in the Proceedings of the 5th

Materials Research Symposium, Solid State Chemistry, National Bureau of Standards, (1971).

[49] Swanson, A. B. , D. Phil. Thesis, Oxford University (1968).

[50] Koch, D. F. A. and Becker, H., Personal communication quoted by G. H. Taylor, J. Solid

State Chem. 1, 359 (1969)

.

DISCUSSION

G. K. Johnson : I guess this question is for either you or Dr. W. L. Roth. Would you

comment on what size crystals can be grown of this material and what techniques are used?

R. A. Huggins : Walter, why don't you answer that?

W. L. Roth : Most of the work was with crystals obtained from the Carborundum Corporation'. The crystals were frequently 1 or more centimeters in diameter, but only one or twotenths of a millimeter thick. They are mica-like and the quality of thick individuals is

poor. We have grown crystals in the laboratory that were a bit better in perfection and

thickness, but only one or two millimeters in size.

G. K. Johnson : Well, what's the general method that is used for producing these?

W. L. Roth: We passed current between carbon electrodes inserted in a large mass of

sodium carbonate and AI2O3. The melting point is around 2000 °C and the materials react and

crystals of 6-AI2O3 appear to grow from the melt.

154
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

EXPERIMENTAL STUDY ON THE lONICITY IN THE TiO PHASE. AN APPLICATION

OF THE NEW METHOD OF DETERMINING THE STRUCTURE FACTOR

BY HIGH VOLTAGE ELECTRON DIFFRACTION

D. Watanabe and 0. Terasaki

Department of Physics

Tohoku University

Sendai, Japan

It was reported recently that the second order reflection in electron diffraction

vanishes at a certain accelerating voltage E^, owing to the many -beam dynamical interaction

combined with the relativistic change of electron mass [Watanabe, Uyeda and Kogiso, Acta

Cryst. , A24 , 249 (1968).]. A measured value of makes it possible to determine very

accurately the Fourier coefficient of the potential for the first order, and thus the

corresponding value of the x-ray scattering factor [Watanabe, Uyeda and Fukuhara, Acta

Cryst. A24 , 580 (1968), A25 , 138 (1969)].

In the present study, the method has been applied to the disordered TiO phase. The

accelerating voltages E^, for which Kikuchi lines of the 400 reflection vanish, have been

measured using a 500 kV electron microscope. .The measured values are 340, 354, 389 and

425 kV, respectively, for TiOo.82' TiOo,96» TiOi_ie» TiOi.25- To compare the

experimental values with calculation, the values of E^ have been calculated for TiOg _82

and Ti0i,25» using theoretical scattering factors of titanium and oxygen atoms of various

atomic states. The calculations have been made for free neutral atoms Ti*^, 0°, monovalent

ions Ti^+, 0^" and divalent ions Ti^+ , 0^". The structure factors of the first order have

been determined using the measured values of Eq.

Comparison of the experimental values of E^^ and the first order structure factors with

theoretical ones enables us to discuss the ionicity in a TiO crystal. The result shows that

the ionicity depends on the oxygen concentration in the crystal, i.e., titanium and oxygen

atoms in the oxygen-deficient TiO crystal are considered to be almost neutral, while the

elements in the titanium-deficient crystal appear to be in the ionic states.

The possibility of applying the present method to a Ti02 cjrystal of the rutile type

is discussed as well.

Key words: Critical voltage for the 400 of TiO; critical voltage for the 110 of Ti02

(rutile) ; determination of structure factor by high voltage electron diffraction;

disappearin'g effect of the second order reflection in electron diffraction; ionicity

in TiO crystal; many-beam dynamical interaction in electron diffraction; structure

factors for electrons of TiO.

1. INTRODUCTION

It was found by Watanabe, Uyeda and Kogiso [1]^ that the second order reflection in

electron diffraction disappears at a certain value of the incident electron accelerating

voltage E^ owing to the many-beam dynamical systematic interaction combined with the

relativistic change of electron mass. The effect has been observed on Kikuchi lines

with a 500 kV electron microscope for f. c. c. and b. c. c. metals, such as Al , Fe , Ni

,

Figures in brackets indicate the literature references at the end of this paper.

155
and Cu [2, 3], Nagata and Fukuhara [4] and Fisher et al. [5] observed a similar

effect in the vanishing of the second order extinction contour in electron micrographs

at the critical voltage E^. A measured value of makes it possible to determine veiry

accurately the Fourier coefficient of crystal potential for the first order Vi , and thus the

corresponding value of the x-ray atomic scattering factor f^, assuming those for the second

and higher order reflections. Previously, the values of E^ were measured for the 220

reflection of Fe and the 222 reflection of Al, Ni, and Cu, and the x-ray atomic scattering

factors for the first order reflection ff were determined by many-beam calculation, with

an accuracy as good as that obtained by the most accurate x-ray measurement [2,3].

In the present study, the method has been used for accurate determination of the

structure factors of titanium monoxide TiO . The NaCl type TiO phase exists over a wide

range of composition depending on temperature, e.g., from TiOo.y to TiOi .25 at 1400 °C and

TiOg.g to TiOi,25 temperatures below about 990 °C, and its crystal structure has a large

number of vacancies [6,7]. At the composition TiOi,0' about 150% of both metal and oxygen

sites are vacant, and titanium-rich crystals have more of the metal sites filled, together

with an increase in the number of oxygen vacancies, and vice versa. The vacancies are arranged randomly in the NaCl type structure at temperatures above 990 °C, while ordering

of vacancies occurs at lower temperatures [8] . The present method was applied to the disordered phase.

Since atomic scattering factors for electrons at small scattering angles are very

sensitive to the configuration of outer atomic electrons, accurate determination of the

structure factors for low angle scattering from the TiO crystal would be very useful to discuss the ionic state. The present method provides one of the most sensitive means of

measuring low angle structure factors.

The purpose of this paper is to give a brief description of the principle of the method

and to report the result obtained from the NaCl type TiO crystals. In addition, the

possibility of applying the present method to Ti02 crystal of rutile type will be discussed.

2. PRINCIPLE

In high energy electron diffraction many weak beams are generally excited in addition

to strong ones. Among weak beams, the effect of higher and lower order reflections of the

main reflection (systematic interaction) does not depend on the crystal azimuth around the

normal of the reflecting plane and is always important; while the effect of other

reflections (accidental interaction) depends on the azimuth and is generally small unless

simultaneous reflections occur. For the second order reflection at the exact Bragg

condition, the intensity I2 depends not only on the Fourier coefficient of the second

order V2 but also on Vj , V3 , V4 , etc. I2 depends, at the same time, on the accelerating

voltage E due to the relativistic effect. That is, I2 is expressed by the relation,

I2 = f (Vi, V2, V3, . ..; E) . (1) The theoretical description of this effect has been given by the many-beam dynamical theory

[4] as well as by Bathe's second approximation [9] and higher-order approximation [10].

In terms of Bethe's second approximation, the apparent value of the structure factor

of the h reflection Uj^(E) is expressed by

U;(E) = R[U, (0) - R'd^E" "g^'-" '\-g'°^ ] , (2)

if the effect of accidental^ interaction can be neglected. In (eq 2), R = 1 + (eE/mgc^)

,

mgc = 511 kV, Ug = (2moe/h^)Vg, d is the lattice spacing of the first order reflection

and

I" means the summation over positive and negative integers except for g = 0 and h.

For the second order reflection, U2 (E) is given by

156
U^(E) = R[U2(0) - R-d2|ui(0)2 - |ui(0)-U3(0) - (0) -Ui^ ((

- •:j^U3(0) -UsCO) - ^U4(0) -06(0) ...}]• (3)

If the value of Uj (0) is large and U2 (0) is positive, the apparent structure factor of the

second order reflection (E) decreases with increasing accelerating voltage, vanishes at

a certain voltage (E^,) and increases its absolute value with further increase of the voltag

At the critical voltage E^^, (eq. 3) is reduced to

U2(0) - (1 + ^-^) d2|ui(0)2 - -Ui(0)-U3(0) - --U2 (0) -U^ (0) moc^

15

I3 (0) -Us (0) 24

(0) -Ue (0) . . .[ = 0. (4)

If Ec is determined experimentally, can be calculated assuming the values of V2 , V3 , etc

and the value gives the atomic scattering factor for electrons f^ at the first order

reflection and thus that for x-rays, f^.

The percentage error of f thus obtained can be estimated as follows. From (eq. 4)

,

|AUi/Ui| is roughly given by the relation

ui ' ~2 1 2 ^ ' U2 y

*

^ ^ moc^ + eEc ^

(5)

From this equation and the well-known formula

STT^moe^

(4TTsin6/A) 7~ ' (6)

|Afi/f]^| is expressed approximately by the equation

eE~

ry ^

ff moc^ + eE

j Aff

I 1 Z - f^

ff

" 2

AE,

Z - f^

|Af

f2

(7)

Since (Z - ff) /ff - 0.4 and ff/CZ - ff) - 0.8 - 1.0 in many cases, the contribution of Aff

to |Aff/ff| is about 1/6 - 1/5 of |Aff/ff|. If Ec - 400 kV, then eEc/(moc2 + eEc) -4/9 and

therefore the contribution of AEc to |Aff/f?| is less than one tenth of I AE^/Ec • X

I J. i. I IX X Contributions of Af3 etc., are less because the factors multiplying |Af3/f3| etc., are much

smaller.

In the experiment, the accelerating voltage of each diffraction pattern is determined

from the analysis of the Kikuchi pattern with an accuracy of 1% [11] , and the value of Ec can be determined with an accuracy of 10 kV by examining a series of diffraction patterns

taken at various accelerating voltages. In the calculation of the scattering factor, the

theoretical Hartree-Fock values of f?, f?, etc., [12] for the free atoms or ions are used.

X

^ -J The errors of f2 estimated from reliable theoretical and x-ray experimental data are about

1-2% for f . c. c. and b. c. c. metals such as Al, Fe, Ni and Cu [3] . Since Ec is usually

measured at room temperature, the values of V2 , V3 , etc., including the Debye-Waller

factors exp (-Bsin^O/A^ ) must be used in the calculation of Vi . For many crystals the

Debye characteristic temperature appropriate to crystal diffraction have been accurately

measured, and these can be assiamed in the evaluation of Vq. The contribution to the error

of f^ from that of the assumed B values, AB, is estimated to be, for example, less than

0.2% for AB = 0.05 A^

.

157
The calculations of and therefore fj^ can be carried out by Bethe ' s second approximation, (eq. 4), taking eleven beams (g = -4, -3, .., +6) into account, and also by an orthodox many-beam theory [13] covering nine beams (i = -3, -2, +5) . In the many-beam

calculation, the accelerating voltage at which two main branches of the dispersion surface

contributing to the second order reflection contact with each other is defined as a critical

voltage E;-.. The results of both calculations agree almost exactly for f. c. c, b. c. c. metals and for NaCl type crystals.

The values of f^ at the 110 reflection of Fe and the 111 reflection of Al , Ni and Cu

have been calculated from the measured values of Eq and compared with the theoretical and

x-ray experimental data [3]. The estimated errors of ff were in fact less than 1%, i. e., about 0.6% for Fe, Ni and Cu and 0.9% for Al . It is to be noted that the values of f^ are smaller than those for the free atoms calculated by Freeman and Watson [14] by 0.5% for Ni,

0.9% for Al and Fe and 1.6% for Cu, but agree well with the values for the atoms bound in a crystal obtained by Wakoh and Yamashita [15] on the basis of band structure calculation.

Recently, the high voltage electron diffraction experiments have been done for V and Cr as well and the x-ray atomic scattering factors f^ for the 110 reflection have been obtained

[16] , which are also in good agreement with the theoretical values obtained by Wakoh and

Yamashita.

3. EXPERIMENTAL METHOD

Four different specimens were prepared by arc melting appropriate mixtures of Ti02

(99.9% pure) and sponge titanium (99.8% pure) under argon atmosphere. Repeated melting was made to ensure the homogeneity in composition. The buttons were rapidly cooled to room temperature in the argon atmosphere.

For determining the specimen composition, lattice parameters of the powdered specimens were measured, using an x-ray diffractometer method and making a Nelson-Riley plot.

Measured values were a = 4.191, 4.184^ 4.174, and 4.168 A, respectively, for four different

specimens, the errors being +_ 0.0005 A. Comparing these values with the lattice parametercomposition relation established by Andersson et al. [7], the compositions of the present

specimens were estimated to be TiOo.82' TiOo.gs/ TiOj.ig, and TiOi.2 5' respectively.

The specimens were thinned mechanically to approximately 0 . 1 mm thickness. Thin foils

suitable for transmission electron microscopy were then prepared by electropolishing at room temperature in a solution of 60% HNO3, 20% HF and 20% glacial acetic acid at 4 V. Final polishing was achieved by chemical thinning in a solution containing 33% HF , 50% HNO3,

and 17% H2O.

The x-ray diffraction patterns showed sharp diffraction lines of the NaCl type structure,

indicating that the disordered state was retained at room temperature. The electron diffraction

patterns contained a distribution of weak diffuse scattering, in addition to the fundamental

spots. The diffuse scattering is due to the existence of some short range order to vacancies.

Thin foils were examined with a 500 kV electron microscope. Diffraction patterns were

taken from areas of 1 ym diameter or smaller by the selected area diffraction technique at various accelerating voltages. Inspecting intensity variation of the 400 Kikuchi line and

contrast change of the middle line of the Kikuchi band [1, 17] with the accelerating voltage,

the critical voltage E^ for the 400 reflection was determined.

4. RESULTS

Figure 1 shows examples of diffraction patterns of TiOo.82 taken at accelerating voltages

325, 345 and 365 kV. The 400 Kikuchi lines are clearly visible in figure 1 (a) and (c) , but

almost invisible in (b) . Moreover, the middle line of the Kikuchi band is clearly seen in

figure 1 (a) and (c) , and vanishes in (b) . Asymmetry of excess-deficient profile of the

middle line is reversed in (a) and (c) . The critical voltages E^ for the 400 reflection

determined from a series of such diffraction patterns were 340, 354, 389, and 425 kV,

respectively, forTiOo.82' TiOo.96/ TiO^^^g, andTiOi^25-

158
800 1

Fig. 1. Electron diffraction patterns from TiOQ.g2taken at

325 kV (a) , 345 (b) and 365 (c) . Arrows in (a) and

(c) show the middle line of the Kikuchi band.

To compare the experimental values with calculated ones, the values of E^^ were calculated

for TiO 0 82 Ti0i_25' using available theoretical scattering factors of titanium and

oxygen atoms or ions of various atomic states. The calculations were made for free neutral

titanium and oxygen atoms Ti ^, 0^, monovalent ions Ti-^"*", 0-^~ and divalent ions Ti^+, 0 ~. For the divalent oxygen ion, three models were considered, i. e., 0^" ion in a hypothetical

potential well with a spherical distribution of +1 or +2 charge calculated by Watson [18,

19] , and 0^" ion model calculated for magnesium oxide crystal by Yamashita and Asano [20,

21]. For neutral atoms, positive ions and monovalent oxygen ions, x-ray scattering factors

calculated by Fukamachi [22] from analytical Roothaan-Hartree-Fock wave functions of

Clementi [2 3] were used. The respective electron configurations are as follows:

TiO K(2) L(8) 3s (2) 3p{6) 3d(2) 4s (2)

,

Til + K(2) L{8) 3s(2) 3p(6) 3d(3) 4s (0) ,

Ti2 + K(2) L(8) 3s (2) 3p(6) 3d(2) 4s (0) ,

oO ls(2) 2s (2) 2p(4) , oi- ls(2) 2s (2) 2p(5) ,

159
The structure factors for electrons TrvgUh of the hOO reflections (h = 2, 4, 14)

calculated for TiOo_82 and TiOi^25 293 K are shown in table 1, where vq is the volume of

the unit cell of the crystal lattice. In the calculation, titanium and oxygen vacancies

have been treated as if they are distributed uniformly throughout the titanium and oxygen

sublattices, respectively, with the probabilities corresponding to vacancy concentrations;

since the vacancies are almost randomly arranged in the NaCl type crystal. The effective

B factors of for TiOo.s 0.80 for TiOi.2 determined by neutron diffraction

experiment of Yamada et al. [24], which include the effect of static atom displacements near vacancies as well as thermal vibration effect, were assumed for TiOg 82 and TiO^ 25' respectively.

Table 1

Structure Factors for Electrons, ttvoU^ (A) , of the hOO Reflections

Calculated for TiOo.82 and Ti0i,25

hOO TiO,oO Til+,0^ Ti2+,o2- (a) Ti2+,o2- (b) Ti 2+,02- (C) experimental

value

200

400

600

800

1000

1200

1400

14.41

5.85

2.60

1.25

0.637

0.327

0. 165

TiOo .82 (d)

14.03

5.87

2.60

1.25

0.637

0.327

0.166

14.20

5.87

2.60

1.25

0.637

0.327

0.165

14.11

5.87

2.60

1.25

0.637

0.327

0.165

13.77

5.84

2.60

1.25

0.637

0.327

0.165

14.59+0.08

200

400

600

800

LOOO

1200

1400

13.55

5.27

2.18

0.947

0.422

0.185

0.078

TiOi .25 (e)

13.23

5.30

2.18

0.947

0.422

0.185

0.078

13.38

5.30

2.18

0.946

0.422

0. 185

0.078

13.26

5.30

2.18

0.946

0.422

0.185

0.078

12.84

5.26

2.17

0.946

0.422

0.185

0.078

13.08±0.11

(a)

(b)

(c)

(d)

0 2- Watson +1 well.

0^~, Watson +2 well.

0^~, Yamashita & Asano.

Occupation probabilities are 0.925 and 0.755 for titanium and oxygen sublattices,

respectively

.

(e) Occupation probabilities are 0.78 and 0.975 for titanium and oxygen sublattices,

respectively

.

160
Table 2

Calculated and Measured Values of Eq (kV^ for TiO.

Ti°,oO Til+,0l- Ti2+,o2-(a) Ti2+,o2-{b) Ti2+,o2- (c) measured

value

TiOo 82 359 414 389 403 447 340 + 5

TiOi .25 359 408 385 403 462 425 + 10

(a) 02-

, Watson +1 well.

(b) , Watson +2 well.

(c) 02- , Yamashita & Asano.

The values of calculated using the theoretical structure factors given in table 1 are shown in table 2, together with the experimental values. Although the values of E^

change considerably with the atomic state of constituent elements, the values for each

model are almost independent of specimen composition. This is due to the systematic changes

of temperature factor, lattice parameter and occupation probabilities of both titanium and

oxygen sublattices with composition. That is, the effects of temperature factor and lattice

parameter changes compensate the effect of occupation probability change, and almost the same values of E^ are obtained. The measured values of Eq, however, change considerably with

specimen composition.

The structure factors 'tvqUx of the first order reflection 200 for TiOo.82 and TiO 1,2

5

calculated using the measured values of Eq and assuming the structure factors of higher

order reflections given in table 1 are shown in the same table. It is to be noted that the

theoretical structure factors of higher order reflections are almost the same for various

models, as seen in table 1. The contribution to the error of the first order structure

factor |AUi/Ui| from that of the second order structure factor IAU2/U2I is estimated to

be less than 0.4%.

5. DISCUSSION

Comparison of the experimental values of Eq and ttvqU;^ with the theoretical ones enables us to discuss the ionicity in the TiO crystal. As seen in tables 1 and 2, the

experimental values of Eq and irvoUi for TiOo.82 are approximately equal to those calculated

for neutral atoms Ti'^ and o'' , while the experimental values for TiOi.25 are far different

from those for neutral atoms. Since the values of E^ calculated for each model are almost

independent of specimen composition, as already mentioned in the preceding section, the

Ec values, 354 and 389 kV, measured for TiOo.ge and TiO 1.15, respectively, can also be

compared with those calculated for various models in table 2. These results mean that the

ionicity in the TiO phase depends on the oxygen concentration in the crystal. That is,

titanium and oxygen atoms in the oxygen-deficient TiO crystal are considered to be almost

neutral, while the elements in the titanium-deficient crystal appear to be in the ionic

states

.

The calculation of the structure factors have been based on the atoms in neutral or ionic states with spherically symmetric electron distribution. Since TiO crystals examined

in the present study have the cubic close packed structure and the vacancies are almost

randomly distributed, the electron distribition in the crystal is considered to be spherically

symmetric. On the other hand, the condition of charge neutrality has not been satisfied in

the present calculation. The correction to this is not possible to make at present,

161

465-504 O - 72 - 12
because t±ie actual electronic structure of a TiO crystal is not yet known. Although an attempt to make this correction is in progress, assuming several models for the electronic

structure, it seems that at least the conclusion for the oxygen-deficient crystal does not

change even if the correction is properly made, since the correction for TiOg^gg must be

negligible.

It should be emphasized that the structure factors Ui of the first order reflection 200

estimated from the measured values of Ej, are most reliable. Since the structure factor at low angle scattering is very sensitive to the configuration of outer atomic electrons

,

the present result on the first order structure factors would contribute greatly to the study

of the electronic structure of TiO crystals.

In order to find the possibility of applying the present method to other compounds with

different crystal structures, the values of Eq for Ti02 crystal of the rutile type were

calculated. The lattice parameters of Ti02 are a = 4.594 A and c = 2.959 K, and the

scattering angles of the 110 and 101 reflections are relatively small, i. e., sin6/A = 0.1539

and 0.2010 A"-^, respectively. Consequently, the structure factors of these reflections are extremely sensitive to the configuration of outer atomic electrons. In fact, the calculated

values of Eq for the second order reflections change remarkedly with atomic state of the

constituent elements, as shown in table 3. In the calculation, the B factor of 0.7

determined by the x-ray experiment of Baur [25] was assumed.

The preliminary experiment on the 220 reflection of a Ti02 crystal was carried out by

use of a 500 kV electron microscope. Figure 2 shows examples of diffraction patterns taken

at 333 and 380 kV, where the 220 Kikuchi lines are clearly visible. Observation of a series

of such diffraction patterns revealed that the critical voltage Eq is about 350 kV, which

can not be explained by any model shown in table 3.

Since it is thought that Ti02 does not retain the spherical symmetry of electron

distribution and has some covalent character in its bonds, the measured value of Eq can not be compared directly with the calculated values shown in table 3. However, it would

be very useful for the study of electronic structure to determine accurately the structure

factors of the 110, 101, and other reflections by the present method. Attempts are in

progress on this line.

Table 3

Calculated Values of E^ (kV) for Ti02 (rutile).

^^reflection

Model ^s^^

110 101

TiO,oO 444 386

Ti2+, 0^~ 502 406

Ti'*+, 0^- (a) 96 58

Ti'+ + , 02- (b) 102 39

Ti'+ + , 02- (c) 104 28

(a) 02-, Watson +1 well

.

(b) 02-, Watson +2 well

.

(c) 02-, Yamashita & Asano

162
6. ACKNOWLEDGEMENT

The electron diffraction experiments in the present study were carried out by using

a 500 kV electron microscope installed in the Institute for Solid State Physics, the

University of Tokyo. The authors wish to thank the ISSP for giving them opportunities of

using the equipment and for financing the present study. They are indebted to Professor

S. Hosoya and Mr. T. Fukamachi for valuable discussions. Thanks are also due to Mr. K. Suzuki and Mr. M. Ichihara for their help in the electron diffraction experiments, and to

Dr. H. Iwasaki of Tohoku University for his aid in specimen preparation. This work was partly supported by a Science Research Grant of the Ministry of Education (1969 - 1971)

.

Grateful acknowledgement is made to the Sakkokai foundation for the provision of a research

grant (O.T. )

.

7. REFERENCES

[1] Watanabe, D. , Uyeda, R. and Kogiso, M., Acta Cryst., A24 , 249 (1968).

[2] Watanabe, D. , Uyeda, R. , and Fukuhara, A., Acta Cryst., A24 , 580 (1968).

[3] Watanabe, D. , Uyeda, R. , and Fukuhara, A., Acta Cryst., A25 , 138 (1969).

[4] Nagata, F., and Fukuhara, A., Japan J. Apply. Phys . , 6_, 1233 (1967).

[5] Fisher, R. M. , Lally, J. S. , Humphreys, C. J., and Metherell, A. J. E., Proc.

septieme congres international de microscopie electronique , Grenoble, 1^, 107 (19 70) . [6] Ehrlich, P., Z. anorg. allg. Chem. , 247 , 53 (1941).

[7] Andersson, S., Collen, B., Kuylenstierna, U., and Magneli, A., Acta Chem. Scand.

,

11, 1641 (1957)

.

[8] Watanabe, D. , Terasaki, 0., Jostsons , A., and Castles, J. R. , The Chemistry of

Extended Defects in Non-Metallic Solids, North-Holland Pub. Co., Amsterdam 238 (1970).

[9] Uyeda, R. , Acta Cryst., A24 , 175 (1968).

[10] Cowley, J. M., Z. angew. Phys., 26, 149 (1969).

[11] Uyeda, R. , Nonoyama, M. , and Kogiso, M., J. Electronmicroscopy , L4, 296 (1965).

163
[12] International Tallies for' x— ray Cirystallogiraphy ^ III, (1962) , Binningham: Kynoch Press.

[13] Fukuhara, A., J. Phys . Soc. , Japan 21_, 2645 (1966) . [14] Freeman, A. J., and Watson, R. E., Acta Cryst., 14_, 231 (1961).

[15] Wakoh, S., and Yamashita, J., J. Phys. Soc. Japan, 30.' "^22 (1971).

[16] Fujimoto, M. , Terasaki, O. , and Watanabe, D., to be published.

[17] Kainuma, Y. , and Kogiso, M., Acta Cryst., A24 , 81 (1968).

[18] Watson, R. E. , Phys. Rev. Ill , 1108 (1958).

[19] Sanger, P. L. , Acta Cryst. , A25 , 694 (1969).

[20] Yamashita, J., and Asano, S., J. Phys. Soc. Japan, 2_8, 1143 (1970).

[21] Fukamachi, T. , and Hosoya, S., Tech. Rep. ISSP , ser. A No. 453 (1971).

[22] Fukamachi, T. , Tech. Rep. ISSP, ser. B, No. 12 (1971).

[23] Clementi , E. , Tables of Atomic Functions, A supplement to the paper appearing in IBM

J. Res. Developm., 9_, 2 (1965).

[24] Yamada, Y. , Terasaki, O., and Watanabe, D., to be published.

[25] Baur, W. H., Acta Cryst., 9_, 515 (1956).

164
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

THE STRUCTURE AND INTERGROWTH OF THE POLYMORPHIC FORMS

OF Zr02.16Nb20g

N. C. Stephenson, J. P. Beale, and D. C. Craig

School of Chemistry

University of New South Wales

Kensington, N. S. W. Australia

The compound Zr02.12Nb205 has been reported to exist in three polymorphic forms, one

of which is isostructural with TiNb2i40g2.

The crystal structures of the remaining two polymorphs have been determined by

examining x-ray data collected from a single crystal of the 3-monoclinic fo2rm. The unit-cell

dimensions are a = 39.693, b = 3.830, c = 35.488 A, 6 = 116.53°. 2948 data were collected

using a single crystal diffractometer and CuKa radiation.

No assumptions were made about the structural features and the basic subcell unit was deduced from the Patterson function. Modifications of this subcell give rise to the

remaining two polymorphs, which contain blocks of 3x3, 4x4, and 3x4 corner sharing octahedra.

The 3x4 blocks are all at the one level and form sheets running parallel to (100) . The

3x3 and 4x4 blocks form sheets which alternate with those just described. The manner in

which the sheets fit together determines which polymorph is formed.

Although the structures were solved using standard x-ray procedures , the solutions

were facilitated by using feat\ires of electron transmission micrographs. These consisted of

a regular array of dots and streaks (plane group p2) arranged in lines parallel to c. The

spacial distribution and contrast of these dots and streaks, together with their arrangements at antiphase boundaries and fault areas, impose certain restrictions upon structures

that can be derived by modifications of the basic subcell.

In terms of structure, the areas of contrast on transmission micrographs can be

identified with the different types of block junctions.

Key words: Crystal structure; intergrowth; lattice-image; polymorphism; zirconiumniobium oxide.

1. INTRODUCTION

The compound Zi?02 • 12Nb205 was first identified by Roth [1] as the initial product

of the reaction of the component oxides in 1:12 proportion. It was shown to be isostructural

with TiNb2i+0g2 [2], (fig. 1), but on annealing it transforms to a much more complex structure.

Single crystal x-ray studies of the transformed material suggest-ed that the unit cell was monoclinic with a=c=71.04 A, b = 3.82 A, and 3=90°.

In a later study, Allpress and Roth [3] investigated this monoclinic form using electron

diffraction and transmission microscopy. It was shown that the transformed material

contained two polymorphs which were capable of intergrowth at the unit-cell level. These

polymorphs were called the 3 and y forms of Zr02.12Nb205 while the product of the initial

reaction was called the a form. The relevant crystallographic data are given in table i.

Figures in brackets indicate the literature references at the end of this paper.

165

/
ig. 1. An idealized model representing the structure of the a form

of ZrNb2it052 . Each square represents an octahedra viewed

down a body diagonal, the lighter and darker squares being

centred on parallel planes 1.9 A apart. The circles

represent metal atoms in tetrahedral coordination.

Table 1

Crystallographic Data for the ZrO„.12Nb„0^ Polymorphs

2 2 5

a(A) b(A) c(A) a e Y 29.78 3.821 21.21 90° 94.9° 90° (cell dimensions of

TiNb24 062)

39.693 3.830 35.488 90° 116.53° 90°

a-Form

B-Form

Y-Form 35.5 3.83 35.5 90° 90° 90=

The identification of the 6 and y polymorphic forms of Zr02.12Nb205 which intergrow

in a single crystal formerly thought to have the enormous unit-cell dimensions reported by

Roth [1] , beautifully demonstrates the power of combined electron diffraction and optical

techniques

.

Figures 2 and 3 are reproduced with the permission of Drs . Allpress and Roth. The

hOl reciprocal lattice plane of the 3 phase (fig. 2a) can be identified in the combined

hOl data from the 3 and y forms (fig. 2b). Apart from the fact that these photographs are easier and quicker to obtain than corresponding x-ray photographs, the information contained

in figure 2(b) is nevertheless available in the x-ray photographs. Early recognition of

intergrowth phases is however facilitated by the use of electron transmission microscopy

(fig. 3b)

.

2. ELECTRON TRANSMISSION MICROGRAPHS OF Zr02.12Nb20g

Figure 3a shows a lattice image of a fragment of a-Zr02 • 12Nb205 . Most of the fringes

have a separation of 15 A, which is the characteristic spacing between shear planes parallel

to c in the TiNb2i+052 structure. The 17 A separations are indicative of the intergrowth

of planar slabs of the H-Nb205 structure and show that the original preparation was slightly

off stoichiometry

.

166
c

II III !V V

X X O O S> S) _ x_x x_x _ xx^xx

X XX X XX XX X X o o o ® • • • \ • • X

' • • o • • y •

Fig. 2. Electron diffraction photographs.

(a) The hOl reciprocal lattice net of the 3-polymorph

.

(b) The hOl reciprocal lattice net taken from a crystal containing

twinned domains of the B-polymorph and domains of the y-polymorph.

(c) A diagrammatic representation of the component reciprocal

lattice net evident in 2 (b)

(i) basic tetragonal subcell lattice;

(ii) a domain of the 3-polymorph;

(iii) a domain of the 3-polymorph related to the previous

one by a two-fold axis;

(iv) a domain of the y-polymorph;

(v) a combination of (i)-(iv).

The contrast in figure 3b consists of an array of white dots and this lattice image

was formed with the electron beam incident a few degrees to [010] . This photograph clearly

shows intergrowth domains of the 3-form (area H) and y-forms (area S) . Area H, is a domain of the 3-form in different orientation to H.

Allpress and Roth [3] were able to postulate structures for the 3 and y Zr02.12Nb205

phases. They did this by modifying the structural components of a tetragonal subcell

which was evident from the distribution of spots on electron diffraction photographs. These

modifications were carried out on the basis of the contrast shown in figures 3c and d. The

lattice image in figure 3c, taken with the electron beam parallel to the b axis of the

3-form, shows regular rows of dark dots and streaks. Faults are evident at P, Q, and R. Previous studies [4] have shown that sites occupied by tetrahedral atoms (0-positions) in

block structures produce strong contrast in the form of dark dots in lattice images of

suitably oriented framgents. An 0-position is shown in figure 4a while the other remaining

way of joining 4 blocks gives rise to an x-position (fig. 4b) . The structures proposed by

Allpress and Roth [3] were felt to be inadequate in that they did not satisfactorily

explain the streak contrast in figure 3c. The regions which give this contrast were

correlated with x-positions, of which there were too many and which previous studies [4] have indicated to give only slight density contrast in lattice images.

167

/
Fig. 3. Lattice image micrographs.

(a) of a crystal of a-Zr02 • 12Nb205 tilted to reveal the shear planes parallel

to c with spacings of 15 A. The spacings of 17 A correspond to planar

slabs of H-Nb205 which form disordered Wadsley intergrowth defects.

(b) taken with the electron beam incident a few degrees away from parallism

o , with the short (3.8 A) axis. The area contains distinct domains:

(1) H contains the monoclinic 3-polymorph.

(2) Hj is a domain of the 3-polymorph but in twinned orientation to H.

(3) S contains the tetragonal ypolymorph

.

168
Fig. 3. Lattice image micrographs.

(c) taken with the incident beam exactly parallel to the short b axis of the

6-polymorph. The contrast may be approximately described as an array of

dots and streaks arranged in lines parallel to c. Faults are evident at

P and Q.

(d) similar to (c) but with OOi reflections dominating the diffraction

patterns. Another type of fault occurs at R.

169

/
X X

x:

X

X

X

X

X X x^

IS

X

X

X

X

X

Hxi

X

X X

SI

IX

U14 X

X

X

XT

IE

X X

X

X

X

X X

X

X

X X

X

X X

X X

X

X X

X

1^

X

X

X X

X

X

o e

x^

X

X

O vssilion

Fig. 4. Block junctions showing the formation of X- and 0-positions (full circle

and open square respectively). Other positions in the blocks, marked with

an open circle or cross, represent centres of symmetry if the blocks are respectively (2n x 2n) or (2n + 1 x 2n) octahedra in size. Vectors across

these centers are shown distributed about an origin.

The work described below involves the determination of the structures of the 3 and y forms from x-ray diffraction data but with due regard to the spacial distribution and

contrast of the lattice image dots and streaks in domains, fault areas and antiphase

boundaries

.

3. EXPERIMENTAL

Crystals of the compound were mainly fine needles, with twinning and intergrowth

particularly common, and it was necessary to examine several by the Weissenberg method

before a suitable one was found. The crystal chosen for data collection had dimensions of

0.017 X 0.012 X 0.15 mm.

A Siemens A. E. D. four circle diff ractometer controlled by a PDP-8 computer was used

for data collection; crystal orientation and angle calculation were accomplished using

the method of Busing and Levy [9] . Cell dimensions were determined from selected high

angle reflections, which were used also for the refinement of the approximate initial UB

matrix

.

Integrated intensities for hOl reflections were obtained with CuKa radiation using a 6-29 scan and a "four value" modification of the "five value method" [10] of measurement.

In this modification the third stage of the measurement is omitted, resulting in the peak

intensity being obtained as the run of two partial scans, and background measurements being

made on each side of the peak. This affords a considerable time saving over the "five

value method", and yet maintains the valuable check scanning symmetry obtainable by

comparing the values from the two partial scans. The scan range varied from 0.8° at low

theta to 1.3° at theta of 70° the limit of the instrument.

The scan rate is controlled by the computer and varies from 6 sec/deg. for the most

intense reflections to a maximum, set in this case at 120 sec/deg. for the weak reflections

Attenuation filters are inserted automatically when necessary to keep the count rate within

the linear range of the equipment.

Intensities were corrected for instrumental drift, if any, using a periodically

measured standard reflection as a reference. Background was assumed to vary linearly

though the scan range of each reflection, and corrections for this, Lorentz, polarization

and absorption were applied using programs written in this laboratory. Standard deviations

(a) were assigned on the basis of counting statistics, and a reflection was regarded as unobserved if its net intensity was less than 2.58a, and its intensity was then assigned

as 2.58a.

170
4. DETERMINATION OF THE STRUCTURE OF THE 3-POLYMORPH

4.1. SUBCELL STRUCTURE

The advantages of working with two dimensional hOii data far outweigh the disadvantages,

which relate mainly to atomic overlap in projection and to standard deviations in parameters.

Overlap in projection is, in fact, minimal because of the short length of the projection

axis (3.83 A) whereas computing and phase determination problems are greatly reduced by using

only hOl data.

The Laue symmetry of the reciprocal lattice (2/m) indicated that the crystal class is

probably monoclinic. It could, in fact, be triclinic with the heavy metal atoms in a more symmetric array than some of the lighter oxygen atoms. In this case however the form of the

two-dimensional Patterson function

A{x,z) = h=o 1=- F hoa exp.-2iTi (hx + Iz) (1)

is independent of either symmetry requirement and was therefore calculated and contoured.

It was immediately apparent from the distribution of peaks that the structure is based upon

blocks of corner sharing octahedra similar to the many examined by Wadsley and co-workers.

If the crystal calss is monoclinic then the plane group of the (010) projection of the

unit-cell contents, or fundamental set, must be p2. It would therefore be possible to choose a line from the origin of A(x,z) to a vector point corresponding to a pair of

centrosymmetrically situated points in the fundamental set. Image seeking functions [5] based upon this line should not be subject to false symmetry and represent the fundamental

set.

The expected location of these centric vectors are shown in figure 4. These were

readily identified on the Patterson projection and a number of minimum functions were

contoured from superimposed Patterson maps.

The 'fundamental set' which repeatedly resulted from these superposition methods is

shown in figure 5. It consists of blocks of 4x3 corner sharing octahedra which are themselves joined by edge sharing. The actual unit-cell is shown dotted and corresponds to the

'tetragonal subcell' which was described by Allpress and Roth [3] . There are four of these

subcells in the unit-cell of the 3-polymorph.

Fig. The 3-polymorph structure as determined from the Patterson function by

image seeking methods. The monoclinic unit cell axes are shown as dashed.

The tetragonal subcell is shown dotted.

171
4.2. MODIFICATION OF THE SUBCELL STRUCTURE

The relationship between the subcell (dotted) and the true unit cell of the 3-polymorph

(dashed) is shown again in figure 6. Blocks of corner sharing octahedra are represented

by rectangles whose edges run through the centers of the peripheral octahedra.

There are four 0-positions in the 3-phase unit-cell depicted in figure 6 (shown as dotted circles) . Lattice images of the 3-phase (fig. 3c, d) show that there are only three

0-positions and one "modified" 0-position (appearing as a streak). The only way to remove,

or modify, an 0-position is to convert it into an X-position by expanding one of the blocks

so that it shares edges with some octahedra in an adjacent block at the same level. This

position is shown marked with an X in figure 7. The trial partial structure shown in figure

7 thus has the following features:

(1) There are only three 0-positions in the 3-polymorph unit-cell and these agree in

positions with the distribution of dark dots in figure 3c.

(2) The structure is only a very slight modification of the subcell structure derived

from x-ray diffraction data.

Pig. 6, Block diagram of the subcell structure shown in figure 5. The

4x3 blocks are represented by rectangles. 0-positions are shown as broken circles and four such block junctions occur in

a unit-cell of the 3-polymorph.

Fig. 7. The initial trial partial structure for the 3-polymorph which was obtained from the siabcell structure by eliminating one 0-position

(marked with an X) and reducing the sizes of the remaining blocks

to allow for expansion in either of two directions.

172
(3) The block sizes (mainly 3x3) and positions are such that they can be expanded to

3x4 (or 4x3) in either of two directions or some can be made 4x4 blocks if atoms

are located in the appropriate positions. It is important that the "right" atom be

omitted from a trial structure in order to give the structure the utmost flexibility

during modification.

(4) The plane group symmetry is pi. If, in fact, the symmetry is higher, then this

will become evident as the determination of the true structure from the experimental

data proceeds.

4.3. THE TRUE STRUCTURE

Metal atom positions which correspond to the blocks drawn for the trial structure were obtained from the minimum function. The positions of the remaining metal atoms can be

located by successive cycles of structure factors (Fc) and difference Fourier syntheses.

This involves calculating the function

+ 00 +00 Ap{x,z) =i ,1 ( lFol-|Fc|)cos[27T(hx + lz)-cx] (2) A h=0 !=-<»

where a is the phase angle of individual Fc values and Ap (x, z) is the residual electron

density at the point x,z in the unit-call. As additional metal atoms are found they are included in the calculation of Fc for the next cycle.

After 12 cycles the 99 metal atoms in the asymmetric unit-cell were located. The plane

group is pi and there remained to find over two hundred oxygen atoms. These were located

in the manner just described but with the following refinement procedures applied to metal

atom parameters and, eventually, to the oxygen atoms.

4.4. REFINEMENT PROCEDURES

Full matric least-sequares methods [6] were used to refine the atomic parameters.

Values of T. w ( |Fq|-|f^|)2 were minimized, where w is the weight of |Fq|-|F(,| and

estimated for each observation from counting statistics. The atomic scattering factors

for neutral atoms Nb^ and 0 were computed from numerical Hartree-Fock wave functions using

the method of Cromer and Mann [7] . A correction for the real component of the anomalous

dispersion of CuKa by Nb was made [8] . An IBM 360/50 computer was used for all calculations

together with local versions of well established programs.

A s\mmary of the refinement cycles is given in table 2 and atomic parameters are listed

in table 3. Fractional shifts were introduced to rationalize parameter shifts and after

cycle 16 the metal atoms were assigned anisotropic temperature factors of the form

exp [-(3iih^ + 633!^ + 23i3hl)]. Metal atoms, in projection are to a certain extent overlapped by the oxygen atoms which are displaced b/2 A for them along the [010] direction.

Provided the metal atom is located at the center of the octahedron then considerable overlap

occurs. These octahedra are usually found in the center area of blocks. Octahedra lying

around the periphery of blocks are associated with crystallographic shear planes and metal

atoms are significantly displaced towards the body of the block. In these cases the degree

of metal-oxygen overlap is lessened and the effect is to elongate the metal peak in projection.

An over simplified way of treating these differing degrees of overlap is to treat the com- posite atom as Nb + 0 and assign anisotropic thermal parameters.

The slow rate of convergence of the least-squares cycles is due, in part, to the

non-centric arrangement of the atoms and, in the main, to the parameter interdependence

brought about by the underiding symmetry of the subcell. The same difficulty was experienced

during the refinement of the Ta205 - WO3 structures [11] ; atoms not related by the symmetry

elements of the real cell are nevertheless related by the symmetry elements of the

(tetragonal, in this case) siibcell. Correlation coefficients are high and standard

deviations in atomic positions are large. Standard deviations in the x and z positional

Nb and Zr were assumed to scatter in an identical manner and all metal atoms were treated

as niobium atoms.

173
Table 2

A Summary of the Refinement Cycles

Atoms in Number of Number of Type of Total Number Type of Fractional R(a) WR(b)

Asymmetric Variables Cycles Thermal of Parameters Parameter Shifts

Unit Parameters entered varied

79

79

88

92

92

97

99

226

226

247

247

247

247

247

TRIAL STRUCTURE

202

222

184

184

292

198

256

256

298

298

298

197

197

Overall B

Number of Obersvations l^bb

Individual B

(ANISO, Metal

ISO Oxygen)

476

530

554

554

584

596

1358

1358

2719

2719

2719

2719

2719

Metal X,Z

Metal X,Z

Metal X,Z

Metal X,Z

Metal X,Z,B

Metal X,Z

Oxygen X,Z

Oxygen X,Z

Metal

Sl3' ^33

Metal X,Z

Metal X,Z

.50

.50

.50

.50

FULL

FULL

.25

.25

.25

.25

FULL

.30

FULL

43.2

39.8

35.6

33.0

30.8

28.0

26.9

23.2

23.0

22.0

21.2

20.2

19.5

18.5

47.9

38.1

32.5

30.6

27.8

23.7

23.1

19.4

19.0

18.3

17.7

16.7

16.1

15.1

(a)

(b) The normal R factor I - F, The weighted R factor [Ew(|Fo| - | F^, | ) ^/^w | Fq | ^

]

parameters of the niobium atoms are of the order 0.05 A, which is exceptionally large and

reflects a degree of intractability in the refinement of the structure.

The large number of parameters associated with atoms in the asymmetric unit imposes

an upper limit, approximately 300, on the number of parameters that can be varied in each

cycle of least-squares on the IBM 360/50 computer. It is not possible to vary all the

parameters of all atoms at the same time. This computing problem, together with the

inherent intractability described above, contribute towards a difficult and costly refinement.

The refinement of this present stage cannot be considered as complete. Nevertheless,

structural details are sufficiently well resolved to allow for the following discussion.

174
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X M-( M-I Q) M O

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r-l II M-I S-) 0

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tn 3 -P ^ifilfl|||llMiilIfli|ll|Ii|y = |y ^^Pl

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175
5. DESCRIPTION OF THE STRUCTURE OF THE g-POLYMORPH

The structure of the unit-cell of the 3-polymorph is shown in [010] projection in

figure 8. The blocks of distorted, corner-sharing octahedra are either all 4x3 at one

o level or 4x4 and 3x3 at another level. The two levels are separated by a distance of b/2 A

along [010].

The idealized structure is shown in figure 9 and differs from the real structure in

that the blocks are composed of regular octahedra with no distortions at the shear planes.

Fig. 8. An (010) projection of the real structure of the g-polymorph of

Zr02 •16Nb205 . One unit-cell is shown (dashed) which contains

99 metal and 246 oxygen atoms. One metal atom has tetrahedral

coordination. The other 0-position is empty (marked with an E)

.

Fig. 9. An idealized block diagram of the unit-cell of the $-polymorph.

The full circle represents an atom in tetrahedral coordination

(0-position) , the open circle is an empty 0-position, intersecting shear planes are marked with a cross *, and two of the X- positions are shown.

176
The 4x3 blocks form strings'* parallel to [001] in which adjacent blocks are oriented

perpendicular to each other while in a direction perpendicular to [001] these blocks are paralleled in pairs with adjacent pairs at right angles to each other. The blocks at the

other level again form strings which run parallel and at right angles to c.

The corners of adjacent blocks are joined by either

(i) the sharing of three octahedral edges. There are four of these X-positions in the

unit-cell

;

(ii) an atom in tetrahedral coordination. There is one 0-position (dark circle) per

unit-cell;

(iii) an empty 0-position (open circle). There is one modified 0-position per unit-cell;

(iv) the sharing of one octahedral edge. This new type of block joining is marked

by a cross in figure 9. It will be referred to as a Y position.

These are the four different types of block junctions.

Bond distances and angles for individual coordination polyhedra have not been

calculated because of the large number of these polyhedra (99) and because of the large

standard deviations which make detailed comparisons useless. The interest is rather in

the structure at antiphase boundaries and fault areas and in the interpretation of the

dots and streaks which appear in lattice image photographs.

6. THE INTERPRETATION OF DOTS AND STREAKS IN LATTICE IMAGE PHOTOGRAPHS OF THE 6-POLYMORPH

A surprising feature of the structure of the 3-polymorph is that the three 0-positions

which were left as such in the trial partial-structure (dotted circles, figure 7) have

each been converted to X-positions. Two alternative tetrahedral sites have developed;

one site is occupied with a metal atom (shown as a block dot in figure 9) whereas the other

tetrahedral site is vacant (shown as an open circle in figure 9) . There is only one

true 0-position in the unit-cell.

0-positions are regions of high electron density; regions where crystallographic shear

planes intersect and where an additional tetrahedrally coordinated metal atom is located.

Such positions produce dark dots in lattice image photographs.

Similar positions of high electron density are shown as crosses in figure 9. These

Y-positions are at the intersection of shear planes and their contrast effect in

transmission micrographs is therefore unknown. If, however, one assumes that they also

give rise to a dark dot then the regular alternation of these positions and the 0-position

(* ° * in figure 8) would give rise to a line of dark dots, parallel to c and separated

by c/2 A.

o Displaced from the * ° * line by a/2 A but again parallel to c is a line * ° *. Empty 0-positions, i.e., unfilled tetrahedral sites, have not been observed previously

and their contrast effect in transmission micrographs is again unknown. They are, however,

regions of appreciable electron density -and may very well give rise to a streak, particularly

as the intersecting shear planes do not intersect precisely at 0 but are displaced slightly.

When the above positions are represented by either dots or streaks then their spacial

distribution, shown in figure 10, can be correlated with the arrangemet of dots and streaks

in tramsmission micrograph 3c.

A close inspection of transmission micrograph 3c shows areas of lighter contrast which

lie between the dark dots and streaks adjacent to each other in the same (102) planes.

These lighter areas can be correlated with X-positions (fig. 9) which have been shown by

Allpress [4] to be distinguishable from 0 (or Y) positions by their lighter contrast.

What appear to be strings in projection are actually sheets in three dimensions.

177

465-504 0 - 72 - 13
Fig. 10. A domain of the 3-polyinorph. One unit-cell is shown dotted. 0- and

Y-positions are marked as large dots. Empty 0-positions are streaked.

The distribution of these block junctions agrees with the distribution

of dots and streaks on lattice image 3c.

The distribution of the four various types of block junctions therefore satisfactorily

explains in terms of numbers, spacial arrangement and contrast, the features of the

transmission micrograph shown in figure 3c.

7. THE STRUCTURE OF THE Y-POLYMORPH

The structure of the 3-polymorph has been described above in terms of sheets of blocks

of octahedra which run parallel to (100) . A sheet of alternating 4x4 and 3x3 blocks has on either side of it a sheet of 4x3 blocks. These sheets can be displaced parallel to c but remain in the same sequence along a to give the arrangement shown in figure 11. This

structure has the same composition as the 3-polymorph but the unit-cell has a = b 35.8 A

The structure is that of the ypolymorph reported by Allpress and Roth.

The distribution of dots and streaks in transmission micrographs of the y-polymorph

can be correlated with the distribution of 0 (and Y) positions and empty O~positions is

the structure drawn in figure 11. The x-positions, located midway between any four

adjacent dots and streaks can be identified on the micrograph as areas of lighter contrast.

It is thus possible to explain the contrast features of lattice images of the Y~polY~

morph in terms of the distribution of the various types of block junctions in the structure.

8. MICRODOMAIN INTERGROWTH AND FAULT STRUCTURE

The faults evident in micrographs 3c and d are labelled as P, Q, and R. Those labelled

Q are one unit-cell wide and involve a displacement along [001] of approximately c/2 A. (Most readily seen in figure 3d) . Faults R are two unit-cells in width and involve the

domains either side of it in a relative displacement of c A along [001] .

Faults Q and R can be regarded as the intergrowth of domains of the y form in a matrix

of the S form. These structures are shown in figures 12 and 13.

Faults of the P type are of a different character; the displacement along [001] is

approximately c/4 A. Figure 14 illustrates the structure of the P fault. The domain on

the left hand side of the fault is displaced by half a unit cell in the b direction from the

domain on the right hand side of the fault. Thus the 4x3 blocks on the left hand side

are at the same level as the 3x3 and 4x4 blocks on the right hand side of the P fault.

178
I I ^ I

°

I I »

I

IP

Fig. 11. A domain of the y "Polymorph . A unit-cell is shown dotted.

The different types of block junctions are marked as in the

3-polymorph and correlate with the contrast shown in

transmission micrograph 3c.

Fig. 12. Structural details at the Q fault. The Q fault can be regarded

as a slab of the Y~polyinorph , one unit-cell wide, inserted

between two domains of the 3-polymorph.

179
180
9. DISCUSSION

A unit cell of either the g or y polymorph contains 99 metal atoms and 246 oxygen

atoms, which corresponds to a composition of Zr02 . 16Nb205 . Each unit cell contains the

unit 3Zr02.48Nb205.

It would appear, therefore, that the 3 and y forms are not polymorphs of a-Zr02 • 12Nb205

but are polymorphic forms of a substance with stoichiometry Zr02 • 16Nb205 .

Allpress and Roth observed that the initial product of their reaction between Zr02

and Nb205 was slightly off stoichiometry and contained slabs of ZrNb2it0g2 and H-Nb205 . These intergrowing domains were readily detected on transmission micrographs of the a form (figure 3a) . It would be reasonable to assume that the effect of prolonged annealing

is to react the excess Nb205 with the domains of Zr02.12Nb205 to form a new compound(s)

e.g., with composition Zr02 • 15Nb205 . such a reaction to occur there would need to be

twice as many intergrowth slabs of Nb2 05 than appear in figure 3a. This may be the case since the crystal area imaged is but a small fraction of the bulk specimen.

The crystal structure as it stands is the result of the combined use of x-ray diffraction

methods and electron diffraction and microscopy techniques. Atomic coordinates are derived

from the x-ray data but the identification of intergrowth domains and the use of contrast

features to modify subcell structure can only be made using electron optical data.

The work described above represents an attempt to correlate the contrast features of

electron micrographs with structure. We believe that the dots and streaks of varying

intensities, which result from imaging with the electron beam precisely parallel to the

crystallographic b axis, can be correlated with the different types of block junctions

that occur in the structure of Zr02 . 16Nb205

.

We have seen transmission micrographs at this conference [12] in which the contrast

features are not merely dots and streaks; these micrographs enable the actual block sizes to be determined merely by inspection. It is clear that a knowledge of block sizes would enable

a much better trial structure to be propounded and thereby reduce the uncertainty and the

work involved in the refinement of the real structures of these very complicated oxides.

10. ACKNOWLEDGEMENT

We are indebted to John Allpress and Robert S. Roth for permission to reproduce figures

1, 2, and 3 and for providing a sample of the zirconium niobium oxide.

11. REFERENCES

[1] Roth, R. S., unpublished results.

[2] Roth, R. S., and Wadsley, A. D. , Acta Cryst., 18, 724 (1965).

[3] Allpress, J. G., and Roth, R. S., J. Solid State Chem., 2_, 366 (1970).

[4] Allpress, J. G. , Mat. Res. Bull., 4_, 707 (1969).

[5] Buerger, M. J., in "Vector Space", John Wiley and Sons., Inc., New York, p. 227 (1959).

[6] Busing, W. R. , Martin, K. O. , and Levy, H. A., ORFIS , USAEC Report ORNI-TM-305 (1962).

[7] Cromer, D. T. , and Mann, J. B., Acta Cryst., A24 , 321 (1968).

[8] Dauben, C. H., and Templeton, D. H., Acta Cryst., 8_, 841 (1955).

[9] Busing, W. R. , and Levy, H. A., Acta Cryst., 22_, 457 (1967).

[10] Hoppe, W. , Angew, Chem., 7T_, 484 (1965).

Ill] Stephenson, N. C. , and Roth, R. S., Acta Cryst., B27, 1010 (1971).

[12] Allpress, J. G. , "The Application of Electron Optical Techniques to High Temperature

Materials", page 87, this volume.

181
DISCUSSION

R. S. Roth: I don't want you to feel bad when you say that the composition of the crystal might be different from what I had originally made it up to be. Since the paper that

John Allpress and I published on this phase , I have been trying to obtain equilibrium data,

hopefully, for the polymorphic transitions. I believe that they might have stable equilibrium

relationships. So I have re-made a lot of specimens in the high Nb205 end of this system

using the same oxides, the same two end-members (from the same batches) that I had used ten

years ago. I found that it was completely impossible to duplicate the number of phases present in a given starting composition two days in a row. I came to the conlcusion that the

zirconia that I was using, which was an ultrapure, ultra-spec-pure, zirzonia, had a very abnormal distribution of volatile hydrated material with amorphous zirconia. One can simply not

accurately weigh out this "amorphous zirconia". Therefore, it was necessary for me to go to

a different technique. I had a metallurgist arc-melt titanium and niobium metal in the proper

proportions and I oxydized it. A 10 gram batch at 600 °C took about a month to completely oxydize. You end up with a nice, almost amorphous oxide that you can then equilibrate at higher

temperatures. I can now get a single phase x-ray pattern that looks very much like what my

old x-ray pattern looked like at the 12 to 1 composition. I don't know what the 16 to 1 ratio

would give me.

N. C. Stephenson : Could I ask John Allpress a question, since we didn't ask John questions? In your photographs we saw white features which were the tunnels in the blocks and then

we saw the shear planes appearing as dark rims, but you couldn't see what was at the block

junctions, everything was just black. Now is it possible to identify the different types of

block junctions, not just the tunnels by contrast features?

J. G. Allpress : The detail that you actually see depends very critically on focus and so

on, but in fact you can see all those features in the pictures that I showed which were taken

at Arizona State (see Allpress, Figs. 14, 15.) The resolution in the pictures I took previously (see Stephenson, Fig. 3) was insufficient to reveal the same details. I'm sure that some good high-resolution images of the same material , recorded under the appropriate conditions of focus, etc., should provide the answer, and enable us to reconcile the various observations which we have made already.

S. Andersson : May I just ask, what kind of R-f actor did you get?

N. C. Stephenson : Well, I was afraid you would ask me that. The R at present is fourteen percent. The reason for this is that it takes three and a half hours a cycle and the R comes down by one per cent. The reason for this I believe is....

S. Andersson : But it ' s going down anyhow?

N. C. Stephenson : Oh, it's coming down every time. As soon as we can get a Saturday to spare, we race in and use the computer for 3 1/2 hours, and drop our R. It's come down from

43 to 14 in about one per cent steps.

S. Andersson : That's very good!

N. C. Stephenson : There is a lot of interdependence of parameters in these supercell

structures. Atoms that aren't related by supercell symmetry are related by the subcell symmetry, and the correlation coefficients are extremely high. Standard deviations are very high.

The standard deviations for the metal atoms in this structure are .05 of an angstrom and that

is due to parameter dependence, as Dr. H. Evans very well knows with his barium titanate.

J. G. Allpress and R. S. Roth, Jour. Solid State Chem. 2_, 366 (1970)

182
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

SUPERSTRUCTURE OF THE ORTHORHOMBIC Nb205-6Zr02 TYPE PHASE(S) IN THE

Nb205-Zr02 AND Ta205-Zr02 SYSTEMS

Robert S. Roth, J. L. Waring, W. S, Brower and H. S. Parker

National Bureau of Standards

Washington, D.C. 20234

The phase previously described as Nb205'6Zr02 has been found to have a composition

varying from a Nb205:Zr02 ratio of about 2:9 to 2:15. The solidus temperatures of the

intermediate compositions studied seem to follow a smooth curve from 1435 °C to 1640 °C

rather than a stepwise function expected from a series of compounds. The x-ray diffraction

powder patterns indicate a series of phases with subcells similar to a-Pb02 and orthorhombic

symmetry. Superstructure lines indicate that these phases have a multiple Jb axis . The com- position 2:9 corresponds approximately to a structure with a i-axis multiplicity of seven. The 2:11 composition appears to have a multiplicity of eight, 2:13 a multiplicity of nine

and the last composition 2:15, a multiplicity of ten. The intermediate compositions 1:5,

1:6 and 1:7 show superstructure lines halfway between those of the simpler phases on either

side, corresponding to multiplicities of 15, 17 and 19 respectively. These multiplicities

and compositions thus appear to belong to a homologous series M^_i02n where n varies from

14-20. However the phase equilibria data do not rule out the possibility of a homologous

series Mn02n+i- Compositions in the Ta205-Zr02 system apparently have the same composition

vs multiplicity arrangement, however, their melting points are considerbly higher.

Single crystals of these phases, prepared by both direct cooling of a melt and utilization of a barium vanadium oxide eutectic flux, have enabled the multiplicities to be

completely verified and are now being used for crystal structure determinations. This

stabilization of the high pressure form of Zr02 (the orthorhombic structure type) by means

of higher valence cations provides an alternate process to the anion deficient stabilization

of the cubic fluorite phase.

Key words: Equilibrium; Nb205-Zr02; ordered defects; a-Pb02-type phase(s); single

crystals; superstructure; Ta205-Zr02.

1. INTRODUCTION

Zirconium dioxide has long been an attractive material for high temperature applications

needing only to be "stabilized" to avoid disruptive phase transitions. Unfortunately most

of the additives used for "stabilization" have certain drawbacks and the material is often

"destabilized" with use. The systems Nb205-Zr02 [1,2]^ and Ta205-Zr02 contain a phase which

appears similar to the a-Pb02 structure type [3] instead of the "stabilized" cubic (or

tetragonal) Zr02 phases found for MgO, CaO or Y2O3 stabilized ZrOg. This phase is therefore

either cation deficient or anion excess as opposed to the anion deficient phases found in

the other systems.

Zr02 and Hf02 are both known to have a high pressure polymorph with orthorhombic

symmetry [4,5,6] (fig. 1). The published x-ray pattern [4,6] of this high pressure phase

is very similar to that of the a-Pb02-type structure. Apparently the high pressure phase is

stabilized by lowering the average radius of the cation with addition of Nb"^^ or Ta"*"^.

1 Figures in brackets indicate the literature references at the end of this paper.

183
T

\ 1 r

ZrOa

2400 r\

N _ S

AFTER BENDELIANI

1 1 1 1 1 1 Zr02

1200 - -

•c

800

TETRAGONAL V :

400 \

MONOCLINIC

\ 0RTH0RH0M8IC

1 t 1 \ 1 1 1 20 40 60

kb AFTER SOCOUILLON

Fig. 1. Pressure- temperature phase diagrams for Zr02f

after Bendeliani et al. [4] and Bocquillon

and Susse [5]. The polymorph labelled orthorhombic has an x-ray pattern similar to Ci-Pb02.

However no study has been made of the nature of the defects which occur in this system,

although Trunov et al. [2] have indicated the probable existence of a superstructure.

One of the most interesting problems in the field of solid state chemistry is the

nature of the non-stoichiometric phases which occur in systems of this type. By a combination of phase equilibria studies, crystal growth, x-ray powder and single crystal diffraction

and electron microscopy and diffraction, the methods by which nature compensates a crystallographic phase for non-stoichiometry are gradually beginning to emerge.

The block principle, crystallographic shear and Wadsley defects have been shown to be

the major factors affecting non-stoichiometry in Nb205-type phases [7,8,9]. Ordered oxygen

"vacancies" or "distortion planes" causing localized reduced cation coordination is apparently the controlling factor for the appearance of superstructure in low-Ta205-type phases

[10,11] . "Stabilized" cubic Zr02 appears to have random anion vacancies which may be

ordered at low temperatures with the addition of small cations [12] . The systems Nb205-Zr02

and Ta205-Zr02 have therefore been re-examined to determine the nature of the non-stoichiometric orthorhombic phase (s) found in these systems.

2. SPECIMEN PREPARATION AND TEST METHODS

One gram batches of the appropriate compositions of Zr02 and either Nb205 or Ta205 were weighed, mixed in a mechanical shaker and pressed into disks at about 10^ psi. The

disks were placed on Ft setters and calcined in air at 1000 °C for 10 hours, ground, re- pressed and recalcined at 1350 °C for 60 hours. For both heat treatments the specimens were heated and cooled at the rate of approximately 3°C/min. After these preliminary heat treatments the specimens were ground and small portions placed in Ft tiibes and heated in the

quenching furnace at appropriate temperatures and for various periods of time.

The Ft tubes, open on one end, were quenched either into ice water or onto a chilled

metal plate, opened and examined by x-ray diffraction techniques. These specimens were invariably too fine grained for single crystal x-ray diffraction methods. A high angle

recording Geiger counter-powder dif f ractometer and Ni filtered Cu radiation was used in the

study. The Geiger counter was rotated at 1/4 deg/min and radiation was recorded on the

chart at 1 deg/2e/in. The unit cell dimensions reported can be considered accurate to about

±2 in the last decimal place listed.

In order to obtain unambiguous indexing of the powder diffraction patterns it was necessary to grow small single crystals. This was accomplished in two ways. One consisted

of direct cooling of a melt rich in Nb205 (60 mol% Nb2O5-40 mol% Zr02) which had been heated

by induction in a Pt crucible and allowed to slowly cool through the liquidus before being

rapidly cooled.

184
The second method consisted of mixing various proportions of Nb205 and Zr02 with a premelted BaO - V2O5 eutectic flux (32.2 wt% BaO:67.8 wt% V2O5) . These mixtures were heated

to 1200 °C and then cooled very slowly (l°/hour) to 800 "^C and removed from the furnace.

3- RESULTS AND DISCUSSION

The experimental data is shown in table 1 and the phase diagram derived from this data

is shown in figure 2. This diagram differs appreciably from the previously published phase

diagram for this system [1] (fig. 3). The orthorhombic phase (s) is shown to have considerably less area than previously thought and the composition and temperature of the maximiom

1471

li.92 1550 1600 . phase + L-Kb;Oi

1399

1623

liiiS

;h. phase + 12;1

.ally orch. phase + L-Nb;Os

1379

, liOCF,

orth. phase + L-Nl

1400=

14 30

14 36

. phase + 12:1

a-4.947. b-5.137-15

1422,,

14 3&^-' 1452

liiTS

1550

phase + L-KbjOs

15.38 84.62 39.70

39.45

14.28i 65.715 —A/

(1:6) liiOO-' 1432 1482

1499 ..965. b-5. 126-17

39. iO 39.31 39.40

39. 3Z 39.23

1554

1608

1617

39.15

38.85

36.80

3B.76

1-4.971, b-5.122«9 39.06

;=5.2e5 39.10

572

1417 168 1546 139

14 12-' 64 1566,, 19

1575^-' 168

38.88

36.84 36.85

11.76 88.24

(2:15) 1594

1600

1617, 89 1626- 168 1635 17 1657 17 orth. phase + L-Nb^Oj

38.72

38.70

38.68

38.65

1605^' 240

1606 17 1641 16

, phase + Hon ZrO;

• given cwo pre i350°C - 60 hrs uii

1 phase, probably (onseS 1

185
L

1435"

50 60

1640

e

a- e

I

70 8C mol % Zr0290

1750

1650

-1550

1450

ZrO,

Fig. 2. Proposed phase equilibrium diagram of a portion

of the system Nb205-Zr02

• - not melted

o - partially melted

e - melted

- previously equilibrated at

higher temperature

1400

0 20 40 60 80

NbzOi COMPOSITION, MOL %

100 Zr02

Fig. 3. Previously published phase diagram of the

Nb205-Zr02 system after Roth and Coughanour

[1] .

stability phase is slightly different. The reasons for the differences are probably due to

the differences in techniques which in turn are due to improvements in "the state of the

art". For the present diagram considerably more specimens were examined; they were heated

for much longer periods of time and quenched instead of slow cooled. The solidus temperature could be found with considerably greater accuracy by the onset of the appearance of

a low-Nb205-type phase in the x-ray powder diffraction pattern. Low-Nb205 is the phase

which recrystallizes from a Nb205 rich liquid upon quenching.

186
The x-ray powder diffraction pattern of the orthorhombic phase (s) was found to be

different in several important details from the two previously published patterns (tables

2 and 3) . The stronger lines of the powder pattern could be completely and accurately

accounted for on the basis of an a-Pb02-like orthorhombic subcell with a, b, and c approximately 5 A. This indexing as listed in table 3 and shown diagramatically in figure 4,

Table 2

Previously Published X-ray Powder Diffraction Patterns

of the Orthorhombic Phases in the System Nb205-Zr02.

srence [1] Reference

d d

A KX

4.92 100 4.97

3.61 101 3.623

- - 3.298

- - 3.140

2.95 Ill 2.953

- - 2 . 839

2.64 002 2.635

2.56 020 2.556

2.48 200 2.488

2.35 012 2.343

2.31 021* 2.326

2.244 201*/210 2.2475

2.179 112* 2.187

2.091 121 2.084

2.020 211* 2.025

- - 1.952

- - - 1.9363

1.838 022 1.8354

1.809 202 1.8087

1.782 220 1.7816

- - 1.7417

- - 1.7246

1.706 212 1.7055

1.6822

1.660 103 1.6570

1.6288

1.579 113 1.5756

1.545 131 1,5402

1.511 311 1.5105

1.478 222 1.4762

1.456 023*

1.435 032

1.393 123

1.321 004

1.281 040/014

1.243 400

etc

1/

hk£ reported by [2] have the hkJl values transposed

to be in accord with present indexing scheme.

* These hkl values do not obey the extinction rules

hk£:h+2.=2n and hkO:k=2n

187
5, ^immmmmmim

s-2 I I sss;

, 1 1

H mmmmm

~ s a" - s 2 s 5 3 "

~

I mmmmmmmmnmim

5, ~ KS"|SSSS='|--SS31-"3S2

1

1 m'mmmmm

mmmm

S " S " S I

S S " 2 " 2

nmmmi

mmim

nil

uu

I I I I

ii ii 5i -I

\ 11

i

\

5 I

il nnll Si

188
a-Pb02

(SUBCELL)

hK/:h + i = 2n hK0:K=2n

2:15 CO)

1:7 (19)

I

1

1

\

0?0

1 1

1

20

022

012 »

1 1

1

1

IJ 220

11} 212 lOJ

1

1 1 m

Jl

222

1 0J2

1 1

^ \

a.ia.0

1 II . , 1 1 . .

\

1 1 11 1 . . Li 1, 1

^ \

1 1 , ll 1 ' ' L 1 il i 1 —LJ

^ \

1 1 . . ll 1 1 , 1

. \

1 1 1 ll 1 . . 1 .1

\

1 , . 1, ,

1 1 I

1

1 , . 1, , .

1 .1 1

2e.cuK3

Fig. 4. Diagramatic representation of a portion of the

x-ray diffraction powder patterns of the orthorhombic phase (s) in the system Nb205-Zr02.

obeyed the extinction rules hkS, :h+2.=2n and hkO:k=2n when using the convention for the subcell a<b<c. All lines which cannot be indexed on this basis are actually superstructure

lines. The d-spacings of the superstructure lines were found to be very strongly dependent

on composition and heat treatment. For instance, the peak at d = 2.31 A mistakenly reported

with hk£= 021 by Roth and Coughanour [1] was found to vary from 29^^^ =39.98° (2.2532 A) at the 1:4 Nb205'Zr02 ratio to a value of 38.67° (2.3263 A) at the 1 :8"nS205 :Zr02 ratio under

equilibrium conditions. These two compositions were found to be just on either side of the

single phase boundaries. Although other peaks were also found to change positions considerably this peak is the best diagnostic indicator for the change in the superstructure and has

been labelled as the "characteristic" peak in tables 1 and 3, similar to the nomenclature

used for the low-Ta205-type phases in a previous publication [13]

.

In order to arrive at the correct indexing of the superstructure peaks it was necessary

to examine single crystals. The specimens prepared by direct melting and by BaO - V2O5 flux

growth were used for this purpose. Typical crystals from the flux growth experiments are shown in figure 5. These crystals were invariably twinned as shown in the photograph. The

twin axis was found to coincide with the c axis of the subcell. The b axis was always the

axis perpendicular to the crystal plate. All superstructure spots in a single crystal x-ray

diffraction precession pattern were found to occur only along the b axis of the subcell.

The tabular crystallographic habit is therefore consistent with the general rule that the

short axes grow relatively fast while the long axis grows much more slowly.

From the single crystal photographs shown diagramatically in figures 6, 7 and 8, it

can be demonstrated that the only possible hk£ value for the "characteristic" peak occurring

o between 2.253 and 2.326 A is the OkO superstructure spot occurring immediately after the 020

substructure reflection. For those compositions where the multiplicity is the smaller whole

numbers 7, 8, 9, or 10 the index of the 020 substructure peak would then be (0,14,0) , (0,16,0)

,

(0,18,0) or (0,20,0) and the index of the characteristic peak would have a k value of 2 greater or (0,16,0), (0,18,0), (0,20,0) or (0,22,0) respectively. However, for the more

complex intermediate compositions where the multiplicity is 15, 17, or 19 and the (020)

substructure peak is (0,30,0), (0,34,0) or (0,38,0) the k value of the characteristic peak

would be 4 greater or (0,34,0), (0,38,0) or (0,42,0) respectively. The orthorhombic phase(s)

in these systems always have only a b axis superstructure so that this characteristic line

can be used directly to calculate the true unit cell. The distance between this superstructure peak and the 020 s\ibstructure reflection increases directly proportional to the

189

/
ill iTi^i1r---'^-^^'^''^*'^'^liP^^^^^

Fig. 5. Photographs of

n

typical twinned crystals of the orthorhombic

phase (s) in the Nb205-Zr02 system grown in the BaO:V205 flii;

composition. The distance between the spots is the greatest at the higher Nb205 concentration

and the least at the highest Zr02 concentration.

All of the superstructure lines in the x-ray powder diffraction patterns can be

accounted for on the basis of a i3-axis multiplicity varying from approximately seven times

the subcell value at a composition of about 2:9 Nb20 5:Zr02 to a value of exactly ten times

the subcell at a composition of about 2:15. For those specimens which have been most com- pletely equilibrated by heating at temperatures within about 10 °C of beginning of melting

for extended periods of time, it was found that the i-axis multiplicity was as follows:

Nb205:Zr02 Multiplicity

2:9 ~7 1:5 15

2:11 8 1:6 17

2 :13 9 1:7 19

2:15 10

Specimens which had not been heated long enough and/or at high enough temperatures

always showed the characteristic peak at lower d values (higher 26) than was achieved at proper equilibriation. However once the specimen had achieved equilibrium it could not be

reversed to its former condition by reheating at lower temperatures.

190
SCALE lcm= 2mm Mo^

34 i? 30 18 16 W

33 Kl^n IS W 8 6 • • • S3 S !S 19 IT iS a

25 6 9 1

343230 »

4? 40 38 32 ?6 24 K 18 e 14 8

• • • •

35 33 31 19 17 6

48 40 32 24 16 8 0 8 16 24 32 40

Fig. 6. Diagramatic representation of superimposed {hO£)

and ihll) single crystal precession patterns of

the orthorhombic phase with superstructure of

eight times the subcell. Spots are labelled

in upper left quadrant. Numbers below the spots

indicate those present at the hOi. level and

n\imbers above the spots indicate those present

on hl£ level. Indices of spots obey the extinction rule hkJi :h+k+£=2n.

SCALE lcm-2mm MOk mm hkO:htk=2n

• • • 66 62 56

71=15

• • • J4 30 26

• •

4 0

• • •

34 32 30

n = 8

• • •

18 16 N

• • -

2 0 4

6'2 58

5*4 36 j'2 28 2*4 6 2 33 31 2*9 19 IT 15 15 3 i 3

64* 56

• • • 34 30 26

• •

4 0 M* M

• • •

18 16 14

• • -

2 0 2

56 32 2*8 2 55 33

3' 19 IT 15 i

1

• • • 64 60 56

• • • 34 30 28 J

?1?2 30

• • •

18 16 14 J . 0

• • •

' n (864"='7 ...

38 34 30

• •

4 0

• ••

"

42 4038 ...

22 2018 •• -

2 0 4

70 66 62 40 56 2

2*8 6 2

4' 39 51 23 3 1917 3 i 3

• • •

12 68 64

• • •

58 34 30

• •

4 0 •• •

4 2 40 38

• • • 22 2018

. • -

2 0 2

4 0 36 32 2 43 4' 39 23 a 19 i

1

Fig. 7. Diagramatic representation of upper left portions

of (hO£) single crystal precession patterns of

the orthorhombic phase (s) with superstructure of

15, 8, 17 and 10 times the subcell. Indices of

spots obey the extinction rule hk0:k=2n.

191
NbgOsiZrOg

i;5

2:11

1:6

2:13-

1:7

2:15-

(OKO)

64 60 56

34 32 30

42 40 38

34 30 26 fr16 14

22 20 18

20 15

mok^ radiation

Fig. 8. Diagramatic representation of the left hand portion

of the (OkO) level of single crystal precession

patterns of the orthorhombic phases with superstructures of 15, 8, 17 and 10 times the subcell.

This picture illustrates the way in which the superstructure spots approach the subcell spot as the

composition approaches Zr02

.

The above results most nearly correspond to a group of phases (or a solid solution)

which belong to a homologous series Mn-l'-'2n*

Mn-l02n

n M:0 Nb205 :Zr02 Formula m

14 M13O28 -2:9 Nbi+Zr902 8 ~7

15 M11+O3O 1:5 Nbi+ZrigOso 15

16 M15O32 2:11 Nb4Zrii032 8

17 M16O34 1:6 Nbt+Zri2034 17

18 M17O36 2:13 Nb4Zri303e 9 19 MI8O38 1:7 Nb^Zri^Ojg 19

20 2:15 Nb^ZrisOtto 10

However the real compositions of the specimens are probably not accurately enough

known to eliminate the possibility of a homologous series Mj^02n+2'

192
Mn02n+2

n M:0 Nb205 : Zr02 Formula m

14 M11+O30 1:5 Nbi^ZrioOso 7 15 Ml 5O32 2:11 Nbt^Zri 1O32 15

16 1:6 Nbi^Zr 12O34 8 17 M17O36 2 :13 Nb^ZrigOse 17 18 Ml qOo a 1:7 NbuZr T uOqo 9 19 M19O1+0 2:15 Nb4Zri504o 19

20 M20O52 1:8 Nb4Zrig042 10

Actually no region containing two orthorhombic phases has been seen in this system.

It seems unlikely that a two phase region exists and completely or almost completely

ordered mixtures of the above phases must exist at all compositions in the single phase

region. This rather untenable conclusion may seem more reasonable if stated another way.

At low temperatures a metastable solid solution region exists with some type of structural

defect containing very little long range order and no superstructure peaks. As the com- position is equilibrated at higher temperatures the structural defects tend to diffuse

through the individual crystallites and regroup into ordered arrangements. This clustering

of defects continues until equilibrium is established. Further heat treatment will then no longer affect the ordering process.

Electron microscope lattice image photographs show only fringes characteristic of the

b axis unit cell. However electron diffraction patterns were very complex, often requiring

much larger multiplicities than the x-ray data would indicate. Only specimens from the two

phase region containing the m=10 phase co-existing with monoclinic Zr02 allowed the same

simple explanation for both x-ray and electron diffraction. A possible explanation for this

disagreement is that the specimens are not exactly at equilibrium and/or at exactly the

intended composition (all electron microscope and diffraction data were obtained by J. Allpress, CSIRO, Melbourne, Australia).

4. REFERENCES

[I] Roth, R. S. and Coughanour, L. W. , J. Res. NBS 55_ [4], 209-213 (1955).

[2] Trunov, V. K. , Vladimirova, Z. A., Kovba, L. M. , and Komissarova, L. N. , Izv, Akad.

Nauk. SSSR Neorgan. Materials 1 [7], 1152-4 (1965).

[3] Roth, R. S. and Waring, J. L. , Am. Min. 49, 242-246 (1964).

[4] Bendeliani, N. A., Popova, S. V., and Veres chchagin , L. P., Geokhimiya 6, 677-683

(1967). -

[5] Bocquillon, G. and Susse, C. , Rev. Int. Hautes Temper, et Refract. 6, 263-266 (1969).

[6] Bocquillon, G. , Susse, C. , and Vodar, B., Rev. Int. Hautes Temper, et Refract. 5,

247-251 (1968). ~

[7] Roth, R. S. and Wadsley, A. D. , Acta Cryst. 19_ [1], 26-47 (1965).

[8] Wadsley, A. D. and Andersson, S., in Perspectives in Structural Chemistry III,

ed. J. D. Dunitz and J. A. Ibers , pp. 1-58 (1970). John Wiley & Sons, New York.

[9] Allpress, J. G. and Roth, R. S., Solid State Chem, 3_, 209-216 (1971).

[10] Roth, R. S. and Stephenson, N. C. , in The Chemistry of Extended Defects in Nonmetallic Solids, ed. L. Eyring & M. O'Keeffe, pp. 167-182 (1970). North Holland

Publishing Co. , Amsterdam.

[II] Stephenson, N. C. and Roth, R. S., Acta Cryst. B27 , 1010-1044 (1971).

[12] Thornber, M. R. , Bevan, D. J. M. , and Graham, J., Acta Cryst. B24 , 1183-1190 (1968).

[13] Roth, R. S. and Waring, J. L. , J. Res. NBS 74A [4], 485-493 (1970).

465-504 O - 72 - U

193
DISCUSSION

W. R . Cook : 1 noticed the shifting of the superstructure lines with respect to the

substructure lines. We have observed this on another zirconium compound. I don't know

whether it's characteristic of zirconium or not, but if you dope lead zirconate with a little strontium or lanthanum and titanium you get a tetragonal anti-ferroelectric structure which has weak superstructure which, working from powder diagrams, shift in the same

way. You can always convince yourself that you can resolve individual phases out of these

apparently continuous shifts, but you are never sure that you've got it.

R. S. Roth : My answer to that is, I think, a very important point, namely you can

do all sorts of things with x-ray diffraction powder patterns, but I don't believe them

anymore. You have to have a single crystal and at least look at the single crystal x-ray

diffraction data or obtain electron diffraction data or something else to help. Now, my

guess is that what you are talking about is probably some kind of Ruddlesden-Popper type

phases, maybe ordered, maybe disordered. If there really is this continuous type of a structure in the lanthanum titanate-lead zirconate system, then this is something new, and

if you can prove it with single crystals, then it's not a Ruddlesden-Popper phase.

D. J. M. Bevan : Perhaps I can just comment very briefly. This sort of phenomenon

seems to be cropping up rather more . We have much the same sort of thing in the rare earth

oxide-fluorides where you have an anion excess. There is a region of composition in the

yttrium case between YX2 . i 3 or there-abouts to YX2.22 where X is oxygen plus fluorine. On

the evidence of both single crystal and powder data, both sets of which correlate very

nicely, I believe we have a virtual infinity of ordered phases, some with very large superstructures. I think the biggest we've seen so far is a one dimensional stack of fluorite

unit cells, 57 fluorites in length. I think the i-axis of the orthorhombic system is some- thing of the order of 350 angstroms in this case. This is within the fluorite type structure and hasn't gone as far as the a-Pb02 type.

J. G. Allpress : One possible explanation that we have come up with recently is that

you may have a super-lattice which extends for a long period in one direction and then has

a kink in it. We have been looking at chromium titanium oxides of the a-Pb02 type which

have shear planes in them. The shear planes can go in either of two directions. They seem

to go in one direction for a long time and then a small segment in the other direction. If

you build up a very large superstructure on this basis, I think you may be able to explain

some of the orientation anomalies in the diffraction patterns. We're following this up

right now.

B. G. Hyde : I might interpolate. I think this has been seen in several places, and

is due to exactly that. In fact, I have noticed throughout this afternoon that several of

the micrographs that have had wavy plane images in them, have the waves very closely correlated. If the correlation were perfect this would give rise to very high index ordered

planes.

L. A. Bursi 11 : Earlier this year we published a paper on what we call swinging shear

planes in reduced rutile-'- and that will be discussed in the next paper by Mike O'Keeffe.

In this paper we discuss a simple model whereby you can produce very high index planar

faults in crystals. You can have a continuous rotation of the planes from one simple plane

to another. We also suggested this as a new way of accommodating nonstoichiometry, instead

of varying the shear plane spacing we have an ordered variation in orientation. You have

two reciprocal lattices, one due to the superstructure and one due to the subcell, and these

rotate relative to each other. This explains the orientation and spacing anomalies on the

single crystal diffraction patterns. This type of special reciprocal lattice geometry will

not be restricted to shear structures alone.

R. S. Roth : Yes, that wavy lattice image which John Allpress made of poorly annealed

Nb205:5Zr02 definitely must be telling us something about the method of approaching equilibrium in this system. I don't think that we should be led astray by the very, very large

apparent unit cells that one can get in a system where there is a continuous infinite series

of phases with no two-phase regions between them, i think we are looking at some phenomenon

that isn't quite a series of isolated phases. I don't know what it is, but I am not inclined

to believe myself these 300 angstrom unit cells. Certainly not in terms of it being a phase.

194
a structure all by itself because you never find two-phase regions. We need an explanation

for why these systems do not have two-phase regions.

B. G. Hyde : Bob, you didn't have the spacing on that wavy plane picture. What was the

interplanar spacing there, do you remember?

R. S. Roth : It would have been on the order of magnitude of about 19 angstroms.

Note Added in Proof: During the course of this study it became apparent that the "Zr02"

used in this study did not have reproducible weight losses (see discussions after papers by

N. C. Stephenson and by B. Gatehouse - this proceedings) . After personal discussions with

Drs. J. Galy, S. Andersson and J. Allpress during the meeting, it was decided that a few more experiments to determine the correct compositions of the phases would help to determine

the crystallographic nature of this material. Therefore specimens were prepared of four

Nb/Zr alloys by arc fusion of the pure end member metals. The compositions used were 2:5,

2:6, 2:7, and 2:8 Nb:Zr ratios. These specimens were oxidized at 850 °C, each specimen

taking about one week for complete oxidation of the alloy. The specimens were then ground

and reheated at 1000 °C (with repeated intermittent grindings) for another week. These

specimens then represented 1:5, 1:6, 1:7 and 1:8 Nb205:Zr02 ratios with compositions known

to a much higher degree of accuracy than was true of the original specimens.

A small portion of each specimen was then heated for approximately one week just below

solidus temperatures in a high temperature quench furnace as described in the text of this

paper. The 1:5 specimen could now be indexed on the basis of a multiple cell very close to

m=7. The 1:6 phase, Nb2Zr50i7 was now found to have a multiplicity of exactly m=8. The

1:7 phase had a multiplicity very close to m=9 and the 1:8 composition was now essentially

single phase with a multiplicity of m=10.

It can be concluded from the above experiments that the original specimens were actually

low in Zr02 content compared to their "as prepared" mole ratios. Each specimen is approximately 1/2 - 1 1/2 mole percent lower in Zr02 than the stated value. The results of these

experiments can be interpreted as indicating that these orthorhombic phases belong to the

homologous series Mn02n+2 rather than Mn-i02n ^i^d are anion excess fluorite type phases

rather than cation deficient a-Pb02 type compounds (see L. Nagel and M. O'Keeffe, Matl.

Res. Bull. 6_, 1318 (1971) for discussion of similarity of these structures) .

^Bursill, L. A., Hyde, B. G. , and Philp, D. K. , Phil. Mag. 23_, 1501, (1971).

195

/

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

PHYSICAL AND GEOMETRICAL PRINCIPLES OF CRYSTALLOGRAPHIC SHEAR IN RUTILE

L. A. Bursill and B. G. Hyde

School of Chemistry

University of Western Australia

Nedlands W. A.

M. O'Keeffe

Department of Chemistry

i Arizona State University

Tempe, Arizona 85281

Recent studies by electron microscopy and diffraction have elucidated many of the strutural patterns of fojrmation of homologous series of oxides derived from the rutile structure

by crystallographic shear. In this paper, the physical and geometrical principles underlying

the formation of planar defects are considered. It is shown that the only crystallographic

shear planes expected in systems derived from rutile are those containing <111> as observed

e.g. in Ti02_x ^^'^ Ti02 —Cr203. These results enable us to establish likely criteria for

the development of homologous series in oxide systems. The kinetic consequences of the ex- istence of disordered shear planes (Wadsley defects) are further examined in the light of

these developments.

Key words: Crystallographic shear; rutile; swinging shear planes; Ti02 ; Ti02-Cr203

system.

1 . INTRODUCTION

The study of the "homologous series" of reduced oxides M02_jj with structures derived

from that of rutile (Ti02) has played a central role in the development of our knowledge of

the crystallographic and chemical behavior of Wadsley defects in solids. In this paper we

examine some of the physical principles possibly important in dictating that non-stoichiometry shall be accommodated in some instances by Wadsley defects (in the M02_jj systems under

consideration here, these are crystallographic shear, CS , planes) and in other cases by

point defects. We shall be guided by the now extensive accumulation of experimental data

mainly obtained by x-ray and electron diffraction and by electron microscopy of Ti02-x

Tii_2xCr2jj02_x. These data have been the subject of a recent review [1]-^ to which the interested reader is referred. Here we simply wixl quote the appropriate experimental observations when pertinent.

The first question to which we must address ourselves is: Why are extended defects

rather than point defects observed in non-stoichiometric crystals? Some clues are provided

by an examination of the physical properties of the host crystal and the insight they give

into the nature of interionic forces. The second question is: Why do particular extended

defects, in this case CS planes of certain indices, occur and not others? The essence of

the answer to this question is to be found in a consideration of crystal structure and it

will prove necessary to particularize here to the case of rutile-derived materials.

1 Figures in brackets indicate the literature references at the end of this paper.

197

/
2, POINT DEFECTS VERSUS EXTENDED DEFECTS

An observation that we feel has received insufficient attention is that Wadsley defects

of the CS plane type appear to be confined to materials containing ions of high formal charge

and in crystals which either have a very high dielectric constant (>100) or are ferroelectric.

Local fields due to an asymmetric distribution of charge in such crystals will therefore be

screened rapidly by polarization of the surrounding matrix and polarization energy will be of

some importance. As a result the ionic description of these materials must be employed with

caution and the contribution of ionic and electronic polarization to the total energy must

be considered. The situation is exacerbated by the fact that in materials exhibiting high

dielectric constants, the Lorenz correction to the local field is quite different from the

normal value of 4Tr/3 so that ionic polarization/ or displacement from the normal site, is

accompanied by large local electric field and a large energy contribution from electronic

polarization of the anions which in turn stabilize the ionic displacements.

In the case of rutile, calculation of the Lorenz correction [2] satisfactorily accounts

for the high dielectric constant (ca. 200) [3]. Examination of the normal coordinates of the

corresponding soft IR-active modes [4] shows that the response of this crystal to an electric

field is mainly an off-center displacement of the titanium ion in the Ti02 octahedra (see

fig. 1).

A recent calculation on Tii^Oy by Anderson and Burch [5], based on a rigid ion model,

found no significant difference in electrostatic energy for an ordered vacancy structure and

the (observed) shear structure. In view of the above remarks, it is hardly surprising that

the less symmetrical shear structure is indeed observed.

It is worth noting also that rutile-structure materials also exhibit a soft Raman-active mode which suggests that the crystal can also accommodate local elastic strains without

large stresses [6]. In general one might expect unsymmetrical structures, coherent intergrowth, etc., in systems based on parent crystals with such properties. The term compliant

crystals [7] is proposed for materials of this type.

Fig. 1. Normal coordinates of the low-frequency infraredactive modes of rutile. Large open circles represent

oxygen and small filled circles titanium. The A2u

mode makes the main contribution to e^^. The

which makes thfe main contribution to is doubly

degenerate , displacements in the second E mode are obtained by rotating to displacement vectors by 90°

around the c-axis (vertical in the figure)

.

198
In what follows we shall suppose that the interaction of two titaniiom ions in close

proximity, corresponding to TiOg octahedra sharing faces, can be fairly readily accommodated

by displacement of the titanium ions towards the opposite faces of the octahedra. The occurrence of this configuration in hexagonal BaTi0 3, which is very close in energy to the cubic

form, is already familiar. An octahedron sharing two opposite faces will present a much

less favorable configuration, as in this more-symmetrical arrangement off-center displacement cannot occur.

3. STRUCTURAL ASPECTS OF DEFECTS IN RUTILE

3.1. THE RUTILE STRUCTURE

It proves convenient at this stage to slightly idealize the rutile structure by con- sidering that the anions are in hexagonal close packing (hep) 2. In this description (100)

layers of anions are hexagonally close-packed and the [100] direction corresponds to the hep

c-axis. The octahedral sites, of which half are occupied by cations in rutile are primitive

hexagonal: it is these upon which we shall focus. There are, of course, also tetrahedral

sites. However, the experimental work has largely been confined to date to systems containing

in addition to Ti^"*", ions such as Ti^"*" and Cr^"^ with strong octahedral site preferences, so that the possibility of tetrahedral site occupancy is not considered.

Figure 2 shows the two layer repeat-sequence of cation sites in Ti02 - The pattern of

filled sites in one layer is immediately above and below empty sites in adjacent layers. A

useful geometric property to keep in mind is that the octahedra around the cation sites share

edges with adjacent octahedra within a close-packed layer, share faces with octahedra immediately above and below in adjacent layers and share corners with the next nearest octahedra

in adjacent layers. Thus in rutile each TiOg octahedron shares edges with two other such

octahedra and corners with eight octahedra (fig. 2)

.

3.2, DEFECTS IN RUTILE

An interstitial octahedrally-coordinated ion inserted in the parent structure will be

in close proximity to two other cations: its coordination octahedron will share two faces,

four edges and only two corners with neighboring octahedra. As discussed above, this is

likely to be a high-energy configuration so we search for other ways of accommodating extra

cations without destroying the oxygen close packing.

An important step in the argument is to recognize that extra cations can be introduced

with octahedra sharing only one face in the region of antiphase boundaries (APB) in the crystal. The only possible APB that does not change the connectivity of coordination polyhedra

(specifically that does not introduce face-sharing) is that derived by shear by the vector

1/2<011> in planes of form {Oil}. Only vectors of the type l/2<oil> connect full and empty

octahedral sites and leave the oxygen lattice invariant. The plane must, therefore, be of

type (.hll) . The restriction on face-sharing in turn requires h = 0. Figure 3 represents

two cation layers in rutile with such an APB.

r» *

a o o q p o o

o o d b o o

o o o o o o

Fig. 2. Two (100) layers of cations in rutile (filled and

empty circles respectively) . Solid lines connect

cations in edge sharing octahedra and broken lines

connect cations in corner sharing octahedra.

2As hep and body-centered cubic (bee) are closely related, the structure could also be idealized to have the anions in a bcc array. This latter was the representation preferred by

Anderson and Hyde 18]

.

199
Systematic examination of possibilities shows that cations can be added to the crystal

with octahedra sharing not more_than one face in just one way. This involves "chains" of

face-sharing octahedra along [111] and the simultaneous production of a step in the APB. A

chain terminating within the crystal will require the presence of either a vacant cation site

(neighboring octahedra less connected than normally) or octahedra sharing more than one face.

Such a chain is illustrated in figure 4; we return below to a fuller description of its geometrical properties.

We observe at this point that the normal terminology of point defects is not adequate

for the description of structural defects such as those under consideration. Part of the

difficulty arises because it is not clear which are normal and which are interstitial sites

in the proximity of an antiphase boundary. It is more useful, therefore, to discuss defects

•••••/OO

O O Q p/i • • • •HI^tHO O o o o d / « • «

• ••/oooo

o o • • «

Fig. 3. Cations layers in rutile with an antiphase boundary.

Symbols as in figure 2.

•O •O #0 #0 #0

•O #0 •O #o

•O #0 #0 #0 #0

a #0 #0 #0 O #0 #0 #0

•O •O #0 #0

•O •O •O #0 #0

(>• o« o# o©

0# €>(>• 0« 0«

b 0# 0« 0«

o# 0« (>• (>• (>•

OO OO (>• o«

o« o# o# o# o«

Fig. 4. The small circles on the right in (a) and (b) represent (100) cation layers in

rutile and in rutile with an antiphase boundary as in figures 2 and 3 respectively.

The larger circles on the left in these diagrams represent two (Oil) cation layers.

Open circles represent cations in the plane shown by a line on the right, filled

circles represent cations in the layer underneath. Cations in edge-sharing octahedra are connected by a line. In (c) , the same projections are shown by a [111]

chain of face-sharing octahedra in an APB. Cations in face-sharing octahedra are connected by a double line. In (d) the octahedra coordinating the open-circle

cations of (c) are drawn.

200
at a higher levelof organization - in this instance in terms of the connectivity of coordination polyhedra. In rutile each octahedron shares edges with two and corners with eight of

its neighbors. This situation is unchanged by introducing an APB. In the chains of facesharing octahedra described above, there is introduced for each extra cation a pair of octahedra that share one face, three edges and six corners in the place of one "normally" con- nected octahedron. The topology of the structure requires that these pairs of octahedra

occur in chains along [111] in an APB unless other connectivity defects are introduced. For

the sake of completeness it should be noted that in general the connectivity of empty octahedra should also be considered. For example, a cation vacancy corresponds to an empty Og

octhhedron sharing two faces, etc., in the same way as does an occupied TiOg octahedron cor- responding to a titanium interstitial. Here we are considering cation-excess structures so only occupied (i.e. TiOg) octahedra are discussed.

3.3. EVOLUTION OF SHEAR STRUCTURES

A formal description of the process of reduction of the crystal can now be given. We

will consider later the evidence as to whether, and under what circumstances, this might

correspond to the actual steps occurring.

Loss of oxygen at the surface will produce a local excess of cations. Either a preexisting APB or a fragment of an APB nucleated at this point can accommodate a chain of facesharing octahedra containing the extra cations in a step on the APB plane. Figure 5 illustrates how the step can migrate into the crystal by a cooperative series of cation jumps a- long [Oil] transporting the cation excess into the crystal. A second step corresponding to

a new [111] chain can now form at the surface. Eventually we might envisage a number of

steps in the APB being formed.

The chains of pairs of face-sharing octahedra producing steps in the APB contain an excess of cations and require polarization of the surroundings for stability, so it is

plausible to suppose that the next stage in the development is that they order in the plane

to maximize the distance between adjacent steps. When this occurs we no longer have a (Oil)

APB but a new plane whose indices depend on the spacing between steps. A detailed account of

the geometry has been given elsewhere [1,9]. Here we simply note that if there are n rows of

"normal" ions between each step the indices of the plane are (1 n+2 n+1) , the limiting case

n = 0 corresponding to (121) planes. The last illustration in figure 5 shows one layer of

cations intersecting a (132) plane (n = 1) .

(a)

op

u w u O ' • • • • • • / O O O O cop

ooooooo

•

o

O O O O O o • •

(c)

• • / o o o o o

o o

• ' O O O O O O

O O O o • • • •

• • • • o o o o

o o o

ooooooo*

o ooooo® •

•

• • • • o o o

(d) o o o a

Fig. 5. Two (100) layers of cations in rutile with

(a) an antiphase boundary, proceeding by the

jumps shown in (b) and (c) to a segment of a

(132) CS plane in (d)

.

201
Intermediate cation densities can and do occur. For example, regularly alternating

n = 1 and n = 0 will result in a (253) plane. In fact, progressive reduction of Ti02 , and more particularly increasing chromium concentration in (Ti,Cr)02-xf results in a great

number of planes of different and very high indices being observed [9] by electron-optical

techniques as the plane "swings" from (132) to (121) . In every instance, however, the

observed planes can be considered as derived by ordering of chains of pairs of face-sharing

octahedra in an APB in the manner we have described. The occurrence of only particular types

of CS planes is seen therefore to be required by the particular structure of rutile and by

the principle of minimizing face sharing of octahedra without disrupting the oxygen framework.

The final stage in the evolution of the structure corresponds to the situation in which

there is a high density of extra cations and hence a high density of CS planes. Again the

requirement of polarization of the surrounding medium suggests that at least at short interplanar distances shear planes will tend to order to maximize the interplanar spacing, producing the now familiar families of reduced oxides [1] . An analysis [10] of interplanar

spacings of isolated groups of (132) CS planes has demonstrated this short-range repulsion

and shown that in addition there is a longer-range attractive force between pairs of CS

planes. This latter is difficult to interpret but may be related to the tendency to eliminate

the out-of-phase material between the two APBs.

The particular system of CS planes found in an ordered structure will depend on the

balance between the tendency on the one hand for CS planes to order as far apart as possible

and on the other hand for the individual chains within a plane to order likewise. One can understand qualitatively in this way the evolution from (132) planes at small degrees of re- duction to (121) planes at greater cation/anion ratios.

4. MASS TRANSPORT MECHANISMS

In the absence of detailed kinetic studies, a discussion of mass transport mechanisms

must be somewhat speculative at this state. However, we can recognize [1] a number of re- lated, but distinct, processes that might occur in oxidation or reduction of Ti02 or in interdiffusion of e.g. Ti02 and Cr203. These processes will probably occur simultaneously but

their relative importance will to some extent at least depend on the degree of reduction and

previous history of the crystal.

4.1. NUCLEATION AND GROWTH OF SHEAR PLANES

It was suggested earlier [8] that the first stage of reduction of rutile might occur by

the aggregation of anion vacancies into planar regions ("discs"). Local collapse and shear

of the lattice subsequently produces a region of CS plane surrounded by a partial dislocation.

In view of the above discussion a more attractive possibility would now appear to involve

nucleation of a CS plane at the surface, eliminating the need for mobile point defects. In this mechanism an APB (which may terminate inside the crystal at a partial dislocation) acts

to allow easy incorporation of a cation-rich step of [111] chains of face-sharing octahedra.

Cooperative jumps of a line of atoms by 1/2 [Oil] moves this chain into the crystal (cf fig.

5) . This process moves a step on the APB into the crystal and leaves a "perfect" APB ex- tending back to the surface ready to accommodate another step. Ordering of steps then produces a shear plane of appropriate indices.

4.2. SWINGING SHEAR PLANES

A closely related process that is favored by a certain stoichiometry [1,9] involves

change of indices of a CS plane. As should be clear from the above discussion, this re- quires the identical process of cooperative jumps by 1/21011] by strings of cations, and is

a logical extension of the process of nucleation.

4.3. LATERAL DISPLACEMENT OF SHEAR PLANES

The observation of well ordered crystals with large regions of uniformly spaced CS

planes requires that CS planes can move laterally after growing into the crystal. This process can also occur by 1/21011] jumps [1,11], the difference now being that cooperation of a whole plane of atoms is reguxred. Clearly such a process will not be thermally activated

but will require repulsion between adjacent CS planes to provide the driving force 111]

.

202
4.4. CONSEQUENCE OF THE MODEL

There are some interesting consequences of the model we have described. A key role is

played by the APB in providing a path for incorporation of extra cations in the early stages

of reduction. Nucleation of a CS plane/APB would appear to be a difficult step and asymmetry

in oxidation and reduction in both the kinetic and thermodynamic aspects is expected in cer- tain ranges of stoichiometry . Indeed hysteresis in oxidation-reduction isotherms can be satisfactorily interpreted in terms of this method [1]

.

Surprisingly there have been no measurements of chemical diffusion in the Ti-02 system.

As well as expecting different rates of oxidation and reduction, it is entirely possible that

there will be memory effects, in that APBs left on reoxidation of a slightly reduced sample

will provide sites for subsequent reductions. Experiments designed to test these ideas are planned.

Recently a study was made [13] of interdiffusion of Cr203 and Ti02. Some features of

those measurements are worthy of attention here. Most striking was the observation of a lack of any prono\inced anistropy in the interdiffusion coefficient D. Now every step in ox- idation or reduction we have discussed involves atomic jumps on the type 1/2 [Oil] so that

the net flux in each process will have components, on average, of a/4 = 0.12 nm and c/2 = 0.14 nm. Transport along the c- or a-axes will therefore occur at comparable rates. We

can also understand qualitatively the variation of the magnitude of D with composition (fig.

6) . The initial rapid rise of D with chromium concentration corresponds to nucleation of increasing numbers of APB/CS planes. The almost constant D at higher chromium concentrations

corresponds to cooperative movement of planes of atoms

.

It should be remarked that the above account is really too facile and a completely satisfactory account of interdiffusion, particularly in ternary systems, remains to be given.

Conspicuous among the difficulties for ternary systems is that counter-diffusion of e.g. Ti

and Cr is necessary (in the binary system electronic conduction assures the appropriate Ti'*+/

Ti^"*" ratio at all times) . Movement of a CS plane incorporates new atoms into the plane and

strands the atoms originally in face-sharing octahedra in regions of "perfect" crystal; a mechanism must exist to return Cr^"*" to the CS plane.

A second point which has not received the attention it deserves is that a CS plane migrating due to cation displacements does not move parallel to the normal to the plane but

along [Oil] . For a CS plane extending right through the crystal this can only be accomplished

by adding cations (or siibstracting oxygen) at one surface and removing them (adding oxygen)

at the opposite surface. The role of gas phase transport of material should therefore not

be discounted.

-12

log(D,

-13

0.1 0.2

Cr/Cr +Ti

Fig. 6. Interdiffusion coefficient, 'b , for interdiffusion

of Ti02 and Cr203 at 1450 °C. Based on experiments

by T. J. Ribble [13]

.

203
The difficulty is mitigated to some extent when systems of defects are considered. For

example, ions stranded by one moving CS plane can be incorporated into an adjacent one. Changes in stoichiometry can also occur by movement of a coherent interface [1] between two

regions of different density of CS planes.

Clearly many more experiments are needed before the full picture will emerge with any

clarity. When this happens, however, we will have sxabstantially enhanced our understanding

of the way in which inorganic materials can change in composition.

5. ACKNOWLEDGEMENTS

This paper is based on experimental research at Perth supported by the Australian Research Grants Committee, the U. S. Air Force Office of Scientific Research and the University

of Western Australia. One of us (M. O'K) would also like to acknowledge support from the

National Science Foundation and a grant from Arizona State University which helped make possible a visit to Western Australia.

6. REFERENCES

[I] Bursill, L, A. and Hyde, B. G., Progr. Solid State Chem. , in press (1?71)

.

[2] Parker, R. A., Phys. Rev, 124 , 1713 (1961).

[3] Parker, R. A., Phys. Rev. 124 , 1719 (1961).

[4] Tray lor, J. G. , Smith, H. G. , Nicklow, R. M. , and Wilkinson, M. K. , Phys. Rev. B3, 3546

(1971) . [5] Anderson, J. S. and Burch, R. , J. Phys. Chem. Solids, 32_, 923 (1971).

[6] Nagel, L, E, and O'Keeffe, M. , Mat. Sci. Bull. 6, 1317 (1971).

[7] Nagel, L. E, and O'Keeffe, M. , to be published.

[8] Anderson, J. S. and Hyde, B. G. , J. Phys. Chem. Solids 28_, 1393 (1967).

[9] Bursill, L. A., Hyde, B. G., and Philp, D. , Phil. Mag. 23_, 1501 (1971).

[10] Bursill, L. A. and Hyde, B. G., Phil. Mag. 23_, 3 (1971).

[II] Anderson, S. and Wadsley, A. D. , Nature 211 , 581 (1966),

[12] O'Keeffe, M. , Proc. Brit. Ceram. Soc. 19_, 1 (1971).

[13] O'Keeffe M. and Ribble, T. J., J, Solid State Chem. 4_ (1972) in press and unpublished

results

.

204
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

STRUCTURES AND CHEMICAL BOND PROBLEMS IN VANADIUM OXIDES

Dr. Paul Hagenmuller

Service de Chimie Minerale Structurale de I'Universite de

Bordeaux I associe au CNRS, 351 Cours de la Liberation,

33 - Talence, France

In the transition metal oxides the d-electrons may be either in a localized or a collective state depending essentially on the structure, the transition element and its oxidation

state. Some significant examples will be given resulting from recent investigations in the

field of the vanadium oxycompounds

:

1. A study of the magnetic and electrical properties of the phase K2-xV3+2x08+2x±k in

the system V2O5-VO2-K2O shows that it can be written formally as

K2-xV'++vf±3x+2K (V^i+2K ) subst . (V2x) ins .08 (02x±K ) ins

.

K2V3O3 is actually an insulator in which the V^"*" and v'*'*' ions occupy well defined sites

(K2V'^+ (V^"*") 203) • It does not become a conductor until the progressive appearance of delectrons in the V^"*" sites as a result of a hopping mechanism. The variation with x of the

Curie constant shows that the vanadium, inserted in the form of chain links (O) -V-O-V- (O) in the tunnels emptied by the potassium, also occupies a particular site. These properties

were confirmed by the determination of the structure: the phase <)), which is isostructural

with Ba2TiSi20g, is actually made-up of three types of cationic sites.

2. VO2 has an allotropic transformation at 340 K of the type homopolar bondingi^metal

.

This transformation is characterized by a change of symmetry from monoclinic to tetragonal

of the rutile type. The replacement of vandium 4+ by cationic substitution of the type

2v^+=m5+ (Nb^+f .e. ) +v3+ or by anionic substitution v'*+ + O^" = v^"*" + F~ results in the lowering

of the transition temperature. It seems to be the result of the progressive occupancy of a

TT band. On the other hand the transformation temperature is raised by a substitution of the

type 2V^+ = M^"*" (Cr^+f .e. ) + V^+, and there appears an intermediate semi-conducting phase of

orthorhombic symmetry. The existence of this phase can be explained by the ferroelectric

distortions due to vanadium 5+. The change of the physical properties with the substitution

rate is analyzed on the basis of the obtained structures.

3. The phase Lai_xSrxV03 {CXx<0.40) with a structure derived from GdFe03 is characterized by an evolution from semi-conductor to metal with increasing x. This latter results

from the strengthening of the tt (B-0) bond which is a consequence of the weakening of the

a (A-0) bond and the partial replacement of vanadiim 3+ by vanadium 4+. This change is less

sensitive for the phase Gdi_xSrxV03, Gd^"*" being more acidic than La^"*" and hence a (A-0)

stronger and tt (B-0) weaker.

These results are compared with those obtained for the homologous LnT03 phases, Ln being

a lanthanide and T a 3d- transition element, on the basis of Goodenough's covalent mixing

parameters X and A . The influence of various factors on the physical properties is

discussed.

Key words: Covalence parameters; insulator-metal transitions; perovskite like structures;

relations between structures and physical properties; vanadium oxides.

205

I
1. INTRODUCTION

The interest in vanadium oxycompounds lies in the fact that the d-electrons may be either

localized or delocalized through the lattice. The degree of localization is intimately related to the V-0 distances. In other words, it depends on the structure. Factors such as the

average degree of oxidation of vanadium, nature of other elements present, temperature, etc., can influence this localization. We are going to show, on the basis of some examples, that

the crystal structure of these vanadium oxides and the properties resulting from such an electronic localization are closely related. One is largely responsible for the other. We shall

also stress the influence which other cations present can exercise on these properties and

therefore on the structure.

2. THE SYSTEM V2O5-VO2-K2O

The first example deals with the phase (j) of the system V2O5-VO2-K2O. In the ternary diagram at 500 °C this phase extends from the composition K2V3O8, for which one atom of vanadium

in three has an oxidation state of 4+, to the line of the vanadates (IV) in which vanadium is

exclusively tetravalent (the composition limits are here K2V5O13 and K2V8O17) (fig. 1) [1] ^

.

The phase (f) is tetragonal with parameters which do not vary perceptibly with the composition

(a = 8.897 ± .001 A, c = 5.246 ± .002 A for the composition K2V3O8)

.

The unit cell of K2V3O8 contains two formula units. A comparison of the density measured

by a very precise hydrostatic method [2] and the densities calculated for various structural

hypotheses allows one to assign to a segment inside of the homogeneity range of phase ((> a structural formula y'2-^3+2yp8+2x^^^9 • 2). Outside of this segment the amount of included

oxygen can be either greater or lesser than 2x. The formula can be written as K2-xV3+2x'-'8+x±k:

for the entire range. In other words the phase (j) is derived from K2V3O8 by replacing the

cations K+ by the chains (0) -V-O-V- (0)

.

The electrical and magnetic properties along the K2-xV3+2x08+2x segment [3] have been

studied. When we assign to the vanadium atoms their formal degree of oxidation, this formula

can be written ^2-x^^'^^^-3x^'lx'^8+2x- This means that during the departure of x K"*" ions, 3x

atoms of vanadium pass from the 5+ state to the 4+ state, and 2x atoms insert themselves in

the available sites in the form of chains of average length 0-V-O-V. The formula can now be

written as: K2-xV'++vi±3x (V^J) subst . (V^+) ins. Og (Ogx) ins

.

K,0'

; \

^

Fig. 1. Homogeneity range of the phase

at 550 °C in the equilibrium

diagram V2O5 - VO2 - K2O.

^Figures in brackets indicate the literature references at the end of this paper.

206
d

2,00

'""^ 2^00 3,00 —* \

Fig. 2. Determination of the structural formula of

the phase K2_xV3+2x08+2x 't> by comparison of

the calculated and observed densities for

various hypotheses.

K2V3O8 is an insulator at room temperature with a resistivity above 10^ Q. cm. One can deduce therefore the absence of a hopping mechanism, the two vanadium 5+ atoms occupying

crystallographic sites different from that of vanadium 4+. The conductivity increases with

rising x along the K2xV3+2x08+2x segment: at room temperature it is approximately 10"^ ohm~^

cm"-^ for X = 0.33, 10~^ ohin~l cm~^ for x = 0.67. The activation energies decrease also as x increases: at 600 K it is 1.2 eV for x = 0.33, 0.79 eV for x = 0.50, 0.67 eV for x = 0.60

and 0.16 eV for x = 0.67. Apparently it is the substitution of vanadium 5+ by vanadium 4+

for x > 0 which allows a hopping mechanism in the ij) phase.

Magnetic measurements indicate that the phases K2-xV3+2x08+2x at sufficiently high temperatures obey the Curie-Weiss law. The low value of the Weiss constant (Tp = -18 K) observed

for K2V30g could indicate that the vanadium 4+ occupies distant and isolated crystallographic

sites. But the fact that the Neel temperature does not vary as x increases allows us to as- sume that not only the inserted v'*'^, but also those of the host oxide lattice are arranged in

clusters of two (fig. 3)

.

The molar Curie constant varies linearly (fig. 4) : = 0.37 + 0.59.

Whereas in K2V30g the effective magnetic moment is 1.73 per V^+, for each v'++ added

either by substitution or insertion, the moment becomes on the average 2.17 pg. This result

confirms that, when x > 0, V^"*" occupies three different sites in the lattice.

The structural determination by x-ray diffraction confirmed these conclusions. The phase

K2V3O3 has the same structure as Ba2TiSi20g [4] . The lattice is formed by layers of composition (K2V303)n- The pentavalent vanadium has a tetrahedral coordination, the tetravalent vanadiuiTi is surrounded by five oxygens forming a square pyramid. The potassixim occupies the

tunnels of pentagonal cross-section. In the network of the i> phase potassium is replaced by

(0) -V-O-V- (O) chains. Figures 5 and 6 show the projections of the structure of K2V30g on the

xyO and xOz planes.

3. THE TRANSFORMATION POINT OF VO2

The next example deals with the influence of substitution on the transformation point

of VO2 at 340 K VO2, which has a rutile structure, is metallic. Below 340 K VO2 becomes

monoclinic and semi-conducting. This change results from the formation of d-d bonds between

pairs of neighboring atoms. The distance V-V is alternatively 3.12 and 2.65 A, these pairs

twist slightly about the c axis in creating ferroelectric distortions [5 to 13]

.

207
Fig. 4. Variation of the molecular Curie constant of

the phases K2_xV3+2x08+2x ^ function of x.

208
Fig. 5. Projection of the structure of the phase

K2V3O8 <}) on the (001) plane.

^2^3 ^8 projech'on on

(010)

Fig. 6. Projection of the structure of the

phase K2V3O8 ())on the (010) plane.

The change in the transformation point is different depending whether the substitution

gives V^"*" or V^"*".

The chromium doped CrxVi-x02 oxide has been studied in a detailed manner [14] . Three

phases have been found in place of two: a rutile phase R at high temperature derived from the

corresponding VO2 phase, which cannot be stabilized at room temperature even by very quick

quenching, an orthorhombic variety 0 closely related to the previous one (aQ^aR/2, bo<ap/2,

cq-cj^) , and a monoclinic phase M at low temperature. The transformation points Tj and T2 were determined by DTA and x-ray analysis:

Ti T2 R ->-> O M (fig. 7 and 8) .

Ti increases with rising x while T2 decreases: in other words the homogeneity range of

the orthorhombic phase increases while the rate of substitution of chromium increases. This

result is confirmed by the variation of the magnetic susceptibility as a function of temperature for various values of x (fig. 9) . The amplitude of the two magnetic discontinuities

decreases with rising x, T2 is no longer observable for x > 0.10. The existence of the two

209

465-504 O - 72 - 15
Fig, 7. Transformation temperature

and R as determined by DTA. between phases O

20 40 60 2 9

~20 40

1^

60 2 9

M

40 60 28

Fig. 8. Diffraction patterns of the phases R, 0

and M of composition Crg . o i^o . 99'-'2 •

transition temperatures is also shown by conductivity measurements as a function of temperature (fig. 10) . The phases M and O behave as semi-conductors, while R is metallic as x is

small, for x > 0.10 the R phase becomes in turn semi-conducting.

All these facts now allow one to construct a phase diagram of the three phases as a function of x and temperature (fig. 11) (*).

The similarity of the parameters cq and Cj^ shows that the d-d bonds that exist in the

phase M are all broken in the phase 0. The comparison of the parameters aQ, bg and aj^ indicates that in the orthorhombic phase a ferroelectric distortion takes place in the

vanadium surroundings (fig. 12). This distortion is itself a result of the substitution:

2v'^+ = Cr^"^ + in the CrxV^_j,02 phase. One can assiime that vanadium 5+ having a much

smaller size induces the distortion of the coordination octahedron. The increase of T^ with

X can be explained by the fact that the energy necessary to transform O to R is higher as the V^"*" atoms become more numerous

.

—A recent Guinier investigation shows that for x<0.05 the intermediate phase is actually

monoclinic with only 50% of the d-d bonds broken, whereas the rupture is complete in the

orthorhombic phase. It was detected the first time by Marezio, McWhan, Remeika and

Dernier [ 33]

.

210
211
On the other hand the replacement of vanadium by chromium brings about a progressive

rupture of the d-d bonds which are characteristic of the phase M, and so T2 should decrease

as X increases.

The metallic properties of phase R for small values of x result, as in the case of high

temperature VO2 / from the delocalization of d electrons which occupy, according to Goodenough'

model, a part of the levels available in the t^ band characteristic of the bonds between va- nadium atoms along the c axis, and in the a Tr*tj_ band, which overlaps it, due to the tt (V-O-V)

bonds perpendicular to the c axis (fig. 13) [15 -to 17]. As x increases, the progressive de- crease in the metallic character results from the presence of Cr^ 10ns which break the se- quence V-V-V and intercalate between the vanadium atoms

.

The structural change seems to be analogous in the phases AlxVi_x02 and Fex^i-x^2 characterized respectively by substitution such as: 2v'*+ = Al3+ + and 2V^'^ = Fe^+ + V^"*".

The aspect of the phase diagrams obtained are completely different when the substitution

creates vanadium 3+. Various authors have studied the system V02-Nb02, and have shown that

it is characterized by the formation of a compound NbxVi_jj02 which for x < 0.50 can be denoted

by the substitution: 2V^'^ = Nb^^ + [18,19].

Studies by x-ray diffraction, DTA, electrical conductivity and thermoelectric power measurements indicate that, at least for x < 0.15, two phases only appear: the rutile phase R

at high temperatures and the monoclinic phase M. The transformation point decreases about

11° per Nb °/o introduced (fig. 14) [20]

.

For X > 0.10 the phase R passes gradually from metallic behavior to semi-conducting,

with an increasing activation energy. One is tempted to attribute this change, which is

analogous to that observed for Cr^Vj _x02 (R) , to the interruption of the sequences V-V-V by

the Nb^"*" ions.

The lowering of the transformation point with increasing x can be attributed either to the decrease of the number of d-d bonds by the introduction of niobium 5+, or to the introduction of supplementary electrons, due to V^"*", into a distinct antibonding band TT*tj.. The

absence of phase 0 can be explained by the absence of V^"*" ions able to induce a ferroelectric

distortion.

[4] 4p —

4s

3- [4;

[2] — — 2 pg 2 5 -I 2

[6]

VO2 rut. 2 0

Fig. 13. Band structure of the high temperature

variety of VO2.

lelragonal (rutile . type)

Iransilion region

200

0,10 Q.2Q

Fig. 14. Phase diagram of the compound

NbxVi_x02 for x < 0.15.

212
An analogous diagram has been observed in the neighborhood of VO2 for the substitutions:

2V'++ = Ta5+ + v3+, 3V^+ = MoS+ + 2v3+ and 3V^+ = + 2V^+ [21,22,23] . The lowering of the

transformation point is particularly fast in both last cases.

This analogy reappears again in the system V02_xFx obtained by partial replacement of

oxygen by fluorine, the substitution relation can be written here as: V^"*" + 0^~= V^"*" + F

[24,25] . The decrease of the transition temperature is about 12° C per F °/o . The absence

of any cation other than vanadium suggests the conclusion that the lowering of the transition point results effectively from the appearance of d electrons in the TT*tj_ band.

The structures of the phases derived from VO2 are therefore closely related to the

degree of oxidation and to the temperature.

The last example deals with series of compounds of structure derived from the perovskite

in which the vanadium has an oxidation state intermediate between 4+ and 3+. Let us consider for instance the case of the series Lai_xSrxV03 [26]. For 0< x< 0.40

it forms, at 1100 °C, a phase with the GdFeOs structure with a slight rhombohedral distortion

(fig. 15).

The effective magnetic moment seems to follow the Curie-Weiss law. However, instead of

decreasing as one could predict by the progressive replacement of V^"*" by V^^ with increasing

X, it rises rapidly with x and then levels off (fig. 16) . The paramagnetic Curie temperature

tends towards very high values (fig. 17) . Electrical conductivity measurements as a function

of temperature show that the activation energy which is about 0.10 eV for x = O tends towards

zero for x - 0.20 (fig. 18) . All these properties are characteristic of a progressive transition with X of the type semiconductor -> metal.

4 PEROVSKITE RELATED COMPOUNDS

z

y X

Fig. 15. Relationship between the parameters of the ciibic,

tetragonal (or orthorhombic) and hexagonal perovskite

unit cell (ah = ac/2, ch = 2acv^3) .

213
1000

500

0,1 0,2

Variation of the effective magnetic

moment as a function of x for the

phase Lai_xSrxV0 3.

0,10 Q20

Fig. 17. Variation of the Curie paramagnetic

temperature as a function of x for

the phase Lai_jjSrxV03

.

214
This phenomenon can be explained by the compositional change in this phase. The replacement of the lanthanum by strontium gives rise to an average weakening of the bond a (A-0) due

to the reduction of charge at the A site. This weakening in turn causes a strengthening of

the bond tt (B-0) with which the a (A-0) bond is in competition. The corresponding tt* band be- comes broader as the substitution increases. Since this band is only partially filled, it

gradually results in metallic conductivity (fig. 19). This broadening of the tt* band is en- hanced by the progressive increase in the average oxidation state of vanadium which strengthens the bonds a (B-0) and tt (B-0) . The covalence parameters A and of Goodenough are now

X > X > X^, Xp being the critical value above which the d electrons are collective [17].

a TT ^

A similar phenomenon is observed in the case of the orthorhombic Gdi_xSrxV03 phase

(O < X < 0.17) of the type GdFe03. Figure 20 allows the comparison of the activation energies

of Lai_xSrV03 and Gdi_xSrxV03: the a (Gd-0) bond being stronger than the a (La-0) bond, AEcd

is greater for the same value of x. For two phases of homologous composition the metallic

character is more pronounced in the case of lanthanum than in that of gadolinium. This

result shows conclusively that the change in the physical properties is not due exclusively

to the charge increase on the vanadi\im atom.

However, one can wonder whether the semiconductor-^metal transition is not the result of

a structural evolution induced by the substitution. The Goldschmidt critical radii increase

with X (rsr^+ = 1.16 A, r^a^"^ ~ ^, ^Gd3+ = 0.94 A, in the Shannon and Prewitt classification) , this results in a small increase of the angle V-O-V which tends towards 180° and

therefore in a strengthening of the tt (V-O) bond, whose metallic character is enhanced. This

explanation is in agreement with the fact that the activation energy of LaV03 is smaller than

that of GdV03 , as the angle V-O-V is larger in the former case than in the latter. It is not

sure that the competition between bonds has a greater influence than the bond angles on the

mechanism of conduction.

It is of interest to compare the properties of LaV03 and GdV03 with those of the corre- sponding compounds of the first series of transition elements having a perovskite type

structure.

LaTi03 is metallic and Pauli paramagnetic, whereas GdTi03 is semiconducting and antiferromagnetic at low temperatures [27,28]. If X^^ is the value of the covalence parameter

for which the Curie-Weiss electronic correlations give rise to Pauli paramagnetism (X^ > X^)

,

X > Xw for LaTi03 and X^ > X > X^ for GdTi03 , the weakening of the tt (Ti-0) bond is still

due to the fact that a (Gd-0) is stronger than a (La-0) . The difference of behavior between

LaTi03 and LaV03 results from the much greater extension of the titanium tjg orbitals

('^W ^ -^^c ^

'*^TT LaV03 and GdVOs) .

On the other hand LaCr03 and GdCr03 , whose t2q orbitals are less extended than those of

LaV03 and GdV03 , have localized d electrons (X^j >

'^c> X ) .

215

/
Fig. 20. Variation of the activation energy as a function of

the rate of substitution in the compounds Lai_xSrxV0 3 and Gdi-xSr^VOs.

LaMn03 and GdMn03 show a Jahn-Teller distortion and a A type magnetic structure due to the presence of manganese 3+ (t2g egM . Under these conditions the d electrons are obviously

localized and Aq > > A77. A localization is also observed for LaFeOj and GdFe03 , where the

high value of the intraatomic exchange energy for the Fe^+ ions (t2g eg) implies that X and are becoming smaller.

LaCo03 has simultaneously Co^^^ ions in the low spin state (t2^ e^) and €0^+ in the

high spin state (t2g Sg) , p^^^ GdCoOs the Com ions exist alone at low temperatures and

the Co3+ ions at high temperatures. It has been shown that in both phases a transition

temperature exists for localized electrons t- collective electrons (of different nature)

.

One can conclude in both cases that X^-Xq for the eg electrons in the high spin state of

cobalt [29,30] . The difference in behavior with the analogous iron compounds can doubtlessly be explained in part by the greater tendency of cobalt, whose nucleus has a greater

charge, to give to the ions a low spin, and also by the decrease in the intra-atomic

exchange energy.

The behavior of the nickel 3+ compounds confirms this point of view. These compounds

have been recently prepared under an oxygen pressure of 4 kbars, and their physical properties studied in detail [31] . Nickel is found to exist in the low spin state in the whole

temperature range studied (t2g ^g) • LaNi03 is metallic (A^ > A^^) . To the contrary YNi03

and LuNi03 are Curie-Weiss paramagnetic, but the absence of the Jahn-Teller effect gives

rise to a magnetic structure of type G(A^^ > Aq > A^) . The only explanation for this weakening of Aq is the decrease in the bond angle Ni-O-Ni as the size of the A^"^ ion decreases.

In brief the properties of the oxides of the rare earths and transition elements having

perovskite-like structures; depend not only on the nature of the bonds, in particular the

a (A-0) bond, but also on their crystal structures. The results concerning these various

phases are condensed in figure 21.

216
LaTi O3 Gd TiOj

LoV Oj

GdV O,

LaCr O3 Gd CPO3

Lo Mn 03 GdMn P3

La Fe Gd Fe

]

]

]

]

La Co O3" Gd Co O3

Lo Ni O3" Lu Ni O3

'29 *9

.2 0 29 9

'29

'29 '29 '9

A,

A,

A,

Srrucr

cub. perov. Gd FeOj

Gd Fe O3 dist. Gd Fe O3 Gd Feq3

Gd Fe O3

GdFe03 disr. GdFeQs disr. Gd FeC^

Gd FeOj

Gd FeP3

GdF«03

rhomb. GdFff03

Fig. 21. The change in the covalence parameters of Goodenough

in some phases with perovskite-like structure containing

a lanthanide in site A and a transition 3d ion in the B site

.

REFERENCES

1, 1958.

Mat. Res. Bull., 6, 119, 1971.

Pouchard, M. , Galy, J., Rabardel, L. , Hagenmuller, P., C.R. Acad. Sc. 264 , 1943, 1967,

Rabardel, L. , Pouchard, M. , Hagenmuller, P., brevet CNRS n° 72.118, 1966.

Pouchard, M. , Casalot, A., Villeneuve, G. , Bull. Soc. Chim. Fr. 1, 81, 1968.

Galy, J. , Andersson, S. , private communication.

Morin, F. J., Phys. Rev. Letters, 3_, 34, 1959.

Kitahiro, I., Ohashi, T. , Watanabe, A., J. Phys. Soc. Japan, 21, 2422, 1966.

Paul, W. , Mat. Res. Bull., 5_, 691, 1970.

Rudorff, W. , Walter, G. , Stadler, J., Z. anorg. allg. Chem. , 297 , Minomura, S. , Nagasaki, H. , J. Phys. Soc. Japan, 19_, 131, 1964.

Andersson, G. , Acta Chem. Scand. 10_, 623, 1956.

Adler, D., Brooks, H. , Phys. Rev., 155 , 826, 1967.

Goodenough, J. B. , id., 117 , 1442, 1960.

Zinanon, Z. , Mott, N. F. , Phil. Mag., 21_, 881, 1970.

Villeneuve, Bordet, A., Casalot, A., Hagenmuller, P, Bongers, P. F. , Sol. State Comm. 3_' 275, 1965.

Knoeugue, K. , J. Phys. Soc. Japan, 22.f 551, 1967.

Goodenough, J. B. , Progress Sol. State Chemistry V, Pergamon, 1971.

Rudorff, W. , Marklin, J., Z. anorg. allg. Chem., 334 , 142, 1966.

Trarieux, H. , Bernier, J. C, Michel, A., Ann. Chim. 4, 183, 1969.

Villeneuve, G. , Casalot, A., Bordet, A., Hagenmuller, P., Pouget, J, Lederer, P., J. Chem. Phys. Sol., to be published.

Israelsson, M. , Kihlborg, L. , Mat. Res. Bull. 5^, 19, 1970.

Nygren, M. , Israelsson, M. , id., 4, 881, 1969.

Rao, C. N. R. , Natarajan, M. , Subba Rao, G. V., Loehman, R. E., J. Phys. Chem. Sol.

32_, 1147, 1971.

Chamberland, B. L. , id., 6_, 425, 1971.

Bayard, M. , Reynolds, T. G. , Vlasse, M., McKinzie, H. L. , Arnott, R. J., Wold, A.,

J. Solid State Chem. 3_, 484 (1971).

Dougier, P., Casalot, A., J. Sol. State Chem.

Koehler, W. C. , Wollan, E. O. , J. Phys. Chem,

Bozorth, R. M. , Williams, H. J., Walsh, D. E. Raccah, P., Goodenough, J. B. , J. Appl. Phys.

Casalot, A., Dougier, P., Hagenmuller, P., J. Phys. Chem. Solids, 32_, 407, 1971.

Demazeau, G. , Marbeuf, A., Pouchard, M., Hagenmuller, P., J. Solid State Chem. 3, 582 (1971)

.

P., Launois, H.

, 2, 396, 1970.

Sol. 2, 100, 1957.

, Phys. Rev., 103 , 572, 1956.

, 39, 1209, 1968.

217
[32] Goodenough, J. B. , id. 3_, 490 (1971),

[33] Marezio, M. , McWhan, D. B. , Remeika, J. P., Dernier, P. D. , private communication.

DISCUSSION

p. B. McWhan : I just wanted to emphasize the point that Professor Hagenmuller had made

with regard to VO2 and chromium in VO2 . It has been traditional to explain the insulating

properties and the lack of magnetism in the low temperature form of VO2 entirely on the basis

of the d-electron being pulled up into covalent bonds. Of the four studies that I am aware

of, in the chromiiam doped VO2 system, only the one at Bell Labs has been done on a single

crystal refinement. As Professor Hagenmuller has said, it shov/s that only half of the vana- dium atoms are paired. Therefore, we have to go back and reexamine our simple picture of the

metal to insulator transition because the chromium doped VO2 at low temperatures is still insulating. It is still non-magnetic but only half of the vandiums are paired. As we learn more about the band structures of the rutile phases from the careful work that is being done

on Ti02 and 4d and 5d oxides, we can hope to go back and get a more realistic picture of this

transition.

P. Hagenmuller : I agree with you. Both phases, your monoclinic phase for a very low

value of X and our orthorhombic phase are semiconductors. I hope that the contributions we

can make from both sides will offer the opportunity for a practical cooperation.

J. B. Goodenough : I am making a response , Paul , to the last remark by McWhan rather than

to your paper and I hope that you will forgive me. Ten years ago we emphasized the metal-metal bonding as a way in which one could tie up the electrons in homopolar bonds and therefore

explain the lack of magnetic order as well as the semiconducting properties. Since that time we have taken note of the fact that there are displacements of the vanadium 4+ ions within the

octahedra, which you have described in a vague way as a twisting. These form one short vana- dium oxygen bond very characteristic of a ferroelectric or an antiferroelectric type displacement of the cations . I think such a motion makes an important contribution to the semiconductor-to-metal transition. One of the things of interest in this class of materials is to determine what is the driving mechanism for this transition. Is it the desire to form the metalmetal bonds or is it a softening of the vibrational mode associated with the ferroelectrictype displacement? I personally find the Bell result most interesting, because they find a 50-50 contribution in their monoclinic phase. It appears that both are contributing about the same amount of driving mechanism. Half the chains form homopolar bonds. The other half,

which does not form homopolar bonds, actually shows the antiferroelectric type of displacements,

ments, forming one short metaloxygen bond in the material. Antiferroelectric displacements

along the chains are also enough to account for the semiconductor-to-metal properties in this

particular material. I won't go into the reason at this point, but both mechanisms, homopolar

bonding and antiferroelectric displacements, are playing a role. That's all I wish to emphasize at this point. If one considers both these mechanisms, I think one can understand why we find a metal-to-insulator transition. I will make one other comment. It is about the addition

tion of fluorine, thereby introducing vanadium 3"*" ions. A vanadium 3"*" ion does not participate in the ferroelectric-type displacement. Therefore, it does not encourage that particular

component of the distortion. In addition, vanadium does not form a close bond with the fluorine. Therefore, that also discourages any antiferroelectric-type displacement in this particular material. So one gets a rather sharp decrease in the transition temperature, or addition of fluorine favors the rutile phase all the way down to lowest temperatures, for both

those reasons [32]

.

P. Hagenmuller : I agree completely. It seems the orthorhombic phase is a consequence

of a type of ferroelectric distortion and there are two arguments to support this. The

first one is that in the case of the chromium-vanadium oxide system the transition temperature

increases all the more when one has vanadium 5+. The second argument is given by the fact

that one never obtains the orthorhombic or McWhan monoclinic phase, as long as one has

vanadium 3+.

218
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

PREPARATION AND STRUCTURE OF A PYROCHLORE AND PEROVSKITE

IN THE BiRhOg^^ SYSTEM*

J, M. Longo,^ P. M. Raccah,'*' J. A. Kafalas , and J. W. Pierce

Lincoln Laboratory

Massachusetts Institute of Technology

Lexington, Massachusetts 02173

The pyrochlore structure with general formula A2B2O7 is formed with a wide variety of

ions and tolerates a high degree of nonstoichiometry on the anion and A cation sites e.g.

Pbi , 5Nb206 . 5 . We have found that the reaction of Bi203 with either Rh metal or Rh203 (Bi/Rh

=1:1) at 600-1000 °C in air or oxygen forms a compound with a face-centered cubic unit cell

(a = 10.238 ± .008 A) and the pyrochlore structure. X-ray fluorescence for the Bi/Rh ratio

and thermogravimetric analysis for the oxygen content gave Bi2 . gRhz

.

qOs . 8

•

In the pyrochlore structure the cations are in fixed positions, and there are two types

of oxygen. Six oxygen atoms are of one type (O^) with one position parameter and form the

octahedra around the B cations. The last oxygen (O2) is fixed and coordinated only to the

A cations. It is not essential to the B206-octahedra network. Taking the origin at the B cation, we have refined the position parameter for 0^, the occupancy factor (OF) for O2 and

atomic temperature factors (B) by R-factor minimization of integrated powder diffraction intensity data. The results are as follows:

B„. = 0.7, B^^ =0.1, B„ =0.1, B„ =0.0,x„ = 0.326, OF^ =0.7.

Bi Rh Oi O2 Oi O2

The position parameter for 0^ is in agreement with those found in other pyrochlores

,

and the occupancy factor (OF) is consistent with the chemical analysis. Resistivity measurements on sintered samples at room temperature gave p = 3.2 x 10"^ f2-cm. We will discuss

the stability of the defect structure in terms of the availability of the "inert pair" of

electrons of the A cation.

When Bi203 and Rh203 were reacted in sealed, evacuated quartz tubes at 750-1100 °C, the

product could not be identified. When the same reactants were placed in platinum capsules

and subjected to over 65 kbar pressure at 1000-1300 °C for 1/2 hour, the perovskite BiRh03

was formed. Its unit cell is orthorhombic (a = 5.354 ± .005 A, i = 5.813 ± .005 A, c = 7,776

± .005 A) as in GdFeOs or the series of LnRh03. The relationship between the defect pyrochlore and perovskite structures will be discussed.

Key words: BiRhOs; defect structures; perovskite; pressure-synthesis; pyrochlore.

1. INTRODUCTION

As part of a broad study of mixed metal oxides, the previously unreported Bi-Rh-0 system was investigated in the vicinity of the bismuth to rhodiiim ratio 1:1.

2. EXPERIMENTAL METHODS

When intimately mixed Bi20 3 and Rh20 3 were reacted at 800 °C for 20 hours in air (rhodium metal or a variety of bismuth salts could also be used) , a single-phase, black compound

*This work was sponsored by the Department of the Air Force.

tpresent address: Esso Research & Engineering Co., Linden, New Jersey 07036

Present address: Belfer Graduate School, Yeshiva University, New York, New York 10033

219
was formed. X-ray powder diffraction patterns of this new phase were subsequently indexed

on the basis of a face-centered-c\ibic unit cell with a = 10.238 ± 0.008 A. A chemical analysis was then performed to eliminate composition ambiguities arising from the volatility of

bismuth (III) oxide and the variable oxidation states of both rhodium and bismuth. The bismuth to rhodium ratio as determined by x-ray fluorescence was 1.00 ±0.03 and a weight loss

of 14.85% was observed when the bismuth-rhodium oxide sample was reduced under flowing 15%

hydrogen/85% argon in a du Pont Thermogravimetric Analysis System. The observed bismuth to rhodium ratio and the assumption that the weight change could be totally attributed to loss

of oxygen lead to the formula BiRhO 3^ 1^.

All identification and structural investigations were made on powders using a Norelco

dif fractometer with CuKa radiation and a LiF crystal diff racted-beam monochromator . X-ray

intensity data used for the refinement of structural parameters were collected by slow scan- ning (l/4°/min.) through each peak and accumulating both time and counts. Background cor- rections, determined from a smooth plot of values between peaks, were subtracted from each

observation. Where reflections could not be resolved, they were recorded as a single peak

and similarly treated in the refinement. A total of twenty-one intensities were collected

in this way over the interval 20° < 26 < 120°.

The x-ray intensity profile, cell dimensions, and observed stoichiometry lead to the

conclusion that the structure of the new phase was similar to that of pyrochlore , space group

Fd3m. In this structure the bismuth atoms would have a six plus two oxygen coordination

while the rhodivim atoms would occupy slightly distorted octahedra that share corners with

other_ rhodium octahedra to form a three dimensional network as shown in figure 1. The site

with 3m symmetry was chosen as the origin, and the atomic positions given in table 1 were assigned to each atom.

We then refined the single variable-position parameter for the oxygen of the octahedron,

the occupancy factor for the oxygen atom associated only with bismuth, and the isotropic a- tomic temperature factors for Hi, Rh, 0^ , and O2 using a simplex program developed in our laboratory for minimization of the function R = 100 x E | Ipj^g-I^al | /^^obs • refinement,

the atomic scattering factors for Bi^"*", Rh^"*" [1] , and 0 [2] were corrected for the real

and imaginary parts of the anomalous-dispersion term [3] . The tlieoretical polarization cor- rection for a LiF diffracted-beam monochromator was also applied to our data. The parameters

3. RESULTS AND DISCUSSION

Fig. 1. Octahedra network in the pyrochlore structure.

1 Figures in brackets indicate the literature references at the end of this paper.

220
resulting from the final refinement to R = 3.3, are given in table 1, and table 2 lists the

observed and calculated intensities for comparison. The refined occupancy factor 0.7 ± 0.1

(70% of the O2 sites filled) is within experimental error of the 0.8 found by chemical analysis. The occupancy factor for 0^ always remained at 1.0 when allowed to vary, so it was fixed at unity during final refinements to increase the data to parameter ratio. The crystal

chemistry of pyrochlores shows that the seventh oxygen (O2) is not essential to the stability

of the octahedra network [4] and that the oxygen content can vary from six to seven (Pb2Ru2

Oe [5], Pb2Pt20e.7, and Pb2Rh207 [6]).

The position parameter for 0^ (x = 0.326) is well within the range of reported values

(0.305 < X < 0.355) for all pyrochlores and is very close to the values found for trivalent

rare-earth pyrochlores (0.32? < x < 0.333). A thorough discussion of the pyrochlore structure

and the values of all known u-parameters has been given by Sleight [7] . A list of all Rh-0

and Bi-0 distances as well as selected 0-0 distances and interatomic angles is given in table

3. Figure 2 shows a rhodium octahedron edge-shared to the bismuth polyhedron and includes

some important interatomic distances. The six equivalent Rh-0 distances of 1.97 A agrees

exactly with that predicted assuming 80% Rh^'*"/20% Rh^''" and the ionic radii of Shannon and

Prewitt [8] . The average Bi-0 distance is also in excellent agreement with that predicted

[8] for Bi"*"-^ in eight-fold coordination. The 0-0 distances found range from 2.66 A to 3.65

A and are similar to those found in most mixed metal oxides.

The resistivity of Bi2Rh20g_8 was determined using a four-probe technique on sintered

material. At room temperature p = 3.2 x 10"^ ficm. while p = 3.0 x 10"^ ^cm. at liquid-nitrogen temperature. These values are characteristic of metallic oxides. Similar resistivities have been foiind in sintered samples of Pb2Ru20g [5], Pb2lr20g_5 [6] and Bi2Ru207 [9]. In fields to 14 kOe the magnetic susceptibility of Bi2Rh20g.g was less than the 10"^ emu/g

sensitivity limit of oior vibrating sample magnetometer over the entire range from room temperature to 4.2 K. Such behavior is consistent with the small, temperature-independent sus- ceptibility characteristic of the Pauli paramagnetism often observed in metallic oxides.

When Bi203 and Rh203 were sealed in evacuated silica tubes and reacted at 700-1000 °C,

the pyrochlore did not form and the products could not be identified. However, when the same reactants were subjected to high pressiire (65-90 kbar) and high temperatures (1000-1300 °C)

,

a compound with an orthorhombic perovskite structure was formed along with a small amount of

a second phase. The composition BiRh03 was assumed and was not confirmed by chemical analysis since we could not obtain pure material.

In a typical high-pressure experiment, the well mixed reactants are tightly packed into

a cylindrical (4 mm dia. x 10 mm) platinum capsule that is inserted into a high-pressure cell

equipped with a graphite sleeve heater. The entire assembly is next placed in a belt apparatus capable of developing 90 kbar and subjected to the desired pressure. The sample is then

brought rapidly to the desired temperature and held there for five to thirty minutes. At

this point the sample is quenched before the pressure is released.

Table 1

Crystallographic Data for Bi2Rh20g g

Space Group : Fd3m

Unit Cell Parameter: 10.238(8) K Cell Content: 8Bi2Rh20g_e

Rh in (16c) (0,0,0; 0,1/4,1/4; 1/4,0,1/4; 1/4,1/4,0) F.C.

Bi in (16d) (1/2,1/2,1/2; 1/2,1/4,1/4; 1/4,1/4,1/4; 1/4,1/4,1/2) F.C.

01 in (48f) (X, 1/8, 1/8; X, 7/8, 7/8; 1/4-x, 1/8, 1/8; 3/4+x, 7/8 , 7/8) tr ; F.C.

02 in (8b) (3/8,3/8,3/8; 5/8,5/8,5/8) F.C.

Occupany Factor (O2) = 0.7

B. = 0.1 B = 0.1 B = 0.0 Rh

221
Table 2

Comparison of Observed and Calculated Intensities for Bi2Rh20g g

"""obsd ""'calc "^calc

5.8 5.51 311 3.087

100.00 100.00 222 2.955

39.5 36.97 400 2.559

7 .

3

7 . 03 331 2 . 349

0.4 0.45 422 2 .090

3.3 4.03 333

511

1.970

46 .

1

46 .07 440 1 . 810

2.7 2.42 531 1.731

48.9 47.64 533

622

1.561

11.5 12.24 444 1.478

1.1 1.14 551

711

1.434

1.0 1.44 553

731

1.333

7.5 7.22 800 1.280

0.6 1.11 733 1.251

21.7 21.14

555

751

1.182

-L . 1 / 4 16.7 17.51 840 1.145

0.8 1.13 753

911

1.124

14.4 14.79 844 1.045

0.6 1.00

933

755

771

1.029

17.0 18.36

951

773

666

1022

0.990

0.985

6.4 5.97 880 0.905

222
Table 3

Interatomic Distances and Angles in Bi2Rh206.8'

Bi-0: Bi-60i = 2.54

Bi-202 = 2.22

Rh-0: Rh-60i = 1.97

0-0: O2-6O1 = 3 X 3.06

= 3 X 3.65

O1-8O1 = 4 X 2.66

= 4 X 2.91

Ol- 1 -Bi- Ol -2 (6) Ol- 1 -Bi- Ol -3 (5) Ol- 1 -Bi-Ol -4 02- 1 -Bi--Ol -1 (3 ,5)

02- 1 -Bi-Ol -2 Ol- 1 -Rh--Ol -2 (8) Ol- 1 -Rh--Ol -7 (9)

63.1°

116.9°

180°

100.2°

79.8°

84.8°

95.2°

a/ Notation consistent with figure 2.

(001)

(110)- O Bismuth O Rhodium OOxygen

Fig. 2. Ruthenium and bismuth coordination with oxygen,

223
The lattice parameters for high-pressure orthorhombic BiRhOs, as refined by the minimization of the differences between 26 obs and 26 calc for 26 peaks over the range 22° < 26

< 84°, were a = 5.354 A, b = 5.813 A, and c = 7.776 K with about 0.1% error. The intensities of diffraction peaks were then assigned on a 1 to 100 basis and are compared in table 4 to intensities calculated assuming that the atoms of BiRh03 are in positions corresponding

to those found in orthorhombic GdFeOs [10] . Table 4 also lists for comparison the observed

and calculated interplanar spacings

.

Meaningful electrical and magnetic measurements were not possible on the high-pressure

material since it was not prepared as a single phase.

The high-pressure perovskite phase could be retained at atmospheric pressure and withstood heating to 800 °C in nitrogen. Such stability is similar to that observed in other

quenched, high-pressure, perovskite-related phases [11,12].

In the Bi-Rh-0 system, the pyrochlore structure is stable when reaction is carried out

in air. The rhodium atoms adjust their oxidation states to a formal +3.8. The formation of

partially filled bands allows all rhodium to be equivalent and is the origin of the metallic

conductivity and Pauli paramagnetism found for Bi2Rh205^8' The oxygen vacancies resulting

from inability of the rhodium atoms to achieve a full +4 oxidation state in this structure

are directly associated with the bismuth atoms. These 02-vacancies are located at the centers of bismuth tetrahedra and are stabilized by the high polarizability of bismuth. The

Table 4

Comparison of Observed and Calculated Intensities for High Pressure BiRhO

d(obs) d(cal) I (obs) I (cal) hk£ d(obs) d(cal) I (obs) I (cal)

101 4.410 1.79 040 1,453 1.453 1 0.96

110 3.940 3,939 8 5.56 115 1,447 1.447 1 0.88

002 3.892 3.888 4 4.89 041 1,429 1.428 5 3.36

111 3.513 3.513 13 13.39 224 1,383 1.383 10 10.53

020 2.908 2.906 24 20.94 025 1,371 1.371 <1 1.20

112 2.764 2.767 100 100.0 042 1,361 1.361 <1 0.69

021 2.722 2.722 11 10,29 400 1,338 1.338 5 3.10

200 2.677 2.677 23 24,83 331 1,295 1,294 6 3.00

022 2.326 2.328 5 2,85 411 * 1,288 * 1.01

211 2.320 2.321 * 2.29 043 1.268 1,268 3 1.92

202 2.205 2.205 8 5.72 402 * 1.266 * 0.31

113 2.166 2.165 7 4.63 241 1.260 1.260 6 3.90

122 2.136 2.135 1 0,42 332 1.244 1.244 6 3.16

212 2.061 2,062 2 0,43 116 1.231 1.231 8 8.01

220 1.969 1,969 15 20,58 225 1.221 1.220 3 1,90

004 1.945 1.944 13 13,27 420 1.216 1.216 7 2,54

023 1.935 1.935 7 4,64 242 * 1.213 * 0.49

221 1.908 1,909 11 7,97 421 1,201 1.201 4 1.42

131 1.774 1,774 19 13,04 324 * 1.198 * 0.24

213 * 1,773 * 0,85 026 1,183 1.184 6 0,11

114 1.743 1,743 3 1,61 135 * 1.183 * 3,33

310 1.706 1,706 2 0,60 305 1,171 1.172 6 0,09

311 1.666 1.666 3 1.75 333 * 1.171 * 3.04

132 1.650 1.650 12 9.27 413 1,165 1.165 5 0.77

024 1.616 1.616 12 8.62 044 * 1.164 * 0.70

204 1.573 1.573 18 11.11 315 1,150 1.150 <1 0.60

230 * 1.570 * 0.28 24 3 1.146 1.146 6 3.27

223 * 1,568 * 3,71 150 1.136 1,136 1 1.10

312 1,562 1,562 20 17,80 151 1.124 1,124 6 3.04

133 1.491 1,491 7 6,71 * not separable from above line

224
bonding possibilities of Bi^"^ ions in the defect-pyrochlore structure is analogous to that

of Pb^"*" ions [5] . A discussion of the bonding possibilities has also been given by Bouchard

and Gillson [9]

.

It is interesting to note that the only transition-metal pyrochlores formed with all, or a significant fraction, of the anion sites vacant have Tl"^^ , Pb^"*", or Bi^"*" ions as the A

cation. In all cases, these A cations have 6s^ core electrons that are easily polarized because of a relatively small hybridization energy. We speculate that compounds like Pb2Ru20g

[5] and T2,2Nb205 [13] are stabilized by a transfer of electron density from the A cation to the vicinity of the anion vacancy, thus forming what Goodenough has called a trap-mediated

bond [14] . The exact extent and location of the core-electron density is not easily established, but it has been discussed in considerable detail for Pb2Ru20g [5,11], The compound

Ag2Sb2 0g also crystallizes in a defect-pyrochlore structure [15] , In this case it appears

that the relatively small effective charge on the Ag"*" ions plus the relative instability of

180° Sb^'^-0^~-Sb^"^ bonds [15,16] allows this structure to be competitive with the perovskite

structure

.

Transition-metal BiT^+O oxides do not generally form perovskite structures at atmospheric pressure. BiCrOs and BiMnOs, for example, require high pressure for their formation

(17] and, like BiFeOs, have distorted perovskite structures [18]. This is in marked contrast

with the rare-earth hnT^+O^ perovskites, which generally form stable perovskite structures

if the t3+ ion is able to have octahedral coordination [18]. Furthermore, with the smaller

t3+ ions low spin CoHI, low spin Ni^H and Al'^+ , the reported BiT3+03 phase [19] stable at atmospheric pressure appears to have a structure similar to that of KSb03 [20] . If the stoichiometry of this phase is ABO3, then a Bi^^-ion array consisting of linked clusters of six

cations unscreened by any intervening anion is indicated, and Goodenough has pointed out to

us that a trap-mediated bond may be implicated in these phases also.

The perovskite structure (ABO3) is strongly favored by high pressure, since it consists

of close-packed AO3 layers having B cations occupying all the all-anion octahedral sites,

which share common corners because of cubic stacking of the AO3 layers. The defect pyrochlore Pb2Ru205 (PbRu03) transforms to the orthorhombic perovskite structure at 1400 °C and

pressures P > 90 kbar [11] , and it is reasonable to anticipate that all transition-metal A2

B20g pyrochlores would also transform similarly at high pressures. The formation of highpressure BiRh03 is consistent with this idea.

4. ACKNOWLEDGMENT

We wish to thank J. B. Goodenough for many stimulating discussions, E. B. Owens for chemical analysis, and D. A. Batson and C. H. Anderson, Jr. for valuable technical support.

5. REFERENCES

[I] Cromer, D. T. and Waber, J. T. , Acta Cryst. 18, 104 (1965).

[2] Tokonomi, M. , Acta Cryst. 19_, 486 (1965).

[3] Cromer, D. T., Acta Cryst. 18_, 17 (1965).

[4] Jona, P., Shirane, G. , and Pepinsky, R. , Phys . Rev. 98_, 903 (1955).

[5] Longo, J. M. , Raccah, P. M. , and Goodenough, J. B. , Mater. Res. Bull. 4, 191 (1969).

[6] Sleight, A. W. , Mater. Res. Bull. 6, 775 (1971).

[7] Sleight, A. W. , Inorg. Chem. ]_, 1704 (1968).

[8] Shannon, R. D. and Prewitt, C. T, , Acta Cryst, B26 , 1046 (1970).

[9] Bouchard, R. J. and Gillson, J. L., Mater. Res. Bull. £,669 (1971).

[10] Geller, S., J. Chem. Phys. 24_, 1236 (1956).

[II] Kafalas, J. A. and Longo, J. M. , Mater. Res. Bull. _5, 193 (1970).

[12] Longo, J. M. and Kafalas, J. A., Mater. Res. Bull. 3, 687 (1968).

[13] Belyaev, I. N., Lesnykh, D. S., and Lupeiko, T. G., Zh. Neorg. Khim. 14, 648 (1969).

[14] Goodenough, J. B., Chemical Bond in Crystals, N. N. Sirota, Ed. (HAYKA TEXH KA, Minsk,

1969) p. 94.

[15] Sleight, A. W. , Mater. Res. Bull. 4, 377 (1969).

[16] Kafalas, J. A., this conference

[17] Sugawara, F., lida, S., Syono, Y., and Akimoto, S., J. Phys. Soc. Japan 2£, 1529 (1965).

[18] Goodenough, J. B. and Longo, J. M. , Landolt-Bornstein Tabellen Neue Serie III/4a

(Springer-Verlag, Berlin, 1970) p. 126

225

465-504 O - 72 - IS
[19] Bucci, Joseph D., Ph.D. Thesis, University of Missouri-Rolla (1971).

[20] Spiegelberg, P., Arkiv for Kemi , Min. Och Geol 14_ (5), 1-12 (1940).

DISCUSSION

E . Banks : Did you mention anything about the properties of this perovskite?

J. Af. Longo : No, we were really unable to measure any meaningful properties because we had small amounts of a second phase which we were unable to separate out.

P. Hagenmuller : Don't you believe it would be interesting to try to introduce some fluorine. Very often when one is able to replace holes by oxygen or oxygen by holes if you prefer,

it is interesting to have an intermediate situation by using fluorine.

J. M. Longo : Yes, certainly pyrochlore is known to accept fluorine, hydroxide or even sulfide ions, on that seventh site and one can certainly speculate on a compound which would

have no vacancies and they would be taken up by fluorine.

B . Pos

t

: There usually is a high degree of correlation between the occupancy factor and

the temperature factor. I noticed that you had a rather low temperature factor for vacancies

on O2 sites, namely zero. Of course, this is what came out of your computer. Supposing you

had changed the occupancy factor to .9 regardless of the stoichiometry . Did you try anything

like that?

J. M. Longo : As I recall, we did change temperature factors because, as you noted, things

like oxygen were very small, zero, and bismuth was .7 and we looked for some correlation

there. The way I recall it there wasn't really very much change in this 0.7 occupancy factor.

Even trying to hold oxygen temperature factors at a value of .2 or .3 and allov/ing it to refine, the occupancy factor did not change very much and we just got an increased R factor.

B . Pos

t

: Well, there is something wrong, seriously wrong!

R . Ward : I'd like to ask one question myself. Are all these oxygen deficient pyrochlores associated with elements which have lone pairs, or do you have oxygen deficiencies without them?

J . M. Longo : The pyrochlore compounds which have the oxygen deficiency are certainly

most prevalent with lead 2+, thallium 1+, and bismuth 3+. Also the silver antimony oxide is

known where the seventh oxygen position is totally vacant. To my knowledge that's the only

exception to the vacancy type where there would not be the inert pair. Perhaps John Goodenough would like to make a comment there

.

J. B. Goodenough : I would just like to point out that the original motivation for this

work was because the lead compounds had no oxygen in that site and seemed to be associated

with a lone pair. We tried with the bismuth compound and there was a certain disappointment

that we actually had Og . 9 instead of Og^O- answer to your question, let me say that, as John Longo has pointed out, silver antimony oxide is the exception of a cation that has no lone pair and still forms a defect pyrochlore structure. However, as Jim Kafalas , in the last

paper this morning will point out, we believe that is a peculiarity of the antimony 5+ ion.

A 180 degree antimony 5+-oxygen-antimony 5+ bond does not like to form because of the very

strong covalent bonding with the oxygen, and there are no d-orbitals involved. Antimony 5+,

therefore, is willing to go into this particular structure with the silver in order to avoid

having to make that particular kind of a bond connection. So I think it is a peculiarity of

antimony 5+ that induces the silver ion to be stabilized in this defect-pyrochlore structure.

226
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

PRECIOUS METAL PYROCHLORES*

A. W. Sleight and R. J. Bouchard

Central Research Department

E . I . du Pont de Nemours and Company

Experimental Station

Wilmington, Delaware 19898

Rare earth pyrochlores of the type A2M2O7 where A is a rare earth and M is Ru, Ir, Pd, or Pt have been reported, but little is known of their physical properties. We have grown

crystals of the rare earth ruthenate and iridate pyrochlores. Four-probe electrical resistivity measurements on single cirystals show that both rare earth ruthenates and iridates are semiconducting with an activation energy of about 0.1 eV for the ruthenates and about 0.08

eV for the iridates. Very different behavior is found for the iridate and ruthenate pyrochlores when the A cation is a post-transition metal. Although TZ2^'^z'-'7 also semiconducting, it has an activation energy of only about 0.01 eV. Metallic conduction is found for

12.21^207, T£20s207, Bi2Ru207 , and Bi2lr207. Magnetic susceptibility measurements confirm the

localized electron behavior for the semiconductors and delocalized electron behavior for the

metallic compounds. Structural refinements have been carried out for Nd2Ru207, Yb2RU207, and

Bi2RU2 07. The Ru-0 distance is 2.00 ± .01 A for all three compounds; however, an anomalously

high temperature coefficient was found for Hi.

Key words: Metallic conductivity; oxides; pyrochlore structure; semiconductivity

.

1 . INTRODUCTION

Precious metal oxides with the pyrochlore structure and the formula A'^^M^^Oy have been

known for some time where M is Ru or Ir and A is a rare earth [1,2]^. Recent high pressure

work has extended M to include Pd and Pt [3] . Another recent development is the use of posttransition elements (In, R , Pb, and Hi) as A cations [3-8]. When the A cation is Pb, the

formula is generally better represented as Pb2M207_jj, and phases of this type will not be

considered here.

An extensive program on precious metal pyrochlores is underway at this laboratory, including the preparation of new phases, crystal growth, crystallographic studies, and numerous physical measurements. Some of the results are given in this paper.

2. EXPERIMENTAL

The methods of preparing polycrystalline samples as well as Tl2'Ru.2'^7 crystals have been

described previously [6,8]. Single crystals of Bi2Ru207 and Bi2lr207 were grown in a Bi203

flux. Single crystals of rare earth ruthenates and iridates were grown hydrotherroally or in

a rare earth chloride flux.

Electrical resistivity was measured on single crystals when they were available. However,

sintered bars of T£2M207 compounds were used except for TJ2.2RU207 . In all cases the fourprobe method was used.

* Contribution No. 1871.

1 Figures in brackets indicate the literature references at the end of this paper.

227
3. RESULTS

Table 1 siiramarizes some results on precious metal pyrochlores. All the precious metal

pyrochlores are black and appear to be ciibic (Fd3m) . Ruthenates are the easiest to obtain

in a highly pure form, and ruthenate crystals are the easiest to grow.

3.1. RUTHENATES

Electrical resistivities of the ruthenate single crystals are given in table 1 and fig- ure 1. All rare earth ruthenate pyrochlores are semiconducting with an activation energy of

about 0.1 eV. A very low activation energy is found for T£2Ru207 , and Bi2Ru207 is not semiconducting at any temperature. Seebeck coefficients of +350 yV/°C for EU2RU2O7 , +20 yV/°C

for T£2Ru207, and -7 yV/°C for Bi2Ru207 also indicate a change from semiconducting to metallic

behavior

.

Extensive magnetic susceptibility data on the ruthenate pyrochlores have been obtained

[9]. However, octahedral Ru"*" is nonmagnetic in its ground state, and this leads to complex

magnetic behavior. Nonetheless, these data are compatible with localized Ru electron behavior

when A is a rare earth or T£ and delocalized behavior when A is Bi

.

Single crystals of T2,2RU20 7 and Bi2Ru207 were examined on a precession camera and found

to have the Fd3m space group. Structural refinements have been carried out on semiconducting

Nd2Ru207 and LU2RU2O7, and metallic Bi2Ru207 . The details will be published elsewhere. The

Ru-0 distance is 2.00 + .01 A for all three pyrochlores, and the 0-Ru-O angles are likewise

very similar. Thus, it appears unlikely that the change from semiconducting to metallic properties can be attributed to changes in Ru-0 distances or O-Ru-0 angles. A high Bi temperature

factor is the only result which distinguishes Bi2Ru207 from Nd2Ru207 and LU2RU2O7. This high

Bi temperature factor appears to be characteristic of inert pair cations on high symmetry

sites.

3.2. IRIDATES

Rare earth iridates are semiconducting with activation energies somewhat lower than

fo\ind for the ruthenates. Metallic behavior is indicated for Tii2lr207 and Bi2lr207. Thus,

the iridate pyrochlores show the same trend found for ruthenate pyrochlores

.

Table 1

Electrical Data and Cell Dimensions

Compound

p298 K,

ohm- cm Ea or R^^^

0 a, A

Nd2Ru207 2.0 0.07 eV 10.33

EU2RU2O7 1.2 0.08 Ev 10.25

Gd2Ru207 0.2 0.10 eV 10.23

Yb2RU207 1.0 0.12 eV 10.09

EU2lr207 7 X 10-2 0.09 eV 10.29

Dy2lr207 0.2 0.06 eV 10.21

T2.2RU2O7 2.3 X

10-"* 0.01 eV 10.20

Bi2RU207 2.5 X

10""^ 1.2 10.30

T£2lr207 1.5 X 10-3 1.2 10.21

Bi2lr207 1.1 X 10-3 1.6 10.33

T«,2Pt207 0.25 0.03 eV 10.13

T£20S207 1.8 X lO-'* 1.4 10.31

T2,2Rh207 6 X

10-*+ 0.03 eV 10.16

Resistivity ratio (R = P298 k/Pi+.2 k) given for the metallic compounds; for semiconductors, the activation energy is given in electron-volts.

228
10-4 _

I 1 1 I \ I I 1_

0 100 200 300 400 500 600 700

T, °K

Fig. 1. Resistivity vs. temperature for some ruthenate pyrochlores

.

4. DISCUSSION

other metallic oxides containing Ru'*''* or Ir+'* are RUO2 , Ir02 , SrRu03 , and Srlr03 [10,11

12]. Presumably, this metallic behavior results from a partially filled it* band [10,13] which

arises from an interaction between oxygen p and metal orbitals. In perovskites, Goodenough [14] has argued that the A cation competes for these oxygen p orbitals. This competition becomes stronger as A becomes less basic. Eventually the tt* band may break down and

localized electron behavior will be observed. Thus, the semiconducting behavior of the rare

earth pyrochlore vs. the metallic behavior of SrRu03 and Srlr03 may be due to the less basic

character of the rare earths.

The Ru-O-Ru angles, which are close to 180° in the perovskite structure, are around 130°

in the pyrochlore structure; this difference in angle may contribute to the localization of

electrons in the pyrochlore structure. However, this same geometry is present when A is Bi

and then the electrons are apparently not localized. Furthermore, Bi and T£ are much less

basic than the rare earths, and thus they should compete even more strongly for the oxygen p

orbitals. Therefore, the rules developed for the perovskite structure seem to fail for the

pyrochlore structure.

Ruthenium-oxygen octahedra share only corners in both the perovskite and pyrochlore

structures. There is some distortion of the octahedron in SrRu03 and SrIrOs as well as in

the pyrochlores, but these distortions are small. A more significant difference lies in the

arrangement of A cations around Ru. In the perovskite structure, the A cations are positioned

around Ru at the corners of a cube; the six A cations around Ru in the pyrochlore structure

are in the same plane as Ru. Thus, strong crystal fields may be present in the pyrochlore

structure, which would tend to trap electrons at Ru. This field would be stronger when A is

a rare earth than when A is a post-transition metal. We can now rationalize trapped, localized electrons when A is a rare earth and delocalized electrons when A is H or Bi . The activation energy should be a measure of the trap potential; it should increase as the cell dimension and A-M distance decrease, and in fact this appears to occur (table 1). Finally, Ti

229
should exert more of a trapping influence than Bi because (a) T£ is slightly more electropositive than Bi ; (b) Tl is smaller than Bi which leads to smaller A-M distances; and (c) the

inert pair of Bi is probably directed toward the M cations. The question remains as to whether

the crystal field of the A cations is really sufficient to cause localization; thus, alternate models are being developed.

The pyrochlore structure may be viewed as two inter-penetrating networks (fig. 2) , and

the formula rewritten accordingly is A20'-2M03. The schematic MO diagram given in figure 3 emphasizes this two-network feature in that the strongest bonding is within the two separate

networks. However, the half-filled band arises from an interaction between the two networks.

Since Bi is linearly coordinated to two close oxygens, s-p bonding is assumed. Thus, the

"inert pair" of Bi now has only p character. In this model the metallic properties of Bi2Ru2

O7 are due to delocalization of this inert pair, and the Ru electrons could be localized.

Since TJ2,+ ^ has no inert pair, the half-filled band would be empty in TII2RU2O7, but there

would be only a small gap between this conduction band and the lower energy Ru electrons. In the rare earth ruthenates this conduction band would be at much higher energies.

Fig. 2. Stereoscopic view of the pyrochlore structure as two interpenetrating networks. The smallest atoms

(M cations) are in octahedral coordination, the next

largest atoms (A cations) are in linear coordination,

and the remaining larger atoms are the anions

.

B12 RU2 Oe 0'

Fig. 3. Schematic MO diagram for Bi2RU20

230
Further studies of precious metal pyrochlores are in progress, and we hope to determine

whether or not one of the qualitative models described here, or a combination of them, is

basically correct.

5. ACKNOWLEDGMENTS

We thank J. L. Gillson for electrical measurements, J. F. Weiher for magnetic measurements, and M. S. Licis and C. M. Foris for crystal lographic data. Helpful discussions with

W. Bindloss and D. B. Rogers are gratefully acknowledged.

6. REFERENCES

[I] Bertaut, E. F., Forrat, F., and Montmory, M. C, Compt. rend. 249 , 829 (1959).

[2] Montmory, M. C. and Bertaut, E. F., Compt. rend. 252 , 4171 (1961).

[3] Sleight, A. W. , Mater. Res. Bull. 3_' 699 (1968).

[4] Hoekstra, H. R. and Siegel, S., Inorg. Chem. 7_, 4171 (1961).

[5] Longo, J. M. , Raccah, P. M. , and Goodenough, J. B., Mater. Res. Bull. 4, 191 (1969).

[6] Bouchard, R. J. and Gillson, J. L. , Mater. Res. Bull. 6, 669 (1971).

17] Sleight, A. W. , Mater. Res. Bull. 6_, 775 (1971).

I8J Sleight, A. W. and Gillson, J. L., Mater. Res. Bull. 6, 781 (1971).

[9] Weiher, J. F., Private communication

[10] Rogers, D. B., Shannon, R. D., Sleight, A. W. , and Gillson, J. L., Inorg. Chem. 8_, 841

(1969) . [II] Callaghan, A,, Moeller, C. W. , and Ward. R. , Inorg. Chem. 5_, 1572 (1966).

[12] Longo, J. M. , Kafalas , J. A., and Arnott, R. J., J. Solid State Chem. 3^, 174 (1971).

[13] Goodenough, J. B., Bull. Soc . Chim. France 4, 1200 (1965).

[14] Goodenough, J. B., Phys. Rev. 164, 785 (1967).

DISCUSSION

E, Banks : I'm going to steal Post's thunder this tinje. It seems to me that in this

phase where you have a very large temperature factor for bismuth and bismuth only, it might

have been very informative if you could have done a low temperature single crystal study. I don't mean necessarily on the low temperature phase, which I assume you are probably planning

to do, but if you could have determined whether that was a real temperature factor or due to other considerations, like disorder or something.

A. W. Sleight : This has been done and unfortunately, it was hard to get everything in

this talk. We have measured intensity data as a function of temperature at about six temper i- atures below room temperature and we find that the tei.iperature factor of bismuth stays anom^

alously high all the way down. Of course below the transition we are not truly measuring a temperature factor anymore. However, the apparent temperature factor drops slightly when we

go through that transition. The drop is really within experimental error, I mean the temper

ature factor appears to drop 2.1 to about 1.8 through that transition. Our error is probably

greater than that change, but it's significant in that all the points lie on a nice line.

F. Jellinek : This high temperature factor of bismuth looks like what you could call a dynamic ferroelectric distortion. If this is so, you would expect an anomaly in the dielectric properties. I wonder whether you have done any measurements of that kind.

A. W. Sleight : Well, it's metallic so I don't think it-'s really possible to measure the

dielectric constant. I think a dielectric anomaly is what you would expect for an insulator

but for a metal I think this is exactly the kind of effect you expect to see. A break in the

resistivity curve at the Curie temperature could in fact be a peak in resistivity because

that could be where you have a maxim\am in the scattering. I don't think we can really measure a dielectric constant in a metal

.

E. Kostiner : Are your thermal parameters based on powder diffractions measurements or single crystals?

A. W. Sleight : They are based on powder diffraction data.

231
E. Kostiner : I think that the point made by Professor Post before is very important

here. Perhaps you should consider a single crystal structure analysis even at room temperature. You are measioring thermal parameters from very few data. You probably have a fairly

low data : parameter ratio and I question what those high thermal parameters really mean. Certainly you can get much more information out of a single crystal study.

A. W. Sleight: Well, I won't agree with that. I think it would be way over determined

in the single crystal. I think it's very adequately determined already. There is only one positional parameter to determine.

E. Kostiner: Are you sure about your stoichiometry (your occupancy factors)?

A. W. Sleight: The occupancy factor was allowed to vary at the same time that the temperature factor was allowed to vary and there was nil correlation between the two, and the oc- cupation parameter stays at one. Chemical analysis indicates that there is one bismuth for one ruthenium.

E. Kostiner : I believe that you should still investigate this possibility using single

crystal data.

iV. C. Stephenson : I was just wondering what sort of a scattering curve you used for the

bismuth

.

A. W. Sleight: Well, I don't remember. We've generally used both atomic and ionic and

I don't think in this case it made much of any difference but I don't really recall now.

B. Post: Was there any evidence of preferred orientation in the powder data? I mean

everyone talks about the programs , what about the data?

A. W. Sleight : No, there was no evidence for preferred orientation in the sample that we ended up using. I should perhaps point out that the single crystal photographs show ex^

actly the same trend as we see in the powder data and that we can compare the two. There

are reflections for which the cation contributions add and there are reflections for which

they subtract and you can see in the single crystal photographs that in bismuth ruthenate

these reflections are acting entirely differently as you go out in theta, in confirmation

of the powder data.

J. B. Goodenough : Just a quick comment. Certainly there is a difference between the rare earth ion and bismuth in that the bismuth ions have a lone pair . I wondered if you had

any information as to what the energy of the lone pair electrons was on the bismuth, relative

to the d-levels on the ruthenium.

A. W. Sleight : No, we don't have any evidence on that and I think that is something

that has to be considered. In the paper submitted in conjunction with this talk, I did

discuss the possibility of bismuth oxygen bands and I think this is something which can't

be ruled out entirely.

232
National Bureau of Standards Special

of 5th Materials Research Symposium,

Publication

issued July

364,

1972

Solid State Chemistry, Proceedings

PHASES IN THE SYSTEMS Ba0-Ni0-0-C02 AND BaO-CoO-O-CO^

T. Negas and R. S. Roth

National Bureau of Standards

Washington, D.C. 20234

Several new materials apparently related to the aragonite form of BaC0 3 and to the 2H

form of "BaNi03" were prepared at elevated temperature in air. The phases Ba3NiC^0g_y and

Ba3Ni2Cjj09_y ( [Ni+C] < 3) were prepared in powder and single crystal form. Both phases are hexagonal with a-axes related to the 2H "BaNi03" by a ; ^2}i^^' Single crystal x-ray and electron diffraction patterns of the Ba:Ni = 3:1 phase reveal c ; ^^2H* The structure was re- fined in space group P6 to R = 5.9% using 539 x-ray reflections. BaC03-3:2 (Ba:Ni) phase

composite crystals were prepared by decomposition of 3:1 phase crystals in air at 800 °C.

The structure for these composites is discussed. A similar 3:2 compound, Ba3Co2CjjOg_y , con- taining low-spin octahedral Co^''" , was prepared in powder form.

Although 2H "BaNi03" is not stable in air, single crystals of two phases near Ba:Ni = 1:1 were obtained. Both are rhombohedral with hexagonal a z ^211^^ and large c-axis multiplicities but exact stoichiometries are unknown. Two-layer-like forms of BaCo0 3_jj can be

prepared in air, however, below 890 °C. Similar phases exist at compositions slightly deficient in cobalt. A 12-layer form of BaCo0 3_j^ exists from 890° to 925 °C. It transforms to

a phase of unknown structure above 925 °C. The compound Ba2Co0i| , related to Ba2Ti04 , can be

prepared above 825 °C. Ba2Co0ij. has a reversible, non-quenchable , monoclinic J orthorhombic

inversion at 145 °C. The Co^+ is in a high-spin, tetrahedral , configuration.

Key words: Ba/Co-oxide phases; Ba/Ni-oxide phases; crystal structure; phase equilibria;

transition-metal oxides.

1. INTRODUCTION

Determination of phase relations in oxide systems containing transition metals is com- plicated by the familiar tendency of the metals to exist in variable oxidation states. Stoichiometry therefore becomes dependent on P[02]. However, the importance of other available

and possible components such as H2O and CO2 has been generally overlooked, especially in investigations at ambient atmospheric pressure. The systems BaO - "cobalt oxide" and BaO - "nickel oxide" provide excellent examples of these potential problems.

Subsolidus relations over a wide range of Ba/Me (Me = Co or Ni) ratios were deduced at

ambient atmospheric pressures and <1000 °C. Only the high baria portion of the nickel system

was investigated in any great detail. As the important Ba:Ni = 1:1 ratio was not studied at

temperatures >850 °C, phase relations are considered tentative.

Several Ba-Me oxide phases, especially at the 1:1 ratio, have been reported. Strauss

et al. [1]^ prepared cubic BaCo02 72 (a = 4.82 K) , a BaCo02^3i phase, and a cubic perovskite

BaCo02,23 phase (a = 4.072 A). The x-ray powder data reported for the cubic forms, however,

cannot be indexed completely on the basis of the a dimensions given. Gushee et al. [2] prepared BaCo02.85/ similar to BaCo02.72 [1]/ at 680 °C in air. They found that this phase

was hexagonal (a = 5.59 K, c = 4.82 K) rather than cubic, and that it was apparently isostructural with the "BaNiOs" phase reported by Lander [3,4]. This phase as well as, for

1 Figures in brackets indicate the literature references at the end of this paper.

233

;
example, BaMn03 [5] is commonly referred to as a 2H phase. It consists of two hexagonal

close-packed Ba0 3-layers perpendicular to c. Infinite strings, parallel to c, of face-sharing

oxygen octahedra containing transition metals further characterize the 2H structure. Recently,

Greaves [6] using thermogravimetric techniques, studied BaCo03_x-type phases at P[02] = 1.0,

0.10, and 0.316 atm in the range 350° to 1000 °C. Although his interpretation of the x-ray

data is improbable the gravimetric data appear to be reasonably reliable.

While the data for this study were in preparation for publication, Krischner et al. [7] reported the preparation of BaNi03 by oxidation of BaNi02 in flowing oxygen between 450-600 °C,

Their phase is hexagonal and of the 2H form with a = 5.631 K, c = 4.808 A. They also prepared

BaNiOx phases with x between about 2.75 and 2.55 at lower P[02]. These phases are similar

to BaNi0 3 but have considerably larger a and smaller c subcell parameters.

2. EXPERIMENTAL PROCEDURE

Various combinations of starting materials were used. Sources for BaO included spectrographic grades of BaC03 and Ba(N03)2- Spectrographic grades of 00301^ (calcined at 800 °C in

air), Co (NO3) 2 •6H2O and NiO provided the transition metal oxides. Weighed starting materials

were mixed under acetone, packed in Au trays and calcined at 750-800 °C for two weeks with

almost daily remixing. The 1:1 Ba:Co composition was also calcined at 1000 °C for 3 days,

followed by six weeks at 600 °C. Compositions formulated from nitrates were slowly (~l°/min)

heated from room temperature to the calcining temperature. Portions of the calcined materials were equilibrated in Au tubes within a vertical tube resistance-type quench furnace. After

sufficient heating they were quenched in solid-C02 or liquid-N2 . The temperatures were meas- ured with Pt-PtlO%Rh thermocouples calibrated against the melting points of NaC£ and Au. The quench furnaces were controlled by a-c Wheatstone bridge-type instruments capable of

maintaining temperature to at least ±2 °C.

Phases were identified at room temperature by x-ray powder diffraction using Ni-filtered

Cu radiation and a 1/4° 2e/min scanning rate. Interplanar d-spacings from x-ray powder diffraction measurements were used to compute unit cell dimensions by a least squares refinement

computer program. Unit cell dimensions are estimated to be accurate to within three standard

deviations. When obtainable, single crystals were investigated with an x-ray diffraction

precession camera. Quantitative intensity data were collected with an automatic diff ractometer

using MoKa radiation. Computer programs from The X-ray System, 1970 [8] were used for structural analysis and least squares refinement.

Chemical analyses for several phases were performed by a company independent of the

National Bureau of Standards.

3. EXPERIMENTAL RESULTS AND DISCUSSION

3.1. THE BaO- "COBALT OXIDE" SYSTEM

Subsolidus phase relations in air for starting Ba/Co ratios are shown in figure 1 which

was derived from the data of table 1. Chemical analyses for various phases are given in

table 2. As will become evident, the system is not binary, as O2 and CO2 must be considered

as additional components. Nevertheless, phase relations can be depicted in the simplest manner as a function of temperature and Ba/Co ratio.

3.1. a. Ba^CoO^

At the 2:1 Ba:Co ratio a red-brown phase of stoichiometry Ba2Co0tt exists from -790° to

at least 1050 °C. Above 1050 °C, which precludes use of Au, experimental difficulties are encountered as the material reacts with Pt-containers . At room temperature, the phase is

monoclinic with a = 5.909 K, b = 7.617 A, c = 10.406 K and 3 = 91°6.8'. Indexed powder data

are given in table 3. Ba2Co0it appears to be isostructural with Ba2Ti04 [9] which is a distorted form of the orthorhombic K2SO14 structure type. The transition metal has tetrahedral

coordination. A high temperature x-ray investigation showed that Ba2Co04 has a reversible,

non-quenchable, monoclinic to orthorhombic transition near 145 ± 10 °C. Magnetic susceptibility measurements to be published [10] are consistent with tetrahedral Co'^+(d^) in a high-spin state.

234
Table 1

SusDaxy of Subflolidua D^tM In Air For Ifie System

BaO-"Cobalt Oxlde"2/

Caopoaition Heat Treatment Phase Analysis

B«/Co ratio Temp. <°C) Time(hr)

7:3 721 432 BC + 3:2 phase

754 763

168

264

EC

BC

+ 3:2 phase +3:2 phase reheat of 890" specimen initially consisting of ortho.—Ba2Co04 (88)+ (tr.)BC

638 1344 tho.-Ba2Co04(BB)+ BC<tr.) reheat of 754''C specimen

890 166 ortho.-Ba2C0O4(BB)+ BCCtr.)

917 ortho.-Ba2Co04(os)+ BC(tr.) 953 264 ^rl-hn -R«->ro04(3S)+ BC{tr.) T^l 754

763

168

264 BC + 3:2 phase +3:2 phase reheat of 998*C specimen conBisting

of mono.-Ba2Co04

838

917 1344

144 no.-Ba2Co04

no.-Ba2Co04

reheat of 754"C specimen reheat of 998*0 specimen

953 264 no.-BajCoO^

976 168 no.-Ba2Co04

998 120 no. -BajCoO^

3:2 700

721

750

144

432 264

33

3

2 phase

2 phase

reheat of 750''C specimen

reheat of 763''C specimen

754

763 166

264

3

3 2 phase reheat of e90°C specimen oontaining mono.~Ba2Co04+{tr.) (1:1)bs

771 eoo

14448

3

3

2 phase

2 phase reheat of 836'C specimen containing mono.-Ba2Co04+ (tr. ) (1:1) ss 814 168 3 2 phase + (tr. )mono.-Ba2Co04

+(tr.) (l:l)fls reheat of 771''C specimen

3:2 phase not canplctely decomposed

B38 1344 ano . -Ba2Co04+ (1 : 1) ss

' reheat of 754°C specimen

884 96 3no.-Ba2Co04+(l:l)ss

890 168 3no . -Ba2Co04+ (1 : 1) ss 903 268 3no.-Ba2Co04+(l:l)ss

917 144 ano . -Ba2Co04+ ( 1 : 1 ) ss 935 144 jno.-Ba2Co04+(l:l)S3 reheat of 884°C Bpeclnen

953 264 ano. -Ba?CoC4+ {1 : 1) SS 29:21 721 754

636 890

953

432

168 1344

168

264

3

3 2(ss)+BaC03_j^ 2H-type 2(SS)+(1:1)SW=(1:1)SS

3no.-Ba2Co04+(l:l)s3

14:11 754

890

168

168

3 2(ss)+(l:l)xx=(l:l)3S

3nO.-Ba2Co04+(l:l)xX=(l:l)SB

53:47

754 166

3

3 2(ss)+BaCo03_j( 2H-type 2(S3)+(l:l)ss

' 763 264 3 2{ss)+(l:l)S3 reheat of 890*0 specimen

838 1344 ( 1 ; 1 ) 3 s+ { tr . ) mono . -Ba2Co04

890 168

953 264 YTj 600 240 BaCo03j2H-type rehVaVof a specimen "heated

4 dy at llOO'C

721 432 BaCo03_x,2H-type

763 BaCo03_jj reheat of 976''C specimen

771 144 BaCo03_x+ ( tr . ) 2H-type incomplete reaction

814 168 BaCo03_j. 814 168 reheat of 771 "C specimen

884

^^96 BaCo03_^

BaCoOj.x

890 168 BaCo03_j(+12-layer BaCo03_j( BaCoO incompletely deconpoaed

907 166 12-layer BaCo03_y reheat of 917"'C specimen

907 288 reheat of 890*0 specimen

917 144

917 144 reheat of 890*C specimen

935 144 12-layer BaCo03_j.+ unknown inccDplete dccamposltlon of 12-layer

BaCo03_^ phase

935 144 Incomplete decomposition of 12-layer

phase; reheat of 664*0 specimen

953 264 unknown BaCoO^.^ phase

976 168 976 168 reheat of 814*0 specimen

1003 192 reheat of ei4*C+ 976*0 specimen

903 268 12-layer BaCoO,,^* (1 :1) ss between 53:47 and 1:1

2:3 721 432 BaCo03_jj , 2H-type+Co304

763 264 BaCo03 +C03OJ reheat of 903 *C specimen

614 168

838 1344 864 96 903 288 12-layerBaCoO3_jj+Co304

935 144 unknown BaCoO,_ +C03O4 reheat of 884*0 specimen

953 264 976 168 +C0O

1003 192 +C0O reheat of 976*0 specimen

At

t include pr

, temperature

binary be- calc:

with atmospherii

ere heated in Ai

COj and O^.

BC » Ba003; (tr.) = trace; ss = solid solution) ortho. = orthorhoinbic ; mono. = monoclii

3:2 phase = carbon -containing oxide phase at 3:2 Ba/Co ratio. See table 2 for chemica

(l:l]gs - cobalt deficient oxide phases similar to those at BaiCo = 1:1. BaCo03-x> 2H-type = two-layer hexagonal, oxygen deficient phase. 2H-type = two-layer hexagonal f^ase. 12-layer BaCo03_x ° 12-layer hexagonal, oxygen deficient phase. un)mown BaCo03-x = oxygen deficient phase similar (but not identical) to a perovsitite • BaCo03_j, = oxygen deficient phases related to 2H-type structure (see text). illerite-like pha

235

/
Table 2

Summary of Chemical Analyses for Ba/Co - Oxide Phases

7o Analysis Formula 7o Calculated —

! ^

1 0.00 Ba^CoO,

c i 0.00 2 4

Ba \ 68.32 69.083

Co 14.48 14.822

0 16.095

Ba/Co \ 2.02 2.00

1

1 #1

2 c

1 0.00 BaCoOn

Ba f 56.61 600°C, in air 56.22

Co j 24.02 24.13

0 ? I 19.65

Ba/Co i 1.01 1 1.00

#2 f c 1 0.00

Ba > 55.56 BaCoO^

Co 23.11 #1 specimen

0 1 annealed in

Ba/Co 1.03 j 300-350° 1.00

#1 i C 1.37 1.75

Ba 61.27 ! 60.07

Co 16.93 1 Ba Co CO 17.18

0 20.14 j 3 2 9 20.99

Ba/Co 1.55 1 1.50

#2

C I 1.38 1 1.33

Ba 61.00

i ^^^°2S.75%.5* 61.05

Co V 18.06 17.46

0 f. 20.15

Ba/Co 1.45 1.50

; #3 ;

i C

i 1.71 1t

I Ba 61.10 s Co 17.61 1 0 Ba/Co 1.49 1.50 — Based on the proposed formulas.

The analyses are not unequivocable but appear to represent formulas

within these compositions.

236
Table 3

X-ray Powder Data for Ba2CoO^

.a/ calc hki- obs

170

287 577 502 446

201

156 3.068

3.051

3.016

2.953

2.739 2.713

2.600

2.565

2.466

2.416 2.336

2.284

2.272 2.258

2.178 2.140

2.118

2.051 2.009

1.9750 1.9509

1.9229

1.8975

1.8886 1.8134

1.7879

1.7839

1.7431

1.7296

1.7205 1.6981

1.6752

1.6461 1.5788

1.5322

1.5179

1.4769

5.181 4.284

3.576

3.501 3.448

3.201

3.156

(3.073\

\3.069) 3.050

3.017

(2.9661 (2.954 1 2.739 2.713

2.601

2.564

/2.467'J

< 2.462 > I2.452J

.416

.334

.287 1 .285 i2.282

12. 280) (2.272 \ \2.270 ( 2.258

2.176

(2.142) t2.138)

2.117 2.049 /2.008\

I2.OO7 / 1.9748

.9508)

.9504) 1.9228

1.8976 1.8890

(1.9508) (1.9504/

8133

78821 7874/

7838 i.7433

(1.7300) <1.7300>

(1.7270)

7202 6983

1.6749 1.6460

1.5782

1.5315

1.5180

1.4770

6

719

37 41

32

31

7954

55100

8 1210

26

35

8

7

21(b)

20(b)

8 1321(b)

15

1320

513(b)

10

99

8 16

1522

29

10

7 10

811

6

612

— Indexed on the basis of a monoclinic cell with a = 5.909±0.001 X, b = 7.617+0.001 A, c = 10.406i0.002 A, and B = 91° 6.8+1.2'.

(S) = shoulder

(b) = broad

237
1000

950

T(°C)

800

750

700

1

1 1

1 1 _ BaCOj

y IN BaCoOy

3a2Co04,

:(!(ss)

J oriho. nnono. ^Ba2Co04 145 -r .

1 [Poj=0.3l6atm],

1 AFTER GREAVES

-•

-

-2

• • •

1

1 1 • 1r

(1969) .J

(DISSERTATION) _

• _

• & •1 1 - — 3

tS*

1 b —2.50=y

- •

tho.

B' *—256—(i;i)ss *-

IS BojCoO^ + diDcc I ^ — 1 Co- OXIDE J

1

,

1 • • * i

' <- ' J + •

- . -ao° \

. BoCoOj-x I

1 PHASES *

-

1 \ BOjCoaCs-s) 1 -2.75 —

•

1 ^ —2.77 :

• _ BaCOj

+

: 1» • • \

1 \ —2.78 -

- • BojCoz

1l. . , "1

1

'

1 —Z82=y *

"

1 1" 60

^ 0% Co 100% Bo

55

Ba/Ba + Co(%)

50 45 40 JOO^Co

0%Ba

Fig. 1. Subsolidus phase relations in air for the system BaO-"cobalt

oxide". The system is not binary because of reactions with

atmospheric C02 and 02. Compositions are plotted in terms of

cation (%) of starting mixtures. (1:1) ss = phases similar to those found at the 1:1 Ba/Co ratio. See table 2 for probable

stoichiometries of indicated phases

.

• - quench runs , solid

o - unknown Ba/Co ratio near 1:1

When exposed to air (at room temperature) for extended time intervals Ba2CoOi^ is unstable,

reacting apparently with CO2 . Although BaC03 is easily identified as a decomposition product

the cobalt must remain in a non-crystalline oxide form as its presence is not evident in powder patterns. Near 790 °C, Ba2Co04 reacts with atmospheric CO2 to form BaCOs plus a phase

with Ba:Co = 3:2. The reaction is reversible but decomposition is so rapid that Ba2Co04 can- not be brought to room temperature by a "slow-cooling" process. In oxygen, Ba2CoOt^ does not

decompose.

Evidence for a Ba2Co0i+ (ss) region was obtained from Ba:Co = 7:3. The orthorhombic form

(plus a trace of BaC03) can be retained at room temperature. This indicates that the monoclinic orthorhombic transition temperature is lowered by addition of excess barium car- bonate. X-ray diffraction powder data for the orthorhombic phase obtained from the 7:3 com- position are given in table 4. A comparison of pertinent x-ray data for Ba2Co0i^ , Ba2Ti0i^

,

and K2S0tt [11] is provided in table 5.

The physical nature and magnetic properties of Ba2Co0i4 (ss) are siibjects for future investigation. It should be of interest to determine whether stabilization of the orthorhombic

solid solution is structurally accomplished by excess Ba or deficiency in Co content or is one involving stabilization by an additional component such as CO2 (i.e. - a BaCOs - Ba2Co04

solid solution)

.

3.1.b. THE 3:2 Ba:Co RATIO AND BaCoO^

Below about 810 °C in air a single phase material exists at Ba:Co = 3:2. Above 810 °C

it decomposes reversibly to Ba2Co0i4 plus a phase near the 1:1 ratio [shown as (l:l)gg in

fig. 1]. On each side of the 3:2 ratio two-phase assemblages exist except for a narrow solid

solution region in the cobalt-rich portion. This region is inferred because the unit cell of

single phase 3:2 and 3:2 in equilibrium with 1:1- type phases are similar but not identical.

238
Table 4

X-ray Powder Data for Ba CoO (ss)—

obs calc ''"obs

5 . 106 5.109 110 5 4 .250 4. 246 111 6 3.584 3.583 012 15

3.462 3.463 121 75

3.201 3.201 102 34

3.148 3.147 031 27

3.073 3.074 022 50

3.058 3.059 112 80

2 .975 2.977 130 88

2 .935 2 . 936 200 100

2.722 2.723 122 15

2 .589 2.590 040 8

2 .562 2 .562 032 20

2.472 2.472 013 30

2 .452 2 .453 041 6 2.422 2 .423 221 15

2 . 328 2 . 328 202 5

2 .278 2.278 113 16(b)

2 .272 2.271 212 20(b)

2 .147 2.147 231 23

2.124 2.123 222 38

2.050 2.049 033 15

2.000 2.000 051 12(b)

1.9541 1.9542 150 8

1 .9306 1.9303 232 21

1.8910 1.8912 213 20

1.8156

1.7916

(1.8158).

\l.8157/

1.7915

|104|_

1043)

024

10

15

1.7886 1. 7885 114 25

1 .7808 1.7 807 321 15

1.7418 1 . 7420 302 11

1 .7351 1.7347 143 28

1.7179 1.7179 312 17 1.7031 1.7031 330 8 1.6805 1.6805 233 6 1.6518 1.6512

J. • O 1 oo 1 A 1 Q 1 1 . D 1 7 X

1lOA11 1.5300 1.5301 341 5 1.4680 1.4682 400 12

^- Obtained from a 7:: 3 Ba: Co ratio composition. Contains a trace < which is excluded from the data. — Indexed on the basis of an orthorhombic cell with a = 5.873±0.001 A,

b = 10.362±0.003 A, and c = 7.637±0.001 S.-

(b) = broad

239
Table 5

Comparison of Similar A2BO4 Structure Types

Ba2Ti04 Ba2Co04 Ba2Co04{ss)— K2SO,

monoclinic orthorhomibc

Space Group P2i/n Pmcn

a (A) 6.12 5.909+0.001 5. 873±0 .001 5.772

b (^) 7.70 7.617±0.001 10. 362±0 .003 10.072

c (A) 10.50 10.406±0.002 7. 637±0 .001 7.483

e 93^8' 91° 6.8±1.2'

(Bland, 1961) (Swanson et al. 1954)

(this study)

— From a 7:3 Ba:Co ratio composition. Contains a trace of free BaCO

The powder pattern of the 3:2 phase, given in table 6, is of excellent quality and shows

no evidence of unreacted starting materials or other Ba/Co phases. It can be completely and

unambiguously indexed on the basis of a hexagonal cell with a = 9.688 A and c = 4.757 A. BaCo03 was prepared at the 1:1 ratio and 600 °C in air. This material was annealed at 300 - 350 °C as suggested by Greaves [6] to maximize anion content. The x-ray powder pattern, given

in table 7, represents the phases prepared in air and in O2 . Furthermore, magnetic susceptibilities [10] of both phases were identical within experimental error. The magnetic data

are consistent with octahedral Co'*+ in a low-spin state. BaCoOa was indexed on the basis of

o o a hexagonal cell with a = 5.648 A and c = 4.756 A. Based on the similarity of their cell

dimensions and line intensities, this phase appears to be isostructural with 2H BaMnOs [5].

The x-ray data are in particularly good accord with those of Greaves [6]. Our x-ray evidence,

however, does not support a doubling of the c-axis . Additionally, strong lines indicative of

the presence of cubic-type stacking are absent.

The powder patterns of BaCo03 and the 3:2 phase are strikingly similar as shown by

pertinent portions of each in figure 2. The similarity suggests that the 3:2 phase has a structure related to the 2H form. Several additional lines, however, appear in the 3:2

pattern which can only be accounted for by choosing a cell with the relations a2H*^3 = 23;

2

and C2H ~ <^3:2' This choice creates several problems involving the stoichiometry of the

phase and especially the oxidation state of Co. Chemical analyses (table 2) unequivocally

established the presence of carbon in the material and yield possible formulas ranging from

Ba3C02'^"'"Co . 75O3, 5 to Ba3Co2^''"C0g . The structural implications will be discussed later.

Magnetic susceptibility data [10] are not identical with those of BaCoOs but remain consistent

with octahedral, low-spin, Co^. Electron diffraction data confirmed the a2H'^3 = <33:2 relationship but also suggested that the true c-axis is at least four times that determined

from x-ray powder data.

3. I.e. BaCoO, AND (1:1) PHASES

3-x ss BaCo03 releases oxygen to form BaCo03_x-type phases from 600 °C to near 740 °C. As

shown in figure 3, a increases while c decreases slightly with increasing temperature. Powder

patterns show very little change from 2H BaCo03. If the gravimetric data of Greaves 16] are nearly correct the maximiom value of x in BaCo03_jj must approach -0.20 for this series. A

second series of BaCo03_jj phases appears above 740 °C. As shown in figures 3, 4, 5, and 6 this series is characterized by an abrupt increase in a and decrease in c near 740 °C. The

240
a dimension remains essentially constant while c gradually decreases up to about 890 °C . The

gravimetric data of Greaves suggest that x varies from -0.20 to 0.35 in this range. From

powder data alone it cannot be ascertained whether this second series represents an oxygen

deficient solid solution or a series of discrete, ordered, 1:1 phases. It is clear, however,

that for either case the basic structural framework is a close packing of Ba and 0 atoms similar to the 2H structure. Furthermore, the a and c parameters shown in figure 3, represent

those of a subcell. Each phase, however, has at least two weak-medium intensity x-ray lines

in the vicinity of d = 1.97 A and 1.54 A. As their exact position is temperature dependent,

they are not considered to be lines of a second phase. They cannot be indexed on the basis of

a simple 2H cell. Recently, Krischner et al. [7] reported a similar phenomenon for BaNiOs.j^

phases. Their subcell a-axes remained essentially constant (5.705 A) while subcell c decreased

from 4.335 to 4.311 A between x = 0.25 and about 0.45.

As shown in figure 1, a second 'BaCoO-^_y. series extends to Co-deficient compositions.

This region, labelled (l:l)ssf extends to temperatures at least 60 °C above the last similar

phase observed at the 1:1 ratio. The dashed solvus curve was placed between Ba/Co = 53/47

and 1:1 as the former was always a two phase assemblage. From powder patterns of the 53/47

ratio, siibcell parameters were calculated for the (1:1)^^ near the solvus. As shown in figure 3, a remains relatively constant to 953 °C while c decreases with increasing temperature.

Although (1:1) ss patterns are similar to BaCo03_jj it is clear that the corresponding a and c subcell parameters are significantly different. As in the case of BaCo03-x it remains unclear

whether the (l:l)g3 region includes a series of Co and oxygen deficient solid solutions or re- presents a series of ordered compounds. For convenience a solid solution series is depicted

in figure 1. Table 6 a/

X-ray Powder Data for the 3:2 Ba:Co Ratio Phase —

d , d -, hki — '"ob s

.

obs, calc .

8.402 8.390

3.392 3.394

2.797 2.797

2.422 • 2.422

2.379 2.379

2.328 2.327

2.158 2.158

2.135 2.135

1.8309 1.8310

1.8125 1.8120

1,7087 1.7088

1.6970 1.6971

1.6146 1.6147

1.5068 /l.507l\

( 1.5070f

1.4963 1.4963

1.4509 1.4509

1.3985 1.3984

1.3361 1.3360

1.3266 1.3267

1.2930 1.2930

1.2055 1.2055

1.1985 (1.1987\

\l.l986/

100 14 111 94

300 100

220 7 002 10

310 4 221 77 112 19 410 4 302 11 411 30

222 18

330 20

113)

8 .510/

322 3 412 13

600 18

332 5 223 7 521 14 602 5 f413\ 7 [530/

004 3 441 6 522 7 304 3

1.1894 1.1893

1.1735 1.1736

1.1700 1.1698

1.0945 1,0945

See table 2 for chemical analysis data.

b/ ° — Indexed on the basis of a hexagonal cell with a = 9.688±0.001 A and

c = 4.757+0.001 A.

241

465-504 O - 72 - 17
Table 7

X-ray Powder Data for BaCo03—

d

obs

.

calc

.

I , obs

.

3.409 3.410 101 66

2. 825 2.824 110 100

2.447 2.446 200 iu

2. 378 2. 378 002

2. 174 2 . 175 201

2.140 2. 139 102 31 1.8192 1.8191 112 •7 1.7227 1.7232 211 20

1.7049 1. 7050 202 20

1.6306 1.6305 300 15

1.5078 1.5082 103 6 1.4592 1.4596 212 12 1.4124 1.4120 220 12

1.3305 1.3304 203 5 1. 3042 1. 3046 311 7

c/

— Prepared at 600 °C in air and annealed in

oxygen at 300-350 °C. —/ Indexed on the basis of a hexagonal cell with

a = 5.648+0.001 A and c = 4.756±0.001 A. c/— All peaks are broad.

Fig. 2. Portions of x-ray diffraction powder patterns illustrating

the similarity between the 2H-type BaCo0 3 and the carboncontaining compound existing at the 3:2 Ba:Co ratio.

242
5.72

5.70

5.68

a [A]

5.66

5.64

T 1 r T i

1 1 1 a Ba;Co

(53/47) o—0-0--0- —BaXo

° II Cn=6

Ba:Co (11)

c Ba:co(i:i) /

n=l >^

n=l "° Ba Co . (53/47)

_L

-4.80

4.70

460

c/n(^)

4.50

4.40

430

600 700 800 900 1000

T(°C), IN AIR

Fig. 3. Variation of a and c parameters of quenched 1:1 BaCo03_x-type

and (1:1) -type phases. The latter were determined from the

53/47 Ba/Co ratio which is in a two phase field (see fig. 1)

.

All parameters above 750 °C represent subcells except the a associated with the symbol A .

)

(101) (110)

77l°C/6days

IN AIR

a = 5.707 &

c = 4.527 K

' ^' subcell

T

1 1 r

(101)

72rC/l8days

IN AIR

a = 5.661 K

C=4.7I8 A

-J I I \ I

I I 26 28 30 32

' 3? 39 Ba/Co=|:| 29,CuKa

Fig. 4. Portions of x-ray diffraction powder patterns illustrating

the changes in BaCo03_x from 721 °C to 771 °C in air.

243
"1—I—

r

(201)

1—

r

1—I—I I r

(101) (110)

838 °C/56 days

IN AIR

a =5.707 A

.c = 4.504 A

subcell

T—

r

(102)

26 28 30

Ba/Co 20,CuKq

Fig. 5. Portions of x-ray diffraction powder patterns illustrating changes

in BaCo03_3j from 814 °C to 838 °C in air. Compare with fig, 4.

1 1 1 1 1 1 1

(107) 907 °C/ 7 days

1 1 1

(110)

1" 1 1 1 1 1 1 1

(207)

1

IN AIR

hex. a = 5.664 A

c = 28.496

A

"J^'

(106)

(108)

(205)

(203)

1 (0.0J2) (101?) A

A (204) 1 (206)),

"T ' I I—I—I—nn—I—I—I

\—

r

(201)

aSI'CMdays

IN AIR a = 5.707 X

c

subcell (002)

(200) » /

(102)

J 1 1 1 1 1 1 I I I L,iJ I I I I I II I 22 24 26 28 30 32 36 38 40 42 44

Ba/Co=l:i 2e,CuKa

Fig. 6. Portions of x-ray diffraction powder patterns illustrating

the transformation of a 2H-like BaCo0 3_jj to a hexagonal

twelve-layer BaCo03_x phase. Compare with figs. 4, 5.

244
Near 890 °C and Ba:Co = 1:1 a sluggish transformation to a third modification occurs as shown in figures 1, 3 and 6. X-ray diffraction powder data are completely indexed on the

basis of a hexagonal cell with a = 5.664 A and c = 28.496 A in table 8. Based on the a dimension which is typical of a close packing of Ba and 0 and assuming an average thickness of

about 2.4 X for a Ba03-type layer it is suggested that the compound is a 12-layer (12 x 2.4 = 28.8 A ; c) form of BaCo03_jj. Furthermore, the appearance of the powder pattern strongly

suggests that the stacking is of the mixed hexagonal-cubic type rather than purely hexagonal.

The International Tables for X-ray Crystallography [12] lists 42 possible hexagonal (non-rhombohedral) cases for the stacking of 12-close-packed layers. Until powder pattern intensities

for each case are calculated or single crystals are available the structure cannot be assigned

unambiguously.

Above approximately 925 °C the 12-layer form transforms to yet another modification

which is stable to at least 1000 °C in air. Powder data for this phase are given in table 9. The data resemble that for a perovskite or brownmillerite-type phase but cannot be indexed on either basis. The phase slowly deteriorates upon exposure to air at room temperature.

3.2. THE BaO - "NICKEL OXIDE" SYSTEM

Portions of the nickel system were investigated in air partly for the purpose of preparing an analogous 3:2 Ba:Ni phase and partly to prepare other possible carbon-containing

phases. From structural considerations to be later discussed it became apparent that a phase at Ba:Ni = 3:1 might exist. Very little work was done with Ba:Ni = 1:1, a particularly

formidable and entirely separate project. The system as shown in figure 7 therefore represents subsolidus relations only in air and is incomplete with respect to 1:1. Some of the

data points (table 10) represent conditions under which single crystals were grown.

3. 2. a. THE 3:2 AND 1:1 Ba:Ni RATIOS

At the 3:2 Ba:Ni ratio a phase analogous to that of cobalt is easily prepared. The powO der pattern given in table 11 was indexed on the basis of a hexagonal cell with a = 9.671 A,

c = 4.836 K, The phase is pseudocubic and suspiciously similar to Lander's [3,4] BaNi03

{3 = 5.580 K, c = ^'^-^^ A). If the a dimension reported by Lander is multiplied by /3 the new

cell with a = 9.665 A would strongly resemble that herein reported. Furthermore, Greaves

[6] reported the formation in air of what he considered to be a 1:1 phase with a = 5.596 A,

1200

II 00

1000

TCC)

900

8001-

J. L WARING \ PHASE (X)

NiO

PRECESSION PATTERN PHASE (X) a= 10.0 I& = 5.78y3~

c =38.38^=4.26X9

LAUE = 3m

RHOMBOHEDRAL

PRECESSION PATTERN PHASE (?) 0=9.69^ = 5.59/3"

c =I2.79A =4.26X3

LAUE = 3 m

RHOMBOHEDRAL

BajNij -NiO

BojNij BaCOj

BqO

80 60

Ba/BoK

40

Ni (%) 20 NiO

Fig. 7. Phase relations (incomplete) in air for the system BaO-"nickel

oxide". The system is not binary because of reactions with

atmospheric O2 and CO2 . Compositions are shown only in terms

of cation content. See table 12 for probable stoichiometries

of Ba3Ni- and Ba3Ni2-oxides . Single crystals of phases (X) and phase (?) were grown under conditions shown in the figure.

245

/
Table 8

X-ray Powder Data for the Twelve-Layer

Form of BaCo03_^ ^/

obs

.

4.037

3.720

3.411

3.131

2. 883

2.832

2.463

2.416

2. 374

2. 320

2.252

.180

,137

,101

,036

2.020

2.010

1.8800

1.8590

1.8196

1.7942

1.7632

1.7060

1.6874

1.6526

1.6446

1.6353

1.5829

1.5662

1.5076

calc.

hk£:b/

4613

4342

4160

3705

1. 3467

1.3081

1.2904

1.2794

1.2160

040

718

412

132

882

832

464

417

2.375

2. 375

2.319

2.253

2.179

2.137

2.101

035

020

009

8800

8589

8197

8196

1.7942

7630

7060

6872

6528

6446

6351

5831

5663

5077

5076

4614

4342

4160

3706

3467

3467

1.3079

3078

2903

2795

1.2162

1.2162

104

105

106

107

108

110

1,0,10

202

'0,0,12'

204

205

206

1,0,12

207

0,0,14

208

1,1,10

1,0,14

2,0,10

) 213 » ^1,1,12'

214

215

2,0,12

217

1,1,14

218

300

0,0,18

2,0,14

12,1,111

*1,1,16'

2,1,12

1,0,19

220

2,1,14

'3,0,12'

•l,0,2l'

317

2,0,19

'2,2,12 '

obs

.

4(b)

12

1162

10

100

5(b)

3

3 13

5

8 40

89(b)

9(b)

10

57(b)

3(b)

3(b)

1024

3

5 18

35(b)

5

5 19

5

3(b)

10

54(b)

a/

b/

Prepared at 907 °C in air; x in BaCo03_x

unknown

.

Indexed on the basis of a hexagonal cell with

a = 5.664±0.001 K and c = 28.496±0.004 K.

(b) broad

246
Table 9

X-ray Powder Data for BaCo03_j^ Above 925 °C in Air.

obs

3

oJds

4. 15 10

4.01 3 3.36 8 2.914 100 vb

2.882 25 s,l 2.842 20* b

2.577 8 b

2. 382 11

2. 208 7 2.069 15

2.052 15

1.937 14 1.835 6 b

1.751 6 b

1.686 15

1.614 7 b

1.456 7 b

1. 334 5 vb

1.212 5 vb

1.119 5 vb

./

— This is a poor powder pattern, a characteristic

of this phase. The pattern further deteriorates

with time.

b = broad/ vb = very broad, s = shoulder

* Increases to this intensity from a much weaker,

broad line upon long exposure to ambient conditions.

247
Cl Da & D. + M -P -H (1) <D £ C O QJ (U U

10 a) (1) -H >,

t/1 U) o ^

•H -H

C >, z z 3 U

C 4J -P -P -H H 10 ro 3

10 J3 o P (1) 0) -H C m w o o 0 fO n3 -H -t-) u j:: x: -p u) 1 a ft CO u -3 CP CT" (0 C C 01 H -H C O

fO 4-1 -P -rH -H

01

CC

X !<

H

OOO

O

OO I I >i I I H H

.H

C

C 2 2 O — O O

10 rO - - H

,H nH 73

(0 fO <U 01 ' C C J= £ 0 0 0 0

CP Di ^ to 10 g

g

XX o o

(1) <u j:: £ g m " " " " o o a> (D ^ ^ o o ft Ul o. X

i4 to (0 (0

— ^

CO x: x:

4-1 Oi

a <u <u < II mm t-( CM to to

•• j= x:

1^ cu 0.

248
Table 11

X-ray Powder Data for the 3:2 Ba:Ni Ratio Phase—

obs

.

calc

.

hki-"^ "^obs

8. 378 8.375 100 14

4,837 4.835 110 2 3.420 3.419 111 100

2.792 2. 792 300 92

2.418

2.418 J 2.418

2201

002 '

2. 322 2,323

12.323

1021

310' ^

2.163

2.163 J 2.163

f 2.094

112,

221*

i202

/ 0

2.094 2.094

'2.094

311|

400

5

1.9215

,1.9216

'1.9214

j212.

'320'

•J

1.8277 < fl.8278

U.8276

302I 1410

)

J. *i

1.7099 (1,7097 ^ 1.7096

1222^ Ullj

1.6122 1.6118 3 30 18

1.5290

11.5293

(l,5291

(1,5043

jll3l

j331

1

322

7

1.5043 1,5042

(1.5042

421

510

3

1.4578 1.4580 412 13

1.3958 1,3958

1.3412 (

600

223

14

1.3413 1.3412

1. 3411

332

520

10

1.2925 1.2923

1.2090

j

521

004

12

1. 2088

1.2090

1.2089

1.2088 1 1,1729 (

413

602

440

114 1

11

1.1728 1.1728 < 1.1728

522 ^ 441 - 11

1.1092 ||-|°^^ '1.1093 '710' 4 1.0814 224

1.0811 1.0812

1.0812

442

711

8

1.0551 1.0552 630 6

1.0307 1.0310 J 1.0309

5231

63lf 3

1.0082 ,1,0084

'1.0083

414>

712* 3

— See table 12 for chemical analysis data, — Indexed on the basis of a hexagonal cell with

a = 9.671 0.001 & and c = 4.836 0.002 A. The

phase is pseudocubic,

249
c = 4.847 A. This phase was admixed with BaC0 3 + NiO. If his a were multiplied by /3,

^new ~ 9.692 A, the cell would again resemble the 3:2 phase of this study. Since both 1:1

and 3:2 phases exist in the cobalt system, the 1:1 ratio was investigated below 850 °C. If

the 3:2 phase is truly of 1:1 stoichiometry an additional phase such as BaC0 3 should be

apparent in powder patterns. This is not the case. If the phase is of 3:2 stoichiometry

then a possible 1:1 phase should be similar to BaCo03. If BaNi03 does not exist, the 1:1

composition must then consist of 3:2 plus free NiO. The portions of powder patterns shown

in figure 8 clearly demonstrate the latter case, with free NiO evident in both the 1:1 and

1:2 Ba:Ni ratio patterns. Although some of the NiO lines are nearly coincident with those

of the 3:2, the (220) line of NiO is clearly present in the compositions richer in Ni. It

is therefore concluded that at least in air or in an oxidizing atmosphere containing a sufficient P[C02], BaNi03 is unstable. Further evidence for this was obtained from an experiment involving the compound BaNi02 [3,4]. At 20,000 psi air and 600 °C this compound

instead of oxidizing to BaNi03 decomposed completely to BaC03 + NiO. The CO2 pressure was sufficently increased to prevent even the formation of the 3:2. Additional evidence for

the behavior of BaNi03 was provided by preparing the compound at 810 °C and 1000 psi oxygen.

Cell parameters for this phase which has a powder pattern shown superimposed on that of

3:2 in figure 8, are a = 5.631 A and c = 4.797 A. Greaves [6] prepared a similar phase at low temperature in flowing O2 . His phase, also different from that which he prepared in air,

has a = 5.637 K and c = 9.618 The c-axis was doubled (4.809 A x 2) because of several

weak lines in his powder pattern. Our patterns do not show these lines nor is the phase

(even with a doubled c) isostructural with the 4H form of BaMn03 [5] as suggested by Greaves.

Recently, Krischner et al. [7] prepared BaNi03 with a = 5.631 A, c = 4.808 & in O2 . The

data of Greaves [6], Krischner et al. [7], and this study for BaNi03 are consistent with

our view that the phase observed in air is the 3:2.

Electron diffraction data for the 3:2 phase confirmed the a/3 axis but showed streaking

and additional spots along c* indicating at least a doubling of that axis. Chemical analyses

(table 12) unequivocally established the presence of carbon in this phase. The composition

appears to lie near Ba3Ni2C08 although Ba3Ni2C09 is not precluded. The first (or possible

formulas intermediate in oxygen content) suggests the presence of Ni^+ or perhaps a disproportion to Ni'*+ and Ni^"*". Magnetic susceptibility measurements by Lander [3] on his "BaNi03"

T—I—I—I—I—

r

BaNiO,

(221)

(112)

GRE4VES(I969) LANCER (1951) (THESIS) P6jmc(PSEU00CUBIC) AIR a = 5.580 2 5.596 5.637 ] + a/T' 9.665 I 9.692 BaCO,

c = 4.832 I 4.847

1 &

4.809(i2)J NiO

KRISCHNER eial(l97l) THIS LAB. a = 5 631 0=5.631

c = 4.808 c = 4797 SlOWhrs/IOOOpsiOj

(Prep.byJ.L.WAfilNG)

(220)

(002)1 +

NiO

Ba/Ni=|:2

800°C/AIR

29, Cu Ka Fig. 8. Summary of x-ray diffraction powder data for "BaNiOs" and the

3:2 Ba:Ni ratio phase. Compositions Ba:Ni = 1:1 and 1:2 show

free NiO. The dashed overlay pattern in the bottom powder

pattern represents BaNiOs (this lab)

.

250
Table 12

Chemical Analyses for Ba/Ni-Oxlde Phases

% Analysis Formula Calculated

3:2 Ba/Nl Phase

H9O -- CO2 6 .96 6.57

BaO 67.98

XJCt TIN 68.72

NiO 22.67 22.32

0 -- or

2.39

Ba/Ni 1.46 1.50

Ni/C 1.92 2.00

COp Ba2Ni2C0g 6.42

BaO 67.11

NiO 21.80

0 4.67

#1 3:1 Ba/Ni Phase

C 2.52 2.48

Ni 10.30 *Ba|^2Ni4C503o 9.69

\jI INI 1,20

#2

c 3.03 *Bai2Ni4C503o 2.96

Ni 10.29 9.64

C/Ni 1.44 1.50

1/ Based on the proposed formulas.

Possible formulas indicating between 5 and 6 carbons per unit cell.

See structural discussion, of 3:1 Ba/Ni in text.

suggested a moment corresponding to 0.8 unpaired electrons. Greaves [6] and Krischner et al.

[7] , however, found their BaNi03 to be diamagnetic as might be expected for octahedral Ni'*'*' (d^) . This discrepancy is understandable if Lander really measured a phase containing the

non-diamagnetic (d^) ion Ni^"^. His x-ray and magnetic data appear to be more consistent with

the 3:2 phase of this study.

3.2. b. THE 3:1 Ba:Ni RATIO

Above 875 °C, the 3:2 phase decomposes reversibly in air to an unidentified phase near

1:1 and a reddish-brown (in fine powder form) phase with a 3:1 Ba:Ni ratio. This latter ma- terial has a reversible minim\im in air near 825 °C, decomposing to BaC03 plus the 3:2 phase.

The x-ray powder pattern given in table 13 was completely indexed on the basis of a hexagonal

cell with a = 9.587 A and c = 4.880 A. The portion shown in figure 9 clearly shows the apparent similarity with the 3:2 Ni and Co phases as well as with the 2H BaCo03 structure.

Cell dimensions for the 3:1 phase show a larger c and smaller a by comparison with the 3:2.

The compound melts incongruently above 925 °C in air to a solid phase (?) , possibly near 1:1,

plus a liquid which is especially reactive with Au containers. Chemical analyses (table 12)

clearly established the presence of carbon in the compound and suggest the ideal formula to be between BasNiC^ .25O7, 5 and Ba3NiCi ^ 503 .25 or Ba2NiCi _ 5O7 _ 5

.

3.3. SINGLE CRYSTAL GROWTH AND ANALYSIS OF Ba/Ni PHASES

3. 3. a. PHASE (?)

Small black crystals (<0.1 mm) of a phase (?) were easily grown by melting the 6:1 or

3:1 ratios above -925 °C [within the primary field of phase (?) ] . Precession photographs re- vealed that this phase is rhombohedral (Laue = 3m) with a = 5.59 /3 = 9.69 and c = 4.26 x

(3) = 12.79 A. The cell dimensions and subcell suggest a similarity with 2H BaNi03_jj and

the l:l-type Ba:Co phases previously discussed. From powder patterns and without evidence

251
Table 13

X-ray Powder Data for the 3:1 Ba jNl Ratio Phasea/

obs. calc

.

I , obs.

8.292 8.303 100 34 4.792 4.793 110 13 3.415 3.420 111 100

2.765 2.767 300 63

2.441 2.440 002 6 2.396 2.397 220 12 2.302 2.303 310 8 2.174 2.175 112 11 2.150 2.151 221 52

2 .079 j2.082(

J2.076(

(3111

<400' 4(b)

1.9259 1.9263 212 3 1.8309 1.8303 302 14 1.8121 1.8118 410 5 1.7746 1.7744 321 2 1,7099 1.7099 222 8 1.6990 1.6985 411 23

1.5976 1.5978 330 16

1 .5705

jl.5720j

)1.5691

(5011

U20' 4(b)

1.5406 "1.5405 113 5 1.5019 1.5015 322 3(b)

1.4934 1.4938 421 3(b)

1.4545 1.4547 412 8 1.4258 1.4261 511 3 1.3841 1.3838 600 7

1 . 3454 1.3460 223 3(b)

1.3371 1.3368 332 2 1.2829 1.2827 521 11 1.2663 1.2661

J 610 2(b)

1.2097 )1.2104

)1.2071

|413.

\ '104' 4(b)

1.2033 1.2037 602 5 1.1672 1.1675 522 3 1.1638 1.1638 441 5

— See table 12 for chemical analysis data.

Indexed on the basis of a hexagonal cell with a = 9.587±0.001

and c = 4.880+0.001 K. Single crystal precession pictures

indicate that the true c-axis is (4.880) (2) = 9.760 A.

(b) = broad

252
(—),

1—I—I—

r

(101),

'2H ^""'2H Ba/Ni = 3:l 875°C,IN AIR

hex. a = 9.587 A

c = 4.880 A

J I I 1_ 10 26 28 30 32 37 39 41

25, Cu Ka

Fig. 9. Portion of the x-ray diffraction powder pattern for the 3:1 Ba:Ni

ratio phase illustrating its similarity with 3:2 Ba:Ni and Co and

2H-type phases. Compare with figures 2 and 8.

of superstructure lines Krischner et al. [7] suggested that phases between BaNi02.73 and

BaNi02.55 are rhombohedral with tripled subcell c-axes (4.355-4.311 &x3) and subcell a-axes

(5.705 A) which are multiplied by /3. If our phase (?) is a (1:1) or even near a 1:1 ratio

in composition it appears that Krischner et al. made a rather good educated guess about their

powder patterns. Our precession photos clearly show superstructure spots. All crystals ex- amined, however, are twinned with variable twin volume ratios.

3.3.b. PHASE (X)

Unrelated to the "in air" equilibria is an experiment conducted using the 1:1 ratio.

This was heated at 1175 °C (3 weeks) in a sealed Pt-tube and quenched. Resulting products

were black single crystals (<0.1 mm) of a phase (X) and considerable quantities of NiO plus

a white amorphous material. Precession photos of phase (X) are similar to phase (?) . The

material is rhombohedral (Laue = 3m) with a = 5.78/3 = 10.01 A but with c = 4.26x(9) ~ 38.38 A,

3 . 3 . c . 3:1 CRYSTALS

By heating compositions more Ba-rich than 3:1 within the primary field of the 3:1 phase

(see fig. 7), small hexagonal prisms (<0.1 mm) are easily obtained. Precession pictures show

6/m Laue symmetry. With no extinctions, possible space groups are P5, P6 and P6/m. Furthermore, the c-axis is doubled, c = 4.880 x (2) = 9.760 A, although this is not evident in x-ray

powder patterns (see table 13) . The a and c parameters were confirmed by electron diffraction

3.3.d. TRANSFORMATION OF 3:1 to "3:2 CRYSTALS"

Crystals of the 3:2 phase could not be grown by conventional techniques as the phase has

a decomposition maximum at relatively low temperature. Crystals of the 3:1, however, were

available. As the 3:1 has a decomposition minimum, the 3:1 crystals were heated at 800 °C within the stability field of BaC03 plus the 3:2. The idea was based on the ass\xmption that

since the 3:1 and 3:2 phases appeared to be structurally similar there was a good possibility

that BaC03 would segregate or diffuse from the 3:1 leaving the 3:2 phase in essentially single

crystal form.

The transformation (followed by powder and single crystal patterns) , was completed

within 15 days. Within the first day, the 3:1 crystals did not transform to 3:2 but seemingly

changed to the higher hexagonal Laue group 6/mmm. This conclusion ultimately proved incorrect

after x-ray intensity data using an automatic ditrractometer were collected. For example.

253
although the (.hkl) , I = odd data showed equivalency consistent with 6/inmin Laue synunetry, the

(hkl) , I = even data remained consistent with 6/m. A Laue group check using 2507 measured

x-ray reflections and a sorting - averaging routine for equivalent reflections (written by

Dr. A. D. Mighell, National Bureau of Standards) yielded an R = 1.6% for equivalent reflections based on 6/m. It was concluded that a symmetry change does not occur since the agreement factor in 6/mmm was 11%. At this time we do not understand why the 3:1 when annealed

at lower temperatures (even at 350 °C for 10 min.) exhibits rather large x-ray diffraction

intensity changes particularly for (hk£) , I = odd. The intensity changes are continuous

with annealing time.

With continued heating the 3:1 crystals slowly transform to BaCOs and what appears to be

the 3:2 phase. The precession pictures (figs. 10, 11, 12) for the transfomned crystals are noteworthy in that they consist of intergrowths or at least oriented domains of BaC0 3 intergrown with the 3:2 phase. If the additional spots shown as BaCOs in figures 10, 11, and 12,

belong to the 3:2 phase unusually large a and c axes must necessarily be chosen. Fortunately,

the extra spots were easily identified by their d-spacings as the strongest reflections of

BaCOs. These are also somewhat streaked indicating that BaCOs probably not truly single

crystal in nature. Significantly, the a and c axes of orthorhombic BaCOs coincide with a*

and c* of the 3:2. The i>-axis of BaCOs coincides with an [hhO]* direction. The assemblage

is an oriented, intimate intergrowth of two phases. The cause of this assemblage is the ex- perimental conditions imposed for crystal growth. Although a 3:1 single crystal initially more Ba-rich than 3:2 must exsolve BaCOs to form a two phase assemblage, BaCOs simply does

not diffuse to the crystal surface but remains as domains or perhaps as an intracrystalline

growth with 3:2. Structural implications will be discussed in following sections. Neglecting the spots belonging to BaC03, the remainder of the precession pattern is consistent with

the powder data for the 3:2 phase. The Laue symmetry appears to be 6/mmm. No superstructure

along c* is apparent. The x-ray pattern of crystals which were powdered showed BaC03 plus

the 3 : 2 phase

.

4. STRUCTURAL CONSIDERATIONS

4.1. GENERAL

It is possible to account for the chemistry, thermal behavior, and possible structure of

non-1 :1 type phases by considering the structure of the 2H modification. The structure of a 2H-type A^+B^+Os is shown as the cell with the shortest a dimension in figure 13. Ideally

the cell contains the formula A2B2O6 . The space group is P63/mmc or P63mc. Typical a and c dimensions are -5.7 A and -4.8 K respectively. A larger hexagonal cell with a' related to a by the factor /3 and with a content AgBgO^g can also be chosen as shown. Tfiis unit, of

course, is not the smallest repeat unit consistent with ABO3 stoichiometry , although it could

become the real unit cell if the stoichiometry and particularly the A/B ratio were varied.

The two simplest ways of achieving the aj/3 configuration, starting for convenience with

A5B5O18 stoichiometry are:

a) "removal" of the two Me (B) cations from the corners of the a/3 cell or

b) "removal" of the four Me cations from the 1/3 2/3 z and 2/3 I/3 z sites.

The resulting ideal stoichiometries which would justify the choice of an a/3 cell are

AgB[^0]^3 and AgB20i3. These are not satisfactory with respect to oxygen content as charge

compensation must necessarily be accomplished by increasing the charge of the transition metal (B) . The formula Ag+Bi^0i8 requires a while A2+B20jg requires a b12+. Both clearly

are unrealistic. To maintain a b'++ oxygen vacancies can be hypothesized yielding AgBi^O^^^

and AgB20]^g stoichiometries. The resulting structures would be skeletal in nature with quite

large voids. This mechanism is not particularly feasible. The only remaining possibility is

the incorporation of an additional component which, a) would permit the B cation to exist in

a reasonable oxidation state and, b) would coordinate with available oxygen to preclude large

structural cavities. The 3:2 (6:4) Ba:Ni (and Co) and 3:1 (6:2) Ba:Ni phases have the two

simple A/B ratios described. Furthermore, these phases are characterized by /3-type cells.

The only missing link is the identity of the additional component. From the known affinity

254
Fig. 10. X-ray precession photograph, hko view, of a BaC03 - 3:2 Ba:Ni

composite crystal. The a* directions for orthorhombic BaC03

and the hexagonal 3:2 coincide while b* for BaC03 coincides

with one of the [hho]* directions (unfiltered Mo radiation).

255

/
Fig. 11. X-ray precession photograph, hO£ view, of a BaC03 - 3:2 Ba:Ni composite crystal

The c* directions for both phases coincide. The (204) of BaC03 is very very

weak (unfiltered Mo radiation)

.

256
Fig. 12. X-ray precession photograph, hhl view, of a BaCOs - 2:2 Ba:Ni composite crystal.

The c* directions of both phases coincide and (hhi) spots for orthorhombic BaCOs

are present (unfiltered Mo radiation)

.

of BaO for CO2 and from the structural nature of BaC03, it appeared likely that this component was CO2 . Chemical analyses later verified this assumption. Consider the dashed-line

cell in figure 13. The unit cell outlined may be regarded as being orthorhombic with

^ortho. ~ '3hex.' ^ortho. = '^hex.^^, and c^^^Yio. = <^hex. This cell is nearly identical with

that of the structure of BaCO^ which has a = 5.314 K, b = 8.904 K, and c = 6.430 A [11] . The

Me cations must be removed from the centers of the face-sharing octahedra and replaced with

carbon within the triangular oxygen groups. Except for an expansion of c from ~4.8 K to 6.430 K necessitated by, a) the tendency of parallel CO3 groups to maximize their separation

and, b) the "staggering" of adjacent CO3 units to form "puckered" oxygen layers, the disposition of atoms in figure 13 is similar to aragonite . It is also obvious that for a close

packing of large A cations and oxygens, space is inherently available for carbon within

nearly perfect trigonal oxygen groups.

The 2H, a/3, and BaC03-type cells all appear to be related. It was therefore not sur- prising to find the oriented intergrowth of BaC03 and 3:2 Ba:Ni. The systematic c-axis ex- pansion in, for example, the Ba:Ni series:

257

465-504 0 - 72 - 18
/« a ^

Fig. 13. A close-packing of barium and oxygens with octahedrally coordinated transition

metals (Me) . Atoms, projected on (001) , have fractional z coordinates. The

small (heavy line) hexagonal cell describes the 2H structure. The larger (fine

line) hexagonal cell is related to 2H by the factor v/3. The orthorhombic

(dashed) cell represents the aragonite form of BaC03 only in the general disposition of atoms excluding Me atoms. See discussion in text.

4.797 A (no carbonate^ 1:1) ^ 4.836 A (3:2, carbon containing) -> 9.760/2 = 4.880 A (3:1,

carbon containing -> 6.430 A (BaCOs) ,

is in accord with incorporation of increased amounts of carbonate. The high temperature decomposition of the 3:2 phases appears to reflect the structural instability due to loss of

CO2

.

4,2. THE 3:2 BatNi-BaCO^ COMPOSITE CRYSTALS

Using an automatic dif fractometer, 1385 x-ray reflections were measured for the 3:2

Ba:Ni - BaC0 3 composite crystals. The BaC0 3 maxima were ignored. The data were sorted and

equivalent reflections based on the assumed 6/nuTim symmetry were averaged to yield 111 independent observations. It was anticipated that the quality of the intensity data would be

poor considering the nature of the 3:2 crystals grown. The agreement factor for "equivalent"

reflections, for example, was somewhat high at 10.1%. Although it was further realized that

the electron diffraction data for the 3:2 indicate a tendency toward at least a doubling of

c, a structural analysis was nevertheless attempted.

A three-dimensional Patterson map suggested the coordinates xoz, z % 1/4 for six Ba

atoms but also was characterized by, a) numerous additional maxima which could not be

reconciled with Ba-Ni, Ni-Ni, or Ba-0 vectors and, b) a "smearing" out of the Ba-Ba vectors

along [oow] especially for o < w < 1/8. The following structural observations proved to be

consistent with these features of the Patterson. The condition hho£, I = 2n derived from

the data suggested the space groups P63cm or P63/mcm. Using P63cm and the 5(c) site with

X ; 2/3, z = 1/4, Ba would not refine. The x parameter refined to 0.6817 ± 0.0019 but z was

258
shifted to a numerically huge coordinate effectively outside the unit cell. The isotropic

temperature factor, however, remained positive and < 1.0. Refinement of Ba was possible in

6(g), xO 1/4, of P63/mcm, The x parameter refined to 0.6804 ± 0.0019 when z was fixed at 1/4.

The R-f actor was 35.4%. A difference map at this point immediately revealed several problems.

Two Ni atoms were clearly evident at (000) and (001/2) but the remaining two were distributed

in the 4(d) site, (1/3 2/3 0), indicating possible disorder. Of greater importance, however, were maxima, approximately 1/10 the magnitude of Ba in 5(g), related by the xoz coordinates

of the 12 (k) position. Three distinct sets were evident with the following parameters:

12(k) ; X ; ^, z . i

3 6 12(k) ; X = ^, z ; ^

• 3 6 12 (k) ; X ; ^, Z ; 0

It is proposed that the atoms in 12 (k) are bariums which are arranged in layers perpendicular

to c. Consider layers of the 2H structure- type as generated by the bariums in 5(g) . Eight

o o of these layers separated by ~ 2.4 A yield a distance along c of ~ 19.2 A. In the BaC03

structure, Ba-layers are separated by 1/2 c or (5.43/2) ; 3.2 A. Six BaC03-type layers

therefore can occupy the space provided by a distance of 19.2 A. A mixture of the two types

of layers together with the symmetry imposed by P63/mcm can generate a composite cell with

c z 4.8 A (19.2/4) . This "average" cell accounts not only for the Ba in 6(g) but also for

the possible Ba in 12 (k) . Although the ratio of the two types of layers remains unknown,

the Ba in 12 (k) together with the Ba in 5 (g) yield vectors which are consistent with the Patterson. The precession pictures in figures 10, 11, and 12 further substantiate this interpretation. Based on these observations the conclusion that the 3:2 crystals are not perfectly

ordered but are BaC03-3:2 composites seems justified. This interpretation may not be true

for a 3:2 phase grown "on composition" but seems applicable to those crystals grown purposely

(and from necessity) from a more Ba-rich composition.

Confronted with the possibility that the asymmetric unit could not be deduced by con- ventional methods the refinement was continued. Instead of partially occupying the 12 (k) sites with unknown multiplicity factors (which may also be refined) it was decided to vary

the 333 parameter of the Ba in 6(g) . This is realistic since the z parameters near, for example, 1/4, are ~ 1/5 to ~ 1/3. The 5 Ba (anisotropic) and 2 Ni in (b) , refined to 17.1%.

Addition of the half-occupied 4(d) nickel site plus 6 oxygens in xO 1/4 (x = 1/6) and 12 in

xy 1/4 (x ; 1/2, y ; 1/6) also observed in the difference map gave R = 13.5%. The oxygens

in 6(g) provide for octahedral coordination for Ni in (b) . Those in 12 (j) are associated

with the partially occupied nickel 4 (d) site but were approximately 1/2 the magnitude of ox- ygen in 5(g) in the difference map. The oxygen in 12 (j) refined but has a large

(12.185 ± 5.97) isotropic temperature factor. This was expected since, a) the oxygen is

associated with the partially occupied 4(d) Ni site and, b) the oxygen multiplicity factor

was not permitted to vary. The refinement was terminated at this stage as further information

about the structure especially with respect to the light atoms could not be derived.

4.3. THE 3:1 Ba:Ni PHASE

Using 639 independent reflections collected with an automatic diffractometer a structure

analysis of the 3:1 Ba:Ni compound (a = 9.587 A, c = 9.750 A) was initiated. Of the possible

space groups (without extinctions) of Laue symmetry 5/m, P5 contains symmetry elements which

permit a close packing of Ba and 0 atoms. After an analysis af the Patterson map, the structure was refined to R = 5.9% using full-matrix least squares and successive F^^^ and/or

^diff. ni^PS. The asymmetric unit was not clearly established, however. Positional coordinates are given in table 14. The preliminary structure is shown in figure 14 and 15. Refinement proceeded normally until the very last stages. Refinement of the atoms in the unit

Bai2Nii+C202i gave R = 6.5%. The Ni atoms are in strings of face-sharing octahedra parallel

with c (fig. 15). They are separated by a normal distance of . 2.50 A as in the 2H structure.

The two carbon atoms are located within triangular 0 groups centered about 2/3 1/3 z, near z

z 1/3, 2/3. This ap|>ears to accoiint for the doiabling (2 x 4.880 A) of the c-axis. They are separated by ~ 3.40 A, nearly that observed in BaC0 3. The C - 0 distances, 1.28 - 1.30 A

are typical for a C0 3-group, A possible third carbon at (000) was observed in difference

259
Table 14

Summary of Positional Coordinates from

Single Crystal Data for the 3:1 Ba:Ni-Oxide Phase

Space Group - P6 639 reflections

Ba-]^2'^i4C202i x y z

6Ba {I 1 0.3296 (5) 0. 3115(5) 0. 2426 (2) 3Ba (k 1/2 0.0223 (4) 0. 3268 (5) 1/2

3Ba (j 1/2 0.3206(5) 0. 0067 (5) 0 2Ni (g) 1/3 0 0 0. 122 (1) 2Ni (g b/

1/3 0 0 0. 378 (1) 6 0 [i] 1 0.836 (4) 0. 842 (5) 0. 242 (2)

3 0 (k b/ 1/2 0.831 (5) 0. 013(5) 1/2

3 0 (j b/ 1/2 -0.006 (6) 0. 838(8) 0

3 0 (j c/ 1/2 0.531(4) 0. 330 (4) 0

6 0 (j d/ 1 0.536 (2) 0. 196 (2) 0. 326 (2)

2 C (i 1/3 2/3 1/3 0. 318 (4)

Possible Carbonate Groups from Maps:

3 0 [l] l/2e/ 0.195(4) 0.665(5) 0.031(4)

3 0 («,) l/2e/ 0.196(8) 0.649(8) 0.446(6)

3 0 (£) l/2£/ 0.205(8) 0.542(8) 0.260(5)

R = 6.5% for Baj2Ni4C202]^ R = 5.9% after addition of half-occupied oxygens of the possible carbonate

groups

.

Suggested Stoichiometry (chemical analysis)

:

Ba.^Ni C^O^^ or Ba,^Ni c^O^^

12 4 5 30 12 4 6 30

—'^multiplicity factor (occupancy)

b/— oxygens of the octahedra associated with Ni

c/— potential carbonate group

d/— carbonate group

e/— normal multiplicity is halved (half-occupied oxygens) (see text)

.

260
• o

Fig. 14. Proposed structure, (001) view, of the hexagonal 3:1 Ba:Ni phase.

Fractional coordinates are approximate z parameters . Space group

= P6. Oxygens that are dashed are images observed in F^^^^^ maps

and are possible carbonate groups

.

# Ni, ^ , ^-0, FRONT • C , if ) , ^- 0, BACK

A,B-"GHOSTS" OF TRIANGULAR 0-GROUPS OBSERVED

IN F^j,,. MAPS

Fig. 15. Proposed structure, (110) view, of the hexagonal 3:1 Ba:Ni phase.

_ The Ni atoms are in strings of face-sharing octahedra. Two carbonate

groups at z ; 1/3, 2/3 are shown. The triangular oxygen group around

2/3 1/3 0 is a probable carbonate group. Groups A and B are "ghosts" or images of possible carbonate groups observed in Fjj-j^ff^ maps. All

cannot exist in the structure. Barium atoms are not shown. See

discussion in text.

261

/
maps within the triangular oxygen group centered about 2/3 1/3 0. When refined, the isotropic temperature factor for this atom was slightly negative at -1.6 ± 0.5, Of greater importance are "images" (in F^j_ff maps) of possible C03-groups centered about 1/3 2/3 z as shown labelled A and B in figure 15. Both A and B groups cannot exist simultaneously within

the same cell as the distance between parallel groups is far too short, ranging from 0.58 to

2.25 A. With a c-axis of 9.76 K, space is available for a maximum of three parallel CO3-

groups separated by 3.2 The three groups in set A or B would be satisfactory although the

o corresponding distances range from ~ 2.9 to ~ 4.3 A. These distances were derived after a refinement in which the oxygens in sets A and B were half-occupied (see table 14) . The R- factor dropped slightly to 5.9%. Prior to refinement, the oxygens were positioned where they were observed in difference maps. From z parameters initially at 0.06, 0.24, and 0.43 they

shifted in the refinement to .03, 0.26 and 0.45, respectively. The initial set of z parameters more closely resembles the appropriate distances of 3.2 - 3.4 A for parallel carbonate

groups. As multiplicity, temperature factor, and z parameters are strongly correlated, the

refined parameters may not be particularly accurate. It may be concluded that these groups

are disordered to remain within the confines of P6 . Other possibilities for the observed

phenomenon include, a) absorption_effects for which correction was not made, b) twinning from

a lower symmetry space group to P6 and/or, c) the data is so dominated by heavy Ba and Ni

that a possible monoclinic or orthorhombic space group cannot be discerned. Chemical analyses

established the number of carbon atoms per cell to be between 5 and 6. It is seen (fig. 15)

that a maximum of 6 C can be distributed within triangular oxygen groups observed. Two are

at z ; 1/3, 2/3; one is possible at z = 0; and three are physically reasonable within either

the A or B groups. If the correct number of carbons is 5 then the stoichiometry Ba^ 2^11+05 O30 [Baj 2 (NiitO;^ 2) (CO3) 5 ( O3) ^; V - vacant] yields an oxidation state of 4+ for nickel. If

the number is 6 the Bai2NiitC603o [Bai2 (Niu0i2) (CO3) 5] stoichiometry yields Ni^""". Magnetic

susceptibility data should elucidate this aspect of the problem.

5. SUMMARY

Phase relations in the systems BaO-" cobalt oxide" and BaO-"nickel oxide" are directly

influenced by the presence of CO2 . In air and at elevated temperatures carbonated phases

related to a 2H-type structure are stable and easily prepared. The presence of CO2 causes decomposition of Ba2Co0tt and prevents the formation of 2H-BaNi0 3.

6. ACKNOWLEDGMENTS

We wish to thank Dr. J. G. Allpress , University of Melbourne, for the electron diffraction data and Dr. A. D. Mighell, National Bureau of Standards, for numerous discussions con- cerning the computer programs used in this study. J. L. Waring, National Bureau of Standards,

prepared several 1:1 phases in the nickel system.

7. REFERENCES

[I] Strauss, S. W. , Fankuchen, I., and Ward, R. , J. Amer. Chem. Soc. 73_, 5084 (1951).

[2] Gushee, B. E., Katz, L., and Ward, R. , J. Amer. Chem. Soc. 79_, 5601 (1957).

[3] Lander, J. J., and Wooten, L. A., J. Amer. Chem. Soc. 73_, 2452 (1951).

[4] Lander, J. J., Acta Cryst. 4_, 148 (1951).

[5] Hardy, A., Acta Cryst. _15, 179 (1962).

[6] Greaves, J. R. , Thermodynamic Properties of Mixed Metal Oxides (dissertation), Oxford

Univ., England (1969).

[7] Krischner, H., Torkar, K. , and Kolbesen, B. 0., J. Solid State Chem. 3_' 349 (1971).

[8] The X-ray System, edited by J. M. Steward, F. A. Kundell, and J. C. Baldwin, Univ. of

Maryland Computer Science Center, 1970.

[9] Bland, J. A., Acta Cryst. 14_, 875 (1961).

[10] Candela, G. A., and Negas , T., to be published.

[II] Swanson, H. E., Fuyat, R. K. , and Ugrinic, G. M. , NBS Circular 539, Vol. Ill, p. 62,

1954.

[12] International Tables for X-ray Crystallography , Vol. II, p. 342, Kynoch Press,

Birmingham, 1959.

262
DISCUSSION

R. Ward: May I ask one question? The position of the carbons couldn't possibly be

within an octahedron could it?

T. Negas : No, all our electron density indicative of a carbon was always in or near

the oxygen plane. There is this idea now that carbonate groups are no longer truly planar

and indeed the two carbons that were actually well refined, pulled out of that trigonal

plane very, very slightly, but not into the center of the octahedron. The possible octahedra

within that 110 plane which you saw--these were devoid of nickel, completely devoid of nickel.

R . Ward : They will be sharing faces. In the carbides, the carbon is always in the

octahedral sites, and it looks like that would be a good place for carbon to be.

T. Negas : Yes, but they were definitely well within the triangular oxygen group, not

at a lower elevation. This is definitely a carbonate phase, not a carbide.

263

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

PREPARATION OF SrFe Mn. 0, „ AND CaFe Mn, ^0, CRYSTALS AND SOME OF THEIR PROPERTIES

X 1 X o~y X |~X o~y

E. Banks, O. Berkooz ^ and T. Nakagawa

Department of Chemistry

Polytechnic Institute of Brooklyn

Brooklyn, New York 11201

Single crystals of SrFe^Mn^ ^3-y ~x^3 "V grown by the usual technique

from fluxes of excess SrCl2 and CaCl2, respectively. Apparently cubic perovskites were obtained in the SrFe Mn, system where x is in the range 0.4 < x < 0.7 and in the xl-x3-y-^ — —

CaFejjMn^_jj02_y where x is 0.2 <_ ^ < 0.4. Hexagonal crystals, isostructural with the reported

high temperature phase of BaMn03 , were obtained in the SrFe^^Mn^ x'^S-y ^h®^^ ^ is 0.1 and 0. Chemical analysis showed that the values of Fe:Mn ratio in these crystals were very close to the expected ones. From the density and X-ray measurements the existence of substantial a- mounts of oxygen vacancies (0.26 <_ y <_ 0.44) in the perovskite crystals was observed. For

the hexagonal crystals, lower concentrations of oxygen vacancies (y ~ 0.11) were observed.

The Mossbauer spectra of crystals having x = 0.4 - 0.7 in the SrFejjMn^_j^03_ system were

found to consist of two kinds of quadrupole- split lines of Fe^"^ ions, Fe^+{I) which are present in regular oxygen octahedra and Fe^'*'(II) which are associated with oxygen vacancies.

From the magnetic measurements, Ne^l temperatures in the BrFe^^Mn^.j^O^.y were found to be

% = 130 K, 35 K and 20 K for x - 0.7, 0.5 and 0.4, respectively. Using the experimental

data of the densities, the Mossbauer effect and effective magnetic moments, discussions

concerning the amount of oxygen vacancies in the perovskite compounds are given.

The perovskite-like phases exhibited semiconducting behavior with activation energies

of about 0.16 eV, which was almost independent of composition.

Key words: Antif erromagnetism; CaFe^Mn^ _^0^_y ; defect structure; mixed metal oxides;

Mossbauer effect; oxygen vacancies; perovskite; semiconductivity ; SrFe^Mn^ 0^ y

1. INTRODUCTION

Oxygen deficiencies have often been observed in perovskite-type oxides containing transition metal ions. It is well known [1-4]^ that the deficiencies can be tolerated over wide

ranges of composition without changes in structure. Investigations of the perovskite phases

in the systems SrFe02_ [5-7] and CaMnO^.^ [8,9], have shown that the oxygen concentration

is dependent upon the temperature and oxygen pressure at which samples are equilibrated and

that their magnetic and electrical properties are greatly affected by the oxygen deficiencies

This report describes the preparation of single crystals in the systems SrFe Mn, „0.

and CaFejjMn j^Oj_ , and some observations on their magnetic and electrical properties.

Work sponsored by U.S. Army Research Office (Durham) Grant No. DA-ARO-D-31-124-G-1036 and

Air Force Office of Scientific Research, Grant No. F 44620-69-C-0047

.

2 Permanent address: 11 Azar Street, Holon, Israel.

3 Permanent address: Department of Physical Electronics, Tokyo Institute of Technology,

Ohkayama, Meguro-ku, Tokyo, Japan.

h Figures in brackets indicate the literature references at the end of this paper.

265
2. EXPERIMENTAL PROCEDURES AND RESULTS

2.1. PREPARATIONS OF SAMPLES AND CRYSTALLOGRAPHIC PROPERTIES

Sinqle crystals of SrFe Mn 0, and CaFe Mn 0 were grown by slow cooling from

fluxes of excess SrCl2 and CaCl2, respectively. Sintered powders with compositions

SrFexMni_x03_y and CaFexMni_x0 3_y , produced by mixing SrC03 or CaCOs, Fe203 and MnC03 and

firing at 1100 °C in air for 12 hours, were used as starting materials.

For the preparation of SrFej^Mn _^0^_^ crystals, weighed amounts of the starting materials

and reagent-grade SrCla with a molar ratio of 1:4 were heated in 40 ml platinum crucibles at

1330 °C for 12 hours so as to allow complete solution. The furnace was then cooled at 5-10°

per hour to 900 °C, at which temperature the crucible was removed from the furnace. For the

crystallization of CaFexMn^.^^Oj-y the best results were obtained from a soaking temperature

of 1280 °C.

The crystals were separated by leaching in dilute hot nitric acid. Crystals were located

mostly at the surface on the crucible wall. Cubic crystals generally about 1 x 1 x 1 mm in

dimension were obtained in the SrFexMn^ .xO^.y system (0.4 < x < 0.7) . Fox higher manganese

concentrations (SrMnO^ and SrMn^ g^^Q 1*^3 ^ hexagonal crystals were obtained. In the

CaFe^^Mn^.j^Og. system, ^nly cubic crystals w^re obtained in the range 0.2 _^ x <_ 0.4. The

largest crystals obtained were 3 x 3 x 3 mm in dimension for a composition of CaFeg _ i+Mng ^ 6^ 3-y

•

X-ray diffraction measurements were made on powdered samples of these crystals using

monochromatized CuKa radiation. The powder patterns of cubic crystals are consistent with

a cubic perovskite structure. The lattice constants in the SrFexMn^_x03_y system are plotted

in figure 1. The powder patterns of hexagonal crystals were indexed on the basis of the high

temperature phase of BaMn0 3 [10] . The lattice constants were calculated from the high angle

reflections

.

Crystals from several different runs were chemically analyzed. Results of crystallographic properties and chemical analysis of selected crystals are shown in table 1. Observed values of the Fe:Mn ratio in these crystals are found to be very close to the nominal

compositions

.

Densities of the crystals were measured with a pycnometric method using toluene at room temperature. Observed values of the densities in the perovskite phase, BrFexMn^^ x'^3-y' plotted in figure 2. Solid lines in the figure show the calculated x-ray densities, assuming

oxygen vacancies based upon y = 0, 0.25 and 0.5, respectively.

SrFexMn,.^03-y

Fig. 1. Variation of the lattice constants in the

SrFCjjMn^.jjOg.y system.

266
Table 1

Chemical Analysis and Lattice Parameters of SrFe Mn 0 and CaFe Mn, 0^ X 1-x 3-y X 1-x 3-y

V^i ICIU J. C^CL J. miClJ.^O-LO

o Lattice parameters (A)

SrFe^ ^Mn„ 0

.7 0.3 3-y SrFe„ ^„ Mn„ 0 0.703 0.300 3-y

a = 3.868 + 0.001

SrFe^ Mn 0

.6 0.4 3-y

SrFe Mn 0 0-648 0-349 3-ya = 3.862 ± 0.001

SrFe

0 Mn 0 • .5 0.5 3-y

SrFe Mn 0 0.526 0.446 3-ya = 3.856 ± 0.001

SrFe

0 Mn 0

,4 0.6 3-y

SrFe Mn 0 0.421 0.553 3-ya = 3.849 ± 0.001

CaFe

0 Mn 0

•4 0-6 3-Y

CaFe Mn 0^ 0.378 0.624 3-ya = 3.760 + 0.001

CaFsQ

.3 0.7 3-y ^^^^0 .283%.733°3-y a = 3.754 ± 0.001

Fig. 2. Observed values of the densities (dots) in the

materials SrFejjMni_x03_y

.

It is interesting to note that for all the compositions the vacancy concentrations lie

in the region between y = 0.25 and y - 0.5. The existence of substantial amounts of oxygen

vacancies in the CaFej,Mn^ _j^02_y crystals was also observed in the same way.

For the hexagonal crystals, on the contrary, lower concentrations of oxygen vacancies

were estimated. The results are shown in table 2 together with the Ca-Fe-Mn-0 system, in

which oxygen vacancy concentrations, y, were estimated from the experimental values of unit

cell volume and density.

267

/
Table 2

Density and Oxygen Vacancy Concentration, Y, of CaFej^Mni_jj03_y

and Hexagonal SrFexMni_jj0 3_y

Sample Density (g cm^

)

y

CaFe Mn

0.4 0 . b 3 —

y

4.32 ± 0. 01 0.30

CaFeg^jMng

.7 3-y

4.35 ± 0. 01 0.26

CaFe Mn

0.2 0 0.8 3-y

4.32 ± 0. 01 0.30

SrFe„ Mn„

0.1 0 0

.9 3-y

5.37 ± 0. 01 0.11

SrMnOg 5.37 ± 0. 01 0.11

2.2. MAGNETIC PROPERTIES

The Mossbauer spectra of the perovskite single crystals, SrEe^Mn, „0 , which had been

c "7 " i "X 3 crushed to powder, were measured at room temperature using a Co(Pd) source. A typical ex- ample of the Mossbauer spectra of SrFeQ 5MnQ^502_ , is shown in figure 3. The spectra of the

samples having x = 0.4-0.7 were found to consist of two sets of quadrupole split peaks of Fe^' ions, Fe^+(I), and Fe^+(II) indicating Fe^"*" ions are located in two nonequivalent sites.

Isomer shifts of Fe^"*'(I) and Fe^"'"(II) are about 0.50 mm/sec. and 0.30 mm/sec, respectively,

which are in reasonable agreement with literature values for high-spin Fe^+ [11]

.

Fig. 3. The Mossbauer spectrum of SrFeg . sMng . 5O 3-y at room

temperature.

268
In the iron rich compound, SrFe^ ^Mn^ sO,- / the presence of small amounts (~ 15%) of

Fe ions (IS = -0.17 mm/sec.) [6] was detected^in the spectra (fig. 4). The Mossbauer data

in SrFe^Mn^ _jj0 are summarized in table 3.

Fig. 4. The Mossbauer spectrum of SrFeg . yMng ^ 303,^ at room temperature

.

Table 3

Mossbauer Data for SrFexMni_x0 3_y

.

Sample Ion

Isomer shifts*

(mm/sec.

)

Quadrupole splittings

(mm/sec ,

)

SrFe„ Mn 0 0.7 0.3 3-y

Fe'++

Fe3+(I)

Fe3+(II)

-0.17

0.50

0.30

0

0.57

0.90

SrFe Mn 0 0.6 0.1+ 3 -y Fe3+(I)

Fe^+dl)

0.50

0.30

0.66

0.96

SrFe Mn 0 0.5 0 .5 3-y Fe^+d)

Fe3+(II)

0.50

0.30

0.66

1.02

SrFe Mn 0 0.4 0.6 3-y

Fe3+(I)

Fe^+dl)

0.50

0.30

0.60

1.02

relative to ~^'Co in Pd source.

269

/
The magnetic susceptibilities (x) of selected compositions in the Sr-Fe-Mn-0 system with

X = 0.7, 0.6 and 0.45 were measured with a Foner-type magnetometer between 4.2 K and room

temperature. There was no appreciable magnetic moment for these compositions down to 4.2 K. These samples were found to become antiferromagnetic with Neel temperatures of 130 K, and

30 K, respectively. The 1/x vs T curve of SrFe^ g^ng ^^0 _^ is shown in figure 5. The linear

portion of the 1/x T curve yielded an effective momenl. of about 4.23 Pg. The asymptotic

paramagnetic Curie temperature of this compound is -48 K. The magnetic properties of

SrFe Mn, 0^ are shown in table 4. X i-x 3-y

2.3. ELECTRICAL PROPERTIES

Electrical resistivity was measured from liquid nitrogen temperature to about 500 K. Surfaces of the crystal were polished and contacted to the platinum electrodes using In amalgam for ohmic contact. Appreciable semi conductivity in the perovskite compounds,

Sr-Fe-Mn-0 and Ca-Fe-Mn-0, was observed. Room temperature resistivity of these compounds is

about 10^-10^ ohm- cm regardless of composition. Semilog plots of resistivity against temperature are straight lines. Typical examples of temperature dependence of resistivity are shown in figure 6. The activation energies of these compounds 0.16 eV, are almost equal for

all the samples. The resistivity of the hexagonal crystals, SrMnO^.y and SrMn^ g^^g I'^s-y' was rather high, approximately ~ 10^ ohm' cm at room temperature.

.10^) 1 1

1 1 1

3.0

2.0

TnBp

= 3 5 °K

- -4 8 -K

l.O

Peff = 4.2 3

o 1 1 1 1 1 O 50 lOO 150 200 250 300

Temperature f°K)

Fig. 5. The reciprocal magnetic susceptibility as a function

of temperature for SrFeg . gMnQ ^ i+O 3_y

.

Table 4

Magnetic Properties of SrFe Mn 0 X 1-x 3-y

Sample

Neel temp.

(K) Effective magnetic moment

Paramagnetic

Curie temp. (K)

^^^^0.7^0.3°3-y 130

^^^^0.6%..°3-y 35 4.23 -48

^^^^0..5%.55°3-y 20 4.43 -58

270
Fig. 6. Variation of log resistivity versus 1/T

for SrFeo_itMno. 60 3-y' SrFeQ . sMng _ sOg-y

,

SrFeo.yMno. 303_y and CaFeQ , i+Mno . eO 3_y.

3. DISCUSSION

The lattice constants of the perovskite phases, Sr-Fe-Mn-0 and Ca-Fe-Mn-0, vary almost

linearly with the change of Fe:Mn ratio, indicating the formation of simple solid solutions.

Besides the diffraction patterns of the simple cubic perovskite structure, no superstructure

lines due to the ordering of Fe and Mn ions or oxygen vacancies were detected by the conventional x-ray diff ractometer . Owing to the similarity of the x-ray scattering factor of the

Fe and Mn ions, we might not expect to observe the superstructure lines but it may be safely

said that the difference of the ionic sizes and charge between Fe^"*" and Mn'^'*''^'*' ions is too

small to promote any long range ordering.

Gallagher, et al. [6] reported that the oxygen deficient perovskite phase, SrFe03_y,

could exist stably in the range 0<y<0.25 depending upon the temperature and oxygen pressure

of the sample preparation condition. Recently Mizutani , et al, and Negas and Roth [12] both

reported that they could obtain the perovskite SrMn0 3_y by rapid quenching from 1500 °C. Their results indicate that y ^0.26 and the perovskite can be reoxidized at ~300 °C to SrMn0 3.

From the density and x-ray data, the perovskite crystals of SrFejjMni .^Os-y and

CaFexMni_x0 3-y were shown to have a high concentration of oxygen vacancies (0 . 25 <

y < 0 . 44)

unlike the previous SrFeOs.y, However, under present crystal growth conditions, the brownmillerite-type crystals such as SrFe02.5 and SrMn02.5 were not formed.

271
As for the hexagonal crystals, SrMnO^.y. and SrHn^ gFe^ I'^^-y' lower concentrations of

oxygen vacancies were observed (y = 0.11). This indicates that, in the perovskite structure,

oxygen vacancies can be tolerated over a larger range of composition than in the hexagonal

structure although the major difference between the perovskite structure and hexagonal structure is in the mode of stacking of layers consisting of AO . 3 Mossbauer spectra of the material SrFej^Mn^_j^Oj_^ with 0.4 <_ x <_ 0.6 showed only Fe^"*" ions, with large quadrupole splittings. With better resolution of the spectra we could

assign the two kinds of Fe^"*" ions, Fe2"^(I) and Fe2"'"(II) ions, in the following way.

n _i_ There are two Fe (II) ions which are associated with every oxygen vacancy in addition

to Fe^+(I) ions which are present in regular oxygen octahedra. The location of an oxygen

vacancy adjacent to the Fe^'''(II) ions would be expected to introduce a larger quadrupole

splitting than that of Fe^+d) ion. If we assume that vacancies are randomly distributed in

the crystals, simple calculation gives the result that there would be 50% Fe^+Cll) ions for

compositions such as SrFe^^Mn^ _j^02 75 and 100% Fe^+lII) ions for SrFe^^Mn^ .j^O^ 5. Alternatively,

one can estimate amounts of oxygen vacancies from the Mossbauer data in the perovskites,

SrFexMn^_j^O^_y. This gives a value for y of approximately 0.35 ± 0.05, which is close to the

values obtained from density measurements.

There appear to be about 15% Fe^"*" ions for the iron rich composition SrFe _Mn„ ,0, 0.7 0.3 3-y

The effective Bohr magneton numbers calculated from the straight line part of 1/x - T curve were 4.43 for SrFeo^i+sMng 5503_y and 4.23 g for SrFeg _ gMnQ _ 3_y , respectively.

Using the values of y obtained from the density measurements , the change distributions for

these crystals are estimated to be SrFeo^t^5Mno"J"29Mno"''2602 63 ^^'^ SrFeo"'"60^o"''2i+'^"o"'"l602 58 ' respectively. The measured moments were smaller than the expected values (spin only) of

5.02 Mb for SrFeg _ It sMng _ 5503_y and 5.27 Pg for SrFeg _ gMng , i+03_y . This may be due either to the incorrect estimates of the charge distribution in the crystals or inaccurate extrapolation of the linear part of 1/x - T curve, which was obtained in a relatively narrow

range of temperature.

The Ne^l temperature is reported to be 138 K in SrFeO, [7] . The Neel temperature of

SrFe02 gg has decreased to 80 K with the increased concentration of vacancies [7] . The

Nedl temperatures in the present perovskite system Sr-Fe-Mn-0 (T^ = 130 K, 35 K, and 20 K for x = 0.7, 0.6 and 0.45, respectively) were found to be much lower than for stoichiometric

orthoferrites

.

The main exchange interactions in the Sr-Fe-Mn-0 system would be Fe^"'"-Mn^''' , Fe^"'"-Mn^"'" and Mn^"'"-Mn'*''' , although there are various combinations of exchange interactions such as Pg3+_pg3+ owing to the random distribution.

All the perovskite compounds exhibited semiconducting behavior with large temperature

coefficients and activation energies of about 0.16 eV, which were almost independent of

composition. It also appeared that the room temperature electrical resistivity of the

perovskite compounds fell in the region of about 10^-10^ ohm- cm.

Investigation of the La^ g^^a^

^ gFe^^Mn^.^^Og [13], and La^ _j^CajjFe-|^ _^Mnx03 [14] system

suggested the conduction mechanism for hopping might be:

Mn^"^ + Mn^"*" t Mn3+ + Mn'^"'" and Fe^^ + Fe'*+ t Fe'^^ + Fe3 +

The electrical conductivity in the present perovskite phase may be attributed to the mixed

valence states (Mn^"*" and Mn'*"^) ; however, we cannot deny that there might be a large

contribution from lattice defects. Further study is necessary to clarify these problems.

4. REFERENCES

[1] Erchak, M. , Fankuchen, I., and Ward, R. , J.Am.Chem.Soc. 68_, 2085 (1946).

[2] Strauss, S.W., Fankuchen, I., and Ward, R. , ibid. Ti_, 5084 (1951).

[3] Kestigian, M. , Dickinson, J.G., and Ward, R. , ihid. 79, 5598 (1957).

[4] Brixner, L. , ibid. 80_, 3214 (1958).

[5] Watanabe, H. , J.Phys.Soc, Japan, 12_, 515 (1957).

272
[6] Gallagher, P.K., MacChesney, J.B., and Buchanan, D.N.E., J.Chem.Phys . £1, 2429 (1964).

[7] MacChesney, J.B., Sherwood, R.C., and Potter, J.F., ibid. 43_, 1907 (1965).

[8] Yakel, H.L. , Acta Cryst. 8_, 394 (1955).

[9] Jonker, G.H. , and Van Santen, J.H., Physica 16^, 337 (1950).

[10] Hardy, A., Acta Cryst. 15_, 179 (1962).

[11] Stevens, J.G. , and Stevens, V.E., Mossbauer Effect Data Index, Plenum Publishing Co.,

New York, 1970.

[12] Mizutani, N. , Ohkuma, N., Kitazawa, A., and Kato, M. , Kogyo Kagaku Zasshi 73, 1103

(1970)

.

Negas, T. and Roth, R.S., J. Solid State Chem. 1^, 409 (1970).

[13] Jonker, G.H., Physica 2£, 1118 (1954).

[14] Banks, E., and Tashima, N. , J. Appl. Phys. 41, 1186 (1970).

465-504 O - 72 - 19 273

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

La Sr, RuO,: A NEW PEROVSKITE SERIES*

R. J. Bouchard and J. F. Weiher

Central Research Department

E. I. du Pont de Nemours and Company

Experimental Station

Wilmington, Delaware 19898

The compound LaRu03 was prepared for the first time. It appears to be metallic and

antiferromagnetic. Solid solutions with ferromagnetic SrRu03 of the type LaxSr]__xRu03 exist

for all values of x. All compounds have the orthorhombic GdFe03-type perovskite structure.

The ferromagnetism observed for SrRu03 (x = 0) diminishes rapidly with increasing La content, and antiferromagnetism or parasitic ferromagnetism sets in at approximately 35% La. All compounds show Curie-Weiss behavior at fairly low temperatures. The properties of

LaRh03 are also discussed.

Key words: Antiferromagnetism; Curie-Weiss paramagnetism; ferromagnetism; metallic

conductivity; oxide; perovskite; solid solution.

1 . INTRODUCTION

The number of compounds with the perovskite structure having the general formula ABO

3

is legion. Typical oxidation states are A"'"^B''"^03 and A"'"^B''"^03 , and the crystal structure

is usually cubic or orthorhombic (D^^-Pbnm, Z = 4) , as typified by GdFe03. Magnetic and

electrical transport properties can vary from metallic and Pauli paramagnetic, e.g., LaNi03

[1] ^ , through metallic and ferromagnetic, e.g., SrRu03 [2], to insulating and antiferromagnetic, e.g., LaCr03 [1]. SrRu03 is particularly interesting since it represents the

only known example where ferromagnetism results solely from a 2nd row transition element.

The metallic conductivity has been attributed [2,3] to a 2/3-filled, six-fold degenerate,

TT*-type band formed by the interaction of the t2g orbitals of Ru with suitable directed p orbitals of oxygen. We were interested in examining the effects on the magnetic and

electrical properties of SrRu03 caused by substitution of the Sr"*"^ with a large trivalent

cation like La . This process would change the number of electrons in the tt* band, adding

one electron/La"*"^ as the formal valence of Ru changed from +4 in SrRu03 to +3 in LaRu03,

simultaneously progressing from a 2/3 (d'*)- to a 5/6 (d^) -filled band. In addition, we consider LaRu0 3 itself to be unusual, representing the only known example of Ru in a formally trivalent state in an oxide lattice.

2. EXPERIMENTAL

The starting materials for the LaRu0 3 end member were La203 , RUO2 , and Ru metal,

accurately weighed according to the reaction:

2La20 3 + 3Ru02 + Ru 4LaRu0 3

The La203 was high purity, heated to 1000 °C -16 hours, kept in a vacuum dessicator, and

weighed quickly because of the well-known tendency of this oxide to react with atmospheric

water and carbon dioxide. Preparation of "reactive" La^Oo, by decomposition of the oxalate

_ Contribution No. 180 3.

1 Figures in brackets indicate the literature references at the end of this paper.

275
did not affect the reaction rate or the crystallinity of the product. The Ru metal was high-purity 325-inesh powder, which was also used to prepare the RUO2 starting material by

heating in O2 at 1000 °C for ~12 hours, grinding for 1 hour in a mechanical mortar grinder,

and refiring at 1000 °C in O2 for another 12 hours. The resulting product had a singlephase rutile x-ray pattern and hydrogen reduction indicated RUO2 stoichiometry within

experimental error. SrRu03 was prepared by firing SrC03 + Ru in O2 at 1000 °C, after Randall [4] . The

SrRuOs and the components of the LaRu03 (La203, RUO2 , and Ru) were mixed in the proper

ratios to give LajjSr]^_jjRu0 3 where x = 0.1, 0.25, 0.50, 0.75, and 1.

These starting materials were ground together for approximately 1 hour under dry nitrogen and quickly pressed into a pellet in a small hand press . The pellet was then preheated

to red heat in a silica tube under vacuum to remove any trace water picked up during the

pressing operation and sealed in a Pt tube under vacuum. The tube was heated at 1300-1350

°C for approximately 48 hours, then at 1100 °C for approximately 48 hours, and cooled in

the furnace. When silica tubes were used for the firing, or the 1100 °C heating cycle was omitted, excess Ru was always present in the x-ray patterns.

A pellet of LaRh03 was also prepared. An equimolar mixture of La203 and Rh203 was ground for approximately 1 hour, pressed, sealed in Pt under vacuum, and fired at 1200 °C

for 16 hours. While the resultant product was reasonably well sintered and suitable for

gross electrical characterization, x-ray examination revealed a trace of unreacted La203.

Another sample was prepared by reaction at 1300 °C and 3 kb external pressure for 12 hours,

slow cooled at 50 °C/hr. to 900 °C, after which the furnace was shut off to cool. The product was now single-phase and noticeably more crystalline. This sample was used for obtaining x-ray data.

The products were examined with a Guinier-Hagg x-ray camera using an internal KCl

O standard (a^ = 6.2931 A) and monochromatic CuKa radiation. The films were overexposed to emphasize the weak reflections. Cell dimensions were derived from a least squares refinement of the d-values. For the ferromagnetic samples, a vibrating-sample magnetometer was used for magnetic susceptibility data, while a Faraday balance was used for the antiferromagnetic and diamagnetic compounds. Electrical resistivity was measured for two of the

samples, using bars cut from polycrystalline pellets. Standard 4-probe techniques were

employed. Attempts to grow single crystals by flux reactions for accurate electrical data

were unsuccessful.

3. RESULTS AND DISCUSSION

3.1. CRYSTALLOGRAPH I

C

The products were single-phase, fairly well-crystallized orthorhombic perovskites.

The space group Pbnm (same as GdFe03) was verified by the occurrence of the 021 reflection

and the absence of the 201, which is not allowed. The refined lattice dimensions are listed in table 1. The parameters for LaRu03 are similar to those reported for LaRh03

[5] with a very slightly larger unit cell volume, reflecting the larger size of Ru"*"^ vs

Rh"*"^ [6] . The refined lattice constants for LaRh03 are also included in table 1. They are

in good agreement with reference [5] . The d-values and relative intensities for LaRu03 are listed in table 2. Volumes of the solid-solution unit cells vs increasing x in La^^Sr j^_^Ri03

will be the resultant of two opposing factors: (1) substitution of the smaller La"'"3(1.18 A)

for Sr+2 (1.25 K) and (2) substitution of the larger Ru+3 (0.68 A) for Ru+^ (0.62 A), using

Shannon-Prewitt radii for the six-fold B-ion and eight-fold A-ion coordination in the

orthorhombic perovskite [6] . The observed cell volumes increase with increasing x, indicating factor 2 to be dominant. The lattice constants vs x are plotted in figure 1. While

the unit cell volume increases smoothly with x, the a, b, and c-axes do not. The a- and c- axes appear to go through a maximum and there is a crossover from a > b to a < b at x -0.5.

Most striking is the rapid increase in b, the rate of increase becoming much larger at higher x. The large decrease in the b axis from LaRu0 3 to SrRu0 3 suggests that a factor

other than size considerations may be important. Also, the dimensions for SrRu0 3 are much

closer than LaRu03 to being cubic (a = b = for cubic symmetry). This behavior may be

related to the occurrence of ferromagnetism at the Sr-rich end of the solid solution series

as discussed in the magnetic section. Because the orthorhombic perovskite structure is

276
Table 1

Compound a (A) b(A) C(A) V(a3)

LaRuO 3 5. 4944(6) 5 .7789(5) 7 ,8548(7) 249.40(3)

La^75Sr_25Ru03 5. 5648(7) 5 .6278(7) 7 .8800 (12) 246.78(4)

La_ 5Sr_ 5RUO3 5. 5777 (2) 5 .5749 (8) 7 .8881(5) 245.28(3)

La i+Sr 6^^^03 5. 5798(7) 5 .5652 (9) 7 .8780(8) 244.63(4)

La^25Sr_75Ru03 5. 5782 (7) 5 .5488(6) 7 .8646(12) 243.44 (4) La iSr 9RUO3 5. 5745(7) 5 .5397 (7) 7 .8554(12) 242.58(5)

SrRu0 3 5. 5702(4) 5 .5324(4) 7 .8494 (7) 241.89 (2) LaRh03 5. 5226(3) 5 .7024(4) 7 .9857 (6) 248.65(2)

Refined lattice dimensions for the LajjSr2_jjRu0 3 compounds and LaRh03. Numbers

in parentheses are standard deviations in the last place.

5.80

5.76

5.72

5.68 (A)

5 64

5J60

5 56

552 -

5401 I I I I I I I I I I 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 SrRuOs LaRuOj

X in LaxSr,_xRu03

Fig. 1. The variation in lattice parameters vs. x in

La^Sr^ _j^Ru02 . c/^/tT is plotted rather than c so as to better illustrate the distortion from

cubic symmetry.

277
Table 2

]^ d

oJds C8.X C

1 1 1 0 3,9812 3.9818

1 0 0 2 3.9256 3.9274

11 1 1 1 3 . 5498 3 .5516

15 0 2 0 2.8882 2.8894

100 1 1 2 2.7970 2.7961

23 2 0 0 2.7477 2.7471

5 0 2 1 2.7114 2.7117

£i 21

10 ll

31 Z9 • JD JOc p

1 0 2 2 2.3273 2.3274

2 2 0 2 2.2521 2.2511

3 1 1 3 2.1879 2.1877

1 1 2 2 2.1423 2.1430

18 2 2 0 1.9910 1.9909

12 0 0 4 1.9639 1.9637

2 0 2 3 1.9401 1.9402

6 2 2 1 1.9300 1 .9299

5 1 3 1 1.7711 1.7710

1 3 1 1 1.7042 1.7042

5 1 3 2 1.6498 1.6496

5 0 2 4 1 . 6241 1.6241

17

2

3

0

1 2^ 1. 5968 1. 5975

2 2 2 3 1.5854 1.5848

2 1 3 3 i.4932 1 .4932

1

1

2

1

3

5 I 2f 1 .4620 1 .4613

1 0 4 0 1.4447 1.4447

1 0 4 1 1.4208 1 .4208

co

2

1

24 of X . OX X . jr70U

1 0 2 5 1.3795 1.3801

2 4 0 0 1.3733 1 .3735

1

3030 \\ 1.3087 1.3087

X-ray data for LaRu03. The intensities were estimated from

relative peak heights on a diffractometer tracing. The observed

d-values were taken from a Guinier-HSgg film, and the calculated

d-values resulted from a least-squares treatment of the Guinier

data.

somewhat complex, the relationship between the unit cell axes and individual MOg octahedra

involved in superexchange interactions is obscured, especially for large departures from

cubic symmetry. It is clear, however, that the RuOg octahedra in SrRu03 are more symmetrically arranged, suggesting that overlap of Ru and O orbitals is maximized.

Wold et al. [5], who first reported LaRhOs, noted that NdRhOs could also be prepared,

but not SmRh03 or YRh03. It was assumed that the smaller size of Sm+2 and Y"*"^ could not

satisfy the tolerance factor requirements for the stability of the perovskite phase. That

is, for a given B"'"^ ion size, there is a minimum size requirement for the A ion, below which

no perovskite can form. Since Ru"*"^ is larger than Rh"*"^ , it should be even more difficult to prepare any MRUO3 where M is a rare earth ion smaller than La. This is in accord with

experimental observations. GdRu03, NdRu03 , and PrRu03 could not be prepared under the same conditions used for LaRu03. Instead, the pyrochlores, A2RU2O7, were the major phases.

278
(However, single-phase NdxSr2^_xRu03 solid solutions could be prepared up to x -0.3.) It therefore appears that compared to MRh03 , the phase field defining the perovskite structure

for MRUO3 compounds is shifted further to the left in the lanthanide series so that only

La"*"^, the largest ion, is included. In this connection, it may also be significant that no La2Ru207 pyrochlore exists.

The almost universal adoption of the tetravalent state for Ru in oxides would seem to indicate a special stability. Therefore, Ru"*"^ should oxidize in air to Ru"'"'* at some rea- sonably low temperature. Surprisingly, LaRu03 can be heated in air to 700 °C, suffering

only a slight broadening of x-ray diffraction peaks after about 16 hours. At 900 °C, the

x-ray pattern becomes almost amorphous indicating destruction of the perovskite lattice.

3.2. ELECTRICAL

The electrical data plotted in figure 2 show a fairly low resistivity of approximately

5 X 10"^ ohm-cm for both LaRu03 and La^ 5Sr _ 5RUO3 . The positive temperature dependence is

characteristic of metallic materials, but the low resistivity ratio and relatively high

resistivity suggest that these oxides are poor "metals". It is fair to assume that the

resistivity of single crystals would be considerably lower. Although the electrical results

are qualitative, they do point to the same type of metallic-like behavior found for other Ru

oxides like SrRu03 and RUO2 [2,7].

From qualitative band model considerations of the type discussed by Goodenough [8] , LaRu03 should be metallic with a 5/6-filled iT*band formed from (Ru) t2g- (0) pir covalent interactions. A Seebeck coefficient of +42 ijV/°C was measured on a sintered piece of LaRu03

(hot junction = 60 °C; cold junction = 27 °C) . The small positive voltage is consistent

with hole conductivity in a nearly full band. The relatively high values for the resistivity may indicate that the conduction band is very narrow, leading to high masses and low

mobilities; more likely, they result from the difficulties associated with resistivity

measurements on polycrystalline samples.

If a model with a conduction band composed mainly of t2g (it) states is valid, the

electrical properties of LaRu03 should be considerably different from LaRh03. For the

latter, the 6-fold degenerate iT*-band should be completely filled (trivalent rhodium has a 4d^ configuration), leading to semiconducting properties, rather than metallic. Electrical

T(°K)

Pig. 2. The resistivity of LaRuOg and La^5Sr_5Ru03 vs. temperature. Arrows indicate measurements

taken on heating (->) or cooling {<-) .

279
conduction would then become an activated process, via transfer of electrons from t2g (n) to eg (o) levels, which would presumably also exist as band states, o-bonding being stronger

than 77-bonding. A crude 2-probe resistivity of about 1 x lo'* ohm-cm was measured on a pellet of LaRh03 at room temperature. This difference in resistivity of approximately seven

orders of magnitude between LaRu0 3 and LaRh0 3 is consistent with a partially filled con- duction band in the former and a filled band in the latter.

3 . 3 MAGNETIC

Magnetic susceptibility was measured as a function of temperature on five solidsolutions. The 1/x vs T plots are shown in figure 3. To assure that the upper temperature

portions of the curves correspond to the paramagnetic (Curie-Weiss) region, one sample was taken to high temperatures (fig. 4) . The calculated magnetic parameters are listed in

table 3. No corrections were made for temperature-independent contributions to the susceptibility because of the difficulty in accurately estimating this term. In addition to the

negative contribution from core diamagnetism, there should be a positive Pauli contribution

from conduction electrons. These are small, about the same order of magnitude, and tend to

cancel one another.

All the compounds appear to show Curie-Weiss behavior at the higher end of the temperature region scanned. The straight line to 700 K for one sample supports this conclusion.

The values for the paramagnetic moment are in the range 2.4-2.8 B.M. , with no particular

dependence on composition. Part of this fluctuation may be experimental error, although

error propagation analysis indicates that the standard deviation in p should be no greater

than ~2% or ~ ± 0.05 B.M. Another factor that is probably more important is the temperature

range of the Curie-Weiss portion of the susceptibility data, which may be too small for the

derivation of very accurate C and 0 values. This is illustrated by the low and high-temperature measurements on La_ ysSr _ 2 , as shown in figures 3 and 4, respectively. Data in

both temperature ranges were taken on the same sample preparation. From the high-temperature run, p = 2.56 B.M. and 6 = -127 K (table 2). The corresponding low-temperature data

are 2.70 B.M. and -118 K. Given such scatter, no particular significance can be attached

to the variation of y with composition.

0 100 200 300 400 500

TCK)

Fig. 3. Inverse susceptibility vs. temperature of various

members of the Laj^Sr^_^Ru02 solid solution series.

The data for x = 0 (SrRu03) were calculated from

reference (b) and are included for comparison.

280
300

200 300 400 500 600 700

T (°K)

Fig. 4. Inverse susceptibility at high temperatures for

La ^ Sr RuO,

.

75 .25 3

Table 3 1

(H ^ 0, C ^emu°K

mole Oe

y P e T

c T -> 0) Compound (B.M.) (°K) (B.M.) (°K) emu/gm

SrRu03 2.65 + 160 .85 160

La iSr 9RUO3 .709 2. 39 +142 .75 133 17.4

La_25Sr_ .809 2. 54 +59 .35 79 7.75

La 5Sr 5RUO3 .946 2.75 -107

La^ 75Sr^25Ru03 .817 2.55 -127

LaRuO 3 .841 2.59 -160

Magnetic parameters for La Sri ^RuOq. The SrRuO^ data were taken from reference (2) X X— X

-J ~> r 3k T 1 /9 and are included for comparison. The paramagnetic moment Up = L^^2 X(T-6)J ' from

susceptibility data in the Curie-Weiss region.

The formulas for the solid solutions can be written as LaxSr2^_jjRux"Ru^^^03 . It can be

safely assumed that both Ru"*"^ and Ru"*"^ are in the low-spin state because of strong covalency

effects (large ^g~'^2g splitting) characteristic of 4d-ion interactions. An ESR study [9] of Ru"*"^ in a corundum (AI2O3) matrix confirms this even for the trivalent ion, where cova- lency should be weaker. The spin-only moments corresponding to the low-spin states of Ru"*"^ (d^) in LaRu03 and Ru''"'+ (d^) in SrRu03 are 1.73 and 2.83 B. M. respectively. Although

SrRu03 appears to exhibit a paramagnetic moment near the spin-only value, the LaRu03 moment

is considerably higher than expected. However, d^ systems can show greatly enhanced paramagnetic moments [10,11] because of spin-orbit contributions and various other factors.

While it may be tempting to contemplate the effect of a distorted octahedral environment of

the Ru ion, a structure determination [12] of GdFe03 has shown that the distortion effected

by the orthorhombic symmetry is mainly borne by Gd+3, the Fe"*"^-© octahedra remaining almost

purely octahedral.

The most obvious trend in the magnetic properties of La^jSr^.j-RuO 3 is the appearance of

antiferromagnetism with increasing x. The f erromagnetism characteristic of SrRu0 3 disappears at approximately 35% La, where the Weiss constant G becomes negative (fig. 5).

281
+ 200 1 I—I

\—I

\—,—I—I—

r

Fig. 5.

The shapes of the 1/x vs T curves for those samples which exhibit a negative 6 are not

completely typical of anti ferromagnets . The lack of a pronounced minimiJin may mean weak

parasitic ferromagnetism or trace ferromagnetic impurities. The only reasonable ferromagnetic impurity in the solid solution system would be SrRu03. Since the effect is present

even for LaRu0 3, however, this seems unlikely to be the cause. Also, some of the curves

are very similar to that of CaRu03 [3,13], which is thought to be an example of band antif erromagnetism with parasitic f erromagnetism below Tj^. In addition, the fact that an orthorhombic distortion almost by definition prohibits exactly compensated antiferromagnetism

suggests that parasitic ferromagnetism is a reasonable explanation for the magnetic behavior

at low temperatures

.

In an ABO 3 perovskite, both the A- and the B-ion compete in a covalent sense for the

oxygen electrons. In SrRu03 , Ru"*"^ is able to interact strongly because of its relatively

high charge and small size. The two unpaired electrons in Ru t2a levels are not localized

on the Ru ^, and can take part in ferromagnetic band interactions at low temperatures.

Although paramagentic behavior is found above T^, the moment is below the spin-only value,

consistent with some delocalization. When La"*"^ is siibstituted for Sr"*"^ , its smaller size

and higher charge enable it to compete more strongly for oxygen electrons . At the same

time, the Ru"*"^ resulting from the substitution is less strongly bonded than the Ru"^*^

,

because of its larger size and smaller charge. These effects are additive, both leading to

a decreasing Ru-0 interaction, and presumably a narrower TT*-band. At LaRu03, the bandwidth

has been sufficiently decreased so that antiferromagnetic behavior is observed which appears

to be more characteristic of narrower bands [3] . The paramagnetic moment is considerably

higher than the spin-only value; this may result from orbital contributions and has been

observed, for example, in Ru complexes [14] where presumably the electrons are localized

rather than collective. Evidence that the bandwidth has not decreased to zero is provided

by the metallic-like electrical behavior.

282
similar reasoning was used [3] to explain the contrast between CaRu03 (antiferromagnetic, unit cell volume V = 227A^) and SrRu03 (ferromagnetic, V = 242a3) . In that

example, the more acidic Ca"*"^ decreased the strength of the Ru''"^-0 interactions in CaRu03

to such an extent that antiferromagnetism resulted, for the same number of d electrons per

Ru ion. Clearly, the sign of the superexchange interaction between Ru ions is determined

not so much by the number of d electrons in the tt* band as by other considerations such as Ru-0 covalency and bandwidth of the tt* states.

Finally, the magnetic properties of LaRh0 3 should reflect the filled t2g band previously discussed. This is essentially confirmed, with minor complications. A value of Xa ~ 1.2 X 10" emu/gm was found at 300 K. However, there was a small but definite temperature

dependence and slight field dependence. The temperature dependence indicates a small amount

of paramagnetic impurity {C^ = 0.0082, p|ff = 0.066; corresponds to 0.2 mole % of an S =

5/2 ion) . The field dependence corresponds to a trace ferromagnetic component with a magnetization of Og = 5.5 x 10 ^ emu.

4. ACKNOWLEDGMENTS

Mrs. C. G. Frederick is thanked for the magnetic measurements on the ferromagnetic

compounds, as is Mr. J. L. Gillson for the electrical resistivity data. The comments and

suggestions of Dr. D. B. Rogers are gratefully acknowledged, as are several helpful discussions with Dr. A. W. Sleight concerning the crystallographic details of the perovskite

structure

.

5. REFERENCES

[I] Goodenough, J. B. , J. Appl. Phys. 37_, 1414 (1966).

[2] Callaghan, A., Moeller, C. W. , and Ward, R. , Inorg. Chem. 5_, 1572 (1966).

[3] Longo, J. M. , Raccah, P. M. , and Goodenough, J. B., J. Appl. Phys. 39_, 1327 (1968).

[4] Randall, J. J., and Ward, R. , J.A.C.S. 8]^, 2629 (1959).

[5] Wold, A., Arnott, R. J., and Croft, W. J., Inorg. Chem. 2^, 972 (1963).

[6] Shannon, R. D. and Prewitt, C. T. , Acta Cryst. B25 , 925 (1969).

[7] Fletcher, J. M. , Gardner, W. E., Greenfield, B. F. , Holdoway, J. M. , and Rand, M. H.,

J. Chem. Soc. 1968A , 653.

[8] Goodenough, J. B., Bull. Soc. Chim. France 1965 , 1200.

[9] Geschwind, S. and Remeika, J. P., J. Appl. Phys. 33 (s) , 370 (1962).

[10] Kotani, M. , Prog. Theor. Phys. (Kyoto) 14, 1 (1960).

[II] Figgis, B. N. , Lewis, J., Hyholm, R. S., and Peacock, R. D. , Disc. Faraday Soc. 26 , 103 (1958).

[12] Coppens, P. and Eibschutz, M. , Acta Cryst. 19_, 524 (1965).

[13] Goodenough, J. B. , Longo, J. M. , and Kalafas , J. A., Matl. Res. Bull. 3_' ^71 (1968).

[14] Figgis, B. N., Lewis, J., Mabbs , F. E., and Webb, G. A., J. Chem. Soc. 1966A , 422.

DISCUSSION

E . Banks : Did you try to make any Seebeck coefficient measurements?

R. J. Bouchard : Yes, the Seebeck coefficient of lanthium ruthenate is plus 40, which

is in the metal range-and it is also the right sign for nearly filled band, incidently.

P. Hagenmuller : It would be interesting, of course, to be able to prepare the other

rare earth compounds . Did you try to increase the Goldschmidt factor by working with high

pressure?

R. J. Bouchard : I think we did make a 65 kilobar run when we' tried to prepare neodymium

ruthenate, NdRuOs. Again we got the pyrochlore phase. It is very, very stable for these

compounds

.

P, Hagenmuller : The pyrochlore phase, of course, is in competition with the formation of

a perovskite.

283
J . M. Longo : You pointed out that you didn't expect to get the perovskites with the rare earths because of the analogy to the rhodium compound. From what we reported this

morning on bismuth rhodate, would you expect bismuth ruthenate to be perovskite at pressure

where the others did not form.

R. J. Bouchard : Well, we only tried it with bismuth up to 65 kilobars, and again we

got exactly the same thing we got under autogenous conditions.

284
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

HIGH PRESSURE SYNTHESIS AND CRYSTAL STRUCTURE OF

COBALT SESQUIOXIDE AND ITS LOW-SPIN ^ HIGH-SPIN TRANSITION

M. Marezio and P. D. Dernier

Bell Telephone Laboratories, Incorporated

Murray Hill, New Jersey 07974

J. Chenavas and J.-C. Joubert

Laboratoire d 'Electrostatique et de Physique du Metal

CNRS , Grenoble , France

This note reports the high pressure synthesis of C02O3 with the corundiam structure. Two

different syntheses were performed. In the first the starting material was Co^+Cr^ + Oi^ . By

applying a pressure of > 90 kbar and 1000 °C in the presence of a small amount of water,

CoCrOit was found to decompose into C02O3 with the corundum structure and a solid solution of

CoOOH and Cr02 with the orthorhombic distortion of the rutile structure. The decomposition

occurs according to the formula

:

1 3

(I) 3 CoCrOit + 2 ^ 4 (Cr02) ,75 (CoOOH) _25 + C02O3 + ^02

The second synthesis was based on the following reaction at 80 Kb and 850 °C:

3 (II) 2 C0F3 + 3 Na202 ^ 6 NaF + C02O3 +^02

Unfortunately some reduction occurred under pressure and the quenched material contained

some C03O4.

The x-ray powder pattern of C02O3 was indexed on a hexagonal cell, a = 4.782 K, c = 12.96

A, c/a = 2.710, V = 258.5 A . It resembles closely that of a - AI2O3 as far as the sequence

of the d-spacings is concerned, but the intensities of the reflections are similar to those

of V2O3. This indicates that the Co^"*" ions must be in the low spin state. On the other hand

the arrangement of the structure of C02O3 should be different from that of AI2O3 as the relative intensitites indicate.

By annealing C02O3 at 400 °C for a half hour in air, this oxide transforms to a corun- dum structure with a different volume and c/a ratio. The new values are a = 4.882 A, c = 13.38 A, c/a = 2.742, V = 276.2 A^. Since the unit cell volume and the d-spacings of this

C02O3 are nearly the same as those of a-Fe20 3, the Co^"^ ions must be in the high spin state.

The transformation C02O3 (low spin) C02O3 (high spin) is accompanied by an increase in volume Av/V(l.s.) = 6.7%. These results seem to indicate that C02O3 (high spin) is the cobalt

sesquioxide stable at atmospheric pressure whereas C02O3 (low spin) is the high pressure

phase

.

Preliminary refinements of the two structures based on powder intensities gave average

Co-0 distances of 1.90 A and 1.99 A for C02O3 (low spin) and (high spin) respectively. These

values are in fairly good agreement with those calculated from Shannon and Prewitt ionic

o o radii, 1,92 A and 2.01 A respectively. The Co-Co distances across the shared face between

two octahedra are quite short in both compounds. Relative to the ionic radii it is smaller

in C02O3 (high spin) . Also the Co-Co distance across the shared edge is anomalously short

in C02O3 (high spin)

.

285
According to the general trends in the transition metal sesquioxides , C02O3 (high spin)

should be a magnetic insulator, whereas C02O3 (low spin) a nonmagnetic insulator. In octahedral coordination the Co^+ ions in the low spin state have the configuration t2g^g which

corresponds to a zero magnetic moment. The filled t2g band would be compatible with the

predicted insulator character of C02O3 (low spin)

.

DISCUSSION

_^ p. Hagenmuller : A comment, we found always at any pressure a low spin state for nickel

3 which is consistent with your results. The question, at what temperature do you begin to observe a loss of oxygen from the cobalt sesquioxide. That's the major difficulty with your

interpretation of the data.

M. Marezio : We have tried to prepare nickel sesquioxide with the same methods; it does

not work. The reason why it doesn't work, we believe, is because it is difficult to make the

nijkel_|_ions in the low spin state even at these pressures. If one takes the compound

Ni ^Cr ^Oi^ in the presence of water at 90 kilobars and 1000 degrees one obtains an x-ray pattern of a corundum structure, which we believe is NiCr03 . The lines are very sharp, including

the back reflection region, which indicates a single phase of NiCrOs , One could claim that we have made Ni203 but we don't believe it.

P. Hagenmuller : We don't speak about the same compound. I spoke about the ternary com- pounds of the rare earths. One has to work with high oxygen pressure.

M. Marezio : We do lose oxygen, in fact, in some preparations we obtained C03O4. We lost

oxygen even in an oxidizing environment. In one preparation we used sodium peroxide, which is a very strong oxidizing compound, and we still lost oxygen at 850 °C.

P. Hagenmuller : But there's a problem. In this case you have cobalt 2"*" and there is a question concerning the interpretation of the magnetic moments, but maybe we speak later about

it.

B. Chamberland : That particular compound, the NiCr03 , was prepared using nickel oxide

and chromium dioxide at high pressure and nickel is definitely 3+ with a high spin.

M. Marezio : Thank you.

286
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

INFLUENCE OF MADELUNG ENERGY AND COVALENCY ON THE STRUCTURE OF A+B^+O- COMPOUNDS*

J. A. Kafalas

Massachusetts Institute of Technology

Lincoln Laboratory

Lexington, Massachusetts 02173

The large Goldschmidt tolerance factor t = 1.06 in BaTi03 appears to be related to its

ferroelectric properties and also suggests that relatively large effective charge at a Ti'*'^ ion inhibits formation of the hexagonal-perovskite polytypes generally associated with

t > 1.0. In order to test these ideas, RbNbOs and RbTa03 (t = 1.08) were prepared under

very high pressures. RbNb03 is an orthorhombic perovskite isostructural with ferroelectric

BaTi03, and it decomposes on heating without formation of an hexagonal-perovskite polytype

.

Only at 90 kbar and 900 °C did KbTa03 form a ciibic , or nearly cubic, perovskite. Unlike the

transition-metal ions, Sb^"*" and Bi^"*" have never been stabilized in a cubic perovskite structure. AgSb03 forms a defect pyrochlore, NaSb03 and KSbOs have ilmenite structures, although

a cubic (Pn3) form of KSb03 is stabilized by prolonged annealing above 1000 °C. A bodycentered-cubic , disordered form of the cubic KSb03 having space group 123 was prepared in

five minutes at 20 kbar and 800 °C. Preparation of RbSbOs at 20 kbar and 1000 °C yielded a phase with the same structure. These results are interpreted to mean that strong covalent

bonding inhibits the formation of 180° Sb^"'"-o2~-Sb^"'" linkages.

Keywords: A"'"B^"'"03 compounds; ferroelectricity ; perovskites; phase stability.

Many oxides, fluoride, chlorides and sulfides of chemical formula ABX3 crystallize in one of the hexagonal-perovskite polytypes [I]"''. These structures consist of ordered, closepacked AX3 layers stacked in cubic or hexagonal or mixed cubic and hexagonal stacking

sequences. The smaller B cations occupy all the interlayer X-anion octahedra , and stabiliO zation of these structures requires not only that the larger A cation have a radius rj^>0.9A,

but also that the B cation be stable in an octahedral interstice.

If the stacking of AX3 layers is entirely cubic (fig. la) , the B-cation octahedra share

only corners to form the 3C structure of cubic perovskites. In this structure the A cations

are confined to a cubic cage of edge B-X-B, where the B-X bond length is a characteristic of

the B and X ions that requires considerable energy to increase. This cage creates an upper

limit on the A-cation size that can be accommodated in a given BX3 cubic array. This geometrical reasoning led Goldschmidt [2] to define a tolerance factor

such that the ideal cubic structure should occur at t = 1.0. For t < 1.0 the BX3 array may

be distorted from cubic to orthorhombic or rhombohedral symmetry so as to optimize the A-X

bonding. If this distortion is too large, other structures become competitive, which places

a lower limit on t. Therefore the cubic perovskite phase is stable in the interval

1 . STRUCTURES OF ABX3 PEROVSKITE POLYTYPES

(1)

(2) u

*This work was sponsored by the Department of the Air Force

•^Figures in brackets indicate the literature references at the end of this paper.

287
(o) (b)

where tJie upper limit is expected to fall close to t^ = 1.0.

If the stacking of AK 3 layers is entirely hexagonal (fig. lb), the B-cation octahedra

form face-shared linear chains parallel to the c axis of the hexagonal (2H) cell. Since

these chains are isolated from one another, relatively large A cations can be accommodated

by adjustment of the c/a ratio. Therefore this hexagonal perovskite structure is competitive for larger t>l. However, accommodation of the larger A cation is at the expense of

considerable Madelung energy, a large electrostatic repulsive force occurring between B cations in face-shared octahedra.

In a narrow, intermediate range of tolerance factors three intermediate stacking

sequences have been identified in stoichiometric ABX3 compounds: two-to-one cubic to hexagonal stacking (cchcch of the 6H structure, fig. Ic) , a one-to-one stacking (chch of the

4H structure, fig. Id), and a one-to-two stacking (chhchhchh of the 9R structure, fig. Ic)

.

In these intermediate structures the loss of electrostatic Madelung energy is minimized by

displacing oppositely-along the c axis the B cations in face-shared octahedra. However,

changing the stacking sequence within a structure introduces an energy loss that limits the

stability range of these phases, and in the halides the 4H structure is entirely suppressed.

In a comprehensive survey of ABF3 polytypes, Babel [3] summarizes the stability of the

various f luoroperovskites as follows:

Orthorhombic (GdFe03-type t = 0.78-0.8J

Cubic (3C) t = 0.88-1.0

Hexagonal (6H, BaTiOs-type) t = 1.0-1.06

Hex-Rhombo (9R, CsCoF3-type) t = 1.07

Hex (2H, CsNiF3-type) t = 1.08

In the oxides the upper tolerance-factor limit t^ and the range of tolerance factors for the

inteirmediate polytypes are not well defined: they depend more strongly upon the covalency

and effective charges of the B cations. The purpose of this study was to investigate

further these effects in A+B^+03 oxides, for which no hexagonal polytypes have been reported.

Hydrostatic pressure stabilizes a higher cation coordination, which reduces the lower

tolerance- factor limit t£ . It also favors a more regular cation coordination, which stabizes cubic vs hexagonal stacking [4] and raises t^. This latter trend is illustrated in

figure 2 [5] , which shows the effect of B-cation size and pressure on the stability of

CSBF3 polymorphs, and in figure 3 [6], which shows the effect of A-cation size and pressure

in the system Bri-xSrxRu03 . Since high pressure extends the tolerance-factor rante t|^<t<tu

at both ends, it always favors formation of the perovskite structure. Therefore high pressures were used in this study for the preparation of several A"'"B^+03 compounds.

288
60

20

- 6 6 \ P\ P PEROVSKITE - \ 9 9 LAYER

6 6 eX p 6 » 6 LAYER

2 • 2 LAYER

- \ \

T » 700°

C

9. -[§] A \

^ CsBFj

-[9] \

\6

p

J 9 Y

_ \ \ \ 9- \ .A

Mg Ni ZnCo

^ i

Fe Mn

1 , * 1

P

Cd

P

Co

li 070 0.74 0.78 082 Q86 090

IONIC RADII (A) OF B CATIONS

Fig. 2, Effect of pressure and B-cation size on structure

of CSBF3 compounds.

• PEROVSKITE

N. O 6 LAYER

'^v^ •4 LAYER

\ • 9 LAYER

\

(X)Ba Sr RuO,

l-x X 3

Fig. 3. Pressure-composition phase diagram in

the system Ba]^ _xSrj.Ru03 .

2. TENTATIVE CONCLUSIONS FROM KNOWN A'*"B^"^03 STRUCTURES

A striking feature of the known A"'"B^"'"02 structures is a lack of face-shared octahedra

containing B^"*" ions. Thus no hexagonal A"'"B^"'"03 perovskites have been reported. Furthermore, compounds containing Sb^"*" or Hi B cations tend to form different structures than

those containing Nb^"*" or Ta^"*" B cations . These observations suggest two conclusions: (1) The electrostatic repulsion between B cations of large effective charge reduces the stability of the hexagonal-perovskite polytypes , so that these phases are no longer competitive

if the B cation has a formal valence B^"^. (2) B cations, such as Sb^"'" or Bi^+ ions, that

form strong covalent bonds with their oxygen ligands will not be stabilized in structures

289

465-504 O - 72 - 20
having 180° Sb^"'"-0^~-Sb^''" linkages. Structures that permit the anion to use different p orbitals in covalent-bond formation with two neighboring Sb^"*" ions will be competitive, so

90° Sb^"'"-0^"^-Sb"'" or 120-140° Sb^+-o2~-Sb^"'" linkages are expected in the stable A"'"Sb5''"03 structures (Electrostatic forces would tend to open from 120° the tetrahedral angle appropriate to sp^ hybridization)

.

The first of these conclusions provides a significant perspective for interpretation

of the ferroelectric compound Ba^"'"Ti'*"'"0 3 , which crystallizes in the cubic (3C) perovskite

structure at high temperatures even tho t = 1.06 is considerably larger than the geometric

limit t^5 = 1.0. Of all the A^'^b'^+Os compounds, the cations of largest effective

charge would be those furthest to the left in the Periodic Table (Ti^+, Zr^"*", Hf . The

fact that cubic BaTiOs can be stabilized even though t = 1.06 indicates that the effective

charges on the Ti^"*" ions are too large for the hexagonal structures to be competitive, although the 6H polytype is formed in reduced BaTi03_6. Since a t^ > 1.0 implies stretching

of the B-:x bond length, the elastic forces that would inhibit ferroelectric-type displacements of the cation toward one or more near-neighbor anions is sharply reduced. Therefore

BaTi03, unlike CaTi03 or even SrTiOs, exhibits ferroelectricity with a high Curie temperature. BaZr03 (t = 1.007) and BaHf03 (t = 1.005) are cubic and have no ferroelectric-type

distortions

.

Where the A cation is small enough to be accommodated in sixfold-coordination, an ilmenite structure might be anticipated. However, in this structure a B^"*" cation and an A"*" cation share a common octahedral face, and the electrostatic repulsion between the ions may

be strong enough to stabilize alternate structures. In LiNb03, for example, the small Li+

ion is displaced to the far octahedral-site face midway between the Nb^+-occupied interstices;

and in LiSbOo the Li+ ions fill one-third of the c-axis octahedral-site chains so that the

Sb^+ ions may occupy every other octahedral site in the remaining two-thirds of the c-axis

chains. Ordering of the c-axis chains makes -130° Sb5+-o2--sb5+ linkages in the LiSbOs

structure.

The compounds NaNb03 and NaTa03 (t = 0.94) crystallize in cubic perovskite structures

that are distorted to orthorhombic symmetry as a result of Na''"-ions displacements [7,8].

However, NaSb0 3 crystallizes in the ilmenite structure even though t = 0.95. Clearly the

formation of 180° Sb^"^-0^~-Sb^"'' linkages requires the loss of more energy than the formation

of face-shared Na"*" and Sb^"*" ions. KNb03, which has a t = 1.04, is ferroelectric like BaTiOs

below 435 °C, whereas KTa03 (t = 1.04) is cubic at room temperature [9], although an orthorhombic BaTi03 form has been reported [10]. Again a t>t^'^ = 1.0 is associated with a large

effective charge on the B cation, which inhibits formation of the hexagonal polytypes , and

with ferroelectric- type displacements of the B cations. Surprisingly, KSb03 has the ilmenite structure (a = 6.8144 A, a = 46°20') [11] even though t = 1.05 and the large K""" ion is

stable in twelve-fold coordination. Generally this structure is stable only for t<t£.

Therefore the 180° Sb^"'"-0^~-Sb^"'' linkages of the cubic perovskite phase must be relatively

unstable. Spiegelberg [11] further reports that KSb0 3 transforms to a cubic = 9.56 A)

form if heated at 1000 °C for several weeks. The cubic structure (space group Pn3) consists

of Sb20jQ groups of edge-shared octahedra sharing common comers, as illustrated in

figure 4. The Sb5+-o2~-Sb5+ linkages make 90° and about 130° angles. Clustered about the

origin, located at the center of the front face of figure 4, are four K"^ ions forming a tetrahedron, each at 0. 15/3a from the origin, and four on the other body diagonals a distance 0.25/3a from the origin. This arrangement results in pairs of K+ ions between the

origin and half the body-center positions, in single K"*" ions midway between the origin and

the remaining four body-center positions. The cubic cell is about 3% more dense than the

ilmenite form, and I found that treatment of the KSb03 ilmenite for five minutes at 800 °C

and 20 kbar is adequate to transform the ilmenite phase to a body-centered, disordered

(The twofold and single K+ positions on the eight <^111)> directions are randomized.) form

of the cubic structure. The body-centered space group is 123. In this structure clusters

of K"*" ions form unscreened near neighbors, but the associated loss in Madelung energy is

apparently smaller than that associated with face-shared Sb^"*" ions in the hexagonal perovskite structure or with the formation of 180° Sb^+-0^"-Sb^+ linkages. Similarly NaBiOs

has the ilmenite structure; KBi03 and RbBi03 have the body-centered cubic structure [12].

The silver compounds AgNb03 ^'^^ AgTaOs = 0.94) form cubic perovskites above 550 °C and 485 °C, respectively, and are distorted to monoclinic symmetry at lower temperatures as

a result of Ag+-ion displacements. AgSb03 (t = 0.95), on the other hand, forms a defectpyrochlore structure in which are clusters of four unscreened Ag+ ions. The Sb^"'"-0^~-Sb^"^ 290
Fig. 4. SbOg octahedra network in KSb0 3.

linkages form angles of ca 135°. Again the loss in Madelung energy associated with the

Ag'^-ion clusters is apparently less than the loss in covalent-bond energy to be associated

with 180° Sb5+-o2--sb^+ linkages.

3. NEW SYNTHESES

In order to test further these tentative conclusions, the following new compounds have

been synthesized under pressure: RbNbOs, RbTa03, and RbSb03.

RbNb03 and RbTa03 have a large tolerance factor (t = 1.08) , but it did not seem to be

too large for the ciibic perovskite structure to be accessible under very high pressure.

Synthesis of RbNb03 was achieved at 65 kbar and 900 °C, and the atmospheric phase at room temperature was an orthorhombic perovskite (a = 3.9965 K, b = 5.8360 A, c = 5.8698 A)

isostructural with the orthorhombic form of ferroelectric BaTiOs- Once again f erroelecrric

distortions are associated with a t>t„'^ = 1.0. Preliminary DTA measurements indicate that

rhombohedral and tetragonal ferroelectric phases also exist. However, heating above 500 °C

leads to disproportionation without the formation of any hexagonal-perovskite polytype.

This is to be contrasted with the A^+b'^+Os compounds in which a metastable, cubic-perovskite

(3C) phase is stabilized by high-pressure snythesis. Heating of these latter compounds to above 1000 °C induces transformations to the hexagonal-perovskite polytypes stable at atmospheric pressure. Synthesis of RbTa03 required 90 kbar and 900 °C, which is at the limit of

my apparatus , and it was not possible to obtain the high-pressure form as a pure single

phase. The structure at atmospheric pressure was cubic or nearly c\±iic (a = 4.035 A).

The compound RbSbOs was synthesized at 20 kbar and 1000 °C. It forms the Pn3 structure

of ordered KSbOs with a = 9.6985 A.

These additional syntheses lend considerable support to the tentative conclusions

that motivated this research.

4. ACKNOWLEDGEMENTS

I would like to express my appreciation to Dr. J. B. Goodenough, who shared in the

strategy and interpretation of these experiments. I am also indebted to Drs . J. M. Longo

and J. W. Pierce for many stimulating discussions and to D. A. Batson and D. M. Tracy for

their technical assistance.

291
5. REFERENCES

[I] Goodenough, J. B. and Longo, J. M. , "Landolt-Bornstein" , Vol. III/4a, Springer-Verlag

,

Berlin (1970). Note: Material not specifically referenced in the text of this paper

may be found in this general reference

.

[2] Goldschmidt, V. M. , Akad. Oslo I. Mat-Natur 2_, 7-117 (1926).

[3] Babel, D. , Structure and Bonding _3» 1 (1967).

[4] Goodenough, J. B., Kafalas , J. A., and Longo, J. M. , "High-pressure Synthesis", in

Preparative Methods in Solid State Chemistry, P. Hagenmuller, Ed., Academic Press

(to be published)

.

[5] Longo, J. M. and Kafalas, J. A., J. Solid State Chem. 1, 103 (1969).

[6] Longo, J. M. and Kafalas, J. A., Mater. Res. Bull. 3_' 687 (1968).

[7] Wood, E. A., Miller, R. C., and Remeika, J. P., Acta Cryst. 1273 (1962).

[8] Kay, H. F. and Miles, J. L. , Acta Cryst, 10, 213 (1957).

[9] Vousden, P., Acta Cryst. 4, 68 (1951).

[10] Wyckoff, W. G., Crystal Structures, Vol. 2, 405 (John Wiley & Sons, Inc., 1964).

[II] Spiegelberg, P., Arkiv for Kemi , Min. Och Geol 14A, 5, 1 (1940).

[12] Zemann, J., Mineral. Petrog. Mitt. 1^, 361 (1950).

DISCUSSION

g . Banks : Ferroelectric phases in the perovskite structure can't be quite as simple

as your comments indicate. Right there on the board you had a very good example when com- paring potassium and rubidium niobates and tantalates. The temperature scale for any ferroelectric transition in the tantalates is of the order of 10 smaller than in the niobates.

Here you have nominally equal radii and essentially the same lattice paramters if you con- vert them to equivalent vol\ames and you still don't have ferroelectric phases in tantalates

and you do in the niobates

.

J. A. Kafalas : True, but tantalum has less of a tendency to accept four-fold coordination than niobium does and the ferroelectric distortion is just a tendency toward four-fold

rather than six-fold coordination. However, I agree with you, though, to a certain extent.

I had mentioned that I did some DTA measurements on the riibidium niobate and that we did

obtain the orthorhombic form. We find that there is a first order transition at something

like -15 centigrade and another one at 155 and another one at about 300. One could certainly

suggest that these are the same kinds of ferroelectric transitions that you find in barium

titanate.

B . Cox : You ascribed the structures of your niobates and tantalates to the high charge

on the niobium and the tantalum. Do you have a measured value for the ionicity in these

struc tures?

J. A. Kafalas : Not really, no.

B . Cox : Would you speculate on what the actual charge is?

J. A. Kafalas : I'd rather not at the moment.

J. B. Goodenough : l just wanted to say something with regard to Professor Banks'

question. You'll notice that Jim was very careful to say that when he had a tolerance

factor greater than one, it enhanced any tendency toward going to a ferroelectric transition. He didn't say that that was a sufficient condition, and certainly there are other

conditions that are involved. One of these is, as he mentioned, the need for a near equivalence in the site energies for the ion in tetrahedral and octahedral coordination. That

condition certainly provides an important difference between the tantalum and the niobium

ions

.

A. W. Sleight : 1 was wondering, Jim, whether you or perhaps John Goodenough would

like to tell us why it is that antimony does not like to form the 180° bond with oxygen.

J . A . Kafal as : Do you want to take that one , John?

292
J. B. Goodenough: Well, the working hypothesis we had in setting up this series of

experiments was simply that an antimony 5+ ion is going to have a very strong covalent bond

with the oxygen. Greater covalency per antimony occurs if the oxygen ion uses different porbitals for bonding rather than shares the same p-orbital with antimony on either side.

So, if the Sb-O-Sb linkages can make a 90° bond or something approaching a tetrahedral bond

angle, than the oxygen ion can use two different p-orbitals. Presumably a certain amount of

covalent-bonding energy is sacrificed by sharing the same p-orbital on two sides. That was

the idea we had, and we wanted to see whether one could force the antimony into 180° angles

in a perovskite structure. As you can see, we were unable to do it. So it seems as though

there is a fair amount of energetics involved in that consideration.

R. Ward: 1 think you can get antimony in perovskite structures, in the ordered perovskites.

J. B. Goodenough : That's correct. But there, of course, you are dealing with an ion on the opposite side that is not an antimony 5+ and that isn't bonding strongly in a covalent

way. There is no reason for the antimony 5+ not to want to be in a perovskite structure if

it can form an SbOg cluster that is not so tightly bound to the ion on the opposite side of

the oxygen ions. So, I think, that fits in very well with the explanation I was giving to

you.

293

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposiiom, issued July 1972.

DEFECTS IN OXIDES

J. S. Anderson

Inorganic Chemistry Laboratory

University of Oxford

Oxford, England

Defects in ionic crystals, such as the metallic oxides, are so intimately involved in

diffusion, reactivity and electronic properties, that an understanding of defect structure

is a necessary background for a variety of problems in the chemistry, physics and technology

of materials. In the present context consideration will be restricted primarily to thermodynamic defects: the inner equilibrium of oxide structures, stoichiometric changes that

displace that equilibrium, and solid solutions in which replacement of one cation by another

of different valence involves an analogous change in the ratio of cations to anions in the

crystal structure. This paper is largely concerned with structural matters and has two purposes: the first is to draw together what is known about highly defective oxide structures

(stoichiometrically variable and solid solution phases) ; the second is to consider, in more

detail, one or two systems that exhibit a remarkable capacity for organizing their defect

structures

.

It has been customary to treat these problems within the framework of point defect theory. This viewpoint, well rooted in statistical thermodynamics, is certainly applicable to highly ionic uni-univalent crystals (alkali halides) and, perhaps generally to highly dilute

defect systems - e.g. 10^'^ cm~^ or less. We are concerned with concentrations two orders of

magnitude greater, with ions of greater formal charge, and (in the important transition metal oxides) with a considerable measure of orbital overlap between cations and anions and, in some cases, direct cation-cation bonding. These last considerations raise questions about

the effects exerted by defects, such as anion vacancies, on charge screening and cation re- pulsions, and about the preservation of cation coordination so as to maximize charge screening and optimize the covalent component of the bonding.

We shall try to trace a progression in our classification of defect structures, and in

doing so we shall find effects both of chemical specificity - the electronic configuration,

as well as the size of cations - and of influences exerted nonspecifically , by crystal structure type

.

Key words: Block structures; crystallographic shear; defect clusters; defect models;

high resolution electron microscopy; oxide defects; rutile structure; Wadsley defects.

1. THE SIMPLE DEFECT MODEL

Dissociation of an oxide such as rutile is customarily represented as forming an inherently nonstoichiometric phase:

Ti02 Z Ti02-x + f

02

through the formation of point defects - anion vacancies or interstitial cations. For a vacancy model, the basic step is

O^^ - Vo"" + I

02

where Vq is a vacant anion site with two trapped electrons, which may ionize in two stages

to furnish electrons in the conduction band:

Vq'' t Vo" + e"

Vq* * + e- •

Application of the law of mass action relates the concentration of defects in each stage of

ionization to the chemical potential of oxygen, through the relevant equilibrium constants.

295
For an oxide such as rutile

,

with a very low intrinsic electronic conductivity

and

It is readily shown

[e-] = 2[Vo-'] + [V^-]

f^o^ total = [^o""^ ^ f^o-] + [V^--]

[1] ^ that depending on the vacancy ionization equilibria, the pressuredependence of the deviation from stoichiometry might vary from p"-^- to p~-^. Only if a single

stage of the ionization process dominates the situation is a simple pressure dependence to be expected.

If the defect structure involves interstitial cations, the defect reactions may be

written as

Ti02 O2 + Ti^

. X ^ . m+ Ti^ t Ti^ + me"

and the stoichiometric defect becomes proportional to p~^^ (m+1)

_

Numerous careful studies of rutile [1,2,3], Nb205 [4] and other oxides have been

analyzed on this basis. I^ the case of rutile, Kofstad and Forland considered that the

results agreed with the p~'^ law indicative of fully ionized oxygen vacancies over a composition range from TiOi.999 to TiOi.ggy (1050 °C) and TiOi . 992 3 (1194 °C) [3], or to TiOi.9905

(1227 °C) [1] . Whatever the structure may be at very low deviations from stoichiometry, this

fit between experimental data and the point defect model extends into a composition range

where as will be seen (below) , there is direct evidence that the real structure is quite

different. One must conclude that thermodynamic measurements do not suffice to discriminate

between alternative structural models, even for defect concentrations at which it might be

hoped that the behavior would be simple.

Point defects are customarily regarded as charged entities, located on regular sites

of the crystal lattice or on interstitial sites between them, and it is often (though not

necessarily) assumed that the interstitial positions are the special sites of high symmetry.

In calculations of defect energies, the ions surrounding a defect site are taken to relax

symmetrically from their idealized positions under the influence of coulomb forces and

repulsions. Various authors have drawn an analogy between defects in a crystal, with their

ionization equilibria, and ions in electrolyte solutions, with their protonation equilibria

[5,6]. On this basis, such processes as direct defect association and Debye Hiickel effects

can be treated. The analogy is useful and can be taken further. We are reminded that ions

in solution may profoundly modify the local structure of the solvent and that ions of high

charge interact so strongly with dipolar solvent molecules that a localized chemical transformation takes place: there is no such species as a Zr^"*" cation in aqueous solution; it

is transformed, at the expense of destroying water molecules, into a hydroxo complex. Similarly, relaxation of the system (point defect in a crystal) may go far beyond a simple re- balancing of coulomb forces, and may effect a structural transformation of the 'solvent'

crystal lattice. We can probably summarize the effects of such profound relaxations, and

of progressively stronger mutual interaction between the result: ng defect centers, as in

table 1.

2. APPROXIMATION TO THE SIMPLE DEFECT MODEL

The closest approximation to a random point defect description is afforded at first

sight by the NaCil structure monoxides of titanium and vanadium. These are remarkable com- pounds, with surprisingly high concentrations of cation and anion vacancies - 15% vacant

sites in each sublattice even in the stoichiometric phases, as is shown by figure 1 [7].

These defect concentrations are so high that, on a simple interpretation, they would imply

an absurdly low energetic cost of defect creation. The first thing to note is that these

oxides are metals; the formally +2 cations have occupied d-orbitals of sufficient radial

extension to overlap, so that there is strong cation-cation metallic bonding throughout the

r

Figures in brackets indicates the literature references at the end of this paper.

296
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297

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structure. This has two consequences. The first is that the excess negative or positive

charges arising from stoichiometric charge are completely delocalized, rather than being

trapped as cations of +1 or +3 charge, and the effect of stoichiometric change is only to

raise or lower the Fermi level ; the states concerned are probably in the non-bonding or antibonding levels of the d-band. The second is that the usual role of cation vacancies

and anion vacancies as charge trapping centers is effectively screened by the metallic electrons. As a result, coulomb interaction between the vacancies is greatly attenuated. Nevertheless, there are quite strong interactions.

These interactions show themselves in the transformation of the random, high temperature, nonstoichiometric oxides into ordered phases of fixed stoichiometry , below 1000° C. The structure of the TiO ordered phases has been worked out by electron diffraction [8]

.

There are two distinct structures, at TiO;^_oo '^^^1^25' shown in figure 2. It will be

noted that both structures are superlattices based upon the NaC!i type, with every occupied

lattice site assignable to a site of the parent structure. The vacant sites are now not

defects but are part of the structural pattern; they are a virtual ternary component of a fully ordered crystal pattern; because of this relation to the NaC2. structure, the two

definite compositions are dimensionally compatible with one another and can intergrow coherently. It has been shown that at compositions between TIOi^qq and TiOi^25 ordering leads to an unmixing into lamellae of the two separate ordered structures, only a few tens of Angstroms

wide. The structure at compositions below TiOi^gg in the ordered state has not been worked

out, but from analogy with the suboxide Ti20, in which oxygen atoms are located in octahedral

interstices of the hexagonal titanium structure, it is a plausible prediction that oxygen

atoms and oxygen vacancies will order themselves on {ill} planes of the sodium chloride

structure, with the possibility of giving other additional ordered stoichiometric phases in

intergrowth with TiOi^goIn the light of this evidence we return to the question whether the high temperature

phases are really random point defect structures. Strongly suggestive evidence to the con- trary comes from the fact that although high temperature VO and TiO have similar vacancy

concentrations, they are almost immiscible in the solid state, suggesting that they differ

in an incompatible way in the ordering of their defects on a short range basis. If the

random structures do not actually contain microdomains of the same kind of ordering as can

be fully developed in the low temperature phase, along the lines of Ariya's concept of defect solids, [9] , then at least it is likely that there is a strong correlation between the

positions of vacant sites. My colleague Fender and his pupils have shown that in the some- what analogous NaCJl type carbide structures, the carbon deficient NbCi_x phase shows strong

298
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coherent intergrowth.

correlation, with vacant carbon sites preferentially located in third nearest neighbor

positions.

The next stage in the deviation from a point defect model can be exemplified by the ox- ygen excess fluorite structure oxides such as U02+x- Here the coulomb repulsion between defects - formally identified as oxygen interstitials - reinforced by closed shell repulsion

within a crowded structure, modifies the structure of the parent crystal and transforms a point defect into a defect complex. The Willis structure for UO2+X -"-^ shown in figure 3; in the simplest form of the defect complex, the 2:1:2 complex, each interstitial oxygen displaces 2 oxide ions from their lattice sites, creating 2 vacancies, so that there are, in

fact, 3 associated interstitial oxygens, located on two sorts of general, interstitial site.

The number of such complexes in a crystal is, indeed, given by the number of oxygen atoms

introduced; the hyperstoichiometric oxygen is indeed interstitial; the thermodynamics of the

system approximates to that of a simple interstitial oxygen model. What has been completely

lost is any equivalence between the number of oxygen atoms introduced and the number of

point defects which contribute to transport and other properties. The defect complexes interact with one another and can be ordered, as in U4O9; they can be imperfectly ordered but

must still be quite closely correlated in the oxygen-rich region of the nonstoichiometric

UO2+X phase field.

It may be noted that this type of defect transformation appears to be common to hyperstoichiometric fluorite structures of ionic type. It is found in the CaF2YF3 solid solutions,

as Fender and Cheetham have recently shown.

3. NON-RECONSTRUCTIVE DEFECT CLUSTERS

The next stage we may recognize in the progression is a stereochemically specific asso- ciation of point defects, to form defect clusters without significant change in the atomic

positions of the "solvent" crystal lattice. This is exemplified by what is found in the

substoichiometric binary and ternary fluorite type oxides. Bevan has shown that, in these.

299
'L>.

• Uranium atoms. O Normal oxygen atoms. © Intentitial oxygen atoms 0*. • Inteittilial oxygen atoms 0".

Fig. 3. Model for UO2+X structure. Normal

oxygens, at A and B in U02,oO'

replaced by interstitial atoms 0" at C , D and 0 ' atoms at E (2:1:2

structure) or at E and F (2:2:2

structure)

.

unoccupied anion sites are paired up across the body diagonal of the cubic coordination polyhedra (fig. 4). Depending upon the size of the cation in this polyhedron, which may be symbolized as [MO5V2] , there may be little or no distortion of the f luorite-type cube. Since

every anion site is 4-coordinate , each vacant site is shared with three other cubes, and

the whole represents a dumb-bell shaped cluster which could be assigned the symbol [M0gV2]

[MO7V] g . Every site in this cluster corresponds to a site in the f luorite crystal structure

and the whole is dimensionally compatible with the f luorite crystal structure. It constitutes a unit which, if infinitely repeated, builds up a crystal MiM50i2 in Pr70i2 and

the ternary oxides of similar fonnula) . It is a sort of 'lattice molecule' which may be

plugged into the fluorite oxide structure (or oxyfluoride structure M-'--'--'-0 F) in place of a corresponding group of [MXg] polyhedra [10] . Substitution may be uncorrelated (or imperfectly correlated) , or the units can order themselves in one dimension, along their trigonal axis. They can give rise either to the variable composition a-phases of Ce02_x °^

to the ordered binary and ternary phases. Bevan has advanced evidence that there is a con- siderable degree of linear ordering of such strings of complexes even in the nonstoichiometric apparently random phases. Treating the vacant anion positions as potential electron

trapping sites, the cluster is an electrostatically neutral entity. However, if the ionization energy is small, then the carrier concentration depends only upon the numbers of rare earth cations in the 2 valence states +3, +4, i.e., upon the stoichiometry of the crystal,

and is little dependent upon the actual structure. The electronic properties of the substoichiometric rare earth oxides are simple functions of composition; their structures are

not. On the other hand, the mass transport properties of the crystal depend on mobile defects. The formation of such clusters almost completely removes the isolated anion vacancy

which is the unit of diffusional mobility. Such mobile vacancies can be formed only by what

is effectively a dissociation of the cluster, as represented by the notional equation

[MOg] + [MO5V2] [MOyVjg 2 [MOyV]^

anchored, paired, Isolated defect

structural empty anion vacancy,

anion sites

300
Fig. 4. The Bevan cluster in hypostoichiometric fluorite

structures. Creation of mobile point defect

vacancies involves dissociation of the tightly

bound paired empty anion sites (right)

.

If the clusters are well ordered, unoccupied anion sites are no longer to be regarded as defects; they are again structure elements of the crystal as it is. Even if the clusters are fully randomized, their stereospecif ically paired vacant anion positions are distinct from

the anion vacancies of the point defect equilibrium.

4. RECONSTRUCTIVE CLUSTERING

By reconstructive clustering is meant a rather more profound interaction between introduced defects and the crystal structure, which substantially modifies the occupancy of parent

lattice sites around the defect and emphasizes the role of non-coulombic interactions, crystal field effects etc., in determining the location of cations of different valence. The case to be considered is the ferrous oxide phase Fei-^O which exists only as a highly defective structure with 5 - 15% of vacant cation sites (on the point defect description; the

real concentration of vacant sites is much higher). Mn^.j^O is probably analogous. This is an example of a system where the sparse, but good, thermodynamic measurements of Darken and

Gurry and later workers look as if they follow the p~^ law required for a point defect model,

though later and more data intensive oxygen potential measurements [11] show complexities

and have not been fitted explicitly to the real structural situation.

The actual structure has now been investigated by a variety of methods, though only on

too limited a number of discrete compositions, and on quenched samples: by x-ray diffraction (by Manenc; Koch and Cohen) : by Bragg neutron scattering (Roth) ; by diffuse neutron

scattering (Fender and Childs) and by Mbssbauer effect. There is always some doubt about

the validity of deducing the structures of high temperature phases from quenched samples.

It is therefore important that the structure of ferrous oxide at high temperatures, in equilibrium with its gaseous environment, has been investigated by Bragg neutron scattering

(Fender and Cheetham) and by Mbssbauer methods (Howe) . These combine to give a picture which

is still incomplete, but from which the main conclusions seem assured. Roth's work showed

conclusively that some of the Fe^"*" cations moved from octahedral sites to tetrahedral sites,

thereby creating additional cation vacancies, and the minimum unit would therefore appear to be a complex of a tetrahedral cation bracketted by a pair of vacancies, the octahedral sites;

the analogy with the spinel structure of Fe304 is obvious but slightly misleading, and attempts have been made to fit the thermodynamics of the system to a defect structure based on Roth complexes. [12] At low temperatures, in its metastable existence range, the FeO phase

can undergo a considerable amount of superstructure ordering, and from the partially devel301

/
oped superstructure Koch and Cohen [13] deduced that the actual complex was the unit con- taining four tetrahedral iron atoms and 13 octahedral vacancies, figure 5. In other words,

there has been a considerable aggregation of empty iron sites to the units created by the

Roth complexing process. Such a structural unit is virtually a single cube of the zinc blend

structure type, and it bears a net anionic charge. It must therefore be surrounded by an ionic atmosphere containing other Fe cations in the octahedral sites of the surrounding

structure, which can indeed be described as of the NaCl structure type. This basic unit, of

Koch cluster plus its atmosphere, defines a certain minimum distance of approach between defect centers, which will tend to order themselves under coulombic forces. There are several

ways in which superlattice ordering can take place, which accounts for the apparent variable

and fractional multiplicity of the superlattice observed. The diffuse neutron scattering of

Fender and Childs gave results compatible with the Koch-Cohen cluster and its partial ordering, but is probably equally compatible with the slightly different structure deduced by

Howe from an analysis of the complex Mossbauer structure. This involves the creation of tetrahedral groups, with 5 tetrahedral Fe^"*" atoms and 16 cation vacancies. The high temperature

equilibrium work shows that the defect complexes are not an artifact of quenching and low

temperature ordering. The ratio of tetrahedral iron to total Fe^ in oxygen-rich FeO (e.g. Feo 85O) is consistent with either the Koch-Cohen or the Howe models; it is hardly possible

to discriminate on the basis of the evidence. The essentials of the structure are thus re- tained when long range correlation is lost and a nonstoichiometric phase of pseudo-NaCl type

is formed. The rather subtle thermodynamic differences between different parts of the

Wustite phase field, discovered by Vallet and Raccah and confirmed by Fender and Riley, can probably be attributed to some change in the type of defect complex that is present. Within

any one part of the phase field, a change of composition is reflected by a change in the ra- tio of sites that properly be described as FeO structure to sites that are taken up in the

complexes and their ionic atmosphere, without a change in the nature of the defects. In fact, at the oxygen rich end of the phase field it might be more correct to describe Wustite

as a coherent solid solution of FeO in a disordered superstructure oxide, of irrational formula given by the Howe or Koch-Cohen complex, than as a defect FeO phase. At the iron rich

end of the phase field (i.e., about Fbq 93© to Feg.gsO), and at very high temperatures, the

structure is less clear. The basic unit appears to be a tetrahedral ion Fe^"*" bracketed by

\

moves to tetrahedral site, creating a Roth- type

cluster. B. The Koch-Cohen cluster of 13 empty

cation sites and 4 tetrahedral Fe^+ . C. Alternative cluster with 5 tetrahedral Fe^"*" and 16

empty sites, and possible superstructure ordering.

(Howe) D. The basic cluster unit common to B and

C.

302
4 empty octahedral sites, which may be the defect center at the iron rich high temperature

end. With increasing concentration, such defect centers aggregate, with the absorption of

additional cation vacancies, to build up the more complex clusters. It will be noted that

there is again a profound difference between the real defect structure and the inferences

to be drawn by applying the point defect concept to the variable composition phase. It re- mains as a net vacancy structure, in the sense that the anion sublattice is more or less

completely occupied and the cation sublattice contains fewer cations than the sites available. The number of unoccupied cation sites is not simply related to the composition, nor can the empty sites within the complexes be regarded as defect vacancies in the usual sense. The diffusion properties become more complex. Chemical diffusion, such as transmission of a composition change in oxidation or reduction, requires a cooperative step whereby the location and average distance between the complex clusters is changed. It probably requires a cooperative diffusive mechanism in which, however, the mobility of the isolated vacancy dissociated from the complexes may be the unit diffusive step. The concentration of such isolated vacancies, is, however, much smaller than the number of vacancies that are subsumed in

the clusters. The electronic properties are also likely to be complicated, since the direct

electron transfer between cations on equivalent sites, but in different valence states, involves not all the Fe^"*" but only those in the ionic atmospheres of the clusters. From the

standpoint of statistical thermodynamics, it must be noted that the incorporation of a high

proportion of the vacant cation sites and of the cations of different valency into clusters

of definite structure has the effect of considerably diminishing the conf igurational entropy

of the system. As a consequence, the factor determining the stability, the oxygen potentials

and the structure assiamed by the material is shifted entirely in the direction of a gain in

enthalpy. The factors that enter into this are more subtle than could be extracted from a simple calculation of coulombic energies.

5. ELIMINATION OF DEFECTS BY CRYSTALLOGRAPHIC SHEAR

In the foregoing sections, it is clear that there may be an energetic advantage in processes that reduce the number of defects by subsuming them into larger, but less numerous,

extended defects; these may themselves be clustered and partially ordered. In the oxides of

the (formally) highly charged transition metal cations a particularly interesting situation

arises. It is evidently advantageous to maintain the screening of the cationic charge and

the character of the covalent component of the bonding by preserving octahedral coordination

and changing the coordination number of anions only. The effective size, charge and d-character of the cations are the determining factors. Relaxation then takes the form that has

been termed crystallographic shear, in which the changed coordination of the anions brings

about a closer linkage of coordination polyhedra along some defined crystallographic plane,

and thereby eliminates a complete sheet of anion sites from the crystal. This is a cooperative process; its mechanism is open to debate, but it virtually amounts to a two dimensional

ordering of anion vacancies, followed by a collapse of the structure across the crystallographic shear plane. It provides a basis both for generating a very large number of mixed

valence intermediate phases without any profound change in crystal structure and, as will be

seen, of eliminating point defects down to some very low concentration.

Thus in Re03-tyDe structures (e.g., idealized WO3) , the coordination number of oxygen

is increased from 2 to 3 by changing apex-linking to edge sharing of octahedra: in rutilebased structures, oxygen coordination is changed from 3 to 4 by face-sharing of octahedra.

In each case there is a reduction in cation-cation distances across the shear plane; this causes some distortion of the coordination octahedra, which is propagated out into, and progressively attenuated in, the slabs of parent structure between shear planes, and this may

be one of the (repulsive) elements in shear plane interaction. , Between the cations of face

sharing octahedra there may well be direct cation-cation bonding, sensitive to the nature

and d-character of the cations concerned.

We deal first with the mixed valence intermediate phases. These are formed by recurrent

shear, so as to enclose slabs of unchanging parent structure between crystallographic shear

planes of a particular orientation at regular intervals. If the slabs are of absolutely regular width, a crystallographically new structure of definite stoichiometry is forraed, with a composition that depends upon two factors: (a) the number of anion sites per cation site

that are eliminated in the shear plane, and (b) the width of the slab of parent structure

between shear planes. For any given shear plane orientation, the latter is a variable, so that a whole homologous series is generated, with the possibility of a very fine scale of

303
gradation in composition between successive members. If the slabs of parent structure are not of absolutely regular width, then a one-dimensional disorder is introduced, which gives

rise to the possibility of a new type of nonstoichiometry . It may be noted that the shear

planes, in general, extend by cooperative action across the full width of any crystal. A shear plane that terminates within a crystal must do so at a dislocation and it is energetically advantageous to propagate the shear plane across to the free surface. It can be shown

that disorder of shear' planes makes a very small contribution to the configurational entropy

of a crystal, so that the inner equilibrium is dominated by the enthalpy; ordering is ener- getically favored and the shear phases do not undergo significant disordering of their shear

planes at high temperatures. Such ordering does, however, involve longerange interactions -

O not yet satisfactorily interpreted - between shear planes that may be from 10 to >40 A apart.

The driving force behind ordering therefore falls off with the spacing. The evidence so far

is that the lower members in all series are rather well ordered, although the higher members,

with wider shear plane spacings, frequently do not attain perfect order within the time scale

of laboratory experiments.

Investigation of such problems is entirely dependent upon electron microscope techniques.

The existence of disorder, with narrow domains of a given member of the homologous series,

may be inferred from the streaking of electron diffraction spots, but for the detailed investigation of order the only available method is the purposive use of direct lattice imaging

as pioneered by Allpress. Thus Allpress and Gado found a considerable degree of randomness

in well crystallized W20O58/ ^ single crystal, homogeneous to x-rays, showed spacings between

successive shear planes (as measured on direct lattice images) varying between the values cor- responding to '^i2^3k (^62^3333) and W29O82 (WO2.9285) ^^'^ varying in distribution from isolated lamellae to strips of homogeneous structure wide enough to give discrete electron

diffraction spots (fig. 6) .

Of the crystallographic shear structures, the one most intensely studied is the rutile

structure, and this merits more detailed consideration. It is of interest because, (as indicated earlier) the native defect structure of rutile has been a matter of dispute;

opinions have been divided whether the n-type conductivity produced on reduction is associated with oxygen vacancies or with titanium interstitials . All the studies of rutile up to 1959, and practically all the physics even today, have been discussed in terms of the point

defect model. In fact, the composition range ostensibly covered by point defects in the ru- tile structure has shrunk progressively as the system has been more carefully investigated.

Crystallographic shear not only generates intermediate phases but operates as a means of

eliminating point defects in the rutile phase itself.

The real structural situation in reduced and slightly reduced rutile appears to be as summarized by table 2. There are two distinct series of shear phases, both with the general

formula Ti^02i^_i ' covering different ranges of composition and with the shear plane on two

different orientations. The {121} shear plane family oxides [14] can be obtained as well

ordered solids; the { 132} family [15] are almost invariably obtained in a one-dimensionally

disordered state, with lamellae of different compositions. Occasionally larger domains with

a single shear plane spacing are formed, but the thermodynamic individuality of these phases,

as will be seen in a moment, is so ill-defined that the driving force behind ordering is relatively small. Between the compositions TiOi 900 about TiOj 937 there has to be a re- orientation of the shear planes and we return to this point later. The {132} shear plane

phases extend to a composition about TiOi_g73, with n around 37 and the shear planes more or less ordered at distances of about 40 A_. Material with a yet smaller oxygen defect contains

coherently intergrown domains of the {132} shear plane oxides with domains of rutile structure; [15] [16]_these contain randomly disposed shear planes, not now lined up but on all

the possible (132} orientations. An isolated shear plane of this kind represents a two dimensionally 'infinite' fault, and has been termed a Wadsley defect. Hyde and Bursill [17]

have shown that in material brought by coulometric titration to the composition TiOi^ggsg

shear planes still line up in packets of 2-25, to define lamellae of the intermediate oxides,

and that, from the concentration and spacing of the random Wadsley defects in the rutile

structure (which is now the bulk of the crystal) , the composition of material in apparent

equilibrium with the nearly ordered packets of shear phases is around TiOi 999 . Mutual

alignment and aggregation of shear phases is thus obviated only at compositions still closer

to the ideal formula, and even then much of the oxygen defect is taken up and eliminated by

the random Wadsley defects. It follows that the true point defect concentration in reduced

rutile must be 10~^ or less.

304
lOOA

10 -

20

7o

WO.

2.666

2MS

^0

1920

10

-

16 W 24 28 32 ^

(a) The structure of W20O58: recurrent {130} crystallographic shear planes in the Re03-type structure.

(b) Single crystal 'W02.9o'= varieible spacing between

CS planes. (c) Corresponding distribution of CS plane

spacing in a "W20O58" crystal; proportions of lamellae

of different members of Wn0 3n-2 series.

305
Table 2

Summary of the Structural Situation in Reduced Rutile.

Thermodynamics

Composition Structure -G (1300K},kJ mol'

2 Equilibration behaviour

{121} crystal lographic shear phases ^in°2n-l 4 < n « 10 500 - 455 Hysteresis

Shear plane orientation changes

from {121 } to {132 }. Either: (a) Discontinuity: intermediate phases of two series coexist;

or (b) Continuous change; shear planes pivot around at roughly

constant spacing.

455 - 445 Good reversibility

TM1.9375 - =^ ^^°1.973 {l52} crystallographic shear phases

Ti 0. , , 16 i n « ca 37

n 2n-l'

445 - 43- Hysteresis

ca TiO^_g^3 - ca TiO^^ggg {132} shear planes group in lamellae defining high members of {l52} family, within rutile saturated with {132}

Kadsley defects

431 - ca 350 Probably hysteresis

TiOj^ggg - TiO^.^ Wadsley defects on all {132} orientations, too widely spaced to interact and aline

350 - 250

^i°2-x - ^iO2.00000 Point defects in rutile structure

X «0.0001

The subtlety of these changes in real structure obviously have thermodynamic implications. Some of the older, careful measurements of the oxygen potentials at compositions

close to the ideal overlap into the region where it is now seen that Wadsley defects replace

point defects. Thus all the attempts to analyze the results in terms of point defect theory

and a simple p~i law become meaningless. We may set aside older work on the {l2l} shear

phases , which showed that they were thermodynamic individuals but that transformations were

very sluggish except at very high temperatures , and focus attention upon recent worJc by

Hyde and Merritt, which correlates the themodynamics with the new information on structure.

The structural information shows that a very large number of discrete steps of composition

have to be fitted in to a relatively small total change of chemical potential between TiO^^ys

and TiO2,00' ^° that each step in chemical potential must be very small. Hyde and Merritt

found that, over each range corresponding to a single set of shear phase compounds, there

was gross hysteresis, at the temperature of the experiments (1300 K) , at least. The width

of the hysteresis loop was very large compared with the height of individual steps within

it. In such circ\amstances , maintenance of internal order and establishment of univariant

two-phase equilibria are hardly to be expected. Between these two distinct structural

ranges, however, there was a range of composition over which the behavior was truly reversible, and this was just where the shear plane orientation changed over from {l2l} to {132}.

This is very remarkable, and contrary to all that one would intuitively foretell.

Consider what is happening as composition of the oxide is changed by oxidation or re- duction, or is perturbed by the process of measuring an equilibrium situation. Over the

two end ranges, any composition change implies that shear planes have been eliminated or additional shear planes introduced into the crystal and then, for maintenance of order, all

shear planes have to adjust themselves to adopt a new regular spacing. It appears that either the creation and annihilation step or the migration and ordering step are kinetically

306
hindered, slow and responsible for hysteresis. In the middle range the situation is different. The distance between recurrent shear planes in any homologous series is given by the

formula „ , , ,

>

D = d^, „ (n-X) cs hk£

where d^^g is the interplanar distance in the rutile crystal between the planes upon which

the shear vector operates and X is the collapse factor in the process of shear (ideally,

X = 0.5). When we consider how the shear plane spacing changes in the two homologous series,

it becomes apparent that the upper end of the {121} series and the lower end of the {132}

series, as found experimentally, have slabs of parent structure of much the same width.

This means that, to a first approximation, a change of composition can take place without

changing the number of shear planes per unit volume, but by changing only their orientation.

Intuitively, it would seem that this should be a complex process productive of disorder,

sluggishness and hysteresis. In fact, it corresponds to ready reversibility. How does it

occur? The clue can be obtained with a high degree of probability from work on the ternary

anion-def icient rutile oxides, particularly the Cr203-Ti02 system.

The anion to cation ratio can be changed by introduction of ions of a different valency

and suitable ionic radius, as well as by oxidation and reduction. It must be borne in mind,

however, that there is one profound difference between nonstoichiometric binary systems and

ternary solid solution systems. In the former, a redistribution of cations in different

charge states can be mediated by electron transfer alone, without atomic movement. In the

ternary systems , the distribution of charge is firmly anchored to the distribution of atoms

of the two kinds. Hence any relaxation process may depend upon an ordering of the heteroatoms in the structure, and self-diffusion processes, which become important at high temperatures, may interfere with or destroy the charge distribution which is necessary for some extended defect structure. In the crystallographic shear phases, considerations of local

electroneutrality suggest that the +3 cations must be associated with the shear plane itself,

so that formation of Wadsley defects or of ordered shear structures would depend on cation

ordering. If this is not achieved, the crystal is left with some type of local structural

defect; either cations in interstitial positions or vacancies which may be bound by coulomb

association with the altervalent cations.

A second difference from binary systems is that chemical specificity may enter into the

behavior of the ternary defect oxides. Ionic radius differences will bring about small but

significant changes in both coulomb attraction and repulsion terms of the lattice energy.

The electronic configuration, particularly the d character of the hetero-cations , may have

far reaching effects on the non-ionic component of the binding.

Because VO2 gives rise to its own series of { 121} shear phases it is generally assumed

that titanium-vanadium ternary oxides will differ little from rutile itself, and the system

has not been thoroughly investigated. Doping with chromium brings to light a number of interesting effects that are significant for the understanding of_the rutile system. The first

is that ordering to shear phases takes place with ease. The {121} series of chromium titanium oxides was known earlier from Swedish work, [18] and electron diffraction and microscopy indicates that this extends roughly up to the member with n = 11 i.e., Cr2Ti9 02i

.

Preparations with higher oxygen to metal ratios display a remarkable phenomenon which probably sheds light on the behavior of the middle range of the binary oxide system. Between

the compositions indicated by n = 11 and n = about 22 at least, the well annealed oxides

show very good ordering, with regularly recurrent shear planes, demarcating slabs of rutile

structure of nearly constant width, about 20 A. The orientation of the shear planes swings

round progressively in the [111] zone, from (121) to close to (132) in a continuous progression, (fig. 7,8) as has been established by Hyde and Bursill [19] and independently by Gibb

[20] in my Laboratory. Only at compositions corresponding to n = 27 or thereabouts, obtained by annealing at lower temperatures, does the shear plane lie in or very close to the

[132] orientation. At about this composition the well-ordered shear phases coexist with

rutile structure; (fig. 9) this proves to be a chromium doped solid solution phase, the saturation composition of which varies markedly with temperature, the limiting chromium content

going up to about 5 atoms % at 1600°, [21]. This oxygen deficient solid solution does not

contain Wadsley defects, except perhaps when some slight reduction of Ti'^''" to Ti^"*" has taken

place. Since the unbalance between anions and cations is not eliminated by a crystallographic shear rearrangement, we are obliged to consider that there are localized defects in

this structure.

307

/
Fig. 7. Cr2Tin-202n-l / 12 < n < 22: superlattice direction

lying ieti^een [211] and [312].

Fig. 8. 'Pivoting' of shear planes: change of

composition in Cr2Tin-202n-i series

(n variable) achieved by rotation of

CS planes at nearly constant spacing.

Dotted lines show how CS plane spacing

and CS plane orientation would be

related for given, fixed values of n.

308
Fig. 9. Cr2Tij^_202n-l S-t low Cr'"^ content, 2natile str^act^ore without

Wads ley defects (left hand side) coexists with fairly well

ordered limiting-composition shear phase. At right, corres- ponding diffraction pattern.

At higher chromi\m contents, the {121} shear phase family ends with Cr2Ti3 0o, n = 5. Cr2Ti207 , n = 4, has a different structure, and phase analysis has identified it as a non- stoichiometric compoiind with a composition range that broadens considerably at high temperatures. At low temperatures, it narrov/s to a 'line phase', but does not come to the ideal composition, [21]. Reid in 2'Ielbourne has recently elucidated the constitution of this,

and shown that we have another nonstoichiometric phase based on random intergrowth of shear

structiires. These are not derived from irutile, but from the a-Pb02 structure and over the

composition range of the Cr2Ti2 07 phase there is a random intergrov7th of the meiriiers with

n = 3, 4 and 5 of the a-PbOp shear chase series CrpTi „0„ ,

. (fig. 10) ^ ~ ^ n-2 2n-l

In view of the surprising ease with which Cr^"^ generates v/ell-ordered shear structures

at low concentrations, it is of interest to examine the behavior of other trivalent cations

and bivalent cations of similar ionic radius as controllers of the anion-cation ratio and to vary, in particular, the electronic configuration of the doping cation. The Al203-Ti02 system shows only a narrow range of irutile solid solution, in equilibriiim with the pseudo-brookite phase Al2Ti05, and the solid solution shows no extended defects of any kind \inder any

conditions that we have examined [22] . It must therefore contain only localized defects.

Fig. 10. Recurrent crystallographlc shear in the

a-Pb02 stJTUcture, as in Cr2Ti207.

309
This may be a size effect, or might be associated with the absence of d orbitals available

for covalent bonding. If then one turns to Ga203-Ti02 systems, with the same outer shell

configuration but a somewhat better radius fit for the hetero-cation, one finds that the

gross features of the phase diagram are similar to those of the Al203-Ti02 system. As before,

there is a rutile solid solution range and a phase Ga2Ti05, but the rutile solid solution is now laced with Wadsley defects in the form of planar boundaries but on a new orientation,

{210} (fig. 11). It emerges, further, that there is an intermediate range of composition in

which these {210} planar defects order themselves in regular recurrence, to build up a new family of homologous oxides with the formula

Gait Tin_i+ ^2^-2 (7 < n < 11)

These are moderately well ordered but show some variations in stacking (fig. 12) ; they have

Fig. 11. {210} planar boundaries in Fe203-Ti02 solid

solutions; Ga203-Ti02 similarly.

Fig. 12. Ga203-Ti02: Incompletely ordered recurrent

(210) planar boundaries in crystal of

GattTin_tt02n-2 / defining lamellae with

variable values of n.

310
not been grown as crystals for crystal structure determination, but consideration of the

structural principle, dimensions and the displacement vector across the boundary, as determined from electron microscopy, suggests only one structure for them. This is related to the shear structures but involves a twinned orientation across each boundary. It is a type

of recurrent collapsed twinning.

This difference in planar boundary structures cannot be attributed simply to the availability or non-availability of d orbitals for covalent bonding. The Fe203-Ti02 system re- sembles the Ga203-Tio2 system in having a solid solution range with Wadsley defects on the

{210} orientation. This time, however, there is no ordering into discrete intermediate

phases with regularly recurrent boundaries, even after long annealing in the laboratory. It

may be, however, that all our laboratory experiments are too short, and that the longer diffusion paths attributable in the course of geological time, even at relatively low temperatures, would enable some ordering process to take place. Professor Buseck and I have therefore recently examined high quality natural rutiles, and it is found that in low temperature

hydrothermal rutiles there are both isolated Wadsley defects on the {210 } orientation and a regular long periodicity, suggesting that the collapsed twin boundaries have lined up very

regularly at very long spacings indeed. This is not the whole story. Rutiles formed and

annealed for geological periods at relatively high temperatures, and possibly under pressure

with compositions lying in the solid solution range show a remarkably well developed superlattice ordering of a different type, but it would be premature to discuss this now.

This brief survey of the behavior of rutile emphasizes the role that crystallographic

shear can play in the elimination of defects, as well as in the formation of intermediate

phases. It is appropriate to ask if this is general. The short answer is that the other

oxides that generate shear structure intermediate phases also appear to tolerate only minute

concentrations of point defects, and replace them by Wadsley defects for very small deviations from ideal stoichiometry

.

Thus WO3 has been examined by Tilley, Allpress and Sienko [23] [24] , who have found that

slightly substoichiometric material, in the composition range W02_99 to WO3 qO' obtained by

loss of oxygen in vacuum at high temperatures, accommodates the oxygen deficit by forming

disordered crystallographic shear planes parallel to {l20 }. These were already sufficiently

numerous to cluster into small groups in W02.99 88» ^^'^ were rare, but present, in WO2.9999;

in WO2.993 they had become more or less ordered, albeit imperfectly, at spacings of 40-50A,

to define lamellae corresponding to members of the homologous series Wjj03j^_i , with n around

30-50 (about W02,967 to W02.98)-

It will be noted that this group clustering of shear planes - and indeed, the formation

of a simple Wadsley defect - implies that a defective crystal spontaneously assumes a spatially inhomogeneous composition. The problem of how crystallographic shear takes place is, as yet, unsolved. During a reduction process, oxygen atoms can presumably be removed from

the crystal over the whole surface: by cooperative displacements and diffusion, the conse- quences of that oxygen loss are concentrated and organized at a single sheet of crystallographic sites. Possible mechanisms have been discussed by various authors [24] [25] [26],

but the processes of formation and mutual ordering are still obscure. In Ti02 and WO3 , there

is no evidence that oxygen vacancies have to be ordered or collected in a vacancy disc as a precursor to shear collapse. In M0O3 , Bursill [27] has found that a preliminary superlattice ordering of vacancies, at about the composition MoitOoOll99' take place but does not

appear to be an essential step in the formation of shear planes (in this case on { 120}jy[QQ^ ) .

For each of these examples, the shear plane orientation adopted by isolated, random

Wadsley defects is neither the only observed shear plane nor, necessarily, that found in

well characterized intermediate phases; in each case, however, the shear vector remains

constant:

In WO3 : initial shear on {l20}j^go <" compounds Wj^03j^_2 (Wi^qO]^ 18 '^20053)

have {l30}j^gQ shear planes. Shear vector i <110>

311
In M0O3 : initial shear on {120}mo02 ^ f^HlMoO^ (Mon03n-i ,Moi 3O3 1

)

{311}moO (MOn03n-2'Moi8052) {411} MoO ('^°n*-'3n-3 '^°26'-'75)

3 3 all with shear vector a, b, . [6]

2 7 "

In Ti02 : initial shear on {132}; (132) family Tin02n-1 (121)

family Tij^02n-1 /' shear vector (idealized) ^ <Oii>

There is evidence, as has been seen, that this reorientation of shear planes can take

place continuously: each shear plane is, strictly, pleated into a regularly puckered interface, but its trace remains straight as the mean orientation pivots around. In WO3 however

Allpress [29] has produced striking evidence that - in some circumstances at least , 'possibly

relating to non-equilibrium conditions - the shear planes may kink abruptly from the (120)

to the (130) orientation.

6. DEFECTS IN BLOCK STRUCTURES

Related to the crystallographic shear structures are those that have been interpreted

by Wadsley and designated 'block' structures [30] [31] , fomed particularly by niobium in its

binary oxides between Nbi2 02 9 (Nb02^m7) and Nb2 05, and in ternary oxides derived from these

These are based on the Re03 structural type, and the modified linkage of coordination octahedra, required by the stoichiometry , is accommodated by edge sharing, as in the Re03 -based

shear phases. They can be roughly described in terms of two sets of shear planes on (1^0^^^

and (OOl)j^gQ^, although not strictly derived from the Re03 structure by recurrent shear.

The ribbons of shear plane-like structure demarcate columns or blocks of Re03 -structure

,

(mxn) octahedra in cross section, are infinite along the b axis. They have been fully described in a number of places [31] [32] , and attention need be given in this place only to those aspects that are relevant for the discussion of defects. These substances lend themselves particularly well to the exploitation of direct lattice imaging methods: they have

fairly large unit cells, their structural principles are well understood and the lattice

images can be interpreted in some detail and with considerable conf idence .

( f ig . 13) In a series of elegant papers, Allpress has shown how much detail can be derived about defects

and fluctuations in the local ordering pattern, especially for the ternary niobium oxides

containing titanium (Ti,Nb Ox:0/Ti+Nb < 2.500) and tungsten (W,Nb Oj^ : 0/W+Nb > 2.500) [33].

During the past year or two, a great deal of evidence has been accumulated at Oxford about

the binary oxides NbO2 . 500 to Nb02.[+i7, in relation to nonstoichiometry

.

The feature that emerges unmistakably from these studies is this combination of flexibility with a high capacity for local ordering, in response to very small changes in anion:

cation ratio. The relation of the block structures to the Re03-type subcell imposes a com- mon metric on all the possible structures, while providing extreme possibilities for co- herent intergrowth of isolated blocks or rows of blocks of different sizes, or with different linkages between sets of blocks at the same level. This flexibility is subject to cer- tain constraints as the crystal optimizes its microstructure . The sheared Re03 substructure

must be conserved in the orientation of the [MO5] octahedra and the location of metal atoms

and equatorial oxygen atoms. The assembly of blocks must be space-filling. The permitted

sizes of blocks is restricted by considerations of local electroneutrality - one can regard

the block structure oxides as assemblages of rod-like anionic structures extending along the

h axis, balanced by cationic rods constituted by shared corners of blocks, or tunnels filled

with tetrahedrally coordinated cations, but the local acc\imulation of charge must not be

excessive

.

Subject to these constraints, the compounds reveal a remarkable capacity for discriminating between very small changes in the anion: cation ratio and forming new extended ordering patterns in response, and for assimilating yet smaller compositional fluctuations into

1-dimensional , highly localized structural rearrangements. Changes in composition - in the

proportions of the constituents in the Ti02-Nb205 and W03-Nb205 ternary oxides, for example,

or through oxidation-reduction processes for the mixed valence oxides between Nb2 05 and

Nbi2029 ~ can be assimilated, through the coherent intergrowth of a dimensionally compatible

but different structure, identifiable as lamellae of a different compound [33] . If these

are regularly recurrent, a new ordered intergrowth compound is formed - e.g., the M53O132

312
Fig. 13. Lattice image of the (5x3)_^ structure M15X37 (MgNbj 1^03 5F2

)

showing correlation between lattice image and crystal structure

(inset) . Note twinning and a dislocation.

phases TiNb520i32/ Nb530i32 formed by alternation of unit cell-wide strips of the H-Nb205

(Nb2807o) and the M25O52 structures. If the proportion and the distribution of the lamellae

are irregular, the crystal is inherently nonstoichiometric . If the strips of new structure

associate into packets, several or many unit cells wide, the crystal assumes a domain structure which poses questions - at present with no answers - about the thermodynamic behavior

and thermodynamic characterization of the materials. Which of the above configurations minimizes the free energy of the system? The experimental evidence so far - e.g., from the

reduction of Nb205 - is that rearrangement to new block sizes and block linkages can take

place at relatively low temperatures (below 1000 °C) and usually results in a small-domain

arrangement of the simple structural types. Thus both reduction of Nb2 05 and solid state

reactions of Nb02 with Nb205 at 1000° C yield crystals with domains of the H-Nb2 05 structure

of the (3x4)2 structure of Nb25052 ^J^d of the (3x4) structure of Nbi2029' coherent inter

growth. At 1300° C, such domain crystals transform slowly to form large domains of the

regular intergrowth structures [34] . (fig. 14)

During the past year, systematic high resolution electron microscopy at Oxford has provided information about the modes of faulting, in block structures, that are permitted by

the constraint of conserving the Re03 basic structure. The first type is that which creates

planar domain boundaries while preserving the stoichiometry of the crystals. These include

twinning modes that change the orientation of rectangular blocks , or that reverse the direction in which blocks at the same level are linked in ribbons; because they have to be com- patible with the integrity of the basis structure, the possibilities for such boundaries

vary considerably from one block structure to another. Different block structures may have

the same stoichiometry (e.g., the (3x4) ^ + (3x5)^ structure of H-Nb205 and the two variants

of (4x4)^ structure found in M- and N-Nb205) . Strips of different structure can therefore

be incorporated, as intergrown lamellae or as part of a twinning mechanism, without change

of stoichiometry. Small deviations from stoichiometry can arise not only from changes in

oxidation state, but also from the incorporation of impurities that may catalyze the production of a particular, possibly metastable, crystal structure. Thus, N-Nb205, most readily

313

/
o) (hC3) lattice fringes shc.-'irj diicrvi.r (x750,050)

1 igbt on plate

iDcjococlocL cc'dc c|o c c ! 0 c c:

D Cioc C|0 CIO c|dc|dcc ,'2 C C ;

b} '.

i crcdens i tcr:eter trace across A-A

C DC OC O CCD CC I)

it C-1 i tno oxi , ; c-^;-';'e(U i V i nlcsgro .;itii '-^i^- ) <2-

Fig. 14. Nonstoichiometry in Nb205-x:

1-dimensional (hoo) lattice

fringes show intergrowth of

Nb39097 and Nb530i32 in Nb28O70

(H - Nb205)

.

obtained in the presence of F~ ions, tends to be doped with a low concentration of fluorine

in place of oxygen, to give crystals with 0+F/M slightly greater than 2.50000. In these

circumstances, the evidence indicates that, as has been seen previously, the stoichiometric

defect is concentrated into a localized fluctuation of composition that expresses itself in

a local element of new structure, with different block sizes and/or block linkages from that

of the surrounding matrix. Short range order is maintained. This may be illustrated by fig.

15, a lattice image of N-Nb205; the relation between the idealized block structure and the

contrast distribution in the lattice image is shown on the m.icrograph. Over the field as a whole, the ribbons of linked, square (4x4) blocks can be recognized. At A, a strip of (4x3)

blocks - unambiguously identified by their dimensions - is coherently incorporated, and this

implies a local change in stoichiometry concentrated into this sheet of the crystal. The

fault is finite; it terminates within the crystal at B, and reconstruction of the block structure, from the measured fringe positions, leaves no doubt that the crystal reconciles the

fit of the blocks meeting at that point by building in a single linear fault - a single tunnel providing an array of tetrahedral cation sites.

These ways in which local order is strongly preserved, by a process analogous to the

readjustment of shear plane spacings, prompt the question whether, (as in the crystallographic shear structures themselves) point defects are virtually eliminated. It is not possible,

at the present time, to settle this question definitely, but the balance of evidence seems

to favor the existence of anion vacancies or cation vacancies in some form. Allpress and

Roth [35] have made a careful statistical study of the number and distribution of Wadsley

314
Fig. 15. Lattice image of N-Nb205 ((4x4)^ structure, inset).

At A, C, D strips of different ((4x3)^) blocks.

Faults A, C terminate at B in a single tunnel of

tetrahedral sites.

defects in Nb205-rich WNbi2033 (composition range MO2 . 5000~ ^^LSSSs")- There are regular

intergrowth phases in this system, with regularly recurrent ribbons of (3x5)^ blocks inserted in the (3x4)]^ structure of WNbi2'-'3 3' low excess concentrations of Nb205 , isolated

ribbons of (3x5)^ blocks appear as Wadsley defects. In the most carefully annealed preparations, at compositions between W03.6Nb205 (M02,5385) ^nd W03.8Nb205 (MO2.5294)/ the density

of Wadsley defects was too low, and their mean spacing too great, to account for the deviation from the composition of the (3x4) ;^ block structure. Similarly, in the reduction of

H-Nb205 , as mentioned above, the first step is that of conversion to the (3x4)2 structure of

Nb25052, and this appears at 1000° in lamellar domains, which are incorporated at higher

temperatures into intergrowths of Nb530]^32 (NbO2,4906) Nb390g7 (Nb02^i4872) [34]. At

compositions between NbO2 . 5000 ^^"^ about Nb02.i+95, however, few Wadsley defects (lamellae of

(3x4)2 tilocks) can be found. In both these instances there appears to be a narrow but ex- perimentally significant range of anion:cation ratio in which there is a metal excess, with

respect to the observed structure, not accounted for by extended defects. Since it is a metal excess, it cannot be explained by a variable occupancy of tetrahedral sites [32] , but

would seem to imply anion vacancies, interstitial cations or localized defect complexes

based upon such point defects.

7. CONCLUSION

The theme underlying this paper has been that information about the real ultramicrostructure of defective crystals is essential for a theoretical treatment of their properties.

The evidence advanced has been selective, but it is representative of those structures and

systems about which most is now known. It is clear that, in the present state of the subject, no simple generalized treatment is feasible. The common property is an inbuilt ten315

;
dency towards attainment of order on a local scale if not at long range. Lattice energy

calculations by Burch [36] , confirm not only that ordered configurations are advantageous

as compared with random distributions at significant defect considerations but that, as far

as the electrostatic part of the lattice energy is concerned, there is little between radically different ways of achieving order - as between ordered vacancies and crystallographic

shear in the rutile structure, for example. How crystals deal with defects thus depends on

the more subtle and non-coulombic interactions. Specificity enters in this way, and no one model can embrace the whole of chemistry: neither crystallographic shear nor superlattice

ordering is a universal explanation. At the end, and especially in ternary solid solution

systems, we are left with localized defects, without information, as yet, whether they are point defects or extended defects. One obvious requirement is an extension of experimental

methods to study such problems.

8. REFERENCES

[I] Kofstad, P., J. Phys. Chem. Solids 23_ 1579 (1962).

[2] Hurlen, T. , Acta Chem. Scand. 12 365 (1959).

[3] Forland, K.S., Acta Chem. Scand. 1£ 1267 (1964).

[4] Kofstad, P. and Anderson, P.B., J. Phys. Chem. Solids 21_ 280 (1961), Blumenthal, J.B.,

Mason, J.B. and Whitmore, D.H., J. Amer. Ceram. Soc. 4£ 620 (1965).

[5] Kroger, F.A. , Chemistry of Imperfect Crystals, North Holland Publ. Co. Amsterdam Chap.

IX (1964) . [6] Reiss, H. , Robert A. Welch Foundation Conference on Chemical Research XIV Solid State

Chemistry, Houston 1970: in publication.

[7] Banus, M. D. and Reed, T. B. , Extended Defects in Nonmetallic Solids, North Holland

Publ. Co., Amsterdam, p. 488 (1970).

[8] Watanabe, D. , Terasaki, O. , Jostsons, A., Castles, J.R., Extended Defects in NonMetallic Solids, North Holland Publ. Co. Amsterdam, P. 238 (1970)

.

[9] Ariya, S.M. and Morozowa, M.P., Russ. J. Chem. 28_ 2647 (1958), Ariya, S.M. and Popov,

Y.G., Russ. J. Gen. Chem. 32.2077 (1962).

[10] Bevan, D.J.M., Baker, W.W. and Martin, R.L. , Rare Earth Research Vol. 3, p. 441, Gordon

s Breach N.Y. (1965); Parks, T.C., Thornber, M.R. and Bevan, D. J.M. , J. Solid State

Chem. 1 536 (1970). Thornber, M.R. , Bevan, D.J.M. and Summerville, E., J. Solid State

Chem. 1 545 (1970)

.

[II] Vallet, P. and Raccah, P., Mem. Sci. Rev. Metall. 62_ 1 (1965). Fender, B.E.F. and

Riley, F.D., J. Phys. Chem. Solids 3_0 793 (1969).

[12] Kofstad, P. and Had, A.Z., J. Electrochem. Soc. 115 102 (1968.

[13] Koch, F. and Cohen, J.B., Acta Cryst. B 25 275 (1969).

[14] Andersson, S. and Magneli, A., Naturwiss 43_ (1956).

[15] Bursill, L.A., Hyde, B.C., Terasaki, O. and Watanabe, D. , Phil. Mag. 20 347 (1969),

Bursill, L.A. and Hyde, B.G., Acta Cryst. B27 210 (1971).

[16] Anderson, J.S. and Tilley, R.J.D. , J. Solid State Chem. 2_ 472 (1970).

[17] Bursill, L.A. and Hyde, B.G. , Phil. Mag. 23. 3 (1971).

[18] Andersson, S., Sundholm, A. and Magneli, A., Acta Chem. Scand. 13_ 989 (1959).

[19] Bursill, L.A. Hyde, B.G. , Phil. Mag. 23.1501 (1971).

[20] Gibb, R.M. and Anderson, J.S., J. Solid State Chem. In course of publication.

[21] Florke, O.W. and Lee, C.W. , J. Solid State Chem. 1 445 (1969).

[22] Gibb, R.M. and Anderson, J.S., In course of publication

[23] Tilley, R. J.D. , Materials Res. Bull. 5_ 813 (1970).

[24] Allpress, J.G. , Tilley, R.J.D. and Sienko, M.J. , J. Solid State Chem. 3_ 440 (1971).

[25] Anderson, J.S. and Hyde ,, B . G .

, J. Phys. Chem. Solids 28_ 1393 (1967), Hyde, B.G.,

Extended Defects in Nonmetallic Solids, North Holland Publ. Co. Amsterdam p. 347 (1970).

[26] Andersson, S. and Wadsley, A.D. , Nature 211 581 (1966).

[27] Bursill, L.A. , Proc. Roy. Soc. A. 311 267 (1969).

[28 [ Kihlborg, L. , Arkiv. Kemi 21_ 443 (1963).

[29] Allpress, J.G. , Personal communication; in course of publication.

[30] Roth, R.S. and Wadsley, A.D. , Acta Cryst. 19 42 (1965), Wadsley, A.D. , Helv. Chim.

Acta Alfred Werner Volume p. 207 (1967)

.

[3]] Wadsley, A.D. and Andersson, S., Perspectives in Structural Chemistry, Vol. Ill Wiley,

New York (1970)

.

[32] e.g., Anderson, J.S., Problems of Nonstoichiometry , Ed. A. Rabenau, North Holland

Publ. Co. p.l (1970)

.

316
[33] Allpress, J.G., Sanders, J.V. and Wadsley, A.D. , Acta Cryst. B25 1156 (1969, Allpress,

J.G., J. Solid State Chem. 1. 28, 66 (1970); 2_, 78, 366 (1970).

[34] Nimmo, K.M. and Anderson, J.S., To be published.

[35] Allpress, J.G. and Roth, R.S., J. Solid State Chem. 3^ 209 (1971).

[36] Burch, R. and Anderson, J.S., J. Phys . Chem. Solids and unpublished work.

DISCUSSION

p. Hagenmuller: I would like to make a comment about the rather important question you

raised: do we have two phases or one phase in a given specimen? My question would be , do we really have an equilibrium situation because the phase rule only corresponds to an equilibrium situation?

J. S. Anderson : This is a very difficult point to decide, as Dr. Hyde knows from, his

very careful work on rutile. It is exceedingly difficult to get anything, in operational

terms, which corresponds to the purely hypothetical concept of thermodynamic equilibrium

and a thermodynamically reversible process. Anything we do perturbs the system and it never

can recover. I don't know. I don't know whether one can say any more than that we see steady

state situations.

J . M. Honi

g

: I was wondering, in connection with your earlier discussion, whether you

could not get screening of point charges in solids whenever you have a lot of mobile electrons

around so that you could turn the long range coulomb forces off. In which event I would

imagine that those materials would be subject to the laws of independent point charges. Is this a correct assumption?

J. S. Anderson : Certainly, it is a closer approach to it. All I know is that in some materials, not necessarily oxides, but for instance the carbon deficient niobium carbide

phase, there is a strong site preference for a third nearest neighbor and this is not some- thing that you control by any simple coulomb interactions, I think.

R. S. Roth : 1 want to go back to the first comment of Professor Hagenmuller. I think we must remember the original statement that Dave Wadsley made after John Allpress took the

first lattice image pictures of the niobium-tungsten oxide shear phases. Wadsley 's statement

was that "The definition of equilibrium depends upon the wavelength used to examine it."

The second point I wish to emphasize is the following. As John Allpress and I have demonstrated with these phases-^, if after examining with the electron microscope and realizing

you have not reached equilibrium, you then make a really concerted attempt to obtain equilibri\im in such a specimen by month-long heatings just below the melting point, you can order

up these phases. I think we have to say that when you are looking at a system that has

random shear planes, Wadsley defects, it is a non-equilibrium situation. It is neither one phase nor two phases. Perhaps I should coint a new word for a poorly equilibrated specimen,

it is gunk, and that is all you can consider it. It may be a little more than just a physical

mixt\ire, but it is still a non-equilibri\im situation.

J. S. Anderson : Well, I agree with you it is a non-equilibrium situation. What I say we do not know is what an arbitrary composition would come to when it was finally brought

to equilibrium. I strongly suspect that some of these might really present your concept of

an infinity of ordered structures. They would find some way of accommodating any possible

composition within some, if necessary very complex, stacking or ordered arrangement.

J. G. Allpress and R. S. Roth, J. Solid State Chem. 3_' 209 (1971).

317

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

OXYGEN DISSOCIATION PRESSURES AND PHASE

BEHAVIOR IN THE TRANSPLUTONIUM OXIDES*

T. D. Chikalla and R. P. Turcotte

Fuels and Materials Department

Battelle Memorial Institute

Pacific Northwest Laboratories

Richland, Washington 99352

The results of recent oxygen vapor pressure measurements over nonstoichiometric AmO^^,

CmOjj; and BkOj^ are presented. These include derived information concerning the phase relations and partial thermodynamics of oxygen solution over the range 1.5 < x < 2.0 and 300 < T

< 1200 °C.

The americium-oxygen system has been examined by thermogravimetric techniques in the

single phase a region for 1.80 < x < 2.00 to yield relative partial molar heat and entropy

data. Supporting information obtained by quench methods and x-ray diffraction analysis ex- tend the results to lower compositions and, additionally, demonstrate the existence of a bcc

a phase over a wide composition range. Phase relations in the curium-oxygen system have been

defined by a series of isobars in the pressure range 2 < pq^ (mm) < 730. In addition to a and a phase, compounds of more narrow compositional width are seen at CmO^ 72 and Cm0i.g2,

and a plausible phase diagram is constructed. Differences obtained on two curium isotypes

of greatly different radioactivity are discussed. The berkelium-oxygen system has been ex- amined using a novel capacitance manometer system and a 1.2 mg sample. A set of five isotherms was obtained over the range 852 < T (°C) < 1150. The isotherms show a regular variation across a. and a regions separated by a diphasic field at x ~ 1.79. In addition, a narrow

two-phase region exists between BkO;[ and BkOi_93. Certain similarities are shown to exist

between this and certain other fluorite related ternary oxide systems.

In addition, melting behavior of the di- and sesquioxides and polymorphism in the ses- quioxide is described over the entire actinide series.

Key words: Actinide oxides; actinide sesquioxides; americium oxides; berkelium oxides;

curium oxides; melting points of actinide oxides; nonstoichiometry ; oxides; thermodynamics .

1. INTRODUCTION

The recent investigations of transplutonium oxides in this laboratory and others have

progressed to the point at which compilation of the existing information is of value. Indeed,

understanding of the actinide oxide systems in the M^+ - m'^''" regime is yet primative by com- parison to other areas of solid state science. In detail, the behavior in each of the systems for 1.5 < X < 2.0 in MOj^ (where M = Am, Cm, Bk) is markedly different and we observe

the systematic trends ascribed to these elements as a family only in a coarse comparison.

* This paper covers work performed by Battelle-Northwest under AEC Contract No. AT (45-1) -1830

319
At the end member compositions (x = 1.500 and x = 2.000) , the behavior through the se- ries is more regular, and phase relations (polymorphism) in the sesquioxide are now well

documented for both the actinide and lanthanide series [1,2]^. It is our primary interest

to consider the phase behavior in what would normally be considered the nonstoichiometric

field where 1.5 < x < 2.0 and the sesquioxide is of the fluorite related C-type structure.

In an effort toward completeness, the high temperature phase diagram and melting behavior of

the stoichiometric end member oxides is discussed in the first section. We call attention

to a previous discussion of the fluorite related actinide oxide systems that serves as a basis in some respects for the extension presented here [3]

.

2. M2O3 AND

The melting behavior of the actinide dioxides and sesquioxides has recently been reviewed [2] . In addition, polymorphism in the sesquioxide has been correlated with ionic radii

for both the actinide and lanthanide series.

There are no melting point data for oxides higher than curium. As shown in figure 1, a reasonably linear decrease in the melting point of the dioxides with increasing Z is observed,

while the opposite trend is true for the sesquioxides. The heats of formation of the actinide

dioxides decrease in a similar manner which reflects the lowering of bond energies with increasing atomic number. The increasing stability of the sesquioxides with increasing Z parallels behavior in the lanthanides , where the melting point increases to a maximum at Gd203,

whereafter it remains essentially constant [1]. If the same behavior occurs in the actinides,

this maximum may exist at 0^203, which, based on electronic configuration, is the actinide

homologue of Gd20 3.

Phase transformation behavior for both lanthanide and actinide sesquioxides shows a good correlation of the thermal stability domains of the various polymorphs and ionic radii

(fig. 2) . The five crystallographic modifications for the sesquioxide include A (hexagonal)

,

B (monoclinic) , C (cubic) , H (hexagonal) , and X (cubic) forms. It is interesting to note

that the high temperature H-form sesquioxide is probably the only crystal structure common

to all of the lanthanide and actinides with the exception of Lutetium. Relevant to later

discussion, the metastability of the C-type structure relative to C B or C A transitions

in the < 1000 °C temperature range should be pointed out. This is really to be expected at

these temperatures, where necessary cation movement is slow.

3400

3200 -

3000 -

2800 -

2600

2400

2200 -

2000

92 93 94 ATOMIC NUMBER

Fig. 1. Melting points of actinide di- and sesquioxides.

1 Figures in brackets indicate the literature references at the end of this paper,

320
IONIC RADIUS (A)

Fig. 2. Stability diagram of polymorphic forms of

lanthanide and actinide sesquioxides

.

• - high temperature transformations (ref. 1).

0 - Cm203 transformation temperatures (ref. 2).

- Pm203 transformation temperatures (ref. 2).

A

- Sm20 3 transformation temperatures (ref. 2)

.

V - low temperature transformations (ref. 23).

3. AmO

X The early dissociation pressure measurements of Asprey and Cunningham [4] with a milligram-size sample demonstrated the existence of an Am02-x (ct) phase to at least x = 0.15.

More recent work at lower temperatures by Chikalla and Eyring [5] by a tensimetric method

agreed with the early measurements and allowed accurate determination of the partial thermodynamic quantities. The isotherms (fig. 3) are smooth curves over the entire measured range

1.80 < 0/Am < 2.00. Thermodynamic equilibrium was demonstrated at all but the lowest temper

ature where data were taken in reduction only. There is a notable change in slope in the

isotherms at 0/Am = 1.98-1,96, reflecting a change in defect structure, at this time undefined. The partial molar entropy and enthalpy obtained by the relations

AS„ = - 9(AG„ )/8T (1)

Ai = R 3 (In p^ )/8 (1/T) (2) U2 U2

are given in figure 4, again indicating a larger rate of change at the high composition end

of the a field.

An x-ray diffraction analysis of quenched samples was made across the entire compositional width 1.50 < 0/Am < 2.00 [6]. These show the formation of a bcc phase (o) in the

range 1.50 < 0/Am < 1.67. Samples annealed in the a region could not be quenched but alway

gave a two-phase mixture of Am02.oo ^^'^ ^ phase of estimated composition AmOj^s- By implica

tion, it was suggested that another diphasic region must exist in the interval 1.67 < 0/Am < 1.8.

321

465-504 O - 72 - 22
E

OxygTi/Ampncium

Fig. 3. Dissociation pressure isotherms for AmO^.

Oxygen / Americium

1.80 1.85 1.90 1.95 2,00

2.00 1 .fl5 1 .90 1 .85

Fig. 4. Partial molar entropy and enthalpy for

AmO^.

322
These results may be compared to a recent investigation of the system by ceramographic

and DTA methods by Sari and Zamorani [7] . A phase diagram is suggested which closely parallels that for the PuOj^ system but which is at some variance with these earlier data. A miscibility gap of two a phases shows closure at 1000 °C . The low composition phase intersects

the a field at 0/Am - 1.98, while the high composition phase approaches 0/Am - 1.98 at a temperature of ~ 850 °C.

As discussed above, the x-ray work [6] would suggest a greater complexity in the 1.67-

1.80 region and that the a field extends to the 1.50 composition rather than to 1.63 as indicated by Sari and Zamorani [7] . Clearly, these differences can be resolved only by equilibrium studies over the full range of composition, most importantly by high temperature

diffraction methods.

4. CmO^

Posey et al. [8] reported the first thermograms for the decomposition of Cm02, followed

shortly after by Mosley [9] , whose effort concentrated on the sesquioxide as a candidate isotopic fuel. Chikalla and Eyring [10] published results of a detailed study of dissociation

pressure - composition - temperature relations obtained using a thermobalance technique.

O h Q Most recently, a similar study of CmO^^ has been completed on a sub-milligram sample using

an automated capacitance manometer system [11] . All previous studies were made on ^^^Cm,

which is an alpha emitter with a half life of 18.1 years compared to 3.7 x 10^ years for the

7 U R Cm isotope. It was the objective of this study to assess possible differences in the

chemical nature of the Cm-0 system due to radiation damage.

Since only 0.68 milligram of ^"^^Cm oxide was available, classical microbalance methods

for studying dissociation behavior could not be used. The differential capacitance manometer system employed (fig. 5) is capable of detecting gaseous uptake or evolution of < 10" -^^ moles of gas. The major problem in realizing an accuracy approaching this sensitivity level

is the elimination of system effects either due to physical or chemical changes. The capabilities of the system and detailed information concerning its construction and reduction of

data have been reported [12]

.

For the ^'^^CmO^ sample, isobaric traces were recorded with a sensitivity which allowed

composition to be estimated to 0.001 in x. In the present case, the assumption of three

(P-T-x) points (x = 1.500, 1.714, 2.000) was used to fix correction curves (APgygtem versus

T) for each isobar independently of any other run. The corrections were very small at lower

pressures ( < 50 mm Hg) , but at 760 mm Hg, approached values as high as 30% of the pressure

change due to complete sample reaction. Analysis of the data suggests an uncertainty of ± 0.003 in 0/Cm for the stoichiometry measurement.

HIGH VACUUM

BEIiOWS SEAl£D V*IVES

Fig. 5. Capacitance manometer system.

323

;
The '^^^CmOjj results [10] demonstrated the existence of a number of intermediate phases

in close parallel to the behavior of the rare earth systems CeOj^, PrO^ and TbO^^, now well

established. (See [3] for references.) Representative isobars are given in figure 6. The

decomposition is seen to proceed through a narrow region of Cm02_jj (a) , to phases CmOi 82+x

(6) and CmOi^72 (i) and f inally CmOi^5+jj (o) . Complete reduction to the sesquioxide was not

achieved even in a H2 atmosphere.

These results may be compared to isobars of the ^'*^Cm02 decomposition at an oxygen pressure of 735 mm Hg in figure 7, The similarities are evident. The major apparent differences

are the shift of composition for the 6 phase to CmOi 80 + x^^'^ ease of reduction to the

sesquioxide at - 865 °C. The three isobars shown demonstrate that the degree of completion

of the a -> Cm203 decomposition relates directly to the subsequent oxidizability of the product. The oxidation resistance of the B-fom sesquioxide has been discussed by Mosley [9]

,

where no oxidation was observed in 1 atm O2 except for 250 < T < 520 °C. Thus, we interpret

the break from a to lower compositions as a a -> B - Cm203 decomposition. This interpretation

is, however, not consistent with the kinetic data [9] for the transformation C -> B since no conversion occurred below 900 °C and 1290 °C was required for completion. We ascribe this

difference to impurity or crystallite size differences and note the long history of different

temperatures reported for the rare earth oxide polymorphic phase transformations.

The ^^'^Cm and ^^®Cm results may be more completely compared by the phase boundary plot

of figure 8. There are marked temperature shifts for several of the reactions and differences

in entropy values (slopes of the RT In PQ2 versus T lines) . The vertical lines obtained in

the low temperature region of the a-6 boundary and the a B boundary are taken to indicate

non- thermodynamic behavior (kinetic limitations) , while the remaining reaction boundaries

give reasonable changes in entropy - 40-60 eu. It is remarkable that the ^^'^CmOj^ data for

a-6 do show an acceptable temperature dependence even though occurring at temperatures ~30 °C

lower. We ascribe this increased oxygen mobility to self-radiation, and point out the recent

observation of Noe and Fuger [13] that 2'*'^Cm02 may release oxygen even at room temperature

when in vacuum.

? u ft The large temperature shift m the a -> i boundary to higher values in °Cm0^ and the

marked change in slope of the \ a reduction are not well understood. It is to be expected

that effects due to radiation damage are much reduced at these temperatures due to annealing.

OXYGEN/CURIUM

Fig. 6. Selected ^^^CxtO^ isobars.

324
400

200 —

0

P„ = 735 mm Hg

2 lOC/MIN

600

J L

130 1.60 1.70 L80 1.90 2:00 o;cm

Fig. 7. Isobars for ^^^CmO^ at 735 mm Hg O2

"1 r

CmO

n 1 1

PHASE _x_

a 1.95 - 2.00 6 1.79 - 1.85

i 1.714 0 1.50 - 1.65 B 1.500

Fig. 8,

400 500 600 700 800 900

TEMPERATURE (°C) Partial molar free energy versus T at

phase boundaries in CmOj^.

Sample purity of the ^^°CmO^ at 99.9 mol % was higher than for the ^^^CmO^ sample which con- tained 2.5 mol % Am02 and approximately 0.4% other impurities, mainly Fe and Si, Purity and

other physical differences must play some role in these types of reaction, at a level, however, which is unknown.

325
The phase diagram for the CmO^ system (fig. 9) has not been altered from that given previously [10] . The ^'^^CmOj, results suggest only minor changes and any significant revision

will require a detailed high temperature x-ray diffraction examination of the system under

controlled oxygen pressures.

5. BkO

X with the exception of a few x-ray diffraction studies on Bk203 and Bk02 , the only work

on the BkOjj system was by Turcotte, Chikalla and Eyring [14]. The paucity of data is readily

attributable to its scarcity and short (314 day) half life. The decay mechanism predominantly

involves a 114 KeV beta, introducing californium-249 {ti/2 = 360 yrs) at the rate of about

1 . 5%/week

.

Since only milligram samples of this element were available and the weight loss for a Bk02 BkOj.s decomposition is 34.2 yg per milligram of Bk02 , balance techniques were ruled

out and the capacitance manometer system was developed as described earlier. The 1,22 mg

sample was investigated in the temperature interval 852-1150 °C and oxygen partial pressures

from 10-'^ to 10~2° atm.

The low oxygen pressures required to attain equilibrium with various nonstoichiometric

BkO^ compositions were set by appropriate CO2/CO mixtures. The equilibration of a given gas

mixture with the sample was made isothermally followed by cooling to 500 "C in vacuum. At

this point, the reduced sample was quantitatively oxidized to Bk02^o0' Repetition of this

procedure with various CO2/CO ratios and with appropriate evacuations and flushings resulted

in the isotherms shown in figure 10. The data shown are grouped according to ^^^Cf content

which varied from 3 to 13% during the course of the experiment. The conditions of oxidation

of the substoichiometric BkO^ preparations (7 mm O2 and 500 °C) were not sufficient to oxidize

the Cf present significantly above 0/Cf = 1.50. The ingrowing californium was thus treated

as an inert impurity in correlating the raw data and 0/Bk values. Structurally, it is virtually certain that the Cf+^ was fully incorporated in solid solution and the data obtained

refer to the ternary (Bk^, Cfi-y)Ojj. It is likely, however, that the dissociation pressures

are little different for the pure BkO^^ system as suggested by the present results and by the

small changes observed in other studies as in Ui_2Ce202-x [15] relative to CeO^^ and in

UyThi_y02+x [IS] relative to UO2+X.

The interpretation of the plateau regions shown in figure 10 and by the derived thermodynamic quantities (fig. 11) is complicated by a variety of possibilities suggested by phase

relations in other binary and ternary fluorite related oxide systems. Without x-ray diffraction analysis, we can only speculate as follows: a single phase BkO^^s+x (0) region extends

1.50 1.60 1.70 1.80 l.W 2.00

Oit>^en/Curium

Fig. 9. Phase relations for CmO^j.

326
130 135 1.(0 1.6S LTD 1.75 1.80 1.85 l.W 1.95 iOO

0/Bk

Fig. 10. Dissociation pressure isotherms for BkO^.

- 20

1.50 i.M 1.70 1.80 1.90 2.00 0/M

Fig. 11. Partial molar entropy and enthalpy for BkO^^.

from low compositions up to a maximum 0/Bk which is a function of temperature (1.73 at 1150

°C and 1.78 at 852 °C) . A two-phase region separates a from the Bk02_x (a) region which

extends to near the dioxide composition unperturbed at 1075 and 1150 °C but which is broken

into a and a ' regions at the lower temperatures

.

Alternatively, the observed plateaus (fig. 10) at 0/Bk ~ 1.92 may be related to recent

observations of several phases of narrow composition width in the ternary systems (U,Ce)Ojj

[15], (Zr,Sc)Ojj. [17], (Hf,Sc)Ox [18] and (Hf,y)Oj^ [19]. We note in these systems also that.

327
in general, the major intermediate formed is not MOj^yn^ (as for the pure Ce , Pr, Tb and Cm

oxide systems), but the nonstoichiometric pyrochlore phase (mean 0/M = 1.75) predominates.

Although unobserved in any of the binary systems, radii considerations relative to Roth's

data 120] do not rule out this possibility as explaining the mid-field plateau observed at

0/Bk = 1.73 - 1.82 in the (Bk,Cf)Ox system.

6. CfO„ AND HIGHER Z OXIDES

X The isotopes including californium and all those of higher atomic number, have not been

examined tensimetrically . Baybarz et al. [21], however, have prepared ^^^CfOg by oxidation

of Cf203 in approximately 100 atm O2 or by use of atomic oxygen. During the course of these

preparations, samples of intermediate compositions were obtained which tended to cluster

about compositions 0/Cf = 1.56, 1.70 and 1.80 as estimated by lattice parameter considerations.

By analogy to the rare earth systems, the better crystallized preparations of the 1.7-1.8

compositions showed rhombohedral distortion.

The heavier actinides offer isotopes of increasingly lower half-lives. Einsteinium-253

(ti/2 = 20 days) and fermium-257 {ti ^2 = 94 days) will likely be the last elements amenable

to solid state studies (excluding possible stable super-heavy elements) if and when they become available in suitable quantities.

7. SUMMARY

In summary, the chemical behavior of the transplutonium actinide elements as seen through the behavior of the (M^"^, m'*''") oxides supports the concept that they should be generally similar, but in detail they are clearly individual. Of this series, berkelium would

seem anomalous if indeed curium and californium are as similar as indicated. This is perhaps related to the half-filled 5f subshell of Bk (IV) or to perturbation by the ingrowing

Cf in the sample studied. On the other hand, AmOjj does not appear to form the ordered intermediate phases suggested for CmO^ and CfOj^.

The thermodynamics obtained from these studies have no general theory to which they can

be compared and the influence of impurities on entropy changes, for example, have not been

adequately investigated. The structural details to which correlation must be made are not

available, particularly in the grossly nonstoichiometric regions.

For the actinide oxides, the question of future studies is related to both the stability and very small quantities in existence as already noted and to the oxygen pressure range

and temperatures experimentally accessible. In figure 12, we have compared oxidation-reduction potentials for the m^-'--'--mIV couple [22] with dissociation pressures over MO^ gg at 900

°C using the known data for Pu, Bk and Am oxides. Error bars for the redox potentials of ± 0.2 V are high and the very excellent fit of the three points should not be taken as too

meaningful. The data do predict correctly, however, that the Cf higher oxide requires greater O2 pressures for formation than Cm. It is clear that measurement of oxidation of Es^+

and the heavier elements will be virtually impossible even considering the reduction in dissociation pressures of approximately 15 units in log Pq^ for a temperat\are reduction to 400

°C and another approximately 8 units if one considers a composition M0j_5;^. More clearly

stated, the dissociation pressure over a hypothetical EsOi c-i oxide at 400 °C would be on

the order of 10^-^ atmospheres of oxygen. It is worth pointing out here that a consideration

of the lanthanide III-IV potentials reveals that all but Ce, Pr and Tb have similar or lower

values than Es and indeed none have been prepared in the +4 state.

A summary of the known phases in the (III-IV) field is given in table 1 for all of the

actinides. The progression from high stability for the +4 ion at Th proceeds with increasing

Z through a crossover to the case of a highly stable +3 oxidation state as already indicated.

It is the inteirmediate group from Np through Cf which offers the formation of compounds of

mixed valence as the pure oxides and a host of ternary systems all showing behavior which in

detail we are only now beginning to examine at a level necessary for full understanding and

possible utilization.

328
3 0

-

/ Fm

/a

- /Cm

- P km

/ NP O FIT MOj^ raPc

1 —1 1 1 1 I 0 1 -2 -3 -i -5 -6 -7

Ej",,,. IV, 'VOLTS.

Fig. 12. M-'--'--'- redox potentials versus dissociation

pressures over MO^^gg 900 °C.

Table 1

Fluorite Related Phases in the Actinide Oxides

OBSERVED PHASES + 4)0

X M MO, , 1.5+x ^Ol.714 '^02.000 C 0 i 5 a F Th y y

Pa y

U y y

Np y y

Pu -y y y y

Am y y y y

Cm y y y y y y

Bk y y y y

Cf y y /(?) y y

Es ym

8. REFERENCES

[1]

[2]

[3]

[4]

[5]

Foex, M. and Traverse, J. P., Bull. Soc. Fr. Miner. Crist. 89, 184 (1966).

Chikalla, T. D., McNeilly, C. E., Bates, J. L. and Rasmussen, J. J., High Temperature

Phase Transformations in Some Lanthanide and Actinide Oxides, BNWL-SA-3818 , presented

at the International Colloquium on High Temperature Phase Transformations, Odeillo,

France, September 1971.

Eyring, L, Adv. in Chem. Ser. #71, Chapter 6, 1967.

Asprey, L. B. and Cunningham, B. B. , USAEC Report UCRL-329, (1949).

Chikalla, T. D. and Eyring, L., j. Inorg. Nucl. Chem. 29, 2281 (1967).

329
[6] Chikalla, T. D. and Eyring, L,, J. Inorg, Nucl. Chem. 3£, 133 (1968).

[7] Sari, C. and Zamorani , E., J. Nucl. Mat. 3T_, 324 (1970).

[8] Posey, J. C, Kuehn, P. R. and McHenry, R. E., Abstr. & Papers, 150th Meeting ACS,

Atlantic City (1965)

.

[9] Mosley, W. C. , paper presented at ACS Symposiiim on Macroscopic Studies of the Actinides

,

San Francisco, 1968.

[10] Chikalla, T. D. and Eyring, L., J. Inorg. Nucl. Chem. 3_1, 85 (1969).

[11] Turcotte, R. P., Chikalla, T. D. and Eyring, L., unpublished data.

[12] Turcotte, R. P., Chikalla, T. D. and Eyring, L. , Anal. Chem. 43, 958 (1971).

[13] Noe, M. and Fuger, J., Inorg. Nucl. Chem. Letters 421 (1971).

[14] Turcotte, R. P., Chikalla, T. D. and Eyring, L. , J. Inorg. Nucl. Chem. 33_, 3749 (1971).

[15] Markin, T. L. and Crouch, E. C, J. Inorg. Nucl. Chem. 32_, 77 (1970).

[16] Aronson, S. and Clayton, J. C, J. Chem. Phys. 32^, 749 (1969).

[17] Thornber, M. R. , Bevan, D. J. M. and Sommerville, E., J. Solid State Chem. 1, 545

(1970) . [18] Kalinovskaya , C. A., Spiridinov, E. M. and Komissarova, L. N., J. Less Comm. Metals

17, 151 (1969)

.

[19] Didcot, M., Vicot, J. and Deportes , C, J. Solid State Chem. 2, 236 (1970).

[20] Roth, R. S., J. Res. NBS 56_, 17 (1956).

[21] Baybarz, R. D., Haire , R. G. and Fahey, J. A., ORNL, private communication, submitted

to J. Inorg. Nucl. Chem.

[22] Nugent, L. J., Baybarz, R. D. , Burnett, J. L. , and Ryan, J. L. , J. Inorg. Nucl.

Chem. 33, 2503 (1971)

.

[23] Warshaw, I. and Roy, R. , J. Phys. Chem. 65, 2048 (1961).

330
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

BINARY SOLID SOLUTIONS OF PaO^^ AND OTHER ACTINIDE DIOXIDES

AND THEIR EXCHANGE EQUILIBRIA WITH MOLTEN SALT REACTOR FLUORIDES^

C. E. Bamberger, R. G. Ross, and C. F. Baes , Jr.

Oak Ridge National Laboratory

Oak Ridge, Tennessee 37830

The dioxides of thorium, protactinium, uranim and plutoni\im all are relatively insoluble in molten mixtures — containing LiF, BeF2 / ThFi^ , PaFi^ , and UFi^ or UF3 — which serve as the fuel of the molten salt nuclear power reactors (MSR's) . Since these dioxides can form

substitutional solid solutions, exchange reactions of the type

X X Th02(ss) + MFtt(d) :^ ThFi+(d) + MO? (ss) ; Q^^ =

_Th£ij.

Th X„ „ X.„ Th02 MF4

involving the solid solution (ss) and the molten fluoride phase (d) become possible. It is

of interest to study such exchange equilibria not only because the inadvertent precipitation

of fissile oxide solids from an MSR fuel should be avoided, but also because such reactions

might provide a means of separating and recycling the fissile and fertile elements.

A study of the exchange reaction involving Pa*^"*" and Th'*"*' has been carried out in which

Pa02-Th02 solid solutions (Xp^02 t 0-33) were formed by equilibration of Th02 with molten

LiF-BeF2-ThFi+-PaF[+ (72-16-12-0.05 mol %) in the temperature range 570-730 °C. The resulting

values of the distribution quotient Q^^/ along with previously measured values of and a value of Q^^ derived indirectly from other previous measurements , are consistent with the

following expressions

2 ^ MO2

I^qM . 106 A-318 ± .03

^Th I T

wherein the activity coefficients in the solid solution are related to the difference in the

lattice parameters (Aa = ar[,j^Q2 - aj^02^ suggested by Hietala's model.

Key words: Activity coefficients in solid solutions; equilibrium of actinide oxides and

molten fluorides; heat of mixing in solid solutions; ion exchange between solid oxides

and molten fluorides; lattice parameter of actinide oxides; molten fluorides; molten

salt reactor; oxide solid solutions; equilibria with molten fluorides; plutonium dioxide; protactinium dioxide; thorium dioxide; uranium dioxide.

•^Research sponsored by the U. S. Atomic Energy Commission under contract with Union Carbide

Corporation.

331
1 . INTRODUCTION

Molten salt reactors (MSR's) are nuclear power reactors in which the fissile material

can be either ^^^UFi^, ^^^UFi., or ^^^PuF3 dissolved in a molten salt consisting mainly of

^LiF and BeF2 [1]^. When ^^^ThFi^ is added, it is converted by a neutron capture and successive 3-decays first to ^^^Pa and then to fissile ^^^U. Such reactors thus can replace a portion or all of the fissile material they consume, or even produce (breed) more fuel than they

consume. The oxide chemistry of these actinide elements in this fluoride media is important

because: (a) their inadvertent precipitation by oxide impurities within the reactor core could compromise reactor safety; (b) such oxides might be useful in separating and recycling

the actinide elements.

If a soluble oxide is added to the LiF-BeF2-ThFtt molten mixture which serves as the

solvent salt for the fuel of an MSR, Th02 is precipitated. When UFi^ is present, the oxide

precipitate formed at equilibrixam is a solid solution of UO2 and Th02 which undergoes the

exchange equilibrium

Th02(ss) + UFtt (d) ThFit (d) + U02(ss) (1)

(where d and ss denote, respectively, species dissolved in the molten fluoride phase and in

the oxide solid solution phase) . In a study of this equilibrium [2] , it was found that the

distribution of u'*''", which strongly favors the oxide phase, was not significantly dependent

on the composition of the fluoride phase but did depend on the composition of the oxide

phase; i.e., the equilibrium quotient (Qjlj^) was given by

X X log = log = (2101 + 550 X )/T (2) Th02 UFn

(wherein X denotes mole fraction) . The form of this dependence suggested that the solid solution was a regular solution in which

^U02 = (2^^/^)^Th02 ^'"^

^Th02 = (2^^/^)^U02 ^'^^

The proportionality of the log of Q^^^^ to 1/T indicated, as might have been expected, that the

entropy of the exchange is nearly zero.

In a subsequent study [3] it was found that plutonium, which is trivalent in MSR fluorides, can be oxidized and precipitated as a Pu02-Th02 solid solution. The equilibrium,

measured in LiF-BeF2-ThFi+ (72-16-12 mol %) , was

PuF3(d) + l/2NiO(c) + 3/4Th02 (ss) ^: 3/4ThF[t (d) + l/2Ni (c) + PUO2 (ss) (4)

wherein the oxidant was NiO. From the two measured values of this quotient it is possible

to derive values (table 1) for the equilibrium quotient Q^i^ of the exchange reaction

Th02(ss) + PUF14 (d) X ThF[+ (d) + PUO2 (ss) (5)

The resulting values (table 1) are clearly insufficient to determine the dependence of

on temperature or oxide composition; however, the indicated 60-fold change in Qj^^ over only

a 100° change in temperature and for relatively dilute PUO2- solutions in Th02 is too great

to be consistent with the expected zero entropy for the exchange reaction.

The oxide chemistry of protactinium in these fluorides was first explored by Schaffer

et al. [4] who found that protactinium could be precipitated quantitatively even at very low

Fig\ires in brackets indicate the literature references at the end of this paper.

332
Table 1 Estimation of the Equilibrium Quotient Q^|^ for the

Exchange of Pu^+ and Th'*+ Between Oxide and Molten Fluoride Phases

615 °C°^ 715 °C

Ref.

2 4 Th02 (ss) +-NiO (c) +-PuF3 (d) ThFt^ (d)+^Pu02 (ss)+^Ni (c) 1.45 0.14 0.03 [3] (a)

PuFi+ (c)+-Pu02 (c)

-> 4 1 -PuF3 (c)+-02 (g) -0.53 -0.41 0.03 [9]

|Ni(c)+io2(g) -> o-NiO(c)

3 6.26 5.33 0.03 [10]

4-PuFa (c)

->

-«- |puF3 (d) -2.97 -2.49 0.03 [11]

PuFtt (d) PuFtt (c) -0.59 -0.74 0.72 (b)

Th02 (ss)+P\iFi+ (d) ThFi+ (d) +PUO2 (ss) 3.63 1.83 0.72

(a) Calculated for .67LiF-. 3 3BeF2 from measurements in .72LiF-. 16BeF2-.12ThFt, , using the

corresponding activity coefficients for PUF3 (d) and ThFt, (d) from ref. [12]

(b) Assumed to be the same as for UF4 (d) J UF4 (c) ref. [7].

Table 2

Equilibrium Data Obtained for the

Reaction Th02(ss) + PaFi+ (d) J Pa02 (ss) + ThFi^ (d)

Sample Temperature

(°C)

^ZO^^^ ^PaF, ^Pa02

^Pa

log^ Qrr,,. ^Th a

(i)

A 567.0 0 .35xlO~3 4.38x10"'* (.324) 2.12±.48

B 567.0 0 .58 10~3 4.10x10"^ (.291) 2.08±.26

C 567.0 1 .08xlO~3 3.40x10"^ (.292) 2.16±.15

D 663.0 2 .78x10"^ 3.38x10"^+ (.167) 1.85±.13

E 727.0 2 .70x10"^ 4.16x10-'+ (.109) 1.55±.08 (e) F 567.0 2 .83x10-3 2.71x10"^* .175±.02 (c) 1.97±.06 5 .5926± .0003

G 730,0 14 .88xl0"3 1.91x10-'+

.073±. 004(d)

(.050)

1.69+.05

1.52±.10

5. 5910± .0002

H 567.0 8 .88xl0"3 0.75x10-'* (.062) 2.02±.10

I 567.0 8 .88x10"^ 0.69x10-'* (.063) 2.07±.10

(a) Total moles of oxide added per mole of solvent (LiF+BeF2+ThFi^ ) . (b) Nimber in parenthesis were calculated by material balance.

(c) Determined by x-ray fluorescence.

(d) Determined by y-spectrometry

.

(e) Value assumed for calculating Q , , „ (Sec. 3.2)

333
concentrations by oxide. Recent studies by us [5] have confirmed this and have shown that

the insoli±ile oxide involved is either Pa205 or an addition compound of it with fluoride. In

an MSR fuel, however, protactinium will be in the tetravalent state and the precipitation of

Pa(V) by traces of oxide will be easily avoided under the reducing conditions which will be

normally maintained.

The behavior of Pa (IV) in the presence of oxide remained to be determined. It is to be

expected that Pa'^''" would form solid solutions with Th02 and UO2 . Roberts and Walker [6] have

reported the formation of solid solutions of Th02 containing both PaaOs and Pa02 . The purpose

of the present study was to confirm the exchange equilibrium

Th02(ss) + PaFit(d) t ThFi+ (d) + Pa02 (ss) (6)

and determine the corresponding equilibrium quotient (Qij^) • With these results, along with

previous estimates of qI^^^ and Q^]^, it should be possible to determine at least approximately

how such exchange quotients , and perhaps the properties of these binary solid solutions depend

on the lattice parameters of the separate oxides.

2. EXPERIMENTAL

All the work described here was performed with ~ .4g of ^^-^Pa in glove boxes suited for

work with a-emitters. The procedure and apparatus for purification of the solvent salt,

LiF-BeF2-ThFit (72-16-12 mol %) , for equilibration with the solid oxide phases, and for sam- pling of the melt was similar to that described in the previous studies of plutonium [3]

.

The protactinium solution was prepared by extensive hydrofluorination , at 700 °C, of a mixture of the salt with Pa205. After this treatment the temperature was lowered to 560 °C.

Since this caused no detectable precipitation of the very insoluble Pa (V) oxide, it was con- cluded that the oxide removal was essentially complete. In order to convert all the protactinium to the tetravalent state and to remove the metallic impurities present (Ni^^, Fe^"*") , the solution was next extensively reduced by sparging with hydrogen at 720 °C and then at

560 °C. The extent of the reduction was followed by measuring the HP evolved. The reduction

was considered complete when the partial pressure of HF reached 2.6 x 10"^ atm (2.63 N/m^)

at 560 °C. This pressure limited the amount of Pa^+ to no more than ~5 ppm (0.3% of the total

protactinium present) [5]

.

The equilibrations of the protactinium solution with various amounts of oxide phase

(added as Th02 microspheres) were conducted by stirring both phases under a flowing hydrogen

atmosphere. This maintained reducing conditions while the rate of HF evolution, which was monitored, provided an indication of the rate and amount of oxidation by impurities. Filtered samples of the melt were obtained at various times and at several temperatures, and

the content of ^^'Pa was determined by yspectrometry using a lithium-drifted germanium crystal. Equilibriiam was assumed if the protactinium concentration remained constant to within

± 5% (the analytical uncertainty) for at least 48 hours.

Two samples of the equilibrated oxide phase (40 to 120 mg) were isolated, one at the

end of a series of stepwise additions of oxide. The salt was drawn off through a filter and

the remaining fluorides were removed from the residue by washing with a solution of versene,

boric acid, and citric acid, followed by two washings with 7N nitric acid at 70 °C. The oxide residue was finally washed with acetone and dried. The protactinium content of the ox- ides was deteinnined by Y~counting of a weighed sample. Emission spectroscopy and chemical

analysis revealed no elements other than Pa, Th, and 0 to be present in significant amounts

(1700 ppm F, less than 200 ppm each of Li, Be, Cr, Fe, Ni) . The samples were examined by x- ray diffraction and in a scanning electron microscope. The latter permitted an analysis of

individual oxide crystals

.

3. RESULTS

4+ 4+

3.1. THE Pa -Th EXCHANGE QUOTIENT

While the first oxide sample (F in table 2) was found by x-ray diffraction to contain

two c\ibic phases, the scanning electron microscope (SEM) revealed that only one of these con- sisted of relatively large (15 to 25pm) crystals of the type expected to be formed by equilibration with the melt. The second phase was present as small (<1 pm) irregular particles

334
or aggregates, relatively rich in protactinium (Xp^Qg ~ 0.44 by x-ray fluorescence) . The

latter material was probably an artifact produced by oxidizing impurities introduced during

the filtration procedure used to isolate the equilibrated oxide phase. The second oxide

sample (G in table 2) was found to consist almost entirely of well formed, relatively large,

crystals with a small amount of an extraneous oxide phase. Since the x-ray fluorescence of

individual crystals in both samples revealed the presence of both thorium and protactinium

there can be little doubt that these crystals were solid solutions of thorium and protactinium oxides

.

The analysis of the first sample (F in table 2) is based on the x-ray fluorescence spectra measured for single crystals. (The ycounting results for the entire sample were complicated by the presence of the second protactinium-rich phase.) The result (Xpa02 = .175) is

consistent with the composition which could be crudely estimated from material balance.

Two compositions are shown for the second oxide sample. One is based on direct ycounting of a weighed portion and the other on material balance, which here is more accurate because of the larger amount of precipitated oxide present in the reaction mixture. X-ray flu- orescence was not sufficiently sensitive to give an accurate analysis of this more dilute

Pa02 solid solution. The small amoiint of extraneous oxide phase probably explains the discrepancy between the two analyses shown.

The lattice parameters measured for these samples (table 2) , when plotted (along with

the previous results of Roberts and Walker [6]) vs. the composition of Th02-Pa02 solid solutions showed in one case a positive deviation from, and in the other good agreement with

Vegard's law. While we are not yet sure of the reason for the positive deviation, possibly

a result of radiation damage, it is important to note that if any Pa (V) had been present in

the solid solution the expected effect would have been in the opposite direction.

The entries A-D in table 2, which resulted from stepwise additions of oxide but without

isolation of an oxide sample, include extimates of the composition of the equilibrated oxide

solid-solution based on the following material balance calculation: First the total moles

of oxide present (^n,-,) at the end of the series of equilibrations A-E was calculated from

(X^ -X \ / (1-X „ ) \ ^

PaQ2 / \ ThFtt /

The first term on the right represents the moles -of oxide phase , where xj^p^^ would be the

mole fraction of PaFi^ if none had been precipitated, and Enp is the sum of the moles of LiF,

BeF2, and ThF^ . The other term represents the moles of oxide in solution, based on the solubility quotient of Th02

2s(Th02) " ^ThF^ ^02"/\h02

The values of this quotient finally used (sect. 3-2) are given by the expression

2g(Th02) = "^'^^ " ^'^^

The total moles of oxide thus calculated to be present at the' end of the run exceeded the

total added by a small but significant amount, assiamed to have been present initially. This

amount was used to correct upward the total amount of oxide present at each other step in

the run. Xp^Q^ was then calculated by an iterative solution of equation 7. The remaining

entries H and I resulted from equilibrations where a large amount of oxide (introduced at G) was present; hence, the uncertainty in the composition of the precipitated phase when calculated by material balance, was significantly reduced. The uncertainties assigned to the

resulting values reflect the effect of estimated uncertainties in the direct determinations of Xpa02 ^PaFi+' ^ \incertainty of a factor of two in Qs (ThOz) '

335
within their larger uncertainties, the Q^^ values derived from the material balance calculation are quite consistent with the results of the two equilibrations in which the oxide

phase was analyzed directly. This is most clearly shown by the points plotted in figures 1 and 2, wherein the anticipated effects of temperature and oxide composition have been taken

into account (see sect. 4) .

3.2. SOLUBILITY OF ThO^

When the material balance calculation was applied to the equilibration at 727 °C (E in

table 2) , it was found to be very sensitive to the value assigned to the solxibility quotient

of Th02 (eq 8) , In particular, the very fact that some Pa02-Th02 solid solution remained

undissolved at this relatively high temperature (as was clearly shown by the protactinium

missing from solution) placed an upper limit on Qs(ipj^02) ^^•'^^ within the previously es- timated range of values. Indeed, it was found by reversing the calculation and introducing

an estimated value of Q^fi' ti^sed on the present results at lower temperatures, that it was possible to derive a value of Qs(Th02) conditions of this equilibration which is probably more accurate than any prior estimates.

Noting that this soliibility quotient may be related to the equilibri\im constant by

2s(Th02) " ^s(Th02) '^ThOg'^^^O^" ^ThF^^ ^'^^^

ORNL-DWG 71-11947R

2

io' ' ' ' '

'

' 0 0 2 0.4 0.6 0 8 1.0

Fig. 1. Exchange quotient Q^j.^ as a function

of the composition of M02-Th02 solid

solutions (in mole fractions y^]^02)

at 600 °C. The points are measurements, corrected to 600 °C, in which

the composition of the oxide phase

was determined directly (•) or by

material balance (0) . The lines were calculated by means of eq. (25)

.

336
ORNL-OWG 7(-((946 _

10'

PuOg

(0 = >.396 Vi

NpOj ^((7-5.425 AlUO2 /

Ko =5.41' p^fl4 POIN rs P0O2

(0 = 5.509* )

— Thn_ j^^^ (17 = 5.5975 A)

0.178 0.180 0.182 0.(84 0.186

Fig. 2. Equilibrium constant for exchange

reactions as a function of the

reciprocal of the lattice constants

(1/a) of the pure actinide dioxides

at 600 °C. The points are derived

from those in figure 1 using eq.

(26).

2s(Th02) vary with both melt composition and oxide composition. Since the melt com- position was not changed significantly from LiF-BeF2-ThFi4 (72-16-12 mol %) in the present

measurements, and since the solid solutions were all >67 mol % Th02 wherein Ypp}^02 ^^^^-'-'^ quite close to unity (see sect. 4-1), we may assume here that Qs(Th02) ^ constant dependent only on the temperature. The expression (eq 9) adopted to represent this dependence is

based on the above deteirmination of Qs(Th02) "^^"^ ^ previous estimate of the entropy

of the reaction [7]

,

Th02(c) = Th^""" + 202~ (12)

4. DISCUSSION

4.1. BINARY SOLID SOLUTIONS OF ACTINIDE DIOXIDES

Hietala [8] has successfully accounted for the observed heats of mixing of alkali metal

halides in binary solid solutions in terms of a simple model which involves the displacement

of the common ion in a fixed lattice of the randomly mixed counter-ions. The result is of

the approximate form

where di and d2 are the cation-anion distances for the two pirre salts. The constant C contains no adjustable parameters, being a function only of the molar volximes and compressibilities (and their temperature coefficients) of the two pure salts.

While an analogous treatment has not yet been completed for siibstitutional solid solutions with the fluorite structure such as those of the actinide dioxides, it is clear that

337

465-504 O - 72 - 23
the result will be of the same form. Hence we will approximate the heat of mixing of M02-

Th02 solid solutions by

2 AH = m

\ \h02 /

X X MO2 Th02 (14)

where aj^Q2 is the lattice parameter of the pure oxide. From the heat of mixing found for the

U02-Th02 solid solutions [2] , we obtain

A = 2,440 ± 300 kcal/mole (= 10,210 ± 1260 J/mole)

.

If we assume random mixing in these solid solutions, the activity coefficients are given by

In YMO2 RT ^Th02 /

Th02

(15a)

In YThOc

^ A_ / \hO? ^MO? Y MOc

(15b)

Considering the series of binary solid solutions of Th02 with Pa02 , UO2 , Np02 , and PUO2

,

these then should show an increasing positive deviation from ideality. In the case of Th02-

PUO2 solutions, this deviation should be the largest with

AH 3.17 X1X2 kcal/mole (~ 13.26 J/mole)

and

In Y PuOc 1>590 2 T Th02

'

From this it is predicted that Th02 and PUO2 will not be completely miscible at temperatures

below about 500 °C.

4.2. ACTINIDE (IV) EXCHANCT: EQUILIBRIA

Considering next the exchange reaction

Th02(ss) + MFit (d) t ThFi+ (d) + MO2 (ss) (16)

we might expect the entropy change for this reaction to be zero for all the tetravalent actinides from Pa'*'*' to Pu'*'*'. Furthermore we might well expect that the enthalpy change

^"m02(c) "Th02(c)^ " ^"MF4(d) " "ThF4 (d) (17)

would depend on the reciprocal of the M-F and M-0 distances, i.e.

AH° = - B' (d d

M-0 Th-0

) + B" ( d- d

M-F Th-F

(18)

where B' and B" are constants characteristic of the actinide dioxides and of the actinide

tetrafluorides dissolved at low concentrations in a molten fluoride solvent. If this last

expression is rearranged to _

AH° = B'-B"

fd d Th-0 M-0

d , d

Th-F M-F

Th-F M-F

Th-0 M-0 Th-0

(19)

338
we see that the bracketed term ought to be nearly constant for the series Pa^"*" - Pu^"*", especially since the ion radii of and F are quite similar. Hence we might expect the

following relationship to be a good approximation

(20)

or, replacing d by a

(21)

The equilibrium constant for the above reaction then should be given by

\^M02 ^Th02 / m i = I- I — — \ (22) Th RT ' - -

'

From the results for the Th02 - UO2 solid solution we estimate

B = 2,620 ± 53 kcal/A (= 10,960 ± 220 J/&)

M M The exchange quotient Q^j^ is related to Ki^^ as follows

^ \o? \hFit . ^MDp^MFt^ ^ ^M09^ThFu _ ^^3)

"^^ ^Th02^MFit ^Th02'^MF4 '^^ '^Th02^MFit

We will assume that the ratio of activity coefficients YThFi+Z'i'MF tetrafluorides in

dilute fluoride solutions is a constant independent of the composition of the solvent. This was found to be the case for the ratio YThFi^/'^UFit f^] . By choosing the standard states for

the tetrafluorides such that Ym-u,-,, /Yk^, is unity, we may then write inr 4 Mr 4 M M

\h = ^Th ^M02/^Th02 ^'"^

expression for

Th ' 'MG2

Th

a„, „ -a. ,M B/1 1\.A / ThO? MO? 1

Introducing the expressions for K^^^ (eq 22) , Yj^q^ ^Th02 ^® obtain the following

= I 7-- - -7-) - 1^ ( ^^7^^^'] (2X^ - 1) (25)

\

MO2 Th02 f \ Th02 /

^

Thus we expect the log of the quotient for a given exchange to increase linearly with

^M02' amount of the increase varying directly as Aa^ . Further, we expect the log of the

quotient to increase directly as the difference A (1/a) for the oxides involved.

The present results for QS,^/ along with the previous measurements of and the value

calculated (table 1) for

Q^J^

at 615 °C are compared with these expectations in figures 1 and

2. In figure 1 the data have been normalized to a temperature of 600 °C by invoking the as- sumption that the entropy of exchange is zero (and hence that' In is proportional to 1/T K)

The curve drawn through the values for was arrived at previously by a least squares fit

of the data. The other curves were constructed from equation 25. Values of K^^^ at 600 °C were then calculated according to the expression ~~ m = m - I-

/'^ho, -^MoA ' _ Th ^Th RT I a„^^ } MO2

y

Th02 /

and these are compared with a line based on equation (22) in figure 2.

339
As is seen, witJiin their accuracy, the present results and the estimates for Q^^ at 615

°C agree quite well with the expected behavior. The results for Q^}^ at 715 °C derived in

table 1, which is not shown in figure 1, would fall far below the curve, being low by a factor of about 40. This discrepancy, we are fairly certain, arises from some unsuspected

error in the previous measurement of the equilibrium quotient for reaction (4) at 715 °C.

The apparent change in this quotient by a factor of about 10 over the temperature range 615-

715 °C is far greater than one would predict from the expected small entropy change for this

reaction. The most likely explanation is that the NiO introduced into the system had been

reduced at the higher temperature by reaction with lubricant leaking into the system through

the stirrer seal.

5. CONCLUSIONS

The present measurements of Q^^ are insufficient to test the dependence of AH^ on (Aa/a)

suggested by Hietala's appealingly simple model. The composition range of the Pa02-Th02 solid

solutions and the expected deviations from ideality are too small „ We hope to test further

this dependence by making direct measurements of the Pu^+-Th'*"'" exchange between Pu02-Th02

solutions and a molten fluoride. Here AH^^^ should be much larger and hence so should be the

dependence of Q^'^ on the composition of the oxide phase. These measurements will also test

more fully the apparent dependence of K^j^ on A (1/a) .

The application of Hietala's model to these oxide solid solutions with the fluorite

structure is still in progress. We hope to include solid solutions containing more than two

components , since this should permit the treatment of the important case of the simultaneous

exchange of more than two actinide ions (in an oxide phase) with a molten fluoride phase.

For the present, it seems likely that the correlation suggested here (eq 25) will be

usefully accurate (1) for predicting binary exchange of cations, (2) for relating the solubilities of the other actinide dioxides to Th02 , and (3) for estimating thermochemical values

for actinide fluorides in solution from such data for the corresponding dioxides.

6. ACKNOWLEDGMENTS

The authors would like to express their appreciation to the following members of the

Analytical Chemistry Division of Oak Ridge National Laboratory: H. Dunn for the x-ray diffraction analyses, L. Hulett for the examinations with the Scanning Electron Microscope,

and J. Emery for the Y~spectrometric analyses. We are grateful to D. Sood, on leave at ORNL

from the Bhabha Atomic Research Center, for his invaluable help in isolating the oxide

phases

.

7. REFERENCES

[I] Grimes, W. R. , Nucl. Appl. Tech. 8, 137 (1970).

[2] Bamberger, C. E. and Baes , C. P., Jr., J. Nucl. Mat'l 35., 177 (1970).

[3] Bamberger, C. E., Ross, R. G., and Baes, C. F. Jr., J. Inorg. & Nucl. Chem. 33./ 767

(1971) . 14] Shaffer, J. H., Grimes, W. R. , Watson, G. M. , Cuneo, D, R. , Strain, J. E., and Kelly,

M. J., Nucl. Sci. Engr. 18, 177 (1964).

[5] Ross, R. G., Bamberger, C. E., and Baes, C. F., Jr., MSR Prog. Semiann. Progr. Rept.

for Period Ending Aug. 31, 1970, ORNL-4622, p. 92 (1971).

[6] Roberts, L. E. J. and Walker, A. J., Physico-Chemie du Protactinium, 51 Centre National

de la Recherche Scientifique , Paris (1966).

[7] Baes, C. F. , Jr., in Nuclear Metallurgy (Symposium on the Reprocessing of Nuclear Fuels,

edited by P. Chiotti) vol. 15, USAEC-CONF 690801 (1969).

[8] Hietala, J., Ann. Acad. Scient. Fennicae Series A, VI Physica 121-123 (1963).

19] Dawson, J. K. , Elliot, R. M. , Hurst, R. , and Truswell, A. E., J. Chem. Soc . 558 (1954).

[10] Elliot, J. F. and Gleiser, M. , Thermochemistry for Steelmaking, American Iron and Steel

Institute, Addison-Wesley , Reading, Mass. (1960).

[II] Barton, C. J., J. Phys . Chem. 64, 306 (1960).

[12] Baes, C. F., Jr., MSR Prog. Semiann Progr. Rept. for Period Ending Feb. 28, 1970, ORNL4548, p. 149 (1970) .

340
DISCUSSION

p. Hagenmuller : Did you find any evidence of substitution of oxygen by fluorine in your

solid phase?

C. E. Bamberger : No sir, at least not in an appreciable amount. Because we could not

correlate the lattice parameter of the Pa-rich solid solution with its Pa content, we had

considered the possibility that we had formed a Pa (IV) oxyfluoride. So, this sample was ana- lyzed for fluorine and for metallic impurities. The results, in ppm, were 1700 F, 0.1 Be,

10 Li, and 30 each of Ni and Cr, and 200 Fe, The concentration of Li and Be indicated that

while the amount of fluorine present did not correspond to residual solvent salt, neither

was it sufficient to indicate the presence of an oxyfluoride phase.

Note added in proof : However, from the results obtained, the substitution of oxygen by

fluorine cannot be entirely ruled out. The concentration of fluorine would correspond to a maximum of 0.03 mole fluorine per mole of MO2 (solid solution) or 0.17 mole fluorine per mole

of Pa02 present in the solid solution.

341

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

GROWTH AND X-RAY STUDIES OF SINGLE CRYSTALS OF

HIGHER OXIDES OF PRASEODYMIUM AND TERBIUM

Z. Lowenstein, L. Kihlborg, K. H. Lau,

J. M. Haschke and L. Eyring

Department of Chemistry

Arizona State University

Tempe, Arizona 85281

Single crystals of higher oxides of praseodymium and terbium have been grown successfully using hydrothermal techniques. Cold seal reactors were utilized to study the crystallization process over a temperature range of 600-900 °C and at pressures up to 3.1 kilobar.

Crystal growth conditions were optimized using controlled pressure and temperature cycling.

Any oxide of praseodymium may be used as starting material. Nitric acid served both as a mineralizer to promote solubility and as a source of oxygen. Two predominant crystal habits

are observed; octahedra and trigonal prisms. Faces are smooth and well defined.

Single crystals of praseodymium dioxide have been reduced to PrOi.833 the homologous

series Prj^02n-2 with crystal integrity maintained. X-ray data have been obtained on these

crystals using Weissenberg and Hagg-Guinier cameras. The phase has a f luorite-type sublattice with a superstructure of monoclinic symmetry (space group P2i/n,C2h) and a unit cell

having a = 6.6874 A, b = 11.602 K, c = 15.470 A, 6 = 125.257° and V = 979.6 P. Indexing of

the powder pattern of this phase has been completed on the basis of this cell. The relationship to the fluorite subcell is shown.

Key words: Higher oxides; hydrothermal crystal growth; oxide structures; praseodymium

oxide; single crystal; terbium oxide.

1. CRYSTAL GROWTH

1.1. INTRODUCTION

The system is ideally suited as a model system for the study of solid state

reactions. Its crystal system resembles those of about one third of the known elements; it

exhibits polymorphism in its phases of nearly fixed composition; it possesses ordered intermediate phases of narrow composition range belonging to an homologous series; ordered intermediate phases are observed to disorder to nonstoichiometric phases of wide composition

range at higher temperatures and pressures; and, in addition, such interesting features as chemical hysteresis and pseudophase formation occur in many regions of its existence range.

All these chemical and structural features are accessible at oxygen pressures between vacuum

and one atmosphere at temperatures up to 1100 °C.

There has long been a great need for a model system to be thoroughly studied from all

points of view including thermodynamics, kinetics and structure. Systems for which structural data are most completely known are frequently very difficult to study thermodynamically and kinetically and vice versa. Structural and some specific kinetic studies on the

PrOx-02 system (which is ideally suited to themodynamic and kinetic measurements) have

until now been prevented because of the unavailability of single crystals of most of the

oxide phases. While powder diffraction studies have resulted in a model for the structural

relationships between the phases, these cannot be tested without single crystals.

343
Growth of single crystals of praseodymium oxide by the Verneuil technique has produced

only high temperature A-type sesquioxide crystals which shatter upon oxidation due to the

reconstructive transformation required to produce the fluorite related major sequence of

oxides. Similar failures to obtain crystals in the cubic related system have been experienced in flux growth techniques which successfully grew fluorite Ce02 and Th02 crystals [1,

2, 3]^. The early report of Shafer and Roy [4] made hydrothermal techniques appear well

suited to produce the C-type sesquioxide of the rare earths. It was assumed that the C-type

sesquioxide could then be oxidized to the intermediate oxides and Pr02 without loss of

crystal integrity.

Experiments by Haschke and Eyring [5] demonstrated that in the presence of an oxidizing

medium the oxide produced was Pr02 or a mixture of Tb0i.7ii+ and TbOi.818 in the praseodymium

and terbium oxide [6] systems respectively. An experimental program was inaugurated to perfect the conditions for crystal growth.

1.2. EXPERIMENTAL PART

The basic apparatus and technique has been described previously in detail [5, 7]. An

externally heated stellite cold seal reactor was utilized for the hydrothermal vessel. The

reactor was connected either to a gas driven water intensifier or to a gas driven diaphragm

compressor. In the latter case, argon was used as the pressurizing fluid. Pressure was measured with a bourdon gauge to a. 34 bars and temperature was measured by means of a thermocouple in a well on the outer surface of the reactor. External temperatures were calibrated

to internal temperatures (±25 °C) which are those reported. The reactors were heated by

concentrically wound Kanthai furnaces with the temperature regulated by proportional

controllers

.

The rare earth oxides used were 99.999% pure provided by Lindsay Division of American

Potash and Chemical Corporation. Other chemicals were reagent grade. Since the reactants

attack stellite at high temperature and pressure, sample containers were constructed of thin

gold tubing (5.0 mm OD, 4.5 mm ID) . The tubing was crimped on one end in a three- jaw chuck

and welded shut. The sample was weighed into the container; the other end was then crimped

and welded. Volatile reactants were frozen in the capsule by cooling it and the chuck with

liquid nitrogen before final welding. Leaks were detected by weight loss after extended

heating at 110 °C in a drying oven.

1.3. RESULTS

Haschke and Eyring [5] reported that, starting with A-Pr203 (A-form) , a source of oxygen

such as NO3 was necessary for the oxidation to Pr02 . (Some experiments with H2O2 produced

Pr02 but were considered less satisfactory due to decomposition of the peroxide before the

capsules could be welded.) The presence of a neutral or acidic medium was also demonstrated

as a necessity for dioxide formation. A lower temperature limit of 700 °C was found, below

which Pr(0H)3 was the only product. At temperatures above 700 °C A-Pr203 gave only trihydroxide while 3 disproportionated into Pr(0H)3and Pr02 . With this information as a start, a series of studies was initiated to determine the conditions necessary for preparation of

larger single crystals of Pr02

.

A selective sample of these exploratory studies is shown in table 1. The reactor was pressurized cold to the desired pressure. A preheated furnace was placed around the reactor

which was brought to temperature as quickly as possible (1-3 hours) with the pressure maintained constant. The reactor was sealed off from the pressurizing system and maintained

at temperature and pressure for the period shown.

Different cooling methods were explored as shown in figure 1. Curve A represents rapid

cooling produced by replacing the furnace with a water-cooled jacket. The reactor cools to room temperature in about 20 minutes. Curve B represents cooling produced by switching off

the furnace but leaving it around the reactor. The initial cooling rate is 6 °C/min and the

system reaches room temperature in about five hours. Curve C represents cooling by switching

Figures in brackets indicate the literature references at the end of this paper.

344
off the furnace, with the furnace removed at 700 °C . Curves D and E represent slow cooling

with a motor-driven temperature controller. Cooling rates of 5-20°/hr were maintained either

to 700 °C (D) or to room temperature (E)

.

Starting

Materials

Table 1 Selected Hydrothermal Reaction Experiments

1 = A-Pr203, 2=3 3 = Pr02 , 4 = Pr(N03)3

5 = Pr(0H)3 6 = Hydroxynitrates

Unless noted, HNO3 = 70% tr = trace

Ratio

Oxide: Temp Press Time Depressur- Cooling Products

HNO3 (C°) (bar) (hr) izations Curve

Pr02 Size

1 800 1150 60

1+30%H202 800 1150 65

1+lM HNO3 800 1150 48

1+4 800 1150 96

5 500 1000 60

1+4 900 900 21

1+4 800 900 21

1+4 700 900 21

1+4 600 900 21

1+4 850 1150 21

1+4 800 1150 21

1+4 700 1150 21

1+4 600 1150 21 1+4 800 1500 21 1+4 700 1500 21

1+4 600 1500 21

1+4 700 2000 21

3+HNO3 6 800 1150 20

3+HNO3 1.5 800 1150 20

3+HNO3 1.2 800 1150 12

3+HNO3 1.5 800 1150 12 3+HNO3 1.4 810 1150 12

3+HNO3 1.5 820 1250 12

2+HNO3 1.5 820 1250 12

I+HNO3 1.5 800 1150 10

3+HNO3 1.3 800 1650 14 3+HNO3 1.1 810 1650 20

3+HNO3 1.5 740 2150 15

I+HNO3 1.4 740 2150 15

2+HNO3 1.5 740 2150 15

2+HNO3 1.5 820 1650

3+HNO3 1.1 730 3000

3+HNO3 .9 730 3000 11

3+HNO3 .9 730 1750 12

3+HNO3 .9 955 3100 18

1300 in 2 hr

1200 in 4 hr

1250 in 50 hr

1250 in 50 hr

1250 in 50 hr

1000 in 16 hr

up to 1150

2000 in 18 hr

on cooling to 340°, P goes

to 2500 in 3hr

A 5 A 3, 5 powder

A 3, 5 powder

A 3, 5 powder

A 6 A 3(tr) , 5 A 3 (tr) , 5 A 5 A 5 A 3(50%) , 5 powder

A 3 (30%) , 5 powder

A 3(tr) , 5 A 5 A 3(10%) , 5 powder

A 5 A 5 A 5 A 3, 5(tr) small , poor

A 3, 5(tr) .08-.1 mm A 3, 5(tr) .05-. 08 mm

B 3(60%) , 5 < . 1 mm, smooth

E 3(10%)

,

5 < . 1 mm

B 3(60%)

,

5 .05-.1 mm

B 3(60%) , 5 .05-.1 mm

B 3(60%) , 5 .05-.1 mm

B 3(80%) , 5 small, poor

B 3(80%) , 5 < . 1 mm, smooth

C 3(90%) , 5 . 07- . 3mm , smooth

C 3(90%) , 5 . 07- . 2mm, smooth

C 3(90%) , 5 .07-. 2 mm

B 3(90%) , 5 . 1- . 3 5mm

,

biggest

B

' 3(tr)

5(50%) , 6 B 6 B 3(90%) , 5 .08-. 2 mm

345

;
Time

Fig. 1. Cooling Curves

Depressurization at constant temperature was explored. Pressure leak rates varied from

30 to 600 bars/hr. When the reactor reached final pressure it was cooled isobarically to room temperature by switching off the furnace (B)

.

1.4. DISCUSSION

Several generalizations can be made. Higher temperature and starting pressure (within

the limits of the apparatus) tend to result in larger crystals. Long te2rm heating at temperature and pressure (up to 96 hrs) seemed to have no effect on crystal growth. Slow coolling below 700 °C (curve E, fig. 1) resulted in the trihydroxide as the sole product. Depressurization followed by rapid cooling resulted in large crystal clusters but few individually well-foirmed crystals. Slow cooling produces much larger crystals than fast cooling,

the same is true for depressurization. If the pressure drops below 900 bars at high temperature, crystals of dioxide obtained are fractured and disintegrate to powder on touch. The

final form of the dioxide crystals seems to be independent of the starting material but is

dependent on the relative amounts of starting material (only powder is found if PrOj^rHNOs > 1.5). The largest crystals obtained to date were grown under the following conditions.

PrgOii (or Pr02) and 70% HNO3 (1.4:1 weight ratio) were used as starting materials.

The reactor was pressurized to 1650 bars and heated to 820 °C. The pressure was leaked to 1000 bars over a 16 hour period and then raised to 1150 bars and held for two hours. The

furnace was switched off and the reactor cooled to room temperature isobarically at 1150

bars. The reactor was depressurized at room temperature; crystals were treated with

.2N HNO3 to dissolve the small amount of Pr(0H)3 present, filtered and dried in a desicator.

From the conditions required to obtain single crystals of Pr02 one can propose a plausible mechanism for the crystallization process. While the oxides of praseodymium are soluble in concentrated nitric acid, the mole ratios are such that there is insufficient acid

for complete reaction and too little water for complete solution (after an initial reaction

on mixing, with O2 released, the reaction mixture is equivalent to a 1:1.85 mixture of

PrOi 833 ^^'^ Pr (NO3 ) 3 • 6H2O. Such a starting mixture gives identical results to the Pr02-HN03

starting mixture) . At reactor temperature and pressure the nitrate decomposes to N2 and O2 and the remaining oxide will convert to an intermediate phase, (perhaps I (PrOi^y^) or a (Pr02_x) ^ • '-'^ cooling or depressurization Pr should come out of solution as the intermediate phase, growing on some of the undissolved material present. If the cooling or depressurization is slow enough, one might expect the selective dissolution of smaller crystallites in favor of larger single crystals (as in crystallization from solution under "normal"

conditions) . The result should be large single crystals of the intermediate phase.

346
If these crystals are maintained in a temperature range where Pr(0H)3 is the favored

phase, one would expect (and actually obtains) hydrolysis to the trihydroxide . If, however,

the crystals are passed rapidly through this region of trihydroxide stability, they should

reach a temperature where the kinetics of the hydrolysis reaction permits them to remain.

At low temperatures with at least 1000 atm. of oxygen pressure the oxidation to the fluorite

structure, Pr02, should proceed with crystal integrity maintained.

The concentrated nitric acid reacts at low temperature to provide water and to solubilize some of the starting oxide. At higher temperatures it decomposes to provide a high

oxygen pressure within the sample capsule. Mass spectrometric data on the residual gasses

within the capsule are shown in table 2. These data confirm the complete destruction of

HNO3 under reaction conditions. It is interesting to note the increase of N2:02 ratio when

a reduced oxide (requiring excess oxygen for dioxide formation) was used as starting material,

A product diagram of the type shown in figure 2 is suggested from the experiments sum- marized in table 1. However, further work will be required to locate exactly the regions

of stability.

The suggested mechanism for crystal growth tends to be confirmed by preliminary studies

on the TbOjj system. With the same starting conditions as with PrOx, a mixed crystalline

system of TbO^ 7m and TbOi^aiS was obtained. When the TbO^rHNOs ratio was decreased to 0.8,

a single crystalline phase, TbO^^siS' obtained. This is in agreement with the increase

in oxygen engendered by the increased HNO3 content. The oxygen potential is not great

enough to produce Tb02

.

These results suggest that the hydrothermal method can be a most useful technique for

the growth of single crystals of the rare earth oxides for structural and kinetic studies.

At present crystals up to 0.5 mm on an edge but having a wide range of sizes have been

routinely prepared. These crystals have been spherodized by grinding against emory paper as they are swirled about by a low pressure gas flow [8] . These spherical crystals appear suitable for oxygen diffusion studies by a heterogeneous isotope exchange technique.

2. X-RAY STUDIES OF REDUCED CRYSTALS

Now that crystals of Pr02 of sufficient size and perfection have been grown, a thorough

program of structural investigation is begun. The immediate questions to be answered are whether the intermediate oxides can be prepared by reduction without their fracture and if so to discover the details of their structure.

Pr02 crystals were reduced by heating for various periods of time at 450-475 °C and

Po2= 0.5-1 bar which is within the stability region of the 3 phase [9].

In the first experiments the crystals were allowed to cool relatively slowly at constant

oxygen pressure. The diffraction patterns from these crystals consisted of two sets of re- flections; sharp spots corresponding to the lattice of Pr02 and weaker, diffuse ones cor- responding to the lattice of 3 phase, in parallel orientation. Apparently, the crystals had

Table 2

Gaseous Capsule Contents

Mass No. HNO3 HNO3 + Pr02 HNO3 + A-Pr203

18 .009 (a) .065 ,20

28 .57 .74 .93

30 .002 .002 .003

46 .007 ,005 .004

(a) Peak Height Ratio to 32 (O2)

347
r

"

a

OL n

nh

H NHOO 0 0

0

h 0

0 00

0

h

5 6

T X 10"

8

Fig. 2. Product Diagram. Lower case indicates PrOx

Upper case indicates PrOx + HNO3 , o = Pr02

,

n = hydroxynitrate.

+ Pr (NO3) 3. h = Pr (OH) 3,

oxidized coherently during cooling with smaller regions of the reduced phase remaining

within the "single" crystals.

When the crystals were cooled slowly to 400 °C (still within the 3 region) and from

there rapidly with pumping to avoid oxidation, they remained monophasic. An x-ray powder

pattern taken of some of the crushed crystals showed the faint superstructure lines characteristic of the 3-phase [10] . The single crystal patterns revealed a f luorite-type sublattice

with a superstructure of monoclinic symmetry. Super-structure unit cell dimensions obtained

by least squares refinement are as follows: a = 6.6874±8 A, b = 11.602±2 A, c = 15.470±3 A,

B = 125.257±3°, V = 979.6 A^ . Its relation to the f luorite-type subcell, with the three

lattice vectors a^i , _a2 and ^3 is

11 3 ^ =-2^1 ^ ^' k" z + .§2) r c, = 2 (^1 + a2) (1)

as shown in figure 3. The volume is six times that of the subcell. (It should be pointed

out that the above cell is not the reduced one, but chosen so as to make the c axis fall in

3 3 the a.2 &2 plane. A less oblique cell is obtained with c = 2^2 ^3*)

Indexing of the powder pattern of the 3 phase has been accomplished on the basis of

this unit cell and is shown in table 3. The systematic absences of reflections are those

required by the space group P2i/n(C2h with a nonstandard choice of axes). Data are now being

collected for a complete crystal structure determination of this phase, Pri2 022'

In a preliminary run a Pr02 crystal was reduced under less carefully controlled conditions by heating in air at a temperature in the range 500-600 °C and then rapidly cooled.

According to the equilibrium diagram [9] this is within the stability region for the a-phase.

The single crystal pattern indicated a subcell with an edge about 0.7% larger than that of

the 3-phase, which suggested that the crystal was considerably more reduced. Weak superstructure reflections were visible in the high angle region of the Weissenberg photographs.

348
Table 3

Powder Pattern of PrgOn Recorded in a Guinier-Hagg Focussing

Camera with Th02 as an Internal Standard (a/27°C/=5 . 59712 A)

d , (A) obshki d - (A) calcd ^ (A) obsd , (A) calc

1 6.574 101 6.584

1 6.320 002 6.316

1 5.541 112 5.542

2 5.266 021 5,272

3 4.609 113 4 .605

3 4.271 122 4.270

4 4.203 101 4.206

3 3.980 120 3.976

s

3 . J-ob3 . Ibz

^004

<i30

I204

3.158

3.156

3.154

1 3,064 105 3,064

2 3.044 214 3.044

2.736- |l34 2.735

s 2.731 1200 2.730

2 2.672 103 2.671

1 2.659 210 2.658

2 2.635 142 2.635

1 2.562 140 2.562

1 2.557 225 2.555

1 2.452 216 2.452

3 2.400 231 2.399

2 2 . 388

(043 2.389

U41 2.388

4 2.188

\243

2.188

2.187

4 2.178 142 2.177

4 2.157 315 2.157

5 2.114 107 2.115

4 2.105 006 2.105

4 2.082

(124

(324

2.083

2.081

2 2.039 231 2.038

1 1.943 ^317

(311

1.943

1.941

1.936-

1.929

1,910

1.896

1.848

1.767

1.751

1.737

1.702

1.673

1.649-

1.646

1.604

1.594

1.578-

1,576

1.566

1,542

1.480

1.478

1.476

1.381

1.367

1.366

1.355

208

060

134

334

105

252

155

|l44

1344

247

320

(346

1342

(233

(301

138

064

264

338

204

330

M04

(425

\072

355

!008 260

408

163

340

272

107

433

(276

(235

268

400

410

934

934

933

931

911

897

850

769

767

752

737

702

702

672

671

649

649

649

648

648

647

646

1.605

1.603

1.595

1.579

1.578

1.577

1.566

1.542

1.480

1.478

1.476

1.383

1.380

1.367

1.365

1.356

The intensities of the strong f luorite-type substructure lines are indicated by s; the intensities of the weak superstructure reflections

are visually estimated on a scale from 1 to 5

.

349
Fig. 3. Relationship between the monoclinic superlattice of Pri2022 face-centered,

f luorite-type siiblattice, twelve unit cells

of which are indicated.

and these, as well as the strong spots could be indexed on the basis of the following unit

cell,

^=2 "-^2 + 2a3) , b = f (-^1 +^2) / ^ = 2^1 +^2 +33) • ' (2)

This lattice is rectangular apart from a possible small distortion of the f luorite-type subcell and the volume is 45 times larger than the volume of the subcell. The fact that the

superstJTUcture-ref lections are relatively few and confined to high angles makes the derivation of the unit cell somewhat uncertain, however. Although the oxygen content of this

phase is uncertain it is obviously less than in the g-phase. The weak superstructure lines

indicate long range ordering in either a-phase or some member of the homologous series

formed during rapid cooling.

3. ACKNOWLEDGMENTS

We are grateful to the United States Atomic Energy Commission for support of the

research of which this is part.

4. REFERENCES

[1] Vinokurov, I. V., Zonn, Z. N. and loffe, V. A., Soviet Physics—Solid State, 7_, No. 4. October 1965.

[2] Finch, C. B., and Clark, G. W. , J. Appl. Phys. , 37_, 3910 (1966).

[3] Linares, R. C. , J. Phys. Chem. Solids, 28_, 1285 (1967).

[4] Shafer, M. W. , and Roy, R. , J. Amer. Ceram. Soc, 42_, 563 (1959).

[5] Haschke, J. M. , and Eyring, L. , Inorg. Chem. In press.

[6] MacChesney,* J. B., Williams, H. J., Sherwood, R. C, and Patter, J. F. , J. Chem. Phys.

44, 596 (1966)

.

[7] Laudise, R. A., and Nielsen, J. W. , Solid State Physics, 12, 149 (1961).

[8] Whitmore, R. I., J. Sci. Instrum. , 31^, 223 (1954).

[9] Hyde, B. G., Bevan, D. J. M. and Eyring, L. , Phil. Trans. Roy. Soc, London, Ser. A, No. 1106, 259, 583 (1966),

[10] Sawyer, J. O. , Hyde, B. G. , and Eyring, L. , Bull. Soc. Chim. Fr. , 1190 (1965).

* The preparation of Tb02 by a technique similar to that described above but utilizing

HC10(^-2H20 as an oxidant, was called to our attention by Dr. MacChesney at the time of

presentation of this paper. No mention was made as to the crystallite size of the unstable

Tb02 prepared.

350
DISCUSSION

R. S. Roth : I don't want to comment on the praseodymium oxide or fluorite system, I want to comment on the crystal growth technique. I think it is really going to be a very

useful method. At a conference that Aaron Wold gave, at Brown University in 1967, Prof.

Roland Ward asked the audience "Does anybody know how to make a crystal of two layer hexagonal BaNi0 3?" I think for the first time there is a possibility, with this method, that

somebody might be able to grow that sort of cjrystal, and I bet this method will work in a lot of other systems too.

A. S. Nowick : You pointed out that there was an instantaneous transformation as you

went from one slide to the other. What change produced that transformation? Was it the

temperature?

L. Eyring : Oh, this is a very hostile environment. These crystals are very unstable

in the environment of the electron beam in a high vacuum so they are losing oxygen all the

time. This sequence of superstructure is the natural result of looking at a crystal of decomposing Pr02 in the electron microscope.

E. Banks : In your introduction you mentioned terbium oxides and 1 was wondering whether

you had succeeded in growing any crystals of the Tb02 phase.

L. Eyring : The highest oxide we get is TbO^ 818' ^® delta phase. Utilizing a similar

technique MacChesney et al. [see reference [6] in the manuscript] have prepared Tb02

.

J. M. Honig: Did you find any nitrogen inclusion in your single crystals?

L. Eyring: There has been no analysis of the crystals other than the gravimetric

analysis of a large sample of single crystal material, but this wouldn't show up small amounts

of nitrogen. We have no way of saying that there is no nitrogen; I'm sure there is only a very small amount, if any.

351

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

DEFECTS AND MASS TRANSPORT IN REDUCED CeO^ SINGLE CRYSTALS

Y. Ban^ and A. S. Nowick

Henry Krumb School of Mines

Columbia University

New York, New York 10027

A study is made of reduced Ce02 in the form of large single crystals grown by arc fusion. It is shown that, so long as y ^ 1.67 in the formula CeOy, all structural changes on reducing Ce02 occur without loss of coherency of the original fluorite lattice. Comparison

of length and lattice parameter changes shows that only oxygen vacancies (and no detectable

Ce interstitials) are present in the reduced state. For y > 1.67, it is shown that oxidation

(in air or in O2) takes place at reasonable rates just above room temperature. The kinetics

of this anomalously rapid mass transport are studied in some detail, including the effects of

sample thickness and of oxygen partial pressure. The results show that the kinetics are neither diffusion nor surface controlled. A model of the process is developed which explains the

major results. The low temperature oxidation process does not terminate in the pure 01 (Ce02)

phase, but in a metastable structure, here called a^, for which y is very close to 2.0. The

properties of a' are discussed.

Key words: Ceria; crystal defects; diffusion; mass transport; nonstoichiometry ; oxides.

1 . INTRODUCTION

In the study of nonstoichiometry, considerable interest over the past decade has been

focused on those rare earth oxides which span the range of composition from the sesquioxide

R2O3 to the dioxide RO2 • The specific oxides of interest have been CeO^, PrO^ and TbOy, all

of which take on the fluorite structure in the dioxide. There have been many studies of

phase relationships, mass transport and electrical properties of these materials, usually using samples in polycrystalline form. Careful thermal and x-ray investigations have revealed

that at the lower temperatures a series of intermediate phases of narrow composition limits

is found in the range from y = 1.5 to 2.0. These phases appear always to belong to a homologous series of fomnula Rj^02n-2 • Thus, for CeOy, the projected phase diagram of Sevan and

Kordis [1]^ is given in figure 1 showing three intermediate phases 6 , c and i, which appear

at y = 1.82 (n = 11) , 1.78 (n = 9) and 1.71 (n = 7) , respectively.

The availability of large single crystals of Ce02 through a cooperative project between

Columbia University and the Materials Research Corporation (MRC) has resulted in the present

study of these crystals. The MRC crystals are grown by arc fusion in a carbon arc [2]. The

starting material is ~ 99.98% pure and the final crystals have about the same purity. The

lack of a high degree of perfection, probably due to the rapid solidification in the arc, is

shown by a lack of transparency of the resulting crystals. Nevertheless, x-ray Laue photographs of crystals annealed in oxygen show sharp spots, indicating "good" single crystals.

The present work , explores the question of the type of defects that are present in reduced

Ce02, and observes an anomalously rapid rate of mass transport in the low-temperature reoxidation of the reduced material. A major part of the work (section 3) is directed toward an attempt to understand the nature of this rapid oxidation process

.

Now with Fujitsu Ltd. Co., Kawasaki, Japan.

Figures in brackets indicate the literature references at the end of this paper.

353

465-504 0 - 72 - 24
2. OBSERVATIONS CONCERNING DEFECTS AND STRUCTURE

2.1. RESULTS OF REDUCTION-OXIDATION CYCLING

The phase diagram in figure 1 shows that at high temperatures the fluorite (a) phase is

maintained down to y = 1.7, while at low temperatures a series of three intermediate phases

occurs. It has generally been regarded [3] that these intermediate phases may be considered

as distorted fluorite structures produced by appropriate ordering of oxygen vacancies. With

the large single crystals now available, it becomes possible to see whether these various

structures are, in fact, all formed continuously from the fluorite structure. Thus, we have

carried out a series of reductions of <111> oriented Ce02 crystals and examined the Laue x-ray

diffraction pattern at each stage. Reductions were carried out in the range 700° - 900 °C in

CO/CO2 or H2/H2O mixtures and the samples were then quenched to room temperature. The most

extreme reduction produced by this procedure was to y = 1.67. In all of these cases, the Laue

photograph of the reduced crystal still showed the original 3-fold symmetry along the <111>

axis^, although the spots were more blurred than for the fully oxidized material, indicating

a distortion of the original cubic structure. When the samples were reoxidized by heating in

air at ~ 500 °C the original sharp Laue pattern reappeared in all cases. This result shows

that, so long as y > 1.67, all changes during reduction and reoxidation occur in such a way

that the fluorite lattice, although distorted, is maintained intact. From the phase diagram

(fig. 1), this result may have been expected for y-values down to 1.71, but it is rather sur- prising that it also holds in the range 1.67 to 1.71.

To achieve a more drastic reduction to Ce203 , a crystal was sealed in vacuum in a quartz

tube with titanium chips, heated for several hours at 800 °C , and rapidly cooled to room temperature. In this case, the Laue photograph shows portions of rings, indicating that the

sample is no longer a single crystal. Reoxidation to Ce02 also verifies that the sample is now polycrystalline . It is concluded that, iinlike the intermediate phases, the sesquioxide

forms by nucleation and growth of the new phase at the expense of the original fluorite structure .

1200-

1000

UJ

a:

ID

I-<

UJ

a.

800-

600 =

400-

Fig.

2.0

1. Temperature-composition projection of the

CeOy - O2 phase diagram.

However, the pattern for y = 1.67 differs in the number of diffraction spots from those of

y = 1.8 or 2.0, probably due to the fact that the 1.67 composition corresponds to the bcc

(so-called C-type) structure which has a lattice constant nearly twice that of Ce02

.

354
2.2. COMPARISON OF LENGTH AND LATTICE-PARAMETER MEASUREMENTS

Although the intermediate phases produced by reduction of Ce02 are usually regarded as formed by the ordering of anion vacancies on the fluorite lattice, suggestions persist in the

literature [4,5] (based on the dependence of properties, particularly electrical conductivity,

on oxygen partial pressure) that Ce interstitials are the primary defect involved in reduced

Ce02 . It was therefore decided to examine this point by the most direct method, viz., com- parison of macroscopic (length) with microscopic (lattice parameter) measurements. The basis

for the interpretation of such measurements is the relation

V = Nv (1)

where V is the sample volume, v the volume of the primitive unit cell and N the number of

unit cells. Thus, if reduction occurs by formation of oxygen vacancies, the nijmber of unit

cells is unchanged, and one obtains

AV/V = Av/v (0 vacancies) (2)

as the relation between the fractional changes in the macroscopic and the microscopic volumes.

(The symbol A is conveniently taken as the difference between the oxidized and the reduced

states.) On the other hand, if cerium interstitials are formed, it is easy to see that AN/N

= Ay/2 where Ay is the change in composition of CeO^ associated with the reduction. Thus

AV = Av + A^ (Ce interstitials) (3) V V 2 .

In practice, it is more convenient to measure lengths, i.e., macroscopic length L, and lattice parameter d, in a given orientation. The corresponding relations to equations (2) and

(3) are then

AL/L = Ad/d (0 vacancies) (4)

and

AL/L = (Ad/d) + (Ay/6) (Ce interstitials) (5)

under the reasonable assumption that the change in number of unit cells produces dimensional

changes isotropically

.

The present experiment involved a series of careful micrometer measurements of the thickness of a crystal before and after reduction to y = 1.81, i.e., to the 6 phase. The crystal

involved was 1.05 mm thick and its thickness dimension was parallel to <111> . The result of

the measurements may be summarized as

(L - LJ/L = - 0.017 ± 0.001

a 0 a where the subscripts a and 6 refer to the phases, i.e., to y = 2.00 and 1.81, respectively.

Correspondingly, the change in lattice parameter is available from the work of Bevan [6].

However, we have repeated these measurements in an x-ray diffractometer and obtained somewhat

more precise values for d-values along <111>:

(d„ - d5)/dc( = - 0.0164 ± 0.0003

(The value of da can be obtained from the lattice parameter of the ciobic fluorite structure,

but d(5 must be measured directly, since the 6 phase is actually rhombohedral) . Comparison of

these results shows that the agreement with (eq 4) is excellent, and since Ay/6 = 0.03, that

(eq 5) is in complete disagreement. If we allow for the possibility that both defect types

may be present simultaneously, these results lead us to conclude that at least 97% of the

defects are oxygen-ion vacancies. Thus, we have found no evidence for the formation of Ceion interstitials upon reduction.

355

/
2.3. THE LOW-TEMPERATURE REOXIDIZED STATE (a')

It was found, both for the MRC single crystals and for sintered polycrystalline samples

reduced to y ^ 1.67, that reoxidation takes place in air at ambient temperatures with a re- turn to a y-value close to 2.0. Oxidation is so rapid, in fact, that if a thick sample is

used and cooling precautions are not taken, the sample heats up appreciably as a result of

the exothermic oxidation process'^. The kinetics of the low-temperature oxidation will be

discussed in detail in the next section. Here we are concerned with the state to which the

sample returns after this oxidation process. This state is characterized by the following

features

:

(a) Appearance: The color of the reoxidized crystal remains black, like that of the

crystal in the reduced condition. In order to bleach this crystal to the yellowish color of

the fluorite (a) phase, it must be heated in air at a temperature of 350 °C or higher. When

the bleached crystal is brought back to room temperature, it is stable indefinitely. It is

concluded that the low-temperature reoxidized state is a metastable one; henceforth, we shall

call it the a/ state.

(b) Composition: The y-value in the a' state is very close to 2.0. Samples taken

through the bleaching transformation, in a Cahn microbalance , show that the increase in y-value

which accompanies the transformation a' ^ a is roughly 0.005. In order to determine whether

a" -> a is primarily a thermally activated structural transformation, or whether the small a- mount of oxidation that occurs is essential to the transformation, we heated samples sealed

in quartz capsules. These samples did not bleach when brought up to 500 °C, while similar

samples heated in air are fully bleached. It is therefore concluded that the small amount

(6y < 0.01) of additional oxidation is an essential part of the process by which the metastable a' is transformed to a.

(c) Diffraction Pattern: A Laue photograph of the state is similar to that of a except that the spots are blurry for and sharp for a. For more careful examination, sintered powder samples in the low- temperature reoxidized state were examined in a diffractometer. Figure 2 shows a comparison of (331) reflection for the and a structures. On the

76.2 76.4 766 76.8 77.0 77.2 29

Fig. 2. Comparison of the x-ray (331) reflection

for the a' structure, labeled B, with

that of the fluorite (a) phase, labeled

A. (The doublet in each case is due to the Ka^ and Ka2 x-radiation.

)

The occurrence of this low temperature process is only briefly mentioned in the early literature [6] .

356
one hand, a' shows a slightly larger lattice parameter (~ 0.2% larger) than a, but most

strikingly the line is distinctly broader than the corresponding one for the a phase. The

broadening of the other reflections is about in the same ratio. This line broadening cannot

be interpreted as resulting from a two-phase mixture of the a and 6 phases, since the lattice

parameters of these two phases is sufficiently different that the lines would be well resolved.

Instead, it is most reasonably regarded as indicating a microdomain structure [7], i.e., the

presence of small regions, of dimensions ~ 100 - 1000 atom distances, which differ in composition from the a phase but are coherent with it.

(d) Chemical Reactivity: A reduced CeO^ crystal sealed in a high humidity chamber reacts rapidly with moisture and disintegrates into a powder which probably consists of a hydroxide. On the other hand, the structure is relatively inert toward reaction with moisture .

(e) Electrical Conductivity: The electrical properties of a' are similar to those of

the reduced material, viz. a conductivity a - 10~^ (ohm-cm) On the other hand, upon

bleaching to a, the conductivity drops five decades to a ~ 10-^ (ohm-cm) Figure 3 shows

the change in conductivity during very slow heating and subsequent cooling. Note that once bleaching has occurred, the crystal remains a relatively good insulator at room temperature.

The question of how this metastable a' structure arises will be discussed when we con- sider the theory of the kinetics of oxidation in the next section.

-I 10 IolO" I I I I 1 I

I I I I J

O 200 400 600 800 1000 TEMPERATURE, "C

Fig. 3. Changes in conductance with

temperature upon heating

(solid circles) and subsequent

cooling (open circles) of a Ce02 crystal which had been

reoxidized at low temperature.

Conductivity = conductance x 0.25.

357
3. KINETICS OF THE LOW-TEMPERATURE OXIDATION (5 -> a')

The oxidation of reduced Ce02 in the vicinity of room temperature is an example of re- markably rapid mass transport, considering that Ce02 has a melting point of ~ 2600 °C and,

therefore, a Tammann temperature^ ~ 1200 °C. In order to try to understand the nature of

this rapid mass transport, a detailed study of the kinetics of the process was carried out.

It was hoped that by using single crystals, mass transport along grain boundaries would be

eliminated from consideration.

3.1. EXPERIMENTAL METHODS

To avoid the necessity for mounting and handling the sample after the high temperature

reduction, we gave up the idea of using an electrobalance , and instead adopted a classic sys- tem employing a fine quartz spring, as shown in figure 4. The quartz spring used was made

by Worden Quartz Products, Inc. It allowed a maximum load of 2g and had a sensitivity of

0.039 g/cm. The elongation of the spring was measured by a cathetometer . The samples used

were attached to the quartz spring by means of a fine platinum wire. The system was com- pletely enclosed and offered the ability to transfer the sample rapidly from a hot zone to a cool zone (both regulated in temperature) , as well as to change the gas flowing through the

system. By using thin samples and maintaining a gas flow, it was found that the problem of

heating up of the sample during oxidation could be avoided. The procedure, following the

mounting of the sample, is as follows:

(1) The sample is oxidized by holding it in the hot zone at 850 °C under an oxygen atmosphere for 10 hours

.

(2) The oxygen is replaced with argon over a period of about 1 hour.

(3) The argon is replaced by a gas mixture 99.9% CO/0.1% CO2 and the sample is held

for longer than 12 h at 850 °C in this atmosphere. According to Bevan and Kordis [1] , these

conditions produce an equilibrium y-value of 1.79 ± 0.02,

(4) The sample is then brought down to the point B in figure 4 over a period of a few

seconds by turning the ground joint F, while maintaining the flow of CO/CO2 (at 0.8 cm/sec)

.

Region B is then at 0 °C.

(5) The tube is then flushed with argon, and the point B is then brought to the desired temperature of measurement (20 - 42 °C) . The temperature of point B is controlled to ± 0.02 °C by a mercury relay attached to an immersion heater in water bath I. When this temperature is reached the argon is replaced by oxygen or dry air . This event is taken as the

time t = 0 for the kinetic curve. The flow rates of the Ar and O2 gases are 0.5 cm/sec.

Most of the experiments were carried out on two samples, both from the same MRC crystal.

Each had a cross section of 8 mm x 10 mm and its small (thickness) dimension was parallel to <111>. They did differ, however, both in thickness and in surface condition, as follows:

Sample Thickness Surface

A 1.45 mm polished

B 1.08 mm cleaved

The surface of sample A was polished with emery paper (#180) while that of B was as cleaved.

Sample B, therefore, had a much smoother surface than A.

5 The Tammann temperature, roughly 0.5 of the melting temperature (in K) is the point below

which atom movements usually cease, for all practical purposes.

6 The results described earlier (section 2.1.) , which show that all changes upon reduction and

reoxidation occ\ir without destruction of the basic structure of the fluorite lattice, indicates the absence of any incoherent boundaries in the reduced structure.

358
Fig. 4. The quartz spring balance and

associated equipment. A - specimen position for reduction

at high temperature; B - specimen

position for oxidation at low

temperature; C - cathetometer

;

E - platinum wire; F - ground

joint; G - furnace; I - temperature

regulated water bath; P - quartz

spring; , S2, S3 - stopcocks.

3.2. RESULTS

Figure 5 presents the kinetics of oxidation at four temperatures for sample A, starting

T, °C

42

35

1000 TIME , minutes

Fig. 5. Kinetics of oxidation of sample A at four different

temperatures in pure oxygen.

359
in each case from a y-value near 1.8. In this figure the changes in weight have been con- verted to y-values for greater ease of interpretation. In doing so, the reference value of

y = 2.00 is taken as the value for a sample heated in oxygen at 850 °C prior to reduction''.

In figure 6, kinetic curves are compared for samples A and B at two temperatures. Although the oxidation of sample B seems to begin more rapidly in both curves, the overall re- sult is that there is surprisingly little difference between these two samples, which indicates the absence of a thickness dependence. Unfortunately, however, the fact that the surface conditions of the two samples are not identical places a possible reservation on this

conclusion. This point will be discussed later.

In order to determine the activation energy of the rate controlling step, a series of

horizontal cuts have been made through the cuirves of figure 5, each at a different y-value,

say yj_. The corresponding times t-j_ to reach the value yi are then plotted as log t-j_ versus

1/T, as shown in figure 7. If oxidation over the entire range is controlled by a single ac- tivation energy, E, the slope of these plots should be independent of yj_. In the present

case, there are departures from a constant E at the initial and final stages of the curves, but these regions are also where the precision is poorest. The data of figure 7 shows that

for the intermediate range, E is fairly constant at 0.7 eV (16 kcal/mol)

.

In order to determine the oxygen-pressure dependence of the kinetics of oxidation, the same sample A as had been run in pure O2 was re-run under dry air, i.e., under oxygen pressure a factor of five times smaller. Figure 8 shows that under higher Pq^ the rate of oxidation is faster. If we take the rate of oxidation in the form

dy/dt = k f (y) (6)

the data of figure 8 show that the ratio of rate constants, kQ^/kair/ is 1.5 from the 42 °C

2.00

1.95

>. « 1.90

o

c^ 1.85

1.80

SAMPLE X

" 35° C^-*-^^-*-

• A

- B

X

1 1 1 1 500 1000 1500

TIME, minutes

2000

Fig. 6. Comparison of kinetics of oxidation of samples A

and B at two temperatures.

7 The fact that the 42 °C curve of figure 5 appears to exceed y = 2.0 is a source of concern. Comparing with other experiments, we cannot yet say whether a y-value slightly in excess of

2.0 actually occurs, or whether such a reading is due to experimental error by the spring

balance, or the pickup of some CO2 by the crystal.

360
Temperature ('C) 42 35 27 20

-1 .

I

.

I J_

3.1 3.2 3.3 1000 /T CK)

Fig. 7. Plots of time, t^, to reach a given value yj^ as a fiinction

of reciprocal absolute temperature, obtained from the data

of figure 5.

y in CeO„

1,000 1,500 Time, minutes

Fig. 8. Effect of oxygen partial pressure on oxidation

curves of sample A at two different temperatures.

curves and 1.65 from the 35 °C data. If it is assumed that k <^ P02' these ratios correspond

to n = 0.25 and 0.31, respectively.

Finally, some preliminary experiments were carried out on a set of small flux grown

crystals (supplied by C. Finch of the Oak Ridge National Laboratory). For these crystals,

oxidation does not take place at room temperature but seems to require temperatures near

100 °C. The reason for this difference between the flux-grown and the arc-fusion grown

crystals is not clear at present. It may be related to the very smooth external surfaces or

361
to a higher degree of internal perfection of tlie flux-grown crystals. Either reason may impose an additional rate-limiting step which was not present in the case of the MRC crystals.

This matter will be studied further in the future.

3.3. DISCUSSION

In attempting to understand mass transport processes in reduced Ce02 , one might first

turn to the available high temperature oxygen diffusion experiments [8,9]. Extrapolation of

data taken near 1000 °C for y ~ 0.9 gives a diffusion coefficient D < 10"-^^ cm^/sec at 35 °C.

Such a value is far too small to allow penetration of oxygen through a sample ~ 1 mm thick in

reasonable lengths of time. From the phase diagram, however, it is clear that the structure

at high temperatures, consisting of random oxygen vacancies on the fluorite lattice, is en- tirely different from the structure with which we are concerned near room temperature . Accordingly, it is clear that any explanation for the anomalously rapid mass transport at low

temperatures, must be given in terms of the structure of the reduced material at low temperatures .

There are several strong indications that the low temperature oxidation is not a diffusion controlled process

:

(a) The solution of Pick's second law for a thin slab of thickness a, under conditions

of constant composition at the surface gives [10] a result which initially takes the form

Ay - (Dt)^/^ (7a)

and then, over most of the range obeys

In [1 - (Ay/Ay^) ] = - tt^ Dt/a^ + In (S/tt^) (7b)

Here D is the diffusion coefficient, while Ay is the instantaneous average change in y-value

and Ayq is the total change. The form of (eq 7) disagrees with the kinetic curves of figure

5, since the observed initially increasing slope is not predicted.

(b) In a diffusion controlled process, except for the initial part of the kinetic curve,

the time to a given y-value should vary as , as predicted by (eq 7b) . The results of figure 6, which compares two samples of different thickness, are in clear disagreement with this

prediction.

(c) The observation of an appreciable pressure dependence is difficult to explain on a diffusion model, since the equilibrium y-value is very nearly independent of Pq^ in this

range of temperature and pressure.

(d) Finally, the value of the measured activation energy, 0.7 eV, is too high to be

consistent with a simple diffusion model. For, if it were the activation energy for a diffusion jump, the mean j\imp time at 35 "C would be^ x 10" exp (0.7 eV/kT) ~ 10"^ sec. Thus, in the half-time of the experiment (700 min at 35 °C) there would be - 10^ jumps, or a mean diffusion over ~ lo'^ lattice spacings. Such a distance is far smaller than the sample

dimensions

.

If the observed oxidation process is not diffusion controlled, it is reasonable to con- sider next the possibility that the rate controlling step is the surface reaction by which

oxygen is incorporated into the crystal. In such a case, however, the rate constant k in

(eq 6) should be proportional to the oxygen pressure (i.e. n = 1) which is not observed.

Also, the initial kinetics should be linear [11], i.e., Ay <^ t, contrary to the observations.

Finally, we have the comparison of two samples (A and B) of different surface condition, in

figure 6. The situation is complicated by the fact that two variables, viz. surface and

thickness, are changed simultaneously. However, in the early part of these curves where the

thickness effect should be least important, if anything, the smoother sample B shows the

faster kinetics. This result is opposite to that which would be ejcpected based on a surface

In virtually all atom and defect jump processes in crystals, a frequency factor of 10

sec"-^ is obtained.

362
controlled reaction. In view of these arguments, it seems necessary to reject the idea of a surface controlled step.

Accordingly, we turn to the following simple model which seems generally to account for

the experimental observations. In this model, we assume that the appropriate defect is interstitial oxygen within the reduced 6 phase. This suggestion is not in conflict with the

earlier evidence (section 2.2.) that reduction of Ce02 involves exclusively vacancies, since

the present interstitials are taken relative to the stoichiometric 6 phase. Since the oxidation is not diffusion controlled, it is reasonable to conclude that the interstitial defect

migration process is one of very low activation energy 0.4 eV) , i.e., sufficiently small

to produce diffusion through the entire specimen in times much less than the time of the ex- periment. In view of this rapid interstitial migration, equilibrium of these defects with

the external atmosphere should be quickly established. If the oxygen interstitials are singly

ionized, the reaction is (in the Kroger-Vink notation [12]) :

02 J 20^ + 2 ®

which leads to the mass action equation

[0-]2[ ® ]2/Po2 = Ki(T) (8)

Since [0^] = [ ® ], it follows that [0^] °t Po2^'^^ • other hand, if the interstitials were unionized or doiible ionized, their concentration would go as Pq2^/^ and p^ , respectively.

The second assumption of the model is that nuclei of the a phase are already present in

the quenched material, e.g., at structural imperfections. The final assixmption is that the

rate limiting process is the transfer of an interstitial oxygen ion in the 6 phase over to

the a phase at the 6-a phase boundary.

This model explains why diffusion is not rate controlling, and therefore, why results

are independent of sample thickness. It is also consistent with the observed pressure dependence (see below (eq 6) )

, if one assumes that the singly ionized state of the interstitial is

predominant. The model also predicts the shape of the oxidation profiles of the type shown

in figures 5, 6 and 8. Thus, if the growing particles of a are initially spherical in shape,

the rate of growth is given by

dy/dt = k^n^ • 4Trr^ (9)

where y is the average composition of the entire sample, r the radius of a growing a region,

nQ the number per unit volume of such growing particles (i.e., the original number of nuclei)

and kQ a rate constant. Because the rate is controlled by the surface reaction, we also have

r = Kt, so that Ay t^ for the initial portion of the curve. Figure 9 shows that this initial cube law is obeyed reasonably well. The point at which the oxidation curve departs from

the cube law and the slope begins to decrease is then interpreted as the beginning of interference of the growing a regions

.

Finally, this model permits us to understand why the metastable state is the end

product of the low temperature oxidation process. For, only so long as the 6 phase is continuous can oxygen be rapidly transported to the growing interfaces. As soon as small regions of 6 phase are isolated, the process of further growth requires transport of oxygen

through regions of the a phase. This is a much slower process and, therefore, cannot take

place until the temperature is further elevated. This interpretation seems to lead to the

prediction that the a' structure is a two-phase mixture of a and 6. However, if the 6 regions are small enough, they will be severely strained by the a matrix, since the two are coherent. Accordingly, such small regions would behave more like microdomains than as particles of an independent second phase, which is consistent with the type of diffraction pattern

shown in figure 2.

In summary, the present model provides a basis for understanding of several of the key

facts associated with the anomalously rapid mass transport of oxygen in the low temperature

oxidation of reduced Ce02. On the other hand, the reader should note that, in the data pre363

I
4 0

3.0

<l

2.0

A

1

B / C

/ • /

°

Curve T(*C) _ope Slo e A 42° 3.0

B 35° 2.7

C 27° 2.5

D 20°

1

2.3

2.0 3.0 4.0

log t (min) Fig. 9. Log-log plot of initial

change in length of quartz

spring versus time at four

temperatures. The slopes

of the curves are given in

the inset.

sented here, the variables are not always controlled as well as required. For example, whereas the model assumes that the initial reduced state is completely the 6 phase, the actual yvalues at the start of the runs used to obtain figures 5 and 9 fall somewhat below the ideal

value of 1.818 of the 6 phase. The structure at the start may therefore be more complex than

that assumed in the model. Another example is in figure 6 in which both sample thickness and

surface condition have been varied simultaneously. Finally, there is the question of why

flux grown crystals show slower oxidation kinetics. It is clear, therefore, that further

kinetic studies which will provide a more stringent test of the model are required. Such

studies are currently under way in this laboratory.

4. ACKNOWLEDGMENTS

This work was supported by the Advanced Projects Research Agency. The authors are also

grateful to Messrs. H. Tuller and S. P. Ray for their valuable assistance in carrying out

some of the x-ray and electrical conductivity experiments.

5. REFERENCES

[I] Bevan, D. J. M. and Kordis , J., J. Inorg. Nucl. Chem. 26_, 1509 (1964).

[2] Defects and Mass Transport in Single Crystals of Refractory Oxides, Semiannual reports

to ARPA under Contract DAHC-15-68-C-0129 , May 1, 1968 and Nov. 1, 1968.

[3] Sawyer, J. O., Hyde, B. G. , and Eyring, L., Bull. Soc. Chim. France 1190 (1965).

[4] Kofstad, P. and Hed, A. Z., J. Am. Cer. Soc. 50_, 681 (1967).

[5] Blumenthal, R. N., Lee, P. W., and Panlener, R. J., J. Electrochem. Soc. 118 , 123 (1971).

[6] Bevan, D. J. M. , J. Inorg. Nucl. Chem. 1^, 49 (1955).

[7] See, for example, Anderson, J. S. in Problems of Nonstoichiometry , ed. Rabenau, A.,

North Holland, Amsterdam 1970, Chap. 1.

[8] Steele, B. C. H. and Floyd, J. M. , Proc. Brit. Cer. Soc. No. 19, March 1971, p. 55.

[9] Vinokurov, I. V. and loffe, V. A., Sov, Phys. -Solid State 11, 207 (1969).

[10] Levin, R. L. and Wagner, J. B. , Jr., Trans. AIME 233 , 159 (1965).

[II] Childs, P. E. and Wagner, J. B., Jr., in Heterogenesus Kinetics at Elevated Temperatures

,

ed. Belton, G. R. and Worrell, W. L. , Plenum Press, New York, 1970, p. 269.

[12] Kroger, F. A. and Vink, H. J., Solid State Physics 3_, 310 (1956).

364
DISCUSSION

A. D. Franklin : Do you know the source of the extremely high conductivity in the

alpha prime phase; is it ionic or electronic?

A. S. Nowick : We think it is at least partially electronic, but in view of the

observed rapid migration, it must also have a substantially ionic component. We are just

now in the process of determining the transference numbers.

L. Eyring : Do I understand that at none of these temperatures up to 45 °C did you

see a completely bleached end product?

A. S. Nowick : This is correct. The composition levels off at a final value which

represents the metastable state. To produce bleaching is not a matter of a slight increase

in temperature or of waiting a somewhat longer time. The kinetics are very slow at the

end of each run; to produce the bleaching one must go up another 150 degrees at least.

L. Eyring : So, its something like 200 °C.

A. S. Nowick : Yes, that is correct.

W . Van Gool : I don't see how you are able to deduce something from this defect

chemistry by just comparing the macroscopic and lattice dimensions. I should expect that

even when you have an interstitial model you should find the same relationship as you

found experimentally. You are working here with volumes and the differences between the

two defect situations is a difference in mass, but not in volume.

A. S . Nowi ck : The difference between the two defect situations (oxygen vacancies as against cerium interstitials) is not a difference in mass, but a difference in the number

of unit cells in the lattice. The macroscopic dimensions are sensitive to the number of

lanit cells, while the x-ray lattice parameters are not.

365

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

ANION CENTERED COORDINATION POLYHEDRA AND RELATED

PHYSICAL PROPERTIES IN RARE EARTH OXIDES AND OXYSALTS

Paul E. Caro

Centre National de la Recherche Scientifique

Laboratoire des Terres Rares

Bellevue, France

The structures of rare earth oxides and oxysalts can be conveniently described in terms

of linkages of anion centered coordination polyhedra, namely tetrahedra, yielding two-dimensional or three-dimensional frameworks. A complex "lanthanyl" cation (LnO)^''" can be recognized. It has two different arrangements of tetrahedra, one of them being identical with

the well known "bismuthyl" cation (BiO)fJ'*", The structural elements are similar to the

classical Si02 and Sij-Oy ones; SiOt^ tetrahedra frameworks, used for silicates structures

classification. Other anions than oxygen (sulfur and halides) yield isomorphous networks.

Such types of structures imply some sort of covalent bonding. The covalence of the

bond can be shown from optical measurements on solids. For (OLnL|.) compounds the absorption

spectrum is displaced to the red (nephelauxetic effect) , a phenomenon which corresponds to

the lowering of the Racah's parameters of the 4 f'^ configuration. The mixing of the | 4 f'^> wave functions with ligand wave functions also yields larger transition probabilities and

the (LnO)fJ+ materials are very effective phosphors.

The layered oxide structures also yield textured thin films which exhibit epitaxial

continuity and intergrowth between the rare earth oxides phases

.

The layered polymolecular complex cation concept can be applied to rare earth extended

non-stoichiometric systems. It can be shown that the chemical composition of all the known

phases of those systems can be accounted for in term of the succession along a main crystallographic axis of four planar chemical units ABCD. Non-stoichiometry occurs because a layered structure AB is able to be interleaved through another layered structure ADCD. A general chemical formula for the ordered phases was derived, for the bastnaesite family of

compound (AB = bastnaesite, ADCD = synchisite) , the Ln203-LnF3 systems (AB = tysonite

,

ADCD = trigonal EuOF) , the LnO^ systems (AB = LngOio, ADCD = Lni2022) and the LnCl3-LnCl2

system (AB = LnCls, ADCD = LnCl2). All of the compounds contain layered polymolecular

complex cations

.

Key words: Complex ions; coordination polyhedra; 4 f'^ configurations; non-stoichiometry; polymolecular frameworks; refractory materials; rare earth optical spectra;

rare earth oxide; thin films.

1. INTRODUCTION

A few years ago [1] ^ we introduced a structural description of the rare earth sesquioxides , and of several other rare earth compounds we called "oxysalts", based on the

recognition of the importance of the coordination of the oxygen atom. The process is to abstract coordination polyhedra of metallic atoms (the cations) around the oxygen atom and

to describe the structure in term of linkages of corners, edges, or faces, whatever is

convenient, of these polyhedra together. This is a very well known and successful descriptive scheme for structures in inorganic chemistry, but the abstraction is usually applied

1 . Fxgures in brackets indicate the literature references at the end of this paper.

367
only to cations coordination polyhedra. Anion centered coordination polyhedra are described

but very occasionally [2]. Nevertheless, they sometimes offer a challenging and provocative

way to the understanding of structure and bonding.

We think this is indeed the case for a score of rare earth compounds. It turns out

that the proposed description applies specially well to those compounds of the rare earths

which are high-temperature materials. It may also help to understand some of their fundamental properties and high-temperature behavior. We shall consequently restate briefly,

first, our unified description of rare earths oxides and other pertinent refractory materials .

2. THE TETRAHEDRAL COORDINATION OF OXYGEN IN RARE EARTH OXIDES AND OXYSALTS.

The rare earth sesquioxides exhibit, along the rare earth series, three fundamental

structural types: A-type Ln203 (we shall use the symbol Ln as a convenient one for the

whole rare earth group cations) which is hexagonal, B-type Ln203 which is monoclinic, and

C-type Ln203, cubic. At high temperatures there is also two other additional phases the H (hexagonal) and X (cubic) , but their structure are still unknown. The rare earth oxides

structural pattern versus temperature was investigated up to the melting point by Foex and

Traverse and their papers [3], [4] provide all the informations on transition temperatures,

stability domains and the like.

C-type Ln203 is derived from the fluorite structural type by removing a quarter of the

anions. The fluorite structure is the basis for the understanding of the non-stoichiometric

rare earth oxide systems LnOj^ (Ln203-Ln02 )

, which exhibit several sharply defined compounds

as the thermodynamical and structural studies of LeRoy Eyring and his school have shown [5]

,

[6]. Of those intermediate compounds only one is of a known structure at the present time,

it is the most stable of them all, Ln70;^2' '^^^ fluorite structure can be conveniently

described in terms of anion centered coordination polyhedra. The oxygen in Ln02 is at the

center of a tetrahedron of metallic atoms and the whole structure may be seen as three-dimensional framework of OLni^ tetrahedra linked together by their six edges. Then, from the

known position of oxygen vacancies in C-Ln203 and Ln70i2 it is easy to show that C-Ln203 is

a three-dimensional building of OLni+ tetrahedra linked together by four out of six edges, and

Ln70i2 a three-dimensional building of the same OLni+ tetrahedra, but linked together with five

out of six. In other words, for the two structures, all of the OLn^ tetrahedra have identical linkages and are topologically equivalent. Curiously enough, the observed structures

are the only ways to pack tetrahedra into space by linking together only four or five of

their edges (although there are other ways for linkage of five edges but far less symmetrical than the one observed in Ln70i2 and of a different stoichiometry)

.

A OLnij tetrahedra packing appears conspicuously in A and B-Ln203. However this time,

there are two types of oxygen atoms in the structure, one is inside a tetrahedron of metallic atoms, the other one is six-coordinated and is further removed from the rare earth atoms

o o than the former one (d. 0-Ln = 2.70 A versus 2.40 A, in A-La203) . The remote oxygen atom can be replaced by other chemical species: the familiar example is S^~, yielding the

oxysulfide (LnO)2S which is isomorphous to the A-type oxide. We proposed to formulate

A-Ln203 : (LnO) 2O because the structure is made along the hexagonal c-axis of a succession of

slabs of a "complex group" (LnO) ^^"'"-built of OLni^ tetrahedra edge-linked in a manner derived

from the fluorite structure - separated by planes of oxygen anions. The layered character

of A-Ln203 is very clearly exhibited by the easy cleavage of the single crystals perpendicular to the c-axis [7]

.

B-type Ln203 is very similar to the A-type but is monoclinic because the hexagonal

symmetry is lost following a small displacement of the (LnO)J^"'" slabs with respect to each

other, together with a tetrahedra distortion induced by the lanthanide contraction. The

close relationship between A and B-Ln203 was demonstrated by the author and his associates

[8] from electron diffraction and microscopy on thin oxide films.

Other rare earth oxysalts exhibit edge-linked 0Lni4 tetrahedra which also develop into

a (LnO)JJ"*" slab but with a different symmetry. This other type of slab is usually associated

with monovalent anions (Cl~, 0H~) and the best structural example is the rare earth oxychloride (LnO) CI.

368
Now, the two types of (LnOjJ"*" structural slabs, or layers, are simply slices of the

fluorite (Ln02) structure. One of them (A-Ln203) , is a slice perpendicular to the C3 axis

in the fluorite cake and involves a Ln-O-O-Ln succession of fluorite planes parallel to

(111) , the other one is a slice perpendicular to a Ci+ axis and involves a Ln-O-Ln succession

of planes. Both slices have the same overall formula (LnO)^+. To distinguish the two

arrangements we will, from now on, label them as (LnO)^"*" (C3 ) for the type encountered in A

(or B)-Ln203 and (LnOf}""" (Ci^) for the one found in (LnO)Cl. The labelling does not implies

that the layers imperatively always exhibit a C3 or Ci^ symmetry axis perpendicular to them

through the atomic positions, this fundamental symmetry can be slightly distorted (as in

B-Ln20 3) . An interesting character of both layers is that they do not have a plane of

symmetry perpendicular to the C3 or Cn axis. (That means there can be "up and down" layers

with respect to an oriented C3 or Ci+ axis) , (figs. 1 and 2) .

Numerous rare earth compounds exhibit one or the other type of complex cation. Such

compounds can be recognized, or suspected, easily because for a large number of anions the

Q_i_ rare earth derivatives come m two forms: one is a true Ln-^^ salt, it is usually highly

reactive, soluble, has a low melting point or decomposes easily (for instance the rare earth

halide series); the other one is an oxycompound and contains the (LnO)[J"'" unit, it is on the

contrary chemically inert, strictly insoluble, has a high melting point or decomposition

temperature. Two good examples are the oxynitrates (LnO)N03 which are insoluble (a character which is not common for a nitrate) , and the oxycarbonates (LnO) 2CO3 , which at the beginning of the rare earth series exhibit the highest decomposition temperature for an inorganic

carbonate ((LaO)2C03 - 950-1000 °C) [9, 10].

The rare earth oxycarbonates (LnO)2C0 3 are polymorphous materials. There is three

forms, I (quadratic), la (monoclinic) and II (hexagonal). Two of them, I and la, correspond

apparently to (LnOjJ"*" (C14) , the other one to (LnO)^"*" (C3) . This is the only oxysalt for

which both infinite cations were reported. At the beginning of the rare earth series, the

C3 oxy carbonate appears to be more stable than the Ci| types. In the middle of the series

the Ct| oxycarbonate type I is easier to prepare, and at the end the mere existence of an oxysalt is in doubt. The C3 oxycarbonate decomposes to A-type Ln203 , but the C14 types

decompose to C-Ln203.

Fig. 1. The "hexagonal" (LnO)j^ (C3) polymeric

cation. The smaller balls are the

oxygen atoms

.

465-504 0-72-25 369
Fig. 2. The "quadratic" (LnO)j^ (C^) polymeric

cation. The smaller balls are the

oxygen atoms

.

As a general rule, the rare earth oxysalts are far more easy to synthetize for the

-eerie group. Their easy occurrence is, in fact, a fundamental chemical property of the

eerie group. After gadolinium in the series, the oxycompounds are not so well defined.

This is due to the increased difficulties to conserve the compact, fluorite derived, layers,

in view of the progressive lanthanide contraction which reduces the Ln-0 distance beyond

the limit acceptable for the oxygen to oxygen distance in the OLni^ tetrahedra close packing.

In C-type Ln203, however, the tetrahedra form a less rigid three-dimensional network, they

can distort themselves more easily, and the structure, being able to adjust to the reduced

cation radii, becomes the stable one in the rare earth oxide series.

(LnO)^"*" (Ct^) has a well known counterpart in bismuth chemistry. It is the so-called

bismuthyl cation {BiO)^"*". The crystallography of the bismuthyl compounds is known from the

work of the Swedish scientist Sillen [11] . (LnO)n+ (Ci^) and (BiO)f}+ are strictly identical

and the salts of both cations are isomorphous and can exhibit large domains of solid solutions when the Ln-0 distance is compatible with the Bi-0 one (2.29 A). Because of that

analogy it may be convenient to adopt the word "lanthanyl" to qualify the (LnO)^^"'" (Ci|) and

(LnO)^"*" (C3) compounds. The bismuthyl group (BiO)J^''" appears as a layer in the structures

of numerous complex oxides and complex oxyhalides of bismuth (Wells [12]), providing a good

example of the type of structural entities to be expected from the occurrence of such a type of bonding. We will return to the bismuth case in connection with the problem of non- stoichiometric systems.

The structural elements we have discussed so far have nothing unusual, but for the fact

that the primitive unit is an oxygen centered coordination polyhedron. It will be easily

noticed that what we are describing is analogous in principle to the scheme used to classify

and describe the silicon oxides and the silicate families [12] . The primitive unit is in

that case a cation centered coordination polyhedron which is also a tetrahedron. In the

silicon compounds the SiOi^ tetrahedra are linked together by their corners , instead of edges

for the OLni^ tetrahedra. Depending on the number of corners joined together SiOi, tetrahedra

develop complex cations, rings, chains, or bi-dimensional sheets. The sheets are formed by

3. THE SILICON COMPOUNDS ANALOGY

370
the sharing of three corners, their overall composition is (31205)^'^", and they can exhibit

different geometries (6 ring sheets like in the micas or an alternance of 4 and 8 rings in

such minerals as apophyllite) . These two (Si205)n'^~ sheets are seen to have a formal analogy with the two (LnO)J^+. If the SiOtt tetrahedra share all of their corners we have threedimensional structures. Those are the different forms of silica Si02 . There the formal

analogy is to the three-dimensional framework of OLni^. tetrahedra in Ln02 , Ln70i2 and C-Ln203.

The structures of layered silicates are rather complex and impressive. The negatively

charged sheets can be held together by cations (of course the (LnO)^''" sheets are corres- pondingly held together by anions) , or they can be in structural continuity with other

(positively charged) frameworks (like layered hydroxydes) , as does the bismuthyl cation in

several oxides of bismuth. Also the complexity of the properties come, in part, from the

possibility to siibstitute another cation, with a different charge, Al^+, for the silicon

in the (81205) (and also in other types of SiOt^ frameworks) . Similarly the structures

in the PrOjj system must accommodate two differently charged cations Ln^"^ and Ln^"*". Polymorphism in layered silicates is frequent because the layers can undergo translations with

respect to each other. For (LnO)!^"*" compounds the same phenomenon yields polymorphism (A

and B-Ln203, type I and la (LnO)2C03) and can be a cause of structural disorder (i.e.

poorly defined powder patterns are frequent for oxysalts , and intense twinning is the rule

in B-Ln203 crystals)

.

The correspondence we are trying to establish between the classical picture of the

well-known silicon family and our descriptive structural scheme for rare earth oxides and

oxysalts of high temperature interest is not entirely intended as an illustrative trick.

We do mean that the two groups of compounds, although of unequal nature and complexity, have

in common a fundamental component. In the silicon family, there is, of course, a strongly

covalent a bonding between silicon and oxygen in the SiOi^ tetrahedral unit. Because of the

bonding, one, two, or three-dimensional polymeric atomic frameworks are easily built (see

also the Huggins theory of "structons" [13] ) . We then claim that the occurrence of formally

analogous structural entities in the rare earth compounds is a sign of the existence of a formally analogous, not, evidently, identical but practically as efficient, bonding process

between the oxygen and the rare earth ligand (in fact the mode of bonding is more likely to be distributed through the complex atomic association) . Because of the efficiency of the

bonding and its "polymolecular" nature both the silicon and the rare earth compounds are effectively high temperature materials.

4. OTHER TYPES OF ANION CENTERED COORDINATION POLYHEDRA AND LAYER STRUCTURES IN RARE EARTH

COMPOUNDS

Complex entities, strictly analogous to the (LnOj}"*", can be formed with other anions

than oxygen, namely and F , as work undertaken in Professeur Flahaut's laboratory in

Paris by Dagron and Thevet has shown recently [14] . In the structures of the rare earth

halogenosulfides LnSF, LnSBr, and LnSI , (LnX)j^ structural layers appear made of XLni^ tetrahedra sharing edges. X is fluorine in LnSF, sulfur in LnSBr and LnSI. The layers are held

together by two planes of the remaining anions. The complex layer exhibits, like (LnO)^"*",

the two C3 (SmSI) and (CeSI) polymorphs.

Still another, but different, type of apparent "complex polymeric cation" is exhibited

by the rare earth fluorine association in the tysonite structure of the eerie rare earth

fluorides LnF3. There exists a plane, perpendicular to the c-hexagonal axis, which contains

the same amount of rare earth and fluorine atoms, in an array which can be conveniently

described as triangles of rare earth atoms having at their center a fluorine, each metal

corner being common to three triangles. The overall composition is (LnF)^"^"*". It is known

from NMR experiments, that one of the fluorine atoms in tysonite is more strongly bonded to

the rare earth than the other two [15] . The tysonite sheet is specially important because

it is seen associated with a well documented case of nonstoichiometry and microdomain formation, in the structure of the bastnaesite family of rare earth f luorocarbonates : (LnF)C03

and its associations with calcium carbonate. Similar (LnF)^"^"*" sheets were just reported in

LaSeF (a) and Ce2SeF4 by Nguyen-Huy-Dung from Flahaut's laboratory [16]. As a pleasant

contribution to the power of the tetrahedron abstraction let us mention the discovery by

the Flahaut group [17] that the supposed 3 form of Ln2S3 was in fact a ternary compound

with a formula LnigSi^O and a structure organized around a single isolated OLni+ tetrahedron!

371
Corner sharing of OM^. tetrahedra (M is not restricted to a rare earth) has been described [18] as a convenient way to visualize the pyrochlore structure. This A2B2XgX'

structure is interpreted as two interpenetrating networks, one is a network of classical BXg

octahedra, but with the B atoms forming a rigid tetrahedron skeleton, the other one is a network of X'Ai^ tetrahedra sharing corners in an anti-cristobalite way. The AX 'A angle

stays remarkably close to 110° through the whole range of stability of the pyrochlore

structure (for a position parameter x running from 0,300 to 0,375). In that perspective

the pyrochlore structure appears to be closely related to the Si02 ones and to such classical structures as CU2O which can also be entirely viewed in terms of OCu^ tetrahedra

sharing corners. Other familiar examples of structures easily described in terms of linkages of anion centered tetrahedra are zinc-blende and wurtzite.

5. EVIDENCES ON THE BONDING FROM THE OPTICAL PROPERTIES

The bonding in such materials as rare earth oxides is generally considered to have an entirely ionic character on the basis of Madelung's constant calculations [19]. However,

as Jorgensen explains [20] , a good agreement between the Madelung energy and the heat of

formation of a crystal does not mean that the crystal is purely ionic. On the contrary one should expect between 95 and 105% agreement for a covalent compound (but only 90% for a purely ionic one, because of the repulsion between electrons in close shells) . Sophisticated

methods of evaluating bonds, such as LCAO-MO, have been widely used for organic molecules,

but have not been applied extensively to continuous solids. If the compounds under discussion were not rare earths ones, the treatment of the bonding would be restricted to highly speculative models. However, the rare earth atoms having ground 4 configurations

and the ^^"""^Lj levels of the free ion keep their identity in the solid. They are not greatly

affected by the crystal field like the ^S+l^^ levels of the d"^ configurations: the overall

splitting is generally less than 500 cm"-*. The levels split depending on the symmetiry at the rare earth site, into 2J+1 (n even) or 3+1/2 (n odd) Stark components at the maximum.

The transitions between the levels are well defined and give rise to the sharp lines in the

absorption or emission spectra of the rare earth compounds. Rare earth crystal field

splittings yield information on the symmetry at the rare earth site and the number of

different crystallographic sites, and are generally used as local structural probes sensitive

to short range order. Jorgensen (see ref. [20] for an extensive treatment of the spectroscopic problem) pointed out that the change in the position of the barycenter of the Lj

levels with respect to the free ion, or an arbitrary basis compound, was linked to the nature

of the bond supported by the rare earth atom. Increased covalency (i.e. progressive overlap

of the ligand wave functions with the transition electron wave functions) brings a decrease

of the positions of the barycenters in the energy scale with respect to the free ion: the

absorption spectra is shifted to the red. This is the nephelauxetic effect. The red shift

corresponds to a decrease of the Racah parameters describing the matrix elements of the

interelectronic repulsion hamiltonian. Because of the sharp rare earth spectra, the

nephelauxetic effect, though small, can be quite precisely measured. However it is always

necessary to record the absorption spectra at liquid helium temperature, in order to observe

transitions to the excited levels, from the lower ground state Stark component only.

Fluorescence experiments, or room temperature absorption, must be used to determine the

Stark splitting ground state itself and its barycenter (the zero line for the 4 f'^ con- figuration energy levels) [21,22]. The barycenters of the excited levels are usually easily

determined from the liquid helium absorption spectra. From their positions, the Racah 's parameters of the configuration can be calculated through a computer program [23] . From

those experiments a relative scale of covalency can be established. The method measures

the extent of the pertubation of the 4 f"^ electron wave functions by the environment. This

does not imply that the 4 f"^ electrons participate extensively in the bonding. The bonding

may be simply strong enough to carry over a bit of information down to the deep-core 4 electrons beneath the complete 5p^5s^ shells.

We have recorded the absorption spectra of several characteristic structural types of

neodymii:im compounds. The results are reproduced in figure 3 [24], on the form of the

position of the Isvel (which is not split by the crystal field) of the 4f^ configuration above the lower Stark component of the ^19/2 ground state. The reason for using the

lower Stark component is that for several compounds the ground state barycenter cannot be

easily determined. However the crystal field being more or less of comparable magnitude

from compound to compound the succession on figure 2 is a reasonably good nephelauxetic

scale supported by the full calculation of the Racah parameters [23] . Several reliable

data from the literature were used to help construct figure 3 , pertinent references and

372
228 229 230 231 232 233 23 4 235 236 237 ^ —1 1 1 1 r— 1 1 i I '

I Nd ' *

: L a F3

- - I Nd 2(003)3^ 8 HjO Sii)

1 Nd2(C03)3, 8 H2O S (2)

I Nd(Br03)3,9H20

I Nd (C2H5SO J3, 9 H2 0

I Nd2(C03)3, 3H2O S(i>

I Nd^*: La Al O3

1 Nd2(C03)3,3H^O S (2)

I (Ndo,iLao9)Cl3,7H20

I Nd [(6h)o,5'^o,5]

I N d [(OH)o.e^o.i] 3

I A-NdOHC03

I NdCI 3, 6 HjO

I Nd(0H)3

I Nd LaCl 3

I Nd(DPM)3 Si2)

I Nd(DPM )3 S (1 I

I N d 2 Y A G

I Nd ^'i La Br3

I (NdO) 2 CO3 Type II hex .

I Nd ^ ThO 2

I NdOC

I

1 C - N d203

I Nd 00 H

I Nd^*:C-Y203

1 A-Nd203 ,„2 -1

I (NdO)2 5 , 228 229 230 231 232 233 234 235 236 237

Fig. 3. Position of the levels of neodymium 4f^

above the lower Stark component of the ground

level ^19/2- (liquid helium temperature).

further details are given in reference [23] . A careful comparison shows that the levels

are shifted by an amount proportional to their energy, a fact which incited Jorgensen to introduce a nephelauxetic parameter B.

Energy ^S+1lj (compound)

g = —Energy ^^''"'Lj (free ion or basis compound)

From figure 3, one sees that 6 runs from 0.96 to 1.00 (if the basis compound is chosen

to be the fluoride)

.

It is clear from figure 3 that the compounds which have the largest nephelauxetical

effects are the rare earth oxides and the salts of the (LnOJJ"*". The preferential bonding

to the oxygen shows up by the fact that the (LnO)^"*" salts are quite close to each other on the scale, and well separated from the other compounds (compare for instance (NdO) OH and

Nd(0H)3). The other immediate fact is, that the effect increases from the fluoride, to the

chloride, then to the bromide. This is what is generally observed: the effect depends first on the ligand, and for a given ligand, it depends on the distance between the rare earth

atom and the ligand. The method is quite sensitive for the measurement of distances: Nd-0

in Nd203 is 2.34 A, 2.35 A in NdOCl 2.48 A for Nd(0H)3 and one can see that the two crystallographic sites in Nd2 (CO3) 3 ,8H20 with mean distances of 2.60 and 2.61 A, respectively, are well differenciated. A smaller distance means generally a chance for a tighter bonding, the

nephelauxetic effect shows that the 4f electrons wave functions are affected by the presence

of a closer ligand.

The relative "covalency" scale exhibited on figure 3 is in agreement with recently [25]

reported measurements through Mossbauer spectroscopy of "relative covalency" in a series of

europiimi compounds. As in our studies the europium sesquioxide was found to be the more

covalent one and the fluoride the lesser.

373
An interesting character of the compounds on figure 3, is that all of those which have

the largest nephelauxetic effect from (NdO)2S to Nd(DPM)3 inclusively, and excluding the

bromide, have structures characterized by the existence of a Nd-O-Nd angle close to the

tetrahedral value 109°. This is true for Nd(DPM)3, a 3-diketonate where the rare earth

atoms came in pairs in a dimerized molecule, with a seven coordination very similar to the one in the A-type oxide (the molecule is volatile at 150 °C under 10"^ mmHg) , and also for

the garnet where the oxygen atoms in the irregular eight coordination polyhedron of the rare earth are in a tetrahedron of metal atoms, however badly distorted.

There is another proof of the perturbation of the 4 f"^ configuration in the (LnO)^"^

compounds. It comes from the intensities of the transitions between the ^S+Il^ levels.

Theoretically, only magnetic dipole transitions should be observed between those levels and

only ifAJ=0±l, aO^O transition being excluded. In fact the transitions are more

often of an electric dipole character, mostly because there are a very few crystallographic

sites, where the trivalent rare earth is sitting, which exhibit a center of inversion. But

those electric dipole transitions must borrow their intensities from a parity mixing in at

least one of the energy levels involved. It is well known that the -^Lj levels must be

described in intermediate coupling as a sum of | ^ -^L > with the same J, however parity

mixing needs the inclusion of levels from another configuration, 4 f"~-^5d the next higher

configuration is, for instance, a convenient one. The other parity component can be introduced through mixing with the orbitals of the ligands, as is done classically in MO theory.

A strong intensity of the transitions is the sure indication of an important degree of

mixing. It will be enough to say, to prove the importance of this phenomenon for (LnO)^+

compounds, that the most efficient rare earth phosphors used for color TV applications are rare earth oxysalts , specially oxysulfides. All rare earth oxysalts, and the oxides, are very bright phosphors. It has been shown [26] that the intensities of the transitions

increases exponentially with the magnitude of the nephelauxetic effect.

There is consequently little doubt, from an optical point of view, that the rare earth

atom is feeling something in the oxides and oxysalts. However the 4 f"^ orbitals are obviously not responsible for the main part of the bonding. The (LnO)^"*" compounds, and the

oxides, show strong absorption bands in the ultra-violet (beginning at 2700 A for A-Nd203)

.

The U.V. absorption bands in Si02 quartz and corund\jm AI2O3 beginning about 1500 A were recently interpreted [27] on the basis of a covalent LCAO-MO type of bonding extended

through the crystals, because an ionic model was inadequate to explain the data. It should

be at this point remembered that al\amin\m replaces silicon quite easily in the frameworks

of silicates and that Si02 and AI2O3, like the rare earth oxides, are rather good refractory

materials. However a serious model of bonding for the rare earth compounds should obviously

wait until more simple and more classical structures can be precisely described in LCAO-MO,

or other appropriate scheme. Anyway, sp^ hybridization seems to be a logical starting point

for the oxygen atom.

6. THE ORIENTED TEXTURES OF RARE EARTH OXIDE THIN FILMS

Rare earth oxide thin films were produced by oxidation of rare earth metal thin films.

Their thickness (500 A to 2500 A) allows observation by electron diffraction and microscopy. Large crystals (several dozens of microns) of the two layered oxides A and B-Ln203

can be grown from the low temperature C-type phase small crystals by directly heating the

film with the electron beam. Those films have a preferred texture as shown on figures 4 and 5. The plane of the film is perpendicular to the c-hexagonal axis (i.e. parallel to

(002) for the A-type) and parallel to the (201) plane for the B-monoclinic type. Both

orientations correspond to the planes of the two infinite (LnOjJ"*" layers in the structures.

Large crystals of the C-type can also be grown, but only for those oxides whose C-type is

stable at very high temperatures. The crystals then have also a preferred orientation, the

plane of the film being parallel to (111) cubic as shown on figure 6. The image of the

crystal (C-Dy203) is shown on figure 7.

It is technically interesting to be able to grow large oriented crystals of these

refractory materials from the small crystals produced by the oxidation of a thin metal film.

Dysprosium is specially interesting because the metal is volatile, the oxide is refractory

and, being an yttric earth, it is also quite insensitive to atmospheric agents contrary to the eerie oxides.

374
Fig. 4. Electron diffraction of a crystal of A-Nd203.

The electron beam is along the c-hexagonal

axis. Plane of the thin film is parallel to

(00.2)

.

Fig. 5. Electron diffraction of a crystal of monoclinic

B-Sm203. The electron beam is along [101], 3.5°

off the plane of the thin film which is parallel

to (201) .

375
Fig. 6, Electron diffraction of a crystal of €-07203.

The electron beam is along [111] , the plane of

the thin film is parallel to (111)

.
Electron diffraction and microscopy shows several modes of crystallographic relations

between the rare earth oxides phases. The epitaxial continuity between A and B-Nd203 was measured after producing B-type crystals (fig. 8) inside the A-type crystals by application

of a thermal stress. The B-type bands on figure 8 run in a characteristic zig-zag way.

The epitaxial relationship is as follows: (00.2) and (11.0) of the hexagonal A-Nd203 are parallel respectively to (201) and (313) of the monoclinic B-Nd203 [28] . The situation

is complicated by the existence of intense twinning in B-Ln203 (because there is four

possible glide directions in distorting the (LnO)^"*" sheets in A-Ln203 from above one

another) [8] . Twinning occurs principally with respect to {ill} and {313} of B-Ln203.

The appearance of the twinned crystals is shown on figure 9. At high temperature B-Dy203

grows epitaxially on C-Dy203 with (201) of B parallel to (111) of C and (111) of B parallel

to (110) of C [29]

.

Fig. 8. Characteristic zig-zag and triangular domains

of B-Nd203 in crystals of A-Nd203 (X 30.000).

Fig. 9. Twinning and dislocations in B-Sm203. Twins

are {313 } and {ill} (X 30.000).

377
Twinning and epitaxy keep the continuity of the (LnO) layers . The contact planes

are usually perpendicular to the layers. However all the phenomena have not been yet

investigated and only the most obvious ones were analyzed. The epitaxies can only be

studied very briefly (A and B-Nd20 3) or at very high temperatures. The B-phase twinning

is very complex, a (201) twinning (reversal of the layers) was for instance suspected.

The thin film studies entirely confirm, as does the single crystal cleavage habits,

the layered character of the (LnO) 2O oxides. The crystallographic axis, with respect to which the layers are stacked, is always perpendicular to the plane of the thin film. This

main crystallographic axis turns out to be very important when one considers the implications for non-stoichiometric rare earth oxides.

7. LAYERED POLYMOLECULAR CATIONS AND NON-STOICHIOMETRY

The layered frameworks of atoms (LnO)JJ"'" {C3) , and(LnO)^''" (C4) and (LnF)^"^"*" behave as individual cations with their own chemistry. A question may arise as to their possible

part in the occurrence of non-stoichiometric compounds in several rare earth systems.

The behavior of the bismuthyl cation (BiOj^J"*" may be a clue to this problem. Very

complicated structures are known in the complex oxides and oxyhalides of bismuth. The

(BiO)J^^ group in those compounds appears to be in epitaxial continuity with other types of

structures and interleaved with them. For instance, there is an association of a pseudotetragonal symmetry with a perovskite type of structure, and the crystallography depends on

the numbers of perovskites layers involved (1,2,3 or 4) between the (BiO)^'*'.

Another striking example are the well known, and rather fascinating crystals in

"syntaxic intergrowths" formed by the bastnaesite group of minerals LnFCOs (bastnaesite)

2LnFC03CaC03 (parisite) 3LnFC03 2CaC03 (roentgenite) and LnFC03 CaC03 (synchisite) [30].

The different phases have pseudohexagonal structures and can coexist in the same "single

crystal" as a succession perpendicular to c (interface, planar, parallel to 00.1) of layers

of the different minerals (there is also a three-dimensional intergrowth like the one of A and B-Ln203 in thin film) . The structure of the individual compounds is made of a succession perpendicular to c of the same (LnF)^'^"'" planes we described previously for tysonite

Op o _ (LnF3) , of Ca planes, and of two types of carbonate ion COg planes. We shall see later

how these planes organize themselves

.

Other complicated non-stoichiometric compounds are the microphases found in the LhF3 - Ln203 systems. Bevan et al. [31] suggested the formula (Ln^^Oj^. ^^+2^ Compounds for n=7

(yttrium) and n=5 (Erbium) were isolated. Tanguy and Portier [32] found several symmetry

types in Eu(0,F)j^ 1,5^ x 3, system. A rhombohedral phase occurs for 1.96 <r x <2.06

(EuOF) , a cubic phase (a high temperature one) for 1.96 -3" x -3~2.42 a quadratic phase for

2.16 V X \V~2.20, an orthorhombic one for 2.31 ^ x ^ 2.40. The system exhibits also at high

temperature, above 800 °C, a phase of a tysonite type (LnF)F2. The optical examination of

the Tanguy and Portier phases shows that only three of them have well defined local crystallographic sites for the rare earth. Those are EUF3 (orthorhombic) , EuOF (rhombohedral) and

C-type EU2O3 . The other have broad absorption or emission lines, with however a pattern

changing regularly with x. A structure has been proposed for rhombohedral EuOF by Mann and

Bevan [33] . Along the (III) fluorite axis there is a succession of planes Ln-O-O-Ln-F-FLn-O-O-Ln. . . Such a succession is what is to be expected for the structure of the fluoride

of (LnO)!^"*" (C3) . The oxyfluorides are the only salts not clearly identified because of the

uncertainty in the structures and the possible competition with the (LnF)^ri''" cation. In the

Mann and Bevan structure the two fluoride planes between the (LnO)JJ'*' (C3) layers are equivalent to the two fluoride planes between the (LnF)^'^"'' layers in tysonite LnF3 (hexagonal) . We shall see that the combination of these elements is necessary to the understanding of the system.

The writer and J. D. Corbett [34] reported a most unusual series of non-stoichiometric

phases associated with thermal analysis phenomenons in the TmCl2-TmCl3 system. N. A. Fishel

from H. Eick Laboratory at Michigan State reported [35] that YbCl2 with which TmCl2 is isostructural, is of the structural type of CeSIa, which made it a chloride of a complex cation

of ClTm4 tetrahedra in Ci^ symmetry equivalent to the (LnO)!^"*" (C4) according to the structures reported by the Flahaut group for the halogenosul fides [14]

.

378
For the famous Ln203-Ln02 systems , we have already tried [1] to interprete the chemical

composition of some of the compounds by using the (LnOjJ"^ concept. We found a satisfactory

agreement by using (LnOn"*" (C3) slabs separated, like in the (BiOj^"*" compounds, by layers

of fluorite structure with one sixth of the anions missing in each oxygen plane. If there

is no (LnO)n+ the stoichiometry of this hypothetical phase is LngO^Q which is an unknown

member of the supposedly Lnj^02n-2 family of compounds. However there is a three-dimensional

structure made of OLni^ tetrahedra topologically equivalent joined by five edges out of six

which corresponds to that stoichiometry but the framework looks less symmetrical than the one for Ln70i2»

From a comparison between the non-stoichiometric systems, we were able to isolate, in

each of them, four different planar entities whose succession down a main axis of symmetry

(c pseudo-hexagonal or [111] fluorite) defines the chemical composition. Let us call them

A B C D. Some of the planes (or double planes) are anionic, others cationic. We will

consequently have a rule according to which B will be always followed and preceded by A and

C will be always followed and preceded by D. In table 1 we have identified our choice of

the structural elements in the systems with each one of the code letters A B C D.

The notation "doiible plane" in table 1 indicates that one consider as a single chemical

individual two sequential planes of identical composition. The complex cations may also be

represented by a succession of letters, such as DCD, which stands for (LnO)J^"^ (C3) . Each

of the systems under consideration is characterized by the presence of a structural element

corresponding to one or the other of the complex polymeric cations defined previously in

this paper.

Table 1

Code for the Identification of the Four Planar

Chemical Units in Rare Earth Non-Stoichiometric Systems

Code

letter

Bastnaesite

system

Ln20 3-LnF 3 LnO

x LnCl3-LnCl2

A (LnF)2n+

(as in tysonite)

Doiible plane of

fluoride ions

F~ - F~

(as in tysonite)

Two planes of

fluorite oxide

ions with one

sixth vacancies

in each

Two planes of

chlorides ions

B a plane of

"vertical"

col"

(LnF)2n+

(as in tysonite)

a Ln plane

as in fluorite

3_l- a plane of Ln and a plane of

chloride ions

C a plane of

Ca^"*" ions

a double plane

of oxide ions

without vacancies

as in fluorite

a double plane

of oxide ions

without vacancies

as in fluorite

a plane of chloride ions similar

to the oxygen's

one in (LnO) CI

D a plane of

"twisted" Co|~

a plane of Ln^"^ as in fluoritea plane of Ln

as in fluorite

a plane of Ln

Complex

ion

unit

A is

(LnF)2n+

the succession

DCD

is

(LnO)n+ (C3)

B is (LnF)2"'^

the succession

DCD

is

(LnO)J^+ (C3)

the succession

DCD

is

(LnCDj^"^ iCi,)

379
Then, most, if not all, of the known chemical compositions for the phases in all non- stoichiometric systems can be accounted for with the same succession of letters if the

chemical code in table 1 is respected.

Results are condensed in table 2.

Inspection of the table shows that the non-stoichiometric system occurs because a layered structure AB is able to be interleaved through another layered structure ADCD (the

reciprocal is not true) . The A elements insure the epitaxial continuity. The result is

that an infinite series of compounds can occur in the binary system between the phases AB

and ADCD. However ADCD is generally not one of the extremity of the phase diagram under

consideration. It is Lni2022 in LnO^^, LnOF in Ln203-LnF3. It is remarkable also that in

all the systems one of the simple combinations AB or CD does not exist as a known chemical

entity. Whether or not this must be so, is not clear.

Table 2

Experimentally known, chemical compounds in the rare earth non-stoichiometric

systems identified and connected by a succession of four coded letters.

Chemical

repetitive

unit down

the axis

coded by

letters

(see code table 1)

Name and

formula of

compound

bastnaesite

system

Ln = eerie group

Formula of

compound

LnF3 - Ln203

system

Ln = Eu, Y, Er

Formula of

compound

LnOj^(Ln3+/Ln'+''')

system

Ln = Ce, Pr, Tb

Formula of

compound

LnCl3 - LnCl2

system

Ln = Dy , Tm

AB bastnaesite

LnFCO 3

tysonite

LnF3

LngOjo

DOES NOT EXIST

LnCl3

AB ADCD parisite

2LnFC0 3 .CaC0 3

LngOgFs

(LnF) (LnO) 2F4

LnOi ^778

(or LngOig)

LnsCl?

(Cl/Ln = 2.33)

AB ADCD ADCD roentgenite

3LnFC0 3.2CaC0 3

LnsOi+Fy

(LnF) (LnO) LjFg

LnOj _ 80 0 (or LnjoOig)

extended series

of LnCljj com- pounds between

AB ADCD ADCD ADCD •p LnyOgFg

(LnF) (LnO) eFs LnOi _ 80 9 X - 2.31 and

X = 2.00

AB (ADCD)t^ 7> ? LnOi_815

AB (ADCD)

5

7> 7> LnOi^818

(or Lnii02o)

AB (ADCD) m(n+1) (LnFCOs)

n (CaC03)

LnnOn-lFn+2

(n odd)

Li^6n+30l ln+5 Lnj^Cl2n+l (n.odd)

ADCD synchisite

LnFC03.CaC03

LnOF

(trigonal)

LnOi, 83 3 (or Lnj2022)

LnCl2=[LnCl] CI

structure (CeS)I

CD EXDES NOT EXIST DOES NOT EXIST Ln02 DOES NOT EXIST

380
Because of the excellence of the experimental work done on the LnO systems the agreement between the theoretical formula and the experimental composition is very good. One can see that the Lnn02n-2 classical formula is in error. The real one is Lngj^^. 3011^1+5. It emphasizes the fact that LnOi^833 is the last compound in the system. It was known that

there was no other phases between x = 1.833 and 2.000. Of course, the LnO^^ comounds which

are three-dimensional frameworks of topologically equivalent OLni+ tetrahedra (Ln203, Ln70i2'

Ln02) , not being layered structures, does not come out in the table. The importance of the

OLn^ tetrahedron unit can be seen from the fact that the stability of the Ln70i2 phase is

greatly reduced if one tries to make a mixed compound (i.e., Tb and Pr, or Pr and Ce) [36],

This is because the OPri^ and OTbi^ tetrahedra, for instance, do not have the same size, and

consequently edge-linking is difficult. Epitaxial continuity and syntaxic intergrowth are

to be expected between the layered compounds because of the bastnaesite system correspondence. In LnOjj the presence of the complex cation (LnOjJ^""" (C3) and the blackness of the

phases indicates that the bonding may be able to take care of the charge equilibrium between Ln^"*" and Ln'*"*' . Recent Mossbauer experiments [37] show a single signal for 141 Pr in Pr 12022' That signal is intermediate between the one for Pr02 and the one for Pr203

which is itself very close to the signal of the pure metal. This indicates that the

praseodymium atoms are more or less equivalent. In ^ic^iz'^ZZ ^1-'- °f the praseodymium atoms

belongs to (LnO)^"^ (C3) complex groups, the chemical bonding may insure the fractional

valency implied by the Mossbauer results.

The description of rare earth non-stoichiometric LnO^ compounds as being capable of

syntaxic intergrowths brings a correspondence between the fact that Donnay and Donnay were

able to selectively dissolve by chemical action one or the other of the bastnaesite family

intergrowth constituents [30] and the fact that the LnO^ compounds can be leached by atmospheric agents (water, CO2) , or mild chemicals, to yield the end member of the system, pure,

very well crystallized, Ln02 , which is (compare Ce02) chemically inert [38].

The layered polycations offer a way to the interpretation of the chemical compositions

of the phases in non-stoichiometric rare earth systems. The scheme does not offer a way to

understand the crystallography of those phases. This is because it is clear, from the

bastnaesite family example, that the sequences will orient themselves differently: they have

the polytypic choice, the three ABC sites (in the familiar notation AB hep, ABC fee) . This

amounts to a possibility of rotation of the chemical planes around the pseudo-hexagonal or

(III) fluorite axis. The unit cell may consequently be very wild. As a consequence,

crystallography does not bring out, at all, the fundamental chemical relationship underlying

the basic existence of rare earth non-stoichiometric compounds.

8. CONCLUSION

The recognition of polymolecular chemical entities constituted of linked together anion

centered coordination polyhedra appears to be quite helpful to understand the basic chemical,

optical, and mechanical (thin film textures) properties of several rare earth compounds,

especially oxides and oxysalts. The concept extended to non-stoichiometry gives an instantaneous key to the chemical composition and structures of the compounds in the most famous

rare earth non-stoichiometric systems. The existence of a layered polymolecular cation is

found to be the basic reason for the existence of those systems. As clearly shown by the

optical studies, the chemical bond inside the polycation is the ultimate factor responsible

for the observed phenomena. This is the problem of explaining the real nature of the bonding

of transition elements in solids.

Table 3 collects the layered rare earth polycations discussed in this paper.

381
Table 3

Rare Earth Layered Polycations

1) (XLrii^) tetrahedra sharing edges

X Structural type of

layered polycation

Typical

Compound

0

(LnO)"^ (C.) n i

(LnO)""*" (C.) n ^

A - I'n^O^

LnOCl

s

(LnS)""^ (CJ

n i

(LnS)""*" (C.) n H

Sm SI

Ce SI

F (LnF)2n+(c;)

n h La FS

CI (LnCl)'^'^(C ) n 1+ Yb CI

2

2) XLrij triangles sharing corners

.

X Structural type of

layered polycation

Typical

Compound

F (LnF)^"^ (C.) n 0 LaFjtysonite

9. REFERENCES

[I] Caro, P. E. , J. Less Common Metals 16, 367 (1968).

[2] Bergerhoff, G, and Paeslack, J., Z. Krist 126 , 112 (1968).

[3] Foex, M. and Traverse, J. P., Rev. Int. Htes Temp.:et Refract. 3_ [4], 429 (1966).

[4] Foex, M. and Traverse, J. P., Bull. Soc. Franc. Miner. Crist. 89_, 184 (1966).

[5] Eyring, L. and Holmberg, B. , Advan. Chem. Ser. 39.' (1963).

[6] Sawyer, J. 0., Hyde, B. G. , and Eyring, L. , Bull. Soc. Chim. France, 1190 (1965).

[7] Lejus, A. M. and Collongues , R. , Personnal communication.

[8] Boulesteix, C. , Caro, P. E. , Gasgnier, M. , Henry la Blanchetais , C. , and Pardo, B.

,

Acta Cryst. B27 , 216 (1971).

[9] Turcotte, R. P., Sawyer, J. O. , and Eyring, L. , Inorg. Chem. 8_, 238 (1969).

[10] Caro, P. E. , Achard, J. C. , DePous , O. , Collogue International du C.N.R.S. sur les

Elements des Terres Fares, Vol. I, 285 (1970). C.N.R.S., Paris.

[II] Sillen, L. G. , Nature 30., 318 (1942).

[12] Wells, A. F., Structural Inorganic Chemistry , 3rd Ed., p. 671 and 765, (1962) Clarendon

Press, Oxford.

[13] Huggins, M. L. , Inorg. Chem. ]_, 2108 (1968).

[14] Dagron, M. C. and Thevet, F. , Ann. Chim. 6_, 67 (1971).

[15] Goldman, M. and Shen, L. , Phys. Rev. 144, 321 (1966).

[16] Nguyen-Huy-Dune , These Doctorat-es-sciences , Paris (1971).

[17] Carre, D. , Laruelle , P., and Besancon, P., Compt. Rend. Acad. Sci. Paris, 270C , 537

(1970) . [18] Pannetier, J. and Lucas, J., Matls. Res. Bull. _5, 797 (1970).

382
[19] Barker, W. W. , Graham, J., Knop, 0., and Brisse, F. , in The Chemistry of Extended

Defects in Non-Metallic Solids, Eyring, L. and O'Keeffe, M. , Ed., p. 198, North

Holland, Amsterdam (1970).

[20] Jorgensen, C. K. , Modern Aspects of Ligand Field Theory, p. 263-264, North Holland,

Amsterdam (1971)

.

[21] Dieke, G. H. , Spectra and Energy Levels of Rare Earth Ions in Crystals, Interscience,

New York (1968)

.

[22] Wybourne, B. G. , Spectroscopic Properties of Rare Earths, Interscience, New York (1965).

[23] Caro, P. E. and Derouet , J., Bull. Soc. Chim. France, 46_, (1972).

[24] Caro, P. E. and Derouet, J., Compt. Rend. Acad. Sc. Paris, 271C , 1370 (1970).

[25] Dulaney, G. W. and Clifford, A. F., Proceeding of the 8th Rare Earth Research

Conference, Reno, Nevada, p. 641, April 1970.

[26] Henrie, D. E. and Choppin, G. R. , J. Chem. Phys. 32., 639 (1968).

[27] Reilly, M. H. , J. Phys. Chem. Solids, 3]^, 1041 (1970).

[28] Boulesteix, C. , Caro, P. E. , Gasgnier, M. , Henry La Blanchetais, C, and Schif fmacher

,

G., Acta Cryst. A27 , 552 (1971).

[29] Boulesteix, C. , Caro, P. E. , Gasgnier, M. , Henry La Blanchetais, C, and Schiffmacher

,

G., Collogue International du C.N.R.S. sur 1' etude des Transformations cristallines

au-dessus de 2000 °K, Odeillo, 1971 (to be published C.N.R.S., Paris).

[30] Donnay, G. and Donnay , J.D.H., Amer. Mineralogist 38./ 932 (1953).

[31] Bevan, D.J.M. , Cameron, R. S. , Mann, A. W. , Brauer, G. , and Roether , V., Inorg. Nucl.

Chem. Letters 4_, 241 (1968).

[32] Tanguy, B. and Portier, J. , Personnal communication.

[33] Mann, A. W. and Bevan, D.J.M. , Acta Cryst. B26 , 2129 (1970).

[34] Caro, P. E. and Corbett , J. D. , J. Less Common Metals 18_, 1 (1969).

[35] Fischel, N. A., Dissertation Abstract 31_ [11], 6477B (1971),

[36] Kordis, J. and Eyring, L. , J. Phys. Chem. 72./ 2044 (1968).

[37] Kapfhammer, W. , Maurer, W. , Wagner, F. E. , and Kienle, P., Proc. Intern. Conf. in

Hyperfine Structure Detected by Nuclear Radiation, Rehovot, Israel, p. 120, Sept.

1970.

[38] Clifford, A. F.,in Rare Earth Research II, K. S. Vorres , Ed., Gordon and Press, New

York, p. 45 (1964)

.

DISCUSSION

B. G. Hyde : A beautiful model, I would just like to ask, you predict in the rare earth oxides the known structures, that is the known compositions.

P. E. Caro: Yes, the normal composition. I cannot say anything about the structure

because it is only a chemical repetition.

B. G. Hyde : Do you predict any that are not known?

P. E. Caro: Well, I don't know. You know by that game of coherent intergrowth, you

say there is an infinity of phases as you approach the composition LnOi^eSS' instance.

If you make a design of it you could see that this is, as a matter of fact, intergrowth of

one of the preceding structures and the LnOj^esS- So where do you stop? It is just like

a card game, you know you have four cards, for instance, and you just stack that card game

with some rules. If you let red and black cards represent anionic and cationic sheets then

it's just a mathematical game. You have to have some sort of a distribution as long as you

have four chemical units to stack. But, of course, that says nothing about the crystallography .

383

National Bureau of Standards Special

of 5th Materials Research Symposium,

Publication

issued July

364,

1972

Solid State Chemistry, Proceedings

PLASMA-SYNTHESIZED SUBSTOICHIOMETRIC SCANDIUM OXIDE^

J. E. Young, Jr. and M. J. Sienko

Baker Laboratory of Chemistry

Cornell University

Ithaca, New York 14850

Crystals of substoichiometric scandium oxide have been grown in high frequency, induction-coupled, argon plasmas. The composition of the crystals could be varied by addition of

small percentages of hydrogen or oxygen to the argon stream. Chemical analysis by reoxidation

indicated an oxygen deficiency that could attain 4% before metallic films appeared, concentrated at grain boundaries. The chemical composition of the films could not be established.

X-ray studies of the bulk crystals indicated retention of the C-type rare earth structure of

SC2O3 with but slight shrinkage of the cubic cell parameter. Transmission electron microscopy showed no evidence for shear plane formation. Attempts to measure Hall voltage and con- ductivity by a van der Pauw technique gave conductivity values, both a.c. and d.c, too small

to measure. Faraday susceptibility measurements from 1.6 to 300 K indicated a very small

effective magnetic moment, which decreased below 10 K. Possible models are F and F' centers

in thermal equilibrium or Sc+^ ions with thermal equilibrium between and or and

states

.

Key words: Crystal growth? F centers; flame fusion? magnetic susceptibility; nonstoichiometry, scandium oxide.

1 . INTRODUCTION

Several years ago Morin 11]^ suggested that the electrical-conductivity properties of

the transition metal oxides could be interpreted, at least qualitatively, by a model in which

the conduction band is made up of overlapping d-orbitals . In such a model, the P|_j-orbitals

of the oxygen combine with the d(eg) orbitals of the transition metal to form a lower, bonding

and an upper, antibonding set. The bonding set is believed to be completely populated, cor- responding to a filled valence band. The antibonding levels, corresponding to a* orbitals,

are believed to lie from five to ten electron volts higher and, under normal conditions, are completely empty. In the gap between the two sets of levels are the d(t2g) levels. If the

transition metal atoms are close enough together and if the spatial extent of the t2g orbitals

is large enough, overlap results and a conduction band is formed. Morin went on further to suggest that the extent of orbital overlap should increase as one proceeds from right to left

in a row or from the top to bottom in a group of the periodic table. In this view, the

widest d bands would be formed in the transition metal oxides of the elements toward the left

and bottom of the periodic table. For the first row sequence, the probability of d-orbital

overlap would be greatest for the case of scandium oxide, SC2O3.

As a result of this model, it would appear interesting to investigate the carrier characteristics of scandium oxide in comparison with the carrier characteristics of Ti02 , V2O5,

and Cr03. If the bandwidth in SC2O3 is indeed the greatest of these oxides, one would expect

to find the greatest carrier mobility. The problem, however, is to introdi'ce carriers into

This research was supported by the Air Force Office of Scientific Research and the Advanced

Research Projects Agency.

Present address: Gulf Research and Development Co., P. O. Drawer 2038 Pittsburgh, Pa. 15230

Figures in brackets indicate the literature references at the end of this paper.

385

465-504 O - 72 - 26
the oxides. In their highest oxidation states, the transition metals form oxides that are insulators. They have been described as "electronless metals" because, although they may

have conduction bands of appreciable width, the cation has an argon configuration and there

is no electrical conductivity because there are no carriers. For example, Ti02 is such an insulator. The Ti^"*" ion in stoichiometric Ti02 has no electrons to supply to a d conduction

band. The lower oxides of titanium, however, are fairly good conductors. Electrical conductivity and Hall effect measurements on oxygen-deficient Ti02 [2] indicated conduction electrons with moderate mobility, decreasing with increasing temperature in a way expected for

metals. TiO is a very good metal [3]; Ti203 exhibits a semiconductor-to-metal transition in

the vicinity of 450 K [3] . Morin has suggested that the semiconductor-to-metal transition

is due to a splitting of the 3d band by the crystal field into d^ and d^ sub-bands. Below

the transition temperature, the Fermi level is believed to be in the energy gap between the

occupied dy and the empty d^. bands, but at Tj^, the sub-bands collapse into a single, partially-filled band, causing metallic conduction.

One can imagine two approaches for introducing carriers into the scandium oxide structure. One might substitute a tetravalent atom for a portion of the trivalent scandiiam atoms,

hoping that the substituent atoms would act as donor centers for contributing electrons to the conduction band. The other possibility would be to remove oxygen atoms from the SC2O3

structure. As has been shown by Sienko and Banerjee [4] for the case of WO3, extraction of

each oxygen atom contributes two conduction electrons in the same way as if two alkali metal

atoms had been added. In general, the removal of an oxygen atom from any transition metal

oxide should leave two electrons free for carrier properties.

Because the original effort in this research, to insert an easily ionized donor into

the SC2O3 structure, proved to be unsuccessful, the alternate approach chosen was to remove

oxygen. However, removal of oxygen from SC2O3 is extraordinarily difficult. There have been

reports of lower oxides of scandium in the literature [5,6,7], but close examination of this

work indicates the possibility that the so-called lower oxides were other compounds, for ex- ample, carbides of scandium. It is no simple matter to remove oxygen from the SC2O3 structure,

the lattice energy of which is among the greatest of any oxide. Still, a simple thermodynamic argument suggests that extraction of oxygen should be feasible by a thermal method.

Writing the chemical equation as

:

SC203 (s) SC203_jj(s) + 1/2 x 02(g)

we can see that no matter what the AH for this reaction, a sufficiently high temperature

should lead to a negative AG because the entropy term must eventually dominate. In the re- action, the entropy change must be positive because there is formation of gas phase. In a preliminary investigation, we tried to produce substoichiometric scandium oxide by heating

scandium oxide in a hydrogen-oxygen flame. However, the maximum temperature one can realize

with such a flame is just barely greater than that of the melting point of SC2O3, namely 2400

°C. Hence, although we were able to fuse SC2O3 powder and form multi-crystalline boules by

use of the Verneuil technique, we were not able to get oxygen deficiency. It was not until

we went to the plasma technique that we were able to achieve temperatures high enough to make

the free-energy change favorable for the above reaction.

SC2O3 has been the subject of very few investigations. The only electrical conductivity

measurements have been made on sintered powders. Noddack et al. [8,9] found in the temperature range 873 - 1573 °C that the conductivity in air varied from 0,02 x 10"^ to 47 x 10~^

ohm"'^ cm"-'- wi-th an average activation energy of 1.70 eV and an ionization energy of 6.7 eV. Zyrin et al [10] measured the electrical conductivity and thermoelectric power in air and in vacuum from 1100 to 1600 °C obtaining values for a of 1 x 10"^ ohm~^ cm"-^ at 1100 °C and 1.6 X 10"^ ohm"-' cm"-' at 1600 °C, an activation energy of 2.2 eV, and a thermoelectric power of

230 yV/degree. At a pressure of 10"^ torr, the conductivity was approximately a factor of

eight smaller, with an activation energy of 2.6 eV and thermoelectric power of 760 pV/degree.

Companion [11] observed the diffuse reflectance spectrum of SC2O3, measuring a band gap

of 5.4 eV. Tippins [12] studied the ultraviolet absorption spectra of single crystals at room temperature and at approximately 80 K. His results agreed with those of Companion, and

he calculated a band gap of 6.0 eV at room temperature and 6.2 eV at 80 K. Barta et al [13]

have measured the refractive index of SC2O3, arriving at a value of 1.91, which would yield

a value of 1.38 for the dielectric constant at optical frequencies.

386
Scandium sesquioxide crystallizes in the C-type rare-earth structure. This structure is

essentially a body-centered cubic array of eight fluorite-type cells, with 1/4 of the oxygen

sites unoccupied in the following manner: the vacancies occur in pairs such that 75% occur

along the face diagonals of the anion cubes while the reamining 25% occur along the body diagonals. All the scandium cations are six coordinated, with 25% surrounded by a nearly regular octahedron of oxygen ions and 75% surrounded by a highly distorted octahedral environment of oxygen ions. There have been two recent refinements of the crystal structure: Geller

[14,15] reports a lattice constant of 9.844 A; Norrestam [16] reports a value of 9.849 A. Reid and Ringwood [17] have reported the existence of a monoclinic B-type rare-earth form of

SC2C3, produced at 130 kilobar pressure and 1000 °C. The calculated density of this form

represents an increase of 8.3% over the density of C-type SC2O3, reflecting an increase in

coordination from six to seven fold for 2/3 of the scandium ions. No other properties of

this form have been reported.

The chemistry of scandium is very similar to that of yttrium and the rare-earth metals.

Borchardt [18] observed the formation of a blue-black oxide film resulting from oxidation of

metallic yttrium; x-ray analysis showed it to be Y2O3, with lattice constants identical to

those of stoichiometric Y2O3. He interpreted this as the presence of metallic yttrium dissolved in stoichiometric Y2O3. Miller and Danne [19,20] have reported the preparation of

oxygen-deficient oxides of gadolinium, yttrium, erbium, and lutetium. These compo\inds corresponded to the formulas GdO^^i^gs, ^'^1.^9' ElrOj^^sg, and LuO^^LfSS (crystallizing with the cubic

C-type structure) and GdOi^i+g3 (crystallizing with the monoclinic B-type structure.) They

were produced by vacuum melting of the stoichiometric oxide or by co-distilling and co-melting the rare earth metals with the respective sesquioxide. X-ray and density information indicate that the sesquioxides had lost oxygen, forming Schottky defects in the anion lattice.

These defects serve as effective positive ion sites capable of trapping the electrons released

by the cations in a lower oxidation state. Miller reports that the magnetic susceptibility

data of GdOji^i+93 indicate an anti ferromagnetic transition at 3.35 K. The cubic GdO^.i^gs or

ErOi.i+89 demonstrate no such transition, although the magnetic susceptibility of both these

materials takes a sharp upturn below 20 K indicating possible magnetic ordering at these temperatures. Muller-Buschbaum [21] has reported the preparation of nonstoichiometric La203_x

by melting in a high-frequency, induction plasma in a vacuum. X-ray data indicate a structure

identical to that of LaaOs, but no other properties have been reported.

2. EXPERIMENTAL PROCEDURE

2.1. CRYSTAL GROWTH

The scandium sesquioxide used in these studies was obtained from Australian Mineral Development Laboratories, South Australia. It contained nominally 99.5% SC2O3 with the major

impurity being silica. An emission spectrographic analysis, performed by the analytical facility of the Cornell Materials Science Center, showed that the starting material contained

0.01 - 0.1% calcium, 0.01 - 0.1% magnesium, 0.01 - 0.1% iron, and 0.001 - 0.01% silicon

whereas the plasma-grown crystals contained no detectable calcium, no detectable magnesium,

iron at 0.001 - 0.1%, and silicon at 0.001 - 0.01%.

2.2. PLASMA

The equipment used in these experiments consisted of a TAFA Model 58 torch powdered by

a Lepel 10-kw, rf generator operating at a frequency at 3.8 megahertz or, in later stages,

by a Lepel 20-kw generator, operating at 4.0 megahertz. The powdered oxide was injected into

the plasma through a water-cooled copper probe at the center axis of the torch. The powder

had to be introduced into the plasma in finely divided form as large particles would disturb

the plasma to such an extent that it would be extinguished. The powder-feed mechanism con- sisted of a bed-type hopper in which the dry powdered oxide was fluidized by gas flowing from

a jet at the bottom of a cone. A small portion of this finely divided powder then left the

hopper through an exit tube in the upper portion of the hopper. In order to insure smooth

flow of the powder, the exit tube extended continuously through the hopper and the watercooled probe of the torch, terminating just at the tip of the probe. The powder was kept

from forming "channels" for the gas flow by continuous vibration of the hopper with an electric

vibrator attached to the hopper support.

387

/
The gas used for the plasma was generally argon, with small percentages of hydrogen or

oxygen occasionally added. Addition of any diatomic gas caused a drastic reduction in the

size of the plasma zone and increased the rate of heat transfer to the torch itself, frequently resulting in early torch failure. The torch could be operated reliably only with pure ar- gon, argon mixed with up to 5% hydrogen, or argon mixed with up to 50% oxygen. No efforts were made to operate with nitrogen or air.

The crystals were grown on the end of a 5-mm diameter, 15-cm length magnesia rod which

was mounted on a long boron nitride rod, attached to a motor-driven positioning apparatus.

The position of the crystal pedestal could be varied over a range of approximately 15 cm; it

could also be rotated at a rate of 100 rpm.

Procedures and operating conditions for growing crystals with a plasma technique are difficult to reproduce. Proper compensation for variations in these conditions was developed

only after many failures. A reasonably typical set of conditions was as follows: Total flow

of gas was 1800 - 2200 liters per hr. The majority of this gas enters through the Iciminar

flow jets; up to 25% may be introduced through swirling flow jets, producing vortex stabilization of the plasma zone. The plasma is initiated by inserting a grounded carbon rod into

the center tube of the torch while increasing the power output of the rf generator. The car- bon rod couples with the rf field, eventually becoming red hot. At this point the argon gas near the hot rod becomes thermally ionized, coupling with the field and initiating the plasma.

The crystal pedestal is raised to a point approximately 8 cm from the end of the torch, just

in the lower portion of the plasma tail. The powder flow was begun very gradually, as a quick

burst of powder would immediately extinguish the plasma. The total gas flow through the powder feed hopper was approximately 100 liters per hr. — from 0 to 50 liters per hr. through

the powder fluidizing jet and the balance through an auxiliary carrier gas opening. If the

powder were introduced at a lower total gas flow rate, it would "bounce" off the surface of

the hot plasma zone, flowing around the outside surface and missing the pedestal completely.

The higher gas flow was necessary to punch a hole partially through the plasma in order to inject the powder into its center. After the powder flow was initiated, a very high rate of

flow was used to build up an approximately 5-mm layer of sintered powder on the end of the

magnesia pedestal. At high temperatiires , SC2O3 reacted with MgO to form the spinel phase

MgSc20ij , which served to bond the SC2O3 boule to the pedestal, while the thick layer of sintered powder prevented contamination of the boule by the magnesia. Eventually a cone of the

sintered powder was built up, at which time the powder flow was reduced and the pedestal raised lantil the tip of the cone was 5 to 10 mm from the end of the torch. The tip of the cone then melted, spread out, and a cap of molten oxide was formed. During growth of the boule,

the powder gas flow rate was approximately 15 - 30 liters per hr. through the fluidizing jet.

The pedestal was slowly lowered as the molten cap increased in size, allowing the lower portion of the cap to solidify. The boule was allowed to grow until it was approximately 2 cm

long, the powder flow terminated, the rf generator turned off, and the boule immediately raised until it was entirely inside the quartz tube of the torch. In this way, the boule was cooled in the flowing gas constituting the plasma, without contact with the air.

The resulting boule was 3 to 12 mm in diameter. The surface of the upper portion frequently showed grain boundaries in the polycrystalline mass. The lower portion of the boule

was covered with a dendritic growth of various colors depending on the conditions during

growth. The arms of these dendrites grew at 90° angles and were 0.1 to 0.5 mm thick. At the

base of the dendrites, there were frequently clusters of whiskers up to 0.5 mm long and approximately 0.01 mm thick. If the plasma contained a high concentration of oxygen during the

crystal growth, the resulting boule was nearly clear, but had a brownish haze. The dendrites

at the base were clear. When the boule was fractured, the smoky color was evenly distributed

throughout the mass. When the boule was grown in a pure argon plasma, a black-colored mass

was obtained. The dendrites at the base were dark red in color and were frequently covered

with a metallic-appearing film that was blue, violet, red, gold, or silver. The interior of

the boule varied from dark red (nearly black) to bluish black. When the crystals of the

boule were bluish black, there were frequently observed in the grain boundaries the same multicolored metallic films observed on the dendrites. When the plasma was doped with hydrogen

during crystal growth, the boule was the same bluish black in color but with considerably

more of the multicolored metallic films on the dendrites and in the interior grain boundaries.

388
Because of the metallic appearance of the films, the electrical resistance of various

portions of the boule was measured with a conventional ohm-meter. It was found that many of

the multicolored films, in the interior of the boule or on the surface of the dendrites, demonstrated a resistance of less than 10 ohms, but the resistance of any other portion of the

boule was so high as not to be measurable. The colored films were stable in air, demonstrating no change in appearance or in electrical resistance even over a period of a year. Treatment of various portion of the boule with dilute acid showed for a period of approximately 1 hr a very slow evolution of gas bubbles. During this time, the metallic films would disappear, but no apparent change occurred in the dark, nonmetallic crystals. All of the materials

were stable in pure water.

2.3. STRUCTURE INVESTIGATIONS

Samples of two boules were selected for structure investigation, electrical and magnetic

measurements, and determination of stoichiometry . Crystals were removed from the boules with

great care to exclude the metallic films appearing in the grain boundaries. The lattice parameters were measured from x-ray powder patterns taken on a Guinier-type , focused beam camera with CuKot radiation. SC2O3 was photographed on the same film and the SC2O3 pattern was used

as an internal standard. The measured values for the lattice parameters are listed in table

1. The diffraction patterns corresponded exactly to that of SC2O3 with the exception of a slight shift in line positions toward slightly smaller values of d. Because of the similarity in powder diffraction patterns, a small, nearly spherically crystal of Sc203_jj was aligned

along the [100] direction and a rotation photograph was taken with C\aka radiation. This was compared with a rotation photograph taken of a crystal of SC2O3 obtained from the hydrogenoxygen flame fusion work. No extra reflections or extinctions were observed, and the relative

intensities of the reflections agreed between the two photographs.

Electron micrographs and diffraction patterns were kindly taken for us by Professor J.

G. Allpress of the University of Melbourne, Australia. He found that the diffraction pattern

of all fragments of the material corresponded closely to that expected for SC2O3 except that

some of the reflections, which are forbidden by the space group, appeared strongly. This effect was due to multiple scattering and was a consequence of the technique used, rather than

any function of sample stoichiometry. None of the patterns contained additional reflections,

diffuse scattering, or streaking. There was no evidence for crystallographic shear formation

[23].

2.4. ANALYSIS FOR STOICHIOMETRY

The oxygen content of the Sc20 3_jj crystals was measured by reoxidation. Crystals which

were free of metallic films were selected and crushed with an AJI2O3 mortar and pestle to pass a 50-mesh sieve. Several portions of each sample, weighing approximately 30 mg each, were placed in small platinum boats and fired to constant weight at 1000 °C in a slow-flowing

stream of oxygen. All weighings were made to the nearest microgram on a Mettler model M5

microbalance . Corrections were applied for the small amounts of platinum vaporized in the

oxygen stream. The results of the analysis are shown in table 1. An additional sample grown

in a hydrogen-doped plasma and containing many of the metallic films in the grain boundaries

showed a composition corresponding to Sc202,5i6 + 0.0 05-

Table 1

Sample Compositions and Lattice Constants

Starting

Sample Material A B

Lattice

Constant

Formula

9.845 A

Ref. [22]

SC2O3

9.831 A

±0.005

SC2O2 .922

±0.008

9.826 A

±0.005

SC2O2 .885

±0.008

389
2.5. ELECTRICAL PROPERTIES

Attempts were made to measuire the electrical conductivity and Hall effect of the SC2O2—

x

samples by the van der Pauw technique [24] . The crystals selected for study were approximately

Immx 2 mmx 0.2 mm in size, chosen with extreme care to insure that no metallic films were

included. The resistance of the Sc20 3_j^ crystals proved to be so high that it was impossible

to obtain meaningful data by dc measurement techniques, using an electrometer. Because of

space charge effects, the electrometer was replaced with a Princeton Applied Research model

HR8 lock-in amplifier with an FET input operational amplifier as an impedance matching device,

but again the crystal resistance proved to be too high to be measured. Because accurate electrical conductivity data were not obtained. Hall effect measurements were impossible. The

conclusion was that the electrical resistance of the crystals was equal to or greater than

the input impedance of the measuring instruments — i.e., 10-^^ ohms.

2.6. MAGNETIC SUSCEPTIBILITY iyiEASUREMENTS

The Faraday method was used for the measurement of the magnetic susceptibility. The

magnet was an Eastern Scientific Instruments Model 7 electromagnet supplied with 18-cm diameter pole caps giving a gap of 3 cm. The force-sensing balance was a Cahn Model RG electrobalance, an electrically recording-type balance with an ultimate sensitivity of 0.1 microgram

with a maximum weight of one gram for the sample plus suspension. Temperature was varied

over the range from 1.5 to 300 K. The dewar was constructed of stainless steel with the ex- ception of the tail, which was constructed of copper to eliminate any possible effects on the

magnetic field. The temperature was measured and controlled by a regulator designed by J. Garland of the Cornell University Department of Physics. The regulator consisted of a resistance bridge driven by an oscillator operating at approximately 200 hertz with the unknown leg

being one of two carbon resistors used as thermometers. The imbalance of the bridge was am- plified and detected in a lock-in-type amplifier synchronized with the bridge drive oscillator. The sensitivity of the measuring circuit was such that a change of resistance in the

thermometer of one part in 10,000 could be detected. The thermometers were calibrated at

three temperatures, room temperature, 77 K, and 4.2 K. The latter two points were determined

accurately by measuring the vapor pressure over the boiling liquid-nitrogen or helium in the

cryostat and applying the appropriate temperature and hydrostatic head corrections. The

three calibration points were then fitted to a semi-empirical equation proposed by Clement

[25,26] for the temperature-resistance relationship of the carbon radio resistors.

The magnetic field was mapped with the aid of a 0.6 mm-diameter platinum bead, hung from

quartz fibers of various lengths. The vertical position of the bead with respect to the peak

of the magnet pole caps was measured with a cathetometer . The force was found to be constant

within 2% in a region approximately 1 cm high and 5 mm wide. The maximum field used was 12 kilogauss. The field was calibrated using platinum [27,28] and mercury tetrathiocyanato co- baltate [29] as standards.

The force measured by the balance at any given value of the magnetic field is the sum of

the force due to the quartz sample bucket and that due to the sample itself. The necessary

corrections were determined by measurements on the empty bucket at the same values of the

magnet output as those used in the field calibration, throughout the temperature range 1.6 K

to 300 K. The correction was temperature-independent from 300 K to approximately 60 K, then

its magnitude decreased as temperature decreased. This latter effect was undoubtedly caused

by trace impurities in the quartz. Apparently, the distribution of such impurities in the

quartz is not uniform since the correction varies somewhat from bucket to bucket. Hence, a measurement of this diamagnetic correction was made for each bucket used in the apparatus.

A slight field dependence was found for the samples of Sc203_j^ as well as for the SC2O3

starting material, suggesting the presence of trace ferromagnetic impurities. These were corrected for by the extrapolation method of Honda [30] and Owen [31] . The plots of Xh

- were very nearly linear in the range of 5 kilogauss to maximum magnet output , so extrapolation to i = 0 was a simple matter. The molar susceptibility was also corrected for the diamagnetism of the ion cores. The value for Sc^+ was taken as -6 x 10"^ [32] and that for

0^~ as -10 X 10"^ [4]. As indicated previously, the SC2O3 and the Sc203_x contain small a- mounts of iron which, according to Geller et al. [33], dissolves in SC2O3 by substitution of

Fe^+ for Sc^+. The SC2O3 starting material contained 0.01 - 0.1% iron, and the plasma-grown

390
crystals exhibited a factor of 10 reduction in the iron content. Assuming the presence of

0.02% iron in SC2O3 and 0.002% in the samples of Sc203_j^, a correction was made to the observed molar susceptibility by using the equation x = Ny^/3kT, where N is the number of Fe^+

ions per mole of SC2O3 and u is the effective magnetic moment of Fe^"*" (in this case, 5.9 Bohr

magnetons)

.

3. DISCUSSION

The reduction in impurity levels in the plasma-grown crystals probably results from the

fact that sufficiently high temperatures are reached in the plasma to result in vaporization

of a considerable amount of the powdered scandium oxide. At high temperatures the vapor pressure of iron or its oxides is higher than that of scandium oxide [34,35], so portions of this

impurity, as well as calcium and magnesium, are simply boiled off prior to crystallization of

the SC2O3, resulting in effective purification of the Sc203_x.

In the temperature range 2400 - 2570 °C, i.e., very near the melting point of SC2O3, SC2

O3 sublimes [36] with the following equilibriTM:

SC203(s) t 2ScO (g) + 0(g)

The vapor pressure of ScO at 2440 K is 0.001 torr and at 2630 K, 0.01 torr. At 2550 K the

ScO partially dissociates to form Sc and 0 atoms in a ratio of 1 Sc to 8 ScO. In a rapidly

moving plasma stream, one could expect a portion of the Sc and ScO vapors to be quenched and

dissolved in the molten cap and on the surface of the boule before recombination with oxygen

could occur. The net result would be an excess of scandium in the molten cap, but this could

have only limited solubility in the solid material. Apparently the composition of sample B is nearer the limit of solubility of scandium in SC2O3, because of greater amounts of a second

phase precipitated in the grain boundaries. Unfortunately, the metallic films could not be

produced in sufficient quantities for chemical analysis. Their multicolor character could

not be attributed to light interference patterns resulting from varying film thickness; the

films themselves are metallic, and light penetration would be insignificant. The films could

be due to precipitated, colloidal, metal particles of varying size or they could consist of

lower oxides of scandium with continuously varying oxygen content. Photoelectron spectroscopy

or x-ray microprobe analyses of these films might yield useful information.

Correction of the observed magnetic susceptibility of SC2O3 for diamagnetism of the ions

cores and for the contribution due to Fe^+ impurity yields a slight paramagnetism that is es- sentially temperature independent. This has been observed previously in the case of SC2O3 , Ti02f snd V2O5 [37] ; it is just the Van Vleck paramagnetism [38] . Because the structures of

SC2O3 and Sc203_jj are the same, the Van Vleck paramagnetism should be subtracted from the observed susceptibility of the oxygen-deficient samples in order to study the magnetic contribution of the defects. The resulting plot of the reciprocal susceptibility as a function of

temperature is shown in figure 1. Figure 2 shows the temperature dependence of the effective

magnetic moment per mole of Sc20 3_j^ calculated from the relation Pgff ~ 2.83 /xj^jT. The error

bars at high temperatures are sufficiently large that a linear relation of the Curie-Weiss

type, X = C/(T-e) cannot be ruled out, but the actual data points do indeed show a definite

curvature throughout the entire temperature range of measurement.

It can be seen from figure 2 that the effective magnetic moment is extremely small. It

would be more meaningful to calculate the y^f^ per mole of defect rather than per mole of SC2

order to do this one must know the nature of the defects and their concentrations

in the samples. The most probably defects are: Sc^ , either interstitial or at a scandium

site; Sc''"-'- or Sc+^ , probably at a scandium site; and F center, consisting of a single electron

trapped at an oxygen vacancy; or an F' center consisting of an electron pair trapped at an oxygen vacancy. Each of these defects would make a different contribution to the magnetic

susceptibility. The contributions are listed in table 2. Col\imn I gives -the types of defect

and Column II, corresponding formulas of samples A and B. Column III shows the experimentally

observed Peff P^r mole of defect at three temperatures: 300 K, 77 K, and 4.2 K. Column IV

indicates the spin state S of the defect, and Column V, the magnetic moment expected from spin

only. In all cases, the observed Peff less than the y predicted for any of the paramagnetic species, thus implying that more than one single species, one paramagnetic and the other

diamagnetic, must be contributing to the net magnetic moment. The temperature dependence of

the moment suggests either an equilibrium between two species or an equilibrium between two

391

;
Temperature , ° K

Fig. 1. Reciprocal net molar magnetic susceptibility versus absolute

temperature for oxygen-deficient scandium oxide. Values have

been corrected for diamagnetism, temperature-independent

paramagnetism, and trace iron impurity.

Q4

0.3 ^ 02 ^ 0.1 I

0

CD ^ ^ 0.3 02 ^ 0.10

EFFECTIVE MAGNETIC MOMENT

"I—'—I—I—I—I—I

<— "1 I I

«—I—I—I—1—I—I—I—1—I—I—

r

^'^2°Z885

^^2*-^Z992

' ' ..U ' ^—'-^—'—i^^H—'—'—'—'—' ' '

I 'I

'

I 1

I I 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

Temperature , "K

Fig. 2. Effective magnetic moment versus temperature per mole of Sc20 3_j^.

states of the same species. The diamagnetic state or species would have to be more stable

at low temperatures.

Of the species listed, there could be an equilibrium between an F center and an F' center. However, F" centers are stable only over a relatively narrow temperature range and then

only in the vicinity of 70 K in the case of alkali halides. The other possibility arises with

the Sc+-^ ion. The energy difference between the ^D(s^d-^) ground state and the ^D(sM-^ antiparallel spin) is 2541 cm"-^ ; that between the ground state and the ^S(s^d'^) level is 11736

cm~-^. However, ligand-field effects may be sufficient to make either the -^D or the very

close in energy to the ground state. Furthermore, the orbital moment of the ground state

may not be completely quenched, yielding an additional component to the Van Vleck temperatureindependent paramagnetism.

The observed electrical properties are not inconsistent with the above models. If the d

electron of Sc"*" were delocalized in a d-conduction band as postulated by Morin [1] , there

should be strongly enhanced conductivity; this was not observed. Apparently, the electron is

trapped at a localized site. Application of Goodenough's criterion for metallic conductivity

392
Table 2

Comparison of Calculated and Observed Magnetic

Moments Asstiming Different Defect Models for Sc 0

I Defect

II FormulaIII Obsd.p

err

IV

Spin

State

V

Calc

.

Temp. A B M

ScO

300 K

77 K

4.2 K

Sc3+Sc° 02- ^^2 ^0 . 052 2 - 922 Sc3+Sc° 02-

^^2 ^^0-076^2-885

1.18 1.34

1.01 1.16

0.79 0.80

1/2 1.73

Sc+1

300

77 4.2

3^^1^922^4. 07802:922 ^^1 .885^'=0. 115^2-885

0.97 1,09

0.82 0.94

0.64 0.65

1 3d

0 ^D or ^S

2.83

0

Sc2+

300

77 4.2

SCjtgi+i+Sc^+^ggO^^g^^ Sc^+ Sc2+ 0^-

1 -770 0-230 2-885 0.68 0.77

0.58 0.67

0.45 0.46

1/2 1.73

F

300

77 4,2

Sc^+O^- e~ ^2 2-922^0.156 Sr^+O^- p2 2-885 0-230

0.68 0.77

0.58 0.67

0.45 0.46

1/2 1.73

F'

300

77 4.2

Sc3+02- 2e2-

2 2-922 0-078

Sc3+02- 2e2-

2 2-885 0-115 0.68 0.77

0.58 0.67

0.45 0.46

0 0

[39] would give a critical cation-cation distance for SC2O3 of 3.00 A, The actual nearest

neighbor Sc-Sc distance in SC2O3 is 2,14 A, but this distance is not repeated consecutively;

it occurs at isolated sites in the lattice, hence could not contribute to extensive electron

delocalization. Furthermore, the application of Goodenough's empirical relationship to the case of scandium oxide is questionable. It was derived from electrical studies of the oxides

of titanium, vanadium, chromium, and iron, and is expressed in terms of the nuclear charge of

titanitim. Also, as Goodenough suggests, the relationship is valid only when the cations are distributed with octahedral coordination in a close-packed array of oxygen ions. The coor- dination sphere of oxygen around three fourths of the scandium is so distorted that it is difficult to call it octahedral.

There remains the possibility that the poor electrical conductivity observed is the result of passivation of the SC203_x crystal by a film of stoichiometric SC2O3 although the

electrodes for electrical measurements were attached with the aid of an ultrasonic soldering

device. If the film were rejuvenated as rapidly as it was broken, then the oxide barrier at

the electrode-crystal interface could still inhibit the electrical conductivity, leading to space charge effects such as were observed during the measurements. Unfortunately, electrodeless conductivity measurements are not feasible on intermediate and low conductivity materials.

4. REFERENCES

[1] Morin, F. J., Bell System Tech. Jour. 21' 1047 (1958).

[2] Breckenridge, R. G. and Hosier, W. R. , Phys. Rev. 91_, 793 (1953).

[3] Morin, F. J., Phys. Rev. Letters, 3, 34 (1959).

393
[4] Sienko, M. J. and Banerjee, B. , J. Amer. Chem. Soc. 83_, 4149 (1961).

[5] Petru, F. and Dufek, V., Z, Chem. 6_, 345 (1966).

[6] Dufek, v., Petru, F., and Brozek, V., Monat. Chem. 98, 2424 (1967).

[7] Dufek, v., Brozek, V., and Petru, F. , Monat. Chem. 100 , 1628 (1969).

[8] Noddack, W. , Walch, H. , and Dobner, W. , Z. Physik. Chem. 211 , 180 (1959).

[9] Noddack, W. and Walch, H., Z. Elektrochemie 63_, 269 (1959).

[10] Zyrin, A. V., Dubok, V. A., and Tresvyatskii , S. G., Khimiia Vysokotemperaturnykh

Materialov, Trud, Vses. Soveskch. 2nd, Leningrad, 1965, pp. 59-65 (pub. 1967).

Companion, A. L., J. Phys . Chem. Solids 25_, 357 (1964).

Tippins, H. H., J. Phys. Chem. Solids 27_, 1069 (1966).

Barta, C, Petru, F. , and Hajeck, B., Naturwissenschaften 45_, 36 (1958).

Geller, S., Romo, P. and Remeika, J. P., Z. Krist. 124 , 136 (1967).

Geller, S., Romo, P. and Remeika, J. P., Z. Krist. 126, 461 (1968).

Norrestam, R. , Arkiv fur Kemi 29, 343 (1968).

Reid, A. F. and Ringwood, A. E. , J. Geophys. Res. 74_, 3238 (1969).

Borchardt, H. J., J. Inorg. Nucl. Chem. 26_, 711 (1964).

Miller, A. E. and Daane, A. H., J. Inorg. Nucl. Chem. 27_, 1955 (1965).

Miller, A. E., Ph.D. thesis, Iowa State University (1964).

Muller-Buschbaum, H. K., J. Inorg. Nucl. Chem. 30_, 895 (1968).

Swanson, H. E. and Fuyat, R. K. , National Bureau of Standards Circular 539, Vol III,

NBS, Washington, D.C., 1953, p. 27.

Allpress, J. G., private communication,

van der Pauw, L. J., Philips Res. Rpts. 1_3, 1 (1958).

Clement, J. R. and Quinnell, E. H., Rev. Sci. Instr. 23_, 213 (1952).

Hoare, F. E., Jackson, L. C, and Kurti, N., Experimental Cryophysics, Butterworths

,

London, 1961, p. 234.

Kojima, H. , Tebble, R. S., and Williams, D. E, G. , Proc. Roy. Soc. (London) 260 , 237

(1961)

.

Hoare, F. E. and Walling, J. C, Proc. Phys. Soc. B64 337 (1951).

Figgis, B. N. and Nyholm, R. S., J. Chem. Soc. 1958 , 4190.

Honda, K., Ann. Phys. 32./ 1048 (1910).

Owen, M., Ann. Phys. 32' ^57 (1912).

Selwood, P. W. , Magnetochemistry 2nd edition, Interscience , New York, 1956, p. 78.

Geller, S., Williams, H. J., and Sherwood, R. C, J. Chem. Phys. 35./ 1908 (1961).

Fedesov, V. N. and Nadolskii , A. P., Trudy Irkutsk. Politekh. Inst. 27, 80 (1966).

Nesmayanov, A. N. and Trapp, G., Zh. Fiz. Khim. 38.' 2931 (1964).

Semenov, G. A., Russ. J. Inorg. Chem. 10_, 1300 (1965).

Landenburg, R. , Z. fiir Phys. Chem. 126, 133 (1927).

Van Vleck, J. H., The Theory of Electric and Magnetic Susceptibilities , Oxford University

Press, London, 1932, p. 302.

[39] Goodenough, J. B. , Collogue Internationale du C.N.R.S., No. 149, Bordeaux, 1965, pp. 162-

169.

DISCUSSION

J. H, Perlstein : You grew the crystals on MgO pedestals, I think you indicated,

M. J, Sienko: The pedestal was so far down that we didn't have any of that: we just

took the top part.

J. H. Perlstein: 1 was going to ask you if there could have been magnesium diffusion

up the crystal?

M. J. Sienko: There was no evidence of magnesium in the spectroanalysis . There was

no detectable magnesium.

E . Banks : Have you been able to look at any optical spectra?

M. J. Sienko: No, the black is so black that it is hopeless. One might be able to do

something with reflectivity, but certainly not with transmission. Incidentally, these things

are relatively inert. As I mentioned, those films would stick around for a year or so. If we put the boules in water, they just stayed there. If we put them in acid, there would be

394
a very slow evolution of bubbles which would continue for hours. We were not able to collect

any gas to make an analysis of it, but we assumed it was hydrogen. ^

W . VanGool : Are you sure there was no hydrogen in your crystals?

M. J. Sienko : No, one is never sure that there is no hydrogen. That is always a possibility, but being in an argon plasma instead of hydrogen-oxygen flame suggests that it was not hydrogen that was producing these properties. Also, I think that hydrogen would probably

give reasonable conductivity in these structures because of the proton jump.

R. S. Roth : If we wanted to accurately measure the melting point of scandi\jm oxide for use on an international practical temperature scale and we were going to do this in a vacuum

in a tungsten crucible, would we run into the problem of reduction of scandium oxide?

M. J. Sienko : No, I don't think so. No, I think that my first argument would apply.

The Ah for oxygen loss must be very large.

F. Holtzberg : I wondered if you looked for any rare earth impurities?

M. J. Si enko : The effective moment, as you saw, was of the order of 0.3 Bohr magnetons;

any rare earths would immediately make this climb up. But you have a point there; there could

be traces. We considered that, didn't we John (Young)?

J. E. Young : The detailed spectroanalysis did not really investigate the rare earth

possibility to any great extent. They did not look very closely for rare earths.

E . Banks : I think that scandium oxide has a C-rare earth oxide structure, is that correct? In that structure you have two non-equivalent scandium sites in the ratio of three to one, and I would just like to ask whether your ESR spectrum could be partially resolved in

terms of a three to one intensity?

M. J. Si enko : That's a very good point and this is precisely what we are trying to do

now. The ESR spectrum offers promise of indicating what the nature of the defect is.

395

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

CRYSTAL CHEMISTRY AND COMPOUND FORMATION IN THE SYSTEMS RARE EARTH SESQUIOXIDE-WO3

G. J. McCarthy, R. D. Fischer-"- , G. G. Johnson, Jr. and C. E. Gooden

Materials Research Laboratory

The Pennsylvania State University

University Park, Pennsylvania 16802

Compounds with the following stoichiometries have been prepared in the rare earth ses- quioxide-tungsten trioxide systems: RE6WO12/ RE10W2O2I' REl 1+^1^033/ RE2WO5 , RE2W2O9. Compounds of the first three stoichiometries prepared at 1400 °C have structures apparently

related to that of fluorite. REgW0i2 has three structural classes whose symmetries are dependent on the rare earth ionic radius: La-Pr, cubic or pseudocubic ; Nd-Gd, pseudotetragonal; Tb-Lu, Y, rhombohedral . RE10W2O21 is stable only for RE = Gd-Ho, Y and has the same pseudotetragonal symmetry as the intermediate REgW0]^2 compounds. REi[|Wlj03 3 has a pseudorhombohedral s-tructure related to the third RE6WO12 structure. The rhombohedral RE6WO12

compounds are known to be isostructural with RE7O12 oxides and it is suggested that

RE10W2O21 and REi[+Wij033 may be structurally related to RE^Oy and REgOn respectively.

KE2WO5 compounds with RE = Pr-Dy have a monoclinic scheelite-related structure. The RE2W2O9

compounds, also wi-th a complex monoclinic structure, are stable only for RE = Ce-Gd (or Tb)

.

Compounds of the stoichiometries REitW3 0i2 and RE2W3O12 were not studied, but -the literature

infoirmation on them is noted. A discussion of the probable sub-solidus phase relations in

RE-W-0 systems is also included.

Key words: Fluorite-related structures; rare earth tungstates; rare earth tungsten

oxides; RE2O3-WO3 compounds; RE-W-0 systems.

1. INTRODUCTION

As part of a continuing study of rare earth-transition metal oxide chemistry, we have

completed a preliminary examination of the crystal chemistry and compound formation in the

systems rare earth sesquioxide-tungsten trioxide. These compounds are of considerable interest in science and technology as phosphors, laser hosts and nuclear control materials,

and in crystal chemistry because of the opportunity to examine the behavior of certain

structure types as a function of the rare ear-th ionic radius.

2 There have been several previous investigations of compound formation in RE2O3-WO3

systems. Ivanova et al. [1]^ studied the system La203-W03 and reported compounds of the

molar ratio 3La203'W03, 3La203-2W03, La203 -WOs , La203-2W03 and La203 -31^03. In the system

Nd203-W03 Rode and Karpov [2] found the following compounds: 3Nd203 -WOs , 2Nd203-W03,

Nd203 -W03, Nd203 -2^703, Nd203-3W03. Chang et al, [3] listed 3Sm203 -W03, 7Sm203-4W03,

Sm203-W03, Sm203*2W03 and Sm203-3W03 as the stable compounds in the system Sm203-W03. Finally

in the earliest systematic RE2O3-WO3 study, Borchardt [3] reported the following compounds

in the system Y2O3-WO3 : 3Y2O3-WO3 , 9Y203-4W03, 15Y203-W03, Y2O3 •WO3 , Y2O3 -31^03.

1 Present address: Institute for Biophysical Chemistry, Max Planck Gesellschaft, Gottmgen,

West Germany.

2 RE = rare earth

3 Figures in brackets indicate literature references at the end of this paper.

397

;
Certain stoichiometries are common to all four investigations: 3RE2O3-W03 (REgW0i2)

f

RE2O3 • WO3 (RE2WO5 ) and RE2O3 • 3WO3 (RE2W3O12) • However, enough variation existed among the

reported stoichiometries to justify a compositional study. The systems Nd203-W03, EU2O3-WO3,

and H02O3-WO3 were chosen for careful study. The stoichiometries of compounds and the range

of stability deteirmined later in the study were: REgW0i2 RE = La-Lu, Y RE10W2O21 KE = Gd-Ho, Y KEiitW4033 RE = Nd-Lu, Y (La-Ce were not examined)

RE2WO5 KE = Nd-Lu, Y (La-Ce were not examined)

RE1+W3O15 RE = La-Nd

RE2W2O9 RE = Ce-Gd (La and Tb were not examined)

RE2W3O12 RE = La-Lu, Y

Only two temperatures were used in this preliminary study: for the range 0-45 mol % WO3

,

1400 °C; for 46-100 mol % WO3 , 1150 °C. Thus, the existence of other stoichiometries at

higher or lower temperatures cannot be eliminated and this should be kept in mind. Also, some of the compounds studied probably show a small range of stoichiometry , but it is on the

stoichiometric compound that the x-ray powder data were determined and crystal chemistry com- parisons were based. It was not feasible in this study to determine the stoichiometry range

of each compound for each rare earth.

In reference to nomenclature, the terms "tungstate", "normal tungstate", "oxytungstate"

,

etc., sometimes applied to these compounds have been avoided in favor of the stoichiometric

formula.

The larger part of this report will be devoted to the f luorite-structure-related com- pounds RE6WO12, KE10W2O21, and REiitW4033. They were especially interesting because of their

probable isostructural relationship to the RE202n-2 oxides.

2. EXPERIMENTAL PROCEDURES

starting materials were high-purity rare earth sesquioxidea and tungsten trioxide-'.

Tb203 and Pr203 were prepared by hydrogen reduction of "Tb^Oy" and PrgOn at 1400 °C. The

oxides were thoroughly dried, weighed to the appropriate ratios to one part in ten thousand,

thoroughly ground and mixed in an agate mortar and pressed into pellets at 60,000 psi. These

pellets were heated in air (or in argon in the case of compounds containing Tb, Pr, and Ce)

for from three to seven days at either 1400 °C (for RegW0i2' RE10W2O21, REmWi^033) or 1150 °C

(for RE2W0g and RE2W20g) . At least once during the heating schedule the pellets were re- moved from the furnace, reground, and repelletized.

Phases were identified by x-ray powder diffraction. Mea^^surements were performed on a Siemens dif f ractometer using Nickel-filtered CuKa radiation (X = 1.54178 A) . The diffractoo o meter was calibrated with high-purity silicon (a^, = 5.4301 A) and gold (a^ = 4.0786 A) . Data were refined to yield cell parameters using the least squares computer program of

Appleman et al. [5] . Reported intensities are derived from relative peak heights.

3. RESULTS AND DISCUSSION

3.1. RE6WO12

The RE6WO12 compounds were all prepared

intermediate regrindings. They were grouped

apparently related to the fluorite structure,

rare earth cation.

at 1400 °C with six days total heating and two

according to three structural classes, all

whose symmetry depended on the size of the

La-Pr Cubic or Pseudocubic

Nd-Gd Pseudotetragonal

Tb-Lu, Y Rhombohedral

Research Chemicals, 99.9%

^Fischer Scientific, "purified"

398
Cell parameters for all of these compounds are listed in table 1.

3.1. a. La-Pr

La6W0]^2 first studied by Chang and Phillips [6] . They presented powder data indexed on a face centered cubic (f.c.c.) cell with ao = 11.18 A and suggested a disordered

pyrochlore or ordered defect fluorite structure. We also prepared LagW02 2 confirmed the

powder data and cell parameter of Chang and Phillips [6] . However, it should be noted that

only two weak reflections [(200) and 422)] could not be indexed on a halved f.c.c. cell with

a„ = 5.591 A.

CegW0;L2 snd Pr5W0i2 ^^'^ very similar diffraction patterns except that the (200) and

(422) reflections were not observed. Several weak reflections which could not be indexed on

a single or doubled f.c.c. cell were present in CegW0i2 ^^'^ it is for this reason that the

symmetry is termed "pseudocubic" in table 1. Powder diffraction data^ for Ce5W0]^2 is given

in table 2. Also given in table 2 is the powder data for Ce02 as listed in the Powder Diffraction File [7]. Both have f.c.c. symmetry (or pseudosymmetry) and there is a striking

correspondence between their relative intensities. The pseudocubic cell parameter of

Ce6W0i2 is only 2% larger than that of Ce02(ao = 5.411 X). This behavior tends to support

the suggestion of Chang and Phillips [6] that the structure of these compounds is closely

related to that of fluorite.

Table 1

Cell Parameters of REgW0i2 Compounds

Compound Co Symmetry

Lag WO 12 11. 182 (1) K Cubic

LaeW0i2 (a) 11. 18 Cubic

Ce6WOi2 5. 518 (1) Pseudocubic

PrgWOi

2

5. 486 (1) Cubic

Nd5WOi2 5. 467 (1) 5. 446 (1) A Pseudotetragonal

Nd6WOi2 (b) 5. 470 5. 442 P s eudo te tragona

1

SmgWOi

2

5. 409 (1) 5. 389 (2) Pseudotetragonal

Sm5WOi2 (b) 5. 412 5. 405 Pseudotetragonal

SmgW0i2 (b) 10. 80 Cubic

EugW0i2 5. 384 (1) 5. 362 (1) Pseudotetragonal

GdgW0i2 5. 352 (2) 5. 327 (2) Pseudotetragonal

TbgW0i2 9. 842 (1) 9. 406 (2) Rhombohedral

Dy6WOi2 9. 796 (1) 9.,371 (2) Rhombohedral

HOgW0i2 (c) 9. 755 (1) 9. 308 (2) Rhombohedral

ErgWOi

2

9. 723 (1) 9. 270 (1) Rhombohedral

ErgW0i2 (b) 9. 712 9.,264 Rhombohedral

TmgW0i2 (d) 9. 679 9.,230 Rhombohedral

YbgW0i2(d) 9.,640 9.,188 Rhombohedral

LugW0i2 (d) 9.,618 9.,145 Rhombohedral

YbgW0i2 (d) 9.,757 9.,317 Rhombohedral

(a) after ref. [6] (c) after ref. [12]

(b) after ref. [8] (d) after ref. [10]

'We determined the x-ray powder diffraction data of every compound listed in the cell parameter tables. However, only selected examples are given in this report. The remaining

powder patterns have been submitted to the Powder Diffraction File of the Joint Committee

on Powder Diffration Standards [7] and, if accepted, will appear in sets 22 and 23.

399
Table 2 X-Ray Powder Data for Ce5WOi2 and Ce02

ceeW0i2 Ce02 (a)

d , calc obs / ^ obs / J. w

111 3 . 186 3 . 184 100 3 . 124 100

200 2 .759 2. 758 35 3 .706 29

2. 215 2

2. 164 >1

2. 123 >1

220 1. 9508 1. 9507 45 1. 913 51

311 1. 6636 1.6634 40 1.632 44

222 1. 5927 1. 5925 9 1. 562 5 400 1. 3794 1.3791 6 1.353 5 331 1. 2658 1. 2658 18 1.241 15

420 1.2338 1.2339 12 1. 210 6 422 1.1263 1. 1263 10 1.1044 12

511 1.0619 1.0617 9 1.0412 9 440 0.9754 0.9753 4 0.9505 5 531 0.9326 0.9328 16 0.9146 13

(a) From reference [7] #4-0593

.

Data collected by

Swanson and Tatge of the U.S. National Bureau

of Standards. a,, = 5 .411 A.

The AX2 fluorite structure has four formula units per unit cell with the eight-fold co- ordinated A cations in the (4a) equipoints of space group Fm3m and the X anions in (8c)

.

For RE5WO22 to have a simple fluorite structure, the model for the unit cell must be

(RE3'^i43 Wg 57) (Og . 86 1 . 1 4) i.e., with every seventh oxygen missing and random distribution

of KE3+ and W on the (4a) and oxygen defects on the (8c). The extra reflections, and thus

doubling of the simple cell, in the case of La6W0]^2 are probably a result of ordering of

cations or oxygen defects or both. When a single-crystal structure analysis is performed,

it would not be surprising to find the oxygen defects clustered around the tungsten since

W^"*" in most oxides has four-fold coordination and in the rhombohedral RE6WO12 compounds described below) , a coordination of six, and thus would favor the site with the lowest co- ordination associated with oxygen defects.

In Ce5W02 2 and Pr5W0;^2 there is the possibility of removal of the oxygen defects by

partial substitution of RE'++. This may explain why the diffraction patterns of Ce6W0]^2 and

PrgW02 2 are not identical with La5W02 2' Because of difficulties in preparing and storing

stoichiometric Ce203 , Ce6W0i2 was prepared by heating the appropriate mixture of Ce02 and

WO3 in a purified argon atmosphere according to the usual schedule. The possibility of incomplete reduction of Ce^"*" to Ce^"*" exists. If there is a mixed Ce valence the oxygen defects

could be removed giving the simple fluorite model {Cel'^ic^Ce'i^'^^gVlQ 57)03. When our "Ce6W0i2" was heated in air at 1400 °C it gave a complex x-ray powder pattern with Ce02 as the major

constituent. In the case of PrgW0i2 (prepared from Pr203 and WO3) there were no reflections

which could not be indexed on a simple f.c.c. cell with ao = 5.486 A. When it was heated in

air at 1400 °C the cell parameter decreased slightly to ao = 5.482 A, probably reflecting

the partial substitution of the smaller Pr'*"*' for Pr^"^.

3.1.b. Nd-Gd

As the size of the rare earth in the RE5WO12 compounds was decreased, many of the strong

f.c.c. reflections showed a slight but resolvable splitting with the addition of a few new weak reflections. This was first noted by Trunov et al. [8] in Nd6W0i2 and Sm5W0i2 prepared

at 1256 °C for 50 hours. Their cell parameters are listed in table 1. The weak reflections

400
of KE5WO12 compounds in this group could not be indexed on this tetragonal cell or one related to it by simple multiples (2, 3, /2, /3) of a^ and c^ , and for this reason the

symmetry has been termed pseudotetragonal in table 1. The x-ray powder diffraction pattern

for NdgW0i2 is given in table 3. We observed significantly fewer unindexed weak reflections

than Trunov et al. [8], but this may be due to their lower preparation temperature's favoring

further ordering and thus yielding stronger superlattice reflections.

Sm5W0i2' Eu6W0i2» Gd5W0i2 were found to be isostructural with Nd5W0i2' In a recent

study, McCarthy [9] prepared EU6WO12 also at 1400 °C, but with a single one-day heating.

The product was cubic with a^ = 5.366 A, not tetragonal. We repeated this preparation and

derived the same cubic phase. Similarly, Chang and Phillips [6] prepared Sm5WOi2 at 1400 °C with a 6-hour heating and reported a phase with f.c.c. symmetry and a^ = 10.80 K. Again,

two very weak reflections required doubling of the 5.40 A f.c.c. subcell. We also observed

the same behavior in Gd6WOi2 heated for 12 hours at 1400 °C. These results imply that con- siderable heating time is required in order to develop the equilibrium pseudotetragonal

structure.

3, I.e. Tb-Lu, Y

The KE5WO12 compounds with RE = Tb-Lu, Y have the well known KE5MO12 (M = Mo, W, U) structure first elucidated by Aitken et al. [10] . The structure of this class of compounds

was described by Bartram [11] who performed a structure analysis and refinement on Y5UOi2-

It is a rhombohedrally distorted fluorite (space group R3) in which the c-axis of the hexagonal cell lies along the [111] axis of the f.c.c. fluorite cell. The Y(RE) ions are coordinated with oxygen ions in highly distorted octahedra, while the U(W) ions form regular octahedra with oxygen. These U (W) octahedra alternate along the c-axis with similar octahedra

not containing a U(W) ion.

TmgW0i2' Yb5WOi2/ ^^i,^0i2' ^^'^ "^6^012 have been prepared as pure phases by Aitken et

al. [10] . Their hexagonal cell parameters of the rhombohedral cell are given in table 1. They also reported that the structure type extended to at least Dy5WOi2 but were unable to prepare any of these other compounds as pure phases. We have prepared the RE5WO12 compounds

with RE = Tb-Er as pure phases without particular difficulty. We reported on H05WO12 in a

Table 3 X-Ray Powder Data of NdgWO^ 2

2 100

(35(a)

118

2 (30

45

j30

~^30 16

( 326 15

hk£ calc obs

3. 62

111 3 .153 3. 153

200 3 .735 2. 735

002 2 .723 2. 722

2. 225

220 1 .9337 1. 9336

202 1 .9297 1. 9296

311 1 . 6484 1. 6483

113 1 .6430 1. 6432

222 1 . 5765 1. 5766

400 1 .3674 1. 3673

004 1 .3212 1. 3613

331 1 .2544 1. 2545

313 1 .2521 1. 2522

420 1 . 2230) 222 402 1. 1 .2219/"

204 1 . 2187 1. 2189

422 1 .1156 1. 1158

224 1 .1131 1. 1131

I\

10

10

(a) Indicates overlapping

reflections

465-504 O - 72 - 27 401
recent study of the H02O3-WO3 system [12] . The hexagonal cell parameters of these compounds

are also given in table 1 along with the data of Trunov et al. [8] for ErgW0i2- The extra

reflections observed in the powder diffraction patterns by Aitken et al. [10] may have been

due to incomplete reaction and the presence of the RE10W2O21 or KEii^WtjOss phases described

below.

3.1.d. Phase Transitions

It is important to note that the results just reported for RE5WO12 compounds probably

pertain only to the 1400 °C isotherm of a temperature vs RE^"*" ionic radius structure diagram.

As a check on the possibili.ty of lower temperature phase transitions, we did water-quench

one example of each of the KE6WO12 structure types from 1400 °C to see whether the same phase as that from the usual slow air cooling would form. In each case the rapid-quenched

and slow-cooled products were identical. This does not, however, rule out the possibility

of a completely reversible phase transition at some temperature below 1400 °C.

If our results are valid for the 1400 °C isotherm, they show that this isotherm intersects the cubic-pseudotetragonal boundary between Pr and Nd and the pseudotetragonal-rhombohedral boundary between Gd and Tb. Using the Shannon and Prewitt [13] effective ionic radii

of RE-' in oxides listed in table 4 we can derive the approximate structure boundary- isotherm

intercepts. For 6-fold coordination of the KE^'*' these intercepts are about 0.99 A and 0.93 A

respectively.

An interesting extension of the research reported here would be a study of the stability

of these three structure classes as a function of temperature. Borchardt [4] has reported

o that rhombohedral YgW0i2 undergoes a phase transition to a f.c.c. phase with a^ = 5.275 A

somewhere between 1700 °C and its melting point (above 2200 °C) . Thus it is likely that

many of the rhombohedral KEgW0i2 compounds will transform to the pseudotetragonal and/or the

cubic structure at higher temperatures.

In a recent study of the system H02O3-WO3, McCarthy and Fischer [12] described a pseudotetragonal f luorite-structure-related compound with the stoichiometry HO]^o^2'^21" Isostructural compounds of the stoichiometry RE10W2O21 were found among the other rare earths only

for RE = Gd-Ho, Y. For the other rare earths, mixtures with this bulk composition subjected

3.2. RE W 0 10 2 21

Table 4 Effective Ionic Radii of the Rare Earths

in Oxides (a)

RE 3 + Six

Coordination

Eight

Coordination

1.045 K

O La

Ce

Pr

Nd

Sm

Eu

Gd

Tb

Dy

Ho

y

Er

Tm

Yb

Lu

1.18 A

1.01

0.997

0.983

0.958

0.947

0.938

0.923

0.912

0.901

0.900

0.890

0.880

0.868

0.861

1.14

1.14

1.12

1.09

1.07

1.06

1.04

1.03

1.02

1.015

1.00

0.99

0.98

0.97

(a) After Shannon and Prewitt,

reference [13]

402
to the usual 1400 °C heat treatment yielded products which consisted of REgW0i2 plus

REiitWit03 3 . Cell parameters of the RE10W2O21 compounds are listed in table 5. A typical x- ray powder pattern, that of DyioW202if is given in table 6. After allowance for the shifts in interplanar spacings due to the lanthanide contraction, one sees that the RE10W2O21 x-ray patterns are virtually identical to those of the

pseudotetragonal RE5WO12 (^E = Nd-Gd) compounds (compare table 3 with table 6) . The stability fields of this pseudotetragonal structure overlap at Gd, and as expected there is com- plete solid solution between Gd5WOi2 and GdioW2021' The cell parameters of the GdioW202i

end member are somewhat smaller than those of Gd5WO]^2 because of the partial substitution

of the smaller W^"*" for Gd3+.

The case of Y10W2O21 is interesting. In his study of the system y203-W03 , Borchardt[4]

described a compound with the oxide ratio 9Y203-4W03 (30.8 mol % WO3 ) . This composition is

between Yj^gWaOai (28.6 mol % WO3) and Yii4W^03 3 (36.4 mol % WO3 ) and indeed a check of the

powder data reported by Borchardt for this "compound" indicated a mixture of about three

parts Y10W2O21 to one part Yii|Wi^033 . Y1QW2O21 sets the lower limit of the stability field

of KE10W2O21. In table 4 the radius of y3+ is between that of Ho^+ and Er2+ but closer to Ho^+. At 1400 °C, the approximate 6-coordinated KE^"^ ionic radii limits for RE10W2O21 are

0.94 and 0.895 K.

In his study of the system Y2O3-WO3 , Borchardt [4] also described a compound with the

molar ratio 15Y203'8W03 (34.8 mol % WO3) . The powder data given for this compound were very

similar to those given by Trunov et al. [8] for llEr203-6W03 (35.3 mol % WO3) and (allowing

Table 5 Pseudotetragonal Cell Parameters of

REi 0W2O21

Compound a 0 c 0

GdioW202i 5.,340 (2) A 5. 317 (2) A

TbioW202i 5.,327 (1) 5. 312 (1) DyioWaOai 5.,309 (1) 5. 292 (2) Hoj 0W2O2

1

5.,287 (1) 5. 268 (2) Y10W2O21 5.,285 (1) 5. 266 (1)

Table 6 X-Ray Powder Data of DY1QVI2O21

"hkl d

' dT TZ calc obs /lo

2 100

/30(a)

\20

(30

t45

j30

"^30 15

i 3 {[_

(a) Indicates overlapping

reflections

3. 52

111 3. 062 3. 062

200 2. 655 2. 655

002 2. 646 2. 648

220 1. 877 1. 878

202 1. 875 1. 874

311 1. 600 1. 601

113 1. 596 1. 596

222 1. 5311 1. 5310

400 1. 3274 1. 3275

004 1. 3228 1. 3230

331 1. 2179 1. 2177

313 1. 2162 1. 2163

403
for larger interplanar spacings) to the data of Chang et al. [3] for 7Sm203-4W03 (36.4 mcl % WO3) . McCarthy and Fischer [12] found a similar compound in the system H02O3-WO3 and determined its stoichiometry as Hoii+W^033 (7H02O3 • 4WO3 ) . A similar examination of part of the

systems Nd203-W03 and EU2O3-WO3 as part of the present investigation also indicated a

REii^Wi^03 3 stoichiometry. . .

All of the rare earths from Nd-Lu, Y (La-Pr were not studied) had a compound of this

stoichiometry. The powder diffraction patterns of these compounds were similar, but minor

variations caused them to be classed into three groups. The basic pattern strongly resem- bled that of the rhombohedral REgW0i2 compounds. However, there were extra weak reflections

and splitting of strong reflections which could not be indexed on a simple rhombohedral

cell. Since satisfactory indexing of all the reflections could not be obtained by the usual

trial-and-error methods, the powder data were referred to this rhombohedral pseudocell using

only unsplit, unambiguously indexed reflections in the cell parameter refinements (see table

7) . The group of REmWi^03 3 closest to rhombohedral in symmetry were RE = Er-Lu. All of the ten strong reflections (to d = 1.3 A) were unsplit and gave an excellent refinement on the

rhombohedral cell. The powder data are given in table 8. In the second group, RE = Ho, Y,

three of the strong reflections [the (214), (413), and (422)] were split and could not be

used in the refinement based on the simple rhombohedral cell. McCarthy and Fischer [12]

suggested indexing of HO]^i|Wi^03 3 based on doubling the hexagonal c^ of the rhombohedral cell

in order to account for the weak reflections and the observed splitting. However, this did

not yield a satisfactory refinement when applied to ^ii^^i^O^'i which had a sharper, stronger

pattern and better development of the weak reflections. Neither did the cell of Trunov [8] with a doubled hexagonal a^. In the Powder Diffraction File (#15-559) [7], Dr. Benjamin

Post suggested indexing for Borchardt's 15Y203*8W03 data based on the hexagonal cell a^ = 7.34 A and c^, = 9.36 A. This cell did not yield a satisfactory refinement when the weak

reflections and splitting not observed by Borchardt were included.

The third group of compounds, RE = Nd-Dy, showed a more pronounced distortion of the

basic rhombohedral symmetry in their powder patterns. Table 8 lists the powder data for

GdmWi^03 3 side by side with that of Luji^Wij03 3 . It should be noted from this table that

only four major reflections of Gd]^i^W^03 3 remain unsplit. The pseudorhombohedral cell parameters were calculated and refined from these reflections only. This explains the comparatively large standard deviations of the cell parameters listed in table 7 for RE = Nd-Dy.

3.4. RELATION OF RE^WO,^, RE^^W^O^, AND RE, ^W^O^^ TO RE 0^ ^ 6 12 10 2 21 14 4 33 n 2n-2

Borchardt [4], in communication with Professor LeRoy Eyring , was the first to report

that a RE6WO12 compound (Y5WO12) was apparently isostructural with the higher rare earth

oxides Pr70i2 and Tb70i2- Aitkan et al. [10] later confirmed that the rhombohedral

Table 7 Pseudorhombohedral Cell Parameters of

REmWij03 3 Compounds

Compound a c

NdiitWi+033 10.,055 (3) A 9.762 (6) A

Smii^WL^03 3 9,.963 (5) 9.622 (8) EU11+W1+O33 9.,902 (2) 9.598 (6) Gdi4W403 3 9..894 (4) 9.600 (4) DyittWi+033 9.,787 (2) 9.465 (3) H014W4O33 9,,748 (2) 9.402 (3) Eri4W4033 9,.735 (1) 9.347 (2) Tmi'+Wi+03 3 9,.688 (1) 9.318 (1) YbiitWitOss 9,.654 (1) 9.263 (1) LuittWit03 3 9,.635 (1) 9.238 (2) Y11+W4O33 9 .747 (2) 9.401 (3)

404
Table 8 X-Ray Powder Data of Gd]^tfW)^03 3 and LU2i^Wi^03 3 Gdi 4Wt,03 3 Lui uWt,03 3 hki, d ^ d , I d ^ d , I ._ calc obs /lo calc obs /lo

3.079

2.985

2.605

003 3. 187 187 30

075, . (a) 061

55

211 3. 067

( • 100

122 2. 681 2. 681 50

214 1. 923

{I:

927

921

14

35

410 1. 869

871

866

30

30

125 1. 646 /I. 648

644

16

14 413 1. 613

(1. 617

610

12

30

241 1. 596 1. 596 30

1.8634

1.8209

1.5943

1. 5674

1. 5545

006 1.5397

422 1.534 {t'll^ 1 1.4924

4. 49 <1

3. 73 4

3. 080 40

2. 985 100

2

.

884 ]_ 2. 768 2 2

.

605 65

2. 310 2 2. 168 1

1

.

951 2

1. 884 2

1. 8636 45

1. 8213 45

1. 7741 1

1. 6598 3

]_ ^ 6491 2

1. 5944 20

1. 5675 40

1. 5546 25

1. 5399 6

1. 4925 18 530

244 1.341 1.341 12 1.3023 1.3023 14

(a) Indicates split reflection

REgM0i2 compounds were isostructural with RE70i2' McCarthy and Fischer [12] recently suggested that RE]^ 0^2^21 REitt^^OsSf which have metal-oxygen ratios of 4:7 and 6:11 respectively, might be isostructural with "Tb^Oy" or PrgOn. Professor Eyring will report on the

structure of PrgOji and other KEj^02n-2 compounds elsewhere in these Proceedings. He recently told us of a probable isostructural relationship between REi)4Wi+033 and PrgOn [14].

3.5. RE WO^

2 6 A number of investigators have studied RE2WO5 compounds. Borchardt [16] prepared all of

the compounds for RE = Pr-Lu, Y. He did not determine the structure type but noted that the

powder patterns fell into two groups, Pr-Dy and Ho-Lu, Y. Blasse [15] also examined these

compounds and found the same two types of powder patterns. He was able to index most of the

reflections of each type on monoclinic cells typified by the examples

g Pr2W06 5.30 A 5.55 A 17.15 A 88.0°

Gd2W06 5.17 5.38 16.65 88.4

Y2WO5 5.50 5.34 15.15 88.3

Trunov et al. [8] prepared Nd2W0g , Sm2W0g , Er2W0g , and Y2W0g and reported being able to index

most reflections on the monoclinic cells, examples of which are

405
6

Sm2W0g 5.473 A 11.30 A 5.260 A 91°45'

YaWOg 5.505 16.00 5.056 91°46'

A later version of the cell parameters for the two structural types of RE2W0g compounds was reported by Pokrovskii et al. [17] . They confirmed that the structural change occurred between Dy2W0g and H02WO6 and provided monoclinic unit cell parameters for all of the compounds.

For the two examples shown above, these were

Sm2W06 16.81 A 11.27 A 5.464 A 110°39'

Y2WO6 11.35 5.333 7.589 104°26'

In a recent crystal structure determination on Nd2W05 , Polyanskaya et al. [18] and Wyant et

al. [19] described a monoclinic scheelite-related structure with the space group l2/c (No.

15) in which the Nd ions are approximately eight-coordinated and the W ions are approximately

five-coordinated

.

We prepared the RE2WO5 compounds with RE = Nd-Gd, Dy and were able to index all the observed reflections on a monoclinic cell similar to that given by Polyanskaya et al. [18]

.

The cell parameters of these compounds are given in table 9 and a typical powder pattern,

that of Dy2W05 , in table 10.

No structure determination has been performed on the second type of RE;.2W05 structure.

We prepared all of the compounds for RE = Ho-Lu, Y and noted many similarities of the strong

reflections of the powder patterns to those of the first group. However, we were unable to obtain satisfactory indexing and refinement for their complex powder patterns based on any

of the cells described above. We did obtain satisfactory indexing and cell parameter refinement on a cell even larger than any listed above by trial-and-error methods. For example,

for Y2W0g, the cell a„ = 11.010(4), b„ = 15.962(8), c„ = 10.081(4), B = 91°46(3)' satisfactorily accounted for all 42 reflections observed out to an interplanar spacing of 1.6 A. Further work on this group of compounds is in progress.

3.6. RE,W^0,„

4 3 12 Compounds of this stoichiometry are reported for RE = La-Nd only. It is emphasized in

the three studies describing these compounds [20, 21, 22] that they cannot be prepared by

sintering the appropriate RE2O3-WO3 mixtures. They have been prepared only as single crystals by hydrothermal or flux techniques. Thus, on the RE2O3-WO3 phase diagrams they may be

metastable compounds or compounds with a very limited range of stability with respect to temperature. The cell parameters of these compounds are listed in table 11. Typical powder

patterns are given for Lai^W30i5 by Timchenko et al . [20] and for PrijW30i5 by Kharchenko et

al. [21] . The structure has been described by Polyanskaya et al. [22] . Tungsten ions are 6-fold coordinated in two distinct types of octahedra, and Nd ions are 8- and 9-fold coor- dinated in three types of polyhedra. The space group is P42/nmc (No. 137) with four formula

units per unit cell.

Table 9 Cell Parameters of RE2WO5 , RE = Nd-Dy

Compound a b^ c^ 3

Nd2W06 15. 858 (4) A 11. 387 (3) A 5,.523 (2) A 91049 (1)

' Nd2W0g (a) 15. 92 11. 39 5,.508 92°

Sm2W0g 15. 731 (2) 11. 264 (1) 5..466 (1) 91°41 (1)

' EU2W0g 15. 686 (3) 11. 219 (3) 5..422 (1) 91°41 (1)

' Gd2W0g 15. 619 (4) 11. 186 (4) 5..412 (2) 91°38 (2) • Dy2W06 15. 505 (3) 11. 064 (2) 5..365 (1) 91°35 (1)

'

(a) After reference [18]

406
Table 10

hk£ dcalc d

obs I /lo

Oil 4 .83 4 .83 3 211 4 .14 4 .14 4 130 3 . 588 3 .588 7 321 3 .116 3 .117 100

J z X J . Uoo o

-3 . 059 80

J oU J . 002 3 . 002 2 All oz . o o c ^

. yoD j DR ±U1 n z

.

. yoD^

2 .985 6

,<1 J ± Z .. oj.4 2

,

. 815 3 z

,

. /OD 2

,

. 766 30

002 2,.681 2..681 25

600 2..583 2,.583 20

341 2.,208 2,.209 2 132 2..1413 2,.1412 5 512 1. 9687 1.. 9688 2 541 1. 9380 1.,9381 1 042 1. 9252 1.,9253 30

640 1. 8878^

887 602 1. 8866/1. 45

602 1. 8351 1. 8352 12

451 1. 8010)^ 8010 550 1. 8009)

1. 6 361 1. 6567)^

741 1. 6556/ 1. 656 15

361 1. 6476 1. 6477 12

Table 11

Cell Parameters of Ndt^W30i2

Compound a^, b^,

Lai+W30i5(a) 10.06 (3) A 12.63 (6) A

PritW30i5(b) 9.962 12.584

Ndi^W30i5(c) 9.92 12.50

(a) After

(b) After

(c) After

ref. [20]

ref. [21]

ref. [22]

407
3.7. RE^W^Og

The first reports of a compound of this stoichiometry were of Sin2W209 by Chang et al.

[3] and of Nd2W20g by Rode and Karpov [2] . Klevtsov et al. [23] and Borisov et al. [24]

prepared single crystals of Ce2W209 , Pr2W20g , and Nd2W209 and performed a partial structure

analysis on Pr2W209 . They found that the W ions formed deformed octahedra with oxygen which

shared edges to yield [(W209)^~] zig-zag chains and that there were two typesof Pr ions with

8- and 9-fold coordination respectively. The space group was P2;^/c (No. 14) with four

formula units per unit cell.

We attempted to synthesize all of the remaining RE2W2O9 compounds. For RE ions smaller

than Gd^"*" ( or Tb^"*" which was not studied) this stoichiometry was not stable and the products were mixtures of RE2WO5 and RE2W30i2- Based on the powder data of Nd2W20g , Sm2W209

,

EU2W2O9 , and Gd2W209 , cell parameters were refined and these are listed in table 12. A typical powder pattern, that of Nd2W20g , is given in table 13. The powder data of Sm2W209

and Nd2W20g were in good agreement with the unindexed data of Chang et al. [3] and Rode and

Karpov [2] . The unindexed powder data of Ivanova et al, [1] for La2W20g did not appear to be similar to the rest of the RE2W20g compounds.

3.8. RE2W30^2

The crystal chemistry and compound formation in this group of compounds have been studied in detail by Nassau and co-workers [25, 26]. A review of this stoichiometry by Dr. Nassau is found elsewhere in these Proceedings.

3.9. RE-W-0 System

We recently completed a study of the subsolidus phase relations and compound formation

in system Eu-W-0 [27]. In addition to the RE2O3-WO3 compounds discussed above, we found a tungsten bronze solid solution EUjj.W03 (previously reported by Ostertag [28]) and a scheelite

structure solid solution EUxWOij . This latter compound contains all Eu^"*" in its end member

EUWO14 . McCarthy and White [29] have demonstrated that it is only with europium that one is

likely to have stable lower oxidation states of the rare earths in oxide compounds prepared

at high temperatures. The bronze REj^W03 has been prepared for all of the other rare earths

with a value of x of at least 0.1. Thus, except in the vicinity of the bronze, the subsolidus phase diagrams of RE-W-0 probably consist of a series of compatibility lines connecting W metal with the appropriate RE2O3-WO3 phases described in the preceding sections.

Borchardt [4] has found this to be the case for a large portion of the system Y-W-0 sub-solidus phase relations. Near the bronze the phase relations will be more complicated and

involve the phases REj^W03 , RE2W3O12' WO2 , W^gOi^g, W2o05g, and WO3

.

4. ACKNOWLEDGMENTS

We appreciate the technical assistance of Maribeth Lovette in the last stages of this

study. This work was supported in part by the Joint Committee on Powder Diffraction

Standards

.

Table 12

Cell Parameters of RE2W2O9 Compounds

Compound

Pr2W209 (a) 7.70 9.84 9.27 105°30' (a) Nd2W209 7.638 (2) 9.829 (4) 9.218 (2) 107°32 (1)'

Sm2W20g 7.596 (3) 9.762 (4) 9.188 (3) 107°38 (2)'

EU2W2O9 7.590 (1) 9.732 (1) 9.178 (1) 107°40 (1)

Gd2W209 7.572 (2) 9.697 (3) 9.149 (3) 107°42 (2)'

(a) From ref. [24]

408
Table 13

X-Ray Powder Data of Nd2W209

calc obs

I ,^ /lo

110 5.85 5.86 10

ill 5.53 5.53 9 020 4.915 4.915 12

111 4.404;

002 4.395 ^ 4.396 2 102 4.394;\ 121 3.959 3.957 5 211 3.538 3.537 7 102

202

3.344)

3.343]

> 3.345 100

022

122

3.276]

3.276J

^ 3.275 95

112

212

3.165]

3.164/

> 3.164 95

031 • 3.071 3.071 6 221 3.003 3.001 16

130 2.988 2.987 70

131 2.942 2.941 20

220 2.926 2.926 75

113

211

2.918)

2.917j

[ 2.917 25

013 2.807 2.809 4 122

222

2.7651

2.764J^ 2.766 11

131 2.728 2.728 1 032

132

2.6261

2.626J

j> 2.626 30

213

' 2.619 2.617 10

123

221

2.595:

2.595,|- 2.595 8 023 2.517 2.516 2 311 2.463]

202 2.463 } 2.463 20

302 2.462]( 040 2.457 2.457 8 310 . 2.357 2.357 45

141

104

2.306]

2.306J

^ 2.305 2 114 2.244 2.244 14

123 2.209 2.209 3 222

322

2. 202' 2.201J

\ 2.202 8 004

202

2.198]

2.197J

^ 2.197 6 033 2.184 2.172 11

313 2.173 2,172 11

409
5. REFERENCES

[I] Ivanova, M.M. , Balagina, G.M. and Rode, E. Ya. , Izv. Akad. Nauk SSSR, Neorg. Mater.

6, 914 (1970), [Eng. Trans. 6, 801 (1970)].

[2] Rode, E. Ya. and Karpov, V.N. , Izv. Akad. Nauk SSSR, Neorg. Mater. 2, 683 (1966), [Eng.

Trans. , 2, 587 (1966) ] . [3] Chang, L.L.Y., Scroger, M.G. and Phillips, B. , J.Inorg. Nucl. Chem. 28_, 1179 (1966).

[4] Borchardt, H.J. , Inorg. Chem. 2, 170 (1963).

[5] Appleman, D.E. , Handwerker , D.S. and Evans, H.T. , Jr., Annual Meeting of the American

Crystallographic Association, Cambridge, Mass., Program pp 42-43 (1963).

[6] Chang, L.L.Y. and Phillips, Bert, Inorg. Chem. 3_/ 1792 (1964) . [7] Powder Diffraction File of the Joint Committee on Powder Diffraction Standards,

Swarthmore, Pa.

[8] Trunov, V.K. , Tyushevskaya , G.I. and Afonskii, N.S., Zh. Neorg. Khim. _13, 936 (1968)

[Eng. Trans. 13_, 491 (1968)].

[9] McCarthy, G.J., Mat. Res. Bull. 6, 31 (1971).

[10] Aitken, E.A., Bartram, S.F. and Juenke, E.F., Inorg. Chem. 3_' 949 (1964).

[II] Bartram, S.F., Inorg. Chem. 5_, 749 (1965).

[12] McCarthy, G.J. and Fischer, R.D., Mat. Res. Bull. 6_, 591 (1971).

[13] Shannon, R.D. and Prewitt, C.T., Acta Cryst. B25 , 925 (1969) and B26, 1046 (1970).

[14] Eyring, LeRoy, Personal Communication.

[15] Blasse, G. , J. Inorg. Nucl. Chem. 28_, 1488 (1966).

[16] Borchardt, H.J., J. Chem. Phys. 39_/ 504 (1963).

[17] Pokrouskii, A.N. ,Rybakov, V.K. and Trunov, V.K. , Zh. Neorg. Khim., 14_, 2344 (1969)

[Eng. Trans. 14, 1233 (1969)].

[18] Polyanskaya, T.M. , Borisov, S.V. and Belov, N.V. Dokl. Akad. Nauk. SSSR, 193 , 83 (1970)

[Eng. Trans. 15_, 636 (1971)].

[19] Wyant, J. Klevtsov, P.V., Kharchenko, L. Yu. and Polyanskaya, T.M. , Bull. Soc. Fr. Mineral. Cryst. 93_, 536 (1970).

[20] Timchenko, T.I., Petushkova, L.V., Pobedinskaya, E.A. and Pashkova, A.V. , Dokl. Akad.

Nauk SSSR, 185 , 573 (1969) [Eng. Trans. 14, 188 (1969)].

[21] Kharchenko, L. Yu. , Polyanskaya, T.M. and Klevtsov, P.V., Izv. Akad. Nauk. SSSR, Neorg.

Mater. 6, 1720 (1970). [Eng. Trans. 6, 1517 (1970)].

[22] Polyanskaya, T.M. , Borisov, S.V. and Belov, N.V., Kristallografiya 15_, 1135 (1970),

[Eng. Trans. 15, 991 (1971)].

[23] Klevtsov, P. v., Kharchenko, L. Yu. and Klevtsova, R.F., Dokl. Akad. Nauk. SSSR 176 , 575 (1967) [Eng. Trans. 12_, 851 (1968)].

[24] Borisov, S.V. and Klevtsova, R.F., Kristallografiya 15_, 38 (1970) [Eng. Trans. _15^, 28

(1970)]

.

[25] Nassau, K. , Levinstein, H.J. and Loiacano, G.M. , J. Phys. Chem. Solids 26_, 1805 (1965).

[26] Nassau, K. , Shiever, J.W. and Keve , E.T., J. Solid State Chem. 3_, 411 (1971).

[27] McCarthy, G. J., Fischer, R. D. , and Sanzgiri, J., J. Solid State Chem. (in press).

[28] Ostertag, W. , Inorg. Chem. 5_, 758 (1966).

[29] McCarthy, G.J. and White, W.B., J. Less-Common Metals, 22, 409 (1970).

410
DISCUSSION

p. Hagenmuller : We investigated in Bordeaiax some rare earth alkalir-metal-tungstates and we always found tungsten in coordination 6 or 4 in the wolframite or scheelite-like phases.

So one can suppose that your anionic siiblattice in the fluorite related structures is distorted, giving a coordination number of 6 or maybe of 4. Have you any evidence about the

surrounding of tungsten in these fluorite related structures?

G. J. McCarthy : I do not have any evidence of tungsten coordination in the fluorite rer- lated compounds based on powder d'ata^ . Structures have been determined in the case of

RE4W3O15, RE2W2O9 and RE2WO6. All of these were determined in the USSR^, and the two with

Professor Belov's^ participation are, I believe, quite good. Tungsten is in Gi-fold coordination in the first two and in approximately 5-fold coordination in RE2WO5. You don't get

4-fold coordination until the higher WO3 content RE2W3O2 2 compounds with scheelite related

structures which Dr. Nassau will talk about this afternoon.

M. J. Si enko : I believe that Tilley at Bradford*^ is studying the europium tungsten

bronzes and related systems. He is finding a series of block-type sturctures, as I recall,

with varying integral structural units put together.

G. J. McCarthy : I've been in contact with Ian McColm who is working with Tilley at

Bradford. He was quite interested in learning more about the phase relations around the

bronze composition range. I have not yet seen their crystallographic results, but I'm looking

forward to it.

^Since it is very likely that the fluorite related RE5WO12 compounds with RE=Tb-Lu,Y are

isostructural with Y5UO22 in which uranium has a regular 6-fold coordination, we can infer

that tungsten will also have regular 6-fold coordination in these compounds (see Section 3.1.C).

^References [18], [20], and [24].

^N. V. Belov, Academy of Sciences of the USSR.

'^See J. Solid State Chem. £, 199 (1971) for an article on related Sn^WOi, phases.

411

/

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

PREPARATION OF OXIDES AND RELATED COMPOUNDS BY CHEMICAL TRANSPORT

Harald Schafer

University of Miinster

Munster, GERMANY

In a temperature gradient it is possible for solids to migrate by sublimation, by

catalytic sublimation ^^^^^/^z") • dissociative sublimation and by chemical transport.

Reversible heterogeneous reactions are utilized in chemical transport. The phenomenon

is complex but can normally be treated as gaseous diffusion between spaces in which thermodynamic equilibrium has been established between solid and gaseous phases. The partial

pressure drop between these spaces is the quantity which determines the suitability of a chemical reaction for transport processes.

Information is given regarding working techniques and transport agents which have been

employed hitherto.

In further chapters there is an account of the binary oxides which have been chemically

transported up to now and there is also an account of the types of reaction used for transport.

Using zinc oxide transport as an example, a demonstration is given of the selection of

transport reactions on the basis of thermodynamic considerations.

There is a discussion of syntheses in a temperature gradient and of "solid/solid

reactions", with regard to the preparative employment of chemical transport processes.

This discussion is illustrated with several examples. There is in addition a review of the

transport of ternary compounds and of the decomposition of ternary compounds which can occur

\inder the influence of the transport agent.

Examples are given of the crystallization of metastable modifications out of the gas

phase

.

Key words: Chemical Vapor Transport; crystal growth; oxides; synthesis.

1. INTRODUCTION, PRINCIPLES

1.1. MIGRATION OF SOLIDS IN A TEMPERATURE GRADIENT

If in a reaction space there exists a temperature gradient and if in that space a solid

(or a liquid) migrates reversibly through the gas phase from point 2 to point 1 with the

temperature T2 and T^ , this can be a consequence of five distinct causes:

1.1. a. SUBLIMATION

^2(3) = l2(g) (1)

LiF(s) = LiF(g) (0.5 Li2F2(g)) ' (2)

413
l.l.b. SUBLIMATION WITH SUPRESSION OF A THERMAL BREAKDOWN

TiCl3(s) = TiCl3(g) (0.5 Ti2Cle(g)) (3)

(in the presence of TiCli^ (g)

NbCl,+ (s) = NbCl4(g) (4)

(in the presence of NbCls (g)

)

The gaseous chlorides TiCli^ or NbCls prevent the disproportionation of TiCl3 or NbCli+

,

however they are not involved in siiblimation in the thermodynamic sense.

l.l.c. CATALYTIC SUBLIMATION

There are solids in whose structure the volatile species do not occur as building

blocks at the outset, so that during transition into the gas phase it is necessary to break

atomic bonds, to rearrange atoms and to establish new atomic bonds; such solids possess

lower volatilization coefficients [l].'^ This also applies to the transition of the threedimensionally linked lattice of red phosphorus into the Pif-molecule . It has been found [2] that red phosphorus sxiblimates rapidly upon the addition of iodine. It is not a chemical

transport through phosphorus iodide which is taking place but rather a catalyzed reversible

reaction (5)

.

4 Pred = Pi+ (g) (5) (l2, PIS/

1.1. d. THERMAL DECOMPOSITION AND RECOMBINATION

(Dissociative Sublimation)

NH4Cl(s) = NH3 + HCl (6)

3SbSI(s) = Sb2S3(g) + Sbl3(g)

CdO(s) = Cd(g) + O.5O2 (8)

l.l.e. CHEMICAL TRANSPORT

(2 (2.5) lo)

Nb(s) +\ ^\ = Nbl4(g) (Nbl5(

) (9)

Ti02(s) + 2Cl2 = TiCli+ (g) + O2 (10)

ZnS(s)+ I2 = Znl2(g) + 0.5 82(5) (11)

2GaAs(s) + Gal3(g) = 3GaI (g) + 0.5 Asi^ (g)

^-^^^

1.2. DISTINGUISHING BETWEEN PROCESSES

When it is necessary to determine which of the processes 1.1. a. through l.l.e. is

operative in an observed migration of a solid, this can be accomplished on the basis of a thermodynamic calculation -- or if data is lacking, on the basis of an experimental

equilibrium investigation. In the course of making this deteirmination it will become apparent

when several processes overlap.

However, it often happens that quite simple observations supply sufficient information.

Figures in brackets indicate the literature references at the end of this paper.

414
Only the processes 1.1. a. and 1.1. d. also occur in a vacuum; the other processes require

the presence of a foreign gaseous partner.

In the processes 1.1. a. through l.l.d. the forward reaction is in each case endothermal

;

the solid is used up in the wanner zone (T2) and precipitated in the cooler zone (Ti )

.

On the other hand chemical transport is possible both with endothermal and with exothermal

processes. If in the temperature gradient a solid migrates into the warmer zone (Tj ^ T2)

then it is clearly a chemical transport which is taking place.

1.3. THE COMPLEX NATURE OF CHEMICAL TRAKISPORT AND ITS POSSIBLE SIMPLIFICATIONS

Chemical transport between points 2 and 1 having temperatures T2 and T^ requires gas

motion and a partial pressure drop P2 - Pi

.

The relationships become clear when a known gas flow transports material from an equilibrium space 2 into an equilibrium space 1. In principle this corresponds to equilibrium measurement by the flow method. If a high degree of precision is required

in the computation of transport efficiency then this procedure should be used.

Practically more important, especially for preparative purposes, is chemical transport

in closed cylindrical ampules. Here the process is complex indeed. Problems arise both in

the unambiguous description of the gas motion and in the partial pressure drop. An exact

treatment would have to take the following details into consideration:

(a) Diffusion together with its temperature dependence along the transport path.

(b) The diffusion-coupled flow of the entire gas mass, during reactions involving

molecular number change, which moves towards the side where the reaction takes

place with decreasing molecular number.

(c) Individual diffusion coefficients, whenever more than two gaseous components are present. •

(d) The flow of the entire gas mass by thermal convection with its dependence upon

tube dimensions and upon the position (inclination) of the tube in the temperature

gradient.

(e) Gas separation by thermodiffusion.

To these factors relating to the gas motion should be added those factors

affecting the partial pressure drop:

(f) In the simplest case the equilibrium pressure is established at the surface of the

solid phase. When the tube content is known and whenever only two gaseous materials

occur, the partial pressure drop P2 - Pi is unambiguously derivable from the

thermodynamic calculation.

(g) When the gas phase contains more than two substances the calculation of the gas

composition at the solid phase requires that the individual diffusion constants

be taken into consideration also in the case of equilibrium.

(h) Along the gas path homogeneous reactions can occur (I2 = 21^ ; H2S = H2 + O.5S2)

which influence the diffusion characteristics and the partial pressure drop.

In addition there are the deviations from the equilibrium case:

(i) The precipitation of the substance requires a certain supersaturation of the gas

phase.

(k) In the case of rapid gas movement the heterogeneous reaction (and not the gas

motion) becomes the factor which determines velocity.

(1) Finally in the case of small quantities of the transport agent and large surface

area of the solid, difficulties can arise. The adsorption of gas constituents

at the surface of the solid can significantly affect the given gas composition [3]

It appears hopeless to take all these effects into account exactly. But fortunately

in the practically important range of IP and T many of these effects are not substantially

significant and hence for practical purposes may be neglected:

415
(a') The diffusion is calculated for the mean temperature of the diffusion path.

(b') The one-directional flow of the total gas mass occurring in the case of reactions

with molecular number change is to be neglected whenever the diffusion formula

is applied to those varieties of molecule occurring in small concentration (and

is not applied to a principal constituent) [4]

.

(c', g') In calculations the same mean diffusion coefficient is used for all molecules.

(e' , h') One proceeds on the basis of a model which assumes that a volume element of

the gas is carried unchanged from point 2 to point 1 and reacts there.

(d') Thermal convection acquires significance only for Ep >1 atm. , when, for example,

one is working with ampules of 18 centimeter length and 2 centimeter diameter.

The effect of convection can also be easily checked experimentally: In the case

of pure diffusion the inclination of the ampule in the temperature drop is without

significance; in addition the quantity transported is proportional to the tube cross -section

.

(f, i', k') Normally at EP >10~^ atm. equilibrium pressure is established at the

solid phase with sufficient exactness. If nucleus formation has taken

place in the separating zone (or if seed crystals are assumed to be

present) then supersaturation of the gas phase need not be considered.

(1') If the solid phase does not have an unusually large surface then at total

pressures greater than 10 atmospheres adsorption will also no longer play a disturbing role.

In closing it should be emphasized that the uncertainty in the thermodynamic numerical

values is frequently of much more weight than simplifications in the calculation of the gas motion.

1.4. THE SIMPLIFIED CALCULATION OF TRANSPORT EFFICIENCY [4]

Transport experiments were frequently carried out under the following experimental

conditions

:

Ampule length 10 - 20 cm Ampule diameter < 3 cm Temperature > 600 K Total pressure, lower limit 0.001 - 0.01 atm., upper limit 1-10 atm.

Under such conditions one can proceed from the assumption, based upon available experience

with many chemical systems, that heterogeneous equilibrium exists at the solid phase and

that the gas motion by diffusion is the slowest component of displacement which contributes

to determining the velocity.

For a transport reaction

iA(s) + kB(g) = jC(g) + lD(g) + .... (13)

the molecular numbers moving between points 1 and 2 are in the ratio k: j: 1, in the

stationary state. Thus one can base the calculation upon the absolute values of each of the

partial pressure drops APg, Ap^^, Ap^ (Ap = P2 - Pi). However on account of the flow of the

entire gas phase (cf., 1.3 b, b'), connected with the diffusion, for the calculation of Ap one selects the smallest (or in any case a small) partial pressure; with Pg >> Pq thus

Pq [sic] .

The diffusion formula then gives

D q t

s R T AP„ [Mol]

(14)

416
where D is the mean diffusion constant for the given experimental conditions, q is the cross- section and s the length of the diffusion path, t is the duration of the experiment and T

is the absolute temperature of the diffusion path.

With an average diffusion coefficient for hydrogen-free systems Dq (273 K, 1 atm.) = mm^/sec

follows [4] 0.1 cm /sec. and with the introduction of the functional dependence of D upon P and T there

ep

n^ = gram molecules of transported solid phase

i,j = coefficients of the reaction equation

Apc = difference of the equilibri\am pressures (atm.).

Zp = total pressure (atm.) T = mean temperature of the diffusion path (K) q = cross-section of the diffusion path (cm^)

t' = duration of experiment (h)

s = length of the diffusion path (cm)

This simplified equation has proven to be useful for the approximate calculation of

transport efficiencies. When using another value of Dq it is only necessary to change the

numerical factor proportionately.

Evidently the quoted AP/EP is of decisive significance. In conjunction with the above

equation and with the usual experimental conditions (T = 1,000 K; q = l^ir; s = 10 cm) as well

as with the gram molecular weight of 100 for the transported solid substance, one can calculate a transport efficiency of around 1 mq/100 h, if AP/EP = 10"^, (5). This value

of AP/EP can be used generally as a practical lower limit. If significant amounts of solid

phase are to be transported over distances amounting to centimeters, then a reaction must

be selected with the aid of thermodynamic considerations for AP/EP > 10~^.

At the same time it is to be noted that EP cannot be arbitrarily lowered, because as a

2rule at Ep < (0.001 to 0.01) atm. diffusion no longer determines the velocity (cf . , 1.3 (k) (k'), and also 1.3. (1)). These considerations are applicable in the case of a transport

path (diffusion distance s) of 10 cm. If the reactions between two mingled solids are enhanced by chemical transport (Section 5.3.), then the diffusion paths in the gas space are only of the order of magnitude of 10"^ cm. Because of the proportionality between transport

efficiency and one/s there is then a lowering of the AP/EP-lirait to 10"^ x 10"^ = 10~^(!)

.

1.5. THE PARTIAL PRESSURE DROP (4)

1.5. a. THE EQUILIBRIUM POSITION

As the simplest case let us consider transport of A with the reversible reaction

A(S) + B(g) = C(g) - ' ^^gj

Everywhere in the closed tube which lies in the temperature gradient T2 - Tj , EP = Pg + Pq.

Further, we have for the partial pressure drop AP = P2 - Pi in absolute values [APgl =|APc| . If now the equilibrium (16) lies far to the left or to the right side then one of the

partial pressures and hence also AP will become very small:

"A noticeable chemical transport cannot occur at an extreme equilibrium position"

.

465-504 O - 72 - 28 417
Between these extremes there exists a maximum:

"A large transport effect is to be expected whenever a reaction is chosen for which log

Kp , , does not differ too much from zero" [4] .

This qualitative rule is useful for the selection of the reaction and is sufficient for many

purposes {cf., also Section 4). More extensive questions, such as "under what conditions

of P and T is a maximal transport rate to be expected for the selected reaction?", require

a more precise thermodynamic discussion.

1.5.b. THE SIGN OF THE REACTION ENTHALPY

From the temperature dependence of the equilibrium position it follows that exothermal

reactions transport the solid into the warmer zone -> T2 and endothermal reactions

transport it into the colder zone (T2 ^ Tj). Here the solid is always written on the left

side of the equilibrium reaction which is being considered.

I.5.C. MULTICOMPONENT SYSTEMS

Often in a given transport system only one reaction is responsible for the chemical

transport or is at least so strongly predominant that it suffices to consider this reaction

only.

In those cases in which several reactions participate to a comparable extent in the

formation of the equilibrium gas phase, the situation can be dealt with without difficulty;

for example

MeO(s) + CI2 = MeCl2(g) + 0.5 O2 (17)

MeO(s) + 2HC1 = MeCl2 (g) + H20(g) (18)

CI2 + H2O = 2HC1 + 0.5 O2 (19)

AP = AP(MeCl2) = AP(H20) + 2AP(02)

A closer view of the matter is provided by systems of the type (20) — (23)

.

Si(s) + Sil^ (g) = 2SiItt (g) endothermally (20)

Si(s) + 212(g) = Sili+ (g) exothermally (21)

Si(s) + 4Ig = Sili+ (g) exothermally (22)

l2(g) = 21(g) (23)

Here the effective AP does not come from the difference of the total Si-contents in the

spaces 1 and 2 expressed in each case by P(Sil2) + P(Silit), but from the difference of the

Si-contents P g-;^ reversibly taken up by the gas phase (and capable of being again precipitated

out of it in the case of T-change)

;

P*Si = 0.5[P(Sil2) - P(l2) - 0.5 P(I)] (24)

AP = P(Si*, T2) - P(Si*, T2) ' (25)

This expresses the fact that in the case of T-reduction only the Sil2-portion disproportionates with Si-precipitation, which is not converted into Sili^ by I2 or Ii [4] .

If both exothermal and endothermal reactions participate in the chemical transport,

then P passes with increasing temperature through a maximum or a minimum. Thus there occurs

418
a change in the transport direction in the temperature drop (T2 > Ti ) . During the Sitransport discussed above, the events are governed at lower temperatures predominantly by the

endothermal reaction (2) (T2 Ti) while at a higher temperature the exothermal reactions

(21) and (22) prevail (Ti ->- T2) [4].

For the thermodynamics of chemical transport cf. , also [5]

.

1.6. WORKING TECHNIQUE AND TRANSPORT AGENTS

If transport reactions are to furnish information regarding the controlling gas species

then a highly refined working technique is required. The ampule material (normally fused

quartz) must be heated thoroughly in high vacuum and the materials — as pure as possible — and transport agents which are employed must be introduced with particular care. All

this is superfluous for normal preparative purposes.

Preparative transport reactions are as a rule carried out in closed ampules made of

glass or quartz glass. Typical dimensions are 10-20 centimeters in length, 1-2 centimeters

in diameter. After being loaded up with the solid phase (e.g., 1 g) and with the transport

agent quantity calculated, for example, for 1 atm. at the experimental temperature, the

ampules are sealed off and heated in a tube furnace possessing two independently controllable

heating zones.

At the end of the experiment is is advisable to cool off that side of the ampule on which the initial solid s\ibstance lay. The content of the gas phase then precipitates

there and not upon the transported substance.

For further suggestions regarding the filling of the ampules, cf., [4].

In special cases ampules can be used having linings made of porcelain or of sintered

corundum or having a carbon coating. It is also possible for procelain, sintered corundum,

nickle or platinum to be used directly as ampule material.

Table 1 presents a synopsis of transport agents which have been frequently used up to now

.

Table 1

Examples of Transport Agents

X2 HX NHi+X (X = F, CI, Br, I)

HgX2 AIX3 SiXi+ NbXs

H2 H2O CO CO2

O2 S2 Se2 Te2

Frequently it is more convenient to introduce the corresponding ammonium salt in place

of HCl, HBr, HI.

When very great purity or a very precise amount of the transport agent is required,

the latter can be generated by a quantitative chemical reaction and condensed into the

transport ampule. Examples appear in Equations (27), (28); for further reactions in the

synthesis of transport agents cf., [6].

AgCl + 0.5 H2 = Ag + HCl (27)

2CuI + 0.5 O2 = CuO + I2 (28)

419

;
2. BINARY OXIDES WHICH UP TO THE PRESENT HAVE BEEN CHEMICALLY TRANSPORTED, A SYNOPSIS

In recent years numerous binary oxides have been chemically transported in situations

where the focus of interest was the production of crystals or of thin layers. Tables 2 and 3 give a qualitative synopsis (certainly not a complete one) of the present state of

this subject. With regard to each particular modification of the crystals growing out of

the gas phase (for example Ti02, Nb205) the reader must be referred to the original

literature: In addition cf . , Section 5.5. Simultaneously, the tables referred to furnish

the foundation of the next sections.

Table 2

Chemically TransDortable Binary Oxides

Li

Na

Be

Mg

K Ca Sc 0 0 Cr

Rb Sr Y El Mo

Cs Ba La Hf

Fr Ra Ac Th Pa 0

Mn Fe Co Ni Cu

Tc

Re

Ru Rh Pd Ag

Os Ir

Zn

Cd

Al

Ga

In

Si

Pt Au Hg Tl Pb

He

N 0 F Ne

P S Cl Ar

As Se Br Kr

Sn Sb Te I Xe

Po At Rn

Elements, whose oxides have been transported previously, are marked with

Table 3

Chemically Transported Binary Oxides

Oxide Transport

agent

Temperature

°C

Reference

Li20 H2O '\. 1000 [4] , BeO H2O 1500 [4] , BeO HCl 1100 ^ 800 [4] MgO H2O 'V 2000 [9] MgO HCl 1000 ^ 800 [4] , MgO CO 1700 -> 1600 [11]

B2O3 H2O 900 [12]

AI2O3 CI2 1240 ^ Tl 14]

AI2O3 HCl ^ 1100 -Tl [4] , AI2O3 H2 2000 -> Tl [4] , Ga203 I2 + s 1150 ^ 1100 [16]

In20 3 I2 + s 1150 ^ 1100 [16]

Si02 H2O hydrothermal [4] Si02 HF 200 ^ 500 [17]

Si02 TaCls 1000 [4] Si02 Tal5 ^ 1000 [4] Si02 Sil2/Sili+ 1270 ^ 1000 [4] Si02 CrCli+/Cl2 1100 ^ 900 [4] Si02 H2 1400 ^ Tl [4]

[7]

[8]

[10]

[13]

[14] [15]

[18] , [19] , [20]

420
Table 3 - continued

Oxide Transport Temperature Reference

agent °C

Ge02 roil Ge02 H2/H2O /uu ^ DbU

Sn02 H2O / U ^ IDUU

Sn02 n( L L4J / r 0/1

1

L -^4 J Sn02 HBr rn , _v Q r\ A

1 \ ^ oUU r 0

1

1^-3 J Sn02 b

Q 0 A -V m . cSUU ^ 1 2

r 0 R T Sn02 rir2 + 3 xiutxe b

rn _ _v Q A A i \ ^ oUU

Sn02 Br 2 + large amount S

Q A A rn oUU ^ 1

2

Sn02 H2 A^ AAA yuu 14J Sn02 L.U 900 L4J Te02 H2O "7 A A -V £^ A A /UU ^ bUU l^6J ,

r o"? T [Z / \ Ti02 CI2 1AAA XUUU —V^ oUU QAA r OQ

1

L -^y J Ti02 rlL- J. L4J , r "3 Ai

L 3UJ ilU2 be/ L.±2 JLUUU 1 A A n -i- ^ oUU QAA r oQ 1 L^y J Ti02 -_lxuu ^ yuu r OQ 1 HU2 T « -t- C 12 ^ b

1 1 C A -4. 11 AA XXDU ^ xxuu LXb J 112^3 n.L.± XUUU 1 nnn ^ qha yuu L j1 J Zix U2 T ^ _L C ±2 ^ XUDU 1 A c; A _i. ^ XUUU 1 A AH LX6J V2U5 rl2 n, A A dUU r TO 1

L J/

J

V8"15 1 eL-xi^ L J J J V7U13 XUDU r Qyl 1

L J4J

vg'Ji 1 1 eL-X^. XU4U TA^A -V^ QOA yzu r 0 R

1

V5U9 rod Li6J V4O7 TeClt^. 1050 [34]

TAylA _v AOA iU4U ^ ^J.u [35]

Kb20 5 CI2 1000 Ti r 0 "7

1

L37 j Nb2 0 5

A^ T AAA -> rn , XUUU ^ i

I

Tool L38J , [37] , r "5 A T

- [39]

iND2U 5 CI2 + Te 1 AAA ^ OAA XUUU oUU r /I A

1

L40J

Ml-, _ n 1- iNiJ2 5

( 12 + NDLX5 A . T A A A —V m a ^ ±UUU ^ il L3yj , r / 1 1 r /I 0

1

, L42J

1NJJ2 5

" XUUU ^ X^ [41] , l4J ,

r / 0 1 NbOo *^^2 c-v • 5 X NbBrs " XUUU r /I 0

1

[4]

i>*j-»u^

. 5-x NDi 5 boU ^ DDU [4] ,

r 0 Q

1

[39] ,

r /I 0 1

L'i'i J NbOp uru NbCl5/NbOCl3 1250 Ti L rt J NbO2.it 17 Nbl5 920 840 [461

(Nbn oOoq)! 74n fiSn r47i LI / J Nb02 lo 1000 [471 r4i

rjDU I2 QCA -V 11AA you ^ XXUU 14 / J , r/11 [4 J Ta2 05 CI2 QAA -i. *7 A A yuu ^ /uu L4J Ta2 05 HCl 1000 600 [4] Ta2 05 TaCls 750 550 [48] , [4] ia2U5 OAA yuu -V^ '7 A A /uu L4J ur2U3 02 *s 1 AAA ^ XUUU r/i 1 14 J (_r2U3 CI2 OAA C A A oUU ^ bUU

you ^ odu

r 0 Q

1

L3y J

(-r2U3 CI2 + ^2 OAA A A oOO 600 r[49] >i m

Lr2U3 Br2 ; Br2 + O2 800 600 r /I n 1 149 J vio u 3 n2U 'Vj 700 14J , r c A

1

L->OJ M0O3 CI2 500 400 [51]

riOU2 I2 1000 800 r y1 A 1 [49] , [52] ,

- [53 j WU3 H2O 1100 Tl [4] ,

r c A

1

[50]

WU3 CI2 T AAA AAA 1000 ^ 900 [54]

T*7n WU3 HCl 1000 900 [4] , [54] , reel [55]

WU3 CCli| 700 [34]

W20O58 HCl 900 [56]

W18O49 I2 + H2O 900 ^ 800 [58]

W4O1

1

H2O (+ H2) 1000 ^ Tl [4] WO2 H2O (+ H2) 1000 ^ Tl [4]

421
Table 3 - continued

Oxide Transport

agent

Temperature

°C Reference

W02 1000 - 800 [57] , [58] , wo 2 HCl ^ 900 [56]

Clo 980 -> 860 r391 CI2 + O2 800 -> 600 [591

Mn ^ Oll HCl 1000 ^ 800 [10] , [60]

MnO HCl 980 900 [41 . [391

j\c2>-' / HoO (+ Oo) 180 ^ Tl [611 To 400 ^ 370 [621 [631 , Re02 To2 700 -> 600 [631

r e2>-'3 Clo 980 -> 860 [41 , [391 Feo 0 a HCl 300 400 [65]

Fgo 0 0 HCl 1000 800 [4] Feo 0 0 HBr 600 [25]

Fe -jOi. HCl 1000 -> 800 [4] , [66] , FeO HCl [4] RUO2 Oou2 1280 ^- Tl [41 , [681

OSO2 Oo 960 900 [4] , [69] , COQ Oli HCl 900 -> 700 [60]

Clo 980 ^ 860 [39]

CoO C15 1000 - 900 [39]

CoO HCl 970 ^- 900 [39]

Ir02 Oo 1100 ^' 900 [4] Ir02 C12 + 02 900 Tl [72]

NiO Clo 980 -> 860 [39]

NiO Bro 930 Tl [73]

NiO HCl 930 -> Tl [73] , [10] , NiO HBr 940 -> 915 [73]

CuO HCl 800 ^- 700 [74]

Cu2 0 HCl 600 > 900 [4] CU2O HCl 1100 ' 900 [4] ZnO Ho"Z [75]

ZnO rio 1000 -' 800 [761 , [291 , ZnO ny L,J.2 1000 - 800 [291 , [61 ZnO HCl 1005 -- 935 [39] , [29]

ZnO Bro 1010 990 [77]

ZnO lo 800 700 [78]

CdO l2 540 -> 510 [46] , [39]

760 700 [79] . [78]

U3O8 O2 > 1300 [80] , [81]

U3U8 1000 850 LoZ J UltOg HCl 1000 -> 850 [82]

UO2 HCl; Br2;

Br2 + S 1000 -- 850 [82]

The arrow indicates the transport direction in1 the T-drop. To the ext

[52]

[64]

[67]

[70] , [71]

[39]

action has already been covered in [4] , the reader is referred to the original literature

cited there.

TYPES OF REACTION

The transport aaent is highly volatile and transforms the solid, which is to be

transported, reversibly into volatile reaction products.

Frequently employed transport agents are listed in table 1 (Section 1.6.). Further

variations are possible particularly in the case of the metallic halides.

The following, naturally incomplete, picture (for literature citations cf., table 3) is the result of an attempt to make it possible to survey the quite disparate reaction

types employed for chemical transport from a unified point of view.

422
3.1. THE FORMATION OF VOLATILE ELEMENTS OR SUB-COMPOUNDS

The reactions (29) through (31) give examples.

MgO(s) + CO = Mg(g) + CO2; 1700 -> 1600 °C (29)

Al203 (s) + 2H2 = Al20(g) + 2H2O; 2000 °C -> Ti (30)

Si02(s) + H2 = SiO(g) + H2O; 1400 °C -> T2 , (31)

Such transport processes reauire relatively high temperatures which however are still

substantially lower than those of a comparable purely thermal volatilization of the solids.

3.2. THE FORMATION OF VOLATILE COMPOUNDS WITH NORMAL OR HIGHER OXIDATION STATES

The volatility of the MeX^ compounds increases with the magnitude of n. This is a consequence of the diminution of the crystal lattice bonding with increasing n and of the

simultaneously increasing screening of Me by the X ligands in the gas molecule. For this reason in chemical transport the formation of compounds with monovalent ligands (halides)

is frequently a controlling factor. If gaseous oxide-halides or oxides are formed then

for the same reason these are, as a rule, of a type having a higher Me oxidation state.

32)

Examples:

Mn203(g) + 2CI2 = 2MnCl2 (g) + 1.5 O2

NiO(g) + 2HBr = NiBr2 (g) + H2O (33)

(34)

(35)

(36)

CdO(s) + I2 = Cdl2(g) + 0.5 O2 -

Fe203 (s) + 6HC1 = 2FeCl3 (g) + 3H2O

Si02(s) + 4HF = SiFit + 2H2O

Si02(s) + 2TaCl5(g) = SiCli+ + 2TaOCl3 (g)

(37)

NbO(s) + I.5I2 = NbOl3(g) (38)

1^12029 (3) + 19NbCl5(g) = 29NbOCl3 (g) + 2NbClit (g) (39)

(40)

Ta205(s) + 3TaCl5(g) = 5TaOCl3

2Cr203 (s) + 5Cl2 = 3Cr02Cl2(g) + CrCli^ (g)

Mo03(s) + CI2 = Mo02Cl2(g) + 0.5 O2

WO2 (s) + I2 = WO2I2 (g)

Mo03(s) + H2O = Mo02(0H)2(g)

Re207(g) + H2O = 2Re03 (OH) (g)

0s02(s) + OsOit(g) = 20s03(g)

Ir02(s) + 0.5 O2 = Ir03(g)

3.3. THE COMBINATION OF TRANSPORT AGENTS

(41)

(42)

(43)

(44)

(45)

(46)

(47)

The heterogeneous reactions become relatively complicated whenever, for stoichiometric

reasons, gaseous compounds must arise havina various oxidation numbers: cf . , (eq. 39,41).

423
If in the contemplated system there exists onlq one gaseous compound of the metal which

is under consideration then it must be made possible to control the oxidation number by means of the simultaneous use of several transport acjents: (eq. 48) .

Wl80i+9(s) + + 13H2 = 18W02l2(g) + 13H20 (48)

It can also be particularly useful to improve the equilibrium position in a thermodynamically

predictable manner by means of added supplements; (eq. 49 through 51) ; also cf. , [4]

.

Si02(s) + CI2 + CrCl4(g) = SiCl4(g) + Cr02Cl2 (g) (49)

Zr02(s) + 2I2 + 0.5 S2(g) = Zrli, (gj + SO2 (50)

Cr203(s) + 2Cl2 + 0.5 O2 = 2Cr02Cl2 (g) (51)

In the transport of Ti02 with CI2 the addition of Te proved to be especially favorable.

However, we still have no clear picture of the gaseous species (Te02, TeOCl2?)

.

3.4. UNEXPECTED TRANSPORT PHENOMENA

As a rule one knows the gas molecules which lie at the basis of the observed transport

processes. However, it happens repeatedly that an observed transport effect is not interpretable by means of known gas molecules. If the transport effect persists when the

experiments are carried out with a thorough exclusion of impurities suspected of being

transport agents (water from the wall of the quartz ampule!), then a more detailed

experimental thermodynamic investigation would be desirable. For example it was in such a way that it became known that the molecule which is essential for the functioning of the

iodine lamp is not tungsten iodide but is the oxide iodide W02l2- This led to the transport

of WO2 with I2 on the basis of (eq. 43)

.

For the transport reactions of M0O2 and Re0 3 with I2 the gaseous oxide iodides M0O2I2

and ReOsI were, from the outset, assumed to be of controlling importance. In support of

this assumption there is the sequence:

NbOl3 M0O2I2

WO2I2 RsObI

and the fact that corresponding oxide-bromides and oxide-chlorides (M0O2CI2, Mo02Br2,

ReOaCl, Re03Br) are known. These ideas have been confirmed by the most recent measurements

[53] made in the case of chemical transport of M0O2 with I2

.

It is not unusual to find that, of the higher halides and oxide-halides of a metal,

the one possessing the heavier halogen is, to be sure, no longer stable in the solid state,

but certainly occurs in considerable concentrations in the gas phase (CrCli+ , Fel3).

Some more examples of unexpected transport phenomena are:

Numerous metallic sulphides were transported in the presence of high sulphur pressures

[83] , with the controlling molecule as yet unidentified.

^^^^3(s) transported by AI2CI6 (g) . The equilibrium study which was carried out in

investigation of this phenomenon led to the discovery of the gas molecule (CrCla • 3 AlCX-s)

[84], [85].

4. THE SELECTION OF TRANSPORT REACTIONS, ILLUSTRATED BY THE EXAMPLE OF ZINC OXIDE

For the transport of zinc oxide, all those eQuilibrium reactions are to be discussed

in which, besides the solid ZnO, only gaseous reaction partners participate. The only Zn- containing gas species having sufficient thermal stability are Zn and ZnX2 (X=halogen)

.

Thus it is only in this form that the zinc can migrate through the gas phase. Hence, we

424
have the followincr reaction eauations:

ZnO + H2 = Zn(g) + H2O

(g)

(52)

ZnO + CO = Zn(g) + CO2 (53)

(g) + 0.5 O2 (X = CI, Br, I) (54)

ZnO + 2HX = ZnX2(g) + H20(g) (55)

ZnO + HgCl2(g) = ZnClz (g) + Hg(g) + 0.5 O2 ^^^>

Further selection takes place on the basis of thermodynamic considerations.

At a given total pressure the transport rate is proportional to the partial pressure

drop: AP = P2 - Pi (Section 1.4.). Of course the magnitude of AP is not equally critical

for every preparative purpose.

In the case of powder reactions (section 5.3.) having transport distances of the order

of 1 - lOOy, very small values of AP suffice (cf . , section 1.4.). In the case of syntheses

in the temperature drop (section 5.2.) or in the case of the production of small crystals

the selection of a larqe value of AP is necessary if the reaction times are to remain within

limits and for growinq large crystals the selection of the maximum AP is especially important — a fact which nevertheless has evidently not been sufficiently taken into account up to

the present. This topic will be discussed in a later paper.

According to section 1.5., AP is large whenever log Kp for the transporting reaction

lies near zero. Thus in selecting the transporting reaction, one first studies the

equilibrium position and its dependence upon temperature. Figure 1 provides data in this

connection

.

Since one has to stay above the condensation temperature of zinc or of zinc halide

and on the other hand, to avoid attacking the quartz, an unnecessary high temperature should

be avoided, it is desirable to set the temperature region, in which ZnO is to migrate

through the gas phase, at 1,000/900 °C. Then, referring to figure 1, one can make the

following statements

:

The saturation pressure of the solid ZnO is so low that it can be ignored. The

dissociative sublimation of the zinc oxide requires higher temperatures.

With log Kp ranging between -2 and 0 for the corresponding reactions, I2, CO, H2 , and

HgCl2 are suitable transport agents for ZnO, with the special suitability of HgCl2 deserving

particular emphasis.

In reactions having positive values of log Kp it should be taken into consideration

that the saturation pressure of the fluid zinc halide ought not to be exceeded (ZnCl2 boils

at 1005 K, 1 atm) . Hence one selects a total pressure which is not too high.

Of the remaining transport agents, Br2 and HCl are especially suitable. However, CI2

is also usable, as corresponding experiments have confirmed.

The use of HBr as a transport agent leads to an exothermal reaction (AH° = -5.4 kcal)

.

Hence transport into the warmer zone is to be expected. But because of the quite large value

of log Kp the transport properties are not favorable.

These qualitative statements made on the basis of figure 1 are sufficient within our present context. They are confirmed by a more extensive quantitative treatment, in which,

at the total pressure prescribed by the condition Ep = 1 atm., a calculation is made of the

gas composition and of the magnitude of AP(Zn) or AP(ZnX2).

425
-15 -

1000 soo-c

1300 1200 1100 1000 900 800 °K

0.7 0.8 0.9 1.0 1.2 1.3 1.4 lOOO/T

Fig. 1. Equilibria with ZnO as solid phase. Kp refers to the reaction of 1 Mol ZnO.

5. PREPARATIVE USE OF CHEMICAL TRANSPORT

5.1. SYNOPSIS

In the basic process of chemical transport the solid which is initially introduced is

chemically identical with the transported material which is precipitated out of the gas

phase. This process is suitable for, e.g., crystal growing.

The combination of chemical transport with other processes gives rise to many preparative

possibilities. Here chemical transport generally has the effect of furthering equilibration

or in other words of promoting the fomation of the thermodynamically stable solid phase

(for a limitation cf . , section 5.5.). The latter, at no particular expense, will usually

contain crystals suitable for x^ray purposes.

One can classify the applications of chemical transport in the following way:

A. Crystal growing, precipitation of thin layers

\^

B. Purification of solids {cf . , van Arkel-method, and also [4], [86], [87a]

C. Doping of solids

D. Promotion of syntheses (solid + gas) in a temperature gradient [4] , [86]

426
E. Promotion of reactions between solids [4], [86]

(a) Partial transport of one component only (e.g., of oxygen)

(b) Transport of one solid partner only

(c) Transport of the reaction product

(d)

It Production of closely adjacent phases (Hagg-Magneli-phases)

;

a buffered gas phase

: transport using

(e) Production of mixed crystals [86]

F. Synthesis with spatially separate precipitation of reaction products [5]

G. Transport of ternary compounds

H. Precipitation of metastable modifications

Of these niomerous possibilities only D, E(c) , G and H will be discussed in further

detail in what follows:

5.2. PROMOTION OF SYNTHESES (SOLID + GAS) IN A TEMPERATURE GRADIENT

During reactions of solids with gases (e.g., O2 , S2) the reaction product often forms

a surface layer which delays the progress of the reaction. With the aid of a transport

agent, the reaction product can be transported away and, at another location in the reaction

space, be precipitated in crystals (normally at a lower temperature). In this way the reaction

is at the same time substantially accelerated. Examples:

Iridium oxide is formed when iridium is heated at 1000 °C in oxygen (1 atm) . The Ir02-

surface layer much impedes the reaction. But if the reaction is carried out under transport

conditions then Ir02 precipitates out of the gas phase separately from the Ir and the

reaction is complete [4], [86a]. Here oxygen itself has the effect of a transport agent.

The behavior may be described by means of the processes (57) and (58) , that is to say by

Ir02-formation and transport-away.

Ir + O2 = Ir02 (s) (57)

Ir02(s) + 0-5 O2 = Ir03(g) (58)

If one is v/orking at a temperature of the iridium which is so high that an Ir02 -surface layer

is not stable at O2 = 1 atm. , then the reaction sequence is (59) , (60) .

Ir + 1.5 O2 = Ir03(g), T2 1150 °C (59)

Ir03(g) = Ir02(s) + 0.5 O2 , Tj 1000 °C (60)

The situation is similar in the case of synthesis of ruthenium dioxide [4] , [68]

.

Likewise, in the reaction of excess tungsten with oxygen in a sealed tube with formation

of the dioxide, the transport of WO2 with I2 (1000 ^ 800 °C) is advantageous [29]

.

The oxides Re02 and ReO^ are obtained as crystals if the synthesis out of elements in

the sealed tube is combined with transport by means of iodine - [63] ; cf., also table 3.

Also in the case of synthesis of sulfides , selenides and tellurides the reaction-layer

formed on the metallic grain or on the molten metal ( ! ) can severely impede the course of

the reaction. Hence the removal of the chalcogenide layer by means of iodine decidedly

accelerates the course of the reaction. Comparative observations of this sort exist with and

without addition of I2 as a transport aaent in the synthesis of ZnS, ZnSe , CdS , CdSe, AI2S3,

Al2Se3 and CrTe [4] , [86]

.

Syntheses of binary, ternary and quaternary chalcogenides from the elements, with iodine

being added, were carried out primarily by Nitsche and co-workers [87] , [88] , [89]

.

427

/
The addition of a transport aaent has a similarly favorable effect, for example, in the

synthesis of metallic arsenides out of the elements.

In general it is possible in the presence of the transport agent, on account of the

reversibiliti) and mobility which it creates, to combine the most conveniently accessible

materials, e.g., the elements, into the desired stable compound.

5.3. PROMOTION OF SOLID/SOLID REACTIONS [4], [86]

The recombination of two solids by heating the aggregate of the powdered components is

the classical preparative procedure of solid state chemistry. It still plays an important

role today although it exhibits clearly recognizable disadvantages:

(a) Diffusion in the solid state requires time and high temperatures.

(b) Diffusion must take place over just a few "contact-bridges" between the grains.

Because of the volume reduction which normally occurs during the reaction, this

contact becomes steadily worse as the reaction progresses.

(c) Such reactions possess no selective mechanism. Contaminants which have been

brought in with the initially introduced material or by reaction with the wall

of the vessel, remain in the reaction product.

(d) Because of the absence of selectivity, chemical analysis of the products has

scarcely any demonstrative value since one finally recovers only the aggregates

of material which have been used.

By the addition of a transport agent these difficulties can be overcome. Even when

only one of the initially introduced materials (e.g., the material A) is chemically transportable, the reaction is substantially accelerated. The non-transportable substance B is

then to some extent heated in a gaseous solution of A. For this the entire surface of B is

available for the reaction. Mechanical contact bridges are no longer a bottle-neck and in

fact a mechanical contact between A and B is no longer required.

Still more favorable is the frequently occurring case in which A, B and the product

AxBy are transportable. In this situation all the above named difficulties (a, b, c, d) are overcome. The reaction product is precipitated out of the gas phase as pure crystals.

The combination of two binary compounds into a ternarv as for example occurs in the

preparation of spinels or of ternary sulfides can be carried out in the same working

procedure along with the chemical transport. Thus if it is desired to secure crystals of

the ternary compound the preliminary synthesis of this compound by another route (e.g.,

by means of a pure solid/solid reaction) is not necessary.

Table 4 shows examples of reactions of oxides carried out in the presence of transport

agents. The table is in no sense complete. Thus for example the closely neighboring phases

("Hagg-Magneli phases") occurring between Nb02 and Nb205 are obtainable in crystalline form

by the reaction of Nb205 with Nb or a lower oxide in the presence of a transport agent (cf .

,

table 3) . The members of the analogous family of the vanadium oxides are attainable in

crystalline form from V2O5 and a lower oxide in the presence of the transport agent TeCli^

(cf . , table 3)

.

The same principle of synthesis is also used with other classes of compounds.

During the investigation of multi-component systems with determination of the phases

occurring in the sub-solid domain, the promotion of equilibration by addition of a transport

agent is an essential help [100]

.

5.4. THERMODYNAMIC CONSIDERATIONS RELATED TO THE TRANSPORT OF TERNARY COMPOUNDS

If two solids A and B exist side by side then they compete for the transport agent X. In consequence the transport of A and B is modified in a predictable way in contrast to the

isolated transport of these substances. If the solid compound A^B^ is formed in addition, then

from the thermodynamic point of view very different situations can arise.

428
Table 4

Reactions of Oxides in the Presence of Transport Agents

Temperatures Around 1000 °C

Starting Product Transport Reference

Material Agent

Nb + Nb205 NbO CI2 [4] Nb + Nb205 NbO I2 [4] Nb + Nb205 Nb02 l2 [47]

W + WO3 WO 2 I2 + H2O [58]

Ti + Si02 Ti203 + TiSi TiCl3 [4] V + Si02 VO + V3Si l2 [90]

Nb + Si02 NbO + Nb5Si3 H2 [4] Nb + Si02 NbO + Nb5Si3 l2

Ta + Si02 Ta205 + Ta2Si l2 [4] Ta + Si02 Ta205 + Ta2Si TaCls [4] TiO + Til2 + B2O3 TiBOs H2O (HI) [91]

V2O5 + V + B2O3 VBO3 H2O, HCl [91]

Cr203 + B2O3 CrB03 H2O, HCl [91]

MgO + Cr2 03 MgCr2 0[+ O2 [4] MeO + Cr2 03 - MeCr2 0it CI2 [92]

(Me = Mn, Co, Ni)

NiO + Cr2 03 NiCr20it O2 [4] MeO + Fe203 MeFe2 0i+ (Me = Mn, Ni, Co) HCl [93]

(Me = Mg, Co, Ni, Zn) HCl, CI2 [94]

NiO + Fe203 NiFe20it HCl [95]

CoO + Si02 Co2Si0it HF [96]

FeO + Ge02 FeGe03 NHt+Cl [97]

CaO + Sn02 Ca2SnOi+ H2, CO [4] SrO + Sn02 - SrSnOs H2, CO [4] MeO + Sn02 Me2SnOi+ NHttCl [98]

(Me = Mn, Co, Zn)

CoO + Sn02 Co2Sn0it CI2 [92]

MeO + Ti02 MeTi03 CI 2 [92]

(Me = Mg, Ni)

Me203 + Nb205 MeNbOit CI2 + NbCls [39]

(Me = Cr, Fe)

MeO + Nb205 MeNb205 [39]

(Me = Co, Ni, Ca) CI2

(Me = Fe, Mn) CI2 + NbCls

(Me = Mg, Zn) HCl

Me205 + Nb205 Me (Nb902 5) CI 2 (+NbCl5) [92]

(Me = V, As)

Ge02 + Nb205 Ge02 • 9 Nb205 CI2 [92]

Me203 + Ta205 MeTaOtt Cl2(+ TaCls) [92]

(Me = Fe, Cr)

MeO + Ta2 05 MeTa2 06 Cl2(+ TaCl5) [92]

(Me = Mg, Mn, Co, Ni)

MeO + M0O3 Me M0O14 CI2 [92]

(Me = Mg , Mn , Co

,

Ni)

MeO + WO3 MeWOi+ CI2 [92]

(Me = Mg, Mn, Fe, Co, Ni, Zn)

FeO + WO3 FeWOtt HCl [4] Fe203 + Cr203 Me203 - mixed cryst.

CI2 [92]

Th02 + U3O3 Me02 - mixed cryst.

O2 [99]

ZnO + MnO + Fe203 (Zn, Mn) Fe20n HCl [25]

429
It frequently happens that ternary compounds are transportable when this is true,

under the same circumstances, for the isolated binary compounds. This means that the free

enthalpy of formation for the process aA(s) + bB(s) ^ AaBb(s) is not large. If this is not

so then different cases are conceivable:

Transport of the ternary compound can occur although the same is not true for one or both components because for these the transport equilibrium lies too far to the right.

Transport of the ternary compound can fail to occur (or be very much diminished)

although both components are in themselves transportable. In this case the transporting

equilibrium has been pushed too strongly to the left by the exothermal compound formation.

Emmenegger [92] has already discussed qualitative ideas of this sort. Such situations

are to be treated quantitatively according to the usual rules of chemical transport on the

principle of heterogeneous equilibria. This applies also to the somewhat more complicated

question which inquires under what circumstances the reaction of the phase A^Bj-, — in itself

thermodynamically stable — with the transport agent leads to precipitation of one of the

components A or B. There exist familiar examples of this: In the attempt to transport

CuFe20i+ with CI2 , CuO precipitated in the colder zone while Fe203 remained in the warmer

zone as a residue [101]. The analogous experiment with garnet Y3Fe50i2 and HCl as the

transport agent leads to Y203-precipitation in the warmer zone [102], cf . , also [95].

Wehmeier [102] has already studied this question. The solution which he suggests is in

principle as follows:

One considers the equilibria (61) and (62) (for simplicity formulated without stoichiometric coefficients) for the given temperature and the selected mixture in the reaction

chamber.

AB(S) + 2X(g) = AX(g) + BX(g) = Kg 1 (61)

B(s) + X(g) = BX(g) : K62 (62)

With the equilibrium pressures of (61) one calculates the K52-analogous expression Q61,62 =

Pg 1 (BX) /Pg 1 (X) . With Qgi,62 > K52 the component B(s) precipitates, together with AB(s),

under the influence of the transport agent.

The analogous statement is valid for the precipitation of A(g).

In the extreme case the reaction can lead to complete consumption of ABj^^ , (eq. (63))

^(s) ^ ^(g) = ^(g) ^ ^(s)

Naturally this also depends upon the amounts of the solid phase and of the transport agent

which are used.

The following considerations are likewise of interest:

(a) By addition of AX(g) to the system (61) the decomposition of AB(g) can be

repressed. Example:

Addition of FeCl3 in the transport of Y3Fe50i2 [102].

(b) It can suffice (!) to use an increased AB - initial amount and an increased amount

of the transport agent. Then a portion of AB(s) is used, with precipitation of

B(g) , in the construction of the equilibrium gas phase; however the remaining

portion of AB^gj can be chemically transported.

(c) During decomposition of AB(3) under the influence of the transport agent it is

nevertheless possible, after sufficient transport duration, for AB^gj to exist at

Ti:

Step 1 AB(g) + X(g) = AX(g) + Bfg) T! ^ (64)

Step 2 AX(g) = A(s) + X(g) at Tj (65)

430
This process proceeds until there is no more AB(s) present at T2 : One then has A(s) at Ti

and B(s) at T2.

Step 3 Now the B-transport begins, T2 T2

^(s)+ = BX(g) at Tj (66)

Step 4 Re-formation of AB(g)

A(s) + BX(g) = AB(3) + X(g) at Ti (67)

Steps 3 and 4 are not compulsory. It can also happen that the process comes to a stop

after Step 2 because the equilibrium gas generated by the presence of A(s) at T^ interferes with the B-transport. In such a case one could achieve renewed formation

of AB(s) by an advance provision of B(s) in the zone with Ti . Of course it would not

be possible to grow crystals by this method.

(d) The possibly advantageous transition to another transport agent or the use of

an additional transport agent for B^^j were not included in the considerations of

the present study. In addition it was assumed that the simultaneous presence of

A, B and X does not lead to the formation of new gas molecules. As a rule this is

the case but for the system Cu/Fe/Cl the possibility should not be excluded.

Quantitative statements can likewise be attained regarding the effectiveness of the arrangements (a) or (b) and regarding the stable solid phase in zones 1 and 2 of a transport tiibe. They can be derived from the calculation of the composition of the gas phase over the solid

phase AB(3) and B(g) at the temperatures and T2 and at constant total pressure in the tube

Such a computation will not be carried out here because the thermochemistry of the two systems which are familiar along these lines CuO/Fe203 and Y203/Fe203 is still too uncertain.

5.5. PRECIPITATION OF METASTABLE SUBSTANCES

In the ideal model chemical transport by gas motion between equilibrium regions is

described. In the practical case this model is valid to a degree of approximation which is

sufficiently good for the thermodynamic calculation to constitute a basis for the selection

of transporting systems and for determining transport rates. In addition the mobility

provided by the transport aaent favors recrystallization (mineralizer effect [4] ) and leads

to a transition of the solid phase into the thermodynamically stable state. Also useful,

during investigation of phase diagrams, is the decided improvement — due to transport agents — of the equilibration in the sub-solid region [100]

.

Naturally, the equilibration becomes all the more difficult the less the solid phases

differ from one another in energv content. Under such circumstances, even in the presence

of a transport agent a longer isothermal tempering can be required for the formation of the

stable phase -- as has appeared in the case of the Nb205-modif ications [41]

.

In such systems, durinq normal transport experiments in the temperature drop, the

precipitation of metastable modifications is also possible. The following review presents

examples of polymorphisms.

^^2^5' numerous modifications of Nb205 those designated by the letters B, H, M, N,

P, R, and T can be obtained by chemical transport in crystalline form [41] , [38] . H-Nb205

is thermodynamically stable at temperatures > 700 (j^ 50 °C) . Below this temperature the

B-form is stable. Ah (transformation H-Nb205 B-Nb205) ^ -2 kcal [41] . The other

modifications, so far as we know up to the present, are metastable.

In our experiments [41] powdered H-Nb205 served as the initially introduced substance.

However the modification of the initial substance was without effect upon the transported

product. The following is a synopsis of the formation conditions

:

B-Nb^O^: (a) Transport with NbCls + CI2 , 850 ^ 750 °C; often in a mixture with the modifications N and P [41]

.

431

;
(b) Transport with Nbis (700 550 °C)

NbCls (1000 ^ 700 °C) or

[42a]

(c) Transport with HCl or HCl + CI2 or CI2 + H2O;

750 -> 700 °C [37] : H-Nb^O^: Transport with NbCls + CI2 , 1100 1000 °C [41], [37].

M-Nb^O^: (a) Transport with NbCls + CI2 1000 -> 800 °C

in a mixture with the H-fonn [41]

.

(b) Transport with NbCl 5 + CI2, 970 ^ 860 °C

in the presence of Sn0 2, which strongly promotes the formation of the M-form,

without the incorporation of significant amounts of Sn - [37].

N-Nb^O^: Transport with NbClj + CI2 , 940 ^ 840 °C, in a mixture with the modifications M

and H. The addition of a small amount of F~ (as Nb02F) strongly promotes the

formation of the N-form [41]

.

P-Nb 0 : Transport with CI2 + H2O, 800 ^ 600 °C; then the P-form is markedly preferred

[41], [37].

R-Nb 0 : (a) Transport with HCl, 800 ^ 600 °C, besides P, at times also besides B- and

T-Nb205 [38].

(b) R-Nb205 was also observed in transport with NbCls/NbOCls besides other

modifications. Slight additions of Nb02-F appear to promote the formation

of the R-modifi cation [38]

.

T-Nb^O^: (a) Transport with NbCls + CI2, 890 ^ 835 °C. As a rule besides B- and N-Nb205.

Nucleus selection is possible [41]

.

(b) Transport with CI2 , 850 ^ 750 °C, in a mixture with P-Nb205 [37].

riO^. Rutile is the modification which is thermodynamically stable at all temperatures.

Rutile was obtained (without admixture of anatase) with TeCli^ (or CI2 + Te) as the

transport agent at 1100 900 °C [28] . At 1000 -> 800 °C rutile precipitated in one part

of the experiment but in others rutile with anatase was precipitated [29]

.

Anatase without admixture of rutile precipitated with CI2 as the transport agent at 1000

800 °C. [28], [29]. However, under comparable conditions both modifications often appeared

together [29]

.

Mixtures of Rutile and anatase were obtained in many experiments (1000 -y 800 °C; 900 700 °C) with CI2, CI2 + S, CI2 + Se, CI2 + Te, CI2 + P, CI2 + C as transport agents [2

Brookite has not yet been observed in transport experiments.

ZnS . By transport with iodine below 1000 °C, e.g. , at 850 750 °C pure cyrstals of zinc

blend are obtained but at 1170 -> 1150 °C crystals of wurtzite were obtained [100] , [88]

.

Ah (transformation, wurtzite -> zinc blend) = -3 kcal. Possibly wurtzite is the stable high

temperature form.

In Se . Of four modifications, three are producible in crystalline form by transport with

I2 [103].

NbS . Two polymorphic modifications (2s and 3s) were obtained by transport with I2 at

different temperatures [104]

Taking into consideration that this is not very extensive observational data, one reaches the following conclusions:

432
In the transport experiments with Nb205 and with Ti02 the metastability is manifested by

the simultaneous occurrence of several modifications.

In all cases the difference in energy content of the occurring modifications is small,

In consequence nucleus formation and nucleus growth acquire significance.

Even at transformation heats of 8 kcal/Mol(Y a-FeaOs) and 15 kcal/Mol (y ^ a-Al203)

chemical transport produces only the thermodynamically stable modification. Transport

experiments specially conducted to obtain y -Fe203-crystals always produced ct-Fe203 [94]

.

In general one can expect the preparatively — and of course also structurally —

interesting metastable modifications to have the highest probability of occurrence when

the energy difference is small in comparison with the stable phase and when the precipitation

temperature is made as low as possible. It would also be possible for transport under

conditions of non-equilibrium, e.g., at small total pressure, to promote the formation of

metastable modifications. However there exists no data on this subject.

If several modifications occur together then as a rule they can be easily separated

mechanically because of the size of the crystals.

In addition there exists the possibility of promoting the formation of metastable

modifications by the selection of other transport agents {cf . , the case of Ti02) or by

additions to the transporting system [cf . , Nb205 , addition of Sn02 , F) . Here to be sure

one is dependent upon empirical experiments. Certainly in the cases which have been

mentioned, owing to the small amount of incorporated foreign material aagregates, one is

not dealing with a stabilization in the thermodynamic sense but with a kinetic effect

during nucleus formation or during crystal growth.

6. REFERENCES

[1] Brewer, L., and Kane, J. S., J. Phys . Chem., 59_/ 105 (1955).

[2] Schafer, H., and M. Trenkel, in Z. anorg. allg. Chem., to be published.

[3] Kleinert, P., Z. anorg. allg. Chem., in press.

[4] Schafer, H. , Chemische Transportreaktionen , Weinheim 1962; Chemical Transport

Reactions , New York, London 1964.

[5] Schafer, H. , J. Crystal Growth, 9_, 17 (1971).

[6] Schafer, H., to be published in W. Bardsley, D. T. J. Hurle, and J. B. Mullin,

North Holland Series on Crystal Growth, Vol. I. (North Holland Publishing Co.,

Amsterdam)

.

[7] Berkowitz-Mattuck, J. B. , and Buchler,A., J. Physic. Chem., 67, 1386 (1963).

[8] Budnikov, P. P., Kusakovskij , V. I., Sandulov, D. B., and Butra , F. P., Izvest.

Akad. Nauk. SSSR, Neorg. Mater., 2_, 829 (1966).

[9] Alexander, C. A., Ogden, J. S., and Levy, A., J. Chem. Physics, 39_, 3057 (1963).

[10] Kleinert, P., in J. W. Mitchell, R. C. DeVries , R. W. Roberts and P. Cannon,

Reactivity of Solids, J. Wiley 1969.

[11] Budnikov, P. P., and Sandulov, D. B. , Kristall u. Techn., 2^, 549 (1967).

[12] Schmid, H., J. Physic. Chem. Solids., 26_, 973 (1965).

[13] Kerrigan, J. V., J. Appl. Physics 34_' 3408 (1963).

[14] Sears, G. W. , and DeVries , R. C, J. Chem. Physics., 39_, 2837 (1963).

[15] Ready, D. W. , and Kuczynski, G. C. , J. Amer. Ceram. Soc. , 49_, 25 (1966).

[16] Nitsche, R. , Crvstal Growth, Sunpl. to J. Phys. Chem. Solids., C 1, 215 (1967).

[17] Schmid, H., Z. anorg. allq. Chem., 327 , 110 (1964).

[18] Chu, T. L., Gavaler, J. R. , Gruber, G. A., and Kao , Y. C, J. electrochem. Soc,

111 , 1433 (1964)

.

[19] Chu, T. L., and Gruber, G. A., Trans. Met. Soc, AIME , 233 , 568 (1965).

[20] Gruehn, R. , see Schafer, H. , Festschrift fur Leo Brandt, Westdeutscher Verlag Koln

and Opladen 1968.

[21] Chu, T. L., and Gavaler, J. R. , J. Inorg. Nuclear Chem., 27_, 731 (1965).

[22] Faktor, M. M. , and Carasso, J. I., J. electrochem. Soc, 112 , 817 (1965).

[23] Ugai, Y. A., Lavrov, V. V., Anokhin, V. Z., and Averbakh, E. M. , Izv. Akad. Nauk

SSSR, Neorg. Mater., 6_, 750 (1970).

[24] Schrocke, H. , N. Jb. Min. Mh. , 1963, 18.

465-504 0 - 72 - 29 433
[25] Scholz, H. , Aachen, Privatmitteilung 1966/67.

126] Glemser, O, , Haeseler, R. V., and Muller, A., Z. anorg. allg. Chem. , 329 , 51 (1964).

[27] Malinauskas , A. P., Gooch, J. W. , and Redman, J. D. , Nucl. Appl. Technol., 8_, 52

(1970)

.

[28] Niemyski, T. , and Piekarczyk, W. , J. Crystal Growth 1_, 177 (1967).

[29] Schafer, H. , and Trenkel , M. , unpublished (1971).

[30] Anikin, I. N. , Naumova, I. I., and Rumjanzewa, G. W. , Kristallografi ja, 10 , 230 (1965).

[31] Hauptman, Z. , Schmidt, D. , and Banerjee, S. K. , Collect, czechoslov, chem. Commun.,

32_, 2421 (1967) . [32] Glemser, O. , and Muller, A., Z. anorg. allg, Chem., 325 , 220 (1963).

[33] Nagasawa, K. , Bando, Y., Takada, T. , Horiuchi , H., Tokonami , M. , and Morimoto, N.,

Jap. J. Appl. Physics, 9_, 841 (1970) . [34] Nagasawa, K. , Bando, Y., and Takada, T. , Jap. J. Appl. Physics., 8_, 1262 (1969).

[35] Nagasawa, K. , Bando, Y., and Takada, T. , Jap. J. Appl. Physics., 8_, 1267 (1969).

[36] Nagasawa, K. , Bando. Y., and Takada, T., Jap. J. Appl. Physics., 9_, 407 (1970).

[37] Emmenegger, F. P., and Robinson, M. L. A,, J. Physic. Chem. Solids, 29_, 1673 (1968).

[38] Gruehn, R. , J. Less-Common Metals, 1_1, 119 (1966).

[39] Emmenegaer, F. P., and Petermann, A._, J. Crystal Growth, 2^, 33 (1968).

[40] Schafer, H. , and Wiemeyer, M. , unpublished (1971).

[41] Schafer, H., Gruehn, R. , and Schulte, F., Angew. Chem., 78_, 28 (1966).

[42] Schafer, H., Schulte, F. , and Gruehn, R. , Angew, Chem., 7^, 536 (1964).

[42a] Laves, F. , Moser, R. , and Petter, W. , Naturwissenschaften , 51 , 356 (1964).

[43] Schafer, H. , Gruehn, R. , Schulte, F., and Mertin, W. , Bull. Soc. Chim. France, 1965

1161.

[44] Gruehn, R. , and Norin, R. , Z. anorg. allg. Chem., 355 , 176 (1967).

[45] Gruehn, R. , and Norin, R. , Z. anorg. allg. Chem., 367 , 209 (1969).

[46] Schafer, H., and Odenbach, H. , Z. anorg. allg. Chem., 346, 127 (1966).

[47] Schafer, H., and Huesker, M. , Z. anorg. allg. Chem., 317 , 321 (1962).

[48] Schafer, H., and Sibbing, E., Z. anorg. allg. Chem., 305 , 341 (1960).

149] Schafer, H. , and Schwarzer, B. , unpublished, 1967.

[50] Glemser, O. , and Haeseler, R. V., Z. anorg. allg. Chem., 316 , 168 (1962).

[51] Tillack, J., and Schafer, H. , unpublished (1963).

[52] Ben-Dor, L. , and Conroy, L. E. , Isr. J. Chem., 1_, 713 (1969).

[53] Oppermann, H. , Z. anorg. allg. Chem., 383 , 285 (1971).

[54] Kleber, W. , Hahnert, M. , and Muller, R. , Z. anorg. allg. Chem., 346 , 113 (1966).

[55] LeBihan, R. , and Vacherand, C. , Croisance Composes Miner. Monocrist. , 2_, 147 (1969).

[56] Kleber, W. , Raidt, H. , and Dehlwes, U. , Kristall u. Technik, 3_, 153 (1968).

[57] Dettingmeijer, J. H., and Meinders, B. , Z. anorg. allg. Chem., 357 , 1 (1968).

[58] Dettingmeijer, J. H. , Tillack, J., and Schafer, H. , Z. anorg. allg. Chem., 369 , 161 (1969).

[59] Schafer, H. , and Schwarzer, B. , unpublished, 1969.

[60] Kleinert, P., Z. Chem., 3_, 353 (1963).

[61] Muller, A., Krebs, B. , and Glemser, 0., Naturwissenschaften, 52 , 55 (1965).

[62] Ferretti, A., Roaers, D. B. , and Goodenough, J. B. , J. Physic. Chem. Solids, 26,

2007 (1965)

.

[63] Bode, M. , and Schafer, H. , unpublished (1967).

[64] Ouinn, R. K. , and Neiswander, P. G., Mater. Res. Bull., ^, 329 (1970).

[65] Kleinert, P., and Schmidt, D., Z. anorg. allg. Chem., 348, 142 (1966).

[66] Hauptman, Z., Czechoslov. J. Physics, 12_, 148 (1962).

[67] Kershaw, R. , and Wold, A., U. S. Air Force Syst. Command, Air Force Mater. Lab.

Tech. Rep., AFML, 1967 ; TR-67-2 39, 24-31

[68] Schafer, H., Schneidereit , G., and Gerhardt, W., Z. anorg. allg. Chem., 319 , 327

(1963)

.

[69] Ruff, 0., and Rathsburg, H. , Ber. Dtsch. chem. Ges., 50^, 484 (1917).

[70] Greedan, J. E., and Willson, D. B., and Haas, T. E., Inorg. Chem., 7_, 2461 (1968).

[71] Thiele, G. , and Woditsch, P., J. Less-Common Metals, 1^7, 459 (1969).

[72] Bell, W. E., and Tagami, M. , J. Physic. Chem., 70, 640 (1966).

[73] Stolpe, C. van de , J. Physics Chem. Solids, 21_, 1952 (1966),

[74] Schafer, H., and Jagusch, W. , (1966) vgl. bei [4].

[75] Hoffman, J. W. , and Lauder, I., lUPAC Congr. , Australien 1969, Referat R 11 Mon 52.

[76] Kleber, W. , and Mlodoch, R. , Kristall and Techn.., 1_, 249 (1966).

[77] Widmer, R. , J. Crystal Growth, 8_, 216 (1971).

[78] Schafer, H. , and Wehmeier, F. , unpublished (1963). _

434
[79] Schafer, H., and Fuhr, W. , unpublished (1964)

.

[80] Karkhanavala , M. D. , and Momin, A. C, J. Nuclear Materials, 11_, 114 (1964).

[81] Ackemann, R. J., Thorn, R. J., Alexander, C, and Tetenbaum, M., J. Physic. Chem.,

64, 350 (1960) . [82] Naito, K., Kamegashira, N., and Nomura, Y. , J. Crystal Growth, 8_, 219 (1971).

[83] SchSfer, H. , Wehmeier, F., and Trenkel, M. , J. Less-Common Metals, 16_, 290 (1968).

[84] Lascelles, K. , and Schafer , H. , Anqew, Chemie , 83^, 112 (1971).

[85] Lascelles, K. , and Schafer , H. , Z. anorg. allg. Chem., 382 , 249 (1971).

[86] Schafer, H., in P. Hagenmuller, Preparative Methods in Solid State Chemistri^

;

Academic Press, in press.

[86a] Schafer, H. , Heitland, H. J., Z. anorg. allg. Chem., 304, 249 (1960).

[87] Greenaway, D. L. , and Nitsche, R. , j. Phys. Chem. Solids, 26, 1445 (1965).

[87a] Schafer, H.,Chemische Transportreaktionen . Ihre Grundlagen und Anwendungen, besonders

fiir Trennvorgange. Reinststoff probleme IV., (Chemical Transport Reactions. Their

Foundations and applications especiallq for separation processes. Pure substances

Problem IV.), Editor, M. Balarin, Akademie-Verlag Berlin (1971).

r OQ

1

Loo J Nitsche, R. , Bolsterli , H. U, , and Lichtenberger , M. , J. Phys. Chem. Solids, 21_, 199 (1961)

r on 1 189 J Nitsche, R. , Sargent, D. F. , and Wild, P., J. Crystal Growth, 1, 52 (1967)

.

[90] Spear, K. E . , Gilles, P. W. , and Schafer, H., J. Less-Common Metals, L4, 69 (1968)

[91] Schmid, H.

,

Acta Cryst., 17_, 1080 (1964).

[92] Emmenegger

,

F., J. Crystal Growth, 3, 135 (1968).

[93] Curtis, B. J., and Wilkinson, J. A., J. Amer. Ceram. Soc, 48, 49 (1965).

[94] Kleber, W.

,

Noack, J., and Berger, B., Monatsber. dtsch. Akad. Wiss. , Berlin, 7,

157 (1965)

[95] Kleinert, P . , Z. Chem., 4, 434 (1964).

[96] Schmid, H.

,

Z. anorg. allg. Chem., 327, 110 (1964).

[97] Royen , P .

,

and Forwerg, W. , Z. anorg. allg. Chem., 326, 113 (1963).

[98] Tromel , M.

,

Z. anorg. allg. Chem., im Druck.

[99] Karkhanavala, M. D., and Momin, A. C, J. Nuclear Materials, 11, 114 (1964).

[100] Nitsche, R. , J. Crystal Growth, 9_, 238 (1971) . [101] Berger, H.

,

Lecture at the symposium on crystallization by chemical transport

reactions

,

Berlin 11. - 13 April 1967.

[102] Wehmeier, F . H., J. Crystal Growth, 6_, 341 (1970).

[103] Medvedeva

,

Z. S., Guliev, T. N., Neorg. Mater., 1, 848 (1965).

[104] Nitsche, R. , and Wild, P., J. Crystal Growth, 3, 153 (1968).

DISCUSSION

R. S. Kirk : What did you use as a container for your hydrogen fluoride transport?

H. Schafer: „, , , ^-u -i j. That was made with platinum.

J. M. Honig : Is there usually a danger of incorporating some of your transport gas

in the crystals that you grow? Is any systematic information available on that point?

H. Schafer : First of all, the concentration of gas species per cc is small compared

to the flux method and therefore the danger is not too high, but I don't wish to escape the

question in this way. We looked for the introduction of iodine in sulfides and found that

this depends on the system. For example you can have amounts of hundredths of a per cent of

iodine in sulfide in some cases, but it depends on the formation of holes. You see, if you

introduce an iodine instead of a sulfur then the charge is not balanced and therefore you

must have a hole on the cation sites. We did such investigations, and if you go to more

highly charged cations , for example to hafnium sulfides , then the introduction of iodine is

too small to be measured because now it's too hard to get a four valent hole.

R . Ward : I wonder in the chemical transport and formation of the silica phase, was it

tridimite?

H. Schafer: Yes.

435
R . Ward : What was the transport agent there?

H. Schafer : HF

.

R

.

Ward : HF? Was there any incorporation at all of fluorine in the crystals?

H. Schafer : There are a few, not too much.

R. Ward: I think tridymite is a clathrate, I think there must be something there.

T . Chen : I just wonder if all the tungstate and molybdate phases required the same kind of transport agent. The ternary systems. What kind of agent?

H. Schafer : Yes. Mostly they use chlorine usually.

J. W. McCauley : I have two questions. Have you ever tried to grow carbonates by this

technique? Have you ever tried to limit the number of crystals and grow one large one with

any of these materials?

H. Schafer : We have never grown carbonates, but I believe it must be possible for such

things like siderite or manganese carbonate also. We would like to try as it has not been

done up to now. We are not crystal growers, that is to say, primarily, but I know that

"people using such an ampule in a temperature gradient make single crystals from gallium

phosphide. They can be obtained some centimeters in size. Zince oxide crystals are made

by Fischer with a length, I believe, five centimeters and a diameter of five or six millimeters .

436
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

PRECISION PARAMETERS OF THE FERROELECTRIC RARE EARTH MOLYBDATES Ln2(Mo04)3*

L. H. Brixner, P. E. Bierstedt, A. W. Sleight and M. S. Licis

Central Research Department

E . I . du Pont de Nemours and Company

Wilmington, Delaware 19898

o Lattice parameters to an accuracy of better than ±0.001 A have been detearmined for the

ferroelectric Ln2(Mo04)3 compounds with Ln = Pr , Nd, Sm, Eu, Gd, Tb , Dy and Ho. X-ray patterns were obtained with a Hagg-Guinier camera and the data was refined by a least-squares

method using selected reflections. Parameters obtained this way exhibited a systematic

trend of the b-a dimension as a function of the cation size for the orthorhombic Pba2 room

temperature structure. A linear relationship between the cell volume and the cube of the

ionic radius of the rare earths has been observed. The first seven compounds are metastable at room t^emperature and transform from the f erroelectric/f erroelastic Pba2 structure to the parent P42im structure between 140 and 235 °C. Only H02 (MoOi^) 3 is stable in the Pba2

phase at room temperature and transforms into the tetragonal structure at 121 °C. The high

temperature structure for this compound is orthorhombic, space group Pnca. The transition

temperatures have been accurately determined by differential scanning calorimetry, differential thermal analysis, dielectric measurements and hot-stage optical techniques and are discussed in relationship with the degree of b-a distortion. Lattice parameters have also been

determined for the stable monoclinic modification of Sm, Eu, Gd, Tb and Dy-molybdate and

their transition temperatures, ranging from 800 to 1000 °C, as reported.

Key words: Ferroelectric molybdates of rare earths; lattice parameters; phase transitions.

1 . INTRODUCTION

Certain rare earth molybdates of the type Ln2 (1^00^)3 such as Nd2(MoOi^)3 have been known

for many years [1] '• . More recently, Borchardt [2] grew single crystals of many rare earth

molybdates and showed that some members of this group of compounds are ferroelectric. There

still was considerable argument about the true structure of the ferroelectric room temperature phase, which is complicated by the fact that for most compounds it only exists in a metastable state. Abrahams et al. [3] and Jeitschko [4] have given detailed accounts of

this orthorhombic structure, but even to date some authors 15] insist that the structure is

tetragonal. There was also disagreement on the extent of the existence of the Pba2 phase as well as the nature of the stable room temperature a phase. Newnham et al. [6] only included

the Sm to Dy-compounds in their parameter studies of the ferroelectric rare earth molybdates

and stated that "the orthorhombic distortion i -a is constant within experimental error."

Nassau et al. [7] carried out a comprehensive study of these rare earth molybdates, recognizing the profusion of different structural types, further complicated by temperature-dependent

polymorphisms. Concerning the stable low temperature a structure, Nassau [7] stated that it

is unknown.

In the present paper we will show that actually 8 rare earths Ifrom Pr (59) to Ho (67)

,

excepting Pm, which does not occur naturally] crystallize in the Pba2 structure of Ln2(Mo04)3

and that there exists a pronounced dependence of b-a upon the ionic radius of the rare earths.

Contribution No. 1801 ' \ -

' 1 Figures in brackets indicate the literature references at the end of this paper.

437

/
We will also show that the a structure of the compounds of Sm, Eu, Gd, Tb and Dy is actually

identical with the structure previously described for Eu2(WO:j)3 [8]. The remaining non-ferroelectric Ln2(MoOi^)3 compounds fall into two categories: 1) an isostructural group including La, Ce, Pr and Nd-molybdate , crystallizing in a monoclinic structure different from that

given by Jamieson et al . [12] for aNd2(MoOtt)3 and 2) an isostructural group, crystallizing

in the orthorhombic Pnca space group and including Sc, Y, Er, Tm, Yb and Lu-molybdate . Parameter refinements have been obtained on all of these compounds and will be the subject of a forthcoming publication [13] .

2. EXPERIMENTAL

2.1. SAMPLE PREPARATION

All compounds were prepared by standard solid state techniques using Kerr-McGee Co.'s

99.99% pure rare earth oxides and M0O3 prepared by decomposition of Climax Molybdenum Co.'s

ammonium-molybdate (NH14 ) 5M07O211 • 4H2O . The a-phase compounds had to be prepared below the

transition temperatures reported in table 3. Since this temperature may be as low as 800 °C,

extensive firing periods of up to 60 hours were necessary to achieve homogeneous products.

2.2. X-RAY STUDIES

For the x-ray studies, powder patterns were obtained at 25.0 ± 0.5 °C with a HaggGuinier camera using KCl (a^ = 6.2931 K at 25 °C) as an internal standard. These data were refined by a least-squares method using selected reflections which could be indexed as single

lines. As a guide for the 3' modifications, powder pattern intensities were calculated based

on the known 3'Gd2(Mo04)3 structure [4]. Intensities for aGd2(Mo0t|)3 were estimated with

diff ractometer data as well as the Guinier data.

2.3. TRANSITION AND DIELECTRIC STUDIES

The Curie temperatures as well as the a/3 transition temperatures and melting points were measured with a Du Pont 900 thermal analyzer. Heating and cooling rates of 1 °C or 0.5 °C/min were employed, ensuring accurate T^ values. A sensitive digital voltmeter was used to monitor the output of the thermocouple; thermal hysteresis in the T^, values was always observed, but in no case did it exceed 1 °C.

Dielectric measurements were made at 1 kHz and 10 kHz with a General Radio (Type 716c)

capacitance bridge. A Princeton Applied Research Lock-In Amplifier (HR8) was used both as the generator and detector. The output of the detector was fed into an x-y recorder for

plotting of the capacitance vs. temperature curve. In addition, the DTA apparatus was adapted so that dielectric constant measurements could be made in the DTA cell, and then the thermal anomaly (DTA) and the dielectric anomaly could be measured simultaneously. C-cut single

crystals were used for this purpose, and it was observed that the peak in the dielectric con- stant occurred at the same time as the peak in the DTA signal. The precision of the T^ values

is +0.2 °C.

The Curie temperatures were also measured by observing through crossed polars the disappearance and reappearance of the ferroelectric domains as the specimen was heated and cooled through the 3'/3 transition. A Mettler FP hot stage was used to heat the sample, and it

was observed that the transition occurred over temperature intervals less than 0.1 °C. The

temperatures were measured with a calibrated platinum resistor and the agreement with T^

values obtained by dielectric and differential thermal analysis techniques was within 0.2 °C.

3. RESULTS AND DISCUSSION

Jamieson et al. [12] have postulated a structure for aPr2(MoOi+)3 and aNd2 (MoOit ) 3 . We

have shown that isomorphism actually exists from La2(Mo04)3 to Nd2(MoOtt)3. In going to

Sm2(MoOtt)3, there is a structural change for the oiphase which persists through Dy2(MoOit)3.

Nassau et al. [7] report that the low temperature modifications of Sm2(MoOt|)3, Eu2(MoOi+)3,

and Gd2(MoOi|)3 are isostructural with each other, but they claim that these compounds are not isostructural with any other known molybdates or tungstates. We have found that there

are low temperature modifications of Tb2(MoOtt)3 and Dy2(MoOi+)3 which are isostructural with

aSm2(Mo04)3, aEu2(Mo04)3, and aGd2(Mo04)3. Furthermore, these are in fact isostructural

438
with the normal modifications of Ln2(W0tt)3 compounds where Ln is La through Dy. The cell

dimensions of the aLn2(Mo0i4)3 phases where Ln is Sm-Dy are given in table 1 assuming space

group C 2/c^. These may be compared with the cell dimensions of Eu2(W0tt)3 which are [8]: a = 7.676 A, b = 11.463 A, c = 11.396 A and g = 109.63°. Intensity calculations were carried

out for aGd2(MoOi^)3 using the published [8j positional parameters for Eu2(W0i4)3. The agreement between the calculated intensities and the powder intensities is qualitatively very

good (table 2) . A comparison of the last 2 columns in table 1 shows that we are dealing

with rather substantial differences (-20%) in densities for the 2 structures. This suggested

that the application of pressure may have a significant influence on the transformation of

the metastable low density, high temperature 3 structure into the stable, high density, low

temperature a structure. At 30 kbars of pressure the 3 a transformation for Gd2(Mo0L|.)3 was indeed observed at 555 °C, more than 300 °C below the ambient pressure transformation

o point"'

.

Table 3 summarizes the lattice parameters, shear angles. Curie temperatures and transition temperatures of the ferroelectric rare earth molybdates. Figure 1 shows a graphic

representation of the various phase relationships for the different rare earth molybdates as

a function of temperature.

It is apparent from the data in table 3 that there is a systematic trend for the b-a

parameter of the Pba2 structure going from a maximum of 0.053 A for the Pr compound to a minimum of 0.021 A for the Ho compound. In going from the ferroelectric mm2 point group to the paraelectric 42m point group, the a and b lattice constants become equal and it requires

a higher temperature to effect this rearrangement of atoms for the praseodymium compound than

for the holmium compound.

The trend for the a/3 transformation temperature is in the same direction, that is, going up as the size of the ionic radius of the rare earth increases. The melting point, on

the other hand, goes up in the opposite direction due to the fact that the cell volume decreases with a corresponding increase in cohesive energy.

The one minor deviation from a linear relationship between Curie temperature and composition in figure 1 is 3 ' Tb2 (MoOi^ ) 3 . This compound had essentially the same Curie temperature as the Gd-composition , while the b-a difference is smaller. A recent paper by Keve [lOJ

also gives a higher Curie temperature for 3' Tb2(Mo0i+)3 but lists a higher b-a difference.

Conceivably, small deviations in stoichiometry may account for this discrepancy.

Table 1

Cell Dimensions (a) of the a-Rare Earth Molybdates and a Density Comparison

Compound a> K

0 b, A c/ A 3 V, A^ ct(b) i' (c) Sm2 (M0O4)

3

7. 562 11.509 11. 557 108.98 951.1 5.450 4..405

EU2 (MoOtt) 3 7. 554 11.459 11.497 109.08 940.6 5.533 4

,

.463

Gd2 (MoOt^) 3 7. 575 11.436 11.424 109. 28 934.1 5.647 4,. 555

Tb2 (M0O1+) 3 7. 529 11.379 11.401 109.21 922.3 5.743 4..708

Dy2 (M0O1+) 3 7. 514 11.344 11. 364 109. 31 914.1 5.847 4.,628

(a) The cell is C-^centered

.

(b) Calculated densities based on the x-ray volumes

(c) Density of the 3' form at room temperature for comparison.

C c as the alternative space group has been ruled out based on a negative second harmonic

generation test carried out on a-Sm2 (MoOi+) 3 (courtesy Professor Cross, Pennsylvania State

University)

.

In a recent paper, Nassau [9] also listed an a modification for Ho2(Mo04)3. We were unable

to obtain this form even through extended (10 days) sintering between 600 °C and the reported transition temperature of 750 °C. We only obtained 3' Ho2(Mo04)3.

439
Table 2

X-ray Powder Pattern for a-Gd2 (MoOt^) 3

-3}

d , obs

-I) 6.047

0 5.705

2 5.384

1 5.045

H 4.741

2.723

"""obs '''calc 26

3.361 ^ ^^^> 5

3.074 ,„'X> 7

10

15

2 2 19 22

18 16

2 - 3.923 - 1

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J 2

2^

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-3f 3.560f 17

5

1 -1 3.158 3.158 100 100

<1

<1

3 3.043 3.043 84 79

0 - 3.031 - <1

-2 - 3.029 - <1

0 2.858 2.859 27 27

3 - 2.770 - <1

-4 - 2.768 - <1

1 - 2.764 - <1

6

3 4 - 2.696 - <1

-I) , I

2 2.608 2.609 15 15

-4 2.605 2.605 14 15

2 2.526 2.526 3 3

-1 2.447 2.450 1

-2 2.449 <1

4 - 2.438 - <1

2 - 2.374 - <1

-4 - 2.371 - <1

°l 2 333 2.333) 1 -3/ 2.33lf <1

31 2.285i <1

-4[ 2.281 2.284[ 2 <1

1' 2.282) <1

440
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C !h 0) CM rH rH fH rH rH rH -p

p >i 0 ;D c n) nJ -H U (U u M

4J P 1 u >^ M 0) D C u (C g

(C cn o c rtJ TI

Eh o OJ >H •H CD in , T! C Sh +J U o ni 0 0 0) T) C H Hi CO u 0 •H Ti 0)

nJW -pC cn -p •H +J c m u r-- rH O rH in ro H W <0

w

U 0 co rH CO in ro o inCM

H c 01 Ol CTi CO CO oo ro CO 0 H C o P 0 Eh ft O -P (C u O

•H rH 0) !h rH

(/) en ca !h •P 01 (0 c \ Eh —- (3 XI U a ca W c , 0) f (0 z Q IH u in

Cn ri

— rH

rH c in rH CN

H rN CM in 4J

w +i iH H P U CO (N CN (C !h

QJ +J

C 0 o o rH rH

H rH Csl iH !h (U o •H rH rH rH rH rH rH rH rH 0) 0 +J OJ

<u 0 m 0)

O rH

s; ^ H Cn

0) T!W c

+J 01

u c OJ 0 m cn cn CO CO CO CO CO 01 p g !h •H U) m H 4J -T J- -3- J- J- J- J- J- 01 (C 0) TI 0)

-rH

O o o o o o o O 01 XI x;

M 0 o 0 0 0 o O

H

g

H

u cn 0 s s s s

<N CM IN CN Cvl 0 U e p -a 0 O ft S cn w u

441
Figure 2 shows a plot of the cell volume of the g' molybdates vs. the cube of the ionic

radii. The numbers used for the radii are those of Shannon and Prewitt [11]. Based on the

cell volume obtained for Pr2(Mo04)3, a correction of the ionic radius for Pr"^^ in octahedral

coordination from 0.997 to 0.991 K would seem indicated.

3. SUMMARY

In conclusion, the ferroelectric rare earth molybdates constitute a highly interesting

group of compounds which combine a number of unusual physical properties in the metastable

Pba2 room temperature structure. The structure is highly sensitive toward substitutions and

tr^ansforms at relatively low temperatures (121-235 °C) into the more symmetrical tetragonal

P422m structure. Prepared below the a/3 transformation temperature, the molybdates with Ln = Sm-Dy are isostructural with rare earth tungstates of the type Ln2(W0i|)3 where Ln is La-Dy.

200-

100

STABLE a and METASTABLE /3 REGION

_ METASTABLE /3' REGION

I \ i Pr Nd Pm Sm Eu Gd Tb Dy Ho

Fig. 2. Ionic radius vs. cell volme

of the 6' modifications.

442
4. ACKNOWLEDGMENTS

We are grateful to J. W. Rooney and B. F. Gordon for technical assistance in carrying

out this work.

5. REFERENCES

[I] Hitchcock, F. R. M., J. Am. Chem. Soc. 522 (1895).

12] Borchardt, H. J., U. S. Patent 3,437,432.

[3] Abrahams, S. C. , Kurtz, S. K. and Jamieson, P. B. , Phys. Rev. 172 , 551 (1968).

[4] Jeitschko, W. K. , Naturwiss. 57, 544 (1970).

15] Drobyshev, L. A., Sov. Phys . -Crystallogr . 15_, 835 (1971).

[6] Newnham, R. E. , McKinstry, H. A., Gregg, C. W. and Stitt, W. R. , Phys. Status Solidi 32./ 49 (1969)

.

[7] Nassau, K, Levinstein, H. J. and Loiacono, G. M. , J. Phys. Chem. Solids 26.' 1805 (1965).

[8] Templeton, D. H. and Zalkin, A., Acta Cryst. 1£, 762 (1963).

[9] Nassau, K. , Shiever, J. W. , Keve , E. T. , J. Sol. State Chem. 2_, 411 (1971).

[10] Keve, E. T. , Abrahams, S. C. , Nassau, K. and Glass, A. M. , Solid State Coramun, 8^, 1517

(1970)

.

[II] Shannon, R. D. , Prewitt, C. T. , Acta Cryst. B25, 925 (1969), and ibid, B26, 1046 (1970).

[12] Jamieson, P. B. Jamieson, Abrahams, S. C, Bernstein, J. L. , J. Chem. Phys. 50, 86 (1969).

[13] Brixner, L. H. , Bierstedt, P. E. , Sleight, A. W. and Licis, M. S., Mat. Res. Bull. 6_, 545 (1971)

.

DISCUSSION

F. Holtzberg : Do I understand that the metastable transition that you showed, takes

place reproducibly at the indicated temperature?

L. H. Brixner : No. You have to prepare the alpha gadolinium molybdate material below

the transformation temperature of 800 °C, where it is stable. If you heat that up, it converts rather quickly into the beta structure. Now, if you rapidly quench the beta structure

through 850 °C, it will survive. So, in other words, below 850 °C it is at least kinetically

stable. If you sit with a crystal of the beta structure at or below the transition temperature, it will convert in a matter of days or perhaps weeks. If it's fine powder, it will go

much faster. Thus, equilibrium favors the a phase but the reaction rate is quite slow. The

density comparison of a and 3 indicates the structures are very different, which is consistent

with the notion of large energy barrier between 3 and a.

443

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

STRUCTURAL AND PHASE RELATIONSHIPS AMONG

TRIVALENT TUNGSTATES AND MOLYBDATES

K. Nassau and J. W. Shiever

Bell Telephone Laboratories, Incorporated

Murray Hill, New Jersey 07974

The trivalent tungstates L2(W0tt)3, molybdates L2(MoOtt)3, and mixed systems, L2(Wi_^MOjj

Oit) 3 have been studied between room temperature and the melting points (up to 1650 °C) . Single cirystal and powder x-ray diffraction at room and elevated temperatures, differential

thermal analysis, and crystal growth were among the techniques used to characterize phases

and determine relationships.

Among the molybdates of the lanthanides. In, Sc , Fe, Cr, and Al, at least five structures

were observed: the tungstates show at least three. Particular attention was devoted to Tb2

(MoOtt)3, which, like Gd2(MoOi+)3, shows transitions at 800, 1040 and melting at 1155 °C and a ferroelectric transition at 163 °C in the metastable phase region; not all of these transitions are easily reversible.

Pseudo-binary tungstate-molybdate phase diagrams and structural parameters were determined for the La, Nd, Sm, Gd, Ho, and In systems. Based on' struct\iral determinations together

with phase diagram interpretations and crystal growth evidence on the nature of various transitions (destructive or nondestructive) , structural relationships were used to organize the

many structures into three groupings and relate the results to the radii of the trivalent

atoms :

i) The small size tungstates and molybdates, the Sc2 (WOlj) 3 type family, with at least two members, form 6-coordinated structures with unit cell or subcell based on Pnca; with rising temperature this family extends to larger size atoms.

ii) The large size tungstates and molybdates form 8-coordination structures with scheelite related subcells; this a-Eu2 (WOi^) 3 type family includes at least 4 structiires.

iii) The 3-Gd2 (M0O4) 3 type family of structures, occurring only in the intennediate

size molybdates, have 7-coordinated trivalent atoms; except for Y2 (MoO^) 3 they are stable

only above 800 °C, although extensive metastability does occur with ferroelectric transitions

in the metastable form near room temperature.

Key words: Crystal structure; lanthanide compounds; molybdates; tungstates.

1. INTRODUCTION

Insight into crystallochemical relationships can be obtained by the study of the variation of structure in a series of closely related compounds. Suitable variables can include

the temperature and the substitution of cations of similar size and electronegativity. Structural determinations on single crystals (or powders when crystals are not available) as well

as the study of phase transitions and pseudo-binary phase diagrams have been used by us and

our co-workers [1-7] ' to clarify the structural relationships here studied.

1 Figures in brackets indicate the literature references at the end of this paper.

445
The hexavalent tungsten and molybdenum ions have essentially the same size and electronegativity, and the range of these same parameters in the lanthanide series is also limited

(6-coordination ionic radii [8] range from La = 1.06 A to Ln = 0. 85 ^) . By comparison with

other series of rare earth compounds one might therefore expect at most three structures to occur in the trivalent lanthanides tungstates and molybdates of the formula Lnl"*" (M^'^0^)3.

In fact, no less than eight distinct structure types occur, at least four of which show

evidence of containing additional variants. Four of these structures have been determined

and enough is known about the other three and some of the variants that several patterns can

be discerned.

The seven structures may first of all be grouped into families [6] as shown in figure 1. The smallest trivalent cations yield the C* family tungstates and molybdates, where the trivalent cation is 6-coordinated. A number of outer transition metal ions also occur in this

family, and in the tungstates this structure occurs in the very wide size range from Al

(0.53 A) to Gd (0.94 A)

.

Intermediate size molybdates contain 7-coordinated trivalent cations. With the exception of Y2(Mo04)3, these have stability regions only at elevated temperatures but nevertheless do exist metastably at room temperature, showing interesting dielectric, ferroelectric,

and ferroelastic properties and serving as laser host lattices [5,9-11].

The largest size trivalent cations yield tungstates and molybdates in the A family

structures with 8-coordination , similar to that in the scheelite structure (CaWO , tetragonal

J4i/a) . This A family contains four structure types as shown in table 1, namely A, D, M*

,

and N*, the asterisks on the last two indicating that variants occur. The variability of

structures within this A family can be understood by viewing them as derived from the scheelite structure with two trivalent ions replacing three Ca ions, one vacancy (designated

resulting; one may then describe the substitution as the electroneutrality maintaining transformation: 3 Ca2+ WO4 Ndl"*" (t)°(W0i^)3.

This substitution, however, does not occur without an increase in energy, and the strain

may be relieved in at least three different ways. First, there may be a change to an arrangement involving other than 8-coordination. With elevated temperature the tendency is to obtain

7-coordinated trivalent cations, with smaller trivalent cation size 6-coordination is observed

A second way of lowering the energy results from a distortion of the unit cell shape.

This occurs, for example, in the A type tungstates (e.g. a-Eu2(W04)3, monoclinic, C2/c [12])

where the occupancy arrangement is simple (every third layer of Ca sites in the scheelite

structure figure 2a, is vacant as shown in figure 2b) but where the scheelite type sxib-cell

angle is 94° instead of 90°.

6 COORDINATION

IONIC RADIUS

OCCURENCE OF

6 COORDINATION

OCCURENCE OF

7 COORDINATION

OCCURENCE OF

8 COORDINATION

8 COORDINATION

IONIC RADIUS

1.06 1.013

1 1 0.995 0.85 0.79 0.53

1 III

1= =

6 COORDINATION RADIUS RATIO RANGE

(=== = = = = = =

C FAMILY TUNGSTATES

'^"""-^ MOLYBDATES

1== = = = =

1=

L FAMILY MOLYBDATES > STABLE AT ROOM

TEMPERATURE

STABLE AT ELEVATED TEMPERATURE ONLY

1 1 1

i FAun Y MOLYBDATES """-^ TUNGSTATES

1 8 COORDINATION RADIUS RATIO RANGE i 1.18 1.02 1.00 0.97 0.92

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 La Pr Pm Eu Tb Ho Er Yb In Fe A.f Ce Nd Sm Gd Dy Y Tm Lu Sc Cr

Fig. 1. Occurrence of structure families, coordination

about the trivalent cation, and ionic radius of

the trivalent cation in Ln(W04)3 and Ln(Mo04)3

(after [6]).

446
Table 1

Structure Types of Ln2 (W04) 3 and Ln2(MoOtt)3

Structure Example

A Family (8-coordinated)

A

DM*

N*

a-Eu2 (WO1+) 3 6-Nd2 (W0[+) 3 a-Tb2 (M0O1+) 3 a-Nd2 (MoOtf) 3

L Family (7-coordinated)

6-Gd2 (M0O1+) 3 e-Gd2 (M0O1+) 3 Y-Tb2 (M0O1+) 3

C* Family (6-coordinated)

C* Sc2(W0Lf)3

Fe2 (MoOi^) 3 a-Tm2 (MoOit) 3

S pacegroup

C2/C

C2

Pba2

P42i/m

Pm2m or subgroup

Pnca

Siibcell

'scheelite" y 7^ 90

'scheelite" y 7^ 90

scheelite" y / 90

scheelite y = 90

tetragonal

tetragonal

Pnca

Pnca

'after table 3 of [6] ; several obvious errors there have been corrected.

a) SCHEELITE - CoWO^ /•A • •'^ /.<

/ / ) • 1 / / 1 • ( '/V

1 • ( / /

b) aNd2(W04)3-A

c) a Ndj (Mo04)3-N • < / /

• 1 > • /A /

e 1 / / 1 • / /I/

7^

' •/! /

' /

Fig. 2. Position of the Ca atoms in scheelite,

viewed down the c (a) ; equivalent view

of the Nd atom positions in a-Nd2 (WO1+) 3, structure type A(b); and in ct-Nd2 (MoO,,) 3

,

structure type N(c).

447
A third way of relieving the strain is observed, for example, in the N*-type molybdates

{e.g. a-Nd2 (MoOtt) 3 / monoclinic, C2) ; here the s\ab-cell remains tetragonal (J4i/a as in scheelite) but the replacement of 2Na^+ for 3Ca^+ occurs in the long range order arrangement of

figure 2c [3]

.

The other 8-coordinated structure types, the D tungstates and the M* molybdates, also

have distorted scheelite-type siab-cells and structures distinct from type A; it may be suggested that when crystals become available and the structures can be determined, both \init

cell distortion as well as disordering of the vacancies will be found.

2. OCCURRENCE OF STRUCTURES

The occurrence of the various structures for the various trivalent tiingstates and molybdates is shown in figures 3 and 4, respectively. This is based primarily on our work [1,3,6]

relevant work by others will be found referenced there.

6 COORDINATION IONIC RADIUS (A) ,800 1-05 1.00 0.95 0.90 0.85 0.79 053

ig. 3. Occurrence of structures in the L2 (WOtt) 3 compounds

(after [6]),

448
These structures are conveniently designated in three different ways. Successive phases

with increasing temperatures are designated a-, 3-, etc. as usual. For comparison among different compounds, alphabetic designations such as "A", "C" , etc. as in table 1 and figures

3 and 4 provide an easily perceived label. An asterisk following such a designation indicates

that the comparison of x-ray powder diffraction data (Debye-Scherrer , Guinier, and diffractometer techniques have all been used) indicates close similarity but not necessarily identity

of structures. Thus in the case of the C* family, a-Sc2 (WOt^) 3 falls into space group Pnca

,

but Fe2(MoOi^)3 is P2i/a, with Pnca as sub-cell. Structures solved in detail are designated

by the specific compound first solved as customary. Thus one may refer to a-Nd2(WOi|)3 as being part of the "A" field and having the a-Eu2(W04)3 structure. Preparation (powder sintering and single crystal growth) and examination techniques (x-ray examination at ambient

and elevated temperatures, DTA (differential thermal analysis), TGA (thermogravimetric analysis), quenching, etc.) have been previously [1,3,6] described. Transition and melting temperatures have been stjmmarized previously [1] with some additions [6] .

Some mixed compounds of the type LaYb(W0t+)3 were also examined and found to have the same structiires as the compound closest to the average ionic radius, Sm2 (WO4) 3 in this instance. Any possible ordering of the cations was, however, not looked for.

The many phases reported by Drobyshev et al {e.g. eight for Pr2 (MoOi^) 3 [13] ) appear to

be inconsistent with this work. Their preparation technique (nonequilibrium , which can produce other nonequilibrium phases by Ostwald's step rule) and x-ray results (only minor intensity changes and invariant diffraction line spacings for many of the phases) make it difficult

to relate their results to those of this series of studies.

The neodymium tungstate-molybdate Nd2 (WOi^) 3 - Nd2 (MoOi^) 3 pseudo-binary system has been

investigated in most detail [3] , and a phase diagram consistent with the data is shown in

figure 5. Both a (room- temperature) forms have scheelite-type sub-cells; the variation of

the sub-cell parameters with composition is shown in figure 6. The addition of as little as 2-1/2% tungstate permits the long range order a-Nd2 (M0O1+) 3 N structure of figure 2b to change

into the highly ordered a-Nd2(WOtt)3 A structure- at first with an a angle of approximately

90°, increasing to 94° as the tungstate content dominates. Whether the A structure can exist

with an a-angle of exactly 90° cannot be decided from these data.

3. PSEUDO-BINARY PHASE DIAGRAMS

i200r

800

700 "-J 0 20 40 60 80 100 NCl2(M004)3 Nd2(W04)3 MOL %

Fig. 5. The Nd2(MoOtt)3 - Nd2(WOit)3 pseudobinary phase diagram (after [3]).

449

465-504 O - 72 - 30
5.20aI-! -I 1 I I I 0 20 40 60 80 100 aNdjIMoO^lj aNd2(W04)3 MOL %

Fig. 6. Scheelite-type sub-cell parameters

in the a-Ndg (MoOt|) 3 - a-Nd2 (WO4) 3 system (after [3]).

The gadolinium tungstate-molybdate system is shown in figures 7 and 8. Both the Nd and

Gd systems show no significant two-phase region, but the La and Ho systems show wide two

phase regions [6]; the sub-cell parameters of the latter are shown in figure 9. In the case of the Sm system [6] the three sub-cell parameters are all continuous between the M and A phases but there is evidence that at least one additional phase may exist in this system.

In the indium system there is complete solid solubility, both end members having the same C structure [6]

.

700

0 20 100

Gd^lWO^lj

Fig. 7. The Gd2 (MoOlj) 3 - Gd2(WOit)3 pseudobinary phase diagram (after [3]).

450
I 11.40A -

5.30Ar

aGdjlMoo^lj 80 100

Fig. 8. Scheelite-type sub-cell parameters

in the a-Gd2 (M0O4) 3 - a-Gd2(WOtt)3

system (after [3]).

0 20

aHO2(Mo04)3 80 too aH02(W04)3

Fig. 9. Scheelite-type s\ib-cell parameters

in the a-Ho2 (M0O14 ) 3 ~ a-Ho2 (WOi^) 3 system (after [3]).

Even though the sub-cell may not show any discontinuities, e.g. between the M and A structures in the Sm binary system [6] , there are nevertheless changes seen in a series of

x-ray powder diffraction patterns across the system that indicate a change in structure.

This was confiinried in the Sm system by the powder second harmonic generation test which showed

a center of symmetry in Sm2(W0i+)3 and in the mixed system to 80% Sm2(W0t+)2 ~ 20% Sm2(MoOLj)3,

but a lack of a center of symmetry in Sm2 (MoOi^) 3 [6]. The report by Brixner et al . [14] that

the A and M compounds are isostructural is based only on x-ray powder diffraction data which

does not necessarily show small differences. The type of long range ordering which characterizes the A* family of structures can only be satisfactorily established by single crystal

work.

4. DESCRIPTIONS OF THE INDIVIDUAL STRUCTURES, THEIR OCCURRENCE, AND CRYSTAL GROWTH

4.1. A FA14ILY STRUCTURES (8-COORDINATED)

4.1. a, STRUCTURE A

This structure is found in the a-form of the tungstates from La to Ho and including Y as shown in figure 3. The structure was first solved for a-Eu2(W0tt)3 which is monoclinic C2/c

451

;
with a = 7.73, b= 11.58, c= 11.48 K, and 3 = 109.6° [12]. There is a scheelite-related

distorted tetragonal siib-crell with a = 5.28, c = 11.58 A and y near 94°. Lattice parameters

for most of the type A compounds , and an indexed x-ray powder diffraction pattern for a-Nd2

(W0i+)3 have been given [1]; the promethium compound was studied by Weigel and Scherer [15].

The structure is related to that of scheelite as illustrated in figures 2a and 2b, with

an ordered replacement of 2Nd for 3Ca. The distortion angle of the pseudo-tetragonal subcell decreases from 94° towards 90° as, for example, Nd2(MoOLj)3 is added to Nd2(W0i^)3. It also decreases as the temperature is raised, being approximately 92° at the transition temperature for a-Nd2 (WOi^) 3 as shown in figure 10.

Single crystals may be grown from the melt, e.g. by Czochralski pulling in inch size

pieces, for the La to Eu tungstates. The D structure to A transition shown in figure 3 is

nondestructive for these compounds; this is not the case for the transition in the remaining

compounds , where destruction of the pulled crystals occurs on cooling through the phase transition from C to A.

4.1.b. STRUCTURE D

This structure occurs in the 3 form of the tungstates from La to Eu as shown in figure

3. Since it transforms nondestructively into Structure A it cannot be examined at room temperature, although a melt sample of La2 (WOi^) 3 was successfully quenched in the 3-form and an x-ray powder diffraction pattern of this sample has been given [1] . High temperature x-ray

diffraction shows a distorted scheelite-type sub-cell with y 7^ 90° as shown in part of figure

10 for 3-Nd2(WOtt)3 with sub-cell dimensions a = 5.3 and c= 11.6 A. On the basis of the ab- sence of a discontinuity in y in the D to A transition of figure 10 one may assimie a structure

similar to the A structure of figure 2b, but with some disorder.

4. I.e. STRUCTURE M*

This structure is found as the a-form of the molybdates of Sm to Ho as shown in figure

4. Since the L form in this region is extremely stable with respect to the L to M* transition,

preparatory sintering must be performed below the transition temperature and a technique to prepare single crystals has not yet been found.

An x-ray powder pattern has been given [1] for a-Gd2 (M0O4) 3 . Monoclinic indexing of the

a-Gd2(Mo04)3 and cell dimensions for the Sm through Dy compounds has been given by Brixner

[14] on the assumption that the structure is C2/c, identical with the A structure of a-Eu2

(W0tj)3. This clearly cannot be the true unit as indicated by the absence of a center of symmetry and other evidence as discussed in section 3. It is probably a sub-cell of the true

cell.

The scheelite-type sub-cell angle deduced from x-ray diffractometer tracings is in the

92 to 94° range. In pseudo-binary tungstate-molybdate systems the angle y and the other sxih- cell parameters are continuous in some instances and discontinuous in others with those of

the A structure (see figures 8, 9, and reference [6]) . This structure again may be assumed

to be related to the A structures with disorder, but different from that found in the A or D structures. Differences are noted as the x-ray powder patterns of this series are compared

and there may be a number of different disorder patterns as implied in the asterisk of M*

.

MELTING-i

94° TRANSITION930

GLE 920

/3-Nd2(W04)3 ^

<

A \^

91° Q-Nd2(W04)5

90° 1_ 1 1 1 1 0 200 400 600 800 1000 1200 TEMPERATURE (°C)

Fig. 10. Sub-cell y values for Nd2(WOtt)3.

452
4.1.d. STRUCTURE N*

This structure is found as the a-form of La, Pr, Nd, and Pm molybdates as shown in fig- ure 4. The structure was solved for a-Nd2 (MoOi^) 3 which is monoclinic C2 with a = 27.02, b = 11,70, c = 11.85 A, and 3 = 105.3° [4]. An indexed x-ray powder diffraction pattern of this

compound has been given [1] , as well as one for the Pm compound [15] . The siib-cell is tetragonal (e.g. Y - 90°) , I^i/a with a = 5.30 and c = 11.70 A. Crystals were grown by temperature cycling the sintering powder containing excess M0O3 near the upper temperature limit of

the stability region. In the pseudo-binary tungstate-molybdate systems this structure occurs

to about 42% tungstate in the La system, but only to about 2-1/2% tiingstate in the Nd system.

As shown in figure 2c there is considerable disorder in the a-Nd(Mo04)3 structure, with

partial occupancy in the barred locations as determined from satellite reflections [16] . The

comparison of x-ray powder diffraction patterns shows differences among the four N* compounds;

all show tetragonal sub-cells and different types of disorder may be assumed.

4.2. L FAMILY STRUCTURES (7 -COORDINATED)

4. 2. a. STRUCTURES L AND L'

These are the g forms of Pr to Ho molybdates and a-Y molybdate as shown in figure 4. The structure was first solved [7] for 3-Gd2 (MoOi^) 3 (frequently abbreviated 3-GMO or, less

accurately, GMO) which in its ferroelectric form at room temperature is orthorhombic Pba2

,

with a = 10.3858, Jd = 10.4186, and c = 10.7004 A. Lower symmetry has been suggested, but

this appears to be an artifact produced by a-b type twinning and [001] rotational mosaic

misorientations . Above the approximate 160 °C Curie temperature, the structure is tetragonal,

p42i/m. An indexed x-ray powder diffraction pattern and lattice parameters on tetragonal inaexing [1] and more accurate parameters on orthorhombic indexing and Curie temperatures [14]

have been given. The structure has been confirmed by Jeitschko [17] . The designation

(and L') may be used for the ferroelectric phase if a distinction between this and the g (and L) paraelectric phase is desired. The ferroelectric characteristics of this group were

first discovered by Borchardt and Biersted [18]

.

Single crystals can be grown in inch size pieces by the Czochralski technique of pulling

from the melt Pr to Tb. For the Eu to Tb compounds the J structure is first formed, but converts nondestructively into L. In the case of the Dy, Ho, and Y compounds, however, the

transformation from C is destructive.

The L structure compounds (except for Y2(MoOt^)3) exist at room temperature in a metastable condition; at temperatures below but close to the transformation temperature the transition to M does occur. Thus a single crystal of Gd2 (M0O1+) 3 transforms completely at 800 °C in

3 days to the M form, but at 600 °C the process is imperceptibly slow. The powder transforms

completely in less than 3 days at 400 °C. For Tb2(Mo0i^)3 the conversion rate is appreciably

slower

.

At room temperature g-Tb2 (MoOi^) 3 and g-Gd2 (M0O1+) 3 are ferroelectric, ferroelastic , and

paramagnetic, and a compilation of properties has been published [5,19]. Laser action has

been reported in B-Gd2(Mo04)3 doped with Nd [9,10]. At very low temperatures gadolinium

molybdates become antiferromagnetic [20]

.

4.2.b. STRUCTURE J

This phase was only recently recognized [6] . It occurs as the y form of the molybdates

from Eu through Dy as shown in figure 4. The DTA curves of figure 11 show that in the case

of Tb2(MoOi^)3 the y phase does not form on heating but only dvuring solidification of the

melt. It should be noted that the amount of heat absorbed during melting, i.e. the area

under the melting peak, depends on whether the y phase is present or not. Quantitative

measurements indicate that for the g to y transition AH1155 = 50 kcals/mole [6]. The powder

diffraction trace at 1000 °C can be indexed as ci:ibic with a = 10.44 A, and is Pm3m or a subgroup [6] . Since the J structure compoxinds transform nondestructively to L and only exist in

a limited temperature region at elevated temperatures, the prospects for single crystal prepation and examination are not encouraging.

453
TEMPERATURE "C Fig. 11. DTA curve (composite) of (MoO;^) 3 (after [3]).

4.3. C* FAMILY STRUCTURES (6 -COORDINATED)

This family of structures occurs as the only form of the molybdates of Er to Lu, Sc, In,

Fe, Cr, Al, the 3-form of Y, the yfo^ of Ho and the 6-form of Dy; also the tungstates of

Er to Lu, In, Sc, Al, and the 3-form of Gd to Y. The structure was first solved [2] for Sc2

(W0i+)3, which is orthorhombic Pnca with a = 9.596, b = 13.330, and c = 9.512 A. An indexed

x-ray powder diffraction pattern of Sc2 (WOi^) 3 and approximate lattice constants for some of

the other C* compounds have been given, [1]

.

Most of these compounds are readily pulled from the melt in large single crystal form.

One of the difficulties in working with the lanthanide C* compounds is that they absorb moisture from the atmosphere to form trihydrates destructively; data for hydrates of the tungstates, designated B, and the molybdates, designated K, has been presented [1]. Early workers

on lanthanide tungstates did not realize that water was present, and this was first recognized

by Bor chard as detailed previously [1] . The nonlanthanide compounds do not hydrate in this

way

.

The In and Fe molybdates have been reported [21,22] to be monoclinic P2ia, but with Pnca

as a siib-cell. Partial examination of a Tm2 (MoOlj) 3 crystal pulled from the melt and protected

from hydration indicated a doiibling of the c-axis dimension with a = 10.00, b = 13.65, and

o _^ c = 19.50 A; this structure has been designated C by Rode et al. I23J . This type of structural variation is the justification for using the "family" concept.

5. CONCLUSION

Factors which have complicated, and in fact even vitiated, early and also some more re- cent work on these compounds include the following:

i) the existence of unexpected components, e.g. Na yielding NaReCW0i^)2 124J and H2O

in the C* structure lanthanide compound hydrates;

ii) metastability , e.g. the slow L-^N, L^M, and L-^J transitions, resulting in phases being overlooked when sintering is performed at too high a temperature, etc.;

iii) sometimes unsuspected nondestructive phase transitions, e.g. J->L and D^A;

454
iv) the occurrence of compounds with highly related but distinct structures within

families such as C*;

v) the presence of long range ordering not apparent in powder x-ray diffraction but

obvious in single crystal investigations, e.g. in the A family M* structures; and

vi) insidious effects which can be produced by deviations from stoichiometry and

Ostwald's step rule in metastable systems.

With allowance made for these complications, several patterns emerge. Three in particular may be singled out:

i) the unexpectedly many structures occurring can be grouped into three families with

coordination numbers of 6, 7, and 8 for the lanthanons , increase in size and decrease in temperature favoring higher coordination as discussed in Section I;

ii) the change from tungstate to molybdate (or an equivalent smaller rise in temperature

[3] has essentially no effect on the coordination but does produce a change from the relatively simple A structure to the more complex members of the A family; and

iii) the various ways in which the A family structures (based on the ordering of vacancies in a scheelite related s\±)-cell structure) can deform: by deviating from the y = 90° of

scheelite with a simple ordering, as in the A structure; by maintaining y = 90° but forming a complex long-range ordering, as in the N* structures; or by doing both, as presumably occurs

in the M* and D structures.

Further understanding of this fascinating group of compounds must await the availability

in single crystal form (permitting structure determinations) of additional compounds, in particular of the D, M* , and J compounds, as well as further variants within the N* and C* structures .

6. ACKNOWLEDGMENTS . -

The cooperation of various co-workers of references lU through. 17] and 116] as well as those acknowledged there is gratefully recognized, as are most helpful discussions with S. C. Abrahams

.

7. REFERENCES

[I] Nassau, K. , Levinstein, H. J., and Loiacono, G. M. , J. Phys . Chem. Solids 26_, 1805

(1965)

.

[2] Abrahams, S. C. and Bernstein, J. L., J. Chem. Phys. £5, 2745 (1966).

[3] Nassau, K. , Jamieson, P. B., and Shiever, J. W. , J. Phys. Chem. Solids _32.' 1225 (1969)

[4] Jamieson, P. B., Abrahams, S. C, and Bernstein, J. L., J. Chem. Phys. 50_, 86 (1969).

[5] Keve, E. T., Abrahams, S. C, Nassau, K., and Glass, A. M. , Solid State Comm. 8_, 1517

(1970) . [6] Nassau, K. , Shiever, J. W. , and Keve, E. T., J. Solid State Chem. 3_, 411 (1971).

[7] Keve, E. T., Abrahams, S. C, and Bernstein, J. L., J. Chem. Phys. 54, 3185 (1971).

[8] Shannon, R. D. and Prewitt, C. T., Acta Cryst. B25 , 925 (1969).

[9] Borchardt, H. J. and Biersted, P. E., Appl. Phys. Letters 8_, 50 (1966).

[10] Borchardt, H. J. and Biersted, P. E., J. Appl. Phys. 38.' 2057 (1967).

[II] Cross, L. E., Fouskova, A,, and Cummins, S. E., Phys. Rev'. Letters 21, 812 (1968).

[12] Templeton, D. H. and Zalkin, A., Acta Cryst. 1£, 762 (1963).

[13] Drobyshev, L. A., Ponomarev, V. I., Frolkina, I. T. , and Belov, N. V., Sov. Phys.

Crystallography 15_, 391 (1970) . [14] Brixner, L. H. , Biersted, P. E., Sleight, A. W. , and Licis, M. S., Mat, Res. Bull. 6_, 545 (1971)

.

[15] Weigel, F. and Scherer, U., Radiochim. Acta 13_, 6 (1970).

[16] Jamieson, P. B. , de Fontaine, D. , and Abrahams, S. C, J. Appl. Cryst. 2_, 24 (1969).

[17] Jeitschko, W. K. , Naturwiss, 51^, 544 (1970).

[18] Borchardt, H. J. and Biersted, P, E., Appl. Phys. Letters 8_, 51 (1966),

[19] Cummins, S, E., Ferroelectrics 1, 11 (1970),

455
[20] Fisher, R. A., Hornung, E. W. , Brodale, G. E., and Giauque, W. F. (to be piiblished)

.

[21] Plyasova, L. M. , Klevtsova, R. F. , Borisov, S. V., and Kefeli, L. M. , Sov. Phys

.

Cirystallogr. 12, 29 (1968) . [22] Plyasova, L. M. , Klevtsova, R. F., Borisov, S. V., and Kefeli, L. M. , Sov. Phys.-Dokl.

11 , 189 (1966) . [23] Rode, E. Y., Lysanova, G. V., Kuznetsov, V. G. , and Gokhman, L. Z,, Russ. J. Inorg.

Chem. 13.' ^"^^ (1968) . [24] Sillen, L. G. and Sundvall, H, , Arkiv For Kemi, Min. o. Geol. 17A, 1 (1943).

DISCUSSION

L. H. Brixner : I'm glad you left my little diagram up there on the board. I'd like to come back to this gamma phase because I still believe it's metastable. Of course, it would

be very difficult to prove really, because one would have to take a high temperature x-ray

diagram of a growing crystal. There are two reasons why I believe it is metastable. One,

I'm convinced we are growing in equilibrium with the tetragonal beta structure because the

macroscopic symmetry of the crystals (as you well know since you've grown enough of them) is

in accordance with tetragonal symmetry, not with cubic symmetry, and I believe you called the

gainma phase cubic. Two, we do find a lower melting temperature, at least in the case of terbium molybdate, for the gamma phase and we are growing at the beta melting point, not the

gamma melting point.

K. Nassau : Two points. First of all, I said that the gamma phase can be indexed cubic,

I didn't say it is cubic. Drastic difference: it may well be tetragonal. Secondly, I believe you are taking as the melting point the DTA peak whereas we are taking the shoulder.

I believe the shoulder is the correct one to take on theoretical basis and this we find does

not change within five degrees from cx to 3. So we disagree: we agree on the data, but we disagree on the interpretation.

L. H. Brixner : No matter what point we take on the DTA plot, the absolute difference

between shoulder or peak is the same.

K. Nassau : We find the shoulders are identical within five degrees.

L. H. Brixner : As best I know you are also using a DuPont analyzer.

K. Nassau : Yes, I'm the first to admit it. However, I should say in line with what

we heard in our first talk this morning, who knows what an "equilibrium phase" is anyway.

All we can do is report what results we observe.

H. Young : Could we have another kind of question?

R. S. Roth : I think that your surprise that molybdenum and tungsten are so different

shouldn't be a surprise. I think, just like niobium and tantalum are so different, molybdenum

and tungsten are different when more than 50 percent of the compound is this ion. When it

is a 1:1 ratio or less, then they are very, very similar. After all, even the oxides themselves are very different.

K. Nassau : If you look at the phosphates and arsenates and so on, you usually find one structural change in the middle of each lanthanide series. Even if the tungstates and molybdates are different, for instance with calcium the tungstates and molybdates aren't the same structure; I still would not have expected eight structures plus numerous variants within two

simple series of compounds like this. I think one is justified at some surprise there. It's

true, after one has seen Wadsley's work one shouldn't be surprised at anything, but then I do

think we are dealing with equilibrium phases here which is not claimed for Wadsley's structures .

I

456
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

CRYSTAL CHEMISTRY OF TETRAHEDRALLY-COORDINATED

OXIDES: LigPO^ DERIVATIVES

A. R. West and F. P, Glasser*

Department of Chemistry

University of Aberdeen

Meston Walk

Old Aberdeen, AB9 2UE , Scotland

The high and low polymorphs of LisPOit are type structures for a large family of tetrahedrally- coordinated oxides. These are readily synthesized by direct solid state reaction

of the constituent oxides or by hydrothermal reaction. The simplest substances which are

Li3P0it-type include LisVOi^ and LisAsOi^, although the high-low inversion in the latter two

proceeds reversibly through one or more intermediate phases which are thermodynamically

stable over a short range of temperatures.

The intermediate phases often undergo further structural distortion during quenching to ambient. Li3P0it itself forms an intermediate .phase in the conversion low high Li3P0i|.

This intermediate phase is readily retained to ambient but is believed to be metastable at all temperatures. More complex Li3P0it derivatives include substances of the general

formula Li2MX0i+ , where M = Mg, Zn, Co^+ and X = Si , Ge'*''". Each compound usually has at

least two polymorphs. These fall into three classes: one which is either high or low

Li3P0it type, one which includes the distortional derivatives of both high and low Li3P0it,

and lastly, phases of related but unknown structures. A full explanation of the polymorphism

of an individual phase is only possible if effects due to solid solution are taken into

account. For example, the stoichiometry of "Li2ZnSi0i+" varies within the system

Lii+Si0it-2n2Si0:+ ; the solubilities of excess Li"*" and Zn2+ have been measured as a function

of temperature. Inversion temperatures, and especially, the occurrence and stability of

many of the distortional derivative structures, are closely related to the stoichiometry.

The possibilities of making other substitutions, such as replacing (Li"*" + M^"*") by A^"*"

,

where A = Ai, Ga^"*", etc., are discussed.

This family of phases is probably of widespread occurrence. We have encountered these

phases in glass-ceramic systems, such as Li20-Mg0-Zn0-Si02 , where they are an important

crystallization product of all glass compositionKey words: Crystal chemistry; kinetics; lithium arsenate; lithium phosphates; lithium

vanadate; phase transformation; polymorphism.

1. INTRODUCTION

The crystal structures of the low and high forms of LisPOi^ have been determined [1,2]^:

the atomic positions are similar in both polymorphs. The oxygen atoms are arranged in

approximately hexagonal close packing, similar to that found in olivines. However, the

simplest olivines have the stoichiometry M|"'"siOi+ , where m2"*' = Mg, Fe, Ni , Co, Mn , and, at

low temperatutes Ca, while lithium phosphate is more cation-rich. Also, the divalent ions

*^Lecturer and Senior Lecturer, respectively.

Figures in brackets indicate the literature references at the end of this paper.

457
are octahedrally coordinated in olivine, whereas in Li3P0i+ all the cations are tetrahedrally

coordinated. Despite these differences, LisPOi^ and olivines exhibit a remarkable similarity

in unit cell dimensions and axial ratios; both have orthorhombic symmetry and the same, or closely related space groups. This relationship can only be fortuitous even allowing for

the similar oxygen arrangement in the two structure types. As a result, much confusion has

arisen in the past over the distinction between lithium phosphate and olivine structures.

Synthetic lithium phosphate was once classified as an olivine 13] and when the low form of

Li3P0i+ was subsequently found in nature as the mineral lithiophosphate 14] , it was thought

to be an olivine 15]

.

After the crystal structure of high LisPOit had been reported 12] , one of the first to recognize and study other LisPOit isotypes was Tarte 16] ; he showed that Li3AsO^ and Li3V0i+ were isostructural with the low fom of Li3P0it, whose synthesis and x-ray powder diffraction

data were first reported by Swanson, et al. 17]

.

The present paper reviews some of the authors recent work on the simple isotypes of

Li3P04 and on the crystal chemistry and stoichiometry of some of the more complex derivative

structures. Phases which are isostructural with low Li3P0i| will be designated ^jj' those

isostructural with high Li3P0i| will be designated Yii- Reasons for using this apparently

more cumbersome nomenclature will become apparent when the crystal chemistry of the

derivative structures is described.

2. LITHIUM PHOSPHATE

2.1. LITHIOPHOSPHATE

Single crystals of lithiophosphate, the naturally occurring form of LisPOit, have been

examined by x-ray rotation and Weissenberg photographs.^ Sufficient photographs were obtained to show that the specimen is isostructural with synthetic 3ii (low) Li3P0i+ . It had

previously been suspected from a comparison of x-ray powder data that the two were closely

related, but that they may not have been isostructural. This uncertainty is now removed.

The slight differences between the powder patterns of the synthetic and naturally-occurring

samples probably arise from their differing degrees of preferred orientation.

2.2. HEATING EXPERIMENTS ON Li^PO^

3 4 A heat effect has been reported to occur at ca. 500 °C on heating low Li3P04 [7]

:

presumably this was due to conversion of tlie 3jj (low) to Yji (high) Li3P0i+ . The reaction

is apparently monotropic: hydrothermal recrystallization can be used to reverse the

reaction [6] . ^j^Li^^Oi^ can also be prepared by direct precipitation from aqueous solution

[7].

We have recently studied the gjj ^ Yh inversion of a commercial grade (Hopkin and

Williams, Ltd.) of low Li3P0i^ . No sharp event was observed by DTA at or around 500 °C,

but instead, a broad endotherm appeared over the range 440° to 520 °C: this heat effect

was not reversible on cooling. A sample removed from the DTA apparatus after heating to

550 °C gave, at ambient, a powder pattern intermediate between those of 3jj and YiiLi3P0^ taken from the same source and heated to 900 °C for 15 hr yielded YiiLi3P0i+. The

differences between the powder patterns of the high, low and intermediate polymorphs are

small, as shown diagramatically in figure 1. A high temperature powder x-ray (HTXR)

photograph also showed that the Yii inversion proceeded via formation, over a short

temperature range, of the same intermediate phase. The thermodynamic stability of this

Li3P0i+ transitional phase is uncertain: it has not yet been obtained by cooling YiiLiaROit

»

and the reverse reaction, Yjj giiLi3P04, has not been achieved except in the presence of

water or water vapor.

Single crystals of the natural mineral, heated rapidly to ca . 700 °C, convert

topotactically to YiiLisPOi^ . The significance of this will be discussed subsequently.

2 This sample was kindly loaned by The United States National Museum, Catalogue number

USNM 121266.

458
All'

1 . 11

1

ll .

FENS T

1 1 z

1 1 ll 18 22 26 30

'20 CuK«

34 38

Fig. 1. X-ray powder diffraction data at 25 °C for the

polymorphs of LisPOi^.

ISOTYPES OF Li3P04

3.1. LITHIUM VANADATE, Li^VO^

3 4 The complex polymorphism of Li3V0it is only partially understood: the present state of

knowledge is summed up in figure 2. In addition to the 3ii(low) form, hi'^VO^ forms a non- quenchable Yh (high) form and a T (= transitional) phase having a stability field and also,

probably a structure intermediate between those of the 3ii and yii polymorphs [8] . Both the

3ii and T polymorphs occur in several variants; these will be discussed presently. The

existence of an additional phase, stable between ca 1050 °C and the melting temperature,

ca 1150 °C, is indicated by DTA [8,9]. This high phase gave only weak and diffuse x-ray

powder patterns so it is not well characterized, but it appears to be structurally unrelated

to the 3, Y, or T phases.

The 3 phase (3ii or one of its variants) appears to be stable up to ca. 650 °C; above

this temperature a T phase forms. The reaction: 3 phase 1=; T phase, is reversible and shows

some hysteresis, especially at the faster rates used in DTA. One variant of 3ii, designated

X' -311, obtained at ambient. It was prepared by annealing a sample of 3jj at ca. 650 °C for several days. X' -3jj ^^Y be the equilibrium phase at 650 °C. However, HTXR photographs

taken at slow heating and cooling rates show that another closely-related phase, designated

X-3ii, appears between ca. 300° and 650 °C. The exact status of X-gjj and X' -3ij is

uncertain; in figure 2 both are shown as being metastable at all temperatures, but this

interpretation is provisional.

Several T-phases may be produced for Li3V0i| . In general, they have a stability field

between ca. 650° and 750 °C, although two variants have also been quenched metastably to ambient. The conversion of a T phase to Yn takes place reversibly, although with some hysteresis. By HTXR, at heating and cooling rates of approximately 1.0 °C min"-"- the variant

designated Tj Li^VOi^ is observed in the conversion 3iit:, Tjt:;Yii. This Tj phase appears

to be the same as that which is obtained by quenching Li3V0i| from ca. 740 °C to ambient.

However, HTXR photographs taken at slower heating and cooling rates (ca . 0.1 °C min~M , show

that a number of minor phase changes occur within the T phases. The different T phase

variants have proved difficult to classify not only because of the small differences between

their x-ray patterns, and the short range of temperatures over which each variant occurs,

but also, because different transformation sequences between variants are observed on the

heating and cooling runs. The broad features of both heating and cooling runs appear to be:

3ll* >X-gjj"fZ^T phases (several variants) ^Z^YiiThe powder patterns of the T phases, especially Tjj (produced by quenching Li3V0i+ from

ca. 1100 °C) , have close similarities to those of 3ii and Yjj: a comparison is shown in

figure 3. Indexed powder data for these phases are presented elsewhere [8] ; it is shown

that many of the differences between the powder patterns can be accounted for by changes

in the c crystallographic dimension of the orthorhombic cell, or pseudocell, which is common to all three phases. With rising temperature, c increases by about 1.0 to 1.5% at

each transition. These discontinuous changes in c are characteristic of a normal, firstorder phase transformation.

459
Li3Pq, Li3AsC^

LigVO^

TSO 1050

7<yo 7yo LUZnSiQ,

L!2MgGeq^

LijCoSiq^ LijZn GeC^

Fig. 2. Schematic temperature-stability relations for the

sequence of phase changes in LisPOtt and related

structures. The ordinate is a schematic measure

of the relative stabilities of the different forms.

Heavy lines show the equilibrium state. Broken

lines indicate phase changes which could be followed

by either DTA or high- temperature x-ray. Small

circles represent transformations which could not

be followed directly, but which must exist. Where

known, transformation temperatures are indicated at

the bottom of each figure. For LiBVOi*, the

crystallochemical classification of the high phase

is not known; hence the question mark. Also, it

is not known if the T^LisVOtt phase which is shown

as stable for a short range of temperature below

750 °C, is the same as or is a variant of the Tj

phase obtained at ambient by quenching; the figure

suggests the latter interpretation.

460
y„ 800 c

=1 1

1 1 ,1 1,1 1 T 25°C

1 1

1 1

-4 .

I I J.1 \I ,JII—. MJ

16 20 24 28 32 36

°2e CuKoc

Fig. 3. X-ray powder diffraction data for some

LisVOit polymorphs.

3.2. LITHIUM ARSENATE

The polymorphism of Li3As04 is shown in figure 2. Like Li3V0tt , it has Yu and Bjj

phases whose stability fields are separated by that of a transitional phase. This phase,

designated Tjj Li3AsOi| , is believed to be isostructural with Tjj Li3V0it , a polymorph which

is probably always metastable in the Li3V0tj system. The Tjj phase of Li3AsO^ forms reversibly

from 3x1 Li3AsO^ on heating and from yii Li3AsO^ on cooling. The transformations exhibit

considerable hysteresis at the faster DTA rates. All three polymorphs may be retained to ambient by a suitable choice of cooling rate for the Yii phase. None of the other transitional

phases or the 3jj variants produced by annealing Li3V0it seem to have any counterpart in the

Li3As04 system.

3.3. STRUCTURAL RELATIONS, KINETICS AND MECHANISM OF THE HIGH -^Z^ LOW TRANSFORMATION IN Li^PO^ - TYPE STRUCTURES

3 4 The structural differences between the high and low forms of Li3P0i+ are not large.

Examination of the atomic positions shows that the oxygens approximate more nearly to hexagonal close packed layers in the low form than in the high, and that one set of lithium

and one set of phosphorus atoms occupy different sets of tetrahedral holes in the two

structures. These differences are largely confined to displacements occurring in the [001]

direction, i.e., the direction which is normal to the close-packed oxygens. Thus, the

two structures appear to be very similar in their ab projections. Rather surprisingly, the

symmetry of the low foirm is higher than that of the high-temperature form.

Associated with each plane of close-packed oxygens are two sets of available tetrahedral

sites, one above and one below the oxygen layer. Only one of these sets is occupied in low

Li3P0i^. By comparison, in high Li3PGi^ there is a division of lithium and phosphorus atoms

into tetrahedral sites on both sides of the oxygen layers. This redistribution of cations

in the high form causes a buckling of the oxygen layers, which results in the c unit cell

edge of high Li3P0i+ being 1-2% larger than that of low Li3P04 .

During the high.* low transformation, half of the cations jump from one set of tetrahedral sites to another and the oxygen framework changes slightly. Evidence for the semidisplacive nature of the transformation is provided by observing single crystals of lithiophosphate which have been heated rapidly to 700 °C. These convert to 'YjjLi3P04 which is

easily preserved to ambient. Microscopic examination shows that these Yjj crystals retain

their optical continuity and orientation, thereby indicating that the transformation is

topo tactic

.

The 3jj^^Yii transformation is much more rapid for Li3V0it and Li3AsOtt than it is for

Li3P04. This could be explained in several ways. Firstly, it should become progressively

easier to rupture bonds in the order: P-0 , V-0, and As-0 . Secondly, more thermal energy

will be available at the inversion temperatures of LisVOii and Li3As0it which are both

approximately 700 °C, compared with approximately 500 °C for Li3P0i^ . Thirdly, the possible

appearance of a transitional phase will presumably lower the activation energy required for

the transition, by allowing the necessary adjustments in atomic positions to occur in two

461
stages. The question arises: if a phase with intermediate structure eases the transformation,

and such a phase occurs during the Li3P0it transformation, why is the gjT ^

*" Yjj transformation

apparently irreversible? One possible explanation is that the transitional phase is, in

fact, metastable and can only appear monotropically on heating the low phase. This possibility

is shown schematically in figure 4. On heating a sample of 3ixLi3PO[| , it follows the free

energy curve a-b-c. Beyond point b it is actually metastable: at point c it inverts

monotropically to a transitional phase. On further heating, the transitional phase becomes

unstable and converts to the equilibrium Yn phase. However, on cooling the Yn phase, it

follows the curve e-b-f: beyond point b, Yji becomes metastable relative to gji but no apportunity arises for the formation of a transitional phase, and a large kinetic barrier

is created which favors the metastable preservation of the Yii phase.

4. DERIVATIVE Li3P04 STRUCTURES: U^l^^'^XO^ PHASES

4.1. INTRODUCTION

A number of compounds have been prepared which have one, or both, the Yu and 3jj

structure types. These include substances where m2+ = Mg, Zn, and Co, and where X = Si^"*" and Ge'*"'". In all cases where both y and 3 polymorphs can be prepared from the same composition, the 3-type phases are stable at the lower temperatures; the polymorphisms of

these compounds are summarized in figure 2. Phases of the type Li2MX0i+ need not conform to

this exact stoichiometry , and the polymorphism of the derivative structures is, in fact,

very sensitive to the stoichiometry. A fuller explanation of the crystal chemistry of these

derivatives and the stability of their various polymorphs, including the effects of changing

composition, temperature of preparation, and rate of cooling to ambient, can only be given

in terms of the phase diagram for the appropriate system.

TEMPERATURE

Fig. 4, Schematic temperature - stability relations for the

polymorphism of LisPOit showing the postulated monotropic

formation of a metastable T (= transitional) phase on heating low (gji) Li3P04. This T phase transforms

irreversibly to Yjj (high) Li3P0i^ on prolonged heating

at ca 600° - 700 °C (shown by vertical arrows)

.

462
4.2. THE SYSTEM Li .SiO -Zn.SiO . 4 4 2 4 4.2.1. PHASE EQUILIBRIA

The phase diagram of this system is shown in figure 5. It was determined by a combination of classical quenching methods and direct, high-temperature investigation [10]

.

LiltSiOLj can accept a considerable amount of zinc into solid solution, but no detectable

solid solution of lithium in zinc orthosilicate occurs. Li2ZnSi04 is a congruently melting

1:1 phase and both 3- and y-type polymorphs occur at this ratio. The most remarkable feature

of the diagram is the very wide range of solid solutions formed by the Yjj polymorph. At

900 °C, the range of single-phase formation extends from approximately 21 to 72 mol % Zn2Si04 . At higher temperatures, the zinc-rich limits of solid solution continue to expand but it

becomes more difficult to fix accurately the lithia-rich limits, owing to the increasing

volatilization of lithia from the sample. It is possible that the narrow two-phase gap,

which at 900 °C separates the fields of Y-]--|- solid solutions from those of Li^SiO^, closes over at higher temperatures, such that complete subsolidus miscibility extends from Lii^SiO^ to ca. 75 mol % Zn2SiO(4. The extensive solid solution in this system, even at low temperatures, is much larger than any previously reported in other comparable orthosilicate systems.

4.2.2, CHARACTERIZATION AND CRYSTAL CHEMISTRY OF THE ORTHOSILICATE SOLID SOLUTIONS

The x-ray d-spacings of y-phase solid solutions ranging in comparison from 25 to 71.5

mol % Zn2Si0i+ , have been measured at 700 °C. The end-member compositions mark the

approximate limits of homogeneous, single-phase formation at 700 °C and this is also the

lowest temperature at which the entire range of solid solutions can be held, without

decomposition, for a length of time sufficient to obtain an x-ray pattern. Figure 6 shows

the variation in unit cell dimensions with composition of the Yji solid solutions at 700 °C

The c-dimension remains nearly constant throughout; a and b change little in the lithiarich solid solutions but show a more rapid rate of change beyond 50% Zn2Si0i|. The calculated

cell volume of Li2ZnSi0i^ increases slightly with both lithium and zinc substitution. It is

thought that the oxygen array remains unchanged throughout the solid solution series and

Fig. 5. Phase equilibria in the system LittSiOi+-Zn2SiOit

,

The data are taken from reference [10]

.

463
330

3.20

3.10

2

80'

270 260

250

T—I—I—I—r—I—

r

(200)

-1 i <-

-4 1 1- -j 1—

(002)

Li,Sil^ 25 40 45550 5560 66 715 Zn^SiC^ MOLE •/. Zn^SiOj

Fig. 6. Variation in the a, b and c unit cell

dimensions of the Yu lithium zinc silicates

as a function of composition, at 700 °C.

The data are taken from reference [10]

.

that the variable lithium-zinc ratios are achieved by introduction of cation vacancies in

the zinc- rich members, and by cation-stuffing in the lithia-rich members. Thus, if the

unit cell formula at the 'ideal' ratio is: Li2ZnSi04, substitution of zinc for lithium

introduces cation vacancies until, at 75 mol % Zn2Si0it, the solid solution has the formula:

( 2Li4Zn2) {Zn^) Sii+Oie where represents a cation vacancy. On the other hand, the lithi

rich solid solutions substitute two lithiums for one zinc, so that at 25% Zn2Si0i+ , the solid

solution composition would be: (Li) 2 (Lie) (Zn2Li2) Si40i6 whereQ^efers to a site, which

is unoccupied in solid solutions containing > 50% Zn2Si0it, but which is gradually filled

in the lithia-rich solid solutions. LittSiOi^ may be regraded as the end-member of this

stuffing process. Its crystal structure is known [11], and at ambient temperatures it can be regarded as a distorted Li3P0i+ type structure in which the extra lithiums are stuffed into

five and six coordinated sites. With rising temperatures, Lii+SiOi^ undergoes a series of

minor phase transformations, until the high form, stable above ca. 720 °C, is obtained.

Judging by the similarities between HTXR photographs of high Lit^SiO^ and , high Lii^SiOt^ is probably even more similar to the Y-j-j phase than is low Lii+SiOt^. This similarity in

powder patterns, especially at higher temperatures, lends support to the view that, at temperatures just below the solidus, it would be possible for the two-phase gap between

LitfSiOtt solid solutions and "^jx solid solutions to disappear.

4.2.3. LOW-TEMPERATURE PHASE TRANSFORMATIONS

At lower temperatures, several types of phase change may occur. ^t equilibrium, Yn

Li2ZnSi0i+ and a small range of solid solutions convert to the Sj]- phase. The inversion

temperature passes through a maximum at the 50% composition, at which composition the

conversion is also kinetically most rapid. At still lower temperatures, the 6jj phase

inverts to another closely related phase, designated 3i , which is a distorted, low Li3P0i^

derivative structure. Under certain conditions, the B-p ^ » 6jj inversion passes through

an intermediate phase designated 3ii' which can be quenched to ambient. This 3jx' phase is

closely related in structure to 3ii Li2ZnSiOi+, its powder pattern differing only in slight

splittings of certain reflections. The nomenclature used is chosen so that Roman subscripts

denote patrials , or members of a particular structural family. Where it has been possible

to study phase transfozTnations between patrials, these are usually second-order, or have

some second-order continuous character: these transformations are characteristically rapid

and are often non-quenchable . Thus, the Yll solid solutions undergo various structural

distortions on cooling to yield other y~ patrial phases. The more lithia-rich members, for

example at 30% Zn2Si0i+, convert to the patrials designated yi and Yq- more zinc-rich

compositions, typically, 60% Zn2SiOi+f progressive cooling of Yu solid solutions yields

first a Yjx and then a new phase, designated phase C. Phase C appears to be structurally

related to Li^POn, but has a characteristic Li20:ZnO ratio in the region 1:2 to 2:3.

464
Two general principles serve as a guide to the type of non-equilibria which can arise

on cooling. One principle is that any reaction requiring conversion of a y- patrial phase

to a 3- patrial will be comparatively sluggish. If a phase fails to convert at an equilibrium

transition temperature it may instead follow a metastable pathway which subsequently leads

to its undergoing one or more metastable inversions. Nevertheless the results obtained by

cooling samples from ca. 900 °C at 1-10 °C min"-^ are so consistent and are so reversible on reheating, that they can be presented as a quasi-equilibrium diagram [12] : this is shown

in figure 7. At higher temperatures, where equilibrium is attained more rapidly, the

sequence of phase transformations tends to become indistinguishable from those which are shown on the equilibrium diagram (fig. 5), but at lower temperatures, the sluggishness of

the Yij 3ii conversion allows the y~ patrial phases to appear metastably across the

central region of the diagram. The Yq ,

* Yi and yi < * inversion temperatures also

pass through a thermal maximum at the Li2ZnSi0i+ composition.

The second principle is that equilibrium reactions requiring the exsolution of an initially homogeneous solid solution tend to be sluggish. Quenching of more zinc-rich

compositions causes a Yn phase to enter a region where it is metastable with respect to the

two-phase assemblage (Yji solid solution plus willemite) ; at lower temperatures, this

undercooled Yj]- phase inverts to a metastable C-family patrial, designated C. Another

example occurs in more lithia-rich compositions; for example at 16% Zn2Si0t| cooling of

Lii^SiOt^ solid solutions yields a new lithia-rich phase, designated phase D, which is structurally-related to Lii+SiOtt and is presumably a more distant relative of the Li3P0t^ structure

types. Powder x-ray data for these phases, as well as more details of their preparation can

be found in the references [10,12]. The combinations of metastable and stable phase transformations tend to produce complicated patterns of thermal activity in DTA runs ; a few of

these sequences have been described in detail [12] . It is also noteworthy that the equilibrium

phase relationships cannot, in general, be determined from an analysis of the phases

present in runs "quenched" to ambient: it is necessary to use a combination of direct, hightemperature methods (DTA, HTXR) to account for the phase distributions observed at ambient.

Lj,SO, 20 40 60 ao Zn,SiCi MOL 1.

Fig. 7. Phase non-equilibrium diagram representing the sequences

of transformations encountered in LittSi0i^-Zn2Si0L,

compositions upon cooling from the liquid, or from

solidus temperatures, at moderately slow rates ranging

from approximately 2 to 20 °C min~^ . The data are taken from reference [12]

.

465-504 O - 72 - 31 465
single crystals of most of the low-temperature phases can generally be prepared by

conversion of a 'high' solid solution having the appropriate composition. In several cases where these crystals have been examined at ambient, the crystals exhibit complex twinning:

this has tended to discourage single crystal x-ray studies. In general, the low-temperature

ordering of the solid solutions prepared initially at higher temperatures , bears a phenomenological resemblance to that which occurs in many complex alloy systems. The

analogy is strengthened because certain solid solutions which are unable for kinetic reasons

to undergo inversion to the stable phase or phases, instead undergo martensitic phase

transformations. The formation of phase D from Lii+SiOi^ solid solutions and phase C from

Yji solid solutions are examples of this.

4.2.4. MECHANISM OF THE y TRANSFORMATION IN Li^ZnSiO^

Evidence has been presented showing that Li3V04 and Li3As04 transform from Yjj to 3ii

modifications via an intermediate phase. Each of the transformations, Yjj ^

* T and

T ^

* Bjj . approximates to first-order. However, in the various derivative structures, the

3jj Yii transformation proceeds in different ways. The Yjj ^

* 6jj inversion for Li2ZnSi0i|

has a different mechanism to that for Yji ^^li LisVOi^. Thus, in one experiment, a homogeneous Yjj Li2ZnSi0i+ preparation was cooled to ambient from 1100 °C over a period of

4 hours. The x-ray powder pattern showed that it contained a mixture of 3- and y~ type

phases at ambient, indicating that partial conversion of the y phase to 3 had occurred. A

peculiar feature of the powder pattern of this partially converted product is the appearance

of the (002) reflections. Corresponding (002) reflections of the 3 and Y phases, are normally clearly resolved in well-crystallized mixtures of the two phases, but in the

partially converted product the two reflections are connected by a continuous band of diffuse

radiation, upon which are superimposed two sharp reflections, one of the 3, the other of

the Y phase. This phenomenon has been interpreted in terms of coherent growth during the

cooling, of 3 crystallites within the host Y~phase crystals. The extra diffuse reflection

band is attributed to disordered or strained regions at or close to the interface. A

number of specimens have been examined which differ principally in their degree of conversion

In this series of powder photographs, the relative intensities of the sharp portions of the

(002) reflections varies, as would be expected, with the relative proportions of Y~ and 3-

phases which are present, but the intensity of the diffuse band always remains approximately

constant so long as both the starting phase (y) and its conversion product (3) are both

present.

The reaction apparently proceeds in the reverse direction - that is, 3

*-y ~ in one

step. A high-temperature x-ray photograph, taken on heating, showed 3 converting slowly

to Y- The reaction was slow, taking several hours to complete, although the furnance

temperature was allowed to rise slowly during the course of the experiment. The powder

pattern thus obtained was characterized by a gradual weakening of the (002) reflections of

the 3 phase while the (002) reflections of the y phase became more intense. Each (002)

reflection remained sharp and no intermediate diffuse zone was noted.

These observations show that the Sjj ^ * Yh transformation in Li2ZnSi0i^ is not

ideally reversible, and provide some support for the suggestion that the Yji phase transforms

to 3 II by a nucleation and coherent growth mechanism.

4.2.5. MECHANISM OF THE Y^..^. ^

*

3^..^ TRANSFORMATION IN OTHER Li^MXO^ PHASES

A few experiments have been done to find out the mechanism of the y ^ transformation

for other derivative phases. Li2CoSi04 transforms in the same way as does Li2ZnSiO[t . On

heating the 3jj phase the conversion to Yu apparently takes place in one step, but upon

slow cooling of Ynf the (002) reflection of 3jj gradually appears, and the (002) reflections

of the two phases are again connected by a diffuse scattering region which persists throughout

the transformation. In Li2MgGeO[t , however, the transformation between Bjj and Yu proceeds

reversibly through a separate intermediate phase, which may be the thermodynamically stable

phase over a short range of temperatures close to 1000 °C. This transitional Li2MgGe04 phase

is probably isostructural with TjjLi3V0i^.

466
4.3. THE SYSTEM Li ^SiO -Mg^SiO

4 4 2 4 Phase relations in this system, shown in figure 8, were studied by the same techniques

as were used for studying the Lii+Si04-Zn2SiO[t system [13] • The magnesium system bears a considerable resemblance to the zinc system, except that the stoichiometry of the magnesiumcontaining Y solid solution is more restricted at any temperature chosen for comparison.

Also, no 3-patrial phases have ever been obtained in this system. Hydrothermal experiments

made in the hope of producing a 3-patrial phase at the Li2MgSiO[| composition yielded

negative results, although 3 solid solutions containing up to 80 mol % Li2MgSi0i+ can be

prepared along the join Li2ZnSi0i|-Li2MgSi04 . Apparently, some zinc is essential to the

stability of the 3-type phase.

The D-patrial phases, which could only be obtained metastably in Li4Si04-Zn2Si0i+

compositions, can be obtained at equilibrium for a range of Mg-containing compositions.

5. SUBSTITUTION OF TRIVALENT IONS IN Li2M^'^X0^

Trivalent ions such as aluminum and gallium may be substituted, often in substantial

quantities, in these structures. In all cases where solid solution was found to occur,

the M^"*" ion substitutes for (Li"*" + M^"*") , rather than by substitution of two M^"*" ions for

(M^"^ + X**"^) . Thus, the solid solutions have the formula: Li2_nM^-n^n"'"^'^4 ' where n is the

number of trivalent ions per formula unit. Table 1 shows the quantitative extent of these

solid solutions, at 1000 °C, for the various combinations tried. Compositions on the join

Li2MgSi0i+-LiAJ,Si0it did not yield a y-phase solid solution: instead large quantities of

lithium spinel formed. Thus the solid solution of Ai in Li2MgSi0i^ is probably negligible.

On the other joins, solid solutions range upwards from ca. 5% of LiA£GeOi^ , or LiGaGeOi^ in

Li2ZnGe0i+ , to ca. 25% of LiGaSiOi^ in either Li2ZnSiO[t or Li2MgSi0i| . Apparently, the most

favorable substitutions are those where gallium replaces either (Li + Mg) or (Li + Zn) in i silicate phase or where either aliminium or gallium replace (Li + Mg) in a germanate phase.

It is not possible from these few experiments to say whether the solid solutions are compatible with the end-members of the replacement series, LiM^"'"XOi+

.

1200

°c

1000

600

^ -^^^^ / Mc^tO^» LIQUID

HIGH-L|,Siq

80 MgjSiO^

Fig. 8. Phase equilibria in the system Lii^SiO[^-Mg2Si04

.

The data are taken from reference [13]

.

467

/
TABLE 1

Solid Solution of M Ions in

Li2M^ XOit Phases

System

Extent of Solid

Solution at 1000 °C

Li2ZnSi04-LiAJlSi0it 10 ± 5%

Li2ZnSi0i+'-LiGaSi0tt 25 ± 10%

Li2ZnGeOit-LiA2.GeOtt 5 ± 5%

Li2ZnGe0it-LiGaGe0it 5 ± 5%

Li2MgSi0i+-LiJV£Si04 0-5%

Li2MgSi0i|-LiGaSi0i+ 25 ± 10%

Li2MgGe0[t-LiA£Ge0i+ 20 ± 10%

Li2MgGe0i| -LiGaGeOi^ 20 ± 10%

6. OCCURRENCE OF Li^PO^ - TYPE PHASES IN MORE COMPLEX SYSTEMS

The interactions between the three orthosilicates : Lii^SiO^, Mg2Si0i+ and Zn2Si04 have

been studied [13] , and it was found that an extensive range of ternary orthosilicate solid

solutions having the 3 or y type structures occur. The extent of this solid solution and

the occurrence of 3 or y phases is very temperature dependent. Figure 9 shows the

appearance of one such isothermal section at 700 °C.

The distribution of Li3P04 - derivative phases in yet more complex systems has

received some study. Data on the quaternary system Lii+Si0tj-Zn2Si0i+-Mg2Si04-Si02 show

that at subsolidus temperatures, all compositions, even those highest in silica, will

contain a Li3P0;+ - type phase on equilibrium cirystallization [14] .

Fig. 9. Phase equilibria in the system Lit|SiOi+-Zn2Si04-Mg2SiOi^ : the 700 °C isothermal section. The data are taken from

reference [13 ]

.

468
7. REFERENCES

[1] Keffer, C. , Mighell, A., Mauer, F., Swanson, H., and Block, S., Inorg. Chem. , 6_, 119

(1967) . [2] Zemann, J., Acta. Cryst., B13 , 863 (1960).

[3] Zaitibonini, F. , and Laves, F., Z. Krist., 83_, 26 (1932).

[4] Matias, W. S., and Bondareva, A. M., Dokl. Akad, Nauk , S. S. S. R. , 112 , 124 (1957).

[5] Fischer, D. J., Amer. Miner., 43_, 761 (1958).

[6] Tarte, P., J. Inorg. Nucl. Chem., 29_, 915 (1967).

[7] Swanson, H. E., Morris, M. C, and Evans, E. H., "Standard X-Ray Diffraction Powder

Patterns", Sect. 4, p. 21, National Bureau of Standards, Washington, D. C, monograph

No. 25, (1966)

.

[8] West, A. R. , and Glasser, P. P., J. Solid State Chemistry, 4_, 20 (1972).

[9] Reisman, A., and Mineo, J., J. Phys . Chem., 66_, 1181 (1962).

[10] West, A. R. , and Glasser, F. P., J. Mater. Sci., 5_, 557 (1970).

[11] Vollenkle, H. , Wittmann, A., and Nowotny, H., Monat. Chem., 99_, 1360 (1968).

[12] West, A. R. , and Glasser, F. P., J. Mater. Sci., 5_, 676 (1970).

[13] West, A. R. , and Glasser, F. P., J. Mater. Sci., 6_, 1100 (1971).

[14] West, A. R. , and Glasser, F. P., J. Mater. Sci., in press.

DISCUSSION

R. S. Roth: I'm wondering if these compounds don't have some water in them that

might account for some of the strange polymorphic behavior and/or some of the non- stoichiometry . Do you have any way to prove or disprove this?

F. P. Glasser: Well, of course it is always very difficult to disprove the existence

of water in a compound, but in the course of doing the experiments on lithiiim vanadate we certainly did do quite a few weight change measurements and there was no evidence of any

water pickup. We have also done some infrared work on these compounds, which time does

not permit me to describe, and there was no evidence of any hydroxy 1 content in them.

Also, in many instances the temperatures of preparation were very high, 1300 or 1400 °C

in a few instances. I would think the evidence is vfery reasonable that there is no essential content in any of these phases. It is possible that some of the annealing

variants which we described might have picked up water during the long annealing at low

temperatures. However, some of these experiments were duplicated in sealed silica tubes

in an attempt to check this and they gave identical results.

W. R. Cook : There is a very great similarity between the low and high temperature

lithi\am phosphates in their structure, which doesn't really seem to require intermediate

phases. I was wondering if you had any information on why, in fact, you get the intermediate phases.

F. P. Glasser : Yes, we had speculated why these intermediate phases arose. Let me

describe the structures very briefly for those who aren't conversant with them. The

oxygens in both phases are hexagonally close packed and all cations both lithiums and

silicons are in tetrahedral sites. But comparing the two structures, half the lithiums

and half the silicons are in different sites. We speculated that the transitional forms

arise because of motions of one set of atoms before the other set begin to move. This

would, of course, require a structure determination of one of the intermediate forins to prove this speculation. As most of the people who have worked on lithium phosphate,

lithium vanadate and so on will tell you, the crystals tend to have a high proportion of

twins. Many of the crystals of the related silicate phases also have very complicated

internal phase domain structures. These have greatly handicapped single crystal investigations. So, at the moment we are reduced to speculation as to why the transitional forms

arise.

I might add that with respect to both questions, I think that all of these oxide

systems, when investigated in more detail, are going to turn out to be very complicated.

They are going to turn out to be just as complicated as metal alloy systems. I think

these intermediate phases and transitional phases will more and more be discovered.

469

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

ON THE SOLIDIFICATION TEMPERATURE AND THE NONSTOICHIOMETRY

OF COBALTOUS OXIDE IN AN OXIDIZING ATMOSPHERE

J. p. Coutures and M. Foex

Centre National de la Recherche Scientifique

Laboratoire des Ultra Refractaires

B. P. No. 5 - 66 - ODEILLO

France

Liquid cobaltous oxide can dissolve a large amount of oxygen depending on temperature

oxygen partial pressure and time. Therefore, the solidification temperature decreases when

the amount of oxygen in the liquid phases increases. During solidification, a "spitting"

phenomena occurs. The behavior (spitting phenomena for example) and the properties of

this oxide (solidification temperature, melt composition, solid composition) are studied by

high temperature techniques.

Key words: C0O-O2 system; melting point depression; nonstoichiometry in liquid CoO;

solar furnace; thermal analysis.

1 . EXPERIMENTAL

In the course of the present study, thermal analysis, thermomanometric , and thermogravimetric, apparatus are used and in each case the oxygen potential in the gaseous phase

is determined by gas chromatography.

The thermal analysis apparatus (fig. 1) , previously described by Foex and Coutures [1]

is used in conjunction with an horizontal axis solar furnace. Controlled atmosphere is

obtained by the interposition of a silica tube (A) between the centrifugal furnace (B) at

the focus of the parabolic mirror. The optical pyrometer works in the visible region (O.eSym).

Melting is maintained for ten minutes in order to obtain thermodynamical equilibrium between

the melt and the oxygen partial pressure of the atmosphere. The volume of the centrifugal

furnace (cooled cooper) is 10 cm^. The dimensions of the cobaltous oxide crucible are: diameter 8 mm, length 23 mm.

Figure 2 shows different cooling curves of cobaltous oxide melted under: A) mixed gas,

20% argon - 80% oxygen, B) mixed gas, 40% argon - 60% oxygen, C) pure argon. It is evident

that only the product melted under pure argon ^ives a good solidification plateau corresponding

to a stoichiometrix oxide (solid composition ^= 1,000). For the other cases, at the end

of the solidification, there is a thermal arrest corresponding to the spitting phenomena.

As an example, figure 3 gives a view of the spitting phenomenon that occurs at the end of the

solidification of cobaltous oxide molten under a pure oxygen atmosphere. The projections

(spitting) are the cause of the thermal arrest on the thermal analysis curves.

A schematic diagram of the thermomanometric apparatus [2] (built in our laboratory)

associated with the vertical axis solar furnace is shown in figure 4. The product is melted

on a small water cooled copper plate which is surrounded by two silica vessels containing

water. The change of the pressure inside the vessel, at the solidification point is measured

by a differential pressure transducer and recorded by a high speed recorder [3] . The response

time of the complete data acquisition system is 2 milliseconds.

Figures in brackets indicate the literature references at the end of this paper.

471
Variable speed de motor

Cooling water

Parabolic mirror

Fig. 1. Thermal analysis apparatus for controlled atmosphere,

A - silica tube, B - sample, C - optical pyrometer.

1850 -

Temperature in "C

^ Time : seconds 20

J I I I 1 I I I I I I I I 1 \ 1 I I I I

Fig. 2. Cooling curves of cobaltous oxide after melting under:

A - mixed gas 20% A - 80% O2; B - mixed gas 40% A - 60%

O2; C - pure argon.

472
Fig. 3. View of the spitting phenomena Fig. 4. Schematic drawing of the thermooccurring at the solidification manometric apparatus associated

of CoO after melting in pure with a vertical axis solar furnace,

oxygen.

Solidification of the sample is obtained through a variable speed DC motor by vertical

translation of the measurement head in the solar heating cone. In such a way the liquid

phase can be cooled at different speeds in the range of 1 °C/sec to 250 °C/sec. Figure 5 shows the pressure change at the solidification of cobaltous oxide melted under pure oxygen

(weight: 230 mg; time of fusion: 1 minute; atmosphere: pure oxygen at 0.83 atm; cooling speed

of the liquid phase: 250 °C/sec) . One can note the beginning of the solidification and the

plateau due to the evolved oxygen. The final peak is caused by the many thermal effects

linked to the spitting [3] . With the help of calibration curves we can calculate the volume

of evolved oxygen and the composition of the melt just before the solidification.

The rmogravime trie data, figure 6, are obtained by a high temperature thermobalance

manufactured by SETARAM (Lyon-France) . This apparatus is composed^o:^^an ^i^^omatic recording

balance with a complete data acquisition chain (weight = f(t) and ~ ^ ^^'^ a high temperature furnace working in oxidizing atmosphere. The graphite heating element

of this furnace surrounds the alumina laboratory tube. The composition of the working

atmosphere (mixed argon-oxygen) is determined by a gas chromatography; the protection of the

resistor is obrained by purified argon flowing through the furnace. The temperature of the

molten product, in this case contained in an iridium crucible, is measured by an automatic

optical pyrometer working at 0.65ijm viewing the crucible through a total reflection prism.

An example of a typical thermogravimetric curve obtained with cobaltous oxide molten

under a gas mixture containing 20% oxygen and 80% argon is shown in figure 6. One can

note, at the beginning of the melting, the weight increase caused by the solution of oxygen

in the liquid phase and the weight loss that occurs at the solidification.

473

/
Temperature evolution K 2093 2093

Fig. 6. Thermogravimetric curve showing the solution of oxygen in CoO

molten under static atmosphere of 20% oxygen in argon.

474
2. RESULTS

2.1. INFLUENCE OF THE PARTIAL PRESSURE OF OXYGEN ON THE REFRACTORY CHARACTER OF COBALTOUS

OXIDE

By analysis of many cooling curves of cobaltous oxide melted under different oxygen

partial pressures one can get some information on the influence of oxygen on the solidification

point. We have collected the most important experimental results in table 1, when T is the

solidification temperature (IPTS 48), AT the depletion of the freezing point (reference:

solidification point of cobaltous oxide melted under pure argon) , composition of the solid

product after melting (ratio ) the nonstoichiometry x for Coi_x 0 as a function of

the composition of the melting atmosphere (mixed oxygen-argon). From these results, one

can make the following remarks

.

The depletion AT of the freezing point is proportionnal to the square root of the

partial pressure of oxygen, and this indicates that the oxygen is dissolved in an atomic

state.

The solidification temperature of cobaltous oxide versus the oxygen partial pressure is

given by the following formula:

T^ = 1830 - 40.5 Po2^/^

(total pressure 0.83 atm, atmospheric pressure of the laboratory).

2.2. INFLUENCE OF THE TEMPERATURE ON THE MELT COMPOSITION

The solution of oxygen for a given partial pressure versus the temperature is studied

by means of the thermogravimetric apparatus. To minimize the oxidation of the wire and of

the curcible of iridi\m and also the noise from the flowing gas, the experiment was performed

under a static oxidizing atmosphere (mixed oxygen 20% and argon 80%) . The temperature range

is between 1815 °C and 1885 °C and the pressure is 0.83 atm. The experimental data are collected on figure 7 where the composition of the liquid phase (ratio—

^ ; 0 = number of

oxygen atoms and Co, the number of Cobalt atoms) is shown versus the temperature. The curve

Table 1

0^ % del

atmosphe

T solidif

i

AT

AT

(0) CO sol

X

X 10^

^2 %

0 1830 0 0 1.000 0

10 1820 10 3.16 3 .16 1 .000 0 20 1814 16 4.47 3.17 1 .002 0.002 0.47

30 1810 20 5.47 3.65 1.005 0.005 0.91

40 1808 22 6.32 3.63 1 .006 0.006 0.94

50 1805 25 7.07 3.53 1.008 0.008 1.13

60 1802 28 7.74 3.61 1.009 0.009 1.16

70 1800 30 8.36 3.58 1.010 0.010 1.19

80 1797 33 8.94 3 .64 1.011 0.011 1.23

90 1795 35 9.48 3 .68 1.012 0.012 1.28

100 1793 37 10 3.70 1.012 0.012 1.20

475
1,02

-1,01

Temperature in "C

1800 1825 1850 1875 1900

Fig. 7. Change in the ratio (Jq obtained in static

atmosphere (20% O2 in A) with temperature.

of figure 7 shows that, above the melting point, the solution of oxygen in the liquid phase

decreases when the temperature increases, which indicates that the heat of the solution

reaction is exothermic.

One can note that in such a case the data obtained under static atmosphere are not

the true equilibrium values because the solution of oxygen produces a decrease of the oxygen

potential near the gas-ligand interface. But, with some improvement, as described previously

(3) , it is possible to obtain the composition of liquid cobaltous oxide, near the solidification, under an oxygen partial pressure of 0.166 atm. The value is (—2~) = 1.074.

Co liq

The data obtained in static atmosphere are however adequate to make some calculations

on the enthalpy of the oxygen solution in liquid cobaltous oxide.

2.3. DEPENDENCE OF MELT COMPOSITION ON TIME

Because of the oxidation of the wire and of the cirucible in iridium it is impossible

to obtain data on the kinetics of oxygen solution in liquid CoO by thermogravimetry . Some

qualitative indications are given by thermomanometry , and the results show that the apparent

reaction is rapid. In fact, at 2000 °C in pure oxygen, the equilibrium value 'liq """^ obtained after only 10 seconds of malting. Nevertheless, data on the oxygen desorption are given with argon at low flow as carrier gas. The bath of cobaltous oxide is first saturated

by a static gas mixture containing 20% oxygen and 80% argon. Figure 8 shows three thermogravimetric curves (A: 209 3 K - B; 2128 K -C; 2153 K) .Am is the weight loss due to the

476
1

5 1 0 1

Time

15 20

1

: min

\\\

^\ - 10 \A

\\

V

-15

\ \

\\\

- 20

\\ \

- 25

lO^(AjL)

M S mm"2

Fig. 8. Thermogravimetric curve obtained for

desaturation of cobaltous oxide melts

previously saturated in 20% A O2/A for

differents temperatures: A - 2093 K; B - 2128 K; C - 2153 K.

oxygen desorption in mg, M is the weight in mg of the sample, and S in mm"^ the exchange area between the liquid and the gas phase. One can see two steps in the rate of weight loss of

the bath. It seems possible that the linear part of the curve is due to the desaturation

of the liquid interface, and that the parabolic part is due to the oxygen diffusion in the

bath.

2.4. INFLUENCE OF THE LIQUID COOLING SPEED ON THE COBALTOUS OXIDE SOLIDIFICATION, SPITTING

PHENOMENON

The thermomanometric apparatus is particularly well adapted for unraveling such a phenomenon, and in this case the experimental conditions are as follows: saturation

temperature 2000 °C, melting time: 1 min, oxide weight: 230 mg, atmosphere: pure oxygen at

0.83 atm, range of cooling speed between 1 °C/s and 250 °C/s. Figure 9 shows the experimental

results given by these experiments. We have drafted, on curve A, the change in the number

of oxygen atoms evolved at the solidification per mol of cobaltous oxide, and on curve B the change in the liquid phase composition just before the solidification. One can see the

great influence of the cooling speed on the intensity of the splitting. Table 2 shows the

percentage of weight loss of the product versus the cooling speed (in the case of the

previously defined experimental conditions)

.

477
1.2

1,1

1

(A)

B c-A

Atome Op

A

0,2

/ /

./ /

y

k \

\ N

B

^ *~ ' 0,1

0

// \

^ A

0 5 0 IC

Co

10 15

oling speed 'C

.0 2(

1

sec

DO 250

1 Fig. 9. Evolution of the number of oxygen atoms evolved at the

solidification of CoO molten under pure oxygen versus cooling speed. Curve A: the change in the number of

evolved oxygen atoms per mole of CoO at solidification.

Curve B: melt composition of such a product just before

the spitting phenomena.

Table 2

Cooling speed 250 200 140 120 100 85 70 40 2 1 °C/s

Weight 28 26 22 21 17 15 15.5 16 7.5 3 %

The examination of these results shows that:

a true melt composition for a given saturation temperature is obtained for cooling

speeds higher than 150 °C/s

- the mechanical effect (projections) of spitting increases when the cooling speed

increases.

2.5. EXAMINATION OF SOLID PRODUCTS

The nonstoichiometry of the products is determined by thermal reduction in hydrogen at

800 °C and knowledge of the thermal history of the liquid. For example, one can see from

table 3 the change in composition of solid cobaltous oxide with the cooling speed of the

liquid phase (experimental conditions are the same as previously)

.

Table 3

Cooling speed 250 200 140 120 100 85 40 2 1

°C/s

(^)s 1.022 1.020 1.019 1.018 1.017 1.014 1.011 1.004

478
The nonstoichiometry of the final product increases when the cooling speed increases.

After (water quenching) the composition ( ^ ) (ratio in solid state of the number of atoms

of oxygen and to that of cobalt) is 1.044. X-ray analysis, however, does not show any

important parameter changes for the above nonstoichiometric cobaltous oxide,

2.6. CONCLUSION OF EXPERIMENTAL RESULTS

On the basis of the experimental results obtained by thermal analysis , thermomanometry

and thermogravimetry it is possible to draft, as shown on figure 10 a diagram of cobaltous

oxide-oxygen system. The heavy lines represent the liquidus and partail pressure of oxygen

This diagram clearly shows: First: the great importance of oxygen in the atmosphere above

the melt and the decrease of the solidification point when the partial pressure of oxygen

increases. Second: the exothermicity of the solution of oxygen in the liquid phase, the

ratio ( Co ) liq decreased when the temperature of the bath increases. Third: the spitting

phenomena is to be explained by the great difference of composition between the liquid and

the phase at the transition liquid = solid.

3. DISCUSSION OF RESULTS

3.1. KINETICS DATA

It is possible to calculate with the help of Arrhenius equation from the different

thermogravimetric curves the apparent activation energy of the two stages occuring during

the oxygen desorption. From the slope of the linear curves we obtained

2000

Tempera

\

\

ture in 'C

\ P 02 = 0,8

\

\

\

\

3 atm

\

\

\ P02 = 0,166

\

\

\

aim \

\

\ 1900

\

\

\ liqu

\

\

\

\

d \

\

L

t-Xl800

—\

\

\V

V-

\

\

\

\

i

1 CoO/r~

/\

Co 0 liquid

1 /

1 /

1 I

1,1

1

0

Co

1,2 • Fig. 10. Diagram of temperature vs composition

for the system C0O-O2

.

479
E desaturation

a 51 K cal/mol

E diffusion 72 K cal/mol

3. 3.2. THERMODYNAMICAL APPROACH TO THE OXYGEN DISSOLUTION

The thermomanometric data have shown that the solution is an atomic solution, because

the quantity of oxygen evolved at the solidification is a function of the square root of the

partial pressure of oxygen in the atmosphere above the melt.

For the calculation of the heat of solution on the assumption of the following equation

(0„)gas = 2 (0) . 2 sol

we consider the reference states to be such that

the gaseous oxygen is under a pressure of one atmosphere

the dissolved oxygen is an infiniting dilute state.

In that case we can write

d Ln (o) AH"

1 - d { 2R

With (o) =

n + X

o

(0) molar fraction of dissolved oxygen, no the number of dissolved oxygen atoms, X composition

of the liquid with all present species except dissolved oxygen.

At that point one must make a remark of great importance. Such a caluclation is

impossible with thermomanometric results because of the non thermodynamic equilibrium

conditions of the experiments. In the case of saturation by oxygen at 20% in argon n

X = n CoO and nQ is very small with respect to n CoO and consequently we can write (0) "^CoO By measuring the slope of the curve showed on figure 11 we determined the enthalpy

of solution of oxygen in liquid cobaltous oxide

AH° , = - 103.5 K cal/mol 0^ sol 2

In conclusion, one can note great effect of the oxygen on the behavior of cobaltous

oxide after melting. For the establishment of correct phase diagrams with this compound,

it is necessary to give the nature and composition of the gaseous atmosphere above the melt.

4. REFERENCES

[1] Coutures, J. P., and Foex, M. , C. R. Acad. Sci., 267C , 1577 (1968).

[2] Foex, M., and Coutures, J. P., C. R. Acad. Sci., 266C , 796 (1968).

[3] Coutures, J. P., Thesis, Bordeaux, Janvier 1971.

480
481

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

THE SYSTEM FeO-Si02-Ti02 AT HIGH TEMPERATURES AND HIGH PRESSURES

E. Woermann

Institut fur Kristallographie

Rhein.-Westf . Technische Hochschule Aachen

West Germany

A. Lamprecht

Frankfurt am Main

Germany

ABSTRACT

The investigations of liquidus and solidus relationships in the system FeO-Si02-Ti02 in

equilibrium with metallic iron at one atmosphere total pressure revealed four ternary invariant points

:

1) L = wustite + fayalite + ulvospinel (1169° C)

2) L = fayalite + tridymite + ulvospinel (1145° C)

3) L + ilmenite = tridymite + ulvospinel (1180° C)

4) L + f erropseudobrookite = tridymite + ilmenite (1254° C)

In the system f erropseudobrookite - tridymite - rutile in equilibrium with metallic iron con- siderable amounts of trivalent titanium are observed at solidus and liquidus temperatures.

The titanium bearing phases thus are located outside of the ternary system FeO-Si02-Ti02

toward the oxygen deficient side.

At elevated pressures the following reactions occur:

1) Ferropseudobrookite = rutile + ilmenite

2) ulvospinel + quartz = fayalite + ilmenite

3) fayalite + quartz = ferrosilite

4) ulvospinel = wustite + ilmenite

Depending on temperature and pressure the iron titanium phases form limited solid solutions

in the system FeO-Si02 , due to the occurrence of defect structures.

483

/

II. BORIDES, CARBIDES, SILICIDES,

AND RELATED MATERIALS

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

CARBIDES AND SUICIDES

Hans Nowotny, H. Boiler and G. Zwilling

University of Vienna

Vienna , Aus tri a

A brief survey of the structural chemistry of transition element carbides will be presented with emphasis on the problem of carbon-void ordering. The scandium carbides including

Sc^sCjg are to be discussed. Complex carbides which derive from octahedral and trigonal

prismatic building elements will be classified. Metal-metal carbides such as VCr2C2 and

metal-nonmetal carbides such as Ti3SiC2, VitP2C, Nb2SC or Ta2S2C will be interrelated. The

role of nitrogen and hydrogen on the stabilization of complex carbides such as Cr3(C,N)2 or Zr2CHo^5 will also be treated. Besides the class of typical interstitial carbides, some ex- amples of metal boro-carbides displaying a two-dimensional boron-carbon network will be given

(YB2C) . In compounds such as Cr2(P,C) carbon plays an intermediate role. The present state

of the problem of chemical bonding in carbides will be discussed.

Binary metal silicides are numerous and occur almost at any composition. They are com- monly classified as valence compounds (electronegative) , metal-like silicides (electro-positive) and clathrate silicides (mainly electroneutral) . Disilicides and related compounds

exhibit a particularly wide occurrence. The continuous change of structural elements and

properties of this group will be dis cussed. So—called defect disilicides of formula Tj^Si2n—

m

(T = transition element) which are derived from the TiSi2 type structure belong to a uniform

building principle, where n presents the number of subcells and m the deviation from the disilicide composition. In many cases a relation of the electronic concentration with m can be observed. In general, lowering of the overall electron concentration diminishes the defect m. Single crystal work on Mn27Sitt7 will be described. This phase, a fifth variety

having a composition in the vicinity of MnSi__i^7, presents the problem of pseudo-homogenous

domains. Some ternary silicides such as E-phases will be discussed from the viewpoint of

ordered structures

.

Key words: Carbides; chemical bonding; defect structures; interstitial compounds;

ordering; silicides.

1 . INTRODUCTION

with regard to the large number of review articles [1-7] ^ it appears to be questionable

to add another to this subject. The main problems are still unchanged; e.g., the lack of a breakthrough concerning the theory of bonding, particularly as the transition element car- bides are concerned. Hence the predictibility of stable solid compounds for binary and multicomponent systems is still uncertain and even the method of classification of phases is not

consistent.

2. CARBON AND SILICON

The striking structural similarity known for carbon in the diamond forms (cubic or hexagonal) and silicon (c\ibic or hexagonal) disappears more or less with metal carbides and the

homologous silicides. The main reason for this is due to the size factor. The silicon atom

is considerably larger than the carbon atom evaluated for a neutral state. The same is true

for the silicon-metal size ratio as compared to the carbon-metal size ratio. Furthermore

Figures in brackets indicate the literature references at the end of this paper.

487
there is quite a difference in electronegativities. The position of the 3d-level may also

occasionally separate the bonding system in silicides from analogous carbides. It is significant to note that the individual features for SiC polytype modifications are equal to a large extent, obviously favored by the strong valence influence of directed sp^ bonds, thus

obeying the octet rule and not violating a critical radii ratio for tetrahedral structures.

3. BINARY CARBIDES

Very early it was recognized that carbon combines with almost every other element of the

Periodic Chart, but all (e.g. copper) do not form carbides. According to the proposed rule

which considers the difference of the ionization potential of the elements, we classify "carbides" as compounds of carbon with metals and with boron and silicon. Such a classification

coincides with a positive sign of the difference in electronegativities of carbon-metal (B,

Si) .

Alkali and alkaline earth carbides (e.g. graphite compounds) exhibit partially ionic

character in that carbon atoms easily form anion aggregates e.g. pairs such as is the case for Ca"^"*" (C2)~. The transition element carbides are metallic and regarded, following the con- cept by Hagg [8] and Goldschmidt [3], as interstitial compounds or interstitial alloys. A

final group consists of Be2C, AHnC^ and SiC type phases. These very likely are of ionic-covalent bond type, obeying the valence rule (octet forming). There is, however, ample overlap

in the neighboring areas as far as the bonding and the structural elements are concerned.

In other words a stepwise change in bonding, struct\iral elements and hence chemical composition can often be observed. The latter fact has also been emphasized by Goldschmidt [3] studying the systematic structural change within a specific group of elements of the Periodic

Chart. The gradual change in bonding is well known as illustrated by the isostructural

series: CaC2 LaC2 UC2. The first compound, however, is not a transition element carbide. The strong ionic bonding between Ca++ ions and the acetylide ions (C=C)^~ can be derived from lattice energy calculations [9] , from the formation of solid solutions CaC2-CaS

[10] , and, as was previously concluded, from the hydrolysis behavior. While the assumption

of the triple bond in (C=C) ^~ is also in agreement with the distance C-C, larger carbon-carbon distances have been observed for R.E.C2 and UC2 , as was shown by Atoji et al. [11]. It was assumed that six valence electrons of the metal atoms in R.E.C2 are distributed over one

(C=C) ^~ and one (C=C) ion [12]. On the basis of hydrolysis experiments, measurements of

specific resistivity, TEF and Hall-coefficients, Makarenko et al. [13] have proposed a similar charge distribution, La+++ (C^C) ^~ (C=C) eT/2' assuming 0.5 conduction electron per

atom. Anotner explanation tor the larger C-C distance in R.E.C2 in comparison to that of

CaC2 has been proposed on the basis that the one electron left fills an antibonding level in

the carbon diombbell particle. The R.E .dicarbides were occasionally considered as salt-likecovalent-metallic carbides [14]

.

o The C-C distance in UC2 increases up to 1.340 A. Increasing C-C distances correspond,

according to Atoji [15] , to higher metal valencies (4 for U; 3.4 for Ce) . The tendency for

increasing C-C distances indicates the competition between pair formation of carbon and isolated carbon atoms in metal carbides. One should emphasize in this context, that the ex- tended C-C aggregations only occur in graphite compounds. This means in a very first approach, that the aggregation of carbon atoms decreases in the carbides going from the left

side to the right side of the Periodic Chart.

3.1. BINARY CARBIDES OF TRANSITION ELEMENTS

The carbides of the very first transition element also reveal in a peculiar way the

stepwise change with respect to the C-C aggregation. Although no complete phase diagram for

the scanditm-carbon system is available as yet, the Sc-carbides unify somewhat the features

of both the carbides of calcium on the one hand and titanium on the other. The phase

ScCg^ 3-0.5/ having a defect NaCil type structure within a large homogenous region, can be com- pared with TiCi_jj etc. (isolated carbon particles) . A superstructure also has been found at the composition SC2C. A carbon-void ordering like Y2C has been proposed by Atoji et al. [16]

,

but a more detailed inspection has been shown to be necessary [17], The scandium carbide,

earlier formulated as Sc2C3_jj [18], was found by Krikorian et al. [19] to be 801^03 with the

Th3Pi^- instead of Pu2C3-type structure. Neutron diffraction experiments carried out by the

latter named authors indicate the presence of single C particles rather than C2 pairs as was derived from X-ray powder diagrams. The metal positions in both arrangements are however the

488
same. Anot±ier scandi\im carbide has been detected beyond this phase [18] , having a composition asstomed to be ScCi _ 2-I . 3 [19] • It turned out that the same phase was also described by

Petru et al. [20] who designated it as "SCC2". A formula SC15C19 (ScCi ^2?) f its best with a proposal of an atomic arrangement based on single crystal x-ray data (figs. 1-3). SC15C19

can be obtained either from heating scandiiom metal and carbon or by reduction of SC2O3 with

Fig. 1. Array of metal octahedra in SC15C19

(a = 7.50; c = 15.00 A, P42ic).

Fig. 2. Positions of the scandium atoms in SC15C19, as seen in the [001] direction.

489
Fig. 3. [ScgC]- and [SC6C2] -groups in SC15C19.

carbon at 2000 °C. The crystal structure of ScjsCjig CScCji^27) consists of metal octahedra

(somewhat distorted) which are filled by single carbon atoms and carbon pairs, with a C-Cdistance of 1.25 K which compares well to that of CaC2 or R.E.C2. As is shown in figure 2 the metal atoms form a parent lattice related to a cubic close packing.

A similar phase, YJ5C29 (YCj ^2?) appears to occur in the corresponding yttrium-carbon

system. According to Carlson et al. [21] a 6-phase was found to exist between 55 and 58 a%

C, transforming to the e-phase above 1200 °C. This phase obviously corresponds to "Y2C3"

earlier reported as of low symmetry. Very recently Haschke et al. [22] described a monoclinic YbCi 2 5+y which most likely also relates to the above mentioned scandium and yttrium

carbides MCi 27' Although the powder diagrams of the respective carbides SC15C19 and 5 C29 clearly indicate an isotypic structiire, it may be that the pseudocubic, tetragonal cell

is only a first approach.

Although a dicarbide occurs in the Y-C system (Y has a larger metal radius than Sc) no such scandium dicarbide could be synthesized. On the other hand, the similarity between

the metal-rich sides in both cases should be mentioned, each having a large region of defect

sodi;am chloride structure (including ordered phases) . In the course of mass spectrometric

measurements by Drowart et al. [23] , the formation of at least five scandiiam carbides has

been described. In addition to SC15C19, Sci+Cs (Sc2C3_jj) and SC2C, the existence of two more ordered carbide phases derived from the NaC£-defect structure has been postulated. No precise measurements of melting points of the Sc-carbides are available as yet. However, a possible eutectic between SC15C19 and graphite lies close to 1800 °C. These carbides seem, therefore, to be thermally less stable than the yttrium carbides. A eutectic between YC2

and graphite is reported to occur at 2300 °C. As Drowart et al. emphasize, the heat of formation of the scandium carbides is in line with that of other transition element carbides

(IIIA, IVA and VA)

.

3.2. CARBON ORDERING

The carbon-void ordering has clearly been demonstrated for subcarbides of transition

elements and more recently for other compositions such as V5C5 or VqCj . The tendency for

carbon ordering is even more pronounced with carbohydrides such as Zr2CH. The problem of

490
ordering in carbides has been extensively discussed by the author [24] . In general, low

temperatures favor ordering. Probable minor amounts of oxygen or nitrogen contaminants quite

often exert an ordering influence upon the transition element carbides. A unique example for

the unambiguous determination by neutron diffraction of carbon ordering has been shown for

V2C having the c~Fe2N-type structure. Here the neutron diffraction scattering stems only

from the carbon positions (fig. 4). Nevertheless, orthorhombic V2C has also been reported

for V2C1 01O0.O2 [25], On the other hand, the existence of an orthorhombic V2C (called aV2C) was found at low temperatures by Rudy et al. [26]

.

Whether the ordering phenomenon takes place in a large homogenous region such as for

ScCi_jj and YC^-x or in a more narrow domain such as for W2C, the most characteristic feature

is obviously the formation of shorter metal-carbon distances than those for randomly distributed carbon atoms in a metal parent lattice with close packed array. Thus the V-C distance

of 2.01 K for the orthorhombic V2C is distinctly shorter than the V-C distance of 2.03 A for

the hexagonal V2C with random carbon positions. Similarly the Y-C distance of 2.27 A in Y2C

(rhombohedral) is remarkably shorter than the Y-C distance of 2.35 A in YC^.^.

Furthermore, it turned out that the metal atoms in some ordered carbide structures, e.g.

VgCy , are also shifted in such a way that shorter neighboring metal-carbon atomic distances

result [27,28] . It has also been shown that shorter distances between metal-carbon-metal

occ\ar than for metal-void-metal. This clearly indicates the significance of the structural

elements [MgC] . The concept of the building elements for the generation of the large class

of complex carbides has been shown to be particularly useful [7]

.

From this concept stacking faults in TaCi_jj ^® understood by gliding in planes in

which a metal-void-metal arrangement occurs. Thus areas at high temperatures may exist with

some stepwise transition from the cubic close packing (monocarbide) to the hexagonal close

packing (subcarbide) . This problem is linked to the C-carbides recently explored by Yvon et

al. [29]. The metal atoms of the fairly \instable i;-phases, {Vi^C^ , Nbt^Cs, Tat^Cs) exhibit a complicated sequence, namely (hhcc) 3 . In this context VTa2C2 detected by Rudy [30], should

be mentioned although this phase (stable up to 2600 °C) represents an intermediate ternairy

carbide, which is characterized by a sequence (hhc) 3 . However, nothing can be said about the

degree of ordering. It has already been emphasized that V^C^ can be built up by V2C and VC

structural blocks. From table 1 the evolution of different stacking sequences in carbides

can be seen. The corresponding c-axes display a simple ratio. As compared to the early

findings of interstitial compounds quite a change has taken place. Still more transition

element carbides are to be expected to occur because of more complex ordering and stackings

.

The mode of stacking immediately influences composition because of the repulsion of two car- bon atoms which come too close together, as was assumed for MoC^.j^ (M03C2) . On the other

hand, there was no carbon ordering found for the C-carbide V1+C3.

70 r

9

87 -

6

-

5A

32

7

C002JW21)

sCnO) sCllD

I

{202) {221)

I s(7J7;

s{130)

(02310 ^0)

^^^^{{132)011)

{310} '

74 700 128 4 7 50 18 12A 4 7 70

I I ' I I I I I I I I I I I I I

'

I ' I I I ' I I I I I I I I I I

I '0 20 30 40 50

28, deg

Fig. 4. Neutron diffraction diagram of V2C, having C-Fe2N-type structure,

s = superstructure lines.

491

/
Table 1

Metal Stackings in Carbides

number of metal c-axis, approxim. ^ , ilx n/ci layers n (A)

3 ABC (cub., hexag. axes) 7.5 (TiC) 1

6 ABCACB 14.7 (Y"MoCi_x) 2 9 ABCBCACAB 22 (VTa2C2) 3 12 ABCACABCBCAB 30 (Tai+Cs) 4

Molybdenum and tungsten carbides have recently been reviewed by Morton et al. [31] who

have measured the superconducting critical temperatures. These authors confirmed the existence of the well known Mo-C phases [4] including the orthorhombic a-Mo2C , which is, according to Jack [32] , stabilized by very minor amounts of nitrogen.

Nevertheless there is no complete agreement between all data reported in the literature.

The same is partially true for the W-C system.

4. COMPLEX CARBIDES (INTERSTITIAL COMPOUNDS)

Only novel carbides of this huge class shall be discussed. For more detail the reader

is referred to the above cited literature [7] . Generally the particular problem of transition between metal-metal-carbides and metal-nonmetal-carbides is to be focused here. On the

basis of the building elements, mainly octahedral or trigonal prismatic groups [MgC] or [MgX]

(X = nonmetal) , so-called H-phases , the filled Re3B-type structure and derivatives offer con- venient examples to demonstrate the stepwise generation of new structure types of complex

carbides. In the H-phase, e.g. Nb2A5,C, the aluminum atoms are still in contact with overall

metal packing "Nb2AJi" (c/3a = 1.49) . No such contact (if neutral S atoms are present) can be assumed for Nb2SC (c/3a = 1.17) . In other words the latter H-phase can be considered as

a topochemical sum of NbC (octahedra) + NbS (trigonal prism) . At this point it is of interest

to note that Goldschmidt has introduced the term "inverse" interstitial compounds, e.g. 2sM0S2, which is, incidentally, an anti-type of the H-phase parent lattice.

4.1. Ta^S^C

No H-phase Ta2SC in the system Ta-S-C has been found so far. However, a complex car- bide, Ta2S2C, was detected in both low and high temperature forms. The transformation is

sensitive to mechanical treatment. As is shown in figure 5, the octahedral structural element

[M5C] linked by edges form a single plane or double plane (Ti3SiC2-type structure) combined

with trigonal prismatic layers (Ti2SC- and Ti3SiC2-type structures) or typical layer blocks

(M0S2-, TaS2 -structure types). Thus ls-Ta2S2C is topochemical ly composed of IS-M0S2 + TaC

slabs, 3s-Ta2S2C of ls-TaS2 + TaC. Because of the weak bonding between adjacent sulphur

layers, mechanical distortion (stacking faults) easily may take place. Both polymorphs are isotypic with valence compounds (Ce202S and Bi2Te2S respectively) [33]

.

The latter mentioned fact indicates the presence of some ionic fraction in the bonding.

One must assume formation of sulphur anions and metal cations. The role of hydrogen in metal

carbohydrides is similar. Within the layer sequence -M-C-M-H-M-C-M (ciibic or hexagonal) the occurrence of H-anions is most probable, as is the case of many metal hydrides, e.g. NdH2

[34] .

4.2. FILLED UP Re B-TYPE STRUCTURE CARBIDES AND V P C.

-J 4 2 The occurrence of the filled Re3B-type structure is shown in table 2. The array represents a simple combination between octahedral and trigonal prismatic building groups. Again

VCr2C2 is a perfect topochemical sum of (V,Cr)Ci_jj (octahedra) + Cr3C2 (trigonal prism).

Similarly Cr3C (Cq ^ 14N0

_ g ) [35] is built up by CrN and Cr3C2 elements with some nitrogen in

CrN being substituted by carbon.

492
B-group element * c

Fig. 5. Transition element sulfocarbides

and related compounds, as seen from layer-like stacking.

M element

Table 2

Occurrence of the Filled Re3B-type Structure

X element Interstitial element

V

V+Cr

Cr

Ga,Ge ,P ,As C

(B,C) ,Ge,P,As

(C) ,N C

C, (N)

Combinations with { ) are missing

As is well known for the Mo-C and W-C system, the octahedral building group is limited

to subcarbides or carbon deficient cubic structures which only occur in a high temperature

region. For the monocarbide of tungsten the trigonal prism is characteristic. Ettmayer has

recently found that nitrogen at high pressures stabilizes MoCC,N) in the WC-type structure

[36] .

, Another interesting example of combined building elements is represented by V4P2C (fig.

6) . Similar to the filled ResB-type structure, the metal octahedra are filled by carbon,

while the trigonal prisms accommodate the phosphorus atoms. The crystal structure has been

derived by Boiler [37J

.

The interchangeability of X-atoms and carbon such as H/C, N/C, B/C is widely extended.

In such a way another concept somewhat different from the intejcstitial principle becomes visible. It was found that phosphorus and arsenic atoms can be replaced by carbon in chromiun

containing carbides. Furthermore, formation of boron-carbon aggregates takes place in metal

borocarbides (carboborides)

.

^V2.6^0.4 Cr2(As,C)

While the Cr-phosphocarbide is a ternary compound, the isotypic Cr2(As,C) develops from

the high temperature form having Fe2P-type structure. The lattice parameters, dependent upon

the amount of carbon, indicates that carbon not only may enter voids but also substitutes for

the X-atom, as is shown in figure 7.

493
5. BOROCARBIDES OF TRANSITION ELEMENTS

Boron/carbon substitution in borocarbides of transition elements is well known for Fe3

(B,C) or Fe2 3(B,C)g. However, carbon atoms in borocarbides such as M02BC do not display a substitutional mode with respect to boron atoms. M02BC, a sum of MoC (octahedral) and MoB

(trigonal prismatic group) behaves as the former (interstitial) compounds. UBC and Cr3(B,C)

C look like intermediates between M02BC and Fe3(B,C). Nevertheless, with borocarbides low

in metal content, the aggregation tendency of the nonmetal atoms becomes a distinct feature.

The boron-boron chains are linked to carbon atoms like a branched chain as is the case for

UBC (fig. 8) . Very recently YBC [38] was found to be of a similar arrangement (fig. 8)

.

While for ThB2C (approximate composition) two-dimensional networks have been assumed, Smith

et al. [39] derived the crystal structure of SCB2C2 consisting of such boron-carbon networks,

built up by 5- and 7-membered rings. In YB2C2 such a network also exists, however it contains

4- and 8-meinbered rings (fig. 9) . The same arrangement obviously occurs in a large number

of lanthanide borocarbides described by Smith et al. [40]. Finally, YB2C also exhibits twodimensional boron-carbon networks characterized by 4- and 7-membered rings (fig. 9)

.

Th.e array represents a sum of the building elements of YB2 (diboride type structure) and

YB2C2 . These complex carbides compare somewhat to the alkaline graphite compounds. From

this analogue one must assume that the boron-carbon layers bear a slightly negative charge.

Within this class of compounds the boron-carbon structural elements constitute a major (covalent) bonding system. No specific data such as melting point for these borocarbides are available as yet.

6. SOME REMARKS ABOUT THE CHEMICAL BONDING IN CARBIDES

The views about the nature of the chemical bonding in transition element carbides are still controversial. There is a particularly wide gap between the various models including

quantum chemical results and experimental facts including structural chemical aspects.

494
Fig. 8. Branched boron-carbon chains in UBC Fig. 9. Boron-carbon networks in YB2C

(below) and crystal structure of YBC (a = 6.769, c = 7.430 K, P42mbc)

(a = 3.38g, b = 13.693, c - 3.627 A, generated out of YBi+ , (above).

Cmmm)

.

Beattie [41] has recently treated this class of compoimds within the "cannonball" structures

where octahedral (and occasionally tetrahedral) voids are filled by so-called small nonmetal

atoms, in agreement with the early geometrical concept of interstitial carbides. Along these

lines the electronic model or "transition-metal like" model has been developed by a number

of authors, assuming a transfer of electrons from the carbon atom to the d-band of the metal

atom. In such a way bonding between metal-metal atoms was expected to be enhanced, thus,

the stability evaluated in terms of the melting point, increases for the carbide over the

corresponding metal. In a more detailed, semiquantitative manner, Engel [42] considered the

bond system from the spin pairing concept. For ZrC (an sp^ state is assumed to be characteristic for the fee array of the metal atoms) the following states are present: Zr(l-,2-,3-,

4s^p^d^, 5sp^) and C^+, yielding five d-bonds (Zr-Zr) , three outer sp^-bonds and in addition, four ionic bonds. The large nuraber of bonds makes one believe that the energy required

for ionization of carbon to c'*"'" can easily be overcome.

Quantum chemical calculations carried out by Costa et al.- [43] also support the "transition metal-like model". According to these authors the M-M bonding is the essential interaction in monocarbides . It is assumed that about 1.5 electrons are transferred from the car- bon atom to the metal atom. In a later paper Costa has expressed the opinion that the d-band

filling of the metal does not produce a noticeable positive charge on the carbon atom because

of the extending and overlapping d-orbitals which screen the nucleus of the carbon atom. A

different approach (using optical data) made by Lye [44] for stoichiometric TiC yields the

approximate electronic configuration 3d^4s^/^4p^/^ for Ti and 2s2sp for carbon which cor- responds to a transfer of 1 1/4 electrons from carbon to the metal atom. The net charge is

said to be smaller because the metal wave functions extend to the carbon sites. The main

result of these concepts may be interpreted in the following way: the metal-metal bonds are

495
found to be the strongest, followed by metal-carbon bonds and surprisingly carbon-carbon

bonds should also exist.

Other quantum chemical calculations [45,46] and more recent work based on APW and self

consistent APW-methods on monocarbides and related compounds [47,48] differ quite a bit with

respect to the calculated density - of - state curves as compared to Lye's conclusion.

Furthermore, based on the more elaborate quantum chemical methods, it was shown that the re- sults do not indicate any transfer at all from carbon to the transition element in TiC and

similar compo\inds (assuming a perfect NaCl type structure) .

The presence of M-M-, M-C- and C-C-bonds has also been proposed by Hench [49] . According to this author the electronic bond consists of mutually overlapping tetrahedral hybrid

orbitals . The well known hybrid state of carbon sp^ combines with one of the stable electronic configurations of the metal atom namely sp^ , d^s, d^sp, dp^ , d^p forming a resonance between alternate cells. The arrangement of the respective cores of Ti and C together with

the centers of high electron concentration is incidentally similar to that proposed for TiC

by Schubert [50] on the basis of a spatial correlation of electrons. There is no doubt that

all calculations and specific models are loaded with a number of assumptions.

6.1. COMPOUND-LIKE MODELS

In a more unorthodox manner, considering an isotypic and isoelectronic series such as: KF-CaO-ScN-TiC or CsF-BaO-LaN-HfC , one must accept a stepwise change in bonding, in which

the formation of N-anions and C-anions appears favorable [51] . In fact calculations of the

lattice energies, particularly for nitrides, yield very satisfactory results on the assumption of M^+ and ions, present in the lattice. This has also been shown in great detail

by Straumanis et al [52] for TiN, which is even more metallic than TiC as seen from the

electrical conductivity.

A similar point of view arose with Rundle's theory [53] on transition element monocarbides which has been expanded by Hume-Rothery [54] and Krebs [55] . In this concept the predominant bonding is believed to be due to a metal-carbon interaction rather than metal-metal

bonding. Besides the result that this theory is connected with a more or less pronounced

electron transfer in the direction opposite to that proposed in the "transition metal-like

model" , it was widely agreed that the bonding nature in metal carbides is usually considered

to be a mixture of covalent and metallic bonding. Hume-Rothery completes the discussion with

the idea that the electropositive nature of titanium relative to carbon or nitrogen results

in a further electronegativity effect which acts as a stabilizing factor.

In agreement with this concept [45,48] the important role of metal-carbon interaction

is distinctly shown by the existence of structural elements in carbides and complex carbides.

A more direct confirmation of the "compound-like" model of transition element carbides

(monocarbides) apparently can be obtained by the results of the ESCA-method as Ramqvist [56]

has reported. From the negative shift of the carbon Is-level and the positive shift of the

metal levels (Is; 2p3/2'' ^'^5/2' ^^7/2^ ^ transfer of electrons from the metal atom to the

carbon atom in monocarbides has been derived, leading to a average charge of 0.3 to 0.5

\inits . The calculated Madelung energy from these data turns out to be 30 - 60 Kcal/formula

;

values which Ramqvist compares to the heats of formation. With respect to the bond system,

present in monocarbides, a statistical approach, proposed by Hoch [57] should also be mentioned. From the energy balance it clearly turns out that M-C bonding is by far the most

important contribution; furthermore, carbon-carbon repulsion takes place which obviously

stems from a Coulomb interaction.

In view of the radius of the silicon atom in comparison to carbon on the one hand and

to aluminum on the other the concept of typical interstitial compounds no longer holds for

metal silicides. They rather occupy an intermediate position [3] between interstitial and

intermetallic compounds. Metal silicides are also characterized by their wide occurrence

and the large variety of compositions which they exhibit. Generally they are line compounds

and for some, ordinary valencies apply, at least in a formal way, for metal silicides having

7. BINARY METAL SILICIDES

496
isolated silicon atoms in the lattice. One can further extend the valence principle by taking into account Si-Si aggregates, so-called pseudoanions , as the tendency to form Si2 pairs,

Si-Si chains etc. is frequently observed in metal silicides. Alkali and alkaline earth silicides , mainly of composition (M2Si-MSi2) belong to the class where the electronegative character is predominary [58]: Lii++ [Si2 ] ; K4+[Sii+]^~; Ca2^+ [-Si-Si-] ^~ etc. It is of interest to notice that a number of these compounds e.g. CaSi , Ba5Si3 are structurally representative of a series of corresponding transition element silicides, although the valence

concept no longer holds for these compounds and a mixed type of bonding (metallic - ionic)

must be assumed. Along these lines, more metallic character develops, although not necessarily in a predictable way. In metal-rich silicides the cationic function of silicon appears as can be seen from a pronounced metal-silicon interchangeability in niimerous phases

displaying typical metallic crystal structures such as polyhedra compounds etc. This is

valid particularly for complex silicides. On the other hand, the silicon like behavior

(tetrahedral bonding) in silicides, is revealed in the silicon-rich clathrate compounds such

as NasSi^g [59] .

7.1. DISILICIDES AND DEFECT-DI SILICIDES

As was early recognized, the formation of stable disilicides extends from Group IIA to VIIIA metals and the gradual change in structure is most characteristic, particularly in the

Si-Si aggregation and bonding. The tendency of Si-Si aggregations decreases in a systematic

way from IIA to VIIIA metal disilicides and will be replaced by metal-silicon networks within

IVA to VIA metal disilicides. While compounds such as CaSi2 or SrSi2 can be explained by

valencies (strong ionic portion considering Si-anion aggregates) , the disilicides of the

latter named group display interchangeability and hence obey regularities of valence electron

concentration

.

The interchangeability of metal-silicon atoms within the so-called supertype compounds

{TiSi2- TaSi2- and MoSi2-type structures [60] is particularly supported by the partial silicon/aluminum substitution, which transforms the various types in agreement with the valence

electron concept. Lowering of the electron to atom ratio (on the basis of the outer electrons) leads to a change from the MoSi2-type structure to the TaSi2-type structure and further

to the TiSi2-type structure [61] . The hexagon array of the silicon atoms in the supertype

which perfectly accommodates the metal atoms (Ti,V,Nb etc.) is demonstrated in R.E. disilicides having A£.B2-type structure or in the ThSi2-type structure. The latter can be generated out of the A£B2-type structure by a shift, as was shown by Parthe [62] . The intermetallic character of the supertype structures parallels with the coordination ntimber of 10, although there are semiconductors among these disilicides (CrSio or ReSi2 at high temperatures)

.

With respect to thermal stability, the disilicides (two-dimensional networks) compete mainly

with monosilicides and silicides of formula M5Si3 (exhibiting Si-Si chain formation)

.

Silicides of the general formula MnnSi2n-m have been detected [64-68] as intermediates

between the supertype structures and 3-FeSi2 [63], 0sSi2 [63], CoSi2 , NiSi2 which crystallize with a distorted or regular fluorite type (C.N, = 8 for silicon)

.

7.1. a. MANGANESE SILICIDES Mn Si^

n 2n-m

Manganese silicides of the above formula corresponding to a defect disilicide MnSi2_jj

exhibit a unique structural principle first discovered with MnnSi^g. As seen from figure

10 the atomic arrangement is generated from the TiSi2-type structure, the siibcell of the manganese (transition element) atoms being identical with the titanium (transition element) a- toms within the TiSi2 cell. The multiple n refers to the number of the transition element

in the formula. The second partial lattice formed by the silicon atoms is expanded, leaving

out m silicon atoms out of 2n silicon atoms for n TiSi2 cells. In this way crystal structures occur occasionally having large c-axes (table 3) . Also, various defect disilicides

have been found to exist either for slightly different compositions in the binary system

manganese-silicon or in partially substituted ternary phases. More recently the compound

Mn2 7Sit|7 (fig. 10) has been characterized by single crystal data. Although the melting mode

in the region of MnSi~2.7 is not unambiguously explored as yet, large single crystals C4cm)

could be obtained by means of the Czochralski method at a rate of 0.45 mm/min. Single crystal data confiirmed the cell dimensions, earlier derived from powder patterns. In accordance

with the regularity for odd m and n, only (Okl) reflections k + 1 = 2n (space group P4n2)

have been recorded. The atomic positions have been derived in a similar way as for the other

465-504 O - 72 - 33 497
Fig. 10. Atomic arrangement of TiSi2, MnnSi^g and Mn27Si^7.

manganese silicides with an R-value of 0.095. While the Si-Si-helix which is centered in the

(110) plane is essentially going clockwise from top to bottom, the adjacent helix centered in

the (110) plane goes anticlockwise (fig. 10) . Also it has been shown by neutron diffraction

experiments that the same multiple n results as has been determined by x-ray techniques.

However the superstructure reflections e.g. (21.11) for Mni5Si25 are remarkably enhanced [69].

The strong contribution of the magnetic scattering seems to be very complicated. No

simple explanation for the magnetic structure of these Mn-silicides can be given as yet. It should be mentioned that the representative superstructure reflections (Weissenberg patterns)

as mentioned above or the (21.20) and (11,47) reflections for Mn27Si47 occasionally have a diffuse character. Even after a long anneal (150 hrs) at about 1000 °C this phenomenon does

not disapper, indicating a domain formation around the multiple n. In this context an observation, reported by Ivanova et al. [70] is of interest, namely microscopically visible

fringes perpendicular to the [001] axis, independent of the direction of pulling of a manganese silicide of formula MnSii_72.

7.2. PSEUDO-SOLID SOLUTIONS OF FORMULA (Mn,T) Si

n n-m

S;ibstitution of some manganese atoms by other transition elements (Cr,Fe,Co) do not es- sentially change the subcell, as can be seen from a plot: volume versus composition of the

defect disilicide (fig. 11) . The dependency mainly reflects the silicon defect and makes

one believe that continuous solid solutions have been formed. Similarly, other properties

such as the magnetic susceptibility indicate solid solutions, as is determined for (Mn,Fe)-

defect disilicides in figure 12. A detailed inspection reveals, however, that the various

498
136

A 9 - « (Mn, Cr) Si\

\ 'n 2n-m A 8 (Mn.Co] Si'

^ 'n 2n-m

Fig. 11. Volume of the subcell as a function of the

amount of silicon for (Mn ,T) j^Si2n-m phases.

substituted silicides differ generally with respect to n and m. This means only pseudo-solid

solutions are present, as is shown in table 3. Some of these phases might develop from one

of the manganese defect disilicides such as (Mng , gsFeg . o 5) l iSii g or (Mng _ g5Cro ^ 1 5) t+Siy. The

latter obviously is related to the compound Mn^Siy which has been characterized by Fujino et

al. [71] and by Karpinskii et al [72] . An analogous behavior has been described for transition element germanides and substituted compounds [7] . From figure 13 it can be seen that

an increase in the outer electrons which occurs with Fe and Co-substitution increases the

silicon defect while chromium siibstitution decreases these defects. This fact is closely re- lated to the regularity of the silicon/aluminum substitution in the supertype structures.

Here again aliaminum, lowering the overall valence electron concentration suppresses the silicon defect, thus stabilizing the supertype structures for Mn (Si , Ail) 2

•

499
Table 3

(Mn,T) Si„ Phases

n 2n-m

Formula n a c c/na

n

2 (Mng , qD D^FenU or) ^ iSii

Q

11 1 .727 5 . 51q 47 . 96 0

.

7914

3 (Mno .gFeo

.

1) 7Sil2 7 1 .715 5 .51o 30 .464 0. 7898

4 (Mno .SsFeo .15) 17Si29 17 1 .705 5 .5O3 73 .865 0. 7896

5 (Mno .eFeo. 2) 23Si39 23 1 .695 5 .49e 99 .797 0. 7895

6 (Mno .75Feo .25) 29Sii+9 29 1 .691 5 .490 125 .685 0. 7894

7 (Mno .7Feo

.

3) 228137 22 1 .682 5 .483 95 •173 0. 7890

8 (Mno .95C00 .05) 25Siit3 25 1 .719 5 .516 108 .950 0. 7901

9 (Mno .95Cro .05) 19Si33 19 1 .738 5 .533 83 .06g 0. 7902

10 (Mno .gcro

.

1) 3lSi5t+ 31 1 .742 5 .534 135 .718 0. 7911

11 (Mno ,85Cro .15) i+Siy 4 1 .750 5 .537 17 .532 0. 7916

12 (Mno •SCro. 2) 298151 29 1 .757 5 .54g 127 .28i 0. 7914

13 (Mno .75Cro .25) 178130 17 1 .763 5 .552 74 .66i^ 0. 7911

7,68

0 10 20 30 40

Fig. 13, Silicon concentration as a function of the

amount of the manganese-transition element

substitution.

An interesting approach to explain the peculair structural principle has been made by

Jeitschko et al. [73]. As the transition element atoms form a subcell lattice which is well

known for the white tin type structure, the defect disilicides are considered as "stuffed"

white tin structures. The silicon atoms act as a filler donating electrons to the white tin

array. Application of this concept leads to an electron/atom correlation which shows a relatively small excess contribution of the transition elements as compared to vanadium to the

overall electron concentration. More recently Pearson [74] treated the same problem in phases

called chimney- ladder structures. From about 40 phases belonging to these super-super-structures a relationship between the transition element valence Vrp and the ratio (2n-m)Vj^/nVrp

has been derived, which is shown in figure 14 (Vj^ = valence of silicon, etc.). The electron

concentration for the subcell of the transition element atoms is limited to 14 per atom or

56 outer electrons in the siibcell. The composition of phases for lower valences Vrp is obviously also controlled by a uniformly decreasing electron concentration (48 outer electrons

in the subcell for Vrp = 4) . For the manganese silicides (Vrp = 7) it is significant to note

that a constant electron concentration per sxibcell governs the stability. However, it is not

possible to explain the varieties of multiple n for a relatively narrow region on the basis

of the above proposed electron concentration per subcell. According to Pearson the similarity of Mn-Si distances (fig. 15) of neighboring atoms along the c-axis may well be responsible for comparable near-neighbor interaction and hence for comparable enthalpy.

500
Fig. 14. Electrons per atom (a) and electrons per

siibcell (b) as dependent on the outer

electrons of the transition element for

chimney-ladder structures.

0.25

0.2

0,15

0,1

0,05

2,0

\ \\

5 9^ .6

o o

oo \ o

/ o ,

/oo

o

I 00\\ / / O O o o \ \/ o /o, oo

o o 00 ^, \

/ / \ \

o\ \

; oo oo ^

QO O o

O OO

/ O) O ^\

J ^°

0,0

o\

1 o^o ^

2.5 3,0

oA

Fig. 15. Mn-Si-distances along c-axis in Mn27Sii^7.

501
8. TERNARY METAL SILICIDES

There are quite a few review articles [3,6] dealing with ternary and multicomponent silicides . The ability of silicon to act as a non-metal on the one hand and as a metal on the

other is clearly demonstrated in a large number of complex silicides. The metal-like behavior can be seen preferentially with metal-rich silicides. This is particularly true in the case of random substitution metal-silicon in equivalent positions such as Mn(Ni,Si)2 or with

metal silicides crystallizing with polyhedric structures such as the y-phase Mog(N,Si)7.

The non metal like behavior of silicon is again centered around alkali and alkaline earth

containing compounds such as Li2BaSi [75] or MgCaSi [58] which obey ordinary valencies. For

ternary silicides, ordered structures derived from the array of binary compounds (salt-like or metallic) are quite characteristic: examples are the ordered CuA£2-, BaA£[^- or the antiPbC2.2-type structures. Thus silicon in NbitFeSi or ThCu2Si2 is surrounded by metal atoms

forming a so-called quadratic antiprism. In such a way silicon compares somewhat to carbon

in metal-rich carbides with a small ratio rrp/r^ such as Cr2 3Cg. Some fifty compounds belonging to the ThCu2Si2 type structure have been described [6,76]. Another group of ternary metal silicides having a wide occurrence is encountered with so-called E-phases having the or- dered anti-PbCl?.2~type structure. Metal trigonal prisms linked by edges surround the silicon

atoms, thus, ignoring three more metal neighbors, some similarity to metal carbides can be

recognized. In addition, as is shown in table 4, the valence compounds MgCaSi and MgSrSi

[58] are the first members of a series of E-phases containing transition elements.

Finally CaA£2Si2 and SrA£2Si2 having an ordered La203-type structure (La202S) can also

be considered as salt-like compounds and obey normal valencies (Sr^lA£5-'--'-Si2^) . A resonance between ionic and covalent bonding must be assumed, as silicon is surrounded by four neighbors, similar to the Mg2Si proposed by Krebs [77]. It would be of interest to extend

Phillips [78] theory on bonding to this class of compounds. ,

Table 4

Ternary Silicides (E-phases)

Mg {Ca,Sr} Si Ti {Ni,Cu} Si V {Co,Ni} Si ^4n {Co,Ni} Si Zr {Fe,Co,Ni,Pd,Pt,Cu} Si Nb {Fe,Co,Ni} Si

Hf {Fe,Co,Ni,Cu} Si

9. REFERENCES

[I] Kieffer, R. and Benesovsky, F., Hartstoffe , Springer-Verlag , Wien, 1963.

[2] Storms, E. K. , The Refractory Carbides, Academic Press, New York - London, 1967.

[3] Goldschmidt, H. J., Interstitial Alloys, Butterworth, London, 1967.

[4] Rudy, E., Compendium on Phase Diagram Data, AFML-Report, 1969.

[5] Samsonov, G. V., Tugoplavkie Karbidi , Na\ikova Dumka, Kiev, 1970; Kosolopova, T. Ya.

,

Carbides Properties, Production and Applications, Plenum Press, New York, 1971 (Russian

text published 1968); Toth , L. E., Transition Metal Carbides and Nitrides, in Refractory

Materials, J. L. Margrave, Editor, Academic Press, New York, 1971.

[6] Gladyshevskii , E. I., Kristallochimia Silitsidov i Germanidov , G. V. Samsonov, Editor,

Izdatelstvo Metallurgi ja, Moscow, 1971.

[7] Nowotny, H., Progress in Solid-State Chemistry, Vol. 5, H. Reiss, Editor, Pergamon Press,

Oxford, 1971.

[8] Hagg, G. , Z. Physik. Chem. B12 , 33 (1931).

[9] Vinek, G. , Neckel, A. G. , and Nowotny, H. , Acta Chim. Acad. Sci. Hung. 53^, 193 (1967).

[10] Juza, R. and Bunzen, K., Z. Phys . Chem. N. P. 17_, 82 (1958).

[II] Atoji, M. , Gschneidner, K. , Daane , A., Rundle, R. , and Spedding, F., JACS , 80_, 1804

(1958)

.

[12] Vickery, R. , Sedlacek, R. , and Ruben, A., J. Chem. Soc . No. 2, 498 (1958).

[13] Makarenko, G. N., Pustovoit, L. T., Yupko, V. L., and Rud' , B. M. , Izv. Akad. Nauk SSSR,

Neorg. Mat. 1787 (1965).

502
[14] Samsonov, G. V., Poroshk. Metall. No. 1, 98 (1965).

[15] Atoji, M., J. Chem. Phys . 35./ 1950 (1961).

[16] Atoji, M., and Kikuchi , M. , Argonne Nat. Lab. ANL-7441, 1968.

[17] Jedlicka, H., Nowotny, H., and Benesovsky, F., Mh. Chem. 102 , 389 (1971).

[18] Rassaerts, H., Nowotny, H., Vinek, G. , and Benesovsky, F. , Mh. Chem. 98, 460 (1967).

[19] Krikorian, N. K. , Bowman, A. L., Krupka , M. C. , and Arnold, G. B., High Temp. Sci. _1, 360 (1969) . [20] Petru, F., Bro^ek, V., Hajek, B. , and Dufek, V., Z. Chem. 71 (1969).

[21] Carlson, O. N. , and Paulson, W. M. , Trans. Met. AIME 242 , 846 (1968).

[22] Haschke, J. M. , and Eick, H. A., JACS 92, 1526 (1970); High Temp. Sci. 2_, 376 (1970).

[23] Drowart, J., Smoes , S., Vander Auwerd-Mahieu , A., and Wagner, S., in press.

[24] Nowotny, H., Progress in Solid-State Chemistry , Vol. 5, Pergamon Press, H. Reiss, Editor,

Oxford etc. 1971.

[25] Alyamovskii, S. I., Shverikin, G. P., and Gel'd, P. V., Zh. Neorg. Khim. 8_, 2000 (1963).

[26] Rudy, E., and Brukl , Ch., J. Amer. Ceram. Soc. 50_, 265 (1967).

[27] Kordes, D. , Phys. Stat. Sol. 2£, K 141 (1967).

[28] Henfrey, A. W. , and Fender, B. E. F., Acta Cryst. B26 , 1882 (1970).

[29] Yvon, K., and Parthe, E., Acta Cryst. B26, 149 (1970).

[30] Rudy, E., J. Less-Common Met. 2£, 49 (1970).

[31] Morton, N., James, B. W. , Wostenholm, G. H., Pomfret, D. G. , Davies , M. R. , and Dykins

,

J. L., J. Less-Common Met. 2_5, 97 (1971).

[32] Jack, K. H., AIME meeting, Atlanta, Ga. 1971.

[33] Nowotny, H., Boiler, H., and Beckmann, O., J. Solid State Chem. 2_, 462 (1970).

[34] Bieganski. Z., Phys. Stat. Solidi , in press.

[35] Ettmayer, P., Mh. Chem. 97^, 241 (1966).

[36] Ettmayer, P., Mh. Chem. 101 , 1720 (1970).

[37] Boiler, H., Mh. Chem., in press.

[38] Bauer, J., and Nowotny, H. , Mh. Chem. 102 , 1129 (1971).

[39] Smith, G. S., Johnson, Q., and Nordine , P. C, Acta Cryst. 19_, 668 (1965).

[40] Smith, P. K. , and Gilles, P. W. , J. Inorg. Nucl. Chem. 29./ 375 (1967).

[41] Beattie, H. J., in Intermetallic Compounds, J. Wiley and Sons, J. H. Westbrook, Editor,

New York, 1967)

.

[42] Engel, N., in Development in Structural Chemistry of Alloy Phases, Plenum Press, B. C. Giessen, Editor, New York, 1959.

[43] Costa, P. and Conte, R. R. , in Compounds of Interest in Nuclear Reactor Techn. , edited

by Waber, J. T. , Chiotti , P., and Miner, W. N., IMD Special Rep. No. 3, Met. Soc.

AIME, 1964.

[44] Lye, R. G. , in Proprietes Thermodynamiques , Physiques et Structurales des Derives SemiMetalliques , CNRS , Paris, 1967.

[45] Bilz, H., Z. Phys. 153 , 338 (1958).

[46] Ern, V., and Switendick, A. C, Phys. Rev. 137A , 1927 (1965).

[47] Schwarz, Kh., Doctoral Thesis, University of Vienna, 1968; Neckel, A., Nowotny, H. , 6th

Plansee-Seminary , Reutte-Tirol 1969.

[48] Conklin, J. B. , Averill, Ir. F. W. , and Hattox, Th. , Colloquim, Centre Europeen de Calcul

Atomique et Moleculaire, Menton, Sept. 1971.

[49] Hench, L. L., Electronic Bonding and Properties of the Carbides, U. of Florida, 1967.

[50] Schubert, K. , Kristallstrukturen zweikomponentiger Verbindungen , Springer, Berlin,

Gottingen, Heidelberg, 1964.

[51] Nowotny, H., Vitovec , F. , in F . Benesovsky, 1st Plansee Seminary, Reutte , Tirol, 1953.

[52] Straumanis, M. E., Faunce , C. A., and James, W. J., Inorg. Chem. 5_, 2027 (1966) . [53] Rundle, R. E., Acta Cryst. 1^, 180 (1948).

[54] Hume-Rothery , W. , Phase Stability of Metals and Alloys, P. S. Rudman, et al. Editors,

McGraw-Hill, New York, 1967.

[55] Krebs, H., Acta Cryst. 9_, 95 (1956).

[56] Ramqvist, L. , Jernkont. Ann. 153 , 1 (1969).

[57] Hoch, M., in Rudman, P. S., Stringer, J., and Jaffee, R. I., Phase Stability in

Metals and Alloys, McGraw-Hill Book Co., New York, 1967.

[58] Schafer, H. , Angew. Chem. Int. Ed. Engl. 9_' ^65 (1970).

[59] Kasper, J. S., Hagenmuller, P., Pouchard, R. M. , and Cros , C, Science 150 , 1713 (1965).

[60] Laves, F., in The Theory of Alloys , Am. Soc. for Met. Cleveland, Ohio, 1956.

[61] Nowotny H. , in Electronic Structure and Alloy Chemistry of Transition Elements, P. A. Beck, Editor, J. Wiley and Sons, New York, 1962.

503
[62] Parthe, E., in Proprietes thermodynamigues , physiques et structurales des Derives Semi- metalliques , CNRS, Paris, 1967.

[63] Engstrom, I., Acta Universitatis Uppsaliensis Soderstrom and Finn, Uppsala, 1970.

[64] Schwomma, O., Preisinger, A., Nowotny, H., and Wittmann, A., Mh. Chem. 95, 1527 (1964).

[65] Flieher, G. , Vollenkle, H. , and Nowotny, H., Mh. Chem. 98, 2173 (1967).

[66] Vollenkle, H., Preisinger, A,, Nowotny, H., and wittmann. A., Z. Kristallogr. 124, 9 (1967) . [67] Flieher, G. , Vollenkle, H. , and Nowotny, H. , Mh. Chem. 99_, 2408 (1968).

[68] Zwilling, G. , and Nowotny, H., Mh. Chem. 102 , 672 (1971).

[69] Flieher, G. , Doctoral Thesis, University of Vienna, 1968.

[70] ivanova, L. D. , Abrikosov, N. Ch. , Elagina, E. I., and Chostikova, W. D. , J. Neorg.

Mater. 5_, 1933 (1969) . [71] Fujino, Y., Shinoda, D., Asanabe, A., and Sasaki, Y., Japan J. Appl. Phys . 3_/ 431 (1964).

[72] Karpinskii, O. G. , and Evsev, B. A., j. Neorgan. Mater. 5_, 525 (1969).

[73] Jeitschko, W. , Parthe, E., Acta Cryst. 22_, 417 (1967). ~

[74] Pearson, W. B., Acta Cryst. B26 , 1044 (1970).

[75] Axel, H., Miiller, W. , Schafer, H., and Weiss, A., Z. Naturforschg . 22b, 1081 (1967).

[76] Rieger, W. , and Parthe, E,, Mh. Chem. 100 , 444 (1969).

'

[77] Krebs, H., Proc. NPL Symposium No. 9, 1958.

[78] Phillips, J. C, Rev. of Modern Phys. 42, 317 (1970).

DISCUSSION

A. L. Bowman : For the intermediate scandiim carbide we always come out with a composition of exactly Scl^C^. Our diffraction data resulted in a complete determination

of the single carbons in the structure which, of course, we didn't expect at all when we started. Structurally, I like to think of the basic structure of the sesquicarbides as being that of the scandium 4 carbon 3 phase. The sesquicarbides of uraniiim and plutonium

would best be thought of, as for instance, PU4(C2)3. Thus we see the exact relationship

between them, even though they seem to be totally different. We seem to find, interestingly

enough, that we can make both phases in some of the rare earth carbides by using pressure

synthesis. Exactly what happens there we don't understand at all, but that's an initial

observation.

H. Nowotny : Well, yes, I agree.

N. C. Stephenson : The manganese silicide structure that you showed there contains

silicon pairs. What sort of condition was the manganese in? Were they just isolated

cations?

H. Nowotny : You mean with respect to the valence state?

N. C. Stephenson : They weren't bonded to anything else were they?

H . Nowo tny : No, the manganese forms a more or less white tin structure and it is in

itself diamondoid. One silicon spiral fits with the same direction, but the other is

anti. I don't know whether I have really answered your question.

R. S. Roth : I would like to ask if, in the phase diagram for a system containing

these ladder-like structures, there are two phase regions between such structures, or are you talking about a continuous ladder-like structure?

H. Nowotny : In this system, manganese silicon, we couldn't find a heterogeneous

domain, but we get either the one or the other and this depends very much on the thermal

treatment and, of course, also on the composition. In a more detailed study. Dr. Zwilling

managed to prepare single crystals of a length of a few centimeters, that means one and

one-half inches, and all parts of this were uniformly of the last structvire, the 27-47

phase. In most of the Weisenberg patterns we nevertheless observed superstructure

reflections with some diffuse character. In other words, it may be that the 27 multiple

is just an average and we have domains around this 27. So such a crystal is very

complicated in its microstructure

.

504
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

INVESTIGATIONS IN THE TERNARY SYSTEM

BORON - CARBON - SILICON

E. Gugel, R. Kieffer, G. Leimer and P. Ettmayer

Forschungs-institut der Cremergruppe

Roedental , Germany

and

Institute fiir chemische Technologie anorganischer Stoffe

Universitat Wien, Austria

Viewing the literature one will notice that the available knowledge about the nonmetallic inorganic systems are rather insufficient and sometimes do not agree with each other.

These systems yield a number of attractive high temperature materials and therefore it is es- sential to improve available information.

The Institut fiir chemische Technologie anorganischer Stoffe (Institute for Chemical

Technology of Inorganic Materials), Technical University of Vienna, and the Research Institute of the Cremer-Group , Rodental- Germany , have systematically worked in this area for several years. This paper will deal with the system Boron-Carbon-Silicon.

In contradiction, some publications confirmed the existence of Bi^C only in the enclosing

system Boron-Carbon. However, Boron Carbide is able to incorporate excess Boron up to the

composition Bg 5 (in solid solution) clearly showing a lattice expansion. Within the enclosing system Silicon-Boron there are the chemical compounds SiBt^_^ (x<l) and SiBi2+x (^^^^ • According to our investigations the ternary system itself, in contrast to some other scientists, does not contain ternary phases as well as no solid solution between enclosing binary

systems. Limited solid solutions exist around Bi^C (+Si) and around SiBtj_j^ (+C) . The x-ray

investigations permit the presentation of phase distributions. By means of a new method for

determination the melting temperatures of high temperature materials the liquidus areas

(melting isotherms) of this system were investigated.

Key words: Binary system; boron; carbon; chemical analysis; melting-point determination;

metallography; phase-field division; silicon; solubilities; ternary system; x-ray investigations .

1. INTRODUCTION

Many of the nonmetallic hard materials existing in nature or those man-made which are used in technology because of their special properties, can be found in the quarternary system, boron-carbon-silicon-nitrogen. These are the elements which combine especially with

the transition metals of the IVa - Via group of the periodic table to form the well known and

very important hard alloys of the carbides, borides , nitrides and silicides.

All compounds of this quarternary system lie as can be seen from figure 1, on the binary

connecting lines. As far as is known till now either ternary nor quarternary compounds exist.

Last time we studied all the four ternary systems (fig. 2). Here we shall deal with

recent work in the system boron-silicon-carbon.

505
Of the three boundary binary systems, vie have reported recently about the system Si-c

[1] as well as about the system Si-B [2]

.

The system B-C, containing the technically very important boron carbide, and therefore

investigated many times, has not been covered until now. Russian and American authors, es- pecially, cannot agree about this system. Therefore, we have studied this system once more

in detail.

Figures in brackets indicate the literature references at the end of this paper.

506
The reason for the very different information one can find in the literature for the

system B-C, as well as for the ternary system B-Si-C, lies doubtlessly in the experimental

difficulties of the investigations. These are caused by the properties of the elements and

compounds. These include the high-melting phases B^C and B, the low-melting element Si with

a high vapour pressure, carbon, non-melting under normal conditp-ons, the incongruent-melting

siliconborides and SiC, which dissociates to vapour and a solid phase. Boron, carbon and

silicon themselves are very reactive at the high temperatures of the investigations and

therefore inert crucibles and furnace equipment are hardly available.

Chemical and x-ray analyses, and metallographic investigations were made on samples

which were hot- or cold-pressed and then tempered under different conditions. Microhardness

,

transverse strength and abrasive strength were determined on some selected samples.

Melting point determinations were made in a resistance-heated furnace constructed specially for this purpose (figs. 3 and 4). Melting occurred under an inert atmosphere using

pyramid-shaped specimens. Possible support materials were studied. It was possible with

this simple equipment to get very exact data.

2. THE SYSTEM B-C

Here we will report only on the results of our own investigations. For the remaining

studies of this system, reference should be made to a publication [3] containing an extensive reading list.

The experiments cover compositions of 0 - 60% C, 100 - 40% B, and the temperature range

of 1800 - 2300 °C.

Fig. 3. Furnace for the determination of melting-points.

1.2.

3.4.

water in 5 . specimen support

water out 6. Pyrex viewing glass

protecting gas 7. vacuum W-heating tube 8. watercooled double casing

507

/
Fig. 4. Electrode arrangement in the furnace for

determination of melting-point.

1. V7-tube 5. H2O - out

2. H2O - out 5. electrode terminals

3. H2O - in 7. floor plate

4. H2O - in 8. plastic seal

Above all, x-ray investigations have shovm that in the system B-C only one carbide

phase exists v?ith a relatively v/ide range of homogeneity. Figure 5 shows the lattice parameters calculated from the x-ray pov^der diffraction patterns as a function of the composition

of the initial samples. A relatively wide variation in the results of the analysis occurs because of the relatively small displacement of the diffraction lines measured at low angles.

Nevertheless, one can recognize a relationship, which could perhaps correspond to the graph

line. Therefore the x-ray constants for pure boron carbide, B1.C, are a = 5.60 K and c = 12.085 K and those for boron carbide in which the carbon is maximally replaced by boron are

a = 5.61 and c = 12.13 K. The increase of the unit cell dimension along the c-axis is very

clear. It is easy to interpret as the substitution of larger B-atoms in the carbon chain

situated on the c-axis.

Comparing this result with the relatively few meas\irements given in the literature [4-8] one can see that previously a much larger increase of the lattice parameter was determined.

However the results confirm in principle the present idea about the lattice of boron carbide

.

Figure 5 shows the melting temperatures determined, in comparison with the liquidus

temperatures stated by Elliot [9] and Samsonov [10]

.

As the "melting point" , the temperature was estimated at v/hich the pyramid-shaped specimens form a hemispherical pearl. Metallographic investigations have shovm that the specimens, even those v/ith a v/ide melting interval, were totally melted in most cases. The stated

values are therefore liquidus tentperatures

.

508
12, le

12,16-

12.10-

12.06-

5,66 -

.5. 64-

5,62-

5,60--

100 0

A= Allen (1953)

S = Schdanow ( 19^8,1954) L = Laves (1934)

M=Matkovich ( 1961 ) CsChark (1943)

,S,C,A

(C-Mxx

0|

B lAt.%1

90

10 —»— 8020

-4~ -4- 7030

60 50 60 50 — C f At. 'A I

Fig. 5. Lattice constants of B^C.

% filled circles-hot pressed specimens

O open circles-cold pressed specimens

A triangles-literature data

Fig. 6. Liquidus temperatures in the system Boron-carbon.

O open circles-tungsten tube furnace

® closed circles-Carbon tube furnace

509
The highest melting temperature in the boron-rich region was measured at 16% C. A eu- tectic between the supposed compounds B13C2 and B12C, as estimated by Schurawlow [11], could

not be detected. Furthermore no support was found for the existence of the compound B12C

with a melting temperature of about 2400 °C. The melting temperatures in the boron-rich re- gion are, however, higher than estimated previously. In the carbon-rich range our own re- sults are in accord with the liquidus temperatures from Elliot [9] whereas here Samsonov [10]

gives too low figures

.

All mixtures investigated with C-contents greater than 24%, begin to melt at nearly the same temperature of 2400 ± 10 °C. This is obviously the eutectic temperature. For the identification of the composition of the eutectic the following observation was of use; that sam- ples with more than 26% C do not melt homogeneously. Apparently the eutectic melt infiltrates the porous graphite support leaving a graphitic skeleton. Therefore it can be stated

that the eutectic composition contains 26% C in contrast to the 28 and 31% given in the literature. An undetectable diffusion from the graphitic support into the specimens could,

however, displace the value to the left side. An eutectic between boron and boron carbide

was not detectable, but from results obtained in the experiments with the ternary system one

can suppose that it is present. Certainly it lies ve2:y close to pure boron and is hard to

find because the melting-point of boron is decreased considerably by small amounts of impurities. The eutectic, estimated by Samsonov JIOJ and Schurawlow IllJ seems to be incorrect.

3. THE SYSTEM B - Si - C

The component elements show many similar chemical and physical properties as a result

of the horizontal (B, C) , the vertical (C, Si) and the diagonal (B, Si) relationship in the

periodic table. They are all metalloids with low densities and great hardnesses (for carbon,

the diamond) . They have, of course, different, but relatively high melting points, are chemically inert and form compoiinds with similar chemical and physical properties. Among themselves they react to extremely hard compounds, which are the s\ibject of this investigation.

Specimens analysed covered the whole range of the ternary system above 1700 °C.

3.1. THE PSEUDOBINARY SYSTEM B,C - SiC

4 Independent of the sintering conditions, x-ray analysis in all cases, showed the two

phase Sic and B^C.

The x-ray diffraction line at 2 0 = 133.5° (copper K-alpha radiation) which exists in

all Sic polytypes was constant in the range of ± 0.2°. A solution of boron in the SiC lattice constants of Bi+C varied with a^relatively intense zone of dispersion between a = 5.58

and 5.61 A and c = 11,99 and 12.11 A. As a rule, the lower values can be found by increasing

sintering temperatures and in samples with increasing SiC-content. The lattice constants lie

below the lowest values we have found in the system B - C and the lowest values we found for

Sic-rich samples. Therefore one can assume the existence of a certain slight sol\ibility of

Sic in BttC. Such a solubility is not confirmed in the more recent literature [12] , but in

older references [13] it seems possible however.

Figure 7 shows the results of the melting-point determinations in comparison with the

literature [12] . Therefore the eutectic is closer to B^C (about 65 mol % Bi^C) and the temperature somewhat lower.

3.2. THE PSEUDOBINARY SYSTEM B,C - Si

4 In all cases Bi^C and SiC were detectable by x-ray determinations. Microscopic investigations indicate the presence of boron silicides, which are required by the stoichiometry

.

Electron-microanalysis indicated a solubility of 2.2 weight % Si in Bt^C. Melting-temperature

investigations made on presintered samples are given in the total presentation of the meltingtemperatures of the ternary system (fig. 8)

.

510
Fig. 8. Melting isotherms and eutectic lines in the system

silicon-boron-carbon.

3.3. THE PSEUDOBINARY SYSTEM B - SiC

X-ray analysis showed in all mixtures the two phases SiC and B^C . Here the formation

of boron silicides is also required. The solubility of boron in 3-SiC at 1800 °C is 4.9 - 5.2 weight %. This value, contrary to Shaffer [14], is very high. Russian authors [13,15,16] on the other hand have announced a considerable solubility of B in 3-SiC. The results of the

melting investigations , with those from the system Bi^C - Bi^Si discussed below are used for

the total presentation of the ternary system.

3.4. PSEUDOBINARY SYSTEM B^C - SiB^ y

As starting powders, the end member components were used. The x-ray analysis of the

samples, which were sintered at 1900 °C, showed in all cases B^C. In addition to this, for

the starting composition with 10 - 80% Bi^Si, SiC appeared as second phase, and for samples

with 80 - 90% Bi+Si, some SiBg as third or second phase. A ternary compound was not detectable. The continuous series of solid solutions as it is stated by several authors [17-21] , if at all, is existent only below 1350 °C. At high temperatures SiC always exists, while

511
SiBit_x dissociates above 1350 °C to SiBg and Si, which reacts with the B^C to SiC. A variation of the lattice parameters of B^C in equilibrium with silicon-boron alloys was not detectable .

3.5. THE TERNARY SYSTEM

The phases Si, SiC, B^^C, Si.Bg, SiB^g+x ^""^ ^ were detected. Ternary compounds were not

found, not even in the compositions which were stated in the literature 118,19] for them.

From melting-point determinations in the ternary system together with those from the boundary

systems and the pseudobinaries , the melting isotherms and the eutectic lines as shown in fig- ure 8 can be presented. Therefore the ternary eutectic lies very close to the binary eutectic

of the system B - Si.

Figure 9, in conclusion, shows the phase-field divisions at two isothermal sections

which would be probable according to the complete results.

4. CONCLUSION

New investigations in the system B - C confirm the statements of Elliot [9] with regard

to which phases occur. The only compound is boron carbide, Bi^C, with a relatively wide range

of composition. With increasing s\:ibstitution of carbon atoms by boron an increase of the

lattice occurs, detectable by x-ray analysis. The liquidus curve of this system has a maxi- mum at 16% C, clearly higher than was assumed previously. The eutectic between Bi^C and C lies at 26% C and 2400 °C.

In the ternary system B - Si - C no indication of the existence of a ternary compound

could be found. The x-ray diffraction patterns of alloys in the range of the solid solution

of Si in Bi^C, also showed no indication of the existence of a phase with the character of a ternary compound. However, it seems possible that Si is accommodated in the Bi^C-structure

,

not statistically, but in certain positions. This phenomenon can be observed sometimes in

the accommodation of extraneous atoms in the boride lattices

.

Based on the results, phase-field divisions at two isothermic sections were determined.

As was to be expected from thermodynamic data on SiC and Bt^C, at not too high temperatures

the Si liquidus is in equilibrium with SiC but not with B^C.

Melting isotherms and the eutectic lines were determined by melting-point examinations.

There were difficulties in the analysis of the solubilities, but the values were in general not high, and were in agreement with those of other authors. The solubility of boron

in Sic was not detectable, neither by x-ray nor by electron-microanalysis . If solid solution

occurs, it would be very low.

The range of composition of the compound SiBg with regard to the three components has

not been investigated, nor has the solubility of carbon in the compound SiB^2+x.

1700 'C 1900'C

Fig. 9. Phase field divisions in the system Si - B - C at 1700 °C and 1900 °C.

512
5. REFERENCES

[I] Gugel, E., Ettmayer, P., and Schmidt, A., Ber. Dtsch. Keram. Ges . £5 Nr. 8, 395-402

(1968)

.

[2] Ettmayer, P., Horn, H. Ch., and Schwetz, K. R. , Microchimica Acta (Wien) , Suppl. IV,

87-95 (1970)

.

[3] Kieffer, R. , Gugel, E., Leimer, G., and Ettmayer, P., Ber. Dtsch. Keram. Ges. 48_, Nr. 9,

385-389 (1971)

.

[4] Allen, R. D. , J. Amer. Chem. See. 75_, 3582 (1953).

[5] Schdanov, G. S., and Mitarb. , J. Phys. Chem. (russ.) 22., 326 (1948).

[6] Laves, F., Nachr. Ges. Wiss. Gottingen, Math.-Physik. Kl., Fachgruppe IV, 1_, 57 (1934).

17] Matkovich, V. J., J. Amer. Chem. Soc . 83_, 1804 (1961).

[8] Clark, H. K., and Hoard, J. L., J. Amer. Chem. Soc. 65_, 2115 (1943).

[9] Elliott, R. P., IIT Research Institute, ARF-2200-12, Final Rep. US At. Energy Comm.

Contract At. (ll-l)-578, Projekt Agreement No. 4, p. 44 (1961).

[10] Samsonov, G. V., Schuravlov, N. N., and Amnuel, J. G., Fiz. Met. Metallovad. Akad. Nauk

.

SSSR Ural. Filial 3, 309 (1956)

.

[II] Schuravlov, N. N., Makenzenko, G. , and Samsonov, G. , IZ west. Akad. Na\ik. SSSR OTN 1_, 133 (1961)

.

[12] Sacrist, D. R. , J. Amer. Ceram. Soc. 47, 127 (1964).

[13] Kalinina, A. A., Shamray, F. I., Doklady Inst. Metall . imeni Baykova, A. A., 151 (1960)

(trans. J. P. R. S. 4045, Sept. 16, 1960).

[14] Shaffer, P. T. B., Mat. Res. Bull. 4, 213 (1969).

[15] Meerson, G. A., Niselson, L. A., Chu-Ming, C, Izw. Akad. Nauk. SSSR, Met. Topt. 1, 67

(1964)

.

116] Meerson, G. A., Kiparisov, S. S., Gurevich, M. A., Den Fen-Syan, Poroshkovaya Met., 2_, (26) , 15 (1965) . [17] Meerson, G. A., Kiparisov, S. S., Gurevich, M. A., Den Fen-Syan, Poroshkovaya Met., _3, 62 (1966)

.

[18] Colton, E., J. Amer. Chem. Soc, 82_, 1002 (1960).

[19] Matkovich, V. I., Acta Crystall. 13_, 679 (1960).

[20] Cline, F., and Sanks, E., Nature 185 , 456 (1960).

[21] Brosset, C, Magnusson, B., Nature 187 , 54 (1960).

[22] Portnoj , K. I., Samsonov, G. V., Solonikova, L. A., Dokl. Akad. Nauk. SSSR., 125 , 823

(1959) . [23] Portnoj , K. I., Samsonov, G. V., Solonikova, L. A., Zhurg. Neorg. Khim, 5_, No. 9, 2032,

C. A. 55, (1960), No. 7, 6329e (1961).

465-504 O - 72 - 34 513

National Bureau of Standards Special

of 5th Materials Research Symposium,

Publication

issued July

364,

1972

Solid State Chemistry, Proceedings

VALENCE BONDING IN SOME REFRACTORY TRANSITION

METAL COMPOUNDS WITH HIGH COORDINATION

Forrest L. Carter

Naval Research Laboratory

Washington, D. C. 20390

Bond formation in transition metal compounds isomorphous with WC and AIB2 is formulated

using the bidirectional orbital approximation (BOA) to establish orbital hybridization and

a simple but self-consistent application of Pauling's metallic radii with charge transfer to obtain the bond orders . For tungsten carbide seven mutally orthogonal bidirectional bonding

orbitals for the negative W atom permits it to simultaneously bond its fourteen neighbors

with up to 6.5 electrons. However, bond polarization results in an effective negative charge

for carbon of 0.0 to -0.3e. For the diborides the metallic radii results indicate that the

group IV diborides have a slightly positive boron which becomes negative with increasing

group number but remains below a charge of -le. Four arguments are given for the pleating

of the boron layer were it to be heavily charged as has been proposed earlier in the isoelectronic analogy to graphite. One of these involves a new definition of atomic volume

based on the Voronoi polyhedron. Bond formation by the boron and carbon atoms in these com- pounds is discussed using the nonpaired spin-orbital [NPSO] approach of Linnett.

Madelung constant and Madelung potentials calculations via the method of Bertaut have

been made for both the tungsten carbide and the AJiB2(Cdl2) structure. These were computed

in order to both estimate the magnitude of the electrostatic stability as a function of

atomic parameters and to provide a basis for the comparison of ESCA chemical shift data with

the calculated effective charge.

The effect of bond formation in distorting the surfaces of constant energy in k space

is also considered in these compounds with the aid of a simple square well potential model.

The principle directions of these distortions of the unreduced Fermi surface are indicated

for the WC structures and as a function of the boron position parameter for the AJiB2 structures .

Finally, we note that in both of these structures almost all the electrons outside the rare gas cores are involved in bond formation; this is in contrast to the refractory

chalcogenides

.

Key words: Aluminum diboride - cadmium diiodide structure; bidirectional orbitals;

effective charge; ESCA; Fermi surface distortion; Madelung constant; Madelung potential;

metallic single bond radii; refractory transition metal compounds; tungsten carbide;

valence bonding; Voronoi polyhedra.

1. INTRODUCTION

The materials of principal concern in this paper are those transition metal compounds

with the tungsten carbide and the aluminum diboride structures. These generally refractory

compounds have in common three features of interest to us

:

1) all outer electrons are used in bond formation (largely true)

,

2) the transition metal atoms have high coordination numbers, 14 and 18 respectively,

and

3) the nonmetals , which are usually first row atoms, also have high coordinations for

which bond hybrids of the usual types do not apply.

515
Understanding these compounds then presents a special challenge to the solid state chemist

since he must devise new bond hybrids for both the transition metal atom and the nonmetal

atom, under the restraint that all electrons outside the rare gas cores are involved in bond

formation. This latter fact is, of course, suggested by the unusual refractory nature of

many of these compounds

.

In view of the commercial importance of some compounds having the tungsten carbide

structure, it is surprising that it has not been the subject of extensive theoretical re- search. That it has not is indicated by the little space devoted to it in reviews such as Nowotny's [1]^ which deal with the bond formation in similar refractory compounds, and in

material bibliographies of metals and alloys treating physical properties sxibject to theoretical interpretation [2] . On the other hand, the diborides which currently are of little

commercial value, though of some promise, have a plethora of theoretical bonding interpretations as is indicated in the review of Post [3] . These bonding interpretations are primarily

of two forms; electron transport to boron and electron transport away from boron.

Of these two diametrically opposed theories, the theory transporting one electron to boron is the simplest and has considerable appeal to chemists. This theory was probably

first proposed by Nowotny [4] in 1950 and Muetterties [5] in 1957, although Pauling [6] had

earlier discussed a tetravalent B~ atom in conjunction with FeB. In this description of the

diborides the boron is assumed to be isoelectronic and isostructural with graphite, with the

boron negative charge neutralized by the intercalated divalent metal ions. For the various

other details of this approach it is well to go to the original articles as reviewed by

Post [3]

.

The case for the opposing theory has been discussed by Kiessling [7] in 1950 from a chemical point of view, by Juretschke and Steinitz [8] in 1958, and more recently by

Cadeville [9] from physical concepts. In the latter two models various numbers of electrons

(3 and 1.7 respectively) are assumed to enter the d band of the transition metal in order to account for experimental mobility and magnetic properties. Taken literally the resultant

high positive charges for boron of +3 and +1.7 respectively are difficult to accept from a chemical viewpoint.

In this paper we want to reexamine valence bonding in refractory transition metal materials as represented by the two classes of compounds with the tungsten carbide and aluminum

diboride structures. In doing so, use will be made of bond distance information as through

Pauling's metallic radii formalism [6; 10, p. 393ff ]

, electrostatic energy calculations, and

atomic volume effects. However, instead of applying Pauling's "resonating valence bond"

theory [6] in a literal sense, an attempt is made to develop bidirectional orbitals [11] for

the transition metal atoms in the two structures and to examine some of the implications of

Linnett's [12,13] nonpaired spin-orbitals (NPSO) approach for bonding by the nonmetal atom.

The desirability of deviating from the resonating bond approach while retaining many of the

desirable features of the valence bond method is related to the incalculable number of different ways of developing equivalent resonant forms in the solid state. The bidirectional

orbital approximation (BOA) reduces the number of possibilities to a manageable few which

can be ordered.

In particular, the tungsten carbide structure is approached from the metallic radii

formalism, electrostatic energy, and valence bond methods in sections 2., 3., and 4.,

respectively. For the diborides similar considerations are applied in the main sections 5.,

7., and 8., while a new concept of atomic volume is developed in section 6. Theoretical and

experimental evidence is adduced, in these four sections, against the existence of a planar

graphite-like layer composed of B~ ions. Finally, in section 9 the effect of bond formation

on the shape of the Fermi surface is discussed in regard to the two different structures

along the lines suggested earlier by the author [11]

.

Prior to proceeding to the body of this primarily theoretical paper, it is of value to the reader to recognize that the most important and difficult portion of working in the area

of these refractory materials is the preparation of single phase, well characterized com- pounds. That this is a nontrivial problem is suggested by the frequency that irregularities

1 Figures in brackets indicate the literature references at the end of this paper.

516
in the metallic radii results are coincident with the questioning in the literature of the

compounds existence.

2. METALLIC VALENCES IN TRANSITION METAL COMPOUNDS

By the use of Pauling's semiempirical metallic radii formalism [6; 10, p. 393ff] it is

generally possible with the data from an accurate structure analysis to obtain estimates of

the following properties: 1) the relative importance of different bonds, 2) the effective

valences Vj , for each atom, 3) an approximate distribution of bonding electrons between the

s-p and d orbitals, and 4) the approximate number of unshared and unpaired electrons on each

atom. For the transition metals the number of unpaired electrons can be checked against

known magnetic properties. In Pauling's approach the atomic valence Vj of atom j is equal

to the sum of the bond orders n-j_j of all important bonds, eq (1). These bond orders are

V. = ^ n. , ...

3 1 i: (1)

d. . = R. + R. - 0.600 log n. . (2)

R. = 1.825 - 0.043Z - (1.600 - 0.100)6 (3) 1 obtained from the bond distances dj_j and the single bond metallic radii R^ via eq (2) . In

eq (3) we give Pauling's formula for estimating the single bond radii Rj_ , for the iron-transition row elements according to 6, the bonding d character, and Z, the number of electrons

outside the rare gas core. These radii are in general a function of the atomic valence, both

through the d character, 6, of the bonding orbitals and through the number of electrons Z,

associated with the atom in question. This latter factor includes electrons involved in

charge transfer but not electrons associated with bond polarization.

In order to apply these equations to a known structure, an Algol program [14] has been

developed that solves the above simple equations in an reiterative manner taking into account

electronegativity effects like the one of Schomaker and Stevenson [10, p. 228], equations

similar to eq (3) for the elements of other rows, and the effect of nonstoichiometry (without site relaxation). While the equations and effects involved are simple, the program is

not, due to an inordinate amount of electron bookkeeping required for a program capable of

handling a general structure which might involve any combination of the elements (actinides

generally excluded) . Presumably the only variable permitted is charge transfer since tables

of the single bond radii and d character have been provided by Pauling 16,10] . In fact it is

often necessary to permit variation of the transition metal d character, 6, in order to achieve selfconsistency between the valence "calculated" by eq (1) and the valence "estimated" from the electrons available and set aside for covalent bond formation (a bookkeeping

operation)

.

In general it is desirable to pay more attention to trends in series of related com- pounds than it is to focus attention to the details of any one compound. This is particularly true in the refractory carbides and diborides discussed in this paper since it is often

the case that the only information reported is the nominal starting preparatory composition

and the lattice parameters. In the general absence of detailed information the author has

little alternative to the suspect assimption that the compounds reported are pure and stoichiometric. Even when the assumption is correct a detailed analysis might be misleading in

a refractory and hard compound since the final structure can be a compromise in which some bonds are stretched while others are compressed. This situation will lead to incorrect bond

orders via the application of eq (2) and to incorrect valences', eq (1), in some cases. Even

so the use of Pauling's metallic radii are much to be preferred on the basis of the new information obtained than any "hard sphere" or ionic radii model. The parameters associated

with the latter models usually are applicable only to a very limited class of compounds

while Pauling's approach has general application to intermetallic compounds, semimetals , and

most semiconductors.

2.1, METALLIC RADII CALCULATIONS FOR THE TUNGSTEN CARBIDE COMPOUNDS

In compounds with the one-to-one hexagonal tungsten carbide structure the nonmetal has

six metal neighbors in the form of a trigonal prism while the metal atom has six basal plane

517
metal neighbors, and two additional metal neighbors above and below the basal plane. Further,

the metal atom has six rionmetal neighbors also in a trigonal prismatic coordination. For the

compounds and their lattice parameters tabulated by Wyckoff [15] the results of various

metallic radii calculations are given in tables 1 and 2. In general we see from table 1 that the strongest bonds are the metal-nonmetal bonds, labeled M-X, which are somewhat better

than halfbonds (bond order equals 1.0 for a single bond). The metal-metal bonds are also

quite significant, being only slightly weaker than halfbonds, except in the compound of MoP

.

Of the metal bonds the vertical pair along the z axis are consistently stronger than the more numerous basal plane bonds. In table 2 it is apparent that the tungsten carbide structure

is characterized by a high metal valence of about 5.0 to 6.5 and by a low charge effect.

Details and limitations of the metallic radii approach are indicated by the first two

entries in table 1 and 2 for tungsten carbide, as calculated under two different charge

transfer restrictions. Under the assumption of 1:1 stoichiometry for tungsten carbide the

application of the metallic radii equations as given by Pauling does not lead to self-consistency without some upward adjustment of the tungsten d character (6, as given by eq (2))

.

Such a change in d character results in a smaller single bond radius {Rj_) and usually a de- crease in the calculated valence. If the d character increases too much {e.g. 10%) or decreases, the experience of the author suggests that the reason may reside in the incompleteness of the material characterization, and that assumptions as to stoichiometry and

purity are inaccurate. In the case of entries 1 and 2, table 2, it is seen that the d character increases from 39% to 42% and to 40% respectively. In the first case, entry 1, no charge transfer was allowed so that all of the adjustment to attain self-consistency was attained by the d character increases. The effective charge of carbon, -0.36, is due to the

polarization of the bond according to electronegativity differences in a manner employed by

Hedberg [16] and Pauling [10] . In the second case, entry 2, sufficient charge was transferred from carbon to tungsten to make the effective charge of each atom zero, where the

effective charge of each atom is taken as the sum of the charge transferred to it plus the sum of the charges due to the polarization of the pure covalent bonds "i" of bond orders nj_

.

This latter case, which we describe as a "neutral cell" calculation (to be discussed shortly) , appears to give the following rather reasonable results for tungsten carbide: 1) first

very little adjustment of the tungsten d character is required, 40% vs 39.7%; 2) electrons

transferred to tungsten are employed in bond formation (no unshared electrons on tungsten)

and 3) all the carbon electrons are also used for bond formation or are transferred. The net

result is that tungsten has roughly 6-1/2 electrons for forming halfbonds with 14 near neighbors and that all electrons outside the rare gas cores of both atoms are bonding electrons,

a situation which is wholly reasonable in light of the refractory nature of tungsten carbide.

Table 1

Metallic Radii and Bond Orders for the Tungsten Carbide Compounds

ENTRY cpd RADII (A) BOND ORDERS

M X M--X M-M (basal) M-M (vert)

WC 1.,322 0 .772 0 .543 0.318 0.416

2. WC 1..333 0 .770 0 .568 0.380 0.495

3. WN 1 ..333 0 .770 0 .486 0.420 0.543

4. RuC 1..276 0 .774 0 .528 0.256 0.356

5. OsC 1..282 0 .774 0 .539 0.266 0.370

6. MoP 1,. 301 1 .108 0 .826 0.090 0.098

7. MoP 1..301 1 .062 0 .693 0.090 0.098

(a) Similar entries of tables 1 and 2 correspond to the same calculations.

(b) Entry 1 was calculated under the restriction of zero charge transfer,

the remainder of the table was calculated using the "neutral" cell

approach

.

518
Table 2

Metallic Radii Summary for the Tungsten Carbide Structure

CALC. 6 UNSHARED

ENTRY cpd. ELEM. CHARGE VALENCE d-CHARACTER ELECTRONS

Trans

.

Eff

.

, (d)

J. w 0 .0 + 0

.

37 5 nn n . 0 C 0 .0 -0. 37 3 .26 0..74

Z •

Ta7 W -0 . 51 0

.

0

c.o . 3 / n n c +0 .51 0. 0 3 .41 0,.08

J m Win Ww -1 . 00 0

.

0 • <c n 0 N +1 .00 0. 0 2 .91 1..08

AHi > PnP Ru -0 .07 0

.

0 5 .41 0 . 46 (

0

. ; 2 .66 C +0 . 07 0

.

0 3 .17 0,.76

5, OsC OS -0 .07 0. 0 5 .57 0..46 (0 .49) 2,.50 c +0 .07 0. 0 3 .23 0,.70

6. MoP Mo -0 .11 0. 0 5 .69 0..43 (0 .43) 0,.42 P +0 .11 0. 0 4 .95 (3.11) 1..78

7. MoP Mo -0 .09 0. 0 4 .89 0,.43 (0 .43) 1,.20 P +0 .09 0. 0 4 .16 0,.04 (0 .0) 0,.75

(a) Similar entries in tables 1 and 2 correspond to the same calculation.

(b) Generally the "calculated" valence equals the "estimated" valence, when this is not

the case the estimated valence is given in parentheses.

(c) The d-character in parentheses is that given by Pauling or calculated from his table

of single bond metallic radii [10]

.

(d) With the exception of entry 1, all results are for the "neutral" cell restriction,

that is, charge transferred is balanced by bond polarization such that the effective

charge on each atom is zero. In this case, however, no charge transfer was permitted.

In those cases where bond polarization in a compound is counteracted by charge transfer,

see Pauling [10, p. 431ff ]

, a polyhedral cell can be devised [17] such that the total charge

in the cell is zero. Such a "neutral" cell about a particular atom is constructed along the

lines of a Voronoi or Wigner-Seitz cell by constructing planes which are both perpendicular

to the inter-neighbor vectors and which divide in half each bond of the atom of interest.

The smallest polyhedron formed by this process is the cell of interest. From atom i, the

distance dp of the plane which divides equally the bonding electrons between atoms i and j is

taken to be

dp = (d. . - R. - R.)/2 + R. = (d. . + R. - R.)/2 (4) i: 1 D 1 i: 1 : where dj_j is the internuclear distance and Ri,Rj are the single bond radii. The polarization

of this bond is assumed to transport through the bond-bisecting plane that amount of charge

to be associated with the electronegativity difference times the bond order [16] . The cell

charge is zero when the total bond polarization charge is equal to that transferred to an- other atom. For tungsten carbide the neutral cells for both kinds of atoms are compared in

figure 1 with their Voronoi polyhedra (to be discussed in greater detail later) . The neutral

cell restriction was employed with the remaining entries of table 1 and 2 in order to clarify

any trends. However, in these materials it seems reasonable that the physical situation is

bracketed between the results under the restriction of zero charge transfer and those of the

519
I

Fig. 1. The Voronoi polyhedron for carbon is the same as that for

the tungsten atom in the tungsten carbide structure. This

polyhedron, whose volume is half that of the unit cell, is

compared with the neutral cell polyhedra for carbon and

tungsten. These cells, which more nearly reflect the volume

associated with the individual atoms almost pack together

perfectly to fill all space. The c axis is vertical.

neutral cell restriction. From table 2, entries 1 and 2, we see that the effective charge

of carbon is negative with a maximum value -0.36.

The neutral cell calculation for tungsten nitride is of interest for several reasons.

In the first place, the largest electronegativity difference of tungsten and nitrogen polarizes the W-N bonds more, so that the neutral cell calculation requires the largest charge

transfer to the metal of any of the compounds in the series of table 2. In the second place,

100% more charge is transferred than seems to be used by the tungsten atom in bond formation

since 0.49 tungsten electrons are unused (unshared). Finally, so much charge is transferred

that the single bond radius of nitrogen is a near equivalent to that of neutral carbon,

table 1.

While the neutral cell restriction seems to be eminently reasonable for application to

intermetallic compounds of good electrical conductivity, perhaps its application to compounds

exhibiting large electronegativity differences is less desirable. On the other hand, th-is neutral cell approach seems reasonable when taken in combination with the meager experimental

data available. Tungsten mononitride is rather different than the refractory tungsten car- bide in that it is reported by Schonberg I18J to decompose at 600 "C to W2N and nitrogen gas. In addition, Schonberg suggested that the compound was not stoichiometric but probably con- tained less nitrogen than 50% atomic. A decrease in nitrogen content will tend to produce

three desirable effects in terms of the neutral cell calculations : 1) The number of electrons transferred to tungsten but not used for bonding will be directly reduced through com- position changes. 2) Similarly, the tungsten charge will also be reduced and appear to more nearly resemble that of tungsten in the carbide. This will have a secondary effect on the

charge transferred as the W-N electronegativity difference will be decreased, 3) Finally,

the nitrogen radius will be larger and the metallic radii calculation will yield a valence

of nitrogen greater than the 2.91 of table 2. These three points taken together suggest that

stoichiometric tungsten mononitride might be difficult to prepare and give reasons for the

comparative stability of W2N, that is, provided it has a related structure.

520
Experimentally little data on the stoichiometry and properties of ruthenium and osmium

monocarbide exist. That more is needed is indicated by the neutral cell metallic radii

calculations; the results of which are given in tables 1 and 2. Since the electronegativity

differences are small, the neutral cell approach may be expected to apply; even so in both

cases, entries 4 and 5, the d character had to be decreased (metal radius increased) by 4%

and 3% in order to obtain selfconsistency . This suggests an interstitial impurity or that excess carbon may be present. Otherwise the results as well as some of the refractory properties are similar to those of tungsten carbide^. The calculated results are similar in the

presence of the high metal valence, an apparent carbon valence of less than four, and good

metal-metal bonds

.

The neutral cell results for molybdenum monophosphide are rather different in regards

to this last point as illustrated by entries 6 and 7 in table 1. Here it seems that the

metal-metal bonds are a fourth as strong as in the remaining members of the tiingsten carbide

series. However, the metal and nonmetal valences are comparable to the other members of the

series. Another difference is the use of a smaller radius by phosphorous than is normal:

this is interpreted as the use of a small amount of d character according to an equation

which is an extrapolation of Pauling's equations and is similar to eq(3) . That the normal

radius is inappropriate in this case is shown by entry 6, table 2, in which the estimated

phosphorous valence of 3.11 is not equal to the calculated valence of 4.95. In order to achieve selfconsistency the insertion of 3 to 8% phosphorous d character was assumed. Entry

7, table 2, gives the results for 4% d character which was approximately the lowest d character giving selfconsistency . At higher d character the Mo-P bond order became more nearly

like a halfbond at the expense of slightly decreased valences. The use of d character by

phosphorous is understandable and is discussed later in terms of bidirectional orbitals for

its trigonal prismatic coordination. An alternative explanation might be metal deficiency;

however, the experimental data given does not bear on this point.

The effective charges for the various members of the tungsten carbide compounds might

be summarized as follows : Carbon in tungsten carbide has a small negative charge due to bond

polarization effects but one which is significantly less than the zero charge transfer case

of -0.36. Nitrogen in WN has a somewhat larger negative charge than its carbon analogue,

but its lower composition ratio will result in a tungsten charge approaching that in the carbide. The remaining compounds should have quite small charges of less than +0.1. Part of

the theoretical information required to verify these expectations is developed in the next

section

.

3. ELECTROSTATIC AND POTENTIAL ENERGY CALCULATIONS

Any model of bond formation in a heteroatomic material will, in effect, associate with

each atom a net effective charge. Accordingly, a comparison of calculated charges with

measured charges would be a useful adjunct in a test of the model in addition to the usual

test using interatomic distances. While accurate determinations of atomic charges has been

attempted by x-ray and optical technic^ues , generally these have not been too successful.

However, new technical advances (x-ray) and interpertations of optical bond data by Phillips

[19] may prove useful. Meanwhile, the method of electron spectroscopy for chemical analysis

(ESCA) has been developed by Siegbahn and his co-workers [20] at Uppsala and this method

promises to be a much more direct and rapid approach to the detennination of effective atomic

charges in a compound. In short, the technique is to bombard the core electrons with a monochromatic beam of x-rays with the energy E^ and accurately measure the energy Ej, of those

electrons which escape the solid without being inelastically scattered. The binding energy

Eg of the core electron is then simply Eg = E^ - E]^. The chemical shift AE is the difference

Eg - E° where E° is the binding energy for that element in some standard state. Simple potential theory suggests that for a free atom a positive AE corresponds to a positively charged

atom. In the case of a crystalline compound the approach must be modified to allow for the

Madelung potential as has been discussed by Siegbahn et al. [20] and Ramqvist [21]

.

Although to date little chemical shift information is available on transition metal

compounds having the tungsten carbide and aluminvmi diboride structure, the corresponding

Nowotny [1, p. 194] reports that Knapton has demonstrated that these reported carbides of

ruthenium and osmium probably were, in fact, tungsten carbide.

521

/
Madelung constant and Madelung potentials have been calculated here in anticipation of the

rapid maturing of the ESCA technique. Two more immediate reasons for the Madelung constant

calculations include the electrostatic estimation of the tungsten carbide heat of formation

as per Ramqvist [21] and concern for the stability of the boron position in the diborides

when charge has been transferred.

The Madelung constant A, and potentials , have been calculated via the method of

Bertaut [22,23]. Using the notation of Templeton [24,25] the appropriate formula for one molecule per unit cell is eq (5) where Wg is the electrostatic energy,

W ?

£ is the electron charge, V is the unit cell volume, L is a standard length taken here as L = v^/^, Zj is the charge of the atom j, and h is the length of the reciprocal lattice

vector (hih2h3) . The structure factor term F is given in eq (6) where the atom j is at the

position (X1X2X3)

.

F = ^ z.

"^2^2 + h3X3)

The function (j) (ot) is simply the square of the Fourier transform of the normalized linear

spherical charge distribution f (r) defined by eg (7) with R as the sphere radius. The selfenergy factor g is readily shown to be g = 26/35 [23,25]

3(R - r)/7TR^

0

r < R

r > R

f(r) =

and the parameter a is defined simply as a = 2TThR

(7)

The potential Vj , at the position of the atom j is readily calculated by the method of

Bertaut [23] at the same time as the Madelung constant,

the electrostatic energy Wg , by the eqs (8 and 9) The potentials Vj , are related to

V. = 6W /6z

.

W = — ^ V .z . E 2 : D :

(8)-

(9)

The equivalence of the carbon and tungsten positions in the tungsten carbide structure permits the potentials to be obtained from the Madelung constant without further calculation,

thanks to eq (9), as is occasionally the case with other simple structures [21]. However,

for the AS,B2 case the aliiminum and boron site potentials must be individually calculated.

Unless otherwise stated, all calculations were made by summing over the points in reciprocal

space out to a limit of h (max) determined by a (max) = 27TRh (max) = 5.0. The value of R in

these hexagonal structures was taken as R = 0.285 A^ where A^ is a basal plane unit cell

edge. In both the tungsten carbide and the diboride structure the closest interatomic approach for any value of the metalloid z parameter is Aq//3. The radius R was chosen to be

less than 0.2887 A^, or half this value, so that no correction was needed for the overlapping

of the charged spheres.

The computer program used [26] is suitable for several simple hexagonal structures and

was tested by verifying the work of Zemann [27] who gave the variation of the Madelung con- stant of the NiAs structure as a function of the c/a ratio. The program was further checked

against the empirical "reduced" Madelung constant of Templeton [28] as indicated in the

appropriate sections below. The results for the Cdl2 structure also generally supported the

work of Hartman [29] who obtained the value A(Rq) = 4.381890 rather than the earlier and

less accurate value of Hund [30] who obtained A(Rq) = 4.71. Both of these values are based

on Rq the shortest anion-cation distance. TaJole 3 gives the present results for the Bozorth

Cdl2 structure (see [15, p. 266]) as a function of a few values of the iodine z parameter

and two values of the c/a ratio. These calculations are based on a cation charge of +1.0,

522
an anion charge of -0.5, and a length L equal to a cube root of the volume. When Hartman's

value is converted to these conditions, one obtains A = 1.73865 which is lower by 0.00030

than the value shown in table 3 for z = 1/4, c/a = 6.855/4.240 = 1.617, and a (max) = 5tt . Jones and Templeton [25] have provided a table of corrections for series termination to be

applied to Madelung constants calculated using the Bertaut series for values of a (max) up to

a (max) = 5tt. In the present case this correction amounts to 0.000034 which is about 1/9 the

amount required to produce agreement between Hartman and the results obtained here. The Cdl2

calculations were repeated for amax = 5 . 5tt and are indicated in table 3 in parentheses.

These results tend to confirm the size of the Jones and Templeton correction and suggest

that Hartman's value may be 0.015% smaller than the best estimate of A = 1.738918.

3.1. THE TUNGSTEN CARBIDE MADELUNG CONSTANT

Using Bertaut 's method as described above, the Madelung constant for the tungsten carbide structure has been calculated as a function of the c/a ratio as well as a function of

carbon z position. In table 4 the Madelung constant A = W^L/e;^ is given for the charges

= +1, Zq = -1 where is the electrostatic energy and L = V-^/^ = Aq (/3 c/2a)^/^. As

the result of this charge choice and the carbon and tungsten position similarity the same

table can be used for the carbon Madelung potential interpreted as VqL/£ , and with a negative

sign as the tungsten Madelung potential, V^L/£^ . The symbol £ represents the electron

charge. The Jones and Templeton correction for table 4 is Q = AAR/2L = 5.7 x 10"^ and is a slowly varying function of c/a. Thus for c/a = 0.85 the numerical magnitude of A should be

decreased by AA = 0.000036 and at c/a = 1 . 2 by AA = 0.000041.

The increase of the electrostatic energy (Madelung constant) with the decreasing separation of the tungsten and carbon layers and the decrease of the Madelung constant with increasing c/a ratio is expected from simple electrostatic considerations. The carbon parameter at z (C) = 0.50 and constant c/a ratio is at the Madelung constant minimum. Experimentally determined metalloid positions in this structure at values other than at 2/3, 1/3, 1/2

are not known to the author. Even so, on the basis of L being the cube root of the molecular volume, the Madelung constant 2.137, of the tungsten carbide structure with c/a = 1.0

Table 3

The Cadmium Iodide Madelung Constants

and Potentials for Selected Parameter Values

METALLOID z = 0.30 0.25 0.20

C/A

1-617 A 1.481751 1.738951 1.957677

(1.481736) (1.738935) (1.957662)

LV^^/e -1.864629 -2.092507 -2.340555

(-1.864609) (-2.092485) (-2.340535)

LV^/e 1.098873 1.385396 1.574799

(1.098863) (1.385385) (1.574789)

1-633 A 1.469607 1.732332 1.956348

(1.469592) (1.732316) (1.956334)

LV^^/e -1.846214 -2.079068 -2.332955

(-1.846194) (-2.079047) (-2.332936)

LV^/e 1.093000 1.385596 1.579742

(1.092991) (1.385585) (1.579732)

(a) Values in parentheses are for a_,,Y = 5.5Tr, others for arn=x ~ 5.0tt.

523
U

+Jupu

+J

CO

OJ •H

£i

fO UC

0) pm

0)N

•rH iH

(C

0)C

(U

(Uo

tn -pc

rO -pc0uc

<1) T!s oo

inoo

iHo

in

INo

COo

in

CM (J) in CM CO o 00 o CO CO CO

in CM 00 CM CO 00 CO CM o n TP in in CO

CM CM CM CM CM C\] CM

<Ti

_

CO CM CJ5 CO 00 in o CO

CM CO i> CM

CVJ CM o 00

CO in in 
 CO CO

CM CM CM CM CM CM CM

in 0^

in CM in in CO

CM CO o CO in in o in CO CD CM CO in in in CO

CO CM CM CM CM CM CM Cvj

CM o o 00

O 00 in CO CO in in CM CO 17) X in

CO CO in o 00

in CO i> rH CM CO

t-i CO CO in in o CM CM CM CM CO CM CM CM

CO rH CO o O 00 CO CO

CO o in CM rH CM CO

00 O)X in CM

X

rH rH rH rH rH rH o O

CM CM CM CM CM CO CM

a> rH CM CM o f~ CM 00 CM in C5 rH CO CO O t> rH CO I> CO CO 00 O

rH r-H rH rH rH o o O

CM CM CM CM CM CM CM CO

-= 0 M U

•H « > aM

CO

D, CME I |CO a

rH CO u I a -c o CO o Q uM <D x:

0) -P o

cj ^ a o

rH CM

£3 \ in in X in CO Ol CT^ C rH o CM CM rH CO CM in X o - CM X o O O X CO MCO o O CO CO O) o CM CM CO •H \

CM CO CO CO CO ^ TP

U rH

-U ~ o CM CM CM CM CM CO CM CM CO

x: CM

X rH in a> rH TP X CM CM CO X 'H 0) X CO in X TP 05 o O -!-> CD C5 rH CM CO CO CM CO •H CM CM CO CO CO CO CO CO ^ m N

CO CM CM CM CM CO CM CM -tH

CO rH \

rH rH

rH COX in CO CM - rt rH CO CO X CO in CO -n CO in in CO rH CM \ O

CO in CO CO CO

m CO rH CO CD CO CM CM CM CM CM CM CM ^ a

cn CM CO CM CM CM CM CM CO 0) H in

Cfi

O

C71 CO rH CD CO o TP CO e X X CM o o X o

CO

X o o rH

X rH 0)

O rH CM rH o in rH

CM CM CM CO CM rH rH rH

x: CO CM CM CM CM CM CO CM -P c

•H

C

CS

0) x: ^ +j O ?H -P 0

-P

0)E U 3 ^in c

cn -H d bJ) H

•H o o

in

rH 0)

C75 CM

XX CM CD +-1 -p CO in rH rH X rH CD rH

TP in CO a> in CO CD s -p CO CO in CO o CO X C 03 rH rH rH rH rH o O no rH

CM CM CM CM CM CM CM rH < in o in o in O in O X 7) CD o o rH rH CM U C3 o o o rH rH rH rH rH D -p x: 0)

524
compares favorably with that of the NaC2. structure, 2.202, and that of the CsCi structure,

2.035.

For timgsten carbide itself with a = 2.9065 and c = 2.8366A we have that the Madelung

constant referred to L is 2.1465 and A(Rq) referred to the shortest anion-cation distance

R , is A(Rq) = 1.7161. This latter value is the same as for Templeton's "reduced Madelung

constant" a defined by eq (10) where the sum is over all atoms in the

a = 2A{Ro)/^z2 (10)

"molecule" [31] . Templeton [28] had shown earlier that a could be approximated by the empirical equation below, eq (11)

a = 1.89 - 1.00/m (11)

where m is the weighted-harmonic-mean coordination number defined as 1/m = (?n. p . ) / (?n . ) . 1 1 1 i 1 Here it is assumed that n^^ atoms of one kind have the coordination number p^^ , where the sum

is again over all atoms in the "molecule" or unit cell. For tungsten carbide 1/m = 1/6 and

the empirical a = 1.72 in good agreement with the reduced Madelung constant of eq (10), where

a = 1.7161.

Having calculated the tungsten carbide Madelung constant, we are now in a position to estimate the negative charge on the carbon atom from the reported ESCA chemical shift data

[31]. Using a combination of metal x-ray absorption edge (K) and ESCA data, Ramqvist [21] was able to obtain the atomic charge for titanium in TiC and the carbon Is Coulomb repulsion

integral Y^is ' ss Zrpj_ = 0.4 and y^-^^ = 0.73 Hartree (atomic units) . From this start he was

able to indicate that the metal charge in a series of cubic transition metal carbides was proportional to the ESCA chemical shift and that the electrostatic energy calculated simply

from this charge and the Madelung constant correlated surprisingly well with the heat of

formation of these various carbides. Using the ESCA chemical shift value of Sqiq = 2.1 eV

reported by Ramqvist for tungsten carbide and his experimental value of the Coulomb repulsion

integral "Yq^qi the carbon charge in tungsten carbide is calculated here to be Zq = - 0.245

from eq (12) as per Ramqvist. The

^Cls = ^C^Cls ^ \ =

^C ^^Cls - (12)

resultant electrostatic energy is calculated from the tungsten carbide Madelung constant of

2.145 to be 65.6 kJ/mole which is in rather poor agreement with the experimental heat of

formation of 40 + 2kJ/mole. This suggests that the estimated charge is about 25% too high

and that a value of z^^ = - 0.20 would be better. The alternative, that Yds should be as large as 0.80 Hartree, seems unlikely since it will later be seen that a strong parallel can

be drawn in the carbon bonding and the use of the carbon p orbitals in the tungsten carbide

case compared to the cubic transition metal carbides. Recent advances in ESCA instrumentation

could be advantageously employed to confirm or deny the Ramqvist reported shift.

The Madelung constant calculations also give support to the ordered carbon position found

by Leciejewicz using neutron diffraction techniques [32] . Earlier it was uncertain whether

carbon was in the ordered position 2/3, 1/3, 1/2 or was disordered between that position and

1/3, 2/3, 1/2. Using the Bertaut method for the case of perfect disorder [33], the author

has employed Madelung constant calculations to show that a statistical distribution of cation

vacancies in lanthanide sesquichalcogenides having the ThsPij. structure is electrostatically

unstable with respect to the complete ordering of vacancies [34] . A similar effect may be

expected here. The case with z (C) = 0.5 has not been calculated; however, the case with one carbon atom at 1/3, 2/3, 0 and charge of -1.0 can be compared with the VB2 - Cdl2 calculations with the boron position z (B) =0 given in a later section (table 7) . In this case we

have two atoms of charge -0.5 at the positions 1/3, 2/3, 0 and 2/3, 1/3, 0; this would correspond to the complete disordering of the carbons. By comparing Madelung constants at various

c/a ratios, we see that the ordered case is more stable by 0.61 units at c/a = 0.90 to 0.67

units at c/a = 1.2. This result, a 25% increase in electrostatic stability, is suggestive

that the ordered case at z (C) = 0.50 is also more stable than the disorder structure, as is

indicated by the neutron diffraction findings.

525

/
4. BOND FORMATION IN TUNGSTEN CARBIDE STRUCTURE

A discussion of valence bond formation in the tungsten carbide type structures will

revolve principally around the approaches used in treating two problems. The first problem

involves finding a suitable basis set of valence orbitals for bonding the tungsten atom to

its fourteen near neighbors, given only nine atomic orbitals. The other problem is that of

devising carbon orbitals which permit the carbon atom to simultaneously bond six neighboring

tungsten atoms. If the tungsten atoms were in an octahedral coordination the three p orbitals

could be used. However, the coordination about the carbon atom is that of a regular trigonal

prism. The approaches to these problems employed here involve the use of bidirectional or- bitals (BOA) to obtain bonds in the fourteen directions required by the tungsten atom 111]

in combination with Linnett's nonpaired spin-orbitals (NPSO) on carbon to obtain six bonds

in the trigonal coordination [12,13].

4.1. TUNGSTEN BIDIRECTIONAL ORBITALS

Twelve of the fourteen neighbors of the tungsten atom have a coordination similar to hexagonal close packing but with a c/a ratio slightly smaller than 1.0 rather than the ideal

1.63. In this case the tungsten atom is surrounded by six metals situated in the basal

plane with three carbon atoms above and below the basal plane in the form of a trigonal

prism. This HOP coordination suggests that a variation of the C-type bonding orbitals used

in a discussion of bonding in the HCP rare earth metals [35] be employed. If a bonding

bidirectional orbital is written in the general form of eq (13) then five other orbitals

d)l=As + Bp + Cp + Dp + Ed +Fd +Gd +Hdo9 + Id o (13) X y z xy xz yz x_y^ y

can be generated from <iii by rotations of 120° and 240° about the z axis combined with a 180°

rotation about the x axis. If this set of six orbitals is required to be orthonormal, then

the coefficients, A, . . I, must satisfy equations (14), (15), and (16)

.

A- + l2 = d2 = 1/6 (14)

c2 + e2 + f2 = + 6^ + h2 = 1/3 ^ (15)

BC = EH + EG (16)

Of the original nine atomic orbitals, one 6s, three 5p and five 5d's, three orbitals

remain which may be hybridized in various ways. Since the two remaining important neighbors

of the tungsten atom are directly above and below it on the z axis and since all the p^

character is employed in the six C-type orbitals as per eq (14) , then a bidirectional G-type

orbital of the form eq (17) first employed by Ganzhorn [36]

(^^ = A s + id s (17) G z

might be applicable. The two remaining orbitals then contain no s, p^, or d22 character.

The orthogonality conditions to be satisfied by these last three orbitals are indicated by

equations (18) , (19) , and (20) where the lower case coefficients

A A + I i = 0 (18)

Cc + Ee + Ff = Gg + Hh = 0 (19)

Cb - Be + He - Eh + Gf - Eg =0 (20)

correspond to the two local orbitals.

526
within the above restrictions for the six C-type orbitals, eqs (14-16), the coefficients

may be selected such that one lobe of the bidirectional orbital is directed approximately

toward a neighbor in the basal plane while the maximum of the other main lobe is directed

toward one of the six atoms out of the basal plane. Previously it had been indicated that an effective variation from a c/a ratio above 1.63 to a ratio of about 1.52 could be achieved

via use of increasing d character in these orbitals [35]. This decrease in c/a is clearly

insufficient for the tungsten carbide coordination. However, if significant s character is

included in the orbital much lower effective c/a ratios can be achieved as is indicated in

figure 2. Since there are nine coefficients in eq (13) and only five restrictions, eqs (14),

(15), and (16), there exists a certain latitude in the choice of the remaining coefficients.

However, such considerations as the relative strengths of the two main lobes and alignment

of lobes along bond directions are of importance and will be considered later.

The strength of the G orbital along the z axis is determined both by the fact that only

one s and one d22 orbital are available and that these must be shared by the G orbital and

the six C-type orbitals in the manner required by the orthogonality restriction of eq (18)

.

It is a happy circumstance that the s and d^2 coefficients in the C-type orbitals are of

opposite sign since this permits, via eq (18), the same signs of these coefficients in the

G-type orbital. As a consequence, this orbital has a strong concentration of electron density along the z axis , thereby permitting the tungsten atom to form halfbonds with its tungsten neighbors directly above and below.

The overall picture for the tungsten atom then may be summ.arized as follows: six Ctype orbitals and one G orbital can employ up to 7 electrons to form bonds simultaneously

with its fourteen neighbors. There are, in fact, two different ways in which the C-type

orbitals can be formed. These different ways can be related by a mirror plane reflection

and are enantiomorphic to one another. However, the G-type orbital is orthogonal to both

sets of orthogonal C-type orbitals. In figure 2 a C-type orbital is indicated in relationship to its bond directions. Corresponding to this C orbital figures 3 and 4 show the overall angular distribution of the electron density for six such orbitals while figure 5 illustrates the orthogonal G orbital. The hybridization strength^ of the two lobes of the C orbital of figure 1 are approximately equal, 2.18 for the carbon directed lobe and 2.09 for

the horizontal lobe in the basal plane. The strength of the G lobes is 2.28 when A = I//2.

The carbon directed lobe of the C orbital is misdirected toward a high c/a ratio by about 5°. It will be seen in the next section that this is probably desirable to maximize overlap with

Fig. 2. This stereogram of a C-type orbital for the tungsten atom shows a lobe (taken as positive) in the horizontal plane for forming the

basal plane metal-metal bonds and a negative lobe for the metalcarbon bond which projects out toward the viewer. The total d

character of the orbital is 60% with the coefficients A = - I = 1/^6

and D = - 1//6.

^See reference [10, p. 108f] for a definition of orbital strength.

527
the carbon bonding orbital which is also slightly misdirected. The C orbital shown in fig- ure 2 is fairly typical of those available from a coarse net of values of the coefficients

of B and H.

Fig. 3. The total angular density distribution of the six orthogonal C orbitals for the metal atom is shown in this slightly asymmetric

stereogram. While the electron density corresponding to the metalcarbon bond has a clear trigonal prismatic configuration the basal

angular projections tend to overlap in pairs near the carbon atoms.

Although the basal lobe maxima are well directed these lobes are not symmetrical about the metal-metal direction; this is also

indicated stereoscoptically in figure 2 and figure 4.

Fig. 4. The stereogram viewed here down the z axis includes the average of

the electron density of figure 3 plus its enantiomorph. While the

corresponding wavefunction has the full crystal symmetry of the

metal site the metal-metal bonds are clearly asymmetric favoring

the region near the carbon atoms . Nevertheless the bond maxima in

the basal plane are only about 5° away from the hexagonal directions.

528
Fig. 5. The remaining two near neighbors which are not bound by

the six metal C orbitals in tungsten carbide are other

metal atoms directly above and below. These neighbors

are bo\ind by the symmetrical (gerade) G orbital shown

above whose angular concentration along the + z and - z direction is controlled by the requirement of orthogonality

with the six C orbitals.

4.2. BOND ORBITALS FOR CARBON

While the BOA method appears to provide a reasonably satisfying set of bond orbitals for

the tungsten type atom, the method is not by itself applicable to carbon in the tungsten car- bide structure since carbon has a trigonal prismatic coordination and only s orbitals and p orbitals are available for hybridizatLon . Later it will be seen that prismatic coordination

using C-type orbitals of low d character, ca. 7.8%, might be considered. However, this gives

a coordination c/a ratio^ of 1.5 which is not a good fit for carbon in tungsten carbide where

its effective coordination c/a is 1.9. More important, even a usage of 7.8% d character by

carbon appears improbable.

The approach which shall be used to discuss the carbon bonding is the non-paired spinorbital (NPSO) treatment of Linnett. In this case the traditional valence pairing of electrons in a single bonding orbital is abandoned and one deals with eight spin-orbitals for

carbon. The real space components of the four of these orbitals for the spin up electron is

generally not orthogonal to the real space orbitals for the spin down electron. Accordingly

by this method one can obtain eight s-p hybrid orbitals from the four traditional orbitals

of carbon. These then may be linked to the bidirectional orbitals of the metal atom to obtain a form of the alternate molecular orbitals (AMO) introduced by P. 0. Lowdin and expanded

by Pauncz and his coworkers 137] . However, prior to considering the implications of these

1+ The_definition of coordination c/a ratio used here defines the height of the metal prism

as c/2 and length of the side of the trigonal base as a. When this definition is used for

a trigonal antiprism a c/a of 1.633 corresponds to a regular octahedral coordination about

the central atom.

465-504 0 - 72 - 35 529
ideas, let us review the variations of bond hybridizations possessing three-fold symmetry.

Such a review will be applicable to the boron element in the Ai'B2 structure and will provide

limitations for the bonding of carbon in the tungsten carbide structure.

The orthogonality conditions for trigonally related s-p hybrid orbitals can be readily

obtained by rotating an orbital of the form a s + b pz about the x axis. The well known

relationship eq (21) then relates

b^ sm Y = 3" (21)

the angle of rotation y to the p character, b^, of the orbital. When y = 90° the three trigonally related orbitals are the familiar planar sp-^ orbitals and the fourth orthogonal orbital

is the p^ orbital. At y = 70° 32' one has the four symmetric tetrahedral orbitals, sp^ , with

one of these being directed along the -z axis. The minimum angle y is 54° 44' and corresponds

to the three pure p orbitals with b^ = 1 . For carbon in the general trigonal prismatic co- ordination one might employ the following scheme: The three trigonally related s-p hybrids

of one spin point to the three metal atoms at the base of the prism with the three trigonal

hybrids of the other spin pointing to the top of the metal prism. Reversing the electron

spins leads to an equally probable situation. Of course in the final wave function these

two different spin arrangements are equally likely to occur in a material of low magnetic

moment

.

The situation in^tungsten carbide is a little bit different from the above. Carbon

has a coordination c/a ratio of 0.975 and a corresponding angle a, as above, of 49° 50".

However, the minimum a for s-p hybrids is 54° 44' corresponding to the three pure p orbitals.

Accordingly, the following applies for the carbon hybridization in tungsten carbide: 1) The

carbon bonding orbital will be mostly p with the fourth orbital for both electron spin up and

spin down being the_2s orbital. 2) The tungsten-carbon bond is bent so that the carbon has a somewhat smaller c/a ratio than observed while the tungsten has a larger c/a ratio than

observed. 3) The maximiam bond order of the tungsten-carbon bond is 0.5 according to this

treatment.

This maximum bond order of 1/2 leads to a maximum valence of three for carbon. That

carbon should be trivalent in a compound known for its strength and extreme refractory nature

is, of course, anathema to all those who believe in the tetravalency of carbon. In the next

section, dealing with phase structures in tungsten carbide materials, we will see that not

only does the unbonded half of the p orbitals play a role in the bonding but appropriately

the s orbital is also important.

4.3. PHASE STRUCTURES IN TUNGSTEN CARBIDE

In the prior two sections bidirectional bond orbital schemes have been devised for both

the metal atom and the nonmetal elem.ents of the second row. Now we would like to link these

orbitals together throughout the structure to form bonds , in a schematic sense , in order to determine the overall selfconsistency of the method. The approach is to match the phases of

the bidirectional orbitals in the bonding region so that bonds rather than antibonds are

formed. In the former case, the phases of the two orbitals should both be positive or negative, while in the case of the antibond the phases are of different signs. Thus, in the

antibond, a nodal surface exists in the region between the two atoms and the resultant low

electron density causes the interbonding force to be repellent. If this were to occur frequently or if many possible bonds were not formed, then one would consider such a "phase

structure" as unstable and not representative of the material's ground state. The use of

bidirectional orbitals usually leads to the formation of cycles within the phase structure

that are composed of rings (cycles) or infinite chains of phase-linked orbitals. Further,

these cycles are usually mutually orthogonal within a single phase structure. However, in

the tungsten carbide case we will find a different situation in the presence of three cen- tered bonds involving one carbon and two tungsten atoms in addition to the above discussed

carbon-tungsten halfbond.

530
In figure 6 we indicate part of a phase structure involving a layer of tungsten atoms

and the neighboring carbons in a view which is a projection down the c axis. The tungsten

atoms are small open circles while the carbons are small filled circles numbered 1, 2 and 3. In this phase structure the C orbitals of all the tungsten atoms are assumed to be all of

the same sense (like right handed) and only two of the six C orbitals for each metal atom

are shown. Also missing are the metal G orbitals and the carbon s and p orbitals. The C orbitals of figure 6 are linked by their lobes in the metal plane to form one-third of the

tungsten- tungsten bonds. Although all of the phases of these lobes are arbitrarily taken

to be positive, we shall shortly find that this leads to a self consistent situation of con- siderable stability. The negative lobes of these C orbitals point toward the carbon atoms

above and below the metal plane. If the carbon 1 is above the plane with one set of NPSO's

overlapping the negative lobes of the C orbitals, then we see from figures 6 and 7 that it

is phase linked through two C orbitals with carbon 2 which is below the plane and which uses

the second set of spin-orbitals . This configuration of phase-matched orbitals might be termed a partial phase structure, iip^iO) , associated with the zeroth layer of tungsten atoms.

This partial phase structure has a repeat unit cell (fig. 6, dotted lines) which is three

times the vol\ime of the crystallographic unit cell (solid outline) . The carbon atoms in

the new unit cell have the coordinates: CI, 0,0, 1/2; C2 , 1/3 , 2/3 , -1/2 ; and C3 , 2/3 , 1/3 , 1/2 . The total phase structure consists of two more partial phase structures, i'-^C^) and i'^iO) , involving different metal C orbitals and a cyclic rotation of the roles played by (and the

spin-orbitals used by) carbons 1, 2, and 3. Notice that the total phase structure, using

'^A'"^B' together, can have the crystallographic unit cell size; and that right handed

and left handed phase structures, employed in equal proportions, give total wave-functions

with full crystallographic symmetry.

At first glance it might seem that these partial phase structures ij;^, etc. are independent of each other, however, we shall now indicate that they are linked through the formation of three centered bonds involving the positive lobe of the carbon p orbitals and its

partial overlap with the central portion of the nearby tungsten- tungsten bond. At the top

of figure 7 we see two C-type orbitals overlapping to foirm a metal bond in the z = 0 plane.

Fig. 6. A partial phase structure, "ij^iO) , in the tungsten carbide

structure basal plane is shown for two of the six C orbitals for each metal atom: the carbon p spin-orbitals

are not indicated. The carbon atoms numbered 1 and 3 are taken as above the plane while number 2 carbon is below

the plane. The repeat cell for '1'^ is indicated by the

dotted lines while the crystallographic unit cell outline

in the (001) plane is shown in the solid lines.

531
W-W Bondf+1) W-W Bond (-1)

Fig. 7. Partial phase structures associated with neighboringhexagonal packed layers of tungsten atoms are shown

to be phase linked by the carbon p spin-orbitals as above. This is seen to involve a metal-metal bond

in the z = 0 layer, two metal-carbon halfbonds, and

two three -centered bonds, such as between a carbon

at z = + 1/2 (- 1/2) and a metal -metal bond at

z = + l.O(-l.O) .

The carbon atom on the right at z = +1/2 uses a p spin^-orbital not only to form a halfbond

with the tungsten atom in the z = 0 plane but also to form a three center bond with the

metal-metal bond in the layer above. Similarly carbon 2 continues the phase matching to the metal bond in the plane below. The net result is that the phases of all the metal-metal

bonds in i'p^t'P^i and can be taken as positive and linked by cycles of six bidirectional

orbitals indicated by the sequences 'J^^ ( 0 ) ( -1 ) { 0 ) and ijj^ (0) -^4;^ (+1) -^ijj^ (0) .

In addition to this special use of the carbon p orbitals, it is seen that the carbon

2s orbital which appears to play only a small role in the direct carbon-metal bond may also

be stabilized by these neighboring metal-metal bonds. This is suggested in figure 6 by

carbon 3. We see that all the metal-metal bonds surrounding it have the same phase, a situation which is uniquely suitable to a stable bonding interaction with the s orbital.

This special stabilization, which is particularly appropriate when the wavevector k is zero, may be expected to disappear as the associated bands (see section 9) become half filled.

The asymmetry of electron density about the basal plane metal-metal bonds may also be ex- pected to contribute to the stability of the carbon atom both through the enhanced carbon

2s orbital stability and through the three center bonds. Their asymmetry is indicated in

the stereogramatic figures 2, 3, and 4 and by the metal bonds near carbon 3 in figure 6. Finally, we note that the unit cell indicated in dotted lines in figure 6 is also the

repeat unit cell for the use of nonpaired spin-orbitals for carbon for the three partial

phase structures iip^,,^^, and Note further that the sum of their composites can also

correspond to the crystallographic unit cell.

4.4. METALLOID BONDING IN MoP

The bonding scheme described above for carbon in tungsten carbide could be applied to MoP. However, the Pauling metallic radii results suggest (table 2) that a few per cent d

character may be involved in the phosphorus bonding. In this section an interpretation of

this possibility will be explored through the use of pure C orbitals. We will seek a set

of bidirectional orbitals of low d character which are suitable for the trigonal prismatic

coordination of phosphorus in MoP.

532
Assume that we have a pure symmetric C orbital of the form + bdjjz and th.en rotate

it about the x axis by an angle a . Two more orbitals are generated from the first by rotations about the z direction of 120° and 240°. The amount of d character, b^ , is determined

by mutual orthonormality and is given in eq (22) derived earlier 138] in a somewhat different

form. In order

(l-b2)cos2a = 1/3 (22)

to see the effect of changes in the angle a, we refer to figure 8 in which we are looking

down the axis (z direction) of a twisted trigonal prism. Assume that the main C orbital

lobes of the first orbital point in the direction of atoms 1 and 1^, figure 8. The triangular top of side length a = a is in solid lines while the prism base is in dotted lines. The

angle in projection between atoms 1 and 1' is taken to be the angle 2a) as shown and the height

of the prism is taken as c/2

.

The results in terms of coordination c/a ratio and a is given in figure 9. Notice that

when 0) is 0° and 60° one has trigonal prismatic coordination and when to is 30° and 90° the

coordination is antiprismatic . The latter case occurs at 54° 44^ and b^ = 0 and corresponds

to the octahedral coordination of three pure p orbitals.

The case of most interest here is for w = 60°. This occurs at a = 53° 4^ and has a d

character of 7.8% which agrees rather well with the metallic radii results (4-8%) obtained

in section 2.1. for phosphorus in MoP. While the correspondence between the observed coor- dination c/a of 1.90 and the ratio 1.50 obtained for 8% d character is less than impressive,

it is hardly worse than the alternative of using pure p orbitals for the phosphorus. In addition, the use of a small amount of d character in these C orbitals raises the bond hybridization strength to 1.91 compared to 1.73 for pure p orbitals.

Before considering the effect of bond formation in tungsten carbide on its surfaces of

constant energy in k-space , we first discuss the transition metal diborides from the same general viewpoints as we have treated the tungsten carbides. While certain similarities

are found, it will be seen that differences in the successes of the treatments raise questions

as to the correctness of the unpleated AJiB2 structure for some of the diborides

,

y

Fig. 8. Looking down the axis of a general twisted

trigonal prism we see that the top triangular

base of side a = a is rotated from the position

over the base triangle by the angle 2 oj. If

the height of the prism is c/2, then the effective

or coordination c/a ratio is c/a.

533
Fig. 9. For a twisted trigonal prismatic coordination using C orbitals the coordination c/a ratio and the angle to is given as a function of the rotation a of the C orbital out of the xz plane. When u = 0 and 60 degrees

the coordination is trigonal prismatic while co = 30 and 90 degrees correspond to antiprismatic and octahedral

coordinations respectively.

5. METALLIC RADII TREATMENT OF THE TRANSITION METAL DIBORIDES

The results for the treatment of the nonrare earth transition metal diborides via the

metallic radii formalism of Pauling [10] are given in tables 5 and 6 for those diborides

listed by Post [3] and Pearson [39] as having the hiB2 structure. These self consistent calculations were not performed under the "neutral cell" restriction since in many of thes2 com- pounds the bond polarization of the boron-metal bonds and the transfer of charge for increased

bond-forming power are effects which act in the same direction. That is, in some diborides

both effects increase the effective negative charge of the boron. Generally it was assumed

also that the boron parameter for planar boron layers, that is z (B) = 0.50, is correct and

that the lattice parameters taken from the literature [3,15, and 39] were for stoichiometric

materials. However, generally speaking, these assumptions are subject to correction as more detailed and critical data is collected. The calculations which are exceptions to these two

assumptions in table 5 and 6 are entries 4 and 5 which deal with the effect of changing z (B) in VB9 , and entries 14 and 15 which are nonstoichiometric results for the tantalum diboride

compositions, TaBj_g7 and TaB2_7o- Also we note here that variations in the boron radius in

table 5 are primarily due to charge transfer effects.

When the boron layer is planar and graphite-like (z(B) = 0.50) each boron has three

short boron-boron bonds and six boron-metal interactions such that the boron sits in the center of a trigonal prism of metal neighbors. The bond orders for these two different kinds

of bonds are given in table 5. It is clear that the strongest bonds are for the B-B interactions and the next strongest are the M-B bonds. The boron valence electrons are, roughly,

equally divided between these two kinds of interactions. Each metal atom has twelve boron

neighbors in the form of a hexagonal prism and six metal neighbors in the basal plane. Table

5 shows that only in the case of SCB2 are the M-M bonds stronger than M-B bonds. In addition,

there are two weaker metal-metal bonds perpendicular to the basal plane whose bond order is

generally three-quarters or less than that shown in table 5 for the M-M bonds. While these

two bonds are included in the metal valences shown in table 6, the author doubts that these

are significant bonds considering the multiplicity and bond order of the M-B bonds. Generally, speaking for the metal atom, we see that more than two-thirds of the metal's valence

electrons are employed in the formation of bonds with the boron atoms and less than a third

534
Table 5

Metallic Radii and Bond Orders for the Transition Metal Diborides

(a) ENTRY cpd. RADIUS BOND ORDERS

Metal Boron B-B B-M M-M

1. ScB2 1.351 0.816 0.43 0.19 0.28

2. TiB2 1.250 0.796 0.64 0.24 0.12

3. VB2 1.230 0.791 0.73 0.30 0.11

4. VB2 1.225 0.800 0.49 0.59 0.11

z = 0.42 0.16

5. VB2^^'^^ 1.227 0.797 0.51 0.54 0.11

z = 0.42

6. CrB2 1.183 0.778 0.84 0.25 0.17

7. MnB2 1.167 0.778 0.77 0.24 0.11

8. ZrB2 1.407 0.809 0.45 0.24 0.26

9. NbB2 1.336 0.795 0.53 0.29 0.16

10. M0B2 ^'^^ 0.295 0.799 0.57 0.38 0.17

11. RuB2 1.202 0.781 1.11 0.43 0.20

12. AgB2 1.318 0.778 0.78 0.34 0.38

13. HfB2 1.384 0.805 0.47 0.24 0.24

14. TaBi.gy^®^ 1.339 0.800 0.53 0.31 0.18

(e) 15. TaB2.70 1.339 0.800 0.55 0.30 0.21

16. OSB2 1.220 0.782 1.06 0.43 0.20

17. AuB2 1.368 0.800 0.43 0.23 0.23

(a) Entries with the same number in tables 5 and 6 correspond to the same calculation.

(b) The position parameter of the boron atom is given by z = 0.42.

(c) The longer boron-metal bonds are not included in the metallic radii calculations.

(d) The high temperature form {A2.B2 structure) of MoBo is stable above 1600 °C and is

metal deficient [3].

(e) The self-consistent calculations were carried out for the stoichiometries as indicated.

535
Table 6

Metallic Radii Summary for the Transition Metal Diborides

CALC. d- UNSHARED

ENTRY cpd. ELEM. CHARGE VALENCE CHARACTER ELECTRONS

Trans. Eff.

1. ScB2 Sc -1.08 -0.70 4 .08 (4..14) 0,.25 (0.,20) 0.0

D + U - J_» z 0 .0 2. TiB2 Ti +0.29 +0.43 3 .71 0. 34(0.,27) 0.0

g U • U

3. VB2 V +0.57 +0.67 4 .43 0. 35(0.,35) 0.0

nD — n 9Q 9 Q \

• zy

;

U . U

4

.

(d) V 0 . 00 +0.15 5 .00 0, 35 (0.,35) 0.0

2=09 . 42 IJR — n HQ . DD to. nn ^ 0.0

5. z=o!^2(^'^^

V +0.22 +0.33 4 .06 0. 35(0. 35) 0.71

13 -n 1 7 n n U . U 6

.

CrB2 Cr + 1.50 + 1.57 4 .192 0. 39(0. 39) 0.30

-0 . 75 -0 . 78 4 .ID) u • u

7. MnB2 Mn +1.44 +1.46 3 .67 (3..12) 0. 40 (0. 40) 1.99

-D 7 T

-3 7 7 ^rtU \ u

.

U . U 8. ZrB2 Zr -0.60 -0.32 4 .58 0. 34 (0. 31) 0.0

B + 0 . 30 +0 . 15 2 7n nu • nu

9. NbB2 Nb +0,33 +0.42 4 .67 0. 40 (0. 39) 0.0

B -D 9

1

•3

, xo J u • u 10. MOB2 Mo +0.08 +0.12 5 .92 0. 44 (0. 39) 0.0

H . T

.

B n nn f

"5 n^ ^ u • u 11

.

RuB2 Ru +1.28 + 1.15 6 . 72 0. 53 (0. 50) 0.0

B -0 . 64 -0 . 58 5 . 90 ( 3

.

nVJ • nu 12

.

AgB2 Ag +1.50 +1.51 6 .69 0. 41 (0. 35) 2.81

-D 7R -n 7R . JO i J ,.ID] n n U • u 13

.

HfB2 Hf -0 .38 -0.07 3 .49 0. 35 (0. 29) 0.0

TaBi.gy^'^^'

0X3 U • U 14. Ta +0.09 +0.27 4 .91 0. 39(0. 39) 0.0

(g) TaB2.70

B -0.06 -0.14 3 .40 (3. 05) 0.0

15. Ta 0.0 +0.19 4 .67 0. 39(0. 39) 0.32

B 0.0 -0.07 2 .98 0.02

16. OSB2 OS + 1.21 + 1.09 6 .79 )

.

53 (0. 49) 0.0

B -0.61 -0.55 5 .78 (3. 61) 0.0

17. AUB2 Au 0.0 +0.10 4 .16 0. 30 (0. 36) 6.84

B 0.0 +0.05 2,.64 0.36

(a) Entries with the same number in tables 5 and 6 correspond to the same calculation.

(b) Generally the "calculated" valence equals the "estimated" valence, when this is not

the case the estimated valence is given in parentheses.

(c) The d-character in parentheses is that given by Pauling or calculated from his table

of single bond metallic radii [6,10].

(d) The position parameter of the boron atom is given by z = 0.42.

(e) The longer boron-metal bonds are not included in the metallic radii calculations.

(f) The high temperature form of M0B2 is stable above 1600 °C, has the AIB2 structure, and

is metal deficient [3].

(g) The self-consistent calculations were carried out for the stoichiometries as indicated.

536
of the valence electrons is involved in the formation of metal-metal bonds. These results

support the observations and interpretations of Post [40,3] who explained the c/a ratios in

the transition metal diborides on the basis of a strong B-B bond and a relatively constant

metal-boron distance in contrast to a weaker metal-metal bond. As Post has indicated, these

conditions permit a qualitative appreciation of what occurs except when the metal atoms are especially large.

Prior to discussing boron charges, magnetic moment, nonstoichiometry , and boron layer

pleating, it is noted that, while the rare earth metal diborides might be properly treated

here, they will not because the metallic radii results for the lattice parameter data [3,39,

and 41] indicate such a high d character increase that an additional complicating effect

must be operating. A similar effect was observed by the author [17] in the rare earth com- pounds having the CaCu5 structure and it was suggested that it was the result of an anisotropic radius of the rare earth atom due to anisotropic f electron shielding [17]

.

5.1. EFFECTIVE CHARGE AND MAGNETIC MOMENT IN THE DIBORIDES

The metallic radii results for effective charges vary in a systematic way as one progresses across the periodic table. Considering only those calculations for z (B) = 0.50, it

is seen by starting with the entries 1, 8, and 13 for ScB2 , ZrB2 , and HfB2 respectively, that

the boron is first positively charged to a maximum extent of +0.54 (SCB2) and then becomes

increasingly negatively charged as one increases atomic number along the row. This appears

to be the case for the 3d and 4d series and would apply to the 5d series were it not for

AUB2 where the effective charge is small because charge transfer is not required by boron

for the formation of bonds and the electronegativity difference is minimal. The maximum

negative charge of the boron for each of these rows is -0.78 (CrB2) , -0.75 (AgB2) and -0.61

(OSB2) . It is seen that this charge picture generally supports no one theory, neither the

transport of three electrons from boron to the metal d band as Juretschke and Steinitz [8] have interpreted their electrical data, nor the loss of 1.7 boron electrons to the metal

atom as magnetic data on CrB2 and MnB2 as has been discussed by Cadeville [9] , nor the gain

of an electron by boron to form a graphite-like plane of B~ ions. This later picture is

discussed by several authors based both on earlier chemical considerations, {e.g., Nowotny

[4] and Muetterties [5]) and on NMR data (Silver, Bray, and Kushida [42,43]). The boron

charges generally range from +0.54 for SCB2 to -0.75 in a few cases where selfconsistency^

was not achieved.

Experimental checks on the above charges are generally not available from the literature,

however, some results for the diborides of titanium and vanadium have been reported by

Ramqvist [21] and Fischer [44] respectively. For TiB2 , shifts in the metal K absorption

edge, the emission edge, and the metal 2p3y2 bonding energy (ESCA) were inconclusive except

to indicate that the absolute metal charge was smaller than 0.5 [21]. In vanadium L x-ray

emission studies of VB2 , the shift to higher energy was interpreted as indicating a charge

flow from the metal to boron [44] . Both of these results are in agreement with the present . studies. However, clearly, much more work in this area is indicated.

Since magnetic data is becoming available, let us now consider the number of unshared

electrons for the 3d elements listed in table 5. For the corresponding diborides, we will

confine our interest to those metallic radii results with the z (B) = 0.50, for the moment.

The elements Sc, Ti and V (entries 1, 2 and 3) have no unshared electrons available, so a magnetic moment is not expected in their compounds. However, in CrB2 and MnB2 the transition

metal is associated with 0.30 and 1.99 unshared electrons respectively (entries 6 and 7)

.

Since these electrons are expected to be essentially d electrons and since only 1.63 and

1.47 d orbitals per metal atom are used in CrB2 and MnB2 respectively for bond formation, we

may expect .H\ind's rule to be obeyed and find these electrons unpaired as well as unshared.

Magnetic susceptibility data for the 3d diborides summarized by Carter and Swartz [45]

supports the above results. From NMR studies, CrB2 has been reported by Barnes and Creel

[46] as anti ferromagnetic with a moment estimated by Castaing, Caudron, Toupance , and Costa

'The maximum negative charge of -0.75 on boron is program limited by reason of the author's

expectation that a metal charge of +1.50 is as large as might be supported by a metal atom

in a good conductor. This forces the program to find other ways to seek selfconsistency

than by massive charge transfer.

537
[47] to be below 1 per metal atom. From a susceptibility curve which cannot readily be

fitted with a Curie-Weiss law [47] above the Neel point, paramagnetic susceptibility has

been analyzed by Cadeville [9] as corresponding to 1.3 magnetic electrons per metal atom.

This is about 1 electron greater both than that estimated in table 6 and that considered to be appropriate to antiferromagnetic CrB2 [47] . Manganese diboride has been found to be

ferromagnetic by both Cadeville [9] and Anderson, Dellby, and Myers [48]. At 0°K the saturation magnetization indicates 0.19 Ug per metal atom while the paramagnetic data gives an effective number of unpaired electrons as 1.55 [9,48] in reasonable agreement with table 6,

The difficulties associated with preparing or obtaining pure CrB2 and MnB2 are considerable in the light of recent attempts at NBS [49] and the NMR data reported by Barnes and

Creel [46] , Anderson, Dellby, and Myers [48] , and Carter and Swartz [45] . Apparently the

sensitivity for the detection of boride impurities in these materials by the NMR technique

is significantly greater than by the usual x-ray powder method. However, if we take ex- ception to the high paramagnetic value of 1.3 magnetic electrons per metal atom in CrB2

found by Cadeville, because he did not report or correct his measurements for the presence

of magnetic second phases, then it is only appropriate to suggest some of the weaknesses in

the metallic radii approach. These are indicated in the next two siibsections where we con- sider the effects of nonstoichiometry and the pleating of the boron layer,

5.2. EFFECT OF NONSTOICHIOMETRY

In applying the metallic radii formalism to nonstoichiometric compounds, it is assumed,

out of ignorance: 1) that nonstoichiometry is the result of vacancy rather than interstitial

formation, 2) that lattice relaxation does not occur at the vacancy site, and 3) that the

vacancy locations are purely random. Under these assumptions the effect of nonstoichiometry

is fairly predictable. For example, let us consider the A?,B2 form of M0B2 , a material which

must be quenched from high temperature if it is to retain its structure. From entry 10,

table 6, we see that selfconsistent results were not obtained since the estimated boron

valence is 3.04 while that calculated from the sum of bond orders is 4.00 electrons. Since

the molydenum d character is 5% larger than its normal value, it is apparent that the calculated valence of the metal would also be too high if the normal d character, and hence

normal single bond radius, were assumed. If it is accepted that the lattice parameters are

reasoncibly correct, then we see that the more reasonable calculated valences would be obtained

if metal vacancies (or boron vacancies) were assiamed. That this is the case is indicated by

the literature [3, p. 342]; however, the lack of sufficient data precludes further calculation.

For tantalum diboride the situation is different in that information on lattice parameters vs composition is available [39] . In entries 14 and 15, table 5, we have given the

results for TaBj^gy and TaB2_7o under the condition that d character of tantalum is constant

at its normal value of 39%. The nonselfconsistency of the calculated boron valence 3.40

compared to its estimated valence 3.05 can be removed by a d character increase of about 1%

and a charge transfer of a couple tenths of an electron. However, for the composition TaB2.7o

(assuming metal vacancies) it is seen that the normal values of Pauling apply and that the

valency of both elements is lowered by the metal vacancies in the ratio AVg/AVrp^^ = 1.75.

Even though the general strength of tables 5 and 6 is weakened by the lack of accurate

compositional and vacancy (density) data, the tables are sufficiently internally consistent

to make certain of its members deserving of critical scrutiny. In particular, note the

extreme disparities between the calculated and estimated boron valences for RUB2 , 5.90 vs 3.64, and OSB2 , 5.78 vs 3.61. These differences exist even though reasonable adjustments of

metal d character have been made and sizable charge transfer has taken place. It would

appear that either the lattice parameters are much too small or that the structure is wrong.

Przybylska, Reddoch, and Ritter [41] have called attention to the anomalous positions of the

ruthenium and osmium compounds on a lattice parameter chart of the diborides. Earlier

Aronsson, Stenberg, and Aselius [50] questioned the interpretation of the osmium and ruthenium boride data and suggested that the composition is more nearly RuBj j and OsB^ 2

/ ^^^^ that these materials have the tungsten carbide-type structure. If this is correct) then the

unusually strong B-B bonds (for the A£B2 structure) of table 5, entries 11 and 16, would be

eliminated and the calculated boron valence would be restored to a reasonable value of about

3. In addition, the high charge transfer would not occur, the metal d character would be

restored to normal, and unpaired electrons might be expected on the metal atoms.

538
The metallic radii results also suggest that further work on the diborides of silver

and gold might be rewarding. These were reported by Obrowski [51] in a simple note without

chemical analytical support. While the lattice parameters for the silver compound are in

line [41] with other diborides, the calculated results given in table 6, entry 12, suggests

the real composition is nonstoichiometric and probably boron deficient compared to AgB2

.

The results for AuB2 are even more suspect both in terms of the "c" lattice parameter [41]

and the decreased, not increased, d character of the gold atom, entry 17. The boron unpaired

electrons indicated by table 6 for this compound are not expected, in fact.

5.3. THE PLEATING OF THE BORON SHEET .

A variable to be considered in addition to stoichiometry is the effect on bonding due

to the variation of the boron position parameter, z(B) , away from the value 0.5. Such a movement conserves the axial symmetry of the boron, as is required by NMR data [42,45,46]

,

and gives rise to a double (or triple) hexagonal pleated sheet in which the borons are alternately vertically displaced plus and minus from the planar graphite positions. The pleating of boron layers in other compounds is well known and the alternation of pleated and un- pleated layers in W2B5 and M02B5 was given a special notation by Kiessling [52] as early as 1947. More recently, it has been found by LaPlaca and Post [53] that the diboride of rhenium

has a pleated structure. In addition, a new (perhaps only) modification of ruthenium diboride has been assigned by Roof and Kempter [54] a pleated structure of a different sort.

On the basis of size considerations alone, one might expect that pleating is most likely

to occur in the A£B2 structure when the transition metal atoms have their smallest radius.

This occurs in the 3d series for cobalt and nickel for which diborides have not been reported.

The pleating of the boron layer might be tested using the lattice parameters of CrB2 and

MnB2 and z (B) as a variable in an attempt to remove the nonselfconsistency for boron in these

compounds, entries 6 and 7, table 6. However, since these compounds are associated with a poorly determined number of unpaired (or magnetic) transition metal electrons, we elect instead to examine the effect for vanadium diboride for which a magnetic moment is unknown.

Accordingly, all outer electrons in VB2 are bonding electrons since unshared electrons on boron are unlikely for that electron deficient element.

In table 5, entries 3, 4, and 5, three metallic radii calculations are carried out for

VB2 under the condition that the d character of vanadium has its normal value of 35% . In the first case for z(B) = 0.5, entry 3, we see that all of the outer vanadium electrons are used for bonding except for 0.29 electrons which are transferred to boron. This gives an estimated boron valence of 3.29 which is 0.7 electrons short of the calculated valence of

3.99. In order to decrease the difference between the estimated and calculated boron valence, let us develop a pleated boron sheet by moving the boron to a z(B) = 0.42 position.

This increases the three boron-boron distances and three of the boron-metal distances, while

it decreases the other three boron-metal distances. The effect of these changes on the re- spective bond orders is indicated in table 5, entry 4. This decreases the nonselfconsistency

in the boron valence to 0.55 electrons, however, the decrease seems small and a weak argument

for the pleated boron sheet.

In entry 5, table 5 and 6, we give the results for the metallic radii under the assumption that the longer boron-metal interaction is nonbonding. This assumption is justified

below (section 8.2) as a combination of the greater distance and the lack of suitable available boron bonding orbitals. In table 6, entry 5, it is seen that overall self consistency

is obtained. The presence of 0.71 unshared vanadium electrons, however, is not in agreement

with experimental data and suggests that z (B) is somewhat greater than 0.42 and that the

assumption of the nonbonding longer metal-boron interaction is too strong.

The results constitute the first of four arguments that the boron layer may be expected

to be pleated in circumstances of small metal radius and high boron negative charge. Applying this approach to CrB2 and MnB2 it is clear that the CrB2 calculation could be made selfconsistent and the boron negative charges could be reduced in magnitude. Experimental evidence for or against this suggestion of a pleated sheet is slight. The single crystal x-ray

results of Post and Miksic have been reviewed [3, p. 350] and show that the boron layer in

TiB2 is unpleated. However, in this case the boron effective charge is small, table 6, and

the metal atom is large and under compression (compare the calculated d character of 34% to

the normal value of 27%) . Evidently more experimental work on other diborides is desirable

in this area.

539
Recent new results in combination with previous NMR studies of the 3d and 4d transition

metal diborides shows that the electric field gradient at the boron site cannot be correlated with either the c/a ratio or the molecular volume. In this work [45] , Carter and

Swartz point out that the pleating of the boron layer may be responsible for the lack of

correlation, which is especially bad for CrB2 and MnB2

.

6. VOLUME CHANGES IN

The variation of the atomic volume change of boron as its positional parameter z (B) de- creases from the value 0.5 will now be considered for the representative case of VB2 . The

results will constitute the second argument against the transfer of negative charge to a boron layer which remains unpleated. We have seen from the metallic radii results above

that there is little evidence for supposing that any transferred electrons to the boron are involved in boron-boron bond formation. If it were the case, the corresponding bond order

would be 1.33 and a graphite analogy would be understandable; however, instead, the boronboron bond order is approximately half that. In view of the absence of such supporting

experimental information, it seems reasonable to argue that negative charge transfer to the

boron should be associated with a net increase in the atomic volume. In the case of a purely

ionic representation, such a vol\ame change with charge is certainly expected, for example,

see the large variation of ionic radii with charge suggested by Pauling [10, p. 512f f] . A

similar, though smaller, change may be argued on the basis of coulomb repulsion for transferred electrons which are covalently employed.

From simple structural considerations, it is quite clear that the effective boron atomic

volume is a minimum when z (B) = 0.50, this is due to the short boron-boron distances. However,

it is not at all clear how the volume of the unit cell should be divided up between the con- stituent vanadium and boron atoms. A hard sphere approach is immediately rejected as it ac- counts for less than 50% of the unit cell volume. A more reasonable definition of an effective atomic volume is developed below.

For atoms of equal size an approach that was published by the mathematician G. Voronoi

[55] in 1908 seems to be most appropriate. Voronoi formed space filling polyhedra about

each member of an aggregate of selected points by constructing perpendicular planes at the

bisecting position of each interpoint vector. The smallest polyhedron about each member

point of the aggregate is known as its Voronoi polyhedron, the complete set of which fill all

space. When the aggregate of points correspond to a single type of crystallographically

equivalent points, these polyhedra are mathematically termed "stereohedra" , although they are better known to the solid-state physicists as Wigner-Seitz cells. In the present case we will have two types of atoms in the unit cell^ and will describe the resultant polyhedra as Voronoi polyhedra or cells.

The boron Voronoi cells were computed [56] as a function of the boron positional

parameter z(B). The boron and vanadium cells are shown in figures 10 and 11, respectively,

for the values of z(B) = 0.50 and 0.43, The volume of two boron Voronoi polyhedra plus that

of a corresponding vanadium Voronoi polyhedron is equal to the unit cell volume. When fitted

together in the ratio of two to one, such cells fill all space. As indicated earlier and

illustrated in figure 12, the volume of the boron Voronoi cell is clearly a minimum in VB2

for z (B) =0.50. This supports the contention, that with respect to negative charge accumulation, the boron planar configuration at z (B) = 0.50 is unstable.

On the other hand, it might be appropriately argued that the original assumption of

equal atomic radii is not a good chemical or physical approximation. This, however, makes

no substantial difference as related polyhedra may be also computed under the assumption that

the atomic radii are different for vanadium and boron. The resultant polyhedra can no longer

be described as Voronoi polyhedra as they are not all-space filling. However, the volume

occupied is almost space filling. In the case radii are assumed to be the single bond

metallic radii as per Pauling (V, 1.224A; B, 0.80A) these new cells may be taken as newly

^Perhaps it is appropriate to extend the generality of the term, Wigner-Seitz cell, beyond its

original usage, where it was exclusively applied to parallellohedra and stereohedra, to the

present case involving two different crystallographic sites, however, the author prefers the

term, Voronoi polyhedra, both for its greater generality and its earlier conception.

540
Z=0.50 2=0.43

Fig. 10. The boron Voronoi polyhedra are illustrated

in the lower two drawings for the boron

position parameter z = 0.50 and z = 0.43.

The top polyhedron illustrates the smaller

volume of the polyhedron obtained by using

the same construction method but with atomic

sizes corresponding to Pauling's metallic

radii

.

Z=0.50 Z=0.43

Fig. 11. These vanadium metal polyhedra correspond to those of boron in figure 10. While the metal

Voronoi polyhedra plus the corresponding boron

polyhedra fill all space the polyhedra associated

with different size atoms do not.

541

;
9.0

8.C

7.0

6.0

Calj Structure

.50 .42

Z

.38 . 34 .30 .26 .22

Fig. 12. The volume of boron Voronoi polyhedra in the

AIB2 structure is seen to increase steadily

in VB2 as the boron layer becomes increasingly

pleated and approaches the Cdl2 structure type.

defined atomic volumes. Now, the total volume is better than 99.92% occupied by these new

cells. The variation of the boron atomic volume for z = 0.50, 0.46, 0.43, and 0.40 is

4.866a3 (7.202) , 4 . 894a3 ( 7 . 254) , 4 . 952A ^ ( 7 . 360) , and 5 .037a3 (7 . 520) where the numbers in

parentheses are the corresponding Voronoi volumes for comparison. Accordingly, we note that

the boron is unstable in the graphite position with respect to volume increase resulting

from an increased negative charge. This is true in terms of the Voronoi cell volume or in

terms of a reasonable definition of atomic volume. In the next section a more forceful

argument, based on electrostatic considerations, will also be used to suggest the boron

planar configuration is unstable when charged.

7. MADELUNG CONSTANTS FOR THE AIB2 - Cdl^ STRUCTURE^

There is no doubt that, from an electrostatic energy viewpoint, the concentration of

charge on a planar boron layer is unstable with respect to a pleated boron layer. This can

be argued on the basis of the short boron-boron distance and the known Bozorth form of Cdl2

which is the resultant structure that would evolve from a continuous but extreme pleating of

the boron layer. In order to provide rigorous support for this third argument for the pleating of the boron layer when negatively charged, we have calculated the Madelung constant for

the A£B2 - Cdl2 structure for a variation of the c/a ratio from 0.8 to 1.8 and a variation

of the boron position from z (B) = 0.5 to z (B) = 0.0. The method used was the Bertaut series

as discussed above (section 3) and the results are given in tables 7 and 8. The Jones and

Templeton correction [25] to be subtracted from the Madelung constants of table 7 varies as

a function of c/a only, from AA = 0.000027 for c/a = 0.8 to AA = 0.000035 for c/a = 1.8.

The associated Madelung potentials (V^L/E) for both the metal and metalloid atoms are given

in table 8 for the convenience of the reader and for the future interpretation of ESCA and

x-ray data. The series termination correction to be made t^ the data of this table is un- certain, however, a correction of the form AV-i_L = 2AAZj_/ (EZ-i_) appears to be consistent with

the current information as in table 3.

For the AiB2 structure with z (B) =0.5, there is uncertainty in the correct calculation

of A(Ro) , of the reduced Madelung constant a, and in the correct manner of calculating a by Templeton's [28,31] empirical relation, eq (11). This is because the anion-anion distance

The AP.B2 and Cdl2 structure belong to the same space group and differ only in the nonmetal

positional parameter (z(B) ^0.5, z(I) ^0.25) and hence coordination.

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M TP 05 TP o O CM in CO CO X in O) rH X in CD X CO X O CD CD CO CM CO CM rH CM rH CM rH CM rH CM rH rH rH O rH <y> rH X rH O CO o d CM1 rH CM rH 1 CM rH M rH 1 CM rH 1 CM1 rH CM rH rH1 rH rH rH 1 rH1 rH rH rH 1

C5 rH CO O) CO rH o CO CM CO o in CO CO CO 05 05 CD <r CO CO in o CM O rH X in X c:5 O OJ CO 05 CD 05 CO X rH CM CO o X rH O 05 CO X CM o 05 o> Tp O CO Tp CO CM in in in CO X rH 05 rH X i> in rH rH CO CD CO 05 CM CO O) in in O X

CO rH o CM

O CM o rHO rH

O

O 05 05

X

XX CD in CD 'J' in o CM1 rH CM rH CM1 rH CM rH CM rH 1

C<11 o rH o1 rH1 o rHO1 rH1 O rH

O1

CO

X 05 rH TP CO CD oi in 05 in CD in in TP 05

X CO rH

X rH

O 05 CD in t~- in CO CM o in rH rH CD

O <T> t- CO CO in O O t>- CM CM CO o 05 TP CO CO CM X t- CO 05 o rH rH o (0 CO <35 CM t~ i> C>4 rH TP CO Tp CO CO CM o O in X 05 in CO rH Tf rH o rH O rH Ol rH O) O X c:5 X CD in in CO CO CM CM rH d CM rH CM rH 1 CM1 o CM O1 CM O1 rH1 O rH O1 rH1 o rH oi rH1 o rH O1

CO rH T}< CM CM CO TP CO r- CD

X CO CM in in rH CO CO CD o rH TP

XX CM CM CM in

X 05

O TP CO rHO CM CD

X inX

TP Tp rH

X CO o> Tp rHX CO in

X CO rH CD CO CO in rH in in o CO cn X o O X 05 in CD O CM TP O o CM C55 rH o rH (J5 rH X O X O CD X in TP CD CM TP O CO rH rH CM d CM rH CM O o CM O CM O rH o rH O rH O rH O rH O rH O o

in

rH

O 05 TP

X CD CM CD rH 05O rH 05 CM

X rH CM 05

X CO 05 in X in in rH rH rH 05 rH X rH in X 05 in O 05 OJ o X O CM in X O in CO CD TP in CD in rH o CO CM CO rH X 05 X

in 05 CO Tp CO CD

X COX TP CMO TP TP TP Tp

X in

rH 05 rH 05 rH

XO 05 CO

X Tp CO CO rH Tp

O CM CM o TP

CMO1 CMO CM1 o CMO1 rHO 1 rH1 o rH

O1 rH

O1 rHO1 1 rH1 o1 rH1 o1 d -a CS 73 rs T3 rt -a CS a CS -O a -a CS a CS D

rH CM rH CM rH CM rH CM rH CM rH CM rH CM rH C<I rH CM rH CM rH CM Xo

05o

544
(B-B) is shorter than the shortest anion-cation distance, usually taken as Rq- If we use a prime to indicate as referring to the boron-boron distance, then for VB2 we have A(Rq) = 1.1939, A{Rq) = 0.8950, and a = 1.5918, and a' = 1.1934. Using the empirical calculation

of a by eq (11) and ignoring the boron-boron interaction, we have a = 1.75 which is in 9%

disagreement with a = 1.592 above. With the boron-boron interaction and the boron-metal

interaction, we have a" = 1.52 which is 4% too small. It is not, of course, surprising that

the simple empirical relation of Templeton should fail in such a case.

The expected instability of the almninum diboride , with respect to the pleating of the

boron layer, is clearly demonstrated in table 7 for all values of the Madelung constant calculated from c/a = 0.8 to 1.8. The position at z (B) = 0-50 for all values of c/a is a minimum of electrostatic stability. This instability for the boron is also emphasized by the

actual reversal in sign for the boron Madelung potential for c/a ratios greater than 1.6.

The increase in the electrostatic stability (Madelung constant) with decreasing c/a ratio is to be expected since all static ionic structures tend to collapse and since a decreasing c/a

ratio- at constant volume tends to separate the ions of like charges, that is, increases the

boron-boron distances and the metal-metal distances in their respective layers.

8. BONDING ORBITALS FOR THE DIBORIDES

8.1. THE TRANSITION ELEMENT

The application of the BOA approach to the problem of finding suitable bonding orbitals

for the transition metal when the boron is in the planar graphite sheet (z(B) = 0.50) does

not yield wholly satisfying results. This will be briefly indicated in this section for

three different conceivable configurations of bidirectional orbitals. The effect of the

pleating of the boron sheet on the coordination of the metal atom will also be considered.

It will be seen that pleating leads to a more satisfactory bonding scheme.

Two of the principal restrictions of the BOA method [11] are: 1) all neighbors should

be simultaneously bonded and, 2) equivalent neighbors should be bonded in an equivalent

manner. When applied to atoms of high coordination, these restrictions are usually sufficient

to reduce the number of possible combinations of bonding orbitals to a few that can be managed in an elementary discussion. When these restrictions are not maintained, the combinations that should be considered in a "resonating bond" description of a three dimensional

structure with high coordination are staggering. Now, when the boron position is at z (B) = 0.5, the metal atom has two boron hexagons directly above and below to give twelve equivalent

boron-metal bonds. These bonds are in addition to the six metal-metal bonds in the basal

plane. If we just consider the twelve boron-metal bonds, it would appear that six general

orbitals as in eq (13) or six C orbitals or G orbitals would be appropriate.

The first approach which might be attempted is to consider six general orbitals

obtained by rotating one of them eq (1*3) by 60° successively five times. This approach,

however, quickly leads to impossible conditions among the coefficients. Similar results

clearly obtain for either pure C or G orbitals under a six-fold rotation. The second approach

which might be considered is two interpenetrating general trigonal prisms formed by C orbitals. For example, if a C orbital in the xz plane is rotated about the x axis out of the

vertical plane by about a = 28° it is seen from figure 9 that the corresponding trigonal

antiprism (co = 30°) has a coordination c/a ratio of about 2.1 in reasonable agreement with

the generally observed ratio of 2.0. The second required trigonal prism may be formed by

reflecting this one in the yz plane. The six C orbitals are not mutually orthogonal,

however. The orbital of their largest overlap is the p^ orbital which is completely used by

either of the trigonal prisms. This requires then that one has "resonance" between these

two sets of C orbitals and that the metal-boron bond orders are 0.25 or less (as is generally

observed in table 5) . The presence of "resonance" is not satisfactory since the two tenets

of the bidirectional orbital approximation (BOA) , as discussed above, are negated along with

many of their advantages.

In the third approach we will attempt to employ six general G-type orbitals of the form

(eq 23). In this case the approach will be general, although the twelve boron-metal

4),, = As + Bp + Gd +Hdo 9 + Ido (23) G -^x xz x^-y^ z^

465-504 O - 72 - 36 545
interactions will be considered as composed by two interpenetrating twisted trigonal prisms.

For the first trigonal prism the orthogonality conditions eqs (24) and (25) , can be obtained

from eq (23) and its trigonally related orbitals.

- = + g2 + (24)

J

= a2 + l2 (25)

By rotating a pure G type orbital (B = 0) of the form as + id^o about the x axis by an angle a a trigonal antiprismatic coordination is obtained. The corresponding coordination

c/a ratio, bond hybridization strength S, and d character is indicated in figure 13. The

introduction of character (B ^ 0) produces a general twisted trigonal prism.

The second of the two interpenetrating prisms is considered to be rotated about the z axis by an angle 6 from the first prism and is accordingly composed of an orbital such as

(})g, eq (26). Mutual orthonormality for this

(j) = A s + b cos6 p - b sin6 p - 2cos6 sin6 h d

g X y xy

+ g sin6 d + g cos6 d + (cos 6-sin6)h do 9+ i d o (26) xz yz X -y^ z^

trigonal prism results in orthogonality conditions such as eqs (24) and (25) but in lower

case symbols. Orthogonality between the two sets of orbitals gives the conditions of eqs

(27) , (28) , (29) , which, from comparison of eqs (28) and (29) is seen to

0 = Aa + li (27)

(28)

Angle a 'from Z axis (deg.)

Fig. 13. when G orbitals without p character are used to bond six atoms in a trigonal prismatic coordination

one is concerned only with the antiprismatic con- figuration. This figure illustrates the corresponding

variation of the coordination c/a ratio, the hybridization strength S, and the percent d character as a function of the rotation angle a.

546
0 = Bb sin6 + Gg sin6 - 2Hh cos6 sin6 (29)

cos 6 - sm 6 _ _2 coso smo

(30) coso

yield eq (30) . This latter equation requires that cos6 ~ + ~

"J ^^d that the corresponding angle 6 is 60° and 120° . The trigonal character of these prisms informs us that these

results correspond to 6 = 180° and 0°, respectively. The former is obtained from the latter

by reflection in a mirror plane containing the z and y axes; or equivalently by no restrictions in the signs of the lower case coefficients. In short, we may assume 6=0° without

loss of generality. We also note that the s orbital and the d^o orbital are completely used

by the orbitals of the two prisms.

In the case at hand, namely the AILB2 structure with z (B) = 0.5, we will want the six

G orbitals for the metal to boron bonds to be in some sense equivalent. This requires from

eq (25) that A"^ = I" = a^ = i^ = 1/6. Now, if we assume that the signs of the coefficients

A and I are positive (A = I = I/Zg") , then we see from the orthogonality condition, eq (27) , that the coefficients a and i must be different in sign, i.e., a = - i = ± l/^G. The net

result, then, is that the two trigonal prisms are certainly nonequivalent , independent of

the values of the other coefficients, B, G, H, b, g, and h. If, for example, the orbitals

of one trigonal prism have high strengths and are thus suitable for bond formation, then the

orbitals of the other prism have low strengths and are more suitable for localized electrons^

than for bonding.

To summarize the above, we have not been able to devise, in the framework of the BOA

method, six equivalent bonding orbitals for the coordination of twelve (or eighteen) in the

form of two (or three) parallel hexagons of ligands. On the other hand, the BOA approach has

been used by the author in the coordination of twelve in a CCP or icosahedral coordination

[35,57], of fifteen [58] in one of Kasper ' s [59] metal coordinations, of sixteen in a Friauf

polyhedron [57] , of fourteen in WC (this paper) , and even of eighteen as in the metallic LaS

in the NaC£ structure. In this latter case, the metal can use six bonding C orbitals to bond the twelve neighboring metal atoms and three pure G orbitals to bond the six neighboring

metalloids. In view of the above indicated versatility of the BOA method and its lack of success in the A£B9 (z(B) = 0.5) case, the question of the local electron stability of this

coordination arises. The feeling that this coordination might be unstable is strengthened

by the remainder of this section which offers bonding orbitals for the metal coordination

when the boron layer becomes pleated.

As the boron position parameter decreases from the value z (B) = 0.50 the coordination

of the borons about the metal atom changes from that of a hexagonal prism to that of two interpenetrating trigonal antiprisms, a long one having a coordination c/a = 4(1-)j)

(c/a) cj-ystal ' ^ short more important antiprism with a coordination c/a = 4p (c/a) ^^^y^^^-j^

where p = z(B) . Different methods of using bidirectional orbitals for bonding in these

antiprisms is indicated by the data in figure 9 for C orbitals (w = 30° or 90°) and figure

13 for G orbitals. In addition, we must consider bond formation between the metal atoms in

the basal plane. This is possible using G orbitals of high d character (89%) as is also suggested by figure 13 at a = 90°. A combination of such G orbitals and the C orbitals of an antiprism for the short boron distances are readily shown to be orthonormal. We further note

that, when z (B) = 0.408, the coordination about the metal atom of the six closest borons and

the six metal neighbors is, from a point of view of bond angles, the same as a cubic-closepacked coordination. In this case, six orthogonal C orbitals could be used [35] to bond the

twelve nearest neighbors. However, we note that bond orders of. the boron-metal bond and the

metal-metal bond are different.

We have seen that just as the hexagonal coordination with z (B) = 0.50 is difficult to satisfactorily formulate, any significant pleating of the boron layer leads readily to a variety of reasonable bonding possibilities. In the following section we will find a similar

but less extreme situation exists for the boron atom.

'If equivalence between the prisms is not required, then six bonding G orbitals are obtainable, three corresponding to a twisted trigonal prism of high c/a and the other prism

with a very low c/a.

547
8.2. BOND FORMATION BY BORON

Valence bond formation in the diborides by the boron atom presents another interesting

problem in that boron has nine neighbors but only four bonding orbitals, the 2s and three 2p

orbitals. The consideration of this problem is quite germane to understanding the diborides

since both the strongest bonds (boron-boron) and next strongest bonds (boron-metal) are involved. We shall attempt to shed some light on this problem by two simple valence bond

discussions in which the vertical location of the boron is treated as variable. In the first

discussion a traditional valence bond approach is employed, in the second some freedom is

added to the general approach by the use of the nonpaired spin-orbitals (NPSO) of Linnett.

The coordination of the six metal atoms about the boron atom in the planar configuration

(z (B) =0.5) is that of a trigonal prism with a coordination c/a ratio of twice that of the

unit cell c/a ratio. If the traditional boron configuration sp^pz is used where the single

Pz orbital is employed for the boron-metal bonds , then the direction of a boron-metal bond

is 49° away from the direction of the p^ orbital. This, of course, gives rise to six rather

badly bent boron-metal bonds. Further, it is to be noticed that since only one boron orbital

is available to form six bonds, the boron-metal bond order must be 1/6 = 0.167 or less. However, the results of the metallic radii calculations suggest that it is almost always greater

than 1/6 and closer to 0.23.

Let us now consider the changes in the traditional hybridization and coordination as we vary the boron parameter away from the planar value of z = 0.5. Independent of electrostatic

considerations, there are several effects which give this approach an air of reasonableness.

Since the boron-boron bond order (n < 1.0) indicates that tt -bonds do not play a role in the

interboron bonding, there is no obvious reason for the stabilization of sp^ hybridization.

Thus as z (B) decreases, the strength of the bond hybridization^ increases slightly from 1.991

for sp^ hybridization to 2.00 for the best tetrahedral hybridization, sp^ , at z (B) = 0.40.

Thus, as far as the boron-boron bonds are concerned, there is little reason for a preference

of z(B) = 0.50.

With respect to boron's metal coordination, there are two significant changes; the first

is that as z (B) decreases the three metal atoms at the top of the prism become more distant

while the base metal atoms become closer. In the exaggerated position at z (B) = 1/3, the

boron has a coordination of six in a twisted trigonal prism having a small boron top directly

opposed to a larger metal base through the central boron atom. The second significant change

which takes place as z(B) decreases from 0.5 is that s character is added to the p^ orbital

so that the bond hybridization strength is 2.00 (z (B) = 0.40) toward the metal atoms in the

base, but only 1.02 in that part of the boron tetrahedral orbital (sp^) directed toward the

top three metal atoms. This suggests that the effective coordination of boron changes from

nine to six with three of the boron metal interactions being decreased in importance, both

because of increased distance as well as bond hybridization and direction. These effects were employed in an earlier section (5.4.) in the consideration of VB2 with z (B) 7^ 0,5.

In the traditional valence bond approach above, the decrease of the boron position

parameter improves the bond strength of the (sp^)^ hybrid, but it increases the misfit between

direction of the boron-metal interaxis and direction (z-axis) of (sp^)^ hybrid. Thus at

z(B) = 0.50, this angle is 49° but at z (B) =0.40 it has increased to 55°. This suggests

that Linnett 's nonpaired spin-orbitals (NPSO) be used to obtain the boron-metal bond in the

form of the pure three p-orbitals which give a good fit at the angle 54° 44'. This is con- ceivable because the boron-boron bond order is less than 1.0 and nearer to 2/3. If the latter

is the case, then at sp^ hybridization for the boron-boron bonds (z(B) = 0.40 assmed) then

1.5 p orbitals are available for the formation of three boron-metal bonds of half-bond order.

This is generally more than required for these compounds. We note that some bending of the

boron-metal bond may be expected, both because it is doiibtful if z (B) becomes as small as 0.40 and because some s character might be employed for energetic reasons. The use of NPSO

for the boron also indicates that the boron-boron bond and the metal-boron bond formation

are not only nonorthogonal in the phase structure sense, but are indeed closely coupled. We

also note that the use of NPSO's are also quite feasible when z (B) is equal to 0.50 since

this gives rise to three boron-metal bonds which are bent only 6° rather than 49°.

'For a definition bond hybridization strength see Pauling [10, Chapter 4].

548
In the next main section, we will inquire into the effect that bond foirmation in the

tungsten carbide compounds and diborides has upon the electrical properties of these materials.

This will be approached in two ways, through the concept of the Fermi surface and through the

use of the orthogonality of some of the phase structures.

9. BOND FORMATION AND THE FERMI SURFACE

The abundance of information inherent in a careful crystal structure analysis is sur- prisingly rich, especially when used in conjunction with a bond formation scheme. For materials like the transition metal carbides and diborides such information enables one to discuss

transport properties at many levels of understanding using rather crude models. The principal

consideration, which will be developed here for application to these materials, is the relationship between the chemical bond and the Fermi surface topology. For the purposes of

clarity, we consider wave number or k-space as a "good quantum number space" of three dimensions which is rigidly attached to the crystal of interest-^ *^ . The Fermi surface may be taken

as the outermost or most energetic of the occupied surfaces of constant energy in k-space.

In the 3rd NBS Materials Research Symposium [11] , we indicated that the equation for a surface of constant energy in k-space could be written as eq (31). Here m is the electron mass

and k is taken as the magnitude of the

~2

n to k k

E, = V, + neglected terms (31) k 2m 2m k

unreduced wave vector in k-space in the first term, but as the corresponding triplet index,

, k2 , k3) , in the subscript use. The second term is an average over the contents of the

unit cell of the momentum squared of the coordinate and periodic part, Uj^ (r) , of the Bloch

wave function of eq (32). The third term, Vj,, is a potential

^^ir) = e^^*"" U^(r) (32)

term which behaves similarly to oj^j^ and need not be considered further here.

By focusing our attention on the first two terms of the energy, one a "crystal" momentum term, the second a "molecular" momentum term, we can readily deduce the effects of bond

formation in a crystal on the Fermi surface of the crystal. We see immediately that the

energy associated with the first term is a minimum (zero) when k = o and large for higher

filled or excited states. Just the opposite situation pertains with the second term. In order to see this, it is desirable to indicate the correctness of the appellation, "molecular

momentum" term. When k = 0 then the -a)o/2m term corresponds to the energy of a "molecule",

which in this case consists of the contents of a single unit cell in its ground state. The

associated energy then is large and negative. However, a molecule in its excited state is

less negative in energy. This is also true for the general -aj]^^/2m term where an increase

in k corresponds to an increasing frequency of nodal planes and a shift of electron density

away from area_s of greatest potential. However, what we really are interested in is the

variation of o)^ with respect to k (magnitude) as a function of the direction of the wave

vector k.

Qualitatively the variation of lo^ with unique directions in a structure can be understood by assiiming that we have a crystal composed of diatomic molecules, one per unit cell,

with the nuclear axis along the x axis. Now for a k vector along x axis, the magnitude of

0)^ will decrease strongly with k (magnitude) as an increasing number of nodal planes perpendicular to the internuclear axis begins to decrease the dens^ity of the binding electrons.

However, the variation of co^ with k in the y or z direction will be much less because the

nodal planes are now parallel to the internuclear axis and most will fall between the molecules in areas of low electron density. When this variation is combined with eq (31) it is

found that surfaces of constant energy in k space will project, in the unreduced zone

scheme, in the directions which are perpendicular to the bond direction. A generalization

of this result will be used below to predict the approximate shape of the Fermi surface for

compounds having the tungsten carbide and the aluminum diboride structures

.

The description of k-space as "momentum space" is seriously misleading unless it is

further understood as a "crystal momentum" space and not as an electron (p) momentum space.

549
First, however, let us verify this result with an exact calculation using a square-well

potential. Figure 14 shows a square-well potential of period c with four potential step

discontinuities per unit cell. The discrete potentials are given by V-[ corresponding to hills and valleys of width d^ . The energy of the electron, W, is indicated by the dotted

line. Although the solution for the two-step discontinuities per unit cell has been available from the work of Kronig and Penny [60] published in 1931, the general solution to the

n-step problem has not been available until recently [61] . Kronig and Penny also indicated

in their classic paper [60] that if the assumption is made that the three-dimensional

periodic square-well potential of a model crystal may be decomposed into a sum of potentials

of single variables, eq (33), the problem of the motion of

V(r) = V + V

X y

+ V (33)

the electron is separable and may be solved exactly. Using this approach in figure 15 we show the effect in two dimensions of the combination of a two-step potential for the y direction (left side of fig. 15) and a four-step potential in the x direction (bottom of

fig. 15). The depth of the potential is indicated by the amount of cross-hatching. Accordingly, we can imagine a molecule composed of two atom cores, dark squares, separated by a binding region of intermediate potential. The lattice-related molecules are at greater distances and separated by potentials which are more positive. The solutions for these two

linear potentials in general are eq (34) , taken from the work of Kronig and Penny, and eq

(35) (Carter [61] ) .

Two-step discontinuities

Cos kc = C2C2

2 L32 ej Si1^2s (34)

Four-step discontinuities

= CiC, C3C4 H 1

h —

2

1 '3i

2 3iJ

1 '31 34"

2 3i

.

1 62 34

2 37.

" 323^, 3133I

.3i33 32314J

SiS2C3Ct+ - —

S1C2C3S4 - -

7~ + "iT" C1S2C3S4

SiS2S3S^

333V

[32

[

P3

3 ^4

S4 ^ 37

SlC2S3Ci^

CiS2S3Ctt

C1C2S3S4

(35)

0 C Fig. 14, A general one-dimensional square well potential

with four step potential discontinuities per

repeat distance is illustrated. The dotted

horizontal line indicates the electron energy

W in comparison to the constant potentials V-j_

.

550
0 'o

Fig. 15. This figure illustrates the use of two one- dimensional square well potentials to construct

a "bimolecular molecule" in a square unit cell.

The potentials shown at the left, Vy, and bottom,

Vx» add to give a molecule whose internuclear

axis is in the x direction.

where c is the unit cell edge, k the wave vector and 3i, , and are defined by eq (36).

V. ^ W

' 1

e

. = /w-v.

V. > w

1

(36)

C. = Cos 3 .d. 1 11

S. = sin 3.d.

1 11

C. = cosh 6.d.

1 11

sinh 3.d.

1 1

The results for the "molecule" of the figure 15 are illustrated in figure 16 for the

square unit cell case where c = = b^ = 5.0 atomic units, dimensions which roughly corre- spond to the van der Waals packing of hydrogen molecules. Here it is clearly seen that for

a surface of constant energy - constant ordinate in figure 16 - that the Fermi surface projects furthest from the origin in the direction perpendicular to the bond direction. While

figure 16 illustrates essentially a core state this condition clearly obtains at large k

values also. Since a potential of the separable form eq (33) gives [60] the total energy

as the sum, eq (37)

,

W + W

y z (37)

it is easy to see that the Fermi surface is roughly ellipsoidal in k when the form of Vl^ (ki)

is... proportional to k- . This ellipsoidal distortion of the Fermi surface due to bond forma9 tion IS not surprising considering 1) the close relationship between co-^ and the p-momentum

distribution for binding, and 2) the ellipsoids of constant p-momentum density found for

diatomic molecules by Coulson in 1941 [62] . What is surprising is how well the molecule of

"rectangular" atoms of figure 15 appears to mimic the results expected for spherical atoms

as used by Coulson [62] . . -

551
-0. 75

Fig. 16. The solution for the 'diatomic' molecule

of figure 15 can be solved exactly if the

potentials are additive. The solution for

the lowest band is indicated here. It is seen that for constant energy the Fermi

surface projects furthest in k-space in

those directions which are perpendicular

to the internuclear axis.

These elementary conditions can then be summed up in a simple model which can be used

for roughly predicting the shape of the Feirmi surface given only the crystal structure, or

in particular, the relevant bond orders and directions of the stronger interactions or bonds

(i.e., n - > 0.05). Using the unreduced zone scheme assume a spherical Fermi surface whose

volume is determined by the number of electrons outside the filled rare gas cores. Now in

the plane perpendicular to each bond imagine a great circle around the sphere which indicates

the outward distortion of the sphere due to that bond. If this construction is made for each

relevant bond and the amount of distortion is taken as indicated by the bond strength or bond

order, then the principal directions of distortion will occur at the intersections of these

great circles. Of course the voliame of the sphere must be maintained constant during these

distortions and the effects of zone boundaries should be considered, especially for insulating materials and the more polar semiconductors or semimetals. The usual reciprocal lattice

translations may be employed to obtain the results of the distortions in the reduced zone scheme, see for example [63] or the standard solid state physics references. In the next

sections this model will be applied to the materials having the tungsten carbide and

aluminum diboride structures.

9.1. THE BOND FORMATION - FERMI SURFACE RELATION IN TUNGSTEN CARBIDE

The Fermi surface is of central importance, of course, in discussions of transport

properties of crystalline materials, however, before considering how the Fermi surface is

distorted by bond formation let us first discuss those electronic transport properties which

may be deduced from our previous description of bond orbitals and their occupancy in the

tungsten carbide structure.

The bonding for the tungsten atom has been described in terms of G orbitals linking

tungsten atoms together along the c axis and C orbitals which link tungsten atoms together

in the basal plane as well as providing the basis for the tungsten-carbon bond. Now the two

552
principal phase structures which correspond to the use of the G and C-type orbitals are orthogonal and are not mixed by the mirror plane symmetry which must be employed to provide

the total wave function with the symmetry of the structure. Accordingly, we then have in

real space, in p-momentum space, and in k-space two orthogonal "bands" which we might term

for the purposes of this discussion a G-band and a C-band and which (both) would be filled

when the corresponding tungsten bidirectional orbitals in the valence state were occupied by

one electron. Thus, the G-band is filled to give halfbonds when each tungsten donates one electron to it and the C-band is filled to give halfbonds when each tungsten donates six

electrons and carbon three electrons. Such a filling would result in a small band gap semiconductor. However, since the valence of tungsten (table 2) in these compounds is more nearly 6.5 than 7.0, we may expect tungsten carbide to be a low mobility p-type conductor.

Since bond order calculations (table 1) suggest that both the W-W (vertical) and W-W (basal)

bonds are less than half filled (0.46 and 0.35 respectively) but more than quarter filled

both corresponding bands would contribute to the hole-type conductivity. Further, since both

bands are intimately involved in bond formation low mobility may be expected.

These results are in agreement with the experimental transport data of L'vov, Nemchehko,

and Samsonov [64] for the case of tungsten carbide which differs qualitatively from the other

transition carbides (NaC£ structure) studied^ ^ . The data are also in agreement with what

would be expected from BOA considerations for body centered cubic tungsten metal if the eight near neighbors form halfbonds

.

The effect of bond formation in reciprocal k-space for t\ingsten carbide type compounds

is s\immarized in table 9 which indicates the principal directions of the distortions of the

unreduced Fermi surface according to the model of section 9. For example, in the first

entry three great circles perpendicular to the metal-metal bonds in the basal plane intersect

in the [001] and [001] directions to give a strong outward distortion of the Fermi surface.

Similarly a medium strength distortion due to the intersection of great circles corresponding

to a tungsten- tungsten bond in the basal plane and to a tungsten-carbon bond occurs in the

direction [102.] , where Z is noninteger and is determined such that its angle with the [001]

direction is 49°

.

Chemical intuition based on training as an organic chemist suggests that carbon should

be in a sense "saturated" and have little character at the Fermi surface. However, one might expect that the amount of carbon character should be largest at the Fermi surfaces

projections involving the tungsten-carbon bonds. Accordingly, the relative amount of carbon

character at the Fermi surface might be expected to increase as one progresses down table 9.

9.2. CONSIDERATION ON THE ELECTRONIC STRUCTURE OF THE DIBORIDES

In the earlier section treating bonding in the transition metal diborides we argued on

the basis of four crystal chemical considerations against the charge transfer by the metal

of one electron to each boron to form a B~ graphite- like net with a valence configuration of

sp^p^. It was also indicated that any significant charge transfer should be associated with

a pleating of the boron layer. Here we would like to discuss in further detail the electronic structure of the transition metal diborides, both with respect to a proposed semiconducting model [65] and with respect to the distortion of the Fermi surface by bonding effects.

The possibility of a new group of semiconducting compounds based on the A2.B2 structure

has been proposed by George, Goodman, Sterling, and Warren [65]. The stated criteria for

semiconductivity included high bond strength (or low thermal motion) and the possibility of

an ionic-covalent bond formulation associated with a small charge separation. Experimental

support for their contention was their careful preparation and 'characterization of high

mobility-low carrier concentration TiBo and ZrB2 . In vapor grown TiB2 the carrier concentration was sufficiently low (~ 8 x 10 electrons/cm^) that the authors were unable to distinguish between the characterization of the material as a semimetal or a highly impure

(nonstoichiometric) semiconductor. However, it was felt that such a low carrier concentration

did largely eliminate the description of TiB2 as a metal. This latter characterization is in

contrast to that applied to the electronic specific heat results of Castaing, Caudron,

In the discussion of these authors [64] for the carbides it will be seen that the case of

tungsten carbide was not considered and should not be included.

553

/
Table 9

Projections in Surfaces of Constant Energy

Due to Bond Formation in the Tungsten Carbide Structure

DIRECTION BONDS STRENGTH

[001] 3 W-W (basal) Strong

[110] W-W

w-w

(basal)

(vert .

)

Med.

[10^] , e = 49°

z W-W

w-c

(basal) Med

.

[101] , e = 68°

z

2 w-c

[110] 2 w-c w-w (vert .

)

Strong

6 = 53°

•7. 2 w-c Med.

(a) Unreduced Zone Scheme

Toupance and Costa [47] who measured the electronic properties of the diborides of Sc, Ti

,

V, Cr, and Mn. However, of these, the electronic specific heat of TiB2 was indeed the lowest

suggesting a minimum in the density of states and partial support for the semiconducting

model

.

The proposed bonding in the model, however, is not consistent with the metallic radii

results. In the model of George et al. [65] , the boron uses three electrons to form single

B-B bonds (n = 1.0) in the graphite network, this n\mber is significantly greater than that

indicated by the metallic radii calculations where for the B-B bonds, n = 0,64 (table 5)

.

Further, the titanium metal atom in the model is to contribute one electron to each boron

P2 orbital for use as a boron valence electron in the formation of the Ti+^-B~ bond. This

results in the use of the four titanium electrons to form twelve bonds with boron of bond

order 0.166; this leaves no electrons for the metal-metal bond, as would be required for the

proposed semiconductivity . However, the metallic radii results suggest that Ti-B bonds are stronger (n = 0.24) and that the metal-metal bonds are indeed significant (n = 0.12) and

sufficient for metallic or at least semimetallic conductivity.

A low density of states model for TiB2 which is related to the semiconducting model of

George et al., but which is in better agreement with the interpretation of the observed bond

1 9 distances will now be given. Let us assume that for the boron layer a bond order ^'^ of 2/3

is to be associated with a low density of states corresponding to either a small or zero energy bond gap. In support of this we will recall that for the p^ orbital occupation in

graphite, Wallace [66] obtained a zero energy bond gap when the orbitals were 1/3 filled.

It would be surprising if a 2/3 's filling did not give similar results. Recall also that

Pauling noted with interest the frequency of occurrence of fractional bond orders [10] . In addition to the p orbital this leaves the boron with one-third of an s orbital and twoz thirds of a Pj^/P orbital available for bond formation with the six equidistant metal neighbors. However, ^sing the valence bond version of the NPSO approach as for carbon in tungsten

carbide it seems likely from bond angle considerations that these bonds will predominantly

be of p orbital character. This gives a maximum Ti-B bond order of 0.278 (or of 0.333 if the

remaining boron s character is available) , and this is somewhat larger than is generally

l^For A£B2 itself Pauling [10] also obtains a bond order of 2/3.

554
observed, table 5. If boron uses two electrons for the formation of its three B-B bonds,

then the corresponding bond is filled and at a low density of states. The weak metal-metal

bonds also appear to correspond to a low density of states since the number of electrons

involved is approximately one per metal atom. Accordingly, one would expect the predominant

character to be n-type associated with high mobility. The latter property might be expected

from the low filling of the metal-metal band and from the high Debye temperature and low

thermal motion [3] of the B layer as well as from the restriction of electron scattering to

a predominantly two-dimensional process

.

Let us now take another viewpoint of the A£B2 type structure and consider the distortion

of the unreduced Fermi surface due to nearest-neighbor bond formation as a function of the

boron position parameter. When the boron layer is unpleated (z = 0.5) , the characteristic

that over-whelms all others is a very strong distorition of surfaces of constant energy in

the [001] direction, not unlike that calculated for graphite by Wallace [65]. This peak is

due to the confluence of three great circles of strong distortion due to the boron-boron

bonds with three weaker (by 1/6 to 1/3) great circles of distortion due to the basal plane

metal-metal bonds. In addition there is a still weaker distortion by another factor of 1/6,

around the equator due to the marginal vertical metal-metal bond through the boron layer.

The other strong peaks of distortion on the surfaces of constant energy are due to the crossing of the great circles of the boron-metal interactions with those of the metal-metal

and boron-boron interactions. For example, in the direction [10£] the metal-boron great

circle adds to the metal-metal distortion; here I is determined by the angle 6^. which measures the angle between the projection and the z axis [001] . This angle is readily calculated

for this distortion as tanO^ = /3z (B) (c/a) . In the [11£] direction with a slightly larger

62 the metal-boron great circle crosses the boron-boron great circle to give a medium intense

distortion. However, as the boron moves away from the planar position this distortion

rapidly weakens

.

Some distortion peaks will change direction as the boron parameter decreases from z (B) =

0.5. This is shov/n in figure 17 for c/a = 1. The calculations for this figure are simple

ones and require little more than spherical trigonometry. From the figure we see that the

strongest peak in the [001] direction rapidly decreases in intensity due to its separation

Fig. 17. The distortions of the unreduced Fermi surface

for VB2 are given as a function of the boron

positional parameter z(B) neglecting zone boundary crossings. The bonds responsible

for the major Fermi surface projections are indicated in the figure along with their

general directions.

555

/
into other peaks. These number nineteen and include the stationary basal metal-metal distortion, six peaks in the [lOil] direction, six in the [llii] direction and six weaker ones in

the [lOil] position at smaller 0^ values. These latter six are not indicated in figure 16.

However, as this peak diffuses the next strongest peak in the [110] direction remains undiminished and unmoved (see fig. 16) . Also shown in the figure is the splitting of peaks in

the [10£.] and [llli] directions with 62 equal respectively to 60° and 45°. This splitting

reflects the splitting of the six boron-metal bonds for each boron into a set of three strong

bonds (heavy dashed line) and a set of three weak bonds (weak dotted line) . These latter become essentially nonbonding at z(B) = ~ 0.43.

The above material is useful in discussing the effect of the boron z parameter on the

density of states N(E). If the length of the normal derivative to a siirface S of constant

energy in k space is |6E/6kj^| then the density of states is calculated [67] as indicated by

eq (38) where V is the crystal

/

N(E) = (V/87t3) / |6E/6k I'^d.s (38) n volume. Now since |6E/6kj^| '• may be approximated as m*/k where m* is the effective mass, we see that the density of states is just the integral of the surface area weighted by m*/k.

Looking at figure 17 it may be expected that as z (B) decreases from 0.50 and the number of

peaks proliferate the surface area will increase. Accordingly, we may anticipate an increase

in the density of states as the boron layer becomes pleated if the effective mass remains

relatively stable-' An increase m density of states has been observed by Castaing et al.

[47] for the diborides on either side of TiB2 . Accordingly, then such information is not inconsistent with the pleating of the boron layers as they become positive (SCB2) or negative

(VB2) as suggested by the metallic radii results.

10. CONCLUSIONS AND SUMMARY

In general it is seen that the description of transition metal compounds with the

tungsten carbide and aluminum diboride structures is possible using a modified valence bond

approach with a fair measure of success. Not only are experimental properties understood

but the anomalous members and compounds which are erroneously included as members are readily

spotted. The fact that a large percentage of the compounds of each group seem to be improperly characterized experimentally is not only indicative of the casualness associated with

the lack of chemical analyses and the tendency to eschew adequate determinations of the

simpler structures but also of the inordinate difficulties associated with the preparation

of pure (single phase) and/or stoichiometric compounds of these refractory structures.

In both of these compound types it was found that the metal-nonmetal bond plays a very

important role, nevertheless the effective charges calculated, and partly confirmed by

Madelung constant calculations, were not excessive and almost always less than 0.5 (plus or

minus) . In the tungsten carbide case the combination of bidirectional orbitals and nonpaired

spin-orbitals led to the expected high valence of tungsten (6.5) and a less than tetravalent

(3.5) carbon atom. However, the presence of three center bonds and a possible high concen- tration of metal orbitals near the carbon atom may not only compensate for carbon's' nontetravalency but may also account for the larger negative effective charge on carbon calculated

from chemical shift data (ESCA) than expected from a "neutral" cell metallic radii calculation.

Effective boron charges in the diborides were found to change sign near the compounds

of the group V elements and become negative. This has not been previously predicted by any

of the more popular models . While the boron bond formation can now be better understood by

the use of Linnett's nonpaired spin-orbitals, the transition metal bonding still remains

obscure if the original tenets of BOA is strictly followed. On the other hand, the boronmetal bond orders are compatible with a simple form of "resonance" using bidirectional or- bitals (nonorthogonal) . For emphasis we note here that the boron-boron bond order is not

compatible with boron-boron single bond as required by several previous models of the

Changes in the effective mass are difficult to predict from this model without parameterization of the distortion with respect to the bond order, bond length, and electronegativity differences. This information is needed in order to obtain the separation of the

Fermi surface from the Bullouin zone faces and hence estimate zone edge effect.

556
diborides

.

For diborides of the smaller transition metals it was indicated that any large negative

charging of the boron should result in the pleating of the boron layer. The arguments for

this included metallic radii results, anionic volume instability at z(B) = 0.5, electrostatic

instability at z (B) = 0.5, and the inability of bidirectional orbitals to form twelve equivalent bonds in a hexagonal prismatic coordination. If compounds of large negative boron

charge are found to be unpleated then a proper response to the above arguments must be made.

The only clues to where such a response may be found are in the Madelung constant calculations

and the fractional boron-boron bond order of 2/3. The special stability of such a bond order

for a planar (only) boron configuration might be found in a band calculation. The Madelung

constant calculations show that electrostatic energy for z (B) = 0.5 increases rapidly for a c/a decrease. The observed [45] c/a decrease as one moves across the periodic table toward

the more negative boron compounds is at least consistent with these considerations.

Finally, we note that Madelung constants and potentials have been calculated for the

WC, Cdl2/ and A£B2 structures as a function of c/a ratios and positional parameters. In addition, Fermi surface distortions due to bond formation in these compounds have been

predicted.

n. ACKNOWLEDGMENTS

It is with pleasure that I acknowledge many useful discussions of the transition metal

diborides with my wife. Dr. G. C. Carter and that I thank Dr. L. Bennett (both of NBS) for

interesting me in this series of compounds. In addition I wish to thank Margaret O'Hara

and Walter C. Sadler for their patient and complete assistance in the preparation of the

figures and their subsequent photography.

12. REFERENCES

[I] Nowotny, H., in Electronic Structure and Alloy Chemistry of The Transition Elements

,

P. A. Beck, Ed., (Interscience Piablishers, New York, 1963), p. 179.

[2] Carter, G. C. , Kahan, D. J., Bennett, L. H. , Cuthill, J. R. , and Dobbyn, R. C, The

NBS Alloy Data Center: Permuted Materials Index. (Spec. Pub. 324, 1971).

[3] Post, B., in Boron, Metallo-Boron Compounds and Boranes , Roy M. Adams, Ed., p. 301,

(Interscience Publishers, New York, 1965).

[4] Nowotny, H. , Berg-und Huttenmannische Monatshefte 9_5_, 109 (1950).

[5] Muetterties, E. L., Z. Naturforschg. 12b, 411 (1957).

[6] Pauling, L. , Proc. Roy. Soc, 196A , 343 (1949).

[7] Kiessling, R. , Acta Chem. Scand. , _4, 209 (1950).

[8] Juretschke, H. J., and Steinitz, R. , J. Phys . Chem. Solids 4_, 118 (1958).

[9] Cadeville, M. C, J. Phys. Chem. Solids 27_, 667 (1966).

[10] Pauling, L., Nature of the Chemical Bond, 3rd ed. (Cornell University Press, Ithaca,

New York, 1960) . [II] Carter, F. L., in Electron Density of States, (NBS Special Publication No. 323, 1971)

p. 385.

[12] Hirst, R. M. , and Linnett, J. W. , J. Chem. Soc. 1035 , 3844 (1962).

[13] Empedocles, B. P., and Linnett, J. W., Proc. Roy. Soc. (London) A282 , 166 (1964); Trans.

Faraday Soc. 62, 2004 (1966).

[14] Carter, F. L. , Algol program. Calculation of Chemical Valences using Paulings Metallic

Radii. Listing can be obtained from author.

[15] Wyckoff, R. W. G. , Crystal Structures Volume 1, Second Ed., (Interscience Publishers,

1965)

.

[16] Hedberg, K. , J. Amer. Chem. Soc. 74, 3486 (1952).

[17] Carter, F. L., in Proceedings of the Ninth Rare Earth Conference Vol. 2, P. E. Field,

Editor (Virginia Polytechnic Institute and State University, Blacksburg, Va.

,

Oct. 1971) p. 617.

[18] Schonberg, N., Acta Chem. Scand., 8_, 204, (1954).

[19] Phillips, J. C, Science 169 , 1035 (1970).

[20] Siegbahn, K. , in ESCA - Atomic Molecular, and Solid State Structure Studied by Means

of Electron Spectroscopy, 1st Ed., (North Holland Publishing Co., Amsterdam-London

1967)

,

557

/
[21] Ramqvist, L., Jernkont, Ann. 153 , 1 (1969).

[22] Bertaut, F., J. Phys . Radium 13_, 499 (1952).

[23] Bertaut, F., Ferroelectric and Dielectric Crystals: Contribution To The Theory of

Fields, Potentials and Energies in Periodic Lattices, (U. S. Air Force Report

AD-22696, July, 1953) , Unpublished.

[24] Templeton, D. H., J. Chem. Phys. 23_, 1629 (1955).

[25] Jones, R. E., and Templeton, D. H., J. Chem. Phys. 25_, 1062 (1956).

[26] Carter, F. L. , Algol program, Madelung Constant Calculations for the WC , VB2 , and

NiAs Structures. Listings can be obtained from the author.

[27] Zemann, J., Acta Cryst. Ij^, 55 (1958). - , [28] Templeton, D. H., J. Chem. Phys. 23_, 1826 (1955). ' i.;;-. [29] Hartman, P., Acta Cryst., 1_1, 365 (1958). '

'

[30] Hund, F., Z. Phys., 34_, 833 (1925).

[31] Johnson, Q. C, and Templeton, D. H., J. Chem. Phys. 34_, 2004 (1961).

[32] Leciejewicz, J., Acta Cryst. L4, 200 (1961).

[33] Brumel, M. , and de Bergevin, F., C. R. Acad. Sc. Paris 260 , 3598 (1965).

[34] Carter, F. L. , Vacancy and Charge Ordering in the Th3Pt^ Related Structures, J. of Solid

State Chemistry, in press.

[35] Carter, F. L., Proceedings of the Fifth Rare Earth Research Conference, held at Iowa

State University, Ames, Iowa (Aug. 30 - Sept. 1, 1965), Book Two, p. 103.

[36] Ganzhorn, K. , Z. Naturforschg . 7A, 291 (1952): 8A, 330 (1953).

[37] Pauncz, R. , Alternate Molecular Orbital Method, (W. B. Saunders Co., Philadelphia 1967).

[38] Carter, F. L. , Rare Earth Research III, L. Eyring, Editor (Gordon and Breach, New York,

1965) p. 495.

[39] Pearson, W. B. , A Hand Book of Lattice Spacings and Structures of Metals and Alloys

Vol. 8, G. V. Raynor, Editor (Pergamon Press 1967) . [40] Post, B., Glaser, F. W. , and Moskowitz, D. , Acta Metallurgica 2_, 20 (1954).

[41] Przybylska, M. , Reddoch , A. H., and Ritter , G. J., J. Amer . Chem. Soc. 85_, 407 (1963).

[42] Silver, A. H., and Bray, P. J., J. Chem. Phys. 32_, 288 (1960).

[43] Silver, A. H., and Kushida, T., J. Chem. Phys. 38_, 865 (1963).

[44] Fisher, D. W. , J. Appl. Phys. 40_, 4151 (1969).

[45] Carter, G. C, and Swartz , J. C, J. Phys. Chem. of Solids 32^, 2415 (1971).

[46] Barnes, R. G., and Creel, R. B., Phys. Letters 29A, 203 (1969).

[47] Castaing, J., Caudron , R. , Toupance , G., and Costa, P., Third International Conference

on Solid Compounds of Transition Elements, Oslo, June 1969.

[48] Anderson, L., Dellby, B., and Myers, H. P., Solid State Commun . £, 77 (1966).

[49] Carter, G. C, personal communication.

[50] Aronsbon, B., Sten>^°fg, E., and Aselius , J., Nature 195 , 377 (1962).

[51] Obrowski, W. , Naturwiss 48, 428 (1961).

[52] Kiessling, R. , Acta. Chem. Scand. 1, 893 (1947).

[35] LaPlaca, S., and Post, B., Acta Cryst. 15_, 97 (1962).

[54] Roof, R. B., and Kempter , C. P., J. Chem. Phys. 37./ 1^73 (1962).

[55] Voronoi, G., J. reine and anr-ew, Math. 134 , 199 (1908).

[56] Carter, F. L., Algol program. Interatomic Distances for Metallic Valence Program and

Voronoi Polyhedra Construction. Listing can be obtained from the author.

[57] Carter, F. L., Proceedings of the Seventh Rare Earth Research Conference, held at

Coronado, California (Oct. 28-30, 1968) p. 283.

[58] Carter, F. L. , work to be published.

[59] Kasper, J. S., in Theory of Alloy Phases (American Society of Metals, Cleveland, Ohio,

1956) , p. 264.

[60] Kronig, R. , and Penny, W. G., Proc . Roy. Soc. A130 , 499 (1931).

[61] Carter, F. L. , work to be published.

[62] Coulson, C. A., Proc. Cambridge Phil. Soc. 37_, 55 (1941).

[63] Carter, F. L., Proc. Eighth Rare Earth Research Conference, Reno, Nevada, T. A. Henrie

and R. E. Lindstrom, Editors, (April 1970) p. 460.

[64] L'Vov, S. N., Nemchenko, V. F., and Samsonov, G. V., Soviet Physics - Doklady 135 , 1334 (1960) . [65] George, W. P. R. , Goodman, C. H. L., Sterling, H. F., and Warren, R. W. , Phys. Stat.

Sol. ^1' 205 (1967) . [66] Wallace, P. R. , Phys. Rev. 71, 622 (1947).

[67] Smith, R. A., Wave Mechanics of Crystalline Solids (John Dickens and Co., Ltd.

Northampton, G. B. 1963) p. 307.

558
DISCUSSION

B. Post : Would this request for single crystal work apply to titanium diboride?

F. £,. Carter : I think it would be interesting to do most of the series.

B. Post : Well, this was done about ten years ago in my lab with extremely high, good

precision. ^ I forget the R factor, but it's a no-parameter structure and if those borons

are not in a plane they are as close to a plane as anything I could imagine. That is, we can detect no contrary evidence whatsoever; they are in just about perfect agreement right

down the line. Actually, everything agrees better than it should; that is, within statistical

error and even better.

F. L. Carter : Is that assuming that the boron can move and checking the space group

statistically for the equivalence of reflections?

B . Pos

t

: Oh, of course, I mean it was a good structure analysis, a complete structure

analysis, and there is no indication at all that the borons are out of plane. This is not

vanadium diboride of course, vanadium has a smaller metal atom. I just thought you would

be interested.

A. L. Bowman : I did the same calculations for both titanium and zirconi\im diboride

looking for the puckered plane and I agree, no indication at all. As soon as I moved the

borons out, all the calculations pushed them back into the plane, but again, I have not

done it with vanadium.

F. L. Carter : In the titanium case we have essentially no charge transferred to the

boron, so that's a case where one might expect not too much electrostatic instability.

S. LaPlaca : You feel that it is particularly important that you have d-orbital

participation in these diborides. What about the stability or instability of AIB2? How

important does this become? You mentioned this in your abstract as the parent compound.

F. L. Carter : I have attempted to xmderstand the diboride structures through the

transition metal diborides where d character is generally available. I have not attempted

to understand compounds like MgB2 and AIB2 for which d character participation is much less

likely and which are much harder for me to understand except through overly naive models.

S. LaPlaca : It is certainly one of the series. It's the structure type. I just might

mention that rather recently lithium diboride has been found and prepared by Paul Schmidt

at Bell Labs and it is isomorphous with this structure. The boron-boron distances in that

structure turned out to be exactly what you might expect, it's down around 1.58 for just a single electron pair bond, and I doubt whether you have any d-orbital participation to any

extent in lithium diboride.

F. L. Carter : On the basis of our current and rather weak understanding of these

compounds it is probably inappropriate to make a priori structure stability predictions.

While such predictions are entertaining and useful in that they lead to new work, both

theoretical and experimental, it should be noted that Mother Nature is able to generate

more and better models from which to chose than are generally available to mere mortals.

1 M. G. Miksic, Ph.D. Thesis - Brooklyn Polytechnic , June 1962.

559

/

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposiiom, issued July 1972.

CRYSTAL CHEMISTRY OF REFRACTORY CARBIDES*

Allen L. Bowman

Los Alamos Scientific Laboratory

University of California

Los Alamos, New Mexico 87544

The crystal structures of most of the refractory metal carbides may be described generally on the basis of a close-packed metal sublattice, with the carbon atoms occupying all or part of the octahedral sites. Close-packed carbide structures have been observed with

composition MC and packing type c, M4C3 and hhcc, M3C2 and hoc or hhc, and M2C and h or c. All of these structures have one octahedral site per metal atom, and thus an apparent

possible composition MC. This is reached however, only with the c-type packing, and it has

been suggested that only one half of the sites adjacent to an h layer can be filled. This

is found to be an upper limit that is not always reached. These carbide structures thus

have carbon vacancy concentrations ranging from ~0 up to ~70%, with a possibility of vacancy

ordering. Neutron and electron diffraction studies have shown ordering to exist in the M2C

compounds and in carbon-deficient VC.

The order-disorder transformation of the carbon vacancies in M02C has been studied in

detail with high-temperature neturon diffraction. The kinetics data are consistent with a nucleation-growth mechanism involving nucleation on grain boundaries and linear growth

across the interface. The reaction between M02C and M03C2, involving the transformation of

the close-packed metal lattice (h ^hcc) has been studied less thoroughly, but the kinetics

data also appear to be' consistent with a nucleation-growth mechanism.

Key words: Carbide; crystal structure; molybdenum carbide; niobium carbide; reaction

mechanism; solid state; tantalum carbide; tungsten carbide; vanadium carbide

1 . INTRODUCTION

The refractory metal carbides to be discussed here are those of the third to sixth

group of the periodic table. Most of these carbides have melting points above 2000 °C,

exceptions being the chromium carbides with melting points of 1500-1800° [1]-^, and the lower

carbides of the third group metals

.

The crystal structures of most of these carbides may be described on the basis of a close-packed metal s\iblattice, with the carbon atoms occupying the octahedral interstitial

sites. The interstitial carbon atom and its nearest metal neighbors may be considered as a coordination polyhedron, and the crystal structure may alternately be described in terms of

the stacking of coordination polyhedra. The latter description is particularly useful for

those carbides that do not have close-packed metal sublattices.

2. DISCUSSION

The known refractory carbide phases are listed in table 1, with holmium arbitrarily

selected to represent the rare-earth metals, and with the non-close-packed structures

separated on the sides. The structures of Y2C3/ H02C3, and U2C3 may be described in terms

of stacking of C2M8 polyhedra, with C2 groups of bond-length -1.3 A. The SC4C3 differs

only in having CM 3 polyhedra, a single carbon atom replacing the C2 of the M2C3 structure. -

*Work done under the auspices of the U.S. Atomic Energy Commission.

1 Figures in brackets indicate the literature references at the end of this paper.

561

465-504 0 - 72 - 37
Table 1

The Refractory Carbides

REFRACTORY CARBIDES

XScoC c

ScC. 1.3

^fYgC c

Tie c

ZrC c

^VgC h V4C5 hhcc *VC c

^^NbgC h Nb4C3 hhcc NbC c

mo^c h M03C2

MoC

hoc

^HogC c H02C3

Hoc,

HfC c

UC c

10403 hhcc ToC c

^WgC h WC(£)_c_

Phases noted by * have well-established ordered

vacancy structures. The close-packed structures

are indicated by their Jagodzinski-Wyckof f symbol,

The dicarbides, YC2, H0C2 and UC2, are approximately close-packed structures with C2 groups

(bond length -1.34 A) occupying the octahedral sites. The crystal structures of the YC^^ 2 and ScC- 1,3 phases have not yet been determined. On the other side of the table, the

structures of WC (a) , Cr3C2 and (probably) CryC^ can be described in terms of stacking of

CMg trigonal prisms. The structure of Cr2 3C6 should probably be considered in terms of

chromium-metal polyhedra bonded together by carbon atoms.

The carbides in the central portion of table 1 have close-packed structures . The

Jagodzinski-Wyckof f symbols for each lattice are also shown (a layer is denoted by h if the

two adjacent layers are of the same type, by c if they are of different types). The (110)

planes of each of the observed stacking arrangements are shown in figure 1. The hhc se- quence, which has been observed in the ternary carbide Ta2VC2 [2], is also included. Since

each close-packed structure has one octahedral site per metal atom, the maximum carbon com- position of each close-packed arrangement would seem to be MC. However, this ideal com- position is approached only with the c-type of stacking, while the maxim\am carbon composition of the h-type carbides is M2C. It has been suggested [3] that where two sites are located above each other in the (110) plane (which occurs with each h-layer) , only one site

can be occupied. Following this argument, which is valid for the h-type stacking, and

assuming complete occupation of sites adjacent to a c-layer, maximum carbon compositions were defined as M2C for h, M3C2 for hoc and hhc, M^C^ for hhcc and MC for c.

The carbon compositions based on 50% vacancies for an h-layer and no vacancies for a c-layer must be considered as upper limits which need not be reached. The composition M2C

appears to be the approximate upper limit for all the h-type phases , while for the c-type

phases, TiC, ZrC, HfC, NbC, TaC and UC reach almost 100% occupancy of carbon sites, but

MoCg.y, WCq , 7 and VCg^g are always deficient in carbon. The c-type carbides of the group

three metals have a maximum composition M2C at low temperature (<1000°) but form a continuous solid solution field with the dicarbides at higher temperatures. The carbides with

mixed stacking sequences are all deficient, with approximate compositions of C/M -0.64.

The close-packed carbides thus tend to have large percentages (up to -65%) of their

carbon sites vacant. Even the c-type carbides with composition MC (except UC) have large

ranges of homogeneity based on carbon vacancies. These vacancies could be either ordered

or random in the c- and h- type structures. Ordered vacancy structures have been identi562
h hcc hhc hhcc c

Fig. 1. The known close-packed carbide structures.

The (110) plane.

fied in the c-type vanadium carbide phase at VgCy (cubic) [4] and VgC5 (trigonal) [5]

.

Above -1200° the VC phase has only random vacancies. A complete long-range ordered vacancy

structure has not yet been clearly observed in the other monocarbides . Ordered vacancy and

identified structures have been observed in all of the M2C carbides, including the c-type

of the third group metals. These structures are listed, and the references cited, in table

2. The structures of the ordered h-type M2C carbides are shown in figure 2 as projections

in the plane perpendicular to the c-axis (V2C has the same structure as M02C) . The c-type

structures have the same vacancy arrangement as Ta2C, with alternate C-planes completely

filled and empty. It appears that all of the M2C carbides transform to the corresponding

random vacancy structure at temperatures ranging from -600° to over 2000°.

The intermediate phases with mixed stacking sequences have two different kinds of

carbon sites, those adjacent to an h-layer (H) , and those that are not (C) . There are thus

three possible types of vacancy arrangement, random distribution over all sites, random

distribution over H-sites with C-sites filled (partial ordering) , and ordered arrangement

among specific sites (more probably H-sites) , as well as possible intermediate states. The

neutron diffraction pattern of M03C2, obtained at 1750°, appears to agree better with the

calculated random vacancy pattern than with the partially ordered vacancy pattern. The

completely ordered structure is not possible. The neutron diffraction patterns of TaitC3

also do not appear to be consistent with even partial ordering, although an ordered structure has been proposed from an electron diffraction study [14]

.

Two solid-state reactions are possible with the close-packed carbides, the transformation between the ordered and disordered vacancy structures, and the reaction with metal or graphite to yield a new phase with a different stacking sequence (the reaction between two

carbide phases to yield a third carbide phase is considered equivalent to the second reaction) . The molybdenum- carbon system is particularly well suited for the study of both

types of reaction, with three possible cases

Mo2C(a) J Mo2C(S)

Mo2C(e) + C t M03C2

M03C2 + C t MoC

(1)

(2)

(3)

The order-disorder transformation of M02C (eq 1) has been studied with high-temperature

neutron diffraction [15] . The volume transformed (^) was measured as a function of time by

following the change of intensity of the (111) peak of the a-phase when the sample temperature was changed across the equilibriiim temperature. The results are shown in figure 3 for

M02C in the presence of Mo and C, for an initial temperature 30° from the equilibrium value

and a final value 15° to the other side. The data are consistent with a nucleation-growth

563

/
Table 2

The Ordered M2C Phases

V2C C-Fe2N [6]

Nb2C a-Nb2C [7]

Ta2C Cdl2 (C6) [8]

M02C CFe2N [9]

W2C £-Fe2N [10]

SC2C

til]

Y2C

Tb2C 1 CdCl2 {C19)

tl2]

H02C , [13]

Fig. 2. The ordered M2C structures. Projection

on plane perpendicular to the c-axis

.

mechanism involving nucleation primarily on grain boundaries and linear growth across the

a-:F=*3 interface. The data were fitted by the method of least squares to the equation

<; = 1-exp {-kit [l-^; exp (-k2t3 [1-3x2 + 2x3])

|

(4)

The rate constants and k2 are composites of the nucleation and growth rates and of the

grain boundary area available for nucleation.

The reaction between M03C2 and M02C (eq 2) involving a change in stacking sequence has

been studied to a small degree by high-temperature neutron diffraction. The data appear to fit the simpler equation

564
1 1 1 1 1

1.0 -

/ ^^^\^^^~fl-»a + C ^^-^

' / ^^^^ p — + WIO

0.5 -

1/ / ^"''o

'/ / ATj -15°

-

0

-

1 1001 1 20011 300 TIME ( MINUTES )

Fig. 3. The rate of the order-disorder transformation

of M02C, in the presence of molybdenum and of

carbon.

? = 1-exp (-kt ) (5)

with n = 3-4. This is consistent with a nucleation-growth mechanism with decreasing nucleation rate, but further work is required to obtain a quantitative final result. The reaction between M03C2 and MoC (eq 3) is too fast to study.

2. REFERENCES

[I] Rudy, E., Compendium of Phase Diagram Data, AFML-TR-65-2 , Part V (1969).

[2] Rudy, E,, J. Less-Common Metals 2£, 49 (1970).

[3] Parthe, E. and Yvon, K. , Acta Cryst. B26 , 153 (1970).

[4] deNovion, C. H. , Lorenzelli, R. , and Costa, P., Compt. Rend. 263 , 775 (1966).

[5] Venables, J. D. , Kahn, D. , and Lye, R. G. , Phil. Mag. 18_, 111 (1968).

[6] Yvon, K. , Rieger, W. , and Nowotny, H. , Monatsh. Chem, 97_, 689 (1966).

[7] Yvon, K. , Nowotny, H., and Kieffer, R. , Monatsh. Chem. £8, 34 (1967).

[8] Bowman, A. L. , Wallace, T. C. , Yarnell , J. L. , Wenzel, R. G. , and Storms, E. K.

,

Acta Cryst. 19_, 6 (1965).

[9] Parthe, E. and Sadogopan, V., Acta Cryst. 16, 202 (1963).

[10] Yvon, K. , Nowotny, H. , and Benesovsky , F., Monatsh. Chem. 99_, 726 (1968).

[II] Atoji, M. and Kikuchi , M. , J. Chem. Phys. SI, 3863 (1969).

[12] Atoji, M. , J. Chem. Phys. 5]^, 3872 (1969).

[13] Bacchella, G. L. , Meriel, P., Pinot, M. , and Lallement, R. , Bull. Soc. franc. Miner.

Crist. 89^, 226 (1966) . [14] Martin, J.-L., Rocher, A., jouffrey, B. , and Costa, P.,' Phil. Mag. 24_, 1355 (1971).

[15] Bowman, A. L. , Wallace, T. C. , and Arnold, G. P., 8th International Congress of

Crystallography, Stony Brook, New York, p. 226 (1969).

Bowman, A. L. , Arnold, G. P., and Wallace, T. C, 25th Southwest Regional Meeting,

A.C.S., Tulsa, Oklahoma, p. 107 (1969).

565

/
DISCUSSION

W. S. Williams : Have you looked at any transport properties through the molybdenum

carbide, M02C, order-disorder transition?

A, L. Bowman : Primarily diffusion you're thinking of?

W. S. Williams : I'm thinking of electrical and thermal conductivity primarily.

A. L. Bowman : No, all we have ever worked with has been powder samples and for this it

just didn't seem worthwhile to bother. We have done a few diffusion studies, and of course many other people have also done this. This is more of what we are interested in, and in

particular what I wanted to find is the change in diffusion as you go through the transition.

We don't really know about the other properties, I'm sorry. I'd like to.

H, Nowotn^ : Your alpha, the ordered alpha Nb2C is our CNb2C?

A, L. Bowman : I believe so. The other one that was found originally that Yvon reported

which agrees with electron diffraction data would seem to be an oxide stabilized phase, not

part of the system.

H. Nowotny : With respect to stabilization, I want to mention that Dr. Jack in the May

meeting of AIME in Atlanta asserts that a nice ordered M02C structure is also stabilized by

nitrogen.

A. L. Bowman : Well, if it is, it is stabilized by nitrogen in the 100 ppm range.

H. Nowotny : Well, it may happen.

A. L. Bowman : That's certainly true, but that's about as low as we can get. Certainly

all of the M2C compounds that I described here seem to be stable with just 100 or 200 ppm of

nitrogen and oxygen. As soon as you add more of the non-metal impurity, other things can certainly happen. It has been shown by Yvon, of course, with the Nb2C that this indeed did

happen, but we don't know beyond that.

R . Ward : I wonder if it's possible that one could have order within the planes and

unless you then have order between the planes also you wouldn't recognize it as an ordered

phase. In other words, you may have order between the planes but there would be no relationship between planes, then you wouldn't see the order. It would look like a random phase.

A. L. Bowman : There are all sorts of very grim possibilities along this line. The

ordering for the zeta phase that has just been suggested by Martin and Costa and others^.

What they are now thinking of is the case where four carbon planes are ordered and then the

next four are also ordered, but these two blocks of four are random with respect to each

other. This is a pretty difficult picture, but it's the best explanation so far for the

data that they have.

1 Yvon, K. , Nowotny, H. , Kieffer, R. , Mh . Chem. 98, 34 (1967).

2phil. Mag. 24_, 1355 (1971).

566
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

A SIMPLE MODEL FOR THE STABILITY OF TRANSITION METAL CARBIDES

Robert G. Lye

Research Institute for Advanced Studies

Martin Marietta Corporation

Baltimore, Maryland 21227

The origins of the unusual and complex combination of physical properties exhibited by

the transition metal carbides remain somewhat obscure despite extensive studies of the problem in recent years. Even the qualitative nature of the bonding has not yet been described

in a manner that accounts satisfactorily for the diverse and sometimes apparently contradictory experimental observations made on these compounds

.

One theme, however, recurring through the years of study, draws attention to the similarity of these compounds to the parent transition metals. This characteristic of the car- bides is considered briefly in the present study in an attempt to provide a qualitative ex- planation for the manner in which the stability of the carbide phases varies with the position

of the parent metal in the periodic chart of the elements. A simple model for the d band

bonding in the transition metals, discussed by Cyrot-Lackmann, is modified for this purpose.

In particular, it is assumed that a major component of the bonding in the carbides arises

from crystalline electronic energy bands derived for the d states of the metal atoms. Because of changes in crystal structure, these bands are modified somewhat from the shape of

the corresponding bands in the parent metal. Of greater importance for the stability of the

carbides, however, is the increase in the width of the band, discussed by Costa and Conte

,

that results from the presence of the carbon atoms within the interstitial positions in the

metal sublattice.

As for the parent metals, the cohesion of the carbides is determined by the number of

electrons in the d band. In the carbides, however, it is assiamed that some of these electrons are provided by transfer from the 2p states of the carbon atoms. Thus, the stability,

as measured by the heat of formation, results from the combined effects of the increase in

the width of the d band and in the number of electrons it contains.

Despite the considerable simplifications employed, an analytical formulation of this

model yields estimates for the heats of formation of the carbides that agree remarkably well

with the experimental data presently available.

Key words: Bonding; carbides; cohesive energy; density of states; electronic structure;

heat of formation; Lii,iii spectra; refractory hardmetals; Ti; TiC; transition metal

compounds

.

1. INTRODUCTION

Transition metals from Groups IV, V and VI of the Periodic Table combine with boron,

carbon or nitrogen to form related series of compounds having remarkable combinations of

properties [1-5]^. In particular, many of these compounds exhibit strong deviations from

Dalton's Lav7 of Constant Proportions, resulting in considerable variations in their physical

properties. Thus, although NbCo_977 has a superconducting transition temperature of 11.1 K

1 Figures in brackets indicate the literature references at the end of tliis paper.

567

,/
and that for an alloy of NbC-NbN is 17.8 K, not far below the highest value yet observed,

NbCo.70 does not become superconducting above 1.05 K [6,7]. Most of these compounds are hard

and brittle at room temperature, reminiscent of covalent solids, yet they exhibit metallic

conductivities comparable with those of the parent metals. In addition, they are highly re- fractory/ TaCo.89 having the highest melting temperature known, 3985 °C [8]. Some of the

carbides become deformable and have remarkably high ratios of strength to density at elevated

temperatures [9] , which suggests numerous possible technological applications if the undesirable brittleness at low temperatures can be overcome.

Although many of the carbide phases extend over broad compositional ranges , a trend is

exhibited, in each transition series, for the region of stability to move toward lower car- bon-to-metal atom ratios as the atomic number of the parent metal increases. Brewer and

Krikorian [10] and Dempsey [11] have noted that the variation of various physical properties

of the carbides approximately parallels that for the metals but is displaced somewhat, as though the carbon atoms contributed additional electrons to the electron energy bands characterizing the transition metals. Similar conclusions have been drawn by Ubbleohde [12],

Umanskii [13], Kiessling [14,15] and Robins [16] from a variety of considerations. This

point of view was provided some support by the results of an LCAO calculation of the electronic energy band structure TiC by Lye and Logothetis [17] , which suggested that the energy

bands derived from the 2s and 2p states of the carbon atom were displaced upward in energy

relative to the bands arising from the 3d states of the metal atom. The resultant disposition of the energy bands required a transfer of approximately 1.3 electrons from electronic

states of 2p symmetry into states of 3d symmetry. Accordingly, the principal component of

the interatomic bonding was associated with electronic energy bands similar in most respects

to those of the parent transition metal but broadened somewhat by the effect of the carbon

atom core potential [18] , and occupied more fully by the electron transfer.

This interpretation of the bonding in TiC has been placed in question by the results of

APW calculations of the band structure by Ern and Switendick [19] and similar calculations

to self-consistency by Conklin and Silversmith [20] , who concluded that the carbon 2p bands

lie relatively low in energy and accept between 2 and 3 electrons transferred from the titaium electron orbitals.

Ramqvist and coworkers [21-26] in a recent series of papers have reported the results

of measurements made by the ESCA technique to determine changes in the binding energy of a- tomic core electrons upon formation of the carbides. In all of the cubic carbides studied,

the binding energy of the carbon Is state was found to be less in the carbides than in carbon, i.e., the Is state is raised in energy in the carbides relative to its position in carbon. For Tic, the displacement observed experimentally, 3.3 eV, agrees in direction and approximately in magnitude with the displacements applied to the 2p level (2.77 Ev) and the 2s

level (4.15 eV) in the LCAO band structure calculation by Lye and Logothetis [17].

Ramqvist equates this displacement solely to ionic interactions arising from charge

transfer between the carbon and metal atoms, and concludes that 0.4 electrons are transferred

from 3d states of the Ti atom into carbon electronic states. According to this argument, the

electrostatic (Madelung) energies of the cubic carbide lattices are very nearly equal to the

heats of formation of these compounds. Ramqvist asserts also that the electrostatic energy

of the carbides is approximately one-sixth to one-third of the total binding energy of these

compounds. He defines the total binding energy of the carbides, however, as the sum of the

cohesive energy of the metal, -AHjuje , and the heat of formation of the respective carbide,

-AHj^ieC' whereas thermodynamic arguments require the inclusion of the cohesive energy of carbon, -AH(^ = 710 kj/mole, in this sum. When Ramqvist 's calculations are revised in this manner, his estimated ionic contributions to the cohesive energy vary from 8% to 13% of the total. Qualitative discussions will be given later in this paper to suggest that the effective

charge associated with the ions in TiC may be approximately one-half the value indicated by

Ramqvist. Thus, the ionic contribution to the bonding would be approximately 4% of the total

binding energy or one-quarter of the heat of formation. For either estimate of the ionic

charge, however, questions are raised again regarding the origins of the principal components

of the bonding.

Additional support for the APW band structure of TiC [19,20] has been offered recently

by Holliday [27] and Fischer [28,29] from the results of their measurements of x-ray emission

and absorption spectra. Although their interpretations are plausible, they should not be

568
considered conclusive. Indeed, Fischer [29] correctly emphasized that the x-ray spectra can- not be correlated quantitatively with the electronic density of states curve unless proper

account is taken of the influence of the electronic transition probabilities. Accepting this

limitation, it may be noted that the titanium Ljj jjj emission and absorption spectra of TiC

can be interpreted in the alternative manner illustrated in figure 1. Shown there are the

Lj-]- spectra of Fischer and Baun [29] , used by Fischer [28,29] in subsequent discussions

also. The emission spectrum is similar to that reported by Holliday [27] , but appears to

exhibit differences in detail. The significance of these slight differences is unclear.

Superimposed on these spectra is a plot of the density-of-states curve derived from the LCAO

band structure calculated by Lye and Logothetis [17] , adjusted in energy so that the Fermi

level lies near the position of the Lji^ni absorption edge. Some uncertainty resides in

this choice [28,30] , so the adjustment has been made to optimize the correlation between the

x-ray spectra and the density-of-states curve. On this basis, the structure in the x-ray

emission spectrum from -4.5 eV to -6 eV may be attributed to charge exchange transitions involving the carbon 2s electrons, the large peak near -1 eV primarily to 3d electrons, and

the shoulder near -2.5 eV to titanium 3d and some carbon 2p electrons. Similarly, the small

feature near +1.5 eV in both the emission and absorption spectra is correlated with a peak

in the density-of-states curve that arises largely from titanium 3d states, although carbon

2p and titanium "4p" states also contribute. The peak in the density of states near 2 3/4

eV arises primarily from 3dg. states, and may cause the abrupt increase in absorption in this

region. Although Fischer and Baun [29] do not place great confidence in the details of the

absorption spectr\am at high energies, their results can be correlated qualitatively with the

density-of-states curve in this energy region also. In particular, peaks in the density of

states curve near 4.8 eV and 5.6 eV, which result from (4s+"4p") states, respectively, agree

rather well with structure in the absorption spectrum. The peak due to "4p" states near 6.6

eV does not correspond to obvious structure in the absorption.

This alternative interpretation of the x-ray spectra differs from that proposed by

Fischer [27] primarily in associating the structure near -5 eV with the carbon 2s electrons.

Fischer [28] , together with Ern and Switendick [19] and Conklin and Silversmith [20] , estimate that the carbon 2s band lies somewhat lower in energy, near -9.5 eV. The titanium K emission spectr\im obtained by Chirkov et al. [30] appears to support the lower energy of the

EIIER6Y (eV)

Fig. 1. Structure in the electronic density-of-states

histogram for Tic obtained by Lye and Logothetis

[17] shows a pronounced correlation with that in

the Ljj emission and absorption spectra observed by Fischer and Baun [30] if the Fermi

level, at the zero of energy, is placed relative

to the x-ray spectra in the manner shown here.

569
carbon 2s bands employed by Fischer in his analysis; but additional confirmation would be

desirable. For either position of this band, however, the carbon 2s electrons would be ex- pected to contribute little to the total binding energy of TiC. To evaluate the principal

sources of the bonding with useful accuracy requires knowledge of the relative positions of

the carbon 2p and metal d bands with greater precision than appears possible using current

techniques of x-ray spectroscopy. The necessary precision may be attainable, however, with

other experimental approaches. In particular, the use of modulated piezoreflectance and similar techniques should permit analysis of both the symmetry properties of the energy bands

involved and the location of the corresponding optical transitions within the Brillouin zone. Lacking quantitative experimental information on the energy distribution of the carbon 2p

states prohibits making a quantitative evaluation of the energy band structures [17,19,20] or of the origins of the bonding. Nevertheless, the qualitative features of the LCAO band

structure [17] are in better accord with the broad spectrum of physical characteristics ex- hibited by the transition metal carbides than is the APW calculation [19,20]. Two aspects

of this LCAO band structure may be considered of primary importance: i) electrons are transferred from the carbon 2p states into bands derived from the metal d states, and ii) the introduction of carbon atoms broadens the energy bands of the carbide relative to the metal

[18] and thereby increases their contribution to the binding energy. In the next section,

these concepts will be employed in an effort to provide a qualitative explanation for i) the manner in which the compositions of the stable carbide phases vary with the position of the

metal atom in each transition series, and ii) the manner in which the heats of formation of

the carbides vary with the position of the parent metal in each transition series and with

carbon content.

2. STABILITY OF THE CARBIDES

An elementary model will be developed in this section to illustrate the concepts mentioned in section 1. For this purpose, it will be supposed that the cohesion of the parent

transition metals arises from the superposition of contributions from an s-p band, Egp^, and

a d band, E(Jq. The s-p band will be assiamed to provide a bonding energy of 20 kcal mol--^ (83.5 kJ mol--'-) . The d band will be represented by a uniform distribution in energy of electron states in a band having the same width for each metal within one series. In that case, the d band provides a contribution to the binding energy dependent on a, the fractional occupation of the band [31]

:

Ed = 4E^in " ^1-TM^ '

where E^^^^ is the maximum value assumed by E^. This parameter will be assigned the values

^dmo = 115' 1^5' °^ ^'^^l i^QO, 690, and 795 kJ mol"^) for the first, second and

third transition series metals, respectively, in their pure state. To produce qualitatively

the variation of the cohesive energies [3] of these metals, the fractional occupation of the

d band is assumed to have the form

where is the fractional occupation and N^^ is the number of electrons in the d band of the

pure metals, and Z represents the number of outer electrons on the metal atom (3 for Sc, Y,

La, 4 for Ti , Zr, Hf , etc.). By using this simple fom for a^, with a constant density of

states in the d band, only the broad features of the cohesive energy variation will be represented, as shown in figure 2; the detailed fluctuations will be suppressed.

2.1. d BAND WIDTH, w,

a

As discussed in section 1, it is assumed that the introduction of carbon to form the

carbides causes the electron energy bands to broaden and increases the number of electrons in

the d band. The increase in the width, w^j, of the d band will be assumed to be proportional

to the atomic ratio, x, of carbon to metal. This increase in width depends on the increase

in the magnitude of overlap integrals between orbitals on adjoining metal atoms, and conse- quently on the change in the effective potential in the overlap region caused by the introduction of the carbon atoms. If it is supposed that the effective potential contributed by

the carbon atoms is the same in all carbides, then

570
(3)

where w^-, is the increase in the width of the d band for a carbon to metal atom ratio of unity.

For this simple model [31] ,

= lOw^/8 (4) dm d

Consequently, for the carbides,

= 10(w^ + xw )/8 = + xE = E ^ (1 + xE /E , ) (5) dm do c dmo c mdo c mdo

where E^ = lOw^/8 is chosen to have the value 170 kcal mol"-^ (710 kJ mol~-^) , in order to be

qualitatively consistent with the results of calculations by Costa and Conte [18J and to provide a heat of formation for TiC approximately equal to the value observed experimentally.

For simplicity, it will be assumed that the carbon atoms increase the cohesion provided

by the s-p band in a manner silimar to that for the d band. In particular, if the ratio

^c/'^mdo approximates the relative strength of the potential in the overlap region contributed

by the carbon, compared with that contributed by the metal atoms, the s-p bonding in the car- bides becomes

:

E = E (1 + X E /E ^ ) . (6) sp spo c mdo

n I 1 1 1 1 1 1. "O 2 4 6 8 10 12 VALENCE ELECTRON NUMBER, Z

Fig. 2. The cohesive energies of the pure

metals from the I, II and III transition series, as represented

by the simple model employed here.

The detailed fluctuations from the

smooth curves observed experimentally [32] are neglected in this

model

.

571
2.2. OCCUPATION OF THE d BAND

If it is assumed that all of the electrons donated by each carbon atom are introduced

into the d band, then for the carbides,

a = N^/10 = (N^ + xn^)/10. (7) a do t

It becomes necessary now to estimate the manner in which n^ varies with the valence electron

number, Z, and with the carbon concentration, x. It is expected that n^ will increase with

Z, because the d levels of the metal atoms are depressed relative to the 2p level of carbon

as Z increases in each series. For simplicity, differences between the energies of the d

bands in the three transition series will be neglected for the present purposes even though

they may be expected to influence the number of electrons transferred. The variation of n with carbon concentration may be understood similarly if the carbon 2p levels are displaced

in energy relative to the d bands by an amount that depends on the carbon concentration in

the carbide. A qualitative estimate may be made for the elevation of the carbon 2p band in

the following manner.

2.3. ELEVATION OF THE CARBON 2p BAND

To be specific, consider a siibstoichiometric cubic carbide. The metal sublattice is

treated as a face-centered cubic packing of spherical metal atoms having radius r = a/2/2,

where a is the lattice parameter. r- The carbon atoms, of radius r„ = (>^-l)r_, are distributed

c m

over the octahedral interstitial sites within the metal sublattice . At the site of a missing

carbon atom, the electron charge distribution associated with the surrounding metal atoms

provides a negative charge, -Zq, within the volume 4/3 (irr^^) associated with the carbon

atoms. This negative charge raises the electron energy levels of a carbon atom inserted into

the interstitial site. If the 2p levels then lie above the Fermi level, n^ electrons per

carbon atom will be transferred into lower lying states, principally into bands derived from

the 3d states of the metal atom. Because of this electron transfer, each carbon atom will

lose a negative charge, -^n^, and each metal atom will gain a negative charge, -xCn^. The new electrons received by the metal atoms also will overlap onto the carbon atomic spheres,

depositing there an additional negative charge, -x3n^.

For a specified carbon concentration, x, the x occupied carbon atomic spheres have a net

negative charge

z = - (z -(;nt + x3nt) , (8) c o

the (1-x) unoccupied carbon atomic spheres have a net negative charge -(Zq + x3n^) , and the

metal atomic spheres have a net positive charge

z-m ~ (zo-xcnt + xgnt) . (9)

If these charges are assumed to be uniformly distributed over their respective atomic

spheres, they provide average potentials <|)^2 ^sxiz carbon and metal atom sites given

by: 2

r 2 e

6_ c

5 r

c (10a)

z e m

(10b)

The presence of these positive and negative charges in the lattice will provide also

Madelung potentials, ^^y[ and For the present purpose, the Madelung potential will be

2 The following discussion was suggested in part by J. W. McClure.

572
calculated by using the positive charge at the metal atom sites and the average negative

charge at the carbon atom sites, where is given by:

z = -x(z -Cn^ + xen^)-(l-x) (z + x3n^)

c o t t o t

= -(zo-xcnt + x6n^) = z„.

Consequently

,

<j) , = -az e/(a/2) (12a)

cM c

4 = -az e/(a/2) , {12b) mM m

where a is the Madelung constant for the carbide lattice. The total potentials at the car- bon and metal atoms are given by:

^ z e 2az e

6 c c / T -> \ A = A + i, = (13a)

c cz cM 5r a

c

^ z e 2az e

^ ^ ^ + <j, = I

EL_ . (13b) m mz mM 5 r a m

The difference, AV, between the potential energies of an electron on a carbon atom and

one on a metal atom determines approximately the upward displacement of the carbon electron

energy levels relative to those of the metal atom electrons. This displacement is given by:

AV = -e(4> -(t) ) c m

= (4.6e2/a) {z -1. 78Cn^ [1-x (0 . 44 + 0.563/?)]} ergs. (14) o t

For Tic,

AV = 15.3 {z -1.78Cn^[l-x(0.44-0.563/C] } eV, . (15) o t

and at X = 1, this equation reduces to

AV(x = 1) = 15.3 {z -n^(?-3)} eV. (16) o t

The effective negative charge on the carbon atoms at the stoichiometric composition is ~q(-, f where

,

r , T AV(x = 1) q = {z -n^ C-3)} = — (17)

c o t 15 .

3

Ramqvist [21-26] has determined experimentally that in TiC the carbon Is levels are displaced

upward in energy by approximately 3.3 eV at x = 1. The effective charge on the carbon atoms

in Tic is indeed negative, therefore, and has approximately the magnitude 0.215 electron

units. It should be noted, however, that this effective charge is the difference between the

negative charge, -Zq, deposited within the carbon atomic spheres by the metal atoms, and the

net negative charge, -n^((;-3) , transferred out because of the elevated position of the 2p

states relative to the d bands. The magnitude of Zq for TiC could be estimated using the

value n^ = 1.33 determined in [17], if {i;-3) were known. The atomic structure calculations

of Herman and Skillman [33] suggest a value of 0.3 for r; , but 3 cannot be estimated so directly. Using very coarse approximations for i) the effects of directionality of the d orbitals

,

and ii) the increased radial extent of the electron wave functions in the crystal relative to the free atom, the charge deposited in the carbon atom sphere is found to be 3s = 0.088 and

3(j = 0.117 for each s and d electron respectively. If the average s and d electron densities.

573
Rg and n^, at the Fermi level are in the proportions n^/n^ = 0.17 [17], then -

_

g = (n e + n,B,)/(n + n,) = 0.11, (18)

' s s a a s a

with a large uncertainty. In that event, Zq has a magnitude near 0.47 electron units.

By assuming that i) ^d independent of valence electron number, and ii) the

numbers of s and d electrons vary in accord with equation (2) , a second estimate is obtained

for Zq:

z = 0.114Z - 0.026 (Z>1). (19) o

This equation yields Zq = 0.43 for TiC, in fortuitously good agreement with the previous

estimate. Despite the admittedly large uncertainties, both estimates of suggest that the

2p levels are elevated in energy considerably by the overlap charge from the metal atoms.

Using equation (19) , the amoimt of this initial displacement, AV^, is found to be

AV = 15. 3z = 1.75Z -0.4 eV. (20) o o

This large upward displacement permits the carbon 2p electrons to relax into lower lying

states. The resulting electron transfer removes charge from the carbon atom spheres, thereby

cancelling a portion of the initial upward displacement. The net upward displacement is given

approximately by equation (15) using equation (19) for Zq.

2.4. THE NUMBER OF ELECTRONS TRANSFERRED

The simple model discussed above may now be employed to estimate the number of electrons

transferred out of the 2p levels of the carbon atoms. For this purpose, as before, the electronic energy bands of the solid are represented by a mean energy and a constant density of

states within a prescribed bandwidth. For simplicity, only three bands are considered, the

d and s bands of the metal and the p band of carbon. The total number of valence electrons,

N, is given by:

N = N + N + N , (21)

S d p

where the N^^'s are the numbers of electrons in the respective bands.

If the mean energy of the d band is selected as the zero of energy, and Ep is the Fermi

level, equation (21) becomes:

N = n [E„ - (E - w /2) ] + n^[E„ + w,/2] + xn [E„ - (E + AE - w /2) ] , (22) sF ss dPd pF P PP

where the n^^'s represent the densities of electron states in the respective bands at x = 1

,

Eg and E are the mean energies of the metal s and carbon 2p bands respectively; the w^'s

represent the widths of the indexed bands, and AE , assumed to be equal to AV, is the upward

displacement of the carbon 2p band discussed in the preceding section. It is implied that

the Fenni level intersects each of these three bands.

For the present purposes, only the s and d electrons of the metal atom, a total of Z,

and the 2p electrons of the carbon atom are included. Thus, the total number of electrons

available for distribution in the three bands is given by

N = Z + 2x, (23)

for a carbon to metal atom ratio, x. This relation may be used in equation (22) to solve

for the position of the Fermi level, Ep:

E = (Z -6 - X + xn (E + AE ) + n E )/(n + n, + xn ) , (24) F pppsssdp

574
where use has been made of the identities HgW^ = 2, npWp = 6 and n^w^ 10,

The numbers of electrons transferred per carbon atom may then be calculated from the

relation:

n 2 - N /x = 2 - {n [E - (E + AE )] + 3} (25) t p p F p p

The result is:

n [ (n + nJ (E + 15. 3z ) - (Z - 6 + n E ) ] - (n + n.) _ p s d p o s s s d \ "

n { (n + n^) (27.40 [1 - x(0.44 + 0.563/?) ] + x} + (n + n^)

p s d s a

(26)

In this form, n^ differs somewhat between the three transition series if, for example,

the one-electron energies of the atoms provided by Herman and Skillman [33] are used to define Eg and Ep, but for each series it increases with increasing Z and x in approximately

the same manner. In keeping with the approximations made previously, these differences will

be neglected in the following discussion and a common form will be used for n^ in the three

transition series. The principal conclusions regarding the heats of formation, discussed in

the next section, are not affected seriously thereby, but quantitative agreement with experiment cannot be expected.

2.5. THE HEATS OF FORMATION OF THE CARBIDES

The heats of formation of the carbides can be estimated by using expressions (1) , (5)

,

(6) and (7) in the relation

- AH^ = [E^(Z,x) + E (Z,x)] - [E_,(Z,0) + E (Z,0) + X ( - AH ) ] (27) f d sp d sp c

where - AH^ is the cohesive energy of carbon, taken to be 170 kcal mol"-*- (710 kJ mol"-^) [32],

If Eg and Ep are assumed to be approximately linear functions of Z, as indicated by

Herman and Skillman [33], and the widths of the s, p and d bands are linear functions of x,

as in equation (3) , expression (26) for n^ assumes the form:

n = (ai + a2Z + a^x + ai+xZ)/(bi + b2X + cax^) (28)

A first approximation to this relation, n^ = constant, when siobstituted into equation (27)

,

yields results that are reminiscent of the behavior observed experimentally [4] , if the value

n^ = 1.332 estimated for TiC [17] is employed. Discrepancies are observed for a constant

value of n^, however, in that large heats of fomation are calculated for the dicarbides of

the elements immediately preceding the transition metals, i.e., Z = 1-3. Somewhat similar

results are found if n^ is allowed to vary slowly with Z.

An improved approximation is given by the empirical relation:

n^ = 1/3(Z - 1)/(1 - x/4) (29)

and n^ < 2

,

which vanishes for Z = 1, matches the value 1.332 for TiCi_o [17], and varies with Z and x in approximately the manner required by equation (26) . When this expression is used to calculate the heats of formation, equation (27) , the results illustrated in figures 3 to 8 are obtained.

As shown in figures 3 to 5 , both the regions of stability and the magnitudes of the

heats of formation calculated in this simple approximation follow the trends of experimental

data in a remarkably consistent manner:

575

;
Fig. 3. The heats of formation, -AHf, of the

first transition series carbides, as calculated from the model discussed

in the text. Experimentally determined heates of formation of some compounds [3] are shown for comparison.

Fig. 4. The heats of formation, -AHf, of the

second transition series carbides,- as calculated from the model discussed

in text. Experimentally determined

heats of formation of some compounds

[3] are shown for comparison.

576
Fig. 5. The heats of formation, -AHf, of the

third transition series carbides, as calculated from the model discussed

in the text. Experimentally determined heats of formation of some compounds [3] are shown for comparison.

o

E

l-mol" ZrC,

<_> ^ 300 <]

1 ^- 200 o

60

40

Exp >^

OF

FORMAT

' 20

- 0

0.5 1.0 1.5 2.0 1—§ -100 .-20 X *

-200 -40

Fig. 6. The variation of the heat of formation

,

-AHf, of ZrCx with carbon concentration,

X, as calculated from the model discussed

in the text, compared with that observed

experimentally. The dashed curve represents the analytic expression for -AHf (x) deduced from experimental data [35]

.

577

465-504 0 - 72 - 38
Fig. 7. The variation of the heat of formation,

-AHf, of NbCx with carbon concentration,

X, as calculated from the model discussed

in the text, compared with that observed

experimentally. The experimental value

of -AHf for Nb2C is shown also. The

dashed curve represents the analytic

expression for -AHf (x) deduced from

experimental data [36].

Fig. 8. The variation of the heat of formation,

-AHf, of TaCx with carbon concentration,

X, as calculated from the model discussed

in the text, compared with that observed

experimentally. The experimental value

of -AHf for Ta2C is shown also. The

dashed curve represents the analytic

expression for -AHf (x) deduced from

experimental data [37]

.

578
i) No stable carbides are indicated for the alkali metals. M2C2 carbides having

small heats of formation have been reported [34] for these metals 2.

ii) Stable dicarbides are suggested for the alkaline earth elements, as is observed

experimentally

.

iii) Stable dicarbides having large heats of formation are expected for the elements

of Group III, but the ionic radius of scandium, being substantially smaller than those of

the Group II metals, would be expected to lead to a reduction in stability when the metal

atoms were separated widely by the introduction of a large concentration of carbon atoms.

Yttrium and most of the rare earth metals, on the other hand, have relatively large ionic

radii and would be expected to accommodate larger concentrations of carbon. Indeed, most of

these elements do form higher carbides, including dicarbides. The present model suggests

that their heats of formation should increase with increasing carbon content until geometric

constraints interfere, but experimental information is not available for confirmation. Uranium also forms higher carbides, despite its small ionic radius, but the heats of formation

per mol UCjj do not appear to change much with composition [4] . The fact that -AHf for UC2

is slightly less than that of UC3/2 i"ay perhaps reflect the influence of geometric constraints. Modest heats of formation are expected for the Group III monocarbides

.

iv) Large heats of formation are indicated for the Group IV monocarbides . The calculated heats of formation continue to increase beyond x = 1, but, as for the Group III metals, geometric constraints probably prohibit the formation of higher carbides.

v) The Group V carbides exhibit maxima in their heats of formation near x = 1, close

to the composition at which the d band is half filled.

vi) Stable carbides are indicated for the Group VI metals only for x < 1. Their maximum heats of formation, appreciably less than those of the Group IV and V monocarbides,

occur near x = 1/2.

vii) Of the Group VII metals, only Mn is indicated as forming stable carbides, in ac- cord with experimental data, and the region of stability of MnC^^ is restricted to x < 0.5.

The calculated maximum heat of formation, near x = 0.25, is small and therefore of dubious

validity, but agrees qualitatively with the small heat of formation of MnCj^/3, 1.2 kcal

mol-^ [34].

viii) None of the iron group metals are indicated as forming stable carbides. The heat

of formation, -AH , for the metastable FeC^ ,3 is reported to be -1.9 kcal mol"-^ (-8 kJ mol"-^)

[33], compared with the value -10 kcal mol"'^ (-42 kJ mol"-^) estimated here.

ix) No stable carbides are expected on the basis of this calculation for the Co group

metals or for the subsequent metals in each transition series, in accord with experimental

observations

.

x) Detailed experimental information is available for the variation of the heat of

formation with carbon concentration for only a few carbides, ZrCj^ [35], NbCj^ [36], and TaCj^

[37] . Analytic expressions for the heats of formation deduced from these studies are given

below and are plotted in figures 6-8 for comparison with the results obtained from the present model calculation:

ZrC [35]: -AH^ = -7.4 + 84 . Ix - 27.2x2 j^cal mol~^ (30) X f

NbC [36] : -AH = -6.60 + 70.95x - 30.75x2 ]zcal mol ^ (31) X f

TaC [37]: -AH = -22.81 + 103. 78x - 46.88x2 1 (32) X f

3 The intercalation compounds of graphite may, perhaps, form another exception at carbon con- centrations much larger than those considered here.

579
Experimentally determined heats of formation for Nb2C [36] and Ta2C [37] also are shown in

these figures . The calculated curves are seen to agree remarkably well with the experimental

data, particularly for the Group V carbides. The good agreement for the latter carbides probably is somewhat fortuitous, however, because no account has been taken here of the energy

involved in the structural transformation of the metal lattice in forming these carbides.

Pettifor [38] has estimated an energy of approximately 5.65 kcal mol"-^ for the bcc-fcc crystallographic transformation in Group V and VI metals. On the other hand, the hcp-fcc transformation of Group IV metals appears to involve a substantially smaller energy (= 0.3 kcal

mol~-^[38]), which has only an insignificant influence on the present comparison.

xi) One experimental point stands in significant disagreement with the calculated

curves. According to the experimental data of Zhelankin and Kutsev [39], the heat of formation of HfCo.67 is approximately 51.8 kcal mol"-"- (216 kJ mol"-^) (fig. 5) . If a stability

ratio, Rg, is defined by the relation:

R (x) = -AH^(x)/(-AH - xAH ), (33)

s r m c

where -AHjj, and -AH^ are the cohesive energies of the parent metal and carbon respectively,

the results of Zhelankin and Kutsev indicate that this ratio is 15% greater for HfCg gy than for HfCg^gg. The present model suggests, instead, that this stability ratio should de- crease as the carbon content of HfC^^ is decreased. Allowing for the considerable uncertainties in these calculations, the present results would suggest that the heat of formation of

HfCg 67 is approximately (40 ± 5) kcal mol"-"- (167 kJ mol"-'-) , rather than the higher value re- ported by Zhelankin and Kutsev [39]

.

3. SUMMARY AND DISCUSSION

A simple model has been proposed to account for the broad trends in the stabilities of

the transition metal carbides for different values of the valence electron number, Z, and

carbon concentration, x. In this model, it is assumed that the principal components of the

bonding in the carbides are similar to those in the parent metals, which are represented as arising from the contributions of an s-p band and a d band. The s-p contribution is assumed

to change little throughout the three transition series, whereas that from the d band is assximed to vary with the level of occupation in the parabolic manner suggested by the simple

"constant density of states" model of Cyrot-Lackmann [31] . The increase in cohesion in each

succeeding transition series is represented as resulting from a corresponding increase in

the width of the d band, with the widths assumed to be constant within each series.

It is assumed further that the effects of carbon on the stability of the carbides are two-fold: i) the carbon atoms provide an additional potential that causes a broadening of

the electron energy bands proportional to the concentration of the carbon [18] , ii) the car- bon atoms contribute some of their 2p electrons to the energy bands derived from the electronic states of the metal atom, principally to the metal d band. An elementary calculation

is given to indicate the manner in which the number of d electrons, n^, transferred from the

carbon 2p states, varies with Z and x (eq (26)) . For simplicity, however, an empirical approximation to this relation is employed in subsequent calculations, the same approximation

for each of the three transition series. The expression for n^ used for this purpose is

fitted to the value estimated for TiCj q ^Y^ and Logothetis [17]

.

It may be noted that this transfer of electrons from the carbon 2p states into the metal d band is consistent with and, indeed, results from the presence of a small negative charge

within the carbon atomic spheres. The LCAO band structure of TiC [17] has been criticized

[21-26] on the erroneous basis that it indicates the presence of a positive charge on the

carbon atoms. Clearly, the upward displacement of carbon 2s and 2p states employed in the

LCAO calculation requires the presence of a small net negative charge, and the upward displacement of these levels is required to permit the transfer of approximately 1.3 electrons

from the carbon states to bands derived from electronic states of the metal atom.

No account is taken in this model of the bonding contributed by the carbon 2p band in

the carbides, nor of the energy involved in crystallographic transformations of the metal

sublattice accompanying the formation of the carbides. Moreover, the contribution to the

bonding from the s-p band is dealt with in a rather casual manner for both the metals and

580
the carbides. A fully consistent model probably should consider the s and p bands of the

metal atoms in a manner parallel to that used here for the d bands.

Despite these inadequacies and numerous other simplifications, the stabilities of the

carbides as calculated from this model agree remarkably well with experimental observations,

particularly with regard to: i) the composition ranges in which the stable carbides occur,

ii) the variation of the heats of fo2n]iation, -AHf , with Z and x, and iii) the magnitudes of

the heats of formation for many of the carbides

.

It should be noted that the variations of -AHf calculated here are a direct consequence

of the transfer of some 2p electrons from the carbon atoms into bands derived from the d

states of the metal atom. It remains to be demonstrated that similar agreement with experimental observations can be provided by a model in which the electron transfer is in the opposite direction. In the meantime, the success of the model discussed here provides justification for accepting at least the principal features of the LCAO band structure for TiC

presented by Lye and Logothetis [17] , in particular the relative positions of the 2p and 3d

bands indicated by that calculation. Additional support for this conclusion is provided by

the good correlation between the x-ray spectra of Fischer and Baun [30] and the electron density-of-states curve of Lye and Logothetis [17] , as shown in figure 1.

Finally, it would appear entirely feasible to make the model presented here more nearly

quantitative: i) by including specific consideration of the metal s and p bands, ii) by using

a more realistic representation for the variation of the density of states within the d bands,

iii) by allowing for variations in the width of the d band within each transition series, iv)

by calculating more precisely the displacement of the carbon 2p levels relative to the d levels and v) by using an estimate for the number of electrons transferred that is specific for

each transition series, rather than the empirical approximation employed for all three series

in the present calculation. Consideration of these factors may be included in subsequent

studies, in which the nitrides and other refractory hardmetals will be examined. Additional

attention should be given, however, to developing improved methods for determining the electronic structures and bonding characteristics of the individual members of this interesting

and useful class of compounds.

4. ACKNOWLEDGEMENTS

It is a pleasure to acknowledge useful discussions with J. W. McClure and J. D. Venables

.

Thanks for due to E. Parkison and W. Furth for some of the computer calculations. Grateful

appreciation is expressed for financial support provided by NASA Research Division, Code RRS

,

Materials Research Branch, under Contract NASw-1290.

5. REFERENCES

[I] Kieffer, R. and Benesovsky, F., Hartstoffe, Springer-Verlag, Wien (1963).

[2] Schwarzkopf, P. and Kieffer, R. , Refractory Hard Metals, Macmillan, New York (1953).

13] Storms, E. K., The Refractory Carbides, Academic Press, New York (1967).

I4J Goldschmidt, H. J., Interstitial Alloys, Plenum Press, New York (1967).

[5] Toth, L., Transition Metal Carbides and Nitrides, Academic Press, New York (1971).

[6] Giorgi, A. L., Szklarz, E. G. , Storms, E. K. , Bowman, A. L., and Matthias, B. T., Phys

.

Rev. 125_, 837 (1962) . [7] Matthias, B. T., Phys. Rev. 92_, 874 (1953).

[8] Rudy, E., Ternary Phase Equilibria in Transition Metal-Boron-Carbon-Silicon Systems,

Part V. Compendium of Phase Diagram Data, Air Force Materials Laboratory, WrightPatterson AFB, Ohio (1969) . [9] Hollox, G. E., Mater. Sci. Eng. 3_, 121 (1968/69).

[10] Brewer, L. and Krikorian, O. , J. Electrochem. Soc. 103 , 38 (1956); Univ. Calif. Rad.

Lab. Rep. UCRL-3352 (1956) . [II] Dempsey, E., Phil. Mag. 8_, 285 (1963).

[12] Ubbleohde, A. R. , Trans. Faraday Soc. 28, 284 (1931).

[13] Umanskii , Ya.S., Ann sect. anal, phys.-chim., Inst, chim.gen. (USSR) 16_, No. 1, 127

(1943)

.

[14] Kiessling, R. , Acta Chem. Scand. 4, 209 (1950).

[15] Kiessling, R. , Met. Rev. 11 (1957).

[16] Robins, D. A., Powder Met. 1/2 , 172 (1958).

581
Kallne, E., Noreland, E.,

Johansson, G. , Gelius, U.

Kallne, E., Noreland, E,,

Soc . AIME , New York

,

2, 243 (1968) .

, and Nordling, C, J. Phys . Chem.

and Manne, R. , J. Phys. Chem. Solids

and Nordling, Phys. Chem.

and Manne , R.

,

J. Phys. Chem. Solids

(1971)

Lye, R. G. and Logothetis , E. M. , Phys. Rev. 147 , 622 (1966).

Costa, P. and Conte , R. R. in Nuclear Metallurgy Symposium, Met. Vol 10, p. 3 (1964) . Ern, V. and Switendick, A. C, Phys. Rev. 137 , A1927 (1965).

Conklin, J. B. and Silversmith, D. J., Int. J. Quantum Chem. Symposium No

.

Ramqvist, L. , Jernkont, Annlr. 153 , 159 (1969).

Ramqvist, L. , Hamrin, K.., Johansson, G. , Fahlman, A. Solids 30, 1835 (1969) . Ramqvist, L. , Ekstig, B.

,

30, 1849 (1969)

.

Ramqvist, L. , Hamrin, K.

,

Solids. 31, 2669 (1970).

Ramqvist, L. , Ekstig, B,

,

32, 149 (1971) . Ramqvist, L. , J. Appl. Phys. 42, 2113 (1971).

Holliday, J. E., J. Phys. Chem. Solids 32_, 1825

Fischer, D. W. , J. Appl, Phys. 41, 3561 (1970).

Fischer, D. W. , J. Appl. Phys. 4]^, 3922 (1970).

Fischer, D. W. and Baun, W. L., J. Appl. Phys. 39_, 4757 (1968).

Cyrot-Lackmann, F. , J. Phys. Chem. Solids 29, 1235 (1968).

Gschneider, K. A., in Solid State Physics, ed. F. Seitz and D. Turnbull, Academic Press,

New York, Vol. 16, p. 276 ff (1964) . Herman, F. and Skillman, S., Atomic Structure Calculations, Prentice-Hall, Inc., Englewood Cliffs, New Jersey (1963).

Wicks, C. E. and Block, F. E., Thermodynamic Properties of 65 Elements-Their Oxides,

Halides, Carbides, and Nitrides, U. S. Bureau of Mines Bulletin 605 (1963).

Baker, F. B., Storms, E. K. , and Holley, C. E., J. Chem. and Eng. Data 14_, 244

Huber, E. J., Head, E. L. , Holley, C. E Chem. 65_, 1846 (1961) . Huber, E. J., Head, E. L., Holley, C. E

(1962) . J. Phys. C 3_/ 366 (1970) . and Kutsev, V. S., Zhur, Fiz. Khim. 38, 562 (1964)

Storms, E. K. , and Krikorian, N. H.

and Bowman , A . L . , J . Phys . Chem

(1969) . J. Phys.

67, 793

Pettifor , D. G.

,

Zhelankin, V. I.

DISCUSSION

B. Post : Were you speaking of x-ray adsorption spectra in the soft x-ray region?

R, G. Lye : The L^-j- x-ray emission and adsorption spectra, yes.

B . Pos

t

: 1 had heard that there was some work done by electron spectroscopy on titanium

carbides and I wondered whether you were familiar with the results.

R. G. Lye : That's Ramqvist 's work-^ that I was talking about. The principal result of

that was that it says that the electron energy levels of the carbon are displaced upward

relative to their position in carbon. . -

B. Post : Well, it's good to know that the carbides resemble the borides in at least

that respect. There are some that think the transfer is to the left and others who think

it's to the right. I think it depends on whether you're a physicist or a chemist and I'm

serious about that, but it's a long story.

Ramqvist, L., J. Appl, Phys. 42, 2113 (1971) and references listed there.

582
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

ORDERING EFFECTS IN NbC AND TaC

J. D. Venables and M. H. Meyerhoff

Research Institute for Advanced Studies

Martin Marietta Corporation

Baltimore, Maryland 21227

Studies of the phase equilibria in the MC transition metal carbides have shown that

they retain their nominal NaCl structure over a relatively wide phase field. Although it

is well known that this wide latitude in composition is accomplished through the incorporation of carbon vacancies in the carbon sublattice, there is considerable uncertainty

regarding the degree of order exhibited in most of the carbides by the remaining carbon

atoms. In this investigation, an attempt has been made to resolve this question for NbC

and TaC using some of the techniques applied previously in a study of ordering in the

vanadium- carbon system.

By means of transmission electron microscopy and electron diffraction, evidence has

been obtained for the existence of long range carbon atom ordering in single-crystal niobium

carbide that has a carbon-to-metal ratio close to the integral composition NbgC^, The

ordering, which gives rise to superlattice and domain structures similar to those observed

in VgC5, appears, however, only in samples that have been cooled slowly (~8 °C/h) through

the order-disorder temperature of 1025 °C. In TaC of similar composition, the ordering,

although present, remains very imperfect even after the crystals are subjected to the same thermal treatment.

The results are interpreted in terms of the electronic structure of the transition

metal carbides as it is currently understood, and their relevance to the mechanical properties of NbC and TaC are discussed.

Key words: Carbides; electron diffraction; interpretation of ordering effects;

niobi\im carbide; ordering effects; superlattice; tantalum carbide; transition

metal compounds; vanadium carbide.

1. INTRODUCTION

In a previous report [1] ^ , evidence was presented that vanadiiim carbide having a carbonto-metal ratio close to the integral composition VgC5 exhibits an ordered structure.

Material of this composition occurs within the nominally cubic (rocksalt) phase field of the

vanadium- carbon phase diagram, but because of the ordering its structure is more appropriately

described in terms of a derivative structure in the trigonal space group, P3]^, or its enantiomorph, P32. Thus, the ordered structure is based on two interpentrating fee lattices,

only one of which (the metal lattice) is completely occupied. -The other is only 83% filled,

but the carbon atoms (and carbon vacancies) are distributed in an ordered manner over the

available octahedral lattice sites.

From an analysis of supplementary spots in electron diffraction patterns, and nuclear

magnetic resonance spectra of the principal vanadium isotope, V^^, it was established that

the carbon atoms and carbon vacancies are arranged so that all the vanadium atoms have

exactly five nearest neighbor carbon atoms in the perfect ordered structure [1] . The

observation that ordering in material of this composition leads to a distribution of atoms

1 Figures in brackets indicate the literature references at the end of this paper.

583
that is homogeneous on an atomic scale is consistent with the model for stability of the

transition metal carbides discussed in the previous paper by Lye [2] . Considerations based

on this model suggest that the most stable composition in the vanadium-carbon system occurs when the carbon- to-metal atom ratio is close to 5/6 and that ordering effect arise in order

to maintain this ratio as nearly as possible on an atomic scale.

On the basis of these same considerations, Lye has also suggested that ordering effects

similar to those observed for VgCs may also arise in the other Group V transition metal

carbides, namely NbC and TaC, with minor modifications imposed by the slight differences

in their electronic structure. Accordingly, in this investigation, an attempt has been made

to examine the structure of these carbides using some of the techniques applied previously

in a study of the ordering in VgCs [1]

.

2. EXPERIMENTAL

2.1. CRYSTAL GROWTH

Single crystals of niobium carbide and tantalum carbide were grown by the floating

zone technique described by Precht and Hollox [3] . Isostatically pressed and sintered rods

of an appropriate composition were heated with an r.f. induction unit, and a molten zone about 1 cm in height was passed along the rod at a rate of approximately 1 cm/h. To obtain

a composition of the crystalline product close to the integral composition MgCs, it was found necessary to add 10% by weight of the appropriate metal to the stoichiometric carbide

powders. The actual compositions of the samples used in the experiments were determined by

lattice parameter measurements [4] and chemical analysis to be NbCg 8^+ ^^'^ TaCg 83'

2.2. PREPARATION OF ELECTRON MICROSCOPE FOILS

Thin foils suitable for transmission electron microscopy were prepared by jet dimpling

3 mm disks with a 20% sulphuric acid - 80% methonal solution at 4-5 volts, followed by

electrolytic polishing in the same solution at the same voltage.

3. RESULTS

3.1. NIOBIUM CARBIDE

3.1. a. EVIDENCE FOR ORDERING IN NbC^^

A typical transmission electron diffraction pattern obtained from an NbCg 84 crystal

in the "as grown" state is shown in figure 1(a) . The pattern exhibits a series of primajry

diffraction spots which map out the (110) reciprocal lattice of the nominal rocksalt

structure of NbC. In addition, a supplementary pattern is observed, which, except for the

diffuse nature of the diffraction spots, resembles those derived from VgC5 [1]. This

evidence suggests that although ordering effects are present in the samples, the long range

ordering parameter is less than unity. The imperfect nature of the ordering in the "as grown" crystals can be improved dramatically with a suitable heat treatment, however.

Previous studies on V5C5 have indicated that the ordering time constant near the orderdisorder temperature of 1250 °C may be as short as lO"** sec [5]. Thus, it is observed that

the high temperature disordered state cannot be retained by quenching with readily attainable cooling rates. On the basis of the considerations discussed in Part 3.2 below, however, the ordering time constant in NbCQ_8tt expected to be at least 5 orders of magnitude

greater than in VgC5. The degree of order exhibited by a crystal of NbC, therefore, may

depend critically upon its prior thermal history. In view of this, sections of the crystal

used in the preliminary examination were heated in vacuum to 1130 °C and then cooled

linearly to 940 °C in a programmed furnace at a rate of 8 °C/h. Although the cooling rate was selected somewhat aribtrarily, the temperature span was chosen after measurements were made to determine the order-disorder (0-D) transformation temperature.

These measurements were made by heating a sample in the electron microscope hot stage

while the degree of order was estimated from visual observations of the superlattice spot

intensities in the diffraction pattern. Initial results were limited in accuracy because

the diffuse nature of the superlattice spots made it difficult to monitor their intensity

584
(a) (b)

Fig. 1. Transmission electron diffraction patterns obtained

from (110) foil of single crystal NbCo , 84

"as grown" condition and (b) after slow cool through

the order-disorder temperature. The pattern in (b) resembles those derived from V5C5 [1] except for

extensive spot doubling (circled) and streaking.

on the fluorescent screen. Nonetheless, the results were sufficiently accurate to establish

reasonable upper and lower temperature limits for the thermal treatment. Later experiments,

in which similar measurements were made on more perfectly ordered material, yielded a value

for the 0-D temperature of 1025 °C ± 25 °C.

The diffraction patterns derived from the slowly cooled material exhibited a marked

increase in the shairpness and intensity of the superlattice spots relative to those derived

from as-grown samples, figure 1(b). Moreover, the samples exhibited a domain structure,

figure 2, which was not evident before the thermal treatment. This evidence suggests that

the long range order parameter was increased to nearly unity by the heat treatment.

3.1.b. CRYSTALLOGRAPHIC STRUCTURE OF Nb^C^

5 5 The crystallographic structure of vanadium carbide having a carbon-to-metal ratio close

to the integral composition VgC5 was determined by combining the results of electron diffraction and nuclear magnetic resonance (NMR) studies [1] . The supplementary spots exhibited

in the diffraction patterns provided infomation regarding the symmetry and size of the

superlattice unit cell, whereas the NMR of the principal isotope, V^-^, exhibited spectra

that provided information about the disposition of carbon atoms within the unit cell. Similar

complementary studies would be desirable to establish the crystallographic structure of

niobium carbide, but unfortunately previous investigations [6] have shown that the NMR

spectra of Nb^^ provide insufficient information to determine the disposition of carbon atoms

in NbC. Thus, Froidevaux and Rossier [6] have observed that second order quadrupolar line

broadening effects in NbC are so great that no satellite line structure is observed in the

spectra. They were unaware, however, that slow cooling rates are necessary to promote a high degree of order in NbC and it is possible therefore that studies on well ordered

material would provide useful information. For the present, however, a determination of the

crystallographic structure of NbCg.s^ been based on a comparison of, the electron diffraction patterns of NbCg^a^ ^6^5 r using as a reference the known structure of VgCs.

Selected area diffraction patterns obtained from (100) and (110) foils of NbC q

gi^ are similar in most respects to those obtained from equivalently oriented foils of V gC 5. However, the NbC patterns exhibit extensive spot doubling and streaking, figure 1(b), which were not so prominent in the VC patterns. Both of these effects are known to result from

the presence of planar lattice imperfections that distort the shape of reciprocal lattice

points into reciprocal lattice rods (rel-rods) . The rel-rods appear as streaks in a dif585
Fig. 2. Bright field transmission electron micrograph of the

domain structure which forms in single crystal NbCg s't after heat treatment. No domains can be resolved in

the as grown material.

fraction pattern when they are tangent to the reflecting sphere, and (except at the origin)

give rise to displaced or extra spots when they intersect the reflecting sphere [7]

.

In the present case, it has been established that the planar imperfections giving rise

to the rel-rods lie parallel to {ill} pl'anes . The orientations of the streaks that appear

in figure 1(b) can be accounted for on this basis, and the position of all the double spots

in the pattern is consistent with ttiis hypothesis also. It is suggested that anti-phase

boundaries, similar to those proposed to account for certain contrast effects observed in

V5C5, [1] may be responsible for the effect.

In the perfect V5C5 structure, carbon vacancies are arranged in an ordered manner on alternating carbon layers in two-dimensional hexagonal nets parallel to {111} planes. The

nets are sequentially positioned along the third dimension so as to define either a righthanded or left-handed triad screw axis [1] . This sequence is disrupted if one or more of

the carbon layers that contain vacancies is displaced by any vector in the {111} plane con- necting nearest-neighbor carbon atoms. Such displacements do not change the near-neighbor

or next-nearest-neighbor distribution of carbon atoms surrounding metal atoms. For this reason, it is expected that faults of this type (anti-phase boundaries) would be low energy

configurations with a high probability for forming in the VgC5 structure.

The presence of anti-phase boundaries alone is not a sufficient condition to promote

the formation of streaking such as that observed in the patterns. The boundaries must

occur in pairs so as to form a thin platelet of anti-phase material embedded in an otherwise perfect matrix. Moreover, the thickness of the platelet, t, determines the length of

the streak, i, on the diffraction pattern. Thus, from the relationship t = k/£. (where k is

a geometrical constant) , the thickness of the platelets may be computed [7] . In the present

586
case, the measured streak length implies a platelet thickness of -10 A, which is approximately

O the spacing, 10.32 A, between four carbon layer planes.

Although there are some indications that similar anti-phase boundaries occur in VgCs,

[1,8] they do not give rise to such pronounced streaking or spot doubling in the diffraction

pattern. This suggests that the spacing between them must be sufficiently great, on average,

that the reciprocal lattice points do not become extended in the same manner as in NbC.

The reason for this difference is not understood, but it could be related to differences in

the driving force for ordering, which, based on the difference in 0-D temperatures, is

expected to be somewhat smaller in NbC than in VC.

In siimmary, a comparison of the diffraction patterns obtained from NbCg qi^ and V5C5

suggest that there are only minor differences between the structures of the two materials.

Both materials appear to contain anti-phase boundaries parallel to {111} planes, but, in

NbCo 84' some of them are spaced close to each other and give rise to extensive streaking

and spot doiibling in the diffraction pattern. Thus, it can be concluded that the structure

of niobium carbide having a composition close to that of NbgCs is isomorphous with that of

the V5C5 structure.

3.2. TANTALUM CARBIDE

The electron diffraction patterns derived from "as grown" samples of TaCg 8 3 '^^ ^'^^ exhibit discrete superlattice spots, but evidence for some ordering is suggested by the

presence of diffuse bands which appear in addition to the primary spots. The geometry of

the bands is consistent with an M5C5 type of ordering, but their diffuse nature suggests

that the ordering is extremely imperfect. Moreover, the ordering is improved only slightly,

figure 3, when the samples are subjected to slow cooling (-8 °C/h) through the temperature

range 1150 °C to 775 °C. On the basis of the following arguments, these results suggest

that the 0-D temperature for TaCo 83 is lower than that of NbCg^s^ ^^'^ occurs in a temperature range where the carbon atom diffusivity is extremely small.

A measurement of ordering time constants in VgC5 [5] has demonstrated that t varys

exponentially with reciprocal temperature

T = T^expCw/kT) (1)

• •

•

• • • • • •

• # •

• •

Fig. 3. Transmission electron diffraction pattern

obtained from (110) foil of a single crystal

TaCo.8 3 sample which had been given a heat

treatment similar to that used to develop

the ordering in NbCg.sif The presence of

diffuse bands, rather than discrete superlattice spots, suggests that the ordering

is very imperfect.

587

/
where W is taken as the activation energy for carbon diffusion. The constant, Tq , may be

evaluated from a knowledge of the Debye temperature since implies a characteristic atomic

vibration frequency, = 6^^ k/h, which will be fully excited at elevated temperatures.

Disordered carbon atoms undergoing these vibrations will have one chance in six tries to

jump into an ordered position in a nearest-neighbor site of the carbon sublattice because,

on the average, 5/6 of the nearest-neighbor sites are already occupied. Thus, the ordering

time at very elevated temperatures is expected to be approximately Tq = 6/Vq. On this basis,

if the 0-D temperature for TaCp 33 were equal to that of NbgCs, it can be shown that the

ordering time constants of the two materials should not be appreciably different. For

example, using values of = 761 K [9] , W = 3.5 eV [10] for NbC and = 616 K [9] , W = 3.7

eV [11] for TaC, the expected ratio of ordering times x (NbC) /x (TaC) =0 . 2 -at 1025 °C. The

experimental results imply a much larger difference in the ordering rates, so it must be

concluded that the 0-D transformation temperature for TaCg 8 3 lies below that for Nb5C5.

Although it has not been possible to make quantitative measurements for the ordering

effects in TaCg 83 » it is interesting to note that the present results establish a pattern

for the Group V transition metal carbide 0-D temperatures . Thus , it appears that the 0-D

temperature of the Group V metal carbides decrease progressively from the first to the third

transition series. This observation has implications for the interpretation of ordering

effects in these materials, which will be discussed in the next section.

The observations presented here, and those which have been discussed previously [1],

demonstrate that all the Group V transition metal carbides tend to form an ordered structure

of the M5C5 type when their carbon-to-metal ratio is close to the value 5/6. In the perfect

M5C5 structure, the metal atoms occupy their normal fee lattice sites, but the carbon atoms

(and carbon vacancies) are distributed on their fee s\±>lattice in such a manner that all the

metal atoms have only five nearest neighbor carbon atoms. The fact that material of this

composition tends to exhibit a distribution of atoms that is homogeneous on an atomic scale

is consistent with the electronic structure of the transition metal carbides as developed by

Lye [2] . Moreover, it appears that the depression of the 0-D transformation temperature in

carbides of the higher numbered series Group V transition metals , relative to those of the

lower series may be accounted for on the same basis.

In particular, Lye has developed a qualitative description of the bonding in these

materials that is based on a semi-empirical LCAO band structure calculations [2] . According

to the model, the outer electrons of the six metal atoms surrounding a carbon atom overlap

onto the carbon atom site depositing a negative charge there. This raises the potential

energy of electrons on the carbon atoms enough to elevate electrons in the upper portion of

the bands derived from carbon 2p states above those of vacant states in the d and s bands

associated with the metal atoms. To minimize their energy these electrons are redistributed

into the lower lying bands, mostly d bands, where they occupy normally vacant states. Thus,

the occupancy of these bands is influenced by the carbon concentration even though the bands

are initially derived from metal atom d states.

In VC those d states whose orbitals overlap in a bonding configuration become completely

filled when the carbon-to-metal atom ratio is close to 5/6 [2] . At this composition the

anti-bonding states are empty, or nearly so, but an increase in the carbon concentration

beyond this ratio would serve to increase their occupancy with electrons contributed by the

carbon atoms. Since the electronic interactions between neighboring metal atoms are important

in determining the band structure as well as the total cohesive energy of the transition

metal carbides, it has been suggested by Lye [12] that the most stable structure would occur when the local concentration of carbon atoms is equal to the integral number five. This

condition is not met in VC if the carbon atoms assume a random distribution on their fee

lattice sites even though the carbon-to-vanadium atom ratio is 5/6, In these cirexams tanees

the fraction, p, of vanadixim sites having n (n^ 6) nearest neighbor carbon atoms is given by

the binominal distribution fiinction

4. DISCUSSION

P(n) = C ^(r)"(l-r)6"'^ (2) n

588
where r is the fraction of the carbon sites that are occupied, and are the binominal

coefficients. Thus, for a random distribution, 33% of the vanadium sites will have six

nearest neighbor carbon atoms, whereas only 40% will have five. On the other hand, the

condition of homogeneity on an atomic scale is readily satisfied without any modification

of the metal lattice, if the carbon atoms assume the ordered arrangement deduced for VgC5.

Similar arguments also appear to account qualitatively for the ordered structure VgCy

which has been described by de Novion et al. [13] . In this case the fraction of vanadium

sites having six, and five, near neighbor carbon atoms would be 45% and 38%, respectively,

for a random distribution, but in the ordered structure the corresponding ratios are 25%

and 75%. Such an ordered arrangement would be expected to exhibit less stability than

V6C5 because anti-bonding d states are necessarily occupied, but it should be more stable

than the random distribution.

The argument that ordering in VC occurs to avoid the occupation of antibonding d states

can be extended to account for the nature of the ordering in NbC and TaC also. For these

materials. Lye's calculations indicate that the bonding portion of the d bands become fully

occupied at increasingly higher carbon concentrations in progressing from the first to the

third series carbides [2], Consequently, it would be expected that the tendency to form an ordered structure should prevail in these materials also, but that the driving force for

ordering would be diminished relative to that in VgCs. The observation that the 0-D temperatures for V5C5, NbgCs and TaCg 83 1250 °C, 1025 °C, and <1025 °C, respectively is

consistent with this hypothesis because, as a general rule, the 0-D temperature of a solid

may be taken as a measure of its ordering energy [14]

.

Finally, it should be noted that Hollox and Venables [15] have demonstrated that the

0-D temperature of VgCs corresponds rather closely to its brittle-ductile transition temperature, both effects occurring within the range 1250 °C to 1300 °C. On the basis of this

observation, it was suggested that the ordering imposes restraints upon dislocation mobilities

in addition to those which arise from the usual Peierls stress. The exact nature of the

hardening mechanism has not been determined, but in any event the results, when interpreted

in terms of Lye's model for ordering, appear to provide an example of the way in which the

electronic energy band structure of solids can influence their mechanical behavior. Moreover, it is reasonable to expect that NbC, and perhaps TaC, will exhibit related effects.

However, the characteristics of their electronic structure which impose a sluggish 0-D

transformation may promote mechanical properties that will depend in a complex manner on prior thermal history.

5. ACKNOWLEDGEMENTS

It is a pleasure to record our indebtedness to R. G. Lye, RIAS , for communicating some

of his results on the electronic structure of the carbides prior to publication. Thanks

are also due to W. Precht, RIAS, who grew the single crystals, and to R. Huntington, RIAS,

who made the lattice parameter measurements. In addition, the authors are grateful for

financial support provided by NASA Research Division, Code RRS , Materials Research Branch,

under Contract NASw-1290.

6. REFERENCES

[1] Venables, J. D. , Kahn, D. and Lye, R. G. , Phil. Mag. 18_, 177 (1968).

[2] Lye, R. G. , this symposium, in paper entitled A Simple Model for the Stability of

Transition Metal Carbides.

[3] Precht, W. and Hollox, G. E. , J. Crystal Growth 3_' 1' 818' (1968).

[4] Rudy, E., Ternary Phase Equilibria in Transition Metal-Boron-Carbon-Silicon Systems,

Part V. Compendum of Phase Diagram Data (Clearinghouse, U.S. Dept. of Commerce,

Springfield, Va. , 1969).

[5] Venables, J. D. , The Ordered Compound VqC^ — Jts Structure and Susceptibility to Radiation Damage, Ph.D. Dissertation, University of Warwick, England (1970).

[6] Proidevaux, D. and Rossier, D. , J. Phys. Chem. Solids 28_, 1197 (1967).

[7] Hirsch, P. B. , Howie, A., Nicholson, R. B. , Pashley , D. W. , and Whelan, M. J.,

Electron Microscopy of Thin Crystals (London, Butterworths , 1965).

[8] Lewis, M. H. , University of Warwick, private communication (1971).

[9] Chang, Y. A., Toth, L. E. , and Tyan, Y. S., Metall. Trans. 2_, 315 (1971).

589
[10] Resnick, R. , Steinitz, R. , and Seigle , L., Trans. Metall. Soc. AIME, 233 , 1915 (1965).

[11] Resnick, R. and Seigle, L. , Trans. Metall. Soc. AIME, 236 , 1732 (1966).

[12] Lye, R. G. , private conraiunication

.

[13] deNovian, C. H. , Lorenzelli , R. , and Costa, P., Compt. Rend. 263 , 775 (1966).

[14] Muto, T. and Takagi , Y. , in "Solid State Physics", ed. F. Seitz and D. Turnbull,

Vol. 1 (Academic Press, New York, 1956), p. 212 ff.

[15] Hollox, G. E. and Venables , J. D. , Proc. Intl. Conf. on Strength of Metals and Alloys,

in Suppl. Trans. Japan, Inst. Metals 9_, 295 (1968).

DISCUSSION

J. S. Anderson : It seems this time that you have been able to get ordering in NbC . My

colleague. Dr. Fender, and one of his pupils, Alan Henfrey, some two years ago examined the

diffuse neutron scattering from materials which had been quenched from 1450° and (I think)

1250°. Henfrey-^ was able to show that in the disordered phase there was still a very strong

correlation; there was a strong third neighbor site preference energy. That, I think, is

precisely the same spacial relation that you have in the defect structure that you've found.

J . Venabl es : As we have pointed out in this paper, the degree of order exhibited in

NbC is critically dependent on the cooling rate through the order-disorder temperature.

The quenched material you describe would undoubtedly exhibit only short range order, but the

atomic configuration should be related to that in the long range ordered structure we've

described here.

H. Nowotny : The band formation you have shown for tantalum carbide also occurs in

vanadium carbide.

J . Venables : Yes, Billingham and Lewis^ have shown similar patterns for low carbon VC. The order-disorder temperature for this material is considerably lower^ than that of V5C5

and is probably in the range where carbon atom diffusivity is low. Under these circumstances,

long range ordering would be more difficult to develop. It appears that this may be the

explanation for the presence of banding, rather than sharp diffraction spots, in low carbon

VC.

Fender, B. E. F. and Henfrey, A. W. , to be published; Henfrey, A. W. , D. Phil. Thesis,

Oxford 1970.

2 Billingham, J. and Lewis, M. H. , Phil. Mag. 24_, 231 (1971).

3 Lewis, M. H. , Univ. Warwick, private communication.

590
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

THE CdP„-Ge SYSTEM AND THE GROWTH OF

^ CRYSTALS OF CdGeP2

E. Buehler and J. H. Wernick

Bell Laboratories

Murray Hill, New Jersey 07974

The macroscopic features of the phase relationships in the CdP2-Ge system have been determined. The tetragonal CdGeP2 phase melts congruently at 790 ± 5 °C. Two eutectics are present: one between CdP2 and CdGeP2 at ~ 700 °C and 20 mol % Ge, and the other, between

CdGeP2 and Ge at ~ 750 °C and 65 mol % Ge. Techniques and results for the growth of crystals

from stoichiometric melts, by chemical transport, and from liquid Cd and Sn are presented.

Key words: CdGeP2; CdP2-Ge sysrem; Ge; phase diagram; single crystals.

1. INTRODUCTION

CdGeP2 , a direct band gap (1.72 eV) [1]-^ diamond-like ternary semiconductor, is one of

a group of isostructural II-IV-V compounds receiving attention in the search for new emitters and detectors of visible and near infrared radiation and new nonlinear optical materials. Shay et al. [1] have reported the electro-reflectance, absorption coefficient, and

energy band structure results for CdGeP2 near the direct energy gap on single crystals prepared by chemical transport. These crystals exhibited resistivities of the order of 10^ ohmcm at room temperature

.

In general, crystals grown by chemical transport are relatively small and growth from

melts is desirable for obtaining large single crystals. CdGeP2 had been reported to melt

congruently at 800 °C [2] and 779 °C [3] and our early x-ray results and metallographic observations were generally in agreement with this piiblished work. The congruent nature of

CdGeP2 is an asset in growth from the melt. On the other hand, it has been known for sometime that glasses of CdGeP2 and CdP2-rich Ge solutions can be prepared [4,5] suggesting that

supercooling and glass formation might be important factors in determining successful growth

from the melt. Since CdGeP2 glass has an energy gap of ~ 0.8 eV, it can be detected by use

of an infrared microscope [1] . Another important feature of the II-IV-V2 phosphides relevant for the choice of growth technique is the rather large dissociation pressures exhibited

by a number of these materials [6] . Since large single crystals of CdGeP2 are required for

a number of electrical and optical studies, the above facts prompted us to investigate some

of the macroscopic features of the phase relations in the Cd-Ge-P system and to develop suitable growth techniques .

In this paper we report the results of our study of the CdP2-Ge join in the Cd-Ge-P^

system and the successful growth of fairly large single crystals from stoichiometric melts.

In addition, we briefly describe our experience in the growth of crystals by chemical transport and from liquid Cd and Sn. Previous workers have grown small crystals from Sn solution

[7] , from the vapor phase [8] and from the melt [9]

.

^Figures in brackets indicate the literature references at the end of this paper.

A complete investigation of the Cd-Ge-P system is in progress and results will be published

elsewhere

.

591

/
2. CdP2-Ge SYSTEM

Differential thermal analysis was used to determine the liquidus and eutectic temperatures. Thermocouples were calibrated against the melting points of pure metals spanning the

temperature range of interest to us . The starting composition for each DTA run was prepared

from CdP2 , Ge, and CdGeP2^ (average weight of charge 0.7 g) and sealed into evacuated quartz

ampoules which contained a thermocouple receptacle as shown in figure 1. An additional

amount of phosphorous was added for each run so as to yield a phosphorous pressure (as F^) of

approximately 10 atmospheres at 800 °C. In all cases, several Si02 granules were added to the charges so as to promote nucleation and thus minimize supercooling. Even so, it was found for cooling rates of 2.9°/min and 3.6°/min, supercooling was observed (as much as 30

°C, for example) for the CdP2 rich melts. Reproducible DTA data were ojDtained for a cooling

rate of 1.7°/min. Typical DTA curves are shown in figure 2. No evidence of a solid state

transformation for CdGeP2 (which occurs for ZnGeP2 at ~ 75 °C below the melting point) was

detected, although the occurrence of one close to the melting point is not ruled out. X-ray

and metallographic examinations were made after each DTA experiment to properly label the co- existence regions

.

The CdP2-Ge join (fig. 3) , determined as described above, shows that the phase relationships are rather simple and the chalcopyrite phase melts congruently. The melting points of

CdP2 and Ge determined in this study are 770 ± 5 °C and 930 ± 5 °C respectively. Berak and

Pruchnik [10] reported 782 °C for CdP2 . The generally accepted value for Ge is 936 °C. We were not able to detect the 3 ^ a-CdP2 transition (~ 420 °C) [10] . Our x-ray results show

only the presence of 3-CdP2 , indicating the sluggishness of this transition [11,12].

We have found that a solution of Br in methanol (1:1000 by volume) is a sensitive etching reagent for metallographic examination of CdP2-Ge alloys. With this reagent, coring,

when present in the primary CdGeP2 phase, can be delineated and is observed for cooling rates

in excess of 2°/min for DTA compositions differing from stoichiometric. This is an important

observation because it indicates to us that a homogeneity region having the CdGeP2 structure

exists at the elevated temperatures. Metallographic and x-ray examination of several CdGeP2

and off-stoichiometric samples homogenized and quenched from 770 °C indicates that the max- imum solid solubilities of CdP2 and Ge in CdGeP2 are less than 2.5 mol %. We have indicated

the existence of a homogeneity range at the elevated temperatures based on the metallographic

observation of coring and the flatness of the liquidus curve, which from thermodynamic arguments, also suggests the existence of a homogeneity region. It is important to note, however, 1 that we do not yet know the maximum solid solubilities and thus the shapes of the solidus

curves and whether or not the stoichiometric composition exhibits the maximum freezing point.

Fig. 1. Ampoules for the DTA experiments

showing the reentrant cavities for

thermocouples

.

Cu OR Ni REFERENCE

'Cd, 99.9999%, P, 99.9999%, and Ge , single crystal, 10 ohm-cm p-type.

592
400 "C

1000 'C 30

700

-760 770

MOLE PERCENT Ge IN PSUEDO -BINARY SYSTEM Ge-CdP

Fig. 2. Examples of DTA curves. The curves for 60 and 70 mol were obtained with an electrically quieter system.

Ge

Detailed equilibrium partial pressure-temperature-composition information in the context of

the whole Cd-Ge-P system is required for a clearer understanding of this phase. The work re- ported here is a step in this direction.

3. CRYSTAL GROWTH FROM MELTS

Early attempts to grow CdGeP2 crystals from stoichiometric melts contained in quartz

crucibles or boats were unsuccessful. The ingots were polycrystalline , contained numerous

cracks, and tended to stick to the quartz. Successful single crystal growth has been carried

out by directional freezing in pyrolytic graphite and vitreous carbon boats sealed into evac- uated quartz ampoules. Charges consisted of stoichiometric amounts of Cd, Ge , and P with or without excess P. When excess P was used, the amount was such so as to yield a P pressure

593

465-504 O - 72 - 39
(as Pit) of 5-10 atmospheres at 850 °C. In order to avoid explosions f the assenibly is usuaXly

heated to 500 °C over a period of 24 hours and then to 850 °C at a rate of ~ 100°/day. The

melt is then cooled to room temperature by decreasing the furnace temperature at rates which

varied from 10-30°/day, depending on the experiment. The furnace gradient established at one end of the assembly is about 4°/cm which we estimate results in a linear growth rate of

approximately 2.5 to 7.5 cm/day through the melting point. Ingots prepared in this fashion

from stoichiometric melts are not completely single, since no seeding is done. They usually

contain from three to ten large crystals. Examples are shown in figure 4. A few cracks are still present and may result from differential thermal contraction or a phase change occur- ring close to the melting point. Nevertheless, the number of cracks present do not hinder

preparing crystals of sufficient size for most electrical and optical experiments presently

underway. The room temperature resistivities of crystals prepared in this manner are essen- tially similar to those prepared by chemical transport (of the order of 10^ ohm-cm) . The

presence of CdGeP2 glass could not be detected by Shay by infrared microscopy and thus the

tendency for glass formation in this system appears not to be an impediment in growing large

crystals from stoichiometric melts. These crystals also yield sharp powder x-ray diffraction

peaks. All 0.1 and 0.2 do\iblets were well resolved.

4. CRYSTALS VIA CHEMICAL TRANSPORT

The procedure we have used consists of placing the desired quantities of Cd, Ge and P with 1-2^ the closed end of a quartz t\±>e (15 cm long, 1.5 cm inside diameter, and .15 cm

wall thickness) , evacuating and sealing. The ampoule containing the charge is placed in a furnace in such a way that on heating over a period of a week , a temperature gradient is

maintained whereby the charge-containing end is the coldest. The maximum temperature reached for the colder end was usually 800 "C. At 800 °C, the alloy is molten. The melt is then

cooled to - 750 °C, where it is solid. The longitudinal temperature gradient is then eliminated because we have found that the largest crystals grow normal to the ingot surface (natural furnace gradient - l-2°/cm) after 10-30 days. Crystals are fewer in number but larger

if the starting charge contains enough Ge in excess of the stoichiometric amount such that

the solid ingot contains Ge second phase . The optimum amount of excess Ge is ~ 15 mol %

.

CM 1 2 3!

Fig. 4. Examples of two directionally

solidified samples of CdGeP2

,

each containing three or four

large crystals.

4 I2 is required for the transport of Ge. Six mg of 12/cc of ampoule volume. For our am- poules, this amounted to ~ 2 wt % of the total weight of charge.

594
Metallographic examination shows the crystals tend to nucleate and grow at those points on

the surface of the ingot which are Ge-rich. Crystals as large as 8 mm^ have been grown by

the above procedure using excess Ge. If the charge is not heated initially to a temperature

where it is completely molten but only to the growth temperature, a Cd-Ge liquid phase is

always present (Cd-Ge eutectic exists below 400 °C) during the growth period and it is found

that only very small crystals are formed under these conditions, similar to that observed for

ZnGeP2 [6]

.

5. GROWTH FROM LIQUID Cd AND Sn

Only a limited amount of effort was expended in this direction. In general, eight mol % of prereacted, polycrystalline CdGeP2 obtained by cooling stoichiometric melts was added to Sn or Cd in pyrolytic graphite boats and sealed into evacuated quartz ampoules . The mixtures

were cooled from 750 °C to room temperature at a rate of ~ 2/hr. The crystals were separated

from the Sn or Cd by heating the ingots in Hg held at 200 °C , followed by etching in concentrated HNO3. The crystals obtained by this technique were generally quite small, ~ 2-4 mm^

,

and the quality, extremely poor, as indicated by powder x-ray patterns; the high angle lines were not sharp.

6. SUMMARY

The macroscopic features of the phase relationships in the CdP2-Ge join of the Cd-Ge-P

system have been determined as a first step towards understanding the results of crystal

growth and physical measurements. The largest crystals of CdGeP2 have been grown from the

liquid state and it appears that the tendency towards glass formation in this system is no impediment for the growth of large single crystals from stoichiometric melts.

7. ACKNOWLEDGMENTS

We thank Messrs. J. D. Wiley and J. L. Shay for their efforts in behalf of the crystal

growth work and helpful comments on the manuscript.

8. REFERENCES

[I] Shay, J. L., Buehler, E., and Wernick, J. H., to be published in Phys . Rev. Sept. 15,

1971.

[2] Masmoto, K., lomura, S., and Goto, W. , J. Phys. Chem. Solids £7.' ^^^^ (1966).

[3] Mughal, S. A., Rayne, A. J., and Ray, R. , J. Materials Science 4_, 895 (1969).

[4] Goryunova, N. A., Kuzmenko, G. S., and Osmanov, E. O. , Mater. Sci. Eng., 7_, 54-56 (1971).

[5] Boltovets, N. S., Borshchevskii , A. S., and Osmanov, E. 0., Mater. Sci. Eng., 1_, 56-58

(1971) . [6] Buehler, E. and Wernick, J. H., J. Cryst. Growth, £, 324 (1971).

[7] Spring-Thorpe, A. J. and Pamplin, B. R. , J. Cryst. Growth, 3-4 , 313 (1968).

[8] Fedorov, A. E., Bychkov, A. G. , and Tychina, I. I., UKr. Fix. Zh. L5: 1568-9, Sept.

1970.

[9] Goryunova, N. A., Ryvkin, S. M. , Spenikov, G. P., Tychina, I. I., and Fedotov, V. G.

,

Phys. Stat. Sol. 28_, 489, (1968).

[10] Berak, J. and Pruchnik, Z., Roczni, Chem. 42_, 1403 (1968); we previously reported a value of ~ 725 °C obtained by DTA for a cooling rate of 3.5 deg/min; Mat. Res. Bull.

6, 303 (1971)

.

[II] von Stackelberg, M. and Paulus, R. , Z. Phys. Chem. B28 , 427 (1935).

[12] Horn, J., Bull. Acad. Polonaise des Sciences, 17, [2] 69 (1969),

595

/

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

HIGH BORON CONTENT RARE-EARTH BORIDES

K. E. Spear and G. I. Solovyev

Materials Research Laboratory

The Pennsylvania State University

University Park, Pennsylvania 16802

Investigations were performed to determine which rare-earth metals form LnBgg phases,

and to measure some of the properties of these compounds. Similar rare-earth borides have

been recently reported with B:Ln ratios of 50 to 100 for metals Y, Gd, Tb, Ho, and Yb. A single crystal structure analysis published on the yttrium compound shows the structure to

be face-centered cubic with an ideal stoichiometry YBgg. In the present studies, ten

representative metals were used: Y, La, Ce, Pr , Nd, Sm, Gd, Dy , Er, and Yb. Boron-rich

compositions were prepared by arc-melting mixtures of the elements. Identification of the

phases in each sample was performed with the use of x-ray and metallographic techniques.

All of the investigated systems except La, Ce, and Pr formed the LnBgg phase, and it is

predicted that all rare-earth metals from Nd through Lu will form this phase. Lattice

parameters were measured and show a general, but not regular decrease with atomic number.

The LnBgg phases are extremely hard, with Vickers microhardness values ranging from about

3600 to 4000 kp/mm^ . Melting temperatures for the LnBgg phases were essentially the same

for all metals, and equal to approximately 2150 °C.

Key words: Borides; lattice constants; LnBgg compounds; melting temperatures;

microhardness; rare-earth borides.

1. INTRODUCTION

Metal borides are very unique and interesting compounds. Their stoichiometric relationships are extraordinary, with common M:B ratios of 4:1, 2:1, 3:2, 1:1, 3:4, 1:2, 1:4, 1:6,

1:12, and 1:66. The more metal-rich phases are most commonly formed with transition metals,

and the boron-rich phases are most commonly formed with lanthanide and actinide metals

.

Nothing analogous to the higher borides with boron contents of 80 at. % and greater is

found in other high temperature materials such as carbides , nitrides , oxides, silicides, etc.; they are unique with the borides.

This paper reports the results of survey studies on the most boron-rich borides of the

lanthanide elements, the LnBgg phases. Ten representative Ln-B systems were studied.

Attempts were made to prepare the LnBgg phases, and lattice constants, microhardness, and

melting temperatures were measured on these boron-rich compounds. Before reporting and

discussing the present results, previous studies on phases of this type will be reviewed.

2. PREVIOUS STUDIES

Seybolt [1]"^ discovered a phase in the Y-B system that was very rich in boron, and

designated it by the formula YByg- Since that time boron-rich phases have been given

formulas of LnB5o, LnBgg, LnByg, and LnB^oO' Lundin [2] tentatively assigned a tetragonal

During the time this research was performed. Dr. G. I. Solovyev was a visiting exchange

scientist at The Pennsylvania State University. His present address is: Moscow Engineering

Physical Institute, Moscow, USSR.

Figures in brackets indicate the literature references at the end of this paper.

597
cell to a material described as YB70 • LaPlaca [3] prepared cubic borides of Tb, Ho, and

Yb with approximate composition LnByg , and later reported [4] he could not prepare these

phases for the larger rare-earth metals. However, the specific metals are not identified.

Smith and Gilles [5] produced similar compounds with Gd and Yb, and gave them formulas

LnBioo* Eick [6] reported the existence of PuBjooRichards and Kasper [7] recently performed a single crystal structure analysis of the

boron-rich yttrium compound and assigned it a formula of YBgg based on this structure

analysis. The structure is face-centered cubic with space group Fm3c, and a„ = 23.440 A o with a standard deviation of 0.005 A. The unit cell contains approximately 1584 boron atoms

and 24 yttrium atoms. A single crystal structure analysis by Naslain, Etourneau, and

Kasper [8] on ThBgg indicates that this phase is isotypic with YB^g.

The basic nature of the crystal structure is not difficult to grasp, as has been

illustrated by Oliver and Brower [9]. Icosahedra made up of thirteen B12 icosahedra are

the basic units of the structure. Figure 1 shows how these 156-atom 612(612)12 groups are formed. One B12 icosahedron is in the center of an icosahedron formed by twelve B12

icosahedra. Two orientations of the 155-atom group are shown because the crystal framework

as shown in figure 2 is made up of two interpenetrating fee lattices of 612(312)12 units

Group

Formulo # Atoms

Sctiemotic Drawing

Group

Symbol

8,2(6,2),

2

156

O

8,2(8,2),

2

156

Fig. 1. Schematic illustration showing the formation of B12

icosahedra from boron atoms, and of a 612(612)12

icosahedra from thirteen B12 icosahedra.

ONE OF Ln ATOMS

IN OCTANT OF CELL

• = Ln atonn in one

of six sites in octant. 0= 0 = B|2 (B,2)|2 group. Qand Q differ by

90° rotation.

UNIT CELL OF LnBgs

1584 Boron Atoms

24 Metal Atoms

Fig. 2. Schematic drawing of the YBgg-type crystal structure.

A description of this structure is given in the text.

598
that differ only by the 90° rotation of these units. Thus, there are eight of these 156-

atom groups per unit cell — or 1248 boron atoms in these icosahedra. The metal atom

positions and the locations of the remaining boron atoms in the structure can be most

easily pictured by referring to an octant of the cell, also shown in figure 2. Six metal

atom sites exist in each octant of the cell, and these are statistically half-filled. The

O sites are located 1.27 A (for YBgg) inside the cell from the center of each face of an octant; one such site is depicted in the figure. The center of each octant is occupied by

either a 36 or a 48 boron atom group. In a random fashion, half of the octants contain

36-atom groups, and half contain the 48-atom groups. The average formula for the structural

units present in one octant of the cell may be written as Ln3[Bi2 (B12) 12^ 1 [^36] 1/2 ^^48^ 1/2

•

Oliver and Brower [9] have grown single crystals of YBgg from the melt by a pedestal

growth technique. Their studies have indicated that YBgg melts congruently at 2100 °C, and

that the YB22-YB66 eutectic temperature is 2050 °C, both values have uncertainities of 50

°C. Smith and Gilles [5] determined that the melting temperature of YbBgg in contact with

more metal-rich ytterbium borides must be greater than 2000 °C.

3. EXPERIMENTAL

3.1. SAMPLE PREPARATION AND ANALYSIS

All samples were prepared from elemental boron and the rare-earth metals. The boron from

A. D. MacKay, Inc. was -325 mesh powder with a purity of 99.5+%. The major impurities

were carbon, 0.20%, and iron, 0.22%. The metals from Research Chemicals had metallic

element impurities of 0.05% or less except for the following: y-Ta (1.0%); Gd-Y (0.5%);

Dy-Ta (0.5%). Most detected impurity elements were present in quantities smaller than 0.01%.

The elemental powders were weighed to give a B:Ln atomic ratio of 80 1 , mixed, pressed

into pellets, and then melted on a water-cooled copper hearth in an argon atmosphere with an arc-furnace utilizing a tungsten electrode. Before melting the samples, zirconium metal was melted to purify the argon atmosphere. The mass of each sample ranged from 5 to 10 grams.

Two of the samples, SmBgg and NdBgg, were analyzed qualitatively by spectrographic

analysis for metallic impurities. The elements Fe and Cu were detected as minor impurities

(0.02-1% range), Mn and Cr were detected as trace impurities (< 0.02%) , and all other

elements including W were not detected. Rare-earth metal impurities were not looked for in

these samples. In addition to the boron as a source of Fe impurity, the prepared samples were ground in a hardened steel mortar. The extreme hardness of the samples probably

resulted in the pickup of at least part of the Fe and Cr detected. The Cu probably

resulted from the arc-melting on a water-cooled hearth.

3.2. HEATING TECHNIQUES

The annealing of samples and melting point determinations were performed in a Centorr

Associates Series 15 tungsten mesh resistance furnace under an argon atmosphere. A borided tantalum setter plate suspended into the hot zone by molybdenum wires was covered

with a powdered layer of SmBg containing a small amount of SmBgg. The samples to be

heated were placed on this powdered layer. The eutectic temperature of 2055 °C for TaB2-B

mixtures [10] , and the boron-like nature of the LnBgg compounds make it likely that a similar eutectic would occur between TaB2 and LnBgg. It was for this reason that the

powdered layer of SmBg was used to separate the LnBgg phases and the TaB2

•

Temperatures were measured with a Leeds and Northrup optical pyrometer by sighting

through an optical window, through holes in the radiation shields, onto the surface of the

sample. In some cases, black-body holes were made in the samples with a spark-cutter.

Observed temperatures were corrected with the use of a calibration based on the melting

point of platinum. The metal was observed to melt at a pyrometer reading of 1710 °C, 59°

below the reported melting temperature of 1769 °C [11] . The melting point of the LnBgg

compounds was determined by observing the rounding of sharp edges on the samples as the

temperature was slowly raised toward this melting point. Some samples completely collapsed

at this point.

599
3.3. CHARACTERIZATION METHODS

3. 3. a. X-RAY DIFFRACTION

X-ray diffraction patterns were taken of all samples with a Siemens dif f ractometer and

Ni-filtered CuKa radiation. Scan rates of 2°/min were used for identification of the phases

that were present, while rates of l/2°/inin were used in determining lattice constants. The

instrument was calibrated with the use of gold and silicon standards. Lattice parameters

were calculated by a least-squares technique and a (cos^e/sinO) extrapolation function.

3.3.b. METALLOGRAPHY

Standard metallographic mounting and polishing techniques were used. The extreme

hardness of the boride samples made the use of a diamond-paste compound necessary for

polishing. The microstructures were examined with the use of a Leitz Panphot photomicrographic apparatus.

3.3.C. MICROHARDNESS

A Leitz Miniload hardness tester was used in measuring the microhardness of samples.

The indentations were made with a pyramidal Vickers diamond using a load of 200p (p = pond = 980.555 dynes). A standard supplied with the instrument (MPA 7760.65) was determined to have a microhardness of 594 kp/mm^ , while the value given for a lOOp load was 581 14 kp/mm^

.

An average of ten measurements was used to calculate the hardness of each sample.

4. RESULTS

A tabulation of the present results is given in table 1. The phase results of attempts

to prepare the LnBgg compounds are given for the ten metal-boron systems looked at, and these

results are followed by lattice constants, microhardness, and melting temperatures of LnBgg

for the systems forming this phase.

The three largest rare-earth metals -- La, Ce, and Pr — did not form LnBgg compounds,

but gave mixtures of the hexaboride and boron. The seven remaining systems studied all

formed the YBgg-type phase. Lattice parameters of these phases were calculated using the

indexing scheme of Richards and Kasper [7] for YBgg. The lines in the diffraction patterns

could be readily indexed, and the intensities were approximately the same as given by

Richards and Kasper and also by Smith and Gilles [5] . The uncertainties given with the

lattice constants in table 1 are computed standard deviations. A general decrease in

lattice constant with atomic number is apparent, but this decrease is not regular. A regularly decreasing trend would require that the SmBgg and DyBgg values be larger.

The microhardness values range between 3610 and 396D kp/mm^ . No systematic trend with

atomic number or cell volume is observed. However, estimated uncertainty limits of + 200

kp/mm^ indicate that not too much emphasis should be placed on differences in these values.

The measured melting temperatures for the LnBgg phases were essentially identical for

all samples. The same value of 2150 °C was given all samples with a rather large, but

realistic uncertainty of + 100 °C. The neodymium and samarium values are probably for

peritectic melting of LnBgg; the other values are believed to correspond to either the

congruent or peritectic melting of single phase LnBgg, but the mode of melting is xinknown.

The evidence used to deduce these results is given below.

The LnBgg samples were single phase except for the NdBgg sample which contained minor

amounts of NdBg, and the YBgg and GdBgg samples which contained trace amounts of second

phase detectable by metallographic, but not by x-ray techniques. In terms of visually

observing the melting of a sample, all samples except the neodymium sample would act like

single phase materials.

Previous studies of the Sm-B system [12] gave evidence for the peritectic melting of

SmBgg to give SmBg plus a boron-rich melt. The microstructure of the neodymium sample in

the present studies indicates that NdBgg melts by a similar reaction. The evidence is not

conclusive, but a eutectic structure was not observed in the two-phase NdBg-NdBgg mixture.

600
Table 1

(a) Experimental Results for Measurements on LnBgg Compounds

(b) ^""^^^(c) (d) Melting

Metal Phases Present Lattice Constant Microhardness Temperature

mj mn tr Ca) (kp/mm^

)

{°C)

Y YB6 6 - YB12 (g) 23 451 +_ 0 002 3860 2150

La B LaBg -

Ce B CeBg -

Pr B PrBg -

Nd NdBee NdBg - 23 508 + 0 004 3910 2150

SmBge - - 23 474 + 0 002 3610 2150

Gd GdBge GdBe (g) 23 476 + 0 005 3660 2150

Dy DyBee 23 422 + 0 005 3840 2150

Er ErBg5 23 .438 + 0 003 3635 2150

Yb YbBge 23 .415 + 0 003 3960 2150

(a) Data were taken on samples quenched from the melt except as noted.

(b) Phases present as determined by x-ray and metallographic techniques:

mj = major, mn = minor, tr = trace.

(c) The uncertainties given with the cubic lattice constants are computed

standard deviations

.

(d) Estimated uncertainty is + 200 kp/mm^

.

(e) Estimated uncertainty is + 100 °C.

(f) Lattice constant and microhardness values were measured on an SmBgg

sample annealed at 2000 °C for 2 hrs . Before annealing, the microhardness was 3710 kp/mm^.

(g) Identification was by color of the trace phase present.

It appears that the NdBg precipitated out first, then NdBgg, but elemental boron or a eutectic mixture of NdBgg and boron was not detected.

The x-ray and metallographic examination of these samples showed no evidence for LnBgg

formation by a solid state reaction occurring after solidification of the melt, which leads

to the conclusion that these boron-rich compounds do not decompose by a solid state reaction

before melting.

5. DISCUSSION

Including the present and previous studies, attempts have been made to form LnBgg phases

with all the rare-earth elements except Pm (radioactive) , Eu, Tm, and Lu. Since only the

three largest rare earths — La, Ce, and Pr -- did not form this phase, it is almost certain

that Pm, Eu, Tm, and Lu will form LnBgg phases.

601
since the starting materials in the present studies were mixed in a molar ratio of

B:Ln = 80 1, it might at first seem surprising that all prepared samples were either

single phase LnB55, or LnBgg plus a more metal-rich phase. One might conclude that the LnBgg

phases actually have B:Ln ratios closer to 80 or higher, as indicated by Smith and Gilles [5],

rather than a ratio of about 66. This explanation could be valid, but another one also seems plausible. From Smith's studies [13] on which rare-earth boride phases vaporize congruently,

one concludes that all of the presently studied LnBgg phases, with the exception of YbBgg,

lose boron preferentially upon vaporization. Therefore, one would not be surprised if boron

were lost during the arc-melting preparation of the samples so that the final B:Ln ratios were less than 80. Careful preparation and characterization studies are needed on these

phases, as they are on essentially all boride phases.

Detailed crystallographic studies of boron-rich chromium samples by Andersson and

Lundstrfim [14] showed chromium to dissolve in 3-rhombohedral boron to the extent given by

the formula CrB^^^- No unique boron-rich phase such as the YBgg-type phase was detected.

In latter studies of solution hardening of 3-rhombohedral boron by Carlsson and Lundstr5m

[15], samples with compositions corresponding to MB20 were prepared with metals Sc, Ti , V,

Cr, Mn, Fe, Co, Ni, and Cu. No unique boron-rich phases were detected. Perhaps with larger

transition metals, YBgg-type or similar type phases will form, but thus far, only some of the

lanthanide and actinide elements and yttrium have produced these compounds.

The powder diffraction patterns of the LnBgg phases studied in the present research

indicate that all of these compounds are structurally isotypic with YBgg. However, no attempts were made to determine the B:Ln ratios of the samples, nor were samples with a specific metal prepared so that lattice parameters of metal-rich and of boron-rich LnBgg

could be compared. Such comparisons would indicate the extent of each phase's homogeneity

range. Compositions either rich in metal or boron could also be annealed at different

temperatures, quenched, and lattice parameters measured. These values would give an indication of the changes in phase boundary composition with temperature.

The hardness values of the LnBgg phases are greater than that of pure 3-boron, which

is given as 3410 kp/mm^ by Carlsson and Lundstrom [15] , and are about the same as the

solution hardened boron values reported by these same authors. The boron was saturated

with the metals mentioned in the discussion above, and gave hardness values ranging from

3610 kp/mm^ for boron containing dissolved V, to 4210 kp/mm^ for boron containing either

dissolved Sc or Mn.

The value of 2150 100 °C given for the melting temperatures of the studied LnBgg

phases is in agreement with the few reported values. Oliver and Brower [9] give a value

of 2100 + 50 °C for the congruent melting of YBgg and 2050 + 50 °C for the YBi2-YBgg

eutectic temperature. Smith and Gilles [5] report that the melting temperature of YbBgg

must be higher than 2000 °C. Although the few reported values are in general agreement, more detailed studies of melting temperatures and behavior are needed on these LnBgg

compounds

.

6. ACKNOWLEDGMENTS

The authors want to acknowledge C. W. Gregg for providing the computer program for the

least-squares lattice parameter calculations, and E. G. Imperato for his assistance in the

experimental portion of these investigations.

7. REFERENCES

[1] Seybolt, A. U. , "An Exploration of High Boron Alloys," Trans. Am. Soc. Metals 52

971-989 (1960) . —

[2] Lundin, C. E., "Rare Earth Metal Phase Diagrams," in The Rare Earths, (F. H. Spedding

and A. H. Daane, eds.), Wiley, New York, Chapter 16, 248 (1961).

[3] La Placa,^^S., private communication quoted on page 330 in Ben Post, "Refractory Binary

Borides," in Boron, Metallo-Boron Compounds and Boranes , (R. M. Adams, ed.). Interscience Publishers, New York, Chapter 5, 301-371 (1964).

[4] La Placa, S., private communication quoted on page 91 in J. L. Hoard and R. E. Hughes, "Elementary Boron and Compounds of High Boron Content: Structure, Properties, and

Polymorphism," in The Chemistry of Boron and Its Compounds, (E. L. Muetterties, ed.).

602
Wiley, New York, Chapter 2, 25-154 (1967)

.

[5] Smith, P. K. and Gilles, P. W. , "Rare Earth Hectoborides , " J. Inorg. Nucl. Chem. 26 , 1465-1467 (1964)

.

[6] Eick, H. A., "Plutonium Borides," Inorg. Chem. 4, 1237-1239 (1965).

[7] Richards, S. M. and Kasper, J. S., "The Crystal Structure of YB^g," Acta Cryst. B25 , 237-251 (1969)

.

[8] Naslain, R. , Etourneau, J., and Kasper, J. S., "Structure Cristalline de la Phase du

Systeme Bore-Thorium. Un Nouveau Borure a Structure Type YBgg," j. Solid State Chem.

3, 101-111 (1971)

.

[9] Oliver, D. W. and Brower, G. G. , "Growth of Single Crystal YBgg from the Melt," Report

No. 71-C-162 (June 1971); General Electric Co., Schenectady, New York 12301.

[10] Rudy, E., "Ternary Phase Equilibria in Transition Metal-Boron-Carbon-Silicon Systems,

Part V. Compendium of Phase Diagram Data," Tech. Rept. AFML-TR-65, 2 , Part V, 209

(May 1969)

.

[11] Hultgren, R. , Orr, R. L. and Kelley, K. K. , private communication in form of "Supplement

to Selected Values of Thermodynamic Properties of Metals and Alloys," University of

California, Berkeley, California.

[12] Solovyev, G. I. and Spear, K. E. , "Phase Behavior in the Samarium-Boron System",

(Submitted for pxiblication J. Am. Ceram. Soc).

[13] Smith, P. K. , "Lanthanide Boride Systems and Properties," Ph.D. Thesis, University

of Kansas, May 1, 1964. Also USAEC Report No. COO-1140-103 (May 1964) . [14] Andersson, S. and Lundstrom , T. , "The Soliibility of Chromium in 3-Rhombohedral Boron

as Determined in CrB^i^i by Single-Crystal Dif fractometry , " J. Solid State Chem. 2_, 603-611 (1970) . [15] Carlsson, J. 0. and Lundstrom, T., "The Solution Hardening of 3-Rhombohedral Boron,"

J. Less-Common Metals 22_, 317-320 (1970) .

DISCUSSION

B. Post: Did you worry about the fact that all the rare earth B66 (R.E.Bgg) compounds

melt within 20 degrees of each other, which is within 20 degrees of the melting point of

boron?

K. E. Spear : Yes, we worried some about it. We melted these on a borided tantalum

setter plate. That's what we were using to anneal samples and the eutectic temperature

between the tantalum diboride and the boron is about 2050°. We were afraid SmBgg or any

of the metal boron 66 (MBgg) phases and tantalum diboride would have a similar low melting

eutectic. Therefore, we put a layer of essentially pure samarium hexaboride powder between

the tantalum diboride and the specimen to be melted. I think the melting points are correct

within + 100 degrees.

B . Pos

t

: What I was wondering about is the possibility that you drove off the metal

and had boron left.

K. E. Spear : No, at least ytterbium was the only possible case. The rest of these

metal borides should lose boron preferentially according to the work of Smith and Gilles^

.

S. LaPlaca : Just to update your phase diagram^, the compound samarium boron approximately 2.1 (SmB2.i) turns out to be Sm2B5. The work in collaboration with Paul Smith at

Bell Labs is being published in Acta Cryst. very shortly.

K. E. Spear : Oh, very good, do you know the crystal structure?

S. LaPlaca : Yes, in fact that is how the composition was determined, by doing the

crystal structure. It is a derivative of the MBt^ structure where you just separate the

layers and put intervening B2 units in.

^P. K. Smith, "Lanthanide Boride Systems and Properties," Ph.D. Thesis, University of Kansas,

May 1, 1964. Also USAEC Report No. COO-1140-103, May 1964.

^Refers to Sm-B phase diagram shown during oral presentation to illustrate melting behavior

of SmBgg. This phase diagram appears in the paper: G. I. Solovyev and K, E. Spear,

"Phase Behavior in the Samarium-Boron System," J. Am. Ceram. Soc. (submitted for publication) .

603
K. E. Spear : Very good! We had x-ray data and it wasn't like any known boride structure, so I'm glad to hear the structure has been solved.

K . Kahan : Is there any evidence that these MBgg phases are intercallation compounds?

K. E. Spear : No, the structure disproves this. The structures are similar to elemental boron in many ways. In fact, the easiest way to answer your question is with two slides that I have. I think I can do this in about one minute. Actually the structure is

fairly simple to see when you look at the slides. It is a face-centered cubic structure

and is made up chiefly from groups of 156 boron atoms. If you consider these groups as individual units, then you can see fairly easily how the 1608 atoms per unit cell are ar- ranged. The first slide (Fig. 1 in text of paper) just briefly shows how you build up the

156-atom groups. You go from single boron to the icosohedra B22 groups. The 156-atom

groups have a B12 group in the center, and 12 such groups around the outside. This gives

you the 156-atora group. I've shown two orientations, of this group, just 90 degrees twisted

because that's the way it is in the structure. If I could have the next slide (Fig. 2 in

text of paper); consider this the sodiiam chloride structure. If you substitute a 156-atom

group for each sodium atom and each chlorine atom in NaCl , then you account for 1248 of the

boron atoms. Other groups of boron atoms are in the center of each octant of the cell. You

have either a 36- or 48-atom group in there. As for the metal atoms, you have an average

of 3 metals in each octant. Just one of the six metal sites per octant is shown. The metal

are statistically placed with an average of three per octant, or 24 per cell. That finishes

filling the cell. This explanation of the structure is a simplified version that I can easily understand.

B. Post : 1 think it should be emphasized that this structure was done by Kasper and

Richards'^ and is really quite a job, it is very good.

Reference 7 in paper under discussion.

604
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

PREPARATION AND CHARACTERIZATION OF BORON SUBOXIDE

D. R. Petrak and Robert Ruh

Air Force Materials Laboratory, Wright Patterson Air Force Base, Ohio 45433

B. F. Goosey

Department of Materials Science, University of Cincinnati, Cincinnati, Ohio 45221

Fabrication techniques have been developed to produce specimens of near theoretical

density by reaction hot pressing of boron and boric acid in vacuum at temperatures of 1900-

2000 °C and pressures of 0.41 kbars . The composition range 80 to 89 atomic % boron was investigated by chemical analysis, lattice parameter studies, pycnometric density determinations, electron probe analysis and infrared analysis. Results support the B12O2 chemical

formula and the R3m space group with twelve boron atoms in the IBh positions and two oxygen

atoms in the 5c positions. Thus, on the basis of the experimentally determined hexagonal

lattice parameters of a = 5.386±0.003 A and c = 12.32610.004 A, the calculated density is

2.602 g*cm~^ and this is in good agreement with the experimentally determined value of 2.600

±0.007 g*cm~^. The occupancy of the 3b position by either boron or oxygen (to allow the Bi^O or B13O2 stoichiometry) is ruled out since this would require increases in density and/or

lattice parameters and none were observed. Also these configurations do not satisfy the

Longuet-Higgins and Roberts counting rule. The boron suboxide phase has been studied by

electron probe and infrared analyses. The oxygen K emission spectra as well as the infrared

reflection spectra are presented. Boron suboxide has been studied by mass spectrometric

analysis and found to decompose to rhombohedral boron and B2O2.

Key words: Amorphous boron,- anhydrous boric acid; boric oxide; boron carbide structure

type; boron suboxide; crystal structure; decompose; electron microbeam probe; infrared

spectrum; lattice parameters; pycnometer; reaction-hot pressing; rhombohedral boron;

x-ray diffraction.

1. INTRODUCTION

Boron suboxide is a material of Air Force interest because of its low theoretical density, high hardness and other characteristics. However, insufficient basic information and

property data were known to adequately evaluate the potential of this material. Thus one of

our research goals has been to determine structure and property relationships as well as processing techniques so that a meaningful evaluation was possible. A review of the literature on boron suboxide has been accomplished in an earlier study [1]-^. This study was a rather broad one and investigated boron suboxide as well as the 80-100 atomic % B composition

range using chemical, metallographic , petrographic , x-ray diffraction, electron probe and

elastic properties analysis. Results revealed that with increasing boron content the phases

present were: B2O3 plus rhombohedral boron suboxide, boron suboxide, boron suboxide plus

rhombohedral boron and boron. Hardness was investigated and values somewhat greater than

those obtained for boron carbide were found. Elastic properties were determined for boron

suboxide and two phase boron-oxygen compositions. Results revealed Young's moduli of up to

4830 kbar for boron suboxide and the value decreasing to 4480 kbar as the composition moved

through the two phase region to boron. Poisson's ratio was found to be 0.156 for boron suboxide and to decrease through the two phase region to 0.130 at the boron composition.

1 Figures in brackets indicate the literature references at the end of this paper.

605
The current investigation was a more basic and detailed analysis of boron siiboxide and

study of the structure as well as the thermodynamic and physical properties. Since boron

suboxide has the same structure type as boron carbide and other attractive high boron com- pounds, information gained in this investigation will help to provide a better understanding

of this whole family of compounds.

2. FABRICATION TECHNIQUES

2.1. STARTING MATERIALS

The compositions studied were prepared from appropriate mixtures of anhydrous boric

acid and amorphous boron powders^ . Emission spectrographic analyses revealed an impurity

level of less than 0.1% for the boric acid and approximately 1% for the boron exclusive of

boric oxide. While the impurity level was relatively high, this was the only boron available with the necessary fine (0.5 pm) particle size.

2.2. REACTION HOT PRESSING

The hot pressing of specimens in this study was accomplished in two steps. The first

was a prepressing operation which consisted of heating the dry mixed starting powders in a steel die to approximately 450 °C at 0.206 kbar. {Under these conditions the boric acid was

molten.) The steel die was lined with Grafoil^ and tantalum sheet before filling with the

powder mixture. The grafoil facilitated easy removal of the specimen from the die while the

tantalum sheet assured a smooth specimen surface. The purpose of the prepressing operation

was (1) to disperse the anhydrous boric acid throughout the compact and (2) to consolidate

the compact and impart green strength.

The second step was a more conventional hot pressing operation. This was accomplished

in vacuum using inductively heated graphite dies with barrier layers of boron nitride and

tantalum sheet. A schematic diagram of the furnace and die assembly is shown in figure 1. The boron nitride was applied to grooved cylindrical surfaces of the die and plungers

using a suspension in toluene. Initial pressings without the tantalim barrier revealed a ring of boron carbide 3 to 5 mm thick on the circumference of the specimen. The use of tantalum prevented the formation of boron carbide in most cases and tantalum was not found to diffuse significantly into the billet. However, as an added precaution, the outer ring of

material was always discarded. A billet size of 5 cm in diameter by 1.2 cm in thickness was used so that adequate material was available for many different analyses and tests.

Fig. 1. Schematic diagram of the furnace and die assembly.

2 U. S. Borax Research, U. S. Borax and Chemical Corporation, Anaheim, California

3 Union Carbide Corporation, Carbon Products Division, Cleveland, Ohio

606
Pressings were made at 1900 to 2000 °C for 15 to 30 minutes at 0.41 kbar. Densification

was monitored by means of a dial guage mounted on the press ram. Densification due to sintering was not observed \intil the 1750 to 1800 °C temperature range was attained. Pressure

was maintained at 0.069 kbar up to the sintering temperature and then increased to 0.41 kbar.

These pressing procedures were found to work equally well for compositions in the 80-100

atomic % boron range and bulk densities of 96-100% of theoretical were obtained.

Boron suboxide reflection data were first indexed on an orthorhombic unit cell by

Pasternak [2] who also determined the composition to be Bg^gO by chemical analysis and the

measured density to be 2.64 g-cm~^. Based on these data, he assigned a stoichiometric formula of B7O. Later LaPlaca and Post [3] showed that the powder pattern for the boron suboxide

phase could be more satisfactorily indexed on a rhombohedral cell of the boron carbide structure type. The ambiguity in indexing the pattern was the result of a special intensity ratio

which existed; namely, [d (qqi) /d (loo) ] = 7. LaPlaca and Post suggested a B13O2 stoichiomet2ry which agreed well with Pasternak's Bg.gO composition but required a calculated density of

2,80 g'cm~^. Rizzo et al, [4] found the composition to be B5O or a B12O2 structural formula,

which was later supported by Post [5] . The B12O2 structure (modified from Silver and Bray

[6] and shown in figure 2) together with the hexagonal lattice parameters of a = 5.395 and

c = 12.342 K determined by Rizzo et al. gave a calculated density of 2.59 g.cm^. The crystal

structure work of both Novak [7] on powder patterns and Corfield [8] on a twinned crystal

support the R3m space group for boron sijboxide. Assuming this rhombohedral symmetry. Hoard

and Hughes [9] have noted that the only dimensionally satisfactory structure that satisfies

the Longuet-Higgins and Roberts electron counting rule [10] for a filled band configuration

is B12O2 where no bond exists between oxygens. This would rule out any stoichiometry range

for boron suboxide analagous to the Bi4C-Bi3C2 range in boron carbide.

In this study precision lattice parameters were determined at room temperature on hotpressed specimens with nominal starting compositions of B^O, B5O, B5O, B7O and BgO. Two different methods were used for determining peak positions, namely (1) slow scan dif f ractometer

traces and (2) Debye-Scherrer film techniques using a camera with a radius of 71.62 mm. Agreement between the two methods was very good. However, the film technique yielded the more precise results, and these results are given. Further description of the experimental

techniques and the computation of lattice parameters were given in an earlier paper [11]

.

The hexagonal lattice parameters for all five specimens were within the range of a = 5.386 ± 0,003 and c = 12.326 ± 0.004 K, thus indicating no significant change. Furthermore, decreasing amovmts of B2O3 were noted in the Bi^O and B5O specimens by x-ray diffraction, while free

boron was found in the B7O and BgO specimens. The free boron in the B7O specimen could not

be detected by x-ray diffraction but was observed by metallographic analysis. As shown in

table 1, chemical analyses^ on the nominal BgO and B7O specimens gave 79.7 and 80.7 wt. %

3, CRYSTAL STRUCTURE

O BORON -ehg

© B0R0N-6h|

0XY6EN-2C

Fig, 2, Proposed rhombohedral unit cell of B12O2

(modified from Silver and Bray [6] )

.

Ledoux and Company, Teaneck, New Jersey

607
Table 1 Nominal and Analyzed Compositions and Phases Present in Boron-Oxygen Specimens

Nominal Phases

Composition Analyzed Composition Present

B (wt%

)

0(wt%) Total

B50 77.5 22.0 99.5 B6O+B2O3

BgO 79.7 20.7 100.4 BgO

B7O 80.7 18.3 99.0 BgO+B

BoO 82.5 16.8 99.3 B5O+B

boron respectively. This would support a B5O stoichiometry of 80.2 wt. % boron. Oxygen

analyses, although not considered as accurate, were performed and gave total boron and oxygen

contents of 99.0 to 100.4 percent.

Pycnometric densities were also determined on all but the B3O specimen. At least 5 grams

of each composition were ground to minus 325 mesh in a boron carbide mortar and pestle, then

boiled in distilled H2O to dissolve any B2O3 present. After filtering and drying the density

was measured using a 25 cm^ pycnometer with butyl alcohol at 24 °C. All density values were within the range 2.600 ± 0.007 g-cm" . This agrees well with a calculated value of 2.602

g-cm~^ obtained by assuming a B5O stoichiometry and the lattice constants determined in this

study. Thus all of the above data support the B12O2 structural formula in agreement with the

Longuet-Higgins and Roberts theory. However the data do not preclude the possibility of a small change in stoichiometry.

4. ELECTRON PROBE STUDIES

Polished specimens of the nominal compositions mentioned previously were studied by Baun

and Solomon [12] using a Perkin-Elmer (Hitachi) XMA-5 electron microbeam probe. Typical Oxygen K spectra for boron suboxide and B2O3 are given in figure 3. It is seen that boron suboxide has two maxima separated by approximately 3 eV^ , while B2O3 has a major peak with a much weaker component at the low energy side

.

The existence of the two peaks indicates the formation of split molecular orbitals. Although a complete molecular orbital treatment has not been performed for boron suboxide , the

two transitions could be explained by the crossover theory. On this basis, transitions from

the boron 2p to the oxygen Is level as well as the oxygen 2p to Is are allowed. Using published values for these energy levels, the two bonds should be 2.5 to 3 eV apart and this

separation was observed.

Baun and Solomon [12], in comparing the spectra from the nominal compositions, have noted changes in the relative intensities of the two peaks. They have explained these changes

on the basis of compositional changes due to boron or oxygen occupying the interstitial sites

in the rhombohedral structure of figure 2. In light of the present work it appears that the

oxygen atoms occupy the 6c sites and that the 3b site is vacant. However the existence of a defect structure cannot be ruled out. The observed changes in relative intensities could

also be explained by the presence of B2O3 in different amounts.

5. INFRARED REFLECTION SPECTRA

The infrared reflection spectra for the BgO phase has been determined by Phillipi [13]

.

The main reflection band at 1060 wave numbers is shown in figure 4. Other weaker reflection

bands were observed at 880, 780, 710 and 420 wave numbers. Similar reflection spectra were observed for the nominal compositions of B4O, B5O, BgO and B7O. However, no large wavelength

shifts that could be related to changes in composition were evident. A multioscillator dis-

^1 eV = 1.6021 X 10~5j

608
I I I

I

I I I I I 518 522 526 530 ENERGY (eV)

Fig. 3. Oxygen K emission spectra from boron suboxide

and B2O3 (after Baun and Solomon [12]).

Fig. 4. The major infrared reflection band at

1060 cm"^ (after Phillipi [13]).

persion analysis is presently being performed on the spectra to aid in the characterization

of these materials

.

6. STABILITY AND MASS SPECTROMETRIC STUDIES

The stability of boron sviboxide was investigated as a function of temperature in a flowing helium atmosphere. A 97% dense hot pressed pellet was repeatedly heated to temperature,

held for two hours, cooled and weighed. Results are presented in figure 5. After the final

heating cycle the specimen had an extremely porous appearance and could be crushed easily.

465-504 O - 72 - 40 609
40

800 1000 1200 1400 1600 1800 2000 2200 TEMPERATURE CO

Fig. 5. Weight loss versus temperature for a solid boron

suboxide specimen in a helium atmosphere.

X-ray diffraction analysis of the decomposed material revealed rhombohedral boron and a small

amount of boron suboxide. This would explain the decrease in rate of weight loss at the

higher temperatures, since most of the boron suboxide had already been decomposed. This work

is in reasonable agreement with that of Rizzo et al. [4] who determined weight loss in helium

for the 1300-1750 °C temperature range.

The vaporization characteristics of boron suboxide were investigated by Carbonara [14]

for the authors to determine the vapor species and the thermodynamic quantities involved.

An analyzed 79.7% boron composition was contained in a BeO-lined niobium Knudsen cell. A Nuclide HT-90-12 mass spectrometer was used to identify the vaporizing species to temperatures

as high as 2000 °C. The predominate vapor components were BO and B2O2 . Small amounts of B,

B2O, BO2 and B2O3 were also found. This information was used to confirm thermal gravimetric

analysis made in an Ainsworth microbalance and the BeO-lined niobium Knudsen cell.

The TGA data were converted to equilibrium total pressure and AH^ and AS^ were calculated for the reaction:

2B60(s) t B202 (g) + lOB(s)

AH^ =90.9 Kcal/mol^

AS^ = 40.2 eu^

X-ray diffraction analysis on the condensed phases after testing gave both boron suboxide

and rhombohedral boron. No reaction with BeO was detected.

The above values for AH^ and AS^ compare well with AH-^ = 94 ± 8 Kcal/mol and AS^ = 41.4

eu found by Inghram et al. [15] for the vaporization of mixtures of boron and boric oxide.

Their work was done in the temperature range 1030 to 1230 °C on molar ratios of boron to boric oxide greater than one. Since Inghram et al . reported no analysis on their condensed

phases an attempt was made to reproduce them. A 2:1 molar ratio of boron to boric oxide was mixed and placed in a covered alumina crucible (Inghram et al. used an alumina Knudsen cell)

.

The crucible was then heated to 1230 °C in vacuum for 7 hours. The condensed phases under

these conditions were found to be boric oxide and boron suboxide with only a small indication

for boron. Since it is doiibtful that this experiment had reached equilibrium it is likely

that Inghram et al. actually observed the vaporization of boron suboxide and boric oxide.

This would explain the similarities in the results of the two mass spectrometric studies.

6 1 Kcal/mol = 4,184J/mol

'^1 eu = 4.184J/mol K

610
7, SUMMARY

Fabrication techniques have been developed to produce dense specimens of boron suboxide

by reaction hot pressing at 1900-2000 °C at pressures of 0.41 kbars in vacu\m. The structure

of boron suboxide has been investigated in light of chemical analyses, lattice parameter

studies, pycnometric density determinations, electron_ probe analysis and infrared analysis.

Results support the B12O2 chemical formula and the R3m space group with twelve B atoms in the

18h positions and two oxygens in the 6c positions. The occupancy of the 3b position by

either boron or oxygen (to allow the Bi^O or B13O2 stoichiometry) is ruled out by chemical

analysis, density and lattice parameter studies, as well as by the Longuet-Higgins and Roberts

electron counting rule. However the experimental data does not preclude small changes in

stoichiometry. Boron suboxide was found to decompose to B + B2O2 by mass spectrographic

analysis

.

8. ACKNOWLEDGMENTS

The writers express sincere appreciation to W. L. Baun, P. W. R. Corfield, T. C. Joyce,

C. M. Phillipi and E. J. Rolinski for helpful discussions, to E. G. Charles for assistance

in the x-ray diffraction analysis, to V. A. Patel for assistance in the density determinations

and to Miss Sally Allen for typing the manuscript.

9. REFERENCES

[I] Rxih, Robert, Petrak, D. R. and Goosey, B. P., Processing and Fabrication and Some Properties of Boron Suboxide , Presented at the Seventy-Second Annual Meeting, The American

Ceramic Society, Philadelphia, Pennsylvania, May 4, 1970 (Society Symposium 4, Ceramic

Armor, No. 7-S4-70)

[2] Pasternak, R. A., Acta Cryst. 12, 612-13 (1959).

[3] LaPlaca, S. and Post, B., Planseeber Pulvermet, Bd 9, 109-12 (1961).

[4] Rizzo, H. F., et al., J. Electrochem. Soc. 109 , 1079-82 (1962).

[5] Post, B., Refractory Binary Borides in Roy M. Adams, Ed., Boron, Metalloboron Compounds,

Interscience P\iblishers, New York, 301-71 (1964).

[6] Silver, H. A., and Bray, P. J., J. Chem. Phys . , ri, 247 (1959).

[7] Novak, R. , RCA Laboratories, private communication, Princeton, New Jersey.

[8] Corfield, P. W. R. , Cheinistry Department, Ohio State University, private communication,

Columbus, Ohio.

[9] Hoard, J. L. and Hughes, R. E., Elementary Boron and Compounds of High Boron Content:

Structure , Properties and Polymorphism in E, L. Muetterties , The Chemistry of Boron

and Its Compounds, John Wiley and Sons, Inc. New York, 25-154 (1967)

.

[10] Longuet-Higgins, H. C. and Roberts, M. dev., Proc. Roy. Soc. (London) 230A , 110-19 (1955).

[II] Domagala, R. F. and R\ih, Robert, ASM Trans Quart. 62_, 915-925 ^(1969).

[12] Baun, W. L. and Solomon, J. S. Boron Bonding Studies Using the Electron Probe Presented

at the Twenty-Second Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Cleveland, Ohio, Feb. 28-March 5, 1971.

[13] Phillipi, C. M. Analytical Branch, Air Force Materials Laboratory, Wright-Patterson Air

Force Base, Ohio, private communication.

[14] Carbonara, R. S., Letter Report on Contract F33615-71-C-1070 Preliminary Experiments on the High Temperature Behavior of Boron Suboxide, Sept. 3, 1971, Battelle Columbus Laboratories, Columbus, Ohio.

[15] Inghram, M. G. , Porter, R. F. and Chupa, J., J. Chem. Phys. 25_, 498-501 (1956).

DISCUSSION

R. S. Kirk : Your slide didn't show what was the temperature stability on your suboxide. How high could it go?

D. R. Petrak : That was the slide that wasn't shown. In a flowing helixam atmosphere

it begins to decompose at approximately 1000 °C.

611

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

TERNARY TRANSITION METAL SUICIDES AND GERMANIDES: ORDERING

AND METAL-METAL BONDING IN Ni2ln-RELATED PHASES

Vancliff Johnson and Wolfgang Jeitschko

Central Research Department*

E , I . du Pont de Nemours and Company

Experimental Station

Wilmington, Delaware 19898

Ternary transition metal silicides and germanides with structures related to Ni2ln

("filled" NiAs) are reviewed. For compositions TT'Si and TT'Ge, where T is a transition

metal from groups IV, V and VII and T' is from the iron group, the structures adopted are TiNiSi (ordered anti-PbCl2) , ordered Fe2P, TiFeSi or Ni2ln. We describe and illustrate how

these as well as the hexagonal MnsSis structure are related.

Metal site occupancies in ternary TiNiSi and Fe2P-type silicides and germanides and

pseudobinaries with Ni2ln and Mn5Si3 structures are also reviewed. We discuss the importance

of the relative size and electronegativity of the transition metal atoms and their d-electron

configurations in determining site preferences.

Bonding in these Ni2ln-related phases, (TT ' ) a-x^-'- ^'^^^ ' discussed. The structures

differ principally in the strengths of the respective T-T, T-T', and t'-T' metal-metal interactions. Questions as to how these are determined by electronegativities, size and d-electron configuration, and how they in turn affect phase stability and metal-site occupancies

are raised.

Key words: Fe2P and Mn5Si3; metal-metal bonding; metal-site occupancies; Ni2ln;

ordered ternary silicides and germanides; silicides and germanides; ternary Ni2ln-related phases; TiNiSi.

1. INTRODUCTION

Ordered versions of the C02P (anti-PbCl2) / Fe2P, and closely-related structures frequently occur among ternary silicides and germanides at compositions TT'Si and TT'Ge where

T and T' are transition metals. These as well as the Mn5Si3 type are all closely related to Ni2ln ("filled" NiAs). True ternary phases, (TT')5Si3 based on the Mn5Si3 structure have

not been found; however, in substitutional solid solutions ordering of the transition metal

atoms occurs. The factors influencing ordering in all these phases pose interesting questions .

2. EQUIATOMIC TERNARY SILICIDES AND GERMANIDES

Many ternary phases are found at the compositions TT'Si and TT'Ge when T is a large,

electropositive transition metal, for example Ti , and T' is from the iron group. With T from groups IV, V, and VII, the structures adopted are TiNiSi (o-rdered anti-PbCl2), ordered

Fe2P, its distorted version, TiFeSi, or Ni2ln. With T from group VI, the known equiatomic

ternary phases possess the MgZn2 structure (T = Mo or W) . The occurrence of these phases

[1-12] is summarized in table 1. The TiNiSi type occurs most frequently with silicides and

germanides while the Fe2P and TiFeSi types occur mainly with rare earths as T component and

elements from the aluminum group replacing Si or Ge [13] . The Ni2ln and MgZn2 structures

*Contribution No. 1879

1 Figures in brackets indicate the literature references at the end of this paper.

613
Table 1

Occurrence of Ternary Equiatomic Transition Metal

Silicides and Germanides TT'Si(Ge).

SILICIDES GERMANIDES

\T'= Mn Fe Co Ni Cu Mn Fe Co Ni Cu

T= \

Ti o • • o 0

Zr 0 0 0 0 D

HfV

no 0 o •

To • •

CrMo X W X X X Mn

Tc Ru Rh Pd Ag Tc Ru Rh Pd Ag

Ti •

Zr o • 0 NbMn

TiNiSi ( onti -PbCl2 ) X MgZn2

o FegP • TiFeSi

occur infrequently at these compositions though the latter occurs in most of the ternary systems in the pseudobinary sections T(T'i_j^Si )2 with x ~ 1/3 [14-16]. The MgZn2 structure is

not apparently related to the others and wi$l not be further discussed.

3. STRUCTURAL RELATIONSHIPS

The Ni2ln structure is generally regarded as a "filled-up" version of the NiAs structure.

In NiAs the metalloid atoms (As) form a hexagonal close-packed array with octahedral and

trigonal by-pyramidal voids. Metal atoms occupy only octahedral voids in NiAs but both in

Ni2ln. MnP and TiNiSi are similarly related. The MnP structure derives from NiAs by small

atomic displacements (figure 1) ; likewise the TiNiSi structure may be regarded as a distorted

Ni2ln structure [17] . The Fe2P type structure is not directly derived from Ni2ln. However,

as can be seen in figure 1, nearest neighbor environments are very similar to TiNiSi. The

TiFeSi structure is very closely related to the ordered Fe2P type structure [9] and nearest

neighbor environments are virtually identical. For the purpose of the present paper it may

be regarded as identical to ordered Fe2P.

In all these structures the basic triangular prismatic coordination of the metalloid

atom is retained; the metalloid has six close metal neighbors in NiAs and MnP while three additional metal atoms are in the center of the rectangular prism faces in Ni2ln, TiNiSi and

Fe2P. Nearest neighbor environments for the metal atoms are summarized in table 2. in TiNiSi

and ordered Fe2P (e.g. TiCoGe) the large transition metal, T, has five Si or Ge atoms as nearest neighbors which form a quadratic pyramid. The small transition metal, T', has four

Si or Ge neighbors in a tetrahedral configuration. The number of nearest metal neighbors is

the same for the corresponding T and T' atoms although their relative arrangements differ

somewhat (figure 1)

.

The Mn5Si3 structure may also be regarded as related to NiAs [18] . Figure 2 shows in

projection the Ni2ln and Mn5Si3 structures. The hexagonal close-packed arrangement of metalloid atoms is retained in Mn5Si3 but 1/3 of the octahedral positions which are filled in

Ni2ln are empty. The remaining octahedral and trigonal prismatic voids of the hexagonal closepacked metalloids are filled. A shift of the T' atoms towards the empty octahedral sites

distorts the structure from the ideal Ni2ln arrangement. These voids are filled with C, Ga

or Cu in Mo<5Si3C^l [19] , Ti5Gait [20] and Hf5Sn3Cu [21] . Transition metal atoms are in two

614
lrSn(NiA5)

O I', MnJi.Zr

• Co, Ni, Ru

O S.,Ge,Sr>

ZrRuSi(Fe,Pl

Fig. 1. Projections of t±ie structures of IrSn, IrSi , MnCoGe,

TiNiSi , and ZrRuSi . The respective structure types

are given in parentheses. Atoms connected by thick

lines are separated by half a translation period in

the projection direction. Atoms and vacancies are connected to emphasize relationships and differences

among the structures [12]

.

Table 2

Atomic Coordinations of the Transition Metal Atoms in Some Ni2ln-related Phases

Metalloid Total Metal

Structure Space Grp Position Coordination Coordination Atom

Ni2ln P63/mmc 2a octahedral 6+2+6 T 2d trigonal bi- 5+0+6 T' pyramidal

TiNiSi Pnma 4c pyramidal 5+4+6 T 4c tetrahedral 4+2+6 T'

Fe2P P62m 3g pyramidal 5^+4+6 T

3f tetrahedral 4+2+6 T'

MnsSi^ P63/mcm 4d octahedral 6+2+6 T 6g trigonal bi- 5+6+4 T' pyramidal

^The three sequential coordination numbers refer to metalloids, metal atoms

of like kind, and unlike metal atoms, respectively.

615
Mn, Si, -Mo, Si, C T,. Go, Hf, Sn, Cu Nijin o Mn Mo Ti Hf o Ni 0 Si Si Go Sn o In or z = 3s • void c Go Cu . o In c\ z - li

Fig. 2. Relationship between Ni2ln, MnsSis and filled MnsSi

structures

.

inequivalent sites (T in 4d and T' in 6g) . The T atom has six metalloid neighbors in a distorted octahedral arrangement. The octahedra share faces along the c axis thus giving two

close T neighbors (figure 3) . Six T' neighbors also forming an octahedron complete the T environment. The T' atom is surrounded by a distorted bypyramid of metalloid atoms, six T' and four T atoms. The T' atoms form octahedra that share faces along c at each corner of

the unit cell. The metalloid atoms are coordinated by 4 T and 5 T' atoms in a distorted

triangular prismatic arrangement.

4. METAL-SITE OCCUPANCIES

4.1. Ni^In-TYPE PHASES

This structure is infrequently found for true equiatomic ternary silicides and germanides but is frequently found among binaries and pseudobinaries with large homogeneity ranges

not including the T2X composition. In fact its nonstoichiometry and frequent existence as a high temperature phase are marked characteristics. This is also true of the parent NiAs

phases

.

For phases with compositions between Fej^gyGe and Fej yyGe it has been shown [22,23,24]

that the vacancies occur on the T' (trigonal by-pyramidal, 2d) sites. Yasukochi et al. [25]

suggest this also for Mn2_xSn, Fe2_jjSn, Co2_jjSn, and Ni2_xSn with this structure. Castelliz

Fig, 3. Mn5Si3 structure showing chains of 4d

metal atoms and chains of octahedra

formed by 5g metal atoms. Si atoms

and octahedral chains at two corners

of the unit cell are omitted [38] .

616
[1] was the first to determine the ordering scheme for MnNiGe from x-ray data and this places

Mn on the T position. This is plausible since Mn is the larger of the two transition metals

and the T position has the higher coordination number. One of the most studied pseudobinary

is (MnFe)2_xGe. Suzuoka et al. [26] have reported an ordered ternary phase Mno.9Feo.9Ge in

which Mn also occupies the T (octahedral, 2a) sites. Austin [27] has also shown that Mn

perferentially substitutes for Fe in the T positions for the part of the (Mn,Fe) 1 ^gyGe system

that has the Ni2ln structure.

4.2. TiNiSi-TYPE PHASES

Ordering of the metal atoms in ternary anti-PbCl2 type structures has been determined by

single crystal x-ray studies for TiNiSi [3] , ZrFeP [28] and MoCoB [29] . In all cases the

larger and more electropositive T atom occupies the site of higher coordination.

It has been pointed out [30] that compounds with the anti-PbCl2 structure can be divided

into two main groups, depending on the a/c ratio (setting Pnma) with considerable differences

in the number of nearest neighbors. The length of the short b axis has been taken as an additional parameter determining the coordination number [29] . A convenient expression for this

is (a + c)/b. The two parameters group the various PbCl2 structures (figure 4). Since the

atomic parameters are similar within any one group, the coordination polyhedra differ only

slightly within the group, but are entirely different going from one group to another. The

ternary anti-PbCl2 phases therefore belong to the C02P sub-group whereas the binary silicides

and germanides belong to the Co2Si sub-group.

An interesting question is whether the size factor is the only factor determining the

site ordering of the metal atoms in these phases. In all cases where the T atoms were found

on the site with the higher coordination number the T atoms also possess a lower number of d

electrons and are more electropositive, hence these results do not separate size and electronic effects. Wappling et al. [31] have emphasized this and have also shown from Mossbauer

0. 6S

Fig. 4. Grouping of PbCX,2 type compounds according

to their axial ratios [29] .

617

/
measurements on Feypo2-x^ R"2-x^®x^ with the anti-PbCl2 structure that the larger atoms

prefer the T site. In both cases, however, the materials could possess large degrees of disorder depending on composition, suggesting that the size factor is not overwhelming.

We have found that MnRhSi has the anti-PbCl2 structure. Since Rh is larger than Mn (Mn

has fewer d electrons) site occupancies for this compound should indicate the relative importance of size and electronic factors. Calculated x-ray intensities for both ordering schemes

as well as a disordered arrangement of Mn and Rh are compared in table 3. The data indicate

that Mn preferentially occupies the T site, while the larger atom, Rh, prefers the T' site^.

These results therefore point to d-electron configuration or electronegativity of the parti c- pating atoms as most influential in site occupancies.

It has previously been pointed out [32] that in phosphides, silicides, and germanides

with TiNiSi and Fe2P structures the ordering energy is apparently large since their homogenity ranges are extremely restricted to ideal compositions such as ZrFeP, NbMnSi and MnNiSi.

For example though atomic sizes are favorable and Ni2Si and Co2Si possess the anti-PbCl2

structure (Co2Si branch) , Mn is not soluble in them to a large extent, but the phases MnCoSi

and MnNiSi are found with the TiNiSi structure. Furthermore the ternary phases also have

restricted phase fields so that mutual s\ibstitution of the metal atoms is probably quite

small. These results also suggest that factors other than size contribute greatly to the

ordering energy.

Table 3

Calculated and observed intensities (powder dif fractometer data; CuKa radiation)

for MnRhSi. Positional parameters of TiNiSi [3] were used for the calculation.

101

002

Oil

200

102

111

201

210

112

202

211

103

013

212

301

113

020

203

302

004

4.681

3.569

3.352

3.100)

3.093f

2.949

2.843

2.401 ) 2,398 / 2.340

2.276

2.221

2.016

1.992

1.985

1.917

1.898)

1.888 f 1.788i

1.785 i

I^/

c

I Geometric Random Valence o Fit2 25 71 24 R

4 0 9 7 27 5 1 2 V,R

27 24 29 19

17 41 72 39 R

0 0 3 100 100 100 100

19 13 9 11 R,V

84 58 35 43 V,R

53 41 29 14 V

21 28 36 32 V,R

2 7 17 17 V

23 28 33 36 V

4 5 7 13 V

37 42 46 50 V

4 5 5 6

a/ Intensity calculations were done for the ordering schemes : Geometric - Mn in tetrahedral

and Rh in pyramidal site; Random - random distribution of Mn and Rh; Valence - Mn on pyramidal and Rh on tetrahedral site.

b/ It can be seen that the data indicate site preferences according to the valence scheme.

2lt would appear that the space-filling principle is violated; however, the coordinations of

these sites probably adjust to give a slightly different structure from that of TiNiSi. A

complete structure determination on MnRhSi should therefore be of interest.

618
4.3. Fe„P-TYPE PHASES

Kripjakevic et al. [33] were the first to report the ordering (table 4) for the equiatomic phases in the systems (Zr ,Hf ) -Ni- (Al ,Ga) . Analogous occupancies were found for CeNiAl

[13]. In these structures the Al atom is on the 3f site, and the T' atom is found on 2c and

Lb which sites correspond to the metalloid positions in TiNiSi . On the other hand, the site

occupancies found for the ternary borides, silicides, gennanides and the pseudobinary phosphides listed in table 4 correspond to the ones found for the TiNiSi structure.

At first it may seem surprising that, for example, the Ni atoms in CeNiAl and ZrNiAl do

not correspond to the Fe atoms in NbFeB. There are, however, structure-chemical arguments

for the support of both ordering schemes [9] : (a) Both Ni and B are the elements with the

smallest atomic volume in their respective compounds; they are therefore well-suited for the

2c and Lb sites which have the lowest coordination number. (b) Although aluminum is chemically

related to boron, silicon and germanium, it is known to behave sometimes like a transition

metal. For example, it is found in such typically inter- transition-metal structures as the

a-phase structure (a-Nb2Al and a-Ta2Al) . This makes the correspondence of the Al atom in

ZrNiAl with the Fe atom in NbFeB at least plausible. (c) In intermetallic phases of the large

transition metals of groups three and four with group eight elements, the elements of the

eighth group frequently occupy the boron positions in structure types such as CrB, FeB and

AIB2 (for examples see the compilation by Pearson [16] ) and thus have a coordination of nine

nearest neighbors which is also the case for the Ni atoms in CeNiAl and ZrNiAl. (d) The isotypy of many borides, phosphides, silicides and germanides , on the other hand, supports the

atomic order of NbFeB, NbMnSi , and TiCoGe.

In all Fe^P-type ternary phases the T atom is on the 3g site which has the larger coordination number. Thus the principle of good space filling is well preserved.

4.4. (TT')^Si^

The number of binary and ternary MnsSis type and the various "filled" Mn5Si;j type phases

is close to 200. In this account we limit ourselves to a review of site ordering on the 4d

and 6g metal positions.

Several (TT')5Si3 systems have been studied. Schachner et al. [35] showed that in the

pseudobinary section Ti5Si3-Mo5Si3 the Mn5Si3 structure extends from Ti5Si3 up to Ti3Mo2Si3

while in Ti5Si3-W5Si3 the substitution of Ti extends only up to Ti3 ,75Wi _25Si3 • In both systems it was shown through x-ray studies that both Mo and W preferentially occupy the 4d

position. In (Mn,Re)5Si3, Re occupies the 6gr position preferentially [36],

Recent Mossbauer effect and magnetic studies of the (Mn,Fe) ^Si3 series have been carried

out by Narasimhan et al . [37] and by Johnson et al. [38]. The two studies are not in complete

agreement but both show that Fe preferentially enters 4d with a small amount of disorder.

Compositional dependence of the lattice parameters, c/a ratios and magnetic irsoments of ferromagnetic compositions are also consistent with this ordering scheme [38]

.

Table 4

Atomi c Order in Fe2P -Type Structures (Space Group P62m

Pyramidal Tetrahedral

Phase 3(g) 3(f) 2(c) and 1(b) Reference

ZrNiAl Zr Al Ni 33

CeNiAl Ce Al Ni 13

NbFeB Nb Fe B 34

NbMnSi Nb Mn Si 6 TiCoGe Ti Co Ge ' 9 ZrRuSi Zr Ru Si 12

MnFeP Mn Fe P 32

CrFeP Cr Fe P 32

619
In all these systems, the larger atom occupies the position of higher coordination;

again, with the exception of (Mii,Re) 5813 , the larger atom is both more electropositive and

has fewer d electrons so these studies do not distinguish what influences atomic order most.

That the (Mn,Fe) ^Si-^ system is ordered despite the relatively small size difference between

Mn and Fe does point to the importance of electronic factors.

5. BONDING

In all the structures discussed, the basic triangular prismatic coordination of the metalloid is retained as in NiAs . This suggests similar metal-metalloid bonding. Axial ratios

of these Ni2ln-related phases indicate that metal-metal interactions are important. We attempt to assess the importance of these for the formation of these phases and in the particular structure type adopted.

For highly positive cations short metal-metal distances introduce core electrostatic re- pulsions, so these structures are not adopted by ionic compounds. However, in compounds of

the transition metals with the less-electronegative metalloids (IIIB, IVB and VB) , the effective charges on the metal atoms are small, and metal-metal bonding more than compensates for

the electrostatic repulsions due to short metal-metal distances. These ideas have been suggested by Goodenough [39] who discussed the crystal chemistry of binary pnictides and chalcogenides with NiAs-related structures. The influence of metal-metal bonding and its increased importance in the highly covalent metalloid phases are illustrated by the following

empirical findings [40]

:

(a) NiAs phases do not occur among the more ionic oxides and halides , nor with

nontransition metals that are not capable of d-electron metal-metal bonding.

(b) The MnP structure, with an even greater number of short metal-metal distances than

the NiAs structure, occurs when the metalloid is of groups IVB and VB but seldom when it is

the more electronegative chalcogen.

(c) There is a tendency to form "metal-filled" NiAs-related structures with more and

shorter metal-metal distances as the metalloid component becomes less electronegative.

Since bonding between transition metals and silicon or germanium is essentially covalent,

metal-metal bonding apparently contributes enough to the binding energy so that "metal-filled",

NiAs-related structures are frequently foimd for phases with these elements. The structures

in general differ in the strengths of the respective metal-metal interactions T-T, T-T' , and

T'-T'2[12]. In TiNiSi and ^^xj^uSi all three interactions are significant whereas in Ni2ln

only the T-T and T-T' are present. In Lhese three types the T-T' interaction is strongest

whereas in MnsSis the T-T and T'-T' interactions are much stronger than the T-T'. The metalmetal interactions are obviously quite sensitive to electronegativities, d-electron configurations, and relative size of the metal and metalloid. The particular structure is therefore

stabilized where these factors are such as to give the optimum binding energy. It has also

been argued [38] that the extremely close approach of metal atoms in 4d of Mn5Si3 may account

for this site preference by the less electropositive atom.

In TiNiSi and ZrRuSi the T'-T' distances are much shorter than in MnCoGe. There is

therefore a larger number of metal-metal bonds in the TiNiSi and ordered Fe2P types than in

Ni2ln. The seeming unimportance of the T'-T' interactions to the stability of the Ni2ln

structure may well account for the frequent occurrence of this structure for phases with ex- tended homogeneity ranges arising from variability in the T' concentration. Conversely,

phases with the anti-PbCl2 and Fe2P structures usually exist over more restricted ranges.

Also, the Ni2ln structure in preference to the Co2Si structure found for iron group phases

with the larger metalloids Ge and Sn presumably because, with Ge and Sn in combination with

the relative small iron group metals, metal-metal bond strengths are necessarily reduced.

This is also consistent with the fact that Ni2ln frequently occurs as a high temperature

phase.

3 The relative strengths of the various interactions can be approximated by the Pauling valence method [38] , or more qualitatively by comparing interatomic distances to radius

sums [12]

.

620
For (Mn,Fe)5Si3, it has been shown I38J that the magnetic moments of the component atoms

can be explained in terms of MO theory if valences of III and II are assumed for and M-j- ^

.

These valences are also consistent with Mossbauer results and Pauling valences of the metal

atoms with respect to Si. High or low-spin configurations for these atoms are not meaningful

concepts since the magnetic moments will depend on the details of the metal-metal interactions

(total d-band structure)

.

6. CONCLUSION

Additional studies of site occupancies and d-electron configurations of the metal atoms

in these phases will allow further insight into the factors that determine stabilities and

site preferences.

7, REFERENCES

UJ Castelliz, L, , Monatsh. Chem. 84, 765 (19531.

[2] Gladysheveskii , E. I., and Kuz'ma, Yu B. , Russ. J. Structural Chem. (Eng. Trans.) _1, 57 (1960) . [3] Shoemaker, C. B. and Shoemaker, D. P., Acta Crystallogr. 18_, 900 (1965).

I4J Ganglberger, E., Nowotny, H. , and Benesovsky, P., Monatsh. Chem. 98_ 95 (1967).

£5] Nickl, J. J. and Sprenger, H. , Natuz^v^issensch. _54, 248 and 515 (1967).

16] Deyris, B. , Roy-Montreuil , J., Fruchart, R. , and Michel, A., Bull. Soc. Chim. Fr. 1968 , 1303 (1968)

.

[7] Roy-Montreuil, J., Deyris, B. , Fruchart, R. , and Michel, A., C. R. Acad. Sci. Paris

262C, 615 (1968)

.

Jeitschko, W. , Jordan, A. G. , and Beck, P. A., Trans. Met. Soc. AIME 245 , 335 (1969).

Jeitschko, W. , Acta Cryst. B26 , 815 (1970).

Jeitschko, W. , Met. Trans. 1, 2963 (1970).

Deyris, B. , Roy-Montreuil, J., Roault, A., Fruchart, R. , and Michel, A., C. R. Acad. Sc. Paris 273C, 47 (1971)

.

Johnson, V. and Jeitschko, W. , J. Solid State Chem. 4_, 123 (1972).

Dwight, A. E., Mueller, M. H., Conner, R. A., Jr., Downey, J. W. , and Knott, H. , Trans.

Met. Soc. AIME 242 , 2075 (1968)

.

Kuz'ma, Yu B. , Gladyshevskii , E. I., and Cherkashin, E. E. , Russ. J. Inorg. Chem. (Engl.

Trans) 9_, 1028 (1964) . Bardos, D. I. and Beck, P. A., Trans. Met. Soc. AIME 236 , 64 (1966).

Pearson, W. B. , Handbook of Lattice Spacings and Structures of Metals and Alloys, Vol 2,

Pergamon Press, N. Y. (1967).

Jellinek, F. , Osterr. Chem. Zeit. 60_, 311 (1959).

Nowotny, H., andParthe, E. , Planseeber. 2, 34 (1954).

Parthe, E. , Jeitschko, W. , and Sadagopan, V., Acta Cryst. 19, 1031 (1965).

P5tzschke, M. and Schubert, K. , Z. Metallkde. 53, 474 (1962).

Rieger, W. , Nowotny, H., and Benesovsky, F. , Monatsh. Chem. 96_, 98 (1965).

Kanematsu, K. and Yasukochi, Ko., J. Phys. Soc, Japan 18, [10], 1429 (1963).

Forsythe, J. B. and Brown, P. J., Proc. Int. Conf. Magnetism, Nottingham, England, 1964,

p. 524.

Adelson, E., and Austin, A. E., J. Phys. Chem. Solids 26_, 1795 (1965).

Yasukochi, Ko and Kanematsu, K. , J. Phys. Soc. Japan 17_, Suppl. B-I, 165 (1962).

Suzuoka, T. , Adelson, E. , and Austin, A. E., Acta Cryst. A24 , 513 (1968).

Austin, A. E., J. Appl . Phys. 40, 1381 (1969).

Rundqvist, S., and Nawapong , P., Acta Chem. Scand. 20, 2250 (1966).

Jeitschko, W. , Acta Cryst. B24 , 930 (1968).

Rundqvist, S., Arkiv Kemi 2£, 67 (1962).

Wappling, R. , Haggstrom, L. , Rundqvist, S., and Karlsson, E. , J. Solid State Chem. 3,

276 (1971) . ~

Fruchart, R. , Roger, A., and Senateur, J. P., J. Appl. Phys. 40, 1250 (1969).

Kripjakevic, P. I., Markiv, V. Ja. , and Melnyk , Ja. V., Dopov. Akad. Nauk, Ukr. RSR

A29, 750 (1967) . Kuz'ma, Yu B. , Dopov. Akad. Nauk. Ukr. RSR A29, 939 (1967).

Schachner, H., Cerwenka, E. , and Nowotny, H. , Monatsh. Chem. 85, 245 (1954).

Setz, S., Nowotny, H. , and Benesovsky, F. , Monatsh. Chem. 99, 2004 (1968).

621
[37] Narasiiahan, K. S. V. L. , Reiff, W. M. , Steinfink, H., and Collins, R. , J. Phys . Chem.

Solids 31, 1511 (1970) . [38] Johnson V., Weiher, J. F., Frederick, C. G. , and Rogers, D. B. , J. Solid State Chem. £,

311 (1972).

[39] Goodenough, J. B. , Lincoln Technical Report 345, 1964, p. 11-12.

[40] Kjekshus, A., and Pearson, W. B. , Prog, in Solid State Chem. 1, 89 (1964).

DISCUSSION

g. Kostiner : You seem to be treating these compounds as having stoichiometries that are

as written. Have you investigated, chemically or physically, deviations of stoichiometry?

V. Johnson : This point has been looked at by several people, in particular for the titanium nickel silicide and the Fe2P type structures. I have looked at this myself and what

was initially quite surprising is that in these two structures the range of homogeneity is

quite narrow. This would suggest that there is very little mutual replacement of the two

transition metal atoms on the two sites. This is not true for the nickel 2 indium (Ni2ln)

structure where the ranges of homogeneity are much, much wider.

622
III. CHALCOGENIDES

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

STRUCTURAL TRANSITIONS OF SOME TRANSITION-METAL CHALCOGENIDES

F. Jellinek

Laboratorium voor Anorganische Chemie

Materials Science Center of the University

Groningen, The Netherlands

A survey is given of some recent investigations on transition-metal chalcogenides (sulfides, selenides, tellurides) carried out in the author's laboratory; particular attention is

paid to compounds undergoing structural transitions at elevated temperatures. Examples are given of transitions involving a change of the coordination of the metal (NbSe2 , TaS2, TaSe2

,

MoTe2 ; Ni3Se2) J of order-disorder transitions (AgCrSe2 and related compounds; chromium sulfides, Ni3±jjTe2) » and of transitions involving distortions of the structure (CrS ; VS , Nbi-^S) . The occurrence of trigonal-prismatic coordination in several transition-metal chalcogenides

is ascribed to d-covalency which stabilizes trigonal-prismatic with respect to octahedral co- ordination for ions with a d° , d-^ or spin-paired d^ configuration. The effect of the metal

coordination on the physical properties of the compound is also described. The distributions

of occupied and vacant metal sites in transition-metal chalcogenides Mi+pX2 are discussed

(chromium sulfides, zirconiiim selenides), as is the concept of "occupation waves" (titanium

sulfides) . In Ni3+xTe2 occupation waves lead to a phase lacking three-dimensional periodicity; the intervention of this phase allows smooth transitions from the disordered high-temperature form to the ordered low-temperature forms (two-step second-order transition)

.

Key words: Dichalcogenides ; intercalation compounds; layer structures; modulated structures; occupation waves; selenides; semiconductor-to-metal transitions; structure transitions; sulfides; tellurides; transition-metal chalcogenides; trigonal-prismatic coordination.

1 . INTRODUCTION

The crystal chemistry of the chalcogenides (sulfides, selenides, tellurides) of transition metals differs greatly from that of the oxides of the same elements. There are several

reasons for this difference in behaviour. Sulfur, selenium and tellurium are much less electronegative than oxygen. While most transition-metal oxides may be described as containing

0^- ions, in several chalcogenides (part of) the non-metal is present as X~ (X = S, Se, Te)

;

often, the X~ ions form pairs (X2)^~ [1]'^. The chalcogenide ions S^~, Se^~ and Te^~ have

much higher polarizabilities than has the oxide ion 0^~. Therefore, layer structures and

other structures with polar surroundings of the anions are quite common among the chalcogenides, but not for oxides. Actually, all dichalcogenides of transition metals have either

layer structures or structures with (X2) ^~ anions. Finally, the chalcogenide ions have dorbitals of accessible energy, which may participate in covalent bonds with the transition

metal. Therefore, the chalcogenide ions often have surroundings that are unusual for oxide

ions, for instance the trigonal-prismatic coordination of the anions found in chalcogenides

of the NiAs type and related structure types [2] .

In the present communication we shall discuss some recent investigations carried out in

Groningen, particularly those on transition-metal chalcogenides that undergo structural transitions at elevated temperatures. It need not be emphasized that such transitions have great

1 Figures in brackets indicate the literature references at the end of this paper,

465-504 O - 72 - 41 625
influence on the high-temperature behaviour of the materials; often, the structure transitions

also affect the mechanical, electrical, optical or magnetic properties which are of importance

for various applications. The examples we shall discuss comprise changes of the coordination

of some ions, distortions of the structures, order-disorder transitions and combinations of

these phenomena.

2. DICHALCOGENIDES

As mentioned, many dichalcogenides of transition metals have layer structures [3] . The

dichalcogenides of Ti, Zr, Hf have structures of the Cd(0H)2 type with axial ratios c/a near

the ideal value of 1.63; the coordination of the metal is octahedral. The same structure

type is found for the ditellurides of some group VIII metals, but here the c/a ratio is con- siderably smaller, probably due the mutual repulsion of the electrons in the dt2|-, levels of

the metals, which levels are more than half filled. These levels are less than half filled

in the ditellurides of V, Nb, Ta, Mo (h.t. form) and W which also have layer lattices with

the metal in essentially octahedral coordination; however, their structures are distorted

due to the presence of (zigzag or more complex) metal-metal chains. In ReSe2 [4], ReS2, and

probably also in the corresponding Tc compounds [5] the metal atoms form clusters which are again linked to chains. ' . _ .

The disulfides and diselenides of Nb, Ta, Mo and W are polymorphic [1,3]. At room temperature these compounds (and also MoTe2) have layer structures with trigonal-prismatic co- ordination of the transition metal. Molecular-orbital calculations indicate that d-covalency

provides a stabilizing factor for trigonal-prismatic with respect to octahedral coordination

for ions with a d^ , d^ or spin-paired d^ configuration. In trigonal-prismatic coordination

the (antibonding) d-level lowest in energy is an a;^ level. This explains that the disulfides

and diselenides of Nb and Ta , where the metal has d-^ configuration, are metallic, while the

corresponding compounds of Mo and W with d^ metal ions are diamagnetic semiconductors [2]

.

At about 850 °C, MoTe2 undergoes a transition leading from trigonal-prismatic to (distorted) octahedral coordination of the cation; this transition is accompanied by a change

from semiconducting to metallic properties, as can readily be understood from a band-structure model [5]. In NbSe2 [7], TaS2 [8,9] and TaSe2 [10] again trigonal-prismatic coordination of the metal is stable at room temperature, octahedral coordination at high temperatures;

in the intermediate temperature range modifications are found in which layers with the two

types of coordination alternate. The structures of the various forms of TaSe2 are shown in

figure 1, their thermal relationships in the following scheme [10]

:

Metal

coordination

:

trigonalprismaticmixed octahedral

Se-rich

;

Ta-rich:

4s(c)

2s (a> 3s (metastable)

790 °C

Is-TaSe'

860

The Is-forms of TaS2 and TaSe2 with structures of the Cd(0H)2 type can easily be retained at room temperature by quenching. Remarkably enough, these forms are diamagnetic semiconductors at low temperatures [9,11] , while the other forms of TaS2 and TaSe2 are metallic.

The diamagnetism of ls-TaS2 and ls-TaSe2 may be explained by considering the term scheme of

a d^ ion in octahedral coordination [12] ; the ^T2g level is split by spin-orbit coupling giving a ground state (r3) with zero magnetic moment, since g = 0. Nevertheless, the spins of

the Ta + ions (S = 1/2) will probably order at low temperatures; indeed, ls-TaS2 and ls-TaSe2

may be diamagnetic antiferromagnets or even diamagnetic ferromagnets at low temperature!

Thus, spin-orbit coupling stabilizes the d-^ configuration in octahedral coordination, while

the stabilization of d^(+d°) is smaller. Probably, this difference in stabilization causes

ls-TaS2 (and also BaTaSs , BaTaSe3) to be a semiconductor at low temperatures, while isostructural VSe2 (and BaVSs) where spin-orbit coupling is much weaker, is metallic [11]

.

625
o

o

Is

c 3s

'a

o ic

o c

2s(i)

2s^)

*•(•)

'8

<s(b)

TaStt.

o

45(C)

Fig. 1. Sections through the hexagonal (110) planes of

the polymorphic forms of TaSe2. Metal atoms

are indicated by black circles, chalcogen atoms

by open circles.

3. INTERCALATION COMPOUNDS A MX„

P 2 The dichalcogenides of Nb and Ta with trigonal-prismatic coordination of the metal exist

in several polytypic forms of nearly the same energy, which differ only in the stacking of

the XMX slabs (X = S , Se ; M = Nb , Ta) . It is understandable, therefore, that stacking faults

are frequently observed, for instance by the broadening and weakening of diffraction lines

with h-k 7^ 3n in x-ray powder patterns. The stacking order is greatly improved if additional

metal atoms are inserted between the NbX2 or TaX2 slabs. This is the case in the phases

Mi+pX2 (0 < p < 0.3 for X = Se 113]) shown in figure 2, and also in ternary phases ApMbX2

and A^TaX2, where A may be Cu or Ag (p ; 2/3), a 3d transition metal (p < 1/2 or 1/3) , an alkali metal (p ; 2/3) or Eu. The Cu and Ag atoms lie in tetrahedral holes between the NbX^

or TaX2 slabs [14] , 3d transition metals [15,16] and the light alkali ions in octahedral holes,

the heavy alkali ions [17] and Eu^+ [18] in trigonal-prismatic holes. The latter surrounding

can be understood by regarding the metal ions as d'^ ions [2] .

In all these phases ApMX2 the Nb or Ta atoms in the MX2 slabs have an electron configuration between d-"- and d^ and again a trigonal -prismatic coordination. In corresponding com- pounds of Mo and W these atoms would have a configuration between d^ and d^ and trigonalprismatic coordination is no longer expected to be stable. Indeed, such intercalation com- pounds derived from M0X2 or WX2 are not known, except for the highly reactive and unstable

compounds ApMoX2 and ApWX2 (p ; 1/2) where A is an alkali metal [19] . CoMo2Sit [20] and

similar compounds have Mo in essentially octahedral coordination.

Many other compounds ApMX2 SLre known where M is a transition metal in octahedral coordination. We mention only a few examples. In ApTiS2 where A is an alkali metal (p = 0.5 - 0.8) , the coordination of Ti is octahedral; the coordination of the alkali metals Li and Na

is also octahedral, but that of K and Cs trigonal-prismatic [21] . In CuCrX2 and AgCrX2 (X =

S, Se) the Cu and Ag atoms lie in tetrahedral holes between the CrX2 slabs [22] , though not

in the centers of these holes. At room temperature Cu and Ag occupy half of the tetrahedral

holes in a polar arrangement, at high temperatures they are distributed over all tetrahedral

holes (fig. 3) . The transition temperature of this order-disorder transformation lies at

200 °C for AgCrSe2, at about 400 °C for the sulfide compounds [23].

4. PHASES M,^ X,

l+p 2 Several transition-metal chalcogenides Mi+pX2 have structures intermediate between the

Cd(0H)2 type (p = 0) and the NiAs type (p = 1) with octahedral coordination of the cations.

Completely and partly (fraction p) filled metal layers alternate (fig. 4a). In most phases

627

;
Fig. 2. Sections through the hexagonal (110)

planes of the phases Nbi+pX2 and

Tai+pX2 (X=S,Se). Chalcogen atoms

are indicated by open circles, fully

occupied metal positions by black

circles, partly occupied metal positions

by crosses.

1V3

Fig, 3. Sections through the hexagonal (110) planes of

(a) NaCrX2 , (b) the low-temperature form and

(c) the high- temperature form of CuCrX2 and

AgCrX2 (X=S,Se). Chalcogen atoms are shown as open circles, Cr as double circles, fully

occupied positions of Na, Cu, Ag as black

circles, statistically occupied positions as hatched circles.

628
Fig. 4. Sections through the hexagonal (110)

planes of phases Mi^.pX2 with octahedrally coordinated metal atoms M. Chalcogens X are shown as open circles,

fully occupied metal positions as hatched circles, partly occupied metal

positions as black dots. The chalcogen

atoms are in (a) hexagonal close packing?

(b) cubic close packing; (c) packing of

the type chch.

Mi+pX2 the distribution of vacant and occupied metal sites in the partly filled layers is ordered, at least at room temperature. A good example is provided by the chromium sulfides

where ordered arrangements of ideal formulas CrySg [24], Cr5S5 , Cr^S^, Cr2+xS3, Cr2S3 [25]

and CrsSs [26] have been established (fig. 5). However, since the surroundings of occupied

and vacant metal sites are almost identical, unusually large proportions of Schottky defects

are present [27,28] and the various chromium sulfides are actually somewhat richer in metal

than indicated by the ideal formulas given [25] . The three-dimensional order of the vacancies in CrySe [24] and CrsSg [29] disappears at about 320 °C, that in CrsSii at 880 °C [30] , but the vacancies remain confined to alternate metal layers.

Many other transition-metal chalcogenides Mi+pX2 have quite analogous structures based

on a hexagonal close packing of the anions. In some cases, however, other packings of the

anions are found, again with the metal atoms in octahedral holes". The structure of Zri+pSe2,

for instance, is based on a hexagonal close anion packing for small values of p, on a packing

of type chch for intermediate values and on a cubic close packing for large values of p [31]

,

as shown in figure 4. Obviously, the radius ratio ^Zr/^Se large for structures with

a hexagonal packing of the anions to be stable, except for small values of p.

Similar arguments hold for the titanium sulfides in the range TiS2 - TiS . In the phases

TiS2 (hexagonal close sulfur packing) , TisSs (packing cchh) , and Ti2S3 (packing ch) completely

and partly occupied metal layers alternate, as in the other Mi+pX2 phases discussed so far.

629
OOOG

CXXXXX) ^^^^

Q0OOO ^^ocxf ©ooo mmmm

Fig. 5. In the room- temperature forms of the chromium

sulfides completely filled metal layers (a) alternate with partly filled layers (b-f )

,

in which the metal atoms (hatched circles)

and vacancies (open circles) are ordered.

Ordering of type (b) is found in CrySg,

(c) in CrgSg, (d) in CrgSi,, (e) in Crg+xSs

and Cr2S3, (f) in CrsSeIn Ti3S[+ (packing chchchh) , Tii^Ss (chchh) , and TisSg (chh) , however, the occupancy of subsequent metal layers is more complicated, as shown by figure 6. The figure suggests that the

occupancy may be described by "occupation waves". There are n such waves for 2n + 1 metal

layers; n = 0 for TiS (NiAs type) , n = 1 for TigSg, n = 2 for Tii+Ss, n = 3 for TisSi^, and n

=ci> for Ti2S3 [32]. The "occupation waves", in this case, are commensurate with the crystallographic lattice.

5. MONOCHALCOGENIDES

TiS is one of the few monochalcogenides which have a NiAs-type structure at room temperature. In several transition metal - chalcogen systems the composition of the NiAs-like

phase Mi+pX2 does not reach the limit of p = 1, in other systems it reaches it only at high

temperatures. In some cases, however, the structures stable at room temperature may be re- garded as simple distortions of a NiAs-type structure. The monoclinic distortion of the

structure of CrS causes the octahedra about the metal atoms to become elongated: Cr has four

sulfur neighbors at distances of 2.43 K, two more sulfurs at 2.88 A [25]. Evidently, the defoirmation of the structure is to be regarded as a Jahn-Teller distortion, due to the freespin d"^ configuration of Cr^+. This stabilization of the d^ configuration causes pure CrS

to be a semiconductor. At about 600 °C a transition to metallic conduction takes place; this

630
Fig. 6. The fractional occupation of successive metal

layers in the phases TiS , TisSg, Ti^Ss, TisSt^, and

Ti2S3; observed values of are indicated by

black dots. The stacking of the sulfur layers

between the metal layers is also given; c = cubic,

h = hexagonal close packed.

transition is not due to a simple structure transformation, but rather to the peritectoidal

decomposition of CrS into the high-temperature phase Cr^.j^S and chromium metal [24]

.

Other distortions of the NiAs type may be ascribed to the formation of chains , clusters

or three-dimensional networks of metal atoms. Three-dimensional networks of metal atoms are found in the hexagonal superstructure of FeS , stable below 140 °C [33] and in the orthorhombic structure (MnP type) of VS , stable below about 500 °C; the transition from the NiAs to the MnP type is of first order [34] . In the case of the phase Nbi_xS (0 ^ x < 0.08) a MnP-type

form is stable at high temperatures; the distortion from the NiAs type is more pronounced

than in VS , resulting in the formation of zigzag Nb-Nb chains (fig. 7a) . At 780 °C a transition takes place to a hexagonal low-temperature form of composition NbiiSi2? the structure

of which again is closely related to the NiAs type; nine of the metal atoms per formula unit

form triangular clusters, the remaining two being isolated, as shown in figure 7b [35].

6. METAL-RICH NICKEL CHALCOGENIDES

The metal-rich chalcogenides of Ni , Ag, and particularly of Cu undergo many structure

transformations of various types. We shall confine our discussion to the transitions of

Ni3+jjTe2 and Ni3Se2 which show some remarkaisle features. Above about 770 °C the phase Ni3+^

Te2 has a f.c.c. structure; the metal atoms are distributed over a n\imber of positions in the

cubic close packed lattice of the chalcogen 136,37]. At lower temperatures structures are

found derived from the Cu2Sb type. In this type the non-metal atoms form a (distorted) cijibic

close packing; half of the metal sites have tetrahedral, half have octahedral (or rather

square-pyramidal) coordination. In Ni3+j^Te2 the tetrahedrally coordinated metal sites are

Fig. 7. Projections of (a) the high-temperature form,

(b) the low-temperature form of Nb]^_jjS. Metal

atoms in alternate layers are indicated by heavy

and light contours, respectively; metal positions

in an undistorted NiAs-type lattice are indicated

by crosses. The sulfur atoms are not shown.

631
fully occupied, while about half of the square-pyramidal sites are vacant (fig. 8) . The oc- cupation of the latter sites is random above about 300 °C (tetragonal structure) ; ordered

arrangements of the atoms in these sites are found below 170 °C (Ni-rich side; monoclinic

superstructure) or 130 °C (Te-rich side; tetragonal superstructure) , as shown in figure 9 [36,38]. In the intermediate temperature range the structure is orthorhombic , but the (single-C2rystal and powder) x-ray diffraction patterns of the phase contain additional reflections which cannot be indexed in terms of the orthorhombic cell. The satellite-like extra

reflections can be explained by assuming a modulated occupation of the square-pyramidally

surrounded metal sites; the period of the occupancy wave is 2.33 times the orthorhombic a- axis [36j . It may be remarked that the room-temperature form of Cu^_^'Ie2t stable below 140

°C, also has a structure derived from the Cu2Sb type and modulated in a similar way [39].

The heat effects of the transitions of Ni3+jjTe2 at about 300° and 150 °C (and of Cu3_jj

Te2 at 140 °C) are very small and the transformations are close to second order. Analysis

in terms of Landau's theory shows that second-order phase transitions from the tetragonal

disordered phase directly to the ordered superstructures of Ni3+jjTe2 are not possible. However, second-order transitions (of type II) are allowed from either of these structures

to the orthorhombic structure which lacks three-dimensional periodicity. It appears, therefore, that the intervenient modulated structure makes a smooth path possible from the disordered high-temperature form to the ordered superstructures of Ni3+xTe2 [36]

.

Another interesting transition is shown by Ni3Se2. At room temperature this phase has

a rhombohedral structure based on a (slightly distorted) body-centered cubic packing of se- lenium. On heating, a transition to a f.c.c. form of the type described for Ni3+jjTe2 occurs

at 600 °C. When Ni3Se2 is cooled again, a transition of the f.c.c. form to a metastable tet- ragonal form is observed at 560 °C ; at about 530 °C this metastable form is converted to the

stable rhombohedral form [40] . The structure of the metastable tetragonal form is of the

(Ni ,Fe) 1 iSeg type [41]; it is based on a cubic close packing of selenium, just as the hightemperature form of Ni3Se2. It is understandable, therefore, that the transition from the

high- temperature f.c.c. form to the metastable tetragonal form is kinetically more favorable

than a transition to the stable rhombohedral form which has a structiire based on a b.c.c.

packing of the chalcogen [37]

.

Fig. 8 The structure of tetragonal

Ni3_^jjTe . Tellurium atoms

are shown by open circles,

fully occupied metal positions

(in tetrahedral coordination)

by black circles, partly

occupied metal sites (squarepyramidal coordination) by

hatched circles.

632
Fig. 9. Low- temperature orderings of metal atoms

(hatched circles) and vacancies (open

circles) in the square-pyramidal metal

sites of Ni3^xTe2 in (a) the monoclinic

superstructure of Ni-rich samples, (b) the tetragonal superstructure of Te-rich

samples. The tellurium and the tetrahedrally coordinated metal atoms are not

shown; cf. figure 8.

Several of the investigations discussed were supported by the Netherlands Foundation for

Chemical Research (SON) with financial aid from the Netherlands Organization for the Advancement of Pure Research (ZWO)

.

7. REFERENCES

[I] Jellinek, F., Chapter 19 in: Inorganic Sulphur Chemistry, G. Nickless, ed., Elsevier,

Amsterdam-London-New York (1968)

.

[2] Huisman, R. , de Jonge, R. , Haas, C, and Jellinek, F., J. Solid State Chem. , 3_, 56 (1971)

[3] Wilson, J. A. and Yoffe, A. D. , Adv. In Physics, 18_, 193 (1969).

[4] Alcock, N. W. and A. Kjekshus, Acta Chem. Scand. , 19_, 79 (1965).

[5] Wildervanck, J. C. and Jellinek, F. , J. Less-Common Metals, 24_, 73 (1971).

[6] Vellinga, M. B., de Jonge, R. , and Haas, C, J. Solid State Chem., 2_, 299 (1970).

[7] Kadijk, F. and Jellinek, F. , J. Less-Common Metals, 23_, 437 (1971).

[8] Jellinek, F., J. Less-Common Metals, 4_, 9 (1962).

[9] Thompson, A. H., Gamble, F. R. , and Revelli, J. F., Solid State Commun., 9_, 981 (1971).

[10] Huisman, R. and Jellinek, F., J. Less-Common Metals, 17_, 111 (1969).

[II] Geertsma, W. , Haas, C, Huisman, R. , and Jellinek, F., Solid State Commun., 10_, 75 (1972)

[12] Ballhausen, C. J., Introduction to Ligand Field Theory, McGraw-Hill, New York (1962).

[13] Huisman, R. , Kadijk, F., and Jellinek, F. , J. Less-Common Metals, 2_1, 187 (1970).

[14] van den Berg, J. M. and Kort, C. W. F. , J. Less-Common Metals, 13_, 363 (1967).

[15] Anzenhofer, K. , van den Berg, J. M. , Cossee, P., and Helle, J. N., J. Phys. Chem. Solids,

31, 1057 (1970) . [16] van Laar, B., Rietveld, H. M. , and IJdo, D. J. W. , J. Solid State Chem., 3_' 1^4 (1971).

633

/
[17] Omloo, W. P. F. A. M. and Jellinek, F. , J. Less-Common Metals, 2£, 121 (1970).

[18] Jellinek, F., Mater. Res. Bull., 6, 169 (1971).

[19] Rudorff, W., Chimia, 19, 489 (1965).

[20] van dan Berg, J. M. , Inorg. Chim. Acta, 2_, 216 (1968).

[21] Grams, G. , Dissertation, Univ. of Tubingen (1961).

[22] Bongers, P. F., van Bruggen, C. F., Koopstra, J., Omloo, W. P. F. A. M. , Wiegers, G. A.,

and Jellinek, F., J. Phys . Chem. Solids, 29_, 977 (1968).

[23] Engelsman, F. M. R. , van Laar, B., Wiegers, G. A., and Jellinek, F., to be published.

[24] Popma, T. J. A. and van Bruggen, C. F., J. Inorg. Nucl. Chem., 3]^, 73 (1969).

[25] Jellinek, F. , Acta Cryst., 10, 620 (1957),

[26] Sleight, A. W. and Bither, T. A., Inorg. Chem., 566 (1969).

[27] van Laar, B., Phys. Letter, 25A , 27 (1967).

[28] Popma, T. J. A., Haas, C, and van Laar, B., J. Phys. Chem. Solids, _32, 581 (1971).

[29] van Bruggen, C. F. and Jellinek, F., Propr. Thermodyn. Phys. Struct, des Deriv. SemiMetal., CNRS, Paris, p. 31 (1967).

[30] Erdos, E., Brezina, P., and Scheidegger, R. , Werkst. u. Korrosion, 22_, 148 (1971).

[31] Salomons, W. and Wiegers, G. A., Rec. Trav. Chim. Pays-Bas, 87_, 1339 (1968).

[32] Wiegers, G. A. and Jellinek, F., J. Solid-State Chem., 3^, 519 (1970).

[33] Evans, H. T., Jr., Science, 167 , 621 (1970).

[34] de Vries, A. B., Dissertation, Univ. of Groningen (1972).

[35] Kadijk, F. and Jellinek, F., J. Less-Common Metals, 19^, 421 (1969).

[36] Stevels, A. L. N., Dissertation, Univ. of Groningen (1969); Philips Res. Reports Suppl.

9 (1969) . [37] Stevels, A. L. N. and Jellinek, F., Monatsh. f. Chem., 102, 1679 (1971).

[38] Kok, R. B., Wiegers, G. A., and Jellinek, F., Rec. Trav. Chim. Pays-Bas, 84, 1585 (1965).

[39] Stevels, A. L. N. and Wiegers, G. A., Rec. Trav. Chim. Pays-Bas, 90_, 352 (1971).

[40] Stevels, A. L. N., Bouwma, J., Wiegers, G. A., and Jellinek, F., Rec. Trav. Chim. PaysBas, 87_, 705 (1968) . [41] RjzJst E. and Haugsten, K. , Acta Chem. Scand., 23_, 1601 (1969).

DISCUSSION

J. M. Honig : The model presented for explaining the semiconductivity of ls-TaS2 would

imply that the band gap is quite narrow and, therefore, the activation energy quite small;

is this correct?

F. Jellinek : The apparent activation energy of semiconducting ls-TaS2 at room temperature

is about 0.02 eV (reference 9), that of BaTaSs (also with Ta'^'^ in octahedral coordination)

about 0.06 eV (R. A. Gardner et al., Inorg. Chem. 8_, 2784 (1969)). Although it is not

certain whether these observed activation energies are the intrinsic values, they are quite

consistent with the model presented.

F. Holtzberg : Can one determine the anisotropy in electrical conductivity in the layer

type dichalcogenides?

F. Jellinek : The measurements on the electrical anisotropy are delicate, since the

crystals we obtained of the layer- type compounds were quite thin. Preliminary measurements

on the metallic forms of NbSe2 and TaSe2 indicate the conductivity perpendicular to the

layers to be somewhat smaller (by about one order of magnitude) than that within the layers.

However, these experiments may have been affected by several types of errors, again due to

the pronounced plate-like habit of the compounds under discussion.

F. Holtzberg : Have optical measurements been performed on layer-type dichalcogenides?

F. Jellinek : Due to the plate-like habit of these compounds transmission spectra

through the plates can readily be obtained (cf . reference 3) . The energy-band diagrams

proposed for these compounds (cf. reference 2) are partly based on such spectra.

A. Wold : In the model presented for ls-TaS2 the t2g level of the metal in octahedral

coordination is split by spin-orbit coupling. However, it is also split if the symmetry of

the environment of the metal is lower than cubic. By taking account of the latter splitting

we could explain some properties and structural features of marcasite-type compounds.

634
F. Jellinek : The term scheme presented (cf. reference 11) refers to a ion in

octahedral coordination. Actually, the environment of the metal in ls-TaS2 has only trigonal

symmetry 03;^ (perhaps even lower at low temperatures) . This leads to an additional splitting

of some of the energy levels, but the essential features of the scheme are not changed; the

ground state still has zero magnetic moment (g = 0)

.

635
I
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

SOLID SOLUBILITY IN THE FACE CENTERED CUBIC Gd Se, SYSTEM

X l-x

F. Holtzberg*, D. C. Cronemeyer, T, R. McGuire* and S. von Molnar*

IBM Thomas J. Watson Research Center

Yorktown Heights, New York 10598

The range of homogeneity has been studied in the face centered cubic GdjjSei_jj system.

The solid solution field is bounded by the composition x = 0.443 for excess Se and extends

through the stoichiometric composition to at least 0.512 for excess Gd. The lattice constant

decreases linearly with decreasing Gd concentration except at lowest values of x. The materials have been characterized by resistivity, reflectivity and magnetic measurements. The

results of the transport and reflectivity measurements are explained on the basis of a simple

single rigid band model. Magnetization measurements show that all compositions order antif erromagnetically with the Ne^l temperature, T^^, varying from ~ 20 to ~ 60 K and 6 from -25

to -135 K with increasing Gd or electron concentration.

Key words: Color-concentration dependence j gadolinium monoselenide ; Hall effect;

homogeneity range; magnetic ordering; reflectivity; resistivity; single crystal growth.

1. INTRODUCTION

The rare earth chalcogenides have been of considerable interest primarily because of the

relationship of their magnetic properties to electron concentration. This has been dramatically demonstrated in the semiconducting divalent europium chalcogenides EuS , EuSe and EuTe

and particularly in EuO , the only confirmed rare earth monoxide [1-5]^. Similar effects have

been observed in the Th3Pi| type RE3Se^-KE2Se3 solid solution systems [6,7]. During a recent

attempt to grow crystals in the Gd3Sei+-Gd2Se3 system in the vicinity of the 3:4 composition,

the primary crystalization phase was found to have a NaCl type structure with a deep blue

metallic color, the remaining phase being a eutectic composition of NaCl and the Th3Pi+ type

defect structures. The blue phase had a smaller lattice constant than that expected for

GdSe.

There has been evidence for some time in the literature, of compositional variation in

the trivalent monochalcogenides . landelli [8] noticed a color variation from yellow gold to red violet in the sulfides and selenides, which he attributed to incomplete or non-homogenous reaction. These were polycrystalline materials which were reacted in quartz at temperatures up to 1450 °C. M. Guittard [9] studied the range of homogeneity of all the rare earth

monosulfides using lattice constant variations of polycrystalline material to explore the

range of solid solubility. She found that the range of homogeneity increased with atomic

number. Furthermore, she determined from density measurements that the solid solubility was

on the metal- rich side with sulfur vacancies for all the rare earth sulfides except Lu, for

which the homogeneity range extended to both sides of the stoichiometric composition. In all

cases the lattice constant increased with increasing sulfur concentration.

*This research was supported in part by the Advanced Research Projects Agency of the Department of Defense and was monitored by the U. S. Army Missile Command under Contract No. DAAH01-71-C-1319.

^Figures in brackets indicate the literature references at the end of this paper.

637
The rare earth monochalcogenides are gold colored because the electron not used in bond

formation is believed to be in a band formed by 5d and 6s wave functions giving rise to the

metallic character. The ^87/2 ground state of Gd'^'^"'" provides an atomic moment of 7yg and is, as a pure spin state insensitive to lower order crystalline field splittings. The Gd-Se system was chosen for a study of compositional variation in the monoselenides since the interpretation of magnetization data does not present the complication of having to consider or- bital contributions to the magnetic moment.

2. EXPERIMENTAL

2.1. SYNTHESIS AND CRYSTAL GROWTH

Since, among other measurements, we elected to examine transport properties and reflectivity as a function of concentration, it became apparent that it would be useful to obtain

single crystals. In order to study the homogeneity range, two large charges on either side

of the stoichiometric composition were synthesized using the following procedure: All materials were handled in a He purged dry box. Metallic Gd sponge obtained from the Lunex Corp.

having a nominal 99.9 concentration and 99.999 Se from the United Mineral and Chemical Corp. were reacted by the vapor transport of Se to the gadolinium side of an evacuated and sealed

dual chamber quartz reaction tube. This reaction was carried out at a maximum temperature

of 500 °C because at higher temperatures there was evidence of quartz attack. Transport was considered complete when the characteristic color of Se vapor disappeared. The product of

this reaction is quite inhomogeneous . The entire charge was transferred to a large tungsten

crucible which was covered and sealed by electron beam welding. The crucible was then heated

to 1600 °C in the vacuum heated RF furnace described below. The two samples were powdered

and chemical analysis gave the Gd rich composition as GdSe^gg and the Se rich composition as Gd^72Se. A series of samples developed from mixtures of these two compositions were used

for crystal growth. Samples of approximately 6 grams were pressed into pellets which were sealed into 3/8 x 2 in. tungsten crucibles. Crystals were grown in an induction heated RF furnace (fig. 1) using a 10"^ torr vacuum to protect the crucible from surface reaction. A

split Ta shield surrounding the crucible reduced gradients and the crucible, suspended from

a fine Ta wire, was positioned to adjust the temperatiire profile along its length. Temperature measurement and control were achieved with an NBS calibrated LSN automatic optical pyrometer, surface temperature having been calibrated with a black body measurement obtained

with the same geometry. Samples were heated to the melting point and cooled at about a degree per minute to 700 °C at which point the power was turned off.

U&CUUM GAG£

PYROMETER

VIEWING PORTTO TURBOMOLECULAR PUMP

I Fig. 1. High temperature vacuum RF furnace.

638
2.2. X-RAY ANALYSIS

X-ray data were obtained with a Guinier focussing camera using Si as an internal standard. A least squares fit to the data gave a standard deviation of 0.001 A.

2.3. CHEMICAL ANALYSIS

Relative sample concentrations were obtained using an ARL EMX-SM electron microprobe

with Gd metal as a standard. The error in concentration from sample to sample was estimated

to be of the order of 0.5%. The composition scale was fixed with wet chemical analysis of

three of the microprobe samples. Gd was determined by a EDTA titration and Se by a permanganometric titration. The error in the analysis was estimated to be of the order of 1%.

An AEl MS-7 double focussing solid state mass spectrometer was used for impurity analysis of the Gd metal and several single crystals of the selenide. Y and Ho were found in the

100-200 ppm range and Cu, Si, 0, C and Na at the 100-300 ppm level. Synthesis and crystal

growth of the selenide led to small increases in Na and Cu concentrations and considerable

reduction in the C and 0 impurity levels. Since the small increase in Na and Cu concentrations (about 50 ppm) was not found to scale with Gd content, the effects of impurities on physical properties were considered to be negligible.

2.4 MAGNETIC MEASUREMENTS

Magnetization data were obtained with a force balance in fields up to 20 Kilogauss in

the temperature range 4.2 K to room temperature.

2.5. REFLECTIVITY

A Gary 14 R spectrometer, modified with a reflectivity jig for 10° incidence was used

for measuring the shift in reflectance spectra with composition. Instrumental corrections

were obtained with an evaporated gold film standard.

2.6 TRANSPORT MEASUREMENTS

A standard 5 probe D.C. technique was used to measure the resistivity as a function of

temperature as well as the Hall effect, wherever possible. Measurements were limited to signals greater than 10"^ volts.

3. RESULTS

A striking result of the crystal growth experiments is the dramatic variation of sample

color as a function of composition. The Gd rich samples were a bright yellow gold color and

as the Gd concentration decreased the color changed progressively to bronze, copper, red

gold, purple and at the lowest Gd concentration, a deep metallic blue. Since there was a small temperature gradient along the crucible during crystal growth, a concentration gradient

developed as the sample crystallized. Each single crystal ingot, therefore, graphically represented the crystallization process of the system. The initial crystallization was found

to have the highest Gd concentration or most gold-like color and the final crystallization

the lowest Gd concentration or most blue-like color, reflecting the range of solidus concentrations for a particular melt composition. Crystals of unifom color were cleaved from an

ingot for analysis and it was found that by carefully matching the color of crystals from

different areas it was possible to reproduce all physical measurements within the error of

each determination. The gadolinium rich compositions were found to melt at approximately

2350 °C. Melting temperatiires decreased smoothly to about 1750 °C for th.e blue, selenium

rich, phase.

Figure 2 is a plot of lattice constant as a function of concentration. The overall

decrease of lattice constant with increasing Se concentration is unexpected and contrary to Guittard's [9] results for Lus. It is possible that density determinations will shed some

light on the nature of the defect structure and provide an explanation for the lattice contraction. A straight line has been drawn through the stoichiometric composition. It is reasonable, however, to expect differences in slope on either side of this concentration. Al639
<S 5.79

Q 5.78 -

5.77

5.76

Fig. 2.

-T GOLD

^f- BRONZE

52 51

! COPPER

-i". RED GOLD

PURPLE BLUE

BLUE PURPLE

.50 49 .48 .47 46

MOLE FRACTION x in GdxSei-x 45 44

Lattice constant ao as a function of

composition x in Gdj^Sei-xthough the data illustrates the general trend shown by the straight line, additional measurements are necessary to show any detailed changes in slope.

In the composition range x = 0.443 to 0.463 the lattice constant goes through a minimum

as shown by the solid line. The lattice constant for the blue phase, (x = 0.443), is 5.770

which is identical with the value obtained from the NaCl pattern of the two phase region.

This composition therefore, represents the limiting concentration of the Se rich field.

It is also possible to draw a horizontal line (dashed line) which just touches the error

bars for the three data points used to define the minimum. Such a line of constant a^ would

indicate that this is a two phase region. This would place the solubility limit in the Se

rich field at x ~ 0.455. However, neither x-ray nor metallographic analyses showed any evidence of a second phase.

The results of the resistivity measurements can be suinmarized as follows: i) The bronze

and gold colored samples, which have comparably low resistivities, p, exhibit a temperature

dependence in p normal for magnetically ordered metals (lower curves in fig. 3) . The resistivity is linear in the paramagnetic region with a knee near Tj^ and drops precipitously as the temperature decreases towards 0 K. This is readily analyzed with three contributions to resistivity

22.5 r

""^0 50 100 150 200 250 300 350 TEMPERATURE CK

)

Fig. 3. Resistivity, p , as a function of temperature

(°K) for four compositions, x, in the Gd^Se^.^

system.

640
p = + p + p , L 1 m (1) where p-^ = lattice, p. = impurity and p^ = magnetic contributions to the resistivity. For

these two samples p^^^ is constant above Tj^ (only spin disorder scattering) which accounts for

the observed curve. ii) The resistivity as a function of temperature for both the blue and

purple samples are plotted in the upper part of figure 3. The room temperature resistivity

is higher (because the free electron concentration is lower) and the linear decrease in

with decreasing temperature reaches a minimum near 75 K, thereafter increasing to a constant

value at low temperatures. Again we might analyze the data with equation (1) with the ass\imption that p^^ includes a critical scattering term. On the other hand Tj^, from magnetic

data has not changed appreciably and it is unlikely that the resistivity will remain constant

below T^.

The Hall effect was measured at room temperature for the purple sample (Gd i+esSe 535)

and the carrier concentration derived by assuming a simple band was n = 1.4 x 10^^ cm~ 3. it

is possible to check the consistency of this number with other independent measurements as follows: if we assume that each Gd contributes one electron to the conduction band, simple

valence arguments lead to the expression

N I3x - 2 (1 - x) ] x2 = N (2) o where Nq = carrier concentration for the stoichiometric composition (x = 0.5) where x = composition. Solving for N^, using the experimental values x = 0.465 and n = 1.4 x 10^^ cm"^

,

one obtains = 2.2 x 10^^ cm~^ . On the other hand we can also calculate using the lattice parameter for stoichiometric material as = = 4/(5.78 x 10~^) ^ = 2.1 x 10^^ cm"^.

The agreement is very satisfying and lends evidence to our model of a simple rigid band in

which the number of free carriers is determined by the stoichiometry

.

It is also tempting to attribute the dramatic changes in color simply to changes in carrier concentration. Figure 4 shows reflectivity data for three representative samples. For

the case that the reflectivity minimum, Rmin' - ' dispersion relation for free carriers yields the following expression:

I I I 1

1 1-

I 2 3 4 5 6

Fig. 4. Percent reflectance R as a function of energy hv

.

641

465-504 0 - 72 - 42
where nig is the effective mass is the high frequency dielectric constant, n is the number

of free carriers per unit volume and ^xnin ^h^ wavelength at which Rj^in occurs. Since

vo= y, (3) can be rewritten as (hv) <^ n, and, assuming that m^ and do not vary substantially throughout the series, a plot of log n vs hv should yield a straight line with a slope equal to 2. We have assumed here that the reflectivity is dominated by free carriers

and that interband transitions, inc. perturb the spectra only slightly. Figure 5 exhibits

the results of such a plot. It is apparent that the curve is consistent with our model with

the exception of the lowest point.

All compositions in the solid solution system order antiferromagnetically . A rough measure of Neel temperatures indicates that they vary from ~ 20 K for x = 0.443 to ~ 60 K

for x = 0.512. A plot of paramagnetic 6 values as a function of composition (fig. 6) is

essentially linear with composition except for x = 0.443. Comparing these with the resistivity results we see that the negative exchange interaction increases strongly with electron

concentration.

109

S

7

6 -T 5

'eucT 4

CVJlOX

1- 3

KC

2

I 2 3 456789 10 he (eV)

Fig. 5. Carrier concentration, n, derived from

experimental composition, x, as a function of hv for which the reflectivity is a minimum. The data is

plotted on a log- log scale to demonstrate that n (hv)^ in the Gd^Se^.^

system.

Fig. 6. Paramagnetic Curie temperature, 6 , as a fiinction of composition, x, for Gd^Sei-x642
As we have shown the relationship between observed experimental parameters and composition is surprisingly direct, and in the case of resistivity and reflectivity is well explained by the simplest of all models, a single rigid band. It should of course be noted that in

all cases the lowest Gd composition appears to be anomolous , but the explanation probably

lies in the breakdown of the free electron approach at lowest Gd concentrations. The possibility of two phases can be ruled out from the lattice constant argument given earlier as well as on the basis of a more detailed examination of the susceptibility data. The limiting concentration of the Gd - Th3P4 solid solution system forming the boundary of the two

phase region is strongly ferromagnetic with 6 positive and equal to 88 K [5] . Measurements

on the eutectic phase also gave a positive 6. Any small amount of this ferromagnetic material in the composition x = 0.443 would show a deviation from the linear plot in figure 6 towards a more positive 0, which is contrary to experimental results.

4. ACKNOWLEDGMENT

We wish to thank P. G. Lockwood for sample preparation, R. B. Hamilton for resistivity

measurements, H. R. Lilienthal for magnetic measurements, J. D. Kuptsis for microprobe

analysis, R. W. Johnson for mass spectrometric analysis and B. O. Olson for chemical analysis.

5. REFERENCES

[1] Holtzberg, F. , McGuire, T. R. , Methfessel, S. and Suits, J. C. , Phys . Rev. Letters, _13, 18 (1964) . [2] Holtzberg, F. , McGuire, T. R. and Methfessel , S., J. Appl. Phys., 37_, 976 (1966).

[3J Von Molnar, S. and Methfessel, S., J. Appl. Phys., 38, 959 (1967).

[4] Oliver, M. R. , Kafalas, J. A., Dimmock, J. O. and Reed, T. B. , Phys. Rev. Letters, 24_, 1064 (1970)

.

[5] Final Report, Contract No. DAAH01-70-C-1309 , IBM, June 1971, AD-729355.

16] Holtzberg, F. , McGuire, T. R. , Methfessel, S. and Suits, J. C., J. Appl. Phys., 35,

1033 (1964)

.

[7] Loginov, G. M. , Sergeeva, V. M. and Bryzhina, Soviet Phys. Solid State, 12_, 2942 (1971).

[8] landelli. A., Rare Earth Research Ed. E. V. Kleeber, MacMillan, 1961, New York, 1_, 135.

19] Guittard, Mile M. , Compt, Rend., 261 , 2109 (1965).

DISCUSSION

M. J . Si enko : What is the magnetic moment? Does it correspond to gadolinium 3+?

F. Holtzbercj : The values or molar Curie constants are very close to theoretical

values for trivalent gadolinium but there is some variation over the concentration range. There have been several discussions with various people at this conference of why this

lattice constant decreases and why the sulfide one increases. One explanation could be,

in this system, and I don't think this is necessarily correct, that at the high electron

concentration you have a d-electron that is localized around gadolinium giving the ion a larger size. As you decrease the electron concentration, the lattice constant would shrink.

I favor the picture that we just have vacancies on the rare earth site and that the lattice

shrinks around those vacancies.

R. S . Roth : Do you think there is any chance of low temperature annealing giving

rise to any ordering in such a system?

F. Holtzberg : We did not anneal below 1600 °C , and I don't have any idea as to whether

we would find ordering at lower temperatures; it is something we should study. We did

examine some samples from the higher temperature annealing but found no evidence of ordering.

J. Flahaut : I want to first say that the monochalcogenides are very difficult to prepare, and you have made a very good contribution to this program. It seems to me that in

your solid solutions through the 1:1 composition don't you observe some discontinuence in

the properties, the physical properties, to the 1:1 composition?

643
F. Holtzberg : That is one of the problems. We don't see it in the magnetization data

but I'm not sure that would be the most sensitive way to look for it. The most sensitive

way would be, I think, to do all the conductivity around that region and to do more samples

at the 1:1. If you noticed, we did not have that composition in time for this slide.

644
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

TERNARY CHALCOGENIDES OF LIGHT RARE EARTH ELEMENTS WITH

TRANSITION ELEMENTS

G. Collin, H. D. Nguyen, 0. Gorochov, M. Guittard,

P. Laruelle and J. Flahaut

Latoratoire de Chimie Minerale - Laboratoire de Physique

Faculte Des Sciences Pharmaceutiques et Biologiques

Universites Paris V et Paris XI - 4 Avenue de 1 ' Observatoire , Paris 6°

Description of three new crystal families. Crystal structures. Magnetic properties.

1) La2Fe2S5-type - orthorhombic A2iam. 2) LasFesS^ 5-type - monoclinic Bm. These two

structures have similarities. The rare earth atoms are 7-8 coordinated. The Fe atoms have

two kinds of environments: 4-coordinated in a distorted tetrahedron of S atoms, 5-coordinated in a distorted octahedron of S atoms. In both cases 2 neighboring Fe atoms are associated by 2 intermediate S atoms. These 4 atoms fo2rm a distorted quadrilateral with Fe-SFe angles not far from 90°. 3) CeCrSe3-type - orthorhombic Pnam. The rare earth atoms are 9-coordinated , and the Cr atoms are 6-coordinated , inside a nearly regular octahedron of se- lenium. As in the preceding structures, 2 neighboring Cr atoms form with 2 intermediate Se atoms a nearly regular square

.

These compotinds are antiferromagnetic at low temperature (Neel temperature for LaCrSeo:

165 K) . Weak ferromagnetism appears at lower temperature.

Key words: Crystal structure; magnetic properties; rare earth; ternary chalcogenides

;

transition metals.

1. INTRODUCTION

We describe here three kinds of new compounds, which contain transition elements - especially Fe and Cr - and light lanthanides - especially La -. There are: La2Fe2S5

LasFesSis

LaCrSe3

The two first are only known with sulfides, the last one exclusively

First of all, the crystal structures were established, with single crystals, before

studying the magnetic and electrical properties. For some of these compounds, the study of

the physical properties is still in progress. The formula of the second compound, which was approximately deduced from chemical evidence as being La2FeSi4 , was definitely established

from the crystallographic study.

2. COMPOUNDS OF THE la^^e^S^ TYPE

2.1. STRUCTURE OF La Fe S^.

2 2 5

The tetramolecular orthorhombic cell has the dimensions:

a = 11.40 A b = 16.55 K . c = 4.055 A.

and related compounds,

exists with selenium.

645
The space group is A 2iain (N° 36) , with all atoms in the special positions (with (000; 1/2,

1/2) + ) : 4a xyO -(x + 1/2) , y, 0

with

:

X y

4 La I 0.058 0.377

4 Lall 0.443 0.376

4 Fe I 0.231 0.702

4 Fe II 0.211 0.071

4 S I 0.098 0.199

4 S II 0.404 0.199

4 S III 0.241 ' 0.849

4 S IV 0.025 0.000

4 S V 0.299 0.542

The reliability factor is 0.068 for 342 independent reflections. The two La atoms (fig.

1) are surrounded by 8 S atoms; 6 of which are on the corners of a trigonal prism, and the

two others in the equatorial plane of the prism, in front of the lateraj. faces. The Fe I atom is at the center of a distorted octahedron with 3 Fe-S distances of 2.43-2.53 K, and 3 other ones of 2.75-2.81 A. The Fe II atom is inside a distorted tetrahedron of S atoms, with

Fe-S distances of 2.29, 2.29, 2.43 and 2.49 A.

Each kind of Fe atom forms a zig zag chain Fe - S - Fe - S parallel to the c axis.

The chain formed by Pe I is directly bonded to the chain formed by Fe II , and together they

constitute a column through the structure, parallel to the c axis. In the column, the interatomic distances are: Fe II - S I : 2.48 A; S I - Fe I: 2.53 A; Fe I - S V: 2.76 A; S V - Fe II: 2.25 A. The Fe I - Fe II distance is 2.98 A.

b

Fig. 1. Projection along the c axis of the

orthorhombic structure of La2Fe2S5.

The iron atoms are black. The

sulphur atoms are large circles

and the lanthanum atoms are small

circles

.

646
Two neighboring columns are bounded by lanthanum atoms. A recent study of this com

pound showed the presence of vacancies on the Pe II tetrahedral positions, in relation to a partial siibstitution of Fe^"*" by Fe^"*". At the limit the true composition would be La2Fe^"'" (Fe|^3 1/3) S5 , with a possibility of a small homogeneity range.

2.2. OTHER COMPOUNDS

The two kinds of Fe atoms have quite different coordinations, and the synthesis of other compounds having this crystal type is in agreement with this observation. Really the

general formula of these compounds is L2BCX5 . The B site can only be occupied by usually

tetracoordinated atoms, as Zn. The C site is only occupied by usually hexacoordinated atoms

Ti", V", Cr" , Mn" , Co". These compounds exist with the biggest rare earth atoms: La in

each case and Ce in a few cases (for Ce2Fe2S5, Ce2ZnMnS5 and Ce2ZnFeS5)

.

3. COMPOUNDS OF THE LagFe3S^g CRYSTAL TYPE

3.1. STRUCTURE OF La Fe,S-_. >

The tetramolecular monoclinic cell has the dimensions

a = 16.55 A b = 10.85 A c = 13.98 A y = 102.91°.

It is related to a pseudo hexagonal subcell, with

a, = 8.10 A c, = 7.24 A

h h

which correspond the only reflections observe on the powder diagrams. This pseudo hexagonal

cell is six times smaller than the monoclinic cell.

The atoms are on the positions 2a and 4b of the space group Bm {N° 8) . The reliability

factor is 0.077 for the 1000 strongest independent reflections.

o o All the La atoms have coordination 7-8, with La-S distances from 2.76 A to 3.20 A. The Fe atoms, as in the preceding structure, have two different environments: in each cell

4 Fe atoms have four-fold coordination, inside distorted tetrahedra and the other 8 Fe atoms

are 6-coordinated , inside distorted octahedra.

In this structure, from which the asymmetric part of the cell is viewed figure 2, the

Fe atoms form clusters with Fe - S - Fe - S arrangements , separated by lanthanum and sulphur

atoms and by large cavities.

3.2. OTHER COMPOUNDS

As in the preceding structure, the two kinds of sites of the Fe atoms should be distinguished, and the general formula of this compound should be L8BC2X15 where the B sites are occupied by usually tetracoordinated atoms, and the c sites by usually hexa-coordinated atoms. At the present time, only four compounds are known with the lightest rare earths:

LagFeaSis, LasMnsSis, LagCrsSis and CeeFeaSis.

4. THE LCrSe^ FAMILY

4.1. STRUCTURE OF CeCrSe . 3 The tetramolecular orthorhombic cell has the dimensions:

a = 8.08 A b = 13.74 A c = 3.952 K. The atoms have the positions 4c of the space group Pnam (N°62)

:

± X, y, and ± + x, i - y, i)

647
La^Fe S

8 3 15 Fig. 2. Projection along the c axis of the

structure of La8Fe3Si5. The iron

atoms are black. The sulphur atoms

are large circles and the lanthanum

atoms are small circles.

with

X y

Ce

Cr

Se I Se II Se III

0.0950

0.3427

0.1907

0.3407

0.4832

0.1711

0.9480

0.7889

0.5040

0. 1099

The reliability factor is 0.046 for 487 independent reflections. This structure is

identical to that of NHt^CdCl3 , which was previously known for 4 ternary chlorides.

The Ce atoms are nine-coordinated. They are at the center of a triangular prism of se- lenium atoms, with three other Se atoms in front of the rectangular faces, in the equatorial

o plane. The Ce-Se distances have an average value of 3.08 A for the 6 Se atoms at the cor- ners of the prism, and of 3.19 A for the 3 Se atoms in front of the faces.

The Cr atoms are at the center of a nearly regular Se octahedron with 6 distances Cr-Se

between 2.50 and 2.59 A. There appears in this structure nearly regular sguare arrangements

of 2 Cr atoms and 2 Se atoms: the lengths of the sides are 2.50 and 2.55 A, and the angles

are 88.25° and 91.35° (fig. 3).

4.2. OTHER COMPOUNDS

The high coordination number of the lanthanide sites is the reason why this family is

only known with the first elements of the rare earths from La to Nd.

Similar compounds do not exist with other trivalent transition elements, or with sulphur instead of selenium. Large single crystals of the La, Pr and Nd compounds were obtained by a flux method using the iodides of the corresponding rare earth.

648
Fig. 3. Projection along the c axis of the

structure of CeCrSe3. The chromium

atoms are black. The selenium atoms

are large circles and the cerium atoms

are small circles.

4.3. MAGNETIC PROPERTIES

The magnetic susceptibility of these four compounds was studied between 7 K and 800 K. Powder and large single crystals lead to the same results. All these compounds are antiferromagnetic and we sum the results in table 1. At a temperature slightly lower than the

Neel point we observed the appearance of an added weak ferromagnetism . But this phenomenon

remains very weak for all low temperatures (down to 7 K) . At high temperature these compounds show a paramagnetic law (X = _£_) . The Curie constant related to chromium as calculated for these compounds is about 1.6'

The curves (fig. 4) show that only chromium is oriented below Neel temperature. On the

other hand the rare earth follows a paramagnetic law at all temperatures.

We interpreted the magnetic properties in direct relation with the crystal structure.

The three kinds of new compounds which have been described above have two different

environments for the transition element: a mixture of 4 and 6 coordination in the La2Fe2S5

and La3Fe3Si5 types, and a 6 coordination with a nearly regular octahedron in the CeCrSe3

type. But in both cases two transition element atoms have neighboring positions; so, direct

and indirect M - X - M interactions are possible. Known magnetic properties show that magnetic ordering appears at low temperature, and depends only on the transition element.

649
(1) w

uu

m

Preparation

A2

A3

Bl

B2

Cl

C2

C3

0 (°K)

P

Table 1 Magnetic Properties of LCrSe3 Compounds

C

+ 99

T^(°K)

160 110

165 <77

160 <77

160 107

165

165 <77

167 77 165 90

160

( °K)

exp

(Mol.)

1.63

Ln

3+=C -C^ 3+

Cr Mol Ln

1.63

0) w

MO

(1) U

Bl

+ 50 171

175

130

135

2.30 0.82 1.48

0) w

uu

CM

Al

Cl + 10 (170) (160-

165)

3.26 1,64 1.62

NdCrSes Al -25 (183) (172) 3.41 1.69 1.72

A

B

C

Tn

ep

Tf

^exp

CLn3+

Ccr3+

preparation from oxides + H2Se at 1200° C. preparation from elements in sealed evacuated tubes,

crystals.

Neel temperature.

Curie paramagnetic temperature,

antiferro ^—- ferromagnetic transition,

experimental Curie constant,

calculated Curie constant for L" Curie constant for Cr^"^.

3 +

Fig. 4, Variation of the inverse of

the magnetic susceptibility,

for 3 samples of LaCrSe3: 2 single crystals and one polycrystal sample.

T'K307

650
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

CRYSTAL CHEMISTRY OF METAL-RICH REFRACTORY SULFIDES*

Horng-yih Chen and Hugo F. Franzen

Institute of Atomic Research and Department of Chemistry

Iowa State University

Ames, Iowa 50010

Systematization of the crystal structures of metal-rich chalcogenides was attempted with

emphasis on the coordinations of a few key metal atoms. This approach gave a more complete

interpretation of many chalcogenide structures, notably those of Ta2S, TagS and Nb2Se, than

did the conventional descriptions using the packing of the coordinations of the chalcogen

atoms. The pursuit of this approach led to the recognition of a polyhedron, which, owing to

its repeated presence in many metal-rich compounds, appeared to be of great importance in

crystal chemistry. It is a two-centered polyhedron formed by the interpenetration of two C. N. 14 Kasper polyhedra in such a way that the center of one of the Kasper polyhedra is the

apex of another. The presence of a very short interatomic distance between the two centers

is one of the important features of this polyhedron. With the help of this polyhedron as the

building block, the structures of Zr9S2, a-V3S and 3-V3S were satisfactorily described and

correlated; the short interatomic distances in the structures could be explained semi-quantitatively; and the structural differences expressed by the different packing schemes of the

polyhedra and the different positions the sulfur atoms occupied in the polyhedra. The description using the two-centered polyhedra as the basic units was extended to the structures

in phosphide systems and provided new structural evidences to the similarities and distinctions among the Zr9S2-, cl-Y^S-, 3-V3S-, Fe3P- and Ti3P-type structures, and to the correlation that the Fe3P structure is the high temperature form of the Ti3P structure. The smooth

correlation between the sulfides, Zr9S2, a-V3S and 3-V3S, and the phosphides and related com- pounds renders further support to the speculation that these sulfides possess the nature of

intermetallic compounds.

Key words: Crystal structure; intermetallic; phosphides; refractory; sulfides; transition metal; coordination polyhedra.

1. INTRODUCTION

Earlier studies on refractory metal sulfides by high temperature techniques were focused

mainly on the composition range from sesquisulfides to monosulfides , In recent year's composition ranges under study were extended to the metal-rich regions, and the results revealed a number of new compounds. Owing to the fact that the compositions of these new compounds are

not predictable on the basis of conventional concepts in chemistry, the identification and

characterization of these compounds relies very heavily on their structure determinations.

Because of the insufficiency in available data the metal-rich sulfide structures have not yet

been systematized, and the descriptions and the interpretations of these structures have, so far, been carried out by the extension of the concepts generally accepted for metal-rich borides, silicides and phosphides. The idea was to regard the structures of the sulfides as being built up of trigonal-prismatic coordination polyhedra for sulfur atoms. In general,

this approach has yielded satisfactory understanding of the sulfide structures. Difficulties

Work was performed in the Ames Laboratory of the U. S. Atomic Energy Commission.

Contribution No. 312 7.

651
were encountered, however, in the application of this description to the cases of Nb2Se [1]^,

Ta2S [2] and TagS [3], in which, particularly the former two, the presence of trigonal-prismatic coordination for the chalcogenide atoms was not apparent. Instead, very clear pictures

could be obtained when the Ta2S and TagS structures were described as the packing of icosahedral tantalum coordination polyhedra. Similarly, the interpretation of the crystal structure

of Zr9S2 can be accomplished with greater ease if the coordination polyhedra of the metal,

instead of the sulfur atoms, are used as the basic building units [4]. Clearly, a new ap- proach to the description and systematization of the sulfide structures is desirable. The

present study was undertaken with the purpose of systematizing the structures of the refractory transition-metal sulfides with emphasis on the coordinations of the metal atoms.

2, SURVEY ON METAL-RICH SULFIDES

Some sulfides and the structure types to which these sulfides belong are listed in table 1. Also listed in the table are the sulfur coordinations and the coordination of the

metal atoms which form the basic units. All the listed compounds are hard and brittle and

exhibit metallic luster. They are refractory and do not exhibit appreciable homogeneity

ranges. Most of the compounds listed were synthesized easily by high tem.perature techniques,

such as arc-melting, high temperature annealing, etc. Nb^i+Ss, however, formed with great

difficulty. More entries to the listing are likely in the near future. Structure-wise,

these structure types can be grouped into four classes as indicated in the table.

Table 1

Structural Classification of Refractory Metal-Rich Chalcogenides

.

Structure

type

Compound Chalcogen

coordination

Metal

coordination

Ta2P Ti2S[5] , Zr2Sl6] , Zr2Se[6]capped tri prism. cubic

Nb2iS8 Nb2iS8[7] , Zr2iS8[6J capped tri prism. cubic

Nbi^Ss Nbi^SstS] capped tri prism. cubic

Hf 2S Hf2S[9] , Hf2Se[6] tri . prism octahedral

Nb2Se Nb2Se[l] incomplete

prism.

tri cubic

Ta2S Ta2S [2] incomplete

prism.

tri. icosahedral

TagS TagS [3] capped tri. prism. icosahedral

a-VjS a-V3S [10] square-antiprism. C.N. 14

Kasper

polyhedral

3-V3S B-VgSllO] square-antiprism. C.N. 14

Kasper

polyhedral

Zr9S2 Zr9S2 [4] square-antiprism C.N. Ka sper

polyhedral

1 Figures in brackets indicate the literature references at the end of this paper.

652
3. STRUCTURE OF COMBINED SULFUR AND METAL COORDINATIONS

The first group of structure types to be discussed contains the Ta2P/ Nb2iS3 and Nbj4S5

structures. These structures have been well recognized for the ubiquitous presence of capped

trigonal-prismatic coordinations of sulfur atoms in the diverse structures. Also clearly observable is the presence of fragments of the body-centered cubic structures of the metals.

Chains of metal-atom cubes perpendicular to mirror planes are formed in a variety of ways in

these structures. The unit of the chains in the Ta2P structure is formed by two body-centered

cubes sharing faces. There are two different kinds of cube-chains in Nbii^S5 and Nb2iS8 structures. In Nb]^i4S5, there is one type of cube-chain made up of two body-centered cubes interpenetrating in such a way that the body-center of one cube is the corner of another, and an- other chain is made up of three cubes arranged in a T-shape. In Nb2iS8 one chain is made up

of four cubes in a cross-shape and another of single cubes. However, because of the complexity of the structiires, the description can only be completed with the additional consideration of the trigonal-prismatic coordination polyhedra of the sulfur atoms. Since the trigonal prism has a very high compatibility with cubes and there is a variety of ways to form the

cube-chains, a large number of compounds, including many borides, silicides and phosphides

[11] , have structures formed with the cube-prism combination. This group of structures is

characterized by the presence of a short axis equal to tlie edge of the cubes and parallel to the cube-chains

.

The two hafnium compounds form a group. In this group there is a short axis but hafnium

does not form cube-chains as has been commented upon by Franzen, Smeggil and Conard [6] , based

on the Engel-Brewer correlation [12]

.

4. STRUCTURES BY PACKING OF METAL-CHAINS

The third group of compounds includes Nb2Se, Ta2S and TagS. While in Nb2Se and Ta2S the

chalcogen coordinations are not clearly trigonal-prismatic, the Ta2S and TagS structures contain one type of Ta-atom which has no sulfur atoms as its nearest neighbor, and the structures

can not be satisfactorily described based on the chalcogen coordinations alone. The difficulties encountered can be avoided if the coordinations of the metal atoms are emphasized in

the structure description. From the point of view of metal coordinations, the description of

the structures of Ta2S and TagS is quite obvious, namely the packing of Ta atoms arranged in

continuously interpenetrating icosahedra with the sulfur atoms filling the voids created in

the packing. In Ta2S , the packing is rectangular and the relatively large voids are filled

by clusters of sulfur atoms forming octahedra with a void in the center. In TagS, it is twodimensional close-packing, and the voids are only large enough to accommodate a single sulfur

atom. It has been suggested that the tendency for tantalum to form icosahedral coordination

is associated with its low-lying d^ state.

This approach can also be successfully applied to the Nb2Se structure. The structure of

Nb2Se is extremely similar to that of Ta2S if the icosahedral chains of Ta atoms in the latter

are replaced with cube-chains of Nb atoms, as shown in figure 1. The basic unit of the cubechains of Nb atoms is formed by the interpenetration of two body-centered cubes as the one found in the Nb2t+S5 structure. The voids created in the packing of the cube-chains are again filled with clusters of chalcogen atoms in an octahedral arrangement. The chains are parallel to the short axis and are packed rectangularly as in the case of Ta2S . Based on the

Engel-Brewer correlation, the preference of Nb atoms to form cube-chains instead of icosahedron-chains , is understandable in terms of the low-lying sd^ state of the Nb atom and the

relatively high-lying d^ state 12]

.

5. COMPLEX PACKING OF TWO-CENTERED POLYHEDRA

The structure interpretation emphasizing the transitions-metal coordinations becomes the

most interesting and probably the most significant when applied to the fourth group of the

sulfides. There are only three known compounds in this group, namely Zr9S2, a-V3S and B-V3S.

However, the conclusions reached can be extended smoothly to include no less than 30 phosphides and related compounds. A tetragonal symmetry and the absence of a short axis distinguish these structures from those discussed earlier. The structures of these compounds have

very similar polyhedra built around metal atoms as basic units, and resemble in many ways the

structures of intermetallic compounds, even though they contain sulfur or phosphorus which

are conventionally not considered as metallic. The complete listing of the compounds known

653
- o o

o o

Fig. 1. Two unit cells of Nb2Se structure

projected on (010) , emphasizing the

units formed by the interpenetration

of the body-centered cubes of Nb atoms

.

in this group, including phosphides and the related compounds according to Lundstrom I13J

,

and the five structure types they belong to, are shown in table 2. The structures of ZxqS2

and a-V3S will be discussed in detail and comparison will be made with the other three structure types

.

Table 2

Sulfides, Phosphides and Related Compounds with the

Two-Centered Polyhedra as Their Structural Unit.

Stiructure Compound

type

ZrgS2 ZrgS2

a-V3S a-V3S, M03P, W3P

3-V3S 6-V3S

Fe3P Cr3P, Mn3P, Fe^P , NisP, Fe3 (Pq ,7iBo _ 29) ' Pd3As,

Zr^Sh, Hf3Sb, Ti3Ge, Ta3Ge (h.t.)

TigP (Feo. 8^60.2)32, Fes (P0.37B0.53) ' ^13?, V3P, ZrsP,

NbsP, Hf3P, Ta3P, Zr3As, Nb3As, Ti3Si, Zr3Si,

Nb3Si, Ta3Si, Zr3Ge, Hf^Ge, Ta^Ge (l.t.)

5.1. ZrgS^

The crystallographic data and atomic parameters for Zr9S2 are tabulated in table 3 and

4, respectively, and the coordinations for the six independent atoms are shown in figure 2. The sulfur atoms are coordinated with eight metal atoms in a square-antiprismatic arrangement as in the cases of a-V3S and 3-V3S. But, for the purpose of this study, the most important coordination is that for Zr(2), around which the two sulfur and 12 zirconium nearest

neighbors form a distorted C.N. 14 Kasper polyhedron [14] . This polyhedron differs from the

icosahedron around Ta atoms in Ta2S and TagS in that two sulfur atoms replace two zirconium

654
Table 3

Crystal Data for Zr9S2.

Composition

Density

Diffraction Symbol

Space Group

Lattice Parameters

ZrqS9&2

'obs 6.38g/cc (cicalc = 6.442g/cc)

14/mmm Body-centered tetragonal system

14i/amd (No. 141)

a = 9.752 A

c = 19.216 K

Number of Atoms

Table 4

Refined Atomic Parameters for ZrgS2.

Wyckof

f

Point

Atom notation sym. X _z_ z e(A2)

Zr(l) 16(f) 2 0.1788 (2) 0 0 0.51(4)

Zr(2) 16(h) m 0 0 3014 (1) 0 3014 (1) 0.39(5)

Zr(3) 16(h) m 0 0 0789 (3) -0 4309 (1) 0.53 (5) Zr (4) 16(h) m 0 -0 .0289 (3) 0 1422(1) 0.51(5)

Zr(5) 8(e) mm 0 0 25 0 ,0106(2} 0.63 (71 S 16(g) 2 0.2723 (4) 0 25 + X 7/8 0.37(10)
atoms at 1 and 3 positions in one of the hexagons. As will be concluded later, the polyhedron is a basic unit of the building blocks of the structure, the sulfur atoms in ZryS2 do

therefore participate in the formation of the basic unit and are not located in the regions

created by the packing of the basic units. The substitution of zirconium atoms by two sulfur

atoms in the hexagon results in a distortion of the hexagon from a planar configuration. The

other hexagon containing only zirconium atoms lies in a mirror plane, but is not a perfect

hexagon either. The distortion of this hexagon is an important feature of the structure and

will be discussed later. The central and the apical Zr (2) atoms are related by the mirror

glane and have a short interatomic distance of 2.889 A, about 10% shorter than the sum, 3.20

A, of the Goldschmidt radii. The prediction, based on a purely geometric argximent, proposed

by Frank and Kasper [14] will yield a shortening of this interatomic distance by about 15%,

which is slightly larger than the 10% observed in Zr9S2 case. Since the lower hexagon in

figure 2c lies in a mirror plane it can be seen that the coordination polyhedra for the two

Zr(2) atoms interpenetrate and form a two centered polyhedron. The axis of this two-centered

polyhedron is parallel to the a^axis , hence perpendicular to the four-fold, or the c-axis

,

and its length defines the value of a. It is proposed here that this polyhedron is the basic

building block of ZrgS2 stinacture and the entire structure can be described as the complex

packing of such polyhedra. To show how the polyhedra are packed to form the structure a projection picture, emphasizing the arrangement of the Kasper polyhedra, is shown in figure 3, It is projected along the b-axis and for clarity only the structure between the two mirror

planes, at y = 1/4 and y = 3/4, is shown. There are two zigzag chains in a unit cell propagating along the a-axis. The chains are formed by the two-centered polyhedra, around a pair

of Zr (2) atoms and with their axes parallel to the jb-axis, joining together side by side

sharing triangular faces. A point to be emphasized is that there is a pair of Zr(2) atoms in

the planar hexagon of the polyhedra, which, at the same time, are the two centers of the other

polyhedra with their axes parallel to the a-axis, in accord with the four -fold screw symmetry.

Thus, each pair of Zr(2) atoms has a dual character: as central atoms for one polyhedron

and as a part of a hexagonal ring for another. No shortening in interatomic distances will

be expected for ring atoms according to Frank and Kasper. Because of the dual character, the

Zr(2) - Zr(2) distance of 2.889 A represents a 10% shortening for the ring atoms and, at the

same time, a lengthening for the central-apical atoms by about 33% of the values for a perfect I C.N. 14 Kasper polyhedron. Mainly because of the presence of a short Zr(2) - Zr(2) distance

in the planar hexagon, the hexagon is distorted. A picture of the structure model constructed by the packing of the two-centered polyhedra is shown in figure 4. It is shown in this

picture that the polyhedra join together along their axes by sharing the apical atoms, and

that the two chains of polyhedra join together at the closest points by forming tetrahedra of

three atoms from one chain and one from another.

O ^"025. © 025<Y<05 . @Y-05. #0.5<t<0.75. © T.0.78

Fig. 3, Crystal structure of Zr9S2 with 0.25 <. y 1. 0.75

viewed along y-axis

.

656
Fig. 4. Crystal structure of ZrgS2 constructed with the

models of the two-centered polyhedra.

5.2. V^S

The structures of a-V3S and B-V3S were reported by Pedersen and Gr0nvold [10] and the

reported structures are reproduced in figure 5. The presence of short vanadium-vanadium

distances was recognized and the structural similarity with 3-W structure was discussed. If

the structure of a-V3S is projected along the [110] direction perpendicular to the four-fold

axis, the view shown in figure 6 is obtained. Again for clarity only the partial structure,

one half unit along the viewing direction, is shown and the presence of the Kasper polyhedral

arrangement of atoms, around V(l) atoms and parallel to the [110] direction, is emphasized.

From this figure it is readily apparent the structure unit in a-V3S is very similar to that

in ZrgS2. The differences between these two structures lies in the packing of the basic

units. In a-V3S, straight chains, formed by the two-centered polyhedra joined together by

sharing triangular faces, propagate along the c-axis. Along the axes of the polyhedra, the

polyhedra join together by sharing, instead of the apical atoms, an edge of the hexagonal

pyramid around the apices. In other words, the apical atom of one polyhedron lies in the

hexagonal ring of another. This last difference in packing gives rise to the difference in

composition between ZTr^S2 and a-V3S. There are no important differences between the two

basic units, and the V(l) - V(l) distance, 2.50 A, is shortening from the sum, 2.72 A, of

radii by about 8.2%.

(0 ) (bl 0^=0 ©Z = l/2 ([D Z =1/4 ® Z =3/4

Fig. 5. The structures of (a) a - V3S and (b) 6 - V3S,

viewed along the four-fold axes. (Data taken

from the paper by Pedersen and GrszSnvold [10] )

. 465-504 0 - 72 - 43

657
-c

0

'v-2

c

h = l/6 h ^ 2/6

Fig. 6. Crystal structure of a-VjS projected along the [110]

direction, emphasizing the C.N. 14 Kasper polyhedral

coordination of Ti(l) atoms.

The structure difference between a-V3S and its low temperature form, 3-V3S, has been rec- ognized as very small. Crystallographically speaking, it lies in replacement of a mirror

plane perpendicular to the [110] direction in a-V3S with a two-fold symmetry along that direction in 3-V3S. From the viewpoint of the two-centered polyhedral unit, the difference

arises from the fact that the two sulfur atoms in the 3-V3S structure units occupy the 1 and

4 positions in the hexagon instead of the 1 and 3 positions as in the cases of a-V3S and Zrg

S2, and the upper part of the two-centered polyhedron is related to the lower gart by a twofold axis, instead of a mirror plane. The short V(l) - V(l) distance is 2.44 A, corresponding to 10% shortening. The polyhedra in 3-V3S are packed in the same way as those in a-V3S.

It is thus quite clear that the interpretation of the crystal structures of metal-rich

sulfides based on the coordinations of the transition-metal atoms is very useful in the discussion of the structures. The presence of some of the atoms, such as Zr(5) in ZrgS2/ Ta(l)

in TagS and Ta(3) in Ta2S , which have no sulfur atoms as nearest neighbors, can be discussed

without relying on any additional model. The presence of short interatomic distances and

their values can also be explained semiquantitatively . The successful structural correlation

among ZrgS2/ oi-V3S and 3-V3S regardless of their significant difference in composition is

very striking. The correlation will be later extended to phosphides with trigonal-prismatic

coordination for phosphorus atoms. Most important of all, this approach sheds some light on

the bonding in the crystal. The present interpretation clearly indicates that bonding situations for sulfur atoms in ZrgS2/ a-V3S and 3-V3S are different from that in Ta2S. Since the

Kasper polyhedral arrangement of atoms is characteristic of intermetallic compounds, the fact

that sulfur atoms can replace the metal atoms in the formation of the Kasper polyhedra indicate the intermetallic characters of these compounds. In other words, sulfur in these com- pounds behaves as a metal and should probably be regarded as utilizing its outer orbitals to take on metallic character.

6. DISCUSSION

The structural similarity among a-V^S, 3-V3S, Ti3P and Te^P has been well recognized

[13]. The fact, established by Rossteutschen and Schubert [15], that the low temperature

form of Ta3Ge has the Ti3P structure type and the high temperature form has the Fe3P structure type, seems to indicate that the a.-V^S to 3-V3S transition is related to the Fe3P to Ti3P transition. There is however no correlation among these structures at present. If a partial structure of Ti3P is projected along the [110] direction the pictvire such as the one

shown in figure 7 will be obtained. The appearance of this picture is so similar to that in

658
Fig. 7. The structure of Ti3P projected along the [llOJ

direction, emphasizing the C. N. Kasper polyhedral

coordination of Ti(l) atoms.

figure 6 for a-VsS that only by a close examination can the differences be revealed. It can

be readily concluded that a similar two-centered polyhedron should be used as the basic

building units of the structure. As it turns out, for the Ti3P structure the two phosphorous

atoms in the distorted hexagon are located at 1 and 4 positions as in the case of 6-V3S, a character of the low temperature form as discussed earlier. Furthermore, the Ti3P structure

has a similar two-centered polyhedral building unit with the two phosphorus atoms at 1 and 3 positions of the distorted hexagon, thus providing the relationship between the phase transitions discussed above. The packing scheme of the polyhedra for Ti3P and Fe3P is identical

to that for the V3S structures, and hence they have the same compositions. The Fe(l) - Fe(l)

distance, 2.41 A, in Fe3P represents a shortening of 5.1% while the Ti(l) distance, 2.712 A

in Ti3P represents a 6.6% shortening. In the polyhedra for the sulfides the apical vanadium

atoms lie on the axes of the polyhedra while the apical atoms of the phosphide polyhedra are

off the axes , shifted toward one of the phosphorus atoms resulting in a very long M-P and a shorter M-P distance. Therefore, the phosphorus coordinations in these phosphides are different from the sulfur coordinations in the vanadium sulfides.

It has been suggested earlier that in Zr9S2 the presence of sulfur atoms in the hexagon

is the major cause for its distortion, and it follows that the distortion will be greater if

the metal atoms are larger relative to the sulfur or phosphorus atoms. It will thus be ex- pected that a compound, M3X, will prefer the Ti3P structure to the Fe^P structure if the r^^/

rjfi is small, where rx and rjj; are the radii of X and M atoms, respectively. In the Ti3P structure, the X atoms will be located in the 1 and 4 positions in the hexagon of the polyhedra,

allowing the distortion forces to come from opposite directions and to cancel one another to

a greater extent, while the Fe3P structure, with the X atoms located off to one side of the

hexagon, can tolerate only smaller distortion and will be stable when r^/r^ is not very much

smaller than unity. This conclusion is in agreement with the one arrived at by Lundstrom [13]

that tlie Fe3P and Ti3P structures are characterized by r^/r^ > 0.82 and r^/x^ < 0.82 respectively .

As a summary of this discussion, the structures of the five types, Zr9S2, a-V3S, 3-V3S,

Fe3P and Ti3P, are compared in table 5 and the models of the five two-centered polyhedra are

shown in figure 8.

The extension of the discussion to include the Fe^'P and Ti3P structures enables one to

show the similarities among ZX(jS2, a-V-^S, 3-V3S and a large group of M3X compounds involving

many heavy Group IVg and Vg elements. Many of these heavy elements have a highly metallic

character. The inclusion of these compounds in the same qroup with the Zr9S2 and V3S com659
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Fig. 8. The models of the two-centered polydra for the

crystal structures: (a) a-VgS, (b) 3-V3S,

(c) FejP, (d) TigP and (e) ZrgS2.

pounds provides further support for the suggestion that these three sulfides should be re- garded as intermetallic compounds.

There are many other compounds between transition metals and Group Hlg/ IVg and Vg

elements, for which the transition metal atoms have the C.N. 14 Kasper polyhedral coordinations, in particular those with the 3-W, W3Si and Mn5Si3 structures. In these structures,

there are present even shorter interatomic distances between pairs of transition metal atoms.

For example, 2.70 & between the Zr atoms in Zr5Al3 [16] and 2.544 A between two Ti atoms in

Ti5P3 [17], corresponding to 15.6 and 12.3% shortening, respectively. All these Kasper

polyhedra as in the cases discussed earlier. The major difference is that the axes of the

Kasper polyhedra in Zr5Al3 and Ti3P are parallel to the six-fold axes and the pairs of atoms

involved do not have the dual characters mentioned earlier. According to Frank and Kasper a shortening of about 15% wiJ.l be expected, in pretty good agreement with the observed values.

While their prediction is useful in the interpretation of crystal structures, it is desirable

that some fundamental study on the chemical bonding be carried out to explain the Kasper poly

hedral coordination and the presence of very short bonds along the axis of the polyhedron.

7. REFERENCES

[I] Conard, B. R. , Norrby, L. J. and Franzen, H. F., Acta Cryst. B25 , 1729 (1969).

[2] Franzen, H. F. and Smeggil, J. G. , Acta Cryst. B25, 1736 (1969).

[3] Franzen, H. F. and Smeggil, J. G. Acta Cryst. B26 , 125 (1970).

[4] Chen, H.-Y. and Franzen, H. F., paper submitted to Acta Cryst.

[5] Owens, J. P., Conard, B. R. and Franzen, H. F., Acta Cryst. 23_, 77 (1967),

[6] Franzen, H. F., Smeggil, J. G. and Conard, B. R. , Mat. Res. Bull. 2_, 1087 (1967).

17] Conard, B. R. and Franzen, H. F., High Temp. Sci. 3_, 49 (1971).

[8] Tuenge, R. , Chen H.-Y. and Franzen, H. F. to be published.

[9] Franzen, H. F. and Graham, J., Z. Kristallogr. 123 , 133 (1966).

[10] Pedersen, B. and Gr^nvold, F., Acta Cryst. 1_2, 1022 (1959).

[II] Aronsson, B. , Lundstrom and Rundqvist, S., Borides , Silicides and Phosphides, John-Wiley

New York (1965)

.

[12] Brewer, L. , Electronic Structure and Alloy Chemistry , edited by A. Beck, 223-235, Interscience Publishers, New York (1963).

[13] Lundstrom, T. , Arkiv. Kemi , 31, 227 (1969).

661
[14] Frank, F. C. and Kasper, J., J. Acta Cryst. 11, 184 (1958); 12, 483 (1959).

[15] Rossteutscher , W. and Schubert, K. , Z. Metal K. 56_, 813 (1965).

[16] Edshammer, L.-E. , Acta Chem. Scand. 16_, 20 (1962).

[17] Lundstrom, T. and Snell, P.-O., Acta Chem. Scand., 23^, 1343 (1967).

[18] Moore, C. E. , National Bureau of Standards Circular 467 (1949).

662
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

MIXED CATION DISULFIDES OF TITANIUM, VANADIUM, AND CHROMIUM* +

Lawrence E . Conroy and Kondayoor Raghavan Pisharody

Department of Chemistry

University of Minnesota

Minneapolis, Minnesota 55455

Mixed cation disulfides of the types Tii_xVxS2 and Tii_xCrxS2 have been prepared with

compositions in the range 0 < x < 1 in the Ti-V system and 0 < x < 0.4 in the Ti-Cr system.

Polycrystalline materials were prepared by direct reaction of the elements in vacuo at 950°.

Single crystals of the Ti-V compounds were prepared by chemical transport reactions, employing

iodine as the transport agent. The Ti-Cr disulfides failed to transport by this technique.

The chemical properties of the mixed cation materials were found to be very similar to those

of TiS2 . X-ray diffraction data indicated a random substitution of V or Cr for Ti in the

normal Ti sites in the TiS2 structure. A regular variation of lattice parameter with the

vanadium content was observed in the Ti-V system. The magnetic properties of both the Ti-V

and Ti-Cr compounds were characteristic of f errimagnetic materials, with magnetic susceptibilities in the range of 3 x 10~-^^m^/g to 12 x 10~-^'^m^/g (corrected) at room temperature.

All of the mixed cation materials exhibited metallic electrical conductivity in contrast

with the degenerate semiconductor behavior of TiS2, with resistivities of the order of 10"^

ohm-m at room temperature. No superconductivity was observed at temperatures above 1.3 K. A band model for the description of the electronic properties of these materials is discussed.

Key words: Disulfides; electrical conductivity; magnetic properties; sulfides; titanium disulfide; titanium-vanadi\im disulfides; vanadium disulfide.

1. INTRODUCTION

The transition metals form numerous dichalcogenide compounds with the group VI elements.

Some sixty-odd have been reported to date. The metals of groups IV, V, VI and VII typically

form layered structures, whereas the group VIII dichalcogenides usually crystallize in the

pyrite or marcasite structure. In electrical properties the dichalcogenides range from diamagnetic insulators like HfS2 to true metals such as NbS2. The entire scope of transition

metal dichalcogenides has recently been treated in an elegant and extensive review by Yoffe

and Wilson [1] . We have been particularly interested in the disulfides of the group IV

transition metals because within this isostructural group of compounds is found the full

range of electron transport properties. Titanium disulfide is metallic, ZrS2 is a semi-conductor, and HfS2 is a large gap insulator [2,3], All crystallize in a layered structure (C6

in the Strukturbericht classification) consisting of close-packed anion planes in a hexagonal

stacking array. The metal atom planes interleave every second pair of sulfur planes to produce a sequence -S-M-S-S-M-S- along the c-axis direction. In the group IV disulfides each

metal atom is octahedrally coordinated to six sulfur atoms in the two adjacent layers. Each

S-M-S sandwich layer is bonded to adjacent layers by relatively weak Van der Waal's forces

with the result that these compounds cleave readily along the layers, i.e., along the a plane of the hexagonal lattice. Although superconductivity occurs in the dichalcogenides of

group V metals , none has been reported among the group IV compounds

.

*Based upon a thesis presented by K. R. Pisharody to the Graduate School of the University of

Minnesota in partial fulfillment of the requirements for the Ph. D. degree.

+This work was supported in part by the U. S. Army Research Office - Durham

^Figures in brackets indicate the literature references at the end of this paper.

663
Previous workers have found that substitutional doping of the layered dichalcogenides

occurred quite readily in the case of the groups V and VI. Thus (Nb/Mo) Se2 and (Ta/W)Se2

mixed cation compounds have been studied [1,4]. This type of substitution offers intriguing

possibilities for the manipulation of the d electron population and the examination of the

effects of that population on the electrical, magnetic, and optical properties of the system.

It is for that purpose that we undertook the preparation and exami.nation of a number of mixed

cation disulfides, with special attention to the 3d compounds which have been less studied

than the heavier metal systems. This paper reports our studies on the (Ti/V)S2 and (Ti/Cr)S2

systems in which mixed cation disulfides with the type formulas Ti2_jjVjjS2 and Ti2_jjCrxS2 were

prepared.

2. EXPERIMENTAL

starting materials were: titanium metal sponge, 99.9% (United Mineral and Chemical

Corp.); vanadium metal powder, 99.9% (Electronic Space Products, Inc.); chromium metal powder,

99.7% (Fisher Scientific Co.); resublimed 99.9% sulfur, and reagent grade 99.9% iodine. Titanium disulfide was prepared by the reaction of stoichiometric quantities of titanium metal

sponge and sulfur in sealed, evacuated (10~^torr) Vycor ampules. Each sample was heated

slowly to 900° and held at that temperature for one week. The product was a yellow, crystalline powder. The x-ray powder diffraction pattern of this material showed only the reflections for hexagonal TiS2. To prepare the Ti2_^Vj^S2 and Ti _j^Crj^S 2 ( 0 < x > 1) materials,

appropriate quantities of vanadium or chromium, sulfur, and TiS2 were mixed thoroughly by

grinding them together in a mortar. Each mixture was pressed into pellets at a pressure of

30,000 Ib/in^. The pellets were heated in sealed, evacuated (10~^ torr) ampules at 950° for

one week. Each sample was examined for homogeneity by recording its x-ray powder diffraction

pattern. Inhomogeneous samples were reheated another week under the same conditions.

The products at this point consisted of polycrystalline masses that exhibited a silvery

luster. For the Ti2_j^V^S2 series, a homogeneous phase was produced for each composition over

the entire range of x values, but the Ti;^ _j^Crj^S2 system yielded homogeneous products only in

the range 0 < x > 0.4.

2.1. PREPARATION OF SINGLE CRYSTALS

Samples containing 1 to 2 grams of each composition of the polycrystalline disulfides,

described above, were employed in chemical transport [5] reactions to produce single crystals

of useful size. Each sample was sealed in an evacuated (10~^ torr) Vycor ampule (25 mm diameter X 15 or 20 cm long) along with 5 mg/ml of resublimed iodine. The technique used for

loading and evacuating the ampules has been described previously [6] . The transport ampule

was heated in a two-zone tube furnace that provided independent temperature control and program for each zone. Initially both zones were heated to 900° and held at that temperature

for 12 hours. The growth zone was then allowed to cool at a rate of 10°/hr to 750°. Transport was carried out in the gradient 900° - 750° for 6-7 days.

2.2. CHEMICAL ANALYSIS

Both titanium and vanadium were determined photometrically [7,8]. Samples were dissolved in a H2S0tt-HN03 mixture and the metals were determined in H2O2 solution. Because of the

interference between these two metals it was necessary to standardize at two wavelengths with

pure standard solutions of Ti and V, and to measure the absorbance of each unknown solution

at both wavelengths . The concentration of each metal could then be determined from simultao o neous equations. Measurements were carried out at 4100 A and 4500 A using a Cary 14 spectrophotometer. On known mixtures this method was found to be accurate within 0.5%. Standard

solutions were prepared from K2Ti (020^)3 and NHi+VOs .

Chromium was determined spectrophotometrically with diphenyl carbazide [7] . Samples were brought into solution by fusion with a 1:1 mixture of Na202 and Na2C03

.

For sulfur analysis the disulfide sample was fused with a large excess of Na202-Na2C03

mixture. The cooled cake was dissolved in water, acidified with HCl, and treated with excess

BaCl2. Sulfur was weighed as BaSOi^ . Analytical results are summarized in table 1 of the

results section of this paper.

664
Table 1

Chemical Analysis Data for {Ti/V)S2 and (Ti/Cr) S2 Mixed Cation Disulfides.

1 Composition Found

Nominal Ti V Cr s Formula

—Composition F— Found

Tin qVn iSt 35 .7 7 .2 _ 56. 9 Tin 01. Vn . i cSo Tin fiVn oSo 33 .8 9 .9 _ 56. 4 TinU.oUQ n VnU .ZUonSoz Tio.5Vo.5S2 21 .1 22 .4 _ 56. 6 TinU.JsVnU , JsSoz. Tio_itVo_6S2 17 .1 26 .7 56. 1 Tio .40Vo .60S2

Tio.2Vo.8S2 7 .0 38 .0 55. 0 Tio .I7V0 .87S2

Tio.lVo.9S2 2 .1 43 .3 54. 6 Tio.O5Vl.oS2

Tio.9Cro.1S2 39 .0 4.0 56. 8 Tio.92Cro.09S2

Tio.sCro ^2S2 32 .9 10.5 56. 5 Tio.78Cro,23S2

Tio.7Cro]3S2 29 .3 14.5 56. 1 Tio.7Cro.32S2

2.3. OTHER EXPERIMENTAL METHODS

X-ray diffraction data were obtained on powdered samples using a Debye-Scherrer camera

and on single crystals by rotation and precession photographs. Nickel-filtered copper radiation was employed. Powder data were refined by a least squares program adapted to Cohen's

method 19]

.

Magnetic susceptibilities were determined by the Faraday method, using an electro-balance. The single-crystal samples weighed approximately 5 mg. Both platinum metal and Hg

iCoCSCN)^] were utilized as calibration standards. The sensitivity of the system was 10"^ g and the reproducibility was within 2% on the smallest forces measured. Measurements were

carried out over temperatures from 78 K to 300 K. Temperatures were measured with a Cu-constantan thermocouple.

Electrical resistivities were measured on single crystals by the method of Van der Pauw

110] . Electrical contacts to a crystal were made with silver conducting paint at the perimeter of the plate-like crystals. All measurements were made in He atmosphere. Temperatures

were m.easured with a Cu-constantan thermocouple in contact with the center of the crystal.

Hall voltage experiments were carried out by both ac and dc methods. The apparatus has

been described previously [11]

.

3. RESULTS AND DISCUSSION

x-ray powder diffraction data showed that in the preparation of the polycrystalline samples (before transport) a homogeneous phase was formed for each composition in the '^^i—y^y^^z

system. In the Ti2_xCrjjS2 system, however, homogeneous products were obtained only for com- positions having x ^0.4. Mixtures containing more chromium always yielded mixed phases,

even after several weeks of heating at 950°. The chemical transport technique was successful

in producing larger crystals (Ti/V)S2 compositions, but all attempts to transport the (Ti/Cr)

S2 compositions were unsuccessful in that only TiS2 was transported. The (Ti/V)S2 crystals

deposited as very thin platelets ranging up to approximately 1 cm in diameter and 200 microns

in thickness. The color ranged from metallic yellow for the titanium-rich samples to metallic

silver for the vanadium-rich compositions. The chemical properties of both the Ti/V and Ti/

Cr compounds were veiry similar to those of TiS2. All were insoluble in water and organic

solvents, and all could be decomposed by concentrated mineral acids, especially oxydizing

acids. These compounds were relatively unaffected by aqueous alkali solutions, but fusion

with strong oxidants, such as Na202 or Na2C03-NaN03 mixtures produced rapid decomposition to sulfates. These siabstances, like TiS2» decompose below the melting point when heated in inert atmospheres, and it is this property that makes necessary the chemical transport technique for crystal growth. Heating in air above approximately 450° rapidly converts these

compoiinds to SO2 and metal oxides. Analytical data on the chemical compositions of the various stoichiometries that were prepared are reported in table 1. Data on the Ti/V composi665
tions are for the crystals prepared by chemical transport, and the Ti/Cr data represent the

compositions of the polycrystalline material. Column 1 lists the nominal compositions that were prepared for the starting mixtures of TiS2 , metal, and sulfur.

Both the (Ti/V)S2 and (Ti/Cr) S2. compositions crystallize in the same C6 structure as does TiS2, having the P^jj, space group (03^ symmetry). Thus both the V and Cr atoms must be

in octahedral coordination with sulfur atoms between alternate sulfur layers. The platelike habit and ready cleavage along the a plane are very similar to those properties of the

other C6 structure transition metal disulfides [1,12]. Lattice parameters for the crystals

are listed in table 2, along with those for nominally pure TiS2. These data show that the

substitution of Ti atoms by V or Cr atoms has negligible effect on the c parameter but causes

a decrease in the a dimension, i.e. within the close-packed sulfur planes. A plot of the a dimension vs. the vanadium fracti.on of the metal, shown in figure 1, indicates a Vegard's

Law proportionality between the lattice constant and the vanadium content. This contraction

O O is consistent with approximate core radii of 0.60A and 0.68A for tetravalent vanadium and

titanium, respectively. It is to be noted that, like TiS2 itself [2] , the Ti/V and Ti/Cr

disulfides usually crystallize with excess metal in the structure. The C6 structure can ac- commodate metal atoms in excess of the MS 2 composition both by adding metal atoms within the

S-M-S sandwich layers, since half of the octahedral sites and all of the tetrahedral sites

are still empty, or by adding them to the nominally empty layers between adjacent sandwiches.

Table 2

Crystallographic Data for (Ti/V)S2 and (Ti/Cr) S2 Mixed Cation Disulfides.

Composition a (A) c

0 (A)

TiS2 3.405 + 0 .005 5 .701 + 0 .006 1.67tt Tio.8i+Vo.i6S2 3,390 + 0 .004 5 .707 + 0 ,006 1.683

Tio .8 0"^0 .20^2 3.382 + 0 .004 5 .710 + 0 .006 1.688

Tio.SOVo .50S2 3.352 + 0 .002 5 .706 + 0 .002 I.7O2

Tio .4V0.6OS2 3.345 + 0 .005 5 .710 + 0 .006 1.707

Tio.i7Vo.87S2 3.318 + 0 .005 5 .710 + 0 .009 1.72i

Tio!o5Vi .0S2 3.296 + 0 .005 5 .666 + 0 .01 1.72i

Tio.92Cro,o9S2 3.395 + 0 .004 5 .701 + 0 .006 1.679

Tio.78Cro.23S2 3.395 + 0 .002 5 .701 + 0 .005 1.679

Tio,70Cro.32S2 3.381 + 0 .003 5 .712 + 0 .006 1.689

o<

OJ

3.3 5

3.3 0

3.25 J I I I I L J I L 0.2 0.4 0.6 0.8

X in Tii.xVxSg

1.0

Fig. 1. Lattice parameter, a, vs. composition, x, for

(Ti/V)S2 mixed cation disulfides.

666
The substitution of Ti atoms by V or Cr atoms must occur on a random basis because our

x-ray diffraction data showed no evidence of ordering beyond that of the C6 structure of

TiS2. Similarly the accommodation of excess metal atoms must take place randomly because no structural evidence of the extra metal was found.

Both the (Ti/V)S2 and (Ti/Cr)S2 systems exhibited paramagnetism at temperatures below

300 K. Figures 2 and 3 show the plots of reciprocal susceptibility vs. temperature for the

(Ti/V)S2 systems, respectively, x' r the susceptibility per gram of Tii_jjMjjS2j has been corrected for diamagnetic contributions using the values (in m^/mol x 10 ) of -6 for Ti"*"^ , -9

for -10 for Cr+^ and -40 for S'^ {13, 14]. 2 The susceptibility data fit a Curie-Weiss

law between 120 and 300 K. Least-squares fits of the linear portions of these plots yield

the magnetic constants that are listed in table 3. The low-temperature deviations from Curie

Weiss dependence are characteristic of f errimagnetic structures. An examination of the magnetic moments tabulated in table 3, column 5, reveals no direct relationship to the vanadium

or chromium content. Thus the magnetic evidence points to the existence of interactions between two or more magnetic sublattices in antif erromagnetic array. We have no evidence thus

far concerning the distribution of the two types of metal ions in the crystals. Our powder

30

n

D)

0)

Io

20

10

0

a x = 0.l6

b x-0.23

c X =0.50

d X = 0.60

e X =0.87

f X = 1 .0

1

100

T. ° K

200 300

Fig. 2. Reciprocal magnetic susceptibility of (Ti/V)S2

as a function of temperature.

n

E

O)O»—X

3 0|— Ti.|_^Cr^S2

a X =0.09

b X = 0.2 3

c X =032

20

1 0

O'O0S>'00

6^'

^oo-o-oo-oob100

T. K

200 300

Fig. 3. Reciprocal magnetic susceptibility of (Ti/Cr)S2

as a function of temperature.

667
Table 3

Magnetic Constants for (Ti/V)S2 and (Ti/Cr)S2 Mixed Cation Disulfides.

1 2 3 4 5 Composition Weiss Constant Curie Constant Magnetic Moment Magnetic Moment

M,x in per Metal Atom per V or Cr Atom

e (K) C at 300 K at 300 K

y (BM) y (BM)

0 V 0.16 -161 ± 19 0.16 0.897 5.6

V 0.23 -120 ± 20 0.24 1.14 5.0

V 0.50 - 97 ± 10 0.30 1.31 2.6

V 0.60 - 92 ± 16 0.30 1.35 2.2

V 0.87 -105 ± 19 0.33 1.41 1.8

V 1.0 - 94 ± 15 0.29 1.55 1.6

Cr 0.09 -257 ± 20 0.21 1.33 1.3

Cr 0.23 -214 ± 20 0.42 1,99 8.7

Cr 0.32 -250 ± 30 0,71 2.40 7,5

x-ray diffraction data could not distinguish any such sublattices occupied by atoms as closely

similar as Ti , V, and Cr.

Electrical resistivity data were obtained on single crystals of the {Ti/V)S2 compositions.

No crystals sufficiently large for electrical measurements were obtained in the transport of

the (Ti/Cr) S2 system. Resistivities were measured in the a plane for all compositions of

(Ti/V)S2. No reliable data could be obtained for resistivity parallel to the c axis because

of the extremely thin flake-like habit of the crystals. The a plane resistivity vs. temperature data for the titanium-vanadium disulfides are shown in figure 4, along with similar data

for pure TiS2. The room temperature resistivity of 2.35 x 10"-^ ohm-m obtained for TiS2 in

this work is in fair agreement with that obtained in earlier work in this laboratory 1.35 x 10~^ ohm-m and reported by Conroy and Park [6] , and with the results of McTaggart and Wadsley

[3], 7.7 x 10~^ ohm-m. The dependence of the electrical resistivity upon the composition is

indicated by the plot in figure 5.

E

I E

o

inO

K

1110

9

8

7

6

5

4

3

2

1

- a o- 00- o- 0—00-0—o —oa X = 0.23

b X = 0.50

c X = 0.60

d X = 0.8 7

e T1S2

b o-o-oo-cP-o-o-ooo

c o- 00 o — o —- 00-

— o-o-o —

o

-0-0

-DO- -oo

oo 00

cP' oO

T, K 100 200 300

Fig. 4. Electrical resistivity of (Ti/V)S2 as a function of temperature.

668
\ \ \ \ \ \ \ \—

r

11 - q

10 -

9 -

8 -

0 0.2 0.4 0.6 0.8 1 X in Tji_xVxS2

Fig. 5. Electrical resistivity of {Ti/VjSo as a function of composition.

A comparison of the resistivity vs. temperature data for the (Ti/V)S2 system (fig. 4) with that for TiS2 shows that the substitution of vanadium for titanium in this lattice has

changed the electrical characteristics from that of a degenerate semiconductor in TiS2 to metallic conductivity. Some preliminary Hall coefficient measurements on this system indicate

that each vanadium atom contributes a fractional additional electron to the system. No superconductivity could be detected in any of these {Ti/V)S2 or (Ti/Cr)S2 materials down to 1.3 K.

The effect of the substitution of vanadium or chromium atoms for titanium atoms in the

TiS2 structure is to confer properties of a paramagnetic (or ferrimagnetic) metal on the system. An energy level model to describe such a nonmetal-metal transition in compounds having

the C5 structure has been proposed by Vellinga, de Jonge , and Haas [15]. Their schematic

energy level diagram is reproduced in figure 6. For trigonally distorted octahedral coordiE

f

—*- M(EI 'C3v)

Fig. 6. Schematic one-electron energy level

diagram for C6 disulfides with trigonally distorted octahedral {C^^)

coordination

.

669
nation, with the metal atom shifted along the trigonal axis (symmetry C3 )

, the ligand field

splitting produces two degenerate e* antibonding levels and a nondegenerate a* (d^.^) level,

with one of the e* levels (dx2_y2 and dj^) being lowest. Employing this model, Vellinga, de

Jonge, and Haas have successfully explained the metallic behavior of 3-MoTe2 . Although TiS2

and our substituted disulfides have the same C6 structure as B-MoTe2, it has not yet been

established in any of these compounds that the octahedral coordination around the metal

is trigonally distorted as it is in 6-MoTe2 . However it is reasonable to expect such distortions since it is found in TaS2 , also a C6 structure. The smaller first row transition metal

atoms Ti , V, and Cr, would be more easily displaced in the relatively large octahedral voids

in the sulfide lattice than would a Ta atom.

Application of the Vellinga-deJonge-Haas model to TiS2 would predict that the energy

bands that arise from the overlap of the antibonding orbitals would all be empty, so that TiS2

would be an insulator or semiconductor. The substitution of the d^ ions of the V^^ or d2

ions of Cr'^'+ would contribute electrons to the low-lying e* band and bring about metallic

conduction. Because of the smaller radial extent of the d orbitals in Ti as compared with Ta, one would expect the interaction with adjacent atoms to be less, so that the conduction bands

would be narrower in TiS2 than in TaS2 . The greater binding of the d band electrons to the

ion cores may be responsible for the observed paramagnetic susceptibility in these substituted

disulfides

,

4. ACKNOWLEDGMENT

This research was supported in part by the U. S. Army Research Office - Durham.

5. REFERENCES

[I] Wilson, J. A. and Yoffe, A. D., Advan. Phys., 18_, 193 (1969).

[2] Conroy, L. E. and Park, K. C, Inorg. Chem. , 1_, 459 (1968).

[3] McTaggart, F. and Wadsley, A. D. , Aust. J, Chem., 11_, 471 (1958).

[4] Brixner, L.' H. and Teufer, G. , Inorg. Chem., 2_, 992 (1963).

[5] Schafer, H. , Chemical Transport Reactions, Academic Press, New York, 1964.

[6] Conroy, L. E., Inorg. Syntheses, 1_2, 158 (1970).

[7] Sandell, E. B., Colormetric Determination of Traces of Metals, 2nd ed. , Interscience

Publishers, New York, 1960, p. 572.

[8] Weissler, A., Ind. Eng. Chem., 17_, 775 (1945).

[9] Cohen, M. , Rev. Sci . Instrum. , 6_ 68 (1935) 7_, 155 (1936).

[10] Van der Pauw, L. , Phillips. Res. Repts., 13_, 1 (1958).

[II] Vergamini, P., M. S. Thesis, University of Minnesota, Minneapolis, Minnesota (1969).

[12] Jellinek, F. , Ark. Kemi . , 20_, 447 (1963).

[13] Angus, W. , Proc. Roy. Soc, Ser. A., 136 , 573 (1932).

[14] Klemm, W. , Z. Anorg. Allg. Chem., 246, 347 (1941).

[15] Vellinga, M. B. , de Jonge, R. ,'and Haas, C, J. Solid State Chem., 2_, 299 (1970).

"To convert to cgs units, divide by 4 tt x 10~°.

DISCUSSION

F. Holtzberg : Did you analyze your compounds for sulfur as well as for metals?

L. E. Conroy : Yes, all components were determined. Samples were oxidized by fusion

with a large excess of Na202-Na2C0 3 mixture. The cooled cake was dissolved in water, acidified, and the sulfur was precipitated as BaSO^. Attempts to determine sulfur as SO2 were

xinsuccessful, apparently because the presence of V2O5 or Ti02 catalyzes the conversion to SO3.

670
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

CRYSTAL GROWTH AND PROPERTIES OF SOME I-III-VI2 COMPOUNDS

H. M. Kasper

Bell Telephone Laboratories, Incorporated

Murray Hill, New Jersey 07974

The I-III-VI2 compounds are ternary analogues to the II-VI semiconductors and are interesting both as possible nonlinear optical materials and as semiconductors. They usually

crystallize in the chalcopyrite structure which belongs to the uniaxial acentric crystal

class 42m. In order to study their optical and semiconductor properties, single crystals of

AgGaS2, CuGaS2 and CuInS2 have been grown by slowly cooling melts of stoichiometric composition, and the conditions of growth by directional freezing are reported. AgGaS2 crystallizes

as yellow and green crystals. The yellow crystals seem to be gallium rich. CuGaS2 does not

melt congruently. Stoichiometric melts first crystallize a composition near Cug . 33Ga;[ , 04^2

as light orange crystals. Later darker, nearly stoichiometric crystals are obtained. CuInS2

crystallizes between 1050 °C and 1000 °C with all crystals transparent to beyond 10 y. There

is a strong absorption in CuGaS2 near 1.8 y, which extends toward the visible and causes the

darker color. The bandgaps are 2.72 eV for AgGaS2 , 2.53 eV for CuGaS2 and 1.55 eV for CuInS2

at 2 K. Both the light and dark crystals of CuGaS2 as well as CuInS2 and AgCuS2 show sharp

line luminescence. The linear and nonlinear optical properties of AgGaS2 , Cuq . esGai _ ottS2 and CuInS2 have been investigated. Unfortunately in both Cuo.88Ga1.04S2 and CuInS2 the birefringence is not large enough to permit three frequency phase matching, but AgGaS2 can be

phase matched in the infrared for both parametric oscillation and second harmonic generation.

With both CuGaS2 and CuInS2 a pronounced structure has been observed in electroreflectance

near the bandgap and at higher energies. From this structure is concluded that the crystal

field splitting of the d bands is about 0.7 eV and that the d bands lie about 2 eV below the

valence band edge in both compounds. Stimulated emission has been observed in AgGaS2 , CuGaS2

and CuInS2. AgGaS2 is usually of high resistivity, whereas CuGaS2 is p-type and CuInS2 can

be made both p- and n-type

.

Key words: AgGaS2; chalcogenides ; chalcopyrite; I-III-VI2 compounds; crystal growth;

CuInS2; CuGaS2; d-bands ; direct bandgap semiconductors; nonlinear optical materials;

semiconductor materials.

1. INTRODUCTION

Luminescent materials, especially zinc sulfide and cadmium sulfide, have been of considerable interest for a long time both scientifically and technically. More recently, encouraged by the success of many useful semiconductor devices, investigators have begun to study

in detail electroluminescent devices, in which minority carriers are injected at a junction

so that light is produced by recombination with majority carriers. These studies have generally focused on two classes of materials, II-Vl compounds [1]^ and III-V compounds [2]. Both

the II-VI's and the III-V's are deficient in some respect insofar as being ideal electroluminescent materials [3] . In the III-V compounds visible light emission is relatively inefficient, while the II-VI sulfides and selenides have so far only been obtained with useful n- type conductivity, so that no efficient electroluminescence has been achieved. ZnTe is only

p-type and CdTe has the bandgap in the infrared. Thus, we were led to consider alternative

electroluminescent materials.

Figures in brackets indicate the literature references at the end of this paper.

671

/
In contrast to our extensive knowledge of the physical properties of the II-VI compounds,

there is presently very little known about ternary compounds related to the II-VI 's. The

most obvious related class is the I-III-VI2 compounds, where the bivalent cation is substituted half by a monovalent and half by a trivalent cation, e.g., in ZnS Zn is substituted

half by the element to its left in the periodic table (Cu) and half by the element to its

right (Ga) . A number of materials in this class were first prepared by Hahn and coworkers

[4], who determined that all ABC2 -compounds (A = Cu, Ag; B = Al, Ga, In; C = S, Se , Te) had

the chalcopyrite (CuFeS 2 type) crystal structure. This structure can be derived from the

zincblende lattice by an ordered substitution at the cation sites. The superstructure formed

leads to a doubling of the c-axis in the chalcopyrite with respect to the cubic zincblende

lattice [5] (figure 1)

.

Previous investigations of these materials [6] have mostly concerned the thermoelectric

properties of the ABC2 members with lower bandgaps. It has been shown that small crystals

of many ABC2 can be obtained by hydrothermal methods [7] . Robertson obtained crystals of

AgGaS2 by a Bridgman technique [8] , and Lerner those of CuGaSe2 and AgInSe2 by zone refining

methods [9] . We have found that CuGaS2 and CuInS2 can be transported with iodine vapor [10]

,

but we were unsuccessful in transporting AgGaS2 • However, sulfides generally incorporate

insignificant amounts of iodine which can change transport and optical properties quite drastically. There have also been some studies on the compound formation of pseudobinaries of

I-III-VI2 compositions with either II-VI compounds as by Hahn [4] and Parthe [11] or with

the III2VI3 compounds as in the investigation of the system CuGaS2-Ga2S3 by Belova and co- workers [12] . We will report here on the preparation and properties of crystals of AgGaS2 , CuGaS2

and CuInS2 , which we have studied more extensively than other members of the I-III-VI2 family

and which have the most interesting electroluminescent and nonlinear optical properties of

those members so far examined.

2. EXPERIMENTAL

In each case crystals were obtained by slowly cooling melts of stoichiometric composition. Starting materials were 99.999% pure copper, 99.999% pure silver, 99.9999% pure gallium, and 99.9999% pure sulphur obtained from United Minerals Corporation. The melts were prepared similar to Belova and coworkers [12] by heating stoichiometric amounts in silica

boats contained in evacuated and sealed silica ampoules. Slowly cooling the melt was used

to initiate directional freezing and crystals up to several mm in size were obtained of all

three materials.

CHALCOPYRITE

CuGaSj • Cu Fig. 1. Model of CuGaS2 crystallizing in the

chalcopyrite lattice.

672
3. RESULTS AND DISCUSSION

(a) Silver gallium sulfide, AgGaS2 - Preparation : The melting point has been reported

to be at 980 °C [12] or 1040 °C [8] , although our quenching experiments indicate that crystallization occurs closer to 950 °C. The melts were cooled from 1020 °C at a rate of about

1 °C/hour. In many cases the silica boats were cracked because of the thermal contraction

of the crystals on cooling. Generally when the starting composition was exactly AgGaS2 the

ingot consisted of a light yellow part, which had crystallized first, blending into a green

part, which crystallized last. Luminescence investigations showed, that exciton emission

was sharper for the green material [13] . Growth experiments where the initial stoichiometry

was Ago . gyGai . 0 1S2 resulted in completely yellow material. On the other hand when oxygen

got into the ampoule, when crystals were formed they were green. Thus, it is apparent that

the color of the crystals depends strongly on the defect concentration and that AgGaS2 does

not melt completely congruently. It is likely that the solid in equilibrium with a stoichiometric melt has Ga/Ag >1. This may be part of the reason for the observed difference of

melting point (980 °C) and the reported crystallization temperature (950 °C)

.

Properties : The lattice constants (a = 5.75 and c = 10.305) of the yellow and green

material did not show any difference within the accuracy of our measurement and agreed well

with previous measurements [4] . The absorption spectr\im for a yellow crystal is shown in

figure 2. The absolute reliability of the absorption coefficient as shown in figures 2, 4,

and 7 is discussed by Boyd et al. [14] . AgGaS2 is transparent in the infrared to about 13

y, where multiple phonon absorption starts. There was some residual absorption in the visible in all the samples measured, and it is not clear at this time how it can be eliminated.

The bandgap deduced from reflectivity measurements by Tell et al. [13] is 2.727 eV at 2 K. It is shifted at 77 K to a slightly higher energy (2.732 eV) in contrast to the decrease of

the bandgap with increasing temperature normally observed for II-VI compounds. This may be

caused by the anisotropic thermal expansion. Unfortunately no measurements of thermal expansion of AgGaS2 are reported in the literature. The indices of refraction at 1 y are Hq = 2.4582 and ng = 2.4053 with a birefringence of 0.0529 [14]. This birefringence in connection

with the acentricity of the chalcopyrite structure and a large coefficient of second harmonic

generation allows phase matched second harmonic generation with the wavelength of the fundamental between 1.8 p and 11 p. Chemla et al. [15] and Boyd et al. [14] have observed the

phase matched second harmonic with a C02-laser output at 10.6 y as a pump. Measurement of

the nonlinear optical coefficient shows that it is about three times that of LiNb03 [14] . However, the residual absorption of unidentified origin below the bandgap and problems with

crystal quality have first to_be worked out before AgGaS2 can serve as a useful nonlinear

optical material. The class 42m of AgGaS2 is nonenantiamorphous and the allowed optical ac- tivity is normally unobservable . Hobden [15] detected optical rotation in AgGaS2 at 4974A

where = n^ and it should also be detectable in CuGaS2 where nQ = ng at 6400A [14]

.

8.00

7.00

6.00

5.00

4.00

3.00

2.00

1.00

0.00 ,

.5 .6 .7 .8.91.0 1.25150 20 2.53.0 40 5.0 6.0 80 10.0 12.5 X (MICRONS)

Fig. 2. Absorption coefficient of AgGaS2.

673

465-504 0 - 72 - 44

AgGaS2

a

(cm"')
Investigation of the electrical transport properties of AgGaS2 have shown no useful con- ductivity [13]. All crystals, both yellow and green, are semi-insulating but of very low

{~10~' Q cm) conductivity and it was not possible to determine the nature of the few carriers.

Various doping and annealing experiments did not change the situation. The low conductivity

is disappointing from a semiconductor point of view, but of course connotes an absence of

free carrier absorption in the infrared which is desirable for optical applications.

(b) Copper gallium sulfide, CuGaS2 - Preparation : The preparation and crystallization

of CuGaS2 is more complicated than that of silver gallium sulfide. Belova et al . [12] studied the pseudobinaary CuGaS2-Ga2S3 system with samples quenched from 1100 °C and measured the

dependence of the lattice constants on composition. In figure 3, which is adapted from their

publication, two homogeneity regions for Cui_jjGai+jj/3S2 with 0 < x < 0.13 and 0.65 < x < 0.9 can be recognized. In the region 0 < x < 0.13 the diffraction pattern corresponds to the

chalcopyrite structure and for 0.65 < x < .9 to an ordered alloy CuGasSe. Cooling stoichimetric melts of CuGaS2 we found that the results depend strongly on three parameters: (1) the maximum temperature to which the melt had been raised, (2) the soaking time at this temperature, and (3) the cooling rate. Generally, it was found that at the beginning of the

crystallization lighter orange crystals formed, while later darker crystals with some black

material crystallized. This indicates that at first gallium richer phases grew and after

some depletion of the melt at lower temperatures more copper rich crystals appeared. When

the melt was raised to temperatures above 1160 °C, invariably the first material crystallizing was yellow and obviously lay in the region 0.65 < -x < 0.9. Below 1160 °C all crystals were always orange and darker. This shows that the jump in the solidus curve of the phase

diagram between Cuo.3tfGa1.22S2 ^^d Cu ^ ssGai . 01+S2 occurs near 1160 °C. The reported melting

point of CuGaS2 is, however, 1280 °C according to Apple and Fischer [17] and >1200 °C according to Belova et al. [12] . We think that the difference is not a supercooling effect but due

to the presence of other valence states such as Cu"^"^ and Ga^^ in the melt, which may make the

treatment of these systems as pseudobinaries inappropriate. We obtained crystals with rea- sonable reproducibility, when we soaked the stoichiometric melt at 1150 °C for a day and then

slowly cooled at a rate of about 1-1/2 °C/hour. The crystals were several mm in diameter

with concoidal cleavage. The first crystals were deep orange or deep red; the later ones darker

.

O 2

• 1

5.30

5.25

5.15 —

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 X

Cu,'l-X

Fig. 3. Lattice constants and their dependence on composition for the system Cuj -xGai+x/3S2

(adapted from Belova, Koshkin and Palatnik

[12]) .

674
Properties : Spectrographic analysis showed that the crystals contained about 5 ppm Si

and Mg, 3 ppm Al and Fe, and 2 ppm Ca. Twenty-nine other elements were checked but not found.

The lattice constants for the orange crystals were a = 5.328A and c = 10.462A, while the dark

crystals had a = 5.351A and c = 10.484A. This suggests (using the data of figure 3) compositions of Cug se'^^l 04^2 ^ = 0.12 for the orange crystals and nearly stoichiometric CuGaS2

for the dark crystals. The absorption spectrum in figure 4 shows transmission in the infrared to 13 p. Reflectivity measurements give 2.53 eV for the bandgap of CuGaS2 at 2 k. In

addition, there is an absorption in the red crystals in the infrared (figure 5) and a much

stronger broad absorption in the dark crystals at about 1.8 y. We suspect that defects con- nected with Cu^"*" are responsible for the absorption in the dark crystals. The indices of re- fraction at 1 y are n^ = 2.5405 and ng = 2.5349 with a birefringence of only n^ - no = -.0053

[14] . The small birefringence does not allow phase matched second haianonic generation at any

wavelength in CuGaS2 . The electroreflectance spectrum of CuGaS2 shows pronounced structure

at about 2.4 eV and between 3.5 and 5 eV (figure 5) . The electroreflectance spectra of the

II-IV-V2 compounds with chalcopyrite structure like CdSnP2 have been very satisfactorily ex- plained by Shay [18] and coworkers with the quasicubic model, which assumes that the band

structure is insensitive if two atoms like In are replaced with an atom to the right and to

the left of In in the periodic table (i.e., Cd and Sn substituting for 2 In). This model

also assumes that the only important change in the band structure going from the zincblende

to the chalcopyrite lattice is due to the relative size of the tetragonal distortion. While

this model works beautifully for the II-IV-V2 compounds, it breaks down for the change ZnS ^

CuGaS2 [19] . This breakdown can be seen from the fact that there is a big difference in the

size of the bandgap in ZnS (3.8 eV) and CuGaS2 (2.40 eV) . The model probably is inappropriate

because of the d-electrons present in copper. We can assign the structure of the electroreflectance spectrum [20] near 4.5 eV to a transition near the F-point from a dg. electron

band mostly on the copper to the s-type conduction band and similarly the structure near 3.8 eV to a transition d^y to the conduction band (figure 4) . This corresponds to a crystal field

splitting for the d-electrons near the copper of 0.7 eV, which is very close to the value

found for tetrahedral Cu^"^ in many oxides [21] . The location of the d-bands in CuGaS2 with

respect to the conduction band edge coincides with the position of the upper valence band

edge in ZnS, which is made up mostly from p-orbitals . Since there is strong orbital overlap

between d and p-electron distribution, we conclude that the breakdown of the pseudocubic model

is due to this interaction. The position of the d-bands ~ 1.5 eV below the valence band

edge is consistent with the observation that the chemically most stable valence of tetrahedral copper in sulfides is monovalent, in contrast to oxidic tetrahedral copper compounds,

where an inversion of these bands would be expected, but instead mostly bivalent copper is

observed

.

20.0

18.0

16.0

14.0

12.0

10.0

8.0

6.0

4.0

2.0

.5.6.7.8.91.01.2 1.5 2.0 2,5 3.0 4,0 5.06.0 8.010.0 15.0 X(MICRONS)

Fig. 4. Absorption coefficient of orange Cuj _xGaj^+x/3S2

.

CuGoS

a

"(cm"

675
Fig. 5. Absorbance log I^/I of red and dark

Cui_xGai+x/3S2

•

-0.01

ELECTROREFLECTANCE

CuGaSj r 300° K

s ELECTRON

OeV CONDUCTION BAND

2.45eV

r

p ELECTRON 5^ ^ VALENCE BAND

r

r

5 " ELECTRON

BAND

2 —

"^'^^^df ELECTRON BAND

\ 1 ^

XIO

\l \

1 —

H

l\\

Il2.5| 3.0

' V

3.5 U

\v

1

' PHOTON ENERGY

\ 1 <ev)

1 1 Y

Ell Z —EiZ

1

^2

C

1 1 1 1 1 1 6000 5000 4000 ^ 3000 WAVELENGTH (A) Fig. 6. Electroreflectance spectrum and simplified energy

band diagram neglecting the ordering of the cations

and tetragonal distortion of the chalcopyrite lattice

and using the band designations of the zincblende

structure (adapted from Tell, Shay and Kasper [20]).

676
The investigation of the transport properties showed that as-grown crystals are mostly

semi-insulating [20]. However, in contrast to all II-VI sulfides, which are semi-insulating

or n-type , CuGaS2 can be made p-type with a resistivity of p ~ 0 . 4 cm and a Hall mobility

pj^

~ 20 cm^/volt sec by doping and annealing procedures [20]. Tell et al. found that as in

the II-VI compounds the conductivity depends strongly on the anion vapor pressure.

(c) Copper indium sulfide, CuInS2 - Preparation : We cooled the melts from 1100 °C at

a rate of about 1 °C/hour and presume that the crystallization temperature lies somewhere between 1050 and 1000 °C. CuInS2 is opaque to visible light; however, it is transparent in the

infrared and crystals were selected by use of a microscope equipped with an infrared image

converter. Although we observed differences in transparency in various crystals in the infrared image converter, we did not note stoichiometry variations as spectacular as in CuGaS2

.

Properties: The lattice constants were determined to a = 5.524 and c = ll.lsA in agreement with previous work [4] . The absorption spectrum of CuInSa is shown in figure 7, and we

see that it is transparent in the infrared to 15 p. The bandgap is 1.55 eV as determined

from reflectivity at 2 K [20] , and is considerably higher than a previously reported value of

1.2 eV [22]. The absorption coefficient shows some absorption, probably due to impurities,

near the band edge. The indices of refraction at 1 u are n^ = 2.7225 and Uq = 2.7067 with

birefringence n^ - nQ = - 0.0158, which is insufficient to allow the phase matched generation

of second harmonic laser light [14]

.

The electroreflectance spectrum of CuInS2 [20] is similar to that of CuGaS2 with a general shift of all structure to the infrared corresponding to the smaller bandgap. The d^- band is about 4 eV and the d.^ band about 3.3 eV below the conduction band edge and the transitions due to the valence band edge are seen at about 1.55 eV . Again we have the disagreement with the quasicubic model in the infrared shift of the bandgap compared with Zno,5CdQ_5S

(3 eV) . The splitting of the d-bands is ~ 0.7 eV as in CuGaS2 . The energy difference of the

d-bands and the valence band edge is here about 0.5 eV larger than in CuGaS2 and the perturbation of the valence band through d-electrons should be slightly less. As grown CuInS2 is

usually low conductive p-type. Annealing and/or doping leads to highly conductive p-type

[20] material with a resistivity p = 7 Q cm and a mobility of 12 cm^/V sec. After better

crystals were available it was found that CuInS2 can also be made n-type with a resistance

p

~ 1 n cm and a Hall mobility p -. 200 cm^/volt sec. Recently rectifying junctions have been

obtained in CuInS2 [23]

.

26.0

24.0

22.0

20.0

18.0

16.0

14.0

12.0

10.0

8.0

6.0

4.0

2.0

0

.7.891.01.2 1.5 20253.0 4.05.06.0 8.010.0 150 \ (MICRONS)

Fig. 7. Absorption coefficient of CuInS,.

CuInS2

\ -

a

'(cm-')

677
4. VISIBLE STIMULATED EMISSION AND POSSIBLE APPLICATIONS

We have already mentioned that AgGaS2 has very desirable nonlinear optical properties.

However, the properties of CuGaS2 and CuInS2 are even more interesting. It is important that

CuGaS2 and CuInS2 are direct bandgap semiconductors with the top of the valence band and the

bottom of the conduction band at the T-point of the Brillouin zone. This implies a strong interaction of valence and conduction band electrons with photons of bandgap energy, and it is

a precondition for efficient semiconductor luminescence. Experimentally, Shay et al. [24]

have recently demonstrated the emittive qualities of AgGaS2 , CuGaS2 and CuInS2 . At ~ 2 K,

electrons were pumped with a pulsed nitrogen laser (3371A) from the valence band to the con- duction band. It was possible to observe stimulated emission in a small solid angle normal

to the incident beam in AgGaS2 at 4620A, CuGaS2 at 500oA and in CuInS2 at 9175A.

For the design of light emitting devices p-n junctions are required in addition to the

luminescent properties. CuInS2, which can be made of both p- and n-type conductivity and

which has a bandgap slightly larger than GaAs, shows all the requirements, of a homojunction

laser material. Fisher [3] distinguishes quasi-homojunctions as defined as a p-n junction

between two materials, one being n-type, the other p-type, which form a complete series of

solid solutions from hetrojunctions made of unrelated materials. Up to now all quasi-homojunctions of the II-VI compounds had to be based on ZnTe, which was the only material with

native p-type properties and which had to be combined with the n-type sulfides and selenides.

The p-type conductivity and the luminescent properties of CuGaS2 make, in our opinion, this

sulfide a much stronger contender for quasi-homojunctions with II-VI sulfides than ZnTe.

5. CONCLUSIONS

We have reported on the preparation and the properties of crystals of the I-III-VI2 com- pounds AgGaS2, CuGaS2 , and CuInS2. We find that growth from the melt is probably the best

way to obtain crystals of I-III-VI2 compounds, which are able to meet the purity and perfection standards required for semiconductor and nonlinear optical applications, in contrast to the preparation of quality II-VI compounds from the vapor phase [25] . AgGaS2 has been shown

to have good potential for nonlinear optical applications. The most remarkable property of

the copper compounds is their p-type conductivity. CuInS2 is the first tetrahedral sulfide

which has shown good conductivity of both types. The outstanding luminescent properties of

the tetrahedral chalcogenides , and specifically sulfides, leads to the expectation that the

p-type conductivity will enable the design of useful visible light and laser sources.

6. ACKNOWLEDGMENT

I would like to thank R. A. Laudise and A. G. Chynoweth for their initiation of and

their continued interest in this woxk. The encouragement and uninterrupted cooperation of

G. D. Boyd, J. H. McFee, G. E. Peterson, J. L. Shay, and B. Tell have been extremely helpful

and they have contributed greatly to the author's knowledge about the physics of these

materials. I would like to thank R. L. Barns for obtaining lattice constants, J. L. Shay

and B. Tell for their enthusiastic investigation of modulation and luminescence spectra and

of electrical properties, G. D. Boyd for his untiring effort to uncover better nonlinear

optical materials and Miss B. E. Prescott for the transmission spectra.

7. REFERENCES

[1] see for example "Physics and Chemistry of II-VI Compounds", edited by M. Aven and J. S. Prener, John Wiley and Sons, New York (1967)

.

[2] See for example 0. Madelung, Physics of III-V Compounds, John Wiley and Sons, New York

(1964) . [3] Fischer, A. G. , Jo\irnal of the Electrochem. Soc. 118 , (6), 139C (1971).

[4] Hahn, H., Frank, G. , Klinger, W. , Meyer, A., and Storger, S., Z. Anorg. allg. Chem. 271,

153 (1953)

.

[5] Gross, R. , Gross, N., Neues Jahrb. f. Min. Bull. 48, 113-135 (1923).

[6] Zhuse, V. P., Sergeeva, V. M. and Shtrum, E. L., Zhurnal technischeskoi Fiziki 28, 2093

(1958); translation: Soviet Physics, Tech. Phys. 2, 1925 (1958).

[7] Cambi, L., Elli, M. , Chimica e Industria 48, 944 (1966).

[8] Cound, V. M., Davies , P. H., Hulme, K. F., and Robertson, D., J. Physics C 3, L83 (1970)

678
[9] Lerner, L. S., J. Phys . Chem. Solids 27_, 1 (1966).

[10] For the vapor transport method compare H. Schafer, Chemical Transport reactions. Academic

Press, New York (1964).

[11] Parthe, E., Yvon, K. , and Deitch, R. H. , Acta Cryst. B25 , 1164 (1969).

[12] Belova, C. K. , Koshkin, V. M. , and Palatnik, L. S., Izvestia Akad Naiik SSSR, Neogranicheskia Materialy 3^, 617 (1967) . [13] Tell, B., Kasper, H. M. , Phys. Rev. B, £, 4455 (1971).

[14] Boyd, G. D., Kasper, H. M. , and McFee J. H., IEEE Journal of Quantum Electronics, QE7 , 563 (1971)

.

[15] Chemla, D. S., Kupecek, P. J., Robertson, D. S. and Smith, R. C, Optics Comm. _3, 29

(1971) . [16] Hobden, M. V., Acta Cryst. A24 , 676 (1968).

[17] Apple, E. F., J. Electrochem. Soc. 105 , 251 (1958); Fischer, A. G. , J. Electrochem.

Soc. 106_, 839 (1959) . [18] See for example. Shay, J. L., Buehler, E., and Wernick , J. H. , Phys. Rev. B3 , 2004

(1971) . [19] Shay, J. L., Tell, B., Kasper, H. M. , and Schiavone , L. M. , to be published (Phys. Rev.

B) . [20] Tell, B., Shay, J. L. , and Kasper, H. M. , Phys. Rev., B4 , 2463 (1971).

[21] Ballhausen, C. J., Introduction to Ligand Field Theory, McGraw Hill, New York (1962).

[22] Austin, G. , Goodman, C. H. L., and Pengelly, A. E., J. of the Electrochem. Soc. 103 , 609 (1956) . [23] Tell, B., and Kasper, H. M. , unpublished.

[24] Shay, J. L. , Tell, B., Kasper, H. M. , Appl. Phys. Lett. 19_, 366 (1971).

[25] Henry, C. H., Faulkner, R. A., and Nassau, K. , Phys. Rev. 183 , 798 (1969).

679

;

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

CRYSTAL CHEMISTRY AND MAGNETIC PROPERTIES OF PHASES IN THE Ba-Fe-S(Se) SYSTEMS*

H. Steinfink, H. Hong and I. Grey-'-

Materials Science Laboratories

Department of Chemical Engineering

The University of Texas at Austin

Austin, Texas 78712

The crystal structures of a number of new phases synthesized in the Ba-Fe-S and Se systems were investigated by x-ray diffraction techniques. Ba2FeS3 is orthorhombic , Pnma, a = 12.087(5) A, b = 4.246(2) A, c = 12.359 (5) A, p^eas = ^-^ g/cc, Pcalc = 4.47 g/cc , Z = 4, m.p.

> 1300 °C. The compound is isostructural with Ba2ZnS3 and the structure consists of FeS^

tetrahedra sharing corners to form an infinite linear chain. Ba2FeSe3 is isostructural with

the sulfide and its parameters are a = 12.350(7) A, b = 4.439(2) A, c = 12.921(5) A. BaFe2S3

is orthorhombic, Cmcm, a = 8.7835(9) A, b = 11.219(1) A, c = 5.2860(5) A, Pmeas = 4.0 g/cc,

Pcalc ~ 4.40 g/cc, Z = 4, m.p. = 765 ± 10 °C. Three dimensional x-ray diffraction data was

used to refine the structure which consists of two FeSi^. tetrahedra sharing edges and this binuclear unit in turn shares edges with others to form an infinite chain. The structure of Ba

Fe2Se3 is essentially the same as that of the sulfide but they are not isostructural. The

selenide is orthorhombic, Pnma, a = 11.878(3) A, b = 5.447(2) A, c = 9.160(2) A, Pcalc = 5.44 g/cc, Z = 4; decomposes above 750 °C. BagFesS^s is tetragonal, I4/m, a = 11,408(2) A,

c = 10.256 (2) A, P„^-,_ = 4.30 g/cc, P = 4.36 g/cc, Z = 2, m.p. 880 ± 10 °C . The structure

was determined from three dimensional x-ray diffraction data and consists of a tetranuclear

unit formed by 4 FeStt tetrahedra sharing corners and these units then share edges to form an infinite column. BasFesSey is hexagonal, P63mc, a = 10.843(3) A, c = 7.384(2) A, Pcalc ~ 5.00 g/cc, Z = 2. The structure was determined using three dimensional single crystal x-ray

diffraction data and consists of isolated trinuclear units formed by edge sharing of three

FeSi+ tetrahedra. The Fe-Fe distances between chains are 5 A, and vary from 2.6 A to 4.2 A

within the chains. The Fe-S distances are 2.3 - 2.4 A, the S-Fe-S angles are tetrahedral and

the Ba-S distances are essentially equal to the sum of the ionic radii. The corresponding

distances in the selenides reflect the larger size of the anion.

The magnetic characteristics of Ba2FeS3, BayFegSji^ and BagFegSi5 were investigated; all

three compounds are antiferromagnets . The values of the exchange forces, J/k , correlate with

the observed Fe-Fe distances.

Key words: Crystal structures of Ba2FeS3, Ba2FeSe3, BaFe2S3, BaFe2Se3 , Ba7FegSii4,

BagFegSis, BasFesSey; magnetic characteristics of Ba2FeS3, BayFegSit^ and BagFegSis.

1. INTRODUCTION

A series of new compounds has been synthesized in the barium-first row transition metalsulfur and selenium systems which is based on a common structural- scheme consisting of tetrahedra linked by corner and edge sharing into linear chains or columns.

The crystal structure of BayFegSjLf [1]^ and the structures and magnetic behavior of Ba2

MnS3 and Ba2MnSe3 [2] have been reported and a preliminary account of the structures of the

other phases has been given [3]

.

— . . _

Research sponsored by the Robert A. Welch Foundation, Houston, Texas

^Present address: CSIRO, Division of Mineral Chemistry, Port Melbourne, Victoria, Australia.

Figures in brackets indicate the literature references at the end of this paper.

681

/
2. EXPERIMENTAL SECTION

BaS, BaSe, Fe, S and Se constitute the starting materials for the ternary compound preparations. Commercial, yellow BaS, containing free S, was heated at 500 °C for 4-5 hours

under a current of H2. BaSe was prepared by the reduction of BaSe03 under a current of H2

at 500 °C for 4-5 hours. The Fe, S and Se powders were nominally 99.9% pure and no impurities were detected on examination of their x-ray powder patterns. Different ratios of BaS, BaSe,

Fe, S or Se were mixed in a graphite tube and sealed under vacuum of 10"^ to lO"'* mm in vycor

tubing and preheated at temperatures of 300 °C for sulfides and 350 °C for selenides for 4-5

hours. The temperature was then raised and kept in the range of 750 °C to 1050 °C for two

days. At the end of the reaction the sample was slowly cooled to room temperature by cutting

off the power to the furnace or was quenched by dropping it into ice water.

Melting points of the compounds were obtained by selecting single crystals and placing

them on a thermocouple j\mction to which an A.C. voltage was applied. Melting temperatures were obtained by observing the crystals microscopically. An x-ray powder diffraction diagram

was obtained after the material had solidified to check whether melting had occurred congruently

.

Densities of the compounds were obtained by the liquid displacement method using benzene

and the values have ± 10% precision.

3. STRUCTURES OF Ba2FeS3 AND Ba2FeSe3

The initial mixtures of 2BaS:Fe:S and 2BaSe:Fe:Se were heated at 850-870° for 2 days.

The x-ray powder patterns of the two products were quite similar indicating that they were probably isostructural . Weissenberg and precession diagrams of a single crystal selected

from the selenide showed that the space group is either Pnma or Pn2ia, with lattice parameters

a = 12.350(7) A, b = 4.439(2) A, c = 12.921(5) A. The powder pattern of Ba2FeS3 was also indexed on the basis of an orthorhombic cell with lattice constants a = 12.087(5) A, b = 4.246

(3) A and c = 12.359(7) A. With an assumed stoichiometry based on the initial composition

and a knowledge of the lattice constants and space group it was found that the compounds

could be isostructural with Ba2ZnS3 [4] . A calculation of the powder intensities for Ba2

FeS3 and single crystal intensities for Ba2FeSe3 using the atomic coordinates of Ba2ZnS3

gave good qualitative agreement and confirmed that the structures were identical. The meas- ured density of Ba2FeS3 is 4.02 g/cc, calculated p = 4.47 g/cc, Z = 4 formula weights per

unit cell; m.p. > 1300 °C.

The projection of the structure of Ba2FeS3 on (010) is shown in figure 1. A linear infinite tetrahedral iron chain, formed by corner sharing, exists parallel to the b axis and

the Fe-Fe distance between shared tetrahedra is 4.246(3) A, the b axis dimension of the unit

cell. In Ba2FeSe3 this distance is 4.439(2) A. Bond distances were calculated on the basis

of the Ba2ZnS3 parameters and the Fe-S distance where S is shared between two Fe ions is

2.45 A, considerably longer than the other Fe-S distances of 2.30 A and 2.38 A. One Ba+2 is

surrounded by six S ions at the corners of a trigonal prism and an additional S ion is approximately centered above one rectangular face. Seven S ions surround the other Ba+2 , four

at the corners of a square plane and three at the corners of a triangle whose plane contains

the barium ion and is perpendicular to the plane of the square. Ba2FeS3 is isostructural

with Ba2ZnS3, K2CUCI3, (NH4)2CuBr3, Cs2AgCl3 , Cs2Agl3 and CuPbBiSs [5].

4. CRYSTAL STRUCTURE OF BaFe2S3

A mixture of BaS:2Fe:2S was prepared and heated at 790 °C for two days and then slowly

cooled to room temperature. Weissenberg and precession pictures indicated space groups

C2cm, Cmc2i and Cmcm. The lattice constants were a = 8.7835(9) A, b = 11.219(1) A, and c = 2860(5) A. The measured density is 4.00 g/cc, p^^^ = 4.40 g/cc, Z = 4; m.p. = 765 ± 10 °C. An examination of lattice constants and space groups for compounds with stiochiometry AB2C3

[5] showed that CSCU2CI3 might be isostructural with the unknown phase. Single crystal intensities were collected using the stationary crystal-stationary counter method with balanced

filters for molybdenum radiation and 336 independent reflections were measured. The data were reduced to F(hk£) in the usual manner.

682
B02 Fe S3

Fig. 1. The projection of Ba2FeS3 on (010).

The numbers inside the circles denote

fractional heights along the b axis.

The atomic parameters for CSCU2CI3 [6] , space group Cmcm, were used as starting parameters for a least squares refinement of the structure and after 3 cycles with anisotropic

temperature factors R was 0.064 and wR was 0.067; (R = z1|Fq| - [f^ ||/e|Fq|, wR = [ZwCFqF(,) 2/EwFq^] 1/2) . The final parameters are shown in table 1, and bond distances and angles

are shown in table 2.

4.1. DISCUSSION OF THE STRUCTURE

Two FeSi4 tetrahedra share an edge with the line formed by the two Fe ions parallel to the

a axis of the unit cell, figure 2. This unit of two tetrahedra, in turn, shares edges with

another unit above it and parallel to the c axis and forms an infinite chain along 1001]

,

shown stereoscopically in figure 3. The Ba+^ is coordinated to 8 sulfur ions, six are located

at the corners of a trigonal prism at 3.29 A and 3.45 A and two are approximately above the

rectangular faces at 3.35 A. Two additional sulfur atoms are located near the third rectangular face of the prism but at 3.92 A and can't be considered as part of the coordination

sphere.

Table 1

Atomic Parameters and Their Standard Deviations in Parentheses

(x 10*+) for BaFa2S3*

Atom x y z Bll B22 B33 B12 Bl3 B23

Ba 1/2 1859 (3) 1/4 66 (3) 41(2) 94(9) 0 0 0 Fe 3464(4) 1/2 0 26(4) 14(3) 33(11) 0 0 0 S(I) 1/2 6147 (9) 1/4 35 (12) 10(7) 70(34) 0 0 0 S(II) 2074(9) 3768(7) 1/4 52(9) 41(7) 50(23) 0 0 0

temperature factor is [exp- (Bllh2 + Baak^ + B33^2 + 2Bi2hk + 2B 13hl + 2B2 3k£) ]

.

683

;
Table 2

2 Fe-Si

2Fe-S2

Fe-Fe

Fe-Fe

Ba-Fe

2Ba-Si

Bond Distances and Angles in BaFe2S3^

Distances (A)

2,28 (1) 4Ba-S2 3 29(1)

2.27(1) 2Ba-S2 3 35(1)

2,643(5) 2Ba-S2 3 92(1)

2.699 (5) 2S2-S1 3 69(1)

3,998(5) Sl-Si 3 69(1)

3.46 (1) 2S2-S1 3 70(1)

S2-S2 3 82(1)

Angles

S2-Fe-Si

S2-Fe-Si

51-Fe-S2

52-Fe-S2

S2-Fe-Si

Si-Fe-S2

108.1(4)

107.6 (4) 108.1(4)

114.9 (4) 108.9 (4) 108.9 (4)

Standard deviations are shown in parentheses.

The number in front of a bond length indicates how frequently this length occurs

Fig. 2. The projection of the structure of

BaFe2S3 on (001)

.

684
Fig. 3. Stereoscopic drawing of the double tetrahedral

chain in BaFe2S3. The horizontal direction is

[100] and the vertical [001]

.

5. CRYSTAL STRUCTURE OF BaFe2Se3

A mixture of BaSe:2Fe:Se was heated at 790 °C for 2 days followed by slow cooling. The

x-ray powder pattern of the material showed great similarity to BaFe2S3 and initially these

two compounds appeared to be isostructural . Weissenberg and precession pictures showed that

the possible space groups were Pnma or Pn2]^a; the lattice constants were a = 11.878(3) A,

b = 5.447(2) A, c = 9.160(2) A; P = 5.44 g/cc , Z = 4; decomposes above 750 °C . The different space group showed that this compound was not isostructural with BaFe2S3 and a search

of lattice constants and space groups for compounds with a stoichiometry AB2C3 [5] indicated

that constants for CsAg2l3 were similar to those of the unknown phase. A single crystal

structure determination was undertaken on the assumption that the compound was BaFe2Se3 and

was isostructural with CsAg2l3.

Single crystal x-ray intensities were collected in the range 3° < 26 < 50° using unfiltered AgK radiation and a scintillation counter. The integrated intensities of 1150 reflections were obtained and reduced to F(hk2.). The atomic parameters for CsAg2l3 were used as starting parameters for a least squares refinement. After four cycles of refinements using

anisotropic temperature factors, R was 0.0725 for 983 reflections greater than o and R = 0.0891 for all 1150 reflections. The final parameters are shown in table 3; bond distances

and angles are shown in table 4.

5.1. DISCUSSION OF THE STRUCTURE

The structure shown in projection on (101) in figure 4 is basically identical with that

of BaFe2S3 but sufficient distortions exist to change the symmetry operations relating the

atoms and the coordination of the Ba"*"^ is thereby affected. The Ba"^^ is surrounded by 5 Se~' at the corners of a trigonal prism with Ba-Se distances of 3.358 A, 3.455 A, and 3.534 A. Two additional Se~^ are above the centers of two rectangular faces of the prism at distances

Table 3

Atomic Parameters and Their Standard Deviations in Parentheses

(xlO^) for BaFe2Se3*

Atom X y z Bll B22 B33 B12 Bl3 B23

Ba 1847 (1) 1/4 5185 (1) 49 (1) 89 (3) 59 (0) 0 15(1) 0 Fe 4947(1) 3(3) 3515 (1) 28(1) 75 (4) 31(1) -2(1) -0(1) 0(2)

Sel 3590 (1) 1/4 2272 (2) 40(1) 71(4) 45(2) 0 -21(1) 0 Sell 5259 (1) 1/4 4915(1) 28(1) 56 (4) 34(1) 0 0(1) 0 Belli 3975 (1) 1/4 8125 (2) 47(1) 92(5) 53 (2) 0 28(1) 0

* The temperature factor is [exp-B^h^ + 622^^ + B^^l^ + '2Bi2hk + 2Bi3h£ + 2B23k£)].

685
Table 4

Bond Distances and Angles in BaFe2Se3^

Distances (A)

r c OCT z9 • J

"50^; r^D (0^ \ J 0

. HDD (±) te 15a. 063 . HDD \XJ

Fe-Se2 2.434(2) Ba-Se;^ 3 .377(2)

Fe-Se2 2.444(2) Ba-Se3 3 .694 (2) Fe-Fe 2.721(3) Ba-Se3 3 .745 (2) Fe-Fe 2,726(3) Sei-Se3 3 .988(2)

B3.~Fe beC — C la

]^ —062 J . H±o \ Z J B6.— Se ]^ Se ]^ ~Se2 3 .753(2)

£5a. oS T 663 be2 QQQ t

') \

Dei O c p 3 QDP,

Oct O tr p 3 . 534 (1) 0 cp 0 cp 3 • 0^ u V ^

/

Angles (°)

Sei-Fe-Se3 112.55 (8) Sei-Fe-Se2 111.32 (6) Sei-Pe-Se2 101.67 (7) Se3-Fe-Se2 107.83 (7) Se3-Fe-Se2 111.35 (6) Se2-Fe-Se2 112.13 (6)

'standard deviations in the last decimal place in parentheses

Bo FegSe

Fig. 4. The projection of the crystal structure

of BaFe2Se3 on (010).
of 3.377 A and 3.694 A from Ba''"^ . The corresponding Ba-S distances in BaFe2S3 are equal. A ninth Se~^ is near the third rectangular face at a distance of 3.745 A while the tenth selenium atom is at a distance of 4.47 A. If the Ba"*"^ coordination is taken as 8 in BaFe2S3

then it can be considered as 9 in BaFe2Se3 . In the former compound the coordination polyhedron is also more symmetric.

6. CRYSTAL STRUCTURE OF Ba^FegS^^

This structure has been published [1] and is included here for the sake of completeness.

The basic structural unit is a trinuclear iron cluster, Fe 35^32/2 ' which consists of three

FeSi^ tetrahedra, where the central tetrahedron shares its two opposing edges with two other

tetrahedra. The trinuclear groups link together by corner sharing of the tetrahedra to produce infinite zigzag chains in the general direction of the "b" axis. The chains are held

together by the packing of the barium ions.

Within a Fe3S7 group, the Fe-Fe distances are unequal, with Fei distances to the two terminal iron atoms 2.747(7) and 2.829(7) A. The bridging angles of Fe-S-Fe are in the range

72-75° and the sequence Fe2-Fei-Fe3 is almost linear (177.1(2)°). These distances and angles

are closely similar to those observed in KFeS3 [7] , containing infinite chains of edge-sharing

tetrahedra . Each of the FeSi^ tetrahedra is considerably distorted as reflected in the large

variation in the tetrahedral angles and in the Fe-S bond lengths. The distance between adjacent iron atoms of two corner-shared trinuclear groups is 3.670(7) A which is considerably

greater than the distances between irons within a cluster. It is, however, shorter than the

Fe-Fe separation in Ba2FeS3. Further details of the structure are presented in reference 1.

7. CRYSTAL STRUCTURE OF Ba.FeoSTt6 8 15

The C3rystal, which eventually was shown to have this stoichiometry , was found in the

product obtained from a quench of a starting mixture having the composition BaS:2Fe:2S which

had been held at 800 °C for two days. It was evident from the x-ray powder pattern that the

product was polyphas_ic. Weissenberg and precession photographs showed that the possible

space groups were 14, 14, and I4/m. The lattice constant were a = 11.408(2) A, c = 10.256(2)

A; Z = 2, P^~^j_ = 4.36 g/cc, P^eas ~ 4.30 g/cc ; the compound melts congruently at 880 ± 10 °C,

(the number of formula weights and calculated density are based on the subsequently determined

stoichiometry)

.

Three dimensional data were collected with MoK radiation. A total of 1033 reflections

was measured, of which 956 were considered to be above background.

The structure was determined by the use of the direct method for phase determinations.

Wilson statistics indicated a centric distribution and I4/m was selected as the proper space

group. The sequence of computer programs FAME-MAGIC-LINK-SYMPL [8] was used to generate

about 300 phases from five symbol assigned reflections. A three dimensional E(hk£) map showed

peaks which could be interpreted as due to two Ba and one Fe atoms. A three dimensional electron density map calculated with signs obtained with these positions revealed additional peaks

which were due to S and it became evident that the compound had the formula BagFesSxs. The

final parameters shown in table 5 were obtained by a least squares refinement. The final

R = 0.0800, wR = 0,0678 for 1034 reflections and R = 0.0714, wR = 0.0673 for 928 reflections

greater than a.

7.1. DISCUSSION OF THE STRUCTURE

The [001] projection of the structure is shown in figure 5. Four FeSt^ tetrahedra share

corners and their arrangement can be described with reference to an octahedron. Two opposing

faces of the upper half of an octahedron, (111) and (111) , form the bases for two tetrahedra

and they share a corner which is the apex of the octahedron; two opposing faces of the lower

half of the octahedron, (111) and (111) , form the bases of the other two tetrahedra and they

share a corner which is the lower apex of the octahedron. The sets of two tetrahedra share

corners which are the 4 points 100, 010, 100, and 010 of the octahedron. This unit of 4 FeSi+ tetrahedra is propagated by mirror planes perpendicular to [001] into an infinite column parallel to the c axis as illustrated in figure 6. The Fe-Fe distances between edge sharing

tetrahedra are 2.81 A and are 3.34 A, 3.54 A and 3.78 A for Fe-Fe distances when tetrahedra

687
Table 5

Final Atomic Parameters and Their Standard Deviations in Parentheses

(xlO^) for BagFeeSis^

Atom X y z BU B22 B33 B12 Bi 3 Bo 3

Bai 0 0 3044 (2) 14(1) 14(1) 25(2) 0 0 0 Ba2 24o4 (1} 1304 ( 1

)

0 lb (1) lb (1) 38 (1) 0 (1) 0 0 Fe 1537(2) 4384 (2) 1365 (2) 13(1) 14(1) 25(2) 0(1) -1(1) 1(1)

Si 790(3) 2700 (3) 2266 (4) 17(2) 14(2) 31(3) 3(2) 6(2) 4(2)

S2 3035(5) 3951 (4) 0 17(3) 15(3) 25(5) 0 0 0 S3 0 1/2 0 12(5) 13(5) 28(7) 4(4) 0 0

Sit 0 0 0 16(8) 16(8) 16 (9) 0 0 0

temperature factor is exp[- (Biih2 + B22k^ + B33^^ + 2Bi2hk + 2Bi 3h£ + 2B23k2,) ] .

I

Fig. 5. The projection of the structure of

BagFegSis on (001)

.

Fig. 6. Stereoscopic view of the infinite column

of tetrahedra in BagFe3Si5. The vertical

direction is [001] of the unit cell.

688

1
share corners. The Fe-Fe distance between atoms in adjacent chains is 6.10 A. The Ba ions

are in ninefold coordination. Eight S ions form a square antiprism around Ba; and the 9th

atom, S[+, is in the center of one square face, along the c axis. The S:. atom is not part of

a FeS(+ tetrehedron. The polyhedron around Bao consists of a capped trigonal prism. The Ba-S

distances are essentially equal to the sum of the ionic radii. The bend distances and angles

are listed in table 6.

The formula of this compound can be written as Ba.'.Fe- (III ) Fe, (11)3- ^ and since the F'-^ ions are crystallographically indistinguishable we can consider the average oxidation number

as 2.25. There is a possibility that electrical conduction can occur via a hopping mechanism

and that this material should display conductivity in one dimension similar to the recently

reported mixed valence square planar complexes, [9].

8. CRYSTAL STRUCTURE OF Ba3Fe3Se7

In addition to Ba2FeSe3 an unknown phase was occasionally observed in the reacted material obtained from an initial mixture of 2BaSe:Fe:Se. The unknown phase, which was later

found to be Ba3Fe3Se7, consisted of black hexagonally shaped crystals.

Weissenberg and precession photographs indicated the possible space groups P62c , PGjmc,

and P53/mmc. The lattice parameters are a = 10.843 (3) A, c = 7.384(2) A; Z = 2 , = 5.00

g/cc. Peak height intensities from a single crystal were obtained with balanced filters and

MoKa radiation. A total of 455 independent reflections was measured of which 397 were con- sidered observed.

Table 6

Bond Distances and Angles in BagFegSj^g

o Distances, A

Fe-S2 2 27(1) Bai-S2 3 23(1)

Fe-Si 2 29(1) Ba I-S2 3 23 (1) Fe-Si 2 30(1) Bai -Si 3 31 (1) Fe-S3 2 36(1) Ba.\ -Si 3 31 (1) Ba2~S2 3 09(1) Ba 1-Sl 3 31 (1) Ba2-S3 3 23(1) Ba 1-Sl 3 31 (1) Ba2-S4 3 20(1) -Si 3 74 (1) Ba2-Si 3 34(1) -S3 3 95(1)

Ba2-Si 3 34(1) -S3 3 67(1)

Ba2-Si 3 36(1) Si -S3 3 61 (1) Ba2-Si 3 36(1) S2 -Si 3 61 (1) Ba2-Si 3 61(1) si -Si 3 95(1)

Ba2-Si 3 61(1) Fe -Fe 2 811 (7)

Ba;^ ~S[^ 3 119 Fe-Fe 3 539 (7) Bai-S2 3 23(1) Fe-Fe 3 783 (7) Ba|-S2 3 23(1) Fe -Fe 3 342 (7) Fe-Fe 6 102 (7) Angles (°)

S2 -Fe-Sj 110. 3 (3) Si -Fe-S3 115. 8(3)

Si -Fe-Sj 118. 8(3)

S2 -Fe-S3 104. 9(3)

Si -Fe-Sg 102. 1(3)

S2 -Fe-Sj 104. 2 (3) Fe -S^-Fe 100. 8(3)

Fe -S3-Fe 106. 8(1)

Fe-Sj-Fe 108. 8(3)

^Standard deviations in the last decimal place in parentheses.

465-304 O - 72 - 45 689
The structure was solved from an interpretation of the three dimensional Patterson function even though the formula was unknown. The interactions observed in the various Marker

sections indicated that the probable space group was P63mc. The positions of one Ba and one

Se were located from the Patterson map and phases were calculated. A three dimensional electron density map based on these phases revealed positions for one Fe and two additional Se

atoms. It was evident now that the compound was Ba3Fe3Se7. The atomic coordinates were re- fined by least squares and after three cycles of refinements with antisotropic temperature

factors and using 381 reflections greater than a, R was 0.0704, wR = 0.071; for all 455 re- flections R = 0.0887, wR = 0.0725. The final atomic parameters are shown in table 7.

8.1. DISCUSSION OF THE STRUCTURE

The structure of Ba3Fe3Se7 consists of isolated trinuclear units formed by three FeSei^. tetrahedra sharing edges, figure 7. The Fe-Fe distances within the unit are 2.85 A and are

5.91 A between iron ions of different units. Ba is in eightfold coordination consisting of

a distorted trigonal prism which is capped on two rectangular faces. The (001) projection of

the structure is shown in figure 8. The Fe and Ba ions lie in planes at z = 0.486 and z = 0 respectively and they are separated by selenium lying in planes at z = 0.311 and 0.590. The

bond distances and angles of interest are shown in table 8. The formula can be expressed as Ba3Fe2 (III) Fe (II) Sey and the crystallographically equivalent Fe can be considered to have the

average oxidation number 2.66.

Table 7

Final Atomic Parameters and Their Standard Deviations in Parentheses

(xlO^) for Ba3Fe3Se7^

Atom X y z Bll B22 B33 B12 Bl3 B23

Ba 1911(2) 3822(2) 0 21(2) 21(2) 69(4) -6(2) 0 0 Fe 2458(6) 4916(6) 486(1) 38(7) 38(7) 5(1) 36(5) 0 0 Sei 4573(5) 9146 (5) 3110(7) 35(5) 35(5) 50(7) 25(4) 0 0 Se2 1252(4) 2504 (4) 5895 (7) 23(5) 23(5) 73(8) 13(4) 0 0 Se3 1/3 2/3 738(1) 17(7) 17(7) 30(1) 0 0 0

2 The temperature factor is exp[-(Biih2 + 622^^ + ^33^ + 2Bi2hk + 2Bi3h£ + 2B23k£)]

Fig. 7. Stereoscopic view of 3 FeSe^ tetrahedra

forming the trinuclear unit in Ba3Fe3Se7.

690
Fig. 8. Projection of the structure

of BasFesSey on (00.1).

Table 8

Bond Distances and Angles in Ba3Fe3Se7^

Distances O

, A

Fe-Sei 2.44(1) Ba-Se3

Fe-Se2 2.39 (1) Ba-Se2

Fe-Se3 2.48(1) Ba-Se2

Fe-Sei 2.44(1) Ba-Se2

Fe-Fe 2.85(1) Sei-Se3

Ba-Fe 3.84(1) Sei-Se2

Fe-Fe 5.91(1) Se2-Se3

Ba-Sei 3.75(1) Sei-Sei

Ba-Sei 3.75(1) Sei-Se3

Ba-Sei 3.41(1) Sei-Se2

Ba-Sei 3.41(1)

Angles, (° )

Sei-Fe-Se3 105.5(5)

Sei-Fe-Se2 110.8(5)

Se2-Fe-Se3 112.8(5)

Sei-Fe-Sei 111.2(5)

Sei-Fe-Se3 105.5(5)

Sei-Fe-Se2 110.8(5)

3.30(1)

3.27(1)

3.26(1)

3.26 (1) 3.92 (1) 3.98(1)

4.06(1)

4.03(1)

3.92 (1) 3.98(1)

^Standard deviations in the last decimal place in parentheses.

9. MAGNETIC PROPERTIES OF Ba2FeS3, Ba^FegS^^ AND BagFegS^^

A Faraday type magnetic balance was used to measure the magnetic susceptibilities of the

BaxFeyS2(Se) compounds. Each datum point is an average measurement on two samples and the

differences are all within 8%. The results are shown in the form of the usual ^/Xp^ vs. temperature (°K) plots; X;^ is expressed in electromagnetic units in the cgs system. The linear

portions of the curves (Curie-Weiss behavior) were extrapolated to obtain a value for the

Weiss constant Q

.

The curve of vs T for Ba2FeS3, figure 9, exhibits a minimum at 110 K and is typical

for an antiferromagnet. A theoretical equation has been proposed for the susceptibility of

a one-dimensional array of Ising spins for S = 1/2, and S = 3/2. A reduced spin model

691
Ng^B^S ( S+1) J 'AT

ihs been applied with good results for S = 2 and S = 5/2. Therefore, log [(3k/N3^)xT] was

.l:.-T:'-d against 1/T in figure 9 for Ba2FeS3 (S = 2) and the data fit the straight line relai.ionship rather well. The intercept, g^S (S+1) , yields a magnetic moment of 5.29 BM which is

;;eadori.ajDle for a tetrahedral iron (II) ion in a weak ligand field having S = 2. The g factor

of 2.16 in Ba Fe.i . shows that the orbital moments are quenched. Table 9 summarizes the magni-cic parameters for the three compounds. The value of Ueff for Ba2FeS3 obtained from the

Cune-Weiss plot is too high for Fe"*"-- and is actually the value for Fe"*"^. A value closer to expected one is obtained from the reduced sjsin plot. A much larger number of experimental

190

150

otl

Bag FeS3

9 =-385 °K

Ueff= 5.98

100 300

T° K

500

ro 5

or_

802 FeS3 : j'/k =-162 "K [g2S(S + l)]'^2 ^5.29B.M

.002 .004 .006 l/T "K"'

.008

Fig. 9. Magnetic susceptibility as a function

of temperature for Ba2FeS3.

Table 9

Compound

Magnetic Parameters

Curie-Weiss Plot

T K y K ^eff

Reduced Spin Plot

J 'A K [g2s (S+1) ] V2 Metal-Metal

o Distances A

Ba-FeS ^ BayFegS;

4

BapFegSi

5

BaPeoS i

110

200

250

600

-385

-152

-937

-395

5.98 (2.44)

5.30(2.02)

5.57(2.15)

4.00(1.64)

-162

-228

-304

-480

5.29(2.16)

5.70(2.18)

4.39(1.70)

4.70 (1.92)

4.246

2.747-3.670

2.810-3.780

2,643

g values are given in parentheses

nearest transition metal distances

692
200

150

0

Ba^ Feg S,^

e = -152.2 "K

Ugff = 5,30 B.M.

_l L. 200 400

T " K

600 800

Fig. 10. Magnetic susceptibility as a function of temperatur;

for BayFef.S 1 1,

.

400

Xa

320 -

ot.

Bos Fee S|5

B = -937 »K

Ueff = 5.57 8. M.

200 400 600

Fig. 11. Magnetic susceptibility as a function

of temperature for Ba5Fe3S]5.

points follow a linear relationship when this interpretation is used and the intercept Is thus much better defined than the slope obtained from the Curie-Weiss plot. The curves of

atomic reciprocal susceptibility 1/X;^ vs. temperature observed for Ba7Fef,Sii4 and Ba,-,Fec S i , figures 10 and 11, show that these materials are also antiferromagnets . The Neel temperatures

are 200 K and 250 K, respectively.

If the trinuclear unit in BayFegSn^ is treated as a single unit, then the zig-zag iron

chain can be considered as a linear chain in which each unit shares corners as observed in

Ba2FeS3. Therefore the reduced spin model was tried and log [(3k/N6^)xT] was plotted against

1/T, figure 12. The intercept, g^sCS+l) , yields a magnetic moment of 5.70 BM which is

reasonable for an iron ion having average S = 2.17. This suggests that the reduced spin model

may be applicable and that the effective spins of the clusters can be considered as forming a one dimensional antiferromagnet

.

693
• 807 F'es S|4 [^S(S+I)]'^=5.70B.M.

J'/K =-228 "K

Boe Fee S15 :(g^S(S-H)]'^=4.39aM,

j'/K =-304 »K

002 .004 .006 .008 .010 l/T

Fig. 12. Plot of magnetic susceptibility as a function of temperature using the

reduced spin model.

The reduced spin model was also tried for BagFesSis and the plot is shown in figure 12. The intercept gives a magnetic moment of 4.39 BM which is unreasonable for iron ions with an average S = 2.125. This suggests that the antiferromagnetism of BagFegSis can not be ex- pressed as a simple linear interaction. This is not too surprising since the linear structure

is columnar rather than a chain. The very high Curie-Weiss constant, G = -937 K, implies a strong interaction among iron atoms.

The slope of the straight line portion permits the calculation of the effective exchange

energy J'/k and these values are listed in table 9. It is evident that the exchange energy

correlates very well with the Fe-Fe distances found in these structures.

10. REFERENCES

[1] Grey, I. E., Hong, H. and Steinfink, H. , Inorg. Chem. 10, 340 (1971).

[2] Grey, I. E. and Steinfink, H., Inorg. Chem. 10, 691 (1971).

[3] Hong, H. and Steinfink, H., Abstracts, American Crystallographic Association, Winter

Meeting 1971.

[4] Schnering, H. G. and Hoppe, R. , Z. Anorg. Allg. Chem., 312 , 99 (1961).

[5] Wyckoff, R. W. G., Crystal Structures, 2_, Interscience Publishers, J. Wiley & Sons, New

York (1964)

.

[6] Brink, C, Binnendijk, N. F. and van de Linde , J., Acta Cryst. 7_, 176 (1954).

[7] Boon, J. W. and MacGillavry, C. H., Reel. Trav. Chim, Pays-Bas , 61_, 910 (1942).

[8] Dewar, R. B. K. , Proceedings of the 1969 International Summer School on Crystallographic

Computing, Ed. F. R. Ahmed, Munksgaard, Copenhagen, 1970.

[9] Minot, M. J. and Perlstein, J. H., Phys. Rev. Lett. 26_, 371 (1971).

DISCUSSION

R. S. Roth : Did you try to determine whether the compounds you have described can be

considered part of a homologues series?

H. Steinfink : There doesn't seem to be a general expression that would cover the various

stoichiometries described in this presentation.

694
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

STUDY OF SULFOSPINELS

R. E. Tressler and V. S. Stubican

Department of Material Sciences

The Pennsylvania State University

University Park, Pennsylvania 16802

Several new compounds with the formula AB2S1J were synthesized. Pressure-induced polymorphism of the sulfospinels was investigated. Sulfospinels which produced new high-pressure phases were NiRh2Stt, FeYb2St^ , In2S3, CrIn2S^ , NiIn2Si4, CoIn2S[^ and MnIn2S4. The only

sulfospinels which transformed to the NiAs derivatives were those in which A and B atoms had

unfilled d-orbitals. P-T phase relations were investigated for a series of sulfochromites

.

Thin films of several ACr2Stt (A = Mn, Fe, Co, Cu and Zn) sulfospinels were prepared by

a flash evaporization technique on the (111) and (100) planes of NaC£ and on the (100) plane

of MgO.

Key words: Flash evaporation; high pressure phases; sulfospinels; thin films.

1. INTRODUCTION

The existence of well defined sulfospinels has been known for some time [1]^. Structures

of complex sulphides with composition M^^M^HSit have been reported by several authors. Hahn

et al. [2], Lotering [3], Bouchard et al. [4], Blasse and Schipper [5], Flahaut et al . [6,7,8],

Pinch et al. [9] , Romers et al. [10] , Omloo and Jellinek [11] , Patrie et al. [12] , Donahue

[13] , Lugscheider et al. [14] , Steigmann [15] , Bouchard and Wold [16] , Bouchard [17] , Plovnik

[18] have studied the preparation and the structure of the M^-'-MlUS^ compound. The purpose

of this paper is to summarize our recent results on (i) the synthesis of some previously un- reported M-^-'-M^I^Si4 compounds (ii) the polymorphism of sulfospinels at high pressures and

(iii) the preparation of thin films of some sulfospinels.

2. EXPERIMENTAL PROCEDURE

2.1. SYNTHESIS OF M^^M^^^S^ COMPOUNDS

Usually the two metals and sulfur were mechanically mixed, pelletized, sealed under vac- uum in fused silica tubes, heated slowly from 200 °C to 800 °C, held for several days, ground,

pelletized, heated at 700 to 800 °C for several days, and then recycled until the sample was

single phase. Exceptions were the use of rare-earth and scandium sulfides, cupric sulfide

and cadmium sulfide. When two sulfides were mixed to form a ternary compound, heat treatment

was begun at high temperatxires

.

2.2. HIGH PRESSURE EXPERIMENTS

The high pressure experiments were performed with externally heated uniaxial devices,

using pistons of cemented carbides and hardened steel. The high pressure apparatus is described fully elsewhere [19]. The samples were pelletized into platinum rings, sandwiched

between two platinimi sheets to assure a closed system, and placed between two pistons on

1 Figures in brackets indicate the literature references at the end of this paper.

695
which hicih x-'i^essure was applied. After 1 to 14 days the specimens were quenched to room temperature by a cold air blast, and the pressure was released. With some specimens, the same treatment was repeated several times to assure equilibrium. Temperatures and pressures were

:.utoinatically controlled to : 5 °C and r 5% respectively

2,3. PREPARATION OF THIN FILMS

The technique of flash evaporation [20] was used to prepare thin films of sulfospinels

'.-;hich contained elements with different vapor pressures. The spinels MnCr2S[4 , FeCr2S4 , Co

?r ,Sij , CuCr Si, and ZnCr2S4 were prepared as previously described. The evaporation was accom- blishea using a Hitachi vacuum evaporator fitted with a copper block substrate heater against

v.-hich the substrate was held by stainless steel clips. The substrates were Harshaw NaCl

crystals cut, and polished on the (111) plane and NaCS. crystals cleaved on the (100) plane.

General Electric MgO crystals cleaved on the (100) plane were also used. A thin wafer of

the spinel was evaporated from the W-strip. The substrate to strip distance was held constant

at 1 1/8". Spinel film could be obtained by preheating the substrate to 170 - 180 °C, evaporating for 2 to 6 seconds, and annealing in place at 210 - 220 °C for 24 hrs . The vacuum before evaporation was consistently 0.9 - 1.0 x 1.0"^ Torr as measured by an ionization gauge,

calibrated against a Stokes McLoad gauge. By weight gain measurements and knowing the spinel

o o o densities, the film thicknesses were calculated to be between 500 A and 1500 A, the 1500 A film being opaque.

The thin films were floated off the substrate in water or alcohol onto a copper grid and

Wore examined in transmission on a Hitachi electron microscope.

3. RESULTS AND DISCUSSION

3.1. SYNTHESIS OF COMPOUNDS

Table 1 includes the conditions of preparation and the proposed structures of the AB2Sit

compounds which were previously unreported.

Table 1

Syntheses of Previously Unreported Compounds

Compound

NiA. iSu,

ZnSc2S4

NiYb2S^*

NiRh2Si^

FeRhoSi.

^

Preparation

300 °C 1 day, 800 °C 4 days

800 °C 1 day, 1200 °C 1 day

(2 cycles) , 950 °C 1 week

400 °C 1 week, 800 °C 1 week

1200 °C 1 day, 950 °C 1 week

400 °C 1 week, 800 °C 1 week

600 °C 6 days, 800 °C 4 days

900 °C 6 days, 600 ""C 11 days

X-ray Diffraction

Results

Isostructural with

Spinel, ao = 10,478

± 0.001 A

Isostructural with

a- CaY2St+

Spinel, aQ = 9.701

± 0.001 A

Unidentified

* CuYb^Si^ , CdYb2SLt , ZnYb2S:^ , ZnLu^St^ , CdLu2St, , and CoLu2S:t were prepared under the sairie conditions as NiYb?Si, and appear to be isostructural with this compound.

.L CrRh;,S4, MnRh^St^ , ZnRhoS4 and CdRhQSi, were prepared under the same conditions as FeRh2S4

and appear to be isostructural with this compound.

696
From the results in table 1 and from literature sources [2-18] the octahedral radius of

the A-'--'- ion can be plotted versus the radius of the B-'--'--'- ion for A-'^-'-B^^-'-Si^ compounds. Sulfides are more covalent than oxides because of the lesser electronegativity of sulfur [21]

.

The use of ionic radii for characterization of a "structural field" has a limited value in

this case. Because of many variables involved (coordination change, degree of covalency,

etc.) no single type of radii is completely satisfactory. However, strictly for the matter

of relative comparison, figure 1 was prepared. Some regularities in this figure are obvious.

For large B-'--'--'- ions there is some overlap of the spinel and a-CaY2S4 structure type. Pressure or temperature polymorphism of the compounds near the boundary is a possibility which

was not investigated. For large B-'--'--'- and A-'--'- ions, the Th3P4-type structure is predominant.

With small B-'--'--'- ions the FeA?.2Si+ type structure, where both A"'--'- and B-'--'--'- ions are in fourfold coordination, overlaps with spinels. The compounds with the spinel type structure surround a central area of compounds with the defect Ni-As structure which has predominately

covalent bonding. With the small B-'--'--'- and large A-'--'- ion hexagonal PbCr2SL( type structure

appears [11] . However, the shortcomings of the presentation of the structural relationships

as given in figure 1 become evident if one considers the polymorphism of some AB2S11 compounds

at high pressure or temperature. NiIn2S^ and other In-spinel containing transition elements,

all form a high pressure phase which is not isostructural with NiAs or CaY2SLj . ZnA£2SL|. possesses a normal spinel type of structure at room temperature. The high temperature polymorph

has a layered structure with an orthorhombic cell [15].

3.2. HIGH PRESSURE RESULTS

The appearance of the NiAs structure field and the known spinel-NiAs polymorphism promoted the investigation of the effect of pressure on other sulfospinels [22] . The results

are listed in table 2. It is evident from table 2 that only spinels which transformed to the

NiAs derivatives are those in v/hich A-'--'- and B-'--'--'- ions have unfilled d-orbitals, i.e., a d-d

interaction is necessary to stabilize the face-shared octahedral arrangement in the NiAs

structure.

In2S3 transformed to a high pressure form which could not be indexed as an NiAs structure. The other In-spinels produced a similar high-pressure phase. The d-spacings for high

pressure In2S3 and NiRh2Si+ are given in table 3.

The chromite series of sulfospinels was selected for quantitative investigation of the

pressure- temperature relations between the spinel and NiAs structures. The experimental P-T

curves for several spinels are given in figures 2A and 2B. The P-T curve for FeCr2Si| was in

excellent agreement with the data of Albers and Rooymans [22] . For the P-T conditions near

1.20

» 0 90

0 50

La

I 1 X SPINEL TYPEr •

1 1 FeAl2S4 TYPE

1

1 A

1 1 1

NiAs TYPE PbCr2S4 TYPE

Ce 0 C0Y2S4 TYPE A A

Nd A Th3 P4 TYPE A AA A

" EuGd A AA A

Dy

Y

- ErTm

Yb

Lu

In

- Sc

8

0

>

>

0

0

° 80 0§

X XX X

XX X

X

X

OOX

X

X

0

oot>

X

oooo

00

oooo

00

OOOO

TiV amam

Rh X XXX

CrCo BHUXB

X XX

a X X ,

" NiGo X a

X

_ Al • • XX*

Mq Ni CuCoZnFe

1 Cr , Mn VTi

1 I Cd Co

1 Hg EuSr Pb __, 1 Cr_j . I I I 1 I I 1 1—

0.65 0.70 0.75 0.80 0 85 0.90 0 95 1.00 1.05 1. 10 1.15 1,20

Fig. 1. Structure of AB2S4 compounds.

697
Table 2

High Pressure Results

Treatment

P T t Compound (kbars) (°C) (days) Phases Lattice Parameters (A)

CoNi2Stt 50 500 2 Disordered NiAs a = 3.42±0.01, c = 5.33±0.01

CuV2Sit 60 415 3 Ordered NiAs a = 5.82+0.01, b = 3.30±0.01

c = 11.44±0.01, 3 = 91.90°

CuTi2Si+ 58 510 4 Disordered NiAs a = 3.44±0.02, c = 5.65±0.05

MnCr2Si+ 60 520 7 Ordered NiAs a = 5.98±0.01, b = 3.45±0.01

c = 11.74±0.05, 3 = 91.2°±0.10°

FeCr2Sit* 55 520 7 Ordered NiAs a = 5.94±0.01, b = 3.44±0.01

c = 11.47±0.01, 3 = 90.85°±0.05

CoCr2Si+ 40 520 7 Ordered NiAs a = 5.91±0.01, b = 3.41±0.01

c = 11.10±0.05, 3 = 91.7°±0.1°

CuCr2Sit** 80 600 4 Spinel No transformation

ZnCr2Stt 80 600 4 Spinel Nc transformation

NiCr2Stt 50 500 4 Ordered NiAs (same as a = 5.90±0.01, b = 3.42±0.01

In2St^ + starting material) c = 11.04±0.05, 3 = 91.5°±0.05°

45 500 3 High-pressure phase. Unidentif. d spacings (table 3) not NiAs

Feyb2Si+ 60 485 3 High-pressure phase, Similar to In2S3, unidentif.

not NiAs

NiRh2S4 45 497 3 High-pressure phase, Unidentif., apparently complex

not NiAs distortion of spinel

* Albers and Rooymans [22] reported hexagonal NiAs cell parameters, a = 3.4 A, c = 5.7 A

^ NiIn2Sit , CoIn2Si| ,CrIn2S4 , and MnIn2S[| all form high-pressure phases isostructural with

high pressure In2Si+

.

** Bouchard [17] reported the transformation of CuCr2Sit to the NiAs type structure.

Table 3

X-ray Diffraction Powder Patterns of High Pressure Phases

In^S^ NiRh^S^

d spacings (A) (I/Io) obs d spacings (I/Io)obs

4.58 30 3.07 20

4.40 60 3.00 100

3.47 50 2.14 15

3.29 70 2.11 40

3.10 80 1.99 10

2.68 80 1.89 25

1.89 100 1.76 10

1.73 60

698
50 NiAs TYPE

the transition, the hexagonal NiAs structure was observed for FeCr2S^ and MnCr2S4 , after they

were held for short times. At longer times and more extreme pressures, the monoclinic NiAs

phase appeared as shown in figure 3. However, for all conditions of treatment in the NiAs

field, CoCr2Si^ transformed directly to the ordered monoclinic NiAs phase. ^ In figure 4, xray densities for the spinel-type and NiAs-type phases are compared. The difference in the

densities of the low- and high-pressure polymorphs increases from 6.6% for FeCr20i^ to 9.1%

for CoCr2S4

.

Considering the equilibrium transition pressure at 600 °C versus the various parameters

for the aH ion, such as ionic radius, number of d-electrons, and octahedral site preference

energy, there are no definite trends. The equilibrium transition pressure decreases with increasing octahedral site preference, however, CuCr2Si^ does not fit this trend. It is evident

from these results that the magnitude of the transition pressure depends on the crystal chemical parameters in a complex way.

3.3. PREPARATION OF THIN FILMS -

The selected area diffraction patterns showed all compositions deposited onto the (111)

plane of NaCJi gave polycrystalline spinel patterns with some preferential orientation on the

substrate. The excellent agreement of lattice parameters determined by electron diffraction

on thin films and by x-ray diffraction on polycrystalline samples showed that the films were

not far from AB2Si^ stoichiometry [23] . 2 In a concurrent investigation, Bouchard [17] obtained also monoclinic high-pressure polymorphs of Mn-, Fe-, and CoCr2S4 well above the equilibrium transformation conditions.

699
FeCr2 S4 20Kb 550°C 2 DAYS

102 (HEX)

FeCr2S4 30Kb 520''C 6 DAYS

(M0N0CL.)II2 FeCr2S4 55Kb 520°C 7 DAYS

1 112

Fig. 3. X-ray dif f ractometer tracings showing

the transition from disordered (hexagonal)

to ordered (monoclinic) NiAs-type structure

in FeCr2Stt.

4 40

56 58 60

ATOMIC WEIGHT OF A^^

Fig. 4. X-ray densities of spinel-type and NiAs-type

structures as a function of the atomic weight

of the A^-'^ ions

.

700
Deposition of FeCr2St^ on the (100) plane of NaC£ at 215 °C and subsequent annealing in vacuum at 200 °C for 24 hrs . resulted in electron diffraction patterns represented by figure

5(A) and figure 5(B). Figure 5(A) appears to be a textured polycrystalline pattern or a single crystal pattern superimposed on a random polycrystalline pattern. Figure 5(B) , taken

from a different area of the same film as in figure 5(A) , appears to be a single crystal pattern with double diffraction and twin diffraction with a weak diffraction pattern of textured

polycrystalline material. From figure 5(A), the preferred orientation can be determined from

the bright diffraction spots which are indexed in figure 5(C)

.

Some spinel crystals grow epitaxially with the {OOl} type planes parallel to the (100)

plane of the NaCl siibstrate. The set of four diffraction points around the (400) point in

figure 5 (B) is typical of the pattern observed for twinning and double diffraction in facecentered cubic metals with (111) twin planes. The spinel situation is analogous with (111)

twinning except the (200) reflection is extinct in spinel causing the satellite reflections

around the primary (400) reflection.

Higher temperature deposition on the (100) plane resulted in flaking of the film possibly due to the vaporizing of contaminants or to the difference in thermal expansion between

the substrate and film.

(A)|

M •

'm i m ^

SbO 840 88C

• • • 6^ ^ ^0 480

' 220 260

040

Fig. 5. (A) and (B) , electron diffraction patterns of a thin film of ^ FeCr2Si^ spinel deposited on the (100) plane of NaCJl; (C) indexing of the strong diffraction spots in (A) ; (D) reflection electron diffraction pattern of a FeCr2S[^ spinel thin

film deposited on the (100) of MgO.

701
Because of the poor insulating properties of NaCJi , it was of technological interest to deposit films on a good insulating substrate. Single crystals of MgO were the logical choice

because the rocksalt structure was known to induce epitaxial growth. FeCr2Si^ was deposited

on the (100) plane of the MgO substrate. Because the film could not be floated from the MgO

without destroying the film, it was necessary to use a reflection electron diffraction technique where the plane of the film and substrate is nearly parallel to the incident beam.

Figure 5(D) is the resulting diffraction pattern. By matching the two strong rings with the

(400) and (440) rings in the spinel pattern and comparing radius ratios R1/R2 = di/d2 the K value for the diffraction pattern could be calculated. The remaining spots on the diffraction

pattern could all be indexed as spinel reflections. Thus the FeCr2Si^ does crystallize on the

(100) plane of MgO as spinel, but no texturing effect could be observed because of the diffraction technique used.

Recently, single crystal films of several chromium sulfospinels were grown by the chemical vapor transport method [24]

.

4. ACKNOWLEDGMENT

R. E. Tressler was supported in this work by the National Science Foundation and the

National Aeronautics and Space Administration.

5. REFERENCES

[I] Passerini, L. and Baccaredda, Atti Accad. Lincei 14_, 33 (1931).

[2] Hahn, H., Z. Anorg. Allgem. Chem. 264 , 184 (1951); Hahn, H., Frank, G. , Klinger , W.

,

Storger, A. D. , and Storger, G. , Z. Anorg, Allgem. Chem. 279 , 241 (1955).

[3] Lotering, F. K. and VanSteen, G. H., Solid State Commun. 1_, 1827 (1969).

[4] Bouchard, R. J., Russo, P. A., and Wold, A., Inorg. Chem. _4, 685 (1965).

[5] Blasse, G. and Schipper, D. J., J. Inorg. Nucl, Chem. 26_ 1467 (1964).

[6] Flahaut, J., Domange, L., and Patrie, M. , Bull. Soc. Chim. France 105 (1961).

[7] Flahaut, J., Domange, L., and Patrie, M. , ibid, pg. 1887 (1961).

[8] Flahaut, J., ibid. pg. 1282 (1962).

[9] Pinch, H. L., Woods, M. J., and Lopatin, E., Mat. Res. Bull. 5_, 425 (1970).

[10] Romers, C. , Blaisse, B. A., and Ijdo, D. J. W., Acta Cryst. 23_, 634 (1967).

[II] Omloo, W. P. and Jellinek, F., Receuil 87, 545 (1968).

[12] Patrie, M. , Guittard, M. , and Pardo, M. P., Bull. Soc. Chim. France Yl_, 3832 (1969).

[13] Donahue, P. C, J. Sol. State Chem. 2_, 6 (1970).

[14] Lungscheider , W. , PinK , H., Weber, K. , and Zinn, W. , Z. Angew. Phys . 30_ 36 (1970).

[15] Steigmann, G. A., Acta Cryst. 23_, 142 (1967).

[16] Bouchard, R. J. and Wold, A., J. Phys. Chem. Solids 27_, 591 (1966).

[17] Bouchard, R. J., Mater. Res. Bull. 2_, 459 (1967).

[18] Plovnik, R. H., Ph.D. Thesis, Brown University, 1969.

[19] Dachille, F. and Roy, Rustom, pg. 163 in Modern Very High Pressure Techniques, ed. by

Wentorf, R. H., Jr., Butteirworth & Co. (Publishers) Ltd. London, 1962.

[20] Harris, L. and Siegel, B. M. , J. Appl. Phys. 19_, 739 (1948).

[21] Wells, Structural Inorganic Chemistry 3rd ed; pp. 31 725 and 427, Oxford University

Press, London, 1962.

[22] Albers , W. and Rooymans , C. J. M. , High-Pressure Polymorphism of Spinel Compounds

,

Solid State Commun. 3_/ 417 (1965) . [23] Tressler, R. E. and St\:ibican, V. S., Mater. Res. Bull. 2_, 1119 (1967).

[24] Pinch, H. L. and Ekstrom, L., RCA Review December, 1970 pg. 692.

702
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

PHASE CHANGES IN CU^S AS A FUNCTION OF TEMPERATURE

William R. Cook, Jr.

Gould Inc ., Gould Laboratories

Cleveland, Ohio 44108

and

Case Western Reserve University

Cleveland, Ohio 44106

The high-copper phase boundary of CU2S deviates from stoichiometry above 300 °C , first

becoming copper deficient, then above ~ 1075 °C becoming copper rich. The maximum copper

content occurs at the monotectic temperature of 1104 °C. The strong effect of oxygen on the

hexagonal-ciibic transition in CU2S was confirmed; the transition was also found to be sensitive to the type of pretreatment of the material. The high temperature tetragonal "Cuj ggS"

phase is stable between Cuj^gsS and CU2S, at temperatures of ~ 90° to ~ 140 °C. The transition to the tetragonal phase is extremely sluggish. The true composition of djurleite has

been shown to be approximately Cui^9 3S.

The phases near the chalcocite-digenite region of the diagram may be grouped into those

with hexagonal close packing of sulfur atoms and those with cubic close packing of sulfurs.

This is important in understanding rates of transformation among the various phases that

occur in this area of the diagram.

Key words: Chalcocite; CU2S; digenite; djurleite; nonstoichiometry ; phase relations.

1. PREVIOUS WORK

Fairly thorough explorations of the Cu-S phase diagram between CU2S and Cu^ _ 7S have been

made by a number of previous workers [1-8]-^. The resulting diagram may be seen in figure 1 taken largely from Roseboom [7] and Ra'u [8] . The principal phases are chalcocite (CU2S) , orthorhombic (or monoclinic [9]) below 103.5° and hexagonal above it; djurleite (~ Cu^^ggS)^,

and digenite (Cu2_xS) , cubic with a wide range of solid solution at high temperatures, pseudocubic rhombohedral below 78° with a narrow range of solid solution. Additional phases which

have been reported but which have not been confirmed as stable phases in the diagram are a tetragonal "Cui^ggS," obtained between ~ 100° and ~ 150° [10-12], hexagonal CuigiS, obtained

by only one group [13] , a hexagonal [14] polymorph of digenite [15] , and a new "stable"

ordering of digenite, known as anilite [16,17].

Several studies have examined the changing stoichiometry of chalcocite. Posnjak et al.

[1] and Jensen [3] found the maximum melting point to be at a composition slightly deficient

in copper. Rau [8] found approximately a linear relation for the maximum copper composition

of chalcocite between Cui^ggeaS 516° and Cu^ ^99398 at 1048°. Wagner and Wagner [18] obtained a limiting composition of Cui^gggg + .0002S at 400°. Wehefritz [19] obtained a formula of ~ CuigggS at 443° (cubic phase) but found no detectable deviation from stoichiometry in the hexagonal phase (i.e. copper content > Cui^ggggS).

1^Figures in brackets indicate the literature references at the end of this paper.

All chemical formulas will be given as the number of atoms of copper per atom of sulf\ir.

All temperatures are °C.

703
Fig. 1. Cu-S phase diagram in the vicinity of

chalcocite and digenite [3, 6-8]

.

Much of the previous work, particularly near room temperature, was done in air on the

assumption that little if any reaction with air occurs. Buerger [2] pointed out that this

assumption was not valid, but his work was later criticized [5] because much of it had been

done in air. Studies on chalcocite crystals chemically converted from CdS [14] re-emphasized

that it was necessary to completely exclude air at all temperatures if the objective was to determine the two component diagram. The only one to have done so is Jensen [3] , and our re- sults are in agreement with his.

2. MATERIALS AND EXPERIMENTAL TECHNIQUES

Raw materials were 99.999% Cu in either rod or 1 mm wire form and 99.999% S, both from

American Smelting and Refining Co. The major impurity in the sulfur is organic material.

The copper was etched in 1:2 or 1:3 HNO3 to remove the oxide and superficial impurities,

washed with distilled water, and kept in vacuiun until use. Copper filings were not used be- cause of the increased amount of oxygen impurity that would be present due to the large sur- face area. The sulfur was kept in vacuiim briefly before use also in order to remove as much

adsorbed oxygen and H2O as possible. Only chunk sulfur was used so that none would be lost.

Compositions were recalculated after weighing and applying the buoyancy correction to give

the exact composition of the mix. From the time they were made, all compositions were kept

sealed in vacuum except when being ground of x-rayed.

For the usual mixes, which ranged between 1 and 2-1/2 grams, compositional uncertainty

was 0.05 to 0.1% in the Cu:S ratio, Cuj 9599 ± 0019S/ for example. For the "whisker" compositions, which were weighed on a semi-microbalance , the estimated precision of the final com- positions was ~ 2 to 4 ppm, equivalent to a formula of Cuo 001151 ± .000005^^ for example.

At this inaccuracy level, impurities can constitute an error up to ten times the weighing

error. However, it is here assumed that due to the similar nominal level of impurities in

the two raw materials, no substantial increase in error existed. If this is incorrect, it

could shift the abscissa laterally in figure 3 by a small amount.

This work used mainly three techniques : observation of changes at high temperature (Cu

"whisker" growth of Cu2S samples) , differential thermal analysis (DTA) , and low temperature

equilibrium at several temperatures, particularly 120° ± 1°, 73° ± 0.4°, and room temperature

(24° ± 2°) . Powder x-ray diffraction patterns were taken on most of the samples using film

or a dif f ractometer

.

704
swrf - • - , j ......... 1

1 1 .

1 J n 1 12 [ 3

SPECw___DATE

Fig. 2. Cu2^ooil5S composition showing the

effect of heating to 608° for 1.3

hours. The upper picture (with cm

scale) shows sample after equilibration at 100° (no whiskers)

.

The lower picture shows the presence

of numerous fine copper whiskers

,

particularly along the bottom edge

of the sample.

After reaction (generally at 600° for 16 hours to several days, followed by slow cooling

over several more days to allow re-equilibration) , most samples were ground, divided into

several parts, and resealed in fused silica. One part was used for the DTA (Dupont 900 unit

with 1600° furnace); other parts were held at 120°, 73°, and room temperature. Where an appreciable vapor pressure was expected, the vapor space was reduced to a minimum by inserting

a hollow slug before sealing. The DTA equipment was calibrated against the melting point of

tin (231.89°) [20], cadmium (320.9°) [20], zinc (419.505°) [21], silver (960.8°) [20], and

gold (1064.5°) [22] , both at the beginning and near the end of the work. The temperature

correction was never more than 3°. Temperatures normally reproduced to better than 1°.

The determination of the copper-rich CU2S phase boundary rests on an observation by

Shiozawa [23] . If a CU2S sample has been saturated with copper at a low temperature and is

heated somewhat hotter, very fine copper whiskers will grow out of the surface of the CU2S

,

indicating it is now supersaturated and is in the two-phase CU-CU2S region of the diagram.

When the sample is cooled the whiskers redissolve in the CU2S. Since very small amounts of

free copper can be detected visually, this is therefore a very sensitive means of plotting

this phase boundary. An example showing the same sample with and without the copper whiskers

is seen in figure 2.

The large samples to be used for the copper-saturated CU2S phase boundary were not

ground after reaction, but were used as is. It is believed that the slow cooling permitted

equilibration as low as 150° . The reaction progressed by copper migrating through the already-formed copper sulfide to the surface, where it reacted with sulfur vapor. This resulted in a hollow core at the completion of the reaction of almost the size of the original

copper rod. Any free copper remaining after the reaction was completed remained as a solid

lump in the hollow core.

705

465-504 O - 72 - 46
A thermocouple (calibrated against a NBS standardized reference thermocouple) was fastened to the outside of the container with the bead aligned with the middle of the CU2S piece,

and the assembly was put in a temperature-stabilized furnace for a length of time necessary

to establish equilibri\im. For low temperatures, > 16 hours was used, while near 1000° times

of 15 minutes to 1/2 hour were sufficient. The length of the samples meant that at high temperatures a small temperature gradient (< 5°) existed within the sample. The magnitude of

the gradient was estimated with the thermocouple, and corrected for.

After heating, the sample was very quickly removed from the furnace and examined for the

presence of copper whiskers. Most of the time, samples not showing copper whiskers were heated in order to see if whiskers appeared, but occasionally the reverse procedure was used:

samples in which whiskers had been formed were heated at a different temperature to see if

the whiskers disappeared. As far as could be determined, both methods gave the same results.

Two observations should be made on problems encountered, in case others should wish to repeat the experiments. Whiskers that formed quickly at low temperatures tended to redissolve

quickly, but if they remained for 16 hours, extensive treatment (usually at very high teirperature) was necessary in order to get rid of them. Thus for the tests involving disappearance

of copper whiskers, the whiskers had to be "fresh". Also at high temperatures, the presence

of a very small sulfur (or copper sulfide) vapor pressure resulted in whiskers converting to CU2S on the surface after a few hours, after which it was virtually impossible to get rid of

them and the sample would have to be abandoned (since one is depending on visual appearance

of whiskers) . This caused premature abandonment of one of the compositions used in this

study, that at about CU2.00115S3. EXPERIMENTAL RESULTS AND DISCUSSION

The results of the present work and the previous literature are summarized in figures

3-5. The values of Rau [8] , Roseboom [7] , Ruhl and Sauer [24] and Wehefritz [19] have been

accepted for the copper-deficient phase boundary of digenite (Cu2_xS) between 130° and 1000°.

LtQUID Ir LIQUID n + CUBIC C

= Cu WHISKERS

> = NO Cu WHISKERS

I ; DTfl OATfl

' ; Rau

v= WAGNER AND WAGNER

Cu + CUBIC CujS

Cu + HEXAGONAL CojS

CUBIC +

HEX

2.003 2.002 2.001 2.000 1.999 I 998

< IN Cu,

S

Fig. 3. The phase boundary between CU2S and

CU2S + Cu.

706
S , X =

Fig. 4. Melting relations from CU2.1S to Cu^ 72S. The

previous literature is summarized along with

results from the present study.

IZOOr

34 35 36 ATOM % S

Fig. 5. Phase diagram from Cu2.oo2 ^° ^^1.72^-

707
3.1. Copper Solubility in Cu^S and High Temperature Phase Relations

The observation of Cu whiskers due to supersaturation with copper was used to determine

the (Cu + CU2S) - CU2S phase boundary between 165° and 1070 °C, as shown in figure 3. At

low temperatures, copper whiskers were most nun.erous at the hottest spot, which follows from

| the shape of the phase boundary (fig. 3) . The copper whiskers varied in length up to half : an inch or more. Long whiskers were usually bent or coiled. Widths of whiskers ranged from 6 barely detectable under the microscope (< 10 microns) to several tenths of a millimeter. One \) whisker was found to be polycrystalline by x-ray diffraction. In at least some cases, the

whiskers grew into the inner void as well as on the outside, but this did not appear to interfere with the observations. When the samples were broken open at the end of the experi- i mentation, a very minor amount of whiskers was found in those samples with more than two ' copper atoms per sulfur, but no trace was found of the original copper core, indicating that

at some stage all of the copper was in solid solution in the CU2S

.

i The initial deviation from stoichiometry is in the direction of copper deficiency as ex- pected. However, as may be seen in figure 3 the boundary unexpectedly curves back towards

copper at high temperature. This is in the opposite direction to what has been reported

^ previously I8j .

j At low temperatures, all three samples with excess copper (x > 2.0) fomed Cu whiskers

on heating above ~ 305 °C. Since all were equilibrated with Cu near 150°, all showed whiskers

at the same temperature, the excess copper at 150° remaining in the core as a solid piece.

It must be only above 300° that the phase boundary deviates significantly from the stoichiometric composition. One sample was heated for long times near 305°, 320°, 400°, 415°, 435°,

and 445° and the amount of free copper was qualitatively observed. At 304.5° no copper was

detected. At 306° one exceedingly small whisker was found. At 320.5°, both the number and

] length of the copper whiskers had increased considerably, but the amount was still small. At

415° a further increase in amount of copper was observed. At 435° and at 445° the number of

whiskers had probably not increased, but the thickness and length were both quite large. The

longest whiskers were probably at least half an inch in length, and strongly coiled. These

qualitative observations are the basis for the shape of the phase boundary below 435° as drawn in figure 3. It is assumed that copper-saturated compositions below 300° are stoichiometric, but the limits of uncertainty are CU2.0001S and Cu^^ggggS from compositions of sam- ples adjacent to the phase boundary and observation of changes in amount of copper whiskers

with temperature above 305°.

High temperature results were supplemented by data from the DTA curves, which showed the

existence of solidus and liquidus curves on both sides of the maximum melting temperature of

the CU2S phase as indicated in figures 3 and 5. The maximum melting point is in the composition range Cui_ggt4.S to Cuj^gsgS, probably at the high copper end of this range, and the

maximum temperature of melting is 1130 ± 2°, in excellent agreement with 1130 ± 1° at Cu^^ggo

± .OC+S and 1129° at Cu^^gggS reported previously [1,3]. It is probable that the occurrence

of the maximum melting point slightly on the sulfur-rich side of CU2S led previous workers to suspect that the copper-rich phase boundary of the CU2S phase was shifted in the same direction

at high temperatures [8,3], which is incorrect or oversimplified as seen above.

j One notices in figure 3 that the "solid solution" of copper in CU2S at 1103° is appreciable. The data points from the "whisker" data just below 1095° indicating no formation of

copper whiskers have been disregarded. The lack of apparent rise of the CU-CU2S phase boundary is due to the circimistance that the specimens needed to be equilibrated at least 20° a- bove the phase boundary for the whiskers to appear. The fact that the sample with composition

CU2.001797S was not supersaturated with copper at 1097° (the highest temperature to which it was heated) is shown by the absence of any core of unreacted copper when the piece was broken

open.

The monotectic was measured at 1103 ± 2° for a composition with appreciable excess Cu

(fig. 4) compared with 1105° determined previously [6,3]. Jensen [3] chose 1105° although

his data contained both 1104° and 1105° as possible data points. The value of 1104° ± 1° is

used for figure 1.

708
3.2. The Hexagonal-Cubic Phase Transition Near 435"

There has been a good deal. of difficulty in determining the transition temperature in

the past due to its sluggish nature, with temperatures between 350° and 470° reported; in

this study it was not a problem, largely because of the rigorous efforts to exclude oxygen

from the samples. The strong effect of oxygen on the phase transition was pointed out by

Roseboom [7] . The minimum temperature hysteresis for the transition was 7° , considerably under most other studies, but still of significant size. Wehefritz [19] explained this large

hysteresis as due to the extremely small heat of transition, estimated by him as 110 ± 40 cal/

mole. This can be expected to be not far in magnitude from enthalpies due to structural defects and therefore arising from other than thermodynamic equilibrixim.

An additional effect on the hysteresis was found arising from the past thermal history

of the sample. All samples in which the composition contained more copper than the stable

limit near 435° showed increased hysteresis with temperature cycling, even when oxygen was

excluded, the increase in hysteresis amounting to a factor of three after several cycles.

The effect was temporary, since re-equilibrating the sample at high temperature sharpened the

DTA peaks and eliminated the excess hysteresis. The transition temperature was unchanged between samples equilibrated at 1105° (near maximum Cu content) and at 835° (near minimum Cu

content). Thus the increased temperature hysteresis is caused by slow kinetics, probably

caused by lattice defects connected with the Cu precipitation, rather than a shift of transition temperature with copper content.

There appears also to be a continued rise of the hexagonal-cubic phase transition as a metastable extension of the phase boundary into the two phase region (dotted in on figure 3) but the increase in temperature is small and is barely significant.

The shape of the DTA curves for the hexagonal-cubic transition in compositions near CU2S

can also suggest a location for the minimum copper content of the hexagonal phase since a single phase sample will transform more sharply than a sample which is a mixture of the limiting hexagonal composition plus a cubic phase. From the curve shapes the limiting low copper

content of the hexagonal phase is no lower than Cu^^ggsS, and may be as high as Cu^^gggi^S.

This uncertainty is indicated on figure 3 by dashed lines. Roseboom [7] by a different method

judged that the solid solution limit of hexagonal chalcocite at 180° was at higher copper

content than Cu^^gggS, which is in agreement.

3.3. Low Temperature Phase Relations

A brief summary is given of other findings, since they affect the structural interpretation of the results.

No evidence was found for solid solution in "orthorhombic" chalcocite at 73° or 76° by

the method of disappearing phases. No evidence near 100° (where solid solution was reported

to be maximum [7]) could be obtained, since samples transformed to the tetragonal phase. By

the same method the composition of djurleite was found to be Cui_g3 + Ol^S. Results were

not precise enough to be certain of the existence of solid solution. It is probable that

previous studies used material that was slightly contaminated with oxygen, and thus contained

less Cu in the lattice than was believed to be the case. Djurleite decomposes at 91 ± 1", in

reasonable agreement with the previously determined [7] 93°.

The transformation to tetragonal "Cu^^ggS" is very sluggish, and may again become more

so in the presence of oxygen contamination. All compositions between CU2.00S and Cuj^gsS

transformed completely to the tetragonal phase in a matter of months between the temperatiires

of 94° and 120°, and partially transferred at 137°. The phase transforms back by at least

146°. Lesser times were frequently insufficient for complete conversion.

•-^l.giS [13], the hexagonal polymorph of digenite [14,15], and anilite [16,17] were not

obtained as stable phases in this study, and are not believed to exist in the equilibrium

Cu-S phase diagram. The details of the attempts to obtain anilite will be reported elsewhere .

709
4. COMPARISON OF THE STRUCTURE OF THE COPPER SULFIDES

x-ray diffraction on small CdS crystals which had been chemically converted to chalcocite,

djurleite, or "hexagonal digenite" demonstrate a great similarity in the structure [14], which

can be explained by assuming that the sulfur atoms remain fixed while the copper atoms, which

are known to be unusually mobile in CU2S [4, 25], rearrange themselves in accordance with

the proportion of copper atoms to sulfur. Chalcocite, both hexagonal [26] and "orthorhombic"

[9,26] forms, has its sulfurs essentially in hexagonal close packing. Psuedo-hexagonal [27]

djurleite and the hexagonal polymorph of digenite are both obtainable from chalcocite as single crystals [14] , indicating the same sulfur arrangement. Eliseev's [13] Cu^ g^S phase

can also be fitted to this sulfur arrangement (fig. 6)

.

The cubic close packed sulfur arrangement typified by sphalerite and hawleyite (cubic

CdS) is found in digenite [28] (or anilite [16,17]) and tetragonal "Cui^ggS" [10]. This is

the obvious explanation for the very sluggish transition between "Cuj^^ggS" and djurleite or chalcocite, and the somewhat sluggish transition between hexagonal chalcocite and digenite at 435°. On the other hand, while the cubic high temperature form of digenite can be at least

partially quenched, the phase transformation to the low temperature ordered phase is sufficiently fast that the DTA peak occurs with no hysteresis. The hexagonal form for chalcocite

is widely reported as unquenchable; the hexagonal-orthorhombic transition, though almost cer- tainly first order and showing 10 to 15° hysteresis, occurs rapidly.

All of the above results are completely consistent with the picture of the two basic

sulfur arrangements with the interstices filled by highly mobile copper atoms. Transitions

between phases with the same sulfur arrangements are rapid while transitions between phases

with different sulfur arrangements are sluggish. This same approach to phase relation among

the copper sulfides has been clearly expressed in a recent paper by Cavallotti and Salvage

[15]. It is obvious that the copper atoms, being highly mobile and able to take a wide variety of orderings , are very poorly bonded to the sulfur atoms. In fact a statistical distribution of copper atoms along channels has been proposed [26] for the structure of hexagonal

chalcocite

.

HEXAGONAL

HEXAGONAL

CujS OR HEXAGONAL

CdS

ORTHORHOMBIC

CHALCOCITE CU2S

Fig, Idealized unit cells in the plane

perpendicular to c for copper

sulfides, showing orientation and

size of unit cells with respect

to hexagonal close packed sulfur

layers

,

710
An additional problem is the reason for the wide solid solution in the structures with

a cubic close packed sulfur arrangement and very limited solid solution in those with hexagonal close packed sulfurs. Cavallotti and Salvage [15] offered the following structural ex- planation. In the cubic type the coppers tend to be in the tetrahedral antifluorite position,

whereas in the hexagonal close packed structures the coppers tend to be in the sulfur layer

and are thus more tightly bonded to three sulfurs than when they are bonded to four in the

cubic arrangements. This favors the cubic sulfiur arrangement when the ratio of copper to sulfur deviates from 2:1.

5. ACKNOWLEDGMENTS

This work was performed while a Ph.D. candidate at Case Western Reserve University, and

was supported in part by Aerospace Research Laboratories, Air Force Systems Command, United

States Air Force, Contract F33615-68-C-1732 . I am indebted to P. 0. Banks and J. Hower of

the Geology Department, Case Western Reserve University and L. R. Shiozawa and J. M. Jost of

Gould Inc. for many stimulating discussions.

6. REFERENCES

[I] Posnjak, E., Allen, E. T. , and Merwin, H. E., Econ. Geol. 1£, 491-534 (1915).

[2] Buerger, N, W. , Econ. Geol. 36_, 19-44 (1941).

[3] Jensen, E., Avhandl. Norske Videnskaps-Akad. Oslo I. Mat.-Naturw. Klasse 1947 , No. 6,

1-14,

[4] Hirahara, E., J. Phys. Soc. Japan 2_, 211-13 (1947), ibib. 6_, 422-27 (1951).

[5] Djurle, S., Acta Chem. Scand. 12_, 1415-26 (1958).

[6] Johannsen F. and Vollmer, H., Erzbergbau u. Metallhuttenw. 1_3, 313-22 (1960).

[7] Roseboom, E. H., Jr., Econ. Geol. 61_, 641-72 (1956).

[8] Rau, H., J. Phys. Chem. Solids 28^, 903-16 (1967).

[9] Evans, H. T. , Jr., Nature Phys. Sci. 232 , 69-70 (1971).

[10] Janosi, A., Acta. Cryst. 17_, 311-12 (1964).

[II] Skinner, B. J., Boyd, F. R. , and England, J. L., Am. Geophys . Union Trans. 45_, 121-22

(1964)

.

[12] Kullerud, G. , Handbook of Physical Constants, Geol. Soc. Am. Mem. 9J_, 323-44 (1966).

[13] Eliseev, E. N. , Rudenko, L. E., Sinev, L. A., Koshurnikov, B. K. , and Solovov, N. I.,

Mineralog. Sb. L'Vovsk. Gos . Univ. 18, 385-400 (1964).

[14] Cook, W. R. , Jr., Shiozawa, L. , and Augustine, F. , J. Appl. Phys. 41, 3058-63 (1970).

[15] Cavallotti, P. and Salvage, G. , Electro-chim. Metal. 4, 181-210 (1969).

[16] Morimoto, N., Koto, K. , and Shimazaki , Y., Am. Mineral 54_, 1256-68 (1969).

[17] Morimoto, N. and Koto, K. , Am. Mineral. 55_, 106-17 (1970).

[18] Wagner, J, B. and Wagner, C, J. Chem. Phys. 26_, 1602-6 (1957).

[19] Wehefritz, V., Z. Phys. Chem. (F'rankfiirt) 26^, 339-59 (1960).

[20] Weast, R. C. , Ed., Handbook of Chemistry and Physics, 45th Ed., Chemical Rubber Co.,

Cleveland, Ohio (1964)

.

[21] Simson, H. F. , NBS J. Res. 65A [3] 139-45 (1961).

[22] Moser, H., Otto, J., and Thomas, W. , Z. Physik 175 , 327-36 (1963).

[23] Shiozawa, L. R. , personal communication, Aug. 1968.

[24] Ruhl W. and Saur, E., Ber. Oberhess. Ges . Natur-u. Heilk. Giessen, Naturw. Abt. 28_, 35-

47 (1957) . [25] Pavlyuchenko, M. M. and Pokrovskii , I. I., Vestsi Akad. Navuk Belarus, SSR, Ser. Khim.

Navuk 1967 (3) , 35-41.

[26] Buerger, M. J. and Wuensch, B. J. Science 141 , 276-77 (1963) ; Wuensch, B. J. and

Buerger, M. J., Mineral Soc. Am. Special Paper 1, p. 164-70 (1963).

[27] Takeda, H., Donnay, J. D. H., Roseboom, E. H., and Appleman,'D. E., Zeit. Krist.

'

125 , 404-13 (1967)

.

[28] Morimoto N. and Kullerud, G. , Am. Mineral. 48, 110-23 (1963).

711
DISCUSSION

H. T. Evans : In connection with your testimony that most natural chalcocite specimens

actually are djurleite, I may say that from my own experience I can confirm this observation.

However, I do not agree that the djurleites are psendomorphous after original low chalcocite.

The specimen labelling is not important because djurleite closely resembles low chalcocite

in physical properties, and djurleite was not known to be a distinct species before 1958. I have found that each has distinct and characteristic crystal habit, and from this evidence

it appears that both have been formed as primary phases in the veins at temperatures below

100 °C. The djurleite crystals are flat, roughly hexagonal tablets, fresh in appearance,

with blue-black submetallic luster. Low chalcocite crystals are more prismatic with dome

terminations, highly striated, and have a dark, reddish brown-black patina resulting from

surface oxidation. X-ray diagrams show that low chalcocite crystals are often intergrown

with djurleite. Allowing for low temperatures of formation that are quite feasible in vein

deposits, these observations are consistent with the equilibrium system you have shown.

W. R . Cook : In all cases but one, the crystals examined were old (mined over 43 years

ago) , and were almost entirely djurleite. One larger crystal that had been attached to copper sulfide matrix was still partly chalcocite, and one crystal which was unattached had

gone all the way to digenite. However, all but one of these crystals (including the digenite)

had shapes explicitly or implicitly hexagonal. Some were flat hexagonal plates, some were hexagonal prisms. The crystal retaining a little chalcocite was prismatic.

Basically, I have trouble visuallizing djurleite being as hexagonal in appearance as chalcocite, which is hexagonal above 103 °C. Therefore, I believe that all of these crystals

were hexagonal to start with, and were chalcocite. The one crystal that was different was

the Bristol Conn, specimen, which had the shape shown for it in Dana. The long axis of the

crystal was the djurleite a axis. This crystal obviously grew below the stability range of

the hexagonal form, and therefore could have been either low chalcocite or djurleite. My

preference is for djurleite, because the composition is "different" and so is the crystal

shape, but it is purely intuitive, and may be entirely incorrect.

712
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

PREPARATION AND PROPERTIES OF THE SYSTEMS

CuFeS^.^ AND Cu^./e^.^S^.^

R. L. Adams, P. Russo, R. J. Arnott, and A. Wold

Division of Engineering

Brown University

Providence, Rhode Island 02912

Stoichiometric samples of CuFeS2 were prepared by direct combination of the elements in

sealed evacuated silica tubes. The products were characterized by x-ray diffraction, density

determination, magnetic susceptibility and MSssbauer spectroscopy. Homogeneous single phase

o products gave a density of 4.18 ± 1 g/cc and cell parameters of = 5.292 ± (5) A and Cq = 10.407 ± (5) A. In addition, all of the iron was found to be trivalent and located on tetrahedral sites. The plot of inverse susceptibility versus temperature was nearly temperature

independent from 77 K to 300 K, and the magnetic susceptibility measurements gave a Xm

~

9.8 X 10"'* emu/mole. Single crystals of CuFeS2 were grown from the melt by means of a modified Bridgman technique.

Samples having the composition CuFeS2_jj were also prepared by the direct combination of

the elements. X-ray diffraction studies indicated that existence of a single phase, tetragonal Y

~ form, when x was varied from 0.17 to 0.24. The compound CiiFeSi^S had cell dimensions of ao = 10.598 ± (5) K and Cq = 5.380 ± (5) A. Contrary to previous reports, this

phase was found to be stable from room temperature to 800 °C. In addition, this phase was

stable at room temperature for a period of time in excess of 250 days. It was concluded from

density measurements that the structure is best represented as a close packing of sulfur with

excess metal ions occupying additional lattice sites.

Compo\inds having the composition Cui-xFei+j^S^ .gO ('^•^^ > x > 0.08) were prepared and

found to be c\ibic with an average cell size of a^ = 5.32 A. However, attempts to prepare

single phase products with a composition of Cui+xFei_jjS2-y were unsuccessful.

Key words: Chalcopyrite ; CuFeS2 , CuFeS2_jj, Cui_xFex+xS2-y; Cu-Fe-S system; CuFeS2

crystal growth.

1. INTRODUCTION

Chalcopyrite (C;iFeS2) has been examined by many investigators [1,2,3,4]-^ and found to have an ordered zinc blende structure (ao = 5.28 A, Cq = 10.41 K) with the c-axis doiibled.

Killer and Probsthain [5] reported that on removal of sulfur from chalcopyrite, a stable cubic 6 phase (CuFeS2-x) was formed; Nambu [6] and Kano indicated that the stability range of

the 6 phase was with x varying from 0.144 to 0.260. This phase was reported [5] to be body

centered with aQ = 10.60 A. In addition, they indicated the existence of a high temperature

Y - form of CuFeS2_j^ which was tetragonal with aQ = 10.58 A and Cq = 5.37 K. This phase was

reported to be stable at elevated temperature and converts slowly to the 3 - phase at room

temperature. VThen heated to 230 °C the 6 - phase transforms to the y ~ phase. Hiller and

Probsthain concluded from density determinations that neither of these phases contains sulfur

vacancies, but that excess metal ions occupy additional lattice sites.

1 Figures in brackets indicate the literature references at the end of this paper.

713
Neutron diffraction studies showed CuFeS2 to be antiferromagnetic at room temperature

[7,10]. Teranishi [7] reported a Neel temperature of 550 °C with a moment at liquid nitrogen temperature of = 8 x 10"^ emu/mole; the susceptibility was temperature independent below the Neel temperature. These measurements were carried out on natural single crystals of

chalcopyrite which had the composition CuFe^ _ 08^2 . 0

1 • Efforts by Teranishi to synthesize

single crystals of CuFeS2 were unsuccessful. There appear conflicting reports in the literature [8,9,10] concerning the oxidation states of the copper and iron in chalcopyrite. A

recent Mossbauer study [10] indicates the probable valence of +3 iron located on the tetrahedral sites. However, +2 iron is undo\ibtedly present in the non-stoichiometric phase.

There are numerous other reports on the preparation and properties of chalcopyrite and

related phases. However, these studies have been carried out on either naturally occurring

minerals or poorly characterized polycrystalline samples. There have been no successful re- ports of the growth of stoichiometric C\iFeS2 single crystals. There appears to be sufficient

confusion in the literature concerning the preparation and characterization of phases related

to chalcopyrite to warrant further investigation.

2. EXPERIMENTAL

2.1. PREPARATION OF SAMPLES

Samples were prepared by the direct combination of the elements. Freshly reduced copper

(Gallard-Schleisenger , 99.999%), iron (Gallard-Schleisenger , 99.999%), and sulfur (GallardSchleisenger , 99.9999%) were combined and sealed in evacuated silica tubes. Initially, the

samples were heated from room temperature to 800 °C at a rate of 25 °C/hour, were maintained

at that temperature for 2 days , and were allowed to cool to room temperature over a period

of 18 hours. This cooling was essential to allow time for the complete reaction of the sulfur. The sintered samples were then removed and ground in an agate mortar and pestle under

a dry nitrogen atmosphere. The materials were again sealed in evacuated silica tubes and

heated at 800 °C for 4 days and slow cooled. This procedure was repeated for two additional

cycles in order to ensure sample homogeneity. It was found that extreme caution was necessary

in order to prevent oxidation of the sample by exposure to air. However, once the reaction

was completed, there was a dramatic increase in sample stability.

2.2. PHASE BOUNDARY STUDIES

The problem of phase analysis was studied by both Thermal Gravimetric Analysis (TGA) and

x-ray diffraction. For TGA studies, samples were heated in a dynamic vacuum, and the weight

loss was measured as a function of temperature. CuFeS2 was heated for a period of time, was allowed to lose a certain amount of sulfur and then was slow cooled; the product was weighed

and x-rayed in order that the phase (s) present in that particular composition could be identified. Small samples (5 mg) were chosen as the optimum size because the final product had

a unifoinm color and appeared homogeneous under microscopic examination. In addition, com- pounds of a specific composition near the phase boundaries, defined by the TGA studies, were synthesized and examined by x-ray diffraction. The use of these two methods resulted in

sharply defined phase boundaries

.

2.3. CHARACTERIZATION OF SAMPLES

Cell parameters of products were obtained with a Norelco diffractometer using monochromatic radiation (AMR-202 focusing monochrometer) and a high intensity copper ttibe. The diffractometer was calibrated relative to a silicon standard.

Densities were determined by a hydrostatic technique using a modified Sartorious model

2604 analytical balance. The density medium, chosen for its ability to wet tlie samples, was 1,1,2,2 tetrachloroethane . This simple method gives precision and accuracy of 0.5%, but care must be taken to outgas the samples throroughly before weighing them.

The bulk magnetic susceptibility of the samples was measured with a Faraday balance from

77 K to 300 K. The susceptibility was also measured as a function of field (Honda-Owens

method [12] up to 10.3 kilogauss in order that the presence of any ferromagnetic impurities

could be ascertained.

714
2.4. CRYSTM, GROWTH

Crystals of CuFeS2 have been grown by a modified Bridgman technique. The samples were

lowered from 925 °C to 825 °C over a period of 10 days at a rate of 1/2 inch per day. The

thermal characteristics of the furnace were such that an extremely slow rate of cooling (2-

3° / inch) occurred during the initial growth period, and then the rate of cooling was con- tinuously increased as the crystal was lowered through the temperature gradient. When the

temperature of the crystal reached 825 °C, the furnace was programmed to room temperature at

a rate of 100 °C/day. The resulting crystal was usually found to be sulfur deficient. The

density of the crystal was measured, and the amount of sulfur to be added was calculated to

give a stoichiometric composition (CuFeS2) . The crystal and sulfur were then annealed in an evacuated silica tube at 700 °C for a period of 5 days and again were slow cooled. The crystal was X-rayed by both Laue (using molybden\im radiation) and dif fractometer methods before

and after annealing. Densities were also used to verify the final composition after annealing.

3. RESULTS AND DISCUSSION

3.1. CxiFeS^

2-x

The results of the phase studies for the system CuFeS2-x summarized in table 1. Tetragonal a - CuFeS2 was found to lose sulfur at 390 °C under a dynamic vacuum. This is

considerably lower than the value of 550 reported in a previous study [5] . Some of the ct - CuFeS2 samples prepared contained magnetic impurities that could be detected by means of

density and magnetic measurements, although they appeared to be homogeneous by x-ray diffraction. For such samples, the measured density was higher than the calculated value of 4.18 ±

(1) g/cc. In addition, the Honda-Owens plot showed the presence of ferromagnetic impurities.

This is evident, in figure 1, by the field dependence of the susceptibility. The presence of

the apparent ferromagnetic impurity is undoubtedly a result of the lack of homogeneity of the

sample. When such samples were annealed, with sufficient sulfur to decrease the density to

4.18 ± (1) g/cc, the magnetic susceptibility showed no field dependency. This can be seen in

figure 1. Magnetic susceptibility can, therefore, be used to determine sample homogeneity,

beyond the sensitivity of x-ray analysis, when a deviation in stoichiometry results in a separation of a magnetic phase.

Table 1

CuFeS^

2-x

Value of x ao (^) ^O Theoretical++

Density (g/cc)

Experimental

Density (g/cc)

Structure c/a

X = 0 5.292± (5) 10.407± (5) 4.18± (1) 4 (CuFeS2)

4.18± (1) a- tetragonal 1.97

X = 0 to

X = .16 MIXED PHASE a+Y tetragonal**

X = .17 to

X = .24 10.598± (5)

5.380± (5)* 4.32±(1)*

8(Cui,iiFei.iiS2.oo

4.30±(1) • y- tetragonal 0.51

* Values given represent composition for x = 0.2.

** It is possible that the g-phase (cubic) is also present as pointed out by Dr. L. J. Cabri

(personal communication)

.

All theoretical densities based on a close-packing of sulfur with excess metal ions oc- cupying additional lattice sites.

715
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 lO^-H

Fig. 1. Magnetic susceptibility of CuFeS2.

Magnetic susceptibility measurements of stoichiometric CuFeS2 gave a value of xm ~ 9.8 X 10~^ emu/mole as compared to the reported value of natural crystals of xm ~ ^ ^

10"*^ emu/mole [7]. The plot of inverse susceptibility versus temperature, shown in figure 2, was nearly temperature independent from 77 K to 300 K. Mossbauer examinations of polycrystalline

samples of CuFeS2 [11] indicated that all the iron was present as +3 and located on tetrahedral lattice sites.

Attempts were made to reproduce the cubic 3-phase reported by Hiller and Probsthain [5] by direct combination of the elements. In all cases, the final products were found to have

the tetragonal yfo^iti- This phase was found to be present in all samples whether quenched

from elevated temperatures or slow cooled and annealed below 230 °C. has a range from x = 0.17 to x = 0.24. For the composition CuFeS^^f

(5) A

The Y-CuFeS2_j^. phase

the cell parameters

are = 5.380 ± (5) ^ which is in agreement with a previous report

[5]. However, whereas Hiller and Probsthain [5] reported this phase to be unstable at low

temperatures, this study indicated the yphase to be stable when quenched from any temperature

CuFeS

Fig. 2. Inverse magnetic susceptibility of

CuFeS2 as a function of temperature.

716
between room temperature and 800 °C; also, the y-phase was stable at room temperature

for an extended period of time (250 days) . In addition, the product does not transform to the cubic 6-phase. The g-phase can be prepared by heating CuFeS2 in a stream of hydrogen at

450 °C, but the pure phase cannot be obtained by the direct combination of the elements. For

compounds having the composition CuFeS2_3j, <3ensity measurements indicate the structure to be

based on a close-packing of sulfur with extra cations occupying additional lattice sites.

This was demonstrated for the composition CuFeSi^s by comparing its measured density (4.30 ±

(1) g/cc) with the theoretical density for the close-packed case (4.32 + (1) g/cc) and the

value for the sulfur deficient model (3.89 ± (1) g/cc). Therefore, the formula for CuFeSi g can be represented as Cui.iFei,lS2 indicating the existence of additional metal occupancy.*

3.2. Cu- Fe, 1-x 1+x 2-y

Attempts to produce polycrystalline samples of Cui_^Fei+j^S2 and Cuj+j^Fei _xS2 were unsuc- cessful. In each case, a -CuFeS2 and other unidentified phases appeared in the diffraction

pattern. However, a single phase could be obtained for compounds having the general formula

Cui_xFei+xS2-y (for 0.25 > x > 0.08 and y chosen as 0.2). The stability range of this phase with respect to sulfur content is still to be determined. The compounds in the above compositional range have a cubic structure with a^ varying from 5.31 A to 5.33 A. This phase

contains no superlattice lines requiring a doubling of the cell edge as is observed in the

cubic 6 case. The change in structure as the copper to iron ratio is varied from x = 0 to

X = 0.25 is shown in table 2. The tetragonal y - phase exists only when the value of the

copper to iron ratio approaches unity. Efforts to prepare Cuj+xFei.j^Si .9 were unsuccessful,

and the phases identified by x-ray diffractions were: CuFeS2 or CuFeS2_x in addition to a bornite solid solution (CusFeS^)

.

3.3. CuFeS^ SINGLE CRYSTALS

The growth of well characterized single crystals of CuFeS2 and associated phases is desirable for the elucidation of both the structural and magnetic properties of the materials.

Earlier work has shown this to be a formidable problem [7]. Crystals grown from the melt,

as discussed earlier, weighed as much as 500 mg. and were 1 cm. in diameter and approximately

1 cm. in length. Density measurements were used to ascertain deviations from stoichiometry

.

The crystals were reannealed with sufficient sulfur to produce the desired stoichiometry. In

all cases, Laue patterns were taken, and the growth of single crystals was verified. However,

the Laue diffraction spots were always diffuse indicating either strain or microtwinning

.

This has also been observed for many natural chalcopyrite crystals.

Table 2

Cu^ Fe, 1-x 1+x 1.

Value of X ao (A) Co (A) Theoretical++

Density (g/cc)

Experimental

Density (g/cc)

Structure c/a

X = 0 to

X = ,01

10.598± (5) 5.380± (5) 4.32± (1) 8.(Cui,iiFei.iiS2.oo)

4.30± (1) y- tetragonal 0.51

X = .02 to

X = .07 MIXED PHASE y- tetragonal

cubic

X = .08 to

X = .25 5.328± (5) 4.28±(1)*

2 (Cu.sgFei _33S2 .00)

4.28± (1)

cubic 1.00

++ Values given represent composition for x = 0.2.

All theoretical densities based on a close-packing of sulfur with excess metal ions oc- cupying additional lattice sites.

717

/
4. ACKNOWLEDGMENT

This work has been supported by the Kennecott Copper Corporation and by the United <{ States Army Research Office, Durham, North Carolina.

The technical support of the Marc Vassiliadis and Roland Beaulieu, in the growth of

chalcopyrite single crystals, is greatly appreciated.

5. REFERENCES

:j|

[I] Burdick, C. L. and Ellis, J. H., Proc. Natl. Acad. Sci . U. S. 3, 644 C1917) , J. Am. | Chem. Soc. 39, 2518 (1917) . [2] Pauling, L. and Brockway, L. O., Z. Krist. 82_, 188 C1932) . [3] Donney, G. , Corliss, L. M. , Donnay, J. D. H., Elliot, N., and Hastings, J. M. , Phys . i Rev. 11^, 1917 (1958) .

j [4] Buerger, N. W. and Buerger, M. J., Amer. Min. 19_, 289 (1934).

| [5] Hiller, J. E. and Probsthain, K., Z. Krist. 108_, 108 (1956).

[6] Nambu, M. and Kano, S., Ganeski Kobutsu Kosho Gakkaishi, 6£ (5), 127-145 (1968).

[7] Teranishi, T., J. Phys. Soc. Jap. 16_, (10) 1881 (1961).

[8] Raj, D. and Puri, S. P., 11, Nuovo Cimento LXB (2), (1969).

[9] Aramu, F. and Bressani, T., 11. Nuovo Cimento LIB (2), (1967). i [10] Frank, E., 11. Nuovo Cimento 58B (2), 407 (1968).

[II] Chen, J., personal communication.

[12] Bates, L. F., Modern Magnetism (Cambridge University Press, New York, 1961).

DISCUSSION

j

L. J. Cabri : I found this paper most interesting since we have been studying these

phases, both as minerals and as synthetic compounds for the past five years and have recently

submitted new mineralogical , Mossbauer, magnetic, and crystal lographic data on talnakhite

(3-phase) , chalcopyrite and mooihoekite (y-phase) for publication and are presenting some

of this work at the 17th Annual Conference on Magnetism and Magnetic Materials in November. | As a consequence, I have a few comments and questions I would like to put to the authors.

|j Firstly, we have prepared homogeneous yphase and found it to be stable at room temperature for a period of over 3 years. But we have observed that it transforms to two hightemperature non-quenchable phases at 165° and 236 °C. This has been confirmed by hightemperature x-ray powder diffraction. These results appear to disagree with the authors'

statement that y-phase is stable from room temperature to 800 °C. Can the authors comment

on this?

R. L. Adams : I did not mean to imply that there were no other phases when the Y~phase

is heated to 800 °C. What was meant was that on quenching from any temperature from room temperature to 800 °C, only lines of the_ yphase appeared on the powder diffraction patterns.

Also, the study presented here did not employ high temperature x-ray equipment.

L . J . Cabri : Secondly, in a recent paper (Cabri and Harris, 1971, New Compositional

Data for Talnakhite, CU13 (Fe,Ni) 15332. Econ. Geol. 66 , p. 673) it was shown that the 6-phase

can be synthesized from the elements provided that a specific proportion of Cu:Fe is employed.

Have the authors determined the composition of the phase they formed by heating CuFeS2 in

hydrogen?

R. L. Adams : No. The composition has not been determined because this phase was not

prepared as a pure single phase material. The preparation was made to obtain some idea as to the diffraction pattern found for this phase. More important, however, was that the

phase was not studied because the area of interest in this work is only with pure single

phase materials and not mixed phases.

718
L. J. Cabri : And lastly, we also synthesized a phase which can be indexed on a primitive cubic cell a-5.32 A for the composition Cug . gsFe^ ^ 27^2 . 00 • However this phase

transforms on heating between room temperature and -200 °C to give a powder pattern which

is similar to that of f.c.c. high-temperature chalcopyrite . This phase is non-quenchable

and can only be observed with a high-temperature x-ray camera.

R. L. Adams : Again, high temperature x-rays were not used in the study. Therefore,

the phases observed at these elevated temperatures were not observed and not studied. The

emphasis in this work deals with materials that are stable at room conditions only.

I believe these comments cover the areas discussed.

719
I
National Bureau of Standards Special Publication 354, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

LASER RAMAN SPECTRA OF POLYCRYSTALLINE ZnS AND Zn^Cd, ^S SOLID SOLUTIONS^

Jacob Shamir and Simon Larach*

Department of Inorganic and Analytical Chemistry

Hebrew University

Jerusalem, Israel

Raman spectra of poly crystalline ZnS and of CdS have been recorded. The instrument

consisted manily of a He-Ne laser, Spectra-Physics, model 125 and a 1400 Spex double monochromator [1] . The lines observed were in good agreement with those observed before in a single crystal [2], Some of these lines are not as sharp and intense as in a single crystal;

however the LO frequency of ZnS at 351 cm"-' is a very sharp and intense line.

In addition we studied the spectra of ZnjjCd;^_xS solid solutions. These materials have

been prepared by firing mixtures of pure ZnS and CdS, in the proper compositions, at 1100 °C,

in an atmosphere of purified Argon. It has been observed that the LO frequency of CdS at

305 cm"-' shifts toward higher frequencies as the concentration of zinc increases. This

behavior indicates a type I change as discussed by Pershan and Lacina [3] , namely a linear

shift of the frequency as the concentration varies from zero to one in the Znj{Cd2-xS. These

results resemble the ones obtained in a Vegard plot of lattice constants as determined by

x-rays

.

Key words: Laser Raman spectra; polycrystalline ; ZnS; ZnjjCd^.j^S.

REFERENCES

[1] Claassen, H.H., Selig, H. and Shamir, J., Appl. Spectr. 23,8 (1959).

[2] Nilsen, W.G. in Light Scattering Spectra of Solids, G. B. Wright (editor) , SpringerVerlag 1959, p. 129.

[3] Pershan, P.S. and Lacina, W.B. , Appl. Spectr. 23, 439 (1959); Phys . Rev. Bl, 1765 (1970)

As this is a post-deadline paper only a brief abstract is presented here.

* Permanent address: RCA Laboratories, Princeton, New Jersey.

721

465-504 O - 72 - 47

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

NOVEL METHOD FOR THE SYNTHESIS OF RARE EARTH CHALCOGENIDES

C. Paparoditis and R. Suryanarayanan

Centre National de la Recherche Scientifique

Laboratoire de Physique des Solides

Bellevue, France

A description is given of an all-metal vacuum system for the synthesis of rare earth

tellurides and selenides by the coevaporation of the elements. The evaporation chamber

is provided with three crucibles so that ternary compounds can also be prepared. Forty

or more deposits can be obtained in a single operation. A wide range of compositions can

thus be obtained if desired. The siibstrates, amorphous or crystalline, can be heated up

to 600 °C. The following compounds have been obtained as polycrystalline, highly textured

or single crystal films: EuTe, EuSe, YbTe, YbSe, YbSe^^^, SmTe, SmSe, SmSe^+g (Th3P^

structure), Eu^.^Pb^^Te, Eu^-xGd^Se, Eu^.^Yb^Te [1], Evidence of high quality is given by

x-ray, electron microscopy, electron diffraction and electron microprobe analysis. Optical

abso2rption spectra up to 6 eV, reflection spectra up to 10 eV, magnetic circular dichroism

spectra in the visible have been obtained. Transition assignments have been proposed for

the first time in the case of Yb and Sm monochalcogenides [1/2]

.

Results of optical and magneto optical investigations have been presented for the

ferromagnetic EuS obtained by coevaporation and for EuO obtained by reactive evaporation.

Finally, electrical and other transport properties of stoichiometric EuO have also been

presented [3] .

Key words: Coevaporation of elements; rare earth chalcogenides ; synthesis.

REFERENCES

[1] Paparoditis, C, et al., ICCG-3, Marseille, July 1971, to be published in J. Crystal

Growth 1972.

[2] Suryanarayanan, R. , et al.. Conference on Rare Earths and Actinides, Durham, July 1971.

[3] Paparoditis, C, et al., Sol. State Comm. 9, 1871 (1971).

As this is a post-deadline paper only a brief abstract is presented here.

723

IV. OPEN DISCUSSION

SUBJECT: NONSTOICHIOMETRY

ORDERING AND CLUSTERING OF DEFECTS

EQUILIBRIUM vs NON-EQUILIBRIUM
1
National Bureau of Standards Special Publication 354, Solid State Chemistry, Proceeding:

of 5th Materials Research Symposivmi, issued July 1972.

THE TITANIUM AND TITANIUM-CHROMIUM OXIDE SYSTEMS AND SWINGING SHEAR PLANES

L. A. Bursill

School of Chemistry

University of Western Australia

Nedlands, Australia 6009

L. Bursill : Earlier this week Mike O'Keeffe and also Professor Anderson talked about

some of our interpretations of electron microscopy and diffraction results on the titanium

and titanium- chromium oxygen systems. I would like to show and discuss our evidence for

what we call swinging shear planes. The first slide (fig. 1) shows a single (100) layer of

reduced rutile idealized so that the anions (white balls) are close-packed. The pattern of

filled octahedral cation sites (black balls) is identical for each layer and these are stacked

to give an approximately hexagonal close-packed anion lattice. You will see what appear to be

out-of-phase boundaries running from top to bottom (X-X) . At the top is n = 8 of V[^02n-\ with

(121) CS planes-^. The (121) structures n = 4-9 occupy the composition range 1.75Vxvl.89. At

the bottom of figure 1 is n = 13 of ^rPzn-l with (132) CS planes. These occupy the composition range 1.930fCL.98. The difference between (121) and(132) will be seen by looking at the

sequence of steps along the trace of the CS planes. Two types of step occur in the (132)

structures, labelled C and A at the right of figure 1. C is a CS step and it consists of an anti-phase boundary [APB) step A plus an extra metal (which of the cations 1 or 2 is interstitial?) . C and A alternate along the CS plane for (132) but for (121) all the steps are Ctype (top of fig. 1) . On stacking the layers in three-dimensions C and A steps become strings

of corundum (e.g., Cr203) and a-Pb02 type structure respectively. These strings are parallel

to [111] rutile.

Fig. 1.

1 The crystallographic shear (CS) plane indices (hk£) define the plane of infinite extent of

basic structure while the shear vector [uvw] is the ideal displacement of the basic structure

across this plane.

727

;
Our problem was to decide which structures occurred in the intermediate composition range

1.89^x<1.93 and we built models like this. We also had some diffraction patterns which showed

rows of spots along (253) suggesting ordered intermediate CS structures. A n=21 (253) structure is shown in the center of figure 1. The sequence along the CS plane is . . .C C A C C A. .

.

and we note that (253) = (121) + (132)

.

R. S. Roth: I would like to give people a chance to interrupt if they want to, so I am going to have these microphones on and if anyone wants to ask you a question, they can.

L. Bursill : Okay. Well I'll go on. The next slide (fig. 2) shows an electron diffraction pattern which is evidence for (253) CS planes. It is a carefully oriented [lllJrutile

zone. Look at the origin 0. There is a row of superlattice spots running out to (253). The

angle between (132) and (121) is 11.5 degrees and the superlattice rows clearly do not go to either of these. Three members of this family with n=23, 24 and 25 were found.

In a parallel study of the Ti-Cr-0 system Don Philp in our laboratory found 12 members

of this family with n=28 to about 40 (1. 93^;i^l. 95) . No (132) structures occurred. At about

x=1.93 the CS plane began to swing. The next slide (fig. 3) shows a very sharp diffraction

pattern, but the superlattice rows run from the origin- we shifted the origin here- to (374) . Figure 4a and b shows rows which, as accurately as can be measured, are along (495) and (5,

11,6). Now you see what is happening. The superlattice pattern rotates from (132) for TiO^-, or (253) for (Ti,Cr)0;f, around towards (121). Figure 5 shows (7,15,8). A striking feature

of the patterns is the sharpness of the spots and this suggests that even the very high index

CS planes are very well ordered. Instead of a disordered mixture of (121) and (132) structures or large grains of e.g., n=9 (121) and n=16 (132) we have many intermediate CS structures. Figure 6a shows a very high index CS plane, very close to (121), giving rise to what

has been called spacing and orientation anomalies . Finally, (fig. 6b) we find the CS plane

has, we think!, swung to (121). This occurs for n=9 for TiO^ but for n=8 for (Ti,Cr)0^.

An important question is "just how well ordered are these structures? Is it an artifact

we see in the diffraction patterns, and as we see no two-phase mixtures on the patterns, are

we really seeing a continuous series of ordered structures with no two-phase regions in

between?" Yes?

F. Carter : How many unit cells does it take to show up good sharp spots like this in

electron diffraction?

L. Bursill: Well, we have very large areas, half to one micron, so we are not worried.

1

I

728
Fig. 3.

Fig. 4a.

Fig. 4b.

729
Fig. 6b.

. w " • • •

• a = oo h = 8

•ooo

730
F. Carter: What is the minimum number?

L. Bursill : I don't know, how sharp do you want the spots? Ten to 100 would give sharp

spots, we have many more than this.

I have now examined a number of compositions in both systems by lattice imaging in the

hope of clarifying the extent of order. Figure 7a shows a lattice image of a crystal indicating (5,11,6) CS on the diffraction pattern (fig. 7b) . As you see both the spacing and

orientation of the fringes are constant and across what appears to be a twin boundary T we find the equivalent CS plane (11,5,6). So this crystal of (Ti,Cr)Ox- appears to be a very

well ordered stable phase. Even more interesting than this is that Don Philp has now oriented at least 77 flakes into the [111] zone, which is the one you must obtain, and at least

50 of these are different, measurably different.

R. S. Roth : What was the method of preparation of these specimens that can produce such

a well ordered phase? At what temperature were they heated?

L. Bursill : Pellets were melted in an argon arc, sealed in air in platinum tubes and

annealed at 1300° C for three days. (The powdered pellets were black (reduced) after melting

but brown (oxidized) on annealing.) No great attempt was made to reach equilibrium.

As I said, of 77 patterns 50 were measurably different. As well as different CS plane

indices a number of different n values occur for each family, although not in the same flake.

All the inteirmediate CS planes may be written (hkJl) =p. (121) +g. (132) and are therefore ordered

intergrowths in this sense (see fig. 14)

.

The next slide (fig. 8) shows an image of a crystal which, on the diffraction pattern,

seemed to have CS plane intermediate between (495) and (5,11,6). We wondered whether these

would order also. It seems from this that you get wobbly fringes, and it is tempting to

Fig. 7.

731
Fig. 8a.

Fig. 8b.

think that we have partly resolved the A steps and that the sequence ...CCCCACCCCC

A. . . is not perfectly ordered. It is very difficult to interpret. The fringe spacing is 15

Angstrom. We need to obtain cross grating images to check this. In the region around the

origin of the diffraction pattern (fig. 8b) the row of reflections B-B is very weak. To re- solve the APB or CS steps we need to use the strong rutile reflections. This means resolution better than about 3 Angstrom. We are attempting this.

In the next slide v/e return to the binary system TiO^- and these patterns (fig. 9) are from a specimen quenched from 1450 C. You see that we have a whole range of streaks, spots

and arcing of spots. We still have the same basic effect but with a whole range of intermediate CS planes in the same small area. On annealing in vacuum at 1000 C TiO;^ specimens

can be made which have quite sharp diffraction spots, but not as sharp as for chromia doped

732
Fig. 9.

rutile. Figure 10a is a lattice image of reduced rutile where the CS plane lies between (132)

and (253), i.e., approximately (385) (see fig. 10b). If you sight along the fringes you can

resolve them into, to a first approximation, units parallel to (132) and (253), which differ

by 4°. The diffraction pattern (fig. 10b) is much better than figure 9 but not as sharp as

the Ti-Cr-0 ones. The CS and APB steps are not ordered as well. Figure 11 shows very wobbly

fringes in TiO^. We cannot interpret this in detail at this stage, but this to me gives an impression of what a nonstoichiometric phase in the strict sense would look like. You have

a variable CS plane. The steps are not ordered and if^ this is the high temperature situation you can imagine a dynamical situation with steps moving to and fro. An oversimplified

conclusion is that the results on TiO^^ provide a nice model for true non-stoichiometry while

those on (Ti,Cr)0;f provide a model system for a continuous series of ordered phases.

The next slide shows a model where by a series of ...

L. Eyring : Before you get too far from those wavy fringes have you taken diffraction

patterns on those particular areas?

L. Bursill : Yes.

L. Eyring : What are they? Are they the ones that we saw just before?

L. Bursill : No, not as bad as figure 9 and sharper than figure 10b. They look sharp

until you compare them with the chromia ones. This is a big problem, even if the CS planes

are wobbly you may still get a sharp diffraction pattern. It just depends how wobbly they

are.

Reduced rutile will oxidize on cooling if any oxygen is present thereby introducing disorder

and there is also evidence that the CS plane, at a given composition, swings towards (121) at higher temperatures

.

733
10a.

\Ov\<T\
Fig. 11.

J. Allpress : Some of those wobbles may be due to dynamical effects, because I noticed

some bend contours crossing.

L. Bursill : In figure 10a yes. I wouldn't interpret it. It is impressionistic. (Note

added in proof: The bend contour runs parallel to the fringes and the crystal thickness

varies slowly in this area so the diffraction conditions are constant along the fringes. The

wobbles must be due to CS plane fluctuations but what the wobbles are in terms of structure

must await higher resolution.)

Figure 12 shows a schematic model mechanism for swinging the CS planes from (132) towards

(121) . Cations (small balls) are added on the surface at APB steps (top left fig. 12) and

these are fed along the CS plane by the hopping mechanism described by Mike O'Keeffe on Monday^. At each hop a cation jumps from a CS step onto an adjacent APB step. The latter becomes a CS step and the fomer an APB step closer to the surface. Thus the CS plane may

swing continuously through all the intermediate high index planes by controlling the sequence

of C and A type steps. Remarkably few hops are required for a perfectly ordered structure

to occur at each stage. It appears that in reduced rutile the sequences disorder at high

temperature but can be made to order at approximately 1000 C but for Ti-Cr-0 the interraediate

sequences are very well ordered at 1300 C. The process is continued in figure 13; after about

(5,11,5) it is difficult to see the complete repeating sequence. We need a bigger model. The

number of steps becomes smaller and it is easier to make a continuous series of ordered

structures

.

The next slide (fig. 14) shows how a n=25 (253) structure may be resolved, at right, into a unit cell of n=9 (121) plus a unit cell of n=16 (132) ; or alternatively, at left, into

two unit cells of n=9 (121) plus a unit cell of APB structure n=l (Oil) . Many other possibilities exist for coherent intergrowth of different CS planes and n values. Not only do the

CS plane indices follow as sums but the structures may also be regarded as ordered intergrowths. We may extend this a little further and note that the corundum-like strips along

[111] at the CS steps contain the correct number of sites to accomodate all the Cr in the

CS structures which therefore may also be regarded as ordered intergrowths of Cr203 plus

Ti02

.

The next slide (fig. 15) shows a more general situation, i.e., two reciprocal lattice

nets, the finer derived from a super-cell corresponding to the coarser net. The dots indicate reflections you might see using x-ray diffraction, i.e., doublets or triplets about

strong sub-cell positions. Now I ask you the question what happens to your powder pattern

as the fine net is rotated relative to the sub-cell? If a reflection is exactly on a subcell position the line will not shift but reflections on either side will, and with increasing distance from the sub-cell position. This is just the kind of diffraction pattern which

is taken to represent a solid solution! No two phase regions will be seen even though we

have a different perfectly ordered crystal at each stage. We believe that this sort of swinging or this sort of behavior in the reciprocal lattice will be a quite general crystallographic phenomenon; it could occur for ordered intergrowth of any two unit cells which have a common face. It will be found in many cases. So we look for similar effects in other systems.

T——See: L. Bursill, B. Hyde and M. O'Keeffe this volume.

735

Fig. 14. Fig. 15.

The next slide (fig. 16) shows a CS plane in the Re03-type structure. It changes from

(120) at the top through (130) , (140) , (150) to (010) at the bottom. Only (120) and (130)

CS structures were known. So we searched to find high index CS planes i.e., swinging shearplanes in Re03-type systems. (unaware of John Allpress' work- this conference)'*. Figure 17 shows some diffraction patterns we obtained from niobia doped WO3 . On the top (fig. 17a) , we have the (140) structure with n about 60 in ^n'~'3n-3 ' ^-s., M02,95.

R. S. Roth : Can you give me a one or two sentence definition of swinging shear planes?

L. Bursill : A composition change occurs by a cooperative change in CS plane orientation, at close to constant shear plane spacing.

On the bottom, figure 17b, we have a mixture of highly ordered (140) and (150)

structures

.

B. Cox : Do these shear planes only rotate in one plane or are they moving in three

dimensions. In other words, do they all remain parallel to one direction?

L. Bursi 11 : All the ordered structures we observe are parallel to [111] j-^^j^-^g or

[001] Reo^.

B . Cox : Then can you be sure that you don't get steps in the other direction?

L. Bursill : Yes. We are very careful in orienting these patterns. (Note added in

proof: we refer only to ordered structures, there may be a low density of faults.)

Figure 18 shows a lattice image of a crystal of (Nb,W) 02^93 (c.f. fig. 10 in John

Allpress' paper). The CS plane spacing is very regular but they change orientation, in this

system (c.f. chromia doped rutile) , over a very small volume - in a few 1000 Angstrom. Note

the stepped fringes at a long row of steps aligned along Y-Y, cooperative inflections in

the CS planes at P, and a (140) CS plane ending at Q. In the large area of well ordered CS

planes from the center to the right of this picture their orientation changes from (140) to

(150) and back again, a range of 2.7 degrees. To the left the CS plane is (010) which is

the one you have in e.g., V2O5. Here all the A type steps have been eliminated. In the re- gion Y-Y steps are regularly organized over quite large distances. These are very high index

CS planes or, if you prefer, regularly stepped (010) CS planes.

Recently Grey and Reid^ reported some shear structure compounds (Cr ,Fe) 2Tin-202n-l

rived from the Gt-Pb02 type structure. The next slide (fig. 19) shows a model of a-Pb02 structure. If the rows of balls A and B are moved to the left and right as indicated, and a zig-

- See J. Allpress, this volume.

5 I. E. Grey and A. F. Reid (1971) J. Solid State Chem. (to be published).

737

465-504 O - 72 - 48
Fig. 16.

738
Fig. 17b.

739

/
740
Fig. 19a.

Fig. 19b.

Fig. 19c.

..g Plane of oxygens is .e.ove. and the gap close, we obtain ^^^^^^^^^J^X^

a CS plane in the a-PbO^ structure ^^^^^^/.^^^ coherently to a slab of M^O^ (derived

inal Sten Andersson structure) is shown (top) 3°J^ed co Y ^^^^ ^^.^ ^^^^^ ^121)

a-PbO,) at the bottom. The CS P^^^^J^^°ire'5o|;ther to'give intermediate CS struc-

^•1 and g unit cells of (110)a_pbO2 ^""^ ^v^t. rntile to a-PbOz • This type of mSS^! I

increases the ^-^^

"^aifsSfo ^he"^:iso;ie°„tatic„^^o.aUes obse.vea

te^ealate CS structure .ay possr.ly e.plar„_^so^^^^^_^^ ^^^^^^ ^^^^

by John Allpress m (Cr ,t ej iin-2^2n-l

. .-v ^ .1-ress that we predict this special type of recip

just before I finish I would Ixke to ^^^^^^ f JJ, particularly the so-called .sorocal lattice behavior will be very cormon .n other system

morphous replacement series in mineralogy.

Fig. 20.

741

/
R. S. Roth : One other thing. I assume with all these beautiful pictures and diagrams

that they have been or will be published in the very near future. Can you give us a reference

of some sort on what you are going to do with them?

L. Bursill : The diffraction patterns for Ti-0 and Ti-Cr-0 were published a few months

ago in Philosophical Magazine^. More of these and the lattice images are being written up. Some of these and a discussion of structural principles and reaction mechanisms will appear

in Progress in Solid State Chemistry Vol. 7. A paper on reduced WO3 and related psuedo-binaries is to be published in J. of Solid State Chemistry.

R. S. Roth : Is there anybody in the audience that would like to explain the effects

that we have seen in these slides today on the basis of solid solution? No? I didn't think

there would be.

J. Allpress : I am not going to do that, but we did find Bob, that if you doped WO3 with

niobium, you can put a couple of mol.% in before you start seeing shear planes'', and I think

that the same is true for chromium in rutile. Is that so Les?

L. Bursill : We have observed that also with chromia doped rutile samples.

J. Allpress : I'd like to know what the reason for that is.

R. S . Roth : 1 think that what you have to say is that there is some other type of defect which occurs at very, very low concentrations and I think that many people have believed

for a long time that there are other ways to make a solid solution. Maybe one of these might

actually exist, who knows?

L. Bursill : What? A point defect? A cluster?

R. S. Roth : One question I would like to ask is what do the x-ray diffraction powder

patterns of a series of compositions across one of these swinging shear plane areas look like?

Do they look anything like the powder patterns that I showed on that niobium-zirconia phase;

that is, substructure not moving much and superstructure moving continuously?

L. Bursill : Well, this is exactly how Sten Andersson has published these for TiCr-0 and reduced rutile.

R. S. Roth : But you can't see that two-phase region.

L. Bursill : No, above TiOi^gg you cannot see two-phase regions.

S. Andersson : If we take the Ti2Cr207 compound, as an example, the low angle superstructure lines move more than the parent lines, but we never saw any sort of two phase region.

L. Bursill : 1 could add that Don Philp has taken Guinier diffraction patterns and has

computed the unit cells for a list of intermediate structures and calculated line positions.

These come out as groups of very closely spaced lines which show up on the diffraction patterns as a slightly unsharp line.

S. Andersson : Of course, we do agree that if you had a tremendous resolution we would

see two phase regions wouldn't we?

L. Bursill : Well, not so, because the samples always show a range, you never get a sample with just two phases.

S. Andersson : No, but you would see doublets here and there wouldn't you?

L. Bursill : Yes, if you have the resolution.

5

' TM ~

^L. A. Bursill, B. G. Hyde and D. K. Philp, Phil. Mag. 23_, 1501 (1971).

R. S. Roth and J. L. Waring, J. Res. NBS 70A , 281 (1966).

J. G. Allpress, J. Solid State Chem. 4 (1971).

742
R. S. Roth : If the specimen was completely equilibrated with a given composition and

the true composition and the theoretical composition derived from the observed shear planes

matched each other, which nobody has really proved, then you should have to see either one

or two phases if you have the proper resolution. But that's practically theoretical.

S. Andersson : It depends on the degree of swinging, doesn't it?

L. Bursill : Yes. You would get a slightly unsharp line. I wouldn't say it was a broad line, at first glance it is sharp, but it is really the superposition of many.

R. S. Roth : Have you examined a specimen of a given composition with respect to how

the shear planes changed with temperature and time of annealing? I would say they should

change, until you reach some certain equilibrium condition, maybe.

L. Bursi 11 : Well this is a big problem. What is the high temperature structure in

the reduced rutile system? Is it wobbly or is it ordered?

R. S. Roth : I was referring particularly to the titanium-chromium oxide system.

L. Bursi 11 : That can be done by annealing because it doesn't oxidize.

R. S. Roth : But at various temperatures will it change?

L. Bursill : We have worked mainly at one temperature so far. If you melt a pellet

and then anneal at 1000°C for three days you do not anneal out the structure of the melt

which is a reduced rutile. That's a mess (c.f. fig. 9). At 1000°C you do not seem to have

the mobility to get an ordered structure and you have to go up in temperature. A further

point here is that to change the CS plane in reduced rutile (fig. 12) no long range diffusion of cations is required (all the cations are the same colour, say red) , Ti^"*" and Ti'*'*' may interchange by electron switching. For Ti^"'"-Cr^"'' you require long-range diffusion of

Cr^"*" (blue balls must diffuse along the CS plane) and this requires a more complex series of

jumps and presumably a higher activation energy.

R. S. Roth : What I am predicting is that for the temperature-time annealing sequence

you quoted, you have, and you see with electron diffraction, two or three or four different

orientiations of shear planes in the crystal because you have not yet approached equilibrium

far enough. As you go to higher temperatures and longer periods of time you should gradually

anneal everything out until any given specimen will show always one set of shear planes. This

would be your equilibrium condition. Now, if you could demonstrate that after you have done

that, if you come down to lower temperatures it changes again then I will take back everything I have said.

B . Hyde : That's a theological statement and not a scientific one.

R. S. Roth : Yes, but it can be checked.

L. Bursill : It should be checked.

R. S. Roth : All right. I think it's about time to give somebody else a chance up here.

743

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

A DEFECT CLUSTER IN MAGNESIUM FLUOROGERMANATE

E. Kostiner

Department of Chemistry

Cornell University

Ithaca, New York 14850

E. Kostiner : I would like to turn away from electron diffraction and describe a defect

cluster which we investigated using single crystal x-ray diffraction. First, let me give

proper credit; my co-workers are Bob Von Dreele (who is now at Arizona State University) and

Paul Bless and Bob Hughes at Cornell.

The genesis of this problem was an investigation of phosphor host lattices, in particular,

the fluorescence of Mn"'"'^ in the so-called magnesium germanate and magnesium f luorogermanate

structures. To completely determine the correct identity of these materials, it was necessary

to grow crystals and do complete structural analyses. It turns out that the material that has

been considered^ to be magnesium germanate with a stoichiometry Mgi+GeOg is in reality Mg2gGeio

0^9^. It is a rather intriguing structure which can best be described as a mixture of cubic

and hexagonal packing of oxygen atoms with a packing sequence (ABACBC)^. Structurally, it can

be described as a layer structure made up of olivine blocks and magnesium oxide blocks. The

space group is P^j^m ^ith a = 14.512(2), b = 10.219(2), and c = 5.944(1) A.

Figure 1 illustrates the structure. What we have, starting from the bottom, is an alternation of magnesium oxide layers with olivine layers in the sequency MgO, olivine, MgO,

olivine, MgO with the packing direction along the a-axis. The olivine layer has the com- position Mg2GeOit; the magnesium oxide layer, however, has two magnesium ions replaced by a germanium ion and a vacancy in an ordered arrangement to produce the stoichiometry MggGeOg

,

rather than Mg30g . The stacking sequence and the orientation of the layers is not the same

as in the norbergite-type minerals which are made up of olivine and brucite [Mg(0H)2] layers.

The full three-dimensional crystal structure analysis was refined completely to an i? = 0.044.

My interest in this problem is the effect of structure on the fluorescence properties

of Mn"*"^ . (We are now investigating these properties, and the manganese evidently substitutes

for an octahedrally coordinated germanium.) It was found empirically by the phosphor people

that by adding magnesium fluoride to the ceramic preparation there was an increase in the

luminescence efficiency and there was discussion as to whether the fluoride actually went into the lattice. It turns out that fluoride is incorporated into the lattice. The composition

of the f luorogermanate single crystals is Mg2 8Ge7 _ 5O38F1 g • In other words, about 9 w/o fluorine substitutes into the structure and charge compensation is accomplished by a deficiency

in germanium. There is nothing unusual about fluoride-substitution in oxide materials; it is

known to occur in perovskites , spinels, garnets, etc.

We grew single crystals of the f luorogermanate and made a detailed crystallographic investigation^ of the defect site (one of the germanium sites) . The germanate and the f luorogermanate are isostructural (crystallographic parameters for the - f luorogermanate are a = 14.343(1), b = 10.196(1), and c = 5.9075(4) A). We had an ample amount of single crystal data

so that a number of possible models for the defect site could be investigated. For example,

perhaps there is not a germanium vacancy but a magnesium ion substitute at the germanium site.

^Robbins, C. R. and Levin, E. M. , Amer. J. Sci., 257 , 63 (1959).

Von Dreele, R. B. , Bless, P. W. , Kostiner, E. and Hughes, R. E., j. Solid State Chem. , 2,

612 (1970) . -

Bless, P. w. , Von Dreele, R. B. , Kostiner, E. and Hughes, R. E., J. Solid State Chem. 4,

262 (1972). -

745
Fig. 1.

(Germanium occupies both tetrahedral and octahedral sites; magnesium could substitute at either site.) The possibility of magnesium surrounded by fluorine, germanium surrounded by

oxygen, germanium surrounded by fluorine was also investigated. The final arguments ^ , which

I will not go into here, are based on occupancy factors, theimal parameters at the various

sites, and a statistical analysis of the resultant R factors.

We found that the basic difference between the two structures, as first deduced from

the Patterson maps, is that the Ge(III) site (tetrahedrally coordinated) is 38% occupied.

This site is illustrated in figure 2. Three of the anions (actually two, since anion VI lies on a mirror plane) have highly anisotropic thermal parameters, while anion IV is nearly

isotropic. These thermal ellipsoids point toward the germanium sites. From our previous ar- guments we felt that the fluorine was localized at these sites. Since one can approximate a thermal ellipsoid of vibration by two fractionally weighted atoms placed along its major axis, we placed two half-weighted fluorines at either side of the center of this axis for each of

the highly anisotropic anion sites. Refinement converged to an = 0.046 with one half-fluorine exactly at the position of the oxygen in the germanate structure and the other displaced

about 0.2 A farther away from the Ge(III) site. It is very tempting to say that when the germanium site is occupied fluorines occupy these sites and when the germanium site is vacant the

anion (possibly oxygen) moves away from the vacancy.

Complex as the basic germanate structure may seem, it is really very simple if one con- siders the building blocks of olivine and magnesium oxide. In the f luorogermanate , the defect cluster is a partially occupied germanium site with the charge compensating anions localized about it. If one has a germanium deficiency one must have some sort of compensation

and in this case it is the substitution of fluorine for oxygen.

We have some other very preliminary information. We have done some electron diffraction,

but rather crude compared to what we have seen here during the past few days. This diffraction work indicates that we may have some sort of lamilar structure. In fact, if we take very

long exposure x-ray photographs, the glide that relates the two Ge(III) atoms in the f luorogermanate is violated. Therefore, there may be some ordering of defects within the structure

as it stands. We are at present investigating this possibility of a lamilar structure.

Thank you.

746
Fig, 2.

R. S. Roth : I would like to take the Chairman's right by asking the first question. I think there are lots of ways that people could think of disagreeing with you if they wanted

to. There are obviously other interpretations. Now, one of the first things that comes to mind is ... I remember the paper that was in the Journal of Solid State Chemistry . .

.

E. Kostiner : That was the germanate structure.

R. S. Roth : The crystals themselves were grown by a flux technique and there was the

question of did they or did they not have manganese fluoride or something like that?

E. Kostiner : They were grown with the activator ion (Mn"^'*) added, that's correct. But

no fluoride was present in the preparation of the germanate.

R. S. Roth : And yet there was no account taken of the manganese in the structure analysis and the question is, how much is in there? How does it affect the x-ray results?

E. Kostiner : That's a very good question. The manganese concentration (by analysis)

is 0.72%, which corresponds to 0.3 atom of manganese per unit cell. It is very small and it

does not affect the structural details at all. One can make the material and grow crystals

of it without the activator ion. It is very handy to use the activator because you just use

a UV lamp to find the crystals. We did spectroscopic analyses for platinum contamination

from the crucible (0.67%), lead contamination from the flux {<0.1%), and they are at a very

low level such that there is a very small fraction of an atom per unit cell. Yes, I did

worry about the possibility of this intentional contaminant causing this layer structure to form. Are you satisfied?

R. S. Roth : I wouldn't say I was satisfied, but right at the moment I don't have any more questions.

Is there anybody else who would like to take a crack at this? From the crystallographer's point of view?

E. Kostiner : I think the structure should stand as it is. It is a good structure.

There are no anomalies in the data. .

'

R. S. Roth: How about the defect data?

747
E. Kostiner : This is certainly an interesting example of what one might call a defect

cluster.

R. S. Roth : I once ran into a similar thing in a germanium partial occupancy problem

that I simply couldn't solve and this, of course, was because I insisted that it was going

to have to come out stoichiometric. This was the germani\jm: 9 niobia which is isostructural

with vanadium or phosphorus: 9 niobia (P2O5 • 9Nb205) Whether it's nine or not, the germania

compound hasn't been proven, but it is some sort of a defect problem which nobody has ever

solved.

B. M. Gatehouse : I don't think you commented on the anisotropic thermal ellipsoids in

the compound without fluoride.

E. Kostiner : We went fully anisotropic in the germanate structure. The thermal parameters for all of the atoms are essentially isotropic.

R. S. Roth : Any more comments? Questions? I think that we should give Dr. Bevan the

next chance.

'^Roth, R. S., Wadsley, A. D. and Andersson, S., Acta Crystallographica 18, 647 (1965).

748
National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

THE ORTHORHOMBIC PHASES IN THE SYSTEM

YTTRIUM-OXYGEN-FLUORINE

D. J. M. Bevan

Flinders Univ. of S. Australia

Bedford Park, South Australia 5042

D. J. M. Bevan : On this same theme of a continuous sequence of ordered phases or an apparently continuous sequence of ordered phases in a nonstoichiometric region, following

on what Bob Roth said the other day and what we have just heard about the chromium doped

rutile systems, I thought it might be of some interest to tell you something of the work

that Dr. Alan Mann and I have been doing on the yttrium oxide-fluoride system. I'll try

and be as brief as I can. The first slide (fig. 1) defines the region of interest. The

X stands for oxygen plus fluorine and you can see that somewhere between about 2.12, or something like that, and 2.22 there is this orthorhombic phase. At the lower end it coexists with stoichiometric rhombohedral YOF; at the high end with stoichiometric YF3

.

The second slide (fig. 2) shows a plot of the orthorhombic parameters of the subcell.

This is very closely related to the fluorite structure. The slightly distorted fluoritetype subcell parameters are about five and a half angstroms or thereabouts. You might think

you have the nice simple sort of situation of 5 or 10 years ago, continuous variation of

lattice parameter with composition.

Phase data for samples investigated by powder and single

crystal diffraction.

Composition Phase Analysis fluorite-type sub-cell

parameters (±0.001A)

"^2. 13(6) orthorhombic phase 5. 425 5 .508 5 .527

^^2. 11(5)

YOF + orthorhombic phase 5. 420 5 .512 5 .527

"

^^2. 14(8)

orthorhombic phase 5. 419 5 .519 5 .529

^^2. 14(9) orthorhombic phase 5. 419 5 .516 5 .527

^S. 16(5)

orthorhombic phase 5. 416 5 .520 5 .528

^^2. 17(1)

orthorhombic phase 5. 413 5 .52 (8) 5 .52(8)

18(3) orthorhombi c phase 5. 410 5 .53(3) 5 .53(3)

^^2. 18(7)

0 rtho rhombi c phase 5. 407 5 .53(3) 5 .53(3)

^^2. 22(0)

YF^ + ortho rhombic phase 5. 402 5 .541 5 .535

^^2. 22(5)

YF^ + orthorhombic phase 5. 400 5 .544 5 .534

25(9) YF

3 + orthorhombic phase 5. 399 5 . 546 5 .535

Fig. 1.

749

/
paraaeters, (8)

5.550

^•"^ /.ISO 2.250 Fig, 2. Composition o = analyzed composition

© = estimated composition {2P)

The next slide (fig. 3) shows the sort of situation that Bob Roth described the other

day. These are three Guinier powder patterns of different compositions. You can see the

(111) f luorite-type line, the (200) fluorite group, and the set of superstructure reflections.

This one, this (lk32) one moving left and the other one, over here, (Ok22) moving right. So this rather gives the lie to the idea of continuous solid solution. The next slide

R. S . Roth : Judge, can I interupt before you move that slide. Why does the (111) or- thorhombic line appear to be split into three lines?

D. J. M. Bevan : Oh, there's an internal standard in there. That's thoria.

R. S . Roth : Thank you, that means the (111) orthorhomibc line is only split into two lines, not three. (There - probably some YOF in this pattern, too.) Comment?

D. J. M. Bevan : Yes, on the lowest of the three pictures. There is, of course, no splitting of the orthorhombic (111) reflection.

<111> <200> Ok22 lk32

Fig. 3.

1 —--

1

1

Th02 (111) OkiO

750
Next slide (fig. 4) . This is a Weissenberg picture of a single crystal which turned

out, veiry fortunately for us, to be a comparatively simple superstructure; a one-dimensional

superstructure which shows seven spaces between the main fluorite type reflections. We have

gone some way towards getting the single crystal structure of this. Sten Andersson has seen

the results. I think the next slide will show you the sort of structure which this substance

has (fig. 5). This is one quarter of the unit cell, which consists of seven f luorite-type

subcells stacked one on top of the other in the b direction. Down at the bottom the distortions are relatively small. As you move up you start to get rather larger distortions and

the additional anion. The ideal formula, for this substance is YyOgFg , it's an M7O15 structure. The additional anions go in here, these A9 anions on the y = 1/4 mirror plane. I'm

not going to say anything more about the structure except this: in its simplest terms you

can think of a layer, a two-dimensional layer of interstitial anions, going in at the y = 1/4

position. Sten Andersson has a very nice geometric model for this (in terms of his geometry)

where the coordination in this region becomes square anti-prismatic. He might like to comment on that later on.

Fig. 4.

Projection onto (001)

o

A3 ©

Projection onto (100) = Y atom projected from near z=l/4 onto (001) or Y atom projected from, near x=l/4 onto dOO)

= Y atom projected from near z=3/4 onto (001) or Y atom projected from near x=3/4 onto (100)

o

= anion projected from near z=0 onto (001) or anion projected from near x=0 onto (100)

j-'-N = anion projected from near z=l/2 onto (001)

Fig. 5. or anion projected from near x=l/2 onto (100)

751
Let me just move on very quickly to the next slide (fig. 6) which again shows the coorr- dination polyhedra. Two of the cations in the asymmetric unit are now 9-coordinated. There

are the additional anions coming in here (A9) . On the next slide (fig. 7) is one attempt that ' we have made to arrive at the structural relationships. This is the coordination polyhedron in * the YF3 phase itself. You can see that there is quite a close similarity, geometrically, to the 9-coordinated metals in the region of the interstitial layer. A crude description might

be given in terms of an intergrowth of the YF3 type structure; a two-dimentional intergrowth

with regions of a fluorite-type sturctvire. However, I don't want to press that analogy too

far. A great deal more needs to be done on the detailed structure before we can say too much

about that. We also have discovered the phase Y5O5F8 , and we believe that there is indeed an homologous series of simple ordered phases, which one can write as YnOn-iFn+2- That's enough

for that slide, thank you.

i

Fig. 6. Metal coordination polyhedra in

(YyOgFg);^ (Primes refer to symmetry

related atoms in adjacent asymmetric

units.)

® = yttrium atom at close to z=l/4.

(a) = anion at close to z=0.

(a I = anion at close to z=l/2.

© = yttrium atom at y=3/4.

- fluorine atom at close to y=0 (and 1/2)

(f^ = fluorine atom at y = 3/4.

Fig. 7. Coordination of metals Y3, Y:^ in (YyOgFg)^,

752
Let us come back for a moment to the powder patterns . Both of the simple homologs n = 7 and n = 6, have been found as single crystals and indexed completely, and this indexing related back to the powder patterns. The superstructure reflections which are of interest are

the ones which move the most and are of the form Ok22 and lk3 2. Then there is another reflection which is one of the fluorite 200 family, which we can write OkjO where, in the case of the

fluorite subcell, of course, this is 2. In these simple homologs, the values of these indices

are related to the number of fluorite subcells in the stack. The index OkjO is simply (0,ri,0)

where n is the number of fluorite units in the stack. This one is (0,n-l,2) and this one is

(0,n+l,2). Let's now move on to the next slide (fig. 8). This just lists the homologs of the

series. The 7 and the 6 homologs have been found. Let me be quite honest and say that we haven't found the 5 homolog in the pure state, although we have certainly found super-superlattices, as we call them, which are quite clearly based on the 5 homolog. The compositions

of the members n = 8 and n = 4, do not fall within the region of what one might call "nonstoichiometry .

The next slide please (fig. 9) . This is another Weissenberg pattern of one of the intermediate phases. As you can see this one is based on the member n = 5. The very strong reflections are the fluorite subcell spots. You can see that there are 5 spaces in between

these, giving the n = 5 homolog superlattice . You then have the super-superlattice on top of

this, where you have the satellite spots occurring. I think, just speaking from memory, that

we have here a b axis of something like 250 angstroms.

Basic unit orthorhombic phases. \

Unit Composition Formula Unit Cell Parameters

a b c

8F YX2. 125 (YgOyFio )k - YqXu not stable as a discrete entity

7P YX2_ 143 (YyOgFg) h = Y7X15 5. 420A° 38.58A°* (=7x5. 512A°) 5.527A°*

6F YX2. 167 (Y6O5F8) 1+ = ^6^13 5. 416A° 33.12A° (=6x5. 520A°) 5.520A°

5F YX2. 200 (Y5O4F7) 1+ = Y5X11 5. 406A° 27.69A° (=5x5. 538A°) 5.532A°

4F YX2, 250 (Y4O3F5) 4 = Y4X9 not stable as a discrete entity

*Originally reported as c = 38.58A°, b = 5.526A° (D. J. M. Bevan, R. S. Cameron,

A. W. Mann, G. Brauer, and V. Roether, Inorg. Nucl. Lett. 4 [4], 241-7 (1968)). This designation has been interchanged in accordance with the structural findings.

Fig. 8

Fig. 9.

465-504 0-72-49 753

/
Now, how to sort this out? What we have been able to do, and I think this is probably shown

in the next slide (fig. 10) , no, I'm sorry this just shows the indexing of the superlattice

lines for the simple members of the homolog. At any rate there is the (n-l)k index and the

(n+l)k index showing up. Next one, please (fig. 11).

Now, this is the way in which we have approached this analysis. I'm not going to go

through this in detail, but what one can do is to get experimental ratios of sine square thetas from the Guinier patterns and these values of sine square thetas can be obtained fairly

precisely from Guinier patterns. We use strictly monochromatic CiiKa^ radiation and the precision in these measured sine square thetas is quite high. Ri & R2 are the ratios of the sine

square theta for the 0,ki,0 reflection, which is one of the 200 fluorite subcell group, and

the sine square thetas for Ok2 2 and lk3 2 reflections respectively. These are experimental

ratios. Now you can match these to the ratios of the squares of integers. In this way you

can see what sort of values for n are within the limit of error, where n now is the number

of fluorite subcells in the stack. You never find more than about 2 or possibly 3 which are reasonable at all. Then you combine this sort of information with the measurements that you

get from those single-crystal Weissenberg patterns showing super-superlattice reflections.

sin^e and {hk£} values for {OkiO} , {0k22} , and {Uk:32} reflections.

Basic

Unit

{o;ciO}

(Fluorite-type)

{o;c22}

(Superstructure)

{1^32}

(Superstructure)

sin^e {hkl} sin^e {hkl} sin^e {hkZ}

7F 0.07811 {0(14)0} 0.09199 {0 6 2} 0.12359 {1 8 2}

6F 0.07786 {0(12)0} 0.09125 {0 5 2} , . 0.12430 {1 7 2}

5F 0.07750*{0(10)0} 0.08995*{0 4 2} 0.12568*{1 6 2}

* . 9 By interpolation of sin^G values from patterns at nearby compositions.

Fig. 10

Fig. 11.

In the orthorhombic system sin^e^^^^^ = h^A + k^B + l^C

where A

_ a24a2

B - —

4i?2

, C = 4c2

Thus for the {0;ci0} reflection: sin^e

{O^ciO}

ki^B

for the {0^:22} reflection

:

sin^e

{o;c22}

k2^B + 4C

and for the {1^32} reflection

:

sin^e {Lk32} lA + k^^B

In these expression the values of A and C are determined quite

precisely from the a and c parameters of the fluorite-type subcells

(see figure 1) since, for any given intermediate phase, these are unaffected by an uncertainty in the number of sub-cells comprising

the one-dimensional (ij-axis) superstructure.

It then follows that two ratios, and R2 , can be defined

, o sin^e

ki^ {OkiO} such that 2 sin^e

Ri = ^^^'^o;c20}-^^

and R2 = k^^ "^^'^OJciO}

k,^ -in'9{i;c32}-^-^^

754
These are not terribly accurate, not good to better than about ± 4% on the b parameter from

those single crystals. I think the next slide shows the results of this (fig. 12). Here are

the experimental ratios as determined from the powder data and the values of the b parameter

as determined from the single crystal data, and then going back again to the powder data, one

comes up with more precise values of b. You see now the biggest we got is 315 angstroms for

a 57 times fluorite stack. This just indicates the niomber of fluorite subcells in the one- dimensional stack.

Overall the picture has been rationalized in terms of an ordered intergrowth of the basic

homologs, and the next slide (fig. 13) shows the possibilities. There is, for example, a 23

stack, 2 lots of eight and one of seven, although the 8 homolog, of course, doesn't occur on

its own. It's outside of the homogeneity region, although it can still be invoked in the

ordered intergrowth explanation. The only other thing I need to add by way of justification

for this is that if this generalization for the indexing is correct, (this is an assumption,

but works out quite well) then one might expect to have the same sort of approach apply in

the case of the ordered intergrowth. So, if you take kj for example, it is obvious that if

you have 23 fluorites, then the k index is going to be 46 because it's a f luorite-type reflection. However, for the two super-lattice reflections of the 23 stack, the k2 index for

a pure 8 phase would be 7, then twice 7 equals 14, and the k2 index for the 7 phase is 6, so the k2 index for this superlattice phase is 14 + 6 = 20. The k3 of this would be twice 9 or

18 plus 8, 9+9+8= 26. On the basis of this sort of rationalization, we claim (whether

we are justified in claiming this or not, I don't really know, but it certainly works,) we can make a distinction between the two possibilities for the 47 stack and the 57 stack,

as shown, because only in the case of this first one do the indices fit. According to this

pattern and the ratios that you get from these indices, only then do these agree with the

measured ratios of the sine square thetas from the powder data.

Unit cells for Intermediate Phases.

Derived

Unit

Cell n Experimental

Powder Pattern Ratios

Derived

Cell

Experimental

Unit Cell b

Derived

Cell

23F Ri = 5.25±0.06 5.29 128 ± 5& 126. 7A

R2 = 3.11±0.03 3.13

7F Ri = 5.46±0.06 5.44 38.5 ±2A 38. 6A

R2 = 3.04±0.03 3.06

19F Ri = 5.66±0.06 5.64 105 ± 5A 104. 9A

R2 = 2.98±0.03 2.98

45F Ri = 5.58±0.06 5.61 248 ± 10& 248. 2A

R2 = 3.0010.03 3.00

6F Ri = 5.7210.06 5,76 331 lA 33. lA

R2 = 2.9410.03 2.94

17F Ri = 5.9010.06 5.90 91 + 4i 94. 0&

R2 = 2.9010.03 2.89

47F Ri = 6.0810.06 6.12 252 1 lOA 260. OA

R2 = 2.8210.03 2.82

57F Ri =6.1610.06 6.14 317 ± 12A 315. 4A

R2 = 2.8010.03 2.81 ' 28F * Ri = 6.4210.06 6.48 155 16A 155. 2A

R2 = 2.7310.03 2.71

28F* Ri = 6.4510.06 6.48 157 16A - 155. 2A

R2 = 2.7110.03 2.71

41F Ri = 6.54 + 0.06 6.51 222 1 9& 227. 4A

R2 = 2.6910.03 2.69

* However, for the two samples with the same (28F) unit cell, a unit with half

the indicated b axis (i.e. 14F) must also be considered, but for the structural

interpretation of this intermediate phase, the ambiguity is, at this stage,

trivial.

Fig. 12.

755
Ordered intergrowth models.

Unit Ordered Interspersion Calculated k indices from

Composition theoretical ratios

^1 ^2 ^3

Zor z X / QT? \ I or ) + J- X / IT? \ ^^2 .130

"71? /r X X t "71? \ ^^2. 143 J. ^ D

Q0

1X X \ ) z X \ or ; ^^2 .15 3 38 16 22

HDt X I IF) +

A X (,br ) VY^ -. ^ ^^2. 155 0 0

or 1X X \ ox } ^^2 ,16 7 12 5 7

X /r X

1X X \.Dr ) "^^2 .176 34 14 20

*± /r X vor ; 7 X \Dc 1 ^^2 .191 94 38 56

7 X (6F) + 1 X (5F) (YX2.170)

57F 2 X (6F) + 9 X (5F) YX2.193 114 46 68

7 X (6F) + 3 X (5F) (YX2.175)

28F 4 X (5F) + 2 X (4F) YX2.2I4 56 22 34 28F 4 X (5F) + 2 X (4F) YX2.2I1+ 56 22 34

4 IF 5 X (5F) + 4 X (4F) YX2.22O 82 32 50

Fig. 13.

So that's the story! This is I think another example of a continuous series of ordered

phases in a range which in the early days, when Zachariasen ^ first studied this system, was thought to be a classical non-stoichiometric phase. It is related to the fluorite system.

Crystallographic shear planes are not involved here and we have a different sort of principle.

Paul Caro thinks that he can explain this in terms of his (LnO)^ cation. I think that we need

to do some more work on that to see if it fits. Sten Andersson has a very nice description of

the square anti-prism coordination polyhedron in the center whereby the extra anions are introduced. Altogether we'll need to sort all these things out before we can give a final definitive statement on this. This preliminary work will be published in the J. Solid State Chemistry as soon as possible. Thank you Mr. Chairman.

R. S. Roth : I have several questions. The first one is the same question that I've

asked everybody else, how did you make the specimens?

D. J. M. Bevan : Solid state reactions, no doubt with the aid of a little bit of vapor

phase transport, in sealed platinum capsules at about 1150° for a week, slow cooled; mixtures

of yttrium oxide and yttrium trifluoride.

R. S. Roth : How near were you to the melting points, to the solidus temperatures?

D. J. M. Bevan : Yttrium fluoride, I think, melts somewhere around about 1350°. We have

some of the specimens which have obviously been close to melting. The crystal growth that

takes place at high temperatures is very, very considerable indeed.

R. S. Roth : My second question is, how near was the experimental composition to the theoretical one derived from the crystal taken from that batch, and how close do you think the

real composition is to that?

1 W. H. Zachariasen, Acta Cryst. 4, 231 (1951).

756
D. 3. M. Bevan : The real compositions were determined by chemical analysis. They didn't

always agree with the as-prepared compositions because the specimens tend to hydrolyze , and

indeed one makes use of this in the analytical procedure. In using this hydrolysis technique,

steam plus oxygen over the specimens at about 1000°, the HF comes off and you have quite a nice method for analyzing the fluorine. You are left behind with pure Y2O3 which you can

weigh, so the analysis is for example 2.155 ± 3 or so in the third figure.

j;. S. Roth : Now the question becomes, how close does the chemically analyzed composition

fit the x-ray theoretical composition?

D. J. M. Bevan : In the case of the seven homolog, that single crystal came from a mixture in which some YOF was present. The analyzed composition was 2.115 if I remember

correctly. The theoretical composition of the 7 phase was 2.143. The chemical analysis of

the 6 phase, which is about 2.186 if I remember rightly, agrees with the theoretical to about

within experimental error.

R. S. Roth : I've been hogging the questions here. Does anybody else wish to contribute?

Do you think that a stacking sequence of 47 or 57 in a unit cell dimension of 315

angstroms has any real meaning?

D. J. M. Bevan : I've only been talking about the facts as observed.

R. S, Roth : Oh, I quite agree with the facts as observed, that wasn't the question.

J. S. Anderson : I think that is a very interesting question. Bob. I really find it

hard to believe that a crystal can remember what it did 700 anas+-roms ago even if it has a faint recollection of what it did 350 angstroms ago. I have a feeling that when one comes to look at these stacking sequences, made up as they are of a number of sub-units, we are almost

bound to find that there is some variation from specimen to specimen, and some disorder. It

seems to me that these questions about the thermal preparation, are particularly cogent in cases like this. It is very hard to believe that some disordering does not take place at

high temperatures. It may be that they are stable right up to the melting points, but I strongly suspect that there will be some randomization of stacking, that it will be very hard

to prepare an absolutely uniform crystal.

R. S. Roth : Well, one point on this is that ... I might be hogging the answers too,

but my feelings on this subject is that you can introduce more order into the system by high

temperatures. This is not a crystallographic shear type system at all that we are referring

to. In this system I feel that you get a better stacking sequence, more order to that sequence

with more time and temperature as more energy is applied to the system.

D. J. M. Bevan : Well, with respect. Bob, because it is not a CS system then your comment

is irrelevant because in fact if you heat these things up at about 400° or 500°, you lose

your super-structure; they disorder. These are low temperature phases.

R_. S._ Roth: How do you know? What experiment has led you to this hypothesis?

D. J. M. Bevan : We have seen the disordering process occur in electron diffraction,

even under normal operating conditions.

J . S . Anderson : You see, this is kinetics versus thermodynamics. One must distinguish

between the real equilibrium state - the absolute minimum of the free energy surface at any

temperature - and the practicability of getting to that state. As prepared, there may be

fluctuations of order and composition within a crystal, leading to variations in local order.

Its properties correspond to some point on a metastable free energy surface . To get to the

absolute equilibrium state, kinetic processes must intervene: diffusion, or next neighbor

place exchange or at least a jump across a potential barrier to a site of different coordination. To achieve a new order in both CS phases and stacking structures, these steps have

to be highly cooperative. This is perhaps why such ordering processes sometimes seem to show peculiar kinetics: they can set in rather abruptly at high enough temperatures, as if

the activation energy was far greater than that of any individual unit step. For example,

in our electron microscopy of the niobium oxides we have found that H-Nb205 reduces rapidly

757
below 1000° to give a product with domains of the Nb2 5062 structure in unchanged domains of

H-Nb205 structure, and can be annealed indefinitely at 1000° without change. The preparation

process already involves cooperative atom movements that shift all the CS planes (using that

term loosely) in the transformed structure. At 1300°, quite rapidly, the CS planes re-shuffle

themselves to transform the domain structure into the large-cell regular intergrowth structures. That would seem in line with Bob's argument, but I believe it is a kinetic effect.

As we go up the temperature scale - and each structure has its own effective temperature

scale - a second kinetic effect comes in. The atoms are not immobile vibrators: they have

a finite mean lifetime on any site, and this is strongly temperature dependent. If the mean

life time is short, a significant proportion of sites of any one type is always 'wrongly'

occupied. On the ultramicrostructural level, perfect order cannot prevail throughout the

crystal at high enough temperatures. Two questions then arise. How much disorder must there

be before we recognise it? How much disorder must there be before the crystal loses track

of the correlations upon which its superstructural organization depends? Returning to the

thermodynamics, there is now no doubt that the coulombic part of the lattice energy of ionic

crystals confers significant disadvantage to random structures as compared with ordered

structures - any kind of order. In CS and stacking structure, the difference in energy between a perfectly regular and an irregular, but locally ordered, stacking sequence is likely

to be much smaller. The energetic gain, the driving force, behind attainment of true order

is small, so that the crystal can hang up on a metastable free energy surface. However, as long as the planar structural units retain their integrity , there is very little entropy to be gained by randomising their spacing. Hence, under these conditions, equilibrium is dominated and the superstructure order can persist - once reached - up to the highest temperatures. However, if the mean life time factor erodes the perfection of the planar structural

units, the situation changes. Instead of involving a small number of entities in a 1-dimensional disorder problem, the configurational entropy arises from a much larger number of

local clusters, or even every site in the crystal. The entropy gain from disorder can then

take control. In principle, these seem to be the considerations behind the range of behavior

that is found.

P . E . Caro : I would like to point out that the strict chemical order I am suggesting

for those phases in terms of a succession of definite planar chemical entities does not

necessarily imply a crystallographic order. This then will be "ordering" but not with the

crystallographic meaning: we may have several polymorphs with the same composition (i.e. a chemical order) . The fact is well known for silicate structures. The chemical order then

came first, and the crystallographic one only second, and more, it may not be necessary after

all.

D. J. M. Bevan : Well, I agree entirely with what Stuart Anderson said, too, because

there is no doubt these things are not perfectly ordered and when we can get around, if ever we can get around to looking at them under the electron microscope then we are going to see stacking faults. That is, if they don't disorder in the process, which I suspect they may

do. I don't think there is any doubt about that, but Bruce Hyde, it was Fujiyawa or someone, wasn't it, who has done a theoretical analysis of these stacking faults? But you still get

the repeat unit.

B. G. Hi^de : Why bother to speculate? Wait and see! .. . -

D. J. M. Bevan : All right, we'll wait and see.

F. Jellinek : I don't think these very large unit cells are really as frightening as they look at first sight. You have two mechanisms of some kind of ordering. You have both

the metal positions which you studied and also the arrangement of oxygen and fluorine which

you have not studied and could not with this method of course. It may well be similar to what we have found to be the case in some other compounds. One of the orderings may have,

say a repetition distance of 4 subcells; the other one a repetition distance of, say, three

and a half subcells and you add up to a unit cell repitition distance commensurable with both

of them, that means in this example 28 subcells (7x4=8x3 1/2) . So if you have two mechanisms,

as you do have, you are bound to have large unit cells if the two mechanisms are not exactly

commensurate. This may well be the explanation of these phenomena you observe.

758
R. S. Roth : Any other comments : Let me get back to my argijment then . You said that

if you have a system that does not have shear planes, then the argument I was making about

high temperature annealing is invalid. I disagree with that. It could be that in your

yttrium oxide fluorides all the super structures disappear at -400°, you hadn't made that

point earlier. However, we can mention other systems that do not contain shear planes, for

instance, consider the paper that Stephenson gave at the Arizona meeting on the tantalum

tungsten oxides^. Now, there are no shear planes in that low temperature form of tantalum

oxide, yet it is a high temperature annealed system where increased temperature causes better order. The same is true of almost any high temperature oxide that I have ever worked

with that has such things, and there are certainly many such. Do you call the Aurivillius

type phases shear planes, or the Ruddelson-Popper type phases shear planes? These phases,

stacking sequence type things, all have similar phenomena, hundreds and hundreds of angstrom

unit cells and increased high temperatures contribute to ordering; contribute to a much

sharper super-structure pattern. Now, that isn't quite the same thing, is it? But this is

the experimental observation. Comment on that?

D. J. M. Bevan : I don't quite understand what you are saying. You are saying that if

I heat to higher temperatures, then I will get better ordered phases on cooling.

R. S. Roth : I didn't really mean your system, although I wouldn't be surprised, yes.

D. J. M. Bevan : Well, obviously you have to heat to high enough temperatures in order

to react the specimens. They will, in fact, react at about 850° and you get perfectly wellordered phases. It might be worth pointing out in this context that this is not the only

system we are looking at. We are looking at the other rare earth oxide fluorides as well.

When you move up to the lighter rare earths, neodymium oxide fluoride, the specimens have

been heated up to about 1600° or thereabouts, and very good single crystals obtained and

there is only a partial ordering of these. The fluorite subcell distorts in a monoclinic

fashion, but none of the super-superlattice phases have been observed, even after six months

annealing at 350 °C. As you go down the series the super-superlattice phases begin to come

in at temperatures where you can expect to have a reasonably mobile system. I believe as far as the neodymium system is concerned that we just cannot achieve this sort of order if

it is stable at temperatures where—well, what I am trying to say is that the way you would

get the ordering is at temperatures so low that you have lost mobility for ordering to take

place. You are beaten by a kinetic problem.

R. S. Roth : Well, maybe the difference is between a mixed cation oxide and a mixed

oxyfluoride with only one cation, but yet I think of Sten Anderson's work on the tatalum

oxyfluoride which was the same structure type as the one I originally referred to.

D. J. M. Bevan : But there again, the mobil species is the tantalum is it not?

R. S. Roth : I wouldn ' t know . ^

Shall we give Dr. Eyring a chance now?

2 R. S. Roth and N. C. Stephenson, in The Chemistry of Extended Defects in Non-Metalic Solids,

p 167, North Holland Publ. Co., Amsterdam

759

/

National Bureau of Standards Special Publication 364, Solid State Chemistry, Proceedings

of 5th Materials Research Symposium, issued July 1972.

PHASE REACTIONS NOT EXHIBITED ON THE USUAL PHASE DIAGRAM

LeRoy Eyring

Department of Chemistry

Arizona State University

Tempe, Arizona 85281

L. Eyring : I thought it would be worthwhile to call attention to some results obtained

by sensitive yet antediluvian methods of observing phase reactions in solids not usually re- presented. I refer to oxygen pressure, temperature, composition studies on rare earth oxides

utilizing thermogravimetric techniques. For example, let us look at the phase diagram of the

praseodymium oxide-oxygen system shown in the first figure^ . This is an interesting phase

diagram, a fraud to say the least, ostensibly describing all the relationships between oxygen

and praseodymium atoms in the temperature-composition limits shown. People have, whenever

this slide has been shown in my presence, rarely asked about the funny spots veering off to

the right of the PrOx.ynt composition at higher temperatures. Well, therein lies a tale.

The fact is that above about 750° at higher pressures this most thermally stable of the

intermediate phases (iota) does not fom as a single phase in reduction (see curve 650 in

fig. 2) . This is true even with annealing for as long as a month—there is simply no measurable drift toward PrOi_7ii+ under these conditions. On the other hand, if the pressure

over a sample at say 850° and high pressure (stranded at higher composition) is reduced to 10

Torr the composition goes immediately to ~ PrOj^yii^ and the sample does not reoxidize upon

returning to the original pressure^. All this in spite of the fact that reaction rates for

phase reactions are very fast under these conditions.

weight change (mg) 0 20 40 60 60 100

I I I I I I I 1 1 1

iOO" 1714 I"6l.8«)'e'8l833

\ 1 1 I I I I

I

i

- 15 16 17 18 19 20

composition (x in PrO,) Fig. 1.

T B. G. Hyde, D. J. M. Bevan and L. Eyring, Phil. Trans. Roy. Soc, London Ser. A, No. 1106,

^ 259 , pp 583-614 (1966).

R. P. Turcotte, M. S. Jenkins and L. Eyring, unpublished results.

761

/
1714 1778 1800 WB 1-833

I 1 I I 1 , [

, '•5* 155 f60 VeS 170 TO 1?0 fsS

(x in PtO,) Fig. 2,

In the region of the delta, epsilon and zeta phases a phenomenon quite analogous to that

just described in the hyperiota region occurs (see fig. 2 curve 45). At low pressures almost

classical isobars are seen yet such curves show marked hypercomposition at higher pressures.

This behavior is inadequately explained and is presently undergoing further study^.

The alpha phase is formed at higher pressures and temperatures as shown in the diagram

by an apparent disordering of the intermediate phases belonging to the homologous series.

At suitable pressures one can cross the alpha region by changing the temperature and when

one does so, the isobars are reversible and reproducible even with very careful measurements.

Curiously there is an indication, outside the limits of error, that the nature of the alpha

phase depends upon its origin. It depends upon what the ordered phases were which formed it

in disordering^. In addition, whereas the high temperature Guinier photographs of the fluorite alpha phase show no superstructure when one is well within the stability region—at

the boundaries there is indication of blackening of the film in the regions where a superstructure appears when the transition to the ordered phase is reached. There is also broadening of the main reflections which are split in the ordered phase being formed^.

Another common feature of the tensimetric or gravimetric studies in the rare earth oxide

system is the occurrence of hysteresis and pseudophase behavior in the two-phase regions.

The next slide (fig. 3) shows this as revealed by an isobaric cycle in the TbOx system between the delta and iota region. (Similar behavior may be seen in the two-phase regions of

figure 2.) Notice that a sample at 380 Torr at a composition TbOj.gis (the delta phase) being heated slowly does not reduce appreciably before a quite sharp decomposition temperature

(~525°) is reached. At this point it reduces smoothly and rapidly but not discontinuously

to the iota phase. If the temperature is then reversed a temperature is reached at which

rapid oxidation occurs but this is below the temperature at which reduction occurred in heating hence a hysteresis loop is formed. Furthermore, before delta phase is reached the loop

suddenly deviates into a bivariant curve which approaches the delta phase more slowly'* (see

dashed curve in fig. 3). This bivariant region is called a pseudophase (6'). Although in

this case the rate of heating in traversing the loop has some effect on its size the occur- rence of the pseudophase is unchanged. The path taken point-by-point with long annealing

3M. S. Jenkins, R. P. Turcotte and L. Eyring in The Chemistry of Extended Defects in NonMetallic Solids, (Eyring and O'Keeffe, eds.) North-Holland Publishing Co., Amsterdam,

1970, p. 36.

k B. G. Hyde and L. Eyring in Rare Earth Research III, (L. Eyring, ed. ) Gordon and Breach,

New York, p. 623 (1965).

762
800

700

600

* 500

400

300-

1.70

Fig. 3.

1.72

(S-t) HYSTERESIS LOOP (S'-J SCANNING LOOP

1.74 1.76 178 1.80 COMPOSITION (x in TbO^)

1.82

times has been observed to shrink the hysteresis loop^ but not the 6' pseudophase. The loop

is also much smaller if one studies single crystals of ~10^ times the volume of the powder

but the 6

' feature remains essentially unchanged^

.

High temperature diffraction diagrams taken over many weeks as the sample is cooled in

the 6' region show a distinct and different pattern from 6 which is formed at the lower temperatures. In this case 6

' is never seen in reduction—always in oxidation^.

Scanning hysteresis loops are being studied at present^. One of the interesting features

is that if one is in the cooling (oxidation) branch of the loop but reverses the temperature

anywhere in the 6' region the sample behaves as a line phase with no loss of oxygen until a decomposition temperature is reached (see fig. 3, the hysteresis envelope is indicated by a dashed line). If cooling is initiated before decomposition of 6 ' occurs the cooling curve is

reversible

.

The point of these remarks is that the tensimetric and gravimetric observations reveal

exceedingly complex behavior not yet explicable but surely associated with coherent intergrowth of neighboring phases of the homologous series resulting in hysteresis and pseudophase formation. This will be an important system to study utilizing the powerful techniques

of electron microscopy and electron diffraction for structure elucidation discussed earlier

by several authors. Such studies are underway. So far it is clear that one can follow the

reduction of a crystal of Pr02 in the microscope vacuum as a result of electron heating. It

appears that the complex reduction path may be interpretable when more experience is gained.

^J. Kordis and L. Eyring, J. Phys. Chem. 72, 2044 (1968).

_^Arthur Lowe and L. Eyring, unpublished results.

L. Eyring, unpublished results.

763

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Upton, New York 11973

Dr. B. G. Hyde

Univ. of Western Australia

School of Chemistry

Nedlands, WESTERN AUSTRALIA 6009

Dr. Donald L. Janes

3-M Center, Building 201-2E

St. Paul, Minnesota 55101

Dr. W. Jeitschko

E. I. duPont de Nemours & Co. Central Research Laboratory

Wilmington, Delaware 19898

Dr. F. Jellinek

University of Groningen

Laboratory of Inorganic Chemistry

Bloemsingel 10

Groningen, NETHERLANDS

Mr. Garrett K. Johnson

Union Carbide Research Inst.

P. O. Box 278

Tarrytown, New York 10591

Mr. Ronald B. Johnson

National Bureau of Standards

Institute for Materials Research

Washington, D.C. 20234

Dr. V. Johnson

E. I. duPont de Nemours S Co. Central Research Department

Wilmington, Delaware 19898

Capt. Thomas E. Joyce

Air Force Materials Laboratory

AFML/LPT

Wright Patterson AFB, Ohio 45433

768
Mr. Z. T. Jugovic

Universal Atlas Cement Division

U. S. Steel Corporation

Buffington Station

Gary, Indiana 46401

Dr. J. A. Kafalas

M.I.T., Lincoln Laboratory

P. 0. Box 73

Lexington, Massachusetts 02173

Dr. A. H. Kahn

National Bureau of Standards

Room A259, Materials Bldg.

Washington, D.C. 20234

Dr. Roy I. Kaplan

Goodyear Atomic Corp.

P. O. Box 628

Piketon, Ohio 45661

Dr. Ronald Karam

Xerox Corporation

Xerox Square (W-103)

Rochester, New York 14644

Dr. H. M. Kasper

Bell Telephone Lab. , Inc. Murray Hill, New Jersey 07974

Dr. Paul P. Keat

Norton Company

New Bond Street

Worcester, Massachusetts 01606

Dr. Richard Keezer

Xerox Corporation

800 Phillips Road

Webster, New York

Dr. Y. S. Kim

Bell Telephone Lab. , Inc.

555 Union Blvd.

Allentown, Pennsylvania 18103

Dr. Robert S. Kirk

Allied Chemical Corporation

P. 0. Box 1021R

Morristown, New Jersey 07960

Dr. O. J. Kleppa

James Franck Institute

University of Chicago

5640 South Ellis Avenue

Chicago, Illinois 606 37

Prof. E. Kostiner

Cornell University

Baker Laboratory of Chemistry

Ithaca, New York 14850

Mr. John Krc , Jr. Parke , Davis & Company

Joseph Campau at the River

Detroit, Michigan 48232

Dipl.Phys. W. H. Kuhlmann-Schaefer

Preussag AG, Erdol und Erdgas

3 Hannover, Postfach 4829

WEST GERMANY 3000

Dr. Richard G. LaBar

The Carborundum Company

Box 367

Niagara Falls, New York

Dr. Irwin M. Lachman

Corning Glass Works

Coming, New York 14830

Dr. D. Laguitton

Universite Laval

Departement de Mines et Metallurgie

Quebec, CANADA

Dr. A. Lamprecht

Institute of Petrologie

Frankfurt/Senckenberganl . 28

Frankfurt, GERMANY

Dr . Sam LaPlaca

Brookhaven National Lab.

Department of Chemistry

Upton, Long Island, New York 11973

Dr. John J. Larkin

AFCRL (LQP) L. G. Hanscom Field

Bedford, Massachusetts 01730

Dr. John I. Lauritzen, Jr. National Bureau of Standards

Institute for Materials Research

Washington, D.C. 20234

Mr. E. M. Levin

National Bureau of Standards

Room B214, Materials Bldg.

Washington, D.C. 20234

Dr. George G. Libowitz

Ledgemont Laboratory

Kennecott Copper Corp.

128 Spring Street

Lexington, Massachusetts 02173

Dr. Jacob W. Lin

Honeywell Corporation

500 Washington Avenue, South

Hopkins, Minnesota 55343

769
Dr. D. J. Lloyd

Service de Chimie Minerals

Universite de Bordeaux

33-Talence, FRANCE

Dr. John M. Longo

Esso Research & Engineering Co.

P. O. Box 45

Linden, New Jersey 07036

Prof. J. Lucas

Universite de Rennes

Lab. de Chimie Minerale D Avenue du General Leclerc

35 Rennes, FRANCE

Dr. Robert G. Lye

R.I.A.S.

1450 South Rolling Road

Baltimore, Maryland 21227

Prof. G. J. McCarthy

Pennsylvania State University

Materials Research Lab.

University Park, Pennsylvania 16802

Dr. James W. McCauley

Ceramics Division

Army Materials & Mechanics Res. Cen.

Watertown, Massachusetts 02172

Mr. C. L. McDaniel

National Bureau of Standards

Room B214, Materials Bldg.

Washington, D.C. 20234

Dr. William J. McDonough

U. S. Naval Research Lab.

Code 6136

Washington, D.C. 20390

Dr. Thomas D. McGee

Iowa State University

Ceramic Engineering Dept.

Ames, Iowa 50010

Dr. Howard L. McKinzie

Brown University

Division of Engineering

Providence, Rhode Island 02912

Dr. James R. McNesby

National Bureau of Standards

Institute for Materials Research

Washington, D.C. 20234

Dr. D. B. McWhan

Bell Telephone Labs., Inc. 600 Mountain Avenue

Murray Hill, New Jersey 07974

Dr. J. B. MacChesney "

.. , Bell Telephone Labs.

Murray Hill, New Jersey 07974

Dr. George D. MacKenzie

TRW Philadelphia Laboratories

401 North Broad Street

Philadelphia, Pennsylvania 19108

Dr. Arnulf J. Maeland

W.P.I.

Worcester, Massachusetts 01609 .

Dr. Massimo Marezio

Bell Telephone Labs., Inc. 600 Mountain Avenue

Murray Hill, New Jersey 07974

Dr. William J. Marshall

E . I . duPont de Nemours & Co

.

Newport, Delaware 19804

Mr. Robert F. Martin

National Bureau of Standards

Institute for Materials Research

Washington, D.C. 20234

Dr. Richard W. Meyer

Owens-Illinois, Inc. 1700 N. Westwood

Toledo, Ohio 4 3607

Dr. Ralph 0. Moyer, Jr. Trinity College

Clement Chemistry Lab.

Hartford, Connecticut 06106

Dr. G. M. Muchow

Owens-Illinois, Inc.

P. 0. Box 1035

Toledo, Ohio 4 3601

Dr. Ronald A. Munson

U. S. Bureau of Mines

College Park, Maryland 20740

Dr. M. K. Murthy

Ontario Research Foundation

Sheridan Park

Ontario, CANADA

Dr. Clifford E. Myers

State Univ. of New York at Binghamton

Vestal Parkway East

Binghamton, New York 13901

Dr. Kurt Nassau

Bell Laboratories

600 Mountain Avenue

Murray Hill, New Jersey 07974

770
Dr. T. Negas

National Bureau of Standards

Room B214, Materials Bldg.

Washington, D.C. 20234

Dr. Gordon L. Nichols

Keystone Carbon Co

.

State Street

St. Marys, Pennsylvania 15857

Dr. Arthur S. Nowick

Columbia University

School of Mines

New York, New York 10027

Dr. H. Nowotny

University of Vienna

Vienna, AUSTRIA

Dr. John J. O'Connor ' i AFCRL (LQP)

L. G. Hanscom Field

Bedford, Massachusetts 07130

Dr. Roger W. Ohnsorg

The Carborundum Company

P. O. Box 367

Niagara Falls, New York 14302

Dr. M. O'Keeffe

Arizona State University

Chemistry Department

Tempe, Arizona 85281

Dr. Jean Pannetier

Universite de Rennes

Lab. de Chimie Mine rale D 35-Rennes, FRANCE

Dr. C. Paparoditis

Laboratoire de Physique des Solides

CNRS

92-Bellevue, FRANCE

Mr, H. S. Parker

National Bureau of Standards

Room B214, Materials Bldg.

Washington, D.C. 202 34

Dr. Jerome H. Perlstein

Johns Hopkins University

Department of Chemistry

Baltimore, Maryland 21218

Dr. Daniel R. Petrak

Air Force Materials Laboratory

AFMS/LLM

Wright Patterson AFB, Ohio 45433

Dr. James W. Pierce

M.I.T., Lincoln Laboratories

244 Wood Street

Lexington, Massachusetts 02173

Dr. Roos H. Plovnick

Cornell University

Materials Science Center

Ithaca, New York 14850

Dr. Ralph H. Plumlee

Sandia Laboratories

Box 5800

Albuquerque, New Mexico 87115

Dr. Ben Post

Polytechnic Inst, of Brooklyn

Department of Physics

Brooklyn, New York 11201

Dr. Stephen F. Prest

Quebec Iron and Titanium Corp.

P. O. Box 40

Sorel, Quebec, CANADA

Mr. Abbaraju Rajxi

Zenith Radio Corp.

1851 Arthur Avenue

Elk Grove Village, Illinois 60007

Dr. J. P. Remeika

Bell Telephone Laboratories

600 Mountain Avenue

Murray Hill, New Jersey 07974

Dr. R. R. Rettew

W. R. Grace & Co.

Washington Research Center

Clarksville, Maryland 21029

Dr. Morton Robinson

Hughes Research Laboratories

3011 Malibu Canyon Road

Malibu, California 90265

Dr. Donald B. Rogers

E. I. diiPont de Nemours & Co. Central Research Department

Wilmington, Delaware 19898

Dr. R. D. Rosenstein

Crystallography Department

University of Pittsburgh

Pittsburgh, Pennsylvania 15213

Mr. Gay Ion S. Ross

National Bureau of Standards

Institute for Materials Research

Washington, D.C. 20234

77 "I
Dr. R. S. Roth

National Bureau of Steindards

Room B214, Materials Bldg.

Washington, D.C. 20234

Dr. W. L. Roth

General Electric Company

Corporate Research & Development

Schenectady, New York 12301

Dr. Robert J. Rubin

National Bureau of Standards

Washington, D.C. 20234

Dr. P. H. Schmidt

Bell Telephone Laboratories

600 Mountain Avenue

Murray Hill, New Jersey 0797

Mr. S. J. Schneider

National Bureau of Standards

Room B214, Materials Bldg.

Washington, D.C. 20234

Dr. S. Scholes

James A. Jobling & Co., Ltd.

Advance Res. & Technology Unit

Brancepeth Castle, Durham, ENGLAND

Dr. H. Schafer

University of Munster

Munster, GERMANY

Dr. Jacob Shamir

Dept. of Inorganic and Analytical Chemistry

Hebrew University

Jeursalem, Israel

Dr. Joseph R. Shannon

E. I. duPont de Nemours & Co.

335 Experimental Station

Wilmington, Delaware 19898

Dr. M. J. Sienko

Cornell University

Baker Laboratory

Ithaca, New York 14850

Dr. Arthur W. Sleight

E. I. duPont de Nemours & Co. Central Research Department

Wilmington, Delaware 19898

Dr. John Smeggil

G. E. Research & Development Center

P. O. Box 8 Schenectady, New York 12301

Dr . Doug Smith

Owens-Illinois, Inc. 1700 N. Westwood

Toledo, Ohio 43606

Dr. Charles A. Sorrell

Dept. of Ceramic Engineering

University of Missouri

Rolla, Missouri 65401

Dr. K. E. Spear

Pennsylvania State University

Materials Research Lab.

University Park, Pennsylvania 16802

Dr. B. F. Spielvogel

Army Research Office-Durham

Box CM, Duke Station

Durham, North Carolina 27706

Dr. Donald A. Stanley

Department of Interior

Bureau of Mines

P. 0. Box L "University, Alabama 35486

Dr. B. C. H. Steele

Metallurgy Department

Imperial College

London SW7, ENGLAND

Dr. Hugo Steinfink

Chemical Engineering Department

University of Texas

Austin, Texas 78712

Dr. N. C. Stephenson

University of New South Wales

AUSTRALIA

Dr. Kurt H. Stem

Naval Research Lab.

Washington, D.C. 20390 •

Dr. G. Bryan Street

IBM Research Laboratory

Bldg. 028, Monterey Road

San Jose, California 95114

Dr. V. S. Stubican

Dept. of Matls. Science

Pennsylvania State Univ.

University Park, Pennsylvania 16802

Dr. George D. Sturgeon

University of Nebraska

Department of Chem.istry

Lincoln, Nebraska 68508

Mr. Robert M. Sullivan

Hercules Inc. , Drakenfeld Colors

P. O. Box 519

Washington, Pennsylvania 15301

Dr. Lydon J. Swartzendruber

National Bureau of Standards

Room B150, Materials Bldg.

Washington, D.C. 20234

772
Dr. Gunter Teufer

E. I. duPont de Nemours S Co. Pigments Department

Wilmington, Delaware 19898

Dr . Robb Thomson

National Bureau of Standards

Washington, D.C. 20234

Dr. Richard E. Tischer

Coming Glass Works

Sullivan Park

Coming, New York 14830

Dr. John L. Torgesen

National Bureau of Standards

Institute for Materials Research

Washington, D.C. 20234

Dr. Louis Toth

Chemical Engineering & Materials Science

University of Minnesota

Minneapolis, Minnesota 55455

Dr. R. P. Turcotte

Battelle Memorial Institute

Pacific Northwest Laboratories

P. O. Box 999 (308 Trailer)

Richland, Washington 99 352

Mr. George A. Uriano

National Bureau of Standards

Institute for Materials Research

Washington, D.C. 20234

Dr. W. Van Gool

State Univ. of Utrecht

A.C.L., Croesestraat 77A

Utrecht, NETHERLANDS

Dr. John Venables

R.I.A.S.

1450 South Rolling Road

Baltimore, Maryland 21227

Dr. Robert B. Von Dreele

Arizona State University

Department of Chemistry

Tempe, Arizona 85281

Dr. John B. Wachtman, Jr. Inorganic Materials Division

National Bureau of Standards

Washington, D.C. 20234

Mr. Fritz Wald

Tyco Laboratories, Inc.

16 Hickory Drive

Waltham, Massachusetts 02154

Dr. Roland Ward

University of Connecticut

Storrs , Connecticut

Mr. J. L. Waring

National Bureau of Standards

Room B214, Materials Bldg.

Washington, D.C. 20234

Dr. D. Watanabe

Tohoku University

JAPAN

Dr. Edward A. Weaver

Owens-Illinois, Inc. 1700 N. Westwood Avenue

Toledo, Ohio 4 3607

Dr. Cletus Welch

PPG Industries, Inc.

P. O. Box 31

Barberton, Ohio 44203

Dr. Paul F. Weller

SUNY College at Fredonia

Department of Chemistry

Fredonia, New York 14063

Dr. William B. White

Pennsylvania State University

Materials Research Laboratory

University Park, Pennsylvania 16802

Dr. M. Stanley Whittingham

Center for Materials Research

Stanford University

Stanford, California 94305

Dr. J. P. Williams

Coming Glass Works

Research & Development

Coming, New York 14830

Dr. Morgan L. Williams

National Bureau of Standards

Room B150, Materials Bldg.

Washington, D.C. 20234

Dr. Wendell S. Williams

University of Illinois

Dept. of Ceramic Engineering

Urbana, Illinois 61801

Dr. David E. Witter

Crystal Product Dept.

Union Carbide Corp.

8888 Balboa Avenue

San Diego, Califomia 92123

Dr. E. Woermann

Institute fur Kristallographie

RWTH Aachen

D-51, Templergraben 55

Aachen, GERMANY

773
Dr. Aaron Wold

Brown University

Division of Engineering

Providence, Rhode Island 02912

Dr. Takashi Yamaguchi

Pennsylvania State University

313 Mineral Industries Bldg.

University Park, Pennsylvania 16802

Dr. Daniel F. W. Ydo

University of Leyden

Gorleans Laboratory

Leiden, NETHERLANDS

Dr. H. Thomas Yolken

National Bureau of Standards

Institute for Materials Research

Washington, D.C. 20234

Dr. Howard Young

Department of Geological and

Geophysical Sciences

Princeton University

Princeton, New Jersey 08540

Dr. John E. Young, Jr. Gulf Research and Development

P. O. Drawer 2038

Pittsburgh, Pennsylvania 15230

Dr. Susan Zador

Department of Metallurgy

University of Toronto

Toronto 5, Ontario, CANADA

Dr. Saul Zolotov

Chemistry Department

Baker Laboratory

Cornell University

Ithaca, New York 14850
AUTHOR INDEX

Adams, R.

L 713

Allpress, J.

G 87

Anderson, J. S 295

Andersson, S 3 Arnott, R. J 713

^strom,A 3

Baes, Jr., C.F 331

Bamberger, C. E 331

Ban,

Y 353

Banks, E 265

Beale, J. P 165

Berkooz, 0 265

Sevan, D. J.

M 749

Bierstedt, P. E 437

Board, R.D 127

Boiler,H 487

Bouchard, R.

J 227,275

Bowman, A.L 561

Brixner, L.H 437

Brower, Jr. , W. S 183

Buehler, E 591

Bursill, L.A 197,727

Caro, P. E 367

Carter, F.L 515

Chen,H 651

Chenavas,J 285

Chikalla, T.

D 319

Collin,G 645

Conroy, L. E 663

Cook, Jr., W.

R 703

Coutures, J. P 471

Craig, D,

C 165

Cronemeyer, D.

C 637

de Jong, B. H. W. S 41

Dernier, P.

D 285

Ettmayer, P 505

Eyring,L 343,761

Fischer, R.

D 397

Flahaut,

J 645

Foex,M 471

Franzen, H.F 41,651

Galy,

J 29

Gatehouse, B.

M ^ 15

Glasser, F. P 457

Gooden, C. E 397

Goosey, B.

F 605

Gorochov, 0 645

Grey, 1 681

Gruehn,

R 63

Gugel, E 505

Guittard,

M 645

Hagenmuller, P 205

Haschke, J.M 343

Holtzberg,F 637

Hong,H 681

Honig, J.M 127

Huggins, R.

A 51,139

Hyde, B.

G 197

Jeitschko,

W 613

Jellinek,F 625

Johnson, Jr., G.

G 397

Johnson,V 613

Joubert, J.-C 285

Kafalas, J.A 219,287

Kasper, H.M 671

Keramidas, V.G 113

Kieffer,

R 505

Kihlborg,L 343

Kostiner, E 745

Lamprecht , A 483

Larach, S 721

Laruelle, P 645

Lau, K.H 343

Leimer,G 505

Licis, M. S 437

Lloyd, D.J 15

Longo, J.

M 219

Lowenstein, M. Z 343

Lye, R.G 567

McCarthy, G.

J 397

McGuire, T.R 637

Marezio,

M 285

Meyerhoff, M.H 583

Miskin, B.

K 15

Nakagawa,

T 265

Nassau,

K 445

Negas,T 233

Nguyen, H. D. 645

Nowick, A. S 353

Nowotny , H 487

O'Keeffe,

M 197

Paparoditis,

C 723

Parker, H. S. 183

Petrak, D.R 605

Pierce, J.

W 219

Pisharody, K.R 663

Raccah, P.M 219

Ross, R.

G 331

Roth, R. S 183,233

Roth, W.

L 129

Ruh,

R 605

Russo, P 713

775
Schafer, H 413

Shamir, J 721

Shanks, H. R 41

Shiever, J. W 445

Sienko, M. J 385

Sleight, A. W 227,437

Solovyev, G. I 597

Spear, K. E 597

Steinfink, H 681

Stephenson, N. C 165

Stubican, V. S 695

Suryanarayanan , R 723

Terasaki, 0 155

Tressler, R. E 695

Turcotte, R. P 319

Venables, J. D 583 von Molnar, S 637

Waring, J. L 183

Watanabe, D 155

Weaver, H. E 127

Weiher, J. F , 275

Wernick, J. H 591

West, A. R 457

White, W, B 113

Whittingham, M. S 51,139

Woermann, E 483

Wold, A 713

Young, Jr., J. E 385

Zwilling, G 487

776
SUBJECT INDEX

absolute ionic mobility, 141

actinide

dioxides, 331,337

exchange equilibria, 338

oxides, 319

polymorphs, 320

tetrafluorides , 338

activation energy, Ce02, 360

activity coefficients, actinides, 333,338

admittance plot, 6-AI2O3, 149

AgGaS2 , 671

AIB2, 534,540

alkaline earth metals, dicarbides, 579

alkali

metal carbides, 579

metal hydride, 20

metal molybdates, 15

metal niobates, 15

rare-earth titanates, 92

americium oxides, 321

antiferromagnetism

(Ca,Sr)FexMni_x03_y, 265

LaxSri-xRu03, 280

antimony

oxide fluorides, 3,11,12

oxides, 3,7

anti-phase boxmdaries, 92

atomic scattering factor, 156

atomic volume, 522

BaFe2S3, structure of, 683

BaFe2Se3, structure of , 685

Ba2FeS3

magnetic properties, 683

structure of, 691,692

Ba3Fe3Se7, structure of, 689

BaeFeeSis

magnetic properties, 694

structure of, 687

BayFeeSm

magnetic properties, 688

structure of, 693

band structure

chalcogenides , 671

V2O3, 125

BaO-

" cobalt oxide", 233

"nickel oxide", 233

batteries, 139

berkeliuiti oxides, 326

Bertaut's method, 534,542,547

beryllium fluoride, 331

beta alumina, 139

composition, 129

diffusion, 129

domains, 132

kinking, 135

structure, 129

binary solid solutions, actinides, 331,337

BiRhOs^ 221

Bi2Rh206.8/ 221

bismuth oxide fluorides, 3,9

bismuthyl cation, 370-378

block structures, 312

bond

boron-boron, 534,548,556

metal-metal, 518,532,534

order, 517,518,534,548

bonding, carbides, 487,494,567,568

boric oxide, 605

anhydrous , 605

borides, 485

rare-earth, 597

borocarbides , 494

boron, 505,605

amorphous , 605

rhombohedral , 605

sxiboxide, 605

boron carbide structure, 607

bronze, molybdenum, 20,21,22

building elements, 63,78,81

CaFexMni_x03_y , 265,267

carbides, 485,517,561

bonding, 487,494

cobalt group, 579

complex, 492

group III, 579

group IV, 579

group V, 580

group VI, 579 • group VII, 579

iron group, 579

NbC, 584

TaC, 587

VC, 585

carbon, 505,572

content in carbides, 570

ordering, 490

cation order, 114

CdGeP2, 591

Cdl2, 523,540

CdS, 721

Ce02

electrical conductivity, 357

reduced, 353

ceria, 353

ceriimi oxides, 379-380

chalcogenides, 623,625,672

rare-earth, 723

synthesis, 723

ternary (rare earth-transition metal) , 645

chalcopyrites , 671,713

chemical analysis, hybrid phases, 63,64,69

chemical transport

Nb205 rich systems, 63,67,68

oxides, 413,426

chimney-ladder structures, 500

chromium sulfides, 629,630

777

/
clustering

reconstructive, 301

shear plane, 301

cobaltous oxide

kinetics, 479

liquid, 471

melt composition, 475

nonstoichiometry , 475

solidification temperature, 475

themal analysis, 471

cohesion, carbides, 557,570

cohesive energy, carbides, 568,575

color-concentration dependence, GdxSej-x, 637

complex admittance method, 149

complex ions, rare earths, 367

composition fluctuations, localized,

NbaOs-xf 314

conductivity (electrical)

electronic, 148

ionic, 144

iridates, 228

LaxSri_xRu03 , 279

ruthenates, 228

CoijNb209, 121

C02O3

high pressure synthesis, 285

low-spin/high spin, 285

C0O-O2 system, 471

coordination polyhedra

metal rich sulfides, 651

rare earth oxides and oxysalts, 367

coordination, trigonal-prismatic, 626,527

corundum structure, 117

covalence parameters, 205

critical voltage

TiO, 158

Ti02, 152 cross grating pattern, 132

crystal growth

alkali metal tungsten bronzes, 51 chalcogenides, 572

chemical transport, 413

CuFeS2, 713

Li3P0^ derivatives, 457

praseodymiijm oxides, 343

SC2O3-X' 387

terbium oxides, 34 3 crystal momentum, 549

cirystallographic shear, M02_x systems, 197

crystallographic shear planes, 95-103

crystals, single

PrOx, 343

SrFexMni_x0 3-y, 255

TbOx, 343

Cui_xFei+xS2-y, 717

C\iFeS2, 713

CuFeS2-x/ 715

CuGaS2, 671

CuInS2, 571

Curie-Weiss paramagnetism, LajjSr i_xRu03 , 280

curium oxides, 323

Cu-S phase diagram, 704,705,707

"Cui^ggS" (tetragonal) stability, 709

CUjjS phase relations, 703,709,710

d-band - . carbides, 557,572 , r CuGaS2, 575

Dalton's Law, 557

dark-field microscopy, 92-94

decomposition potential, 52,53

defect .

. clusters, 299 •.. in fluorogermanate, 745,748

structures, 255 ,, defects, Ce02-x» 353

density of states, carbides, 559,574,581

diborides, 534,553

dichalcogenides , 625

diffusion, 139,202,353,352

directional freezing, chalcogenides, 572

disilicides, defect, 497

disorder, one dimensional, 304

distortions of NiAs-type, 530,631

disulfides, 553

djurleite, composition, 709

domain boundaries, 104-109

E-phases , silicides, 502

effective charge, 518,521,525,537

electrical conductivity, AgGaS2, 674

electrical mobility, 141

electrical properties, SC2O2-X' 390

electrochemical

cell, 139 . - V. ; transducers, 140

electrodes, 53

nonpolarizing, 139 • .: , reactions , 56

electrolysis, 51 ...

- electrolytic

conduction domains, 151

decomposition, 52

electron . . Bethe's 2nd approximation, 156

diffraction, 87-111,155,583

many-beam dynamical theory, 156

microscopy, 87-111,127

microscopy/diffraction .

• _ Ti-Cr-0 system, 727

optical methods, 63,80,87,295

probe, 608

spectroscopy, 521,525

transfer, 558,572,581

electronic

configurations, 4 f^, 357

structure, 558 : _ transference number, 148 ' - electrostatic energy, 521,525

emf measurements, 143

enthalpy change, 331

entropy, of exchange change, 332

equilibriiam conditions, 57,81

equilibrium, selective, 151

ESCA, 521,525

exchange equilibria, 331,334

778
F centers , 391

Fe2P, 613

Fermi surface projection, 549,552

ferroelectric, Ln2(MoOLj)3, 437

ferroelectricity , 290 ' ferromagnetism, SrRuOs, 281

ferrous oxide, 301

fissile material, 332 '

^ flame fusion, 385

fluorides

molten, 338,340

rare earth, 371

fluorite-type phases, ortho rhombic , 749

fluorocarbonates (bastnaesite group)

,

rare earth, 378 • free energy of reaction, 56

fused salt electrolysis, 41

gadolinium monoselenide (Gd^Se^-x) , 637

color-concentration dependence, 637

Hall effect, 639,641

homogeneity range, 637,638

magnetic ordering, 640

reflectivity, 637,638,642

resistivity, 637,640,641,642

single crystal growth, 638,639

Ge, 591

gemanides , ternary, 513

Guinier method, 66,69

halfbond, 518,553

Hall effect, Gdj^Sei-^, 639,641

heat of formation, carbides, 567,575,576,577

heats of mixing, actinides, 337,338

HfCx, 567

hietala, 331,337

high coordination, 515

high pressure synthesis (C02O3) , 285

holes

cube-octahedral (Li2Motj0i 3) , 24

heptagonal (RbsNbs^Oii^g) , 15

homogeneity range

GdxSei_jj, 637,638

Nb205 rich systems, 63,80,81

homologous series, 192

hybrid phases, 63,76

structure, 63,64,77

surrounding of blocks, 76

hydrothermal crystal growth, 343

hysteresis, rare earth oxide systems, 762

icosahedral coordination, sulfides, 652

infrared reflection spectra, boron

suboxide, 608

insulator-metal transitions, 205

intercalation compounds, 579,627

intergrowth, 93-94 , 98-101 ,106-109

phase, 63 rare earth oxides and oxysalts, 378,381,383

zirconium niobium oxide, 165

intermetallic compounds, 657

interstitials

cerium, 355

oxygen, 363

ionic radius, rare earths, 579

iridates, 227

Jahn-Teller distortions, 630

k-space, 549

Kasper polyhedron, sulfides, 655

Kikuchi line, 155

kinetics

LijPO^ derivatives, 457 versus thermodynamics, 757

KjjMoeOiy, 15,20

lanthanide

molybdates, 437,445

tungstates , 445

lanthanyl ions, 370

LaRh0 3, 276

LaRu03, 276

LaxSri-xRuGs , 275 .

. lattice

fringes, 130,132

image, 129

imaging, 19,91,96-109,165

parameters, 605

actinides, 3 34 LnBgg, 597,601

Ln2(Mo0i+)3, 437

layer structures, dichalcogenides , 626

layered polycations , rare earth, 382

lead oxides, 3,4,5,6,7,8,9

least squares analysis, 52

LiEr02 , 123

LiFe02, 123

Liln02, 123

LiLu02, 123

Li2Moi^0i3 (L.T. form), 15,23

LixMogOiy, 15,20

LiNbOs, 117

Li3P0i^ derivatives

crystal chemistry, 457

kinetics, 457

phase transformation, 457

polymorphism, 457

liquid cooling speed, 477

Lii+Si0tt-Mg2Si04 system, 467

Li4SiO[^-Zn2Si04 system, 463 ,

' • lithiophosphate , 458

lithiiim

arsenate, 461

ferrites, 92-94

fluoride, 331

lutetium titanate, 87

magnesium silicate, 457

phosphate, Li^PO^, 457

vanadate, Li3V04, 459

zinc silicate, 457

lone pair

localization and size, 3,5

structure, 29

779
lower oxidation states , 69

Madelung

constant, 522,542

potential, 522,544,572

Magneli phases, 95-97

magnesium

fluorogermanate, 745

germanate, 745

fluoride substitution, 745

magnetic

moment, 517,537

ordering (Gd^Sei-^) , 640

susceptibility (Sc203_x) , 390 massspectrometer, 510

transport, 139,353,358

melt growth, chalcogenides , 672

melting point

actinide oxides, 320

determination (B-C-Si system) , 507

LnBge, 597,599

metal-insulator transition, 127

metal oxides

mixed, 265

Ti-Cr-0 system, 727

metal-metal bonding, 613,620

metal-semiconductor transitions, 526

metal-site occupancies, 613

metallic radii, 517,534

metallography, B-C-Si system, 507

metastable

forms of Ni3Sc2, 632

substances, 431

Mg28GeioOi+8f 745

Mg28Ge7.5038FlO' ^45

MgSb206, 120

MgTi0 3, 117

microdomains , 101,104-109,357

microhardness , LnBgg, 597,600,501

mixed cation disulfides, 663

mixed conductor, 145

MnCx, 579

MnitNb209, 121

MnsSis, 513

MnTi03, 117

modulated structures, Ni3+j^Te2, 632

molecular momentum, 549

molybdates, 23,24

lanthanide, 445

Ln2 (M0O4) 3, 437

molybdeniam

bronze, 15

carbide, 552

phosphide, 532

MoP, 532

Mossbauer spectra, of SrFejjMni_j^03_y , 268

NagWi^O^s, 49

NaxMogOiy, 15,20

NbC, 584

ordering, 584

NbCx, 567,558,579

Nb205-5Zr02, 183

nephelauxetic effect, 372

neptunium dioxide, 331

Nemst equation, 57

neutral cell, 518,520,541

NiAs-type phases, 699

nickel chalcogenides, 631

Ni2ln, related phases, 513

Ni4Nb209, 121

niobates, 15

niobium

carbide, 552

ordering, 584

oxide, 312

oxidefluoride, 53

titanium oxide, 97-103

tungsten oxide, 95-97,104-109

zirconium oxide, 183

pentoxide, 63

Ni3Te05, 119

nonlinear optical crystals, chalcogenides, 673

nonstoichiometry , 92-101, 353,518,538,725

actinide oxides, 320

chalcocite, 703,705

cobaltous oxide, 475

MO2-X systems, 197

niobia-zirconia system, 183

rare earth oxides and oxysalts, 378

scandium oxide, 385

TiOx, 733

tungsten bronze compounds, 51

occupation waves, 530,632

open circuit voltage, 52,54

optical

absorption spectra, 374

properties

chalcogenides, 673 rare earth chalcogenides, 723

orbital, 516,526,545

bidirectional, 515,526,545

C, 527,533,545

G, 527,529,545

non-paired spin, 529

order-disorder, 113-125

transitions, 527

order of vacancies, 629,532

ordered phases, 298

ordering, 513-515

defects, interpretation, 583

effects, 583

NbC, 584

TaC, 578

gemanides and silicides, 613,616

out-of-phase boundaries, 104-107

oxidation

kinetics, 358,360

of PbO, 5 oxides (see also specific material), 1,413

molybdates and niobates, 15

precious metal, 227 rare earth, 367

780
ternary, 428

transition-metal, 233

oxyfluorides , rare earth, 378

oxygen

activity, 58

vacancies associated with Fe^"*", 272

oxysalts, rare earth, 367

p-momentum, 549

Pauling's metallic radii, 517

PbO oxidation, 5 perovskite, 221

hexagonal polytypes, 287

LajjSri.jjRuOs, 275

like structures, 205

phase equilibria

A+B^+Os compounds, 287

B-C-Si, 512

Ba0-Co0-0-C02, 233

Ba0-Ni0-0-C02, 233

borides , 600

GdP2-Ge, 593

Nb205-Zr02, 186 rare earth oxides, 762

phase structures, 530

phase transformation

Li3P0i+ derivatives, 457

Ln2(MoOtt)3, 437

phosphides, 651,652,654,660

photoelectron spectroscopy, of V2O3, 127

plasma torch, 387

platinum tubes, sealed, 66,67

pleating boron layer, 539

plutoniiam

dioxide solid solutions, 331

tetrafluoride , 331

trifluoride, 331

polarization technique, 139

polymolecular frameworks, 367

polymorphism

actinide sesquioxides , 320

Li3P0t^ derivatives, 457

zirconium-niobium oxide, 165

precipitation, 92-94

mixed, 64

preparation of oxides, 413

Nb20 5 rich systems, 63

praseodymium oxide, 343,379-380

pressure-synthesis, BiRh03, 221

protactinium

dioxide solid solutions, 331

oxide chemistry, 342

pentoxide, 331

pseudophase, rare earth oxide systems, 762

pseudo-solid solutions, 498

pycnometric density, boron suboxide, 608

pyrochlore, 221

iridates and ruthenate structures, 227

quartz

closed vessels, 67

sealed tubes, 66,68

Raman spectra, 113-126

CdS, 721

linear frequency shift, 721

ZnCdi_xS, 721

ZnS, 721

random defect structures , 298 rare earth

borides , 597

chalcogenides (magnetic properties) , 645

oxides, 367,761

hysteresis, 762

molybdates, 445

phase reaction, 762

pseudophase, 762

scanning hysteresis loop, 763

tungstates, 397,445

oxyfluorides , 378

oxysalts , 367

RbNb0 3, 291

"RbNbsOg", 15,19

"Rb3Nb5[tOiLt6"f 15,16

RbSb03, 291

PbTa0 3, 291

reaction hot-pressing, 606

reaction mechanisms, 51 molybdenum carbides , 564

reactors, molten salt, 332

reduction

of Ag+, 133,134,135

of Na+, 136

reflectivity, Gd^Sei-x, 637,638,642

refractory

hardmetals, carbides, 567

materials, 367

RE2O3-WO3 compounds, 397

resistivity

GdxSei_x, 637,640,641,642

sodium tungstate, 44

resolution, conducting planes, 132

reversible electrodes, 144

rocksalt structure, 122

Ruddlesden-Popper phases, 123

ruthenates, 227

rutile, 113,197,304

scandium oxide, 385

scanning hysteresis loops, rare earth oxide

systems, 763

scheelite related structures, 445

Schottky defects, 629

Seebeck coefficient, sodium tungstate, 44

selenides , 625

semi conductivity , 678

iridates, 227

magnetic, 723

perovskites , 270

semiconductor-metal transitions, 626,630

shear, recurrent, 303

short-range order, 92-94,107

silicides, 485

E-phases, 502

pseudo-solid solutions, 498

ternary, 613

781

;
silicon, 505

silver

beta alumina, 133

filaments, 133

globs, 133

migration, 129

whiskers, 129

single crystals

alkali metal molybdates and niobates, 15

GdGeP2, 591

GdjjSei_jj growth, 638,639

sodium timgstate ,41

solar furnace, 471

solid electrolyte, 139

applications, 142

solid solutions, 97,101

Pa02-Th02, 335,336

Pu02-Th02, 342,344

SrRu03-LaRu0 3, 277

solid state reactions, 428

molybdenum carbides, 563

solubilities, B-C-Si system, 512

spectra, Lii,iii, 569

spinels, 115

square well potential , 550

SrFexMni_x0 3_y , 265

SrRu03, 276

Sr2Ti0i+, 123

Sr3Ti207, 123

Sri+Ti30io, 123

stability

Nb205-rich systems, 63,76

transition metal carbides, 567,581

stacking faults, 627

stimulated emission, 678

structural transitions, 625

stmcture

A+B^+Os compounds, 287

AB2Sif compounds, 597

aluminum diboride, 540

BaCoOs, 233

Ba2Co04, 233

BaFe2S-3, 683

BaFe2Se3, 685

Ba2FeS3, 691,692

Ba2FeSe3, 683

BasFeSey, 689

BaeFesSis, 687

BayFegSiitf 693

BasNiCxOg-y, 233

Ba3Ni2Cx09-y , 233

BaNi0 3, 233

beta alumina, 129

boron suboxide, 607

cadmium diiodide, 523,542

corundum, 117

defect, 224

fluorites, 397

lanthanide molybdate, 445

lanthanide tungstates, 445

LnBger 598

magnesi\im fluorogermanate, 745

magnesium germanate, 745 rare earth chalcogenides , 645

rocksalt, 122

rutile, 113

sodium tungstate, 43,45

sulfides (metal rich) , 651

(Ti/Cr)S2, 664

(Ti/V)S2, 663,666

trirutile, 119

zirconium-niobium oxide, 183

structure factor, TiO, 156

structures and physical properties,

relationship, 205

sulfides, 625,651,652,654,660

sulfospinels , 695

flash evaporation, 695

high pressure, 695

thin films, 696

superionic conductors, 129

superstructure

carbides , 583

niobia-zirconia, 189

yttri\am oxyfluoride, 753

swinging shear planes, 197,727 - syntaxic intergrowths , 378-381

synthesis

AB2SLf comporads, 696

chemical transport, 413 -

, RbNb03, 291 ,

. RbSbOs, 291

RbTa03, 291

system

B-C, 507

B-C-Si, 505

C0O-O2, 471 , Cu-Fe-S, 714

.

GdP2-Ge, 593

Lii^Si0^-Zn2Si0it , 463

Nb205-ZrP2» 184

RE-W-0, 397

Si-B, 506 .

: Si-C, 506

Ta205-Zr02, 184

Ti-Cr-0, 727

Ti02-Cr203, 197

Y-O-F, 749

TaC, 587

ordering, 584

TaCjj, 579

tantalum carbide, 562,583

ordering, 584

tantalum chalcogenides, 626,627,634

tellurides, 625

tellurites, 29 . tellurium

dioxide ,29 , hypovanadate , 36

terbium oxide, 343

ternary oxides , 69

'tetragonal bronze' structures, 104-109

tetramolybdate , 23

thermal analysis, cobaltous oxide, 471

thermal gravimetric analysis , boron

suboxide, 610

782
thermobalance , high temperature, 473

thennodynainics

actinide oxides, 319

tungsten bronze compounds, 52

the rmomanometrie apparatus, 471

thin films

oxides, 3 74 sulfospinels , 696

thorium dioxide

solid solutions, 331

solubility quotient, 331

thorium tetrafluoride, 331

thulium chlorides, 378-380

Tic, 568,573

(Ti/Cr) S2 chemical analysis, 664

chemical properties, 665

crystal growth, 664

crystal structure, 663,666

magnetic properties, 667

TiNiSi, 613

Ti02, 197

titanium

chromiijm disulfides, 664

monoxide, 156

sulfides, 629

tellurite, 32 vanadium disulfides , 664

(Ti/V)S2

band structure, 669

chemical analysis, 664

chemical properties, 665

crystal growth , 664

crystal structure, 663,666

electrical properties, 668,669

magnetic properties, 667

transference numbers, 148

transition-metal

chalcogenides , 625,645

compounds, 570,583

transport agents, 419

trigonal prism, 533

trirutile structure, 119

tungstates, lanthanide, 445

tungsten

bronzes, 19,51

carbide, 517,552,562

molybdenum bronze, 61

oxides, 95-97

tunnel

heptagonal, 17

hexagonal, 15,17

twinning, 92,104-106

rare earth oxides and oxysalts, 377

UCjj, 579

unreduced zone scheme, 554

uranium dioxide, solid-solutions, 331

uraniiam tetrafluoride , 331

vacancies, oxygen, 355

vacancy order, 629,632

valence bonding, 515,519,536

vanadium

bronze, 61

carbide, 562,583

oxides, 205

vapor transport, 672

VC, 585

Vegard's law, 335

V2O3, 127

Voronoi polyhedron, 520,540

Wadsley defects, 99-104,197,304

WC, 517,552

whisker growth, 133,135

x-ray diffraction, 187

boron suboxide, 610

x-ray spectra. Tic, 569

x-ray structure determination,

zinc oxide transport, 424

zirconia electrolyte, 55

zirconiiom niobium oxide, 165

Zn^Cd^.j^S, 721

ZnS, 721

ZnSb206, 120

ZnTiOs, 117

ZrCx, 577,579

783
\
FORM NBS-114A (t.71) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET NBS-SP-364

2* Gov t Accession No.

3 • Reci pi cnt s Ac cc ss i on No*

A. ill Lt, AINU Dill Ln SOLID STATE CHEMISTRY

5. Publication Date July 1972

W« k ^l. l.\rl.Lllitlt V71 guA*l<^<X. 1 Wll X^L^UV

7. AUTHOR(S)

•R. S. Roth and S. J. Schneider, Co-editors

8. Performing Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/ Work Unit No.

11. Contract/Grant No.

12. Sponsoring Organization Name and Address

Same as No. 9.

13. Type of Report & Period Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) This book presents the Proceedings of the 5th Materials Research Symposium on "Solid State Chemistry" held at the National Bureau of Standards, Gai thersburg,

Maryland on October 18-21, 1971. The symposium was sponsored by the Institute for

Materials Research, NBS. The purpose of the conference was to explore the realm

of new inorganic crystalline materials emphasizing crystal chemical and structural

aspects, providing a forum for discussion of new research problems and techniques.

A total of 56 invited and contributed papers were presented. In addition, the

symposium included three unscheduled talks and an open discussion period consisting

of four impromptu lectures on very current subjects dealing with nonstoichiometry

.

The Proceedings are divided into four main groupings, I Oxides, II Borides, Carbides,

Silicides, and Related Materials, III Chalcogenides, and IV Open Discussion on Nonstoichiometry. An edited version is given of the floor discussion following each

paper.

17. KEY WORDS (Alphabetical order, separated by semicolons) Chal cogeni des i crys tal 1 ographi c shear;

electron optical lattice images; lone pair geometry; nonstoichiometry; oxides;

18. AVAILABILITY STATEMENT 19. SECURITY CLASS

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21. NO. OF PAGES

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I IIiI