NATL INST OF STANDARDS & TECH R.I.C.

A11 100989903

/NBS monograph QC100 .U556 \/l00;1967 C.1 NBS-PUB-C 1959



UNITED STATES DEPARTMENT OF COMMERCE

.Alexander B. Trowbridge, Acting Secretary NATIONAL Bl REAL OF STANDARDS • A. \ . Astin. Director

TRACE CHARACTERIZATION

Chemical and Physical

W. Wayne Meinke and Bourdon F. Scribner, Editors

Institute for Materials Research

National Bureau of Standards Washington. D.C. 20234

Based on lectures and discussions of the

1st Materials Research Symposium

held at the NBS. Gaithersburg, Maryland

October 3-7. 1966

National Bureau of Standards Monograph 100

For sale by the Superintendent of Documents. U.S. Government Printing Office

\^ ashington. D.C. 20402 - Price $4.50

Issued April 28. 1967
Alational Bureau of Standards

^'-^G 1 6 1967

I o 0

ABSTRACT

A symposium on Trace Characterization, Chemical and Physical was

held at the National Bureau of Standards October 3-7, 1966. This

volume contains the texts of invited lectures, and summaries by the

rapporteurs of the contributed papers and discussion sessions. Topics

covered include trace characterization and the properties of materials;

electrical measurements; electrochemical methods; optical and x-ray spectroscopy; x-ray diffraction; optical methods; chemical spectrophotometry; nuclear methods; mass spectroscopy; preconcentration; sampling and reagents; and electron and optical microscopy.

Key Words: Trace characterization, electrochemical methods, x-ray spectroscopy, nuclear methods, electron and optical

microscopy, optical spectroscopy, symposium on trace

characterization.

Library of Congress Catalog Card Number: 66-62907

ii
FOREWORD

Development and improvement of measurement techniques for the

characterization of materials by chemical and physical means is a prime

responsibility of the Institute for Materials Research of the National

Bureau of Standards. The Institute carries out this responsibility by

serving as a focal point for development of measurement methodology

and by encouraging the dissemination of relevant information. Measurement methodology is the essential forerunner to critically evaluated

data on materials of importance to the advance of industry and commerce, one of the major missions of the Institute for Materials Research.

"Trace Characterization — Chemical and Physical," the first annual

symposium of the Institute for Materials Research, was held October 3—7,

1966, in the new NBS Laboratories at Gaithersburg, Maryland. Over

600 scientists representing industry, government, and university from

the United States and from many other countries attended in order to take advantage of this excellent opportunity for dialogue between specialists of varying backgrounds and interests. This volume contains the invited papers presented at the Symposium,

together with summaries of the contributed papers and ensuing discussions by the rapporteurs. Symposia such as this one and those that wiU follow are tailored to provide an opportunity for interdisciplinary

discussions of the state of the art in the broad spectrum of competences

in materials science represented at the National Bureau of Standards.

Gordon K. Teal, Director

Institute for Materials Research.

iii
i
PREFACE

This book represents the formal report of the first materials research

symposium of the NBS Institute for Materials Research, which was held

at the new site of the National Bureau of Standards in Gaithersburg,

Maryland, from October 3 through October 7, 1966. The subject of the symposium was "Trace Characterization — Chemical and Physical."

The Symposium was intended to bring together the leading authorities

both from within the United States and from abroad in the many different

fields which contribute to the physical and chemical characterization of materials, and especially to the detection and determination of trace amounts of defects and "foreign" substances. It was envisioned that

this meeting would provide a forum for the examination of the successes and shortcomings of the present understanding of materials characterization and for the comparative evaluation of experimental methods and

techniques. Its purpose was accordingly to improve the effectiveness

of materials research (1) by summarizing the present capabihties and

the future potential of the more useful tools for trace characterization

of materials, and (2) by prompting the exchange of knowledge among

the various discipHnes upon which a complete and meaningful characterization depends.

In the past there have been a number of symposia which have focused on one or another specific aspect of trace characterization. Unfortunately, these symposia have often mirrored a rather parochial point of

view and have encouraged the exhaustive study of one particular area

of competence without a corresponding attempt to establish the exact

status of that competence within the broad field of trace characterization. For this symposium, therefore, we made a serious effort to bring

together the several groups whose experimental techniques and competences differ but who could find a common ground in meaningful discussions about trace characterizations. Emphasis was placed on a broad

view of materials research as an interdisciplinary effort, and a special

attempt was made to establish lines of communication among the

speciahsts — chemists and physicists — engaged in the several aspects

of materials characterization. In general, the morning sessions were devoted to one-hour invited

lectures by outstanding authorities in the field. The introductory

lecture stressed the important relationship between trace composition

and the properties of materials. The remaining sessions were devoted

to a close examination of the "state of the art" and the future promise of the more useful tools for trace characterization. Among the specialties

V
vi PREFACE

considered were electrical and electrochemical measurements; nuclear

methods; optical, mass, absorption, and x-ray spectroscopy; electron

and x-ray diffraction; microscopy; and methods for sampling and

preconcentration.

The contributed papers, numbering about 90, were distributed in preprint form to all registrants. Instead of an oral presentation of these

papers, a summary of the sahent points was given by a rapporteur who

was, in each case, also an outstanding expert in the particular area under

discussion. The afternoon sessions were, in general, given over to these rapporteur summaries and to discussions in which the rapporteur,

the authors of the contributed papers, and the audience participated.

Included in this volume are the texts of the invited papers and summaries

of the contributed papers and discussions. A detailed hsting of the

contributed papers is given in an appendix.

An undertaking of such a magnitude w^ould not have been possible

without the wholehearted cooperation and assistance of a large group of people within the Institute for Materials Research and the National

Bureau of Standards. Many of these individuals served on Symposium

committees; their names will be found in the list of committees given in the appendix to this book. Particular thanks are due Dr. Roger G. Bates,

Assistant General Chairman, Dr. John K. Taylor, Arrangements Chairman, and Dr. David H. Freeman, Social Chairman of the Symposium.

The members of the Program Committee are to be commended for their

highly effective planning and directing of the scientific program and

their assistance in the publication of this book. The NBS Office of Technical Information under the direction of W. R. Tilley, with special

help from R. T. Cook and J. E. Carpenter and their coworkers, gave

invaluable assistance in many phases of the effort varying from the

initial pubhcity brochures and programs to this final publication of the

manuscripts. Within the Analytical Chemistry Division special thanks

are due to R. Boreni and especially to Mrs. Rosemary Maddock who, more than anyone else, has provided the coordinating effort that has

made early publication of this volume a reality.

W. Wayne Meinke

Bourdon F. Scribner.

December 15, 1966
SESSIONS vii 1st Materials Research Symposium

Trace Characterization, Chemical and Physical

General Chairman

W. Wayne Meinke

Analytical Chemistry Division, NBS Institute for Materials Research Program Committee Chairman

Bourdon F. Scribner

Analytical Chemistry Division, NBS Institute for Materials Research Session Chairmen

(Institute for Materials Research — National Bureau of Standards) (Washington, D.C. 20234) W. Wayne Meinke

Analytical Chemistry Division Robert L. Parker

Metallurgy Division John K. Taylor

Analytical Chemistry Division Marvin Margoshes

Analytical Chemistry Division Ernest Ambler

Inorganic Materials Division Hans Frederikse

Inorganic Materials Division Oscar Menis

Analytical Chemistry Division James R. DeVoe

Analytical Chemistry Division Bourdon F. Scribner

Analytical Chemistry Division Preconcentration, Samphng, and Reagents David H. Freeman

Analytical Chemistry Division Electron and Optical Microscopy John B. Wachtman, Jr. Inorganic Materials Division

Trace Characterization and the Properties of Materials

Electrical Measurements

Electrochemical Methods

Optical and X-ray Spectroscopy

X-ray Diffraction

Physical Optical Methods

Chemical Spectrophotometry

Nuclear Methods Mass Spectroscopy
II
CONTENTS

Page Foreword iii Preface v Session subjects and chairmen vii INTRODUCTION 1 TRACE CHARACTERIZATION AND THE PROPERTIES OF MATERIALS

Hannay, N. B., Lecturer

Introduction 5 Characterization 6 The Relation of Properties to Composition and Structure 7

Electrical Properties 7 Semiconductors 7 Metals 10 Superconductors 14

Ionic Conductivity 14 Optical Properties 15

Alkali Halides 16 Luminescence 17 Magnetic Properties 18 Mechanical Properties 19

Structural Transformations 24 Chemical Reactivity 29

Radiation Effects in Solids 33 Surfaces 35

Characterization and Properties 36 References 38 ELECTRICAL MEASUREMENTS FOR TRACE CHARACTERIZATION

Weisberg, L. R., Lecturer

Introduction 39 Value of Electrical Measurements for Analysis 39

Criteria for Analytical Use 39

Characteristics of Electrical Measurements 40

Applications of Electrical Measurements 42 Fundamental Principles and Apparatus 50 Fundamentals 50

Resistivity 53 Residual Resistivity 57

Hall Effect 60 Thermally Stimulated Currents (TSC) 63 Summary and Conclusions 65 References 67

ix

I
X CONTENTS

ELECTRICAL MEASUREMENTS -Contributed Papers and Discussion

Powell, R. L., Rapporteur Page 69 Introduction Contributed Papers • Discussion References • ^'^

TRACE CHARACTERIZATION BY ELECTROCHEMICAL METHODS

Laitinen, H. A., Lecturer

Introduction 75 Methods Based on Passage of Faradaic Current 76 Measurement of Current as Related to Concentration 76

Classical Polarography 76 "Tast" Polarography or Intermittent Polarography 78

Derivative Polarography 79 Pulse Polarography 80 Square Wave Polarography 84

Alternating Current Polarography 85 Radiopolarography 86

Catalytic Currents in Polarography 88 Adsorption Effects in Polarography 88 Measurements of Current at Electrodes of Constant Area (Voltammetry) 88 Steady state methods

Single sweep and cychc voltammetry 89

Voltage step chronoamperometry 90 Chronopotentiometry 90 Coulometry 91 Coulometry at Constant Potential 91 Coulometry at Constant Current 92 Coulometry of Surface Layers 92 Thin Layer Coulometry 92 Coulometric Titration 93 Chronocoulometry 94

Galvanic Analysis 95

Coulostatic Analysis 95

Stripping Analysis 96

Electrolytic Concentration 101 Methods Based on Electrodes at Equilibrium 101 Direct Potentiometry 101 Electrodes of the First Class 101 Electrodes of Second and Third Classes 102

Glass Electrodes 102 Liquid Ion Exchange Membrane Electrode 103 Precipitate-Impregnated Membrane Electrodes 103

Precision Null-Point Potentiometry 103 Methods in Which Faradaic Current is Unimportant 104 Conductance 104 High Frequency Admittance 104 Double Layer Capacitance Measurements 105 Summary 105 References 107
CONTENTS xi ELECTROCHEMICAL METHODS -Contributed Papers and Discussion Osteryoung, R. A., Rapporteur ^^s*^ Introduction Ill Contributed Papers 112 Discussion 119 References 120 OPTICAL AND X-RAY SPECTROSCOPY

Addink, N. W. H., Lecturer

Introduction 121 Flame Emission and Absorption 122 Experimental Test of Theoretical Considerations 122

Theoretical Considerations Concerning the Influence of Temperature 125 Comparison of Absorption and Emission 129 Analysis of Multicomponent Systems in Solution 129 Future Prospects 129

Classical Emission Spectral Analysis 130 The Arc 130 General Considerations 130 The Significance of the Rate of Evaporation, Sideward Losses and the Temperature of Column and Mantle 133

Additions before Arcing 134

Limits of Detection 134

Impurities Present in Graphite Electrodes 136 Other Methods of Evaporation and Excitation 136 The Spark 136 Future Prospects 138 X-Ray Fluorescence and Microprobe Analysis 139 X-Ray Fluorescence 139 General Considerations 139

Non-linear Working Curves 141 Thin Layers 141 Factors Bearing on Fluorescence Energies 142 Microprobe Analysis 143 Future Prospects (General) 143

Final Conclusions 144 Future Prospects (General) 146 Acknowledgments 146 References 147 OPTICAL AND X-RAY SPECTROSCOPY- Contributed Papers and Discussion

Kaiser, H., Rapporteur

Introduction 149 Contributed Papers 149 Nomenclature 152

Limit of Detection 153 References 164 EFFECTS OF TRACE IMPURITIES ON X-RAY DIFFRACTION

Chikawa, J. and Newkirk, J. B. Lecturers

Introduction 165 X-Ray Diffraction Topography 166 Experimental Methods 167

Berg-Barrett 167 Double Crystal 168
xii CONTENTS

Page Scanning Transmission 169 Anomalous Transmission 171 Causes of Contrast 171 Homogeneous Dilation and Tilt Contrast 172

Direct Image 173 Dynamical Images 173 The Effects of Impurity on Dislocation Images 175

Imperfections Produced From Trace Impurities 179

Precipitates 180 Impurity Segregation: Non-Uniform Impurity Distribution 182

Lattice Parameter Variations Due to Impurities 186 Double Crystal Method. 187 Moire Patterns 189

Effect of Impurities on Integrated Intensity of X-ray Diffraction 191

Integrated Diffracted Intensity in Reflection 192 Impurity Effect on Anomalous Transmission 193 Impurity Effect on Electron Density Distribution 195

Electron Density Map — Difference Method 195

Precise Determination of Structure Factors by Means of Pendellosung Fringes. . . 196 Other Effects of Impurities 198

Influence of Impurities on Phase Stability 198

Influence of Impurities on Solid State Reaction Kinetics 199 Summary 199 Acknowledgements 199 References 199 X-RAY DIFFRACTION -Contributed Papers and Discussion

Peiser, H. S., Rapporteur

Introduction 203

Contributed Papers 205

Discussion 208

References 209 PHYSICAL OPTICAL METHODS -Contributed Papers and Discussion

Frederikse, H. P. R., Rapporteur

Introduction 211

Invited and Contributed Papers 212 References 214 CHEMICAL SPECTROPHOTOMETRY IN TRACE CHARACTERIZATION

West, T. S., Lecturer

Introduction 215

Molecular-Absorption Spectrophotometry 217

Selectivity of Reaction 217 Mechanism of Colour Production 219

Identity of Liganding Atom 220

Steric Hindrance in Organic Reagents 221 Chelate-Cage Reagent Molecules 222 Formation of Ternary Complexes 224 Methods of Ternary Complex Formation 224 The Alizarin Complexan-Lanthanon System for Fluoride Ion 225 The Bis[diphenanthrohnium-silver(I)] BPR Ternary System, etc 227

Sensitivity of Reaction 230 The Sensitivity Barrier 231
CONTENTS xiii

Page Surmounting the Sensitivity Barrier 232

Evolution of Amplification Reaction 233

Evolution of Kinetochromic Spectrophotometry 234

Molecular Absorption Spectrophotometry in the Future 237

Molecular Fluorescence Spectrophotometry (Spectrofluorimetry) 237

Absorption Re-emission Processes 239 Phosphorescence and the Triplet State 242

Extinction of Fluorescence 243 Quenching Processes 243 Chemical Reaction 243

Intermolecular Colhsion and Temperature Effect 243

Viscosity of Medium 244 Nature of Solvent Medium 244

Charge-transfer Processes 244

Dissolved Cations and Ionic Strength 245

Effect of Dissolved Oxygen 245

Radiative Quenching and Delayed Fluorescence 245 Non-Quenching Extinction Processes 246

Instrumentation 247 Choice of Instrument 248

Physical Laws Governing Fluorescence Emission 249

Basic Differences Between Fluorimetry and Absorbance 252 Reagents for Speetrofluorimetric Analysis 252

Character of Reacting Cation 253 Nature of Fluorogenic Reagents 254

Aliphatic Compounds 254 Aromatic Compounds 254

Molecular Configuration 255

Steric Effects. 256

Principal Types of Fluorogenic Reagent 257

Fluorescence Energy Transfer Systems 258

Fluorometric Reagents in Practice 258 Assessment of Molecular Fluorescence Spectrophotometry as an Analytical

Technique 259

Prospects for the Future 266 Atomic Absorption Spectrophotometry 266

Presentation of Atoms for Analysis 267 The Atom Furnace Reservoir 267 Flame Reservoirs 268

Processes in Flames 268

Nebulisation of Solutions 270 Other Atom Reservoirs 271 Hollow Cathode Sputtering 271

Electric Discharge and Plasma Jets 271 Atomic Spectra and the Hollow Cathode Lamp 272

Necessity for Monochromator 273

Multi-element Lamps 273 Monochromated Continuum Sources 274

Spectral Discharge Lamps 274 Microwave-powered Sources, etc 275 Types of Burner 275 Long Flames 276 Types of Flame Medium 277
xiv CONTENTS

Page Conventional Flames 277 The Nitrous Oxide-Acetylene Flame 278 Types of Hollow Cathode Lamp 278 High Intensity Hollow Cathode Lamps 279

Analytical Relationships in Atomic- Absorption Spectrophotometry 279 Choice of Wavelength 279 Assessment of Atomic-Absorption Spectrophotometry as an Analytical Trace Technique 280

Future Developments in Atomic-Absorption Spectrophotometry 283 Atomic Fluorescence Spectrophotometry 284 Types of Atomic Fluorescence Lines 286

Analytical Relationships in Atomic-Fluorescence Spectrophotometry 287

Instrumentation 289

General Arrangement 289 Types of Burner 289

Fuel Gases 290

Excitation Sources for Atomic Fluorescence Spectrophotometry 291

Spectral Discharge Lamps and Microwave-powered Sources 291 Continuum Sources 292

Sensitivity and Selectivity of Atomic Fluorescence Spectrophotometry 292

Determination of Selenium and Tellurium 294 Assessment of Atomic Fluorescence Spectrophotometry as an Analytical

Technique 295

Future Developments in Atomic-Fluorescence Spectrophotometry 297 References 298 CHEMICAL SPECTROPHOTOMETRY -Contributed Papers and Discussion Menis, Oscar, Rapporteur

Introduction 303

Contributed Papers 303

Discussion 305 References 306 RADIOACTIVITY TECHNIQUES IN TRACE CHARACTERIZATION

Smales, A. A., Lecturer

Introduction 307

Activation Analysis 307 General Principles 307

Activating Agents and Irradiation Facilities 310 Slow neutrons 310

Fast neutrons 316 Gamma photons 317 Charged particles 320 Prompt Radiation Techniques 322 Radiochemical Separations 323

Instrumentation 325 Accuracy and Precision 326

Position of Activation Analysis Relative to other "Trace Characterisation" Methods 326

Analysis Using Radioactive Tracers 327

Introduction 327

Isotopic Methods 328

Single isotope dilution 328

Substoichiometric isotope dilution 329
CONTENTS XV

Page Isotopic exchange 330

Non-isotopic Methods 331

Isotope derivative and derivative dilution 331

Isotope displacement 332

Radiorelease 332 Radiometric Titration 333 Assessment of Radioactive Trace Methods 333 Avoidance of Analysis by Means of Tracers 334 Concluding Remarks 335 Acknowledgements 335 References 335 NUCLEAR METHODS -Contributed Papers and Discussion Guinn, V. P., Rapporteur Neutron Activation Analysis 337 Thermal-Neutron 337

Fast-Neutron 340

Photonuclear Activation Analysis 342

Charged-Particle Activation Analysis 344 Other Activation Analysis Topics 345 Other Nuclear Methods 346 References 346 SPARK SOURCE MASS SPECTROMETRIC ANALYSIS OF SOLIDS

Ahearn, A. J., Lecturer

Introduction 347 Mass Spectrometry with Spark Source 348

Analytical Capabihties of Spark Source Technique 350

Factors Limiting Detection Sensitivity 351

Diffuse Background 351 Line Background 355

Factors Limiting Accuracy of Analysis 358

Transmission Stability of Instrument 359

Reciprocity Fulfillment 359 Emulsion Sensitivity — Dependence on Element 359

Cahbration of Emulsion 360 Spark Source Ionization Pattern 360

Integration of Ion Intensity Profile 360 The Relative Sensitivity Problem 361

Ion Samples versus Standard SoHd Samples 362

Precision Capabihties of Spark Source Technique 366 The Homogeneity Problem 370

Standard Sample Needs and Possibilities 371 Summary 372

Conclusion 373 References 374 MASS SPECTROSCOPY -Contributed Papers and Discussion Owens, E. B., Rapporteur

Introduction 377

Analytical Apphcations 377 The State of the Art — Improving Accuracy 378

Sensitivity Coefficients 379

Photoplate Evaluation 380

Ion Charge Distribution 381
XVI CONTENTS

Page Computer Use in Calculations, 381 Molecules Found in Spark Spectra 381

Quantitative Mass Spectrography • 382 Comments from the Authors and Discussion from the Floor 382 References •

• 384 PRECONCENTRATION IN TRACE ANALYSIS

Minczewski, J., Lecturer

Introduction 385

Preparation of Sample 387 The Analyzed Materials and Sample 387 The Technique of Work 390

Hermetization of Operations 390

Laboratory Vessels and Containers 391 Reagents 395

Concentration and Separation of Traces 396 Masking 397

Precipitation and Coprecipitation 398

Extraction 402 Chromatography 406

Volatility 409 Zone Melting 412

Final Remarks 413 Acknowledgements 414

References 414 PRECONCENTRATION, SAMPLING, AND REAGENTS -Contributed Papers and Discussion

Morrison, G. H., Rapporteur

Introduction 417

Preconcentration and Separation Methods 419 Reagents 421 Sampling and Sample Preparation 422

Discussion 424

References 425 THE STUDY OF CRYSTAL IMPERFECTIONS BY MEANS OF OPTICAL

METHODS AND BY MEANS OF ELECTRON MICROSCOPY AND ELECTRON DIFFRACTION

Amelinckx, S., Lecturer

Introduction 427

Historical Survey 428

Structural Defects 431

Dislocations 431

Definition, Displacement Vector 431 Burgers Circuit — Burgers Vector 432

Dislocation Loops 433

Displacem^ent Fields 435

Stress Fields — Cottrell Interaction 437 Energy of a Dislocation 437 Force on a Dislocation; Motion of Dislocations 438

Forces Between Dislocations 440

Multiplication of Dislocations 440

Stacking Faults. Partial Dislocations 441 Arrays of Dislocations 443
CONTENTS xvii

Page Polygonization 445

Observation Methods 447

Surface Methods 447 Growth Spirals 447

Evaporation Spirals 449

Etching 450 Bulk Methods 455

Decoration 455

Birefringence 467

Electron Microscopy and Electron Diffraction 468 Transmission Electron Microscopy 468

Introduction 468

Principle of the Method 469 Specimen Preparation 470

Electron Diffraction in Perfect Crystals 471 Kikuchi lines — Determination of 5 472

Extinction Contours 474 Thickness contours 474

Inclination or Bend Contours 475

Contrast at Dislocations 477

Origin of the Contrast 477

Determination of the Direction of the Burgers Vector. Extinction Conditions... 479

Determination of the Sign of the Dislocations (i.e., the Sense of the Burgers

Vector) ? 483

Determination of the Length of the Burgers Vector 483

Dislocations Inclined with Respect to the Foil; Oscillating Contrast 487

Dislocations Seen End On 487

Stacking Faults 490 Types of Stacking Faults 490

In f.c.c. Crystals 490

In h.c.p. Crystals 492 Antiphase Boundaries: Periodic Antiphase Boundaries and Stacking Faults... 493

Origin of the Contrast 493 Some Properties of Stacking Fault Fringes 496 Displacement Vector Determination 497

Determination of the Type of Stacking Fault 497

In f.c.c. Crystals. 497 Hexagonal Close Packed Crystals 500 The Measurement of Stacking Fault Energies 501 Ribbons 501 Extended Nodes 504 Other Methods Based on Electron Microscopy 508

Contrast at Slip Traces 508

Point Defects and Dislocations 509

Processes Giving Rise to Point Defect Clusters 510 Quenching 510

Irradiation 511

Plastic Deformation 511

Deviations From Stoichiometry 511 Nature of the Defect Clusters 512

Dislocation Loops 512

Stacking Fault Tetrahedra 514

Cavities 516

Helices 516

237-323 0-67—

2
xviii CONTENTS

Page Methods to Determine the Character of the Loops 516 The Geometrical Method 517 The Tihing Method 520 Loops Seen Edge On 520

Stacking Fauh Method 521 The Burgers Vector Method 522 Domain Boundaries 524

Ferroelectric Domains 524

Anti-ferromagnetic Domain Boundaries 527 Domains Due to Interstitial Ordering 527 Ferromagnetic Domain Walls 528 Other Planar Defects 531

Direct Lattice Resolution 531 Moire Patterns 532 The Effect of the Presence of Defects on the Diffraction Pattern 537

Discussion 538 Acknowledgements 540

References 540 ELECTRON AND OPTICAL MICROSCOPY- Contributed Papers and Discussion

Wilsdorf, H. G. F., Rapporteur

Introduction 547

Contributed Papers 549

Discussion 557 References 559 APPENDIX 1. List of contributed papers 561 APPENDIX II. Symposium committees - 567 INDEX 569
TRACE CHARACTERIZATION

Chemical and Physical

INTRODUCTION

W. WAYNE MEINKE and BOURDON F. SCRIBNER

Institute for Materials Research

National Bureau of Standards

Washington, D.C. 20234 The problem of the meaningful measurement of "traces," be they

chemical contaminants or physical defects, has become critical during

the past few years as the field of materials research has developed and

matured. One to two decades ago the appellation "spectroscopically

pure" was sufficient to characterize materials for almost any use, whether in research or in technology. More recently, however, development of special preparation techniques for high-purity materials and the

discovery of unique properties in these highly-purified materials has

resulted in a situation where our capabilities for preparation and

our demands in utilization have often far outstripped our ability to characterize.

Furthermore, there exists at the present time a multitude of methods

and techniques which have the potential for developing characterization information. Many of these methods depend upon physical principles originally discovered and investigated without regard for possible

analytical applications. They often require specialized equipment and

understanding and have remained the concern of special groups of scientists. Each usually serves an important analytical function, and thus

many of these competences have become highly developed and self- sufficient— with their own disciples, their own vocabulary, their own

symposia, and their own societies. Each group explores in depth the

potentialities of its own area and develops elaborate programs for remedying its own deficiencies and limitations. Unfortunately, interest in cross-fertihzation with other parallel competences is often minimal. Specific symposia dedicated to a given

competence rarely permit time for a glimpse of alternate modes of operation. Competing sessions at general meetings discourage the broadening which is so important in the development of a proper perspective.

What the practitioner of any area of characterization should understand is that the ultimate user of his information does not care whether

the effort has come from chemistry or physics, from spectroscopy,

electrochemistry, or nuclear techniques. Nor is he concerned with

whether the result has emanated from a highly developed competence

1
2 TRACE CHARACTERIZATION

with decades of experience and tradition or from a newly discovered

and newly exploited principle of nature. Rather, he wants accurate

characterization information for certain critical aspects of his material

so that he can assure consistent reproduction of this material.

Eleven years ago this need was recognized in the biomedical field and

resulted in a conference on Trace Analysis sponsored by the SloanKettering Institute and the New York Academy of Sciences. This

symposium covered what might be called the "chemical" methods of trace characterization and emphasized the application of these techniques to the elements of biomedical significance at the parts per milhon

level. The papers for this symposium have been published [1]^ and

form a very useful reference. In the past decade the areas of sohd state physics and chemistry have

developed rapidly, with greatly expanded requirements for sensitivity

and accuracy, which have intensified this demand for development of

the best in many types of characterization methods. Two books [2, 3] have appeared which present, side by side, the case for several of the

most important methods. Detailed reviews and bibhographies [4] giving

reference to the original hterature form excellent source material for further exploration of the subject.

The approach of the present volume has been somewhat different. Rather than emphasize an exhaustive treatment, we suggested that the

invited papers consist of candid reports on the present status of efforts

in trace characterization in all pertinent categories of the particular

subject area, together with a forecast of the future potential. In addition, we proposed that the papers should contain some discussion of

basic principles, but we regarded the critical evaluation of the field to be of primary importance. Furthermore, we suggested that the correct emphasis could perhaps be achieved by considering that the author was summarizing the "state of the art" in his specialty for the benefit of experts in the other fields. Selection of the topics evidently had to be arbitrary, but the subjects

chosen included most of the areas which today give the major promise

for future improvements in trace characterization.

This volume then brings together state of the art summaries in most

of the areas pertinent today for trace characterization. The authors

have distilled the experience of many years into their papers and have

also provided a ghmpse of problems to be faced in the future. In addition, the summaries by the rapporteurs of contributed papers and

discussions bring attention to current research in characterization and

round out the treatment of each subject. Consequently, it is our hope

that this book will provide guidance in materials characterization both

for the present and for a number of years to come.

' Figures in brackets indicate the literature references at the end of this Introduction.
INTRODUCTION 3

References

[1] Yoe, John H., and Koch, Henry J., Jr., Eds., Trace Analysis, John Wiley & Sons, New

York, 1957.

[2] Cah, J. Paul. Ed., Trace Analysis of Semiconductor Materials, MacMillan Co., New

York, 1964.

[3] Morrison, George H.. Ed., Trace Analysis, Physical Methods, Interscience, New York,

1965.

[4] See for example Anal. Chem. 38, No. 5, Annual Reviews (1966).

TRACE CHARACTERIZATION AND THE

PROPERTIES OF MATERIALS

N. B. HANNAY

Bell Telephone Laboratories, Incorporated

Murray Hill, New Jersey 07971 1. Introduction

The rapid growth of sohd-state science and technology in recent years

has brought with it a surge of interest in the materials sciences. Physicists interested in the fundamental properties of solids have discovered

that it is absolutely vital for them to have available research materials

with a high degree of chemical purity and structural perfection. And,

at the same time, in nearly every area of engineering there is a demand

for better materials, to do things which are within the limits of present

scientific knowledge but which require materials control or properties

not generally attainable. To illustrate the dependence of engineering on

progress in materials, a survey of a solid-state device development

organization recently showed that over 75 percent of the people were

engaged in materials work of one sort or another. Contrast this to the

situation a few years ago, when materials work was rather incidental to the development of electron tubes, the forerunner of modern solid-state devices.

While the overall dependence of solid-state science and technology on the quality and control of materials is now well recognized, nonmaterials people often fail to distinguish between two clear and distinct aspects of the materials work. Not only must the materials scientist seek preparative methods, but he also needs methods for characterizing

his materials as to purity and perfection, in order to make meaningful

both the advancement of preparative methods and investigations of

properties.

What is characterization? A definition has been proposed in a recent study of characterization by a committee of the Materials Advisory

Board [1] ^ and it is this: "Characterization describes those features of the composition and

structure of a material that are significant for a particular preparation,

study of properties, or use, and suffice for reproduction of the material."

^ Figures in brackets indicate the literature references at the end of this paper. 5
6 TRACE CHARACTERIZATION

The preparation of a material should not have to be included in its characterization, because it is not a property of the material; lacking

perfection in our methods of characterization, however, we may still have to specify preparation method, as a substitute for true characterization. Also, the properties of a material should not have to be included

in its characterization, because the properties result from the composition and structure. Again, however, the lack of sufficiently good

methods for determining this composition and structure may require us

to fall back on the specification of certain properties in the characterization of a material. Eventually, however, one hopes to understand properties in terms of composition and structure, and to eliminate the need

for a description of properties, as well as of the method of preparation,

in characterization.

This symposium focuses attention on the growing awareness of the

necessity for developing and using better methods for characterizing

solids. It is concerned with one large segment of characterization — the

identification and determination of very small concentrations of chemical

impurities or structural imperfections. Many of the most interesting

properties of solids depend directly upon these small concentrations

of impurities and defects, and the illustration of this is a principal theme

of this paper.

II. Characterization

In simple terms our definition of characterization means "what atoms

are present, and where are they." This is all that is required, in principle, for complete characterization.

A closer examination of what is required to specify the atoms present

and their location shows the complexity of the problem, however. Again

looking at the findings of the Materials Advisory Board study, it is con- venient to divide characterization into three main categories: the chemical composition, the major structural parameters of the solid, and the

deviations of the structure from the ideal, i.e., the structural imperfections. This symposium is concerned with many aspects of the first of

these categories, composition, and with the third, crystal imperfections.

Under composition we seek the identification of impurities, and this includes both their valence state and their state of chemical combination; we include also the determination of the concentration of minor phases,

as well as their location and homogeneity. Finally, we require infor- mation about surface impurities.

Under structural imperfections we include point defects, or agglomerates of pointr defects; vacancies, interstitials, and antistructure defects

fall into this category. Also, we include fine defects, or dislocations, and

the characterization of these may be complex as it includes geometrical

information, such as the Burgers vector and the orientation, as well as

dislocation density, impurity atmospheres, etc. Finally we include area
PROPERTIES OF MATERIALS 7

defects, and there are many kinds of these — grain boundaries, twin

boundaries, stacking faults, interphase boundaries — with geometry and

impurity atmospheres to be characterized.

But this is not the whole story, unfortunately. Large categories of

materials fall outside the limits implied by the terms we have used to define composition and structural imperfections. Polycrystalline in- organic solids require much additional information for a complete characterization, including details of grain geometry and composition,

additional phases present, geometry, surface details, and many other

features. Perhaps even more complicated are organic macromolecular

solids, as the characterization of polymers involves questions of molecular weight distribution, chain branching and tacticity, solid additions

and plasticizers, cross-links, network topology, copolymers, polyblends,

crystallinity, free volume, and a host of other characterization parameters.

Our aim in this article is to provide perspective for characterization,

by relating it to the properties of solids. Perhaps we can visualize this relationship by considering [2] the process of transforming, say, a pile of ore into a useful item of hardware:

Raw Material Useful Material Study of Properties -^ Uses

The step from raw materials to useful materials involves both the preparation and characterization of the latter. We will here focus our attention on the inter-relationship between "useful materials" and the

properties. As stated in our introduction, the ultimate goal of materials

work, and therefore of characterization, is to achieve certain properties;

from a scientific standpoint it is the fundamental understanding of properties in terms of composition and structure that is the goal, and from an

engineering standpoint it is the achievement of properties needed for a

particular end-use.

III. The Relation of Properties to Composition and Structure

We shall discuss the role of "trace impurities" — both chemical and

structural — by giving some examples of their relation to the properties

of various kinds of solids. A perception of this relationship will then

make almost self-evident our concluding remarks about the need for improved characterization.

A. Electrical Properties [3]

1. Semiconductors

The electrical properties of semiconductors [4] offer a by-now familiar,

but nevertheless classic example of a profound effect of traces of chemical impurities on physical properties. It is the experience with semiconductors, more than anything else, which has supplied the impetus

237-323 0-67—

3
8 TRACE CHARACTERIZATION

to much of the work on the purification, crystal growth, and characterization of the sohd-state materials of today.

Most semiconductor phenomena depend vitally upon the impurity

content of the material. Concentrations of electrically active chemical

impurities in the range 10~^ to much less than 10"^ determine the

electrical properties, and in compound semiconductors the point defects

(vacancies, interstitials) can be equally important. In a small number

of semiconductors, notably sihcon and germanium, purities in the 10~^

range or better have been achieved, and the whole spectrum of impuritydependent phenomena has been quantitatively studied. As a result germanium and silicon are very well understood in a fundamental way.

(Effects due to point defects are perhaps less well understood than the

effects due to impurities.) In other semiconductors the need for similarly high purities is recognized, but there have been varying degrees

of success in the effort to achieve high purities. The understanding

of a semiconductor is, in general, proportional to the degree of puri- fication which has been achieved with that material. In such semiconductors as germanium and silicon, the carrier (conduction electrons and holes) concentrations are determined primarily

by the concentrations of Group III and Group V impurities present in the material. In compound semiconductors other impurities function

similarly as simple donors and acceptors. A large number of semiconductor phenomena depend directly upon the carrier concentration.

These include: transport properties, such as electrical conductivity,

thermoelectricity and Hall effect: many optical properties, such as electroluminescence, photoconductivity, aftd some optical absorption

effects; and a variety of other phenomena, such as p-n junction behavior, chemical interactions among impurities and imperfections, and

so on. The electron and hole concentrations may also be affected by

the concentrations of point defects associated with nonstoichiometry,

in the case of many compound semiconductors. Any concentration of

donor and acceptor impurities (or point defects) which is at least as great as the intrinsic carrier concentration wiU be significant. Thus

in silicon at room temperature the carrier concentrations will be deter- mined by the donor and acceptor impurities present if they exceed

about one part in 10", and in germanium the corresponding figure is roughly one part in 10^. These semiconductor phenomena depend

primarily upon the number of simple donors and acceptors present, but

not, in general, upon their chemical identity.

Another set of phenomena includes those properties which depend more specifically upon the identity of impurities, whether they be ordi- nary donors and acceptors, or electrically active in a more subtle way.

Several important properties are related to the ionization energies of

the donors and acceptors, i.e., the work required to remove an electron

from a donor in the lattice to a large distance, or to add an electron to an
PROPERTIES OF MATERIALS 9

acceptor. These include the temperature dependence of the electrical conductivity, Hall effect, threshold for photoconductivity, and optical

absorption by impurity centers. The ionization energies will usually vary even among chemically similar impurities, the differences sometimes being very small, and sometimes large. Hole-electron recombination processes, trapping and luminescence characteristically depend

upon the electronic energies for the center at which the recombination

occurs. Recombination processes in germanium and silicon are sensitive to even smaller concentrations of certain impurities than are the

carrier dependent phenomena mentioned earUer. Thus the minority

carrier Hfetime in germanium is reduced one to two orders of magnitude

by concentrations of transition metal impurities, such as nickel, at the

10-9 level. Much of the effort that has gone into semiconductor materials has been

associated with the identification and control of trace impurities and

structural imperfections. In the relatively simple and well-controlled

semiconductors sihcon and germanium, the concentrations of these

centers are usually small, and the problem has been to develop characterization tools of sufficiently high sensitivity. In many compound semiconductors, the variety of defects of importance in a given sample may

be much larger, and the main problem is to sort them out to a degree

which permits an understanding of the electrical properties. This is illustrated in Figure 1 for pure PbS; the concentrations of several of species are shown as a function of the sulfur pressure in equilibrium

with a sample of a given defect concentration. The full Hne shows

the experimentally accessible parameter, the majority carrier concentration; it can be seen that this falls far short of revealing the entire

chemical composition. This is a relatively simple situation, as far as compound semiconductors go, because no impurities or interstitials have been assumed to be present. Practical cases will therefore be even more compHcated and the extent of the information needed for

19.0 P ! n u

18.5 z

z

18.0 o

^

tE 17,5

t-z

111 u

z

17.0 o

u

16.5 (ANION VACANCIES) j (CATION VACANCIES) o

_1 16.0 ^ LOG

Figure 1. Concentrations of defects expected in PbS as a function of sulfur pressure.

Full line gives experimental values for carrier concentrations, \n—p\. After Hannay [4].
10 TRACE CHARACTERIZATION

complete characterization should be apparent. Only a few compound

semiconductors among the many which show this kind of nonstoichiometry have had even the major features of their composition worked out, due to the difficulty in determining the various defect concentrations [5].

2. Metals

Turning next to the study of metals, we note that the last few years have seen an upsurge in the effort to unravel the basic electronic struc- ture of metals. The key to this effort has been the attainment in a number of metals of a sufficient level of chemical purity and of crystalline

perfection to permit the measurement of quantities which are useful in revealing this electronic structure [6]. The relationship between purity and electrical resistivity is one of the

most direct effects of chemical purity and crystal perfection in metals.

Impurities and imperfections increase the resistivity of metals, because

they act as scattering centers for electrons and therefore reduce the mean

free path of the electrons, i.e., the average distance an electron travels between collisions with these centers or with phonons (lattice vibrations).

An ideally pure, perfect metal would have its resistivity determined

only by the lattice vibrations. It would show a zero resistivity at 0 °K,

increasing as at slightly higher temperatures because of the lattice vibrations, as shown in Figure 2. Impure samples would show a higher

resistivity, because of the increased electron scattering by impurities

and defects. The effect of impurities on the resistivity of copper is shown in Figure 3. The resistivity exhibits a linear dependence upon

the concentration of chemical impurities, and there are very great

differences between impurities in their effects on resistivity; Fe in Cu

at 4.2 °K is an extreme case. Table 1 also compares the effect on resistivity of several impurities and structural imperfections.

Table 1. Approximate contributions of impurities and defects to the

resistivity of copper.

(10^ X Ap/% impurity or defect, ohm cm/%)

Chemical Impurities Physical Defects

Ag 0.2 Vacancies 1.3 Ni 2 Interstitials 5 Fe 20

Sn 5 Dislocations, 0.4 to 3 X lO-^^ Sb 9 where A^=cm of dislocation/cm^,

The low temperature resistivity is often used as a practical measure

of purity in metals. As Figure 2 shows, at liquid helium temperatures

most of the resistivity is due to impurities and imperfections, even in quite pure materials; at room temperature the resistivity is primarily
PROPERTIES OF MATERIALS

0 2 4 6 8 10 TEMPERATURE {°K)

Figure 2. Schematic of resistivity of a metal at low temperatures [6].

0 0.002 0.004 0.006 0.008 0.010 IMPURITY CONCENTRATION (ATOM °/o) Figure 3. Resistivity of copper with impurities (4.2 °K) [6].
12 TRACE CHARACTERIZATION

determined by the lattice vibrations. Thus the higher the "resistance

ratio", i?298°K/^4.2°K^ the purer the metal is both chemically and structurally. The resistance ratio is a figure of merit which lumps together

the effects of chemical impurities and structural imperfections, without

regard to their individual importance.

A number of phenomena are useful in studies of the band structure and Fermi surfaces of metals; among them are magneto-resistance,

Hall effect, magneto-acoustic absorption, cyclotron resonance, deHaasvanAlphen effect, thermoelectric power, anomalous skin effect, hehcon waves and Alfven waves. One can see in a general way why these

effects necessitate materials of very high purity. Several of the phenomena, for example, involve the use of a magnetic field, which causes

the electrons in the metal to move in circular (cyclotron) orbits in a plane perpendicular to the field direction. In order to interact with

the lattice in all possible ways, the electron must complete at least one

orbit before it is scattered. Scattering results from interaction of the

electron with chemical impurities and crystal imperfections. One seeks

therefore to use high magnetic fields in order to reduce the size of the

orbit, and to use high purity materials to reduce scattering. It turns out

that the purity demands are quite stringent, as there is a practical limit

to the magnetic field strengths which are available, and the only recourse

in making the measurements feasible is to reduce the resistivity by in- creasing the purity and crystal perfection. Resistivities below about

10"^ ohm cm (at low temperatures) are generally necessary for these

kinds of measurements. One can see from Table 1 that to achieve

these resistivities in copper, purities in the order of half a part per million

for iron are required, and within an order of magnitude of this for other

elements. Copper was one of the first metals for which the Fermi sur- face was determined in detail, and this has been followed by similar

work in a number of other metals.

Resistance ratios that have been achieved for a number of metals in which purification efforts have been most successful are shown in Table 2. Generally speaking resistance ratios of a few thousand are required in order to make fundamental Fermi surface studies.

The effect of point defects, as distinct from chemical impurities, can

be studied in material of sufficient chemical purity by quenching-in the

defects. Concentrations of the defects in excess of the equilibrium

number are achieved by rapid cooling from some high temperature at which the equilibrium concentration is considerably larger. Figure 4

shows the resistivity changes due to "frozen-in" vacancies in gold,

after quenching from various temperatures, Tq [7]. EquiHbrium concentrations of vacancies in metals are of the order of 10 ppm at 1000

°K, since the formation energies are of the order of one eV and the

vacancy concentration [V] = N exp {—EvIkT), where N is the number of

lattice sites in a cubic centimeter.
PROPERTIES OF MATERIALS 13

Table 2. Resistance ratios of some purified metals. (R298/R4 2). (after W. A. Reed)

Al 26,000 Nb 5,000

Be 3,300 Ni 4,000

Bi 500 Pb 100,000

Cd 38,000 Pd 5,000

Cu 25,000 Pt 1,600

Cs 2,000 Rb 2,500

Fe 5,500 Re 55,000

Ga 100,000 Sn 100,000

K 12,000 Ta 15,000

Li 4,000 W

Mg > 100,000 Zn 40,000

Mo 12,000

950 850 750 650 550 450

4

2

10"^

8

64 2O

I 2 I

O< 10-9

8

64

2

io-'o

86

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

'q

Figure 4. Change in resistivity of gold after quenching from various temperatures (Tq). After Swalin [7].
14 TRACE CHARACTERIZATION

3. Superconductors

A number of effects in superconductors arise from impurity concentrations of a few percent or a few tenths of a percent; thus the superconducting transition temperature of various metals and alloys is decreased

by the addition of rare earth metals.

It has also been discovered that very much smaller impurity concentrations can be of great significance in superconductors. Thus when

molybdenum is sufficiently pure it becomes superconducting below

about 1 °K [8]. The transition temperatures for a number of samples

prepared in different ways are shown in Table 3. Table 3. Superconducting transition temperatures for various samples

of molybdenum.

Supplier Transition

temperature

(1) Johnson Matthey. "Specpure" Quality measured as received. The measurements showed the ac resist- ance of this sample to be at least several-fold greater

than the rest of the samples.

°K

None

(2) Johnson Matthey. "Specpure" Molten 15 seconds in arc furnace.

0.58

(3) Johnson Matthey. "Specpure" Molten 3 minutes in arc furnace.

0.92

A quantitative analytical characterization of these samples was not

possible, although the most significant impurity in determining the

transition temperature is iron, in the parts per million range. One part

per million of added iron is sufficient to prevent the quantitative meas- urement of the isotope effect in molybdenum, the isotope effect being

the change in superconducting transition temperature between the

separate isotopes of an element. Similar behavior is found in other

cases.

4. Ionic Conductivity

In insulating ionic compounds, the free electron and hole concentrations may be so low that the electrical conductivity is dominated by ionic

motions, despite their much smaller mobihties [3]. The mobility is closely related to the ionic diffusion coefficient, by the Einstein relationship. Since diffusion in ionic compounds usually proceeds via a vacancy
PROPERTIES OF MATERIALS 15

700 °C

.4 1.2 000/T (°K) Figure 5. Ionic conductivity of KCl with added SrCl2

or interstitial mechanism, the diffusivity, and therefore the conductivity,

depend directly upon the point defect concentration, and any changes

in this concentration will be reflected directly in these quantities.

It is, in fact, quite possible to change the point defect concentration

by simple chemical means, using the principle of charge compensation.

If a divalent cation is added to an alkali halide, for example, for every

added impurity ion there appears in the crystal a cation vacancy, to preserve the overall charge neutrality of the crystal. This is shown in Figure 5, which shows the effect of adding SrCl2 to KCl. At high temperatures the intrinsic, equilibrium concentration of vacancies outweighs

the contribution of the impurities, but at lower temperatures the conductivity is raised by the extra vacancies introduced with the Sr^+. In other ionic compounds (for example, silver halides) interstitial cations

dominate the conductivity. Anions can also be important.

B. Optical Properties

Optical properties of solids are sometimes closely related to electrical properties [3]. We noted in the preceding section that absorption,

luminescence, and photoconductivity in semiconductors may be due to the same impurities or defects which determine the electrical properties.

Similar kinds of centers affect the optical behavior of insulators.
16 TRACE CHARACTERIZATION

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Figure 6. Models for defects in alkali halides (O holes, # electrons).

1. Alkali Halides

Perhaps the most studied of these effects in insulators is the absorption in alkah hahdes arising from "color centers." Proposed models for a number of these are shown in Figure 6 [3]. Each kind of center has a

characteristic absorption spectrum, and the intensity of the absorption

is proportional to the concentration of the center. It is also possible to convert some of the centers into others. Thus if the F-center, which is

Figure 7. Conversion of F-center into F' -center by irradiation. Full line is F-band before

irradiation, dashed line shows absorption spectrum after irradiation.
PROPERTIES OF MATERIALS 17 an anion vacancy with a trapped electron, is irradiated at a wavelength

corresponding to the peak of its absorption, the peak gradually decreases

in size and at the same time the F '-band, peaked at a different wavelength, grows (Fig. 7). The reason for this can be seen from Figure 6. The F '-center differs from the F-center only in the number of attached

electrons; the absorption in the F-band, or "bleaching," ionizes the

center, releasing an electron which wanders through the crystal until it is trapped, either at another ionized F-center or at an un-ionized F-center.

In the latter event it produces an F '-center, with two trapped electrons. The absorption of light by simple chemical impurities or point defects

in semiconductors frequently leads to ionization, in a manner essentially

like the absorption due to F-centers in the alkah hahdes. The photoconductivity arising from this impurity ionization, as well as the absorption

process itseff, have been the subjects of intensive study in semiconductors and have yielded much fundamental information about defect

centers.

2. Luminescence

In the preceding section we referred to recombination processes for electrons and holes in semiconductors. Whenever electrons or holes

occupy states lying higher in energy than states which are empty, transi- tions wiU tend to occur so that the system can return to the equilibrium

condition; the characteristic decay time for this process is the "lifetime."

This recombination may involve, for example, the return of a conduction

band electron to an empty state in the valence band or on an impurity,

or of an electron from a fiUed impurity state to an empty state in the

valence band or on an impurity. It can occur with the loss of the excess energy to the lattice as heat, or as a radiative process — "luminescence."

A variety of methods may be used to raise the electrons initially to the

higher-lying states. These include electron bombardment, optical

excitation, electric field excitation, and excitation by a chemical reaction.

Thus electron bombardment furnishes the excitation for the active screen

materials ("phosphors") of cathode ray tubes, and optical and electricfield excitation are the principal means used in lasers. Phosphors are extremely sensitive to trace impurities [3]. These may

function as "activators," "co-activators," and "poisons." Many of the

important phosphors are very difficult to control chemically, not only

because of this dependency upon traces of chemical impurities but also because of tendencies toward nonstoichiometry and effects due to the

resulting lattice imperfections. A large effort has gone into the understanding and control of the chemistry of phosphors, much of it limited

in effectiveness by insufficiently good characterization methods.

The role of activators in two primary classes of phosphors may be

understood as follows. In the class illustrated by thallium-activated

alkali halides, the thallous ions, which are randomly distributed on cation

sites, are raised to excited electronic states by the absorption of energy
18 TRACE CHARACTERIZATION

in the excitation process. These then decay to their ground states with

the emission of radiation. In sulfide phosphors, such as ZnSiAg,

ZnS:Cu, and CdS:Ag, the excitation produces free electrons and holes. The hole is captured by the impurity center, with the emission of radiation. A later capture of a conduction electron restores the center to a neutral condition and prepares it again to perform its function in the

luminescence process. "Poisons" are impurities which provide unwanted recombination

paths for the holes and electrons. It has been demonstrated in germanium and silicon that recombination centers at concentrations of less than 10~^ can have very large effects, and so the detection and removal

of poisons, or recombination centers, can be a major challenge; impurities in sulfide phosphors in the ppm range have been shown to act as poisons.

"Co-activator" impurities may function in more than one manner. One, certainly, is to facilitate the incorporation into the crystal of the

activator impurities by providing charge compensation. Thus the

addition of trivalent cations to a II-IV compound improves the solubility of the monovalent activators, and the addition of monovalent anions

(Cl~, Br~) does the same. Another way a second impurity, or co- activator, can function is to modify the energy level of the activator

impurity.

The interaction of two impurities, in relation to luminescence, has been

examined in detail in the electroluminescent material GaP [9]. In this case the recombination leading to luminescence involves holes and elec- trons both bound to impurity centers, as distinct from the mode described

above involving a free carrier and an impurity center. An electron on

a donor impurity and a hole on a nearby acceptor impurity recombine

with the emission of light. The wavelength depends upon the energy

of interaction of the two charged impurities, and this in turn depends

upon their distance of separation. Since this is restricted to certain

values by the geometry of the crystal lattice (nearest neighbors, next- nearest, etc.) the impurity separation distances have certain, discrete,

allowable values. Assuming random distribution of the two impurities on their allowed lattice sites, a theoretical calculation of the positions

and intensities of the luminescence spectrum can be made by simply

calculating the coulombic interaction energy; the observed spectra show

a series of fines in quite good agreement with these values, as shown in Figure 8. In this case we see that the important information about

impurities involves not only their identities and concentrations, but also

(the distribution of) their distances of separation. C. Magnetic Properties

While many of the important magnetic properties of sofids are bulk

effects, there has been increasing reafization that there are important
PROPERTIES OF MATERIALS 19

phenomena which ^epend upon impurity concentrations well below the

tenths of a percent range. A good example of such an effect is the

ferromagnetic resonance line width in yttrium iron garnet (YIG) [10]. The Une width at low temperatures has been found to be about 6 oersteds

in normal single crystal YIG, prepared from ordinary yttrium oxide,

which contains significant concentrations of various rare earth impurities.

The spin-lattice relaxation times of these rare earth ions are such that they can appreciably affect the line widths in YIG. An extensive purification program led to the reduction of the rare earth impurity content

to less than 0.1 ppm, and YIG made from this material showed ferro- magnetic resonance line widths of the order 0.1 oersteds, about a

fifty-fold reduction. Still further improvements were achieved by the

removal of silicon down to the ppm range; this tetravalent impurity

reduces an equal amount of the host crystal ferric ions to ferrous because

of charge compensation, and these divalent irons also contribute to the

relaxation rate. The net result of this further purification was to reduce

low-temperature line widths by another order of magnitude (Fig. 9). Interstitial impurities, such as carbon, nitrogen, hydrogen and sulfur,

have important effects on bulk magnetic properties [11 J. In soft iron,

concentrations of these impurities in the hundredths or even thousandths

of a percent can change the permeability by one to two orders of magnitude. Also, aging effects in iron are dependent upon small traces of

nitrogen. Figure 10 shows that the permeability of iron containing

0.001% nitrogen hardly changes with aging whereas material with 0.005%

nitrogen showed a marked decrease in permeability upon aging. The

reduction is due to the precipitation of nitride from a supersaturated

solution, as the solubility limit at room temperature is of the order of 0.001%. The effect can be reversed by heating to higher temperatures,

as the nitride solubility increases with temperature.

D. Mechanical Properties

The mechanical properties of solids are critically dependent upon

structural imperfections. The electronic properties discussed in the

>200

2 100 I

>- 0

^LU t

in '

Ti i ii ilii i iii i i I

1

1 |l I I I II, I I h I ll I I L 2.23 2.24 2.25 2.26 2.27 2.28 2.29 PHOTON ENERGY (eV)

Figure 8. Observed and calculated frequencies and intensities for some of the emission

lines in GaP.
20 TRACE CHARACTERIZATION

Figure 9. Ferromagnetic resonance line width in YIG. (a) normal YIG, (b) rare earth

impurities removed, (c) silicon removed. After G. H. Morrison, "Trace Analysis,"

Interscience Publishers, New York (1965).

preceding sections have been seen to depend importantly upon chemical

impurities, and to a somewhat lesser extent upon point defects. Line

defects — dislocations — also affect some electronic properties but are

of less immediate concern. On the other hand, they are of paramount

importance to the mechanical properties. Chemical impurities sometimes play a major role here, while point defects are less important.

Area defects, are of several kinds; those which constitute gross dis- continuities, such as interphase boundaries or grain boundaries, have

major significance for most properties; the more subtle area defects,

such as tilt boundaries, twist boundaries, twins, and stacking faults are often outweighed in their effects by other structural imperfections,

and we will not be greatly concerned with them in this review.
PROPERTIES OF MATERIALS 21

It has long been recognized that the strengths of real crystals fall orders of magnitude short of those expected for a perfect crystal, which

should have an ultimate strength limited only by the magnitude of the

chemical bonding forces holding the solid together. It is, of course,

well known that dislocations provide the mechanism by which plastic

deformation occurs at yield stresses far below this theoretical limit. Dislocation-free whiskers of certain metals have been observed to show

elastic strains of more than a percent, at least two orders of magnitude

higher than the values for ordinary samples of the metals, before yielding.

It has also been possible to prepare large dislocation-free samples of

silicon and germanium, and to investigate their yield behavior [12]. Results for dislocation-free germanium as well as for samples containing

various dislocation densities are shown in Figure 11. It can be seen

that dislocation densities of the order of 10^/cm^ virtually eliminate the

upper yield point (dislocation densities of this magnitude are somewhat

lower than those found in ordinary samples of metals).

While very pure, nearly perfect crystals show exceptional yield

strengths, the presence of just a few dislocations will decrease the yield

point well below that of an ordinary metal, because the dislocation allows an easy shp mechanism and therefore plastic flow, and there is no

strengthening mechanism to prevent this deformation. Several mechanisms can block this slip resulting from individual dislocations, and

thereby lead to the actual strengths observed in practical metals, which

are intermediate between theoretical strengths for perfect crystals

and those with relatively few dislocations. One strengthening mechanism is the mechanical blocking of dislocation motion by small particles of a second phase (iron carbide in steel, for example). Grain boundaries can also block dislocation motion. Solute impurity atoms provide still another mechanism. They tend to collect in the vicinity of dislocations,

where the lattice is somewhat expanded, during the formation of the

metal at high temperatures which allow impurity mobility; at lower
i 22 TRACE CHARACTERIZATION

1 DISLOCATIO M FREE f

t^"^^ 9 .6 X102/CM2

i4x10~/CM2

lOVCM2 012345678 ELONGATION (per CENT)

Figure 11. Tensile deformation of Ge for various initial dislocation densities. After Patel and Chaudhuri [12]. temperatures they are immobile, and this impurity cloud pins the dis- location because the dislocation cannot move away from the impurities

without an increase in energy. Finally, when dislocations are present

in sufficient number, they can become interlocked and this accounts,

for example, for the work-hardening of even very pure metals.

It is apparent that the elucidation of mechanical strength depends

upon the control and characterization of the material with respect to line and area defects and chemical impurities. The advent of very

pure and nearly perfect materials has at least partly opened the door on fundamental studies of mechanical properties, and on the practical

realization of a number of mechanical properties which have long been

desired but were apparently beyond reach. We shall be interested in both aspects.

Looking first at some of the fundamental studies permitted by the

availability of high purity materials with low defect concentrations, we

saw in Figure 11 the effects of dislocations in the absence of chemical

impurities. The effect on the mechanical properties of a chemical

impurity, oxygen, has also been studied. Unless precautions are taken

in the preparation, silicon can contain appreciable quantities of dissolved

oxygen, which occupies an interstitial position bonded to two adjacent

silicon atoms. When the solid is heated at an appropriate temperature,

the oxygen clusters into -Si04- units, and at higher temperatures into

I
PROPERTIES OF MATERIALS 23

Si02 aggregates. Since the oxygen can be electrically active, electrical conductivity measurements reflect the changes in the structure of the

defect centers. There is also a change in the infra-red absorption spec- trum as each condition has a characteristic absorption behavior. The

maximum yield strength is also decreased substantially by the heat

treatment, and concentrations of a part per million or below are signi- ficant [13]. Extensive studies have been carried out on high-purity lead, to show

the effects of chemical impurities [111. Among the properties measured

were stress-strain, for ''pure" lead and for material with small amounts

of added silver (Fig. 12). The initial slope is steeper, reflecting a

stiffening of the lattice, and an increase in tensile strength clearly re- sults. The effect is due to the formation of a precipitated phase (recall our earlier remarks about the interaction of dislocations and a second

phase); the solid solubility of silver in lead has been exceeded at these

concentrations. In Figure 13 another property of lead is shown, the

dependence of tensile strength upon time, with and without added

arsenic. It is evident that a very small impurity addition rapidly ac- celerates the age hardening of lead. The recent progress in metal purification has had important implications for the practical applications of metals, especially the refractories,

which present great difficulties in fabrication [6]. Most of these effects are due to interstitial impurities such as oxygen, carbon, and nitrogen,

and frequently these are bound chemically so strongly that their removal

is difficult. When the purification is achieved, however, very large

3000

20 30 50 60 STRAIN IN PER CENT (iN 2 INCHES) Figure 12. Stress-strain in Pb. After Schumacher [11].

237-323 0-67—

4
24 TRACE CHARACTERIZATION

6500

MONTHS AGED AT ROOM TEMPERATURE

Figure 13. Age hardening of Pb. After Schumacher [11]. changes occur, and the material can frequently be worked easily. The

brittleness of ordinary tungsten is associated with impurities at around

200 ppm; with impurity concentrations reduced below about 10 ppm,

tungsten becomes ductile. Other refractory metals behave in a similar

way, upon purification. Among these is beryllium, as shown in Figure 14. The extreme difficulty in fabricating ordinary beryllium is well known,

and the development of such ductility is remarkable. The impurity

content of this bar, which has been bent by hand at room temperature,

is of the order of a few ppm. Still another example is titanium, which,

like beryllium, holds oxygen tenaciously. An order of magnitude

reduction in yield stress results from extensive zone refining. The

change in ductility with purity is shown in Figure 15 for two samples of

iron; one was vacuum melted, the other vacuum melted and zonerefined. Despite the somewhat larger grain size of the latter (which

would be expected to reduce ductility, in general), it had a much greater

elongation. In many of the studies of high-purity metals, including some we have

made reference to, chemical analyses are available only on the less pure

samples. The need for characterization of the pure materials is apparent.

E. Structural Transformations [14]

Closely related to mechanical properties are structural transform.ations. Many of these depend on atom movements in the solid phase.

The two primary mechanisms for diffusion in single crystals are provided

by the motion of interstitial atoms, and by vacancy diffusion. In the

latter case we observe that vacancy motion in a given direction is equivalent to the flow of host atoms on normally-occupied lattice sites (or of

substitutional impurities) in the opposite direction. Obviously, then, the
PROPERTIES OF MATERIALS 25

Figure 14. Ductility of pure Be. After Schaub and Cabane, Compt. R^nd. 257, (2), 444 (1963).

t(°k)

Figure 15. Ductility of pure Fe.

point defect concentration is of immediate concern in diffusion-controlled

phenomena. We saw an example of this in Section III.A.4, in our dis- cussion of ionic conductivity in alkali halides.

When grain boundaries, dislocations, etc. are present they may greatly

accelerate the diffusion rates. The general expansion and disruption
26 TRACE CHARACTERIZATION

of the lattice along grain boundaries results in high vacancy concentrations and increased inter-atomic spacings, and these increase diffusivities, as shown in Figure 16 [15]. Dislocations can provide sinks or sources for vacancies, and this also results in a change in diffusion

rates. At any temperature above 0 °K, there w^ill be an equilibrium number of vacancies and interstitials in any solid, and this can be calculated simply

from elementary statistical considerations, providing we know the

energy required to displace an atom from its normal substitutional site to an interstitial position, or to form the vacancy by breaking bonds and

removing an atom to the surface (there is an overall increase in entropy

which results from the disorder associated with point defect formations,

and an expenditure of energy to form the defects; at equilibrium the free energy is at its minimum)^ As noted earlier, vacancy concentrations are

of the order of lO^'^ in many metals. Point defects can also be intro- duced in a controlled way, in compounds, by suitable additions, and our

earlier discussion of ionic conductivity in alkali halides illustrated how

this can be brought about.

We now consider the general problem of structural transformations in solids and their relationship to diffusion process. The development of

a new structure, or phase, when the free energy change for such a trans10"" I \ \ \ \ \ 20 18 16 14 12 10 8 ioVt (°k)

Figure 16. Comparison of volume, surface and grain boundary diffusion, for self-diffusion of Ag. After Brophy et al. [15].
PROPERTIES OF MATERIALS 27

formation is favorable, involves two stages, nucleation and growth.

Nucleation may be homogenous, and result from fluctuations within a uniform solid. It may also be heterogeneous, being facilitated by the

presence of impurity inclusions, grain boundaries, dislocations, etc., for several reasons: homogeneous nucleation must overcome the extra

free energy required to form the new surfaces associated with the nuclei

of the new structure, and if a grain boundary is already present, the

interfacial energy of this existing boundary is available to help overcome

the free energy required for nuclei to form. Also, grain boundaries

and dislocations help relieve the stresses accompanying the nucleation

processes, and these stresses also involve a free energy increase which

must be overcome. Impurity inclusions in grain boundaries also may

catalyze a nucleation process. The second stage of a transformation is growth, and this results from

diffusion. In special cases the motion required is so small — of the order

of a lattice spacing or less — than this stage does not influence the kinetics of the overall process. A notable example of a "diffusionless" trans- formation is the martensitic, in steels. In general, however, the diffusion

processes discussed above govern the growth rate. A specific transformation system which illustrates both nucleation and

growth, as well as the role of defects, is provided by the precipitation of lithium from a supersaturated solution in silicon [16J. The results are shown in Figure 17: the amount precipitated is seen to depend on t^^- for the major part of the precipitation. This implies a spherically

symmetric diffusion to the nuclei of precipitated lithium, and therefore

indicates something about the nature of the nuclei. A different time

dependence would result from different geometries — dislocations, for example, which are common nucleation sites for precipitation (in fact, this provides a useful method for characterizing dislocations, by dis- location "decoration"). The four curves are for different samples, and

the variations in rate reflect differences in the number of nucleation

centers. Sample 2 originally had too few nucleation centers to show

any perceptible precipitation, and so the sample was then exposed to high energy electron bombardment. This produces a profusion of point

defects in solids, and the much faster rate of precipitation observed after the bombardment, together with the spherical symmetry found for the

diffusion field, imply that these defects provided the initial nucleation

centers. The rate of growth of the nuclei in a transformation may be altered by any factors which change diffusion rates. The introduction of vacancies, by bombardment or by the addition of appropriate chemical

impurities (see Fig. 5), can lead to changes in the diffusion rate. Also

the presence of a second chemical impurity which interacts with the

diffusing species can change the diffusion rate. Thus the precipitation

rate of lithium in silicon containing oxygen is greatly reduced, as shown
28 TRACE CHARACTERIZATION

TIME

0 2 4 6 8 10 12 14 16 (TIME)^^yiOO

Figure 17. Precipitation of Li in Si (four samples with different concentrations of nucleation centers). After Hannay [4].

in Figure 18, by an interaction of Li with the oxygen; this interaction

immobihzes a large fraction of the interstitial Li and effectively prevents

it from diffusing, as long as the interaction for any given interstitial Li

persists [17]. The diffusion coefficient is reduced by a factor repre- senting the fraction of Li which is un-bound, and therefore gives the

equilibrium constant for the reaction between Li and O. The effective- ness of dislocations as nucleation centers for precipitation is shown

by the data of Figure 19. Precipitation has been discussed as an example, to illustrate the

nucleation and growth features of a transformation, but other kinds of transformations depend upon the same general principles, and the role of impurities and structural defects is common to all. Many transfor- mations are of very great technological importance, and semi-empirical means have been used to achieve the desired practical results. An

understanding of basic processes in properly characterized materials

could accelerate this process. Thus the realization of the role of solid state diffusion in sintering, together with an understanding of the

principles by which trace additions of chemical impurities can interact

with the host compound through the charge compensation mechanism

to increase vacancy concentrations, have pointed the way to controlled

alteration of sintering rates. Likewise, recrystallization and grain

growth rates, so important in metallurgical processing, have been
PROPERTIES OF MATERIALS 29

1000

10"® lO""^ 10-6 ^Q-A OXYGEN CONCENTRATION

Figure 18. Precipitation of Li in Si containing oxygen. After Pell [17].

explored in terms of chemical purity. Figure 20 shows the recrystallization rate of aluminum, with various concentrations of added copper,

and reveals the extreme sensitivity to impurities [6]. It has even been

possible, in high purity metals, to study the migration of individual grain

boundaries. They have been found to be affected in an important way

by such factors as the angle between adjoining crystallites, certain angles

providing special points of juncture between crystallites where the

crystal structures become more or less continuous. The addition of an

impurity reduces the migration rate for these special boundaries less than for randomly oriented boundaries. While it is not yet possible to give a complete account of grain boundary motion in fundamental terms,

because of the lack of data in high purity systems, the realization of the necessity for high purity, well-characterized materials is a major

step forward.

F. Chemical Reactivity [18] Ordinarily one thinks of chemical reactions mainly in terms of gas and

hquid phase reactions. There are also certain important soHd phase

reactions, however. Conspicuous among these are corrosion, or tarnish

reactions, between a solid and either a gaseous or liquid reactant. The

mechanism by which such a reaction continues again involves material

transport in the solid phase, as the reaction would otherwise soon stop

as the product of the reaction began to develop at the interface and

separate the two reactants. This was demonstrated first in the classic
30 TRACE CHARACTERIZATION

TEMPERATURE (°C) 700 600 500 400

0.8 1.0 t.2 1.4 1.6 1.8 ioVtemperature {°K)

Figure 19. Precipitation of Cu in Ge, showing effect of dislocation density (Np). After Hannay [4].

experiment of Wagner, on the sulfiding of silver (Fig. 21). He demonstrated that after reaction, block II of the Ag^S had gained weight, block I of Ag2S was unchanged, and the block of Ag had lost weight, providing

clear evidence that silver had diffused through the product phase, with

the continuing reaction occurring at the sulfur-Ag>S interface.

Many other tarnish reactions can be understood in the same terms,

and this has led to an understanding of the kinetics of film growth.

Among the most studied of such systems is the oxidation of copper,

which, like the oxidation of a number of other metals, follows the parabolic law (film thickness proportional to t^''^) characteristic of tarnish

reactions which are rate-limited by diffusion through the product film. In the oxidation of copper, copper diffuses by a vacancy mechanism to
J

S !

AgsS *- n

AgaS *- 1 Ag

Figure 21. Experiment to show mechanism of the tarnish reaction sulfiding of silver.

the outer surface, where reaction occurs. More generally, vacancies

or interstitials might contribute to a tarnish reaction, and either (or both)

cation or anion motion might be involved.

A solid-solid reaction can be understood in the same terms. Thus

in the addition reaction of MgO and AI2O3 to form the spinel MgA104,

both AP^ and Mg-" diffuse, and in the double decomposition of CuX

+ BaO to form BaX2 and CU2O, the correlation of chemical reactivity

and point defect concentration (as measured by ionic conductivity)

has been well established. Thus in solid-state reactions, as well as in tarnish reactions, chemical control of point defect concentrations can

alter diffusion rates and therefore, also, the chemical reaction rates. For example, in the reaction of silver with bromine to form AgBr, the

addition of small amounts of Cd to the Ag accelerates the reaction be- cause the divalent cation. Cd-^. in the product phase introduces an

equal concentration of cation vacancies, for charge compensation.

This reduces the concentration of interstitial silver, the diffusing species.

Corrosion reactions between a solid and a liquid or vapor often reveal

another effect of structural imperfections, the enhanced reactivity of
32 TRACE CHARACTERIZATION

the solid in the places where the lattice is disrupted. Grain boundaries,

for example, may react in this way. Another reason for their enhanced

reactivity is that they may collect chemical impurities, for reasons dis- cussed earlier, and therefore represent a different composition chemically. Even a single dislocation produces a sufficient disordering of

the lattice to enhance reactivity, and this has been taken advantage

of in the detection of dislocations through the "etch pits" developed on

the surface at the points where dislocations intersect the surface, as a

result of chemical etching. Figure 22 shows the 1-to-l correspondence

in position of these etch pits with the points of intersection with the

surface of the dislocations, as revealed by "decoration" (discussed in the previous section) for a sample of silicon [19]. As just noted, grain boundary effects can accelerate the corrosion of

solids. Even more subtle variations or inhomogeneities in impurity

content between slightly separated regions of the soHd can also increase

the rate of corrosion, producing "local action cells". These operate

much like an ordinary storage battery; the driving force for the passage

of current, which is accompanied by the dissolution of metal in the local regions that are anodic, is provided by the difference in chemical

potential between regions of the solid with somewhat different impurity

contents.

Figure 22. Termination of dislocations in etch pits. Copper has been precipitated on

silicon dislocations, with photograph taken by transmitted infrared. After Dash [19].
PROPERTIES OF MATERIALS 33

Another familiar solid phase chemical reaction is the photographic

process. In the development of the latent image, metallic silver is nucleated in the silver halide. There must be a mechanism for the

transport of silver ions to the sites where metallic silver is formed, and

this is believed to be interstitial diffusion. Dislocations or grain boundaries may play a role, by providing preferred deposition sites. Chemical

impurities also are clearly important, as indicated by the role of sensitizers. Sulfur sensitization, for instance, apparently involves the

formation of Ag2S at the surfaces of crystallites, where they act as hole-traps and promote the formation of the interstitial silver needed

to continue the image formation.

In decomposition reactions nucleation of the product phase is important (note the resemblance of chemical reactions to transformations, in the importance of both nucleation and growth stages). The thermal

decomposition of KMn04, for example, is enhanced by pre-irradiation,

which shortens the induction time for the reaction (Fig. 23). The ir- radiation produces cation vacancies and interstitials, which then recombine with the release of energy. The local heating decomposes nearby

MnOj ions and increases the number of nuclei of the reaction product,

and the increase in nucleation sites effectively shortens the induction

period. G. Radiation Effects in Solids

We have already had occasion to mention a number of solid state phenomena dependent upon irradiation. A primary effect of irradiation

often is to produce point defects, and we have seen how these can pro- mote transformations or chemical reactions, either by supplying nucleation sites or by increasing diffusion rates. In Figure 24 we show

cr/B /a

TIME (MIN)

Figure 23. Shortening of induction period for thermal decomposition of KMn04, by

irradiation.
34 TRACE CHARACTERIZATION

Fii:ure 24. Schematic oi enlianced diffusion under irradiation: solid line is nitrmal diffu- sion, dashed line is enhanced rate in steady-state condition during bombardment. schematically how the diffusion coefficient can be enhanced by irradia- tion leading to vacancy formation. In the steady state, a concentration

of vacancies above that intrinsic to the crystal is produced in the low

temperature region.

A profusion of complex centers can be produced by irradiation, in addition to simple vacancies and interstitials. For example centers have been identified in sihcon [20| containing small amounts of oxygen

or of phosphorous corresponding to the following structures:

\ / \ /

\ / \ / \ / SI O Sl / \ / \ / \ SL Sl / \ / \

\ / \ / Si .P \ / \ '\ / Si Si / \ I . / \ Si Si / \ / \

In silicon with very low aluminum concentrations, ~ 10"'^, electron bombardment produces interstitial The mechanism suggested is the

primary production of vacancies and interstitial silicon, with later dis- placement of the (substitutional) Al by the mterstitial Si as it diftuses

through the lattice. Many other radiation damage centers are known,

also.
PROPERTIES OF MATERIALS 35

H. Surfaces

We have mainly been concerned with bulk properties of solids, but

it is obvious that many properties associated with the surface are of equal interest, and that the characterization of surface impurities and

defects is vital to progress in these areas. It is only within very recent

years that techniques for the analysis of surfaces have become available,

and already the rewards to be expected from their further development

are apparent. Techniques have been developed for the preparation

and maintenance for appreciable times of atomically clean surfaces,

for half a dozen or so materials. With this have also come techniques for surface characterization, of both the clean surfaces and those with ad- sorbed gases. Among these are flash desorption, field emission and

field ion microscopy, low energy electron diffraction (LEED), and high

resolution electron microscopy. LEED, for example, shows details of structure of the surface layers. While Ni atoms on a clean Ni surface

reflect the arrangement in the bulk, the two or three top layers in silicon and germanium show a complex rearrangement of the surface, with

displacement of atoms both sideward and normal to the surface (Fig.

25a). In an ionic compound, such as LiF, the anions and cations may

be displaced differently. With adsorbed gases, surface structures develop which may be quite unexpected. Thus, while iodine on silicon behaves in the expected manner, oxygen on nickel does not (Fig. 25b).

The relationship of the surface features, as shown by these new characterization techniques, to the physical and chemical properties, largely

remains to be established.

One vast area of interest in chemistry is adsorption and catalysis on

solid surfaces. Few major problems have so eluded efforts to gain a O TOP LAYER

O 2ND LAYER

• 4TH LAYER

• 6TH LAYER

ONI OXYGEN

o o o o o o

o • o • o •

o o o o o o

o • o • o •

o o o o o o

o • o • o • (b)

Figure 25. la) "Reconstructed" surface layers of clean silicon, (b) (100) face of Ni with one-quarter coverage by oxygen (only the top layer is shown).
36 TRACE CHARACTERIZATION

fundamental understanding as has the role of the solid in the catalysis

of chemical reactions. The new techniques for the characterization of

surfaces offer promise for the elucidation of the nature of the adsorbed

layer, and this is clearly a key feature in the understanding of catalysis.

Many attempts have been made also to relate the nature of the bulk solid

to its role as a catalyst, and while certain factors are found to be highly

suggestive, their generality has yet to be established and exceptions can be found. One such factor is the electronic structure of the solid, and

among the clues that have been noted is the semiconducting nature of a number of nonmetallic catalysts. This is thought to be related to the

transfer of electrons back and forth between the solid and the adsorbed

reacting species. The Fermi level in the solid determines the ability for this to occur, and this in turn is determined by the chemical composition, in the usual manner for semiconductors. This is illustrated by the

oxidation of CO to CO2 on NiO. The addition of monovalent ions, such

as Li + , converts an equal number of divalent nickel ions to trivalent ions,

making the material more p-type and lowering the Fermi level. The

addition of trivalent ions, such as Cr^+, removes trivalent Ni^+. The

effect of these additions on the activation energy for the reaction is shown in Figure 26 [21]. Another example of the possible relation of the chemical and defect

composition to the catalytic activity is provided by studies of the H2—D2

exchange reaction on MgO. The catalyst can be activated by irradiation

with y-rays. Electron spin resonance was used to measure the concentration of Fi-centers and there was found to be a strong correlation

between catalytic activity and -concentration as the activity induced

by the irradiation decayed, as shown in Figure 27 [22]. IV. Characterization and Properties

We have reviewed, in a way which was necessarily sketchy, some of

the relationships between the physical and chemical properties of solids,

and the trace quantities of chemical impurities or structural imperfec4 3 2 MOL % Cr203

2 3 4 MOL 7o LLO

Figure 26. Activation energy for the oxidation of CO on NiO with added impurities. After Schwab [21].
PROPERTIES OF MATERIALS 37

1.4 o

A 8

-

0

0 2 4 6 8 10 12 TIME (HOURS)

14 16 18 20

Figure 27. Annealing curves for ultraviolet-irradiated MgO. Ordinates show -con- centration and catalytic rate constant, following the irradiation. After Lunsford [22].

tions which are present in every real material. As we noted earlier, a primary goal of materials preparation and characterization is to facilitate the development and understanding of these relationships. We see

constantly examples in all areas of solid state science and technology

where our abihty to control or comprehend properties is limited by our

inability to do a good enough job of characterization.

We have endeavored, in our choice of examples to illustrate the rela- tionships between properties and trace impurities and structural defects,

to bring out a few of the areas where improvements in characterization

are needed. In the area of electronic materials, for example, the efforts

to study and utilize new semiconducting compounds, of fundamental

research interest or with promising electrical or optical properties for the rapidly growing array of new semiconductor devices, would be

greatly aided by better techniques for extremely low concentration of chemical impurities. Magnetic materials research and development is hampered by our rather crude techniques for determining valence state. Equally poor techniques for stoichiometry determination affect work with

many compounds of interest as electronic materials. Surface effects are of great importance in devices for integrated circuits, and here again our characterization techniques are quite inadequate.

In the area of structural materials we have a pressing national need

for new materials, with improved capability for high-temperature per- formance, or which have high strengths combined with light weights.

We have already noted the intimate dependence of the mechanical

properties of the refractory metals, which of course are of particular

interest for such applications, on purity and perfection, and we are led

to compare our relatively poor analytical techniques for the light ele- ments, such as carbon, nitrogen, and oxygen, with the predominant role of these impurities in the refractory metals. Another pressing national

need in the materials area has to do with the degradation of materials.

Corrosion and oxidation are extremely costly — for example, 25% of our
38 TRACE CHARACTERIZATION

Steel production has been said to be for the replacement of corroded

equipment — and it often is impurity dependent. Polymeric materials

degrade, and we are so unable to characterize them, as a class, that our approaches to the control of polymer degradation often have to be

Edisonian. Radiation damage phenomena involving defects in solids are important in materials ranging in application from nuclear reactors

to electronic devices in satellites. Thus we find that all areas of solid state research and technology have

broad regions where we are limited by the materials we have available

and our abiHty to control them chemically and structurally. It is ap- parent that improved characterization is an indispensable part of the

materials work needed to permit further advances in these areas. V. References

[1| Report of the Committee on Characterization of Materials, of the Materials Advisory Board (to be published).

[2 1 After H. W. Leverenz.

[3] See, for example, C. Kittel, "Introduction to SoHd State Physics," John Wiley & Sons, New York (1956): A. J. Dekker, "Solid States Physics," Prentice-Hall, Englewood

Cliffs, N.J. (1957).

[4| See, for example. "Semiconductors," N. B. Hannay, Ed., Reinhold Publ. Corp., New York (1959).

[5| "Chemistry of Imperfect Crystals," F. A. Kroger, Interscience, New York (1964).

[6 1 See, for example, "Ultra-High Purity Metals," The American Society for Metals, Metals Park, Ohio (1962).

[7| See "Thermodynamics of Sohds," R. A. Swahn, John Wiley & Sons, New York (1962).

[8] B. T. Matthias, T. H. Geballe, E. Corenzwit, and G. W. Hull, Jr., Phys. Rev. 129,

1025(1963).

[9| D. G. Thomas, M. Gershenzon, and F. A. Trumbore, Phys. Rev. 133, A269 (1964).

[10| E. G. Spencer and J. P. Remeika, Proc. Intermag. Conf., T-159, IEEE, Washington,

D.C. April, 1964.

[1 1 1 See, for example, E. E. Schumacher, Trans. AIME 188, 1097 (1950).

[12| J. R. Patel and A. R. Chaudhuri, J. Appl. Phys. 34, 2788 (1963).

[13| J. R. Patel, Discussions Faraday Soc, No. 38, (1964).

[14| See, for example, "Introduction to Solids," L. V. Azaroff, McGraw-Hill, New York

(1960).

[15| See "The Structure and Properties of Materials," (Vol. 2 — "Thermodynamics of Structure"), J. H. Brophy, R. M. Rose, and J. Wulff. John Wiley & Sons, New York

(1964) . [16| F. J. Morin and H. Reiss, J. Phys. Chem. Solids,3, 196(1957).

[17| E. M. Pell, in Symposium on Solid-State Physics and Telecommunications, Brussels,

1958, Desirant and Michiels, Ed., Academic Press, New York (1960).

[18| See, for example, "Reactivity of Solids," J. H. de Boer Ed., Elsevier Publ. Co., Amsterdam (1961): "Chemistry of the Sohd State," W. E. Garner, Ed., Butterworths

Scientific Publications, London, (1955).

[19| W. C. Dash, j: Appl. Phys. 27, 1193 (1956).

[20| "Radiation Damage in Semiconductors," Paris, 1964. Academic Press, New York

(1965) . [21 1 G. M. Schwab, "Semiconductor Surface Physics," Univ. of Pennsylvania Press, Philadelphia (1957).

[221 J. H. Lunsford, J. Phys. Chem. 68, 2312 (1964).
ELECTRICAL MEASUREMENTS FOR TRACE

CHARACTERIZATION

LEONARD R. WEISBERG

RCA Laboratories, Princeton, New Jersey 08540

I. Introduction

The use of electrical measurements for trace characterization has

evoked considerable interest in recent years [1-3].^ There is httle question that if electrical measurement apparatus were available commercially today in a form where the sample could be inserted, a button

pushed, and the results presented on a chart, these techniques might

already be in wide use. However, this is still in the future, since they

are really laboratory methods. The doubt justifiably arises in the

minds of analytical chemists whether or not these techniques are of value, or if they might involve more effort than they are worth. In short,

this is a question of complexity versus utility.

This is certainly an important question, and to answer it better, this paper is divided into two distinct parts. In the first part, the value of

electrical measurements to the analytical chemist will be discussed.

In the second part, the fundamental principles of these methods will be

reviewed, and techniques and apparatus necessary to carry out these

measurements wiU be described. It will be seen that the simplicity of both the apparatus and interpretation is an important feature of these

techniques.

It is particularly significant here that this is the first of a series of symposia on Materials Research. The electrical measurements to be

discussed were spawned in and by materials research; and, as will be

seen later, the interrelationship of analysis with materials research

determines whether or not they should be used in an analytical laboratory.

II. Value of Electrical Measurements for Analysis

A. Criteria for Analytical Use

We first consider what the criteria are for introducing new instruments

into an analytical laboratory. We can determine this by examining those

instrumental techniques that are presently in use, which include instru- ments for emission spectrography, mass spectrography, electron spin resonance, nuclear magnetic resonance, electron probe microanalysis,

'Figures in brackets indicate the literature references at the end of this paper. 39
40 TRACE CHARACTERIZATION

and electron microscopy. What are the common features of these

instruments?

Their most outstanding feature is that they are enormously expensive—

their prices range between $25,000 and $100,000. In fact, none of these

techniques were acceptable until they became expensive — i.e. until a

large effort had been invested in engineering and automating their operation. Thus, we can conclude that cost is not an important factor here,

and instead that the first criterion for a new measurement technique is simplicity of use. The second most important feature is that each measurement has

special advantages, that extend the range or speed of analysis over

previous instruments. This is clearly manifest in the above mentioned

instruments. For example, the mass spectrograph can detect a very

wide range of impurities at one to two orders of magnitude lower concentration than the emission spectrograph.

The third common feature is that each instrument is self-sufficient, i.e. that the defects can be specifically identified in any given matrix, without

requiring supporting information. Therefore, each instrument can

provide a meaningful characterization by itself. B. Characteristics of Electrical Measurements

How well do electrical measurements fulfill these three criteria: simplicity, special advantages, and self-sufficiency? Let us consider

the advantages and disadvantages of electrical measurements in this Hght.

First, we consider the question of simplicity. Here we mean both

simplicity of measurement, and simplicity of interpretation. There

are many electrical properties known that are dependent upon the pres- ence of impurities. Some of these are listed in Table 1, and are also discussed in the paper by N. B. Hannay of this conference. However,

for most of these, the effects are not well enough established to permit

either simple measurement or interpretation. In many cases, results can be ambiguous, especially when the material is structure sensitive. For example, it is well established that impurities can affect the super- conductive transition temperature. However, even if one were told that there were three samples of NbsSn, with transition temperatures

of 18 °K, 17 °K, and 16 °K, one could draw no specific conclusions con- cerning their impurity concentrations since this variation could be caused

by lattice defects. The same sort of problem exists with dielectric relaxation, space charge Hmited currents, cyclotron resonance, internal

friction, and magneto-acoustic absorption. Magnetic properties are

so highly structure sensitive and dependent on major constituents that trace impurities are not easily detected, except in special cases. However, these methods should not be considered out of the question. As

further research is carried out, some of these methods might attain great
ELECTRICAL MEASUREMENTS 41

Utility. For example, later in this book, papers are given on trace characterization by measuring dielectric properties, and by thermoelectric

measurements.

Thus, for routine and simple use in an analytical laboratory, one

should presently consider only the first four properties hsted in Table 1. Each of these requires simple apparatus, and can be constructed using

commercially available instruments. The cost of constructing any of

of these should be below $5,000, and require perhaps about a month

to build and put into operation. Finally, these four techniques cover

the full gamut of electrical properties, including metals, semiconductors,

and insulators.

We next consider self-sufficiency. Unfortunately, the main disadvantage of these electrical measurement techniques is that they are

non-specific — i.e. in general, impurities are not identified by the measurement. Effects of different impurities can be separated in some electrical measurements, but in these cases, the electrical behavior of the

impurity is a function of its matrix. In fact, when effects from different

impurities are not separated, only the dominant impurities are then

detected, and this is a masking problem that can't be avoided. Next,

since it is generally not known which impurity provides the effect, unambiguous impurity concentrations cannot be determined using electrical measurements. Finally, lattice defects can produce electrical effects similar to those of impurities, and many impurities are not electrically

active, which prevents absolute impurity measurements. Instead,

electrical measurements must be used as an analytical tool in conjunction with other main analytical methods. In fact, these measurements

Table 1. Impurity Dependent Electrical Properties.

Resistivity

Residual Resistivity

HaU Effect

Thermally Stimulated Currents

Space Charge Limited Currents

Thermoelectric Power

Dielectric Relaxation

Piezoelectricity

Internal Friction

Cyclotron Resonance

Magneto-Acoustic Absorption

Superconducting Properties

Critical Temperature

Critical Current

Magnetic Properties

Permeabihty

Ferromagnetic Resonance Line Width
42 TRACE CHARACTERIZATION

must be calibrated at higher impurity concentrations versus standard

analytical procedure, before their results can be extrapolated to low concentrations. They can never independently provide a meaningful characterization of trace impurities. Thus, electrical measurements fail the criterion of self-sufficiency.

Turning to the last criterion, special advantages, here electrical meas- urements excel, surpassing all other analytical methods in several

respects, listed in Table 2. Their sensitivity is outstanding, easily

entering the part-per-billion range (i.e., 1 atom in 10^). This is the

most important feature of electrical measurements, and by itself justifies

their use. In addition, their relative precision is very high, within 10%,

which is especially important when comparing impurity concentrations

between samples. Next, they are non-destructive to the sample — i.e., the sample is not consumed during the measurement process. Finally,

the analysis requires a relatively short time — typically from 1 to 100

minutes. The combination of these four properties fully satisfies the

last criterion.C. Applications of Electrical Measurements

We have discussed that four electrical measurements, resistivity,

residual resistivity. Hall effect, and thermally stimulated currents, only

partially satisfy criteria for widespread use in an analytical laboratory.

However, because of their special advantages, they still have potential

value in an analytical laboratory, and the question that arises concerns

exactly where they can be used.

The answer to this question can be found by referring again to the

Table 2. Advantages of electrical measurements.

(1) Very High Sensitivity (to 1 part in 10^)

(2) High Relative Precision (10%)

(3) High Speed (1 to 100 min.)

(4) Non-Destructive to Sample

underlying theme of this Symposium — materials research. Since these

electrical measurements were spawned by materials research, we must

ask the materials researchers where these techniques have been most

useful. Experience here has disclosed three main applications: deter- mination of over-all purity, monitoring purification, and delineating

impurity distribution. In none of these applications is the identification of an impurity essential. These three applications are best described

by presenting some case histories taken from the annals of materials

research, where use of electrical measurements have played a crucial

role. It wiU be seen that, in general, electrical measurements are most

important at very low impurity concentrations, where many other analyti- cal techniques fail.
ELECTRICAL MEASUREMENTS 43

Example 1: General Principles — Purity of Water

First, for illustration, we will consider an example familiar to all analyti- cal chemists — the determination of water purity by resistivity measurements. This example clearly illustrates all the features, both good and

bad, described above for electrical measurements.

Pure water has a resistivity of about 3 X 10^ ohm-cm at 18 °C, and the

resistivity decreases approximately in direct proportion to the ionic

concentration, as shown in Figure 1. The resistivity of a water sample

is determined by dipping commercially available electrodes into the

sample, and reading the resistivity or conductivity from a standard

bridge circuit. Analytical results can be found within a minute, with

a detection hmit below 1 ppm, and an accuracy of a few percent, without

destroying the sample. The apparatus costs only about $100.

The disadvantages are also clearly shown here. Not all impurities

affect the conductivity of water equally, (e.g., Li+ has a mobility an order

of magnitude below H+) and some provide almost no ions at all, such as organic impurities. Thus, the analysis measures only the general

minimum impurity content, and also no knowledge is derived concerning

the identity of the impurities.

Even though the measurement does not fully characterize the purity

of water, the value of the measurement is manifest. One merely has to ask how much time the analytical chemist would have to spend to continually check the purity of water before carrying out other tests, or

.001 .01 .1 I 10 100 PPM OF KCI

Figure L Variation of resistivity with impurity concentration in water at room temperature, (ppm = parts in 10^).

237-323 0-67—
44 TRACE CHARACTERIZATION

to continually determine if a water distillation apparatus was functioning

properly. Countless hours have been saved through the years by the use of this method.

Example 2: Purification of Gallium and Aluminum

One of the most annoying problems in materials research is to perform

a careful purification procedure, and then not know whether or not it worked. Indeed, this problem is encountered quite regularly in the

ultrapurification of metals, when the total impurity concentration is reduced below the order of 1 ppm. At this level, there is no convenient

analytical technique to rapidly detect a broad range of impurities for a

large number of samples. Therefore, progress in purification is badly

impeded. For example, if one is using a chemical treatment to clean

material, one would like to know whether one, three, or ten treatments

are necessary, or even harmful. Another purification treatment is to directionally solidify or zone refine a material in a boat. One hopes that impurities are swept to the tail end of the ingot, but this procedure must

be monitored.

In the purification of gallium and aluminum, residual resistivity meas- urements (described later) played a very important role. In the case of

gallium, the procedure used was directional freezing. Subsequent to freezing, samples were removed from the ingot for emission spectrographic analysis [4], and the results found are shown in Table 3. Despite

very careful emission spectrographic analysis, no variation at all could

be seen along the ingot. However, referring to the last column of the

table, use of residual resistivity measurements clearly showed that the

front end of the ingot was, indeed, purer than the tail end, even though

the difference was less than a factor of two. Use of residual resistivity

measurements actually saved months of work in gallium purification.

Table 3. Variation of impurity content (in ppm) along a directionally

solidified gallium bar.

(After Kramer and Foster [4])

Cu Sn Pb Hg Zn Al Fe Mg Ca Si ^300

R4.2

Front 0.1 nd* nd nd nd 0.1 nd 0.01 0.1 nd 44,000

Middle 0.1 nd nd nd nd 0.1 nd 0.01 0.1 nd 39,000

Tail 0.1 nd nd nd nd 0.1 nd 0.01 0.1 nd 30,000

*Not detected.
ELECTRICAL MEASUREMENTS 45

In the above method, the zone refined ingot must be sectioned to provide samples for measurements. However, this can be avoided.

The ingot can be preserved by placing electrical leads along its length

[5, 6], as shown in Figure 2. Current is passed through the bar, and the

resistivity of any section is determined from the potential drop between

sets of leads. The results for the variation of residual resistivity in zone

refined aluminum [5, 6] is shown in Figure 3. Again, the effect of purification is clearly demonstrated.

Example 3: Impurity Distribution in Germanium

In the above examples, the high sensitivity of electrical measurements

was the major factor determining their use. In the example here, the

high relative precision of the. measurement technique is the significant feature. The dependence of resistivity of germanium on the impurity

content is shown in Figure 4, where a donor is an impurity that can contribute a conduction electron to the sohd. This figure is quite similar to Figure 1, and this is not accidental, but occurs because impurities in a semiconductor are very analogous to ions in a solution. Not only is the

extreme sensitivity manifest here, but above 1 part in 1(F, the resistivity

varies Hnearly with impurity concentration. The resistivity is easily

measured to a relative precision of 2%.

The control of impurity distributions in semiconductors is an extremely

important problem, not only technologically, but also since it can provide

important information concerning the fundamentals of crystal growth

mechanisms. To impart desired characteristics to a semiconductor,

selected impurities are deliberately added to the semiconductor. In growth from the melt, the impurity can be added to the melt before

growth, but then the impurity is segregated to the tail end of the ingot.

CURRENT LEAD

Figure 2. Position of current and potential leads on an ingot for residual resistivity measurements.
46 TRACE CHARACTERIZATION

3000

500 - MATERIAL

0 2 4 6 8 10 12 POSITION ALONG INGOT(INCHES)

Figure 3. Residual resistance ratio of aluminum, zone refined with 20 passes of two zones.

iOO

i 10

1.0 —

I \\\ I I TT

.L_L ^'o.l LO 10 100 1000 DONOR IMPURITY CONCENTRATION (PART PER BILLION, ATOMIC)

Figure 4. Variation of resistivity with donor impurity concentration in germanium at room temperature (parts per billion= parts in 10*^).

While this may be desirable if one is purifying, it is a^desirable if one

tries to achieve highly uniform properties.

After growth, the impurity distribution along the entire length of the

crystal can be rapidly and accurately determined by measuring the

resistivity [7], as is shown [8] in Figure 5, curve (a). By using special

growth techniques to correct for the impurity segregation [8], the impurity

distribution was then held constant to within about 20% over a 20 cm

portion of the ingot, as shown in Figure 5, curve (b). Comparing Figure
ELECTRICAL MEASUREMENTS 47

1 1 r I 1 I r T 1 r

J L

5 10 DISTANCE FROM SEED END(Cm)

15 20

Figure 5. Variation of impurity concentration, as revealed by resistivity measurements,

along the length of a single crystal of germanium grown by (a) ordinary Czochralski method, and (b) special Czochralski method.

5 10 DISTANCE ACROSS END OF CRYSTAL (mm)

15

Figure 6. Radial variation in impurity concentration, revealed by resistivity measurements,

in a germanium single crystal (a) before and (b) after optimizing the thermal gradient.

5 to Figure 4, it is seen that the impurity concentration was easily

measured here to a high relative precision in the range of 5 to 50 parts in

10^. Indeed, the corrected impurity distribution (Fig. 5, curve (b)), was

actually measured to be held constant to 2 parts in 10^ over a 20 cm

length! This remarkable measurement cannot be even approached by

ordinary analytical techniques.
48 TRACE CHARACTERIZATION

J \ \ I 0 0,5 I 1.5 2 2.5 DISTANCE (mm)

Figure 7. Fluctuation in impurity concentration in germanium as revealed by resistivity measurements.

Let us turn up the "magnification" a bit further. In Figure 6 is shown

the radial variation of resistivity, before and after correction [8]. One

division in Figure 5 is equivalent to 2/3 of the entire Figure 6, so that we

are seeing here impurity variations over a fine scale. Even smaller

variations can be seen. In Figure 7 is shown a periodic fluctuation in impurity distribution [9], again detected by resistivity measurements.

The points in Figure 6 are so far apart that this effect would have gone

unnoticed! Note that impurity variations can be seen in distances as small as 0.1 mm in the impurity concentration range below 1 ppm.

Furthermore, the ingot is not damaged by the measurement. Such a measurement by ordinary analytical techniques would be a hopeless

task. Even electron microprobe analysis would not work here, because

the impurity concentrations are too low. Once again, the point here is that not only were many man-months

saved by these measurements, but also that an analytical laboratory could

well be overwhelmed by confrontation with such a task, without using

resistivity measurements.

Example 4: Over-all Purity in GaAs

The purpose of this example is to illustrate how electrical measure- ments are enhanced by coupling them with standard analytical

techniques.

Hall effect measurements (discussed later) are more difficult to per- form than resistivity measurements, but provide a more direct measure- ment of the impurity concentration. They are quite important in semiconductors in accurately surveying the overall purity. In 1958, Hall measurements indicated that 0.1 to 100 ppm of impurities were in GaAs, and varied from sample to sample. The impurity level could not be controlled since the impurity source was unknown. Sulfur was suspected to be the major impurity, since it is a major impurity in the arsenic. Accordingly, a considerable time of unrewarding effort was

spent developing a sufficiently sensitive wet chemical method to detect

sulfur, but this just showed that sulfur was not the suspected impurity.
ELECTRICAL MEASUREMENTS 49

It was also obvious that tracking down other suspected impurities by

quantitative analytical procedures would be too time consuming. In- stead, semiquantitative emission spectrographic data was accumulated

on nearly 100 samples of GaAs, and compared to the Hall effect electrical data [10]. The result is shown in Figure 8, in which it is seen that a oneto-one correspondence existed between the concentration of silicon and

the electron-carrier concentration.

Using this result, the entire course of the GaAs research program

was altered, since the Hall effect measurement could then provide

meaningful and highly accurate information concerning the purity of the

samples. A Hall measurement can be carried out in about 30 minutes,

and provides a measure of the silicon concentration at and below 1 ppm

to an accuracy of ±20%, using a sample weighing about 1/2 gram, and

not destroying the sample. Several crystals were grown per week, and

several samples were removed for analysis from each crystal. It is easily seen that performing highly accurate quantitative analysis in this low concentration range could be problematical for an analytical lab- oratory, if Hall measurements were unavailable.

I 10 100 SILICON CONCENTRATION(ppnn)

Figure 8. Variation of electron concentration with silicon concentration in GaAs single

crystals. Horizontal separation of solid lines indicate limits of accuracy of semi-quantitative emission spectrographic analysis for sihcon (ppm = parts in 10^).
50 TRACE CHARACTERIZATION

III. Fundamental Principles and Apparatus

A. Fundamentals

Each electrical measurement is useful for only a particular class of

materials depending upon its electrical resistivity, as indicated in Table 4. This difference is not superficial, but is related to the way

the impurities affect the electrical properties, which differs in each

case, as is also shown in Table 4.

Table 4. Detection of impurities by their electrical effect in materials

of different resistivities (p).

Method Material Effect of impurities

(1) Residual Metals Scatters current carriers

resistivity (P < 10-^) (lowers mobility).

(2) Resistivity, Semiconductors Adds current carriers

Hall effect (10-4 < p < 104) (electrons, holes, ions).

(3) Thermally stimu- Insulators Traps current carriers. lated currents (p > 104)

In metals, there are so many electrons ordinarily present that they

swamp out any electrons possibly contributed by, trace impurities.

Instead, the important feature is that the impurities can scatter elec- trons, thus raising the electrical resistivity. However, the lattice itself also scatters electrons, and this effect dominates at room temperature.

By reducing the temperature to liquid helium temperature (4.2 ° K), the

effect of scattering of electrons by the lattice is reduced to the point

where it no longer dominates. Then, as shown in Figure 9, the resistivity

is determined by the scattering of the electrons from the impurity

atoms. The purer the material, the higher is the electron mobility,

and the smaller is the resistivity. It was noticed 100 years ago by Matthiessen that the resistivity due to the addition of impurities is ap- proximately temperature independent. Thus, the presence of impurities usually provides a low temperature limit to the resistivity, and

this limit is termed the residual resistivity. The measurement of

resistivity (or conductivity) at 4.2 °K thus provides a sensitive measure

of impurity concentration.

In semiconductors, in contrast, there are relatively few electrons present, and each electron added by impurities has an appreciable effect, so
ELECTRICAL MEASUREMENTS 51

that a direct correlation exists between electrically active impurity concentration and resistivity. Impurities in semiconductors can be fruit- fully compared to ions in solution. This is clearly seen by comparing

Figure 1 for impurities in water to Figure 4 for impurities in germanium.

Concerning insulators, there are almost no current carriers available

at aU, and trace impurities far outnumber the current carriers, which

is the reverse of the condition for metals and semiconductors. However,

in insulators, impurities can act as traps, i.e., they can capture a cur- rent carrier for a certain length of time before releasing it. This occurs because the ionization energies are large and the ionization constants

are small. One then utilizes the trapping effect of impurities to detect

their presence.

Thus, the fundamental quantities affecting the electrical meas- urements are the concentration per cm^ of current carriers, n, the mobility of the carriers, fx, and the concentration of electrons released

by traps, nr. In general, the relation between the resistivity p, n, and /X is given by

where e is the electronic charge. We must distinguish between the

electron concentration n and the impurity concentration N. In a metal,

as mentioned above, n is constant with impurity concentration, so that p is inversely proportional to p,, and p is inversely related to the impurity

concentration A'^. Unfortunately there is no general expression relating

p and N, since the impurity scattering depends upon the particular

impurity and the lattice it is in. Therefore, the residual resistivity

gives only a general and relative measure of the impurity content. One

n=ll{pefJL) (1)

10 100 1000

T(OK)

Figure 9. Variation of resistivity with temperature in a metal.
52 TRACE CHARACTERIZATION

Other restriction on its use should be noted — it cannot be used for metalHc alloys. The presence of the alloying element scatters electrons,

and this masks the presence of trace impurities.

For semiconductors, the situation is simpler. To a first approximation, one can assume that ju, is a constant independent of impurity

concentration. Then n varies inversely with p, and since the impurity

concentration N=n, N then is inversely proportional to p. However,

it is not always true that /x is independent of N. This problem of assuming constant mobihty can be eliminated by

using the HaU effect. An interesting analogy can be drawn between

a Hall effect and a pH measurement. A pH measurement determines the

concentration of ions in a solution, while a Hall measurement determines

the concentration of charge carriers in a solid. However, the method

of measurement is completely different. Here one adds a magnetic

field H across the sample of thickness t, and passes a current through

the sample. The magnetic field deflects the current causing a trans- verse voltage, the Hall voltage Vh, to be set up across the sample, and

this voltage is easily measured. As shown in standard deriviations [11], the concentration of current carriers, and hence the impurity concentration, is given by:

where Vh is expressed in volts, t is the sample thickness expressed in cm, / is the current through the sample in amps, e=1.6XlO~^^ cou- lombs, and H is the magnetic field in gauss. By comparing Eqs. (1) and (2), it is obvious that measurements of both the Hall effect and the

conductivity provides the HaU mobihty /jl of the dominant species:

When p is expressed in ohm-cm, /jl is expressed in the convenient

laboratory units of cm^/volt-sec. The mobility serves as an additional measure of the impurity concentration of a semiconductor both at room temperature, and especially at low temperatures (e.g. 77 °K).

This is demonstrated in Figure 10 for the case of germanium at room

temperature.

In the case of insulators, the important feature is that the escape of charge carriers from a trap is a temperature activated process, and

varies as exp {—ElkT), where E is the activation or ionization energy

associated with each trap, k is Boltzmann's constant, and T is the

absolute temperature. If a trap is filled at low temperatures (e.g. below 78 °K), the carriers cannot escape except after very long times

(hours or even days). Thus, one can "charge up" the traps by shining

hght on the sample at 78° K. Then, as the temperature is raised, a

n = IHlO-^IVHet (2)

p. = l/(Aiep) (3)
ELECTRICAL MEASUREMENTS 53

0.001 0.01 0.1 1.0 10 DONOR IMPURITY CONCENTRATION

100 1000 PPM, ATOMIC)

Figure 10. Variation of electron Hall mobility with donor impurity concentration in ger- manium at room temperature (ppm = parts in 10^).

temperature is reached at which the electron can escape rapidly. When

the electrons escape from eaeh type of impurities, a current can suddenly flow in the sample if a voltage is applied, called the thermally

stimulated current (TSC), causing a ^'TSC peak" in the variation of current versus temperature.

As the sample is heated, the current flows during a TSC peak for a given length of time. By integration of the area under the TSC peak,

the total number of electrons that have flowed through the sample can

be counted. However, this is not the number of electrons that originally escaped from the traps. The ratio of electrons that escaped to those that were actually counted is measured by generating a known

concentration of electron-hole pairs Npc in the sample per unit volume

per sec. This is accompHshed by shining a caUbrated Hght source on

it and measuring the photocurrent A/. The trap (i.e. impurity) concentration N per cm^ is then given by:

N= NtscNpcIM (4) where Ntsc is the number of electrons derived from the integration of the area under the TSC peak. Although this measurement is somewhat

more complex than the previous methods, this is a very powerful and

useful tool. We proceed below to the apparatus needed for the four measurement

techniques.

B. Resistivity

The sample to be measured can be either liquid or solid, and monocrystalline or polycrystalline, unless electrical barriers are known to form at internal boundaries. The main problem exists in making good

contacts to the specimen [12], i.e. both ohmic and low resistance. For
54 TRACE CHARACTERIZATION

purposes of discussion here, a contact is ohmic when its resistance is independent of direction and magnitude of the current. All measure- ments of conductivity should be carried out at least twice, with the current flowing in each direction to check for such spurious effects. In liquids, to minimize polarization and related effects, AC measure- ments are required.

The method employed for the measurement depends on the resist- ance of the formed contact. If the contact resistance is negligible

with respect to the sample, then only two contacts are needed to the

specimen. The resistance is determined by measuring the current

flowing through the sample when a known voltage is applied. A commercial resistivity meter can be used for this measurement if high

accuracy is not essential. Alternatively, the sample can be placed

in a resistivity bridge. The resistivity p is found from the resistance

R by the relation

where L is the separation between the contacts, A is the cross-sectional

area, and it is assumed that this area is constant throughout the sample.

It is possible to determine resistivities without knowing the sample

dimensions, such as for irregularly shaped specimens, by using a four-point resistivity probe, as shown in Figure 11. For many materials,

all that is necessary is to press the probe against the sample, independent

of the shape and size of the sample, provided the sample is large enough

with respect to the probe spacing, so the sample can be assumed infinite. The current is passed between the outer two probes, and the voltage

measured between the inner two. The resistivity is given by

where d is the spacing between each pair of adjacent electrodes, V is the voltage and / the current. Probes with very small spacings can be

constructed. In Figure 11, the contacting wires can be 0.003 in. di- ameter tungsten wires with sharp points, and the spacing d can be

0.010 in. With such a small probe, one can detect variations in re- sistivity at different positions throughout a sample (e.g., see Fig. 5). One simplifying feature here is that four-point probes for resistivity

measurements are now commercially available, such as from the Dumas

Company or the Fels Company (England).

A preferred method of measuring variations in resistivity along a sample is to use a resistivity "scan" procedure [7]. As shown in Figure

12, the current is passed thru the sample, while a probe moves along the

surface to measure the potential drop. This measurement is easily

automated by measuring the potential drop on a recorder, and have

p = ARIL (5)

P = 2TTdVII (6)
ELECTRICAL MEASUREMENTS 55

Figure 11. Four-point probe resistivity measurement.

MOVING PROBE

(MOTOR DRIVEN)

Figure 12. Resistivity scan method of measuring resistivity variation along an ingot.

a motor drive move the probe along the sample. If the impurities are

distributed uniformly, the line drawn by the recorder will be linear, and

any deviation from linearity indicates a non-uniformity. This is the

type of method used to obtain the resistivity variations shown in Figures

5, 6, and 7. For those cases where the contact resistance is comparable to or greater than the sample resistance, the four-contact potential-drop

method must be used, as shown in Figure 13. In a bar-shaped sample,

current leads are placed at the ends of the sample, and two voltage contacts along the sample. If negligible current is drawn in the potential

leads, their contact resistance will not affect the measurement. This can be accomplished by using a null-type instrument such as a potentiometer to measure the voltage, or else a very high input impedance

DC voltmeter. The conductivity is again given by Eq. (5), except that L is now the separation between the voltage probes.
56 TRACE CHARACTERIZATION

VOLTAGE

CURRENT

Figure 13. Four-contact potential drop measurement of resistivity.

Figure 14. Contactless measurement of resistivity by capacitance coupling. After Nishizawa et al., [13]. One of the detrimental features of the above measurement techniques

is that the sample must be directly contacted. This increases the

difficulty of automating resistivity measurements. It would be helpful to have contactless measurement methods, and indeed it is possible

to measure resistivity without contacting the specimen at all by using AC

methods. In one such scheme [13], shown in Figure 14, two capacitive contacts are made to the specimen by placing it against two electrodes

covered with a very thin sheet of mica or polyethylene sheet. The two

electrodes are connected to a circuit having a inductance, variable

capacitor, and a high frequency (100 Mc/s) voltage source. As the

capacitor is varied close to resonance, the voltage drop across the in- ductance goes through a maximum. By calibrating this voltage with
ELECTRICAL MEASUREMENTS 57

known resistances, the resistivity can be determined directly. This

particular system is appHcable for samples with resistivities in the range

10-10^ ohm-cm.

C. Residual Resistivity

In practice, instead of using the residual resistivity directly to measure

impurity content, one employs the ratio of resistance at room temperature to that at liquid heHum temperature. This minimizes ex- traneous factors in the measurement such as sample geometry and

shape [5]. It is even unnecessary then to measure the electrode spacing or sample dimensions. Furthermore, use of the ratio minimizes

effects due to anisotropy, such as in gaUium [14]. The resistivity can be measured to a precision of a few per cent by

using the simple four-contact potential drop method of measurement

(see Fig. 13). The current is supplied from a battery, in series with

controlling resistors, ammeter, and reversing switch. Because of the

low resistances that must be measured at low temperatures, a DC

voltmeter hawng a high sensitivity must be used, such as the Keithley

148 Nanovoltmeter that has a sensitivity of 10~^ V. The potential

should be measured with the current flowing in the forward and reverse

directions to detect and eliminate extraneous effects such as thermoelectric voltages. For a 1 mm-diameter wire-shaped sample of gallium [12], typical, values of the current and voltage at room temperature are 10 ma and 10"^ V, and at 4.2 °K are 2 amps and 10""^ V. Since measurements are made at only one low temperature, 4.2 °K,

the required cryogenic apparatus is quite simple. In most cases, the

storage Dewar itself in which liquid heHum is suppHed can be used

directly, provided the sample and sample holder are smaU enough to

fit directly into its mouth.

A typical sample holder for measuring three smaU wire samples

simultaneously is shown in Figure 15. The Teflon mounting piece is attached to the end of a 6 mm diameter thin (0.2 mm) wall stainless steel tube, 80 cm long. Two 0.018-in, and two 0.012-in. diam. copper wires

pass through the tube to the Teflon piece for current and potential leads,

respectively. Contact to the sample is made with coiled silver wires.

The holder can be inserted directly into a Dewar with a 3/4-in. bore

entrance tube. Before immersion in the helium, the holder is first precooled by immersion in liquid nitrogen. The heHum consumption

is then only 200 cc for each dip of the holder.

It is also possible to measure the resistivity of a sample without

making any contacts, and this can be very important since it facili- tates automation of the measurement. This method depends upon

the characteristic decay of magnetically induced eddy currents [15]. The apparatus involved is shown schematically in Figure 16. For a
58 TRACE CHARACTERIZATION

Figure 15. Sample holder for measuring the residual resistivity of three wire specimens

simultaneously. Two mounted gaUium wire specimens are shown each having a 1 mm

diameter.

DAMPING

RESISTANCE

a- o W>-f- TRIGGER A_J

CIRCUIT

SAMPLE

PICKUP COIL TIME DELAY CIRCUIT

DC

AMPLIFIER O

OSCILLOSCOPE

FIELD COIL

Figure 16. Contactless measurement of residual resistivity by inductive coupling using

eddy current decay.
ELECTRICAL MEASUREMENTS 59

cylindrical specimen with radius R cm, the time constant y of the

exponential decay is related to the resistivity by the equation

2.l7fiRnO-^ , p = ohm-cm (9)

where fx is the permeabiUty (/it = 1 for non-magnetic materials). The

decay of eddy currents induced in the specimen by suddenly removing the magnetic field is displayed on an oscilloscope and photographed.

With this method, an accuracy comparable to that of the four-contact method can be achieved, and resolution to a few millimeters along

a sample is possible. However, this method may give spurious re- sults with anisotropic metals, and to measure iron, a separate magnetic

field must be applied to saturate the iron. Resistivity data has already been accumulated on a wide variety of metals. The resistance ratios achieved for seventeen metals are listed

in Table 5. Copper has been studied most completely, and the sep- arate effects of specific elements on the residual resistivity have been

determined for copper [16-18J, aluminum [17, 18j, gallium [4, 14], and

indium [17], among others. Some difficulty has been found with

gaseous impurities such as oxygen, since they can react with other

impurities and reduce their effect on the resistivity [19, 20]. For

example, the copper with the highest resistivity ratio was not the purest

sample [21]. The variation of the resistivity ratio with impurity content in copper,

for example, is quite pronounced. It increases from about 10 for a purity of 99.9% to 1000 for 99.999%, and to about W for the highest

purity copper [21]. For this reason, residual resistivity measurements

Table 5. Resistance ratios of some high-purity metals.

Element R300IR4.2 Element R300IR4.2

Ag 740 Ni 2,200

Al 26,000 Pd 7,500

Be 3,300 Pt 1,600

Bi 500 Re 55,000

Cd 38,000 Sb 830

Cu 8,000 Sn 28,000

Ga 40,000 W 80,000

In 17,000 Zn 40,000

Mo 12,000

237-323 0-67—

6
60 TRACE CHARACTERIZATION

SAMPLE ®

CONTACTS

0| I©

-TO DC POWER AND

REVERSING SWITCH

-oTO POTENTIOMETER

^OR VOLTMETER

SWITCH FOR POTENTIAL DpnT DROP OR HALL VOLTAGE

REVERSING MEASUREMENT

SWITCH (^AMMETER

Figure 17. Apparatus for measuring the Hall effect and resistivity.

have been used frequently to monitor the purification of a metal, e.g. to determine if a particular purification procedure is effective, as dis- cussed in Section IIC. This is especially important when impurity contents are below the spectrographically detectable limits. The growing importance of the residual resistance in characterizing the

purity of metals is clearly manifest by the increasing tendency of manufacturers of high purity metals to specify the resistivity ratios of their materials as the analytical standard reference.

D. Hall Effect

The apparatus for the usual DC Hall effect measurement is shown

in Figure 17, together with the resistivity measurement. Ohmic

contacts are placed on the sample as shown. The resistivity is measured by the potential drop method, discussed also in the previous

section. The magnetic field of one or two thousand gauss can be pro- duced by either an electromagnet, or a high field permanent magnet.

Two voltages are measured, the Hall voltage, across contacts 2 and 3

(Fig. 17), and the potential drop for resistivity, across contacts 1 and 2. In the voltage measurement, one should draw no current to avoid effects due to contact resistance. It is preferable to use a potentiometer, but

if a DC voltmeter is used, its input resistance should be much larger

than the sum of the sample and contact resistances. Typically, the

range of voltages extends from several microvolts to several milli- volts. In Hall voltage measurements, several spurious potentials can arise. The largest of these is the potential due to the misalignment of the

Hall probes (contacts 2 and 3), which are on opposite edges of the

sample. To eliminate these effects, one measures the Hall voltage

four times: first with the original direction of current and field, second

with the current reversed, third with the current and field reversed.
ELECTRICAL MEASUREMENTS 61

and fourth with just the field reversed. The Hall voltage is then de- rived by adding the first and third, subtracting the second and fourth,

and dividing by four. At times, a sample with the convenient parallelepiped shape shown in Figure 17 cannot be used. However, it is still possible to make Hall

and resistivity measurements on a disk-type sample having an arbi- trary shape using the van der Pauw method [22]. Referring to Figure 18,

four contacts a, b, c, d, are placed around the edge of the disk. A

known voltage is applied first to contacts c and d and the current is measured between contacts a and 6, giving a "cross" resistance Rnbxcd- Similarly, Rbcxda is measured, and the resistivity is obtained from

7Tt {Rabxcd~^ Rbcxda) r P = 2 f

where t is the thickness of the disk, and /is a correction factor which

must be included if the two resistances are not equal. Values for the

correction factor / are given by van der Pauw [22]. Next, a magnetic

field is applied, and the change in the "cross" resistance ARmxoc is measured. The carrier concentration n is given by: n = Hlet\Rhdxac- (8) In some semiconductors (having an energy band gap of only one or two tenths of an electron volt), the intrinsic number of electrons and holes

swamp out the carriers due to impurities, so that room temperature

Hall measurements no longer measure impurity effects. In such

cases, appropriate Hall data can stiU be acquired by immersing the

sample in Hquid nitrogen. Lowering the temperature to 77 °K freezes out the intrinsic carriers, but does not appreciably affect the carriers

introduced by impurities. Furthermore, lowering the temperature

has the additional advantage of reducing scattering of holes and elec- trons by the lattice, so that the Hall mobihty provides a more accurate

Figure 18. Typical sample and contact positions for van der Pauw measurement of

resistivity and Hall effect.
62 TRACE CHARACTERIZATION

measurement of the total electrically active impurities. A container

for the liquid nitrogen, small enough to fit between the pole pieces of

the magnet, can easily be fabricated from a block of "Styrofoam"

plastic.

The most complete Hall effect studies have been carried out on the

elemental semiconductors, germanium and silicon. In these materials,

electrically active impurity concentrations well below 1 ppm are com- monly achieved, so that most other analytical techniques are difficult. A full Hall effect analysis involves high precision techniques, and also includes measurements as a function of temperature [23]. The accuracy

and sensitivity achievable is shown in Table 6 for the case of silicon.

Table 6. Impurity concentrations in two silicon specimens

(After C. A. IQein and W. D. Straub [23])

Specimen Floating-zone grown Pulled from quartz

crucible

Resistivity (ohm-cm) 1330 53

Net impurity cone. 0.2 ±0.001 5.0 ±0.02

(from Hall effect) atoms in atoms in

Note the very low impurity concentration involved here. It is again

clear that these results cannot be matched by other analytical tech- niques. In favorable cases, the temperature variation of the carrier

concentration provides the ionization energy of the impurity, and hence

can be used to identify a specific impurity.

Another example of the widespread use of Hall measurements in semiconductors is the case of the III-V compounds [24]. As mentioned before, the mobility also serves to measure the impurity content. The variation of mobihty has been determined for GaAs [10, 25],

InP [25], AlSb [25], InSb [26], etc., and the Hall mobifity has been

used specifically to monitor purity, for example in the preparation of

GaAs single crystals [27]. Similarly, for many other classes of solid inorganic semiconductors, the Hall effect has been widely employed, and

its use as an analytical tool will continue to grow.
ELECTRICAL MEASUREMENTS 63

E. Thermally Stimulated Currents (TSC)

The sample to be analyzed must have a low enough dark conductivity

for the TSC to be measured. Practically, the conductivity must be

below roughly 10~^ mho/cm at the temperature of measurement, and it is this Hmitation that bars the application of this technique to most

semiconductors. An experimental advantage of TSC measurements

is that single crystalline samples are not required, and even amorphous

materials (such as selenium films) can be analyzed for trace impurities. However, the disadvantage of the technique is that ohmic contacts must be made to the specimen, which is not always possible, such

as with organic samples.

It is usually sufficient to cool the sample to only 77 °K, unless traps

with values of £" less than 0.15 ev are to be measured. Thus, as shown in Figure 19, only a simple liquid nitrogen Dewar is required, with pro- vision for heating and coohng the sample between 77 °K and 400 °K at predetermined rates such as 0.1 to 0.5 °C/sec. For example, if the

sample holder has sufficient mass, the nitrogen can be removed, and

the heating rate of the sample wiU be quite uniform. A thermocouple

is used to measure the temperature of either the sample holder, or preferably the sample itself by attaching it directly to one of the current

contacts. The Dewar or sample chamber must be light-tight, with a window provided to shine Ught onto the specimen, as shown in Figure 19. The electrical measurements are also simple, since only current need

be measured. Only two contacts to the sample are required (see Fig.

19). A known voltage, usually 1 to 100 V, is supphed from a battery,

and a very high sensitivity ammeter is placed in series with the samLIGHT V

SOURCE — —

REMOVABLE CAP

HIGH

] SENSITIVITY AMMETER

(ELECTROMETER

Figure 19. Apparatus for thermally stimulated current measurements.
64 TRACE CHARACTERIZATION

pie, such as a Keithly 610 Electrometer or a Gary Model 31 vibrating

reed Electrometer. It is convenient to use an X-Y recorder (e.g. Moseley Autograf), with the output from the electrometer placed on the

F-axis, and the output from the thermocouple on the Xaxis.

Next, a light source is required that has a variable and calibrated

intensity. An incandescent lamp can be used, and variations in light

intensity are conveniently obtained with neutral wire mesh filters. The

light source must have a wavelength greater than that corresponding to the band gap of the insulator. Three separate measurements are preferably carried out sequentially over the range of temperature of interest: dark conductivity, TSC, and

photoconductivity. The measurement of dark conductivity provides

the base line to which the other two measurements are referred. First,

the sample is cooled to liquid nitrogen temperature, during which the

dark conductivity is measured, as shown in Figure 20. At 77 °K, the

sample is illuminated with a very bright light source, such as a focused

10

10

UJ

q:

a:^ -9 u 10

10

10 2.5

DARK CURRENT

PLUS TSC

DARK CURRENT

3.0 3.5 4.0 4.5 I000/T°k

Figure 20. Variation of current with temperature with 100 V appHed to GaAs crystal: dark current, and dark current plus thermally stimulated current (TSC).
ELECTRICAL MEASUREMENTS 65

microscope lamp. This floods the sample with holes and electrons, and

fills the traps.

Second, the light is turned off, and the sample is heated in the dark.

As the temperature is increased, a current is measured in excess of the

normal dark current, contributed by carriers freed from the traps, and

this is the TSC (see Fig. 20). Upon subtracting the dark current, one

obtains the TSC peaks shown in Figure 21. Finally, the gain is measured

by continuously shining a light having a known intensity on the sample

over the entire temperature range. The excess current as compared

to the dark current is the photocurrent.

TSC measurements have been applied to a wide variety of insulators

and semi-insulators, such as CdS [28], ZnS [29], CdSe [30], Hgls [31], and

GaAs [32, 33]. Figure 21 shows results for GaAs. Typical TSC peaks

for an insulator are shown in Figure 22, where the existence of at least seven traps can be distinguished and their variation in concentration

from sample to sample is shown. The temperature of the TSC peak can

aid in identifying an impurity. At present, most traps in most materials

are of unknown origin. In years to come, an increasing number of traps

wiU be identified with specific impurities and lattice defects, and TSC

measurements will then be of even greater utility.

IV. Summary and Conclusions

The advantages and disadvantages of electrical measurements for trace characterization were reviewed in relation to an analytical chemist's

criteria for accepting new analytical techniques. Of many possible

electrical measurements, only four are believed to be presently suitable

1-z

6

E = 0.57eV

N = 9 ppm

LU 0.10 o

0.34 eV 5 0.3 ppm

0.08

0.06

0.04

0.02

0

1

1

1

1

THERMALLY

STIMULATE

(UNITS

OF

lO'^AMPS)

1

4

3

2

1 0

/ \ /

1 1 1 ^

E = 0.70eV N=7ppm

1 \

-200 -150 -100 -50 0 50 TEMPERATURE, °C Figure 21. TSC current peaks derived from Figure 20 by subtracting the dark current. Values attached to peaks are activation energies E and trap concentrations in atomic ppm (ppm = parts in 10^).
66 TRACE CHARACTERIZATION

for routine application in an analytical laboratory: resistivity, residual^

resistivity. Hall effect, and possibly thermally stimulated currents. These are characterized by very high sensitivity and relative precision,

but are non-specific. Therefore, they are most useful for providing a general measure of purity, monitoring purification, and determining

impurity distributions. Some case histories were presented in which

their application was especially rewarding, including purification of

gallium and aluminum, impurity distributions in germanium, and re- search on GaAs. Results were achieved that are impossible using other

analytical techniques. The underlying principles and main features

of apparatus for these measurements were described. The simplicity

of both the apparatus and the interpretation is a significant feature of

electrical measurements.

A key feature of these electrical measurement techniques is that they were spawned in and by materials research, and achieved their greatest

potential when applied in this direction. It can be concluded that analytical laboratories that are not closely connected to a materials

research laboratory working on metals or semiconductors will have

little use for these techniques at the present. In contrast, analytical lab- oratories deahng with materials research on pure metals would find residual resistivity measurements of immediate benefit. If automated

equipment were made commercially available, these techniques would

be in widespread use, as indicated in the paper in this conference by

A. F. Clark et al. from the National Bureau of Standards.

In the case 6f semiconductors, apparatus for resistivity measurements

is simple to build, and should definitely be useful. Depending upon

problems that arise. Hall effect measurements are less ambiguous, and

can also be of help. Use of these measurements should find their way

into analytical laboratories over the next decade.
ELECTRICAL MEASUREMENTS 67

The question of potential application is less clear for insulators. The

method of thermally stimulated currents is very powerful, but still has some pitfalls. Furthermore, present techniques require that good electrical contacts be made to the sample, which, in the case of many organic

materials, cannot be done. The ultimate potential of this technique for analysis must still be determined. For example, contactless methods

of measurement for organics should be considered here.

Finally, besides the above-mentioned limitation of these methods of organics, it is also noted that these methods have been mostly used for

solids, although liquids are not excluded (e.g. water).

V. References

[1] Weisberg, L. R., in Trace Analysis: Physical Methods, G. H. Morrison, Ed., John Wiley,

New York, 1965 pp. 511-543.

]2] Weisberg, L. R., Annals N. Y. Acad. Sciences 137, 360 (1966).

[3] Weisberg, L. R., Anal. Chemistry 38, 31A (1966).

[4] Kramer, R. A., and Foster, L. M., in Preparation of III-V Compounds, R. K. WiUardson and H. L. Goering, Eds., Compound Semiconductors, Reinhold, New York,

1962, Vol. 1, p. 146.

[5] Kunzler, J. E., and Wernick, J. H., Trans. AIME 212, 856 (1958).

[6] Wernick, J. H., Dorsi, D., and Byrnes, J. J., J. Electrochem. Soc. 106, 245 (1959).

[7] Valdes, L. B., in Transistor Technology, Vol. I, D. Van Nostrand, Princeton, 1958,

p. 131.

[8] Nelson, H., in Transistors I, RCA Laboratories, Princeton, 1956, pp. 66-76.

[9] Ueda, H., J. Phys. Soc. Japan 16, 61 (1961): also see ref. 7, 125-131.

[10] Weisberg, L. R., Rosi, F. D., and Herkart, P. G., in Properties of Elemental and Compound Semiconductors, H. D. Gatos, Ed. Metallurgical Society Conferences Vol. 5, Interscience, New York, 1960, pp. 54, 56.

[11] See, for example, Lindberg, O., Proc. I.R.E. 40, 1414 (1952).

[12] Bridgers, H. E., Scaff, J. H., and Shive, J. N., Eds. Transistor Technology, Vol. 1, D. Van Nostrand, Princeton, 1958, pp. 10-12, 53-58, 136, 141-145, 149-150, 264-

274, 323 ff. [13] Nishizawa, J., et al., in Ultrapurification of Semiconductor Materials, M. S. Brooks and J. K. Kennedy, Eds., Macmillan, New York, p. 636 (1962).

[14] Weisberg, L. R., and Josephs, R. M., Phys. Rev. 124, 36 (1961).

[15] Bean, C. P., DeBlois, R. W., and Nesbiu, L. B., J. Appl. Phys. 30, 1976 (1959).

[16] Smart, J. S., Jr., and Smith, A. A., Trans. AIME 152, 103 (1943).

[17] Chanin, G. et al., Phys. Rev. 114, 719 (1959).

[18] Vassel, C. R., J. Phys. Chem. SoUds 7, 90 (1958).

[19] Smart, J. S., Jr., and Smith, A. A., Trans. AIME 147, 48 (1942).

[20] Redman, J. K., et al.. Bull. Am. Phys. Soc. Series II, 4, 150 (1959).

[21] Kunzler, J. E., in Ultra-High-Purity Metals, American Society for Metals, Metals Park,

Ohio, 1962, p. 171.

[22] van de Pauw, L. J., Philips Research Repts. 13, 1 (1958).

[23] Klein, C. A., and Straub, W. D., in Uhrapurification of Semiconductor Materials, M. S. Brooks and J. K. Kennedy, Eds., Macmillan, New York, 1962, p. 397.

[24] Reid, F. J., in Preparation of III-V Compounds, R. K. Willardson and H. L. Goering,

Eds. Compound Semiconductors, Vol. 1 Reinhold, New York 1962, p. 158.
68 TRACE CHARACTERIZATION

[25] Reid, F. J., and WiUardson, R. K., J. Electronics and Control 5, 54 (1958).

[26] Rupprecht, H., Weber, R., and Weiss, H., Z. Naturforsch. 15a, 783 (1960).

[27] Ekstrom, L., and Weisberg, L. R., J. Electrochem. Soc. 109, 321 (1962).

[28] Bube, R. H., J. Chem. Phys. 23, 18 (1955).

[29] Bube, R. H., Phys. Rev. 83, 393 (1951).

[30] Bube, R. H., and Barton, L. A., J. Chem. Phys. 29, 128 (1958).

[31] Bube, R. H., Phys. Rev. 106, 703 (1957).

[32] Bube, R. H., J. Appl. Phys. 31, 315 (1960).

[33] Blanc, J., Bube, R. H., and Weisberg, L. R., J. Phys. Chem. Solids 25, 225 (1964).
ELECTRICAL MEASUREMENTS

Contributed Papers and Discussion

ROBERT L. POWELL

Institute for Materials Research National Bureau of Standards

Boulder, Colorado 80302 L Introduction

The contributed papers on electrical methods for trace characterization have been made much simpler to summarize by the thorough review

given by Dr. Weisberg. In addition to his general discussion, he cov- ered in detail the advantages and disadvantages and economic aspects

of four of the more useful methods utihzing the electrical properties:

electrical resistivity near room temperature, electrical resistivity at very low temperatures (residual resistivity), Hall effect, and thermaUystimulated "currents. The first two properties are especially practical

for characterizing metals and semiconductors; the third, for semiconductors; and the fourth, for insulators. In January of this year, he

pubhshed a review article in Analytical Chemistry [1]^; last year he

contributed a chapter to Morrison's book. Trace Analysis [2]. The

latter article is particularly useful because of numerous examples and

an extensive bibhography.

Before commenting on the contributed papers of this session, let us review what is desired in the way of microscopic characterization by

solid-state scientists and engineers. It is realized that the total request

is quite impractical at the present. The information generally necessary

to completely determine the properties of solids includes knowledge of the following: A. Impurity levels — type and concentrations —

10~^ to 10~^ for metals, and 10~^ to 10~^^ for semiconductors

and insulators. B. Location of chemical impurities —

in solid solution — interstitial, substitutional, ordered or disordered.

segregated — isolated or grouped in macroscopic inclusions.

^ Figures in brackets indicate the literature references at the end of this paper. 69
70 TRACE CHARACTERIZATION

C. Location and concentration of physical imperfections —

point imperfections such as vacancies, linear imperfections

such as dislocations, or area imperfections such as grain

boundaries.

D. Ionic state of chemical impurities —

Ionized in various valence states, neutralized, or in complex

chemical compounds.

All of the above deviations from the ideal crystalline solid may be

critically important to the observed magnitude or behavior of one physical property or another. But present analytic tools are a long way from

being able to supply the necessary detailed characterization. Therefore,

the highly sensitive, low-detection limit, but very nonspecific, electrical methods must often be used for many materials with trace imperfections

which tax the detection powers of other methods.

At present electrical methods are usually employed only where the

appropriate measuring systems are already in existence for carrying

out other research programs. In general, there are no packaged meas- urement systems available commercially for making trace characterizations using electrical property methods. However, several of us in the

field are trying to remedy this defect by designing general purpose equipment. Publication of reports with detailed construction drawings,

wiring diagrams, and instructions should make the methods more generally available to those presendy inexperienced in electrical measurements.

It is potentially possible to use many different properties as a means of

characterizing materials, particularly solids. Consideration of the

various properties may be systematized by enumerating the relevant

external force fields, variable environments, and observed responses.

For example, the external force fields may include electrical field (either

dc or ac), magnetic field, thermal gradient, or mechanical strain. AU

force fields may occur in specimens with various environments such as

different temperatures or pressures. The measured response signal

may be, for example, electrical potential drop, electrical current, temperature gradient, thermal current, or static electrical charge. Of the

many possible combinations only a few are reasonable as properties

that may be used for characterization. An example of one simple combination is the electrical resistance which involves measurement of the

electrical current caused by an electrical field along a specimen with a

variable or fixed temperature environment. The HaU effect is more

complicated for it involves measurement of a potential gradient across

a specimen when a magnetic field is imposed that is perpendicular both

to a line joining the potential probes and to the electrical current flowing

through the specimen. Both the electrical resistivity and the Hall effect properties are usually strongly temperature dependent. Both of these

properties were discussed in Weisberg's talk and are described in more

detail in the paper by Clark et al, and in the paper by BuUis.
ELECTRICAL MEASUREMENTS 71

II. Contributed Papers

The dielectric constant indicates the magnitude of electrical surface

charges, or rather the variation of them, when an alternating electrical

field is imposed upon an insulating crystal. The paper by Professor

Smakula briefly discusses this property.

Two other examples of the many possible combinations are 1) the

piezoelectric effect where one measures the resultant electric field across

a sample that has a strain field imposed on it, and 2) the thermoelectric

effect where one determines the electric potential difference set up along

a specimen in the presence of a thermal gradient. The latter effect is the subject of the paper by Sparks and Powell.

In the abstract of Professor Smakula's paper he has indicated the

potential usefulness of measurements of the complex dielectric constant

for characterizing imperfections in insulating crystals. For an intro- duction to the concepts used in dielectric studies, J. C. Anderson [3] has recently written a good short book addressed to a general scientific audience. Research and advances in this field have not equalled those

in the science and technology of semiconductors. For general information, progress in dielectrics is well reviewed in an annual series [4]. Though not unknown (e.g., page 45 of vol. 5 of reference [4]), remarks

on the specific effects of chemical impurities, physical imperfections, or inclusions are relatively rare. One example of a direct study of the

effects of imperfections is the thesis on heterogeneous mixtures by

de Loor [5]. Electrical resistivity is the simplest physical property to understand

and was weU covered by Weisberg earHer. The expressions used for

resistivity (or conductivity) are different for semiconductors and metals.

For semiconductors the conductivity (inverse of resistivity) is given by

(T = XiniZiiJii where m is the concentration of carriers, Zi is their charge, and /m

is their mobihty. The concentration and mobihty are generally functions of temperature. For many semiconductors, the mobility is independent of the concentration of carriers. Therefore, the conductivity

at a fixed temperature will be, for those semiconductors, directly pro- portional to the concentration of carriers and, therefore, to the concentration of "effective" impurities. Weisberg has given several perti- nent examples both in his talk and in his earHer papers [1, 2]. Temperature dependence of the conductivity indicates the variation of carrier concentration and, therefore, the ionization energy of the impurities. This measurement is fairly specific for different impurities.

However, the experimental determination of resistivity over a wide range

of temperatures is relatively difficult and, therefore, the method is not
72 TRACE CHARACTERIZATION

widely used. For some semiconductors it is necessary to go to liquid

nitrogen (77 °K) or liquid helium (4 'K) temperatures to reliably measure

impurity effects. For pure metals the carrier concentration does not change with

temperature and does not change significantly with trace impurity variations. However, the mobility, or rather the inverse concepts of timeof-relaxation and mean-free-path, depend strongly on temperature

at moderate temperatures and on imperfection concentration at low

temperatures. The expression used for analyzing electrical resistivity

is: po = Xinipoi.

where n, is again the impurity concentration and poi is the specific

residual resistance of each type of imperfection. For many types of chemical imperfections

poi = ai-^bi{^zY.

where at depends primarily on ionic volume differences and Az indi- cates the valence difference between the host and impurity ions. Fer- romagnetic metals have a very strong effect on the residual resistivity of many metals. A recent book by Meaden [6] gives a very good intro- ductory discussion of the electrical resistivity of metals which is useful for the general scientist or engineer. He has a particularly good

chapter on the resistivity changes caused by chemical or physical

imperfections.

For some time the change of resistance between 0° and 20° or 100 °C

has been used industrially as a measure of the purity of aluminum and

copper wires. However, the ratio of the residual resistance, Ro, to the 0 °C resistance is a much more accurate indicator of the effective

purity. Although use of liquid helium was in the past a barrier for many

laboratories, it should not be one any longer since helium is so widely

available. The instrumentation required for residual resistance meas- urements is quite simple. For these reasons measurements of the

residual resistance ratio, Ro°c/Ro°a, should become more widespread

as a good indicator of trace impurities in pure metals. It is already

widely used to trace the effects of radiation damage and subsequent

annealing and as a method for production control of high purity metals.

Weisberg described several ways to measure the electrical resistance

of metals or semiconductors. They are briefly the two lead, four

lead with separate potential probes, generalized four probe, capacitive

coupling, and inductive coupling methods. The first is usable for high

resistance wires; the second, for low resistance specimens or wires;

the third, for thin films or sheets; the fourth, for very high resistivity

(10 — 10* ohm-cm) plates; and the last for very low resistivity bulk

samples. The latter method, referred to as the eddy current decay
ELECTRICAL MEASUREMENTS 73

method has been used extensively at our laboratories in Boulder to test metals for the Standard Reference Materials Program of the National

Bureau of Standards. The metals tested include high-purity gold,

copper, platinum and zinc. The methods are described in the paper

by Moulder, Clark, and Gniewek. They are relatively easy to use and

should become widely utilized as production controls in the preparation of high purity metals.

For reasons too lengthy to explain here. Hall-effect methods are not

suitable for metals, but they are of tremendous importance for characterizing semiconductors. Dr. BuUis gives in his paper a very good

review of the physical concepts and experimental problems of these

methods.

Of the many additional possible properties, one more of great use- fulness for metallic wires is described in the paper by Sparks and

Powell. That is the thermoelectric power. Again, this method is quite simple and utilizes inexpensive equipment. Liquid helium

is again preferable for obtaining one of the junction temperatures. A

review of thermoelectric properties, including the influences of imperfections, has been given in the small book by MacDonald [7]. The

thermoelectric power of metals is sensitive to minute concentrations of physical imperfections or chemical impurities. However, unlike the

electrical resistivity, the total thermoelectric power is not a simple

additive property. Rather the total is given by

P total where Si is the specific thermoelectric power of a given impurity and

the other terms have their usual definition. The paper by Sparks and Powell gives several examples of the application of thermoelectric power measurements to the characterization of metal wires, both industrial wires and pure metals of the

Standard Reference Materials Program. When combined with re- sistivity measurements, the two methods can give fairly good indications of the specific impurities, if the specific Si and pi are known

from previous controlled experiments. John Cochrane (Johnson,

Matthey, & Co.) has used this method to analyze and estimate the

concentration of separate specific impurities in high-purity platinum.

III. Discussion

Questions from the audience were numerous. Among those answered

by the authors' panel were:

1. Can one determine the specific concentration of impurities in pure lead (say 5 ppm impurities) by electrical measurements? Yes,

moderately well, if both electrical resistivity and thermoelectric power
74 TRACE CHARACTERIZATION

are measured, the specific components are known from control ex- periments, and a general idea of the main impurities is given.

2. Have electrical methods been used for trace characterization

of biological materials? No, not very much, though there are some

isolated exceptions.

3. What effect does oxygen have on the electrical properties of germanium and silicon? The effects are complicated. The chemical

state of the oxygen ions is important; O2 and O4 complexes and oxygen

chains each act differently. The state of the oxygen atoms will depend

on annealing times and temperatures. The various chemical changes

can be followed by measurements of resistivity and Hall effect.

4. Can trace impurities be detected in binary alloys? Generally

no, because the alloy has a relatively large resistivity and small additional changes cannot usually be detected. For some thermoelectric

measurements there is the possibility of detecting impurities however

as illustrated in the paper by Sparks and Powell.

5. Can one measure the purity of iron by the eddy-current decay

method? Yes, if measurements are made in high magnetic fields and

the results are extrapolated to a calculated zero field value.

IV. References

[1| Weisberg, L. R., Anal. Chem. 38, 31A (1966).

[2] Weisberg, L. R., in Trace Analysis -Physical Methods, G. H. Morrison, ed.. Inter- science Publ., New York, 1965, pp. 511-543.

[3| Anderson, J. C, Dielectrics, Reinhold, New York, 1964.

[4] Birks, J. B., and Hart, J., ed.. Progress in Dielectrics, Academic Press, New York.

(Vol. 1, with different authorship, was begun in 1959.)

[5] de Loor, G. P., Dielectric Constant of Heterogeneous Mixtures, thesis, Univ. of Leiden,

1956.

[6| Meaden, G. T., Electrical Resistance of Metals, Plenum Press, New York, 1965.

[7 1 MacDonald, D. K. C., Thermoelectricity, John Wiley, New York, 1962.
TRACE CHARACTERIZATION BY

ELECTROCHEMICAL METHODS

H. A. LAITINEN

Department of Chemistry and Chemical Engineering

University of Illinois, Urbana, Illinois In keeping with the theme of this Symposium, this paper will stress the determination of trace constituents rather than the detection or determination of small absolute amounts by micro techniques. Since

electrochemical methods in general involve solutions, it will be most

meaningful in comparing the sensitivities of various methods to compare

detection or determination limits in terms of solution concentrations

rather than in terms of absolute quantities.

If a method is selective enough to permit the direct determination of a

trace constituent in a solution of the major component, the determination can be made without a prior separation, and the order of magnitude of the percentage of trace constituent bears a simple relationship to the

lowest concentration capable of being detected or measured. If we

take M as the upper limit of concentration of the major constituent and

if C° represents the lowest concentration of trace constituent that can

be detected or measured, then 100 C7M represents the lowest mole

percentage of trace constituent that can be detected or measured. As

a rule, M is of the order of unity, so a method capable of determining a

trace constituent at 10"^ M concentration is applicable at 10~^ mole %.

While not all electrochemical methods are applicable without prior

separation, others represent powerful methods of selective concentration, and stiU others represent sensitive measurement techniques to be

coupled with other types of separations.

Electrochemical methods have been classified by Delahay et al. [1].^ A similar classification, based upon the operational criteria of the proc- esses occurring at the electrodes and the electrical quantities that are

controlled and measured, will be used here. From the historical viewpoint, the development of polarography

marked a spectacular advance in electrochemical methodology, because

it introduced the element of selectivity through control of electrode

potential, an element which was largely lacking in the older electro- chemical methods of potentiometry and conductimetry. Several tech-

• Figures in brackets indicate the literature references at the end of this paper. 75
76 TRACE CHARACTERIZATION

niques, such as coulometry, selective electrodeposition, and polarized

electrode titrations, which antedated polarography, did not flourish

until the theoretical and experimental development of polarography

stimulated their resurgence. This discussion, then, will begin with

polarography and other methods based upon the net passage of faradaic

current. No attempt will be made at an exhaustive survey of the litera- ture, but a selected list of references illustrating notable examples of

sensitive determinations will be presented. A critical appraisal of the

fundamental limitations of each method, as well as some indications of

fruitful and fruitless avenues of investigation in the next few years, will be attempted.

I. Methods Based on Passage of Faradaic Current

A. Measurement of Current as Related to Concentration

1. Classical Polarography

By classical polarography we mean the measurement of time-averaged

currents with the dropping mercury electrode under diffusion control. In general, the response is governed by the Ilkovic equation

irf=605 n C D'l^m^l^T'l^ (1) where id is the diffusion current (microamperes) averaged over the life- time of the mercury drop, r (seconds), m is the mass rate of flow of

mercury (mg/sec), D is the diffusion coefficient of the electroactive

species (cm^/sec), C is the concentration in millimole/liter, and n is the number of electrons involved per molecule of electrode reaction.

For a typical dropping electrode, m=2 mg/sec, t = 4 sec, and taking

D=l XlO~^ cm^/sec, the response turns out to be

-^=3.82 microamperes/meq/liter. (2) nC

It is clear from such a trial calculation that classical polarography would

be capable of great sensitivity if it were simply a matter of a sufficiently

sensitive method of measuring a polarographic diffusion current. Thus,

it is simple to measure currents of the order of 10 "^^ A, which would

correspond to concentrations of the order of 10 ~^ A^. The practical sensitivity is limited by the fact that even at zero concentration of electroactive material, there is in general a finite current due to the necessity for charging the electrical double layer. This

charging current imposes a sensitivity limitation which is rather serious, as is shown by the following sample calculation. The charging current

ich (microamperes) is given by
ELECTROCHEMICAL METHODS 77

ic^=^=^[ACai.{E-Ep.c)] (3) where q is the charge (microcoulombs) carried by the mercury drop, A

is the instantaneous area (cm^) of the drop, C^i is the differential double

layer capacitance (microfarads/cm^) of the mercury-solution interface,

and {E —Epzc) is the electrode potential with respect to the point of zero charge (Epzc) of the mercury surface.

If as a first approximation it is assumed that C^i is independent of

potential over the range of potentials involved in the measurement of the polarographic wave height,

ich = Cdi

^ - Epzc) + ^ Cdi ^ (4)

In classical polarographic measurements, the rate of change of potential

with time is so slow as to make the second term of eq (4) insignificant.

From the first term of eq (4), the slope of the residual current curve is given by

Aich_^ dA

where the rate of change of area with time is to be averaged over the

drop time r, if the time-averaged charging current is to be measured.

If p is the density of mercury (13.55 g/cm^), the instantaneous drop area

is given by

A = f-^y^' 7712/3^2/3 = 8.51 X 10-^7712/3^2/3 MOV/ (o)

and ^=5.67 X 10-377i2/3ri/3cm2/sec. (7) at The time-average rate of growth of area integrated over the drop life T is ^=8.50 X 10-37712/37- 1/3 cm2/sec (8) dt which gives for our typical dropping electrode of 771 =2 mg/sec and

T= 4 sec

1.07 X 10-2 cm2/sec. (9) at
78 TRACE CHARACTERIZATION

For this electrode, the slope of the residual current curve is estimated

from eq (5), taking C^i to be 20 ijFI cm^, as ^= 20 X 1.07 X 10-2 = 0.214 M/V. (10)

Assuming that by graphical or instrumental compensation methods,

this current can be eliminated to within 10% of its value, that a ratio of diffusion current to uncompensated charging current of 1:1 represents

the limit of useful quantitative measurements, and that a typical polarographic wave measurement involves A£' = 0.2 V, we estimate from eq

(2) that the limit of quantitative concentration measurement by classical

polarography is ^ id 0.0428 ^^,, ... ^^^3:82^^:82" = ^-^^^"^/^^'"'

or 10"^ A^, a value in reasonable agreement with polarographic

experience.

While some improvement in sensitivity is effected by introducing a

linear compensation for residual current, the non-linearity due to variation, of Cdi with potential limits the effectiveness of this approach. By

introducing a "curve follower" in addition to a linear compensator, to permit subtraction of the residual current run on a blank solution, and

by special attention to polarograph design, KeUey and Miller [2] were able

to determine Pb++ in the concentration range of 0.2 to 2.0X10"^ M.

Since Pb++ represents a relatively favorable case of a reversible process

occurring at a low potential, it would appear that this can be taken as a

practical limit for classical polarography even with sophisticated instru- mentation. Claims of sensitivities in the range of 10" ^ to 10 " M appear

to be ill-founded [3].

2. 'Tasf Polarography or Intermittent Polarography

Kronenberger, Strehlow and Elbel [4] devised a polarograph which

records the current only during a portion of the drop life, generally

selected to be relatively late but not quite at the end of drop duration.

Since the diffusion current increases with time whereas the charging

current decreases, it is clear that an improvement in the ratio ialich is to be expected by this technique, and that a gain in sensitivity is therefore

to be expected. A reasonable estimate would be a gain of about one

order of magnitude, to permit quantitative estimates at 10"^ M [5].

Other advantages are (1) the violent variations of current near the

beginning of drop formation are avoided and hence damping of the

oscillations is not required and (2) the variation of drop time with potential does not distort the polarograms as in classical polarography.
ELECTROCHEMICAL METHODS 79

3. Derivative Polarography

In principle, the measurement of derivatives of polarograms is attractive for high-sensitivity polarography because the measurement of a peak rather than a plateau is inherently more sensitive, particularly

when the nonlinearity of the base line and the oscillations with drop

formation are considered.

A basic aspect of derivative polarography is that the slope of a polarogram at the half-wave point is at a maximum and is proportional to the

concentration provided that the Heyrovsky-Ilkovic equation

or E = Eii2 +

^In i (reversible) (1 1) nt I E = £"1/9 + — In . ^ (irreversible) (12)

Uaat I

is obeyed and that no uncompensated solution resistance is included in the potential measurements. Clearly, the inclusion of uncompensated

iR drop affects the slope of the polarogram as well as the apparent

half-wave potential.

The most elegant experimental solution to the problem of derivative

polarography is the apparatus of Kelley, Jones and Fisher [6], in which a

three-electrode system using potentiostatic control of the dropping

electrode potential is employed. A special RC filter network is used

to smooth the curves. Schaap and McKinney [7] have considered in detail the effects of the

residual uncompensated solution resistance in the immediate vicinity of the mercury drop and the residual current on the magnitude of the

derivative peak for reversible waves. For the case of most interest

here, i.e., negligible solution resistance and appreciable residual current,

they write

I =-(SCAN)(mV4/^-S) (13) max where 1.i is the total current (faradaic plus residual)

SCAN = dE/dt, the rate of potential scan K = RTIF

S — dirldE, the slope of the residual current curve at the half-wave

potential.

According to eq (13), the sensitivity of derivative polarography is propor237-323 0-67—7_
80 TRACE CHARACTERIZATION

tional to the scan rate, and it might appear that this method would be

capable of unhmited sensitivity. In practice, the scan rate is limited to ca. 40/n mV/min because of time lags introduced by the RC filter net- works [7] if undistorted peaks are to be observed. Equation (13) also shows the importance of the slope of the residual current curve, which

of course varies with the supporting electrolyte.

Cooke, Kelley, and Fisher [8] showed that the limiting factor to sensitivity in derivative polarography is "electrode noise" or non-repro- ducible background behavior due to fluctuations in wetting at the

electrode orifice. By special design of the electrode tip, they were able

in favorable cases to detect metals, e.g. zinc, at 10~^ M, a concentration

at which the normal polarographic diffusion current would have been

only 2 X 10~^^ ampere. Derivative polarograms of Cd(II) are shown in Figure 1.

Although pulse polarography [9] was developed later than square wave

polarography, it is simpler in principle and will therefore be discussed

first. Parry and Osteryoung [10] have recently described a solid-state apparatus, to which reference will be made in describing the performance

characteristics.

Pulse polarography is applicable in two modes. In the normal mode,

the initial potential remains constant at the foot of the wave, and as each

mercury drop forms it is allowed to grow for a period of time at the initial potential, after which a sudden voltage pulse of 50 msec duration is applied. The current is measured 40 msec after the application of the

pulse, to allow time for the spike of charging current to decay. Each

succeeding drop is polarized with a somewhat larger pulse, always

returning to the initial potential for the beginning of drop formation.

The shape of the polarogram thus obtained resembles an ordinary polarogram. The limiting current, however, is larger than in classical polarography, because the concentration gradient at the instant of current measurement is considerably larger. The diffusion limited current in normal pulse polarography is given by the Cottrell equation

The ratio of this current to that given by the Ilkovic equation gives a

direct comparison of the sensitivities of the two methods. Parry and

Osteryoung [10] write

4. Pulse Polarography

(14)

ii (normal pulse) _ ti^^'^ (15)
ELECTROCHEMICAL METHODS 81

1 1 1 1 1 1 2 X lO^/a^Cd"*""^ T l\

0.02 ; i 1 / 1

- 1 Y 1 rs~ & M r H +

+

, ^ 1 A 1 U /K/ L U ir

: 1 \

\

•

I

1 : 1 I / i\ ;

/

\ ^^A»ru

V ; / VI v.. .y-^vJ

CONDITIONS: CONTROLLED-POTENTIAL AND ^ BLANK

I 1

DERIVATIVE POLAROGRAPH

QUADRUPLE PARALLEL-T FILTER ELECTRONIC SCAN

1 I 1 1 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -i.O

£, VOLTS, vs. S.C.E. Figure L Derivative polarograms of Cd(n) in 10~^ M KNO3. Reproduced with permission from W. D. Cooke, M. T. KeUey, and D. J. Fisher, Anal. Chem. 33, 1209 (1961).

where h is the drop time in classical polarography and t2 is the time at which the current is measured after application of the pulse. For

ti=^ sec and ^2=40 msec, the calculated sensitivity ratio is 6.5. A

much larger gain in real sensitivity, however, is achieved through the

virtual elimination of the charging current. The charging current presents a different problem in pulse polarography than in classical polarography, because the growth of electrode area during the pulse period is so small, and the voltage change so sudden, that the charging current is determined by the RCxime constant

of the circuit. Here R is mainly the electrolytic resistance of the solu- tion and C the double layer capacitance of the electrode. For a typical

dropping mercury electrode of area 0.03 cm^, taking Cdi=20 /xF/cm^,

C = 0.6 /xF. The value of R is determmed by the concentration and

nature of the supporting electrolyte, but for typical polarographic conditions may range from 1000 H to a few ohms, depending upon the cell geometry. Taking /? = 1000 O, C = 0.6 /xF, /?C = 6XlO-4 sec. If measurements are made 4 X 10~^ sec after the application of each pulse,

67 time constants are allowed for the decay of the charging current. Since the exponential decay of charging current decreases it 10-fold during each 2.3 time constant, the charging spike would decrease to about 10~^^ of its initial value. Obviously the charging current would

be insignificant except for much higher solution resistances or shorter

measurement times.
82 TRACE CHARACTERIZATION

The other method of appHcation of pulse polarography is in the

derivative mode. In this method, the voltage pulses are superimposed

upon a slowly changing potential (~ 1 mV/sec) (Fig. 2), and the dif- ference in current between succeeding drops is plotted against the

potential. The resulting curve is hump-shaped, approximating the

derivative of the classical polarogram for small pulse magnitudes

(Fig. 3). Thus for small pulses, A^", the peak current is given by [9, lOJ

^2/r2 ID

(16)

whereas for large pulses [9], it is given by

Mr nFAC (17)

Figure 2. Pulse polarography potential-time and current-time behavior: a. potential-time curve, b. charging current only, c. Faradaic current only, d. both charging and Faradaic

current, ti, ta — times at which current is measured, t2 — time at which pulse is applied,

t4 — time at which pulse is removed. Reproduced with permission from E. P. Parry and

R. A. Osteryoung, Anal. Chem. 37, 1634 (1965).
ELECTROCHEMICAL METHODS 83

Figure 3. Derivative pulse polarograms of 2 X 10 - ^ M Cd(ll): a. in 0.001 M KNO3, b. in 0.01 M KNO3. Reproduced with permission from E. P. Parry and R. A. Osteryoung, Anal. Chem. 37, 1634 (1965).

where

cr=exp (AE" nFI2RT).

In the limit, for A£$>RTInF, ( cr— 1)/((t + 1) approaches unity and

^imax becomes the limiting current as given by the Cottrell equation

(eq 14). Thus, in principle, the derivative mode is less sensitive than

the normal mode, but the resolution is better. Calculations show [10] that for reversible waves, a 50 mV pulse amplitude gives a peak height

45, 75, and 90% of the maximum for a very large pulse for a 1-, 2-, or 3-electron process respectively.

Despite this diminution in theoretical sensitivity, the derivative mode

in practice is probably more sensitive than the normal mode, because

of the hump-shaped response curves. According to Barker and Gardner [9], pulse polarography is capable of detecting 10~^ M of a reversible

system, or 5 X 10~^ M of an irreversible system. This represents per-
84 TRACE CHARACTERIZATION

haps a 100-fold increase over classical polarography and a 10-fold increase over derivative polarography.

5. Square Wave Polarography

By a square wave polarograph v^e shall expHcitly mean the apparatus

developed by Barker [9, 10], since it is available commercially and its characteristics have been fuUy described [11-13]. After a time delay

of ca. 2 sec following the beginning of drop formation a small square wave voltage signal of 225 Hz is applied. During each half-cycle of applied square wave signal, the current is measured only during the last 1/12 of the cycle, to allow the charging current to decay to a very smaU

magnitude before the faradaic current is measured. The response curve resembles the pulse method operated in the differential mode.

Considered strictly from the viewpoint of analytical applications at high dilution, the square wave method has disadvantages as compared

with pulse polarography. These are brought about through the shorter

time scale and the smaller AE" values customarily used. As was pointed

out above, the time constant for double layer charging is proportional

to solution resistance, and in fact one of the practical limitations of

square wave polarography is the need for minimization of solution

resistance.

Another important limitation of square wave polarography is that the

response for irreversible electrode reactions depends upon the kinetic

parameters of the reaction. Von Sturm and Ressel [13] give as approximate limits of concentration for quantitative measurements 5X 10~^ M

for reversible systems and 5X10~^ M or higher for irreversible ones. To complicate matters further, the kinetics of electrode reactions are

strongly influenced by adsorbed surfactants, and depending upon the

reaction rate at a clean surface, the presence of a trace of surfactant

may have a greater or lesser effect upon the square wave response. Therefore, pains are taken to avoid the presence of surfactants and in particular the maximum suppressors commonly used in classical polarography are avoided. Fortunately, the response is not sensitive to the

presence of polarographic maxima. Nevertheless, it is clearly a dis- advantage to have such a sensitivity to the presence of surfactants. As in high-sensitivity derivative polarography, a problem is that of "electrode noise" resulting from nonreproducible detachment of mercury drops. This difficulty was largely overcome by a technique

termed "radiofrequency polarography" [9] in which a high frequency

current (100 kHz to 1.6 MHz) is modulated by a square wave signal of 225 Hz. The resulting signal depends upon the symmetry charge transfer coefficient, a, of the electrode process. For a symmetrical, dif- fusion-controlled process (a = 0.5) the output corresponds to the second

derivative of the polarograms, and thus has a positive and a negative

branch. For unsymmetrical processes {a < 0.5 or a > 0.5) or piocesses
ELECTROCHEMICAL METHODS 85

with chemical rate steps, one branch or the other would predominate.

The sensitivity of the method is of the order of 10 ~^ M for reversibly

reduced metal ions and 10"'' M for irreversibly reduced ones. The

method has not received wide study, evidently because of its experimental complexity.

6. Alternating Current Polarography

The AC polarography method of Breyer and his school [14] consists

of the application of a sine wave alternating potential of relatively smaU

magnitude and low frequency superimposed upon the slow linear voltage

sweep of polarography. The direct component of current is blocked

out from the recorder, and the rectified alternating component is dis- played as a function of electrode potential. For reversible reactions

the response curve, neglecting charging current, is the derivative of the

d-c polarogram superimposed upon the residual current proportional to the double layer capacitance at each potential.

An important characteristic of the AC polarographic method is that

it responds only to reversible electrode reactions. This, of course,

limits its applicability, but in some cases can be advantageous in avoiding

interferences.

A fundamental problem is the proper subtraction of the residual current due to double layer charging. The direct numerical subtraction

of blank from response is theoretically improper because of the phase

relationships between alternating current and potential.

For the charging process the admittance is purely capacitative, and

therefore the phase angle between current and potential is 90°. For the faradaic process, in contrast, the phase angle is 45° for a rapid,

diffusion-controlled reaction [15]. For a slow charge-transfer reaction an added resistance (the charge transfer resistance) lowers the phase

angle while decreasing the admittance across the double layer. In the

limit, for a totally irreversible charge transfer reaction, the faradaic

admittance approaches zero and no AC polarographic response is obtained. In general, it is apparent that a direct arithmetic subtraction of the blank is inadequate as a correction for the charging current. Al- though an empirical procedure involving the use of a working curve will be useful for higher concentrations, the method in general is not successful below about 5 X 10~^ M for reversible processes [14]. The response

may be considerably more sensitive for organic suDstances that are adsorbed at the electrode. As in square wave polarography, the response decreases with de- creasing charge transfer rate, but disappears entirely for a totally

irreversible reaction. Thus the effects of surfactants must be taken

into consideration.

Another effect of certain surfactants is the appearance of "tensammetric peaks" at pofentials where adsorption varies strongly with
86 TRACE CHARACTERIZATION

potential. Such peaks can be of analytical utility for detection of surfactants, but they are relatively non-specific and are applicable only

in special cases. The use of phase-sensitive detectors to reject the charging current component is discussed by Smith and Reinmuth [16] and by Underkofler

and Shain [17] for stationary electrodes. The effect of solution resistance

is largely overcome by the use of a three-electrode system with a potentiostat. The difficulties involved in complete elimination of uncompensated resistance are discussed by Schaap and McKinney [6]. The limit of sensitivity is given as 10~^ M by Smith and Reinmuth and as 5 X 10~^

M by Underkofler and Shain. The detection limit is perhaps an order

of magnitude more dilute. Another approach to minimization of the effect of charging current in AC polarography is the second harmonic technique [18]. If the output

signal is observed at twice the frequency of the input, the response curve

for a reversible reaction and small signal approximates the second derivative of the d-c polarogram, which passes through zero at the half-wave

potential. Depending upon whether the absolute or algebraic values

are plotted, the response curve has two maxima or a maximum and

minimum. To the extent that the double layer behaves as a pure fre- quency independent capacitance, it yields no second harmonic response.

The sensitivity, in principle^ should be considerably greater than for conventional AC polarography. Smith and Reinmuth [18] found linear

response down to 5 X 10~^ M for the iron(III)-iron(II)-oxalate system, but

did not push the method to its limits. The third harmonic would have

the advantage of showing a peak output at the half-wave potential.

According to Paynter and Reinmuth [19], however, the magnitude of the

response falls off roughly with the inverse power of the harmonic, and

there appears to be no analytical advantage to the use of harmonics

higher than the second.

Still another approach to suppression of the residual current is that recently proposed by Kambara and Hasebe [20] to introduce an induc- tance into the circuit. An interesting aspect to this approach is that the

inductance acts also to decrease the faradaic impedance, which has a capacitative component, and thereby to increase the sensitivity, as well

as to decrease the background. Although the effect has been demonstrated to occur, and a response has been observed for 2 X 10~^M Pb+ + and 2 X 10~^ M Zn+ + , it has not yet been studied in detail.

7. Radiopolarography

The application of radiochemical detection methods to determine the

concentration of a radioisotope deposited as an amalgam appears to have attractive possibilities for trace analysis. The technique, termed

radiopolarography by Schaap and Wildman [21], involves the isolation and washing of individual amalgam drops, and plotting the activity
ELECTROCHEMICAL METHODS 87

20

E 12

1 \ \ \

\

• 2xlO"^M Tl'"{T|20'>) IN 0.1 M KNO3

o 2xlO-^M Tr(T|204) 10-3 M

0.0

o

° o o o o

6

-0.2 -0.4 -0.6 -0.8 -1.0

Figure 4. Radiopolarogram of 2 X 10~^ M thallium tracer with 0.1 M KNO3 as supporting

electrolyte (solid points) and in presence of 10"^ M Cu + "^ (open circle points). Repro- duced with permission from W. B. Schaap and E. Wildman, Proceedings of Sixth Conference on Analytical Chemistry in Nuclear Reactor Technology, Gatlinburg, Tennessee, October 1962.

against electrode potential. An unusual feature of the radiopolarogram

at depolarizer concentrations below 10"^ M is that the activity continues to rise at potentials where the current reaches the diffusion current plateau (Fig. 4). This effect is due to the further reduction of metal

ions by the excess electrostatic charge held by the drops, as they fall through the solution. It is readily eliminated by the addition of a more

easily reducible metal ion, e.g., Cu+^ in the case of thalhum.

The potentialities of this technique have not yet been fully investigated. In a recent paper, Katsanos, Tassius, and Zeliotis [22] point out that a radiopolarographic wave is obtained for inactive manganese in the

presence of radioactive zinc, because of a displacement reaction between

manganese amalgam (formed at Ei/2 = — 1.51) and zinc ions. The quantitative aspects of such a wave are expected to be ill-defined, however,

because such interaction cannot occur until after detachment of the

mercury drops.
88 TRACE CHARACTERIZATION

8. Catalytic Currents in Polarography

In certain electrode processes a catalytic cycle is so rapid that an

electrolysis current many times larger than the diffusion controlled current of the catalyst system is observed. Because the stress in this Symposium is on inorganic determinations, only bare mention will be

made of catalytic hydrogen discharge waves for detection of aliphatic

amines and alkaloids down to 10~^ M [23], and sulfhydryl-containing

amino acids and proteins [24]. Platinum (IV) can be detected in concentrations down to 10~^ Min the

presence of palladium (II) by its catalysis of hydrogen ion discharge from

2MHC1 [25].

Harris and Kolthoff [26] determined U(VI) quantitatively down to 2X 10~^ M through its catalysis of the reduction of nitrate ion. The

reduction path of U(VI) involves U(V) and U(III); the latter is reoxi- dized rapidly to U(V) at the electrode surface by an excess of nitrate ion. Kolthoff and Parry [27] detected Mo(VI) at 10" ^ M, V(V) at IQ-^ M,

and W(VI) at 10~^ M through the appearance of catalytic waves of

hydrogen peroxide. An intermediate formation of reducible peroxy- compounds is responsible for the catalytic cycle.

9. Adsorption Effects in Polarography

It has long been noted that traces of certain substances have strong

suppressive effects on polarographic maxima. Under certain conditions,

notably in dilute supporting electrolytes, maxima can be very pro- nounced and the suppressive effect can therefore be extremely sensitive. Most surfactants that are exceptionally effective as maximum suppressors are organic in nature. The time-dependent phenomena involved

in diffusion of the surfactant to the dropping electrode, its adsorption

and suppression of the maximum are extremely complex. The effects therefore will not be described in detail. Mention should be made, however, of taking advantage of the supj)ressive effect of adsorbed tetrabutylammonium ion on the reduction of

Cd(II) at the hanging mercury drop electrode, as was done by Phillips

[28]. By measuring the time necessary for the current to drop to a low

steady state value at a fixed potential, he was able to detect tetrabutylammonium ion at concentrations down to 10~^ M.

10. Measurements of Current at Electrodes of Constant Area

(Voltammetry)

a. Steady State Methods. In principle it should be possible to increase the sensitivity of voltammetric methods enormously by in- creasing the electrode area and the rate of mass transfer. Within limits,

this is true. However, increase of electrode area is accompanied by a corresponding increase in residual currents due to electrolysis of im-
ELECTROCHEMICAL METHODS 89

purities, charging current, and oxidation-reduction of the electrode

surface itself. Stirring rates cannot indefinitely be increased, for several

reasons. Even when pains are taken to maintain laminar flow between

electrode and solution, as in the Levich rotating disc electrode [29], turbulence occurs beyond certain limits. With the ordinary rotating

wire microelectrode. turbulence is commonly encountered, with the

consequence that the mass transport-limited current is not entirely

steady, but is accompanied by "noise" or erratic fluctuations. In

addition to this hydrodynamic hmitation, there is the limitation that the mass transport rate should be the sloivest step in the electrode process

to be rate-determining, and any compHcations due to slow charge transfer

or chemical steps are correspondingly magnified by increasing the mass

transport rate. The simple rotating wire microelectrode [30] is easily capable of detecting oxidants and reductants at the 10~^ M level in favorable cases, and the limit can be extended perhaps two orders of magnitude by in- creasing the electrode area and stirring rate. For highest accuracy at low concentrations, it is best suited as an amperometric indicator elec- trode in coulometric titrations {vd). The rotating disc geometry, while

superior for absolute measurements, has no particular advantage for such

end point indication applications and will not be considered further. Other types of electrodes that deserve mention because they offer methods of altering the electrode geometry and rate of mass transport

are the rotated dropping mercury electrode of Kolthoff and Stricks [31], the convection electrode of Kolthoff" and Jordan [32] the streaming elec- trode of Heyrovsky and Forejt [33] which has been studied in detail by

Weaver and Parry [34] and the tubular electrode of Blaedel and co- workers [35]. The latter electrode was demonstrated to be sensitive

to 10~^ M ferricyanide.

b. Single Sweep and Cyclic Voltammetry. The use of stationary

electrodes in unstirred solution was enormously advanced by the development of linear voltage sweep voltammetry, in the single sweep [36] or

cyclic [37] modes. By restricting electrolysis time from a few seconds

to a fraction of a second, extraneous eff"ects such as convection could be

eliminated, to aUow diffusion theory to be applied to the mass transport

process. Nicholson and Shain [38] have presented detailed mathematical studies of the single sweep and cycHc methods for reversible

and irreversible processes with and without kinetic complications. For

the single sweep method, the peak current is given by the foUowing

expressions for reactions without complications due to chemical kinetics

[39].

i„ = 2.72 X 10»n3'2^CZ)'«i'"2 (reversible) (18)

i„ = 3.01 X 105n(an„)"MCD"2i'i« (irreversible). (19)
90 TRACE CHARACTERIZATION

Equation (18) and (19) point out the following characteristics of the linear

voltage sweep method: (a) the response depends upon the reversibility of the electrode reaction, and (b) the response is proportional to the

square root of the scan rate. The latter characteristic constitutes a fundamental limitation to increasing the sensitivity by increasing the

sweep rate, because the residual current due to double layer charging

increases with the first power of sweep rate (eq 4). Linear sweep voltammetry has proved to be a powerful method for trace determination when coupled with stripping analysis, to be dis- cussed below. Although much less sensitive than stripping analysis,

it is competitive with classical polarography. It can be applied to stationary electrodes as well as to the dropping mercury electrodes, and

to reactions for which stripping analysis is inapplicable due to highly

irreversible electrode processes or the formation of solution-soluble

reaction products.

Ross, DeMars and Shain [40] estimated 10~^ M as the limit for quantitative determination and 5 X 10~^ M as the detection limit, for reversibly

reduced metal ions. Tyler [41] in the analysis of blood determined down

to 0.1 /xg of lead in 20 ml solution (2.5 X 10~^ M) using the hanging mercury drop electrode.

c. Voltage Step Chronoamperometry. If the potential of an

electrode is suddenly shifted from a region before a polarographic wave to the potential on the limiting current plateau, the current-time

rather than current-potential relationship becomes important. This

method has already been considered above, under pulse polarography.

Perone and Mueller [42] observed a barely detectable reduction wave

for Cd(II) at 4 X 10~^ M. By plotting the first derivative, they observed

a well-defined peak at the same concentration and concluded that the

derivative technique increased the sensitivity by at least an order of

magnitude.

The technique of staircase voltammetry, originally suggested by

Barker [43] to decrease the effect of charging current, has been experimentally studied by Mann [44]. A beneficial effect of the staircase

method was noted for mercury electrodes but not for platinum electrodes

which show relatively large noncapacitative background currents. Determinations of Cd(II) down to 10~^ M were reported. Similar sensitivity limits were reported by NigmatuUin and Vyaselev [45]. Christie

and Lingane [46] derived theoretical relationships between the current and potential for reversible reactions and found them to be obeyed

satisfactorily.

B. Chronopotentiometry

If a constant current is applied under conditions of linear diffusion

to a solution of initially uniform concentration, the surface concentration
ELECTROCHEMICAL METHODS 91

of diffusing reactant reaches zero at a finite time, the transition time,

given by the Sand equation

T=-^— (20)

Measurement of electrode potential against time allows a measure- ment of the transition time to be made. A fundamental limitation of the method is the difficulty of making proper correction for the charging

current. The difficulty is brought about by the fact that the applied

current is distributed between charging the double layer and producing

the electrochemical reaction in a variable way. Even after the surface

concentration of reactant has reached zero, its concentration gradient

at the electrode surface is finite, and therefore diffusion continues

beyond the transition times.

One or another graphical procedure is generally used in an attempt to subtract out the effect of double layer charging [47]. The method, while

a powerful tool for the study of electrode processes and for quantitative

work at higher concentrations, is fundamentally limited in its applicability at extreme dilution. The situation has been summarized in a recent review by Reinmuth [48] who states, "As yet the feasibihty of trace chronopotentiometry remains unproved."

Couphng of chronopotentiometric measurements with anodic stripping [49] provides a sensitive method for reversibly discharged metals

such as Zn, Cd, or Pb, but certainly no more sensitive than the linear

voltage sweep method customarily used in stripping analysis.

Thin layer chronopotentiometry [50] is most important when run under

conditions of quantitative electrolysis, and therefore is discussed under

coulometry.

C. Coulometry

Because of the tremendous "leverage" of the faraday, coulometry,

in principle, is a powerful method for trace analysis. Until modern

developments in instrumentation, however, its capabihties could not be fully developed.

1. Coulometry at Constant Potential

Quantitative electrolysis at controlled potential is a useful technique

for performing selective electrochemical reactions, and for determinations at higher concentrations [10~^ M or more] [51], but it has inherent

limitations for trace determinations. Generally, the first-order decay

of current fails at very low concentrations due to electrolysis of residual

impurities or of the supporting electrolyte.

Meites [52] determined chromium in amounts of 5 /xg at a concentration of 10~^ M to an accuracy of ±1% by reducing Cr(lll) to Cr(Il)
92 TRACE CHARACTERIZATION

by controlled potential electrolysis, and performing the coulometric

determination upon reoxidation. Booman, Holbrook, and Rein [53]

determined 7.5 fig, uranium at a concentration of 6 X 10~^ M to an ac- curacy of ±2.2% using 5 to 10 min electrolysis.

2. Coulometry at Constant Current

For certain special applications, direct coulometry at constant cur- rent affords a sensitive, simple, and accurate method of analysis. The

coulometric generation of titrant is considered in a separate section.

a. Coulometry of Surface Layers. Coulometric methods can be

applied to the determination of fractional monolayers of oxides on metal

surfaces. A sensitivity of the order of 10~^^ moles/cm^ of platinum oxide on platinum surface can readily be achieved [54, 55]. The use of electrochemically deposited films, such as silver halides

upon silver, or higher metal oxides upon inert electrodes, will be dis- cussed under stripping analysis.

A method called "spot electrolysis," was described by Evans [56]. A drop of solution containing a soluble electro-active constituent is evaporated to form a spot on a gold foil. After adjusting the potential

to the desired value with foil contacting the solution but with the sample

spot above the solution, the foil was suddenly lowered to bring the sup- porting electrolyte in contact with the sarhple spot. The current was measured after a delay of 3 seconds to allow time for decay of charging

current. The method is best suited to the analysis of micro samples

(down to 10~^ moles) but is not exceptionally sensitive for trace concentrations.

b. Thin Layer Coulometry. Christensen and Anson [50] showed

that if a constant current electrolysis is carried out with a layer of elec- trolyte of thickness /, applying a current density of such magnitude that the chronopotentiometric transition time would exceed by 100-fold or more the quantity f^/SD, where D is the diffusion coefficient of the elec- troactive species, the electrolysis will proceed to completion. Thus,

Faraday's law becomes applicable, and the electrolysis time becomes

t = nFCif/I (21)

where / is the applied current density.

If /= 10-3 cm, and D is taken to be 10-^ cm^/sec, /2/3/) =0.03 sec, and

electrolysis times of 3 sec or more would lead to quantitative coulometry.

Hubbard and Anson [57] and Reilley and co-workers [58], devised

electrodes suitable for thin layer studies. Anderson and Reilly [59] achieved a sensitivity of 10"^ M for reasonably accurate determinations

measuring the steady state current. Using thin layer geometry, ReiUey

and co-workers [60] applied a voltage scan coulometric technique to the

determination of hahdes. In general, however, the thin layer method is
ELECTROCHEMICAL METHODS 93

not particularly advantageous at extreme dilution, and although the

sample volume being examined is very small (~ lO""^ to lO""* cm^) the

practical difficulties of introducing new samples into the cell preclude

the use of a small total sample volume.

3. Coulometric Titration

The coulometric titration, especially with amperometric endpoint

indication, has proved to be exceptionally successful at extreme dilution.

It is, of course, necessary to have a sufficiently rapid and stoichiometric

titration reaction at such extreme concentrations, but the end point can

be arranged to correspond to a region slightly removed from the equivalence point to drive the reaction more rapidly.

An excellent example of the potentiahties of this method is the de- termination of submicrogram quantities of manganese (as permanganate)

by Cooke, Reilley, and Furman [61J. They generated iron (h) electrolytically, maintaining a shght excess of iron (ll) at the end point and

during the entire titration for the most dilute solutions (10~^ M) studied.

The current between an indicator electrode and a reference platinum

electrode set at the desired end point potential was monitored near the

end point (Fig. 5). By adjusting the areas of the electrodes and the

generating current, a 'wide range of sensitivities could be achieved. An

accuracy of the order of 5% was reached at concentrations down to 5 X 10~^^ g Mn/ml (10~*^ M). Similar procedures were used for Fe and V

[62], with quantitative measurements being made at concentrations

down to 2 X 10-^ M and 3 X IQ-^ M respectively.

2500

2000

1500

(n

01

Q.<

g 1000 i

o

i 500

0 1 2 3 4 5 SECONDS Figure 5. Titration curve for 0.003 microgram Mn [as MnO?] titrated with electrolytically generated Fe(Il) using generating current. Reproduced with permission from W. D. Cooke, C. N. Reilley, and N. H. Furman, Anal. Chem. 24, 205 (1952).
94 TRACE CHARACTERIZATION

Nikelly and Cooke [63] titrated cadmium and copper at concentrations

of 2 X 10-^ M, lead at 5 X 10"^ M, and nickel and zinc at 10"^ M, using

EDTA as the reagent and a mercury pool indicator electrode.

Swift and co-workers used electrolytically generated bromine [64], chlorine [65], and copper (l) [66] at concentrations of 10~^ to 10~^ M at relative errors of 1 to 2% using amperometric indication of the end point.

Meites [67] titrated Ce(iv), V(v), Cr(vi), and Mn(VIl) with electrolytically generated iron (ll) at concentrations down to 10~^ using a potentiometric equivalence point method. There seems to be no reason why

an amperometric end point could not have been pushed to 10~^ N. Indeed, Christian and Feldman [68] recently determined chromium (VI)

at concentration of the order of 10~^ M by this method.

Bishop and Dhaneshwar [69] used potentiometry at constant current

to detect the end points in the titration of halides using electrolytically

generated silver ion. They succeeded in observing a detectable end

point even in the titration of 2 X 10~^ M Cl~, although it is not clear why

there is any electrode response at concentration levels so far below the

solubility of silver chloride. Bromide gives a response at similarly low

concentrations.

An unusual amperometric titration involving only the diffusion layer

of a rotating ring-disc electrode was described by Bruckenstein and

Johnson [70]. Bromine was electrolytically generated at a rotating disc

and detected amperometrically at a closely spaced but electrically in- sulated ring. Excess bromine over that required to react with arsenic

(III) diffusing from the bulk of the solution gave rise to an amperometric

current. By plotting the amperometric current at the ring electrode

as a function of coulometric generating current and extrapolating to a residual amperometric current, a coulometric current proportional to bulk concentration of arsenic (III) was observed. The method was

successful down to 10~^ M. A limitation to this method is that the

reaction rate must be rapid enough for stoichiometric reaction in the

time interval (ca 0.01 sec) required for mass transport between the disc

and ring electrodes

Anson [71] has applied the name "chronocoulometry" to a method in which a voltage step is applied to an electrode, and the electrical charge

that flows across the electrode-solution interface is measured as a function of time. If the voltage step is such that no current flows before it, and the maximum diffusion-limited current flows after it, the charge-time

behavior is given by the integrated Cottrell equation [72, 73]

where Q is the amount of charge in coulombs that has passed in time t.

4. Chronocoulometry

(22)
ELECTROCHEMICAL METHODS 95

Q^i is the charge required for the double layer capacitance. If Q is plotted against V^7 the slope is proportional to concentration and the

intercept Q^i is a measure of the integral capacity of the double layer.

Up to the present time, the main use of the method has been to estimate the quantity of adsorbed reactant, which adds the quantity

nFT to the amount of charge passed at zero time, where T is the quantity

of electroactive substance reducible without diffusion, in moles/cm^ [74]. Its applicability to extremely dilute solutions is Hmited by the relatively

large value of Q^i.

A double potential-step method, in which the potential is returned to

its initial value after a finite time, r, was suggested recently by Anson

[71], in an effort to achieve rigorous correction for double layer charging.

Here again, the emphasis was upon determining adsorbed reactant,

rather than upon achieving maximum sensitivity. Although further work

to establish the sensitivity Umits is surely warranted, the method does

not appear to have inherent advantages over pulse polarography where

similar voltage steps can be used, but with direct measurement of electrolysis current.

5. Galvanic Analysis

A type of coulometric method in which a galvanic cell is used to generate current has been reviewed by Hersch [75]. The method is a variant

of constant potential coulometry in which an internal rather than external source of potential is used. It is especially suited to the monitoring of flowing liquid or gaseous streams. Using a tubular electrode at low

flow rates the method approaches 100% current efficiency, and is truly

coulometric while at high flow rates the response approaches a voltammetric mass-transport limited current. For example, a cell using a lead

anode and silver cathode in 24% KOH, using a polyvinyl chloride diffu- sion membrane for oxygen, is sensitive to ppm concentrations of hydrogen in the gas phase [76]. Using a porous "filter electrode" or a cell with a long path, the method is useful for monitoring low concentrations

of halogen in water and for many indirect determinations based upon

halogen. Examples of these and other coulometric techniques are discussed by Bard [77].

6. Coulostatic Analysis

A technique involving measurement of the potential of an isolated

electrode (usually a hanging mercury drop) following the application of a pulse of charge, and during the dissipation of the charge by an electro- chemical reaction of a diffusing reactant, has been independently

studied by Reinmuth [78] and Delahay [79], although it had been sug- gested previously by Barker [80].

If, as a first approximation, the double layer capacitance is taken to be

independent of potential, the amount of charge held by the electrode is 237-323 0-67—

8
96 TRACE CHARACTERIZATION

proportional to its potential, measured from the point of zero charge.

For semi-infinite linear diffusion, the flux at the electrode surface varies

linearly with the square root of time. Therefore, as a first approximation, the potential of an isolated electrode under these conditions varies

approximately Hnearly with Vf, the slope of fine being proportional to concentration. Delahay and Ide [81] showed that the method is applicable in a concentration range of ca. 10'^ to 10"'' M.

Although in principle the method possesses selectivity, the analysis

of mixtures is not convenient, and its dependence upon the double layer

properties of the electrode makes it responsive to all factors affecting

those properties. It appears likely that the method will find only limited

application, in especially suitable cases. A potentiometric method for determination of trace quantities of oxy- gen in gases is based on a similar principle [82]. In an air-free solution, a dropping mercury electrode at open circuit assumes the potential

corresponding to the point of zero charge. If oxygen (or any other strong

oxidant) is present in solution, the potential of each mercury drop varies

approximately linearly with VT until the drop falls off. The rate of change of potential during drop life is proportional to concentrations

of oxygen. Although the method is sensitive to fractional parts per

million, it suffers from a lack of specificity. D. Stripping Analysis

The technique known as stripping analysis appears to be one of the

most powerful electrochemical approaches to trace analysis. An ex- cellent discussion of the principles and potentialities has been presented

by Shain [83J. The procedure consists of two steps, a preelectrolysis step in which

the desired component is deposited cathodically or anodically as a solid deposit or amalgam, followed by a reverse electrolysis in which the

component is determined. It is clear that many permutations of pro- cedures are possible in principle. The preelectrolysis step may be

quantitative or it may be arranged to deposit a reproducible fraction of the component from solution. The reverse electrolysis likewise may

be stoichiometric, to yield a coulometric determination, or it may be

nonstoichiometric, to give a response proportional to the amount deposited. By controlling the potential during deposition or dissolution,

the desired component may be selectively deposited or dissolved. More

easily electrolyzed major constituents may be separated out by preelectrolysis.

If a solid electrode is used, the deposition step may be non-stoichiometric or stoichiometric, but the reverse step must be stoichiometric

(coulometric). On the other hand, if a mercury electrode is used, the reverse process may also be non-stoichiometric because it can be ar- ranged to be diffusion limited.
ELECTROCHEMICAL METHODS 97

At first thought, it would seem obvious that the most sensitive deter- minations would be achieved by quantitative depositions. A simple

calculation, however, demonstrates that by compromising quantitative- ness an enormous saving in time is effected with only a moderate sacrifice

in sensitivity. For example, if a preelectrolysis procedure could be

arranged to deposit a component quantitatively from 2 ml of solution

into a hanging mercury drop electrode dehvered from a dropping elec- trode of m = 2 mg/sec, t=S sec to give an electrode of volume 7.4 X 10~^

cm=^ and area 3.9 X 10"- cm^, a concentration increase of 2700-fold would

be achieved by quantitative deposition. If the deposition is carried out under reproducible stirring conditions, its rate follows first-order kinetics,

with a rate constant given by

where A: = fraction deposited per second

A = area of electrode

F= volume of solution

8 = effective diffusion layer thickness.

Under reasonable stirring conditions von Sturm and Ressel [13] found

8 = lO-"^ cm, and taking D^IQ-'^ cm^/sec, ^ = 0.039 cm^, F=2 ml, we

calculate from eq (23), k = 2X 10-^ sec'^ Calculating the enrichment

factor from the first order decay law, we find the figures in Table 1. It

is evident that a totally impracticable time of preelectrolysis would be

required to achieve a quantitative deposition. Using a 500 second

Table 1. Dependence of enrichment factor on time.

% Deposition Time, sec C-amalg/Csolution

0.1 50 2.7

1 500 27

10 4900 270

50 7000 1350

99 23200 2680

preelectrolysis, a concentration increase of 27-fold could be achieved

under the assumed conditions. In actual practice, Shain and Lewinson

[84j achieved a 500-fold increase in concentration in 5 min of preelectrolysis, evidently because of more efficient stirring.
98 TRACE CHARACTERIZATION

Theoretically, it would be possible to take advantage of nonuniformity

of concentration within the mercury drop during the first instants of preelectrolysis and thus speed up the process without a corresponding

loss of sensitivity [85]. However, after a few minutes the amalgam

concentration is essentially uniform [84], and sensitivity can be increased

by prolonging the preelectrolysis time. Hanging mercury drop elec- trodes have generally been of two designs, either following Gerischer

[86] in catching one or more drops from a dropping electrode and sus- pending the drop from a platinum wire, or as advocated by Kemula [87] to avoid contamination of the mercury, squeezing out a mercury drop

by means of a micrometer screw. An electrode consisting of a thin film of mercury on a substrate of platinum, silver, nickel, or carbon [88-92] would theoretically be much

more sensitive than a hanging drop electrode because of its more favor- able geometry. Although early reports indicated poor reproducibility, more recent work by Roe and coworkers [91, 92] has indicated a substantial advantage, both in sensitivity and resolution for thin-film elec- trodes using nickel or carbon as substrates. For a 1 cm^ graphite

electrode with a thin film of electrodeposited mercury, a half-time for plating of 10 min from 15 ml of solution, and a sensitivity of 3 X 10~ M

for quantitative determination of lead was reported. A stripping curve

for several metals from a thin film of amalgam on nickel is shown in Figure 6. Van Swaay and Decider [93] prepared mercury drop elec- trodes by electrodeposition of mercury onto the flush-ground end of a platinum wire electrode which could be rotated. Evidently the platinum was not completely covered by mercury judging from the cathodic limit of the electrode. Of the many possible variations in procedure, the most common with

mercury electrodes is to use predeposition at a controlled potential

under fixed conditions of geometry and stirring for a time of the order

of 5 to 10 min, followed by a linear anodic scan for stripping. Using

the hanging drop electrode, the peak current during anodic scan is pro- portional to the square root of scan rate, whereas with thin film elec- trodes, a direct proportionality is observed [91] because of rapid diffusion

in the thin film. Normally, stirring is shut off during the stripping, but

with thin film electrodes, the reverse scan can be run with stirring.

The applications of anodic stripping using the hanging mercury drop

electrode have largely been confined to a relatively few metals that are

reversibly plated as amalgams. The results, however, have been spectacularly successful. DeMars and Shain [94] determined 10"^ M Cd+ + with a precision of ±2 or 3% using 15 min of preelectrolysis and a linear scan rate of 21 mV/sec. By extending the preelectrolysis to 60 min,

they were able to extend the sensitivity to 10~^ M. Monnier et al. [95], determined manganese at concentrations of 2 X 10~^ M with precision

of 3%, and 2 X lO-^ M with precision of 13%. Kemula et al. [96], de-
ELECTROCHEMICAL METHODS 99

Figure 6. Anodic stripping from thin amalgam film on nickel. Reproduced with permission from D. K. Roe and J. E. A. Toni, Anal. Chem. 37, 1503 (1965).

termined Pb, Cd, Sb, and In in trace concentrations in high purity zinc,

but did not have sufficiently pure zinc samples to test the limit of sensitivity. They reported a detection limit of 2 X 10~^ M for cadmium, and

10~^ M for copper, corresponding to 2 X 10"''% and 3 X 10~^% as weight

percentages of the metal in zinc. They could also determine Sn, Bi,

and Tl, but could not determine iron. They introduced an important

procedure to improve resolution in defining In and Cd. By stopping the

anodic scan after the cadmium peak had been passed, they selectively

oxidized cadmium from the amalgam, and improved the indium peak

upon resuming the scanning. For Sn and Pb, or Bi and Sb, preliminary

separations were necessary. Barker and Jenkins [11] using square wave polarography during the anodic sweep, determined traces of impurities in reagent grade chemicals, at concentration levels of 10~^ to 10~^ M. Von Sturm and Ressel [97] reported limiting concentrations

of 3 X 10-«, 1 X 10-^ and 8 X IQ-^ M respectively for Pb, Tl, and Cd,

using square wave polarography following 2 min electrolysis, and they

Hst relative sensitivities for a series of metals, including Bi,Cu, Sb, Pb,

Sn, Tl, Cd, In, Zn, Mn, and Ba. The absolute sensitivities could no doubt

be improved by extending the preelectrolysis time.
100 TRACE CHARACTERIZATION

Kemula [98] has stressed the importance of intermetallic compound

formation in lowering the sensitivity of anodic stripping analysis. For

example, nickel lowers the peaks for anodic stripping of zinc, particularly at higher Ni:Zn ratios and at higher zinc concentrations for a given

ratio. With solid electrodes using the reverse linear scan method it is not

possible to set up diffusion-limited currents, so it is necessary to set up some form of colulometric measurements such as the determination

of the area under a current-time curve. Because of disturbances such

as undervoltage and overvoltage effects, and the difficulties of making

residual current corrections, relatively few applications of inert solid electrodes have been made. Lord, O'Neill, and Rogers [99J determined

silver at concentrations as low as 5X10"^ M. Nicholson [100] de- termined nickel in concentrations down to 10"'' M by stripping it from

platinum into thiocyanate solution. This is an important example,

because nickel is so irreversibly oxidized that it cannot be stripped

from its amalgams.

Another type of stripping analysis, either anodic or cathodic, consists

of forming an insoluble layer at the electrode surface during preelectrolysis, and stripping if off by reverse electrolysis. In principle, it is not possible to carry the deposition to completion because of the limitation imposed by finite solubility of the layer. The stripping process, however, may be stoichiometric or nonstoichiometric. Such a method

was used by Ball, Manning, and Menis [101] for determination of chloride

using a mercury electrode, and by Shain and Perone [102] for halides

using a silver electrode as anode followed by cathodic stripping. Shain

and Perone determined iodide at concentrations down to 10~^ M and

estimated the Hmit of sensitivity at 10~^ M. Brainina and coworkers

[103] have compared the sensitivities for cathodic stripping analysis

of various anions using mercury electrodes, and have given concentration Hmits of 5 X 10-6 M for Ch, IX 10"^ M for Br", 5 X 10-« M for

I-, 4 X 10-7 for WQ= and 1 X 10-« M for MoO=. In several other

studies, these workers have precipitated hydroxides of metals in higher

oxidation states at electrode surfaces, and determined them by cathodic

stripping. Examples are Mn(ll), Ce(iii) [104], Fe(li) [105], and Tl(i) [106]. Chromate was deposited reductively as a Cr(0H).3 film on graphite and

determined by anodic dissolution [107]. The method of a chemical stripping was introduced by Bruckenstein

and Nagai [108] who determined thallium and lead at concentrations

as low as 2 X 10-^ M by codepositing the metals with mercury onto platinum and measuring the rate of chemical oxidation by measuring

the open-circuit potential as a function of time. A similar method was

studied by Bruckenstein and Bixler [109], who determined Ce(iv) at 10-« M, Mn04- at 5 X 10-^ M and Fe(lll) at 2 X 10-« M by measuring the

time required for chemical oxidation of a known amount of silver de-
ELECTROCHEMICAL METHODS 101

posited on a rotating platinum electrode. The main disadvantage of the method is its nonselectiveness for strong oxidants.

E. Electrolytic Concentration

Electrolysis, in principle, is a powerful method of effecting enormous

concentration of trace substances. The methods described under

stripping analysis, of course, constitute the first step of such concentration methods although they seldom are carried out to completion.

Schmidt and Bricker [110] and Taylor and Smith [111] effected enor- mous selective concentration operations by electrodeposition into mercury and redissolution into a smaller volume of electrolyte.

Phillips and Shain [112J improved the sensitivity of anodic stripping

analysis for tin by shifting from the 1.2 M HCl medium in which deposition was carried out to 0.01 M HCl for the stripping step, thereby avoiding the interference of residual hydrogen ion discharge. Successful

results were obtained on NBS sample 11-g, containing 0.003% Sn. About 10% of the deposited tin was lost during transfer, but reproducible

results could be obtained by careful technique.

Ariel, Eisner, and Gottesfeld [113] applied a similar technique, which

they called "medium exchange," to anodic stripping analysis. The

technique was applied to the determination of copper in the presence

of manganese in much higher concentrations in triethanolamine solutions. In the original medium, electrooxidation of Mn(ll) to Mn(lll)

would have occurred upon stripping. The same technique would of course be applicable to electrolytic concentration. Some attention

would have to be paid to avoiding appreciable "chemical stripping"

during the rinsing and rest periods.

Another technique closely akin to stripping analysis has been re- cently described by Yarnitsky and Ariel [114J. After a cathodic pre- deposition with stirring, followed by a brief waiting period without

stirring, a short oxidation interval is applied at constant potential.

Then a hnear cathodic sweep is applied to make the determination.

A sensitivity increase is achieved due to the increased concentration

in the immediate vicinity of the electrode surface during the oxidation

step. The method appears to have promise especially when reoxidation

must be carried out at potentials near that of mercury oxidation.

II. Methods Based on Electrodes at Equilibrium

A. Direct Potentiometry

1. Electrodes of the First Class

Relatively hmited analytical application is made of the measurement

of electrode potential for the purpose of determining a substance taking

part directly in an electrode reaction. A metal-metal ion electrode,
102 TRACE CHARACTERIZATION

for example, in a cell with liquid junction would respond to the activity of metal ions provided that the problems of elimination of liquid junction potential and single ion activity coefficients could be satisfactorily

resolved as is done in pH measurements. Very few electrodes in practice respond rapidly enough at concentrations of analytical interest

to make such measurements useful. Moreover, the danger of inter- ferences from other potential-determining systems is frequently present. In high temperature systems, however, the direct measurement of electrode potential is often analytically useful. In LiCl-KCl eutectic

at 400-600°, many metals respond reversibly to their ions, and activity coefficient corrections are unnecessary below mole fractions 0.01 be- cause of the constant ionic environment [115J. As another example,

Moebius [116] determined oxygen fugacities down to 10~^^ to 10~^^ atm

in high temperature gaseous equilibrium mixtures using a concentration

cell involving a solid, oxide-ion transporting membrane as the electrolyte.

2. Electrodes of Second and Third Classes

Silver electrodes, coated with a layer of halide or sulfide, are avail- able from several commercial sources for the determination of chloride,

bromide, or iodide at concentration ranges corresponding to the sol- ubilities of the silver salts. Of course, they cannot be used in the

presence of substances forming stable silver complexes, or in the

presence of anions forming less soluble silver salts than the one coating

the electrode.

An especially interesting electrode for determination of metal ion

activity is the mercury-EDTA electrode introduced by Schmidt and

Reilley [117]. The potential determining system, Hg|Hg(ii)(EDTA),

EDTA, M(EDTA), M"+, permits mercury to be used as an indicator

electrode for various metals that form complexes with EDTA. If equimolar concentrations of the Hg(ll)(EDTA) and M(EDTA) complexes

are added to the solution, the electrode potential is given by

£ = £° H.,„, H. + §^ 1" 1^ + p1" «.w- (24)

where Kmy and Kngv are the formation constants of the EDTA complexes

of the metal M and mercury(ll), respectively.

3. Glass Electrodes

Perhaps the most common potentiometric measurement of all, the

pH determination, lies outside the scope of this discussion.

Recent developments in special glass electrodes for metal ions, particularly sodium and potassium ions, have been discussed in a thorough

review by Eisenman [118]. Addition of AI2O3 to ordinary pH glass elec-
ELECTROCHEMICAL METHODS 103

trodes greatly enhances the ''alkaline error" or response to alkali metal

ions while decreasing the pH response. By varying the composition

of glasses of the systems M2O-AI2 0.3-8102 where M2O is Li20, Na^O,

K2O, Rb20, or CS2O, it is possible to vary the selectivity of response

of the glass to each of the alkali metal ions. For example, a selectivity of better than 1000: 1 for Na+ over at high pH and better than

300:1 in neutral solutions can be achieved with commercially available electrodes. For K^, a selectivity of 10:1 over Na+ is possible. By making a simultaneous measurement of Na"^, a correction can be made for its effect. By varying the glass compositions favorable selectivities for Li+, Rb+, and Cs^ can also be achieved. In general, the best glass

composition for a given measurement depends upon the nature of the

other alkali metal ions present.

Although many attempts have been made to develop glasses sensitive

to divalent cations, none is sufficiently selective to be useful in the

presence of moderate concentrations of Na+ or K+.

4. Liquid Ion Exchange Membrane Electrode

An important recent development has been the introduction of a technique for using hquid ion exchange materials as a membrane for use as a specific ion electrode. Although the published literature is sparse, there are indications that such electrodes are useful for direct

determination of calcium in biological fluids [119]. Errors due to trans- port of water and to solubihty of the ion exchanger have been studied

[120]. This field promises to be one of rapid development in the near

future.

5. Precipitate-Impregnated Membrane Electrodes

Pungor and coworkers [121. 122] developed a new class of anion

selective electrodes involving the incorporation of precipitate particles,

e.g., silver halides or barium sulfate, in a matrix of polymerized silicone

rubber. The electrodes appear to respond through the selective ad- sorption of anions upon the precipitate particles. The most selective

and sensitive is the silver iodide membrane electrode, shown by Rechnitz and coworkers [122] to respond to iodide concentrations down to 5 X 10~' M with relatively little interference from common anions.

B. Precision Null-Point Potentiometry

Malmstadt and Winefordner [123] devised a sensitive potentiometric

method for species that yield sensitive potentiometric response. Basically a concentration cell method, the procedure involves adjustment

of the concentration of electroactive species in the "known" half of a

cell until the highly amplified cell response disappears. Liquid junction
104 TRACE CHARACTERIZATION

effects are eliminated through the use of a high concentration of sup- porting electrolyte (e.g., H2SO4) throughout the cell and standard solution. Careful thermostatting to eliminate temperature gradients and

special attention to electrode preparation to avoid asymmetry effects are necessary to achieve optimum results. Malmstadt and Winefordner [123] were able to determine chloride,

using silver chloride electrodes, with an accuracy and precision of 10%

even at 10~^ M. Using silver iodide electrodes, iodide at 10 ppm

(10~^ M) levels could be determined within 5% relative error even in the presence of high concentrations of chloride.

Using electolytic generation of iodine, with precision null-point

detection, Malmstadt and Pardue [124J were able to determine oxidants

and reductants to within 0.02 ppm of iodine (10~^ M I2), corresponding to a quantitative determination limit of lO"*' M.

III. Methods in Which Faradaic Current Is Unimportant

A. Conductance

Electrolytic conductance is such a nonspecific property that only in special situations is its measurement of practical value in analysis. In these situations, however, it is capable of extreme sensitivity.

A familiar nonspecific determination is the control of quality of distilled or deionized water. The limit of determination would be expected

to be of the order of 10~^ M, the ionic concentration of pure water at room temperature. Ehrenburg and Smit [125J determined CO2 at dilu- tions down to 1 : 10^ (2 X 10~^ M) in water or 10""*% in inert gases by

measuring the conductivity of carbonic acid. Determinations of carbon in steel are commonly made by measurement of the decrease in conductivity of Ba(0H)2 caused by the CO2 produced in vacuum combustion. As an example, Kuo, Bender, and Walker [126J used 0.0065 M

Ba(0H)2 in determining carbon in steels in the 20-400 ppm range and

in boron in the 350-1000 ppm range. The sensitivity limit is no doubt

imposed by the combustion step. B. High Frequency Admittance

High frequency measurements permit the determination of changes

in conductance or dielectric constant without the introduction of elec- trodes into direct contact with the solution. Taking advantage of the

great sensitivity of measuring small relative changes in oscillator fre- quencies, Blaedel and Malmstadt [127] were able to carry out conductometric titrations even in the presence of relatively large concentrations

of indifferent electrolytes. In general, however, such titrations do not compete in sensitivity with amperometric ones. Direct measurements of changes in high frequency admittance afford a sensitive and continuous method for monitoring small changes in
ELECTROCHEMICAL METHODS 105

dielectric constant. Winefordner and Williams [128J based a detector

for gas chromatography on this principle. C. Double Layer Capacitance Measurements

The double layer capacitance of a mercury-solution interface is ex- traordinarily sensitive to adsorption of surfactants. Since a monolayer

of adsorbate may cause a several-fold decrease in capacitance, a frac- tional monolayer can easily be detected. Assuming 10% coverage

of an electrode of 10"- cm^ area by an adsorbate occupying 20 A- per

molecule, a detection limit of 10~^^ mole is estimated. Aside from

testing solutions for the presence of surface active impurities, the

method has been of Httle analytical use because of its lack of specificity. In certain cases it is a convenient method for estimating the fraction

of electrode surface covered by surfactant. In a related method, the "tensammetric" measurement in AC po- larography [14|. the admittance peaks in regions v\rhere adsorption varies

strongly with potential are sensitive indications of surfactants. Breyer

and coworkers [129| titrated several metal ions at concentrations of

10~' to 10~^ M by observing the tensammetric peaks of 8-hydroxyquinoHne (oxine).

IV. Summary

If we define the sensitivity limit of a quantitative method as the

lowest concentration at which a determination can be made with a

relative precision of 10% in the presence of a large concentration of major constituent, we may compare various electroanalytical methods

as in Table II. Such a comparison, however, should be viewed with

caution. Most of the methods have been studied with the most favor- able examples and some have not yet been pushed to their limits. It

is also important to keep in mind that the sensitivity limits of a given

method may vary widely with the substance being determined, and that some methods are far more general in applicability than others. As to the future, one may look with pessimism at some aspects of

the field and with optimism at others. It would appear unlikely that spectacular new advances are to be made in the field of trace analysis

by varying the types of electrical signal inputs or readouts. For special purposes, such as following rapid changes of concentration with

time, or with distance, or measurement of surface concentrations,

such approaches still need development. For many applications that are analytical only in the broad sense, such as identification and de- termination of reaction intermediates, or the pulse generation of react- ants we may expect important progress. For the direct observation

of solution concentrations at extreme dilution, however, the various

permutations of electrochemical signals have been pretty well worked
106 TRACE CHARACTERIZATION

Table 2. Quantitative sensitivity limits of some electroanalytical

methods

Sensitivity limit, M Methods

10-4- 10-5 AC polarography, chronopotentiometry,

Thin layer coulometry, Potentiometry

Willi iiieiai-speciiiL ^lass ui iiieiiiDidiie electrodes

10-5- 10-6 Classical polarography, Coulometry at controlled potential, Chronocoulometry, Tensammetry, Precision null-point potentiometry

io-«- 10-7 Tast polarography, Derivative polarography.

Square wave polarography. Second har- monic AC polarography. Phase-sensitive

AC polarography. Linear sweep voltammetry. Staircase voltammetry. Derivative

voltammetry, Coulostatic analysis, Chemical stripping analysis

10-7- io-« Pulse polarography, RF polarography, Coulometric titrations, Amperometry with

rotating electrodes. Conductivity

(aqueous)

10-7- 10-9 Anodic stripping with hanging mercury

drop electrodes

10-^- 10-10 Anodic stripping with thin film electrodes

or solid electrodes

over. Pulse polarography which is sensitive, selective, and general,

offers the greatest immediate promise for extending the enormous

scope of polarographic analysis to greater dilution. The field of stripping analysis deserves special attention, for it offers the selectivity of both the preelectrolysis and analysis steps and also the sensitivity of the final determination. Among the problems appearing to be fruitful for further investigation are the continued study of

thin film mercury electrodes, the study of substrates for thin film amal-
ELECTROCHEMICAL METHODS 107

gam and direct deposition, the study of media (including nonaqueous

solvents) for stripping of irreversibly deposited metals, and the further

study of the deposition of insoluble films other than the metals themselves. Glass electrodes appear to be limited in applicability to the monovalent cations. On the other hand, the area of liquid ion exchange membrane electrodes for specific metal ions seems ripe for rapid progress. V. References

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[84

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14, 1023 (1965).

ELECTROCHEMICAL METHODS

Contributed Papers and Discussion

R. A. OSTERYOUNG

North American Aviation Science Center 1049 Camino Dos Rios Thousand Oaks, California 91360

I. Introduction

In his lecture, Professor Laitinen discussed the general nature of a

variety of electroanalytical methods. Of particular interest was the

indication of factors which affect the ultimate sensitivity of these various

methods. It might be worthwhile to comment on the practical application of these electroanalytical techniques and the applicability of the

contributed papers to trace characterization. Many of us engaged in electroanalytical or electrochemical work often look at these techniques

with selected and favorable examples and samples. (In reference to the electrochemist's tendency to make a "most favored ion" situation, a friend of mine once wanted to know if, in some electrochemical work we were engaged in, we were stiU doing "cadmiumommetry".)

It is my feeUng, from an admittedly Hmited observation point, that,

at present, classical polarography, voltammetry, particularly sweep

voltammetry, coulometry (in particular, coulometric titrations), and

perhaps stripping analysis procedures, are of significant practical importance in trace electroanalytical procedures.

In part, the practical application of a wide host of electroanalytical

procedures ultimately seems to depend on the availability of commercial

instrumentation. This is not itself sufficient; cost, simplicity of operation, rehability — these factors in part must be taken into account. Some

of the techniques discussed by Professor Laitinen — square wave polarography, A.C. polarography, as examples — have had limited commercial

instrumentation available for some time, but the instrumentation is quite expensive and their use is complicated. Hence, these tech- niques—while used for fundamental studies in various laboratories,

normally with home-made apparatus — have not been widely applied to practical trace analytical procedures. Our own work in the pulsepolarographic area was triggered by a feeling that for internal practical

analytical problems pulse polarography would be a very useful tool. While a commercial unit was available, its cost, about $20,000, was such

237-323 0-67—

9

111
112 TRACE CHARACTERIZATION

that we constructed a pulse polarograph to meet our own needs. We

were fortunate, however, in having facihties and sufficient familiarity

with modern electronics to carry this out. The Oak Ridge National

Laboratory, as another example, has pioneered in electroanalytical

instrumentation as a result of its own internal requirements.

One other factor which I feel limits electroanalytical appHcations is that much more background and understanding is required for their successful utilization than, say, would be required to carry out spectrophotometric-colorimetric procedures.

II. Contributed Papers

I would now like to proceed to a brief discussion of the papers contributed to this Symposium. In so doing, I shaU consider them, where

possible, as they relate to the electroanalytical methods previously

discussed by Professor Laitinen.

UtiHzing classical polarography, the papers "Characteristics and

Potentialities of the Chlorite Catalytic Wave for Trace Analysis" by

L. Gierst, E. NicoUs, L. Vandenberghen, and R. L. Birke from the Free

University of Brussels, Brussels, Belgium, and "Application of the Catalytic Behavior of Certain Metal Complex Systems to Trace Analysis"

by Harry B. Mark, Jr., of the University of Michigan at Ann Arbor,

consider using "catalytic" polarographic waves as a basis for electro- analysis. The first of these papers considers the reaction

FeOsH.j + e ^ FeO.H" + OHk/

4Fe02H- + CIO2- + 2H2O ^ 4Fe03H,- + Ch

kb which, carried out in a large excess of chlorite, can be, in principle,

utilized for the determination of iron in an alkaUne medium. (The

general catalytic case 0 + ne^R

k/

R + Z ^ 0 + Products

kb imposes certain restrictions on the material Z. Z must have a high

overpotential for reduction on Hg, must be a good oxidant (to react with

R), and k/ must be large.) Over a limited concentration range, the height

of the catalytic wave is proportional to the concentration of iron. The

reaction itself is very sensitive to pH changes, to ionic strength changes,

and to the addition of almost anything which forms an iron complex.

From a table of redox potentials, couples which may give rise to catalytic
ELECTROCHEMICAL METHODS 113

current with chlorite are indicated. Some of these have been found not

to give rise to the catalytic currents, however.

The second paper deahng with catalytic currents considers catalysis of the type

MY2.- -^"^ + ne MO + xY

k/

M+ " + xY-'";^MY«-'"

k. where the species Y~'" is determined catalyticaUy in a large excess of M+ For this type of catalytic wave to be observed, the reduction of the

complex MYS-""^"* must be easier (more positive) than the uncomplexed

M+ which must be very irreversibly reduced. Again k/ must be large.

The specific example in this work involves the use of nickel ion, which

is normally irreversibly reduced, and which, in the presence of pyridine

or o-phenylenediamine, shows a catalytic wave. The pyridine deter- mination, carried out in solutions 10~^ — 10~^M in pyridine and about

10~^M in Ni(n), requires a calibration curve as the height of the catalytic current is not linear with respect to the concentration of pyridine. The

phenylenediamine system is interesting in that the ortho-isomer gives

rise to the catalytic wave, while the meta- and para-isomers do not. Thus, determination of the ortho-content of a mixture may be carried

out. A number of other compounds giving rise to catalytic Ni(n) waves

are given.

While an understanding of these catalytic waves is interesting and

important from an electrochemical point of view, practical analytical

utility is hmited. The catalytic waves are very sensitive to most solution

matrix changes including both kind and amount of supporting electrolyte,

pH, temperature (to which they are highly sensitive), and probably any

strong complexing agent in solution. In addition, specificity would seem to be low. I would cite the statement of Gierst et al. as the most

optimistic point of view— "As can be concluded, the use of catalytic currents does not have extremely wide apphcability; however, considering their sensitivity, the effort to broaden their domain of utihty is certainly worthwhile." Yet, the sensitivity is not, as indicated in the

present papers, extremely high — i.e., < 10~^M — and the drastic effects of even small changes in solution composition may result in large changes

in the catalytic currents. The contribution "Adsorption Electroanalysis" by Sidney Philhps

of I.B.M. at Poughkeepsie, New York, considers the current-time behavior of a diffusion or mass-transport hmited faradaic process which

takes place concomitantly with the adsorption of a non-electroactive

organic (or inorganic) species at the electrode interface. The electrode

is held at a fixed potential where the faradaic reaction takes place, and
114 TRACE CHARACTERIZATION

1

the current-time behavior is observed. The adsorbed material interferes

with the faradaic process and the time required for the ehmination or diminution of the faradaic current is related, under certain conditions,

to the concentration of the organic material in solution. To consider analytical use, it must be assumed that the adsorption of

he organic material is diffusion limited and that the adsorption coefficient is so large that, up to full coverage of the electrode surface, aU

the molecules which undergo adsorption are adsorbed as soon as they

reach the surface. At the dropping electrode, the time for full coverage

required for the faradaic current to drop to zero is then related to the

inverse square of the bulk concentration of the adsorbing organic.

When the solution is stirred, and one uses a hanging mercury drop, the

time for the initially constant faradaic current to decrease to a new,

lower steady-state value is determined and is inversely proportional to the concentration of adsorbing material. Data presented indicate that concentrations of tetrabutyl ammonium ion in the 10~^M range can be

determined by measuring the time required for the current due to the

reduction of millimolar Cd(ll) to attain a new steady state value. However, it appears that the model presented, (which requires that,

up to the limit of full coverage, all the molecules adsorb as soon as they

reach the surface) cannot represent the situation. Data presented in- dicate that the current does not decrease to the same final value at each

tetrabutyl ammonium concentration, but that the final limiting current

values are dependent on the concentration of tetrabutyl-ammonium ion. The theory utilized predicts that the amount of organic adsorbed is the same at ail concentrations and should therefore interfere, ultimately,

with the electrode reaction to the same extent. The analytical use of this type of precedure is certainly fraught with

difficulty. Every substance must be tested specifically, not only to see that there is an inhibition process but that the inhibition obeys the

derived equations. It is known, for example, that the assumptions of

(a) complete inhibition and (b) diffusion-limited adsorption are not always

obeyed. It is not, to my knowledge, established that the inhibition of

the faradaic process is independent of the concentration of the electro- active species. The complete lack of specificity, if one has mixtures,

again indicates problems. While of interest electrochemically and

electroanalytically, particularly from the point of view of maxima sup- pression and perhaps masking, the particular utility again seems limited. One use of this type of analysis scheme is, however, to test for, or deter- mine, the amount of organic adsorbants in a supposedly "pure" solution. However, general utility seems small. In a paper, "Application of Cathode-Ray Polarography and Anodic

Stripping Voltammetry to Trace and Microanalysis", E. June Maienthal

and John K. Taylor of the National Bureau of Standards, use a Davis

Differential Cathode-Ray Polarotrace to carry out a variety of low-level
ELECTROCHEMICAL METHODS 115

determinations via sweep voltammetry, and the Sargent Fast-Scan

Polarograph for anodic stripping at a hanging mercury drop. A variety

of metals and halides — aluminum, antimony, arsenic, bismuth, cadmium,

chromium, copper, indium, iron, lead nickel, tellurium, thallium,

titanium, tin, zinc, iodine, and bromine, are included in a list indicating

analyses carried out with the Cathode-Ray Polarotrace. Specific results

for Te in cartridge brass and in white cast-iron standards are given.

The results are in excellent agreement with those found by activation

and spectrochemical analysis.

Iodide, as another example, could be determined at the 1 ppm level

to a precision of 5 parts per thousand by a comparative technique, in which the sweep voltammetric system involves two electrodes. One

of the electrodes is in a solution containing the iodide which has been

previously oxidized to iodate; the other electrode is in a solution containing a suitable standard. The difference in the currents is measured

on appHcation of sweep. The differential procedure permits greater

precision than one would ordinarily expect at this concentration level.

It is demonstrated that cadmium, lead and copper can be determined

at the 10 ppb level by means of anodic stripping voltammetry.

The NBS work demonstrates that the sweep voltammetric procedure

is clearly capable of both selectivity and sensitivity. The use of differ- ential or comparative procedures opens the door to good precision at high sensitivities. Extension to electrode materials other than mercury

would permit determination of species, for example, which could be

electrochemicaUy oxidized.

The work of R. J. Joyce and C. L. Westcott of Beckman Instruments,

Inc., FuUerton, California, investigates a particular form of a mercury

electrode for use in stripping analysis procedures. As indicated by

Professor Laitinen, deposition — hence concentration — into a small

mercury drop, followed by oxidation of the deposited material, can be

an extremely sensitive procedure. The use of a thin mercury coating

had been suggested initially by K. W. Gardner and L. B. Rogers [l].^ However, the apparent irreproducibility encountered tended to cause most workers to ignore these electrodes, in spite of certain advantages

which have recently been set forth in some detail by D. K. Roe and J. Toni [2]. Joyce and Westcott report some very practical efforts to assess particularly the ease of electrode preparation and stability. Mercury

plating was carried out on platinum and nickel wires sealed into a sodalead, soft glass. Cleaning of the electrodes, particularly nickel, is found

to be all important. Although the thickness of the deposited film is constant to only approximately ± 20%, this variation may not appreciably

alter the peak current obtained in stripping. This peak current should

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

237-323 0-67—

9
116 TRACE CHARACTERIZATION

be proportional to both the thickness of film and the concentration of

metal plated and, assuming constant plating conditions, the concentration of metal in the film decreases with increasing film thickness.

The films do not have the same electrochemical characteristics as a mercury drop; the hydrogen overvoltage is lower. Exposure to air results in rapid deterioration of the film.

It is stated that the reduction of Pb (ll) and Cd(ll) is less reversible on

the plated electrode than on a hanging mercury drop as evidenced from

the peak of current-potential curves occurring at more cathodic potentials at the film electrodes. This, however, ignores changes in concentration at the surface of the thin-film which would shift the peak

potentials. Peak currents, on anodic stripping of Cd°, are not completely

hnear with the concentration of Cd(ll) in solution, which is disturbing.

Reproducibility is not too good either. However, if the charge passed on anodic stripping were determined, the linearity of charge versus

concentration of species in solution would be considerably better than

the peak current-concentration data. Some evidence of interaction

between different metals plated into the film is also indicated.

From the present work, it is difficult to assess what advantage, compared to a hanging drop, is offered at present by the plated mercury

electrodes. Resolution is claimed by Roe and Toni [2] to be somewhat

better than for the hanging-mercury drop, mainly, it would appear,

because the "tailing" evident at a hanging drop is absent in what is essentially a "thin-layer" type of stripping and this would be of signifi- cant value. However, the difficulty of keeping and preparing the film electrodes, compared to a hanging mercury drop, may well limit their

widespread use until stable or easily prepared films can be obtained.

Further investigation of these electrodes appears to me to be worthwhile

and warranted.

Continuing with the polarographic papers, "Application of Pulse

Polarography to Trace and Microanalyses" by E. P. Parry and R. A. Osteryoung of North American Aviation Science Center, Thousand

Oaks, California, indicates some use of the pulse polarographic technique previously discussed by Professor Laitinen. Some of the possible

trade-offs between sensitivity and resolution which may be obtained by

varying pulse amphtude are indicated. The determination of micromolar amounts of a material in the presence of 10,000-fold excess of a more easily reduced species is possible and is a very real advantage of

this method, as illustrated by the determination of 10"^ to 10 -^M Cd(ll)

in the presence of 10~^M Cu(ll). Small sample size is no drawback,

and, although sensitivity is highest for reversibly reduced species,

manganese, for example, which is irreversibly reduced, is stiU capable

of determination at the 10 -^M level. Pulse polarographic procedures

are at least as sensitive as the voltammetric sweep methods and are operationally simpler. Since oxidation reactions at solid electrodes can
ELECTROCHEMICAL METHODS 117

be carried out, this is an area for future work, particularly since non- metals can be studied by this method. The technique is also useful in stirred or flowing solutions.

The paper of G. A. Rechnitz of the State University of New York at Buffalo, 'Ton Specific Electrodes as Tools for Trace Analysis" considers an area which might be introduced by quoting from one of Dr. Rechnitz's earher pubhcations [3]. "The age-old dream, and nightmare, of

analytical chemists has been that someone, someday, will develop a

series of probes which, when introduced into a sample, will see and

report on a given constituent regardless of the other components present." In essence, the ion-specific electrodes, of which the glass pH

electrode is probably the best known type, serves as a means of deter- mining one species in the presence of other species which may otherwise

interfere. The use of a glass electrode, for Ag(l) determination, and a Pujigor-type

Agl-precipitate-impregnated silicone-rubber membrane electrode for iodide determination are discussed. These electrodes serve as membranes; a solution of fixed activity of the desired constituent is used on

one side of the membrane, with the unknown solution on the other side. The membrane potential indicates, in general, the difference in activity of the species on either side. Of major importance is the "selectivity

ratio", which in essence indicates the ability of a specific electrode to withstand interference from some other species. For instance, at the

O.IM level the iodide/bromide selectivity ratio at the iodide electrode

is about 200, which means that the iodide is two hundred times as effective as bromide as a potential determining entity.

One of the major problems would appear to be the variability of the

selectivity ratio with the concentration of the ion in solution. The

iodide membrane, in a Kl solution, has an essentially theoretical Nernst

response to about 10" iodide. It is not clear, though, at 10 -^M

iodide concentration, that the selectivity ratio for bromide is still 200.

It appears to me that there would be problems since the electrodes

respond to the activity of the ions. Thus measurements involving complexing agents or bulk matrix changes would require calibration in terms of a specific solution at low concentrations.

Recently, calcium sensitive electrodes have come into use (see [4] for a listing of electrodes), while a variety of the Pungor-type electrodes

are also commercially available. As indicated by J. M. Friedman [5] the

sodium sensitive electrodes appear to be as effective in determining

sodium, in the 0.1 molar range, as flame photometry. The use of these

electrodes "in vivo" is, of course, of great interest.

It is apparent that this area is one in which a great deal of work wiU

be carried out. While promising in outlook, we are not as yet in the

dream world indicated by Dr. Rechnitz, but the area will surely be

subjected to a great deal of scrutiny.
118 TRACE CHARACTERIZATION

The last paper, "Determination of Traces of Protolytic Impurities"

by G. Biedermann, L. Newman, and H. Ohtaki, from the Royal Institute of Technology, Stockholm, Sweden, describes, to quote the authors, a

. . convenient potentiometric method for the estimation of the concentration and of the acidity constant of weak protolytes which have been

found to be present at micromolar level in concentrated salt solutions."

Constant current coulometry is used to remove added excess acidity

and in essence effect a very precise coulometric titration. Measurement of hydrogen-ion concentration is made after each burst of coulometric generation. A "reference acid" is added to the solution of

carefuUy prepared salt solutions, and the reference acid is chosen so

that its pKa is at least 2 pK units greater than the constant of the soughtfor weak protolytes.

The coulometric generation of base (or removal of hydrogen ion) first titrates excess of strong acid, which is initially added to suppress

ionization of both the reference and unknown acid, then titrates the

weak acids. By consideration of the equilibria involved, the concentration and pKa of the unknown weak protolyte are determined from the

coulometric titration-hydrogen ion measurements. Most of the trace

protolytic materials encountered are found to have pKa values of about

5 to 6.5. This work is an example of a trace procedure developed for a particular

purpose and under particular circumstances, namely, for studies of metal ion hydrolysis in high concentration of electrolyte, where it is necessary to assess the acidity present in the electrolyte. The impurity

level determined is in the micromolar range and the weak-acid impurities must be taken into account in the metal-ion hydrolysis studies. The

method would appear useful, as the authors indicate, in the coulometric

standardization of dilute solutions of strong acids, and other situations

where a knowledge of trace amounts of acidity may be important.

When I was preparing my remarks, one of the things that I wanted to know was, what is a trace. A rapid scan of the program and of the

papers submitted convinced me that an argument might well develop as

to what is trace characterization. To quote from a recent book [6], "The

connotation of the term trace varies with the background or interests of the reader." At this Symposium we are already in serious difficulty.

"To avoid ambiguity, it is herein considered as a constituent making

up only a small portion of the sample, the upper limit of the trace or microconstituent being about 100 ppm by weight. There is no necessity

for making the boundary a rigid one. Considering the increasing interest

in analyses at the parts per billion level, the term ultratrace may be

conveniently used to designate the region below a part per miUion. Any

sharp division is, of course, superfluous, and will depend on the nature

of the sample to be analyzed, the analytical technique employed and the

analyst."
ELECTROCHEMICAL METHODS 119

One gram of a solid containing 100 ppm of a substance of molecular

weight 100, dissolved in 100 ml of solution yields a 10~^M solution of the sought for constituent. This is clearly in the electroanalytical tech- nique range and under some conditions, identification and analysis of mixtures may be carried out. The same 100 ppm, if contained in 1 ml

of a solution, corresponds to 10~^M. The factors of sensitivity, selectivity, accuracy, precision, cost (both for analysis and for equipment),

time, and appHcabiUty to a number of problems on hand are recognized

factors which determine the choice of a technique. To this I might also add familiarity with an area or a technique, and just old-fashioned prejudice. Sometimes, of course, the kind of practical problem on hand

almost dictates the choice.

Be that as it may, certainly the talk by Professor Laitinen and, I hope,

the summaries of the papers and comments given here indicate some of the electroanalyst's tools, problems, capabihties, and current interests.

III. Discussion

The general discussion at the end of the session was concerned largely

with specific-ion electrodes. Dr. Rechnitz pointed out that this tech- nique is stiU in its infancy. The number of ions for which specific

electrodes have been developed is increasing, and improvement in response has been remarkable during the past few years. The sensitivity and selectivity of these electrodes are interrelated. As

an example, electrodes with sodium-over-potassium selectivity ratios of 20,000 are now available. The selectivity ratio varies to some extent with concentration. Multi-valent ions do not generally interfere with

sodium ion electrodes but high hydrogen ion concentrations are not

readily tolerated. The relation of electroanalytical techniques to other analytical tech- niques was discussed briefly. The high sensitivity and selectivity of the

former make them very attractive. In some cases, they can offer unique solutions to trace analytical problems. Frequently, they may

be used to confirm results obtained by other techniques. The importance of a two-technique approach was emphasized, especially in the case of analysis for certification of standard reference materials.

The selectivity of electroanalytical methods, particularly polarographic

measurements, was cited. When the quahtative composition of a sample is known, which is often the case, procedures can ordinarily be

selected to minimize interferences. In the absence of such information on any sample submitted for analysis, a spectrographic survey analysis

is a valuable prehminary step.
120 TRACE CHARACTERIZATION

IV. References

[1] Gardiner, K. W., Rogers, L. B., Anal. Chem. 25, 1393 (1953).

[2] Roe, D. K., Toni, J., Anal. Chem. 37, 1503 (1965).

[3] Rechnitz, G. A., Anal. Chem. 37, 29A (Jan. 1965).

[4] Chem. and Eng. News, p. 50, May 30, 1966.

[5] Eisenman, G., Bates, R., Mattock, G., Friedman, J. M., The Glass Electrode, Inter- science, N.Y. (1965).

[6] Morrison, G. H., ed. Trace Analysis, Interscience, N.Y. (1965).
OPTICAL AND X-RAY SPECTROSCOPY

N. W. H. ADDINK

Philips Research Laboratories Eindhoven, Netherlands

I. Introduction

In any consideration of the pros and cons of a method of analysis and

its future possibiHties there is some point in reviewing the causes that have led to the resuhs obtained either in one's own experiments or in those of others. In this way it is possible to trace strong and weak

points of a method and to compare it with quite different methods of

analysis. In that case, of course, also those conditions and those

considerations come to the fore which according to the author are of

essential significance in the method of analysis under notice. Sometimes these are lost sight of in a pubhcation because of descriptions of

details and then one cannot see the forest for the trees.

It is not the purpose of this publication to describe a historical de- velopment, for this can be found elsewhere. Nor it is the aim to give an exhaustive summary of present-day working methods. These can

all be found in survey articles [1] ^ or periodicals [2] or in publications

speciaHsing in short abstracts. In this paper the author desires to review the essential backgrounds of methods of analysis based on excitation in the flame, the arc, and the spark, and on fluorescence produced

by means of x-rays. What then are the standards that must be applied in the appraisal

of a method of analysis?

The following criteria are worth considering:

1. Is the method complicated or simple?

2. Is the method of analysis a quick one?

3. Are the results reliable, and how great is the reproducibility?

4. How much sample is required for the analysis?

5. Is the result of the analysis representative of the bulk composition

or of the surface composition of the sample?

6. For which concentration regions are certain methods of analysis most

suitable, i.e., at what concentration is the reproducibility at its best?

7. What about the possible limits of detection?

' Figures in brackets indicate the literature references at the end of this paper. 121
122 TRACE CHARACTERIZATION

8. It is a well known fact that close to the limit of detection a "poor" re- producibility is found. How can this be influenced favorably?

If the processes taking place during atomization, evaporation, dissociation, ionization, excitation at room temperature (x-ray fluorescence

analysis) and at high temperatures (flame and arc) and the processes

of energy absorption and transfer are known, it becomes possible to

start answering the above questions.

Essentially, the author does not wish to become embroiled in discussions of mechanical/technical improvements, in the sense of: the resolv- ing power is determined by the size of the prism used, or by the number

of lines or by the blaze of the diffraction grating in question or by the

distance between lattice planes and the space group of the analyser

crystal; similarly he does not wish to embark on a discussion of the nature of the differences of detection (photographic plate, photoelectric

cell, multiplier, counters, etc.) or to describe the use of the slide rule, of

the calculating machine or of the computer, though it should here be

mentioned that the scientific worker in this field ought by nature to be

"lazy"; the less he has to note down himself, the smaller will be the

number of "human errors." This appHes also, for example, to the

preparation of the sample requiring analysis. This point may be illus- trated as follows: If it is possible to perform, for example, an alkah

determination directly in a solution by lUeans of flame emission or ab- sorption without preliminary chemical separation, then this method of working is preferable to one in which separation or extraction must first be used, for these may give rise not only to human errors but also to unsuspected contaminations, co-precipitations, or absorption processes. On the other hand it should be remembered that with these two latter processes (and also, for example, with electrochemical methods) it is possible to achieve preconcentrations [3] by means of which the Hmit

of detection of an element present in the starting material can be lowered.

But these methods of working will here be left out of account. A consideration wiU now follow of flame, arc and spark excitation and of x-ray fluorescence and electron microprobe analysis.

II. Flame Emission and Absorption

A. Experimental Test of Theoretical Considerations

It will be remembered that in a flame it is possible to distinguish an

inner cone, in which the gases supplied undergo combustion proper, and at a small distance above it the outer cone, also known as the

measuring volume, in which thermodynamic equilibrium prevails.

The substance being analyzed is brought into solution, atomized to form

a fine nebula, and then blown through the inner and outer cones. Let

us confine ourselves to a description of the state of the outer cone.
OPTICAL AND X-RAY SPECTROSCOPY 123

where thermal excitation and ionization or the absorption of light of

a certain wavelength by ions, atoms, and molecules formed in the inner cone and the intervening space take place. Here we shall pay special

attention to

1. ionization of metaUic atoms (M);

2. the equilibrium MO ^ M + O;

3. the number of excited atoms. The object of the test now to be described consists of trying, while

restricting ourselves to Une emission, to give a quantitative explanation

of the results obtained, so that all details are clearly brought to light.

Our data can be taken from Table 1. Table 1. Some results of flame photometric measurements.^

Aqueous chloride Wavelength Peak height (above

solution emitted background)

Ba 0.4 /Ltg at/ml 553 m/x 19.6 mm (arbitrary

scale)

Ca 1.38 fJLg at/ml 422 m/x 190 mm

Mg 2.26 fJLg at/ml 285 m/x 4.5 mm

^ Flame used: acetylene/air (acetylene in excess). The energy of the hght emitted per unit time (intensity 1) is proportional to the number of excited atoms A^e in accordance with

I = NeAhv (1) where ^ = the transition probability = the reciprocal of the life time of the excited state, which is of the order of 10 ~^ seconds,

hv = \hG energy quantum of the wavelength concerned.

Now how big is the number of excited atoms Ne in comparison with

the total number of atoms A^, that are present? The answer to this is given by the MaxweU-Boltzmann distribution law:

Ne = Ngex^ {-EeimiB (2) where = energy of excitation, expressed in eV,

A: = Boltzmann's constant,

r= temperature at which excitation takes place (°K), g= statistical weight factor of the energy level under examination, g being equal to 27 + 1, where J is the internal quantum

number; for numerical values see [4], B = partition function = ^gn exp (— EenlkT).
124 TRACE CHARACTERIZATION

The ratio NeIN is small if Ee is large or T is small, and vice versa. On

combining eqs (1) and (2) we obtain

/ = NgAhv exp (- Ee/kT)/B (3) Many people are stiU under the impression that, in order to give a large

signal (large value of /, corresponding to a low limit of detectability),

the temperature must be chosen as high as possible. But it is then

forgotten that the degree of ionization, which can be calculated after Saha [5], becomes so great that practically no atoms remain. (If one

goes on to measure, for example, resonance lines of the ion one comes up

against measurements that are difficult to perform; for instance, the resonance lines of the sodium atom are found at 5890/5896 A, while

those of the sodium ion he at 370 A.) Table 2 provides some data indiTable 2. Fraction of non-ionized atoms of different elements at various

temperatures [5]. Ionization energy Temperature in °K

Element Vi in eV 2500 °K 4500 °K 6000 °K

Ba 5.2 0.75 0.50 0.002

Ca 6.1 1 0.9 0.015

Mg 7.6 1 1 0.25

(Zn 9.3 1 1 1 ) (Al 6.0 1 0.9 0.015)

eating the factor with which the number of atoms, originating in the

amount of salt supplied in the form of a solution, has to be multiplied

for calculating the real number (TV) concerned with this excitation.

Alkemade and collaborators [6] have shown that the molecular bands

occurring in an alkaline earth spectrum can be ascribed to the oxides.

The conversion to the oxide takes place in the reaction zone (inner cone)

of the flame. In the outer cone, the measuring volume, there is an 2500 °K

equilibrium, e.g., CaO ;=± Ca+0. It is this equilibrium which

determines the intensity of the CaO-bands and that of the discrete

Ca-emission. Since we are trying to determine the discrete calcium

emission at 422 mfji we must estimate, if only roughly, this equihbrium.

In the gaseous state of the equihbrium

CaO(g)^ Ca(3) + 0(fir) thermodynamics gives us the relation

AG = {AH-mS) = -RT In Kp, (4) where AG = change in standard free energy for this process, Kp = equihbrium constant.
OPTICAL AND X-RAY SPECTROSCOPY 125

We can now insert numerical values [7] [8] for the gaseous substances:

A//ca = 46 kcal/g at. Ai^o=^59 kcal/g at. ^^cao^(heat of sublimation of CaO + heat of formation of solid CaO) = (149.5 - 118) = 31.5 kcal/mole.

In eq (4) A// becomes 46 + 59-31.5 = 73.5 kcal/mole, AS = 5(ca) + 5(o) - -5(030) = 37 + 38.5 - 52 = 23.5 cal/mole.

We therefore find at 2500 °K

AG- 73.5 X 10^-2500 X 23.5= 14.8 X 10^ cal/mole, and

log Kp = {- 14.8 X 103)/(4.57 X 2500) = log 0.05. In a hypothetical experiment let us now, in a closed system (pressure = 1 atmosphere), consider the dissociation equilibrium of CaO, where we

have

aV(l-a2) = 0.05; here we have a = pca = Po, and a then has the numerical value of 0.2. Correspondingly the equihbrium at 4500 °K and at 6000 °K can be calculated; the method is also apphcable to other molecules.

Table 3 gives a summary. Tables 2 and 3 now enable us to accom- phsh the purpose of the experiment, namely to determine the discrete

emission of Ca, etc., making use of eq (3). This is shown in Table 4. From this table it wiU be seen that the calculated ratio of the barium,

calcium, and magnesium line intensities is 1:13:0.2, whereas a ratio of 1:10:0.25 has been found by experiment (Table 1), an agreement which

may be termed reasonable in view of the fact that so many factors have been taken into account and the rather crude thermodynamic

calculations. B. Theoretical Considerations Concerning the Influence of

Temperature

Now it may be asked how great the effect is of a change in temperature, not only on the emission but also on the absorption, apart from

Table 3. Shift of the equilibrium U-O^g) ^M(y)+0(y) calculated at different temperatures for various oxides of metals.

Partial pressure of 2500 °K 4500 °K 6000 °K

Ba atoms 0.008 0.4 0.9 Ca atoms 0.2 1.0 1.0 Mg atoms 0.01 0.7 1.0 (Zn atoms 1.0 (3000 °K) 1.0 1.0) (Al atoms ~ 0.0001 -0.15 -0.8)
126 TRACE CHARACTERIZATION

Table 4. Numerical evaluation of equation (3).

X gAhv X e-^el"'' X-XaXb = I B

where a corrects for the sensitivity of the photocell used; and b corrects for self-absorption

in the flame. N gAhv e-^el^-r - a b =

I B

I "correction" I Cone. factors

/xM/ml Saha^ MO^M+O^

Ba 0.4 0.75 0.008 5 X 10« 2.88 X 10-^ - 72 1 =0.83 X 10^ 3

Ca 1.38 1 0.2 3.3 X 108 1.22 X 10-6 1 100 1 _ n x 10^ Mg 2.26 1 0.01 45 X 10« 4.52 X 10-« 1 68 0.5 = 0.16 X W

^ Data from Table 2. Data from Table 3.

the method of excitation. What factors of eq (3) are sensitive to temperature? For the following are subject to change:

1. the ionization (Saha; Table 2), cf. Table 5, column three;

2. the equilibrium MO^M+ 0 (Table 2); cf. Table 5, column four;

3. the proportion of excited atoms (A^e/A^ ~ exp {—EelkT).

Before considering Table 5 with respect to the emission of resonance

lines, some remarks should be made. Any mutual influence of both

equilibria (of ionization and of dissociation) can be neglected if the

correction factors for ionization or dissociation are nearly unity, and

if multiplication of both factors is permitted. Otherwise both equilibria

have to be taken into account. To take the case of Ba45oo °Kr for instance,

although the two equilibria

BaO^Ba + 0

Ba^Ba+ + e

are shifted more to the right, the quantity of Ba-atoms available for excitation appears to remain nearly constant. The following conclusions can be drawn from the results shown in Table 5:

1. For the elements with Vt < 7 eV and of which oxygen compounds

exist at 2500 °K a maximum of the emitted energy is found to he between
OPTICAL AND X-RAY SPECTROSCOPY 127

Table 5. Calculations illustrating the influence of temperature on

line intensities (hypothetical conditions).

Ee

(eV) (eV) (Sahacorrection)

(Dissociation

correction) exp i-EelkT) Product

Gain against 2500 °K

Ba

2500 °K

4500 °K

6000 °K

2.24 5.2 0.75 0.50 0.002

0.008

0.4

0.9

2.88 X 10--^ 2.85 X 10-3

1.25 X 10-2

1.73 X 10-7 0.57 X 10-3

2.2 X 10-^ 30 X 1021.3 X 102 Ca

2500 °K

4500 °K

6000 °K

2.92 6.1

1.0 0.9 0.015

0.2

1.0 1.0

1.2X 10-«

4.7 X 10-4

3.2 X 10-3

2.4 X 10-7

4.2 X 10-4 4.8 X 10-5 20 X 102 2x 102 Mg

2500 °K

4500 °K

6000 °K

4.35 7.6

1.0

1.0 0.25

0.01 0.7

1.0

4.5X 10-«

1.16 X 10-5 2.0 X 10-4

4.5 X lO-'o 0.81 X 10-5 5.0 X 10-5 . 180 X 102 1100 X 102 Zn

0\J\J\J IN. 4500 °K

6000 °K

5.77 9.35

11

1

11

1

1 y 1 0-10 2.8 X 10-^

1.26 X 10-^

1 .<JO lU

2.8 X 10-7

1.26 X 10-5 18 X 102 800 X 102

Al

2500 °K

4500 °K

6000 °K

3.1 6.0

10.9 0.015

~ 0.0001 ~ 0.15 -0.8

4.5 X 10-7 3.0 X 10-4

2.3 X 10-3

-4.5 X 10-11 ~ 4.0 X 10-5 ~ 2.8 X 10-5 ~ 9 X 105 - 6 X 105

2500 °K and 6000 °K (this applies also in the case of low overall pressures, with dissociation practically unity, and also incidentally to the corre- sponding elements having no molecular compounds at high temperatures, e.g. sodium).

2. Elements with Vi > 7 eV do not show such a maximum; for then the

gain factor increases with the temperature, this increase being greater

if no molecules exist at 2500 °K. The gain calculated in comparison

with the intensity of emission at 2500 °K is, however, in part only apparent, for the number of excited atoms at that temperature is extremely

small (cf. the column exp {—EelkT)\ a value of 4.5 X 10 ~^ is still measurable, but only just, if the concentration is in the neighbourhood of 2

/xg at/ml. As a rule of thumb it may be said that a temperature of 2500-3000 °K wiU stiU just bring about a measurable excitation of 4.5-5

eV, while at a temperature of 4500 °K the excitation reaches about 7 eV

and at 6000 °K some 10 eV.
128 TRACE CHARACTERIZATION

It should be noticed that with aluminum dissociation of the aluminumoxygen bond greatly prevails over the ionization of the aluminum atom.

In this connection it is of special interest to observe the absorption

(Table 6). For this the same data may be used as those mentioned in Table 5, with the exception of the number of excited atoms exp (— Eg/kT).

This number is so small in comparison with the number of non-excited

atoms that the total number of absorbing atoms is determined completely

by ionization (Saha, third column) and molecule formation (fourth

column). From Table 6 a maximum value of the gain of free atoms, with

Table 6. Calculations illustrating the influence of temperature on

absorption (hypothetical conditions).

Ee Vi (Saha- (Dissocia- Gain

(eV) (eV) correc- tion cor- Product against

tion) rection) 2500 °K

Ba 2.24 5.2 2500 °K 0.75 0.008 0.006

4500 °K 0.50 0.4 0.2 30

6000 °K 0.002 0.9 0.0018 0.3 Ca 2.92 6.1 2500 °K 1.0 0.2 0.2

^D\J\J is. i.U 4.5 6000 °K 0.015 1.0 0.015 0.08

Mg 4.35 7.6 2500 °K 1.0 0.01 0.01 4500 °K 1.0 0.7 0.7 70

6000 °K 0.25 1.0 0„25 25

Zn 5.77 9.35

3000 °K 1 1 1 4500 °K 1 1 1 1 6000 °K 1 1 1 1 Al 3.1 6.0 2500 °K 1 ~ 0.0001 ~ 0.0001

4500 °K 0.9 -0.15 -0.135 ~ 1350

6000 °K 0.015 -0.8 ~ 0.012 ~ 120
OPTICAL AND X-RAY SPECTROSCOPY 129

respect to a temperature of 2500 °K, is also found to exist at temperatures between 2500 °K and 6000 °K for those elements showing molecular

bands in the spectrum. In the case of an element hke zinc there is practically no question any more of a maximum.

C. Comparison of Absorption and Emission

If in Tables 5 and 6 the "products" (the number of available atoms)

are considered, then the values given in Table 6 are considerably greater.

It should be remembered, however, that for absorption a power of e

also applies: I = Io exp {—kl) (Lambert-Beer)

with /= transmitted energy,

/o = energy of irradiation,

A; = absorption coefficient,

/ = thickness of the absorbing medium.

If a comparison is now made of the approximate measuring sensitivities

(in ppm) applicable to flame emission and atomic absorption of various

elements that can be excited in the flame, this is found to turn out in favour of emission by a factor of between 1 and 15, the mean being 6; see [9]. Nevertheless with a moderate increase of the flame temperature the absorption method permits the determination of a larger number

of elements, the reason being a somewhat greater dissociation of the

molecules. See [10]. If it were possible to increase the temperature of the outer cone by

500-1000°, this would enable the limit of detection in both absorption

and emission to be lowered [11]. The question then arises of whether

the absorption method would enable us to determine a larger number

of elements. Quite certainly in the case of flame emission a spectrograph of greater resolving power than hitherto used in flame photometry

would be required.

D. Analysis of Multicomponent Systems in Solution

Let us now briefly consider whether it is always necessary in wet

chemical analysis to remove the main components before the trace elements are determined by flame photometry (those cases in which the

physicist is interested, for instance the reciprocal influence of the alkaU

metals, have been worked out). An enormous amount of work could be

saved if once and for always such investigations were performed systematically, for example [12] in the case of silver. E. Future Prospects

Tables 5 and 6 reveal that at somewhat higher flame temperatures

(about 3500-4000 °K) flame emission and absorption can be expected to
130 TRACE CHARACTERIZATION

bring a larger number of elements within their field of apphcation. At

the same time a lower detection limit is to be expected in many cases. For achieving a higher temperature one can think of N2O — C2H2 or cyanogen-oxygen flames, as weU as of Langmuir's atomic hydrogen

flame. The possibility can also be considered of utilizing a horizontally

oriented silver (or copper) arc with water-cooled electrodes (possibly

placed in a specific gas atmosphere, e.g., Ar— N2). The supply of the

analysis material, in solution, takes place ultrasonicaUy in the form of a

nebula. The above metals (Ag, Cu) have spectra poor in fines, and

their arc gas temperature will be about 5000 °K. In the designing of new flames it is important always to consider their energy density, for

this must be so great that the temperature equilibrium will not be dis- turbed by the introduction of the amount of material to be analysed. In

this chapter no attention has been paid to excitation in the inner cone. The results of research undertaken on this subject are very encouraging.

in. Classical Emission Spectral Analysis

A. The Arc

1. General Considerations

As already mentioned in the introduction, the best way of testing a method of analysis is to investigate the factors contributing to a complete

description of the process that takes place. It will then be found for arc excitation that non-homogeneous selective evaporation, and an

excitation volume whose temperature is not homogeneous, strongly affect the accuracy of the analysis results. This will be illustrated with our own data. Perhaps it is unnecessary to mention that we follow the method of complete evaporation of a certain amount (5 mg) of the substance to be

analyzed [13]. The diameter of the graphite electrodes is relatively large

(8-10 mm) in order to prevent, after the striking of the arc, a too rapid

rise in the temperature of the tip of the anode, where the sample is placed

(the maximum temperature of the anode tip is 3500 °C). Furthermore,

with such broad electrodes the amount of carbon vapor, which is present during the evaporation of the material, is relatively large. The

electrode gap amounts to 9 mm (current strength 10 amps) and the light

emitted from the center of the discharge, i.e., 4V2 mm above the anode,

is passed through a diaphragm of 0.5 mm (with the diaphragm sfit perpendicular to the electrode axis) and then to the spectrograph by means of a lens which forms the image on the prism or diffraction grating. The

temperature of the column amounts to 6100 °K, and that of the mantle

to about 4000 °K. (These temperature measurements are relative,

depending as they do on the "thermometer element" used. Reference

is made to the measurements mentioned in [14]; with the choice of other
OPTICAL AND X-RAY SPECTROSCOPY 131

"thermometer elements" temperatures in the 10-amp arc of 10000 °K

and more have been found. This resuk is corroborated by the fact that in the same arc there are hnes of C II {Vi = 21.6 eV) in the spectrum,

and also Hnes of Zr ill {Vi of Zr III ~ 24.7 eV).)

The temperature of 6100 °K mentioned in this paper must therefore

be considered as the mean temperature of the core. With the acetyleneoxygen flame we found, when using the elements hthium and sodium

(F/ = 5.4 and 5.1 eV), an average temperature of 2500 °K; with the ele- ments cobalt and iron {Vi = 7.9 eV) there was an average temperature

of 3000 °K. Let us now look at the possibihty of determining transition probabilities of emitted wavelengths from the large number of analytical data

(/^-factors) that have been determined in the course of the years (63

elements, 678 spectral hnes). For this, further consideration must be

given to the significance of the X-factors in connection with the rate of

evaporation S/, so that we can then with the help of eq (5) and Table 8

arrive at final conclusions. By a /^-factor belonging to a certain spectral

fine of a certain element we mean the ratio of the concentration (C) of the element which is present in the analytical sample and the experimentally determined intensity // (=7/ +

^ — /^ = intensity of fine + background minus intensity of background near the fine). This may also be

put SLS K—C for the case of 7=1. The values of the intensities are standardized on an arbitrary scale. In contrast to flame photometry, where aU the material is introduced as a nebula into the flame, in the arc a partial introduction into the measuring volume takes place: the lower the boiling point of the element to be analyzed, the greater the vapor pressure wiU be during the rise in temperature of the anode tip, and the greater the sideward losses [15]. In order to determine these losses we have experimentally introduced a

"fictitious" rate of evaporation Si. In Table 7 a few values of S/, in (rel.) cm/s are given. The absolute values of these sideward losses have not Table 7. Relationship of speed of evaporation (SO and boihng point of some elements.^

Element Boiling point T °C Si rel cm/s

Cd 770 400

Te 1390 220

Cu 2300 80

Fe 3000 40

Mo 3700 20

Th (O2) 4400 10

^ The relationship between Si and T can be expressed by log Si =

2.94-0.44 Tx 10-3.

237-323 0-67— 10
132 TRACE CHARACTERIZATION

been determined, but it is possible to state that the losses with copper

{Si = 80) are twice as great as with iron {Si = 40). These sideward losses are thus something quite different from those reported by CorUss and

Bozman when under the heading of "persistence of atoms in the arc"

they mention sideward losses on account of diffusion into the surrounding

atmosphere, which is dependent on the mass of the atom (atomic weight).

If, in order to determine A (transition probability), we revert to eq (3), then we can rewrite this [16] as

(Reference [16] contains two errors in the calculation: Incorrect application of the formula of Saha, and wrong values of the partition functions.)

But we also have to know (the number of atoms introduced under

standard conditions into the measuring volume) derived from 5 mg of analysis material containing an element of atomic weight a in a concentration of K%. This amounts to 3KX 10^^/a, and after correction for the relative rate of evaporation Si it becomes 3KX lO^VSj X a. Now a correction is still required for* the sensitivity of the photographic emulsion. By means of -factors of four cadmium lines the instrumental

yield was determined, which in our case was 1/1.5 X 10^. In the same way as described in the chapter on flame photometry we

can now include the degree of ionization (Saha) and the degree of disso- ciation of molecules, as well as the temperature of the measuring volume,

in our calculation. In this way the reciprocals of transition probabilities of emitted wavelengths were found (Table 8). Agreement with the data

of the literature may be termed reasonable and proves that practically

all factors having an effect on the spectrochemically determined result have been taken into account.

Table 8. Reciprocals of transition probabilities of emitted wavelengths.

A=IX SINghv exp (- EelkT). (5)

Au 2427 I Ba 3071 I Cd 3261 I Co 3453 I Fe 3719 I Na 3302 I Ti 3349 II V 3185 I Zn 3076 I

This paper

1.8x10-8 5, 1.3xl0-« 5. 170X 10-« 5. l.Ox 10-« 5. 5 X 10-« 5. 18xi0-« s. 0.2 X 10-8 5 0.1x10-85.

200 X 10-8 5

220 X 10-8 5 0.8x10-8 5. 20 X 10-8 5 35 X 10-8 5 0.8 X 10-8 5 0.9x10-8 5.

AUen [17]

Corhss and

Bozman [18] 2.2x10-85.

1.7x10-85.

330 X 10-8 ^ 0.5x10-85.

5 X 10-8 5 6 X 10-8 5 0.3 X 10-8 5 0.5 X 10-85.

230 X 10-8 5^
OPTICAL AND X-RAY SPECTROSCOPY 133

Here it is of importance to observe that in the choice of spectral Hnes

for spectrochemical purposes attention must be paid to the transition

probabihties: a relatively small ^-value produces the chance that energy

that has been taken up will be given off again, not by the relevant dis- crete emission but by energy transfer to a second component that may

be present in the sample (colhsions of the second kind). Spectral lines of this type are the resonance intercombination hnes of atoms and ions, as well as those originating from two electron transitions.

2. The Significance of the Rate of Evaporation, Sideward Losses and the Temperature of Column and Mantle

If this method of complete evaporation is going to be used for series analysis, where standard samples resembhng the specimens in composition are used, no attention need be paid to Si or to the temperature T of column or mantle. This is generally the case with all the variations of

this technique that there are. If, however, one is dealing with a large measure of difference of the samples to be analysed, the above method

is stiU the best to use, in spite of the objection that the properties, such

as melting point, boihng point, vapor pressure, reactivity with carbon,

of the elements, compounds, or mixtures occurring in the specimens are not always known. In the case of volatile salts (hahdes) it is always

advisable to convert these, with nitric acid, to nitrates which at higher

temperatures easily decompose into oxides; in many cases these are reduced by carbon to the metals, which then vaporize with their specific rate of evaporation. Sulfates are in many cases reduced to sulfides and metal. The tendency of a number of metals to combine with oxygen

is sometimes so great that they vaporize as oxides in the carbon arc (aluminum, for example). Other metals, for example tungsten, form

carbides of such a high boihng point that they cannot be vaporized. As

the principal component of a specimen they cannot then be determined

quantitatively other than by subtraction of the sum of the impurities

from 100%.

The elements on the left of the periodic table with their low ionization

potentials reduce the temperature of the column. For example, during

the evaporation of sodium {Vi = S.\ eV) from a glass the temperature of the column, with our method of analysis, falls from 6100 °K to 5600 °K. Elements (or compounds) evaporating simultaneously (for example zinc;

Vj = 9A eV) are then excited much less. For such cases correction curves are naturally available. During the evaporation of calcium

{Vi = 6.1 eV) from a glass a temperature fall of 300° is measured. This

relatively slight reduction in temperature is achieved by the specimen's

rather slow evaporation rate, caused by the relatively large diameter of the electrodes (already mentioned above). Narrow electrodes are the cause of greater sideward losses [19], a larger measure of simultaneous

vaporization, and a greater concentration of the vapor of the specimen.
134 TRACE CHARACTERIZATION

with accordingly greater changes in temperature. By way of orientation

it is recommended to examine moving plate spectra.

Quite generally it may be stated that elements which are excited in the column (Vi atom > 7 eV, and also ionic lines of elements with Vi < 1 eV)

exhibit more reproducible results than elements excited in the mantle

{Vi < 7 eV). The latter, after all, is much more susceptible to temperature fluctuations on account of direct exchange of heat with the surroundings. For an accurate determination of these elements the flame

photometer will therefore have to be used.

3. Additions Before Arcing

Alterations in the temperature of the column, brought about by the

kind of specimen being analysed (components with a low value of Vi), can be suppressed to advantage by addition of an excess of, for example,

a lithium compound [20] in which case it is only necessary to ensure that lithium is present from the beginning of the exposure to the end. Then

the effect is a virtual increase of the mantle at the expense of the column.

This reveals an endeavor to "homogenize" the temperature of the arc. In the selection of an internal standard, either one of the components

of the specimen being analyzed or an additive, it is important to ensure

simultaneous vaporization of the internal standard and of the element

(or compound) to be determined as well as excitation at the same place

in the column or mantle of the arc. In the analysis of refractory materials fruitful use has been made of additives which, on account of their high boiling point and in accordance

with the principle of carrier distillation, carry along all impurities that would otherwise have remained behind in the specimen (classical

example of Scribner and MuUin and many others).

4. Limits of Detection

With the d-c arc, described in section Ill.l.a. and indicated for short

as the K-arc, it is possible to reach limits of detection equal to about

V3 X A^-factor, corresponding on average to 0.001%. The factor Vs is based on the practical experience that with low background a line blackening of 0.03 can still be observed significantly, both visually and

instrumentally. A modification of this K-arc permits the limit of detection to be lowered even further: electrode gap 2 mm (= sum of cathode

and anode layer); 10 mg instead of 5 mg analytical material; the same

current of 10 amps (mean temperature of the arc 6700 °K); all the light

is transmitted to the spectrograph. This arc discharge will be termed

the ^-arc [21]. The vaporization of the analytical material takes place

in a shorter time, and sideward losses and temperature change to a greater extent than in the K-arc. Where the precision of the results
OPTICAL AND X-RAY SPECTROSCOPY 135

(2 X C.0.V.2) with the ^-arc varies between 10 and 2% rel. in the concentration range of 0.1 to 100%, with the ^-arc in the range of 0.001 to 0.0001%

it amounts to 25% or more. (Obviously this percentage can be reduced

if the number of exposures is muhiphed.^

For the determination of concentrations in the ppm range it will be

necessary to examine resonance lines and single lines whose upper

levels he somewhat higher in the term scheme. It has been shown by

experiments that for those elements excited in the column (F, > 7.5 eV)

the relation log (K-factor/^-factor) = 0.24 F/ — 0.64 apphes, while for those excited in the mantle (F; < 7 eV) the relation is log (X-factor/

factor) = 0.04 Fi + 0.86. In the case of sodium, for example, the limit of detection is reduced by a factor of 12 if instead of the K-arc the ^-arc

is used. This is quite definitely not a consequence of the higher temperature of the Q-arc but mainly because all the light of the ^-arc is trans- mitted to the spectrograph. It should be remembered, however, that with the imaging of the light source on the prism, as described above,

the latter is not completely illuminated [22]. Complete illumination can be achieved if the Ught source is imaged on the slit of the spectrograph, so that, in our case with a Hilger large quartz spectrograph, an

increase of signal and noise by a factor of 14 is obtained. The enhancement factor of 14 can be raised to 30 if one starts not with 10 mg but

with 25 mg of analytical material. Furthermore it is sometimes possible

to superimpose spectra, by which means a hundredfold amplification

of signal and background is obtainable in accordance with

Ii+h — h — h

100(7/+,- /ft) =1007,.

This method of analysis will be indicated by s.p.s.: superimposed spectra;

hght source projected on s\lt. This does not mean, however, that a decrease of the limit of detection by a factor of 100 will be found. If a

significant value is to be given, it is necessary to take into account the

variabihty of the background and that of the line. . The above considerations can also be described in a somewhat different way: in the spectrum

of the ^-arc a resonance line of an element may not be observed because

of the fact that the line lies submerged in the background; even though

the photographic plate does not record it, the relationship Ii = Ii+h — If, holds, but both densities lie in the lower (horizontal) region of the characteristic curve. However, if the signals Ii+h and h are amplified a hundredfold, for example, then they give rise to densities lying on the

straight part of the characteristic curve. The spread of the two densi2 c.o.v. = coefficient of variation.
136 TRACE CHARACTERIZATION

ties must be known, and the presence of a line can be determined significantly if the difference with ^-fold amplification comphes with — nh > 2(76 V2 . For a general discussion of the determination of the limit of detection

reference should be made to paper [23]. From a paper on the further

working out of the above principle the following may be quoted [22]: with hundredfold amplification the real gain factor was 45, reduced by

interference with molecular bands to 12 or by impurities present in the

graphite electrodes to 25. In Table 9 the limits of detection (V3 ^-factor

and s.p.s.) of a number of elements are given. The latter values are corrected for the increase in the background above 3100 A.

5. Impurities Present in Graphite Electrodes

When an arc burns between unloaded electrodes the evaporation of the carbon impurities takes place in such a way that a relatively large

fraction does not reach the zone of excitation but is lost sidewards in the stream of air ascending along the electrodes. This means that the

investigation of spectroscopic graphite must not be carried out by having an arc burn between two clean electrodes. The material to be analyzed

has a collecting action, and the effect of collection can be defined as the ratio of the intensities of spectral lines found with and without a material not containing the element in question. In practice we use extremely pure germanium dioxide. It is understandable that the time

in which the material (the specimen of Ge02 being analyzed) is evaporating will determine the collecting action. This effect, described for the first time in [24], and at greater length later in [22], will be described

in detail in a future publication (Witmer and Addink) after routine

experience during three years.

6. Other Methods of Evaporation and Excitation

At the C.S.I. XII (Exeter 1965), the most recent one to be held, various

methods have been described which essentially boil down to a different way of tackling the problem of atomization, viz, the uncouphng of the

samphng of the analytical material from the physical state in the measuring volume, something that has long been standard practice in flame

photometry. Reference should be made to the papers by Margoshes

and those of the school of Kaiser.

Of the application of the laser, which reminded the present author of

the exploding wire technique, long since abandoned, beautiful examples were given by Mme Vilnat. B. The Spark

The spark, which is used so often and which may be considered with

its small measuring volume to attack practically always a fresh part
OPTICAL AND X-RAY SPECTROSCOPY 137

Table 9. Limits of detection of various elements in the D.C. arc, expressed in ppm (/xg/g). Limit of detection

Element Wavelength A ^-method ^ s.p.s. -method ^

oZoU n 1 U. 1 U.Ui

Al 1. U. i 1

.

Ac zoou OU. Z < oU OU. 1i

.

All All ZD / 09z. u.uo

T>£> 9zlQ7 9Z. u.uo

JjC OiOU U. 1 0U. 11 Dl oUO / 1i. • UO

CACa oZOi lU. 11

.

L.0 ZoZl 0. .Ui Cr zooo lU. .Uz L.U ^9/17 oZ'+ / n 9 U.Z ~ o.uz

r e oUZU 9z. — 0.1

Lra Zy^o 9QzlQ 1i. A AO O.Uz

9/^c:i ZOOi 11. A AO O.Uz Zooo Q

o. 0.07

in ozoo 9z. A O U.Z

ir Q99n ozzu iU. 1. 9Q/I

O

Zo^-y iU. A r» U.Z

IVlg ZoOZ n 9 U.Z A AT A 1 U.UI — U.l

iVin zo /o 1. A AO U.Uz Mo oioZ lU. 1. oUUZ Q

o. A A/C U.Uo Us zyuy iU. A O U.Z

T>r ZOOO QOoU. A ^ U.o ro ZOOO 1. A AO U.Uz

o(Jo4 o

z. A AC U.Uo Kn o4o4 lU. 1. Sb 2598 7. 0.2 Se 2413 300.

Si 2516 1. 0.05-0.5

Sn 2840 3. 0.07

Te 2385 70. 10. Ti 3242 10. 1. Tl 2767 20. 0.5 V 3185 10. 1. Zn 3076 20. 1. Zr 3391 10. 1.

^ See Section IILA.4.
138 TRACE CHARACTERIZATION

of the surface, shows a great measure of reproducibihty. In our laboratory for a number of years the main constituents of magnetic steel have been determined accurately: 2 X c.o.v. = 0.5% rel. On account of

greater sideward losses, smaller amounts of vaporized material, and more

ionization it will be difficult to achieve extremely low limits of detection.

Yet it was found possible, by projection of the spark on the sHt of the

Hilger large quartz spectrograph and by extension of the exposure time

by a factor of 3 (1 V2 min 4V2 min), to achieve amplification by a factor

of 60 and a real lowering of the hmit of detection by a factor of 35 [25]. One more aspect should be pointed out particularly: also with the

spark, on account of the high temperature of the sparked spot, there is selective evaporation (and diffusion in the solid towards the sparked

spot). To avoid such effects and possibly the influence of the previous

history of the material being analyzed it might be better to cool the elec- trodes with, for example, liquid nitrogen. In this way the effect of sputtering would be simulated, in other words the composition of the

vapor would be completely identical with that of the solid [26]. Another point worth mentioning is the shortening of the exposure

time in automatic spectrum analysis by increasing the frequency of the

spark. The amount of material converted into the vapor phase wiU be

correspondingly greater, so that the exposure time can be reduced.

A further point to be mentioned is the examination of the composition at the surface of conducting materials (Fig. 1). In this figure

the depth of penetration is plotted against the spark time, and thus

spectra can be obtained in which the thickness of the layer being an- alyzed is established unambiguously.

C. Future Prospects

The d-c graphite arc, though not exhibiting such a large measure of

reproducibility on account of the evaporation of analytical material,

which is coupled to the kind of excitation volume, has its own special

merits as a general method of analysis, especially with its extremely low

limits of detection (Table 9). In consequence of the relatively large

amount of analytical material that can be examined (10-100 mg) the effect of heterogeneity of the sample can be circumvented, in contrast with the

spark source mass spectrometer which has the same or even lower

Hmits of detection but in which the consumption of material is less. The endeavors to uncouple vaporization and excitation deserve

every attention. Raising of the excitation temperature, so far from being

significant, is probably even harmful. "Homogenization" of the temperature of the excitation volume (with greater energy density) as well as exact temperature measurements are aspects to which attention should

be paid, and so is the use of selected gas atmospheres for arc and spark.
OPTICAL AND X-RAY SPECTROSCOPY 139

10 20 30 AO 50 60 sparking time in seconds

Figure 1. Mean depth of penetration, in fx, for various metals and alloys as a function of the sparking time (in seconds). Point-to-plane technique; silver counter electrode

(angle 120°); gap width 2 mm; 15000 V; 0.005 fiF (Hilger Power Supply).

IV. X-Ray Fluorescence and Microprobe Analysis

A. X-Ray Fluorescence

1. General Considerations

While in flame photometry and classical spectral emission analysis

the material to be examined is introduced in vapor form, whereafter

excitation of atoms takes place by collisions with each other or with

electrxDns, the analytical material in the case of x-ray fluorescence

analysis remains unchanged in phase. It is irradiated by a source of

almost completely constant energy, and it is possible in advance to predict a large measure of reproducibihty of the results of analysis. All the same, unless a comparison is made with a standard which is identical as far as composition is concerned, the systematic error may

be large, being caused by changing absorption ofprimary andfluorescent

energy on account of changes in the chemical composition of the analyti- cal material. In general, the following relation holds:

^trans ~ ^prim ^xp (jXm X m) (6)
140 TRACE CHARACTERIZATION

where /prim = intensity of the primary radiation,

/trans— transmitted intensity,

)Ltm=inass absorption coefficient,

m=mass of irradiated material, given by its surface (1 cm^)

and the depth of penetration (expressed in cm).

If the material consists of the elements A, B . . . , we can say, with Ca

as the concentration of element etc.: Mm = fJimA X + IJimB X Cfi + . . . . (7) Now, following Liebhafsky et al. [27], let us consider the contribution of an element A to the fluorescent yield {(IIa) of a small element dm, situated

in such a way that a mass m Hes between dm and the surface. From eqs

(6) and (7) we find, with /c as a proportionality constant,

dlA = kX /prim exp — [{fJimA X + ^mB X Cfi)prim X m]

X exp — [{fJLmA X + fJLtnB X CB)fiuor X X X . (8)

Equation (8) can be rewritten as

diA =kX /prim exp - prim + f^m fiuor) Xm]XdmX Ca = kX /prim exp{-Qm)XdmX Ca • (9) For the sake of simplicity the angles of incidence and reflection have

here been left out of account. On integration over a total mass M, which may be considered infinitely

thick, eq (9) becomes:

dlA = kXlp,i^XCA exp{-Qm)Xdm

jo jo

or

IA = kX /prim X Ca X [1 - exp (- Qm)yQ .

In the case of infinite thickness, we have e

^'" = 0, so that we find:

lA = kxI^,,^xCAlQ. (10)

From the above eqs (9) and (10) it is possible to draw two conclusions:

Conclusion 1, derived from eq (10): if Q remains constant for various

concentrations of the elements A, B, etc., Ia and Ca are hnearly

proportional.

Conclusion 2, from eq (9): if e'^"" is unity, which means that Qm is ap- proximately zero, there is a hnear relationship of Ia to Ca, with no

attention having to be paid to interelement effects and the like.
OPTICAL AND X-RAY SPECTROSCOPY 141

2. Non-Linear Working Curves (First Conclusion; See also [28])

In many cases the concentration range chosen is so small that, above

all* with interpolation, the systematic error is very small. It may happen,

however, that really extreme cases are involved:

/. The determination of a heavy element present in a light matrix; in

this case the analytical curve is concave to the concentration axis and may in fact be practically parallel to it, so that there can be no question any more of an analysis. Such a case is encountered in the deter- mination of lead in a lead glass: lead concentrations in excess of 20%

can in practice no longer be determined. To overcome this difficulty

the relevant sample, in powder form, can be mixed with a heavy element

or its compound in powder form (similar particle size!). The value of Q

in eq (10) is then increased by a large amount, depending on the quantity

added, so that Q becomes practically constant. Analysis results: 2Xc.o.v. = l% rel. In the above case it was always the Pb La-line that was measured. If the Pb M;3-line is measured, the absorption coefficients come to lie closer

to each other: the result is as if a hght element in a Hght matrix were

deterrriined: the objection of strongly bent analytical curves is can- ceUed [29J.

//. In the case of a light element present in a heavy matrix we did not encounter analytical curves strongly bent in such a way that at low

concentrations the curves would tend to run parallel to the concentration

axis. In such an extreme case the addition of a light element (or compound) might be favorable, but where the absorption by the heavy ele- ment is, let» us say, infinitely large the contemplated object is not achieved. This is important for trace analysis of light elements.

3. Thin Layers {Second Conclusion)

An extensive description and discussion of the method followed

will be found in [30|. A few details will here be given: mean layer thick- ness about 0.1 jjl; weight of the material to be analysed about 0.5 mg.

The layer is obtained by homogeneous distribution of a small quantity of the powdered sample on "Mylar" foil; the holder of the foil, with sample,

is turned upside down and tapped gently; the layer is hardly visible; other methods of applying such layers have been described [31], and

there are analogous methods in which a diluted solution is applied to

filter paper which is afterwards dried. According to eq (9) we find under standard conditions of excitation

C = KX I, where C = concentration of the element to be analysed,

/= intensity of the fine in question, and K=a. proportionahty factor,

which is equal to the concentration if / is unity. We can call them

micro-/(^-factors. Their values are given in Figure 2. Although the

c.o.v. is relatively high (2 X c.o.v. in the case of nickel is 3%) it is certain
142 TRACE CHARACTERIZATION

10 A inX units

2.5 1.79 0.49

E« 0.5

0.2

0.1

0.05

0.02

0.01.

K<X micro-K-factors

•/. bv weiaht i —

i

i

-4

r 4-

\t

ff-—

<

54

3 ^ 2 o

o

E 1

0.4

0.3

0.2

0.1

1

/

K/3 micro

•/. b\ -K-factor

f weiqht

i

1—

/

10 20 30 40 50 60 ——^at.no. Z

30 40 50 60

at. no. Z

10 20

Figure 2. "X-Flu" micro-K factors (Ka, La) as a function of the atomic number Z.

that, if the appHcation of thin layers is improved, a fruitful method of analysis can be obtained.

4. Factors Beariiig on Fluorescence Energies

In [30] results are shown of the calculated ratio of the intensities of

the three elements chromium, nickel, and antimony (Z respectively 24,

28, and 51) and these results are compared with the experimentally

determined micro-/^-factors. For this purpose the following factors have

been taken into account, which may in general be considered to apply:

/. the intensity of the primary radiation of continuum and characteristic

emission;

//. the constant K (eq (9)), made up of the fraction of the irradiated

energy absorbed by the layer and the fraction of the absorbed energy

available for the excitation, the fluorescence yield, and the transition

probabihty;

///. the counting efficiency;
OPTICAL AND X-RAY SPECTROSCOPY 143

IV. the length of the analyzer crystal.

The reflection coefficient of the analyzer crystal (mosaic structure) and

the absorption by beryllium, air and "Mylar" foil were neglected, and

then found

/cr:/xi:/sb = 0.23: 1 :0.005; determined experimentally

lIKcr : VK^i : l//^sb = 0.35 : 1 : 0.002. The agreement may be considered reasonable.

Without change in items I-IV above it is only possible to lower the

limit of detection if the number of counts is increased. Experimentally

it has been shown that if the counting time is increased by a factor of

100, which means a decrease in the c.o.v. by a factor of VlOO= 10, a decrease by a factor of 6 has actually been found [32].

B. MiCROPROBE Analysis

While with the above "micro-K" method an amount of material of on

average 0.5 mg was sufficient for an analysis, the smallest amount of

analytical material for the microprobe amounts to 10 ~^ mg. Essential

for this method is that a volume of 1 /x^ can be investigated apart from

neighboring volumes. Since the object acts directly as the anticathode

it is not necessary to take absorption by beryllium and other substances

into account. By the use of polymolecular soap crystals (2d ~ 100 A)

it has been found possible to demonstrate, for example, 0.1% of carbon

in iron. The difficulty encountered in the calculation of the concentrations lies in the lack of the values of the mass absorption coefficients at these relatively long wavelengths [33]. Data for the depths of penetration of accelerated electrons can be taken from the hterature [34]. Incidentally the concentration calculation is analogous to that used in x-ray fluorescence analysis.

C. Future Prospects

Many aspects have been omitted from our considerations: absorption

analysis, discussions concerning accuracy [35] and many more [36]. As far as the analysis of hghter elements is concerned, the following

quotation of Pomey [37] is apposite: "In order to achieve the determination of still lighter elements it is necessary to make a breakthrough more

in the field of equipment than in the methods used." This is a chal- lenge for the instrument makers but it falls outside the scope of this paper.

I
144 TRACE CHARACTERIZATION

V. Final Conclusions

At the end of this paper it is desirable, with the points mentioned in the introduction in mind, to give a brief summary, understanding by

"flame" the analysis by flame absorption and emission, by "arc," in- cluding "s.p.s. arc," and "spark" classical emission spectroscopy, and

by "X-Flu," including micro "X-Flu," x-ray fluorescence analysis, also of thin layers, while "microprobe" refers to x-ray emission electron

microprobe analysis.

7. Is the method complicated or simple?

Answer: Except for "microprobe" the methods are simple. Dissolving

is necessary for "flame," sometimes desirable for "X-Flu" (reduction

of interelement effects and preparation of synthetic standards).

2. Is the method of analysis a quick one?

Answer: Yes, in all cases except "microprobe."

3. Are the results reliable (systematic errors), and how great is the

reproducibility (c.o.v.)?

Answer: Systematic errors are caused by

a. interelement effects ("flame" and "arc": shift of ionization and dis- sociation equilibria, "arc": change of evaporation rate and of the magnitude of the measuring volume);

b. history of the analytical material ("spark");

c. unknown absorption coefficients ("X-Flu" and "microprobe").

The reproducibility is determined mainly by the constancy of the

exciting light source. Arranged in ascending order of c.o.v. we find: "X-Flu," "flame," "spark," and "arc."

5. Is the result of the analysis representative of the bulk composition

or of the surface composition of the sample?

Answer: With appropriate sampling, the methods here described,

except for "microprobe," can be used for the determination of the

bulk composition. With "X-Flu" and "spark" it is possible to perform

very good surface analyses (chemical surface treatment here being left out of account).

6. For which concentration regions are certain methods of analysis

most suitable, i.e. at what concentration is the reproducibility at its best?

Answer: As a rule of thumb, it may be said, at a concentration of at least 3 to 5 times the limit of detection. In this marginal region the

value of 2 X c.o.v. amounts to 20% rel. [22] for the least reproducible

method of analysis (our s.p.s. arc method). For the methods with the

best reproducibility ("X-Flu" and "spark") values of 2 X c.o.v. of 0.5%

rel. apply at relatively high concentrations.

4. and 7. How much sample is required for the analysis?

What about the possible hmits of detection? . Answer: For the former question it is possible to distinguish between
OPTICAL AND X-RAY SPECTROSCOPY 145

the amount of examined material that is involved in excitation, and the

amount of material that can be handled. Of an amount of, for example,

10~^ mg examined with "microprobe" it is no longer possible to say

that it can be handled, though it does merit this epithet if it is contained

in a bigger mass. An amount of 0.2 to 0.5 mg ("micro X-Flu" and "arc"

[38]) can already be handled quite easily, but the relative limits of

detection here He considerably higher than the ppm range. With

"flame," where the work is always performed with amounts in solution

that can be handled, it is difficult to indicate the amount of material

by numerical examples, because of uncertainties connected with the

concentration of the relevant element in the solution and the equipment

used.

In Table 10 a few data have been collected which indicate by way of

orientation the Umits of detection in ppm and /xg, as well as the amount

of analytical material required.

8. It is a weU known fact that close to the hmit of detection a "poor"

reproducibility is found. How can this be influenced favorably?

Answer: With chemical methods of preconcentration left aside, the

reproducibility of "X-Flu" can be improved if the number of pulses is increased and, particularly with the light elements, if pulse discriminaTable 10. Limits of detection of various methods of analysis.

Method

"Arc"

"Arc s.p.s."

"X-Flu"

Mean limit of detection

ppm ixg

0.3(0.01-1;

8(2-15)

Required amount

for carrying out analyses

7(0.01-30) 0.15(0.0002-0.6) 20 mg

("^"P^'^^^^^

\analysis / 0.1(0.003-0.3) 300 mg

0.4(0.1-0.8)

"Micro X-Flu" 2000(200-50000) 6(0.6-150)

50 mg

/ analysis

Vin 6-fold

/single

\analysis , /analysis \ ^ (in 6-fold)

Remarks.

a. Values in parentheses indicate the lower and upper limits, depending on the element.

b. "Arc" and "arc s.p.s." figures, taken from Table 9, refer to a general method of analysis.

c. "X-Flu" figures [25] refer to a number of impurities present in

steel.

d. "Micro X-Flu" figures, taken from figure 2, refer, though with more

restrictions than those of "arc", to a general method of analysis.
146 TRACE CHARACTERIZATION

tion is applied; that of "'arc" and of "spark" can be improved if the

number of exposures is increased and if measures are taken to reduce

the background (controlled gas atmosphere, selective evaporation, and

the like); that of "flame" can be improved by the selection of a some- what higher flame temperature (increase of signal), in which case attention should be paid particularly to the elimination of molecular bands

(low noise). But here it should be remembered that the intensities of bands of N2, CN, and NO, excited in the column of an arc at 6000 °K, are decreased strongly if the temperature is brought down to about

5500 °K, whilst molecular bands of OH and O2 show lower excitation

energies; they are excited at a temperature of 4000 °K [25]. These data

are mentioned here in connection with the choice of the vaporizing gas

to be used.

VI. Future Prospects (General)

Apart , from the remarks made at the end of each section, "flame"

(emission and absorption) and "arc" can be considered to be approaching each other ever more closely, with the desire for a homogeneous,

adjustable temperature and a great energy density of the measuring

volume playing an important role. The supply of the analytical material

need not take place exlusively via an aqueous solution but can perhaps

also take place in powder form (the work described in [39| is pointing

in this direction). Furthermore the aim in view should be a general,

uncomphcated method of analysis, which, as proved by experience (our

K and Q methods) can quickly solve most problems.

YII. Acknowledgments

In his esteemed letter of invitation of 22 March 1966, Dr. W. Wayne

Meinke wrote to me, among other things: "I am convinced that you

will feel a definite sense of satisfaction in broadening your own hori- zons." It is just in this respect that I am so grateful to him, particularly

since in our laboratory in Eindhoven facilities are available to perform

trace analyses with "flame," "arc," and "spark" (automatic and nonautomatic), "X-Flu" and mass spectrometry, as well as with the help

of modern wet methods of chemical analysis (including micro gas

analysis and gas chromatography), electron microprobe and radioactivation analysis and where "a rather parochial point of view," to quote Dr. Meinke, must always be overcome in order to find the best answer to the required analysis.

I am very grateful to Mr. A. Witmer, Dr. C. van de Stolpe, Dr. H. Vink,

Mr. H. Wallace, and Dr. M. Margoshes for the many discussions I have

had with them, and to Dr. M. Klerk for data given to me on electron

microprobe analysis, Mr. F. de Boer for his careful measurements

carried out in the field of flame photometry, and Dr. A. Brii for the

determination of the sensitivity of the photoelectric cell of the flame

photometer.
OPTICAL AND X-RAY SPECTROSCOPY 147

VIII. References

It should be noted that C.S.I, is the abbreviation of Colloquium Spectroscopicum

Internationale.

[1] Margoshes, M., Proceedings of the XII C.S.I. (Exeter 1965) Hilger & Watts, London

(1966) pp. 26-42.

[2] Alimarin, J. P., Pure Appl. Chem. 7, 455-472 (1963).

[3] Oldfield, J. H., and Mack, E. L., Analyst 87, 778-785 (1962).

[4] Moore. Ch. E., An Ukraviolet Multiplet Table. NBS Circular 488.

[5] Boumans, P. W. J. M., Theory of Spectrochemical Excitation. Hilger & Watts, London (1966).

[6] Kalff, P. J., HoUander, T., and Alkemade, C. T. J., J. Chem. Phys. 43, 2299-2307

(1965).

[7] Kubaschewski, O., and Evans, E. L. L., Metallurgical Thermochemistry. Pergamon

Press, London (1965).

[8] Geiseler, G., Z. Physik. Chem. 202, 424-437 (1954).

[9] Mavrodineanu, R.. and Boiteux, H., Flame Spectroscopy. Wiley, New York (1965),

p. 207.

[10] Walsh, A., Proceedings of the XII C.S.I. (Exeter 1965) Hilger & Watts, London (1966), pp. 43-65.

[11] Pinta, M., Recherche et dosage des elements traces. Dunod, Paris (1962), Chapter

XIII

[12] Dean, J. A., and Stubblefield, C. B., Anal. Chem. 33, 382-386 (1964).

[13] Addink, N. W. H., c.s., Appl. Spectry. 10, 128-137 (1956).

[14] Thiel, B., and Krempl, H., Z. Angew. Phys. 14, 341-347 (1962).

[15] Addink, N. W. H.. J. Iron Steel Inst. (London) 194, 199-211 (1960).

[16] Addink, N. W\ H., Spectrochim. Acta 15, 349-359 (1959).

[17] Allen, C. W., Astrophysical Quantities. The Athlone Press. London (1955), pp. 63-78.

[18] CorUss, C. H., and Bozman, W. R., Experimental Transition Probabilities for Spectral Lines of Seventy Elements. NBS Monograph 53 (1962).

[19] Eichhoff, H. J., and Addink, N. W. H., Proceedings of the VHI C.S.I. (Lucerne 1959) Verlag, H. R. Sauerlander & Co., Aarau, Switzerland (1960), pp. 89-92.

[20] Kroonen, J., and Vader, D., Line Interference in Emission Spectrographic Analysis.

Elsevier, Amsterdam (1963).

[21] Addink, N. W. H., Proceedings of the C.S.I. VI (Amsterdam 1956) Spectrochim. Acta 11, 168-178 (1957).

[22] Addink, x\. W. H., and Witmer, A. W., Proceedings of the C.S.I. IX (Lyon 1961), Groupoment pour I'Avanelment des Methodes Spectrographiques, Paris (1962), VoL 2, pp. 340-354.

[23] Kaiser, H., and Specker, H., Z. Anal. Chem. 149, 46-66 (1956).

[24] Webb, D. A., Nature 139, 258 (1937).

[25] Addink, N. W. H., Limitations of Detection in Spectrochemical Analysis. Hilger &

Watts, London (1964), pp. 96-118.

[26] Addink, N. W. H., Werner, H. W., and Witmer, A. W., Proceedings of the XII C.S.I. (Exeter 1965), Hilger & Watts, London (1966), p. 653.

[27] Liebhafsky, H. A., et al., X-Ray Absorption and Emission in Analytical Chemistry.

Wiley, New York (1960), p. 154.

[28] Addink, N. W. H., Kraay, H., and Witmer, A. W., Proceedings of the C.S.I. IX

(Lyon 1961), Groupoment pour I'Avanelment des Methodes Spectrographiques,

Paris (1962), Vol. 3, pp. 368-384.

[29] Groot, T., et al.. Nature, in press.

[30] Witmer, A. W., and Addink, N. W. H., Science and Industry 12, 1-6 (1965).

[31] Eichhoff, H. J., and Bech, K., Publ. GAMS 1962, pp. 339-354.
148 TRACE CHARACTERIZATION

[32] See [25], p. 100.

[33] Klerk, M., and Roeder, E., Chemie-Ingenieur-Technik, in press.

[34] V. Ardenne, M., Tabellen der Elektronenphysik, lonenphysik und Ubermikroskopie,

VEB Verlag Berlin (1956), Vol. 1, pp. 151-152.

[35] Mack, M., and Spielberg, N., Spectrochim. Acta 12, 169-178 (1958).

[36] de Vries, J. L., Proceedings of the XII C.S.I. (Exeter 1965), Hilger & Watts, London

(1966), pp. 81-98.

[37] Pomey, G., Proceedings of the C.S.I. IX (Lyon 1961), Groupoment pour I'Avanelment

des Methodes Spectrographiques, Paris (1962), Vol. 1, pp. 460-462.

[38] Addink, N. W. H., Mikrochim. Acta (1956), pp. 299-303.

[39] Czakow, J., Proceedings of the C.S.I. VIII (Lucerne 1959), Verlag H. R. Sauerlander & Co., Aarau, Switzerland (1960), pp. 114-118.
OPTICAL AND X-RAY SPECTROSCOPY

Contributed Papers and Discussion

H. KAISER

Institut fiir Spektrochemie und An^ewandte Spektroskopie Dortmund. Germany

1. Introduction

There were 15 papers submitted for this session, covering a large

variety of subjects. Most of these deah with special analytical problems of microanalysis or trace determination, giving many details of working procedures, suggestions for technical improvements, and numbers for precision, limits of detection, and sometimes accuracy of cali- bration. F.our papers dealt with questions of primary importance.

These were by Adams and North, Fassel and Golightly, Hobbs and Rees,

and Winefordner. The first one contained general considerations

about terminology and the other three were concerned with the theory

and practice of the limit of detection.

But the question of how the limit of detection of an analytical procedure

should be defined and what limits of detection actually had been achieved

occurred in nearly aU of the papers, and so the chairman of the session

and the rapporteur decided that these principal questions should have

greater attention than details of analytical procedures during the rather

short period of the discussion session, itself. This report then tries to summarize remarks and considerations which were brought forward

during the discussion session, and also many points which were raised

in connection with other topics of the symposium and in the many small

group discussions which took place.

II, Contributed Papers

To give a more complete survey of the contributed papers, it may be

said that three papers dealt with new methods, which seemed to be

promising, but for which the field of analytical problems where they may

be used has not yet been thoroughly explored. There were two papers

dealing with atomic fluorescence. One, by Winefordner, considers

atomic fluorescence when a flame is used to evaporate the sample

and to produce the neutral atoms which may absorb and reemit radiant

energy brought to them at the wavelengths of the resonance lines. Limits of detection are reported for difl'erent elements and shown

149
150 TRACE CHARACTERIZATION

to be in the range of 0.0001 ppm to several ppm. The other paper, by

Svoboda describes the use of a heated graphite crucible to evaporate

the sample into an argon atmosphere.

The paper by Walters et al., described a method which may be used

in the analysis of rare earths to determine traces of other rare earths

by the characteristic fluorescence line spectra of these elements, the

fluorescence being excited by x-rays. The effects of the matrix composition and of particle size distribution on the measured intensities are discussed as are calibration problems. As an example, detection limits

in Y>0:i are reported for seven other rare earth elements and shown

to he in the range from 0.02 to 10 ppm.

Two papers dealt with problems of local microanalysis. One, by

Chaplenko and Landon, revives the nearly forgotten technique of a microspark; the other, by Cunningham and Ryan, uses a laser microprobe to evaporate the material and to excite the radiation with an

auxiliary electric discharge. With both methods the area of the sample

which is analyzed is of the same order of magnitude (several lO's of microns diameter) and the amount of sample may be several nanograms.

Since these two very diff"erent methods were used to solve different

analytical problems no immediate comparison of their relative merits

is possible from these papers. Several papers, particularly those by Adams et al., Adler, Campbell

et aL, and Elfers, consider combination methods for trace determination, different procedures of preconcentration and separation being

discussed; in particular, ion exchange chromatography in the paper by

Elfers on cesium determination. ^^^Cs is used as a tracer to control

the preconcentration and separation reactions. In nearly all of the contributed papers, as in the invited lecture given

by Dr. Addink, the same principal problems raised their dragon's head

and revealed that even such well established methods as atomic emission

spectroscopy and x-ray fluorescence are not thoroughbred if the field of their normal applications has to be extended to microanalysis and

trace determination. There actually is much hidden embarrassment

about basic concepts and about the possibility of comparing the different

methods not just arbitrarily but in a meaningful and universal way.

Many of these open problems are arranged around the central question

of the limit of detection. One such problem is calibrating the analysis

function for the determination of traces. It is not only the preparation

of standards but also the extrapolation of the analysis function from the

range of decent high concentrations down to the dark region of low

concentrations. This brings up the most important task — how to measure correctly the background intensity under the analysis line and how

to make a background correction in practical, routine analytical work.

In the discussion, E. B. Owens, MIT Lincoln Laboratory, pointed

out that the poor hmits of detection which were arrived at by direct
OPTICAL AND X-RAY SPECTROSCOPY 151

reading spectrometers in the analysis of metals were mainly due to the

fact that no individual background corrections are made and that, in many cases, no provisions to make such measurements and corrections may be given. One method to overcome the drawbacks of in- sufficient instrumentation — in this case by scanning the spectrum and

by the use of signal discrimination — was mentioned but did not receive

much attention and further discussion. The question remains open

whether this technique may be only a substitute for continuous observation of background and of line intensity by means of a high resolving

spectrometer or if there are inherent advantages beyond that possibility.

Closely related to the problem of calibration is that of reliable standards of known composition and another one, how to produce samples

which may be regarded as representative for a bulk sample. These

questions are raised in different ways in papers by Adams et al., Adler,

Rigdon, and Walters et al. Influences of matrix composition on the

analytical functions and interelement effects are considered in the

papers by Adams et al., Campbell et al., Chaplenko and Landon, and

Walters et al. There are two other problems which lead immediately to the central

problem of this report, which is the limit of detection. One is the control of reagents for impurities, which may actually determine the practical limit of detection which one may get, in spite of the fact that the

very core of the analytical procedure, itself, may yield much lower limits of detection if only pure substances would be available. The second is the choice of the best optical instrumentation for a distinct analytical

problem.

Going through the contributed papers, the invited papers, and the

topics of this symposium, the reader will detect considerable uncertainty

about this point. Some rather fuzzy statements about instrumentation

may be found in many of the papers, indicating that the problem, itself, has been realized but no solution could be given. Just one quotation

may be useful: "The monochromator must be capable of minimizing

spectral interference, whether line or background, without loss of

sensitivity." A general approach to how instrumentation could be op- timized is offered in the second paper by Winefordner, but so far only

the formal mathematical treatment has been given. It is urgently

wanted to give not only the approach but concrete solutions for many

different spectrochemical procedures.

The present embarrassment is the result of a transient period in the

further development of atomic spectrochemistry and in the winning of new fields of applications or of a wider range of concentrations. Many

private terminologies and private definitions are abundant, which may

not facilitate communication among the workers in different fields. There is a general tendency to hide difficulties in understanding and the

lack of knowledge about the complicated procedures occurring in the

237-323 0-67— 11
152 TRACE CHARACTERIZATION

light sources behind a protecting wall of words or theoretical considerations without practical consequences. One main and general resuh

of the discussions during the colloquium was to make this intellectual

situation obvious and to start efforts of common meditation. The very

important theories of modern physics on the production of radiation are highly important. They may offer valuable guidance to a deeper understanding of the most complicated processes which are going on in spec- trochemical hght sources, but they should not be misused to replace a more pragmatic and direct approach to a problem.

III. Nomenclature

In this situation, agreement on nomenclature and symbols is necessary.

In the paper by Adams and North, some general considerations on nomenclature are given, some questions raised, and some proposals

made. Adams was given an opportunity to add remarks during the

discussion session. The results of the discussion may be summarized

as follows: An agreement on nomenclature cannot be gained by public

discussions alone or by balloting. A systematic approach can only be

made by relatively small and competent committees which have to consider all the proposals and opinions which may have come up in public

discussions.

At present, the ASTM Committee E-2 is especially interested in questions of nomenclature and there are committees within the Analytical Division of the International Union of Pure and Applied Chemistry

(lUPAC) which are working on such topics. The lUPAC Committee V.4 on "Spectrochemical and Other Optical Methods of Analysis" is preparing a document on nomenclature and symbols and since B. F. Scribner,

NBS, V. A. Fassel, Iowa State University, and L. S. Birks, Naval Research Laboratory, are members of this committee there should be a good and constant communication with ASTM Committee E-2.

The general idea about nomenclature seems to be that there are two

classes of terms. Those of the first class have a very precise meaning.

These terms should preferably be defined by a mathematical equation

or by an experimental procedure and not in words. Concepts belonging to this class are "limit of detection" (see below), "sensitivity,"

"concentration," etc. These terms are by nature connected with

numerical values. There is a second class of terms which are used in coUoquial scientific language. They don't require a very rigid definition. Their exact meaning will become clear by the context or by some additional explanations as the case may be. Some guidance may be useful

to avoid misuse, but too narrow regulations will produce a very clumsy

language. Examples for such terms are: "trace," "ultratrace," "major

or minor constituent," etc. For instance, if the meaning of "trace"

shouldn't be clear from the context, the best thing would be to give the
OPTICAL AND X-RAY SPECTROSCOPY 153

range of concentrations (e.g., 1 to 10 ppm) and not to rely on any foregoing statement which may long be forgotten.

There is special confusion about the term "sensitivity." This term

in analytical chemistry is sometimes used to describe that quality of an

analytical procedure which leads to a low Hmit of detection. However,

in most other branches of science and engineering, "sensitivity" is a

differential quotient giving the slope of the characteristic curve for the

measured quantity. In analytical chemistry this might be the slope of the analytical function relating the measured quantity to concentration

values. Therefore, it is advisable to use the word "sensitivity" only

in this latter and more general sense. An analytical method which

yields a low hmit of detection may be said to have a high "power of detection." Such an expression would match well with terms like "re- solving power," etc. IV. Limit of Detection

As to the limit of detection, itself, it has become the general opinion

that only a statistical definition will hold and will give an objective number for a Hmit which is independent of any personal judgment. The

idea is to give a generally applicable criterion when the measured quantity can be detected with a sufficiently high level of confidence among

the unavoidable statistical fluctuations which every measuring device

will show [1].^ Only values which fulfill this criterion will be accepted

as being real; smaller ones are to be rejected. This idea is probably more than 50 years old. It has been used in spectrochemical analysis

for more than 20 years and nowadays it is often referred to as the concept

of "signal-to-noise ratio." This terminology was created by electronic

engineers and it is certainly a good descriptio^i of their actual experience,

since in electronic communication systems the noise is heard and it is always the question whether the useful signal, for instance the words

and phrases in a telephone conversation, can be detected clearly enough

among the "noise."

But it must be said, the use of this term ''signal to noise ratio'' in analytical work should he discouraged. The term "analytical signal,"

perhaps, may be a good one and could be retained but it is certainly

hard to call the possible fluctuations in the contamination in any reagent

a "noise." The use of "signal to noise ratio" may be misleading, since

in many analytical processes electronic devices are used for the amplification and readout systems. But it would be a bad mistake to think

of their electronic noise as the decisive fluctuation which determines the

limit of detection of an analytical procedure. This may be so in some

cases, but in chemical analysis there may be a level of statistical dis- turbances an order of magnitude above the electronic noise. This has

^ Figures in brackets indicate the literature references at the end of this paper.
154 TRACE CHARACTERIZATION

been pointed out in many of the contributed papers, for instance, by

Campbell et al., and by Winefordner. To illustrate this point further, some of the causes of statistical disturbances are hsted below:

1. Counting of single events, Poisson distribution ((t= V/V) (photons,

atoms, electrons . . . ). 2. Receiver (shot noise, dark current, thermal noise of amplifier,

grain of photographic plate).

3. Light source (background, bands, line intensity, temperature,

volatilization, chemical processes).

4. Inhomogeneity of sample.

5. Contamination of sample and reagents.

6. Measuring process, errors and deviations (e.g., balance, recorder,

photometer, etc.). A general definition of the limit of detection which is applicable to any

analytical procedure is given by the following triplet of equations:

x = XM + k'(Tti (la)

c=f{x)

(lb)

g=^'M (Ic)

In equation (la) "jc" is any measured quantity. For instance, voltage,

transmittance or a weight. The bar underneath indicates the limit. The suffix "6/" points to "blank" analysis. Therefore, "xu is the average

value measured in blank analysis, cr^j denotes the standard deviation

of the blank measurements and the star is a "caution mark" to remind

one of the necessity to investigate very carefully to what extent the

standard deviation computed from conventional type blank analysis

actually represents this quantity for the whole procedure in question.

For instance, in spectrochemical analysis when blank values are taken

for the background alone, in the actual analysis two intensity measure- ments of this type have to be combined to correct for background and,

therefore, the essential standard deviation

where ctu is' the standard deviation for intensity measurements at background level.

It should be clearly seen that Formula (la) gives a pragmatic approach.

For any given analytical procedure it is possible to determine experimentally the value of "cr*;" if the procedure is critically considered.
OPTICAL AND X-RAY SPECTROSCOPY 155

It is not necessary to develop a theory of this standard deviation. Sometimes, however, in particular for electronic noise, a theory can be de- veloped and may be used but the determination of the essential standard

deviation (7^,/* is by no means dependent on a theory.

Equation (lb) is used to symboHze the analytical function correlating

the measured quantity "jc" and the concentration "c"; hence, c symbohzes the concentration value at this hmit of detection, determined by

X. Equation (Ic) is added for the case where the Hmit of detection is required in absolute quantities £, for instance in grams, micrograms, etc., M (for magnitude) is a symbol for the quantity of the sample to be ex- pressed in the same units as forg. It is useful to realize that the splitting of the problem by the two equations, (la) and (lb), avoids the appearance

of ghostly negative concentrations in the computation of the Hmit of

detection. Actually, the measured quantity is the analytical signal

which has to be detected among the statistical fluctuations and by no means the concentration, c, itself. There is still some disagreement about the value of the factor "A:" which gives the level of statistical confidence. This, it may be hoped,

can be settled by convention. At present some authors, for instance

Winefordner, Fassel, and Addink, prefer k = 2 while others, for instance

Kaiser and Specker, prefer A- = 3. During the discussion it was mentioned that the theoretical high Hmit of confidence given by the factor

of 3 may not be justified but in many practical cases only a limited number of the tedious blank analyses may be performed and for this reason some additional statistical insurance may be packed into the factor "A:". However, the general opinion seems to be that the factor A = 1 gives too low a level of confidence to be significant at all. Therefore, as long as no international convention has been arrived at, the value of "A" which

has been used in the calculations should be given.

The splitting up of the problem as indicated by (la) and (lb) is a most

powerful means to optimize the parameters of an analytical procedure.

This may be pointed out by the diagram given in Figure 1. This diagram

is very schematic. The abscissa corresponds to the measured quantity,

X, the ordinate to the concentration, c, the straight line symbolizes the

analytical function, and it is assumed that this analytical function has

been determined by standard samples reading I, II, and III in a range of higher concentrations. The double arrow indicates the process of

critical extrapolation to lower concentrations. So this part of the dia- gram corresponds to Equation (lb). By Equation (la) the lower Hmit

of "x" is given and the region x < x_ where the signal can no longer be

detected is the fined section in the diagram. The point where the

analytical function enters this forbidden zone corresponds to the concentration value, c, at the limit of detection.

Now it can be clearly seen that this value depends on two things: the

position of the analytical function in the diagram and the position of
156 TRACE CHARACTERIZATION

X Figure 1. Diagram illustrating relation between analytical function, signal, level of

statistical fluctuations (noise?), and the limit of detection.

the border of the forbidden zone. These two may change quite independently of each other. The parameters of the hght source and of the

optical instruments may act in quite different ways on these two decisive

positions. The reason why many theoretical investigations about the

hmit of detection in spectrochemical emission analysis have become

so complicated and so few successful is that the position of the analytical

function and that of the forbidden zone have not been treated separately.

This point will be taken up later in this report.

It must be clearly realized that this rigid statistical definition of the

hmit of detection by its nature can only be used for definite "complete

analytical methods" and not for general "analytical principles." For

instance, nobody can give general limits of detection for polarographic

analysis, for emission spectroscopic analysis, or for atomic absorption

analysis. The concept of a complete analytical method comprises the statement of the analytical problem. The nature of the sample and the

elements to be determined must be given. Furthermore, the analytical

procedure must be described in all detail together with the instruments

used. Finally, the evaluation of the measurements must be prescribed.

For instance, whether the outcome of single measurements are used

to give the analytical result or whether the average of several measure- ments is taken will cause a considerable change in the limit of detection.

Many misunderstandings have occurred because the strict correlation

between numerical values for the limits of detection and the distinct "complete method of analysis" has not been seen. This was made

clear during the symposium by the discussion of the paper by Hobbs

apd Rees which has the provocative title, "Confident Analysis Above

and Below the Limit of Spectrographic Detection." The obvious con-
OPTICAL AND X-RAY SPECTROSCOPY 157

tradiction occurs since the "limit of detection" in the title refers to a method when only a single analysis is considered; the claim, however,

to detect the element in question below this limit refers to another type

of analysis where many repeated determinations on the same sample are brought together by a special evaluation procedure.

Hobbs and Rees give a rather rough but most useful procedure to get some kind of an average of many repeated runs just by counting the

number of "detected" and "not detected" analyses (yes or no). This can be particularly useful at very low concentrations when only "purity"

of the sample has to be judged. It might be helpful to translate the

notion used by the authors into the more conventional notion so that the

correlation of these ideas might become more obvious.

A good example where by averaging the results of 10 analyses the

hmit of detection is reduced by a factor of VTo, is given by Figure 2 for the case of the photometric determination of iron in a solution with

o-phenanthroline. The solution contained 0.02 mg/ml. In the left half

of the diagram the results of single measurements have been plotted.

The blanks (open circles) and the results from the sample (crosses) are

partly mixed up. The statistical Hmit of detection was computed to be

0.04 mg/ml. Therefore, a concentration of 0.02 mg/ml cannot safely be

detected. The right half gives the average values for 10 single measurements, and now the values for aU measured samples are clearly

distinguished from the values for the blanks. This illustrates that this change in evaluation, averaging 10 single measurements, constitutes a new analytical method and therefore a lower hmit of detection is arrived

at.

97.50

9700 -

96.50 -

SINGLE

c = 0.04 ^g/ml

o o o

AVERAGE OF TEN

c = 0.012 ^g/ml

o

O BLANK

X 0.02 fig Fe/ml 23456789 10 2 3 4 5 Figure 2. Improvement of detection limit by replicate measurements, for the determination of iron with o-phenanthroline.
158 TRACE CHARACTERIZATION

Figure 3 demonstrates, for the photometric determination of nitrate, that the "sensitivity" of an analytical method and the "limit of detection" may be quite independent quantities. It is well known that the

"sensitivity" of a photometric method is proportional to the length of the absorption cell. Thus, the sensitivity for the analysis in the right half of the diagram was 5 times as high as for that in the left part. Also,

the average level of absorbance for the blanks was different in both

cases but the statistically calculated limit of detection practically did

not change. The diagram shows that the statistical fluctuations grew

with the length of the absorption cell [7]. This diagram also demonstrates that the statistical fluctuations which

are described by the essential standard deviation, cr*;, by no means

should be confused with the average value of the blank measurements.

For instance, in emission spectrochemical analysis a constant background can always be corrected for. What prevents the analytical

signal (the analysis line) from being detected is not the size of the background itself, but the unpredictable fluctuations around the average

level of the background. Therefore, the statement which is found in some papers in the literature that the hmit of detection for spectrochemical emission analysis be given by the ratio of line intensity over background intensity is decisively wrong. The cause for this mistake may

be found in the uncritical acceptance of the concept of signal to noise. "Noise" is not simply "background" and — referring to the corresponding

E

0.03

d = 1,002 cm £ = 0,3 mg//

E

0,09

'B

d = 5cm

c = 0,27mg/f

Figure 3. Effect of cell path length on detection hmit for the photometric determination

of nitrate.
OPTICAL AND X-RAY SPECTROSCOPY 159

fact in electronics — it must be said that the electronic noise also does

not contain the constant dc component.

In connection with this well-defined and widely-accepted concept of the limit of detection there is one problem which only recently has found some attention among analytical chemists. This is the problem of what

it means when the search for an element in a sample was in vain and the

report about this analysis says "'not detected." It may be surprising

that this question must not be answered by a statement that obviously

the concentration of this "not detected" element must be lower than

the limit of detection. The lower limit of concentration which can be

given as a guarantee for the purity of the sample is always higher than

the limit of detection for the analytical method. This is so because one must take into account that, in the case of the actual analysis, by some

statistical haphazard, the expected analytical signal may be very low. Further explanation may be helpful. With any homogeneous sample,

analyzed by an accurate method in repeated runs, half of the results

will lie below the actual concentration and half above: the average will be about right. For a sample having the concentration c, corresponding

to the limit of detection, this wiU — by definition — have a peculiar con- sequence: The half of the determinations below the average wiU have an

analytical signal < x, so that they cannot be recognized among the statistical fluctuations. Therefore, this half wiU be recorded as "not de- tected" [3]. This difference is the inevitable consequence of the fact that these concepts are based on statistics; no sophistication can bridge

this gap. This will be even worse if the sample is locally inhomogeneous.

Therefore, the limit of guarantee for purity is always higher than the

limit of detection. The former limit is the result of sample and analytical

method together, w^hile the limit of detection is a quality of the analytical

method alone.

It was said before that the question of how the Hmit of detection of a

distinct anal>1;ical method may depend on the experimental parameters

is split up in two parts by the symbolic equations (la) and (lb). The

usefulness of the old Roman motto "divide et impera" in this case was

demonstrated by an investigation of how the limit of detection of an

emission spectrochemical method depends on the slit width and the re- solving power of the spectrometer or spectrograph used, all other parts

of the procedure, e.g., kind of sample, hght source, radiation detector,

being kept constant.

It has been known for quite a while that the position of the analytical curve within the field of the diagram, Figure 1, depends on the resolving

power of the spectrograph. K. Laqua [2] seems to have first reaUzed

that this analytical function becomes independent of the optical parameters of the spectrograph as soon as the resolving power of the instrument

becomes much higher than that which is required to show the profile of the analysis line as it is produced by the light source. Now, in the
160 TRACE CHARACTERIZATION

range of low concentrations the half width of the hne profile remains

practically constant, as long as no self-absorption or self-reversal is observed. Therefore, this half width AXl may be taken as a characteristic property of the hght source and the element in question.

A resolving power, RL = k/AkL corresponding to this half width can

be defined. It may be called here the "Hne profile resolving power."

Let Ro be the resolving power of the spectrometer, then R = RqIRl can

be used as a measure for what the spectrometer can show of the hne

profile. Now, when the sht width of the spectrometer "5" is measured

in units of the "critical sht width," "50", which describes the half width

of the diffraction image, hence 5 = 5/50, then the caHbration function

for any emission spectrochemical method in the range of low concentrations can be set up as: h ^l + s^ + R^ ... c = cu^-j

lu

In this equation cu 00 is a calibration constant which depends only on the

light source, the sample and the line of the element.

As can be seen, it is that concentration for which line and background

have the same intensity where a spectrometer of infinitely high resolving

power is used. The intensity ratio of line to background, h/Iu, is the

actual value of this quantity as it is measured in a given spectrometer.

It must be said that the intensity of the line must have been corrected

for background. The last term contains aU that enters this relation- ship from the side of the spectrometer. Only the reduced slit width,

s, and the reduced resolving power, R, are of importance in this respect.

This equation has been derived elsewhere [4] and also its general

validity has been discussed; for the moment it may be accepted without

further discussion. Only one assumption may be mentioned to prevent

mistakes. For this equation it is presupposed that the spectrometer

is completely and correctly illuminated and that the resolving power

is not restricted by aberrations, bad adjustment, or by the graininess

of the photographic plate. A generalization of this equation considering

these influences, too, can easily be made.

The third factor in this equation gives the interrelationship of analytical

functions which are measured with different spectrometers or spec- trographs; it is shown in the diagram of Figure 4. The variable parameter

of the different curves is the reduced slit width. All the curves approach

unity at a sufficiently high resolving power. By this function it is possible to translate the calibration constants from one spectrometer to another. Furthermore, by measuring the values cu 00 with a spectrometer of very large resolving power or by computing them from meas- urements with smaUer instruments using equation (2), it is possible
OPTICAL AND X-RAY SPECTROSCOPY 161

to get calibration factors characterizing mainly the Hght source in respect

to the special analytical problem. These constants are truly universal

and they, therefore, should be given in publications, not the ones which

are dependent on the instrumentation which was more or less acci- dentally at hand.

The curves of Figure 4 also show how the limits of detection depend

on the optical parameters, presupposing that the essential standard

deviation cr* is constant and does not depend on the optical parameters. Then it can be seen that the lowest limit of detection is arrived

at with a spectral apparatus having a resolving power much higher than

that characterizing the width of the line. But, of course, this is only one side of the problem, for the optical parameters may have considerable influence on the value of cr*. In a complete theory, allowing

for optimization of the method, these influences must be investigated

for the different radiation detectors. For photographic intensity measFigure 4. Dependence of the analytical function (and, for cr* = const, limits of detection) on the reduced resolving power, R, and the reduced slit width, s.
162 TRACE CHARACTERIZATION

urements, it can be shown that a further decrease of the Umit of detection is possible by using a spectrograph not only of higher resolving

power but also of high linear dispersion, since the image of the line then

covers a greater area on the plate, thus reducing the standard deviation

caused by the graininess of the emulsion.

Yet, there is a remarkable difference whether the quantity of the sample consumed in such an analysis is restricted or not. If it is restricted

sometimes the blackening of the photographic plate which is necessary

to give high precision in photometry may not be arrived at 0.2). Then it may be better to use a smaller instrument, which may yield

higher blackening.

Most of the commerical large grating spectrographs are not large

enough in resolving power and/or linear dispersion to yield the lowest

possible detection limits. What can be done with a spectrograph

having a resolving power of more than one million is shown in Table 1 for different elements in a dc graphite arc. The amount of sample

actually consumed in this analysis was so chosen that a blackening of

0.2 for the background was produced. These values may be compared

with those given in the paper of Dr. Addink for a more conventional

spectrograph. (These tables were first shown by K. Laqua at the Conference on Chemical Analysis at Lindau, April 1966 [5].) It may be

mentioned here that the line-profile-resolving power in conventional

light sources for most elements lies in the range 50 000 to 100 000. Therefore, a spectrograph might well have a resolving power of 500 000

to reduce the limit of detection by optical means. Such general considerations open the door to gathering data, in particular for the coefficients in analytical functions which are independent

of the instrument which was used in the actual measurement. This

would allow us to compare more reliably the different Hght sources and

other steps or devices in the analytical procedure. In their paper,

Fassel and Golightly have given a very comprehensive collection of data referring to flame emission and flame absorption spectrochemical

analysis. These tables allow us to compare the two methods and to decide which one may be the best for a distinct analytical problem. But

these values are bound to the present state of the art and the usual

instrumentation. The last step is missing. It would be important to have such values which are independent of the instrumentation, characterizing only the very heart of the procedure, so that it may become

possible to realize which principal possibilities for further development

are given. . During this symposium sometimes the question arose how the diff'er- ent methods for trace determination might be compared as to the

hmits of detection which have been attained or may be attained. There

is no doubt that even for such old techniques as emission spectrochemical analysis considerable progress may be ahead of us. Beyond
OPTICAL AND X-RAY SPECTROSCOPY 163

Table 1. Relative and absolute detection limits in graphite matrix

Direct-current arc Spark

Element, Ofvc ng mgsample atm /c ng mgsample Ag 1 3280 A A \y 1 A—

9.0 X lU " 0. ID Q37 OO / Air 1 1 V 1

1.1 X iU 6 I'l .0 0 i 00

A 1 TT O AZ!! O Al II 3962 1 C ^ 1 A—

i.O X lU " ZD lOoU As I 2780 1 O 1 A—

1.8 X lU ^ lolU QQ7 8.3 X 10 920 11100 B 1 2498 1 A \y' 1 A—fi l.U X llr" 7/ OoV Air

Ti TT A r C A Ba 11 4554 1 Q V 1 A—

i.O X lU z.u lo4U

T3 TT O 1 on be 11 3130 1 O s/ 1 A—

1.2 X lU n 1

Q

U. lo 1lUA7i ro

Bi 1 306o O O s/ 1 A—f) 2.0 X lU 4oo /Yir 1 /I V 1 A1 .4 X lU 794. 0

'^1L 70lyJ i^a 11 oyo4 1 A 1 A—

l.U X lU n 1

Q

U. lo loZO Ld 1 3261 ^ O X/ 1 A—

6.8 X lU /o 1 1 /I A 1 14U Air 6.8 X 10"-5 9AQA ovou Ce II 4187 1 9 \/ 1 A— ,T I.O X lU ^ 977 z / / 91 OA ZloU L.U2 Co I 3453 O A \y 1 A—fi 2.0 X lU " /I Q 9AA ZOU 1 A V 1 A- 1 .4 X lU -5 1 "^7 O^OU •^Q^O Cr I 3579 0 O \/ 1 A—fi 0.2 X lU " Q Q

O.C) 9AA ZOU Cu I 3247 c A V 1 A-8 D.U X lU U.Z /1 9A 4Z0 A \y Air 1 7 \/ 1 A1. / X lU -6 Zo9« 1 ftlR lO'+o

T?„ T Q'70A be 1 3/20 Q O \^ 1 A-6 117 11 / oOoU

1^ „ T /I 1 "70 Ga 1 41 iZ 1 "7 1 A—

1 . / X lU Q7 91 f\C\ ZlOU rn

_ T onon Ge 1 3039 O /I \/' 1 A—fi 2.4 X lU 1 A 7 10. / oyo Air A W 1 0 V 1 A- 1 .0 X lU 0 < 0 0 ( OU Hg I 2537 1 O N/ 1 A—

1.2 X lU 1 7QA 1 /oU 1 /I /I A 144U

In I 4511 C O \/ 1 A—

O.Z X lU ° o /

1 9Q9 IZoZ

Ll 1 6/08 O Q 1 A—fi O.O X lU " 7 A /.O Vo A \x- Air Mg 1 2852 /.Z X iU n 1

u. lo 991 ZZl Air A V 1 A- 4.0 X lU 7 00.0 1 1 40

A/r„ T 0*70/1 ivin 1 z / y4 "7 A \y 1 A— 7 7.9 X lU ' 1 O /I 1Z.4 loOo Air A W Z.U 9 n VX 1lUA--fi 91 ft 1 OQOO

Mo 1 3798 ^ "7 \y 1 A—

1 . / X lU 1 /I Q 14o Q7AA O /UU L.U2

1VT_ T conn

IN a 1 5890 /I A 1 A-fi 4.y X lu " 1 1 Q 1 lo 9/1 AA Z4UU rc\

iVTU TT onn/i JNb 11 3094 1 f\ \y 1 A—fi /.9 X 1(J " 1/19 14.

1 QA loU A \^ Air A A V 1 A- 4.U X lU ZDO OO^'

JNi 1 3414 1 "7 1 A—fi 1. / X lU " 11/1

1 1.4 A7/I O /4 i^r'i 1 /I V 1 A1 .4 X lU 91^9 ZoZ 1 ROf^ rb 1 4058 O A s/ 1 A— fi 2.y X lu 1 1 o 1 ly /I 1 1 A 41 lU DU T /lOAO Kb 1 4202 1.1 X 10"^ 2740 9/1 QA Z4VU rc\

ci_ T or AO bb 1 2598 A -7 1 A—

V. / X lU " Vo.o AAO 963 Air

c: T oooo bi 1 2882 /I O 1 A—

4.3 X lU ' O.O 1 i^/IA 104U A \^ Air

C „ T OO A A on 1 2840 1.5 X 10"** OA /I oU.4 9A9C ZUZo JS.L.1 Q Q V 1 A- 0.0 X lU -fi QlV14/I 11

1lUUOA

C TT Adno br 11 4078 5.5 X 10"^ C 7

5. /

1 Al 7 lUl / T* T O/; C O la 1 2653 9.7 X 10"'^ 2730 OOOA 282U t^r^i

JS.L-1 1 h II 2837 1.3 X 10"'^ lie 115 QQ9 ooZ CC\

'T*' TT O O /I A

ll 11 3349 9.7 X 10-7 1.3 1 0/; 136 CO2 1 0 \/ 1 A- 1.2 X lU -fi A A4U OOOUQA

Tl I 5350 3.2 X 10-^ 197 614 CO2

U I 3670 1.4 X 10-5 1130 8080 CO2

V I 3185 5.0 X 10-" 6.4 1280 KCl

W I 4009 7.3X 10-« 244 3340 CO2

Zn I 3345 2.2 X 10-5 58 264 CO2 2.2 X 10--4 3610 1640 Zr II 3392 1.3X 10-« 4.6 358 CO2

the question of optical instrumentation lies the still open problem of how the spectrochemical light source can be improved. One point

is how to keep the atoms for a long time within the zone where they can be excited and observed. What can be done in this respect using

absorption spectrometry may be demonstrated by Figure 5 which was shown at the Exeter Colloquium, 1965, by H. Massmann [6|. This
164 TRACE CHARACTERIZATION

10

1

10-2.

10-3-

10-^-

10-5

CONCENTRATION [ppm] FOR 1% ABSORPTION FLAME

a fa a Z3

10-9

10-fo

10-^^

10-^2 GRAPHITE TUBE

QUANTITY [g FOR l7o ABSORPTION

MgCdZn Li Nq K Ag Mn Ca RbCu f=e Cs Sr Cr Co Ni Au Rh Pb Mo Pd Tl 5b Bi GaSn Pt BaHgAl In Figure 5. Limits of detection by atomic absorption with the flame and with a graphite tube absorption cell. Length of cell = 5.5 cm.; sample volume = 0.04 ml.; most sensitive resonance lines measured. diagram gives a comparison of the limits arrived at for 1% absorption

using as the absorption cell a flame or a heated graphite tube as first developed by L'vov in which the atoms stay for a long time after

volatilization. During the symposium there was some kind of competition between

different possible principles of analysis. For instance, sofid state mass

spectrometry or neutron activation may yield very low limits of detection,

but it must be said that the nearly classical methods of emission spectrochemical analysis are by no means exhausted. There are quite a number of new ideas and experimental possibilities for further development,

in particular to provide a high power of detection. But from all the

discussions in the symposium it became quite clear that there may be

no other principle of analysis which has the same universality and such

an enormous information capacity as is incorporated in emission spec- trochemical analysis as a principle.

V. References

[1] Morrison, G. H., and Skogerboe, R. K., in Trace Analysis — Physical Methods, G. H.

Morrison, ed., Interscience, New York, 1965, pp. 1-23.

[2J Laqua, K., Hagenah, W. D., and Waechter, H., presented at XI Colloquium Spectro- scopicum Internationale, Belgrade, Sept. 30-Oct. 4. 1963, Paper No. B-8.

[3] Kaiser,H.,Z. Anal. Chem. 2 1 6,80(1966).

[4] Laqua, K., Hagenah, W. D., and Waechter, H., Z. Anal. Chem., in press.

[5] Laqua, K., Z. Anal. Chem. 221, 44 (1966).

[6] Massmann, H., Proc. XII Colloquium Spectroscopicum Internationale, Exeter, Hilger, and Watts, London, 1965, pp. 275-278.

[7] Specker, H., Z. Erzbergbau u. Metallhuttenwes. 17, 132 (1964).
EFFECTS OF TRACE IMPURITIES ON X-RAY

DIFFRACTION

J. CHIKAWA

Research Associate On leave from NHK Research Laboratories, Tokyo, Japan

and

J. B. NEWKIRK

B. F. Phillipson, Professor

University of Denver, Denver, Colorado

I. Introduction

Modern techniques of crystal growth have produced various kinds of

large and highly perfect crystals. To observe imperfections in these

crystals, numerous x-ray diffraction techniques, collectively called

x-ray topographical methods, have been developed [1].^ Although these

experimental methods are capable of giving a picture of the actual

extended imperfections present, the effects of point defects on x-ray

diffraction have received relatively httle attention, probably because

the magnitude of their contributions is usually too small to permit

accurate measurement. The diffraction effects of homogeneously dis- tributed trace impurities are also expected to be extremely small. However, there are some experimental approaches to the detection

of these small effects which appear to be successful, but which depend

upon minimizing the contributions from other imperfections through the use of highly perfect crystals.

For understanding diffraction from highly perfect crystals, one must

use the so-called dynamical theories of diffraction, in which multiple

reflections inside the crystals are taken into account. These theories

have been developed for ideally perfect crystals and date from the

time immediately after the discovery of x-ray diffraction (Darwin [2], 1914; Ewald [3-5], 1917, 1920, 1924; Bethe [6], 1928; von Laue [7], 1931). In recent years, these theories have been extended to include dis- torted crystals, and have been of great help in the understanding of the

diffraction images of lattice defects. The theories, however, are complex and are stiU in the process of development both in their fundamental

' Figures in brackets indicate the literature references at the end of this paper. 165
166 TRACE CHARACTERIZATION

aspects and in their applications. The relatively small effects of trace impurities on x-ray diffraction are understandable only by exact the- oretical treatments. Such treatments, however, must be based on

the dynamical theories and have not yet been formulated.

Inhomogeneous distribution of impurities results in fairly large

variations of diffracted intensity and in some systems can readily be

observed by x-ray topography. This effect is caused by lattice dis- tortion or lattice parameter variation due to the impurities, and can be

explained by the theories which have been developed for understanding

extended lattice imperfections such as dislocations. Some observations

and explanations for this effect are described in Sec. II. Section III

is devoted to diffraction effects due to impurities which are uniformly

distributed. These latter effects are observed in the integrated dif- fracted intensities as deviations from the theoretical intensities for the

ideally perfect crystal. The distribution of electrons in crystals is also expected to be changed by the presence of impurities. This

change results in very small variations of the crystal structure factor. A precision method for the detection of small changes in the structure

factor is discussed in Sec. IV. Finally, in Sec. V, other effects of impurities on material properties which are somewhat distantly related

to x-ray diffraction are described by two examples.

II. X-Ray DiflFraction Topography

X-ray diffraction topography is concerned with point-to-point varia- tions in the directions and/or the intensities of x-rays that have been

diffracted by crystals. From those variations, certain features of the

defect structure of a crystal may be displayed and examined in the

form of an unmagnified, photographically recorded image of the crystal

specimen.

Methods that mainly measure the local variations of the direction

of the diffracted beam are useful for the detection of gross misorientations such as grains or subgrains but they are not sensitive to impurity

variations. (Methods of Guinier and Tennevin [8], Schulz [9], Weiss- mann [10]). Intensity mapping methods, on the other hand, are chiefly

useful for revealing individual defects such as dislocations, stacking

faults, and local variations in impurity content. Since topographic methods can detect only variations of intensity

and direction within a broad diffracted beam, a perfectly uniform distri- bution of impurity gives no detectable effects on topography. Actually,

however, impurities in most crystals have non-uniform distribution due

to slight variations of the crystal growth conditions or to other imperfections such as dislocations which may or may not have interacted

with impurities. The intensity mapping methods give a topographical

image of the specimen and are quite sensitive to such non-uniform

distribution.
X-RAY DIFFRACTION 167

First, the intensity mapping methods for both the Laue case (dif- fracted beam leaves the crystal by a different surface than the one en- tered by the incident beam) and the Bragg case (diffracted beam leaves

the crystal from the same surface that was struck by the incident beam)

wiU be reviewed and then the causes for contrast will be discussed.

Next in this Section, we shall describe the effects of impurities on other

imperfections such as dislocations and imperfections produced from

impurities, i.e., precipitates and segregation. Finally, the topographic

detection of very small variations of lattice parameters due to impurities wiU be discussed.

Intensity mapping methods have been developed by several workers

independently. Among these have been Newkirk [13], Bonse and

Kappler [14], Lang [15-17] and Borrmann, Hartwig and Irmler [18]. Newkirk used a refinement of the Berg-Barrett technique in which characteristic x-rays are diffracted from the surface of a single crystal speci- men. A reflection method using single crystals was also used by Bonse

and Kappler, but with a double crystal spectrometer for collimating and

monochromatizing the beam. Lang developed a method for using

diffracted x-rays that have been transmitted through the specimen.

Borrmann et al., employed an anomalous transmission method using

relatively thick crystals. These methods will be briefly described here. Other techniques for diffraction topography are known but, on the whole,

are variations of those we shall discuss [19-21].

In this method the crystal is set to diffract the characteristic radiation from a hne focus x-ray source (Fig. 1). By placing the plate close to the crystal, geometric resolutions of ~ 1 /x are realized. Across the

diffracted beam local variations of the reflecting power occur, due to the imperfections in the crystal. Newkirk showed that single dis- locations could be detected by this technique and their Burgers vector can be experimentally determined. Topographs taken by this method

are shown in Figure 2. The corresponding transmission arrangement has been developed by

Barth and Hosemann. [19]

A. Experimental Methods

7. Berg-Barrett [77, 72]

Figure The Berg-Barrett arrangement.

237-323 0-67— 12
168 TRACE CHARACTERIZATION

Figure 2. (a) Light micrograph and (b-d) diffraction micrographs single crystal of LiF. Berg-Barrett method (b) 200, (c) 202 and (d) 220 reflections. Some grain boundaries and

dislocations (diagonal straight lines) can be seen. From the contrast variation of the

dislocations with the various hkl reflections, the directions of the Burgers vectors can

be determined to be < 110>. In the present paper, all the photographs of diffraction topographs are positives of the x-ray photographic plates, i.e., blacker regions correspond

to higher diff'racted intensities [13].

2. Double Crystal [14] X-rays from a line focus are reflected from a perfect reference crystal,

then from the specimen surface, and finally are recorded on a fine grained

film (Fig. 3). In this method the reference crystal and the specimen

are usually made of the same kind of material so that exactly the same

G?-spacing of the diffracting planes can be used in both crystals. As a

result of this arrangement, the shape of the rocking curve is nearly

independent of the spectral distribution of the radiation used (dispersion

is eliminated) and becomes 10-100 times narrower than any spectral

line [22]. This makes the method very suitable for measuring small

local tilts in the specimen lattice. When the specimen is shghtly misset from the exact parallel position, i.e., on one wing of the rocking

curve, tilts of only ~ 0.1 sec of arc result in detectable changes of dif- fracted intensity. This much tilt corresponds to a normal strain of about Ad/d=lO~^ , where d is the interplanar spacing. Strains of this magnitude occur at distances of 50 to 100 jjl from the cores of single dis- locations, depending upon the material examined. Kohra [24] and
X-RAY DIFFRACTION 169

SECOND CRYSTAL

REFERENCE

CRYSTAL

Figure 3. The double-crystal geometry. Renninger [25] have used a first crystal (of the double crystal arrange- ment) with greatly different spacing of the diffracting planes than those

in the specimen crystal, thereby allowing greater dispersion of the beam

than when the G?-spacings are identical. This combination results in appreciable loss of contrast sensitivity. Recently Deslattes [25a]

has shown that if only a shghtly different G?-spacing is used, the small

amount of increased dispersion that resuhs does not seriously reduce

the contrast sensitivity of the method. His results have made it un- necessary to find two identical crystals when using the double crystal

method. The double crystal arrangement may also be used with the

specimen set for transmission [23].

3. Scanning Transmission [16—17]

In this method, a ribbon x-ray beam is coUimated to such a small

angular divergence that only one characteristic wavelength is diffracted

by the single crystal specimen (Fig. 4). A stationary opaque screen

containing a slit allows only the diffracted beam to reach the photographic

plate. A diffraction photograph, made with the diffracted beam passing

through a narrow region of the specimen as shown is called a "section

topograph." On the other hand, a large area/ volume of the crystal can

be surveyed by scanning both the crystal and photographic plate in synchronism past the incident beam. In a transmission method

developed by Earth and Hosemann [19] a Hne x-ray source is used which

achieves much the same result as the Lang method, viz, a horizontally

extended field of view in the image. The drawback of Lang's more

complicated traverse apparatus, however, is compensated by the lower

background associated with the Lang technique, less trouble with simultaneous reflections (because a strongly collimated beam is used), and a higher resolution, since the photographic plate may be placed closer to the specimen.

Many different types of lattice defects have been observed by the Lang

technique. An example is the topograph in Figure 5(a) showing dis-
170 TRACE CHARACTERIZATION

CRYSTAL

FOCUS SCREEN

^

FILM

TRAVERSE

Figure 4. The Lang scanning method.

Figure 5. Diffraction topographs of dislocations with - [2110] Burgers vectors in a CdS

platelet, (a) Scanning transmission method, (b) Section topograph by a divergent beam

from a point focus. The topograph was taken in such a position that the axis of the beam

satisfied the Bragg condition on the dotted line drawn in (a). In (b), each dislocation image consists of two lines. From this contrast the signs of the Burgers vectors can be

determined. Crystal thickness: lO/x, /xo? = 0.86, MoKai, 2110 reflection.
X-RAY DIFFRACTION 171

locations in CdS. Such topographs are caUed "traverse topographs"

or "Lang topographs." Although the traverse topographs are convenient for surveying large areas, section topographs sometimes are more

informative as will be described later.

4. Anomalous Transmission [18] Inside a perfect crystal, the incident and diffracted waves are dynamically coupled. At the Bragg angle Ob, their interaction produces a standing wave pattern fitting onto the set of diffracting planes. Depending on the positions of the antinodes of this standing wave, the energy

transport of the wave field occurs with anomalously high (antinodes

coincident with planes) or anomalously low (antinodes between the

planes, Borrmann effect) absorption. (See Fig. 6.) Therefore, a perfect crystal set at the precise Bragg angle is capable of transmitting

interfering x-rays at crystal thicknesses which would absorb almost all the energy of a non-interfering x-ray beam. It is apparent from this argument that any source of imperfection which moves atoms away from

the geometric planes reduces the transmitted intensity. An example

of this effect is the intensity decrease due to thermal vibrations of the

atoms [26]. Borrmann et al. [18], using this principle to examine

relatively thick crystals, observed dislocations as lines of low intensity on a gray background (Fig. 7). B. Causes of Contrast [12]

It has been mentioned that when the Bragg condition exists in a perfect

crystal the primary wave Ko and the diffracted wave Kf, form the entity of the x-ray wavefield inside the crystal [27]. Depending on the deviaTRANSMITTED

rATOMIC PLANES ^^^'^.ci n

MONOCHROMATIC

X-RAY BEAM

(a) (b) Figure 6. X-ray wave paths inside a crystal, (a) Interaction of two waves in the primary and diffracted beam directions when the Bragg condition is satisfied, (b) The distribution of intensity as a function of position between the atomic planes resulting from the superposition of the two waves in (a). The phases have been chosen to produce nodes

at the lattice planes.
172 TRACE CHARACTERIZATION

wr»20cm

FOCUS

FILM Rh

FILM Rq

Figure 7. The Borrmann arrangement for anomalous transmission topography.

tion of the incident beam from the Bragg condition, the direction of energy flow of the dynamic wave field varies between the incident and

diffracted directions [28, 29). Since the angle between the incident

and diffracted beams is relatively large, variations in the direction of

the energy flow due to lattice distortions, as well as variations in local

intensity, contribute to the image contrast. According to the kind of

distortions that are involved, one can consider the following three causes

of contrast.

If the energy flow of the x-ray wave field produced in each part of a

crystal does not encounter any appreciable variations in dhki or tilt of the lattice, one can treat the contrast by regarding each part of the

crystal as a perfect crystal. The cause for the contrast is that each

part may simply be more or less mis-set from the diffraction peak given

by the Bragg equation k = 2d sin Bb- The mis-setting can be due to either a change of orientation Ob or of dhkh or of both simultaneously. How

large a mis-setting has to be before it causes a detectable intensity change

depends on the "precision" of the diffraction condition, i.e., the width

of the rocking curve (double crystal arrangement) or of the X-spread

(Berg-Barrett, etc.). In any case, the contrast should be proportional to

{W= width of rocking curve or A.-spread respectively). This is the most

straightforward cause of contrast in the double crystal method, where the

image is formed by diffraction from the thin surface region. Owing to the extreme narrowness of the double crystal rocking curve and the

steepness of its slope, this mis-setting is very sensitive in the double

crystal technique. Notice that the sign of the contrast depends on the

sign of the deformation as well as the direction of the mis-setting [30, 31].

1. Homogeneous Dilation and Tilt Contrast
X-RAY DIFFRACTION 173

2. Direct Image

This image is due to strongly distorted regions. The beam deviated

from the Bragg condition for perfect regions of the crystal enters the

distorted region, passing through the perfect region. Then, in the

distorted region, if the beam satisfies the Bragg condition it is diffracted. The diffracted beam then passes through the perfect region of the crystal

between the distorted region and the exit surface of crystal. If the

incident beam has a far larger divergency than the angular width of the

rocking curve, the diffracted beam from the distorted region super- imposes upon the diffracted beam from the perfect region. Therefore,

the images are always observed as intensity enhancements. If the dis- torted region has a mosaic structure, the intensity enhancement is expected to be proportional to the total volume that is distorted. As can be seen from the above argument, the signs of the deformation can be determined by contrast variation with the sign of the deviation of

the beam from the Bragg condition [32-35]. Figure (5b) is a section

topograph which was taken with the crystal in such a position that the

Bragg condition was satisfied on the dotted line drawn in (5a). In (b) the dislocation images can be seen crossing the vertical black band.

The Bragg condition was satisfied exactly on the center of the black band,

and, since the incident beam diverged from a point focus, on the right

side of the center 6 < 6b and on the left side 0 > 6b, where 6 is the actual

glancing angle of incident beam on the reflecting plane and 6b is the

Bragg angle. Each dislocation image in (5b) consists of two hues which

are considered to be located on opposite sides of the dislocation core. Therefore, the two-line images show that almost all the dislocations

have screw components of the right-handed screw type.

3. Dynamical Images

We shall now consider weakly strained regions which still behave

locaUy like perfect crystals, although, taken over longer distances, a continuous change of orientation and spacing of reflecting planes occurs. The wave field can adapt itself to these changes by a continuous variation

of the direction of its energy flow and correspondingly of the ratio hlh of the intensities of its components Kn and Ko [36] in the transmitted

and diffracted beams respectively. In transmission methods, both the bending of the energy flow and

the shift of energy between Ko and Kh are responsible for considerable

contrast effects in the Ko and Kh waves when they leave the crystal

at its exit surface [37-44]. Moreover, the Borrmann contrast may also be counted in this category [43], since it is due to the breaking up or

at least the continuous modification of wave field beams with anomalously

low absorption into highly absorbed wave fields or single waves.
174 TRACE CHARACTERIZATION

In reflection techniques, wave field beams can be bent back to the entrance surface where they add to the beam which is reflected at the

surface itself [45, 46], thereby causing density variations in a topographical image. In the Berg-Barrett method a major cause of the

dynamical image contrast is due to a local change in primary extinction.

This type of intensity extinction is due to the redififraction of a oncediffracted ray back into the crystal in the same direction as the entering

or incident beam. Because of a phase lag of 90° at each diffraction,

the twice diffracted ray is just 180° out of phase with the incident beam

and therefore interferes destructively with it [13]. In the case where the distorted region is fairly strongly strained,

i.e., intermediary between the case of the shghtly distorted region and

that of the strongly distorted region responsible for the direct image,

the waves from the intermediate case form a new wave field between the

distorted region and the exit surface [35]. The new wave field and the

original wave field show very complicated features of interference, and

wiU not be discussed here.

Actually all the above causes may be responsible for contrast simultaneously. For example, the two line images arrowed in Figure 5(b)

have asymmetric contrast. Notice that the right line in each of these

two line images is darker than the left one. This asymmetric contrast depends on the dislocation depth from the crystal surface and is ex- plained as a dynamical effect. That is, some part of the contrast is due

to the dynamical image, although a large part of the contrast may be

due to the direct image. However, depending on the kind of crystals,

crystal thickness, the hkl reflection, etc., one of the above causes usually

is dominant. In the Berg-Barrett technique and in transmission techniques, for /Xo^— 1, the direct image predominates. In the range

where 1 < pto ^ < 10 both direct and dynamical images are visible. With

/Lto ^ > 10 practically only Borrmann contrast is observed.

In the double crystal arrangement contrast is rnainly due to homogeneous dilations and tilts, and, sometimes, to wave field beams which

have been bent back to the surface.

The general condition for the visibility of a defect is that it produce

a sufficiently large disturbance of the set of diffracting planes used.

From this it follows that, for isotropic materials, dislocations can in principle completely vanish only if g • b = 0 and g • n = 0 (g: diffraction

vector, b: Burgers vector, n: vector normal to the slip plane). This

is referred to as the "visibility rule" in the present paper. Since, for dislocations containing both screw and edge components, both equations

cannot be satisfied simultaneously, mixed dislocations can never totally

vanish. In the anisotropic case, dislocations can vanish only if their

direction is normal to a mirror plane of elastic symmetry.
X-RAY DIFFRACTION 175

Table I summarizes the features which characterize the various

x-ray diffraction topography methods that have been discussed.

C. The Effects of Impurity on Dislocation Images

The direction of the Burgers vector of a dislocation can be determined

by applying the above visibility rule to topographs made with various

reflections, aU of which contain the dislocation to be studied. However,

if the crystal contains some impurity, the dislocations may be altered by the segregation of the impurity atoms upon them. The impurity

atmosphere may so modify the strain-field about the dislocation as to make the visibility rule inoperable. Such dislocations are referred to as "decorated dislocations." Therefore an excellent means is provided

for detecting minute traces of impurities. This impurity effect has

been seen in BeO [47], quartz [48], diamond [49], and Si [50] crystals.

Certain dislocation groups are visible in the Lang topographs of Figure

8(a) but are not visible in Figure 8(b) where g and b are perpendicular.

The dislocation group seen in Figure 8(a) was generated by plastic

deformation; therefore, one can assume that these dislocations are

relatively free of impurities. The micrograph shown in Figure 8(c) shows the x-ray image of the same wafer after copper was allowed to diffuse into the wafer at 900 °C for ten minutes. The x-ray image of Figure 8(b) is identical with that of Figure 8(c), except that it was taken

before copper diffusion. The dislocation group and several other dis- locations not seen in Figure 8(b) are clearly visible in Figure 8(c) because

Figure 8. X-ray topographs of a silicon wafer containing a dislocation group generated

by plastic deformation. Scanning transmission method, (a) 110 reflection, (b) Same

wafer as shown in (a). 101 reflection. The dislocation group seen in (a) is not visible here because bJ_g. (c) Same wafer as shown in (a) and (b) after copper diffusion. The picture was obtained by using the same reflection as in (b). These topographs were made by G. H. Schwuttke.
176 TRACE CHARACTERIZATION

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X-RAY DIFFRACTION 177

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178 TRACE CHARACTERIZATION

of the copper precipitation along the dislocation lines. An infrared

micrograph [51] of the wafer used for Figure 8(c) showed the presence

of fine needles at all dislocations. These were presumably precipitated

copper. From the size and spacing of the copper needles, the number

of copper atoms along a 1-cm dislocation line has been estimated to be not more than 10^^ atoms [50]. This concentration of decoration is apparently enough to enable all the dislocations to ignore the visibility

rule, thereby allowing them all to appear in topograph (c). The fine copper needles on the dislocations are not resolved in these topographs.

Under some conditions individual precipitate particles can be seen in diffraction topographs. This is discussed in Part D-1 of this Section.

Undecorated dislocations are defined as those whose visibility in x-ray topographs conforms with the visibility rules, i.e., their visibihty is not modified by strains introduced through the presence of impurities.

However, it cannot be concluded that any dislocation which follows the

visibility rule is entirely free from impurity on an atomic scale; it is unlikely to be so clean. The Burgers vectors of dislocations in some

impurity-doped crystals can be determined by their visibility variation

with the angle between b and g. Furthermore, the contrast sensitivity seems to depend on the kind of impurity but little further is known

about this effect.

It is known that a straight screw dislocation can become a helix

[52-54] by the absorption or generation of point defects at the dislocation

when the point defects are in excess or shortage of the equilibrium concentration. By the copper decoration method. Dash [55] observed righthanded helices in Si containing Au in a concentration of 10^^ cm^^ or

less. These right-handed helices were formed from left-handed screw

dislocations that had been introduced into the crystal by controlled

twist deformation. In this case, the sign of the screw dislocations was determined from the sign of the deformation. From this observation, he inferred that, owing to the low energy of combination of vacancies

and Au atoms, the Au atoms occupy the vacancy sites and, consequently, cause a vacancy deficiency which is responsible for the helix formation.

Such observations also can be made by stereo x-ray topography [13]

without the need for decoration, and thus the sign of the screw dislocations can be determined directly [32-35]. The topographs in Figure 9

show a helical dislocation b=l/3 [2110] in a CdS crystal. Figures

9(a) and (b) are a stereo pair made by the Lang method. They were made using 2110 and 2110 reflections as illustrated in Figures 9(d)

and (e), respectively. The stereo pair shows that the helix is left- handed. Figure 9(c) is a section topograph which was taken in such a position that the Bragg condition was satisfied on the dotted line drawn

in (a). A two-line image in Figure 9(c) can be seen. As in the case

described for Figure 5(b), it can be concluded from this two-line image

that the helix was formed from a right-handed screw dislocation. Since
X-RAY DIFFRACTION 179

•^^^^ ^3

0.3mm ^ 4.

(d) ^'*"^(e)

^X-RAY 4J 11 1^ 1 2ll0\^CRYSTAL-^ / alio

Figure 9. A helical dislocation with a - [2110] Burgers vector in a CdS crystal. (a) and

(b) are the left-eye and right-eye views of a stereo pair as seen in (d) and (e). The

topographs were made with 2110 and 2110 reflections, respectively, using the scanning

transmission method. They show that the hehx is left-handed, (c) Section topograph

taken at the position of the dotted hne drawn in (a). The observation shows that the left-handed helix was formed from a right-handed screw dislocation. Crystal thickness:

70fji;fjiot = 0.S6; MoKax.

the left-handed hehx was formed from the right-handed screw dislocation,

the helix could not have formed by the accretion of vacancies onto the

dislocation. Instead, the presence of some impurity, as in the case of gold in sihcon [55], must have been responsible for the formation of the

helices. A relatively small total number of impurity atoms could

produce this effect. In some materials stacking faults can also be observed by x-ray topography [56-60]. It is well known that the presence of impurities can

lower the energy of a stacking fault, though the local strain field may be

increased. Therefore, it is likely that stacking faults can be more readily

observed in crystals containing trace impurities. If this is so, the ob- servation of stacking faults in a diffraction topograph may be an indication of trace impurities. For example, in CdS crystals, stacking faults have been observed only for impurity-doped crystals [60-62].

D. Imperfections Produced From Trace Impurities

Precipitated impurity particles, systematic variations in impurity

distribution, and even randomly distributed impurity atoms have a large

effect on x-ray diffracted intensity. Each type of aggregation can be

seen by x-ray topography; precipitates especially have been observed

by many investigators.
180 TRACE CHARACTERIZATION

1. Precipitates

There is a tendency for large precipitate particles to be formed from

even trace amounts of impurities in some highly perfect crystals.

This is probably because highly perfect crystals, containing few, if any, dislocations or other crystallographic defects, offer few sites for preferred nucleation of a precipitating phase. Therefore, only a few

stable nuclei appear and the dissolved impurity atoms have only a few

sites on which to deposit. Using the Lang method, Schwuttke observed

individual precipitated particles of copper in dislocation-free Si crystals

containing copper in a concentration of less than 10^^ atoms cm~^

[63-64]. Such precipitates usually give a double crescent shape of

diffraction image [65], i.e., the images have a contrast-free region between

the two crescents, as can be seen in Figure 10. The long direction of

this contrast-free region always appears parallel to the reflecting plane

that is used to make the topograph. The images are formed by the

strain field around the precipitate particles as shown schematically in Figure 11. The contrast-free part of the image can be explained by the

visibility rule which provides that no contrast is produced when the

displacement of atoms is parallel to the reflecting plane. The atom

displacements within a spherical coherent precipitate particle are, to a first approximation, radial with respect to the particle. Any dif- fracting plane passing through the center of the particle contains atoms

which have no component of displacement normal to the diffracting

plane. According to the rule of visibility therefore, no enhanced

intensity will occur from any diffracting plane passing through the center

of the precipitate particle. By the same argument, one would predict

Figure 10. X-ray topographs of impurity-doped CdS (GaCls). Scanning transmission method 1010 reflection. Circular images due to precipitate particles can be seen. See

text for proposed explanation of double crescent shaped images.
X-RAY DIFFRACTION

-DIFFRACTING PLANE181

Figure 11, Schematic cross-section of the strains around convex-lens and concave-lens shaped precipitates. The choice of form apparently depends on w^hether the interplanar

spacing of the precipitate particles is larger or smaller than that of the matrix. The

arrows indicate the directions of displacements of the atoms, and the lines illustrate the curved atomic planes.

increased diffracted intensity from planes which are in the close vicinity of the precipitate particle, but which are enough removed from its center so that the atom displacements have a large component normal

to the diffracting plane. The above discussion leads logically to the

prediction of the double crescent figures which are commonly seen. The sign of the strain around precipitate particles can be determined

[66] in the manner described for Figure 5. Notice that the exact sizes of the precipitates cannot be obtained from

the image sizes because the diffraction images are determined by the

strain field around precipitates rather than by the precipitate itself. However, rough estimation of precipitate size may be possible from the

very faint images of the precipitate particles which are sometimes ob- tained by adjusting the orientation of the specimen so as to maximize

the difference in diffraction direction of the beams from the matrix and

the precipitate particles. Under this condition, the images lie between

the crescent pairs because they are formed by the highly distorted

regions close to the precipitates. The sizes and the population density

of the precipitates may be used for estimation of impurity concentration

as has been done by Furusho [67]. As seen from the image formation mechanism, identification of the

precipitates or the impurity is impossible at present. However, it may

sometimes be possible to obtain a diffraction pattern from precipitates

by a micro-diffraction technique. Furusho [67] has observed topographic

images of disc-shaped precipitates in Si crystals containing 10^ atoms

cm~^ of oxygen. He also obtained a diffraction pattern from a single

precipitate particle by means of a very narrow x-ray beam which was

directed upon the particle. The pattern thus obtained was a diffuse

Debye-Scherrer ring that indicated crystalhne Si02 [68]. No diffrac-
182 TRACE CHARACTERIZATION

tion ring was obtained for a perfect region of the silicon crystal. For

such a small impurity concentration, diffraction patterns of precipitates

cannot be obtained by usual diffraction techniques using an x-ray beam

with larger cross section.

If one can make a diffraction pattern of precipitates by a microdiffraction technique and, in addition, if the average size and population

density of the precipitates can be seen by topography, the identity of the impurity and a rough idea of its concentration may be estimated.

Elistratov and Kamadzhiev [69-70] made an x-ray diffraction study of precipitates from supersaturated solid solutions of Cu and Ge (concentration: ~ 10^^ atoms cm~^) and of Ni in Ge (~ 5X lO^'^ atoms cm~^).

They found that, in spite of the very low concentrations of Cu and Ni

in Ge, extra diffraction spots appeared near the main diffraction spot of the Ge matrix crystals. These extra-spots could not be explained by

scattering from Guinier-Preston zones or from nucleation centers of the

precipitate, because of the very small concentration of Cu and Ni. They

proposed that the anomalous effect may be due to large deformation at micro-cracks of the matrix Ge crystal caused by the precipitate.

Diffraction anomalies such as "spikes" and "satellites" due to high

impurity concentrations have also been studied using topographic

methods [49, 71, 72]. These effects are very interesting but are some- what out of the category of trace impurity studies.

2. Impurity Segregation: Non-Uniform Impurity Distribution

Non-uniform distribution of impurities produces strong contrast

in x-ray topographs. A typical example of this effect is the oxygen

banding which has been seen in Si crystals by Ishii et al. [73], by

Schwuttke [50, 63, 74], and Kohra et al. [75], and others. The oxygen

segregation bands appear to be perpendicular to the growth direction

in Si crvstals which were made in a quartz crucible by the Czochralski

method. Figure 12 is a topograph of the banded pattern which was

obtained using reflecting planes that are perpendicular to the growth

direction. Corresponding oxygen segregation bands [76] have also been

observed by the 9/x infrared absorption method [51]. Variations of oxygen concentration, computed from the absorption coefficient for the

infrared, of as little as 10^^ atoms cm~^ have been recorded by this x-ray technique [74]. Kohra et al [75], found that topographs of certain

silicon wafers, using the 111 reflection perpendicular to the [111] growth

direction, show an array of alternating weak and strong striations, whereas, for the 111 reflection, the positions of weak and strong striations are reversed, as can be seen in Figure 13. Such local failure of Friedel's

law was explained using the theory by Penning and Polder [36] as follows

[77]: We assume variation of oxygen concentration along the growth

direction, as shown schematically in Figure 14(a). Since interplaner

spacings vary with impurity concentration, the interplaner spacing also
X-RAY DIFFRACTION 183

Figure 12. X-ray topograph of a silicon wafer showing oxygen segregation bands. Scanning transmission method, 100 reflection. The crystal growth axis is perpendicular

to the reflecting plane. After Schwuttke.

varies along the growth direction with the same period. A divergent

beam is used for making the Lang topograph. The energy of x-rays which satisfy exactly the Bragg condition flows along the reflecting plane.

Incident x-rays which are sHghtly off the Bragg angle flow mainly along

the incident direction. Consequently, the latter x-ray waves encounter

the variations of the interplanar spacing during their transmission. If the waves encounter an increase of the interplanar spacing, the paths of the waves that are excited on the farther branch of the dispersion sur- face [27] from the origin of the reciprocal lattice are bent around into the diffracted beam direction and, at the crystal exit surface, they split.

Therefore, most of their energy travels in the diffracted beam direction,

with little in the direct beam direction. This results in a diffracted

intensity increase. Similarly, if the waves encounter a decrease of interplanar spacing, the waves that are excited on the other branch of the

dispersion surface contribute to the diffracted intensity increase. In
184 TRACE CHARACTERIZATION

Figure 13. Local failure of Friedel's law seen in oxygen segregation binds of a Si crystal,

(a) 111 reflection, (b) 111 reflection. Scanning transmission method. The strong lines

in the striation pattern of (a) appear at the positions of the weak hnes in (b) and vice

versa. The crystal growth axis is perpendicular to the (111) diffracting plane. After Kohra, Nakano, and Yoshimatsu [75].

the region where the gradient of impurity concentration is smaU, the

intensity contribution of the x-rays which are initially off the Bragg

condition is expected to be small. Therefore, at the places with the

largest gradients of impurity concentration, the maxima of diffracted

intensity appear, as shown schematically in Figure 14(b). Since the waves that are excited on the farther branch of the dispersion surface

are more strongly transmitted than those on the nearer branch, higher

intensities are obtained in the regions where the interplanar spacing

increases along the paths of the waves. Thus, the weak and strong

striations appear alternately as in Figure 13a and as illustrated schematically in Figure 14(b).

Similar striation contrast due to non-uniform impurity distribution has

been observed in BeO crystals [47]. These striations were also perpendicular to the growth direction (see Fig. 15) and are believed to be the

manifestation of variations of impurity concentration, probably Li, Mo,

or Pt. The crystals were flux grown under non-steady thermal conditions. Therefore, varying degrees of BeO supersaturation with time was

not unexpected. Crystals which showed a definite banded structure in
X-RAY DIFFRACTION 185

GROWTH DIRECTION

Figure 14. Schematic drawing of variations in image contrast of a striation pattern ob- served by the scanning transmission method (b), and corresponding impurity concentration in the crystal specimen (a). The contrast variation in (b) is expected to arise from

the concentration in (a) as described in the text. the topograph were sectioned and examined by D. K. Smith, using an

electron microprobe and using proton and neutron radio-activation,

followed by autoradiography [78]. The lower limits of detectability for these methods varies with the impurity for each method. According to Smith, activation analysis can detect as Uttle as 100 ppm in a bulk sample

and perhaps less under favorable conditions. To locate the source of the radiation, film methods are used which have a resolution limit around

10 microns. Within a 10 micron volume, a concentration of about 1%

would be detected. Also, the depth into the matrix will modify the

sensitivity and the resolution. The electron microprobe is said to be able

to detect as little as 10 ppm of a heavy element in a light matrix like BeO,

in a surface area of the order of 5 microns in diameter. The microprobe

identifies and gives the location of the impurity directly but is limited to material within a few microns of the surface. None of these tests by

Smith led to a banded image corresponding to that seen in the x-ray topograph. Apparently, it can be concluded that the negative results

for the three methods just mentioned indicate that the absolute level of impurity concentration in the striations seen in the BeO topographs is probably below 10 ppm.

It is evident from the above explanation that the striation patterns are dynamical images. Lang [79] observed the similar local failure of
186 TRACE CHARACTERIZATION

Figure 15. X-ray topographs of BeO crystals. Scanning transmission method, (a) 0002

reflection, (b) 1010 reflection. Striations appear perpendicular to the growth directions and seem to be due to variations in impurity concentration. The fringes parallel to the

crystal edge in (a) are due to the thickness variation near the edge. (Pendellosung

fringes.)

Friedel's [80] law on the dynamical images of edge dislocations in the case where their slip planes are parallel to the reflecting planes. The

present explanation for the contrast seen in the segregation bands is, in principle, the same as that for the dislocation images. Non-uniform

distribution of impurity can also be observed by the double crystal

method as will be described in the next section. However, the causes

of contrast are quite different in the Lang method than they are in the

double crystal method.

E. Lattice Parameter Variations Due to Impurities

It is well known that impurities cause changes of lattice parameters.

However, thjs effect is very small for trace amounts of impurities.

Minute variations of cell size, due to trace impurities, can be detected

by precise measurement of lattice parameters using such methods as the

powder method [81], and the Kossel technique [82]. Variations of

\Adld\ ^ 10~^ can be detected using the powder and divergent beam

(Kossel) method, whereas, for the double crystal [14, 25, 30, 31] and the
X-RAY DIFFRACTION 187

Moire' methods [83-85] distortions as small as |AJ/g?|> 10^^ can be

measured. In this paper the two topographical methods are described

with examples. The other methods (non-topographical) are adequately

described in the references so they will not be included here.

1. Double Crystal Method

We have shown in section II-A-2 that the double crystal method is very sensitive to tilts of lattice planes and to gradients of interplaner

spacings. Variations of \^(Hd\ ~ 10~^ can now be detected as contrast

variation. Bonse [86] studied striations which were first seen by

Deslattes [25b] in double crystal diffraction topographs of natural quartz

crystals. Figure 16 shows typical striation patterns of opposite surfaces

of a quartz crystal using double crystal topographs (see Fig. 3). Since

the striations on opposite faces of the crystal match precisely, it was

Figure 16. Striation patterns in a quartz crystal observed by the double crystal method. The left picture is the topograph of the (2110) surface of the crystal as visualized by a 4310 reflection and the right shows the reverse side by 4310 reflection. Note the matching of the patterns in the left and right topographs. After Bonse.

237-323 0-67— 13
188 TRACE CHARACTERIZATION

concluded that the striation lines are traces of layers extending through

the thickness of the crystal. From the similarity of these striations to the impurity bands in Si and BeO (II-D-2), it is inferred that they

originated in the crystal growth process by deposition of layers having

different impurity concentrations. It is known that natural quartz

usually contains Al, Na, and Li as impurities [87-88].

For the double crystal method the change in diffracted intensity, A/,

which produces image contrast has been shown to be

M= K{Mld) tan ^w + n^ • n^A^ (1) where ^ is a constant that is proportional in magnitude to the steepness

(with sign) of the slope of the rocking curve, n^, is a unit vector normal

to the plane that is defined by the incident and the diffracted beams.

is a unit vector parallel to the axis of the lattice tilt. Pure dilation ^d/d can be obtained from two topographs taken with -I- n^, and — n^,, since the contribution from tilt Ad simply changes sign. If both topographs give identical contrast, then must be normal to n^. If identical contrast is obtained using two sets of diffracting planes with different

orientations, then the direction of nt has been determined. In principle

the amount of lattice tilt A^ can be obtained from any two topographs

with -hug and — n^, by subtraction, provided has not been chosen

normal to n^

In this way, it was found that the striation patterns in the quartz

topographs are due to the structure near the surface as illustrated in Figure 17. Bulk stresses, which are caused by variations of impurity

concentrations, relax at the crystal surface. The smaller the shear

modulus, the larger will be the depth from the surface at which the relaxation dies out. These stresses may be of opposite sign in adjoining layers

and cause tilts in the transition regions between these layers. From the

magnitude of the contrast, the tilts and the dilations between different

layers were found to lie in the range of 0.25 Sec of arc and Ad/d= 10~^

respectively.

These crystals were colorless before this striation pattern was ob- served. However, after irradiation with x-rays (46 hr 20 kV and 40

mA), a non-uniform coloration began to become visible. The coloration

had the same lamellar structure as in the x-ray topograph. Comparison

of these results with studies on color centers of smoky quartz [87-92] led

to the conclusion that all lamellae contain Al as a main impurity but with

different concentrations and perhaps also in a different structural arrangement. It was also concluded that the striation patterns observed

by the double crystal method are associated mainly with variations of Al

concentration rather than vacancy concentration. Evidence for this is in Bonse's finding that the x-irradiation caused a sHght expansion of the

lattice {Ad/d ~ H- 5 X 10~^) in all the lamellae. This expansion saturated
X-RAY DIFFRACTION 189

FACE I DILATION = - ^0 + 7^0 ^0 -^0 TILT =

BULK

STRESS*

TILT =

0 0

'})))]))))>}

ri

0 0

)]n ))})),}}} + 0

f + — -

0 0 0 0 0

DILATION - -h ;^o FACE 2

Figure 17. Model for surface relaxation of bulk stresses of the layers with different impurity concentrations. After Bonse.

at higher radiation doses. If the cause of tKe expansion were the formation of point defects such as vacancies, then it would be difficuh to understand why saturation occurs at such small dilations. Therefore it is beheved that the expansion is due to an electronic process occurring at defects (impurity atoms) which are already present before the irradiation

and whose number does not increase during irradiation. If this is true, the saturation (maximum) value of radiation-induced expansion would be

proportional to the grown-in defect concentration. To date this suggestion has not been tested.

It should be noticed that the principle of image formation in the

double crystal method is quite different from that of the Lang method

described in Section II-D-2. In the Lang method, the striation contrast is formed only by strain gradients and, therefore, no contrast is obtained for such regions where the impurity concentration is maximum

or minimum (see Fig. 14). It may be impossible in a Lang topograph to distinguish between two regions with even a larger difference in impurity

concentration if the two regions are separated so far that the gradient

in the transition region between them is too small. On the other hand,

in the double crystal method, regions with uniform but different impurity

concentrations can be distinguished by diffracted intensity differences.

2. Moire Patterns

In the experiments with quartz, the layers with different impurity

concentrations are inclined to the crystal surface. In the case where
190 TRACE CHARACTERIZATION

such layers are parallel to the crystal surface, Moire patterns can be

observed by the Lang method. The topographs in Figure 18 show

parallel Moire patterns of a CdS crystal which consist of two layers with

different impurity concentrations [85]. In figures 18(b) and (c), Pendellosung fringes [93-95] appear due to the wedge shape of the crystal

illustrated in figure 18(a). The Moire fringes with spacings of about

100/x are seen parallel to the reflecting planes used. The fringe spacing

of a Moire pattern is determined by a difference in orientation and/or

lattice spacing between two superposed crystals through which the radiation passes successively. For a parallel Moire, the spacing S is given

by [96]

S = dAdBl\dA-dB\ (2) where dA and dg are the interplaner spacings of two superposed crystals

A and B. Using eq (2), it was found from the observed fringe spacing

that the differences in the lattice parameters, ao and co between the two

superposed CdS crystals are 3.6 ppm and 3.4 ppm, respectively. Since

these two values are nearly equal, one can conclude that an isotropic

lattice variation is caused by the impurity. The equidistant fringes

indicate a uniform impurity distribution in directions parallel to the

layer.

Figure 18. Parallel Moire patterns of two superposed wedge-shaped CdS (CuS) crystals as shown by scanning transmission topographs, (a) Shows the wedge shape of the

crystal which consists of two layers A and B. (b) 0002 reflection, (c) 1010 reflection. The topographs show the tip region of the crystal. Pendellosung fringes are visible which are parallel to the c-axis. These are due to the wedge shape shown in (a).

i
X-RAY DIFFRACTION 191

Such crystals were grown in vapor flow from heated CdS powder which

was mixed with CuS to introduce Cu into the crystals. In the initial stage of the crystal growth, platelets were rapidly formed by the dislocation mechanism [62] and then epitaxial growth occurred on one of the

platelet surfaces that faced the direction of vapor flow. Since the

mixed impurity evaporates very rapidly, the platelet grown in the initial stage and the thin layer grown epitaxially on it may have different

impurity concentrations. Red luminescent emission of the crystal was

observed under ultraviolet irradiation. The emission of the substrate

platelet was stronger than that of the epitaxially grown layer, an observation which also indicates that the layers have different impurity concentrations. Nearly straight fringes such as are seen in Figure 18, were

seldom obtained. Instead, almost aU crystals gave irregular fringes,

indicating that the crystals are easily distorted. In Moire interference, smaUer lattice variations result in larger fringe

spacings. Therefore, if large crystals are available, small lattice varia- tions {— Ad/d ^ 10~^) can be detected by this method. For crystals

that have no layer structures, it is necessary to superpose artificially

the doped crystal and a perfect crystal of standard high purity. However, the superposition may be technically difficult.

III. Effect of Impurities on Integrated Intensity of X-ray

Diffraction

The effects of isolated point defects on the intensity of an x-ray reflec- tion has been treated kinematically by several investigators [97-101],

They concluded that strains due to point defects influence diffraction in a manner similar to thermal motion, i.e., the intensity of a Bragg reflec- tion is decreased and a diffuse scattering builds up in the vicinity of the

peak, while the peak itself is not broadened. However, the effects of

trace impurities seem to be so small that they are overwhelmed by the

effects of any other lattice imperfections. Therefore, it is considered

that the kinematic effects of trace impurities can be detected only for nearly perfect crystals. However, for nearly perfect crystals, it appears

that the destruction of the dynamical interaction of x-ray beams within

crystals become dominant. To our knowledge the effects of point strains on dynamical x-ray interaction has not yet been treated theoretically.

On the other hand, the impurity effects on the intensity of reflection have

been detected experimentally by Batterman [102]. Also Efimov and

EHstratov [103, 104] and Patel and Batterman [105] observed the effect of impurities on the anomalous transmission intensity. This is discussed

in greater detail (in Sec. Ill—B). In both cases, crystals with low dislocation density were used, and it was confirmed that the intensity effects due to dislocations were small enough so as not to overwhelm the impurity effect.
192 TRACE CHARACTERIZATION

A. Integrated Diffracted Intensity in Reflection

Batterman [102] measured the absolute values of x-ray integrated

intensities from Ge single crystals using a double crystal spectrometer

(Fig. 3), and compared these values to those that were calculated for ideally perfect [2, 106, 107] and ideally mosaic or imperfect crystals

[108]. He found that, for germanium and CuKa radiation, variations in dislocation density below W cm~^ did not significantly affect the inte- grated intensities and that the measured intensities agree quite well with

theoretical values which were calculated for a perfect crystal by the

Darwin-Prins theory [106, 107].^ He also observed for Ge crystals with a low dislocation density (5X10^ cm"^) that additions of about one part in 10* of substitutional indium or precipitated lithium atoms significantly in- creased integrated intensities. Figure 19 shows the 333 rocking curve

for Ge before the addition of lithium and after lithium has precipitated.

The average half-width increased by only 3 sec of arc. However, the

increase in total diffracted intenstiy is evident from the superposition

of the two curves. The curve for the precipitated crystal has higher and

longer tails, showing the presence of diffuse scattering. The increase

of 24% in integrated diffracted intensity, due to only 0.01% lithium,

presumably shows the high sensitivity of this parameter to lattice strains. For the In-doped crystal, the integrated intensities varied with position

of the x-ray beam across the face of the crystal. The intensities for the

most intense region are approximately 4, 11, and 33% greater than is predicted theory for the 111, 333, and 444 reflections, respectively.

The variation over the crystal face is consistent with the fact that the

impurity densities were known to fluctuate.

Figure 19. Effect of lithium precipitation on rocking curve for a 333 reflection from ger- manium. After Batterman.

' As Batterman indicated, it should not be assumed that dislocation density less than

10^ cm"- will not affect integrated intensities for all crystals and wavelengths. The sensitivity will depend upon the sharpness of the Bragg peak for the perfect crystal which is determined by the scattering factor of the atoms of the crystals and the wavelength used:

the sensitivity is higher for higher order reflections. As can be also expected, less penetrating radiation is less sensitive to low dislocation density. See also J. R. Patel, R. S. Wagner, and S. Moss, Acta Met. 10, 759 (1962).
X-RAY DIFFRACTION 193

Since the impurity concentration by itself is too smaU to contribute

to the x-ray scattering factor, the increase in the integrated intensity is probably due to a decrease in primary extinction caused by distortion of

the lattice due to the impurity atoms. The observed increase of the

intensity with order is consistent with this explanation. In the case of hthium, it is most probable that the precipitate particles themselves

produce the strain. For the In-doped crystal, however, it appears that the regions of large fluctuations in dissolved indium concentration are responsible for the intensity increase, as in the case of the oxygen bands

in Si crystals. These observations show that the total intensity of reflec- tion in a nearly perfect crystal can be a sensitive measure of low impurity

content, expecially if they induce much lattice distortion due to segregation or precipitation. B. Impurity Effect on Anomalous Transmission

From the theory of the anomalous transmission (I-A-4), one can

expect an intensity decrease due to local strain caused by impurity

atoms. Patel and Batterman [105] observed this eftect, using the experimental arrangement shown in figure 20. The first crystal serves merely

as an x-ray monochromator. These authors studied dislocation-free Si

crystals {/JLot ~ 15). Their result is as follows: Heat treatment at 1000 °C

results in impurity clustering, i.e., the formation of strained regions,

which results in a decrease of transmitted and diffracted x-ray intensity

of over two orders of magnitude. Upon heating at 1350 °C, the clusters dissolved and the original perfection of the crystal was restored. From

the kinetics of the impurity clustering, the impurity was concluded to be

oxygen. The changes in the x-ray intensity occur before there is any

detectable change in the infrared absorption band for oxygen, a standard measure of the dissolved oxygen content. Anomalous x-ray transmisFigure 20. Experimental arrangement for the intensity measurement of the transmitted and diffracted beams. R) X-ray tube; Si, S2, S3) shts; M) crystal monochromator; A)

crystal analyzer; Cr) photomultipher in position to record the transmitted beam; C«) photomultipher in position to record the Laue reflection. The hnes drawn across the

crystal show the orientation of the (220) reflecting planes.

R

M
194 TRACE CHARACTERIZATION

sion, therefore, appears to be very sensitive to changes in the early stages

of impurity clustering and should, therefore, be an important tool for the investigation of precipitation phenomena occurring in crystals of high initial perfection. However, these results indicate that, in the

dissolved state, the impurity atoms have only a smaU effect on the

intensity of anomalous transmission.

Efimov and Ehstratov [103] observed a small effect of dissolved impurities in the dissolved state on anomalous transmissions, using very thick

Ge crystals. Using the arrangement in Figure 20 they [109] found experimentally and then verified theoretically that for thick perfect crystals

ifjiot > 30), the anomalously transmitted and diffracted beams, and

Ri, have equal integrated intensity, i.e., Ti = Ri= i, and there is a linear

relation between In i and the thickness t, viz. In i = —^it + yi. The inter- ference absorption coefficient /X; is equal to the slope of the line which

is obtained by plotting the logarithm of the observed integrated intensities against thickness. The value of y, is the intercept found by extrapolating the line to the In i axis. They [110] concluded that a dislocation

density less than 10^ cm ' - does not affect /t, and y\ appreciably. Using

germanium crystals with low dislocation density (~ 10^ cm~'^), they

[103] studied the effects of diffused impurities on fXi and y/. An example

is shown in Figure 21. From the slopes of the two lines for the pure

(curve 2) and the hydrogen-diffused crystals (curve 1), the change in /x, can be seen. Using this method, they observed the change of integrated

intensities due to the impurities H2, Cu, and Ni in the dissolved state and obtained the following results:

1. Small concentrations of hydrogen (—lO^"* cm~^), copper (~ 10^*^ cm~^) and nickel (5.5 • 10^-^ cm~^) cause a considerable decrease in the

integrated anomalous transmitted intensity in nonequilibrium solid

Int ' -17

-16

-15

1 1.5 2 mm

Figure 21. Dependence of In i on t(i = integrated intensity of the diffracted or transmitted beam, ? = crystal thickness). The hnes (1) and (2) were obtained for the specimens from the same single crystal which was grown in a stream of hydrogen. (1) As-grown

specimen, dislocation density N= 1 • 10^ cm"-. (2) Specimen annealed in vacuum for 2 hr at 700 °C, A^=3 • 10^ cm- 2. After Efimov and Efistratov [103].
X-RAY DIFFRACTION 195

solutions in germanium This effect is especially pronounced for large

thicknesses (^to^ ~ 70) and leads to intensity variations of some tens of percents. The value of fJLi increases regularly with increase in the

impurity concentration. No noticeable effect on was observed.

2. The observation indicates that distortion of the crystal lattice caused by the impurity is greater for impurities with low solubihty.

They [104] also studied the effects of impurity precipitates (Ni and Cu) on fjLi and yt, and found that the precipitation from the solid solution gives

greater change in the integrated intensity as compared with the initial sohd solutions. A very thin (~ 35/x) heavily distorted surface layer is formed by the precipitation. Owing to this distorted layer, the values

of In Ti and In Ri fall sharply from the straight hues relating the logarithm

of the intensity to the thickness. After removing the surface layer, the

Hnear relationship is preserved for the main body of the crystals, but

fjLi is greater than that for the solid solution. The decrease of integrated

intensity for the main body is also attributed to the distortion due to the

precipitation.

As can be seen from the above experiments, anomalous x-ray trans- mission is very sensitive to impurities, especially to precipitated impurities. However, the change in intensity is not due to the impurity

itself, but is caused by a lattice strain introduced by the impurity atoms.

Therefore, it appears that impurities are detectable by diffracted x-ray

intensities only in highly perfect crystals, and that it is impossible thus

far to identify the kinds of impurities by measuring the changes in trans- mitted intensity. This method appears to be suitable for studying the

distribution of deliberately added impurities, as in doping operations.

IV. Impurity Effect on Electron Density Distribution

The impurity effects on x-ray diffraction described in the above sectiqns appear through lattice distortion caused by impurities. However,

it is weU-known that the presence of impurities can also cause changes

in various other properties of crystals. For instance we can expect

impurities to change the electron distribution in crystals. We may ask

the question: Are impurity effects on structure factors too small to detect?

A. Electron Density Map — Difference Method

Mohanty and Azaroff [111] showed experimentally that if impurity

atoms are interstitially dissolved, and, if enough of them occupy the same

types of sites in a crystal structure, then their total contribution to the

diffracted intensities can be detected. They studied zinc oxide crystals,

pure and doped with excess zinc. ZnO has a hexagonal structure,

which, when projected along the c axis, contains pairs of superimposed

zinc and oxygen atoms in one unit cell. If the origin of the unit cell is placed at the projected position of the octahedrally coordinated void in
196 TRACE CHARACTERIZATION

this structure, then a small maximum should be seen at the origin of the

cell in the electron density projection of an artificially Zn-doped crystal.

To exaggerate this effect, they used pairs of crystals, one as pure as could be grown by normal procedures and one dehberately doped to saturation in zinc vapor. A "difference" electron density map was

next calculated by subtracting the electron density of the pure crystal

from that of the doped crystal at each point {x, y) in the unit cell, according to the relation: Ap = PD-pp = aiA) {Fo

FpU-o cos 27Tihx + kyl (3)

h k where A is the area of the projected unit cell and the subscripts D and

P refer to the doped and pure crystals, respectively. Such a difference

map not only has the advantage of showing any real differences between

the electron densities of the two crystals, but it also does not suffer from series termination errors, since the terms omitted in each series can be expected to cancel in the subtraction. It is important to realize that the above Fourier series is unlike the usual difference synthesis

used in crystal structure analysis in which the coefficients are differences

between observed and calculated structure factors. Also, since the

differences between two measured values are used in this work, any

systematic errors due to scaling, instrumentation, etc., should be the same for both terms. Such errors, therefore, may introduce small

uncertainties regarding the peak height of the final synthesis but do

not affect its main features. Their difference map is shown in Figure 22. The small maximum is clearly visible at the origin of the projected cell. From this map, it is possible to calculate the number of interstitial zinc atoms present, on

the average, in one unit cell. The volume of the origin peak corresponds

to 6X10 + ^^ atoms cm~^ in the intersticial site, or approximately one

interstitial atom per one thousand unit cells at room temperature.

They also carried out an identical study with CdS crystals, but did not observe any maxima whose magnitude exceed possible effects caused

by errors inherent in the measurement of diffraction intensities [112].

Thus it appears that this method for studying point defects in crystals

is effective only when they are present in fairly large amounts. Conversely, more precise measurements of structure factors should serve to increase the sensitivity of this method.

B. Precise Determination of Structure Factors by Means of

Pendellosung Fringes

The main error in the experimental determination of the structure

factor by intensity measurements arises from the uncertain corrections

for extinction. Actually we can formulate an exact treatment for dif-
X-RAY DIFFRACTION 197

Figure 22. Difference map of the c-axis projection of ZnO obtained by subtracting the

electron density of a '"pure*' crystal from that of a doped one. The zero contour is shown

dashed. The sohd contours are in equal steps of le/A^. Mter Mohanty & Azaroff [111].

fraction only for the cases of the "ideally imperfect" and "ideally per- fect" crystals. In general, however, real crystals have a texture between

both of these extremes. Therefore structure analyses of real structures contain some inherent ambiguity. However, recent technique has

produced highly perfect crystals and it has been possible to treat them as

"ideally perfect crystals". There have been attempts to measure

structure factors using highly perfect crystals and the phenomenon

of PendeUosung fringes which were predicted and described by Ewald

[113] early in 1916. The determination of structure factors from

PendeUosung fringe data observed by electron microscopy has been

reported by several authors [114]. Kato and Lang [93] first observed

the PendeUosung fringes in the x-ray case using topography, but Hattori,

et al. [115], were the first to report structure factors which had been

determined by means of x-ray PendeUosung fringes. According to the

theory [94, 95], the fringe distance A observed when the Bragg condition

is satisfied is given approximately by

l/A = (l/2) {1 + cos2^b) \iljg\ lik cos Ob) (4) where \\ljg\ is related to the structure factor Fg by the weU-known formula
198 TRACE CHARACTERIZATION

where V is the volume of the unit cell, and e, m, and c have the usual

meanings. This approximation is fairly accurate except for the initial few fringes. Hattori et al. [115], observed Pendellosung fringes with

section topographs of wedge-shaped perfect Si crystals and determined

the structure factors from the observed fringe distances by using eq

(4). The absolute value of the structure factor obtained in this way is accurate to within a few percent. The main errors are caused by the

uncertainties in the geometrical measurements such as the wedge angle

and the crystal orientation. It appears that measurement of structure

factors with high accuracy may be possible by improving the geo- metrical measurements. Therefore it is possible that the effects of

small impurity concentrations on structure factors can be detected if the crystals containing the impurity are still perfect enough. Because

the spacings of Pendellosung fringes are contracted by lattice distortion

[41, 116, 117] it may be possible by this means to detect traces of even

the highly soluble impurities, where the lattice distortion is relatively

small for a given amount of impurity, as has been described in Section

III-B. V. Other Eifects of Impurities

Small amounts of impurities may produce other effects on material

behavior which are admittedly only distantly related to x-ray diffraction. Since effects of the type discussed below are apparently not included

elsewhere in this Symposium they are given brief recognition here by

the mention of two examples.

A. Influence of Impurities on Phase Stability

Stadelmaier [118] has studied the impurity stabilization of ter- nary phases of certain transition metals (Mn, Fe, Co, Ni, Pd, Pt), of the B-metals (Mg, Zn, Cd, Hg, Al, Ga, Ge, In, Sn, Pb), and the metalloids (B, C, N). He found that the Cu, Au-type structure could be sta- bilized by the presence of carbon and nitrogen and proposed that the

metalloid partly fills the octahedral hole of the L12 structure, yielding

the perovskite-type structures in extreme cases. Von PhiUipsborn and

Laves [119] found that the presence of small amounts (~ 1%) of oxygen,

nitrogen or carbon stabihzed the Cu3Au(Li2) structure of TisAu and V3AU

in place of the Cr Si(A15) structure which normally forms in the respective high purity binary alloys [120]. They observed that for the (L,2) structure of TiaAu, the radius of the octahedral hole equals O.6OA,

which agrees well with the radius of the oxygen atom (O.6OA) found for solutions of oxygen in metallic titanium (Ehrhck) [121]. Detailed x-ray

diffracted intensity observations also support their idea that the influence

of oxygen in stabihzing the CusAu-type structure is a result of fiUing the

central octahedral hole in that structure.
X-RAY DIFFRACTION 199

B. Influence of Impurities on Solid State Reaction Kinetics

There is evidence that certain types of impurities can have a strong

influence on reaction rates, especially those which are diffusion hmited.

An example of this effect is found in the work of Hendricks, et al. [122],

who studied the influence of small additions of Ca++ to the rate of precipitation of AgCl in NaCl, as observed by small-angle x-ray scattering.

They found that additions of about 150 ppm of Ca++ caused the AgCl

to precipitate about ten times faster than in binary mixtures of NaClAgCl without the added aliovalent impurity. It was assumed that to maintain electrical neutrality in the crystal, the divalent cation impurity

introduced an equivalent number of extrinsic cation vacancies. The

extra cation vacancies were then presumed to promote the diffusion

movement of the silver ions, thereby accelerating the rate of the precipitation reaction. In a sense, therefore, a small amount of an added

aliovalent impurity appears to act as a reaction catalyst, since it does

not take any part in the reaction except to accelerate it. Many other

examples of the influence of minor amounts of impurities or vacancies

to promote or inhibit reaction rates can be found.

VI. Summary

The presence of impurity traces in crystalhne materials can cause

small changes in lattice parameters and large changes (usually an in- crease) in the intensity of x-rays diffracted by that material. If the

identity of a uniformly dissolved impurity is known, a meaningful esti- mate of its concentration can be made from precise measurements of crystaUographic lattice parameters or the structure factor F of its host. X-ray diffraction topography, on the other hand, is an effective method

for observing the distribution of trace impurities in relatively large

crystals if those crystals are otherwise highly perfect. However, at

its present state of development, diffraction topography cannot identify

the impurity nor measure quantitatively its concentration level. Further development of x-ray diffraction techniques toward these ends is conceivable in principle and is currently in progress. VII. Acknowledgements

We are grateful to Drs. G. H. Schwuttke and M. Yoshimatsu for supplying original photographs and shdes illustrating their studies. Also we are indebted to Professors P. A. Beck and L. V. Azaroff; to Drs. K. Schubert, T. B. Massalski, and W. B. Pearson for their helpful comments

during the preparation of the manuscript. VIII. References

[1] See, for example, Direct Observation in Crystals, J. B. Newkirk and J. H. Wernick,

eds., Interscience Publishers, New York, 1962.
200 TRACE CHARACTERIZATION

[2] Darwin, C. G., Phil. Mag. 27, 315, 675 (1914).

[3] Ewald, P. P., Ann. Phys. Lpz., 54, 519 (1917).

[4] Ewald, P. P., Z. Phys. 2, 332 (1920).

[5] Ewald, P. P., Z. Phys. 30, 1 (1924).

[6] Bethe, H. A., Ann. Phys., Lpz. 87, 55 (1928).

[7] Laue, M. von, Ergeb. exact. Naturw. 10. 133 (1931).

[8] Guinier, A., and Tennevin, J., Acta Cryst. 2, 133 (1949).

[9] Schulz, L. G., J. Metals, 200, 1082 (1954).

[10] Weissmann, S., J. Appl. Phys., 27, 389 (1956).

[11] General Reviews, J. B. Newkirk, J. Metals, 14 (1962) 661 ff; also A. R. Lang, The

Encyclopedia of X-Rays and Gamma Rays, Ed. G. L. Clark (Reinhold Pub. 1963>

pp. 1053-1063.

[12] Bonse, U., Hart, M., and Newkirk, J. B., Encyclopaedic Dictionary of Physics, General Review, Pergamon Press, pp. 391-394.

[13] Newkirk, J. B., Phys. Rev. 110, 1465 (1958); also AIME Trans. 215, 483 (1959).

[14] Bonse, U., and Kappler, E., Z. Naturforsch, 13a, 348 (1958).

[15] Lang, A. R., J. Appl. Phys. 29, 597 (1958).

[16] Lang, A. R., J. Appl. Phys. 30, 1748 (1959).

[17] Lang, A. R., Acta Cryst. 12, 249 (1959).

[18] Borrmann, G., Hartwich, W., and Irmler, H., Z. Naturforsch, 13A, 423 (1958).

[19] Barth, H., and Hosemann, R., Z. Naturforsch. 13a, 792 (1958).

[20] Webb, W. W., J. Appl. Phys. 31, 194 (1960); Yoshimatsu, M., and Kohra, K., J. Phys.

Soc, Japan 15, 2367 (1960).

[21] Schwuttke, G. H., J. Appl. Phys. 36, 2712 (1965).

[22] James, R. W., The Optical Principles of the Diffraction of X-Rays, G. Bell & Sons, London, 1950.

[23] Renninger, M., Z. Naturforschung 19A, 783 (1964).

[24] Kohra, K., Yoshimatsu, M., and Shimizu, I., Direct Observation of Imperfections in Crystals, eds. J. B. Newkirk and J. H. Wernick (1962), pp. 461-470.

[25] Renninger, M., Angew. Phys. 19, 20, 34 (1965). [25a] Deslattes, R. D., "Advances in X-ray Analysis", Vol. 10, Plenum Press, and J. Appl.

Phys. 37, 541 (1966); also Deslattes, R. D., and Paxetzkin, B., this symposium.

[25b] Private Communication, Deslattes, R. D., National Bureau of Standards, Washington,

D.C., 1963.

126] Batterman, B. W., Phys. Rev. 126, 1461 (1962).

[27] See, for example, Batterman, B. W., and Cole, H., Rev. Med. Phys. 36, 681 (1964).

[28] Ewald, P. P., Acta Cryst. 11, 887 (1958).

[29] Kato, N., Acta Cryst. 11, 885 (1958).

[30] Bonse, U., Z. Phys. 153, 287 (1958).

[31] Bonse, U., Direct observation of Imperfections in Crystals, New York Interscience

(1962), pp. 431-457.

[32] Chikawa, J., Appl. Phys. Letters 4, 159, 5, 31 (1964).

[33] Chikawa, J., J. Appl. Phys. 36, 3496 (1965).

[34] Lang, A. R., Z. Naturforsch. 20a, 636 (196S).

[35] Authier, A., Proceedings of the 15th Annual Conference on Applications of X-ray

Analysis, eds. J. B. Newkirk and G. Mallett, to be published.

[36] Penning, P., and Polder, D., Philips Res. Repts. 16, 419 (1961).

[37] Bonse, U.,.Z. Physik 177, 385 (1964).

[38] Kato, N., Acta Cryst. 16, 276, 282 (1963).

[39] Kato, N., J. Phys. Soc. Japan 18, 1785 (1963).

[40] Kato, N., J. Phys. Soc. Japan 19, 67 (1964).

[41] Kato, N., J. Phys. Soc. Japan 19, 971 (1964). [42] Takagi, S., Acta Cryst. 15, 1311 (1962).

[43] Kambe, K., Z. Naturforsch. 18a, 1010 (1963).
X-RAY DIFFRACTION 201

[44] Kambe, K., Z. Naturforsch. 20a, 770 (1965).

[45] Bonse, U., Z. Physik 177, 529 (1963).

[46] Bonse, U., Z. Physik 177, 543 (1964).

[47] Austerman, S. B., Newkirk, J. B., and Smith, D. K., J. Appl. Phys. 36, 3815 (1965).

[48] Schlossin and Lang, A. R., Phil. Mag. 12, 283 (1965).

[49] Takagi, M., and Lang, A. R., Proc. Roy. Soc. A281, 301 (1964).

[50] Schwuttke, G. H., Ultrapurification of Semiconductor Materials, eds. M. S. Brooks and J. K. Kennedy (The MacmiUan Comp. 1962) pp. 434-453.

[51] Kaiser, W., and Keck, P. H., J. Appl. Phys. 28, 882 (1957).

[52] Bontinck, W. and Amehnckx, S., Phil. Mag. 2, 94 (1957).

[53] Amehnckx, S., Bontinck, W., Dekeyser, W., and Sehz F., Phil. Mag. 2, 355 (1957).

[54] Weertman, J., Phys. Rev. 107, 1259 (1957).

[55] Dash, W. C, J. Appl. Phys. 31, 2275 (1960).

[56] Fourdeux, A., Berghezan, A., and W. W. Webb, J. Appl. Phys. 31, 918 (1960).

[57] Kohra, K. and Yoshimatsu, M., J. Phys. Soc. Japan 17, 1041 (1962).

[58] Yoshimatsu, M., Japan, J. Appl. Phys. 3, 99 (1964).

[59] Schwuttke, G. H., and Sils, V., J. Appl. Phys. 34, 3127 (1963).

[60] Chikawa, J., J. Phys. Soc. Japan 18, 148 (1963).

[61] Chikawa, J., Japan J. Appl. Phys. 3, 229 (1964).

[62] Chikawa, J. and Nakayama T., 35, 2493 (1964).

[63] Schwuttke, G. H., Direct Observation of Imperfections in Crystals, eds. J. B. Newkirk and J. H. Wernick (Interscience Pub. New York, 1962), pp. 497-508.

[64] Furusho, K., Japan J. Appl. Phys. 2, 585 (1963).

[65] Chikawa, J., Appl. Phys. Letters 4, 25 (1964).

[66] Chikawa, J., Proceedings of the 15th Annual Conference on Apphcations of X-Ray

Analysis, eds. J. B. Newkirk and G. MaUett, to be pubhshed.

[67] Furusho, K., Japanese J. Appl. Phys. 3, 203 (1964).

[68] Furusho, K., private communication. This result was left unpublished because of

his death.

[69] Ehstratov, A. M., and Kamadzhiev, P. R., DAN SSSR, 125, 538 (1959) (Soviet Physics

Doklady 4, 427).

[70] Ehstratov, A. M., and Kamadzhiev, P. R., Fizika Tverd^go Tela, 4, 3492 (1962)

[Soviet Physics-Solid State 4. 2557 (1963)].

[71] Lang, A. R., Proc. Phys. Soc. 84, 871 (1964).

[72] Kamiya, Y., and Lang, A. R., J. Appl. Phys. 36, 579 (1965).

[73] Ishii, S., Filruga, T., Sasaki, Y., and Kohra K., J. Phys. Soc. Japan 15, 206 (1960).

[74] Schwuttke, G. H., J. Electrochem. Soc. 108, 163 (1961) and 109, 27 (1962) J. Appl.

Phys. 33, 2760 (1962).

[75] Kohra, K., Nakano, S., and Yoshimatsu, M., J. Phys. Soc. Japan, 18, Supplement

II, 341 (1963).

[76] Dash, W. C, Phys. Rev. 98, 1536 (1955).

[77] Takagi, M., Read to Japanese Physical Society (1965).

[78] Smith, D. K., Private communication; Lawrence Radiation Lab., Livermore, Calif.

[79] Lang, A. R., An Investigation of Crystal Imperfections by X-Ray Diffraction (Rept.

'for Contract AF61(052)-449) p. 115.

[80] Kato, N., Acta Cryst. 16, 276, 282 (1963).

[81] See, for example. International Union of Crystallography, Conference in Stockholm "The Precision Determination of Lattice Parameters," Acta Cryst. 13,818 (1960).

[82] Ellis, T., Nanni, L. F., Shrier, A., Weissmann, S., Padawer, G. E., and Hosokwawa,

N., J. Appl. Phys. 35, 3364 (1964): Gillen, P., Yakowahz, H., Ganow, D., and Ogilvie, R. E., J. Appl. Phys. 36, 773 (1965).

[83] Bonse, U., and Hart, M., Appl. Phys. Letters 6, 155 (1965); Z. Physik 190, 455 (1966).

[84] Lang, A. R., and Miuscov, V. F., Appl. Phys. Letters 7, 214 (1965). Proceedings of
202 TRACE CHARACTERIZATION

the 15th Annual Conference on Apphcations ol X-Kay Analysis, eds. J. B. Newkirk

and G. Mallett, to be published.

[85] Chikawa, J., Appl. Phys. Letters 7, 193 (1965); Proceedings of International Conference of Crystal Growth, to be published.

[86] Bonse, U., Z. Physik, 184, 71 (1965).

[87] Griffiths, J. H. E., Owen, J., and Wend, I. M., Defects in Crystalline Solids: Report

of Bristol Conference. London: Physical Society 1954.

[88] Bambauer, H. U., G. O. Brunner and F. Laves: Z. Kristallographie 116, 173 (1961).

[89] O'Brien, M. C. M., and Pryce, M. H. L., Defects in Crystalline Solids; Report of Bristol Conference. London: Physical Society (1954).

[90] O'Brien, M. C. M., Proc. Roy. Soc. Ser. A 231, 404 (1955).

[91] Lietz, J., and Hanisch, M. R., Naturwissensch. 46, 67 (1959^

[92] Lietz. J., and Hanisch. M. R.. Fortschr. der Mineralogie 39, 38 (1961).

[93] Kato, N., and Lang, A. R., Acta Cryst. 12, 787 (195y^

194] Kato, N., Z. Naturforsch. 15a, 369 (1960).

[95] Kato, N.. Acta Crvst. 14, 52o, 627 (1961).

[96] See, for example, Hashimoto, H., Mannami, M., and Naiki, T., Phil. Trans. Roy. Soc,

London 253, 490 (1961).

[97] Zachariasen, W. H., Theory of X-Ray Diffraction in Crystals, 1945.

[98] Matsubara, T., J. Phys. Soc. Japan, 7, 270 (1952).

[99] Huang, K., Proc. Roy. Soc (London) A190, 102 (1947). [100] Borie, B. S., Acta Cryst. 10, 89 (1957). [101] Ekstein, H., Phys. Rev. 68, 120 (1945). [102] Batterman, B. W., J. Appl. Phys. 30, 508 (1959). [103] Efimov, O. N. and Ehstratov, A. M., Fizika Tverdogo Tela. 5, 1869 (1963) [Soviet Physics-Solid State, 5, 1364 (1964)]. [104] Efimov, O. N., and Ehstratov, A. M., Fizika Tverdogo Tela. 5, 2116 (1963) [Soviet Physics-Solid State 5, 1543 (1964)].

[105] Patel, J. R., and Batterman, B. W., J. Appl. Phys. 34, 2716 (1963). [106] Prins, J. A., Z. Physik 63 , 477 (1930). [107] Miller, F., Phys. Rev. 47, 209 (1935). [108] See, for example, James, R. W., The Optical Principles of the Diffraction of X-rays, G. Bell & Sons, London, 1950, Chap. H.

[109] Ehstratov, A. M., and Efimov, O. F., Fizika Tverdogo Tela. 4, 2397 (1962) [Soviet Physics-SoUd State 4, 1 757 ( 1963 ) ]

.

[110] Efimov, O. N., and Ehstratov, A. M., Fizika Tverdogo Tela. 4, 2908 (1962) [Soviet Physics-Solid State 4, 2131 (1963)]. See also Efimov, O. N., Fizika Tverdogo

Tela, 5, 1466 (1963) [Soviet Physics-Sohd State 5, 1066 (1963)]

.

[Ill] Mohanty, G. P., and Azaroff, L. V., J. Chem. Phys., 35, 1268 (1961). [112] Mohanty, G. P., and Azaroff, L. V., Phys. Rev. 120, 1224 (1960). [113] Ewald, P. P., Ann. Phys. 49, 117 (1916). [114] See, for example, J. M. Cowley, Fourier Methods in Structure Analysis by Electron

Diffraction, Reports on Progress in Physics, XXI, 165 (1958). [115] Hattori, H., Kuriyama, H., Katagawa, T., and Kato, N., J. Phys. Soc. Japan 20, 988

(1965). [116] Kato, N., and Ando, Y., 21, 964 (1966). [117] Hart, M., Appl. Phys. Letters 7, 96 (1965). [118] Stadelmaier, H. H., Z. Metallk. 52, 758 (1961). 11191 Philipsborh. H. von, and Laves, F., Acta Cryst. 17, 213 (1964). [120] Greenfield, P., and Beck, P. A., Trans. Amer. Inst. Min. (Metall.) Engrs. 2 06, 265

(1956). [121] Ehrlick, P., Z. Anorg. Chem. 247, 53 (1941). [122] Hendricks, R. W., Baro, R., and Newkirk, J. B., Trans. AIME 230, 930 (1964).
X-RAY DIFFRACTION

Contributed Papers and Discussion

H. S. PEISER

NBS Institute for Materials Research Washington, D.C. 20234

I. Introduction

In his opening remarks the author, as the session rapporteur, raised

the question of how relevant and how important were the x-ray diffrac- tion techniques to trace characterization. Were we overoptimistic in our assessment of resuhs obtainable by x-ray diffraction techniques?

It is the very insensitivity of many conventional x-ray measurements

to the presence of impurities which over and over again has enabled

the crystallographer by rather simple methods to interpret measurements

in terms of idealized features of crystal structures. In fact only when we either have exceptionally perfect crystals or use refined and sophisticated x-ray techniques, do we stand a fair chance of answering some

real trace problems. In their paper J. B. Newkirk and J. Chikawa have

shown that these techniques have in fact progressed quite far. The

rapporteur challenged the audience to test the prophetic capabihties

of these authors to make forecasts on the general apphcabilities in trace characterizations of the Pendellosung and Moire fringe techniques

which Dr. Chikawa especially had recently developed.

Dr. Meinke also had convinced us that we were not on the platform

under false pretenses. He had pointed out that this Symposium was

intended to stress the state of the art with all its present limitations and

that no strict definitions of "trace" in terms of ppm or ppb were intended.

Indeed let us go back to percent if that is the best we can do. The highly perfect crystal is the most promising kind of material for reproducibility and with the most varied properties of possible utility.

That the x-ray techniques discussed by Drs. Newkirk and Chikawa were

mostly limited to such crystals may ultimately not be a serious limitation. Moreover, it is well known how some traces can affect the properties

critically. So the determination of these traces is a central aim in the

control of properties and reproducibility.

Before introducing the first contributed paper, Peiser made a general

comment intended as a guiding thread running through evaluations in

this subject area. The chemical analyst's task in the past had been to evaluate quantitatively the composition of materials. He has had, as 203

237-323 0-67— 14
204 TRACE CHARACTERIZATION

Others at this Symposium had emphasized, to answer the chemical

questions "what" and "how much." The characterization of modern

materials requires — and the evidence that leads to this philosophy is compelling — that the additional question be asked: "where in the crystal structure lies the culprit" or, often more appropriately, "where is the crux of the matter?" Closely Unked with the "where" is the topic of

non-chemical impurities. The host atoms can be replaced by vacancies

or they can slip into interstices and thus act hke a trace of foreign atoms. Moreover, everyone appreciated how phase changes may affect properties when in fact there is no change in stoichiometry whatever, and

x-ray diffraction can give useful information in this respect. In this audience everyone could tell a tale or two on how a good quantitative

analysis had lost its significance through bulk contamination of the

specimen surface. However, the discussion should concern traces within crystals. Sizeable three-dimensional inclusions is one possible

location for trace elements. Peiser proposed that one should for the

sake of this discussion assume that such contaminations can be satis- factorily dealt with by preconcentration treatments, the subject of later sessions.

Other traces within crystals themselves fall into three simple classes: those on two-dimensional crystal planes, one dimensional rows, and those

that are of zero-dimensional extent. We know very little about two- dimensional defects — that is, traces concentrated on crystal fault planes,

i.e., typically stacking faults. What little could be said concerns chiefly

stoichiometry rather than trace contamination.

One-dimensional dislocations are much more accessible to study

and permit a few predictions. Quite good crystals have 10^ dislocations

per square centimeter. This is not many, yet in such a 1 cm^ crystal

there are 3 km of fault lines. The crystal stability is undoubtedly in- creased when these 3 km long atomic-scale passage ways are filled with

trace elements of the right size and shape. Up to 10^^ atoms can hide

without introducing much strain. This is only in the part per billion range and the dislocations will be little selective to specific kinds of atoms. It is not difficult to see, however, why crystals will show re- markable resistance to purification at levels below the requirements

for reasonable stabilization of dislocations. Conversely, as was properly emphasized in Dr. Newkirk's talk, dislocations lend themselves to decoration, that is they form rows of contamination with diameters of more than one atom. Grain-boundaries and subgrain boundaries can be regarded as regions of very high dislocation densities. Concentration of trace elements at grain boundaries is a well-known phenomenon.

The most challenging type of trace contamination occurs inside the

otherwise perfect lattice array by atomic substitution, or in structural

interstices. Even here the properties are profoundly aff"ected by the

type of geometric relationship at what we call the point defect, the zero-
X-RAY DIFFRACTION 205

dimensional defect. It is the crystal chemistry of point defects which

undoubtedly will become progressively of greater importance as knowledge of trace characterization advances.

There is a general rule that the better the crystal-chemical fit of a kind of foreign atom in a structure the more evenly distributed these

atoms will be. Such atoms will be subject to the classical orderdisorder phenomena, in itself a wide-ranging subject not covered in

this Symposium. It is these kinds of point defects that are least easily

measured by most of the x-ray diffraction procedures discussed. On the

other hand, the poorer the crystal-chemical fit the greater the tendency

to segregation, constituting a completely different kind of "order,"

and the more likely are compositional fluctuations and lattice strains that will be detectable by x-ray diffraction methods.

II. Contributed Papers

The meeting then dealt, all too briefly, with the contributed papers. The one by R. L. Prickett and F. W. Wahldick was entitled, "A High

Temperature Single Crystal X-Ray Camera." That work [1] ^ takes the

art of x-ray diffraction studies to high temperatures at which precise

x-ray diffraction measurements on single crystals have hitherto been

virtually unobtainable. The fine instrumental work that has gone into

this development was highly praised. Yet, Peiser warned that for most

trace characterization work the word "trace" in connection with this paper should be interpreted as parts per hundred. This limitation

applies even to vacancy concentration determinations unless the

measurements can be combined with good dimensional data. Prickett

pointed out the important and unique potentiahties of the camera for high-temperature diffusion studies.

Next the rapporteur introduced the paper by T. Inouye and H. Nagami,

both originally from the Central Research Laboratory of Tokyo Shibaura

Electric Co., well known for a fine research outlook. Dr. Inouye is now working at MIT. The authors asked the rapporteur to speak for them. They have developed a new method of Fourier analysis of ob- served x-ray powder diffraction Une profiles interpreted in terms of

stress distribution. The rapporteur put their fine work into perspective

in relation to the subject matter of this Symposium. They are describing

work on polycrystaUine materials. As Dr. Newkirk explained, this severely Umits applications to trace characterization. Line shape, moreover, is so complex a subject and so sensitively dependent on a score of other parameters that the interpretation of obtainable results

is full of pitfalls, which these authors fully recognized. Nevertheless,

Mr. Peiser expressed .the view, not challenged by the Symposium members, that the Inouye-Nagami method had two attractive features:

first, it enabled internal strain caused by traces to be directly compared

' Figures in brackets indicate the literature references at the end of this paper.
206 TRACE CHARACTERIZATION

with that caused by externally applied mechanical stresses; secondly,

Fourier analysis of a line profile was in itself a mathematically justi- fiable procedure for deriving more usable information contained in a composite resonance, relaxation or other response curve than is often

obtained by more direct tests and definitions of resolution. R. D. Deslattes and B. Paretzkin had carried out microstrain measure- ments on highly perfect single crystals. The rapporteur's usual warning

to listeners in this instance was based on the remarks in Newkirk's

and Chikawa's paper that their method does not measure the trace atoms

themselves but only the strain effects they produce. Yet these secondary effects give the opportunity to use powerful and sensitive procedures

which may become of great value. It must be remembered, however,

that some trace elements may, in some crystal-chemical sites, introduce no measurable strain. Dr. Deslattes, himself, showed some beautiful x-ray topographs of quartz, silicon, and ruby crystals of high perfection taken by their new

generally usable method of two-crystal topography [2]. In this method

the reference crystal, known to be free of dislocations and observable

microstrain, is chosen so that it is slightly mismatched in d-value with

respect to the crystal under observation. This procedure leads to a small decrease in sensitivity compared with the corresponding one using

precisely matched crystals. However, such a matched crystal method

would need very precise beam collimation and an almost infinite set of reference crystals. For their method the authors had developed a set of six siKcon reference crystals cut for external Bragg reflection from

chosen sets of atomic planes so that virtually any "unknown" crystal of high perfection could be topographically examined. Deslattes answered

questions on the techniques the authors had developed for the cutting,

sectioning and strain-free pohshing of the sihcon crystals. In view of the critical shortage of time and the perceptive treatment of accurate x-ray intensity measurements for trace characterization in Newkirk's and Chikawa's paper, G. Burley's paper was taken as read,

although his analysis follows a different and perhaps even shghtly more conservative line than that of Azaroff et al. presented by Dr. Newkirk. Dr. Burley and some other authors in this country and in Japan

have obtained x-ray atomic scattering factors of high accuracy from

Debye-Scherrer fines. Dr. Burley had pointed out that with these

values it has become possible to compare x-ray intensities of crystal

powders for the quantitative measurement of point-defect content. He has applied the theory of propagation of errors to individual x-ray

lattice reflections. No doubt a similar treatment might be given to the

observation of forbidden reflections. The present state of the art for point defect detection sensitivities by x-ray intensity measurements lies in the region of parts per thousand although detailed predictions vary with atomic weights concerned. The rapporteur emphasized, however.
X-RAY DIFFRACTION 207

that these results are obtainable especially for foreign atoms that give

the best crystal-chemical fit, i.e., for atoms which will form solid solutions

with least fluctuations of composition and lattice strain. If the Pendellosung fringe technique became effective the sensitivity of detection of point defects by x-ray scattering amplitudes might well jump by several

orders of magnitude.

In introducing the last contributed paper by W. van Gool, the rap- porteur expressed pleasure that van Gool had come to participate in the

Symposium. On our question of where in the crystal structure did the

defects lie, his message to us was: we had better develop a good formal

language in describing the relevant locations. In science, a precise

language often precedes understanding.

Dr. van Gool, himself, presented to the Symposium some of the basic

concepts from his recent book, "Chemical Principles of Defect Chemistry

of Crystalline Solids" [3]. Accepting that the progress in experimental

techniques provides the possibility to determine impurities in host

materials in ever decreasing concentrations, the question of the significance of such determinations becomes more important. Two aspects

are essential in answering that question. First, the function of trace

analysis in materials research is to obtain information helpful in the

understanding and control of trace-sensitive properties. Secondly,

native defects (vacancies, misplaced atoms, etc.) may be just as important as impurities for those properties.

The first aspect illustrates why information about certain impurities

may be more valuable than knowledge of some other impurities. The

influence of the different groups of impurities upon the physical properties may differ considerably. Therefore, the experimental possibility of determining certain impurities in very low concentrations does not guarantee that the essential impurities have been detected. The

second aspect shows that even a complete determination of all impurities

by atomic absorption, emission spectroscopy, activation analysis,

etc., still does not guarantee that the essential information has been

obtained.

The problem then is to find methods revealing the actual situation:

first the predominant species and then the defects present in lower

concentrations. Recently some progress in this problem has been made

for inorganic crystalline materials by introducing a generalized description of the defect chemistry. This description permits the interpretation

of measurements of densities, lattice parameters, solubility of impurities,

and deviation from stoichiometry, without assuming special models.

The description is not detailed, but it characterizes the predominant

species of all defect situations reconcilable with the observed data.

It is encouraging that in some situations this generalized description

fulfills already the purpose of the trace determination, viz, the description and the means for control of the trace-sensitive material properties.
208 TRACE CHARACTERIZATION

III. Discussion

Dr. van Gool has given the example of density-sensitive defect properties. This is a topic which leads us right into the subject of the highest

attainable accuracy in density determinations, a subject clearly of direct concern to the NBS Metrology Division. At the invitation of the rap- porteur H. A. Bowman of that Division presented the state of the art in density comparisons, although Dr. H. Kaiser's comment apphes — this

is a single-number characterization — yet a very useful one. Although

the precision of modern density experiments referred to water is better

than one part in 10 million, such measurements are uncertain by several

parts in one million due to the uncertainty in the density of a partic- ular sample of water. Recently, Cook [4] has measured the density of

mercury directly to about one part in a miUion, but difficulties in trans- ferring the accuracy inherent in this density value to other materials

have prevented full utilization of this measurement as a reference in other density work.

NBS is currently developing a family of solid objects which will col- lectively serve as a reference density in comparison work [5] and it is expected that densities derived experimentally from this reference will be uncertain by significantly less than one part in a million. The

Bureau's Cartesian Diver system [6] is a primary tool in this work because

it can detect differences of apparent mass in water of objects weighing

10 grams reproducibly to better than 10 ~^ grams. When specimen

wetting is a problem, a very small addition of a wetting agent can be used

without introducing a significant error. The rapporteur pointed out that Mr. Bowman had also made significant simplifications in technique for density determinations to 1 part

in 10^, so that such measurements can be carried out simply with standard laboratory equipment. Mr. Peiser expressed hope this technique

will shortly be published, as it might prove very useful at least for the

empirical comparison of crystals of differing trace content.

Dr. Newkirk in further discussion emphasized the potentiality of the

PendeUosung method by which an x-ray intensity could be effectively

measured by an angle and a length measurement. This is a very unusual

physical situation which should be exploited because generally in metrology lengths and angles can be measured far more readily than a radiation

flux.Dr. Chikawa commented further on his Moire fringe measurement

by which lattice spacings could be compared between very similar

crystals differing only in trace element content causing lattice expansions

or contractions of the order of 1 in 10^. The method is akin to a vernier

formed by the lattices compared and is not limited by the sharpness of an x-ray emission line, as are other methods in current use. Peiser in thanking the authors of contributed papers summarized his view that x-ray diffraction techniques had an established and important
X-RAY DIFFRACTION 209

place in the characterization of materials. For the time being, however,

the trace analyst should not build too much confidence in existing x-ray

diffraction procedures. Nevertheless, crystal strain measurable by

such methods was an important parameter additional to the trace composition of materials. Furthermore, the most recent developments

in x-ray diffraction methods left the substantive hope that by their use

direct data on trace composition will soon be obtainable.

IV. References

[1] Prickett, R. L., and Wahldick, F. W., A High Temperature Single Crystal X-Ray

Camera, Proceedings of the 13th Annual Conference on Application of X-Ray

Analysis, Denver 8, 86 (1965).

[2] Deslattes, R. D., Torgesen, J. L., Paretzkin, B., and Horton, A. T., Observations of Dislocations in Ammonium Dihydrogen Phosphate: Production of Dislocation-Free

Crystals, J. Appl. Phys. 37, 541 (1965).

[3] Van Gool, W., Chemical Principles of Defect Chemistry of Crystalline Solids, Academic

Press, New York (1966).

[4] Cook, A. H., Precise Measurements of the Density of Mercury at 20 °C, Phil. Trans. Roy. Soc. 254, 125-154 (1961).

[5] Bowman, H. A., The Development of a Working Density Standard, 14.8-4-65, Proc.

I.S.A. Conference, Los Angeles (1965).

[6] Bowman, H. A., and Schoonover, M. R., The Cartesian Diver as a Density Comparator,

J. Res. NBS 69C, 217-223 (1965).

PHYSICAL OPTICAL METHODS

Contributed Papers and Discussion

H. P. R. FREDERIKSE

National Bureau of Standards, Washington, D. C. 20234

I. Introduction

The purpose of this session was to focus attention on optical phenomena investigated as physical effects but hitherto little used as a method

for chemical trace characterization. While in a spectrochemical

analysis the sample is evaporated and the observed optical spectra are associated with the free atoms or ions, the physical effects presently

under discussion are due to atoms, ions, and defects, surrounded by the

host lattice. Hence one could call the latter kind of characterization nondestructive as opposed to the destructive method of spectrochemistry.

The wealth of optical phenomena that lend themselves to exploitation

as a method for chemical analysis is enormous. As in every area of characterization, one will need a catalogue of measured and calculated

spectra and intensities before these effects will be ready for everyday

use by the scientist interested in the purity of his sample. Although a

fair amount of such data can be found in the literature, very little effort has been made to put the results systematically in the handbooks. Only

in the limited area of semiconductors and color centers does one find some systematic listings of absorption and luminescence data. The need for characterization in situ has become more apparent during

the last 10-15 years. Many important solid state effects and electronic

devices depend not only on the nature of the foreign element or defect,

but also on its location and its environment in the lattice. The development of magnetic materials (e.g., ferrites) requires a knowledge of the

position of the magnetic ion. The question of "random-distribution-orclusters" is important in semiconductors and insulators. The maser

and laser provide examples where the crystalline environment of the

"trace-impurity" is essential to the functioning of the device. Electron-, neutron- and other high-energy radiation produces desired or undesired

defects whose nature and location have to be known.

In nearly all cases the important physical effects are caused by

foreign elements or defects present in amount of 10~^ to 10^ ppm.

Concentration changes of one or two orders of magnitude often radically

alter the observed effects. 211
212 TRACE CHARACTERIZATION

The optical phenomena fall into three categories:

(a) electronic excitation (or de-excitation) to higher (lower) states of the

"impurity" or defect itself [1].^ Examples: optical absorption and luminescence of Cr^+ in AI2O3 or Mn in CdS; F-center absorption, bleaching, lumines- cence, photoemission, etc. [2]. (b) electronic excitation from "impurities" to energy bands of the host

lattice [3], Examples: optical absorption and photoconductivity of B in Si or Cu in InSb.

(c) local vibrations or perturbations of the Reststrahlen spectrum

(lattice vibrational or phonon states) due to foreign elements of different mass.Examples: 0H~ in many host lattices (e.g., KCl, Ti02); Ne in soHd

Ar. A great number of optical effects can be observed especially if one

counts also those variations caused by external fields. An incomplete

listing includes: optical absorption, reflectivity, luminescence (also

electro, tribo, thermo, and cathode luminescence), photoconductivity,

photoemission, Zeeman effect. Stark effect, piezo-optical effects and

stimulated emission.

II. Invited and Contributed Papers

Eugene Wong's (UCLA) introductory discussion was concerned with some of the phenomena mentioned under (a) above. He focused attention particularly on the spectra of transition metal ions and rare earth

ions in simple host lattices. These spectra can be understood — at least qualitatively — in terms of the free ion states, the crystalline field sur- rounding the ion, the spin-orbit splitting, and other minor effects affecting

the position and strength of the absorption lines [1]. In the first contributed talk J. A. Baker (Dow Corning Corp.) made a

strong plea to exploit infrared spectroscopy for the detection of trace impurities in semiconductors. He illustrated his point by discussing

five major impurities in silicon: carbon, oxygen, arsenic, boron and

phosphorus. The first two give rise to vibrational bands at 16 fx [4] and

9 fjL [5], respectively. These bands are obscured by the intrinsic absorption bands of the host lattice. However, by employing a difference

technique, using a slice of pure silicon as the reference material in a double beam spectrophotometer, it is possible to measure the carbon or oxygen bands accurately. The limit of detection for these two elements

is 0.2 ppm.

At low temperatures the elements arsenic, boron, and phosphorus

produce absorption bands at 26 jjl, 32 fx, and 32 /jl, respectively. These

' Figures in brackets indicate the literature references at the end of this paper.
PHYSICAL OPTICAL METHODS 213

bands are caused by electronic ionization of the ions. Because silicon

is reasonably transparent beyond 16 /x, no difference technique is re- quired. From comparison with resistivity measurements (on silicon samples containing only one of these elements as major impurity) one

can conclude that the limit of detection is 0.5 ppb.

The method is appropriate for determining the concentration of single

doping elements in silicon and germanium [3], III-V compounds, and

several other semiconductors. The lowest amount that can be detected

and identified depends on the maximum purity attainable for the host

lattice. The contributed paper by Lorimor and Spitzer (University of Southern

Cahfornia) and WiUardson and Allred (Bell and Howell) dealt with a

similar infrared detection method. These authors discussed local modes due to associated pairs of foreign elements. For instance, by

diffusing lithium into boron-doped silicon (p-type) one produces Li-B

pairs [6]. The pairs (as well as the single lithium and boron-atoms) give

rise to local vibrational modes in the 14-20 fJL spectral region. Substitutional impurities lighter than the atoms they replace will increase

the frequencies of the host-lattice modes. An example is the peak at 362 cm~\ resulting from aluminum in GaAs. Table I summarizes the

lower hmit of detectability for several of the impurities considered in

this study.

Table I. Lower limits of detectability for several impurities.

Lower limit of detectability

Semiconductor Impurity

ppm atoms/cc

Si B(-Li) 40 2X10^8

GaAs P 1 4X10^6

GaAs Al 1 4 X 1016 GaAs Te (-Li) 20 1 X 1018 GaAs Zn (-Li) 20 1 X 1018 GaAs Mn (-Li) 20 < 1 X 1018 GaAs Cd (-Li) 20 ~ 1 X 1018 GaAs Si and Si-Li 2 1X1017

T. Chang (NBS) presented a contributed paper advertising the potentialities of electron spin resonance absorption as an analytical tool. The spectrum results from transitions between electronic levels split

by an external magnetic field and is observed in the microwave region.

A commonly used frequency is 9000 Mc (corresponding to A. = 3 cm,

X-band) and the applied field is of the order of 3000 oersted.

Any ion or defect with an unpaired electron can be detected; often low

temperatures are required to observe the spectrum. A vast amount of

theoretical and experimental knowledge is available in the literature [7]. Some of the best known examples are: ions of the transition elements
214 TRACE CHARACTERIZATION

(e.g., Cr^+ in AI2O3), color centers (F-center in KCl), "impurities" in semiconductors (Sb^+ in Ge), free radicals (I~ inCHsI).

The method is extremely sensitive; in some cases as few as 10^^ spins can be detected. More generally, concentrations of 10"^ to 10~^ ppm

in a sample of one gram are easily observable. Often the e.s.r. method is able to identify the trace impurity (e.g., from the hyperfine structure);

also, it can provide information about the location of the center (substitu- tional or interstitial). In this paper the example of transition metal ions in Ti02 was dis- cussed, including Ti^+, Cr^+, Mn4+, Mn^+, Fe^+, Ni^+, Co^+, Ni2+, Cu2+,

Nb4+, Ta4+, Ce3+, and Gd^^ [8].

II. References

[1] Ballhausen, C. J., Ligand Field Theory, McGraw-Hill Book Company, New York, 1962.

[2] Schulman, J. H., and Compton, W. D., Color Centers in Solids, The Macmillan Company, New York, 1962.

[3] Geballe, T. H., in Semiconductors, N. B. Hannay, ed., Reinhold Publishing Corporation,

New York, 1959, Chap. 8. [4] Newman, R. C, and Willis, J. B., J. Phys. Chem. SoHds 26, 373 (1965).

[5] Kaiser, W., and Keck, P. ,H., J. Appl. Phys. 28, 882 (1957).

[6] E.g., Balkanski, M., and Nazarewicz, W. A., J. Phys. Chem. Solids 27, 671 (1966).

[7J E.g., Low, W., Solid State Physics, Suppl. 2, F. Seitz and D. Turnbull, ed.. Academic

Press Inc., New York, 1960.

[8] Gerritsen, H. J., Paramagnetic Resonance, Proceedings of the First International Conference, Jerusalem, 1962, Academic Press Inc., New York, 1963, p. 3.
CHEMICAL SPECTROPHOTOMETRY IN

TRACE CHARACTERISATION

T. S. WEST

Department of Chemistry, Imperial College of Science and Technology,

University of London, London S.W. 7, U.K.

I. Introduction

The principal concern of this contribution is to review the current

status of analytical potentiality within the area of chemical spectrophotometry. This is an extensive area and, for present purposes, it wiU be defined as being associated with the absorption of radiation in

o the range ca. 2000-8000 A, i.e., the spectral range of a conventional

u.v./visible spectrophotometer. In times gone by the word spectrophotometry has been associated almost exclusively with the mechanised

or instrumented aspects of colorimetry in solution. But, recent developments within the past few years have made it patently obvious that there

are uses for spectrophotometers other than the measurement of absorption of radiation by molecules in solution or in the solid state. It has

also become apparent that some of these developments offer very

attractive possibilities for trace characterisation and determination which

were hitherto scarcely thought to be possible.

The absorption of radiation by molecular species has long been used

by analytical chemists, and the basic requirements and characteristics

of the technique are well recognized. However, although the majority

of molecular species absorb radiation of a characteristic waveband, thus

exhibiting a 'colour' corresponding to the sum of the unabsorbed parts

of the visible range of the electromagnetic spectrum, there are many

which not only absorb (primary) radiation, but subsequently re-emit

(secondary) radiation, usually of a longer wavelength. These are fluores- cent or phosphorescent compounds. Based on these phenomena we

have the twin techniques of spectrofluorimetry and spectrophosphorimetry which offer some unique advantages not possessed by absorption

spectrophotometry. These techniques have been grossly neglected

by analytical chemists for reasons which are not easy to define. It is obvious that this neglect is not likely to persist in view of the remarkable

analytical sensitivity and versatility which they offer. In many philosophical arguments of recent years there has been much

discussion of the areas of responsibility of the chemist and the physicist

and the general conclusion appears to be that, broadly speaking, chemists

215
216 TRACE CHARACTERIZATION

should be concerned with molecules and physicists with atoms. However, sharp lines of demarkation are nonscientific in this context and

there has recently been a trend shown in the naming of the departments

of some new universities and government research institutions whereby,

instead of departments of chemistry or physics, we find departments of

'molecular studies' or of 'atomic studies' which cut across the older and

perhaps more rigid ways of compartmentalised thinking. In the U.K.

the Atomic Energy Research Establishment at Harwell has recently

re-designated its former Division of Analytical Chemistry as the Division

of Analytical Sciences, and similar events have probably occurred in many other places. It may yet prove to be the case that the new

designations of university departments wiU be more rigid and inflexible than the older, now rather elastic ones but, be that as it may, it is cer- tainly appropriate that those of us who, in the past, have thought of

ourselves as analytical chemists should now consider ourselves as analytical scientists and cease to worry too much about Liebhafsky's now

classic comment that the chemistry is going out of analytical chemistry

[1].^ This trend tovv^ards analytical science rather than chemistry is certainly very obvious in the programme of this 1st Symposium of the

National Bureau of Standards on Trace Characterisation and it appears

to the writer that these wider horizons are very much to be welcomed.

It is against this background of thought that the words 'chemical

spectrophotometry' in the title of this contribution will, therefore, be

interpreted broadly to include the absorption of u. v. /visible range radiation by atoms as weU as by molecules. The concepts and techniques of atomic-absorption spectrophotometry (AAS) are indeed more familiar

to 'physicists' than to 'chemists,' but the analyst or analytical scientist must not, and indeed cannot, allow any artificial conceptual barrier to hinder or proscribe the development of his researches. The analytical

implications of the absorption of radiation by free atomic species are very impressive indeed. The sensitivity of the technique is uniformly

high and in all known instances it can be regarded as specific for individual elements.

Most atoms wiU absorb radiation in the u.v./visible range of the spec- trum, as will most molecules, so that the coverage of atomic-absorption

spectrophotometry as presently practised extends over a wide area of

the periodic table. But, whereas a relatively small number of molecules

exhibit fluorescence, it appears from our present state of knowledge that the new technique of atomic-fluorescence spectrophotometry (AFS) will have a much wider coverage than molecular-fluorescence spectrophotometry. The author and his colleagues have as yet not failed to find atomic fluorescence wherever they have looked for it within the

hmits of their present experimental capability. Moreover, the technique

' Figures in brackets indicate the literature references at the end of this paper.
CHEMICAL SPECTROPHOTOMETRY 217

offers unique sensitivity as well as specificity of determination and there

appears to be every reason to forecast a very considerable impact for it within the next decade.

These then are the phenomena and techniques which will be principally discussed in this contribution:

1. the absorption of radiation by (dissolved) molecules, MolecularAbsorption Spectrophotometry;

2. the absorption/re-emission of radiation by (dissolved) molecules,

Molecular-Fluorescence Spectrophotometry;

3. the absorption of radiation by (free) atoms, Atomic-Absorption

Spectrophotometry;

4. the absorption/re-emission of radiation by (free) atoms, AtomicFluorescence Spectrophotometry.

Within this framework it is the author's intention to discuss briefly

and non-mathematically the basic principles of these techniques and to review some recent progress, though in most instances this is particularly well done in the biennial reports of these areas published in ''Analytical

Chemistry'' and need scarcely be added to here. It will be an important

consideration to assess the present day capabilities of these techniques

and to try and forecast probable developments in the near future. It is not, however, at all intended that this should be an exhaustive review of the current status of these techniques, but rather that it should show the scene as viewed through the eyes of one person engaged in these particular areas of analytical research.

II. Molecular-Absorption Spectrophotometry

(The absorption of radiation by molecules in solution)

Although there is probably a considerable future for the development

of solid-state absorption spectrophotometry in thin films and for tech- niques allied to diffuse-reflectance spectrophotometry, particularly in view of the increasing attention which is being paid to direct solid-state analytical techniques, this discussion will be limited entirely to the

absorption spectrophotometry of solutions since this is undoubtedly one

of the backbone techniques of modern trace analysis.

The principles and techniques of molecular absorption spectrophotometry are, of course, very well known and little need be said about

fundamental aspects except in as much as it is necessary for the purpose

of discussion. A. Selectivity of Reaction

A molecule may be regarded as possessing two different kinds of energy, kinetic and potential, whereas a beam of radiation may be

regarded as an electromagnetic waveform disturbance or photon (particle) of energy propagated at the speed of light. Before the molecule
218 TRACE CHARACTERIZATION

can absorb radiation it must interact with it and this interaction must

occur within the period of oscillation of the light wave, ca. 10~^^ sec,

i.e., the period during which the photon and the molecule are in contact. There is no possibility of direct interaction between the translational

energy of the molecule and a light beam since a charge separation must

be involved. Consequently, exchange can only occur by interaction

with the potential energy component of the molecule's total energy via

movement of electrons. The energy of photons in the u. v. /visible range

of the spectrum corresponds to ca. 50-150 kcal/mole so that we are concerned here with electronic transitions rather than with vibrational or rotational transitions, though these may also be involved and impart

superimposed fine structure on the electronic absorption bands. Fur- thermore, the electronic levels inside molecules are quantized so that the absorption bands can occur only at definite values corresponding to the energies required to promote electrons from one level to another.

As a result of this the absorption spectrum of a molecule should cor- respond to sharply defined absorption bands, but the effect of the

multiplicity of different vibrational and rotational levels in molecules

and of solvent molecules associated with the solute molecules is to smooth out these bands so that broad, rather featureless absorption

spectra are usually exhibited by almost all molecules in solution. This

at once places a physical restriction on the selectivity of molecularabsorption spectrophotometry, for obviously in a given expanse of

wavelength scale as presented by the resolution of a spectrophotometer one can only obtain a very limited number of absorption bands without

very considerable overlap. Consequently, even where spectra are well

separated, it is only possible to resolve a mixture of a very few absorbing

species without recourse to complicated mathematical analysis in the

process. Although very many organic compounds absorb quite strongly, only a

limited number of inorganic ions do, and it is the normal modus operandi

of inorganic absorption spectrophotometry to add a molecule or reagent

species to the solution of the inorganic ion which will react with it and,

in the process, bring about a marked change in the spectral absorption

characteristics of the reagent. It is necessary that, along the wavelength

axis, the absorption spectrum of the reagent-ion adduct should be well

separated in at least one place from the absorption spectrum of the

reagent itself, though it generally matters little if it is separated from

that of the ion because the intensity of the absorption band due to the

latter is low. In any event, it is common practice to add a fairly large excess of the reagent so that virtually all of the ionic species are caused

to react with the reagent. It is also desirable, though not strictly

essential, that the separation between the two spectra should be good

with respect to the absorbance axis so that the maximal sensitivity of reaction may be forthcoming.
CHEMICAL SPECTROPHOTOMETRY

1. Mechanism of Colour Production

219

As a generalisation, it can be said that most of the organic molecules

which are used as reagents in inorganic absorption spectrophotometry

constitute the chromophore of the absorbing species which is formed

and that the spectral response which is produced can be ascribed to structural changes which are brought about in the reagent molecule

following reaction with the inorganic ion. Usually, a complex formation reaction between the ion and the organic molecule acting as a multi-dentate Hgand is involved. Now, complex formation may be

defined as the union of a ligand, in which a donor atom furnishes a lone

pair of electrons, and a cation, which acts as an acceptor and incorporates

these electrons into empty levels in its own orbitals. G. N. Lewis

defined a base as an electron-pair donor and an acid as an electron-pair

acceptor. It is, therefore, apparent that there is no essential difference

between acid-base and complex formation phenomena. The implications of this for absorption spectrophotometry are clear. Most organic chelating agents are themselves protic acids and dis- sociate according to a well defined pattern, e.g., H2L^HL- + H+ ^L-2 + H+. (1) Obviously there will be serious competition between hydrogen and metal

ions for the ligand molecules. Metal ions which form weakly bound

chelates wiU only be able to react efficiently with the reagent in solutions

of high pH, whereas metal ions which react more strongly will form complexes in solutions of much lower pH. Thus pH control can provide some means of interelement analytical selectivity for those metals which

react in more acidic media than most others. Another more important

implication for selectivity of reaction may also be drawn, however.

Consider the reaction between a metal ion, M+^, and a ligand species,

HL~, to form a chelate complex, ML2 ^ M+ ^ + 2HL- ^ ML.y ^ + 2H+. (2) The net effect of the reaction is that each ligand molecule has one proton

removed in the process. It is not surprising, therefore, to find that in most instances the colour reaction developed as a result of complex

formation closely resembles that which is produced by the addition of the same amount of alkali to the reagent solution to remove the same number of protons per ligand molecule. Although the Lewis theory

signifies that there is not any essential difference between the proton and

the metal ion, M+^, there is, of course, an enormous physical difference

between the two, particularly with respect to size and electronic structure, so that it is not possible to argue that there should be no change of
220 TRACE CHARACTERIZATION

colour as a result of complex formation since each proton is replaced by

one equivalent of another cation. The hydrogen ion constitutes a 'bare' proton, whereas the nucleus of other cations is heavily screened by their

associated electrons. Consequently, the addition or removal of a proton

to a ligand molecule has a marked effect upon the electronic structure

of a chromophore, whereas the addition or removal of other cations,

unless they themselves are deformable or undergo charge-transfers, is usually of little effect. This point is well illustrated by an examination

of the absorption spectra of some of the 1:1 complexes formed between

various metal ions and the dicarboxymethylaminomethyl substituted

1,2-dihydroxyanthraquinone reagent, Alizarin Complexan, cf. Figure 1. Apparently, any metal ion of suitable co-ordination geometry and affinity for the donor atoms in a ligand, can be expected to react with the formation of similarly coloured complexes all of which approximate to that of one of the more highly ionised (i.e., deprotonated) forms of the ligand

molecule. Some divergence of the absorption spectra can only be ex- pected to occur where there is some degree of covalency in the bonding

between ligand and cation. The more covalent the bond the greater the

interaction between the electrons of the ligand' s molecular orbitals and

those of the cation and the greater the divergence of the absorption

spectrum of the chelate away from that of the appropriately deprotonated

metal-free ligand.

2. Identity of Liganding Atom

The implication of this is that one cannot expect to achieve any simple

or easily won degree of analytical selectivity by moving from one reagent

to another relying on the conventional oxygen and nitrogen donor atoms

400 500 600 700

Wavcfength(^mjj^

Figure 1. Absorption spectra of metal chelates of Alizarin Complexan at pH 4.3. (1) Pb;

(2) Th; (3) Ni; (4) Ce(III); (5) Free reagent; (6) Free reagent at pH 7.
CHEMICAL SPECTROPHOTOMETRY 221

that are used almost exclusively in most organic reagents. However,

it is apparent that the introduction of some other donors such as sulphur,

selenium, arsenic and phosphorus should achieve some selectivity of response. Some work has already been done in this area and it is probable that some measure of success will be achieved with this type

of reagent in the future. For example, it is interesting to study the

reactivity of 8-mercaptoquinoline, the sulphur analogue of 8-hydroxyquinohne. Bankovskii and his co-workers [2] have shown that this reagent has high selectivity for metals with a high affinity for sulphur.

Thus rhenium [3] may be determined very selectively at 438 m/Lt in a chloroform extract from 11. 5M hydrochloric acid without interference

from molybdenum and tungsten. Similarly, [4] palladium may be deter- mined at 485 mfjL following extraction from 50% hydrochloric acid in the

presence of some thiourea to mask copper, gold, mercury (II), osmium,

platinum, ruthenium and silver which would also extract. The only

interference appears to be due to molybdenum (VI) and this can easily

be back-washed from the organic phase by 8M hydrochloric acid. It is out of the scope of a brief review such as this to cite other instances,

but a survey of the biennial reviews in Analytical Chemistry wiU reveal

other examples of selectivity gained in this direction by the substitution

in organic reagents of donor atoms other than nitrogen or oxygen. It is also apparent that permutations of the available donor atoms may lead

to some rather interesting gains in selectivity of reaction, and that this

is an avenue of approach which is worthy of further exploration.

3. Steric Hindrance in Organic Reagents

In the past, however, more attention has been paid to steric hindrance

as a means of increasing selectivity of reaction. This has not been

singularly successful, except in one or two rare instances, however. It is, of course, a rather negative approach in that one is trying to suppress

the activity of a reagent towards certain ions and consequently there is danger that aU reactivity may be suppressed or that rather weak complexes may be produced for those cations which still react. Some of the outstanding successes in this area have led to some curious errors

in the literature. For example, remaining with the 8-hydroxyquinohne

model, we have the now classic work of Merritt and Walker [5] who made

the exciting discovery in 1944 that the 2-methyl substituted reagent was

selectively unreactive towards the precipitation of aluminium, whilst it stiU precipitated most other ions in an exactly similar manner to 8- hydroxyquinohne. They ascribed this, not unreasonably, to steric hindrance. Now it is true that 2-methyl-8-hydroxyquinoUne shows no

visible signs of reaction with aluminium and it may have been this that led Hynek and Wrangell [6] to describe an ingeniously specific spectrophotometric method for aluminium. First of all, other extractable

metals were removed by a chloroform extraction with the 2-methyl-8-
222 TRACE CHARACTERIZATION

hydroxyquinoline reagent and then the aluminium was extracted similarly with 8-hydroxyquinoline and determined in the usual way.

However, this method is based on a fallacy, because appreciable amounts

of aluminium are extracted by 2-methyl-8-hydroxyquinohne even at pH

4.5. The author and his co-workers [7] recently showed that a fluorescent

complex (370/480 mfx) is extracted from aqueous solution. Earher

work by Ohnesorge and Burhngame [8] had demonstrated the existence

of a 1:1 complex in an entirely non-aqueous solution. The 'selectivity of steric hindrance' must, therefore, be interpreted rather carefully

within prescribed conditions.

The reagent 2,9-dimethyl-l,10-phenanthrohne or neo-cuproine fur- nishes another example of a similar nature. Because of the steric hindrance of the methyl groups this reagent does not form a coloured

product with iron (II) and it is, therefore, virtually specific for copper (I) [9] though it offers a rather low sensitivity. However, this has led to a suggestion that the reagent may be used as a specific extractant for copper [10], whereas several other metals, e.g. cadmium, cobalt, nickel,

silver and zinc can be quantitatively extracted by it [11] so that it is once

again demonstrated that it is dangerous to extrapolate the meaning of the

words "selectivity" or "specificity" from one context to another.

Once again, these are only two examples of the use of steric hindrance

to gain selectivity of reaction.

4. Chelate-Cage Reagent Molecules

The phenomenon of the clathrate type of compound is well recognized.

This idea can be extended to the realm of absorption spectrophotometry

using chelating agents via the principle of devising chelate "cages"

into which only ions of the requisite size may fit. Close and West [12], for example, devised the reagent cyc/o-tris-7-(l-azo-8-hydroxynaphthalene3,6-disulphonic acid) now known as Calcichrome, which functions on this principle. The reagent. Figure 2, is constituted of three self con- densed diazotized H-acid units which have formed a cyclic trimer involv- ing a three ortho-hydroxyazo bond system in a tight cage in the centre of the molecule. At pH 12 this reagent reacts only with calcium ions

(ionic radius 0.99 A) to form a colour body. Strontium (1.12 A) and

barium (1.34 A) are too big to fit into the cage and other ions which might

be expected to fit are either precipitated at the pH of operation or are present as anionic complexes (e.g., zincate, etc.) and are not capable of reacting with the anionic ligand. The reagent has been used for the

spectrophotometric determination of calcium in the presence of several

thousand-fold amounts of barium or strontium [13] thus forming an

interesting, though not particularly sensitive [eeism/x = 7600] spectrophotometric method for calcium. It must be reported, however, that Russian workers have challenged the cyclic nature of the molecule and
CHEMICAL SPECTROPHOTOMETRY 223

Figure 2. Calcichrome [(Cyclotris-7-(l-azo-8-hydroxynaphthalene-3,6-disulphonic acid)]. have proposed [14] an alternative open-chain structure in which one of the amino groups is replaced by a hydroxyl group, thus terminating the

possibility of ring closure as originally proposed by Close and West.

More recently another 'chelate cage' molecule has been proposed as

a spectrofluorimetric reagent for magnesium. The reagent is N,N'-bissalicylidene-2,3-diaminobenzofuran, (BSAF), Figure 3, which provides a

fairly rigid square planar cavity between the azomethine nitrogen atoms

and the phenolic oxygens suitable for accommodation of ions having an

ionic radius of ca. 1 A [15]. It was found that most of the ions examined

which had ionic radii between 0.5 and 0.8 A reacted, whilst none with

radii greater than 1 A showed any reaction whatsoever. Structurally

similar reagents such as N,N'-6i5-salicylideneethylenediamine and N,N'-

6i5-salicylidene-l,2-diaminobenzene have been examined also [16] [17] but these form complexes with a wider range of ions, many of them

having ionic radii larger than 1 A and, in addition, they form fluorescent

complexes with ions such as aluminium, beryllium, gallium, indium and

zinc, whereas BSAF forms strongly fluorescent complexes only with

Figure 3. N,N'-Bis-salicylidene-2,3-diaminobenzofuran.

237-323 0-67— 15
224 TRACE CHARACTERIZATION

magnesium (0.66 A) at pH 10.5 (475/545 m^t) and gallium (0.60 A) at pH 5 (475/545 m^t). The BSAF reagent furnishes an elegant and sensitive

spectrofluorimetric method for the determination of submicrogram

amounts of magnesium in the presence of preponderant amounts of

calcium [18]. The 'chelate cage' principle has been httle exploited as yet, but it would appear to offer many interesting possibilities for further investi- gation and it will very probably become a much more thoroughly explored avenue of research in future years.

5. Formation of Ternary Complexes

Most of the complex or chelate systems which are used in inorganic

absorption spectrophotometry are binary complexes (mono- or polynuclear as the case may be) in which the test ion 'M' reacts with one

species of ligand, 'L' to form absorbing species of the nature ML, ML2,

ML3, etc. It has already been pointed out that the chances of other

metal ions 'M", 'M'", etc. duplicating the reactions of 'M' are excellent and that the absorption spectra of these other complexes may very

well closely resemble those of each other and of a more fully deprotonated form of the ligand molecule. It is interesting, therefore, to speculate that if one were to devise complexes in which two ligands

'L' and 'R' react simultaneously with a metal ion 'M' to form a 'mixed'

or 'ternary' complex, e.g., MLR, ML2R, or some such body, then the

possibihties of duphcation of such ternary complex formation should

be considerably less. As a result, such ternary complexes should

probably be analytically more selective than conventional binary complexes. Very little work has been done in this area, but that which has

been done has yielded some significant results and may perhaps be illus- trated by two differing reagent systems investigated by the author and

his co-workers.

a. Methods of Ternary Complex Formation. There are two

principal ways in which a ternary complex may be put together. In one of them one can consider that the ion forms a co-ordination unsaturated complex or chelate with the first ligand so that not all the positions on the co-ordination sphere of the ion are taken up by the first ligand.

These positions may then be taken up by the second Hgand if the geometry is suitable to form a ternary complex. A glance at the co-ordination

numbers and principal valences of various ions shows us that for many

ions there is a 2:1 relationship between these two numbers. Thus we

have Ag^='2, Cu;^l4, AUi^, Th^is and so on. These ions will obviously

tend to react with typical bifunctional analytical reagents such as oxine,

Ox,Ti2, to form co-ordination-saturated zero-charge complexes, so that the possibilities of ternary complex formation are low. However, other

ions such as Mg+Jg, Cci„+J6, Be+Jg will obviously tend to form co-ordination-unsaturated complexes with typical bidentate ligands, so that ter-
CHEMICAL SPECTROPHOTOMETRY 225

nary complex formation with these ions is possible according to the first schemxC. In the second mode of formation, ternary complexes may arise where

the first hgand forms purely co-ordinate bonds with, the metal ion or when it has a 'surplus' of ionogenic or purely dative groups so that although the first hgand does form a co-ordination-saturated complex

it does so with the formation of a positively or negatively charged primary complex which may then ion-associate with an anionic or cationic

dyestuff or other body to form a ternary complex.

b. The Alizarin Complexan-Lanthanon System for Fluoride

Ion. The first type of (ternary complex) formation system may be

illustrated by the .Alizarin Complexan reagent system for fluoride which

\ielded the first 'positive' colour reaction to be described for this ion [19].

-\11 previous colour reactions depended on the bleaching of a coloured

metal complex, e.g. ferric thiocyanate by fluoride ion or on the fiberation

of a free dyestuff from the metal lake compound of a metal such as zirconium or aluminium which forms a strong complex with aluminium.

-\lizarin Complexan (3-dicarboxymethylaminomethyl-l,2-dihydroxyanthraquinone) [20] ionises according to the pattern shown in Figure 4

and reacts in its yellow form at pH 4.3 to form red-coloured metal complexes, the absorption spectra of which closely resemble that of the

metal-free reagent ca. pH 7. i.e.. the next higher ionisation stage of the

chromophore, cf. Figure 1. All these metals except thorium react to form 1:1 complexes with the reagent, and the lanthanides in particular

form very stable complexes. hen any of the Ahzarin Complexan

chelates of one of the first six members of the lanthanide series, viz, elements of atomic numbers 57 to 62, is treated with a substoichiometric

amount of fluoride ion a new blue colour body exhibiting a 1:1:1 reagent:

lanthanide:fluoride stoichiometry is formed. The reaction is particularly

intense with lanthanum and cerium (III). The colour formation is unique

in that it is the only known positive colour reaction of the fluoride ion. Furthermore, it is a sensitive reaction, (e ~ 30,000), and it also appears

to be specific for the fluoride ion. This unusual reaction may be exRed, H^I^", pH 6—10

Figure 4. Dissociation pattern of Alizarin Complexan.
226 TRACE CHARACTERIZATION

plained [21] very simply in terms of classical resonance theory by accepting Pauling's postulate that a partial double bond characteristic may

be ascribed to metal-oxygen bonds. Before the entry of the fluoride

ion into the binary complex the latter may be depicted as in Figure 5. The ligand has formed a co-ordination-unsaturated complex with the

lanthanide ion 'M'. Entry of the strongly electrophyllic fluoride ion

into the co-ordination sphere of the lanthanide leads to a general withdrawal of electrons from the Ahzarin Complexan molecule along the

conjugated bond system presented between the lanthanide atom and the

remaining undissociated phenolic group of the molecule, Figure 6.

Figure 5. Structure of typical metal chelate of Alizarin Complexan, e.g., M = Ce(III).

CH2-N

Figure 6. Induction pattern of 1 : 1 : 1 ternary fluoride complex.

As a result, the proton-oxygen bond i/s weakened and the proton dis- sociates even at pH 4.3, although it does not normally do so till ca. pH 12-13. This is borne out by an examination of the close similarity of the spectra of the ternary complex and that of the Alizarin Complexan

reagent alone at pH 12.4, cf. Figure 7. It has already been mentioned

that this reaction is given only by the reagent chelates of the first six members of the lanthanide series, i.e. those metals where the entry of the first '5d' electron in lanthanum triggers off subsequent filling of the

'4r sheU so producing the inner transition series of the lanthanons.

These are the elements which readily form fluorides when their oxides

are heated with chlorine trifluoride. The intermediate lanthanons

(63-68) form fluorides less readily and the higher ones not at all. There

is every reason to suppose that this reaction could possibly be reversed to form very selective spectrophotometric procedures for these particular

lanthanons in the presence of the others, though the sensitivity would

most probably only be good for lanthanum and cerium (III). The danger

implicit in trying to reverse the procedure is, however, that the reaction is essentially a substoichiometric one as far as fluoride ion is concerned. If the ratio of fluoride ion to lanthanon greatly exceeds unity not only will
CHEMICAL SPECTROPHOTOMETRY 227

400 500 600 700

Wavelength {my.)

Figure 7. Absorption spectra of ternary fluoride complex. (1) Alizarin Complexan at pH 4.3. (2) Cerium(III) chelate at pH 4.3. (3) Ternary complex with fluoride at pH 4.3.

(4) Alizarin Complexan at pH 12.4.

the (blue) ternary complex not be formed, but the (red) lanthanon-reagent

complex will be bleached, liberating the metal-free (yellow) reagent in the

process. This danger may indeed arise when attempts are made to determine larger amounts of fluoride [22] though the analysis may easily

be done when due precautions are observed [23]. c. The Bis [diphenanthrolinium-silver (I)] BPR Ternary

System, etc. The second (ternary complex) formation system is well

illustrated by some recent work on the spectrophotometric determination

of silver [24] and more recently still on cadmium, cobalt (II), copper (I) and (II), gold, manganese (II), nickel, lead, zinc, etc. [25]. These

other metals form firmly bound 'primary' complexes with tertiary amines

such as 1,10-phenanthroline in which the metal is bound to the liganding

atoms by purely dative bonds so that the complex species thus formed

still retains the same formal charge as the original cation. These co- ordination-saturated complex cations can ion-associate with anionic

dyestuff molecules to form very intensely absorbing bodies. This

principle is not, of course, a new one. Many methods are known, e.g., for boron [26], gaUium [27] etc., where colourless complex ions may be

associated with solvent-inextractable basic, i.e., cationic, dyes to form

neutral (uncharged) ion-associated species which extract well. The

work of several Russian authors in this area [28] is particularly

interesting. These dyestuffs have high molar absorptivities and the

absorption spectrum of the extracted species is, of course, identical to that of the dyestuff in aqueous solution apart perhaps from some smaU

solvation effects.
228 TRACE CHARACTERIZATION

However, the systems discussed here are different in that we have the

unusual phenomenon of a colour change upon ion-association of the complex cation and the anionic dye. For example, silver ion reacts with the

polyphenolic triarylmethane dyestuff, Bromopyrogallol Red, BPR,

Figure 8, to form slowly a rather nondescript brown compound in which

the silver ion is apparently present as Ag(II) and is united to one ligand

molecule across the vicinal phenolic groups. The process of complex

formation is slow and is very dependent on experimental conditions such

as the volume of the medium in which formation occurs. The course of the reaction can be followed potentiometrically by the release of hydrogen ions from the ligand in the usual way.

However, when the two reactants, viz, Ag+ and BPR are brought

together in the presence of an excess of r,10-phenanthroline an entirely new colour-body which is bright turquoise blue is formed instantaneously

[24]. Furthermore, this compound formation occurs without the release

of hydrogen ion and the stoichiometry of the compound formation cor- responds to [Ag-Phen2] 2BPR. It is, therefore, apparent that the silver ion is datively bonded to two 1,10-phenanthroline molecules and that two

of the monopositive di-phenanthrolinium silver (I) ions thus formed ion- associate with a BPR molecule to form a neutral body. The compound

thus formed is not very soluble and can only be formed successfully

in very dilute solution. It yields a molar absorptivity value of 51,000

which is ca. twice that of the very temperamental dithizone procedure,

and in the presence of EDTA, fluoride and peroxide only gold (III) yields cationic interference. The complex can also be extracted [29] into nitrobenzene away from anionic interferences. Whilst all of this unites to provide a method which is both more sensitive and selective

than any previous absorptiometric method for silver ion it still leaves

unexplained the unique fact that a very profound colour change is obtained, cf. Figure 9, upon ion-association of the primary complex and

the BPR molecule. Work is still in progress on the mechanism of the

colour reaction, but the three principal theories around which current

investigation revolves are that it may possibly be explained (1) as has

the action of adsorption indicators in the past, to distortion of dyestuff

OH

Fig;ure 8. Bromopyrogallol Red.
500 600 WAVELENGTH (myLt) Figure 9. Absorption spectra of silver-bromopyrogallol red — phenanthroline complex,

(a) Bromopyrogallol Red. (b) Ternary silver complex.

molecules following physical adsorption on a colloidal Ag(Phen)2 body,

or (2) to a charge-transfer mechanism in a definite bis [di-phenanthrolinium silver (I)] BPR compound or (3) to a sandwich layer type of mechanism in which BPR molecules are bonded between two layers of silver-phenanthroline molecules. The first explanation does not ex- plain the firm stoichiometry of the compound and the second is difficult to explain in a completely satisfactory manner at present, though

further work may clarify matters. The third possibility is, in some ways,

a combination of the others and may be a closer approximation to the

true state of affairs. More recent work [25] allied systems using 1,10-phenanthroline as the

ligand and tetrachloro(P)tetraiodo(R)fluorescein [trivial name Rose

Bengal Extra, (RBE)] as the counter anion has yielded yet higher sensitivities, cf. Table 1. In these latter systems the complexes have been

extracted into various solvents to provide increased selectivity of deter- mination. Iron (II), which is well known for its reaction with 1,10-

phenanthroline, does not undergo ternary complex formation. This

is probably due to orbital stabihsation which makes the formation

constant for the ^ri^-phenanthrolinium iron (II) complex from the bis- phenanthrolinium iron (II) greater than the first or second. Only a limited number of ions are capable of undergoing ternary complex

formation, principally those mentioned in Table 1, but even amongst

these it is possible to arrange for interelement selectivity. Thus,

copper may be determined specifically amongst 56 cations and in the

presence of most anions by extraction of the neo-cuproine complex of

Cu(I) from an EDTA medium [25]. Conversion to the [Cu(phen)2] RBE

system is made by simple addition of reagents, thus providing a molar

absorptivity of 62,500 and permitting solutions containing only 0.002 ppm
230 TRACE CHARACTERIZATION

Table I. Tentative sensitivities of ternary ion-association systems.

Ion determined Mol. absorptivity coefficient (solvent) M.A.C.

(Dithizone)

Cd 92,000 (ethyl acetate) 85,000

Co 92,000 (ethyl acetate) 59,000

Cu(II) 78,000 (ethyl acetate) 45,000

Mn 65,000 (ethyl acetate) 32,000

Ni 50,000 (CHCI3) 34,000

Pb 70,000 (nitrobenzene) 72,000

Zn 95,000 (ethyl acetate) 94,000

to be readily analysed for copper. The colour system is stable for several days. This again offers a very attractive alternative reagent

system to the well established dithizone procedure. The sensitivities of several of these ternary systems under the conditions established

to be maximal for copper are shown in Table 1, and are compared there

with the recorded data for dithizone, which was certainly one of the most

sensitive reagents hitherto available for the absorptiometric determination of inorganic cations. It is probable that these figures for the

elements other than copper are capable of improvement following routine

optimisation of experimental variables.

It is apparent that these selective ternary complex systems hold out worthwhile possibilities for future development in molecular absorption

spectrophotometry as an inorganic trace technique. The judicious use

of masking agents, particularly 'mass-masking agents' such as EDTA

which is 'selectively unreactive' towards certain ions, e.g., silver, beryllium, copper (I), thallium (I), or of cyanide which is 'selectively unreactive' towards the alkaline earths, aluminium, beryllium, lead, bismuth,

etc., will obviously go a long way to avoiding the tedious separations

which were formerly required and which made trace analysis a very

difficult area. B. Sensitivity of Reaction

The problem of obtaining selectivity of reaction has obviously become

a major preoccupation amongst analytical chemists and this aspect of

absorption spectrophotometry has been featured almost exclusively

in these paragraphs up to this point. However, it is also necessary to take into account the sensitivity of molecular absorption-spectrophotometry as a trace technique because the Umits of detection and

determination are being pushed to ever lower levels by legislation and
CHEMICAL SPECTROPHOTOMETRY 231

manufacturing know-how. There is little doubt that, whereas the

situation seldom arose in years gone by, the analyst must now frequently

wonder if absorption spectrophotometry is sensitive enough for the analysis which he must perform.

The basic law of absorption spectrophotometry relates the absorbance

'A' to the concentration of the absorbing species 'C linearly through

the length of the absorbing layer of solution and the molar absorptivity of the absorbing species, e

i.e. ^ = e-/-C (3) Obviously the analytical signal can be increased for a given concentration

of the reacting ion 'C by increasing the pathlength or by using a compound which has a greater molar absorptivity, e. At first sight it might appear to be simple to increase the sensitivity of any given deter- mination by a factor of 100-fold by replacing the conventional 1 cm ceU

by one measuring 1 metre. This might work reasonably well if the

reagent, which is always added in considerable excess, had no absorb- ance whatsoever at the wavelength of analytical measurement. But

this is rarely the case, and the most efficient reagents usually exhibit

considerable spectral overlap between reagent and complex. Consequently such solutions would be optically so dense as to become useless for analytical purposes. Indeed, even if the reagent does not absorb appreciably, success can only be achieved where the absorbing

species itself has a low absorptivity, and is therefore very insensitive. Yet again, in dealing with long path cells there are even more serious

difficulties from light scattering, internal reflections, stray light and so on.

1. The Sensitivity Barrier

The best hope of increasing sensitivity of determination would, therefore, appear to be to use reagents which yield high molar absorptivities.

This approach has been used extensively. An absorbing molecule can

be considered as a mesh of electrons which is spread in the path of the

beam of incoming photons. Each absorbing molecular species may be

regarded as having a photon-capture cross section and anything which

can be done to increase this cross-section wiU obviously increase the

sensitivity of determination. Now the analogy of the photon-capture

cross-section, taken in conjunction with the realization that the absorption spectrum of a complex wiU closely resemble that of a higher ionisa- tion state of the metal-free reagent reveals that the simple addition of one, two or even three identical ligand species to a metal ion will not cause much increase in selectivity after addition of the first ligand,

whereas the addition of two differing species simultaneously to a metal

ion may cause a substantial increase in photon-capture cross section.

A crude analogy may be obtained by studying the shadow patterns
232 TRACE CHARACTERIZATION

obtained by placing two rigidly aligned sieves in front of a light-source.

If identical sieves are used there will be no deepening in the pattern if one uses two sieves rather than one. If the sieves are of different

design, however, a considerable increase in shadow will be obtained by

using the two sieves simultaneously. A better analogy stiU may be

obtained by consideration of the effects of impurities on the neutron- capture cross-sections of atomic reactor materials. This, in effect,

is what is being done in putting together ternary complexes where two

different ligand species are involved in reaction with one cation.

Another approach to increase of sensitivity using a single ligand

species is, of course, to build up the molecule's electron orbitals so that

it presents a more effective cross-section. This, however, is not an

easy route to sensitivity and it has not always been a very successful one because complex molecules frequently react only unwillingly with

cations and the tendency for spectral broadening to occur may swamp

the effect produced by chelation with the reacting cation.

However, it is interesting to speculate about just how far the photoncapture cross-section of an organic molecule can be increased. This

has already been done by Braude [30] who calculated that the maximal

value of the molar absorptivity would be of the order of 100,000. Now,

common values for the effective molar absorptivity of determination for most inorganic analyses lie in the range 10,000-40,000, though some of the newer methods described above tend to yield values as high as 90,000,

i.e., virtually theoretical values. Some simple arithmetic on this sensitivity barrier reveals that for a 1 cm cell and a value of 0.002 absorbance

unit the minimum detectable concentration would be 2 X 10~^M. For

the purposes of determination a minimum value of 0.01 absorbance

unit is more realistic and for most systems a molar absorptivity of 50,000

is perhaps better than can be expected. This would produce a limit of

2 X 10~''M. If now one remembers that reagents such as buffers, masking agents, the reagent itself, etc., must be added to the test solution, we find that the most dilute solution we could normally expect to analyse

by absorption spectrophotometry would be ca. 10~^M or even 10~^M.

Consequently, there is a very definite limit to the sensitivity of molecular

absorption spectrophotometry as a trace technique in inorganic analysis,

though it is comforting to turn up the textbooks and find that in terms of

molar absorptivities we can still go a long way to improve on existing

methods.

2. Surmounting the Sensitivity Barrier

The idea of amplification reactions is not unfamiliar in analytical

chemistry. Perhaps the best known is the Leipert method for the deter- mination of iodide ion. The latter is oxidised by bromine to give iodate

ion and the iodate is subsequently reduced by an excess of iodide ion
CHEMICAL SPECTROPHOTOMETRY 233

to yield six equivalents of iodine for each iodide ion originally oxidised

to iodate, i.e. I- -^10,

IO3 + 51- + 6H+ ^=^3H20 + 3I2

In this reaction there is a six-fold amplification and it may be considered

to be a direct one. There are numerous other such reactions, most of

which are of an indirect nature, but these cannot be discussed here. Obviously, this is one potential way of surmounting the sensitivity barrier

and though an example of this will be given for absorption spectrophotometry in subsequent paragraphs it is true to say that it is a device which

has not yet been used to any great extent. Another obvious way of overcoming the limiting sensitivity of

e ~ 100,000 is to persuade the test ion to act as a type of catalyst to pro- mote the kinetics of another reacting system. This again is a device

which is theoretically capable of yielding very high effective molar

absorptivities for ions which require to be determined with very high

sensitivity. There are perhaps more numerous examples of this in the

literature, but it is true to say that little or no systematic work has been

done on this approach. The author has suggested the term kinetochromic spectrophotometry for this type of determination [31] and this too wiU be illustrated by some recent work in the ensuing paragraphs.

a. Evolution of Amplification Reaction. Almost simultaneously,

Umland and Wlinsch [32] and Djurkin, Kirkbright and West [33] devised

extremely sensitive indirect amplification reactions for the phosphate

ion. The procedure devised by the latter authors is marginally more

sensitive and is probably less subject to interference by other ions

because of the extractive procedures employed.

In this procedure [34] the phosphate solution is treated in the usual

way with an excess of molybdate ion to form the conventional, 12 M0O3 • POr^, phosphomolybdate ion. The phosphomolybdic acid

thus formed is extracted away from the excess of molybdate ion in the

aqueous solution into a butanol-chloroform solvent. The phosphomolybdic acid extract is then well washed free of excess molybdate

ion and is equilibrated with an ammonia solution. The latter breaks

down the complex phosphomolybdate ion into the original phosphate

ion and twelve associated molybdate ions. The latter can then be

determined by means of Kirkbright and Yoe's reagent, 2-amino-4-

chlorobenzenethiol [35] so that twelve molybdenum chelate molecules

are extracted into chloroform from the aqueous ammonia extract. The method involves a considerable amount of manipulation, but by

virtue of the sensitivity of the reagent used (€710 m/Lt ~ 36,000) a very

sensitive determination is possible. The effective molar absorptivity
234 TRACE CHARACTERIZATION

for phosphate by this amphfication procedure is €710 mix = 359,000

which compares favourably with that obtained by the usual heteropoly

blue methods and which readily allows the determination of nanogram

amounts of phosphate using a simple spectrophotometer with 1 cm

cuvettes. By virtue of Wadelin and Mellon's extractive procedure

which is used in extracting the phosphomolybdic acid [36], there is no

interference from hundred-fold concentrations of other heteropoly acid

formers such as silicon, germanium, antimony and arsenic and up to thirty-fold excesses of tungsten (VI) can be tolerated in the presence of

l,2-dihydroxyazobenzene-3,5-disulphonic acid as a masking agent.

Work is now afoot to arrange conditions so that a sequential deter- mination of several of these heteropoly acid formers, e.g., silicate,

phosphate and arsenate, may be effected by this amplification reaction, and it is very much apparent that much of the manipulative work

may be eliminated by substituting atomic-absorption spectrophotometry

for molecular-absorption spectrophotometry as the means of analytical

measurement.

Umland and Wiinsch's procedure is essentially similar, except that thiocyanate is used as reagent in place of 2-amino-4-chlorobenzene

thiol as absorptiometric reagent and the colour system is developed in the aqueous extract. b. Evolution of Kinetochromic Spectrophotometry. In aqueous solutions of intermediate acidity, zirconium in the form of zir- eonyl ions, ZrO + ^, tends to polymerise to produce rather inactive species.

Thus a freshly prepared solution of zirconyl oxychloride reacts very

rapidly with the reagent Xylenol Orange, Figure 10, to produce a fairly

intense red chelate compound. The speed of this reaction varies

inversely with the age of the solution, however, so that after the solution

has aged overnight very little colour develops within a conventional

development time, e.g., 60 minutes. We [37] have found, however,

that in the presence of fluoride ion the red colour due to the 2:1 zir- conium: Xylenol Orange complex is formed very much more quickly

in such aged solutions provided that the amount of fluoride ion is considerably less than that of the added zirconium. In addition, there is a linear relationship between the absorbance due to the complex and the

Figure 10. Xylenol Orange.
CHEMICAL SPECTROPHOTOMETRY 235

amount of added fluoride over a given interval of time, i.e., the fluoride ion exhibits a limited catalytic effect on the kinetics of production of the complex. If the colour reaction is allowed to proceed for a limited

period of time only, during which the 'blank' reaction between the

zirconium and the Xylenol Orange scarcely proceeds, it is found that there is a firm stoichiometry for the reaction between the three components. This corresponds to a ratio of X.O.:Zr:F = 4:8:1, i.e., each

fluoride ion appears to be responsible for the rapid production of four

zirconium:Xylenol Orange chelate molecules. It must be stressed,

of course, that if the reaction is allowed to proceed long enough, the pres- ence of the fluoride ion will have practically no effect because it merely

speeds up a reaction that is otherwise very slow. In addition, if the

amount of fluoride is more than substoichiometric in relation to the

zirconyl ion the reaction will be retarded or completely inhibited be- cause of the formation of polyfluoro zirconium species.

Because of the acidity of the reaction, no other cations interfere by

forming coloured complexes with the Xylenol Orange and only aluminium

exhibits a negative cationic interference by forming a stable complex with

fluoride ion at 100-fold concentration. None of the common anions

interferes, but some other anions which exhibit a strong complexing

action on zirconium, e.g., phosphate, arsenate and sulphate (and also some complexing organic anions, e.g., oxalate and citrate) exhibit an

effect similar to that of fluoride ion. The practical impHcations of these kinetochromic reactions are very

considerable. The kinetochromic extinction coefficients or effective molar absorptivities for these reactions are as foUows

fluoride €/, 200,000

arsenate ca- ^ 340,000

phosphate €/, 400,000

sulphate Ca- 22,000

For fluoride, arsenate and phosphate these methods of kinetochromic

spectrophotometry off"er sensitivities ca. one order of magnitude greater

than existing spectrophotometric methods. In the case of sulphate

the sensitivity is conventional at ca. 22,000, but it is, to the best of the

author's knowledge, the only 'positive' colour method so far proposed

for the sulphate ion. Furthermore, the system for phosphate, apart

from its high sensitivity is unique in that it does not depend on the for- mation of a heteropoly acid of any kind. Yet again, in relation to fluoride

ion the above system constitutes a considerable advance on the Alizarin

Complexan method [19-23] and is subject to considerably less cationic

interference.

Although work is still in progress on the elucidation of the mechanism

of these unusual reactions, it is perhaps permissible to speculate briefly
236 TRACE CHARACTERIZATION

here on their possible course. The reacting ratios for the other ions

appears to be as follows

X.O. :Zr:P04 = 8:16:l

X.O. :Zr: As04 = 4:8: 1 X.O.rZr: 804 = 2:4:1

The zirconyl oxychloride solution can only be used after it has aged

for twenty four hours and its effective life is ca. five days. The extent

of the catalytic reaction is also temperature dependent. The reacting

ratio between the zirconium and the Xylenol Orange remains constant throughout at 2 : 1 which corresponds to that which would be expected

between zirconium and Xylenol Orange in pure solution. It appears,

therefore, that in all instances the colour body is the zirconium: Xylenol

Orange 2 : 1 complex and this is confirmed by the coincidence of all the absorption spectra. It may be concluded, therefore, that the

fluoride, arsenate, phosphate or sulphate ions activate the polymerised

slow-reacting zirconyl species present in aged solutions by rendering

them labile towards reaction with Xylenol Orange. The aqueous

chemistry of zirconium solutions is, unfortunately, a very obscure area and consequently any theories developed to explain the above reactions can, in our present state of knowledge, only be highly speculative. It

is tempting, however, to wonder if the reaction can be explained on the

basis that several zirconyl ions (or zirconium ions) may be coordinated

around one central anion such as fluoride, phosphate, etc. The possible

existence of such a labile species, e.g., [F(ZrO)„]+(2«- 1) ^j. [F(Zr)„]+ - 1

)

tempts one to suggest further that in the above instance n = 8 since this would explain the apparent X.O. : Zr : F — 4 : 8 : 1 stoichiometry of the re- action. It is certain that the existence of a labile unpolymerised species

such as this would aUow more rapid formation of the Zr2 : X.O. complex.

These matters must, of course, remain a matter of pure speculation at the present time since the apparently firm stoichiometry of these reactions may be coincidental on a combination of the many variables in- volved. What is certain, however, is that these so called [31] kinetochromic reactions present a very valuable and unique technique for the

analysis of these ions. The intercombination of different cations, anions

and reagents presents fascinating possibihties for further exploration.

It must be recognized that there is a very great need for more attention

to be paid to the analytical absorption spectrophotometry of anions.

Even though the principle of these kinetochromic reactions is only

imperfectly understood at present it should be capable of extension to many other reacting systems and it may well be that this will prove the

most fruitful area yet for the development of sensitive absorptiometric

techniques for the determination of trace non-metals in solution.
CHEMICAL SPECTROPHOTOMETRY 237

C. Molecular Absorption Spectrophotometry in the Future

Several possibilities for future development have already been sug- gested in the previous paragraphs, but these have largely been of a fairly

specific nature, although their general implications are apparent. The

use of differential spectrophotometry should allow much more precise

determinations to be made on solutions of high absorbance so that the

upper hmit of the technique may be extended into the domain of macroanalysis. This is inherently important because absorption spectrophotometry is a technique which is easily automated. At the other

extreme, the intelligent use of scale expansion should allow much smaller

amounts of material to be determined with greater precision than is possible by means of conventional spectrophotometers. Another in- teresting possibility for the improvement of sensitivity would be to endeavour to persuade molecules to abandon their random orientation

in solution and to ahgn in the optimal position for Hght-capture. Obviously this may be no easy task for some molecules, but possibilities for such ordered arrangements do exist and the principle appears to be

worthy of investigation.

Means of increasing selectivity of reaction are perhaps more elusive,

but much of the need for this has been removed by advances which have

been made in the use of masking agents, particularly in the realm of compleximetric titration. Some considerable need exists here for systematic examination of the reactions of masking agents, because

most of our knowledge in this area has arisen empirically and largely

by chance observation. It is possibly also true to say, however, that

Httle is likely to be gained in terms of increased selectivity by modification of reagent structure, apart from introducing hganding atoms

other than nitrogen and oxygen. Perhaps the most promising approach

appears to be an increased use of catalytic action since this is most

frequently of a highly selective nature.

Lastly, it can be said that despite the introduction of many new

spectroscopic trace techniques there is as yet no reason to suppose

that this well-tried and much used technique may become obsolescent

within the next decade.

III. Molecular Fluorescence Spectrophotometry

(Spectrofluorimetry)

In the instance of the compounds and reactions which have been

discussed above in connection with molecular absorption spectrophotometry we have not been concerned with the fate of the photons

which have been absorbed by interaction with the compounds. It has been sufficient to know that the absorption of energy has been a proportional process. However, the molecules which have absorbed

the energy have undergone electronic transitions and since they are.
238 TRACE CHARACTERIZATION

therefore, in an excited state, they must be considered as unstable

until they lose their acquired energy and return to the ground state. Now some molecules which are very highly coloured are well known

for their photochemical instability and in these instances we can clearly

consider that the energy which is acquired upon exposure to light is an activation energy for chemical reaction. The coincidence of high

tinctorial power and lack of "fastness to Hght" is all too well known to the dyestuff chemist. However, the great majority of coloured com- pounds are reasonably stable to normal (daylight) radiation and in these

instances the excess energy is largely spent by transfer into increased

vibrational energy and thermal activity of the molecules which result in non-reactive intermolecular collisions so that we can say that the energy

is lost by dissipation of heat. The whole process is generally referred

to under the most misleading title of loss of energy by "radiationless

transfer." This unfortunate designation presumably arises out of the

third category of energy shedding by excited-state molecules which

is the visible (or u.v.) re-radiation of light. There are very many com- pounds which exhibit light emission in this way and those constitute

the general category of luminescent compounds. Although it is very

germane to the consideration of analytical potentiality, particularly in terms of selectivity of reaction, the author is not concerned, for the

purpose of this discussion, with chemiluminescence phenomena whereby

molecules emit energy which they have acquired as a result of chemical

reaction. These compounds and reactions will therefore be excluded

from all further discussion in this context. Fluorescence and phosphorescence constitute the other two categories of luminescence and

of these, fluorescence is the more common and will be chiefly considered. Outwardly it is difficult to distinguish between fluorescence and

phosphorescence since the latter appears to be merely a case of delayed

incidence of the former, but there is a fundamental difference which

wiU be explained briefly in due course. The essential difference be- tween compounds which absorb light and those which absorb and subsequently re-radiate hght is that the latter have unusually stable excited

states so that these molecules can retain acquired energy in a definite energy level for a finite time before they dissipate it and return to the

ground state. Only those compounds which have stable excited state configurations will therefore exhibit the phenomenon. Resonance re- radiation, i.e., re-emission of photons of the same energy as those originally absorbed is, to the best of the author's knowledge, completely

unknown in solution. Invariably less energetic photons are re-emitted

by the luminescent compound so that the fluoresced light has a longer

wavelength or lower frequency than the absorbed light. The fluores- cence is also characteristic of the compound in the sense that the

emission spectrum is always the same irrespective of the wavelength

of the incident light which promotes the fluorescence. It is perhaps
CHEMICAL SPECTROPHOTOMETRY 239

best to outline the reasons for these and other phenomena before dis- cussing the analytical implications of spectrofluorescence and comparing its merits and demerits with respect to other trace techniques,

particularly molecular absorption spectrophotometry.

A. Absorption Re-emission Processes

Figure 11 depicts the electronic energy levels in a molecule, ignoring all the vibrational and rotational levels for the sake of simplicity. Excitation occurs by absorption of energy and translation of an electron from the

ground state, Eo along path AB to the first excited state, Ei, although

excitation may also occur to higher excitation states, E? and £'3, etc., along paths AU and AV. Fluorescence emission occurs when the

electrons follows path CD in falling from the first excited state to the

ground state. The excited state, Ei has a finite life-time of 10~" to 10~^

sec which may be equated to BC on the diagram. Phosphorescence

emission may occur when the molecule has a triplet excited state, Tu

lying below the first (singlet) excited state, Ei. The electron may pass

over into the triplet state, by path EF shown on the diagram, and phosphorescence is emitted when the electron faUs back to the ground state along path XY. Now the triplet state is a 'forbidden' one and this has two main consequences. These are, (1) that direct promotion of the electron into Ti from Eo is virtually unknown because it demands

TIME

Figure 11. Energy levels in molecular fluorescence and phosphorescence.

_ 237-323 0-67— 16
240 TRACE CHARACTERIZATION

simultaneous spin-decoupling so that no singlet-^ triplet absorption

band will be observed and (2) once indirect occupation of the Ti level has been achieved along path ABEF, re-radiation along path XY will be difficult since spin reversal must once more occur so that the life- time of the triplet excited state will be relatively long (ca. lO""*— 10 sec).

The essential difference between fluorescence and phosphorescence is, therefore, that the former involves a singlet^ singlet electronic transition, whereas the latter involves a triplet^ singlet transition. As a consequence of this difference, fluorescence appears to be an instanta- neous process (emission within 10~^ — 10~^ sec after absorption) whereas

phosphorescence can be seen to be time-dependent (emission within

10"'^ — 10 sec). Another important consequence of the life-time of the

excited state arises, however. This is that whilst some deactivation

of excited state molecules may occur as a result of collisions with sol- vent molecules before the energy is re-emitted as fluorescence, this effect becomes preponderantly important in phosphorescence where

the phenomenon is virtually unknown for dissolved molecules and can

only be observed on any scale when the solutions are frozen into glasses

at low temperatures so that collisional deactivation is prevented or at least severely restricted. Consideration of the potential energy diagram. Figure 12, serves to show some more useful explanations of some of the phenomena of fluorescence and phosphorescence. A simple binary molecule AB is considered as having end A clamped so that all vibration along the bond

axis may be considered as motions of B. In the £"0 ground state B will have a vibrational motion XY along the axis with the mean position of B corresponding to the mid-point of XY. If energy is imparted to the

molecule gradually and progressively the amplitude of XY will increase

to levels 1, 2, 3, 4, etc., and the extremities of X and Y will trace out

the potential energy curve for the ground state of electronic energy, £"0. The maximum distances apart AYi, AY2, AY3, etc., will increase steadily

but the minimum distances apart AXi, AX2, AX.-?, will not decrease pro- portionally because of interatomic repulsions between A and B, i.e., the

compression arm of the diagram will have a much steeper angle than the

stretching arm. It would appear that eventually a position AY„ will be

reached when any further addition of energy will cause B to recede to an infinite distance from A so that the AB bond is completely broken.

However, before this happens the molecule will normally adjust to the

increased absorption of energy by undergoing an electronic transition

to the first exicted state, Ei on the diagram or to a still higher electronic

energy level, cf. Ez, E3 on Figure 11. In the first (singlet) excited state, Eu the mean distance apart of A and B will be greater than in Eo, con- sequently the trough of the Ei potential energy curve must lie to the right of that of Eo in the figure. Under normal conditions the molecule AB

may be considered to exist almost entirely in the lowest vibrational
CHEMICAL SPECTROPHOTOMETRY 241

A B

INTeRATOMlC Dr$TANC£

Figure 12. Potential energy curves in molecular fluorescence and phosphorescence.

level of its ground state of electronic energy, Eq. Excitation from

Eq to E\ must occur during the 'life-time' of a photon {i.e., period of

vibration of a light wave) which is 10~^^ sec. Vibrational frequency in a molecule, on the other hand, is ca. 10~^^ sec so that to all intents and

purposes the geometry of a molecule may be considered to be "frozen"

during the transition from £"0 to Ex, i.e., the distance between A and B

will remain virtually constant during the life-time of the transition which

is so rapid that it can be depicted as a vertical line in Figure 12. Thus

the excitational transition does not occur to the lowest vibrational level of El, but rather to a higher vibrational level, e.g., level 4 of £'1. This means that the excitation places the electrons on the compression side of the potential energy trough so that the molecule is set vibrating like a spring by virtue of excitation. The period of these vibrations is ca. 10"^^

sec, whereas the lifetime of the excited state is ca. 10~^ sec. Consequently, during the latter the molecule will have reached the lowest

vibrational level of the first electronic excited state. It is, therefore,

from this position that the molecule re-emits fluorescence radiation

along path NO. Invariably, therefore, the absorbed photon, corre- sponding to BM in this diagram, is more energetic than the emitted

photon NO, i.e., the fluorescence emission band has a longer wavelength than the excitation (absorption) band. Fine structure might
242 TRACE CHARACTERIZATION

arise if the molecule fell back from the ground vibrational level of the

first excited state to various vibrational levels of the ground state £"0 just as fine structure might be similarly expected in the excitation

(absorption) band. However, in the majority of instances in solution

at low temperature vibrational energy is lost in less than the period of a single vibration so that fine structure is almost totally absent. The

main reason why broadband spectra are obtained rather than the line spectra suggested by Figure 12 has been explained in connection with

absorption spectrophotometry and will not, therefore, be discussed

further here.

1. Phosphorescence and the Triplet State Electrons in atomic and molecular orbitals are spin coupled and the

singlet states corresponding to these are typified by the Eq and E\ states shown in Figure 12. However, reversal of the spin of an electron may

occur and by the Pauli exclusion principle a new orbital must be created

to accommodate the uncoupled electron. The molecule may now be

regarded as a diradical and because of the interaction of spins and

orbitals this shows up spectroscopically as a three-band or triplet sys- tem. According to Hund's rule, spin multiplicity favours the ground

state and as a result the triplet excited state, E,, is less energetic than

the E\ state from which it was formed. The energy difference is not

great, however, and consequently there is considerable overlap of energy levels in the singlet and triplet excited states so that intersystem

crossing is readily possible. Thus one electron can readily be passed

over into the relatively long lived triplet state during the hfe-time of the

El state. Higher energy levels E2, Es, etc., were shown in Figure 11 and

transition up to these levels is quite common. These AU and AV

transitions in Figure 11 correspond to higher energies than AB of course, and show up as shorter wavelength bands in the absorption or excitation

spectra. However, the fluorescence emission band is almost invari- ably the mirror image of the longest wavelength absorption band, when

plotted on a linear energy scale, and these higher energy bands have

no counterpart in the emission spectrum. This arises because almost

invariably the higher states Eu E-z, £^3 are more closely spaced than

the Eo and Ei states. Thus considerable overlap of energy levels can

occur and internal conversion or intersystem crossing leads to complete dissipation of excess energy down to the lowest vibrational level of the first excited state, Ei within the life-time of the latter. As a

result, almost without exception, fluorescence (or phosphorescence)

occurs by emission from the lowest vibrational level of the first excited

state (or its associated triplet state). Consequently, fluorescence emission spectra in solution are usually less complex than absorption spectra

and occur at a v/avelength longer than that of the longest wavelength

absorption band.
CHEMICAL SPECTROPHOTOMETRY 243

B. Extinction of Fluorescence

It is now relevant to discuss some of the phenomena which have a deleterious effect on the efficiency of fluorescence of molecular species.

It wiU have been recognized that because of internal degradation of

energ>^ the photon or quantum of energy which is emitted has less energy

than that which was absorbed. The quantum efficiency, <I>, of fluo- rescence relates the number of quanta emitted to the number absorbed.

Ideally, this should have a value of unity and under favourable circumstances some authors [38] have reported very high quantum efficiencies,

e.g., 0.97 for Rhodamine B in ethanol and 0.92 for fluorescein in 0.1 M

NaOH. Factors which reduce the fluorescence may be classified as quenching eff"ects, i.e., those which reduce the quantum efficiency

itself, or as inner-filter effects, i.e., those which interfere mechanically

without having any effect on the value of

1. Quenching Processes

a. Chemical Reaction. One very important quenching efl'ect is the chemical reactivity of excited state molecules and this, of course,

is well recognized in many quarters where u.v. irradiation is used to promote reaction. However, under the conditions of analytical spectrofluorimetry as it is practised at present, the irradiation dose is usually

small since only relatively weak sources and brief exposures are employed. Furthermore, unstable reagent systems will tend to be dis- carded in favour of those which are stable. For these reasons this type

of quenching action will not be discussed further. b. Intermolecular Collision and Temperature Effect. Col- Hsional deactivation of excited state molecules with others, particularly

the solvent molecules, has a very big role to play in the quenching of fluorescence. Generally it is found that an increase in temperature

causes a very marked decrease in the fluorescence as a result of in- creased coUisional frequency, so that negative temperature coefficients of 1-2 percent per degree centigrade at room temperatures are very common. At first sight this might appear to be a serious practical re- striction on the analytical applications of the technique, but it must be

remembered that spectrofluorimetry is usually practised as a technique

in the submicrogram range where an error of up to 5% represents an

insignificant physical difference in the amount of material being re- ported. For this reason it seems to be common practice not to go to any great length to thermostat the apparatus used to measure analytical

fluorescence though this may arise out of the common analytical trace practice of simultaneous standard analysis along with unknowns rather

than from disregard of the temperature effect. It is also interesting

to note in passing, however, that Bowen and his co-workers [39, 40]

have drawn some conclusions from the magnitude of the temperature
244 TRACE CHARACTERIZATION

coefficient. With aromatic systems a low temperature coefficient is taken to indicate deactivation by intersystem crossing to the triplet state which is a process largely independent of temperature, whereas

a high coefficient is indicative of external conversion which is an ex- tremely temperature sensitive process. Because of the longer life-time of the excited state the effect of temperature is obviously much more

critical in phosphorescence than in fluorescence.

c. Viscosity of Medium. Obviously an increase of the viscosity of the medium will have the opposite effect to an increase of temperature

since it will minimise intermolecular collisions. The viscosity effect

is particularly marked where the quenching efficiency is low.

d. Nature of Solvent Medium. The nature of the solvent molecule

has a profound effect in the same way as temperature. For example,

solvents which are capable of operating strong van der Waal's binding

forces with the excited state molecule will prolong the life-time of a

collisional encounter and will, therefore, favour de-activation. Similarly solvents which possess molecular substituents such as bromo-,

iodo-, nitro or azo groups, etc., are undesirable because the strong

magnetic fields which surround their bulky atomic cores promote

spin de-coupling of electrons and triplet state formation. Consequently

these solvents have a marked quenching effect on fluorescence though

they may show promotion of phosphorescence. The mechanism

whereby those exchanges occur is the subject of some discussion.

Kasha [41] assumed that an energetic coUision between the excited

molecule and the quenching solvent molecule was involved whilst

McGlynn and his co-workers proposed a weak charge-transfer sys- tem [42].

Solvent molecules which are strongly polar generally have an adverse

effect on fluorescence relative to nonpolar systems as far as metal

chelate systems are concerned due to their solvation of the complex,

but with purely aromatic systems the situation may be reversed. Thus

Van Dauren [43] has reported the relative fluorescence intensities of

quinoline in benzene, ethanol and water as 1, 30 and 1000.

e. Charge-transfer Processes. Charge-transfer systems are also probably responsible for the quenching which is observed from certain

anions in solution. For example, the fluorescence of fluorescein,

quinine, Rhodamine B, etc., is greatly reduced by the presence of bro- mide, iodide, thiocyanate and thiosulphate which readily act as electron

donors. It is probable that a complex of the type Q* • Br~, is formed in which the charge on the anion is rapidly transferred, Q*" • Br backwards

and forwards between the pair during close proximity. As a result, the

entry of the tt* electron into its vacant orbital in the ground state may

be prevented by the presence there of a donated electron. The fluor- escence of naphthol and of anthranilic acid may be quenched by the reverse process because of charge-transfer with electrophyllic anions
CHEMICAL SPECTROPHOTOMETRY 245

such as iodate, nitrate, etc., so that excited electrons which would

normally be free to fall back to their tt orbital are transferred to the anion

and are not, therefore, available for fluorescence.

Leonhardt and Weller [44J suggest an interesting mechanism for charge-transfer quenching whereby an excited fluorescent molecule E*

forms a charge-transfer complex with the quencher X, giving an ion

pair E~ • which may dissociate to the ground state entities E and X^

dissipating the energy of the former excited state thermally in the process, or to give a triplet state of E and the ground state quenching

molecule with similar dissipation of excess energy.

f. Dissolved Cations and Ionic Strength. Dissolved cations also have a profound effect, particularly when the fluorescent molecule is a chelate former for the cations concerned. Generally only those cations

which are diamagnetic when co-ordinated and are non-reducible will form fluorescent complexes. Generally the transition metals with unfilled outer 'd' orbitals will quench fluorescence completely. On the

other hand, whereas paramagnetic species quench fluorescence they

strongly promote intersystem crossing so that at low temperatures those

cations will be observed to promote phosphorescence.

Fluorescence may also be markedly influenced by variations of the

ionic strength of the medium when the fluorescent species or the quenching agent or both exist as charged species. This arises because ionic

strength has a marked effect on the activity of the ions whilst it may not

affect their analytical concentration in any way.

g. Effect of Dissolved Oxygen. The presence of dissolved oxygen

has a pronounced quenching action on many organic systems though

it does not appear to have very much effect on very many inorganicorganic chelate systems. In many instances the quenching may perhaps

be due to photooxidation, but in others there appears to be no marked

decomposition. Bowen and Wokes [45] in their excellent monograph

on fluorescence, note that the ground state of the oxygen molecule is, in fact, a triplet state and that formation of its singlet excited level requires the energisation of only 24—40 kcal/mole. Quenching may,

therefore, occur by collision or by long range dipole-dipole transfer of a

singlet excited molecule with the triplet ground state oxygen molecule

producing a singlet excited O2 molecule and a triplet state form of the

other. This supposition is certainly a very convincing one in explaining

the extremely efficient quenching action of oxygen on many organic

systems since the dissipation of anything like the necessary 40-100

kcal/mole is difficult to explain by simple collisional quenching.

h. Radiative Quenching and Delayed Fluorescence. There are several other quenching mechanisms which could profitably be discussed

here, but considerations of space dictate that these cannot be considered

in detail. For example, the long range dipole-dipole transfer of energy

has been mentioned as a typical nonradiative quenching mechanism.
246 TRACE CHARACTERIZATION

but there are also some very interesting long range (up to 100 A) noncollisional processes which are radiative. The energy of an excited

state, E*, is transferred to the ground state of another species which

becomes excited, H*, in the process, and subsequently radiates its own

characteristic fluorescence. In this process fluorescence of E* is pre- vented so that H acts as a radiative quenching agent for E*. The pos- session of a common vibrational frequency to allow coupling of energy

appears to be essential and also the presence in H* of a lower vibrational

level than in E* so that internal degradation in H'* dequantizes the

reaction for E. The first recorded instance of such a reaction [46] is that between 1-chloroanthracene and perylene. This process must

clearly be distinguished from that whereby fluorescence emission by

E* is absorbed by H to give H*, etc. Another quenching mechanism which has recently been engaging

attention is the phenomenon of delayed fluorescence. Outwardly this appears to be akin to phosphorescence, but it involves a singlet-singlet

transition and the wavelength of its fluorescence is identical to that of

'normal' fluorescence, whereas phosphorescence invariably has a longer

wavelength. The mechanism is thought to involve decay of a singlet

excited state E* to the triplet E* followed by interaction between two

triplet molecules to give back a radiative singlet excited state and a ground state, E, molecule [47] according to the mechanism:

Many substances interfere with the evolution of fluorescence without

acting upon the quantum efficiency, ^, in any way. The most common

mode of extinction in this way is the inner-filter effect, whereby excita- tion radiation which would otherwise reach the fluorescent molecule is cut off by the presence of another absorbing molecule which is usually

non-fluorescent. Alternatively the inner-filter compound may act as the screen for the emitted fluorescence, thus preventing some of the

radiation from reaching the detector. The fluorescent molecule can,

of course, act as its own inner-filter. This effect is only marked in fairly

concentrated solutions, however. Typical behaviour is shown in Figure

13A and B. In A the excitation radiation, /o, is largely absorbed at the

front face of the cuvette so that little radiation is transmitted, and so

that the fluorescence signal, F, observed in the sector XY is not proportional either to the intensity of the excitation radiation or to the concentration of the fluorescing solute. In B, where the concentration of the

solute is much lower. It ~ /o and absorption and emission is uniform

E*

E* + E*

E*

E* + E

E + hi^

2. Non-Quenching Extinction Processes
CHEMICAL SPECTROPHOTOMETRY 247

B

SATUKATION INNCR FILTSK

/ 1, •

I I

EFFECT

Figure 13. Effect of concentration on fluorescence emission, (a) Strong solution, (b) Dilute solution. throughout the cuvette. This self-absorption can obviously be elimi- nated by appropriate dilution of the solution and in general this device

is useful for minimising all inner-filter effects. Substances which react chemically with the fluorescent molecule by

oxidation, neutrahsation, complexation, precipitation, etc., may also be

very effective in extinction of fluorescence, but these again cannot be

considered as quenching actions and they are common hazards in all solution techniques of trace analysis involving the use of organic reagents.

C. Instrumentation

The apparatus which is used for the analytical application of fluores- cence and phosphorescence phenomena is fairly weU known and Httle need be said of it. The essential parts are:

1. A detector to sense the level of the emitted radiation, usually with an amplifier to enhance the analytical signal;

2. A monochromator or filter system to disperse the fluorescent radiation before it reaches the detector;

3. A cell or cuvette to hold the solution;

4. A monochromator or filter system to disperse the excitation radiation

and

5. A source of radiation of suitable intensity and emission characteristics. For phosphorimetry a device is also necessary to permit examination

of emitted radiation during the interval when the excitation radiation

is shut off from the sample. Instrumentation of spectrofluorimetry and
248 TRACE CHARACTERIZATION

phosphorimetry has been discussed extensively by many authors in recent years and their papers [48-52] should be consulted for a detailed

assessment of various items and of the merits of some commercially

available apparatus. Fluorescence is usually observed at right angles

ta the incident beam of light to eliminate 'contamination' of the fluores- cense signal by radiation of the excitation wavelength, but the use of

efficient monochromators is fairly effective unless there is considerable

overlap of the excitation and fluorescence spectra. Special care must,

however, be taken in this mode that the detector does not "see" the

walls of the cuvette which may otherwise cause serious interference by

self-fluorescence or by scatter and internal reflection. The right angle

arrangement is most used because it is advantageous for dilute solution

(i.e. trace) work. Frontal analysis is most useful for the examination

of solutions of fairly high concentration, cf. Figure 13A, or for the ex- amination of solid specimens. The straight-through system is most used

in phosphorimetry, but Parker and Rees [48, 49] have indicated that in fluorescence it sometimes has advantages not possessed by the other

methods.

The analytical signal which is obtained is, of course, the amplified

output from a photomultiplier tube or other suitable transducer and as such it has no physical significance unless it is calibrated carefully and

the output is converted to quanta of radiation. However, it must also be noted that the response of a photomultiplier tube varies with the wavelength of the incident radiation as does the output of the source with

selected wavelength. These factors will also be modified by monochromator transmission characteristics, cf. Figure 14. Thus the ap- parent spectra which are obtained require to be corrected for these

characteristics of the apparatus before they can be correlated with other

results. Instrumental correction is also possible by devices in which

part of the light from the monochromated source is led onto a thermocouple which generates a signal corresponding to the energy reaching

it irrespective of its wavelength. This signal operates a sht-servo- mechanism so that constant energy is fed into the irradiation cell. A

second servomechanism similarly operates on the fluorescence side of

the instrument. Commercial equipment is now available for this purpose and has been described recently by Slavin et al. [53], and by

Turner [54].

1. Choice of Instrument

However, ^uch refined instrumentation is more suited to physicochemical studies of a fundamental nature rather than to the needs of trace analysis except in certain circumstances where much developmental work is involved. The main choice of instrumentation which

faces the prospective user of analytical fluorimetry is whether to work

with an instrument with monochromators in both the excitation and the
CHEMICAL SPECTROPHOTOMETRY 249

fluorescence beams or with a monochromator in one and a filter in the

other or with filters in both. Briefly, a double monochromating instru- ment is attractive, particularly in the exploration of a relatively unknown

system and indeed such instruments have been used extensively, if rather laboriously, for basic studies in the past. However, for analytical

work the use of an instrument with a filter ir the excitation arm is very

attractive because it allows much more intensity of irradiation and a wider spectrum of irradiation whilst the monochromator in the emission

side allows more precise resolution of the fluorescence radiation. Light

losses inside most monochromating devices are usually rather great.

As a result, when sensitivity of detection or determination is the desideratum a filter instrument is best suited, but when resolution and pre- cision is required, a spectrofluorimeter with twin monochromators should

be used. The signals which are received from filter instruments fre- quently include spurious signals from Raman emission, light-scatter,

etc., which cannot be detected separately and measured readily by such

instruments. Consequently, such apparatus can only be used satis- factorily on a purely empirical basis when the excitation/fluorescence

characteristics of the system are known.

D. Physical Laws Governing Fluorescence Emission

Fluorescence emission is necessarily preceded by the absorption of radiation of the wavelength of excitation. Consequently, the laws which
250 TRACE CHARACTERIZATION

govern the relationship between the activity of a fluorescent species in solution and the intensity of fluorescence arise out of, and depend on, those relating to absorption.

If radiation of the wavelength necessary to excite fluorescence falls upon a solution of the fluorescent substance in a suitable cuvette of absorbing cross-section A, cf. Figure 15, it will be absorbed according

to the Lambert-Beer law. Suppose that the intensity of the incident

light is /o and that of the transmitted light is h, both measured in quanta

per sq cm. This gives us

It = AIo exp °

where e is the molar absorptivity of the substance at the given wavelength of absorption, / is tlie pathlength in cm and a is the activity of the absorbing species. The amount of energy absorbed is, of course, given by ^/o(l — exp «) and it is this energy which will promote

fluorescence. Let the quanta of fluorescence generated be F. If we

consider a small layer of absorbing solution of thickness dx situated at a distance X from the front face of the cuvette, the fluorescence generated

in this layer will be proportional to the amount of energy absorbed, dl,

according to the quantum efficiency, of generation of fluorescence.

i.e. dF = ^dI

The light intensity which falls on the layer dx at a distance of X cm from

the front is AIq exp « whilst the transmitted intensity is AIo exp"^^'^^'^-^^^ Therefore c?/ = ^/o[exp -^-^"-exp -^(^+djc)aj = ^j^ ^^p -^-^ari - exp-^ '^^"] If we assume that we are dealing with a dilute solution and a very thin

incremental layer, dx, therefore

dI = AIoea exp~^ -^-" dx

As a result we can now write

dF = <i>AIo€a exp-^-^ « dx

Figure 15. Production of fluorescence in solution.
CHEMICAL SPECTROPHOTOMETRY 251

The total fluorescence is obtained by integrating over the entire pathlength of the absorbing/fluorescing solution

I.e. F = A<^Uea \

exp-^-^' " dx

Jo

Expansion of the bracketed term gives the factorial function

{e./.aY {e./.af {e.f.af

2! "^3! 4! ]

]

If e./.a is less than or equal to 0.05, ^ 0.025, ^ 0.0004, and

so on, so that virtually all terms save the very first one may be neglected.

It is easily possible to arrange that e./.a should have a small value by

using a very low concentration, c, of the fluorescing solute so that the

activity a ^ the analytical concentration, and by using a fairly short

path-length. This is achieved in effect by arranging that less than 5%

of the incident hght is absorbed by the compound. Under these conditions /, ~ /() and so the distribution of fluorescence throughout the

solution is almost entirely uniform and the situation depicted in Figure

13B results. The fluorescence equation, therefore, simplifies per sq

cm to

However, it is more common to work on a logarithmic (base 10) scale

and to view only a fraction of the total fluorescence generated by surveying a small segment of solution in a direction at right angles to the

incident light beam. If, therefore, we convert our equation to the

base 10 and introduce a fractional factor "p" we arrive at a final equation

F = 2.303 ^hefcp

It should be remarked at this stage, however, that the true fluorescence

yield F is rarely measured in quanta, but is generally replaced for analytical purposes by the signal response of a photomultipher tube

which is sensitive to the fluorescence radiation.

The alternate parameters /o, / and p are instrumental factors. It is apparent, therefore, that the analytical signal for a given chemical sys-
252 TRACE CHARACTERIZATION

tem will vary directly with the intensity of the radiant signal /o provided

by the source, with the path-length / of the cuvette and with the fraction

of the total fluorescence fed to the detector. The remaining parameters

in the equation, <i> and e are functions of the efficiency of the fluorescent

reagent system which we chose to use for the analysis of the trace constituent of concentration c. Obviously a reagent having a high quantum

efficiency should be selected and also one having a high value for its molar absorptivity, though the latter factor can cause some difficulties. E. Basic Differences Between Fluorimetry and Absorbance

The linear equation which has been derived illustrates two very important differences between absorption spectrophotometry and spectrofluorimetry. In the former the basic equation is A (absorbance) = Log /o//f = e./ .c Any increase in lo will be matched by a corresponding increase in It with no net gain in the analytical signal A. With fluorescence, however,

any increase in lo the intensity of the source, is matched by a corre- sponding increase in F. Thus it is possible to 'improve' the analytical

signal in fluorescence. Yet again, any increase in amplifier gain in ab- sorption spectrophotometry will amplify /o audit correspondingly whereas

in fluorescence the analytical signal F will once more be enhanced. For

these two reasons the analytical senstivity of molecular fluorescence

spectrophotometry is inherently greater than that of molecular absorption spectrophotometry and as a generalisation it may be said to be more sensitive by 2 to 4 orders of magnitude so that it is easily possible

by many fluorescence procedures to determine subnanogram/ml. concentrations of traces. This aspect will be discussed further in the subsequent section dealing with the merits and demerits of the technique

as an analytical tool. These same factors do, however, make it difficult to compare the

relative sensitivities of fluorimetric procedures or, even with a given

method, to compare the results obtained on one instrument with those

obtained by another. This is no problem in absorptiometry since

differences in source intensity and detector response are automatically

cancelled out by the lollt signal ratio that corresponds to absorbance.

Comparison is, however, only made more troublesome because it can

easily be done by correcting for source and detector characteristics

and relation to the performance of a standard substance such as quinine

bisulphate (see reference 72). F. Reagents for Spectrofluorimetric Analysis

It is a fact that molecular fluorescence spectrophotometry has not been used to a very great extent in inorganic trace analysis and this, in
CHEMICAL SPECTROPHOTOMETRY 253

view of the rather high selectivity and sensitivity, is rather surprising

at first sight. But it is only recently that instrumentation of a really

suitable nature has become available and it must be confessed that except for a few elements there is a dearth of the fluorogenic reagents

which are necessary since very few simple inorganic species are capable

of yielding any significant fluorescence in aqueous or non-aqueous

solutions. It is also true that whereas the development of reagents for absorption spectrophotometry took place gradually over a fair number

of ' years, based largely on empirical rules and observation, the evolution of inorganic spectrofluorimetry as a trace technique has been a more sudden process. Although we have now a better understanding

of molecular structure and function, it is still unfortunately usually a more rapid and successful process to screen large numbers of com- pounds for reactivity by experiment than to predict and produce a reagent, if indeed this has ever been done.

1. Character of Reacting Cation

However, there are certain guidelines and facts that are extremely

useful for those who wish to pioneer in this area. First of all there are

certain metals for which there appears to be no lack of fluorimetric

reagents of quite widely ranging characteristics, e.g., aluminum, berylHum, the rare earths, zinc, indium, gallium, calcium. These are chiefly

the metals which largely form 'colourless' complexes. The only

fluorimetric methods available for metals such as iron, copper, nickel,

chromium and other metals which readily form 'coloured' salts and complexes are usually based on the extinction of fluorescence of a fluorescent

molecule with which they react. This can clearly be seen with many

fluorogenic reagents, e.g., 8-hydroxyquinoline, which forms fluorescent

complexes with aluminium, beryllium, etc., and non-fluorescent complexes with iron, copper, etc. One of the features which we clearly must

consider here is that in the 'coloured' ions the energy levels for electron

transition must lie close together since the absorption occurs in the

relatively unenergetic visible range of the spectrum whilst the 'colourless' ions must have relatively wide spaced electronic levels since

any absorption which occurs is found in the u.v. region. Close spacing

of excitation levels is conducive to the processes of non-radiative loss of energy. Consequently, the presence of such 'low-level' ions in an otherwise fluorescent molecule may lead to an electron-sink action

which will completely extinguish fluorescence. Yet again, ions which

are paramagnetic promote triplet state formation in a ligand's tt orbitals and cannot offer good possibility for the production of a fluorescent

complex upon reaction with a molecule which is itself non-fluorescent,

though they may well be determined by fluorescence extinction with a

self-fluorescent reagent. Generally speaking, in any given periodic

group the heavier atoms of the series will be found to produce weaker
254 TRACE CHARACTERIZATION

fluorescence than the hghter elements due to the disturbance produced

by the electric fields of their bulkier atomic cores. On the other hand,

this process tends to favour the production of phosphorescence though

this will not be seen in solution at ordinary temperatures. For ex- ample, no fluorescent copper complexes are known, but several are phosphorescent [55]. In many instances there appears to be a type of

pendulum balance between fluorescence and phosphorescence emission

so that where one is lost the other is found.

G. Nature of Fluorogenic Reagents

1. Aliphatic Compounds

It is a matter of considerable comfort to find that generally, whereas

synthesis has produced ever more complex molecules for absorption

spectrophotometry, it is the simpler molecules which are most suited

to fluorescence spectrophotometry. AHphatic compounds rarely show

efficient fluorescence because they show only feeble absorption in the near u.v. or visible range, and consequently cannot be expected to fluoresce strongly anywhere. Moreover they rarely contain sufficient delocalised tt electrons which are necessary. Most aliphatic compounds

which do absorb strongly do so in the far u.v. (< 2000 A) where the energy

involved is so great that decomposition is produced rather than fluores- cence, or even the curious process of predissociation [56] which again

precludes fluorescence emission.

2. Aromatic Compounds

Aromatic compounds, on the other hand possessing good tt bonding

systems are commonly fluorescent and it is interesting to note that re- placement of one of the methyl groups of acetylacetone, which forms no fluorescent metal complexes, by a benzene ring to form benzoylacetone (or both methyl groups in dibenzoylmethane) results in many

fluorescent metal chelate compounds. Most simple aromatic hydrocarbons fluoresce strongly with their fluorescence moving inevitably

ahead of their absorption spectra into the longer wavelengths with in- creasing complexity, e.g., benzene and naphthalene in the u.v., anthra- cene, green; pentacene, red [57]. It is, therefore, generally found

that fluorescence reagents for inorganic trace analysis can best be

built by substitution of chelating groups on an aromatic skeleton. As

a general rule one would only look for fluorescence from molecules

possessing a, good delocalisation of electrons. Electron donating groups

generally favour fluorescence, whilst electrophyllic groups diminish it. Thus alkyl groups, hydroxyl groups, amino groups are favourable,

whereas the presence of nitro groups, halogens, etc., should be avoided.

Inside the halogen group progressive substitution of fluorine by chlorine,

bromine and iodine in monohalogenated naphthalene progressively
CHEMICAL SPECTROPHOTOMETRY 255

decreases the intensity of fluorescence emission and increases the

phosphorescence yield due to the effect of their nuclear field in pro- moting excited singlet-triplet transitions. The introduction of any heavy

atom into the fluorophore, either as a cation at the chelation centre or

as a substituent in the aromatic ring system, generally diminishes

fluorescence and favours phosphorescence. Nitro groups are particularly effective in this respect so that their presence is particularly

effective in supressing fluorescence (usually completely). Many aro- matic carbonyl compounds undergo ai/tt* rather than the usual 77/77* transitions, i.e., non-bonding electrons rather than 77 electrons are promoted. These bands are usually less intense and the excited state has a longer hfe-time than in a 77/77* transition so that fluorescence is most

frequently not observed. On the other hand, the difference in energy

between the excited state and the associated triplet state is usually

much smaller for such systems so that phosphorescence is frequently common. It now becomes doubly interesting to find that substitution

of a hydroxyl or an amino group in a position vicinal to a carbonyl

group on the aromatic skeleton frequently produces a fluorescent molecule because this combination of groups in such close proximity is of importance in producing metal-chelate compounds of importance to inorganic trace analysis. It is probable that the hydroxyl or amino

hydrogen atoms lock up the non-bonding lone pair electrons on the

carbonyl oxygen through hydrogen bonding thus preventing the n/n*

transition and favouring 77/77* excitation. Carboxylic acids behave

similarly. Thus benzoic acid is non-fluorescent, though benzene is, but salicylic and anthranilic acids are both quite strongly fluorescent. The 71/77* system is also largely responsible for the non-fluorescence of many aromatic compounds containing heterocyclic nitrogen atoms. These heterocyclic compounds can, however, function like the carbonyl

and carboxylic acids mentioned above and like the former they are sus- ceptible to the effect of solvent molecules and so on. For example,

quinoline is non-fluorescent in aqueous solution, but fluoresces strongly

in an acid medium due to locking up of the lone pair electrons upon

protonation. Similarly, many aldehydes and ketones [58] and heterocyclic nitrogen bases [59, 60] which do not fluoresce in non-polar sol- vents do so in hydrogen bonding and strongly polar solvents. This must,

however, be contrasted with the behaviour of some metal chelate compounds which fluoresce more strongly in non-polar solvents [61].

3. Molecular Configuration

The configuration of the molecule is, also very significant. Generally

a fairly rigid structure is necessary and preferably a planar one since

molecular vibrations which might otherwise dissipate energy are minimised and coplanarity ensures good delocalisation of 77 electrons.
256 TRACE CHARACTERIZATION

Fluorescein, for example, differs only from the entirely non-fluorescent

phenolphthalein in possessing an oxygen bridge across the two phenol

rings. The absence of the bridge enables free rotation of the phenol

rings about their bonds with the central carbon atom in the latter molecule and ready dissipation of energy, whereas no such dissipation is possible in the rigid planar fluorescein molecule. The presence of

flexible side chains which are free to rotate and dissipate energy should

be avoided in fluorimetric reagents wherever possible, although there

are instances when this can be turned to good advantage. For example,

the presence of an aminomethyl-dicarboxymethyl group in a position

adjacent to the hydroxyl group in the reagent Calcein Blue, cf. Figure 16,

is of interest [62, 63]. When this side chain is not completely ionised,

e.g., ca. pH 7-10, it is fluorescent and has its fluorescence quenched by

many ions, e.g., mercury, copper, etc. In strongly alkahne solution,

however, it is non-fluorescent, presumably due to the removal of the

hydrogen bonding between the amino nitrogen and the phenoHc oxygen

and free rotation of the dicarboxyamino group. At pH 12, however, the

alkaline earths produce fluorescence once more when they react with

the reagent since they will now function as a bridge in place of the former

hydrogen bond which allowed fluorescence at the lower pH values. This

reaction is very selective for the alkaline earths because other metals

are incapable of reacting at such a high pH.

4. Steric Effects Molecules which possess any appreciable degree of steric hindrance

are usually not efficient fluorescers since the close proximity of groups

favours dissipation of absorbed energy which might otherwise be shed

by fluorescence and this effect has been well studied in the case of the

cyanine dyes [60]. It has also been noted that in some compounds which

exist as cis-trans isomers that the trans form is more intensely fluorescent

than the cis. This has been attributed, for example, to steric interaction

of hydrogen atoms in cis stilbene which is non-fluorescent, whereas

trans stilbene fluoresces strongly [64]. A similar, but less marked

observation, has been made in the instance of 2-vinylanthracene which

exhibits fluorescence in both forms, but with a marked difference between the two sets of spectra [65]. This cis-trans effect may have very

considerable implications for trace analysis because a considerable

number of compounds which are of value as fluorimetric reagents are

CH2COOH

Figure 16. Calcein Blue.
CHEMICAL SPECTROPHOTOMETRY 257

based on stilbene and Schiffs base condensation products. Indeed, it might be said that the latter bear the same useful relationship to fluorimetry as hydroxyazo dyes do to absorptiometry where they constitute a good starting off point for those in search of a new general purpose

reagent. Not a few azo dyes exhibit useful fluorimetric activity also, but

the electron excitation levels lie rather closely spaced in azo dyes so

that the longest wavelength absorption band falls well into the visible range with the result that the fluorescence emission band is pushed over

to yet longer wavelengths where detectors are not particularly satis- factory with respect to sensitivity. O,0'-dihydroxyazobenzene has been

used with success for the fluorimetric determination of magnesium [66] and in terms of the aromatic structure about the azo bond, Pontachrome

Blue Black R which is used as an aluminium reagent is probably the

most complex molecule to have been used in this connection (it exhibits

red emission).

Analytically speaking it is significant to note that some of the most

successful types of fluorimetric reagent are based on aromatic ring sys- tems which are bridged by simple conjugated bond systems or systems

which have partial double bond characteristics (by keto-enol tautomerisation for example), cf. Figure 17. For the purposes of trace metal analysis

it is, of course, necessary that there should be a suitable disposition of donor atoms attached to the bridge or the ortho position in the aromatic

skeleton. Generally, in these reagent types the introduction of a metal

ion of suitable electronic character, qv, most probably induces fluores- cence in the appropriate ionisation form of the ligand by the localisation of the non-bonding lone pair electrons on the donor atoms, thus preH. Principal Types of Fluorogenic Reagent

(bl

(C) (d) Figure 17. Types of metallofluorescence reagent, (a) Salicylidene-o-aminophenol (Schiffs Base Link), (b) 0,0' Dihydroxyazobenzene (Azo Link), (c) Benzoin (Ethine Link),

(d) Dibenzoylmethane (J3 Diketone Link).
258 TRACE CHARACTERIZATION

venting the energetically favoured n/jr* transition process and permitting the necessary fluorogenic tt/tt* transition.

It will be seen, therefore, from the foregoing discussion that although

the approach to the development of a fluorimetric reagent is still largely an empirical process there are well recognized pathways to the production of fluorometric ligands and a wealth of necessary associated empirical knowledge from the older technique of absorption spectrophotometry on the selective functionality of co-ordinative groupings towards reaction

with certain ions.

I. Fluorescence Energy Transfer Systems

Before leaving the area concerning the structure of fluorimetric

reagents it is important to note that whereas all the examples already

discussed have had the ligand acting as the fluorophore with the cation

serving merely as a necessary partner in the process, there are some

instances where the metal ion has a direct role to play in the primary

absorption/emission process. In these, the chelate absorbs energy

characteristic of the ligand species, but re-emits energy which is characteristic of the metal. This situation arises where the metal possesses an excited f (or d) level lying just below the first triplet excited state of the liganding species. Thus tt/tt* excitation and f*/f emission is found

in the chelates of many of the rare earths, e.g., those with benzoylacetone

and dibenzoylmethane [67] and even d*/d emission following tt/tt* excitation in some of the 'non-fluorescent' transition metals which possess

partly filled d orbitals [68]. These systems are obviously of unique

analytical importance, particularly in view of the narrow atomic line- spectra which are emitted in place of the usual molecular band emissions.

The reverse process in which the metal undergoes a f/f* excitation and

the chelate emits a TT*/Tr fluorescence is also not unknown [69], and

probably presents an occasion when it is better, analytically, to use the

excitation rather than the (more usual) emission spectrum for analytical

measurement.

J. Fluorometric Reagents in Practice

An excellent coverage of spectrofluorimetric procedures and other matters pertaining to fluorimetric analysis has been given for many years

in the biennial reviews of C. E. White [70] and more recently in conjunction with A. Weissler [71]. Since these are comprehensive and readily

available only a tabular unreferenced summary of selected methods is given here, c/. Table 2. In connection with this table, it must regretfully

be pointed out that the values quoted for sensitivity must not be strictly

interpreted because they depend on the sensitivity of the detector/

amplifier system, the intensity of the source, the geometry of the excita- tion/emission system, etc. These factors have recently been discussed

briefly by the author [72] and will not, therefore, be reported here. In
CHEMICAL SPECTROPHOTOMETRY 259

many cases improvement of the sensitivity should be possible with use

of recent equipment. Naturally, the information on interferences varies

from paper to paper and this column must also be interpreted accordingly.

K. Assessment of Molecular Fluorescence Spectrophotometry

AS AN Analytical Technique

Molecular fluorescence spectrophotometry possesses two unique

advantages as a trace technique for inorganic analysis. Firstly, it is very highly sensitive and may be apphed to the analysis of solutions

100 to 10,000 times more dilute than corresponding absorptiometric

techniques. The reasons for this have been discussed already in con- nection with the derivation of the fluorescence equation. The same

equation also revealed in its derivation that because of non-linearity

fluorimetry must remain essentially a trace or ultratrace technique. An

even more cogent reason is, of course, depicted in Figure 13A, although

the same figure clearly reveals that a frontal examination of the evolved

fluorescence could be used for 'strong' solutions with some measure of success. Secondly, molecular fluorescence spectrophotometry pos- sesses an even more desirable property as a trace technique — selectivity of determination. It has already been mentioned that only certain ions

are capable of producing fluorescence. Even with an unselective reagent

such as 8-hydroxyquinoline only a few ions produce fluorescence, whereas over 30 produce absorption spectra. Even amongst those metals

which are themselves fluorescent, however, interelement selectivity is possible because measurement may be made on the excitation or the

fluorescence emission spectrum and, of course, it is possible to control

the incidence of fluorescence by selecting the wavelength of excitation

so that one metal fluoresces only weakly or not at all, while the other

fluoresces strongly. CoUat and Rogers [73] have shown, for example,

that both gallium and aluminium 8-hydroxyquinoline complexes may be

extracted into chloroform and yield virtually coincident emission spectra.

However, there is a difference of nearly three-fold in the relative ease of

excitation of the spectra so that they were able to carry out a sequential

determination of the two metals by excitation at 366 m/jL and then at 436 m/Lt using a mercury lamp source. In common with absorptiometry,

spectrofluorimetric methods may be used in conjunction with pH control

to achieve selectivity of reaction and, of course, with masking agents

and simple batch extraction. In this respect, because of its own

'built in' selectivity of reaction, molecular fluorescence spectrophotometry is a good deal more selective than molecular absorption spectrophotometry. For example, Dagnall, Smith, and West [74] have recently

shown in this way that aluminium may be determined fluorimetrically

in aqueous solution with salicylidene-o-aminophenol as reagent in the

presence of 46 cations with interference only from chromium (III),

237-323 0-67— 17
260 TRACE CHARACTERIZATION

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CHEMICAL SPECTROPHOTOMETRY-

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CHEMICAL SPECTROPHOTOMETRY 265

scandium and thorium. As little as 27 ng (or 2.7X10~^ ppm) were

determined by the method.

It is sometimes held against molecular fluorescence spectrophotometry as an analytical technique that it is applicable only to dilute solutions. This may well be a limitation for some analyses, but certainly not for trace work. It is also sometimes said that fluorimetric reagents

are pH sensitive, but in this respect they do not differ from absorptiometric reagents. Another objection which is sometimes raised is that fluorescence is subject to quenching effects, and oxygen is mentioned as the chief source of difficulty. This may well be true for certain organic

compounds, particularly those of bio-chemical interest, but it is the

author's experience with metal chelate compounds that quenching is rarely met from oxygen or any other common substance likely to be

present. Temperature coefficients constitute yet another factor which

is raised as a detraction. But, absorptiometric methods are also subject

to temperature coefficients and in any instance the normal convention

of running two standards with every series of unknowns will overcome

any difficulty likely to arise if it is not convenient to thermostat the

ceU compartment. Photodecomposition of the sample under irradiation

is negligible under the conditions of analytical measurement because of the small dose rate involved.

Perhaps the most telling criticism that may be made of the technique

at present is that as far as inorganic trace analysis is concerned there is, in comparison to absorptiometry, a dearth of reagents. This, in itself,

is perhaps inherent in the chemical selectivity of reaction of such

reagents, but it also arises from the fact that it is only recently that serious attention has been paid to the technique and the availability of reagents should increase rapidly. Most metals can, of course, be

determined by fluorescence extinction but direct (positive emission)

methods are now being found for even the transition metals via the

fluorescence energy exhange reactions mentioned above and by indirect

(positive emission) methods such as that described recently by Bailey,

Dagnall, and West [75] for copper (II) in which the ternary ion-association

complex between copper (II), 1,10-phenanthroline and Rose Bengal is caused to dissociate and fluoresce by addition of ammoniacal acetone

to its extract. These authors found no interference from 56 cations or any common anion and even with the IP 28 photomultiplier, which is not very responsive at the wavelength of emission (570 m/x), they were able

to work at levels down to 1 x 10~^ ppm.

The cost of equipment required for analytical measurements based on

molecular fluorescence spectrophotometry is comparable to that for absorption spectrophotometry, though that required for double monochromating instruments is somewhat (though not greatly) more expensive.

Quartz optics and cuvettes must generally be used at least on the excitation side of the apparatus and quartz cuvettes are almost invariably
266 TRACE CHARACTERIZATION

necessary. Maintenance and running costs constitute no great problem

and are indeed much less expensive than those for most other trace methods, e.g.. X-ray fluorescence, spectrography, mass-spectrometry,

etc. Manipulatively, the technique generally presents fewer problems

than many others with the proviso that the cleanliness of handhng

requisite to all trace methods is observed here also. L. Prospects for the Future

There is little doubt that molecular fluorescence spectrophotometry

has a considerable future and will undergo considerable development as an inorganic trace technique over the next few years. There can be few

laboratories that will be able to neglect such an elegantly selective,

sensitive and inexpensive technique. Like absorptiometry it is easily

automated and consequently should play a big part in this rapidly ex- panding area because of its selectivity and sensitivity. Much of the

modern equipment which has now become available commercially is extremely satisfactory and the real surge forward will probably arise from

a systematic development of a range of reagents such as that which is now available for absorption spectrophotometry. Solid state fluores- cence will probably develop fairly extensively, particularly in conjunction with the development of thin-layer chromatography, but a technique

of pulsed short duration high intensit> irradiation from sources other

than Xenon arcs and mercury lamps may well prove to become signifi- cant. The polarisation eff"ects which are associated with fluorescence

have not been mentioned in this survey, but they are undoubtedly

significant. At the lowest level of information the polarisation spectrum

of the fluorescing solution provides additional information cf diagnostic

value, but much more useful analytical work may be centred around the

phenomenon in future developments.

Lastly, phosphorescence has been mentioned only in passing. It is, of course, slightly more complex to practise spectrophosphorimetry

because of the need to operate at low temperatures and to 'chop' the

incident and emission beams out of phase, but it is inherently a more

selective technique than spectrofluorimetry and may be applicable to a wider range of analyses though present indications are that its sensitivity

may be considerably lower. The flexibility of being able to observe one

phosphorescent species in the presence of others by variation of irradia- tion/observation times appears to be an attractive proposition which may

well outweigh the factor of the lower sensitivity. There is as yet,

however, a shortage of suitable equipment available from manufacturers

for the analytical exploration of spectrophosphorimetry.

IV. Atomic Absorption Spectrophotometry

Atoms are capable of absorbing fight in exactly the same way as molecules by interacting with a photon of the energy requisite to promote
CHEMICAL SPECTROPHOTOMETRY 267

an electronic transition from the ground state to one of the excited states of the atom. Consequently, a technique of atomic-absorption spectrophotometry closely similar to molecular absorption spectrophotometry

should be possible, but for a long time many problems stood in the way

until in 1955 A. Walsh of the Austrahan C.S.I.R.O. [76] successfully overcame them and evolved the analytical technique of atomic-absorption

spectrophotometry which has proved to be so successful for inorganic

trace analysis. The physical laws which govern the relationship be- tween the amount of light absorbed and the 'concentration' of the

absorbing atoms closely resemble those of molecular absorption spec- trophotometry and the principle of analytical measurement and the

experimental arrangement of the apparatus are also closely similar in the two techniques, though there are, of course, several points of dif- ference. Much of the discussion given for molecular absorption is applicable to atomic-absorption of radiation and consequently the author

is chiefly concerned with the differences between the two in the following

paragraphs.

A. Presentation of Atoms for Analysis

Analytical molecular absorption spectrophotometry is always pre- sented in dilute solution where the absorbing species are dispersed

uniformly and do not undergo comphcating interactions with each other. Free molecules are, of course, easily obtained by dispersing the absorbing solute in a suitable solvent medium, but free atoms cannot be pre- sented for analysis in this way and it is here that the first essential

difference between the experimental arrangements for the two tech- niques becomes apparent, cf. Figure 18. Free atoms can only be ob- tained in a gas phase and consequently gasification of the sample is one of the first requisites of atomic-absorption spectroscopy.

1. The Atom Furnace Reservoir

Most inorganic compounds can be gasified by the apphcation of

sufficient heat to pass the sohd material through a hquid phase into the

HOLLOW CATHODE LAMP

STAB POWER SUPPLY (MODULATED)

UV/VIS MONOCHROMATOR

NEBULISER

ISPLAY

TUNED

AMPLIFIER PHOTO

MULTIPLIER

Figure 18. Apparatus for atomic absorption spectrophotometry.
268 TRACE CHARACTERIZATION

gas phase or directly so by sublimation. At first sight, therefore, it would appear to be simplest to place the sample in a box having two

optically transparent sides and to heat it to sufficient temperature,

probably under vacuum or at least in the absence of a reactive gas such

as oxygen which forms molecular (oxide) species with most metals which

are only dissociated to free atoms at very high temperatures. The

nearest approach to this type of atom reservoir has been described by

Vidale [77] who was able to analyse 10"'* /Jig amounts with this type of

reservoir. Essentially the solid specimen was placed in a quartz tube

which was heated in another evacuated tube inside a split furnace at ca. 1400 °K. This idea of the atom furnace reservoir has also been used,

in a more sophisticated form than that described above, by L'vov [78] with a fair degree of success down to 10~^ fig but it is difficult manipulatively, particularly for routine analyses and consequently it does not appear to have been used to any great extent. It would appear reasonable, however, to prepare the sample for analysis by chemically converting the trace ion into a volatile species before submitting it to such

an atomisation process. There are known to be very many volatile metal chelate compounds {e.g., many with acetylacetone and other fiP diketones) which could conveniently be passed into such a 'box' either

as discrete samples or continuously in a flowing gas stream with a

suitable carrier gas. The knowledge gained from recent activity in studying the gas phase chromatography of metal chelate compounds

[79] should be most helpful in such a development.

2. Flame Reservoirs

However, the technique which was favoured by Walsh and which is used almost exclusively in present day practise is to generate free atoms

from molecular species within the plasma of a flame rather than to use

the latter as an external source of heat to produce dissociation in some

other milieu. In making this choice Walsh was no doubt influenced by

the information and experience gained in the well established technique

of flame photometry (thermal emission spectrophotometry) and the

choice is both logical and extremely convenient for many elements.

a. Processes in Flames. By various means which wiU be discussed

subsequently, a dilute solution of the test ion, either as a salt or other

compound, in a suitable solvent, is introduced to the reacting gases

of the flame^ in the form of a fine mist. The small droplets evaporate

very quickly in the flame to leave behind even smaller solid particles

(clotlets [80]) composed of the solutes. Depending on their nature,

the solid particles sublime directly into the gas phase or fuse and subsequently evaporate into the gas phase as free atoms. The chain of events for a salt MX then becomes
CHEMICAL SPECTROPHOTOMETRY 269

Nebulisation Evaporation

'Soln 'Mist [MX] Solid (MX)

Fusion

Liquid Evaporation

{MX} Gas

Dissociation {M° + X°} Gas Outside Flame Within Flame

Once the free atoms have been produced they may be considered as

a 'solution' in the flame gases and they are free to absorb radiation in a manner similar to molecules in dilute solution, provided that the supporting medium is transparent (or nearly so) to the radiation.

Perhaps the most important difference between the two solutions

which are presented for atomic absorption and for molecular absorption

measurements is that the latter is a static system where the concentration of the absorbing species can readily be computed for a known solution. The flame, however, is a dynamic system with the gases flowing

at very high speeds, ca. 10^ cm/sec, for a bunsen flame to 10^ cm/sec

for an oxy-acetylene flame. During the few milli- or micro-seconds

while the sample is within the flame it follows, therefore, that all the processes, shown on the right hand side of the dotted line above, must

take place. Many equilibria are involved, but the first stage, where the

boiling point of the solvent is normally < 400 °K, will almost certainly be

quantitative with most flames because of their much higher temperatures, ca. 1200-4000 °K. Consequently, it is a safe assumption that all the material is introduced into the flame as solid particles when a very

fine solution-mist is used. Fusion, however, depends on the flame temperature as do all subsequent steps to a much more marked degree and,

of course, the physical properties of the clotlets will also have a marked

influence. From this point onwards it follows that the efficiency of atomisation will vary from flame to flame and from one clotlet matrix

to another and it is not at all possible to assume that all of the test ele- ment introduced to the flame has been atomised. The situation is, of course, even more complicated by the presence in the flame of highly

reactive free radicals such as those of oxygen, hydrogen, carbon, hydroxy!, cyanogen, carbonyl, etc., which may undergo compound formation with the nascent atoms with very great ease and these adducts wiU

not possess atomic absorption bands. Free atoms also have a finite life-time and even in the absence of any disturbing free radicals they

wiU readily reunite or react with other products in the upper cooler
270 TRACE CHARACTERIZATION

reaches of the flame. Yet again, it must be reahzed that not all of the

molecular species containing the test ion will pass through the reactive

hot regions, for a definite fraction of them must necessarily pass through

the cooler (sheath) outer regions where atomisation may scarcely be

accomphshed in many instances. The latter consideration is probably

most important where premixed flame gases are used.

Despite these complications, however, it is found with a great number

of elements that atomic absorption bands can be observed with a fair degree of intensity in a great number of flames just above the primary

reaction zone of the flame gases so that it is apparent that all the reactions proceed with a good measure of efficiency. It will also be apparent

from the foregoing discussion that the position in the flame where meas- urements are made will vary quite considerably from elements which

are easily atomised to those which are not and from those which react

easily with constituents of the flame to those which do not. Some flames,

e.g., simple H2/O2, CO/O2 flames show a fairly continuous build-up of temperature up to the tip of the flame due to (slow) three body colhsion

propagation processes, whereas hydrocarbon/oxygen flames exhibit

their highest temperatures just above the primary zone since they are propagated by (fast) two body colhsions. This can also aff"ect the region

of the flame best suited to absorption measurements. Free radicals are also much more common in the upper reaches of non-hydrocarbon

flames than they are in hydrocarbon ones. b. Nebulisation of Solutions. The nebulisation process whereby

the solution enters into the flame must also be considered, i.e., the

equilibrium on the left hand side of the dotted line in the equation. This

process is, unfortunately, very frequently referred to as atomisation as a

result of loose terminology borrowed from other areas, whereas it is the

process whereby atoms are produced in the flame or the complete

process from the bulk test solution through to the atomic species that should be so called. There are two main types of nebuliser in common

use. In one of these the solution is drawn bodily up into the inner

regions of the flame and the entire solution is nebulised there. This

wiU be referred to as total consumption nebulisation. In the second

type the solution is nebulised in one of the reacting gases, usually the

oxidant and only the small droplets are carried through into the flame

while the larger droplets are spun off" by cyclone action as, for example,

in the Unicam nebuliser, or are aUowed to faU to the bottom of an expansion chamber, as for example in the Hilger nebuliser. In the highly

successful Evans Electro Selenium (EEL) nebuliser the solution loaded

gas stream is allowed to impinge on a rotating vane which further aids

the process. This type of nebulisation will be referred to as aspiration

nebulisation. It is easily possible to gauge the efficiency of nebulisation

for the latter type of device and for aqueous solutions it is usuaUy of the

order of 10-20%.
CHEMICAL SPECTROPHOTOMETRY 271

Consequently, it will be seen that the complete process of nebulisation

and atomisation in flames appears to be a rather inefficient and haphazard process. In practice, however, it is found to be very reproducible

and the chief detraction is that many elements, e.g., aluminium, niobium,

molybdenum, etc., form refractory oxides in the flame which do not

readily break down whilst others cannot be measured easily {e.g., the

non-metals such as S, etc.) because the flame plasma also absorbs in the same region of the spectrum. However, the flexibility of choice of flame which is available is an attractive feature of flame-based methods.

3. Other Atom Reservoirs

Many other devices have been utilized for presenting or maintaining

a dispersion (population) of atoms for analytical measurement and some

of these, e.g., the previously mentioned L'vov atom furnace are much

more efficient in their atomisation than flames, but it is doubtful at present if any yet devised offers a serious challenge to the present

supremacy of the flame reservoir despite their individual merits.

a. Hollow Cathode Sputtering. The chief challenge most

probably arises from the hoUow cathode sputtering device of Gatehouse

and Walsh [81]. The work was concerned with metallic specimens.

A suitably prepared sample of the metal or alloy was made into an openended cylindrical hollow cathode and a discharge of ca. 500 V was struck

across from it with an anode in a vessel purged with argon and evacuated

to ca. 1 mm pressure. A cloud of atomic vapour arose in the cathode

cavity and absorption measurements were made by directing the Hght

beam through the cloud of vapour in the cavity. The technique is eminently suitable for the analysis of alloys of constant matrix composition

with regard to major constituents, but is otherwise difficult to use on a quantitative basis. It must also be remembered that only the surface

layer of the cathode is sampled in the process and consequently errors may arise from alloy segregation, surface contamination, boundary

effects, etc. However, this could be turned to good effect for the study

of these specific problems, though it is doubtful if it could offer a serious

challenge to electron-probe microanalysis. There is good reason to suppose that the technique has not yet found its major potential and

future developments may well favour a much more extensive application.

Solutions should be capable of being handled by deposition of solute from a layer of solvent evaporated on a suitable demountable hollow

cathode of a compatible material [82] and there is every reason to expect

that this technique has very much to offer, particularly for the analysis

of discrete minute samples as in forensic work, etc. b. Electric Discharge and Plasma Jets. Electric discharges

between two metal or graphite electrodes has long been used in ac and

dc spectrography and Robinson has made attempts [83] to adapt this to atomic-absorption spectrophotometry, but with no great degree of
272 TRACE CHARACTERIZATION

success. The energy available between the electrodes is such that considerable ionisation may take place so that ionic as well as atomic

emission are obtained with consequent depletion of the ground state population. The stability of such a source is generally inferior to that of a flame and the 'windows' in the discharge may be inadequate.

Recent use of the plasma jet in emission work [84] suggest possible

applications of these as flame reservoirs for difficult elements such as aluminium, molybdenum, niobium, titanium, zirconium, etc. They may,

of course, be open to the same detractions as the dc and ac sources, but

they appear to have greater potentialities.

Other devices used as atom reservoirs include flash-heating tubes [85] and shock tubes [86].

B. Atomic Spectra and the Hollow Cathode Lamp

Atomic spectra differ chiefly from those obtained for dissolved molecules in having very narrow profiles so that the hnes are only ca. 0.02 A

wide. This at once introduces another difference between the two

analytical techniques. The band passed by a monochromating device

from a continuous source such as a tungsten or deuterium lamp, cf. Figure 19A, may be monochromatic with respect to the absorption band

of a dissolved molecule, but when it is superimposed upon the absorption

hne due to an atom in a flame, cf. Figure 19B, it will be seen that it is not possible to obtain any measure of the decrease in signal because of

the 'width' of the signal of the incident light. Walsh [76] calculated

that it would not be possible to use light from a monochromated continu- ous light source since a monochromator with a resolution of 500,000

would be necessary in order to be able to make measurement at the centre of the absorption line. For this reason he resorted to the use

of hollow cathode lamps. The principal Hnes emitted from the cathode

'glow' in these lamps are due to emission from the atomic vapour which

is excited in the cavity of the cathode by the electric discharge struck

across to the anode. Consequently, the hnes emitted by the lamp

correspond to those which will be absorbed by an unexcited population

X

f X > X X

Figure 19. Spectral profiles, (a) Monochromator transmission band, (b) Absorption line,

(c) Hollow cathode emission line.
CHEMICAL SPECTROPHOTOMETRY 273

of atoms of the cathode metal when those are present in a flame. Be- cause of the relatively small incidence of broadening effects (Doppler,

Stark, Pressure) in the cathode cavity it is found that the hues emitted

by such a lamp are much narrower than those absorbed in the flame.

Consequently, when a beam of such radiation is shone through a flamedispersion of ground-state atoms of the same metal, absorption takes

place at the centre of the atomic absorption hne in the flame, cf. Figure 19C. Consequently, the continuous source and monochromator

which is used in molecular absorption spectrophotometry is replaced

by a hollow cathode lamp for the element being determined.

1. Necessity for Monochromator

The lamp, however, emits numerous atomic Hues for each element

and, of course, a continuum from the inert carrier gas which is necessary

to provide sputtering in the cathode cavity. If all this light fell upon the

detector the decrease in signal due to the selected transition hne would

be swamped out by the signal from unabsorbed hues and those which

are only poorly absorbed. Consequently, it is necessary to place a monochromator in the system to disperse the unwanted hues so that these latter do not fall on the detector. For most purposes a monochromator similar to that used in a conventional u. v. /visible spectrophotometer is sufficient, though there may be occasions, e.g., in dealing

with line rich spectra such as that of iron, when a monochromator with

a greater than normal resolving power may be advantageous. When the

continuum from the carrier gas of the hollow cathode lamp shows strong

emission over the same spectral region as the absorption line this device will not, of course, be successful, but the problem rarely arises

when commercial hollow cathode lamps are used. Generally the situa- tion obtaining in molecular absorption spectrophotometry where the

monochromator is situated between the source and the absorbing cuvette

is reversed because it is experimentally more convenient for reasons which need not be discussed here.

2. Multi-element Lamps

The fact that a hollow cathode lamp is required for each element is sometimes seen as a disadvantage of atomic-absorption spectrophotometry, but in fact these lamps with their narrow band emissions provide

virtually complete specificity for each element and in comparison to molecular absorption spectrophotometry the manipulative and chemical

prehandling is much less. However, a considerable amount of activity

has recently gone into the development of multielement hollow cathode

lamps [87, 88] in which the cathode is made up of sections or rings of the different metals or alternatively from an alloy containing the elements

blended in the proportions best suited to obtaining emission bands of approximately equal intensity from each. These lamps, unfortunately.
274 TRACE CHARACTERIZATION

leave much to be desired because the intensity obtained from individual

lines is usually weakened and it is said that the more volatile metals

sputter in preference to others so that a film of this metal gradually

deposits on the entire cathode surface, thus strengthening the emission

for that element and diminishing those of others.

3. Monochromated Continuum Sources

Recently, Walsh's supposition that monochromated sources could not be used because of poor resolution, and because insufficient energy

would be available in such a narrow band from a continuum, has been

challenged by Gibson, Grossman and Cooke [89] who used a monochromator with a 30,000 line/inch grating and a focal length of 50 cm to obtain a band-pass of 0.16 A from a tungsten lamp. Whilst this is approximately ten times the absorption Hne width in the flame, they were able to obtain approximately half-strength absorption signals for sodium (in comparison to those obtained with a sodium discharge lamp

as the source) and the detection hmit was equally good. This significant

contribution was unfortunately only published in abstract form, but

subsequently Fassel, Mossotti, Grossman and Kniseley took up the work

[90] and, accepting the previous suggestion of scale expansion, they were able to obtain very excellent sensitivities for atomic absorption

signals for thirty two elements which were either comparable to, or in some instances (barium, indium, lithium, vanadium, and the rare earths)

better than those obtained using hollow cathode sources. Objectors

to the hollow cathode lamp may well see this as one of the most significant

developments yet to have taken place in this area, and it is undoubtedly

a very fine contribution indeed. Ivanov and Kozireva [91] appear to have

made a similar, though somewhat less extensive examination in the

USSR.

4. Spectral Discharge Lamps

Spectral discharge lamps have long been used as sources of monochromatic radiation for several purposes and those for the alkali metals,

alkaline earths, and more volatile elements such as thallium, cadmium

and zinc are useful alternatives to the hollow cathode lamp, particularly

when they are run at currents lower than those recommended by the

manufacturers. This has the effect of reducing the temperature in the

discharge chamber of the lamp and thus reducing the self-reversal which

is rather a prominent feature of this emission [92] and also, of course, pressure and Doppler broadening, etc., though these are less serious.

Generally speaking it is found that the stability of these lamps is not as good as that of hollow cathode lamps and it is frequently advisable to use an attenuating device with them to prevent radiative damage to the light

sensitive cathode of the detector since their radiation intensity is very

much greater than that of a hollow cathode lamp or a monochromated

continuous source.
CHEMICAL SPECTROPHOTOMETRY 275

5. Microwave-powered Sources, etc. In their excellent monograph 'Atomic Absorption Spectrophotometry'

Elwell and Gidley [93] comment on the possible use of Geissler tubes

and of high frequency electrodeless discharge tubes, but these appear

to have found Httle application as yet. We have found [94] that much

better results may be obtained with an attenuated signal obtained from

a microwave powered iron-containing tube operated at 2450 Mcps and

ca. 10 watts than with a conventional iron hollow cathode lamp. We

presume that this is due to the considerably higher energy fed into the resonance line and the higher resolution that may be obtained by nar- rowing the slits of the monochromator. We have also found a similar

improvement for other elements, e.g., Ag and particularly for those which

have resonance lines bordering on the vacuum u.v. region, e.g., Se [95]. Walsh [96] considered the use of an emitting flame saturated with the

necessary atomic species to be unsuitable because of self-reversal and

line broadening, but the continuous source work discussed above [90] may lead to a re-assessment. It is probable, however, that the stability of a flame source would be inadequate without double beam operation.

Strasheim and Butler [97] have recently investigated the use of the timeresolved spark source and have shown that it has merits worthy of further consideration.

C. Types of Burner

Two types of flame have been used chiefly in the study of atomic

absorption phenomena. The first of these is the (pre-mixed gases)

laminar-flow flame obtained from a slotted burner used in conjunction

with an external aspirator-nebuliser and the second is the turbulent-flow

flame from a (unmixed gases) total consumption burner. Both types of burner are well described in the literature of flame photometry and they

will not be discussed here. The long thin laminar flame is best suited

to analytical absorption measurements because it presents the maximum

number of absorbing atoms to the light beam from the source. It is, however, advisable to ensure that no light from the source by-passes the

flame and enters the monochromator. It must also be considered, however, that if the flame is too long and thin, excessive cooling of its outer

regions may occur and consequently it is sometimes found that there is an optimal length of between 5 and 10 cm for many hot flames. The

shape of the flame is also relevant because the number of absorbing

atoms is inversely proportional to the cross section of the flame. Consequently for a given length of flame the highest concentration of absorbing atoms will be obtained by the narrowest flame which is not adversely

aff"ected by cooling.

The small droplets introduced to the flame from the aspirator nebuliser

are also more uniform and are free from large droplets which may cause

a loss of signal by reflection, scatter and even diffraction. In contrast,

237-323 0-67-18

I
276 TRACE CHARACTERIZATION

the (integral nebuliser) total consumption burner presents only a short

pathway for the absorption of light and concentrates all the self-emissive

features of the flame in front of the monochromator slit. The droplets

which are introduced have a wide range of sizes and many of them are too big to be useful. In addition, much insidious incrustation of the burner

tip may occur with solutions of moderate electrolyte concentration and

cause non-reproducible results with no visible sign of deficiencies in nebulisation. A side issue is that total consumption burners are rather

noisy in use in comparison to laminar-flow burners.

1. Long Flames

The absorption of the atoms in the flame is within limits directly

proportional to the length of the absorption path for a uniform population.

The path-length of a total consumption burner is of the order of 1 cm or

less, unless a multiple passage of the light beam is made through the same part of the flame, whereas 10-15 cm flames are common for some

laminar-flow flames with no appreciable increase in volume. However,

adaptations of the turbulent total-consumption flame have been described

which cause similar and much greater extension of absorption path and

these may prove useful in future work. Fuwa and Vallee [98] led the

gases from a total consumption burner into a long horizontal tube with

the tip of the burner just outside the rim and below the central axis. The beam of light from the hollow cathode lamp was passed down the

tube from the other end and the absorption measured by a monochromator/detector situated opposite the burner end. A Vycor, Alundum,

or Zirconia tube of diameter 1-2 cm and 20-90 cm long was used and

best results were obtained with tubes 70-90 cm long and 1 cm diameter.

Koirtgochann and Feldman [99] have described a similar device with a

slightly different disposition of apparatus. The results achieved indicate

a very considerable increase in sensitivity with oxy-hydrogen flames, but

difficulties are experienced when organic solvents or acetylene are used.

High background signals are obtained and whilst the reasons for these

are not apparent, it is probable that the unusual absorption signal is due

to molecular species generated or accumulating appreciably in the tube

which would otherwise not be formed in an unconfined flame. It has

also been observed that the oxygen/hydrogen ratio has a very marked

eff'ect on the absorption due to spraying a constant solution of metal

ions and that this appears to coincide with the visible length of the flame

in the tube [100]. It is probable that the highest signals are obtained

over the narrow range of conditions of gas pressures which successfully

produce a long laminar flow flame in the tube. The life-time of free atoms in the cool regions of the flame or outside the body of the flame can only be of limited duration and it is probable that the device is successful chiefly because it produces a long flame rather than an
CHEMICAL SPECTROPHOTOMETRY 277

accumulation of free atoms in the combusted gases within its confines. In their paper Fuwa and Vallee demonstrated increases in sensitivity

with increase in pressure of the absorption cell and they suggest that the efficiency of the Vycor tube relative to the others is due to internal

reflection and multiple traverse of the tube. Earlier work by Robinson

[83] demonstrated a simpler T piece adaptor which was placed over a turbulent flow flame. Measurement of absorption was made across the

ends of the horizontal arm. No constructional details were given, but

presumably the device gave a path-length comparable to those for lami- nar flow flames. The device does not, however, permit absorption meas- urements to be made low down in the flame which may account for some

of the poor sensitivities obtained for certain metals.

An understanding of the mechanism of the flame production and propagation in devices such as those mentioned above may yet provide a signifi- cant advance to the practice of atomic-absorption spectrophotometry.

2. Types of Flame Medium

a. Conventional Flames. Many different flame gases have been

used in flame photometry [101] and most of them have been examined

for atomic absorption measurements also. Much of the early work was

done on the relatively cool air-propane and air-hydrogen flames. These

have the merit of low emissive backgrounds so that simple defocussing

systems could be used to allow the monochromator/detector to respond

only to the light beam from the hollow cathode which is focussed on the entrance slit to the monochromator. Walsh [76], however, used a modulation system to overcome radiative effects in the flame. The

beam from the hoUow cathode lamp was interrupted at regular intervals

by a rotating sector and the amplifier of the detector system was tuned

to the interrupting frequency so that only the pulsed signal was amplified.

This arrangement has now been modified in most instruments by

modulation of the supply to the hollow cathode lamp. The temperature

of such flames is, however, rather low and whilst at first sight it would

appear that the flames used for atomic absorption need not be so hot as those used for flame photometry since excitation is not required, the

latter process is largely accomplished by mechanisms other than the

application of thermal energy to the free atom. Atomisation, i.e., the

production of atoms within the flame, is the least efficient process in atomic absorption {ca. 1.5% only for magnesium in an oxy-acetylene

flame at approximately 2400 °K [102]) and consequently some very high

temperature flames have been used, e.g., oxy-cyanogen {ca. 4600 °K)

[103]. The use of the plasma jet has also been mentioned, for which

temperatures of ca. 15,000 °K have been claimed [104]. However, very

high temperatures wiU produce serious depletion of ground state populations for easily excited elements and these flames invariably produce
278 TRACE CHARACTERIZATION

higher background noise. In any event it is true that one of the decisive

factors governing the population of atoms is their Hmited Ufe times

(10~^-10"^ sec) so that it may well be true that increase of flame temperature beyond a certain level appropriate to good dissociation of the clotlet species may have little further effect. b. The Nitrous Oxide-Acetylene Flame. The use of fuel-rich luminous flames, e.g. oxy-acetylene, is particularly effective in providing

absorption signals from atoms which form refractory oxides, e.g., aluminium, molybdenum, etc. [105]. These flames do, however, place

a rather heavy radiative load on the photomultiplier. Recently, the use

of the nitrous oxide-acetylene flame by Willis [106] and by Amos and

Willis [107] has provided a significant advance. Good signals were

received for many difficult elements, e.g.. Be, Ti, Zr, Hf, V, Nb, Ta, W,

U, Re, and the rare earths and moderately improved signals for Mo, Sn,

and the alkaline earths. We, ourselves, have found the nitrous oxideacetylene flame easy to handle and have obtained good signals for molybdenum, sufficiently sensitive to permit its determination in steels [108]

and in trace amounts in metallic niobium and tantalum [109].

Most elements appear to be best determined in or very near to the

characteristic red-feather zone of the flame which appears close to the

primary reaction zone. There is every reason to suppose that the low

intensity emission from this zone is due to the CN band and it may well

be that this flame amounts or closely approximates to a sheathed oxy- cyanogen flame (which was used originally by Robinson [103]) with the

burning gases sheathing a zone where free cyanogen is being produced

and combusted. This flame appears to offer distinct advantages over

fuel-rich acetylene flames and to constitute a distinct advance in extending the range and sensitivity of atomic-absorption spectrophotometry.

Species which are easily ionised in a 'hot' flame may frequently be

brought back to the absorbing groundstate by addition of the salt of a more easily ionised metal since this {e.g., potassium) will be excited in preference in the flame and diminish the ionising capacity of the flame

without reduction in temperature.

D. Types of Hollow Cathode Lamp

Hollow cathode lamps are available for most elements, some using

cathodes of another suitable metal coated with a volatile salt of the

required element where the element itself is too easily fused. A range

of multi-element lamps is also available in which several elements compose the cathode or in which alloys are used. Lamps containing individual cathodes which can be separately connected to the source of potential

difference, and de-mountable flow-through lamps have all been used

with varying degrees of success.
CHEMICAL SPECTROPHOTOMETRY 279

1. High Intensity Hollow Cathode Lamps

The only significant advance to have been made in lamp technology is the evolution of the high intensity hollow cathode lamp. In these a secondary discharge is struck across the atomic vapour at the mouth of the cathode cavity. Normal lamps must be run at rather low currents

to prevent broadening, self-reversal and even self-absorption by the

larger cloud of cool vapour which is generated aroung the cathode by

higher currents. In the high intensity lamp, Jones and Walsh [110] used

the secondary electrodes coated with alkah metal salts to pass a cloud

of low energy electrons through the 'cool' ground state vapour in front

of the cathode cavity. The energy of the electrons is insufficient to excite ionic spectra, but causes good atomic emission. These lamps

then permit much more energy to be passed into the cloud of atomic

vapour in a flame and thus allow narrower sHts to be used where resolution is a particular problem and permit lower ampHfier gains to be used

so that the background noise of the electronic circuitry does not cause

serious problems. The length of the hnear zones of calibration curves

are usually significantly increased as a matter of course with these lamps.

It should be noted, however, that the radiant energy from these lamps

is lower than that from microwave-powered sources.

E. Analytical Relationships in Atomic-Absorption

Spectrophotometry

The laws which govern the relationship between the amount of light

absorbed by atoms in a flame and their concentration are subject to the same rules as those for molecules in solution and may be expressed as A = Log /„//r = €.-!•/ • c where A denotes absorbance, /o and h the incident and transmitted

signals, e.4 the atomic absorptivity, / the path-length and c the concentration of the atoms in the supporting medium. In point of fact, however, we are never in a position to know the concentration of the atoms

in a flame because of the many variables in the atomisation process,

the dynamic nature of the system, the Hfe-time of free atoms, parasitic

side reactions, etc. Nevertheless, the law may be used empirically by

calibration curve principles. As a result it is possible to work in exactly

the same way as in molecular absorption spectrophotometry.

F. Choice of Wavelength

Most of the absorption fines used in atomic-absorption spectrophotometry lie in the u.v. region of the spectrum, except for those ele- ments which are easily excited and consequently absorb in the less energetic visible region. The choice of the most sensitive band for
280 TRACE CHARACTERIZATION

analytical measurement in molecular absorption is usually fairly obvious because there are very few bands, but for most atomic species

there is a considerable number from which a choice must be made.

The electron transitions corresponding to most atomic lines are well

recognized, however, and in many instances this knowledge is helpful.

For the majority of elements in virtually all flames the bulk of the atomic

population exists in the ground state so that only those transitions from

the ground state to one of the excited levels need seriously be considered.

In many instances the most sensitive hne used in the technique of flame

photometry proves to be the best also for atomic absorption measurements, but it must be stressed that for most atomic species there is a choice of lines which will yield various sensitivities according to their

oscillator strength. The most sensitive line is not always the same,

however, and may alter according to flame conditions. It is generally now well recognized which lines are most favourable, but where this knowledge is not available it is a simple matter to screen the sensitivities of the stronger lines. Allen [111] devised a photographic method

for complex spectra which indicates the absorbing lines and yields

the most sensitive line by microphotometry, but it is not usually necessary to resort to such a procedure.

G. Assessment of Atomic-Absorption Spectrophotometry as AN Analytical Trace Technique

As an analytical technique, atomic-absorption spectrophotometry

has one unique advantage over the two other trace techniques discussed

above and indeed over most other trace techniques. It may be expressed

in one word — specificity. The method available for each element is virtually specific for it. This arises because of the narrow spectral

profile of atomic absorption lines in flames and the even narrower source emission lines used to measure their mid-point absorption. In terms of inherent specificity there is no comparison to be made in favour of molecular absorption spectrophotometry or even molecular fluoroescence

spectrophotometry. Except in a few instances where unpleasant matrix

components are present it is not necessary to resort to separations and

even then it is sometimes possible to account for the matrix at very high

levels by adding approximately the same amount of matrix component

to the standard solutions. Matrices which cause difficulty in this way

are largely those which form refractory compounds in the flame, e.g., aluminium, niobium, zirconium, etc., and which lock-up the sought

element in clotlets which do not fuse and break down sufficiently in the

ffame. In some instances difficultly fusible or involatile compounds

may be formed in the absence of a matrix of the above nature. Calcium

in the presence of phosphate shows this behaviour [112]. The addition of a hganding species EDTA may be helpful here, because it sequesters the calcium away from the phosphate ion so that even
CHEMICAL SPECTROPHOTOMETRY 281

though the phosphate is present in the clotlet it is either volatihsed away

before the complex dissociates or additionally has insufficient time to bond with it before the exothermal decomposition of the chelate releases

the calcium. Sodium chloride and sucrose [113] exhibit effects similar

to EDTA and this has led Baker and Garton to cast doubts upon the

vahdity of chelation action. However, it must be recognized that any- thing which dissolves or fuses or explodes a refractory clotlet will have

a beneficial effect in increasing the vapour pressure of the sought

element.

There are very few interelement effects shown in atomic-absorption

spectrophotometry which is in marked contrast to the behaviour of

flame photometry. It is also noticeable that whereas the sensitivity of

flame photometry is critically dependent on the temperature of the flame

this is not so in atomic absorption. Yet again, with few exceptions a

fairly uniform high sensitivity is apparent for most elements by atomic

absorption, whereas sensitivities vary greatly in the older technique.

The reasons for these three important differences can be seen at a glance

from Walsh's equation [76] relating the number of atoms, A^o, in the

ground state to that Nj in an excited state of energy Ej through the

absolute temperature T

NolNj = PolPj'exp^

and P() and Pj the statistical weights for the ground and Ej state respectively. Walsh calculated the ratios shown in Table 3 for the number of

atoms in the excited state to those in the ground state. Even for cesium, 99.99% of the atomic species exist in the ground state at 3000

°K. Temperature has Uttle effect on the number of atoms in the

ground state but causes an exponential variation of the number in the

excited state. Consequently it would appear that variations in flame

temperature wiU scarcely affect atomic absorption, but will greatly

alter the signal for flame photometry. Again, it will be seen that if all Table 3. Calculated ratio of atoms in excited state to atoms in ground

state.

Resonance line T = 2000 °K T = 3000 °K T = 4000 °K T = 5000 °K

Cs 8521 A 4.4 X 10-4 7.2 X 10-3 3 X 10-2 6.8 X 10-2 Na 5890 A 9.8 X 10-6 5.9x10-4 4.4 X 10-3 1.5 X 10-2 Ca 4227 A 1.2x10-7 3.7X10-^ 6.0 X 10-4 3.3 X 10-3

Zn 2139 A 7.3 X 10-1-^ 5.6x10-10 1.5 X 10-7 4.3 X 10-6
282 TRACE CHARACTERIZATION

atomic bands had uniform oscillator strengths a uniform sensitivity

would be obtained for equal population of all atomic species in the flame

by atomic absorption measurements. Variation in the sensitivities for different elements can, therefore, be chiefly associated with their

efficiency of atomisation and to a lesser extent with the oscillator strength

of the absorption band. Since the number of excited atoms in the

flame is very small it is easy to see how numerous inter-element effects may arise in flame photometry, e.g., serious deactivation by collision,

preferential excitation of other species and energy transfer processes

in general. Since the ground-state cannot be de-energised such effects are not applicable to most elements in absorption measurements.

Atomic-absorption spectrophotometry is a trace technique which can

be operated in the 1 ppm region for most metals and some non-metals

(over sixty elements) cf. Figure 20 and it involves very little manipulation

other than dissolution of the sample in an aqueous medium or a suitable

organic solvent and spraying it into the flame. With the facility of scale- expansion it can quite frequently be used in the 10~^ to 10~^ ppm range. Rotation of a longe flame burner-head in a horizontal plane about its vertical axis to expose a shorter absorbing path can contract the sensitivity of the method to allow it to be used for stronger solutions [114] or a technique of differential atomic-absorption spectrophotometry may

be appHed. A third alternative is to select a less sensitive waveband

for absorption measurements. The technique is, therefore, ffexible in most respects. The natural sensitivity of the method can also be vastly

increased by the extraction of traces into water-immiscible organic

solvents. Thus, for example. Belcher, Dagnall and West [115] used a solvent system to concentrate silver from aqueous solution and spray

it into an air propane ffame in an unmodulated instrument capable of responding only to a lower limit of 1 ppm of silver and were able to work

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Figure 20. Elements determined by atomic absorption spectrophotometry.
CHEMICAL SPECTROPHOTOMETRY 283

down to 1 X 10~- ppm even without recourse to the hotter flames of most

modern instruments or the availabihty of scale-expansion, both of which

would probably have yielded analyses down to 10~^ to 10~^ ppm.

Organic solvents cause difficulty in flame photometry because they

appreciably alter the flame temperatures, but this effect of solvents

is insufficient to cause any perturbation of absorbance signals. In most

instances an increase of atomiser efficiency up to 60% is easily possible

with organic solvents, though there are occasions when some solvents

may not be used. For example, Kirkbright, Peters, and West [109]

found it impossible to use chloroform as a solvent for molybdenum in nitrous oxide-acetylene flames though butanol was entirely satisfactory.

Because of the minimization of handhng, atomic-absorption spectrophotometry is a rather rapid procedure, particularly for routine analysis

of single elements, and it can easily be manipulated by relatively unskilled staff following development of a method. It is also a process that

is easily automated and in terms of some of the most popular trace techniques, e.g., x-ray fluorescence, mass spectrometry, its cost of

installation and maintenance is very fractional indeed. Current instru- ments cost from ca. $1700 to $8000 according to their complexity. As

it is presently practised the technique has not been applied to sohd

specimens, unlike x-ray fluorescence, mass spectrometry, etc., but there

appears to be no reason why finely pulverised particulate material should

not be examined by adaptation of the technique.

Atomic absorption measurements may generally be made with an

accuracy of ± 1-2% which compares favourably with that of most

other trace techniques. Perhaps the chief restriction for atomicabsorption spectrophotometry at present is that, unlike some others,

it yet remains to be developed as a method for the simultaneous deter- mination of several elements, but it must be recognized that it is as yet

relatively new to the scene. In general its specificity, sensitivity, ease

of appHcation and analytical range make it one of the most attractive

and elegant techniques available for the characterisation of traces. H. Future Developments in Atomic-Absorption Spectrophotometry

It is difficult to forecast the future direction of development of such

a rapidly expanding technique, but it is probable that since good analyti- cal methods are now available for most metallic elements and some nonmetals, that more workers will turn their attention to the development

or improvement of sources, atom-reservoirs and handling methods.

Apart from the hollow cathode the two most promising sources appear

to the author to be the monochromated xenon arc type of source —

preferably used in conjunction with scale expansion and integration and

the microwave powered source. Paradoxically considerable progress

could be made by dispensing with the flame as atom-reservoir but until

I
284 TRACE CHARACTERIZATION

such a development occurs the evolution of the nitrous oxide-acetylene

flame and the long-tube flame are probably most significant. The

restrictions imposed by the necessity to use a flame also include the

need for dissolution of samples and it is hypothetical if much progress

may be made in dealing with solid specimens unless the flame is dis- pensed with. However, in reading the literature of atomic-absorption

spectrophotometry it is startling to find how often an observation that 'such and such' cannot be done (or is impossible) is disproved within

periods as short as twelve months.

Footnote: After this manuscript had been prepared two very fine monographs on atomic-absorption spectrophotometry have been published

by W. T. Elwell and J. A. F. Gidley ('Atomic-Absorption Spectrophotometry', Pergamon, Oxford, 1966) and by J. W. Robinson ('AtomicAbsorption Spectroscopy', Marcel Dekker, Inc., New York, 1966).

These both give first class accounts of the theory and practical applications of the technique.

V. Atomic Fluorescence Spectrophotometry

In proceeding from molecular absorption to molecular fluorescence

spectrophotometry we observed that there was a very considerable

gain in the sensitivity of determination and an improvement in selectivity. It is logical, therefore, to expect a similar improvement in passing from a technique of atomic-absorption to one of atomic-fluores- cence spectrophotometry. No increase in selectivity can be expected,

however, since the technique just discussed is already virtually specific

for each element. It has long been recognized that atoms can emit

fluorescence in a manner similar to molecules when they are irradiated

with light of sufficient energy to promote an electron transition, but the

first description of atomic fluorescence in flames appears to be that of Nichols and Howes [116] who reported weak fluorescence signals

for lithium, sodium and the alkaline earths. Robinson [117] detected

a weak fluorescence of magnesium in an oxy-hydrogen flame using a magnesium hollow cathode lamp as the source of irradiation, but found

no signals for sodium and nickel over and above their thermal emission

in the flame. This, however, is not surprising in view of the extremely

low emission of hollow cathode lamps and the absence of modulation.

However, the latter author was not attempting to develop an analytical

technique and the first serious and successful attempts to do this were

described by Winefordner and his co-workers in a series of four papers

[118-121] pubhshed in 1964-65 and in the latter year by Dagnall, West,

and Young [33', 122]. In atomic-absorption spectrophotometry the eventual fate of the en- ergy absorbed by the atoms was of little concern since it had no effect on subsequent studies. Most of the energy is lost by collisions with

other atomic and molecular species in the flame plasma. However,

the energy which is imparted to an atom creates an unstable situation
CHEMICAL SPECTROPHOTOMETRY 285

since a charge separation has occurred and the electron will be pulled

back into its equiHbrium orbit with the energy released as a photon

characteristic of the difference between the excited state and the

ground state, i.e., characteristic of the atomic species. In molecular

fluorescence spectrophotometry no matter which of the higher electronic

states was excited, vibrational dissipation and intersystem crossing

ensured that within the lifetime of the excited species the lowest vi- brational level of the first excited state was always attained so that irrespective of excitation, fluorescence re-emission was always at the same wavelength with the fluoresced band mirroring the image of the

longest wavelength absorption band.

Such a situation cannot arise in atomic excitation-emission since

there are no vibrational motions of electrons within chemical bonds

to permit such a process. Instead, the energy can only be shed by

coUisional deactivation with other atoms or molecules (which may

subsequently emit their own characteristic fluorescence) or by the

emission of a photon of energy, i.e., by atomic fluorescence. Because

of the simplicity of the system, resonance fluorescence predominates,

i.e., the excited atoms emit energy of the same wavelength as that which

caused their excitation. At this stage it might be asked why this resonance radiation does not cause serious problems in atomic absorption measurements since the

atoms can emit light of the same wavelength as that which they absorb.

The principal reason is that the intensity of the sources which are used

in absorption work is very low. As in molecular fluorescence the in- tensity of the atomic fluorescence signal is proportional to the intensity of the source and consequently the emitted signal must necessarily

be very low indeed. Secondly, in absorption, a long thin flame is used

so that the weak fluorescence is emitted in all directions and that which

passes towards the entrance slit of the monochromator must traverse

a long path through a, population of atoms which is largely in the absorbing ground state. Although they are relatively weak still, it is probable

that fluorescence emission may cause complications in absorption

measurements with the relatively new high intensity hollow cathode

lamps and that appreciable fluorescence signals could be detected

at the end of the flame nearest the lamp when a strong solution of the

metal is being sprayed and the flame is examined at right angles to its axis. It is doubtful, however, whether this will cause serious diffculties under normal circumstances.

Although it has yet to be demonstrated widely it should be possible

to excite atomic fluorescence at very many wavelengths for each element

because of the multiplicity of discrete atomic absorption lines which

are associated with most elements. Moreover, it should be found that the radiation which is emitted as fluorescence should principally have

the same wavelength as the excitation radiation. Consequently, it is
286 TRACE CHARACTERIZATION

theoretically possible to control the spectral range in which incidence

of fluorescence occurs in a manner which is not possible in molecular

fluorescence. Yet again, it is true to say that whilst there are many

absorbing hues which may be used in atomic-absorption spectrophotometry, their sensitivity is dictated entirely by the oscillator strength

of the atomic line. On occasion, in atomic absorption it may be desirable to use a Une other than the principal one because of flame

characteristics or the presence of elements or compounds with continua

in the region, but it may not always be possible to use it because of poor

intensity. With atomic fluorescence it is, however, possible to 'turn up' the sensitivity of such a line by increasing the intensity of irradia- tion or, of course, by increasing the amplification within the limits of

the combined electrical noise of the detector, source and flame. Atomic

fluorescence is in this respect much more flexible than atomic-absorption spectrophotometry.

A. Types of Atomic Fluorescence Lines

Winefordner and Vickers [118] designate three modes of atomic

fluorescence other than resonance re-radiation from an excited state Ex to the ground state ^o- These are direct-line fluorescence produced

by transitions from higher states to lower states other than the ground

state and stepwise fluorescence in which resonance radiation is emitted

following excitation by light of a wavelength which promotes excitation

to a level higher than the first excited state, but in which non-radiative

deactivation has resulted in population of the first excited state. In

sensitised fluorescence one atomic species is excited by absorption of

light of the requisite wavelength and transfers the energy to another

atomic species which subsequently fluoresces its own characteristic

quanta. Examples of this behaviour cited by Winefordner and Vickers

are:

(a) direct-line fluorescence: Tl 5350 A fluorescence following excita- tion at 3776 A;

(b) stepwise fluorescence: Na 5890 A fluorescence following excitation

at 3303 A;

(c) sensitised fluorescence: Tl 535013776 A emissions from a flame containing a much denser population of mercury atoms and irradiated

by the 2537 A Hg fine [123].

However, though all these forms of fluorescence may be observed, resonance fluorescence, at the present limited stage of development,

is the most useful and certainly the most sensitive. Much of what has been said in the previous section relating to atomicabsorption spectrophotometry is directly applicable to atomic-fluores- cence spectrophotometry, particularly in relation to the means of

producing populations of ground-state atoms in flames.
CHEMICAL SPECTROPHOTOMETRY 287

B. Analytical Relationships in Atomic-Fluorescence

Spectrophotometry

The relationship between the concentration of the fluorescing species

in the flame and fluorescence signal has been fully discussed by Winefordner and Vickers [118] and their derivation of an analytical equation

should be consulted for fuU details of aU the factors involved. However,

the exercise is largely of academic interest only, as in the case of atomicabsorption spectrophotometry, since usually the actual concentration

of atoms present in a flame at any given instant is unknown. There

is, however, a very close similarity between the relationship estabhshed for molecular-fluorescence spectrophotometry and that for atomic fluorescence.

The equation may, therefore, be framed in the same terms, viz. F = 2.303 ^.lo.eA.if.c.p.

for dilute solutions of atoms in flames. F denotes the resonance fluores- cence signals, h the intensity of the excitation light, €a the atomic

absorptivity at the wavelength of irradiation, / the pathlength in the

flame, c the concentration of absorbing atomic species and p a proportionality factor relating to the fraction of the total fluorescence observed by the detector. In this instance the same quanta of energy

are emitted as are absorbed, but not all the atoms which undergo excitation exhibit resonance fluorescence. Consequently, a factor relating

to the quantum efficiency, O, of the fluorescence process must be in- corporated into the equation. <t> may be defined as the ratio of the

number of atoms which fluoresce from the excited state to the number

of atoms which underwent excitation to the same excited state from the

ground state in unit time.

The concentration of preatomic species in the solution phase may be

related to the concentration of free atoms in the flame by multiplying

the former by a nebuhser efficiency factor "n" (< 1), which may easily

be established, and by an atomisation efficiency factor, a, i.e., C = Cg.n.a

Unfortunately, we are not in a position to know the number or concentration of free atoms produced from a known concentration of preatomic

species drawn into the flame because of the uncertain efficiency of the

conversion process, the limited lifetime of free atoms, parasitic side

reactions, etc. Consequently, the equation which may be written in the form

F = 2.303 0./o.e.4./.C,.p.n.a
288 TRACE CHARACTERIZATION

is instructive, but has little significance. For a given nebuliser and

instrumental set of conditions the analytical relationship becomes

where K is a constant, i.e., the fluorescence signal is proportional to the

intensity of irradiation and to the concentration of the preatomic species

in the solution. It is also apparent that the intensity will vary from

from one fluorescence Hne to another by variation of O. Both <i) and

a may be altered by alteration of the flame matrix and an optimum value

probably may be found for the two processes with a compromise struck

between increase of the number of free atoms (before ionisation becomes

serious) and an increase in coUisional deactivation and quenching process

as temperatures are raised. The length of the absorption path may only

be used within limits where self absorption and total frontal absorption

cf. parallel in Figure 13A, does not become a serious problem. The

nebuliser efficiency may be increased considerably by the use of organic

solvents and possibly by preheating the vapour and even introducing

ultrasonic frequencies into the fog chamber whilst the 'p' factor may

be increased by light-collection, via lenses, etc., or by use of an ellipsoid

mirror and off axis mounting of the flame as indicated in Figure 21. Although many of the factors in ths equation may not easily be de- termined, its validity is easily demonstrated by the empirical process of

drawing up calibration curves in exactly the same way as in virtually

all spectroscopic processes. It must be remembered that in the con- ventional right-angled mode of operation, atomic-fluorescence spec- trophotometry is only applicable to trace amounts of material, but there

appears to be no reason why a frontal mode using an acute angle between

incident and emergent beams should not be reasonably successful as

in the molecular technique.

F = K.^.Io.C,s

MODULATED SOURCE

(MONO, or CONTINUOUS)

ELLIPSOID MIRROR

FLAME PHOTO MULTIPLIER DISPLAY

UVAIS

MONOCHROMATOR

TUNED ^

AMPLIFIER

Figure 21. Apparatus for atomic fluorescence spectrophotometry.
CHEMICAL SPECTROPHOTOMETRY

C. Instrumentation

289

It must be stressed that in the following paragraphs the work that is being referred to relates only to published work from the University

of Florida and from the writer's laboratory at the Imperial College of

Science and Technology of London University. Other groups are no

doubt very active in the area, but no further information is available at the time of writing.

1. General Arrangement

A schematic set-up is shown in Figure 21 [124]. Light from a suit- able source is focussed on the population of atoms in the flame and the

fluorescence, which is, of course, emitted in aU directions, is examined

in the same plane at right angles to the direction of the incident light.

The light from the flame is then passed through a monochromator to disperse unwanted radiation and the signal is passed to a photomultipher, etc. In our experiments we have simply made use of a conventional Beckman DU flame photometer or the SP 900A Unicam flame

emission/absorption spectrophotometer, principally the latter, with a

suitable source of irradiation placed near the flame and subtending a

right angle with the entrance slit of the monochromator at the centre

of the flame. Winefordner et al. [119, 125], have built special ap- paratus which does not, however, differ substantially from that used

by ourselves.

2. Types of Burner

In most respects flame photometry bears a closer relationship to atomic-fluorescence spectrophotometry than does atomic-absorption

spectrophotometry. Ideally both require the same shape of flame which

should be small and capable of being viewed over as much of its area as possible by the monochromator so that the maximum possible part of the analytical signal can enter the monochromator and fall on the

detector. In all his studies to date Winefordner and his colleagues

have used turbulent flames from total consumption burners. We have

preferred to use laminar flames from a Meker type of circular burner

head, as used on the Unicam SP 900 flame spectrophotometer, with a separate aspirator nebuliser. The near homogeneous dispersion of uniform droplets which enters such a flame produces much finer uniform

particles or clotlets than can be obtained by use of an integral nebuliserburner. This aspect is very important because light-scatter is a much

more critical phenomenon than it is in either atomic absorption or flame

photometry and a powerful source can produce an appreciable scatter

signal. In our experiments we have observed considerably less scatter than that recorded by Winefordner and his co-workers probably because

of the difference in nebulisers and burners.
290 TRACE CHARACTERIZATION

3. Fuel Gases

Winefordner et al. have worked largely with oxy-acetylene and oxy- hydrogen flames and have more recently [125] described the use of what

they call an argon-hydrogen flame but which in fact contains sufficient entrained air to support combustion of the fuel gas with the argon acting

chiefly as a diluent.

We have made a study of air-based laminar-flow flames burning on a

cylindrical burner head perforated by a series of concentric holes with

hydrogen, propane and acetylene as the fuel gases [126]. To study the

background emission of the flames we have used the SP 900A in its emission mode so that the light from the flame entering the monochromator is chopped at 100 cps in phase with the amplifier. We have also used

an EMI 9601B photomultiplier because of its good response in the u.v. region. These measurements were made with distilled water aspirating

through the flame, since this cools it and reduces the background by

ca. 15%. We found that in the air-propane and air-hydrogen flames

background emission could be virtually eliminated by working high

up in the flame but a distance ca. 3 cm above the primary reaction zone was consistent with maximum stability. Background emission with the

air-acetylene flame was much higher and although our early work [122] was done on this flame, we subsequently preferred to use air-propane

or air-hydrogen. Both these flames exhibit an increase in background

with increase of fuel pressure, but although the air-hydrogen flame

exhibits a lower background emission than air-propane at aU wavelengths

except between 2810 and 2850 A and over the OH band (3060-3200 A)

the air-propane system is attractive because of its low burning velocity

and is very convenient in use. We have found that, in general, doubling

the slit width quadrupled the background, but produces a linear response

in fluorescence signal, i.e., the signal to background ratio decreases

with increasing slit width. In measuring the fluorescence signal the SP 900A is held in its absorption mode whereby the light entering the monochromator is not chopped,

but the source was modulated to match the a.c. amplifier. In comparing

the suitability of the three flames for metaUofluorescence, the air- acetylene one was discarded, although modulation eliminates its effect,

because of its higher background and because it produces greater scat- tering under irradiation. We also observed that with air-acetylene we

could only observe cadmium resonance fluorescence at 2288 A [122] but

with the other two flames signals could additionally be observed at 3261

A. With our equipment we also obtained a more stable flame with air- propane than with air-hydrogen. In addition, it was found, both with

zinc and with cadmium at 2139 and 2288 A respectively, that the fluores- cence signal in an air-hydrogen flame was adversely affected by an in- crease in hydrogen pressure whilst variation of the propane pressure

had no effect.
CHEMICAL SPECTROPHOTOMETRY 291

With oxy-acetylene Mansefield, Windfordner and Veillon [121] found

that the signal for thaUium fell away rapidly beyond the luminous tip of the flame whilst in the lower regions thermal emission was greater than

the intensity of fluorescence; best results were obtained at 3776 A with a hydrogen-rich flame. A height about 1 cm above the luminous tip of

the flame was used for both thaUium and mercury whilst other metals,

zinc and cadmium, were measured about 1 cm above the reaction zone

in the turbulent flame.

4. Excitation Sources for Atomic Fluorescence Spectrophotometry

In atomic-absorption spectrophotometry a hollow cathode lamp has

to be used for each element or a multi-element cathode for a restricted

group of metals. This arises because it is essential to have a source which has an emission hne much narrower than the absorption hne

(although recent work has shown that an extremely well monochromated

continuous source may in fact be used [90]). In atomic fluorescence, on

the other hand, it is not necessary to have such a 'narrow line' source.

It is sufficient if the emission brackets the absorption Hne of the atoms

in the flame, although there are obvious occasions when it may be advantageous to use a narrow line source when dealing with a system that

exhibits many Hues in very close proximity to that of analytical interest.

a. Spectral Discharge Lamps and Microwave-powered Sources.

Both Winefordner et aL, and ourselves have made use of the readily

available spectral discharge lamps which have a nominal rating of 18-20

watts and have used these to study the fluorescence of cadmium, zinc,

mercury and thallium and have additionally used microwave-powered

discharge tubes for many other elements, e.g., mercury, indium, gallium

[121] selenium, tellurium [127] and for several other elements, e.g., antimony, arsenic, cadmium, nickel, silver, tin, thallium, etc. [128]. We used an Electromedical Supplies 'Microtron 200' unit operating

at 2450 ±25 megacycles/sec with a small cavity operating approximately

1 metre from the magnetron at the end of a coaxial cable. Our source

tubes are of quartz and operate under < 1 mm pressure of argon. We

have found these very easy to prepare. In most instances we used a small amount of the metallic element sealed in the tube plus a crystal

of iodine to run the tube in. Winefordner et al., used corhmercially

available discharge tubes and a similar 2450 megacycle microwave unit

rated at 100 watts. Both sets of workers operated their tubes at less than full power but whereas we used < 10 watts output (plus loss due to reflected power) the other group operated their equipment in the range

40-60 watts and report some problems due to self reversal of the source. We have noted a considerable stabilisation of output by blowing a stream

of air over the tube in the tuned cavity. We have used several of these

tubes, e.g., those for nickel, iron, silver, selenium, tellurium, etc., for atomic absorption as well as atomic fluorescence measurements and

I
292 TRACE CHARACTERIZATION

have found them to be possessed of a stabihty equal to that of hollow

cathode lamps.

b. Continuum Sources. Both groups have also made use of con- tinuum sources thus demonstrating the source tolerance of the newer

technique. Veillon, Mansefield, Parsons and Winefordner [125] used

a dc 150 watt xenon arc lamp and chopped the excitation beam leading

the fluorescence through a monochromator/detector (LP. 28) into a tuned

amphfier. We [126] used an ac 150 watt xenon arc lamp operating at mains frequency. Under these circumstances continuum radiation

from the flame over the waveband transmitted by the monochromator

is not recognized, though it produces an increase in electronic noise.

The results shown in Table 4 summarise some of the data obtained by

both groups using such a source.

In contrast to the others who reported signals for Ag, Au, Ba, Bi, Ca,

Cd, Cu, Ga, Mg, Ni, Pb, Tl, and Zn, we found no signals for Ga or Ni

and none for Pb at 4058 A though a good signal was obtained at 2833 A

which is the resonance line used for atomic absorption work, whereas

the 4058 A line is usually used for flame photometry. It is possible that our failure to find the Ga and Ni signals is due to the cooler flame used

and the lack of protection afforded by the argon sheathed flame used

by the other workers. It is certainly noticeable that the sensitivities they reported for Ga and Ni are much lower than the others and these

elements are prone to form molecular oxide species in the flame. As

expected, we found no fluorescence at any of the bands we examined for Al, Be, Hg(II), Pd(II), Sn(IV) and Zr in the air-propane and air-hydrogen

flames and with the continuous source. We did not examine Au, Ba,

Bi and Ca which yielded good spectra in the other study [125] but ob- tained good spectra for Co, Fe, and Mn. The wavelengths shown in Table 4 correspond to the strongest fluorescences observed under our

conditions. It must be stressed, however, that alteration of the radiative

characteristics of the source may well alter the relative strengths of the

fluorescent fines since emission is a function of the intensity of the source emission fines as weU as the osciUator strengths of the absorbing

atoms.

It is also noticeable from the table that those elements which are more

difficult to atomise in cool flames (air-propane) gave lower sensitivities than in the hotter oxy-hydrogen flame, e.g., Mg, Ag, Cu, whilst those

which are easily atomised, e.g., Zn, Tl, gave similar signals. Thus one

arrives at the fairly obvious fact that, as in atomic absorption spectrophotometry, the flame must be hot enough to produce a good population

of free atoms.

D. Sensitivity and Selectivity of Atomic Fluorescence

Spectrophotometry

It must also be stressed, however, that Table 4 apparently shows that on the whole atomic fluorescence is less sensitive than atomic-absorption
CHEMICAL SPECTROPHOTOMETRY 293

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294 TRACE CHARACTERIZATION

spectrophotometry. In fact, the reverse is the case, but the table refers

to the use of a 150 watt source which emits energy over the whole of the

spectrum from 2000 A into the infra-red range. The intensity of radiation available from the lamp in any one waveband must be quite small

and it is surprising to find such sensitivity as these show. Using spectral discharge lamps we have found sensitivities of 2 X 10~^^ g for cadmium and similarly for zinc, corresponding to a signal : noise ratio of 1:1. Good rectilinear calibration curves were obtained for cadmium

with 10-^M solutions [122] and with zinc using 5 X lO^^M solutions [126]. In the range 10~^M a percentage standard deviation of 0.7 was found and

with <10~^M solutions ca. 3.0. With cadmium and zinc we found it easily possible to prepare linear calibration curves over the area lO"-'-

10 ''M. Forty-one cations and eighteen anions were examined for interference at hundred-fold concentrations relative to the test ion in both instances and none was found. The ions were NH4+, Ag, Al, As,

Au, Ba, Be, Bi, Ca, [Cd], Ce, Co, Cr, Cu, Fe(II) and (III), Ga, Hg, In, K,

Li, Mg, Mn, Mo, Na, Ni, Pb, Sb, Sc, Se, Sn, Sr, Te, Th, Tl, Ti, U, V, W,

Y, [Zn], Zr, acetate, borate, bromide, carbonate, chloride, citrate, per- chlorate, cyanide, fluoride, iodide, nitrate, oxalate, phosphate, thiocyanate, silicate, sulphite, sulphate, and tartrate. Hydrolysis was

prevented where necessary by the addition of sufficient acid to maintain

a clear solution. Mansefield, Winefordner, and Veillon similarly report near linear curves for zinc over the range 1 X 10 "^ to 10 ppm, 2 X 10~^ to 10 ppm for cadmium, 0.1 to 1000 ppm for mercury and 4 X 10~^ to 1000

ppm for thallium using spectral discharge lamps.

E. Determination of Selenium and Tellurium

More recently, [127] we have employed microwave-powered sources

for selenium and tellurium and have compared their determination by

both absorption and fluorescence on the same equipment, viz, the Uni- cam SP 900A.

The ^P-i ground state in selenium and tellurium is part of a triplet

=^P2, =^P,, =^Po. For selenium the ^P.-^^Si^, ^P, ^81° and =^Po-^S,°

transitions show up as lines at 1961, 2040 and 2063 A whilst for tel- lurium the same transitions resulted in lines at 2143, 2386 and 2383 A. Intercombination Hues at 1900, 2075 and 2558 A correspond to ^P2 — ^82° transitions whilst those at 1915, 2164, 2531 and 5746 A correspond to ^Pi — ^82°. Fluorescence was observed for all three lines for selenium

and tellurium but only very slightly for the intercombination bands.

8ince the ground state hne absorbs ten to five times more strongly

than the metastable ^Pi and ^Po states there is httle doubt that the 2040

and 2063 fines for selenium and the 2386 and 2383 fines for tellurium

arise from direct-line fluorescence.

Difficulties were encountered with the 9601B photomultiplier, which

has a Corning uv. end-window, and the 1961 A selenium fine, but the
CHEMICAL SPECTROPHOTOMETRY 295

photomultiplier gave a satisfactory response with the direct hne at 2040 A. Using a selenium tube under an argon pressure of < 0.1 mm at 40 watts we w^ere able to obtain good calibration curves between 0.25 and 125 ppm (higher Hmit not explored) with a (signal: noise = 1: 1) detection hmit of 0.15 ppm. With tellurium the 2143 A hne was used,

with a tellurium (iodine) tube at ca. 0.1 mm argon and operating at 30

watts as source, to obtain cahbration curves in the range 0.06 to 125

ppm (upper hmit not sought) with a detection hmit of 0.05 ppm. We

anticipate that use of the directly interchangable EMI 9526B photomultipher would increase the sensitivity by a factor of between 10 and

100 fold, particularly for selenium. As before, no interferences were

observed. Using the same equipment for atomic absorption measure- ments we obtained a detection hmit of 1 ppm for each element. The

2143 A resonance hne was used for teUurium and (despite the insensitivity of the photomultiplier) the 1961 A line for selenium.

The fact that the better sensitivity of the photomultiplier could be

used with advantage by the fluorescence technique, whilst it could not by absorption, is a good example of the flexibility of the former tech- nique. The signal obtained in fluorescence was found to be largely

independent of the flame composition and height of measurement in the flame, but a shghtly fuel-rich air-propane flame was used with meas- urement about 3 cm above the burner head.

VeiUon, Mansefield, Parsons, and Winefordner have observed some

very broad scattering bands in the argon (air)-hydrogen flame due to molecular aggregates in the flame, particularly with the total consumption

burner, but we have not detected these using more conventional flame

gases and the laminar-flow flame. As in atomic absorption we have

generally found ^hat the analytical signal can be enhanced by a factor

of four or five times when the element concerned is extracted into an

equal volume of a non-miscible organic solvent. Similar results have

been observed by Winefordner et al. In our work we have been able

to show that the enhancement appears to bear a direct relationship to the increased nebuhser efficiency using organic solvents.

F. Assessment of Atomic Fluorescence Spectrophotometry as AN Analytical Technique

In his recent monograph on absorption spectrophotometry Edisbury

[129] has remarked that atomic-absorption spectroscopy promises to become a major technique because it involves 'the World's most selective possible absorption of light'. This is certainly true also of atomic

fluorescence and, with it, the newer technique promises to bring along a

flexibihty of operation and sensitivity that considerably exceeds those of atomic absorption. The range of elements which have as yet been deter- mined is hmited still by the newness of the technique, but it is, cf. Figure 22, nevertheless very promising indeed. There is every reason

237-323 0-67— 19
296 TRACE CHARACTERIZATION

H He

Li Be B C N 0 P N e

Na %Mg,»

»• • «

1 1 1

Al Si P s CI At

K

» • • «Ca

• ** •

,

Sc Tl V Cr \\\\

;Mn%«

* • • t .Ve\

•

• « * •

t «« *

• • •* • * • • * « • •» *{^^*\

•••*, Ge

* • •• • • • •

• • • • 1 • Set \\%\

Br Kr

Rb Sr Y Zr rrb Nfo Tc Ru Rh Pd

t • t :cd';

1 1

* • • t

• « «

It 1

» • • t .'en .*

• • • •

• • •

«*SbJ

* • • •

• • • t •m* *. I Xe

Cs

• • • • *Ba*«» V.V»

La Hf Ta W Re OS Ir Pt » Au «' % • • « « «

• « «

• « «

%T1 «,

« « * •

• • * «

. • >

1 « • • .ViV. Po At Rn

FT Ra Ac Th Pa U

Ce Pr Nd Pm Sm Eu Qd Tb Ho Er Tm Yb Lu

Figure 22. Elements determined (to date) by atomic fluorescence spectrophotometry.

to suppose that the arguments vis a vis source intensity and amplifier

gain, etc., used earlier in this discussion when comparing the molecular

techniques of absorption and fluorescence apply equally well to their

atomic counterparts.

Atomic fluorescence carries with it the birthright of the 'World's

most selective possible absorption of light' with the added benefit that the light is 'switched on' and may be 'turned up' whereas the absorption technique is a switching off" with the only possibility of darkening

the line being a slight increase in pathway and scale-expansion. It has been amply demonstrated that a continuous source may readily

be used to generate the atomic fluorescence and that only a crude monochromator is necessary. When a continuous source is used for atomic

absorption a monochromator with a very good resolution is required and

an instrument possessing a good scale-expansion facility. In this way

it may be said that atomic-fluorescence does away with the argument

concerning the necessity for individual source lamps for each element

which has (unreasonably) been held as a detraction from the merits of atomic-absorption spectrophotometry. The concentration range over which atomic fluorescence may be applied stretches over a X 10^ range

as pointed out very aptly by Winefordner et al. [125], and there can be

very few techniques capable of such a feat. The apparatus required

is very simple and easy to devise and practically any flame spectrophotometer may be adapted for the purpose without interfering with

its normal mode of operation in any way. The continuous source is very attractive, but where sensitivity is required above all else the use

of individual spectral discharge lamps will provide the necessary subnanogram sensitivity. Only a limited range of these is currently avail- able, but many more could, and no doubt will, become commercially

available upon demand.
CHEMICAL SPECTROPHOTOMETRY 297

However, at present the microwave powered source appears to be one

of the best available. Not only can it be used to provide narrow 'line' sources consisting of individual quartz 'lamps' which can be made at a cost of ca. $0.5 each within a matter of a few minutes [127] but

multielement lamps may also be prepared by suitable blending of the

desired constituents and a continuous xenon, argon, neon, etc., source

as well, simply by ampouhng the necessary gas under a suitably reduced

pressure. Every technique has its Hmitations, and at the present for atomic

fluorescence these are inherently the largely unknown possibilities of interference by quenching and by light scatter. However, in the few

experiments that have as yet been described, they do not appear to constitute a very serious limitation. It will be freely admitted that lack

of commercial equipment may cause some delays in adoption of the

technique, but anyone who has experience of flame spectrophotometry

or atomic absorption and some knowledge of fluorescence phenomena

will not be deterred from exploring such an enticing new area by such

a triviality.

G. Future Developments in Atomic-Fluorescence

Spectrophotometry

Speculation on the future of atomic fluorescence spectrophotometry

is perhaps pointless and foohsh at such an early state of its development, but it is fairly safe to predict that it is a technique which will attract widespread attention and be much used in the near future. Commerical equipment wiU no doubt rapidly become available as manufacturers realise its potential but the adaptation of a flame spectrophotometer is so simple that it need not hold the enthusiast back at aU. The xenon arc lamp and power supply are readily available in many

laboratories and suitable microwave units are in common use in many

hospitals for therapeutic purposes. They cost only ca. $800 and a simple vacuum hne can be devised [127] in a very short space of time to blow

'lamps' by the dozen.

The inexpensive and simple nature of the fluorescence equipment

necessary to do subnanogram analyses with absolute specificity should

be a serious consideration in all laboratories currently considering the

purchase of items such as x-ray fluorescence, etc. As in atomic absorption, the flame is a non-ideal atom reservoir for reasons which have already been discussed. No doubt many more

flame media deserve exploration, but the use of demountable hoUow

cathode lamps, plasma jets, atom furnaces, etc., demand very close

attention, particularly in view of the possibility of working at last on

the non-metals such as sulphur and the halogens. It is not too much,
298 TRACE CHARACTERIZATION

I think, to suppose that the sensitivity and specificity of this new tech- nique will yet make it one of the most widely used and revolutionary

techniques of our time.

VI. References

[1] Liebhafsky, H. A., Pfeiffer, H. G., Winslow, E. H. and Zemnay, P. D., 'X-ray Absorption and Emission in Analytical Chemistry,' J. Wiley and Sons, New York, 1960.

[2] Bankovskii, Y. A., and Lobanova, E. F., Zhur. Analit. Chem. 14, 523 (1959).

[3] Bankovskii, Y. A., levinsh, A. F., and Luksha, E. A., ibid. 14, 714 (1959).

[4] Bankovskii, Y. A., and levinsh, A. F., ibid. 13, 507 (1958).

[5] Merritt, L. L., and Walker, J. K., Ind. Eng. Chem. Anal. Ed. 16, 387 (1944).

[6] Hynek, R. J., and Wrangell, L. J., Anal. Chem. 28, 1520 (1956).

[7] DagnaU, R. M., West, T. S., and Young, P., Analyst. 90, 1066 (1965).

[8] Ohnesorge, W. E., and Burlingame, A. L., Anal. Chem. 34, 1086 (1962).

[9] Smith, G. F., and McCurdy, W. H., Anal. Chem. 24, 371 (1952).

[10] Morrison, G. H., and Preiser, H., 'Solvent Extraction in Analytical Chemistry,'

J. Wiley and Sons, New York, 1957, p. 155.

[11] Bailey, B. W.. Dagnall, R. M., and West, T. S. Talanta, 13, 753 (1966).

[12] Close, R. W., and West, T. S., ibid. 5, 221 (1960).

[13] Herrero-Lancina, M., and West, T. S., Anal. Chem. 35, 2131 (1963); Palkans, P., and Florence, T. M., Anal. Chim. Acta 30, 353 (1964).

[14] Lukin, A. M., Smirnova, K. A., and Zavarikhina, G. B., Zhur. Anal. Khim. 18, 444

(1963).

[15] DagnaU, R. M., Smith, R., and West, T. S., J. Chem. Soc. 1595 (1966).

[16] Freeman, D. C, and White, C. E., J. Amer. Chem. Soc. 78, 2678 (1956).

[17] White, C. E., and Cuttitta, F., Anal. Chem. 31, 2083 (1959).

[18] DagnaU, R. M., Smith, R., and West, T. S., Analyst. 92, 20 (1967).

[19] Belcher, R., Leonard, M. A., and West, T. S., Talanta 2, 92 (1959).

[20] Idem. J. Chem. Soc, 2390.(1958).

[21] Leonard, M. A., and West, T. S., ibid., 4477 (1960).

[22] Bartkiewicz, S. A., and Robinson, J. W., Anal. Chim. Acta 22, 427 (1960).

[23] Belcher, R., and West, T. S., Talanta 8, 853 and 863 (1961).

[24] DagnaU, R. M., and West, T. S., ibid. 11, 1533 (1964).

[25] Bailey, B. W., DagnaU, R. M., and West, T. S., ibid. 13, 753 (1966).

[26] Ducret, L., and Seguin, P., Anal. Chim. Acta, 17, 207 (1957); also Pasztor, L., Bode,

J. D. and Fernando, Q., Anal. Chem. 32, 277 (1960).

[27] Jankovsky, J., Talanta 2, 29 (1959).

[28] Belcher, R., Wilson, C. L., and West, T. S., New Methods of Analytical Chemistry, 2d Edition, Chapman and HaU, Ltd., London, 1964, pp. 264-267.

[29] DagnaU, R. M., and West, T. S., Talanta 11, 1627 (1964).

[30] Braude, E. A., in Determination of Organic Structures by Physical Methods, Volume I, E. A. Braude and F. C. Nachod, editors. Academic Press, New York, 1955, p. 131

et seq.

[31] West, T. S., Chemistry and Industry, 1005 (1966).

[32] Umland, F., and Wiinsch, G., Z. AnaL Chem. 213, 186 (1965).

[33] West, T. S., lecture to Society for Analytical Chemistry, Burlington House, London,

6th October 1965, cf. Analyst 91, 69 (1966).

[34] Djurkin, V., Kirkbright, G. F., and West, T. S., Analyst 91, 89 (1966).

[35] Kirkbright, G. F., and Yoe, J. H., Talanta 11,415 (1964).

[36] Wadelin, C, and Mellon, M. G., Analyt. Chem. 25, 1668 (1953).

[37] Cabello-Tomas, M. L., and West, T. S., unpubUshed studies, cf Ref. 31.
CHEMICAL SPECTROPHOTOMETRY 299

[38] Weber. G.. and Teale. F. W. J.. Trans. Faraday Soc. 53, 646 (1957).

[39] Bowen. E. J., and West. K.. J. Chem. Soc. 4394 (1955).

[40] Bowen, E. J., and Sahu. J.. J. Phys. Chem. 63, 4 (1959).

[41] Kasha, M., J. Chem. Phys. 20, 71 (1952).

[42] McGlynn. S. P.. Reynolds. M. J.. Daigre, G. W., and Christodouleas. N.D., J. Phys.

Chem. 66, 2499 (1962).

[43] VanDuuren. B. L.. Chem. Rev. 63, 325 (1963).

[44] Leonhardt, H., and Weller, A., Z. Physik. Chem. 29, 277 (1961).

[45] Bowen, E. J., and Wokes, F., Fluorescence of Solutions. Longmans Green and Co., London, 1953.

[46] Bowen, E. J., and Brockelhurst, B., Trans. Faraday Soc. 51, 774 (1955).

[47] Parker, C. A., and Hatchard. C. G., Proc. Chem. Soc. 147 (1962).

[48] Parker, C. A., and Rees, W. T., Analyst 85, 587 (1960).

[49] Idem, ibid 87, 83 (1962).

[50] Lott. P. F., J. Chem. Education 41, A 327 (1964).

[51] Cheng, K. L., in Trace Analysis: Physical Methods, G. H. Morrison, editor. Inter- science Pubhshers, iNew York. 1965, pp. 161-192.

[52] EUis, D. W., in Fluorescence and Phosphorescence Analysis, D. M. Hercules, editor, Interscience Publishers, New York, 1966, pp. 41-79.

[53] Slavin, W., Mooney, R. W., and Palumbo, D. T., J. Opt. Soc. Am. 51, 93 (1961).

[54] Turner. G. K.. Science (No. 3641) 146, 183 (1964).

[55] Allison, J. B.. and Becker. R. S., J. Chem. Phys. 32, 1410 (1960).

[56] Kauzmann, W., Quantum Chemistry, Academic Press, New York, 1957, pp. 542-544.

[57] West, W., Chemical Applications of Spectroscopy, Interscience Publishers, New

York, 1956.

[58] Brederick. K.. Fiirster. T.. and Oesterlin, H. G., in Luminescence of Organic and

Inorganic Materials. H. Kallmann and G. M. Spruch, editors, J. Wiley & Sons, New York. 1962, p. 161.

[59] Kasha. M., and El-Sayed. M. A., Spectrochim. Acta 15, 758 (1959).

[60] Kasha. M., Radiation Res. Suppl. 2, 243 (1960).

[61] Popovych. O.. and Rogers, L. B., Spectrochim. Acta 16, 49 (1960).

[62] Eggers, J. H., Talanta 4, 38 (1960).

[63] Wilkins, D. H., ibid. 4, 182 (1960).

[64] Lewis, G. N., Magel, T. T., and Lipkin, D., J. Am. Chem. Soc. 62, 2973 (1940).

[65] Cherkesov. A. S., Dokl. Akad. Nauk. SSSR 146, 716 (1962).

[66] Diehl, H., Olsen, R., Spielholtz, G. I., and Jensen, R., Anal. Chem. 35, 1144 (1963).

[67] Crosby, G. A., Whan, R. E., and Alire, R. M., J. Chem. Phys. 34, 743 (1961).

[68] De Armand. K., and Forster, L. S., Spectrochim. Acta 19, 1393, 1403, 1687 (1963).

[69] Tomaschek, R., Reichesber, Physik (Beihefte Physik Z.) 1, 139 (1944): cf. C. Abstr. 6815g (1947).

[70] White, C. E., Anal Chem. 21, 104 (1949); 22, 69 (1950); 24, 85 (1952): 26, 129

(1954): 28,621 (1956): 30, 729 (1958); 32,47R (1960).

[71] White, C. E., and Weissler, A., ibid. 34, 81R (1962); 36, 116R (1964); 38, 155R

(1966).

[72] West, T. S., Lab. Practice, 1030 (1965).

[73] CoUat, J. W., and Rogers, L. B., Anal. Chem. 27, 961 (1956).

[74] DagnaU, R. M., Smith, R., and West, T. S., Talanta 13, 609 (1966).

[75] Bailey, B. W., DagnaU, R. M., and West, T. S., Talanta 13, 1661 (1966).

[76] Walsh, A.. Spectrochim. Acta 7, 108 (1955).

[77] Vidale, G. L., GEC (USA) TIS Rep., R 60 SD 330 (1960).

[78] L'vov, B. v., Spectrochim. Acta 17, 761 (1961)..

[79] Moshier. R. W.. and Sievers, R. E., Gas Chromatography of Metal Chelates, Per- gamon Press, Oxford, 1966.
300 TRACE CHARACTERIZATION

[80] Menzies, A. C, in Atomic-Absorption Spectrophotometry, W. T. Elwell, and J. A. F. Gidley, Pergamon Press, Oxford, 1961, p. 28.

[81] Gatehouse, B. M., and Walsh, A.. Spectrochim. Acta. 16, 602 (1960).

[82] Goleb, J. A., and Brody, J. K., Anal. Chim. Acta. 28,457 (1963).

[83] Robinson, J. W., ibid. 27, 465 (1962).

[84] Greenfield, S., Jones, I. L. L., and Berry, C. T., Analyst 89, 713 (1964): Mavrodineanu,

R.. and Hughes, R. C, Spectrochim. Acta 19, 1309 (1963); West, C. D., and Hume.

D. N., Anal. Chem. 36, 412 (1964).

[85] Nelson, L. S., and Keubler, N. A.. Spectrochim. Acta 19, 781 (1963).

[86] Parkinson, W. H.. Proc. Phys. Soc. 78, 705 (1961).

[87] Massman, H., Z. Instrumentenk 71, 225 (1963).

[88] Sebens, C., Vollmer, J., and Slavin, W., Perkin Elmer Atomic Absorption Newsletter 3, 165 (1964).

[89] Gibson, J. H.. Grossman, W. E. L., and Cooke, W. D., in Analytical Chemistry 1962, edited by P. W. West, A. M. G. Macdonald and T. S. West, Elsevier (1963). pp. 288-290.

[90] Fassel, V. A., Mossotti, V. G., Grossman, W. E. L., and Kniseley, R. N., Spectrochim. Acta 22, 347 (1966).

[91] Ivanov, N. P., and Kozireva, N. A.. Zhur. Anal. Khim. 19, 1266 (1964).

[92] Russel, B. J., Shelton, J. P., and Walsh, A., Spectrochim. Acta 8, 317 (1947).

[93] Elwell, W. T., and Gidley, J. A. F., Atomic-Absorption Spectrophotometry, Per- gamon Press, Oxford, 1st edition, 1961, pp. 9 and 12. [94] Marshall, G. B., and West, T. S.. Talanta, submitted for publication.

[95] Dagnall, R. M., Thompson, K. C, and West, T. S., unpublished work.

[96] Walsh, A.rin Analytical Chemistry 1962, edited by P. W. West, A. M. G. Macdonald,

and T. S. West, Elsevier, 1963, p. 286.

[97] Strasheim, A., and Butler, L. R. P., Appl. Spectry. 16, 109 (1962).

[98] Fuwa, K., and Vallee, B. L., Anal. Chem. 35, 942 (1963).

[99] Koirtyohann, S. R., and Feldman, C, Develop. Appl. Spectry. 3, 180 (1963). [100] Goodfellow, G. I., and Turner, C, private communication.

[101] Dean, J. A.. Flame Photometry, McGraw-Hill, New York, 1960.

[102] Huldt, L., and Lagerquist, A., Arkiv. Fysik. 2, 333 (1950). [103] Robinson, J. W.. Anal. Chem. 33, 1067 (1961). [104] Margoshes, M., and Scribner, B. F., Spectrochim. Acta 15, 138 (1959). [105] David, D. J.. Analyst 86, 730 (1961). [106] Willis, J. B.. Nature 207, 715 (1965). [107] Amos, M. D., and WilHs, J. B., Spectrochim. Acta 22, 1325 (1966). [108] Kirkbright, G. F., Smith, A., and West, T. S., Analyst 91, 700 (1966). [109] Kirkbright, G. F., Peters, M. K., and West, T. S., ibid. 91, 705 (1966). [110] Jones, W. G., and Walsh, A.. Spectrochim. Acta 16, 249 (1960). [Ill] Allan, J. E., ibid. 15, 800 (1959). [112] Willis. J. B.. Spectrochim. Acta 16, 259 (1960). [113] Baker, C. A., and Carton, F. W. J., UKAEA Rept. AERE R. 3490 (1961). [114] CHnton, O. E.. Spectrochim. Acta 16, 985 (1960). [115] Belcher. R.. Dagnall, R. M., and West, T. S., Talanta 11, 1257 (1964). [116] Nichols, E. L., and Howes, H. L., Phys. Rev. 23,472 (1924). [117] Robinson, J. W.. Anal. Chim. Acta 24, 254 (1961). [118J Winefordner, J. D., and Vickers. T. J., Anal. Chem. 36, 161 (1964). [119] Winefordner, J. D.. and Staab, R. A. ibid. 36, 165 (1964). [120] Idem. ibid. 36, 1369 (1964). [121] Mansefield, J. M., Winefordner, J. D.. and Veillon, C. ibid. 37, 1051 (1965). [122] Dagnall, R. M., West, T. S., and Young, P., Talanta 13, 803 (1966). [123] Mitchell, A. C. G., Zemansky, M. W.. Resonance Radiation and Excited Atoms,

Cambridge University Press, Cambridge. 1961.
CHEMICAL SPECTROPHOTOMETRY 301

[124] West, T. S., Inaugural Lecture at Imperial College, 25th January, 1966, cf. Chemistry and Industry, 1014(1966).

[125] Veillon, C. Mansefield, J. M., Parsons, M. L., and Winefordner, J. D., Anal. Chem.

38, 205 (1966). [126] Dagnall, R. M., Thompson, K. C, and West, T. S., Anal. Chim. Acta 36,269 (1966). [127] Idem, Talanta. submitted for publication.

[128] Idem, unpublished work.

[129] Edisbury, J. R., Practical Hints on Absorption Spectrophotometery, Hilger and

Watts, Ltd., London. 1966, p. 171.

CHEMICAL SPECTROPHOTOMETRY

Contributed Papers and Discussion

OSCAR MENIS

NBS Institute for Materials Research, Washington, D. C. 20234

I. Introduction

At the conclusion of Dr. West's lecture the chairman of the session

reported on the highlights of the contributed papers. Because of the

Umited time, only one of these papers was presented by the author.

Coincidentally, the six papers which were summarized were representative of the several areas covered by the lecture. They included atomic

absorption, fluorescence, spectrophotometry utilizing an organic chelate

with a high molar absorbancy index, ternary complex reactions, and

chelate extractions. In addition, the contributions included studies of problems associated with the recovery of trace elements from sample

dissolution processes.

II. Contributed Papers

The paper on trace elements in marine waters by atomic absorption

spectrophotometry, by D. C. Burrell, evaluated the appHcation of atomic

absorption methods to the determination of ten elements which included

alkaline earth and transition elements. Some of the aspects of interest were: (1) The assessment of the advantages of the laminar flow, premixed

gas burner over the turbulent flow burner; (2) the presence of spectral

interference of the CaO band in the determination of barium; (3) the use

of standard addition technique to overcome the interference of "light scatter" from the sample background; and (4) the use of a two-step

preconcentration technique in which the transition elements were

adsorbed on ferric hydroxide and then separated by solvent extraction.

The paper on spectrophotometric determination of microgram and

submicrogram amounts of silver with Thio-Michler's ketone by K. L. Cheng described the use of 4,4'-bis(dimethylamino)thiobenzophenone,

Thio-Michler's ketone, for the determination of silver. This reagent

forms a complex with silver ion at pH 3 in a water-ethanol solution or, alternately, it can be extracted into isoamyl alcohol. The complex has an absorbancy index of 94,000, thus approaching closely the theoretical

value of 100,000 discussed by Dr. West in his lecture. In the presence

of EDTA and citric acid, it is very specific and only noble metals interfere. 303
304 TRACE CHARACTERIZATION

In the paper on some problems in the assessment of trace impurities

in highly refractory electronic materials, with particular reference to single crystal ruby and sapphire for maser and laser use by E. M. Dodson,

the problem of dissolving small samples (10 mg) of ruby crystals was

discussed. A study with tracer iron-59 revealed losses due to the platinum crucibles used in the alkaline fusion. The mechanism of these

losses was described. It was shown that by the use of zirconium

crucibles and a potassium hydroxide fusion,, these losses could be

avoided.

In the paper on dual atmospheric tracers utilizing the fluorescence of fluorescein and calcium acetylsalicylate by J. D. Ludwick, a procedure was developed for the sensitive detection of certain fluorescent materials

in a study of their possible use as atmospheric tracers. Instrumentation was used which allowed differentiation of excitation and emission spectra.

This permitted independent analysis of the fluorescent materials,

fluorescein and the calcium salt of aspirin, simultaneously collected from

the atmosphere in diffusion studies. Cross-tracer interference was

reduced to a minimum and as little as 5X10~^^ g of fluorescein and

3 X 10"^ g of Ca-aspirin were measured.

Excitation and fluorescence spectra were presented for these compounds. After consideration of these spectra it is apparent that excitation of fluorescein at 490 m/t will not induce fluorescence in Ca-aspirin,

and the excitation of Ca-aspirin at 300 m/t will influence fluorescein

fluorescence to only a smaU extent. In the paper on spectrophotometric determination of vanadium in steel by C. L. Luke, a rapid method for determination of trace quantities

of vanadium in steel was described. It is based on the extraction of

vanadium with a'-benzoinoxime in chloroform and adding 8-quinolinol

for the formation of the colored complex of vanadium. The interferences

which accompany vanadium can be removed with a dilute hydrochloric

acid wash. The control of acidity prior to extraction and oxidation of

vanadium by permanganate are the critical steps in the procedure.

In the paper concerning evaluation of absorptiometric methods for the determination of nanogram quantities of elements in high-purity

materials by O. Menis, R. W. Burke, and T. C. Rains, the analysis of high-purity material, defined as "6-nines" of major component, presented an analytical challenge. As readily recognized, instrumental methods

require calibration in order to assure reasonable accuracy. Since this represents a major difficulty with high-purity materials, analytical

results based on independent methods must be relied upon to minimize

systematic errors. By atomic absorption and spectrophotometric procedures 40 ppb of

copper was found in "6-nines" purity zinc. In the atomic absorption

a TTA-hexone solvent extraction method was used to isolate the copper.

In the spectrophotometric procedure the displacement of zinc from
CHEMICAL SPECTROPHOTOMETRY 305

dibenzyldithiocarbamate chelate provided a means of measuring the

absorbance of the copper chelate at 435 m^t. This appears to be a re- markable process since it occurred in the presence of a millionfold excess

of zinc. The estimation of antimony and (gold 4- thallium) at less than

0.05 and 0.1 ppm respectively was also achieved by means of the Brilliant Green dye reaction [1].

^ The final paper on precision photometric analysis using a jS-excited

isotopic light source by H. H, Ross, was discussed by the author. Early

in 1966, the Analytical Chemistry Division of Oak Ridge National

Laboratory introduced a new technique for making high precision photometric measurements [2]. This new method utilizes the unusual

spectral properties of a /3-excited light source combined with pulseheight measuring equipment. The advantages of the technique include

high stability, controlled sensitivity, simplicity, small power requirements, direct digital output, and straightforward error analysis.

III. Discussion

In the general discussion, H. Kaiser (Dortmund), presented information on a furnace-type excitation cell for atomic absorption. This idea was

originated by a Russian scientist and developed by H. Massman at Kaiser's Institute in Dortmund. With the aid of a slide. Figure 1, he

described the cell. It consists of a carbon tube 5 cm long, inner diameter

of 8 mm and with a wall thickness of 1 mm. In the center of the cylinder

there is a small hole through which as little as 0.04 microliters of test solution or a solid sample can be introduced.

Figure 1. Furnace excitation cell for atomic absorption.

The carbon tube is supported in a copper block. This block is then

heated electrically by means of a low voltage transformer supplying a current of 400 amps. A temperature of up to 2800 °C can be obtained.

The entire chamber is enclosed in an argon atmosphere to prevent the

' Figures in brackets indicate the literature references at the end of this paper.
306 TRACE CHARACTERIZATION

introduction of impurities from inside of the tube by oxidation processes. Furthermore, the movement of argon gas is kept at a minimum in order

to retain the excited atoms within the absorption path inside the carbon

cyhnder. In a second sUde some detection hmits for 1% absorption were shown for cadmium, zinc, and mercury, indicating sensitivity at the

10-10 g level. Dr. Kaiser felt that this technique when fully developed

should be competitive with spark source mass spectrometry.

To a question from the audience as to the memory effect of the carbon

tube Dr. Kaiser replied that these carbon cylinders are relatively inexpensive and should be changed after each test. T. S. West remarked that as far as ultimate sensitivity, atomic fluores- cence offered the best approach for increasing detection limits. Using

relatively simple equipment one can determine 10~^ and 10~^^ molar

solutions with good precision. In his laboratory this has been demonstrated with zinc, cadmium, selenium, tellurium in the presence of over 40 cations and 18 anions. H. Kaiser remarked that in atomic fluorescence an increase in sensitivity by a factor of ten could be attained by changing the optical

arrangement.

Kaiser also added another comment on the subject of high precision

atomic absorption measurement. He proposed a multi-component

monitoring system to provide automatic corrections for the several

variables. First, he would measure the output from the hollow cathode

lamp of a nonresonance line after it passes through the flame source

to correct for background radiation and fluctuation of the hollow cathode

output. Secondly, he would monitor another element as an internal

standard to correct for the variation of solution aspiration and flame

variations. Finally, he would monitor the output from the hollow cathode

outside the flame path. These corrections could then be electronically

compensated and the final measurement would be free from these

systematic errors. IV. References

[1] Burke, R. W., Menis, O., Anal. Chem. 38, 1719 (1966).

[2] Ross, H. H., Anal. Chem. 38, 414 (1966).
RADIOACTIVITY TECHNIQUES IN TRACE

CHARACTERISATION

A. A. SMALES

Atomic Energy Research Establishment, Harwell, Great Britain

I. Introduction

The authors of the chapters in this book were asked to summarise

the "state-of-the-art" in their particular speciahty. This is difficult enough for a speciaHst to do in the area of nuclear techniques even with mass spectroscopy — a nuclear technique of the very greatest importance

in the field of trace elements — detached for treatment elsewhere. But

for one who is really no longer a speciahst, or at any rate tries hard not to be, it might be thought to be even more difficult! However, in the context of this Conference, where this presentation is merely to serve the

dual purpose of (a) acquainting the non-specialist with a reasoned

appreciation of the present possibilities and future potential and (b) being a preliminary to a discussion amongst all the most active specialists

in the area, it may be that there is some value in having the appreciation

made by someone who has experience of a wider range of competent

areas of trace element characterisation, for he may be more sympathetic

to the problems of the non specialist, leaving the real specialists to point

out any omissions or underestimates of their particular line of enthusiasm.

At any rate, this paper cannot be perfect, least of all to its author trying

to distil into a few pages what has taken several conferences and books,

many reviews and a few thousand research papers to describe.

The area can be divided broadly into two sections, (a) activation

techniques where a sample is irradiated to produce radioactive or excited states of elements in the sample and (b) the use of radioactive

materials as tracers for an element or a compound. There are of course many subdivisions of each section — perhaps some enthusiastic pro- ponents of particular subsections may be hurt in that their specialty is not given full sectional status!

II. Activation Analysis

A. General Principles

The general principles have not altered since they were set out with some clarity in a few key papers in the late 1940's and early 1950's,

307
308 TRACE CHARACTERIZATION

though of course it should be remembered that the approach had been

used first by Hevesy and Levi in the mid 1930's. The basic equation for activation is: —

A = (1 - e- ^0 X 6.02 X lO^^ where A =induced activity in disintegrations/sec at the end of irradiation. /=flux of "particles" used in the irradiation, in number/cm^sec.

cr = the activation cross section for the nuclear reaction con- cerned, in cm^.

weight of element irradiated, in grams.

(f) = fractional abundance of the particular isotope of the element

concerned.

M= atomic weight of that element.

X = the decay constant of the induced radionuclide, in sec~^

^ = irradiation time, in seconds.

After the irradiation, the induced activity will of course decay with a

characteristic half life, falling by a factor two in each half life period.

It follows from this equation that there is a limit to the activity that can

be induced under given conditions, i.e. when the term (1 — e~^0 reaches

a value of 1, for practical purposes after an irradiation time of about ten

half lives of the radioactive species induced. It is possible to get an

indication of the potential sensitivity of the method for any element or indeed any isotope of an element (and it is worth pointing out that this method involves a nuclear reaction and therefore cannot give any assist- ance on identifying the chemical form of that element), given the necessary information on the values for the different components of the

equation. Such sensitivities will be discussed later for each type of

irradiation discussed.

In applying activation analysis the generally accepted approach is not

to rely on absolute values of the components of the above equation but

rather to irradiate a sample and a known mass of a standard under

identical conditions so that a simple comparison of the induced activity

gives the mass of element to be determined in the sample.

The above equation is quite general, but is normally used where

species concerned have values of half life comparable with or longer

than the time needed to measure the induced activity after irradiation

is completed, though there is one development which is worth pointing
NUCLEAR METHODS 309

out at this stage and in which there is growing interest. This involves

counting, during the irradiation, what is arbitrarily called "prompt"

radiation. This latter refers to the radiation emitted from species,

usually denoted as "excited states" with very short half lives, perhaps

at the level of nanoseconds or less. A similar dependence of induced

activity on cross section and flux occurs, but a counter observing such

"prompt" radiation will yield a count-rate C which is proportional to the

rate of reaction, i.e., C = KfcrW where /, o", and IF have the same

definition as earlier, and Kis a constant which depends on the efficiency

and geometry of the detector and the proportion of the decay emitting

the radiation to be determined. Such "prompt" counts can be accu- mulated for an extended period of irradiation when the total counts

registered in time 't' will be

Cin = Kf(TWt

This apparently gives the possibility of infinite sensitivity (note the dif- ference from the earlier case, where it was assumed that counting was

done after the irradiation) but in practice a lower useful limit will be

imposed because of the measurement of activity from other sources which interfere with the determination. Nevertheless the approach has some advantage in saving of time and mention will be made subsequently

of examples that have appeared.

In what might be considered as an intermediate state between the

"prompt" approach and the longer established "removed radioactivity"

situations, some work has been done using pulsed irradiations with

induced activities of intermediate half life values comparable to the pulse

time, counting during the interval between pulses.

By far the most commonly used approach to activation analysis,

remains however the "removed radioactivity" method where measure- ment of the radioactivity follows the completed irradiation. Such

measurement can sometimes be made directly on the irradiated sample

using gamma ray spectrometers or even in a few cases simple beta counting, but it still remains generally true to say that for the utmost sensitivity

and selectivity to be attained radiochemical separations are necessary

before counting.

For those still not familiar with what is involved in practice, the ex- perimental steps in a typical activation analysis may be re-stated.

1. Irradiate weighed quantities of the sample and standard in suit- able containers for a sufficient time to give adequate radioactivity in the element to be determined.

2. After irradiation, dissolve the samples and standards and add a known weight of the element being determined as carrier for the small

quantity that has been irradiated.
310 TRACE CHARACTERIZATION

3. Treat the solution in such a way that the carrier and the element

in the sample are in the same chemical form.

4. Carry out chemical separations to isolate the element (or a

suitable compound) free from all other radionuclides: i.e., until it is radiochemically pure.

5. Determine the chemical "yield" by any conventional method.

The fact that this step is included makes it unnecessary for the chemical separation in step 4 to be quantitative, since the final measured

activity will be corrected for losses, using the chemical yield figure.

6. Compare the radioactivity of sample and standard under identical

counting conditions, making correction if necessary for self-absorption,

dead-time losses, decay, etc.

7. Check the radiochemical purity of the isolated active compound

by measuring (a) the rate of decay, from which the half-life may be

obtained, (b) the activity through different thicknesses of aluminium,

from which an estimate of the energy of the rays or particles emitted

may be made, and (c) the gamma energy, using, for example, a scintilla- tion or solid state gamma spectrometer.

In certain favourable cases, steps 2 to 5 may be omitted.

Then the mass of X, the constituent to be determined, is obtained as

follows: Mass of X in unknown _ Total activity from element X in unknown

Mass of X in standard Total activity from element X in standard

B. Activating Agents and Irradiation Facilities

1. Slow Neutrons

There is no doubt that the most generally useful and available activat- ing source for high sensitivity in the determination of trace elements

remains the nuclear reactor with its abundant flux oi slow neutrons, and

because of the relative simplicity with which irradiations can be carried

out. The particular advantage of slow neutrons is that usually only one

nuclear reaction occurs (the n, y reaction, illustrated by ^^As(n, y)^^As)

and that the cross section for this type of reaction is often quite high.

Many tables have been published giving theoretical sensitivities attain- able, each author making his own set of assumptions about irradiation

time, time for chemical processing and/or counting, type of counter used

etc. Perhaps the most generally useful reference to give here is the

book of R. C. Koch [1]^ where are listed sensitivities for all elements

using several types of activating agent. For slow neutrons Koch defines

sensitivity as the mass in micrograms of the trace element which yields

1000 disintegrations/minute of activation product after irradiation in a

flux of 10^^ neutrons/cm^/sec to saturation or for a maximum period of

' Figures in brackets indicate the literature references at the end of this paper.
NUCLEAR METHODS 311

thirty days. The sensitivity for each element quoted by Koch for each

nuclear reaction available with thermal neutrons is assembled as Table 1. Individual users of the information can readily adjust the figures given

to fit in with reactor fluxes available to them. Perhaps the most serious

limitation of the sensitivities quoted in this table apply to those nuclear

reactions producing short lived nuclides. Again the individual user must

make his own allowance for the decay of such a nuclide during operations

following the irradiation such as transport, radiochemistry and counting.

Table 1. Sensitivity for thermal neutron reactions

Sensitivity in Element Nuclear reaction micrograms

Hydrogen 2H(n,7)3H 2XW

Lithium 6X10-6

Beryllium «Be(n,7)^«Be 1X10^

Carbon i3C(n,y)i4C 4X104

Sodium 23Na(n,y)24Na 2X 10-5

Magnesium 26Mg(n,7)27Mg 2X10-3

Aluminium 27Al(n,y)28Al 4 X 10-5 Sihcon 30Si(n,y)3iSi 2X10-3

Phosphorus 3iP(n,7)32p 6x10-5

Sulfur 34S(n,7)35S 4 X 10-3

36S(n,7)37S 4x10-1

Chlorine 37Cl(n,y)38Cl 7x10-5

Argon 36A(n,y)37A IX 10-3

40A(n,y)4iA 2x10-5

Potassium 4iK(n,y)42K 2x10-4

Calcium 4Ca(n,y)45Ca 7 X 10-3

48Ca(n,y)49Ca 7x10-3

4«Ca(n,y)4«Ca^4«Sc 7x10-3

Scandium 45Sc(n,y)46 + 46m 3 X 10-6

Titanium 50Ti(n,y)5iTi 2x10-3

Vanadium ^iV(n,y)52v 3 X 10-6 Chromium 50Cr(n,y)5iCr 5 X 10-5

54Cr(n,y)^5Cr 2x10-3

Manganese ^^Mn(n,y)5«Mn 1x10-6

Iron 5«Fe(n,y)5«Fe 1 X 10-2

Cobalt 5«Co(n,y)60"^Co 1x10-6

5«Co(n,y)6o + «om(^o 4x 10-5

Nickel «4Ni(n,y)65Ni 9x10-4

Copper 63Cu(n,y)64Cu 6x10-6

6^Cu(n,y)66Cu 3 X 10-5

237-323 0-67—20
TRACE CHARACTERIZATION

Table 1. Sensitivity for thermal neutron reactions— Continued

Sensitivity in Element Nuclear reaction micrograms

Zinc «4Zn(n,y)65Zn 1X10-3

6«Zn(n,7)69'"Zn 1X10-3

6«Zn(n,y)6^Zn 1X10-4

Gallium ««Ga(n,7)7«Ga 2X10-^

^iGa(n,y)72Qa 1x10-5

Germanium 70Ge(n,7)7iGe 3X10-5

^4Ge(n,y)75 + 75mQg 2 X 10-4

76Ge(n,y)77 + 77'"Ge 2 X 10-3

Arsenic ^^As(n,y)^6As 4 X 10-6

Selenium 74Se(n,y)^5Se 6x10-4

80Se(n,y)8^Se 9x10-5

80Se(n,y)8i'"Se IX 10-3

82Se(n,y)83Se 6 X 10-2 «2Se(n,y)83.83m3g^83Br 4x10-3

Bromine ^^Br(n,y)80"^Br 1x10-5

7^Br(n,y)80Br 5x10-6

«iBr(n,y)82Br 1x10-5

Krypton 82Kr(n,y)«3'"Kr 5x10-6

84Kr(n,y)«5"^Kr 4x10-4

86Kr(n,y)87Kr 2x10-3

Rubidium 8^Rb(n,y)8«Rb 6 X 10-5

87Rb(n,y)«8Rb 7x10-4

Strontium «4Sr(n,y)8^Sr 2X10-2

«6Sr(n,y)87'"Sr 2x10-4

8«Sr(n,y)8«Sr 2x10-2

Yttrium 8^Y(n,y)^«Y 2X 10-5

Zirconium ^4Zr(n,y)^^Zr 6x10-3

«6Zr(n,y)«7Zr 9x10-3

Niobium ^3Nb(n,y)'^4mNb 3x10-5

Molybdenum ^«Mo(n,y)'^«Mo 3 X 10-4

i«oMo(n,y)i«iMo 1 X 10-3

Ruthenium «6Ru(n,y)«7Ru 2x10-3

i«2Ru(n,y)io3Ru 2 X 10-4

io4Ru(n,y)io^Ru 2 X 10-4

Rhodium io3Rh(n,y)io4niRh 2X10-6

Palladium i<>8pd(n,y)'09Pd 1X10-5

iiopd(n,y)iiiPd 8 X 10-4

iiopd(n,y)iii'i"'"Pd^ ii^Ag 7x10-4

Silver io7Ag(n,y)io8Ag 1 X 10-6

io9Ag(n,y)iio"^Ag 2 X 10-4
NUCLEAR METHODS 313

Table 1. Sensitivity for thermal neutron reactions — Contmwedi

Sensitivity in Element Nuclear reaction micrograms

Cadmium ii^Cd(n.7)ii5"^Cd 2X10- 3 "^Cd(n.7)ii5Cd IXIO- 4 ii6Cd(n,y)ii""^Cd 3X 10--4 Indium ii3In(n,7)ii-i"^In 4X10-• 5 ^i=^In(n.y)ii^In 4X10-4

^iHn(n,y)ii6min 2X10-- 7 Tin i20Sn(n,y)i2iSn 7X 10--4 ^22Sn(n,y)i23Sn 4 X 10- 3 i2^Sn(n,y)i25mSn 3X10- 3 Antimony i2iSb(n,y)i22Sb 9x 10- 6 i23Sb(n,y)i2-iSb 1 X 10- 4 Tellurium i26Te(n,y)i2-Te 2X 10- 4 i28Te(n,y)i29Te 9x 10- 4 i30Te(n,y)i3iTe 5x 10- 4 i30Te(n,y)^3iXe^ 1311 5x 10- 4 Iodine i2q(n,y)i28I 6x 10- 6 Xenon i32Xe(n,y)i33Xe 7x 10- 4 i34Xe(n,y)i35Xe 2x 10- 3 Cesium i3=^Cs(n,y)i34mCs 2x 10- 3 i33Cs(n,y)i34Cs 5x 10- 5 Barium i30Ba(n,y)i3iBa 4x 10- 3 i=^6Ba(n,y)i37mBa 2X 10- 3 i38Ba(n,y)i39Ba 1 X 10- 4 Lanthanum i39La(n,y)i40La 5x 10- 6 Cerium i^oCe(n,y)i^iCe 3x 10- 4 i^2Ce(n,y)i^3Ce 4x 10- 4 Praseodymium i^iPr(n,y)i^2pj- 4x 10- 6 Neodymium i^6\d(n,y)i^"Xd 2x 10- 4 i48Xb(n,y)i49Nd 2x 10- 4 i50Xd(n,y)i^iXd^i5iPm 2x 10- 4 Samarium i52Sm(n,y)i53Sm 1 X 10- 6 i^^Sm(n,y)i55Sm 3x 10- 5 Europium i5iEu(n,y)i52m£^ 6x 10- S i53Eu(n,y)i54Eu 5x 10- 5 Gadolinium i58Gd(n,y)i59Gd 4x 10- 5 i«oGd(n,y)i6iGd 2x 10- 4 i60Gd(n,y)i6iGd^i6ixb 2X 10- 4 Terbium i-^^Tbin^y) 160Tb 4X10--6 Dysprosium i6^Dy(n.y)i6'^"^Dy 3X10-

i6^Dy(n.y)i6'^Dy 8X10--8

I
314 TRACE CHARACTERIZATION

Table 1. Sensitivity for thermal neutron reactions — Continued

Sensitivity in Element Nuclear reaction micrograms

Holmium i65Ho(n,7)i66Ho 7X10-7

Erbium ^68Er(n,y)i69Er 1X10-4

i70Er(n,y)i7^Er 3X10-^

Thulium i69Tm(n,y)i70Tm 2X10-6

Ytterbium i68Yb(n,y)>69Yb 6X10-6

i^4Yb(n,y)^75Yb 2X10-6

^76Yb(n,y)i77Yb 7X10-5

i76Yb(n,y)^^^Yb-^ ^^^Lu 7X10-5

Lutecium i^5Lu(n,y)i76mL^ 1x10-6

i76Lu(n,y)i77Lu 5x10-7

Hafnium i7'*Hf(n,y)i75Hf 8x10-5

'«0Hf(n,y)i«iHf 4x10-5

Tantalum i«iTa(n,y)i82"^Ta 2 X 10-3

i8iTa(n,y)i82Xa 2x10-5

Tungsten i«4W(n,y)i85W 3x10-4

i86W(n,y)i«7W 5x10-6

Rhenium i8^Re(n,y)i«6Re IX 10-6

i«7Re(n,y)i8«Re 1x10-6

Osmium i«oOs(n,y)i«i' i«i"^Os 3x10-5

i«20s(n,y)i«=^0s 8x10-5

Iridium i«ilr(n,y)i^2mjj. 5 X 10-7

'^'lr{n,yy^nr 8x10-7

i«nr(n,y)i«4lr 7x10-7

Platinum i«6Pt(n,y)i'^7Pt 3x10-4

i««Pt(n,y)i«^Pt 2x10-4

i«8Pt(n,y)i9«Pt-^i99Au 2 X 10-4

Gold i«7Au(n,y)i^«Au 5x10-7

Mercury i«6Hg(n,y)i«7' iTMHg 2 X 10-5

202Hg(n,y)203Hg 1x10-4

204Hg(n,y)205Hg 2 X 10-3

Thallium 203Tl(n,y)204xl 1x10-3

205Tl(n,y)206Tl 8 X 10-4

Lead 208pb(n,y)209Pb 0.2 Bismuth 209Bi(n,y)2io'"Bi 3x10-3

Thorium 232Th(n,y)233Th 9x10-6

232Th(n,y)233Th^233pa 5x10-6

Uranium 238U(n,y)239U 2x10-5

238U(n,y)235^U-^239Np 2 X 10-5
NUCLEAR METHODS 315

Now it may be asked why the Koch tables have been chosen to il- lustrate the sensitivities attainable by slow neutron activation rather

than the more modest lists available in some other papers or books.

The reason is that it is important in a conference of this kind that the

potential of a method is made clear, provided that the limitations are

too. A very great deal of the work pubUshed up to the present has been

done using fluxes of 10^- n cm~^ sec~^ i.e., where the attainable sensitivity

for each element is lower by a factor of 100 than is given in Table 1. Broadly speaking, apart from a few special cases, such irradiations have

been found extremely easy, indeed almost routine. Precautions needed

to deal with the total radioactivity of a batch of samples have been

minimal and it has been possible to irradiate most sample materials

without trouble. So, generally, it can be said that Koch's sensitivities,

reduced by a factor of 100, are currently regularly achieved or achievable except in special cases which include that involving very short

Hved nucHdes (say half lives of less than a few minutes). There have

been some successful examples of work in fluxes of 10^^ and 10^^ but

it must be reahsed that with these higher fluxes there may be severe problems of handhng the increased total activity of the irradiated sample,

necessitating quite a different order of laboratory facility, at any rate

for the preliminary stages following the irradiation. There wiU be

problems too in the type of sample material and container which can

be irradiated, but broadly speaking, there seems to be no reason why

the sensitivities quoted by Koch should not be attainable except in those cases where short half lives are the Umitation, where "self shielding"

is significant (see for example H0ghahl [2] and Kenna [3]) or where

nuclear reactions interfere. These latter two possibilities have been

clearly pointed out on many occasions. In particular any attempt to achieve high sensitivity by activation analysis for a trace impurity in a sample containing significant amounts of elements with atomic numbers

very near to that of the trace impurity element (or containing fissile elements in the case of interfering fission radionuclides) must recognise

the difficulty and make sure either that interference is insignificant or

that steps are taken to overcome it. Where the interference is due to nuclear reactions induced by the fast neutron component then a knowledge of the variation of flux with neutron energy in the reactor, and of

the cross sections involved, is necessary to make the calculation of the

extent of interference (see for example Durham [4] and Roy and Hawton

[5]). If such information is not available then measurement of the

extent of interference may be made by irradiation of the sample shielded

with cadmium. Often, such interference can be avoided by choice of

irradiation position in the reactor, but this usually involves a lower

available flux and hence lower sensitivity. In the case of secondary

reactions such as ^^Ge(n,7)^^Ge-^ > ^^As leading to the production,

from the matrix element, of the impurity element being determined.
316 TRACE CHARACTERIZATION

then there is httle if anything that can be done, other than accepting a lower sensitivity, except to make the best use of irradiation time. Ricci

and Dyer [6] have provided graphs showing calculations of this kind of interference for a range of cases. Pre-irradiation concentration of the

impurity is of course possible to avoid such difficulties and it may be

that in the future this will be done on an increasing scale in these

relatively few special cases, but it must be realised that this involves

the forfeiture of the major advantage that activation analysis has over almost all other analytical techniques i.e., the avoidance of the "reagent

blank".

With some types of reactor e.g., the TRIGA, it is possible to use

pulses of about 30 milliseconds per pulse which give bursts of slow neutrons with peak flux of 5 X 10^^. Lukens, Yule and Guinn [7] have shown

that this can be used to give increased sensitivity, in those cases where

direct identification by gamma spectrometry is possible, for radionuclides

of half life of less that about 1 minute.

At the other end of the scale laboratory neutron generators are now

available with thermal neutron fluxes of 10^ or maybe 10^. They may

be of some value for thermal neutron activation in the trace field though

sensitivitity is clearly limited by the low flux. Nevertheless the combination of thermal neutron and fast neutron activation for the modest

capital involved is very attractive and it would be very surprising if over

the next few years most reasonably sized analytical departments did

not consider installation of such a generator to be essential.

2. Fast Neutrons

Consideration was given earlier to the possible interferences in reactor thermal neutron activation analysis due to the fast neutron

component. Clearly from this it can be seen that there is the possibility

of utilising these fast neutrons in some cases for worthwhile purposes.

Yule, Lukens, and Guinn [8] have investigated this possibility by deter- mining the sensitivity of 35 elements with reactor fast neutrons. They

conclude that for 6 elements (O, Si, P, Fe, Y, Pb) the sensitivity is greater

using fast than thermal neutrons, and for 15 others it is only slightly less and may well therefore be superior in certain matrices.

The main interest in fast neutrons however stems from the original

work of Coleman [9]. In particular the possibility of the non destructive

determination of oxygen has led to a boom in the development and sale of commercial 14 MeV neutron generators. It may be argued that those generators at present available have usable fluxes too low to put

this technique really into the "trace characterisation" category. Strain

[10] gives a list of nuclear reactions and realistic lower limits of detection

for short 10 min) irradiations in a 10*^ flux of 14 MeV neutrons. Generally the sensitivity, defined as "based on spectral measurement

at a level of twice background" is from a few tens to a few hundreds
NUCLEAR METHODS 317

of micrograms for the elements N, O, F, Al, Si, P, Cr, Mn, Cu, Y, Mo,

and Nb. Nevertheless the use of samples of several grams puts the

detection hmits at a few to a few tens of ppm for the favourable elements

and because the list includes several of the lighter elements which are

difficult or impossible to determine using thermal neutrons, and give some difficulty with methods other than activation analysis, there has

been tremendous interest in this area. There are available now several

thorough compilations of gamma spectra, reactions involved and sensitivities achieved using neutron generators, one for example being that of Cuypers [11]. The fact that some of the nuclides produced, especially

that from oxygen, have half lives of a few seconds only, has spurred

designers to make available fast sample transport and rapid identifi- cation, measurement and read out of results for industrial use. Indeed some first class work has arisen on automatic computer coupled acti- vation analysis, both for reactor and neutron generator irradiations

at a number of laboratories particularly but not exclusively in the

United States. Further improvements in commercial neutron generators seem

possible; the recent development of sealed tubes has given prospects

of constant neutron flux over many hours and future developments

in higher flux availability seem encouraging — all this well within the

range of modern analytical instrument costs. There has been relatively little work on choosing the energy of neutrons for irradiations aimed at improved selectivity, but in some cases

this can be worthwhile. Steele [12] has shown some of the possibilities

recently. It seems clear that while this approach is likely only to be

used in a few cases, it is worth consideration where particular combinations of impurity element and matrix warrant it.

3. Gamma Photons

The pioneer work [13] and the continued eminence of the French

workers in this field must be mentioned. Not too many establishments

have available a betatron or linear accelerator giving, via bremsstrahlung,

a high flux of high energy photons. Even fewer can have access to such

machines for analytical purposes, but where this is possible then there

is a rich reward in the availability of sensitive determinations especially

of some light elements.

In general the threshold energy for the initiation of y,n reactions,

those used for much the largest part of work in this area, lies in the

region 10-20 MeV for Hght nuclei falhng steadily to 7-10 MeV for the

heavier elements. Similarly the maximum cross sections occur for gamma energies falling from 20-25 MeV for hght elements to about 15

MeV for others, with values ranging from a few millibarns to a few

hundreds of milhbarns [1, 14], so, with electron currents of up to 50 /xA

available in some linear accelerators, it is possible to obtain sensitivities
318 TRACE CHARACTERIZATION

for some elements well below the microgram level. Schweikert and

Albert [15] and Baker [16] give sensitivity calculations and Table 2 is taken from Baker's paper. Again these sensitivities have been calculated for ideal systems free from interferences but are reaUstic when

using a large hnear accelerator under the following conditions:

Accelerator parameters 5 ptA, 30 MeV electron beam 1 mm tungsten

radiator. Sample position 10 cm. behind

radiator.

Irradiation time One half life of induced nucHde or one hr., whichever is shorter. Counting time Immediately following irradiation, for one

half life or one hour, whichever is shorter. Counter Well-type Nal crystal with discriminator set

at 100 keV.

Limit of detection Defined as that weight of an element which

will give a count equal to twice the standard

deviation on the background count, the latter being taken as 120 c/m.

If chemical separation is required before counting then of course the

sensitivity must be halved for each half life delay. (Half lives of under

10 minutes are underlined.)

Albert [17] and Engelmann [18] have given details of much of their

work which was concerned mainly with the determination of light ele- ment impurities in beryllium and other metals non-destructively i.e., using decay measurements only (the products of y, n reactions decay

mainly by positron emission). Carbon was however separated by combustion in oxygen followed by trapping out the carbon dioxide formed, for counting. Although Albert [17] mentions a chemical separation of

nitrogen as ammonia, following gamma irradiation, Engelmann [19] in a

later paper says for nitrogen "no separation with a good and reproducible

yield has been found". Baker [16] at Harwell has used rapid radiochemical separations for both carbon and oxygen. For carbon in metals,

e.g., in molybdenum and in steels, a combustion and trapping method

was used giving figures for steels in good agreement with published

values down to 10 ppm and he quotes a limit of detection of better than

0.1/xg. For carbon in ceramic materials such as MgO and CaO, a borax

flux was used at 1250 °C in a stream of oxygen to evolve the carbon as dioxide. In this case however, due to the high oxygen content, there is interference from the reaction ^^0(7,nQ:)"C which can be eUminated

by reducing the energy of the gamma photons used in the irradiation

below the threshold value of 25.8 MeV, resulting in a rather poorer

sensitivity but still better than 1 /ig. Baker has determined oxygen in matrices such as Fe and Mo which themselves give rise to short lived

activities making it difficult to differentiate ^^O by simple decay measurements. He used a separation based on vacuum fusion in an iron bath
Table 2. NUCLEAR METHODS 319

Sensitivity for gamma activation

Nuclide Half life of Limit of detection y,n product

20.3m 0.01

14N 10.05m 0.01 160 2Jm 0.04

19p 1.87h 0.05

20Ne 0.3 23Na 2.6y 200

0.3 27A1 6.55 0.2

28Si 4.25 0.2 3ip 2.6w 0.05

2.65 0.3 35C1 32.4m 0.08

39K 7.7m 2.0 4«Ca 0.9s 1.0

46Xi 3.1h 0.1 42m 0.1 55Mn 278d 20

54Fe 8.4m 0.2 ^^Co 9h 0.02

58Ni 37h 0.2 9.8m 0.001

^Zn 38m 0.01

75 As 18d 2 6.4m 0.1 18.7d 3

70m 0.03

89Y 105d 7 4.4m 0.01 93Nb 10.2d 0.02

«2Mo 15.5m 0.2 210d 10

107Ag 24m 0.02

ii3in 14.5m 2

3.5m 0.02

127J 13d 0.4

i8ixa 8.1h 0.01 Au 9.5h 0.02

Limit reported

in literature

0.01 fjig in Be

0.1 fjig chemical sep'n

1 ppm in pure Be

1 ppm in pure Be

1 /Ltg chemical sep'n

0.1 fjig in Hf

0.1 jLtg in Bi

1 A^g
320 TRACE CHARACTERIZATION

in graphite at 2000 °C and subsequent purification of oxygen activity by

passing the gas evolved through two copper oxide furnaces, one at 600 °C to oxidise CO to CO2 without loss of radioactive oxygen, the

second at 1100 °C retaining > 99% of the ^^O without contamination by

^^C or other activities. This separation can be carried out in 4 minutes

with a limit of detection better than 1 /xg. There is no doubt that gamma photon activation is a very powerful

complementary technique to reactor thermal neutron activation. While

not having sensitivity quite as high for some elements it competes in several cases and excels in some vital ones such as carbon, oxygen,

nitrogen and fluorine. While it has the disadvantage of producing mainly

positron emitting nuclides, so that gamma spectrometry cannot be as useful as it is for neutron activation, there is, to offset this, the elimination of self shielding problems so that it becomes possible to measure

impurities in high neutron absorption cross section matrices such as boron, tungsten, cadmium, hafnium, etc. Perhaps the only other variety of gamma photon activation worth

present mention in the context of trace characterisation is that instead

of measuring induced radioactivity, the neutron product itself may be

measured. This has usually only been done for the two y, n reactions

whose threshold energies are so low that the reactions can be effected

by y photons from radionuclides. Thus the ^Be(y, n)^Be reaction with

a threshold energy requirement of only 1.67 MeV has been made the

basis for measuring quite small quantities of Be using ^^^Sb or ^^Y as sources, and deuterium has similarly been determined using

or 2'*Na as y sources. The use of the Mossbauer effect to give information on chemical

structure, bonding, etc., might be classified under this general heading

of gamma irradiation and absorption, but at this juncture it seems best

to regard this as a promising technique for future development.

4. Charged Particles

Historically, charged particles were second only to thermal neutrons

in being used for activation analysis. The reason they appear as fourth

in the order in this paper is because they have a major limitation and

yet perhaps a benefit. This reason is that charged particles can penetrate only relatively short distances into matter. Activation therefore

takes place only very near the surface of an irradiated sample. The

benefit of this can be seen as an ability to analyse surfaces and if such

layers can be removed mechanically or chemically, then that ability

extends to the analysis of layers through a sample. The possibility

of irradiating very small areas of a surface by a beam of charged particles

also exists so that location of a trace element is in principle available.

However, the high heat dissipation occurring if large beam currents are used may be a limitation.
NUCLEAR METHODS 321

Nevertheless a variety of charged particle methods has been de- veloped, especially for light elements that cannot conveniently be de- termined by thermal neutrons. If low energy charged particles are used then the nuclear reactions occur mainly with the light elements,

but as particle energies are increased the problems of nuclear inter- ference become more acute. Standardisation is also complicated by

variations in stopping power as the matrix composition alters. Particle energies of 1 MeV or less can be obtained conveniently with

a Cockcroft-Walton voltage multiplier; Van de Graafif generators provide

higher energies (6 MeV for a single stage machine), while yet higher

energies require multiple stage Van de Graaffs, cyclotrons or linear accelerators. Until recently there has been Uttle development of charged particle

machines solely for analytical purposes, but Markowitz and Mahoney

[20] have proposed a small cyclotron for ^He particles of 8 MeV, be- cause they suggest that by using such particles very sensitive methods

are available for a number of Hght elements. It has also been pointed

out by Ricci [21] that if a 100 /LtA beam of 10 MeV ^He ions impinges on a thick lithium, beryllium or boron target there would be available

a neutron yield of from 2 to 4X10^^ n/sec, comparable with that ob- tained from an ordinary neutron generator; and although the neutrons would not be monoenergetic, choice of target material could give some

control over neutron energy and hence to some extent over the nuclear

reactions with different elements involving those neutrons. Ricci

makes the following conclusions about ^He activation: its advantage is that the detection hmits for low atomic number elements, using a 100

beam of up to 10 MeV ^He ions, lie in the range from parts per million

to parts per thousand milhon; its disadvantage is that ^He reactions

with several elements and with comparable sensitivities lead often to the same nuclide and thus interferences may be important in matrices

containing two or more low atomic number elements.

Results of work on other charged particles are somewhat difficult to classify succinctly because of the variety of particles and energies

involved but the same disadvantages noted for ^He are apparent. Engel- mann in two papers [18, 22] gives a useful summary of the situation

for hght elements:

(1) Using a 10 /xA/cm^ beam of 44 MeV alpha particles the estimated

sensitivities for carbon and oxygen are 10"^ ppm and 10"^ ppm with

chemical separation of the ^^C and ^^F respectively.

(2) 10""^ ppm of nitrogen or boron can be detected in any material

after irradiation with protons in the 6-15 MeV range by separating

^^C. But as ^^C is the product of such an irradiation from both ele- ments the method is non-specific and recourse must be made to using

the different energy dependence of the two nuclear reactions involved.

By reducing the proton energy to less than 5 MeV the process becomes
322 TRACE CHARACTERIZATION

more selective for boron, which can be determined in materials containing N/B s£ 100 but sensitivity is reduced by a factor 100, and of course penetration depth is reduced too. By increasing the energy

to 20 MeV, nitrogen gives 3 times as much ^^C as does an equal mass

of boron.

(3) Non destructive determination of nitrogen and boron is possible in beryllium, silicon and tantalum, with sensitivity of 0.1-1 ppm

for a 10 jjiA beam (presumably with the same limitations as in (2) above).

Koch [1] lists values for sensitivity and the nuclear reactions involved

for many elements but in view of the competing reactions mentioned

above it hardly seems worthwhile quoting each one here.

Charged particles emitted as a result of reactor neutron irradiation can occasionally be used, for example the sequence ^Li(n,Q:)^T,

^^0(T,n)i^F has been used with moderate sensitivity for determination

of oxygen by irradiation of the powdered sample mixed with a lithium

compound. Other reactions are available [23] such as ^^0(p,n)^^F

for determination of ^^O using recoil protons from hydrogen containing

matrices or ^^C(d,n)^^N for determination of deuterium in deuterated

organic compounds.

In summary then the position on charged particle activation analysis

is that high sensitivity, especially for light elements, is available, that the technique is especially useful for surfaces or thin layers (this may

of course be a restriction, too) but that great care is needed to ensure

specificity. For the future it seems that small cyclotrons may become

available especially for ^He work, that variable energy cyclotrons with

their high beam current and selective energy choice may play an in- creasingly important part, and that prospects of scanning by use of

coUimated beams are hopeful, especially in cases where prompt counting

is possible. C. "Prompt" Radiation Techniques

There have been only sporadic attempts to measure the "prompt"

radiation emitted with the sample in its irradiation position. Although

this approach to activation analysis has the disadvantage that there is no opportunity for chemical separation before counting, nor even the

possibility of etching to remove surface contaminants once the sample

is in position, and requires a counting method of high specificity, nevertheless there are some potential advantages which make consideration

of the general approach desirable.

Prompt techniques permit the radiation emitted during decay of very

short lived excited nuclear states to be counted rather than of the

radioactive nuclides of "finite" half life used in conventional activation

analysis. As an example, if ^^O (stable) is irradiated with low energy

deuterons a d, p reaction forms ^^O, also stable. But the ^^O is formed
NUCLEAR METHODS 323

in an excited state which reaches the ground state by rapid emission

of a 0.87 MeV gamma photon. These gamma photons, the so called "prompt radiation" can thus be counted during the irradiation and used

as a measure of the ^^O present in the irradiated sample. In principle

the method is therefore faster than conventional activation analysis

because the counting is done during the irradiation rather than after it. Again, the irradiation can be carried on as long as necessary to give a

statistically useful count, saturation activity being reached almost

immediately after the irradiation is started. Using low energy charged particles with all their disadvantages (listed

earlier) rather than penetrating radiations such as neutrons, in order

to simplify the radiation measurement. Pierce [24, 25] has shown some

of the possibilities for determining carbon, oxygen and boron using

Van de Graaff and Cockcroft-Walton machines. For carbon he used

(1) 1.5 MeV deuterons for the reaction ^'^C(d, p)^^C measuring the 3.09

MeV gamma photons from the excited state of ^^C, (2) 0.8 MeV protons

for the reaction ^^C(p, y)^^N measuring the 2.3 MeV first excited-ground

state gamma ray from ^^N (and not using the radioactivity from decay

of the 10 min half life ^^N — > '^C) (3) ^He ions for the reaction

'2C(^He, p^^N measuring the 1.64 MeV gamma ray from excited ^^N. AU three approaches showed that determination of carbon in steel down

to a few hundred ppm was feasible within a few minutes, the most con- venient being the deuteron irradiation. Similar conclusions were

reached for oxygen and boron and although the levels reached in any

of these examples hardly qualify the technique to be included yet in the "trace characterisation" class, the future possibility exists of rapid, on stream measurement and, with modern high current accelerators,

of improved sensitivity. In addition the possibility of scanning, mentioned earlier can now clearly be seen. Prompt or 'capture' gammas have also been used from neutron irradia- tion and Greenwood and Read [26] Lussie and Brownlee [27] and

Isenhour and Morrison [28] have discussed possibilities, the latter using a modulation techique with a fast chopper in a thermal neutron

beam from a reactor. They also make sensitivity calculations for ther- mal neutrons, their conclusion being that while sensitivity by measuring

prompt gammas is inherently better if the same neutron flux is used for each, where neutron beams are used with a consequent large drop in available flux then of course the prompt technique loses in proportion.

Even here however, with a drop in flux of a factor of 10^, sensitivity for ten elements is as good as or better than that by delayed gamma ray

activation analysis (B, Be, C, Cd, Fe, Gd, H, P, Nb, Ti). D. Radiochemical Separations

In spite of the impression that is often given in some quarters that anyone now using radiochemical separations in activation analysis is
324 TRACE CHARACTERIZATION

rather out of date, it remains a fact that in the majority of high sensitivity appHcations, such separations are still essential. Indeed as far ahead as can reasonably be predicted they will be needed, perhaps on

a decreasing scale as improvements in resolution of detectors are developed.

Separation schemes can be very simple involving perhaps only the

removal of much of the major activity component; alternatively, the

separations can be made groupwise, and both such approaches are usually followed by gamma spectrometry to obtain final specific measure- ment of each individual nuclide. Occasionally and especially where

the highest possible sensitivity is aimed for, or where nuclides concerned

are pure beta emitters, really thorough radiochemical purity of each

element is sought so that beta counting with its very low background, can be used. It is worth restating, in an era of heavy spending on instru- mentation, that any analytical chemist wishing to get started in activation analysis can do so with an expenditure of only a few hundred

pounds sterling, provided he is willing to do a little chemistry after his sample is irradiated.

Broadly speaking, it is now possible to devise a radiochemical pro- cedure to separate any single element from any combination of others

given adequate time. The series of monographs on the radiochemistry

of the elements, issued by the U.S. National Academy of Sciences

Sub-committee on Radiochemistry, is an excellent reference set for which all who use it are grateful to its various authors and especially

to Wayne Meinke as chairman of the originating sub-committee. It would

be quite impossible to condense usefully the wide range of available

separation schemes, but there is still scope for ingenuity especially in finding rapid methods for use with short lived radionuclides. Separation

of nuclides with half lives of a minute or two is fairly commonplace

now, and perhaps the stumbling block to further advance is in the

process of dissolution, especially of refractory materials; we are still searching for the universal solvent — and its container! Direct fluorina- tion with subsequent gas phase separations may prove helpful, cer- tainly there will have to be a move from the conventional methods of

attack on materials; high temperatures and pressures with containment

of vigorous reactions may be an approach. One recalls in the present

surroundings the still very useful but unconventional procedure of

Wichers, Schlecht and Gordon [29] for dissolution of refractory platiniferous materials.

Automatic separation methods are now becoming available and it needs but little imagination to visualise the extension of automatic transfer, activation and counting, at present used nondestructively, to include

a further step of automatic radiochemical separation provided the sample

material can be dissolved fairly simply. Girardi [30] and Samsahl
NUCLEAR METHODS 325

[31] and others have already introduced automation into radiochemical

separations elegantly and effectively. E. Instrumentation

This is but a brief picture of the position on detectors, analysers,

computers, etc.. used in the final stage of an analysis by activation,

though mention might be made briefly of the use of computers to cal- culate optimum conditions for irradiation of a given sample too [32].

The most widely used detector in activation analysis is the sodium

iodide crystal, on which is based gamma ray scintillation spectrometry

with multichannel pulse height analysers, and there are available several compilations of spectra enabUng identification of unknowns [e.g.,

33] . The problem of identifying the components of a complex spectrum

has led to the use of computers to make the best use of the data avail- able and there are many reports on how this is best done [e.g., 34].

Suffice it to say that it has been the growth in these spectrometric

techniques which over the past 10 years or so has led to the intensive use of nondestructive activation analysis, with very rapid turnover of samples for which the approach was feasible. So here again can be

seen one of the advantages of activation analysis in some cases — that

of speed of availabiUty of results. Over the last year or two there has arisen the possibility of very much

improved resolution of individual peaks in the spectrum due to the re- placement of the sodium iodide detector by the lithium drifted ger- manium detector. Whereas the former might have a resolution (defined as peak width at half maximum height divided by centre-peak

energy) of say 7% for the 660 KeV gamma ray of ^^"Cs the recent developments in germanium detectors give possibilities of resolutions as good

as 0.1%. This is having a dramatic effect in the field of activation

analysis as might be expected and already examples of applications are appearing [35] . There seems to be no doubt that a great leap forward

will occur in activation analysis exploiting the possibilities of these detectors comparable to that generated say 10-15 years ago in the move

from simple /3 counting to sodium iodide scintillation spectrometry.

But the present limitations of semi-conductor detectors must be rec- ognised: (a) the detectors must be operated at liquid nitrogen temperature, (b) the volume of the detectors is rather limited and hence the

efficiency of counting gamma rays is significantly less than with sodium

iodide, particularly at higher energies (for example a 5 cm^ detector had

1/100 the efficiency of a 3" X 3" Nal crystal at 200 KeV, l/200th at 1 MeV and l/500th at 5 MeV [35]), (c) distinctly improved electronics

are needed for full utilisation. Higher sensitive volumes are however

becoming increasingly available, for example 50 cm^ detectors are now

being used [36] with very much improved efficiencies, so that there is no doubt the new detectors will be extremely important.
326 TRACE CHARACTERIZATION

The increased resolution leads to the desire to have a far greater number of channels available in the pulse-height analyser in order to make

full use of all the information available. There seems in fact to be a trend away from pulse-height analysers to small computers with their

greater versatility and decreasing comparative cost, the bigger computers then being used for complex programmes (as at present) using

the information then obtained.

Coincidence techniques using sodium iodide counters continue to be of value in specific cases [37] and this of course will also apply to the semi-conductor detectors though there are several practical dif- ficulties with the latter, not only that of low efficiency. F. Accuracy and Precision

The main errors which can arise in activation analysis are those due

to self shielding, unequal flux at sample and standard position, inac- curate counting procedures (e.g., differences in self scattering, self absorption, geometry between sample and standard), and of course

counting statistics. Any experienced devotee of activation analysis

knows that errors from these sources can be reduced to levels that are unimportant in most instances. Rather few papers are published

however which demonstrate this fact; occasionally some papers demonstrate the reverse, upon which the experienced devotee usually considers he knows why. One reason for the paucity is the virtual absence

of homogeneous "standard samples" in which the impurities occur

at the desired low level and whose trace element content is known

accurately. A generlisation might be attempted that where no special

difficulties of competing nuclear reactions or self shielding occur, and

where enough activity is finally available to make counting statistics reasonable, then in most cases the accuracy and the precision could

be much better than ± 10%.

G. Position of Activation Analysis Relative to Other 'Trace

Characterisation" Methods

It is either brave or foolhardy to make comparisons of this kind on

a general basis. So much depends on the type of material to be analysed, the individual elements to be determined etc. But if a large

programme were to be postulated requiring the determination of forty or fifty trace impurities at levels of 10 ppm or less, each in a matrix

say of some ceramic containing six major elements, what part would

activation analysis play, assuming the analytical laboratory concerned

had aU available resources?

It would be very surprising if activation did not play some part.

Almost certainly it would be used to supplement results on given elements

from other techniques in an aim to provide a few samples whose impurity levels could really be said to be known. For a few elements
NUCLEAR METHODS 327

at very low levels activation and mass spectrometric isotope dilution

might be the only two approaches with adequate senstivity. But once

good standards were available it might be thought that spark source mass spectrometry (or its successor) would take over the bulk of the

determinations for routine use, leaving perhaps only a few which, per- haps because they were at levels too low for that technique, would be

tackled regularly by activation analysis.

This opinion may cause surprise, but the conditions leading to it must be remembered. There will certainly be specific examples of

materials and trace impurity requirements where automatic activation

analysis of one kind or another will be the choice, but the method has

competitors and this Conference is designed to make each one of us

learn that that applies to every technique discussed.

III. Analysis Using Radioactive Tracers

A. Introduction

The adoption of radioactive tracers to avoid the necessity for quantitative separations in conventional methods of analysis has been sur- prisingly slow. It seems inconceivable to the experienced radiochemist

that someone trying, for example, to separate microgram quantities of elements such as molybdenum, niobium, tantalum, and tungsten prior

to their determination by spectrophotometry or polarography, should

not check on the efficiency of the separations involved by the very simple

technique of adding a measured volume of a tracer to his starting so- lution and counting a measured volume of his final solution. The

equipment needed costs very little, the tracer solutions are no more

expensive than reagents and the laboratory facilities needed are no more

complex than are required for such a conventional determination any- way. And for such a small investment, the return is complete insur- ance against losses of the particular element at all stages subsequent

to the addition of the tracer. Perhaps inorganic chemistry is too quantitative and every separation can be guaranteed. Even if that is so then the experience gained in using the general technique and equipment would surely be of value

as a basis for further adventures into the use of radioactive tracers

for c^e^ermmm^ elements or even for activation analysis.

It is aU too common to find analytical laboratories pleading that they

cannot use activation analysis because they have no reactor in the

locahty. Even though that excuse is becoming more difficult to use with

the spread of reactors, very often it turns out that the same laboratories

will not use radioactive tracers either, when such tracers are as readily

available as normal reagents.

Methods using tracers for determining elements can be broadly di- vided into two types. One type uses a radioactive tracer of the element
328 TRACE CHARACTERIZATION

to be determined (isotopic labelling), the other a tracer of a different element from that being determined (non isotopic labelling). Although

many fancy names have been given to slight variations in each tech- nique (perhaps the use of such fancy names has been one of the reasons

for their relatively httle use?), the broad principle is clear in each case. In iostopic labeUing methods the principle is that if a fraction of the

element to be determined can be isolated (that fraction being determined

by measurement of radioactivity) and if the mass of the element in that fraction can then be determined either by some conventional measure- ment technique or by reacting with an equivalent amount of a reagent,

then the original mass of the element can be calculated. (This is a complicated way of saying that a radioactive tracer is used to correct

for an inefficient separation in a conventional determination!) There

are some extensions of this broad approach designed to avoid the conventional measurement step and they will be dealt with later. In non-isotopic labelling methods the principle is, simply, that pro- vided the element to be determined can react in some quantitative manner with a known excess of a second material, the latter being labelled,

and provided the fraction of the second material thus released can be

measured via its radioactivity, then the original mass of the element can

be calculated. In addition to the two broad types just outlined there is a third ap- proach which incorporates points from both types. This third approach

is usually called "radiometric titration" and involves following the course of a titration either with a labelled titrand, a labelled titrant or a labelled indicator element. The measurement of the change of radioactivity within the system involves a phase separation.

McMillan [38] has recently written a very clear review of all these

techniques, especially from the viewpoint of trace element determinations and his classification has been used in the remainder of this section.

B. Isotopic Methods

All the methods in this class depend on the fact that the specific

radioactivity of a given element is, by definition, inversely proportional

to the concentration of the inactive element, and the various methods

differ only in the manner of using that proportionality.

1. Single Isotope Dilution

The principle here is the simple one already mentioned in section A

above and it seems a pity to complicate matters by explaining the

principles mathematically.

On mixing a radioactive tracer element with its inactive isotopes,

clearly the overall specific activity is reduced.
NUCLEAR METHODS

If the specific activity of the tracer is So and by definition

329

(1)

where Ao is the radioactivity of a weight Wq of the tracer element, then

if activity Ao is added to a sample material containing a weight Wx of

that inactive element, the new specific activity will become

Now Sx can be measured by recovering (and measuring) a pure fraction

W2 of {Wo-\- Wx) and measuring its activity A-z Then r.= ro(J-l) (3)

If Wq is small compared to Wx

then Wx=W2~ (4) A2

In trace element analysis the main difficulty in applying this method

is that of measuring W2, (and as W2 is always smaller than Wx, one might

ask in fact, is it not easier to measure Wx directly and cut out aU this radioactivity nonsense? The answer is that one imagines that this method will only be used where quantitative separations are not readily

possible).

It was to overcome this problem of measuring W2 at very low levels that the method known as Substoichiometric Radioactive Isotope Dilution Analysis was introduced.

2. Substoichiometric Isotope Dilution

In this method equal partial amounts of the element being determined

are removed both from the tracer solution and from the tracer + sample

solution. The radioactivity in each, Ao and Ax respectively, wiU be

directly proportional to the respective specific activities, so that equation

(3) may be rewritten

The problem then becomes one of removing exactly equal amounts

of the element from two solutions of different composition, and possibly

different volume and containing different amounts of the element. Ru-
330 TRACE CHARACTERIZATION

zicka and Stary, in a series of papers, mainly in the journal Talanta, have

used the principle of substoichiometry to solve that problem, i.e., they

add equal substoichiometric quantities of a suitable reagent to each solution, that reagent then reacts stoichiometrically and the product of the

reaction is separated from the unreacted element in each case. Ruzicka

and Stary [39] concluded that only two types of reagent are suitable for

this technique at the submicrogram level, the first type comprising those

organic reagents forming complexes with high extraction constants and

therefore easily separable from the unreacted element by solvent ex- traction, e.g. dithizone and cupferron; the second, those reagents forming complexes with high stability constants that are readily separable

from unreacted elements by ion exchange, e.g., ethylene diamine

tetraacetic acid. Several elements including Cu, Hg, Ag, Zn, Fe, In, have been de- termined by methods such as these, usually in model experiments, some at levels as low as 10~^ and 10~^^^

g. With practical materials

the question of interferences arises and selectivity must be obtained,

e.g., by masking or preseparation.

Of course a major limitation in these methods is the reagent blank, a factor common to all analytical methods requiring the use of chemical

reagents, except activation analysis. For example a recent paper on

the use of substoichiometric isotope dilution to determine zinc in ger- manium dioxide mentions a reagent blank of 1 jjig zinc. But this dif- ficulty though it must be recognised must not be allowed to obscure

the possibilities of this quite promising method.

There have been additional variants on this substoichiometry theme,

for example DeVoe and his colleagues [40, 41] have suggested "double

radioactive isotope dilution" and "double substoichiometric isotope

dilution" but for a discussion of these either the original papers or the

review by McMillan [38] should be consulted. The same workers have

suggested the use of differential controUed-potential coulometry in iso- tope dilution. Clearly the problems and possibilities are being given

the broadest consideration by those workers and already some ingenious

approaches are being studied.

3. Isotopic Exchange

Reactions of the following type are used in this method

M*X + MY-^ (M, M*)Z + (M, M*)F

and MX+ M*Y^ {M, + M*)Y

MX and MY must be easily separable for example by solvent extraction, and the most strongly complexing ligand must be associated stoi- chiometrically with one portion of M prior to exchange.
NUCLEAR METHODS 331

If the amount of M associated with F, [M\y is unknown and that with

[M\x is known, then

{Ml

(D.

where {Dm*)s is the distribution of M* between the organic solvent and

the aqueous phase assuming MX is the extractable species.

To illustrate the method the example of the determination of iodine

in natural waters may be quoted [42]. Iodine tracer is added to the

water and after conversion of all forms of iodine to elemental iodine, an extraction into benzene is made. (The fact that up to this stage re- covery need not be quantitative as any loss can be corrected for by

determining the tracer yield at this point is incidental). The iodine in the benzene is then allowed to exchange with a known amount of iodide

in aqueous solution: —

I* + 1-^(1, P)2 + I*- The quantity of iodine originally present in the water sample can then

be evaluated from the distribution of the tracer together with the weight

of iodide used. At least 1 /^g iodine/litre of water can be determined

by this method. Perhaps it is worth saying at this point that iodine is a

tricky element for isotopic methods because of its rather complex

chemistry, and it must be clearly understood that in these methods,

for determining elements, before any separations are made, all the ele- ment including that in the tracer must be in the same chemical form.

The remarks made earher in section 2 about sensitivity attainable

and reagent blank Hmitations apply equally to this method.

C. NoN-isoTOPic Methods

These methods depend on the fact that the mass of an element is related to the activity derived on its reaction with a labeled reagent. In fact the group of methods is sometimes called "Radioreagent

Techniques".

1. Isotope Derivative and Derivative Dilution

Here, the element to be determined is made to react quantitatively

with a labelled reagent of known specific activity to form a compound

which can be separated and counted. If the recovery is quantitative

then the amount of the element being determined.

Or where ^4^ = activity of compound formed

Sr = specific activity of labelled reagent

and £ = ratio of equivalent weights of the element and the reagent.

237-323 0-67—21
332 TRACE CHARACTERIZATION

For this method to be successful there are two requirements; first to ensure that the reaction is quantitative by choosing the proper re- agent and conditions; second to recover the radioactive compound in a known yield. This latter may be done in any of three ways,

(1) by making the separation completely quantitative

(2) by adding carrier quantities of inactive product and correcting

for loss on the basis of chemical yield

(3) by adding a quantity of product labelled with a different tracer and

correcting for losses radiometrically.

The distinction between "isotope derivative" and "derivative dilution"

methods is that the former uses only (1) above while the latter, which

has been used exclusively in organic analysis so far, uses (1), (2), and (3). Some quite sensitive applications of the isotope derivative method

have been reported, especially in combination with paper chromatography. Welford [43] has briefly reported separation and determination

of less than 0.01 /tg of Pb, Ca, Sr, and Ba using S-35 labelled sulphate

as a spraying reagent, and less than 0.001 fig Be and Zr using ^^P- labelled phosphate. Location of the individual elements on the chromatogram before spraying with labelled reagent was done very neatly

by using two separate sample aliquots to one of which radioactive tracers

for each element had been added and then running the two chromatograms side by side. Welford makes the statement that all elements

which can be isolated chromatographically can be determined at these

low sensitivity levels, so the potential is clear. Though still subject

to reagent blank problems the technique has such simplicity that it seems possible these may be reasonably controlled.

2. Isotope Displacement

This technique uses the differences in stability constants of the complexes of a series of different elements with an organic reagent. Thus

an unknown amount of an element forming a complex of high stability

with a particular reagent will release a proportionate amount of activity

from a labelled complex of that reagent of lower stability. Provided

that the released activity can be separated from that remaining as the

complex, then the amount of either can be used as a measure of the mass of the displacing element.

An example is the determination of as little as 0.1 /i-g of mercury by

displacement of silver-llOm from its di-zi-butyl phosphorothioate complex [44]. The same paper also describes the use of an isotopic exchange

method for mercury, using the same reagent, this time labelled with

Hg-203 and makes some interesting observations in a comparison of the

two methods, each having its advantages and disadvantages.

3. Radiorelease Methods based on this technique depend on the release of a radioactive

species from a labelled material when this reacts chemically with the
NUCLEAR METHODS 333

trace element and may or may not be isotopic with the material carrying

the label. The trace element may react directly or indirectly to release

the radioactivity. Of course the reaction which does occur must be

highly selective and sensitivity is achieved by using a high specific

activity tracer. The technique has been used mainly for trace elements in water and in gases. Examples in the water field are the determination of added inactive

vanadate or dichromate in water tracing work, but could be applied

generally to the elements vanadium or chromium. Silver labelled with

Hom^g reacts in acid solution with vanadate [45] or dichromate [46] to release silver ions, the reaction is stoichiometric and the released activity

is readily measured. Clearly the reaction is not specific, although for these water tracing purposes, masking of naturally occurring inter- ferences such as chloride and iron was possible. Sensitivities of 0.1 /xg/ml and 0.01 /u-g/ml for vanadate and dichromate respectively were

reached.

A similar example though to a direct problem, is the measurement of dissolved oxygen in water by reaction with labelled thallium where very

high sensitivity is potentially available. The gas analysis methods usually rely on the release of krypton-85

from a clathrate compound, or from the surface of a material such as copper which has had krypton-85 implanted or diffused into it. These methods are all highly sensitive but not usually specific.

However in simple cases they are very useful and have the advantage

that they can readily be adapted to automatic operation.

D. Radiometric Titration

This method, as explained earlier, spans both the isotopic and nonisotopic methods and depends on using changes in radioactivity within

the system to follow the course of a titration. A labelled titrand, titrant or indicator may be used; in fact more than one species may be titrated and more than one titrant used, with, perhaps, different tracers being

employed for the different stages. Measurement of the activity requires

a phase separation such as precipitation or solvent extraction, though

the former is hardly applicable to trace element analysis. Using chelate

extraction, cobalt and zinc have been determined at 0.1 /itg levels but in general the method has not played a very important role.

E. Assessment of Radioactive Tracer Methods

It seems inevitable in trying to assess the "state of the art" in tracer methods that there should be comparison with activation analysis. The

freedom from reagent blanks makes the very high theoretical sensitivity of activation analysis readily attainable on a practical basis in straight-
334 TRACE CHARACTERIZATION

forward cases, and it would usually be the preferred method assuming

availability of irradiation facilities. Nevertheless there are perhaps two broad reasons for the continued

interest in tracer methods. One is that tracer methods offer a real alternative in cases where activation analysis runs into difficulty. For

example activation analysis may be unsuitable where sensitivity is very

low either because the cross section involved is low or the induced activity is of very short or very long half life; or where the bulk material

of the sample has such a high cross section that severe self shielding

would occur; where the overall radioactivity of the irradiated sample

is too high for the facilities available; or where interfering nuclear

reactions prove limiting. The other reason is that tracer methods are very simple in practice, and require only low cost equipment usually. In fact this has led to the applications in automatic instrumentation as mentioned earlier. So it could be predicted that most analytical lab- oratories should take up these tracer methods if only as an introduction

to radioactivity. Once confidence had been gained then the laboratory

personnel would be able to make a balanced judgement as to when

to proceed to the further investment needed for activation analysis.

F. Avoidance of Analysis by Means of Tracers

Many requests for analysis arise from research in other departments

involving processing operations, for example purification of a commercial

starting material to produce a high quality product. Usually the starting

material and the product are submitted to the analytical department for analysis for the trace impurity elements of interest, in order to measure

the extent of the success of the purification. Analysis of the impure

starting material is usually fairly easy because of the relatively high

level of the impurities, whereas the product analysis may be much more

difficult. If radioactive tracers had been added to the starting material

then with a knowledge of the impurity levels in that material, some

very simple radiochemistry or even direct gamma spectrometry could

make very easy the measurement of the remaining fraction of each tracer and hence of the fraction of each remaining individual impurity.

Far too Httle use is made of this approach to trace element problems.

While "avoidance of analysis" may be too strong a term, certainly

"simpHfication of analysis" is justified in such cases. Of course, not

all trace element analysis can be dealt with in this manner, and there is

still need for development of any technique of high sensitivity analysis.

But surely the analytical laboratory should lead the way in using these

tracer techniques and prove to their colleagues in other parts of the

research department that collaboration before the request for analysis

would be mutually beneficial.
NUCLEAR METHODS

IV. Concluding Remarks

335

This paper does not claim to be comprehensive. There are recog- nised omissions, for example no mention is made of scattering techniques

nor of the use of radioactive nucHdes for X-ray fluorescence spectrometry. There may well be unrecognised omissions, if so then perhaps

these will be pointed out during the subsequent discussion. But at least it may be said by one with a third of a century's experience in analytical chemistry including a quarter of a century's experience in radioactivity, that nuclear methods are right in the forefront in solving

problems of trace characterisation. There seems no reason to doubt

that they will continue to be so, as far ahead as can be predicted. There

are exciting possibilities — the analytical chemist must be among the

leaders in exploiting them.

V. Acknowledgments

The author acknowledges with humility and gratitude the contributions made by his colleagues. He has had the benefit of seeing a recent review of parts of the field by R. F. Coleman and T. B. Pierce [47] as well

as those by C. A. Baker and by J. W. McMillan already referred to. He

has benefited much by discussions with D. Mapper, T. B. Pierce, R. K. Webster, C. A. Baker, and others.

VI. References

[I] Koch, R. C. Activation Analysis Handbook, Academic Press, New York and London,

1960.

[2] H0gdahl, O. T., Radiochemical Methods of Analysis; I.A.E.A. Vienna, 1965. Vol.

1. p. 23.

[3] Kenna, B. T., and Van Domelen, B. H.. Inter. J. App. Rad. & Isot. 17, 47, (1965).

[4] Durham, R. W.. Navalkar. M. -P., and Ricci, E., Proc. Int. Conf. Modern Trends in Activation Analysis, A. & M. College of Texas, College Station, 1961, p. 67.

[5] Roy, J. C. and Hawton, J. J., Atomic Energy of Canada Ltd., Report AECL-1181.

Dec. 1960.

[6] Ricci, E., and Dyer, F. F., Nucleonics 15, 447 (1964).

[7] Lukens, H. R., Yule, H. P., and Guinn, V. P., Nucl. Inst. & Methods 33, 273 (1965).

[8] Yule, H. P., Lukens, H. R., and Guinn, V. P., Nucl. Inst. & Methods 33, 277 (1965).

[9] Coleman, R. F., Analyst 86, 39 (1961): 87, 590 (1962).

[10] Strain. J. E., in Guide to Activation Analysis, W. S. Lyon, Jr., Ed. D. Van Nostrand

Co. Inc., New York, 1964, p. 43.

[II] Cuypers, M., and Cuypers, J., Gamma-Ray Spectra and Sensitivities for 14 MeV Neutron Activation Analysis, Texas A & M University, College Station, April 12, 1966.

[12] Steele, E. L., Proc. Int. Conf. Modern Trends in Activation Analysis, Texas A & M

University, College Station, 1965, p. 102.

[13] Basile, R., Hure. J., Leveque, P., and Schuhl, A., Compt. Rend. 239, 422 (1954).

[14] Strauch. K.. Ann. Rev. Nucl. Sci. 2, 105 (1953).

[15] Schweikert, E., and Albert, P., Radiochemical Methods of Analysis, I.A.E.A., Vienna

1965,1, 323.

[16] Baker. C. A., A.E.R.E. Report R 5265. 1966.
336 TRACE CHARACTERIZATION

[17] Albert. P., Proc. Int. Conf. Modern Trends in Activation Analysis, A & M College of Texas, College Station. 1961, p. 78.

[18] Engelmann, C. Proceedings Salzburg Conference 1964. I.A.E.A., p. 341.

[19] Engelmann, C. Cabane, G.. Proc. Int. Conf. Modern Trends in Activation Analysis, Texas A & M University, College Station, 1965, p. 331.

[20] Markowitz, S. S., and Mahoney, J. D., Anal. Chem. 34, 329 (1962).

[21] Ricci, E., Proc. Int. Conf. Modern Trends in Activation Analysis, Texas A & M University, College Station, 1965, p. 200.

[22] Engelmann, C, Radiochemical Methods of Analysis, I.A.E.A. Vienna, 1965, 1, 405.

[23] Aumann, D. C. and Born, H. J., Inter. J. App. Rad. Isotopes 16, 727 (1965).

[24] Pierce, T. B., and Peck, P. F., Proc. S.A.C. Conference, Nottingham, 1965, p. 159. W. Heffer & Sons Ltd., Cambridge, England.

[25] Pierce, T. B., 1st Int. Meeting on Practical Aspects of Activation Analysis with Charged Particles, Grenoble, June 1965.

[26] Greenwood, R. C, and Reed, J., Proc. Int. Conf. Modern Trends in Activation Analysis,

A & M College of Texas, College Station, 1961, p. 166.

[27] Lussie, W. G., and Brownlee, J. L., Jr., Proc. Int. Conf. Modern Trends in Activation

Analysis, Texas A & M University, College Station. 1965, p. 194.

[28] Morrison, G. H., and Isenhour, T. L., Anal. Chem. 38, 164, 167 (1966).

[29] Wichers, E., Schlecht, W. G., and Gordon, C. L., J. Res. Nat. Bur. Std., 33, 363. 451, 457 (1944).

[30] Girardi, F.. Proc. Int. Conf. Modern Trends in Activation Analysis, Texas A & M

University, College Station, 1965, p. 337.

[31] Samsahl, K., Aktiebolaget Atomenergi Reports AE 159 (1964), AE 215 (1966).

[32] Isenhour, T. L.. Evans, C. A., and Morrison, G. H., Proc. Int. Conf. Modern Trends in Activation Analysis, Texas A & M University, College Station, 1965, p. 123.

[33] Heath, R. L.. Gamma-Ray Spectrum Catalogue 2d Ed., IDO 16880-1; U.S.A.E.C., 1964.

[34] O'Kelley, G. D. (Ed.) Applications of Computers to Nuclear and Radiochemistry, NASNS 3107, U.S.A.E.C., 1962.

[35] Prussin, S. G.. Harris, J. A., and Hollander. J. M.. Proc. Int. Conf. Modern Trends in Activation Analysis, Texas A & M University, College Station, 1965, p. 357.

[36] Glos, M. B., Nucleonics 24, (5), 44, 1966.

[37] Reed. W. P., and DeVoe, J. R.. N.B.S. Tech. Note 276, p. 52 (1966).

[38] McMillan, J. W., A.E.R.E. Report R., 5266 (1966).

[39] Ruzicka, J., and Stary, J., Atomic Energy Review, 2, (4), 3 (1964).

[40] Landgrebe, A. R., McClendon, L. T.. and DeVoe, J. R., N.B.S. Tech. Note 248, p. 10, 1964.

[41] Landgrebe, A. R., McClendon, L. T.. and DeVoe, J. R.. N.B.S. Tech. Note 276, p. 124, 1966.

[42] Richter, H. G., Anal. Chem. 38, 772, 1966.

[43] Welford, G. A., Chiotis, E. L.. and Morse, R. S.. Anal. Chem. 36, 2350, 1964.

[44] Handley, T. H., Anal. Chem. 36, 153. 1964.

[45] Gillespie, A. S.. and Richter, H. G.. Anal. Chem. 36 , 2473, 1964.

[46] Richter, H. G., and Gillespie, A. S., Anal. Chem. 37, 1146, 1965.

[47] Coleman. R. F.. and Pierce, T. B.. The Analyst, in press.
NUCLEAR METHODS

Contributed Papers and Discussion

VINCENT P. GUINN

General Atomic Division, General Dynamics Corporation San Diego, California 92112 Although nuclear methods of trace analysis other than activation

analysis methods are also included in the scope of this program on

nuclear methods — and are represented by a number of interesting

contributed papers — this discussion will be largely limited to the subject

of activation analysis methods. This narrowness of presentation is not due to the author's lack of interest in, or lack of appreciation of, the

other nuclear methods — nor entirely to his ignorance of such methods —

but rather is due to the fact that the activation analysis methods are much

broader in their range of applicability.

The general theory and nature of activation analysis have been ad- mirably treated by A. A. Smales — in his "state-of-the-art" paper at this Symposium — so need little further discussion by the present author.

Instead, this author will present some additional remarks to fill in small

gaps, reemphasize certain especially important points, and make a few

comments concerning some of the contributed papers on activation

analysis. He will also draw upon some developments in this field re- ported in the recent literature, and upon some of the recent work of

his colleagues in the activation analysis group at the laboratories of

General Atomic.

1. Neutron Activation Analysis

A. Thermal-Neutron

Thermal-neutron activation analysis is the most fully developed

and most widely applicable form of the activation analysis method.

For most elements, it is the most sensitive form. The great bulk

of the pubUshed literature in the field is concerned with this form

of the method. Smales has pointed out above the tremendous sensitivity attainable for some 75 elements of the periodic system, if a very high (10^^ n/cm^-sec) thermal-neutron flux is used, and if very long

(30-day) irradiations are employed — for the longer-hved induced activities. Under such rather extreme conditions, he indicates defined limits of interference-free detection ranging from as low as 6 X 10"^ /ig (Eu)

337
338 TRACE CHARACTERIZATION

to as high as 0.2 ^ig (excluding the very insensitive elements, hydrogen,

berylhum, and carbon). The median limit of detection for these ~ 75

elements is approximately 10~^ /Ltg. This is obviously an ultra-sensitive

method of elemental analysis, under these conditions, but these are indeed heroic conditions!

What about the limits of detection that are more usually attainable —

in many laboratories around the world — employing a nuclear-reactor

thermal-neutron flux of 10^^ n/cm^-sec and more reasonable irradiation

periods (one or a few hours maximum, rather than 30 days)? As shown

in Table 1, even with a flux of 10^^ and a maximum irradiation period

of one hour, excellent sensitivities are still attainable: ranging from

about 10"^ fig (Dy) up to about 10 fig (Fe), with a median limit of detection of about 10~^

fj.g (these hmits are defined in a way slightly different

from those of Smales — namely, they are those defined by Buchanan [1].^ Thus, even with more common and practical conditions of irradiation,

excellent sensitivities are still attainable for most elements — and with- out some of the complications that set in when very high fluxes and very

long irradiations are employed (such as extensive sample radiolysis and

decomposition, appreciable recoil effects, container problems, excessive

sample heating, etc.). In the author's laboratory thriee reactors are used for neutron activation analysis (NAA) work at thermal-neutron

fluxes of from 2 X lO^^ to 2 X lO^^ n/cm^-sec.

A wide range of sample sizes can be accommodated by this method,

namely, from micrograms to tens of grams. The use of large samples,

if available, is very helpful in improving the concentration limits of detection and also in improving the representativeness of sampling — if the

sample material is quite heterogeneous. The limits of detection cited

in Table 1 can be achieved for many of the elements shown purely in- strumentally (nondestructively) — if the matrix is fairly simple, from the

neutron activation analysis standpoint (i.e., matrices such as water,

organic compounds. Be, C, etc.), or if the major induced activities,

because of their half lives or radiation energies, do not interfere with

the gamma-ray detection of the trace-element activity of interest. Even

where mild or severe interfering activities are encountered, they can

be removed by radiochemical separations with carriers and hold-back

carriers — thus still enabling one to attain the limits of detection shown.

Normally, one employs the purely-instrumental method, based upon

multichannel gamma-ray spectrometry, for the simple reason that it requires less of a chemist's time than the more tedious radiochemicalseparation procedure. However, if the one technique will not work

satisfactorily, the other almost certainly will. In neither form of the

method (instrumental or radiochemical) is there any blank correction —

the bane of many other methods for micro-level or micro-concentration

analysis.

^ Figures in brackets indicate the literature references at the end of this paper.
NUCLEAR METHODS 339

Table 1. Interference-free limits of detection for 75 elements by

neutron activation analysis at a thermal-neutron flux of 10^^ n/cm^-sec

(for 1 hour maximum).

Median sensitivity = 0.001 fxg Limit of Detection,

Micrograms

Elements

1-3

4-9

1-3

4-9

1-3

4-9

1-3

4-9

1-3

4-9

1-3

4-9

1-3

4-9

1-3

4-9

xlO-^

X10--

xlO-«

X 10-6

xlO-5

X 10-5 xlO-^

xlO-^

xlO-3

xlO-3

xlO-2

xlO-2

xlO-i

X 10-1

Dy

Eu

Mn, In, Lu

Co, Rh, Ir Br, Sm, Ho, Re, Au

Ar, V, Cu, Ga, As, Pd, Ag, I, Pr, W

Na, Ge, Sr, Nb, Sb, Cs, La, Er, Yb, U

Al, CI, K, Sc, Se, Kr, Y, Ru, Gd, Tm, Hg

Si, Ni, Rb, Cd, Te, Ba, Tb, Hf, Ta, Os, Pt, Th

P, Ti, Zn, Mo, Sn, Xe, Ce, Nd

Mg, Ca, Tl, Bi

F, Cr, Zr Ne

S, Pb

Fe

Many of the potential sources of error in thermal-neutron activation

analysis are discussed very clearly by G. W. Smith, D. A. Becker, G. J. Lutz. L. A. Currie, and J. R. DeVoe (aU of the National Bureau of Standcirds), in their Symposium paper on the determination of trace elements

in standard reference materials by NAA. These possible sources of

error are weU known, and can all be minimized to essentially neghgible

levels, but they cert£iinly must be recognized by the analyst who is en- deavoring to carry out NAA to obtain absolute accuracies of the order

of ± 1% of the value. The paper at this Symposium by J. Blouri, T. Chaudron, and P. Albert

(of the Centre d'Etudes de Chimie Metallurgique, Vitry, France), on

the NAA determination of traces of sulfur and several metals (especially

Fe, Na, Mn, and Zn) in zone-refined carbazole, is an excellent example

of a combined attack on a difficult problem — employing both the instru- mental and the radiochemical-separation forms of the NAA method.

Smales has referred to the reactor-pulsing NAA studies carried out

at General Atomic. Earlier studies [2] showed that the sensitivity

enhancement attainable in a 1,000-megawatt pulse, compared to saturation irradiation at the usual 250-kilowatt level of operation of the TRIGA

Mark I research reactor (shown in Figure 1) is equal to 70/T, where T

is the half life of the induced activity (thermal-neutron or fast-neutron),
340 TRACE CHARACTERIZATION

Figure 1. View of the core of a modern research-type nuclear reactor. TRIGA Mark I Reactor, General Atomic, San Diego.

in seconds. Thus, sensitivity improvements of 700-fold, 70-fold, and

7-fold should be attainable for elements with induced activities having

half hves of, respectively, 0.1 second, 1 second, and 10 seconds. A new

pneumatic tube, with a transit time, from reactor core to counter, of

0.1 second, has now been installed and is in use. Several quite practical

applications of this sensitivity enhancement via reactor pulses have now been develope'd in the author's laboratory, particularly by H. R. Lukens.

B. Fast-Neutron

As mentioned already by Smales and others, some elements can

be more sensitively detected, or more conveniently detected, by activa- tion with fast neutrons than with thermal neutrons. Some common

elements that fall into this category, for example, are the elements

nitrogen, oxygen, silicon, phosphorus, chromium, and iron. In particular, oxygen is now determined in many laboratories by activation

with 14-MeV, neutrons, to form 7.35-sec ^^N via the ^^O (n, p) ^^N reaction.

The gamma radiation emitted by ^^N is exceptionally high in energy

(mostly 6.13 MeV, with a little at 7.13 MeV), so there are essentially no

interferences (if, however, fluorine is present to an appreciable extent, a correction must be applied — since it also forms ^^N, via the ^^F (n, a) '^N

reaction).
NUCLEAR METHODS 341

It has been shown [3], that the large fast-neutron (fission-spectrum)

flux that is present in the core of a nuclear reactor can be used to ad- vantage in fast-neutron activation analysis. The principal difficulty,

however, is that the activation of other elements in the sample by the

very high thermal-neutron flux also present may greatly complicate

the detection of fast-neutron products, especially instrumentaUy.

Shielding the sample with cadmium or boron during the irradiation, as

is well known, reduces the extent of (n, y) activation by the thermal and

epithermal neutrons (while not affecting the fast-neutron activation),

but often not sufficiently. Thus, at least in many instances, one prefers to use an accelerator as a pure source of fast neutrons for such

work.

The usual small accelerator source is a 100-200 keV Cockcroft-Walton

deuteron accelerator. Using a water-cooled metallic tritium target

(1—10 curies) and a D"^ beam current of 1—2 milHamperes, a fresh target

will isotropically produce ~ 2 X 10^^ neutrons per second. These neutrons are formed by the highly exoergic (d, n) ^He reaction, and have

energies of about 14 MeV. Thus, a tiny sample placed very close to the

target can be exposed for a short time to a 14 MeV neutron flux of about

10^*^ n/cm^-sec; larger samples to an average flux of about 10^ n/cm^-sec.

Thus, the limits of detection published by Strain (and referred to by

Smales) may be overly conservative, since they are only for a flux of

10^ n/cm^-sec. His 10-minute maximum irradiation period is certainly

reasonable, in view of the rapid dechne in neutron output of the tritium

targets at high deuteron beam currents. In the General Atomic Laboratory, three high-output 14-MeV neutron

generators are used for fast-neutron activation analysis work. One

is set up as an automated system for routine high-sensitivity oxygen

determinations. It employs an automatic sample input loading rack,

dual pneumatic tubes (for sample and standard), a spinning device (to spin sample and standard during irradiation), a pair of 5-inch X 5-inch

Nal(Tl) detectors for the activated sample, and a single 3-inch X 3-inch

Nal(Tl) detector for the activated standard — cross-cahbrated with the

sample detector system. Total analysis time on this system, for oxygen,

is less than one minute. The limit of detection for oxygen, with a fresh

target, is about 10 ptg, i.e., 10 ppm in a 1 g sample, or 1 ppm in a 10 g sample. At levels well above the limit of detection, precisions and absolute accuracies of about ± 1-2% of the value are attained. On this system, many thousands of -samples (many kinds of metals, organic

materials, etc.) are analyzed per year for oxygen.

The paper by K. Perry, G. Aude, and J. Laverlochere (of the Centre

d'Etudes Nucleaires, Grenoble, France) at this Symposium represents an interesting assessment of the capabihties of a 14-MeV neutron generator that is not so familiar to U.S. workers, namely, that of a French

accelrator that can accelerate deuterons up to energies of 400 keV,
342 TRACE CHARACTERIZATION

at beam currents up to 2 milliamperes. Their neutron-output measure- ments at deuteron energies of 150, 250, and 350 keV show relative out- puts of about 1, 3, and 7 — showing the advantage of having a somewhat

higher-energy machine to work with. Of course, there is the disadvantage that, in general, the higher the energy of the accelerator, the more it costs. They report measurements on the determination, with

this accelerator, of oxygen, fluorine, and boron with various detector sys- tems (boron via the ^^B(n, p)^^Be reaction). Beryllium-11 has a half

life of 13.6 seconds.

II. Photonuclear Activation Analysis

This type of activation anfdysis, involving activation by bombardment

with high-energy photons, has also been well described by Smales. It

is also the subject of two of the contributed papers at this Symposium.

Photonuclear activation analysis has one advantage also possessed

by NAA — namely, the high degree of penetration of the bombarding

particles (high-energy photons in this case, instead of thermal or fast neutrons) in most matrices. With typical electron linear accelerator sources of bremsstrahlung photons, samples can be exposed to photon

fluxes (above the threshold of the reaction in question) in the range of

10^^-10^^ y/cm^-sec. Since, for most elements, the (y,n) reaction cross

sections are one or two orders of magnitude smaller than the thermalneutron (n, y) cross sections, photonuclear activation analysis, al- though still fairly sensitive, is less sensitive than high-flux thermal

NAA. However, there are a number of important exceptions to this generalization — especially the low atomic number elements carbon,:

nitrogen, and oxygen. For these elements, far better sensitivities are

attainable by photonuclear activation analysis than by either thermal or

fast NAA.

The pioneering work in this field has been carried out by Engelmann

and his co-workers at Saclay (Centre d'Etudes Nucleaires de Saclay,

France), and his paper at this Symposium mentions some of their most

recent work in this field. As in the work of the author's group, Engel- mann determines carbon, nitrogen, and oxygen via their (y, n) products:

20.4-minute ^^C, 10.0- minute i=^N, and 2.07-minute ^^O. Since all of these

are pure positron emitters, their gamma-ray spectra are exactly the same. One must therefore either (1) resolve the 0.511 MeV )8+ annihilation photopeak in the sample spectrum into its radioisotopic com- ponents—by mathematical analysis of its dechne with increasing decay

time, or (2) radiochemically separate the species of interest (^^C, ^^N, or

1^0) from the other species present. Both the author's group and Engelmann's group have found that the purely-instrumental procedure is sufficient in some instances, but that the radiochemical-separation

procedure must be used in more complicated cases. The multiscaler

mode of operation, and a computer least-squares procedure, are nor-
NUCLEAR METHODS 343

mally employed if the instrumental method is used (some additional

pure emitters sometimes present to a significant degree are 1.87-hour

9.73-minute ^^Cu, and 7.7-minute ^^K). In his Symposium paper, Engelmann has described excellent rapid means for the radiochemical separation of ^^C (combustion, then absorption of CO2 on Ascarite), ^^N (reductive fusion, then absorption of N2 on

molecular sieve at low temperature and ^^O (reductive fusion in graphite, oxidation of CO to CO2, the absorption of CO2 on Ascarite). At a 100 /xA beam current of 30 MeV electrons, his hmits of detection for C,

N, and O are 2 X 10-^ g, 4 X 10-^ g, and 5 X IQ-^ g, respectively. He

also discusses the interferences in the carbon determination resulting

from the ^^N(y,t)^^C and ^^0(y,Q:n)^^C reactions; in the nitrogen deter- mination from the i^0(7,t)i^N reaction; and in the oxygen determination

from the ^^F(y,tn)^^0 reaction.

It is worth remarking that the (y.n) method of determining oxygen can

be quite useful in distinguishing between oxygen distributed throughout

a metal sample (bulk oxygen) and oxygen present just in the surface

oxide layers of the sample (surface oxygen). The sample may be simply

activated and counted, to obtain a measure of the total oxygen present —

then it can be activated again, but this time etched for 30-60 seconds

before counting. The etching removes all of the oxide film, so the

resulting value gives a good measure of the bulk oxygen content. This

technique has been used to advantage at General Atomic, by G. H. Andersen, to determine the bulk oxygen content of low-oxygen beryllium

samples. In some such samples, it was shown that specimens with a

total oxygen content of about 30 ppm actually had a bulk oxygen content

of about 8 ppm (incidentally, giving excellent agreement with the metallurgical properties) — the rest of the oxygen being present as surface

oxide. Such work is carried out with two high-current (500 /jlA) electron

linear accelerators — os maximum energies of 17 MeV and 45 MeV,

respectively.

Some of the photonuclear activation analysis studies at the Los Alamos

laboratories are described in a Symposium paper by D. M. Holm and

W. M. Sanders. This particular study is one in which they succeeded

in greatly minimizing the interferences from 2.60-year ^^Na and 7.7- minute ^^K in the photonuclear determination of low levels of oxygen

in samples of metallic sodium (which typically contain 100-200 ppm K

impurity). They utilize coincidence counting techniques to distinguish

between the pure positron emitter, ^^O, and the positron/coincident

gamma-ray emitters, ^^Na and ^^K. They cite several counting arrange- ments studied, in which the ^^Na and ^^K interferences were reduced by

anywhere from 20% to 90%.

To date, studies in photonuclear activation analysis have been limited

to just a handful of laboratories that possess the necessary, quite expensive, linear accelerators. Perhaps, as mere and more useful applica-
344 TRACE CHARACTERIZATION

tions of this technique are developed, there may be enough incentive for some group to develop and market a suitable but less expensive accelerator, perhaps costing around $200,000.

III. Charged-Particle Activation Analysis

This form of the activation analysis method, although by no means

new, is still only slightly developed — except for a few low atomic number

elements in a few matrices. The method has some inherent complications which tend to limit its applicability. It's chief complications are

related to the rather small penetration of accelerated charged particles

(protons, deuterons, helium-3 ions, and alpha particles — at energies in the range of 1-30 MeV) in typical sample matrices. The penetration

depths are only in the range of perhaps ten to a few hundred microns,

depending upon the particle used, its energy, and the stopping power of

the matrix. Thus, such analyses really only give a measure of the sur- face composition of the sample. Sometimes this can be shown to be

identical with the bulk composition — but often it is not. Of course, if one is especially interested in the surface composition (oxide layers,

corrosion layers, etc.), this is an advantage.

P. Albert has employed a technique of activation with charged particles, followed by a controlled etching to a desired depth before counting,

to eliminate the effect of a different surface composition, thus allowing

him to measure bulk composition. Allowance must be made for the

fact that the reaction cross sections change markedly with particle

energy (the particle, of course, is continually slowing down as it penetrates into the sample). One also encounters severe sample heating

and often many interfering nuclear reactions in charged-particle work.

Because of Coulomb repulsion barriers, the method is generally much

more sensitive for low Z elements than it is for high Z ones. In their Symposium paper, M. Deyris, G. Revel, and P. Albert (of the

Centre d'Etudes de Chimie Metallurgique, Vitry, France) give an excellent and detailed account of their utilization of various charged particles

(protons, helium-3 ions, and alpha particles) for the determination of trace levels of oxygen in high-purity aluminum. Careful consideration

is given to the effects of various possible interfering reactions — and their energy dependences. Whereas, under their conditions, practical limits of detection of about 1 ppm oxygen in aluminum were found — using

either protons or alpha particles — a practical limit of about 0.02 ppm was

attainable with ^He ions. The product detected is 1.87-hour ^^F, formed

by the i60(3He,p)i8F and i60(3He,n)i«Ne^ i^F reactions. Results

obtained nondestructively with He^ agreed well with results obtained by

proton bombardment — followed by radiochemical separation of the F^^ formed by the ^^0(p,n)^^F reaction. The ~ 40 A thick oxide film was

etched off, after activation, in each case, so as to determine the bulk

oxygen content of the aluminum.
NUCLEAR METHODS 345

In his Symposium paper, Engelmann discusses not only photonuclear

activation analysis (mentioned earlier), but also some determinations of

boron and nitrogen employing activation with deuterons (at a beam cur- rent of 10 /lA, in the energy range of 5-20 MeV): via the ^'^B(d,n)^^C and

^^N(d,an)^^C reactions. In this energy range, Hmits of detection for boron of from 10~^ to 10"^*^ grams, and for nitrogen of from 10~^ to 10 ~ grams, are attainable.

During the past few years, interest in the use of charged-particle

activation ana/y5i5 — especially using ^He ions and especially for the

determination of trace levels of low Z elements in medium or high Z

metals — has increased considerably. The recent commercial availability in the United States of medium-cost (~ $200,000) small cyclotrons,

suitable for such work, should stimulate further development of the

method. Two companies now produce such cyclotrons.

IV. Other Activation Analysis Topics

Time does not permit an in-depth discussion of some of the other

important developments in the field of activation analysis: the use of hthium-drifted germanium semiconductor detectors for high-resolution

x-ray and gamma-ray spectrometry: the use of coincidence and anti- coincidence techniques: the use of various computer programs for data

processing: new areas of application: and prompt gamma-ray techniques.

Brief reference has been made at this Symposium to the advantages,

in certain cases, of the use of Li-Ge detectors — namely, in the papers by

T. B. Pierce, of the Atomic Energy Research Estabhshment, Didcot,

England (the paper being mainly concerned with analysis via prompt

gamma rays emitted during charged-particle activation), and by D. E. Fisher, L. RanciteUi, J. F. Lawrence, R. L. Currie, and E. Berkey, of Cornell University (paper mainly devoted to the instrumental NAA of

meteorites). In their Symposium paper, K. K. S. PiUay and W. W.

Miller, of the Pennsylvania State University, describe the detection of electron-capture and internal-conversion characteristic x-rays in NAA

work, using gas proportional counters at the lower energies and thin

Nal(Tl) scintillation crystals at the higher energies. In such work,

Li-drifted Si or Ge detectors should also be very useful. Coincidence and anti-coincidence techniques are described by D. M.

Holm and W. M. Sanders in their Symposium paper (already referred to), and by D. E. Robertson and R. W. Perkins, of the BatteUe Northwest

Laboratory, in their Symposium paper (mainly concerned with the instru- mental NAA detection of various trace elements in sea water).

The only Symposium paper devoted to computer techniques in activation Analysis work is that by H. P. Yule, presently at Texas A & M

University. This paper describes a very useful computer method for obtaining firm (3cr) upper limits for concentration for as many as seventytwo elements from instrumental NAA data.
346 TRACE CHARACTERIZATION

In the areas of applications of NAA techniques, there are several

interesting Symposium papers: those by (1) G. W. Leddicotte, of the

University of Missouri, on trace-element studies in the biomedical field,

(2) N. E. Erickson, S. S. Krishnan, and A. K. Perkons, of the Attorney

General's Laboratory, Toronto, Canada — on applications in the field of

scientific crime investigation (a subject of great interest to this author

also), (3) H. H. Kramer, W. J. Hampton, V. I. Molinski, and W. H. Wahl,

of the Union Carbide Nuclear laboratories, on the geographical characterization of chromium ores via their trace elements, (4) D. E. Fisher et al., mentioned earlier, on meteorite analyses, and (5) D. E. Robertson and

R. W. Perkins, also mentioned earlier, on oceanographic applications.

V. Other Nuclear Methods

Time only permits a brief mention of the several interesting papers

contributed to this Symposium on nuclear methods of analysis other than

activation analysis methods. These are papers on (1) thickness measurements, by J. Krugers (Hewlett-Packard Company), (2) substoichiometric

radioisotopic dilution applications, by A. R. Landgrebe, P. A. Pella, L. T. McClendon, and J. R. DeVoe (National Bureau of Standards), (3) fission track etching, by H. S. Rosenbaum and J. S. Armigo (General Electric

Company, Vallecitos Laboratory), (4) radio-gaschromatography, by R. M.

Statnick and F. Schmidt-Bleek (Purdue University), and (5) ion-exchange

membrane radiochelatometric titrations, by J. Tolgyessy, J. Konecny,

and T. Braun (Slovak Technical University, Bratislava, Czechoslovakia

and L. Eotvos University, Budapest, Hungary).

VI. References

[1] Buchanan, J. D., Proceedings of the 1961 Int'l. Conf. on Modern Trends in Activation Analysis (Texas A & M University, College Station, Texas), pp. 72-77.

[2] Lukens, H. R., Yule, H. P. and Guinn, V. P., Nucl. Instr. & Methods 33, 273 (1965).

[3] Yule, H. P., Lukens, H. R., and Guinn, V. P., Nucl. Instr. & Methods 33, 277 (1965).
SPARK SOURCE MASS

SPECTROMETRIC ANALYSIS OF SOLIDS

A. J. AHEARN

Bell Telephone Laboratories, Incorporated

Murray Hill, New Jersey 07971

I. Introduction

Solid state physics, chemistry, and technology have grown rapidly in the past two decades. This in turn stimulated the development of new

analytical techniques [1] ^ for determining the chemical composition of

materials — particularly the detection and measurement of trace quantities of impurities in solids. The demands of our semiconductor technology stimulated the initial development of one of these new methods of analysis. As an example,

the electrical properties of germanium and sihcon are markedly changed

by the introduction of as httle as 10 ppba (parts per bilhon atomic) of

copper [2] into the former or 2 ppba of gold [3] into the latter. But there are many other properties of materials that are appreciably

influenced by the presence or absence of selected impurities in the low

ppm region. Ordinary tungsten [4] is quite brittle but when it is purified

to a level below 10 ppm it becomes readily machinable. At 15 °K the

thermoelectric power of gold [5] is increased by a factor of 100 when the

cobalt content is reduced from 200 ppm to 20 ppm. The ductility of beryllium [6] increases by a factor of 40 when impurities therein are reduced to a few ppm.

The superconducting transition temperature of molybdenum [7] is degraded from 0.9 °K to 0.3 °K by introducing 100 ppm of iron. With

titanium [8] containing less than 5 ppm manganese and less than 2 ppm

iron the transition temperature is 0.42 °K, whereas with 30 ppm manganese and 20 ppm iron it is depressed to 0.17 °K, and with 100 ppm

manganese, it is below 0.06 °K. In the recrystaUization of lead [9], the

grain boundary velocity is reduced by a factor of 1000 by a few ppm of

silver. The efficiency of graphite [10] in a nuclear reactor is markedly

reduced by the presence therein of only 2 ppm of boron.

The magnetic permeability of iron [11] is increased from a few thousand to a few hundred thousand when its carbon, sulfur, nitrogen and

oxygen content are reduced from a few hundred ppm to a few dozen ppm.

* Figures in brackets indicate the literature references at the end of this paper. 347

237-323 0-67- 22
348 TRACE CHARACTERIZATION

Reviewed elsewhere [12] are many more examples of solid state properties that are appreciably affected by trace impurities in the ppm

to ppb region. This is the region in which one of the new analytical

techniques — spark source mass spectrometry [13] — can effectively

contribute by identifying the trace impurity and by determining its approximate concentration.

II. Mass Spectrometry With Spark Source

This spark source technique is not the first instance in which mass

spectrometry has been used for solids analysis. Semiconductors and

metals have been analyzed using an electron bombardment type source

of positive ions [14]. Very high detection sensitivities for certain ele- ments have been obtained by isotopic dilution [15] techniques. Ions sputtered from a solid under ion bombardment have been employed to study solid surfaces [16]. Professor A. J. Dempster [17] was the first to do mass spectrometric

analyses with positive ions from a spark source. As the spark source

[18] is usually employed, a radio frequency voltage of several tens of

kilovolts is applied between two electrodes of the material under investi- gation. When the gap between these electrodes is ^ 100 microns, the

electric field is high enough to produce a field current — an emission of

electrons from the cathode. These field currents appear when the

average applied field is substantially lower than that predicted by theory.

Consequently the electrons probably come from surface irregularities

such as whiskers or other sharp projections where the field is enhanced.

Some heating and vaporization of the cathode material occurs at these

projections. In turn the anode is locally heated and vaporized by these

electron beams. Electron bombardment ionization of cathode and

anode atoms occurs in the interelectrode gap. Under positive ion bombardment, cathode material is sputtered some as neutral atoms and some

as positive ions. These vaporization and ionization processes yield ion currents that, to a first approximation, represent the electrode material

[13]. The degree of this approximation will be discussed later. Spark source mass spectrometry as a technique for the analysis of

solids has grown in use enormously in the past decade or so because of two inherent advantages. First, its detection sensitivity is high whether

defined in terms of the low concentration of an impurity that can be

detected [19] in a matrix or in terms of the total amount of sample [20] needed to detect impurities.

The second outstanding advantage of the spark source as an analytical

tool is its nonselectivity — its mass spectrum reveals all elements in the

sample with approximately the same detection sensitivity [13]. This

presents a great advantage over a thermal ion source for example where

elemental sensitivities vary by several decades. This nonselectivity

makes the spark source the preferred ion source for general analytical
MASS SPECTROSCOPY 349

work on solids primarily because the demands of modern physics and

chemistry of soUds cover most if not all of the elements in the periodic

table. The spark source is used widely in spite of a number of disadvantages

[13] from which it suffers. It is an erratic ion source — it requires almost

constant adjustment to keep it running and in spite of this nearly con- tinuous monitoring, the ion current fluctuates widely with time. Consequently, in nearly all work with the spark source an integrating detector

is used. The spark source being a high voltage device, the positive

ions therefrom are not monoenergetic. Experiments show that they

have a spread in energy of two to three kilovolts [21]. In addition to the

usual requirement of direction focusing whereby ions within some small

solid angle are focused, this ion energy spread imposes the additional

requirement of velocity focusing [13] in the mass spectrometer used

with the spark source. Such double focusing mass analyzers add considerably to the complexity and cost of these instruments. Moreover

this velocity focusing can be achieved only over an energy band of a few

hundred electron volts. Consequently, much of the ion current must be

discarded leaving a relatively small useable ion current of about 10"^^

amperes.

The erratic nature of the spark source would require that an electrical detector measure the ratio of a mass resolved beam to that of the total beam entering the mass analyzer. The small magnitude of this latter beam makes this ratio measurement so difficult [13] that in practice an

integrating detector in the form of a photographic plate is usually used.

The requirement of photographic detection added to the need that the

entire periodic table be encompassed in the recorded mass spectrum has

resulted in the widespread choice of a particular geometry — the Mattauch-Herzog geometry [22] of double focusing. Every commercial

make of spark source mass spectrograph [18] uses this geometry.

This geometry is sketched in Figure 1. Ions from the radio frequency

spark source after acceleration are limited to an appropriately small

solid angle by apertures in electrodes Si and 52. They next enter the

electrostatic analyzer where velocity dispersion occurs. The aperture

in the electrode S3 passes an appropriately narrow energy band of ions

to the magnetic sector where mass analysis occurs. Consider the two ion trajectories that delineate the angular divergence

of the beam. Those of mass mi and m-z and energy Ei and Ez are sketched in Figure 1. Two nondivergent beams emerge from the electrostatic analyzer. In the magnetic sector where mass separation occurs

the various ion paths of each mass are brought to a focus at a plane

beyond the exit of this analyzer.

This focusing of all masses on a given plane is a necessary and suffi- cient requirement for photographic detection for general analytical work

where a wide range of elements needs to be simultaneously registered on the photographic plate.
350 TRACE CHARACTERIZATION

SOURCE 1

Figure 1. Double focusing in a Mattauch and Herzog type spark source mass spectro- graph. After Hannay, N. B., Science 134, 1220 (1961).

III. Analytical Capabilities of Spark Source Technique

The radio frequency spark can be used to analyze many different

kinds of materials. With electrical conductors and semiconductors,

the spark can be formed directly between electrodes of the sample.

Moreover, techniques have been developed whereby an electrical insulator [23] contributes to a spark thereby enabling its analysis to be

obtained.

Samples of metals, semiconductors and insulators in powder form are sometimes presented for analysis. Techniques [24] have been developed for sintering powders or for mixing with suitable binders, or con- ductors which after compacting into rod form are suitable for sampling

with the spark source. The preparation, cleaning, and handling of samples [24a] is critical since less than a monatomic layer of surface contamination [25] is readily detected. With liquid samples a clean surface of a suitable

material is deliberately contaminated [25] by the liquid, or a wet sludge

[26], with a suitable powder, is compacted into a dried electrode.

When there is plenty of sample and it can easily be machined, the

sample should be in the form of rods about 20 mm long and 2 or 3 mm in diameter.

On the other hand, samples from solid state devices or crystal growing

set-ups frequently are small enough to be termed microsamples [27]. There are techniques for sparking and analyzing such small samples.

This spark source technique is usually employed to detect trace impuri-
MASS SPECTROSCOPY 351

ties but in the case of microsamples where the total amount of material

available is too small to examine by other analytical methods, it is fre- quently used to determine major components.

The high detection sensitivity is one of the two distinguishing features

of spark source mass spectrometry. With a few exceptions, all elements can be detected under favorable conditions when the trace element in the ion samples presented to the detector is in the neighborhood of a part per biUion [19] atomic (ppba) fraction of the major component.

In general, the ion sample presented to the detector does not accurately represent the soUd sample comprising the electrodes of the spark

source. However, for most elements the concentration of a trace element in the ion sample usually differs from that in the solid sample by

less than a factor of ten [13]. This small selectivity is a most important

feature of spark source mass spectrometry for analytical work because

it makes the technique so widely apphcable.

The detection sensitivity of a few ppb, quoted for this spark source

technique, was carefully qualified as applying to "nearly all elements"

and "under favorable conditions." What are these "favorable conditions" and how poorly are they reaUzed in practice? How serious are the corresponding losses in detection sensitivity? What can be done

to retrieve these losses? To what extent, as a general analytical method

is this spark source technique limited by less than "favorable conditions."

The second feature of the spark source technique is its nonselectivity

but again this characterization was carefully qualified — "for most ele- ments the concentration of a trace element in the ion sample usually

differs from that in the solid sample by less than a factor of 10." If this misrepresentation or selectivity is neglected, the spark source technique

concentrations could be in error by a factor of 10. How serious is this? In general is it not sufficient to know trace concentrations to within a

factor of 10 particularly in the ppm to ppb region? What are the important factors determining accuracy and precision with this analytical

technique? How can the latter be improved?

These are the questions and considerations treated in the forthcoming

sections of this paper.

IV. Factors Limiting Detection Sensitivity

A. Diffuse Background

What are the favorable conditions under which it is possible to detect

a trace element in the ion sample presented to the photographic detector

when this trace element is present at about 1 ppba? The weakest mass

line that can be detected visually or instrumentaUy on the photographic

plate determines the detection sensitivity under a given set of conditions.

This is a signal-to-noise problem, where the noise is the diffuse background in the emulsion in the presence of which the mass line must be
352 TRACE CHARACTERIZATION

detected. As the exposure is increased, elements with progressively

lower concentration will appear but the background increases also. Consequently there is an optimum exposure beyond which still lower

concentrations are not uncovered. With modern commercial spark

source instruments this optimum exposure is about one microcoulomb

[28].In addition to the intrinsic background of the emulsion, two other

factors contribute background. Some ions in transit are scattered from

the beam by collisions with residual gas molecules. Those scattered in the magnetic analyzer may reach the emulsion. Ions that undergo a charge transfer in a collision with a residual gas molecule by picking up

one or more electrons are frequently revealed by rather sharply terminated bands of diffuse background [13]. The end points of the band

correspond to charge transfers at the emulsion and between the electrostatic analyzer and the magnetic analyzer. In modern commerical instruments, high vacuum techniques [28]

such as metal gasket seals, high speed pumping and baking are employed

to minimize this ion scattering and background. The minimal ? -pat- tering thus achieved permits the detection of elements in the ppba range

provided these elements are substantially greater or smaller in mass

than the major component ions of the sample.

For those elements near the major component, particularly for those on its high mass side, the diffuse background is substantially greater [29]. Ions in a spark source mass spectrograph on striking the photographic

emulsion, produce a mass line spectrum plus one or more of the following

secondary products: x-rays, luminescence, negative ions, secondary

electrons, reflected and/or sputtered positive ions all of which would fog

the emulsion. The magnetic field would return the negatively charged

particles to the low mass side of the incident ion, and the positively

charged ones to the high mass side. The fogging generated by the x-rays and luminescence would probably not be thus directionally limited.

This fogging is appreciable when the integrated ion charge is sufficient

to detect an element in the ppba region. This limitation in detection

sensitivity has been partially circumvented in different ways. In our own laboratory, the photographic plate and plate holder were modified

as shown in Figure 2. The plate was split at the mass position of the

major component ions. At this position rectangular shaped apertures were cut in the backing plate and the plate holder. By this simple

device, the major component ion beam (d) passes right through the

assembly without striking the photographic plate at all. With the MS7

being used, this ion beam thus enters a cavernous space in which the

dimensions are large compared with the rectangular opening thereto. Consequently, it should serve as an efficient Faraday collector to trap not

only the incident positive ions of the major component but also their secondary products.
MASS SPECTROSCOPY 353

Figure 2. Modifications of standard photographic plate holder for MS-7 mass spectro- graph to bypass the major component of the sample, a. Plate holder, b. Backing plate,

c. Photographic plate, d. Major component ions. After Ahearn, A. J., and Malm, D. L., Appl. Spectr. 20, 411 (1966). The suppression of fogging by the modifications of Figure 2 is indi- cated by curve B in Figure 3. Here the sample was gaUium arsenide

and, to accommodate the arsenic singly charged ion and the two singly

charged ions of the gallium isotopes, the widths of the rectangular

apertures in the backing plate and plate holder were made 11 and 13 mm

respectively. The optical transmission of the plate is plotted on the

vertical axis. In this measurement the microphotometer was set at 100 percent transmission at a place where the emulsion was removed

from the glass. To simplify the presentation in Figure 3 the spikes

corresponding to the various mass lines have been omitted and only the

diffuse background is presented in curve B. Mass number is plotted on the horizontal axis. For comparison, curve A in Figure 3 gives the corresponding diffuse

background when the standard plate (not split) and standard plate

holder were used.

Q- inn i I I I I I I I I I I I I 20 40 60 80 100 120 140 160 180 200 MASS NUMBER

Figure 3. Diffuse background in mass spectrum of gallium arsenide. A. Standard

photographic plate and plate holder. B. Modified unit to suppress fogging by trapping

major component ions. After Ahearn, A. J., and Malm, D. L., Appl. Spectr. 20, 411

(1966).
354 TRACE CHARACTERIZATION

Curve B shows that with this spHt plate modification of Figure 2, the

low transmission of 80 percent at the high mass end of the plate is maintained down to about mass 90. Consequently there is little or no loss

in sensitivity from the high mass end of the spectrum to about mass 90. On the other hand, with the standard plate as shown in curve A, the

background rises to about 20% transmission at mass 90. These corre- spond to detection sensitivity losses, by factors as high as 30, that are

retrievable by this split plate technique. The abrupt rise in background

below mass 90 on curve B is not understood. It may be caused by

secondary products of major component ions escaping back through the

wide (10 to 12 mass units) aperture system to fog the plate. It may be

due to major component ion scattering. One with a charge transfer

from +5 to + 2 would introduce background that would bunch near and

terminate approximately at mass 90. The background on the low mass side of the major components is approximately the same for A and B in Figure 3. Doubtless it could be

reduced on the high mass side of the doubly charged major components

by splitting the plate there and introducing a second set of apertures to capture these ions and their secondary products.

In curve A and B of Figure 3, the measured monitor exposure was

1 X 10~^ coulombs requiring about 2 hours in each case with an object

slit vddth of .006 inches. The spark source was run at a repetition rate of 300 cps and a pulse length of 25 microseconds. In each case the

analyzer and source pressure were the same — about 1 X 10"^ torr with

the spark not running.

The background shown in curve A is not an extreme case. Substantially lower transmission values have sometimes been recorded at this exposure — 1 X 10~® coulombs. The degree of fogging depends to some

extent on the magnitude of the ion current to the photographic plate,

being larger for large currents. This could mean that the secondary

products depend in part on the amount of electrostatic charging of the

emulsion or that they vary nonlinearly with current such as would occur

if the mechanisms involved two or more steps.

H. Mai [30] employed a split plate technique similar to that of Figure 2 with similar diminution of plate fogging.

This method of trapping major component ions suppresses the fogging

produced by their secondary products more completely than did our 1954 technique [13] in which a grounded metal mask was placed on the

emulsion at the position of incidence of the major component ions. This simpler technique recently has been adapted and modified by painting a strip of graphite paint [30a] on the emulsion at the position of the

major component ions, the strip being grounded. Some diminution

of fogging is reported.

An entirely different approach to the suppression of this fogging,

produced by these 15 to 20 keV ions incident on the photographic emul-
MASS SPECTROSCOPY 355

sion, has recently been made by Kennicott [31]. The assumption was made that the secondary products would be lower in energy than the

incident ions. This suggested that the latent image produced by the

secondary products would be closer to the surface of the silver bromide

crystals of the emulsion than the latent image of the incident ions

themselves. A developing procedure was devised wherein a latent image on or near the surface of the AgBr crystal was bleached out after which the internal image produced by the 15 to 20 keV incident ions was developed.

A substantial reduction in fogging as compared with D19 developing

is reported. The improved signal-to-noise ratio enables one to slightly

extend the detection limit of this mass spectrometric technique in spite of a loss in absolute sensitivity of the emulsion.

In a broad program to improve on the properties of the conventional

emulsion of silver bromide crystals in a gelatin matrix, Honig, Woolston

and Kramer [32] reported on a gelatin-free photographic detector consisting of a thin film of silver bromide crystals deposited on a glass plate.

Among other advantages indicated by experiments in progress, the

fogging with this gelatin-free detector is substantially smaller than with

the Ilford Q2 gelatin emulsion. This suggests that the secondary prod- ucts of ion bombardment come in part from the gelatin in the Q2 emulsion.

The spht plate technique is cumbersome particularly with a sample

like gaUium phosphide where two splits are needed to bypass the major

component ions. Perhaps the split plate or its equivalent in the form

of a miniature but near perfect ion collector [33] at the proper position on the plate and supplemented by internal image development is the best

alternative for the present. Perhaps a high electrical conductivity

glass with a gelatin-free photographic detector is an alternative.

B. Line Background

Traces of hydrocarbons [19] are not uncommon in high vacuum sys- tems of the character of commercial spark source mass spectrographs.

In this high voltage ion source, such hydrocarbons are fragmented in

part. As a consequence, mass lines due to hydrocarbons or fragments

thereof sometimes appear. Fortunately, the resolving power available

in these spectrographs is usually adequate to separate these ions from

elemental ions of the same nominal mass. Consequently, line background from such hydrocarbons can usually be circumvented.

One of the advantages of this mass spectrographic technique derives

from the simple spectrum that is obtained — simple by comparison with

that of the spectrochemical technique. Nevertheless with this high

voltage spark ion source which produces many multiply charged ions,

many elements have mass lines (mass/charge values) of the same nominal

value as other elements and masking occurs unless the resolving power

is adequate. Singly charged molecular species consisting of 2 or more
356 TRACE CHARACTERIZATION

major component atoms are also produced in the spark. With some

elements, molecular species consisting of as many as 30 atoms [34] have

been recorded. In addition to oxides, hydrides, hydroxides, and

carbides of the major component that may appear, complex molecular

ions [35] like GaP2 and Ga2P have been recorded. The isotopes of these

molecular ions and multiply charged ions occupy a not negligible portion

of the mass spectrum. The resolving power needed to separate them

from the elements of the same nominal mass is not alv^ays available.

The limitations imposed on this spark source mass spectrometric

technique for solids analysis by available resolving power can be considered in the following context. What resolving power would be needed

to detect almost any element in almost any simple matrix? The mass

differences that need to be resolved for this purpose have been compiled

from the Sandia Corporation Monograph "Table of Atomic Masses."

This table compiled with the spark source in mind includes ion masses

of most but not all isotopes up to 6 electronic charges and includes the

singly-charged ions of most but not all isotopic polymers up to mass 210. Figure 4 [36] shows the percentage of the elements resolved from their nearest neighbor as a function of the resolving power Af/AM needed for

this separation. Figure 4 shows that with a resolving power R = 1000

only 10 percent of the elements are resolved from their nearest neighbors,

but with R = 2000, 35 percent of the elements are resolved. Now with

today's modern spectrographs, resolving powers in the 2000 to 3000

range are available. It is evident that the separation of additional

elements requires large increases in resolving power. For instance,

3000 4000 5000 10,i SEPARATION (M/AM)oF ELEMENT AND

000 NEAREST

100,000

Figure 4. Resolving power needed to separate singly charged ions of elements from the nearest m/e matrix ions in spark source mass spectrometry.
MASS SPECTROSCOPY 357

with a resolution of 5000, only 52 percent of the elements would be

separated from their nearest neighbor.

In Figure 4 the elements and their nearest neighbors are listed in columns according to their mass difference M/AM. For example, with

R = 1000, only hydrogen, lithium, beryllium, boron, dysprosium, erbium,

holmium, and thulium are resolved from the matrices that are the nearest

neighbors. Many of the cases calhng for high resolving powers cor- respond to nearest neighbors in the form of oxides. One might argue

that their inclusion is not realistic, but since we are frequently concerned,

in this technique, with ppb concentrations, this presumes either a very

low oxide concentration or a very high degree of dissociation in the spark.

Moreover, the situation is not markedly improved if these oxides are excluded from consideration.

In compiling the data of Figure 4 the most abundant isotope of the

element in question was not necessarily used. An arbitrary decision was made to sacrifice abundance by a factor of ^ 3 if by so doing a less abundant isotope of the element has a more remote nearest neighbor,

i.e., if thereby a lower resolving power sufficed for mass separation.

This decision to sacrifice some abundance and therefore some detection sensitivity where necessary although arbitrary is not unrealistic. Even this sacrifice in sensitivity by a factor of 3 is not an available

alternative for the 27 percent of the elements that are monoisotopic.

It should be emphasized that what is plotted on the horizontal axis in Figure 4 is the limit of resolution — where the valley between the two mass lines in question just disappears. Doublets near this limit of resolution could be identified as doublets only if they were substantially

above the limit of detection but below the point of line broadening

characteristic of the approach to saturation. Moreover, at this extreme,

the doublets could be detected as such only if the two lines had nearly

the same intensity. Furthermore, quantitative measurements of optical

transmission and line width would be worth little with a vaUey between

the doublet lines of less than 50 percent.

The limitations portrayed in Figure 4 can be circumvented in some

elements by resorting to a low abundance isotope of the element but this

is necessarily at a corresponding sacrifice in detection sensitivity. For

monoisotopic elements, this circumvention can only be achieved by

resorting to a multiply charged ion of the element. But since the intensity of a doubly charged ion may be less than 10 percent of that for the

singly charged ion, this also entails an appreciable loss in detection

sensitivity. In Section III, it was indicated that even under the favorable conditions

specified earlier in the present section, there were exceptions among the

elements to the generally high detection sensitivity of a few ppba.

These principal exceptions are hydrogen, carbon, nitrogen, oxygen and

their products. Carbon and oxygen are of particular interest. The
358 TRACE CHARACTERIZATION

minimum apparent concentration observed for carbon and oxygen is usually not below a few ppma [37]. This concentration is labeled

"apparent" because these elements coming from the solid sample are not readily distinguished from instrument background due to dissociation of carbon monoxide, water vapor and/or hydrocarbons.

However, recently Socha and Willardson [38] reported experiments on mass spectrographic measurements of apparent concentrations of

gases in solid samples as a function of pumping speed and of the partial

pressure of the gases in the source chamber. Table 1 summarizes their

determinations of the contribution of source chamber gases oxygen,

nitrogen, carbon monoxide and water vapor to the mass spectrum of

gallium arsenide when the partial pressure of each gas was 1 X 10""^torr. This indicates that oxygen in samples at much less than 2 ppma would

be lost in the noise of the instrument background, but that nitrogen and

particularly hydrogen and carbon in a sample can be detected at substantially lower values.

Table 1. Contribution of source gases to the mass spectrum at a partial

pressure of 1 X 10 ~^ torr. Source gas Ion Contribution in PPMA

O 16o+ 2 N 14n+ 0.3 CO 12c+ 0.01 ^ CO 28co+ 0.02

H2O 1h+ 0.02 b H2O 18h,o+ 0.01

^ Estimated.

^ Includes contribution from H2. (Socha, A. J., and WiUardson, R. K., presented at the 14th Annual

Conference on Mass Spectrometry and Allied Topics, Dallas, 1966.)

V. Factors Limiting Accuracy of Analysis

Spark source mass spectrometric analyses of solids are normally made

as follows. A graded series of exposures is made covering the range

10~^^ to a maximum of 10~^ coulombs measured by a monitoring elec- trode located at S3 of Figure 1. At the lowest exposures ideally some of

the isotopes of the major components are recorded in the linear portion

of the response curve of the photographic emulsion. As the exposures

are progressively increased, impurities of progressively lower concentration appear in the mass spectra. The concentration of an impurity in

its matrix is then derived from the inverse ratio of exposures [39] of

impurity and major component that produce the same response on the

emulsion. In deriving sample composition from these spectra the fol- lowing factors are important.
MASS SPECTROSCOPY 359

A. Transmission Stability of Instrument

The electric charge delivered to the emulsion is assumed to be directly

proportional to the charge measured by the monitor, i.e., the monitor

aperture passes a fixed fraction of the charge incident on the monitor.

Data [13, 20] indicate that this assumption is justified.

B. Reciprocity Fulfillment

The assumption is made that when the response of the emulsion pro- duced by an isotope of one element equals that for an isotope of a second

element, then the charge producing each mass line is the same. This

is true only if the response is first corrected for its dependence on ion mass [39] and ion energy [39], and if the reciprocity relation is satisfied. This requires that in the relation R — It^ for the response R, the ion current / and the exposure time t, the power x be equal to unity, i.e., that the photographic response is determined by the total charge regardless

of the rate of arrival of the charge. Franzen and Hebeda [40] used 30

keV singly charged ions of argon, neon, and krypton in which the exposure

time on Ilford Q2 emulsions was varied from 0.07 to 240 seconds —

a

range of 3300. Their ion currents varied from 1.4 X 10" to 4 X 10"

amperes. Over this range of time and current they found that the x was

greater than unity by less than 1 percent. Less accurate measurements

on 19 keV singly charged ions of boron [13] and antimony over a current range of about 10^ and with gold [20] ions over a range of 10^ did not

indicate any departure from reciprocity. Although the current ranges

in these reciprocity tests are smaller than the 10^ range used in analyses

by this spark source technique, the assumption that the reciprocity rela- tion is satisfied is probably justified.

C. Emulsion Sensitivity— Dependence on Element

The sensitivity of Ilford Q2 plates to ions in the neighborhood of 20

keV energy is assumed to vary as M~^. Experiments confirm this relation [41] and suggest an x value between 0.5 and 0.8 which may

depend on mass. When a mass spectrum is recorded on an emulsion, in addition to the latent image that is produced in the silver bromide crystals at each

of the mass line positions, these crystals are doped by ion implantation

with the particular element responsible for that mass line. Some of these dopants wiU be electrically more active than others in the AgBr

crystals. One would expect that the active elements would not fall on

the simple curve for sensitivity as a function of mass M. Only

about 16 elements [41] have been so tested of which only 7 are above mass 40. Consequently there are wide gaps in the region above mass

40 which need fiUing before the simple relation should be accepted.
360 TRACE CHARACTERIZATION

D. Calibration of Emulsion

The next assumption made is that the photographic emulsion can be

adequately calibrated to express ion intensity as a function of the

darkening of the emulsion as revealed by optical transmission measurements. Sometimes this is done by making a graded series of exposures

in which the ion intensity is given by electrical measurements at the

monitoring electrode [39] at S3 in Figure 1. The precision in such electrical measurements is usually poor. Another method uses a single mass spectrum of an element with a number of isotopes that vary considerably in abundance [39]. The

relative ion intensity of the various isotopes is given by their relative abundance. Electrical measurements of ion intensities are not necessary. For this purpose tin is the most satisfactory element to use; its ten isotopes are adequately spaced in abundance to cover the range of the Ilford Q2 emulsion.

In the Churchill two line method [39], graded values of optical trans- mission are obtained from many pairs of mass lines corresponding to a

specific pair of isotopes of a given element. The corresponding ion

intensities are derived from the relative abundance of the two isotopes

in question. Electrical measurements are not needed.

A modification of this Churchill technique is reported [42] which

employs a single pair of mass lines of the selected isotopes of a given

element. Here the graded series of optical transmissions are read

directly from corresponding points along the optical transmission profiles of the two mass lines. Electrical measurements are unnecessary.

E. Spark Source Ionization Pattern

Usually trace concentrations are derived by comparing the singly

charged ion intensities of impurity and major component. This assumes

that the ionization pattern — the relative abundance of the ions of dif- ferent electronic charge — is the same for impurity and major component.

This assumption is not justified since the singly charged ions of one

element may be 95 percent of the total ionization of that element and

that of another element may be as low as 60 percent.

This difficulty is easily circumvented by determining the total ioniza- tion in each case. An adequate measure of this is usually given by the sum of the singly and doubly charged ions. Sometimes the doubly charged ions of impurity and major component

are compared. This is obviously a very dangerous practice.

F. Integration of Ion Intensity Profile

The optical transmission profile of a mass line on an emulsion can be

converted to an ion intensity profile [43] by means of an emulsion calibration. The ion charge recorded on the emulsion is obtained by integrating
MASS SPECTROSCOPY 361

[44] this intensity profile. This integration is time consuming. However a reasonably adequate measure of the ion charge is given by the

product of the ion intensity corresponding to the peak optical transmission and the half width — the mass line width at half of the peak ion

intensity [39]. The peak ion intensity alone is an adequate measure of the ion charge

only provided the hne widths for lines being compared are the same.

This assumption is not justified. Under controlled conditions this line width varies Hnearly with the square root of the ion mass. However, in an analysis where a trace element is being compared with a major component this line width relation may not hold and hne width measurements

are therefore preferable.

A promising alternative to the integration of the ion intensity profile

is the integration of the optical transmission profile [44a]. G. The Relative Sensitivity Problem

The preceding assumptions have been concerned with the analysis

of the ion sample, but, as pointed out in Section III, the composition of the ion sample in general does not accurately represent the composition

of the sohd sample. Presumably, the factors contributing to this lack

of fidelity in the ion sample are selective evaporation and ionization in the spark source and selective transmission by the double focusing mass

spectrograph.

Woolston and Honig [45] made measurements on the ion energy

distribution at the position of S3 in Figure 1, for a number of solids. Typical results are shown in Figure 5. Considerable variation is shown

18.6 19.0 19.4 19.8 20.2 20.6 21.0 21.4 21.8 TOTAL ENERGY(KV)

Figure 5. Energy distribution of ions in spark source mass spectrometry. After Woolston,

J. R., and Honig, R. E., Rev. Sci. Instr. 35, 69 (1964).
362 TRACE CHARACTERIZATION

in the width of the energy distribution curves for different materials and

also in their position on the energy scale. The double focusing capabilities of the Mattauck and Herzog geometry

[22] are limited to an ion energy band of a few hundred electron volts energy. In some cases the ions have an energy spread of a few keV as shown in Figure 5. In those cases only a fraction of these ions are passed by S3 of Figure 1. Moreover for any given element the fraction

passed depends on this distribution shape and on its location relative

to the pass band. The energy band passed by S3 may misrepresent

the total ion sample presented to S3 by an appreciable factor, thereby

contributing to the overall misrepresentation of the solid sample, by the

ion sample presented to the detector.

This lack of fidelity in the ion sample can best be determined experimentally by measurements on standard samples. This problem is treated in the following section.

VI. Ion Samples vs. Standard Solid Samples

Gorman, Jones, and Hippie [46] at the National Bureau of Standards

first analyzed standard samples with a spark source double focusing

instrument. Since high concentration (one percent or more) components

in a stainless steel sample were studied, electrical measurements could

be made. The concentrations derived from these measurements were

significantly different from the certified values of the standard sample.

They interpreted this to be a lack of fidelity in the ion sample and

calculated an empirical correction factor now called the Relative

Sensitivity Coefficient (RSC) — the ratio of the concentration of an ele- ment to that of its certified value. Measurements on a second standard

sample containing the same components as the first but with different

concentrations were then made. The calculated concentrations, cor- rected by the above RSC, were in excellent agreement with the certified values of this second standard sample.

The importance of this RSC is directly proportional to the amount by

which it differs from unity. The author compiled available data [47] in 1963 showing RSC values ranging from 0.21 to 6.5 — about half of the

values falling in the range 1.0 to 1.5. Table 2 lists similar data available since 1963. Some of these deal

with well established iron and copper standard samples. Much of it is based on concentrations determined by other methods thought to be

reliable. Examples of these are spectrophotometric measurements of

dopants in GaP and radiochemical, electrical, and spectrochemical

measurements in silicon and GaAs.

The data of Table 2 are summarized in Figure 6. Here the fraction of

the values within a given interval is plotted as a function of the RSC

value irrespective of the element or matrix involved. About 70 percent
MASS SPECTROSCOPY 363

35 1

1 2345 6789 10 RELATIVE SENSITIVITY COEFFICIENT (RSC)

Figure 6. Distribution of relative sensitivity coefficient values in Table 2.

of the values are in the range 0.5 to 2.0 Most of the remainder are greater than 2.0. Dejardins [50] found that the RSC values for a given element in several

different matrices were grouped around an average with a standard

deviation of about 25 percent. This degree of independence of an element from its matrix was observed for a number of elements, particularly cobalt and manganese.

Copellen, Conzemius and Svec [49] measured 12 impurities electrically

and photographically in 8 National Bureau of Standards iron standards.

The photographic data for most of the elements gave average values with

average deviations clustered near 20 percent.

Other measurements indicate that Relative Sensitivity Coefficients

determined from standard samples have standard deviations that usually

are not below 30 percent and may be above 50 percent.

A number of theoretical calculations [18] of Relative Sensitivity

Coefficients have been made but the uncertainty in the present experimental values makes comparisons difficult. The certified values, for the components in a standard sample, are average values for the volume sampled by the particular technique

employed in establishing this standard, and these values tell nothing

about the distribution of components within this volume. The use of any standard sample in any analysis is based on the assumption that the
TRACE CHARACTERIZATION

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366 TRACE CHARACTERIZATION

components are homogeneously distributed on the scale appropriate to the technique employed, i.e., that the volume of the standard that is sampled accurately represents the standard sample.

But many of the standard samples that have been employed in spark

source mass spectrometry have been standardized by techniques requiring substantially larger volumes than that sampled by the spark source. Measurements supporting or refuting the above assumption of homogeneity are important. This problem has been treated by Halliday [20]

and his collaborators. The homogeneity requirement becomes more

stringent for samples of higher impurity concentration since a smaller

sample is consumed by the spark. For impurities in the 10 to 100 ppma

range, the linear dimensions of the sample volume consumed are in the

range 15 to 300 microns [18]. This homogeneity requirement can be circumvented in two quite

different ways. Samples in the form of solid cyUnders are rotated about

their respective axis by appropriate arrangements [56]. In this way,

the spark samples an area large enough so that the volume consumed

is representative of the gross sample. This technique is of course only

applicable to samples that are available in cylindrical form. In the

second technique the sample consumed is increased by continuous

running of the spark but turning the ion beam on only intermittently [57]. This is a deliberate debasement of the sensitivity in terms of the amount

of sample needed for an analysis. For sufficiently small samples this practice can only be employed at the expense of detection sensitivity.

Because these techniques for circumventing sample inhomogeneities

have limited applicabihty, the problem of homogeneity of standards and

unknown samples remains one of considerable importance.

VII. Precision Capabilities of Spark Source Technique

The generally large scatter particularly in inter-laboratory comparisons

of samples has led to questions about the precision with which ion beams

can be measured with spark source double focusing mass spectrographs.

The author undertook measurements with an MS7 Mattauck and Herzog

geometry instrument using Ilford Q2 photographic plates. As pointed

out earlier, the ions of the various components of a sample do not always

accurately represent the solid sample. Moreover, this misrepresentation

may fluctuate in an uncontrolled way. Furthermore minor components

may not be homogeneously distributed in a sample. In order to circumvent these uncertainties, the measurements were made on the major

component - mass lines of reasonably pure elements. In this way, a

fixed fraction of the major component ions that are electrically measured

at the monitor electrode (S3 in Fig. 1) are simultaneously recorded on

the photographic plate.

Samples of platinum, tantalum, and tin were tested principally be- cause they have isotopes whose relative abundances were appropriate
MASS SPECTROSCOPY 367

for these tests. Using dual sample holders, 12 platinum and 12 tantalum

or tin replicate exposures were recorded on a given photographic plate

under specified conditions.

From the optical transmission profile the ion peak intensity and the

half width (width at half peak intensity) were obtained with the aid of a cahbration curve. The product of these was taken as the photographic measure of the ion charge of a specific mass line of a particular isotope.

Since multiply charged atomic ions and molecular ions are formed, their contribution must be considered. In practice the sum of the singly and

doubly charged ions was assumed to be adequate since this sum comprised about 95 percent of the total ionization. The 12 replicate spectra from each of the 2 elements on a given plate

yield an average value and standard deviation for the number of ions of the particular isotope in question. These data are summarized in Table

3 giving the plate number, the corresponding isotopes of the platinumtantalum comparison or the platinum-tin case as well as the quantity E

for the monitor measure of the exposure in coulombs. The quantity R

is the photographic measure of the number of ions for the given isotope

where / and W represent the peak ion intensity and half width as dis- cussed earher. The next 3 columns for platinum, tantalum, and tin respectively give the values of R/EF where F is the fractional abundance

of the isotope in question. R/EF is a measure of the plate sensitivity

for the particular element. The Hsted standard deviation described the

fluctuations of {I^^W\-{- I^-W-z) about R since the exposure was ter- minated automatically when E reached its preset value. The last 3 columns give the contribution of the singly charged ion in terms of the

total ionization as measured in these tests. With the spark source, the ionization pattern — the distribution of the

ions according to their charge — may fluctuate even though controllable

parameters are kept constant. These data indicate that for tin the standard deviation in R/EF when R includes only the contribution of the singly

charged ions might be almost as small as when the doubly charged ions

are included in R, but in the case of tantalum the standard deviation

probably would be larger.

The standard deviation values for the tin data range from 10 to 20

percent while that for the tantalum averages below 5 percent. Some of the platinum data gives standard deviations that average below 5 percent

and the rest is in the 10 to 12, percent range. Inspection quickly reveals

that it is the value of E that determines whether the standard deviation

is high or low. When £" = 1 or 2 X 10~ ^, it is below 5 percent not only for tantalum but also for platinum. On the other hand, when E = 3X 10~^^

it is largely in the 10 to 20 percent range for platinum as well as for tin. Among the factors that contribute to the fluctuations summarized in Table 3 are the following: (1) the precision with which the integrating

circuit measures monitor charge, (2) the precision with which the ratio

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370 TRACE CHARACTERIZATION

of charge passed by the monitor to that intercepted by the monitor is maintained, (3) the variation in sensitivity of the photographic plate.

These three factors are independent ones and therefore the fluctuations

that each introduces must be within that given by the standard deviations

of Table 3 which in many cases are below 5 percent. However, for monitor exposures of 3 X 10~ coulombs and presumably for still smaller

values, the fluctuations in R arise principally from those in E, i.e., the

precision with which the integrating circuit measures monitor charge

is degraded to a standard deviation of 10 to 20 percent.

Because it was somewhat unexpected, it is of special interest that the

fluctuations in sensitivity along the 2 inch width of the Ilford Q2 plates are within the 5 percent standard deviation of Table 3. This uniformity

within a given plate is accompanied by comparably small fluctuations

in sensitivity from plate to plate ^ as shown by the R/EF values for any 1 of the 3 elements tested. As shown at the bottom of Table 3, the average

RjEF value for such data carries a standard deviation of about 14 percent.

Every plate containing platinum and tantalum spectra consistently

gives higher R/EF values for the platinum. This is contrary to the M~-^ mass dependence discussed in Section V.C. and lends credibility to the

suggestion there that some elements may not conform to this simple mass dependence. On the other hand, the platinum-tin plates consistently give higher R/EF values for tin in qualitative agreement with the

simple mass dependence M~^. In summary, these measurements

indicate that under optimum conditions the MS7 spark source double

focusing mass spectrograph with Ilford Q2 plates can measure ion beams

with a precision of less than 5 percent standard deviation. In addition,

the evidence that the uniformity of these photographic plates was within

this precision was reassuring.

Many studies have demonstrated that even better precision can be

obtained in photographic measurements of isotopic abundance ratios,

However for such cases a small scale plate uniformity is sufficient. Therefore such tests do not establish the large scale (2 inch) plate uni- formity indicated by Table 3. VIII. The Homogeneity Problem

Having established the precision with which ion beams could be

measured by this technique, the measurements were extended to ele- mental dopants in Johnson, Matthey copper standard samples CA2 and

CA4. In these tests a platinum probe electrode was sparked to the

copper electrode which was electrically tied to the dc accelerating

voltage. After each exposure of a replicate series similar to those sum2 The R/EF value for platinum in plate 347 is not given as the R value is obviously high. Probably the monitor exposure was inadvertently made greater than the indicated value by a factor of 4 or 5.
MASS SPECTROSCOPY 371

marized in Table 3, the copper electrode was moved about 0.5 mm so

that a fresh spot on the copper was sampled by the platinum probe.

Prehminary experiments demonstrated that the platinum ions contributed not more than 5 percent of the ion sample to the detector. That

this nearly negHgible contribution by the platinum ions persisted was

verified by interspersing 4 appropriately short exposures among the

replicate exposures on each plate.

Preliminary measurements indicate that the replicate exposures yield

average values for the dopants with standard deviations between 5 and

12 percent in the case of the CA2 standard. For the CA4 sample, the

corresponding standard deviations were in the 10 to 20 percent range. However on one plate, the CA4 chromium dopant gave a standard deviation of 45 percent.

In addition to the three factors itemized in Section VII, others that could contribute to the fluctuations, characterized by the above standard

deviations, are the following: (1) The dopants may not be homogeneously

distributed in the copper. (2) Any misrepresentation in the ion sample,

due to selectivity in the vaporization and/or ionization of the dopants

in the copper, may fluctuate in an uncontrolled way. All of these five factors are independent and therefore the fluctuations that each intro- duces on a statistical basis must be within that given by the above standard deviation values. The measurements in progress on these copper standards suggest

that the standard deviation for some of the dopants in CA2 may not be

significantly higher than the upper limit of 5 percent indicated in Table

3 for major components and that the sample homogeneity is within this Hmit. For the other dopants, the sample homogeneity is within the 12 percent limit. The CA4 measurements suggest that in this standard,

the dopant inhomogeneities may be as high as 20 percent and in the

specific case of chromium it may be as high as 45 percent. Evidence for comparable inhomogeneities was observed by J. R. Woolston [57a] in similar replicate tests on another rod of this copper CA4 standard.

It should be remembered that in tests of this sort, the spark source mass spectrograph determines the degree of homogeneity of a sample

on exactly the scale desired for spark source mass spectrographic work.

IX. Standard Sample Needs and Possibilities

A wide array of standard samples with components not only in the

ppm range but also well below this are seriously needed for spark source mass spectrometry. Furthermore the degree of homogeneity must be

appropriate to this spark source technique.

Standards in the ppb range are needed to supplement and confirm

detection sensitivities derived by other methods [58]. For these pur- poses samples consisting of dilute solutions of selected elements in appropriate matrices should be useful. The selected elements should
372 TRACE CHARACTERIZATION

be polyisotopic ones with a spread in relative abundances and those with an isotope of very low abundance would be particularly useful. The

doping level could be high enough to determine the absolute value of

the concentration by established techniques with good accuracy, while

the low abundance isotopes reach into the low ppm and even into the

ppb region. Such a standard sample consisting of a dilute solution of

platinum in gold [36] has been used by the author. Elements like sulfur,

osmium, barium, tellurium, tantalum and calcium have equally attractive

distributions in relative abundance.

Perhaps the more urgent need for standard samples is for the accurate determination of Relative Sensitivity Coefficient (RSC) values. For these

purposes two classes of standard samples are needed. The first would

be an array of non-interfering elements in a matrix. These elements

need not be simultaneously in a given matrix since this may not be feasible in many cases. The second would be an array of the same elements

in a number of different matrices which again may have either simultaneous or individual element doping.

Such an array of standards, with dopants and matrices composed of

elements with properties covering a range of values, should help to answer the following questions. Is the RSC of element x the same in many or all matrices? Could empirical relations be established to predict the RSC of element x in matrix y? It would be of considerable

importance, if, from known properties of dopant and matrix or from

empirical relations, it were possible to calculate the RSC of element x

in matrix y without the aid or need of a standard sample.

X. Summary

1. Plate fogging from secondary products generated when the ion

sample strikes the photographic emulsion results in a serious loss in detection sensitivity — a factor of 30 or more. Plate splitting although

helpful is cumbersome at best. Efficient miniature ion collectors and/or

emulsions insensitive to secondary products are needed.

2. The resolving power available in commercial instruments precludes

the study of many elements in many matrices. The fraction of these

excluded combinations would be diminished only slowly even with substantial increases in resolving power.

3. Heretofore, instrument line background of carbon, oxygen, hydrogen, nitrogen, etc., limited the detection of these elements in samples

to a few ppma. Recent studies indicate that with partial pressures of

about 1 X 10'~^ torr, nitrogen, hydrogen and carbon can be detected at substantially lower values.

4. There may be appreciable departures from the simple (Mass)"-^

relation for the variation of emulsion sensitivity among the elements.

This could introduce serious errors in determining the concentration

of an element in a matrix.
MASS SPECTROSCOPY 373

5. Since the ionization pattern for a dopant and its matrix may be

significantly different, the ratio of singly charged ions of dopant and

matrix may give an erroneous measure of the dopant concentration.

6. In general, the composition of the ion sample presented to the detector does not accurately represent the composition of the solid sample.

Accurate values of Relative Sensitivity Coefficients (RSC) to correct for

this misrepresentation are needed.

7. The scatter in RSC values, obtained by comparing spark source mass spectrographic analyses with the certified values of the standard

sample, is serious.

8. In general the standards used were based on analytical techniques

requiring samples that were substantially larger than the spark source technique consumes. Information on the homogeneity of such standards on the spark source technique scale is needed.

9. Under optimum conditions with this spark source technique, an

ion beam can be photographically measured with a precision of less than

5 percent standard deviation.

10. Replicate measurements indicate that the variation in sensitivity of Ilford Q2 plates is within a standard deviation of 5 percent.

11. Items 9 and 10 indicate that the homogeneity of a sample on the

scale needed by the spark source technique can be established by

replicate measurements with the spark source technique itself. 12. Replicate measurements in which a platinum probe sampled

different areas of a copper standard indicate that the minor components

were not all homogeneously distributed.

13. A wide range of standard samples is needed. The homogeneity

of these needs to be appropriate to the spark source technique. Dopant

concentrations should be in the ppma to ppba range. Dilute solutions

of selected polyisotopic elements in compatible matrices are suggested

for some standards.

14. The accuracy and precision of the spark source technique at present is not adequate to characterize the role of trace impurities in the physics and chemistry of solids. Two examples of the latter given

at the beginning of this paper illustrate this inadequacy. A tenfold

change in the concentration of cobalt in gold produces a 100 fold change

in its thermoelectric power. A tenfold change in the concentration of

manganese and iron in titanium changes its superconductivity transition

temperature by a factor of 2.5.XI. Conclusion

The background problem remains a serious one. Probably plate

fogging by secondary products can be adequately circumvented. Ion

scattering by residual gases might be appreciably reduced by faster pumping and/or the introduction of a helium cold finger in the magnetic

sector. These two pumping aids also near the spark source might sub-
374 TRACE CHARACTERIZATION

stantially reduce the instrument background lines of carbon, oxygen, and

nitrogen.

It might be possible to increase the transmission of these double focusing mass spectrographs in two ways. It might be done by ion focusing

techniques since it is unlikely that the present simple geometry of the

spark source yields the optimum current. Another possibility would

be to introduce ion energy bunching techniques.

A substantial increase in transmission could be very useful. Times

required for exposures would be correspondingly reduced. This would

be important for long exposures and for microsamples. An alternative use of the increased transmission would be to reduce S2 and S3 of Figure

1. The smaller solid angle and the smaller energy band involved in the double focusing might yield an increase in resolving power. This

could be very useful in selected cases in spite of an undesirable selectivity that might be introduced by the narrower energy band passed by

S3.The variation in emulsion sensitivity among the elements needs

further investigation in view of the wide gaps in the experimental data

and the possible consequences of the ion implantation suggested in Section V.C. Because the contribution of multiply charged ions to the

total ionization is not generally negligible, the dependence of emulsion

sensitivity on ion energy is important particularly in view of the discontinuities in this relation reported by Woolston, Honig and Botnick [59]. The spark source mass spectrographic technique is capable of measuring the ions of a given mass/charge in an ion sample with a precision

of 5 percent standard deviation. With a standard sample that is ho- mogeneous on the spark source scale, the degree by which the ion sample misrepresents this standard sample, should be measurable with

corresponding precision and accuracy. The present accuracy and

precision may or may not be improved when these conditions are fulfilled. If they are not improved, must one then conclude that there are uncontrollable parameters in spark source mass spectrometry that

limit the accuracy and precision of solids analysis to the present unsatisfactory v£ilues? XII. References

[1] Morrison, G. H., Trace Analysis — Physical Methods, Interscience Publishers, New

York, 1965.

[2] SHchter, W. P., and Kolb, E. D., Phys. Rev. 87, 527 (1952).

[3] Bemski, G., and Struthers, J. D., J. Electrochem. Soc. 105, 588 (1958).

[4] Uhra High Purity Metals, American Society for Metals, Metals Park, Ohio (1962),

[5] Pearson, W. B., Reference 4. [6] Schaub, B., and Cabane, G., Compt. Rend. 444 (1963).

[7] Matthias, B. T., Geballe, T. H., Corenzwit, E., and HuU, G. W., Jr., Phys. Rev. 129,

1025 (1963).

[8] Falge, R. L., Jr., Phys. Rev. Letters 11, 248 (1963).

[9] Rutter, J. W., and Aust, K. T., Trans. Met. Soc, A.I.M.E. 2 1 8, 682 (1960).
MASS SPECTROSCOPY 375

[10] Hausner, H. H., and Roboff, S. B., Materials for Nuclear Reactors, Reinhold Publishers, New York, 1955.

[11] Schumacher, E. E., Trans. A.I.IVI.E. 188, 1097 (1950).

[12] Hannay, N. B., in Reference 1 — Pfann, W. G., Zone Melting, Wiley Publishers, New

York, 1965.

[13] Hannay, N. B., Rev. Sci. Instr. 25 , 644 (1954). Hannay, N. B., and Ahearn, A. J., Anal. Chem. 26, 1056 (1954).

[14] Hickam, W. M., Phys. Rev. 74, 1222A (1948); ASTM Bull. 149, 17 (1953); Honig,

R. E., Anal. Chem. 25, 1530 (1953); J. Chem. Phys. 22, 1610 (1954).

[15] Inghram, M. G., ASTM Bull. 149, 1 (1953). Inghram, M. G., J. Phys. Chem. 57, 809 (1953).

[16] Honig, R. E., J. Appl. Phys. 29, 549 (1958); also Reference 18.

[17] Dempster, A. J., Proc. Phil. Soc. 75 , 755 (1935); Rev. Sci. Instr. 7, 46 (1936).

[18] Honig, R. E., in Mass Spectrometric Analysis of Solids, Ahearn, A. J., ed., Elsevier Publishers, Amsterdam, 1966.

[19] Hannay, N. B., Science 134, 1220 (1961).

[20] HaUiday, J. S., Swift, P., and Wolstenholme, W. A., in Advances in Mass Spectrometry, Vol. HI, Mead, W. L., Editor, Institute of Petroleum Publishers, London, 1966.

[21] Woolston, J. R., and Honig, R. E., Rev. Sci. Instr. 35, 69 (1964).

[22] Herzog, R., Z. Physik 89, 447 (1934); Mattauch, J., and Herzog, R., Z. Physik 89,

786 (1934); Mattauch, J., Phys. Rev. 50, 617 (1936).

[23] Guthrie, J. W., in Reference 18.

[24] Guthrie, J. W., in Reference 18. [24a] Brown, R. A., Craig, R. D., James, J. A., and Wilson, C. M., Conference on Ultra

Purification on Semiconductor Materials, Brooks, M. S., and Kennedy, J. F., Editors, MacMillan Piibhshers, New York, 1962, Duke, J. F., ibid.

[25] Guthrie, J. W., in Reference 18.

[26] Guthrie, J. W., in Reference 18.

[27] Hickam, W. M., and Sweeney, G. G., in Reference 18. Guthrie, J. W., in Reference 18.

[28] Elliott, R. M., Craig, R. D.. and Errock, G. A., Instruments and Measurements, von Koch, H., and Lyungberg, G., Editors, Academic Press Publishers, New York, 1961.

[29] Ahearn, A. J., and Malm, D. L., Apphed Spectroscopy 20, 411 (1966).

[30] ,Mai, H., in Advances in Mass Spectrometry, Vol. III. Mead, W. L., Editor, Institute of Petroleum Publisher, London, 1966.

[30a] Witmer, A. W., Proceedings of the Sixth Annual MS7 Users Conference, Manchester,

England, March 28, 1966.

[31] Kennicott, P. R., Anal. Chem. 38, 633 (1966).

[32] Honig, R. E., Woolston, J. R., and Kramer, D. A., presented at the 14th Annual Conference on Mass Spectrometry and Allied Topics, Dallas, March 1966.

[33] Blosser, E. R., Battelle Memorial Institute, Columbus, Ohio, private communication.

[34] Dornenburg, E., and Hintenberger, H., Z. Naturforsch. 14a, 767 (1959).

[35] Ahearn, A. J., and Thurmond, C. D., J. Phys. Chem. 66, 575 (1962).

[36] Ahearn, A. J., presented at the 11th Annual Conference on Mass Spectrometry and

Allied Topics, San Francisco, 1963.

[37] Consensus of American MS7 Users Conferences.

[38] Socha, A. J., and Willardson, R. K., presented at the 14th Annual Conference on Mass

Spectrometry and Allied Topics, Dallas, March 1966.

[39] Owens, E. B., in Reference 18.

[40] Franzen, J., and Hebeda, E., Z. Naturforsch. 17a, 476 (1962).

[41] Burlefinger, E., and Ewald, H., Z. Naturforsch. 16a, 430 (1961). Owens, E. B., and Giardino, N. A., Anal. Chem. 35, 1172 (1963).
376 TRACE CHARACTERIZATION

Wagner, H., Ann. Physik 7, 189 (1964). Werner, H. W., Philips Res. Repts. 21, 63 (1966).

[42] Dejardins, M., private communication.

[43] Hull, C. W., presented at the 10th Annual Conference on Mass Spectrometry and

Allied Topics, New Orleans, 1962.

[44] Paulson, P. J., and Branch, P. E., 14th Annual Conference on Mass Spectrometry and Alhed Topics, Dallas, 1966. Kennicott, P. R., ibid. [44a] Kennicott, P. R., private communication. iSkogerboe, R. K., Harrington, W. L., and

Morrison, G. H., Anal. Chem. 38, 1408 (1966).

[45] Woolston, J. R., Honig, R. E., Reference 21.

[46] Gorman, J. G., Jones, E. J., and Hippie, J. A„ Anal. Chem. 23, 438 (1951).

[47] Ahearn, A. J., presented at the 11th Annual Conference on Mass Spectrometry and AUied Topics, San Francisco, 1963.

[48] Harrington, W. L., Skogerboe, R. K., and Morrison, G. H., Anal. Chem. 37, 1481 (1965).

[49] Capellen, J., Conzemius, R. J., and Svec, H. J., presented at the 13th Annual Conference on Mass Spectrometry and Allied Topics, St. Louis, 1965.

[50] Dejardins, M., Corning Glass Works, Corning, N.Y., private communication.

[51] Goshgarian, B. B., and Jensen, A, V., presented at the 12th Annual Conference on Mass Spectrometry and Allied Topics, Montreal, 1964.

[52] Auhnger, F., private communication to Honig, R. E., Advances in Mass Spectrometry, Vol. HI, Mead, W. L., Editor, Institute of Petroleum Publishers, London, 1966.

[53] Chupekhin, M. S., and Glavin, G. G., Zh. Anal. Khim 18, 618 (1963) (translated by

Assoc. Tech. Services, East Orange, N.J.).

[54] Klein, H. M., and Larrabee, G. B., Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Feb. 21-25, 1966.

[55] Ahearn, A. J., Trumbore, F. A., Frosch, C. J., Luke, C. L., and Malm, D. L., presented

at the 14th Annual Conference on Mass Spectrometry and Allied Topics, Dallas, 1966.

[56] Blosser, E. R., Battelle Memorial Institute, Columbus, Ohio, private communication.

Franzen, J., Max Planck Institute f. chemie, Mainz, Germany, private communication.

Aulinger, F., Proceedings of the Sixth Annual MS7 Users Conference, Manchester,

England, March 28, 1966.

[57] Franzen, J., Schuy, K. D., and Hintenberger, H., presented at the 12th Annual Meeting on Mass Spectrometry and Allied Topics, Montreal, 1964.

[57a] Woolston, J. R., private communication.

[58] Hull, C. W., and Blanchard, C. G., presented at the 13th Annual Conference on Mass

Spectrometry, St. Louis, 1965.

Elliott, R. M., and Swift, P., presented at the 13th Annual Conference on Mass Spectrometry, St. Louis, 1965.

[59] Woolston, J. R., Honig, R. E., and Botnick, E. M., presented at the 14th Annual Conference on Mass Spectrometry and Allied Topics, Dallas, 1966.
MASS SPECTROSCOPY

Contributed Papers and Discussion

E. B. OWENS

Lincoln Laboratory * Massachusetts Institute of Technology

Lexington, Massachusetts 02173

I. Introduction

We have six contributed papers to discuss. Four of the papers deal

with analytical applications, and we will discuss these four first. Each

paper has features which we might profitably consider, and some of

these points of discussion are found in more than one paper. In order

to give due credit to each contributor, I propose to present very briefly

the major contribution of his paper. Then I will discuss the other ideas

contained in these papers in a general fashion. The two remaining

papers will then be discussed.

At the close of my remarks, each contributing author will have the

opportunity to make additional comments if he feels that my presentation has not done justice to his paper. After these additions to the presentation, I will bring up one by one points from these papers for general

discussion.

II. Analytical Applications

The analysis of trace impurities in beryllium and uranium by spark

source mass spectrometry is described in the paper by Bourguillot,

Cavard, Cornu, and Stefani. They used the usual system of sparking

solid, self electrodes and, with minor modifications, rather generally

accepted methods of densitometry and data handling which incorporate

most of the corrections discussed by Dr. Ahearn. They report very

good results for the analysis of uranium for aluminum, silicon, manganese, chromium, iron, nickel, and copper. These results were ob- tained using sensitivity coefficients derived from the analysis of known

samples of uranium. The average error given is 19% compared to the

value obtained from chemical analysis. For the beryllium analysis,

they evidently did not have known samples from which they could obtain

sensitivity coefficients. This may explain the large errors of their re- ported results. The average error in this case was 37%. This paper is an excellent example of the work that can be done when standards are

available.

^Operated with support from the U.S. Air Force. 377
378 TRACE CHARACTERIZATION

In his paper entitled "Trace Impurity Analysis by Spark Source Mass

Spectrometry" Desjardin discusses some rather novel ways of handling

samples of various forms. A graphite film may be evaporated onto the

nonconducting film which is to be analyzed or the graphite film may be

put down as a mesh instead of a solid film. Special systems are shown

to shorten the distance between the supporting conductor and the spot

of sparking, thereby allowing the use of insulators as self electrodes.

This paper uses the same methods of densitometry and data handling

as did the previous paper except that a computer is used in the calculations. The paper reports values for the sensitivity coefficients of a number of elements in various matrices. These will be discussed later. The paper is a good illustration of the efforts that have been made to increase the versatility of the spark source method.

In a paper on trace analysis in oxidic matrices by solids mass spec- troscopy Oblas, Bracco, and Yee discuss a method using pressed elec- trodes made from mixtures of powdered oxide samples, graphite, and an

internal standard. Sensitivity coefficients were obtained from the

analysis of synthetic standards. The densitometry and data handling

methods conform to accepted practices and include corrections for

line width and the mass effect on photoplate sensitivity. The paper

reports a relative deviation of 20% of the true values on the analysis

of other synthetic samples, but the data of one of their tables showed

that much larger errors were sometimes encountered. The techniques

used for powdering samples are well illustrated in this paper. The paper by Strock and Oblas on the spark source mass spectrometric analysis of refractory metals gives preliminary results on the

analysis of tungsten wire sparked as the metal, and as the oxide mixed

with graphite and pressed to form electrodes. Sensitivity coefficients are reported for seven elements, apparently from the analysis of known

samples; but no comparative analytical results are given from which

the accuracy of the analysis could be evaluated. The preliminary results on the carbon, oxygen, nitrogen, and hydrogen content indicated cor- relation with certain physical properties. This paper is a good reminder

of the fact common to most trace analysis methods, namely, that even

preliminary analytical results often are found to have useful correlations

with some other properties of the material investigated.

III. The State of The Art - Improving Accuracy

Before I begin to discuss the other ideas these papers present, I would

like to make' a few comments not limited to the papers of this symposium

but including all current publications in spark source mass spectroscopy.

The work in analytical applications can be classified as either semiquantitative or quantitative. The semi-quantitative work assumes and

accepts large errors. Many papers give data to indicate the size of the errors for a given matrix. Others correlate the analytical data with
MASS SPECTROSCOPY 379

Other properties of the materials. Both types of paper are valuable

despite the large errors. Much of the work in the field today is aimed at reducing the large

analytical errors, i.e., at making spark source mass spectroscopy truly

quantitative. In this endeavor people are investigating the relative ion yields in the spark discharge, the uniformity of transmission of all ions through the instrument, the properties of the photoplate as an ion

detector, and methods of interpreting the data on a photoplate. The

present state of the art has moved away from the large error factors of semi-quantitative analysis and is moving encouragingly along the path

to quantitative analysis. I make these general remarks now to place

the following discussions in proper perspective. Much of what we will discuss will be these efforts to reduce the analytical error. A. Sensitivity Coefficients

Several of the papers that we had considered use the term "sensitivity coefficient". In Dr. Ahearn's review this sensitivity coefficient

is defined as the ratio of the concentration of an element as determined

by mass spectroscopy to the true concentration. An element for which

the method consistently gives high answers has a sensitivity coefficient

greater than one. The method has high sensitivity for that element.

This high sensitivity can be due to one or more of a number of factors. The spark discharge may produce a disproportionately large amount of

ions for an element. Addink [1] ^ has suggested that the high ion yield

may be a function of the relative volatility and diffusion coefficients of the elements. He has had some success in calculating sensitivity coefficients from these properties. Oblas, Bracco, and Yee feel that their

data show good agreement between the sensitivity coefficients and the

boihng points. The paper of Bourguillot and coworkers state that a number of parameters were carefully chosen to avoid a selective effect.

It would be of great value if during the discussion they would tell us which variables had the greatest effect on selectivity and what tests they

made to evaluate such effects. Dr. Ahearn has pointed out that selective transmission of ions through

the mass spectrograph may also contribute to high or low sensitivity

coefficients. Franzen and Hintenberger [2], and Woolston and Honig [3] have shown that the ions of the various elements do not all have the same energy when they leave the spark discharge area. Consequently,

different energy spectra are formed for the various elements as the ions

pass through the electrostatic analyzer. Since the energy slit permits

only a small portion of the energy spectrum to pass into the magnet field, the elemental composition of the ion beam passing into the magnetic

field is likely to be quite different from the composition of the ion beam

which passed through the electrostatic field. The transmission through

' Figures in brackets indicate the literature references at the end of this paper.
380 TRACE CHARACTERIZATION

the electrostatic field and energy slit is higher for some elements than

for others. The ratio of these transmissions will stay constant only if the energy spectrum relationships stay constant. However, the high

degree of reproducibility achieved by a few workers shows that the rela- tive instrumental transmission and the relative ion yield can be held constant when the sparking parameters are carefully controlled. We have seen so far that relative sensitivity coefficients are produced

by relative ionization factors and relative instrument transmission factors. We must add to this list the relative response characteristics of the photoplate. Fortunately, the response characteristics of the photoplate can and have been evaluated. We know how to calibrate the photoplate,

how to correct for line width and background, and how to correct for the effects of ion mass and energy on the photoplate response [4]. However, some workers use none or only a few of these corrections.

This, of course, affects their accuracy and, adds appreciably to the large

differences seen in the comparisons of relative sensitivity coefficients. In terms of quantitative analysis, a relative sensitivity coefficient value

is unique for a given element in a given sample, for a given set of sparking parameters, for the transmission characteristics for a given instru- ment, and for a given method of photoplate evaluation. Change any

one of these factors and you change the sensitivity coefficient value. The values are not interchangeable between laboratories. There are some who think they are interchangeable and that changing the matrix

has no effect. But they are talking about semi-quantitative analysis.

Desjardin states in his paper that most of the elements for which he

presents data possess a sensitivity coefficient which appears to be

independent of matrix. But a look at the data in one of his tables shows

the semi-quantitative nature of his observation. We have seen from

Bourguillot's paper that a quantitative accuracy of 19% can be achieved

with sensitivity coefficients obtained from the analysis of known samples

of the same matrix as the unknown.

B. Photoplate Evaluation

As was mentioned previously, there is disagreement among the many

laboratories on the number of corrections used in evaluating photographic data. We see some of this disagreement in the papers in this symposium. In one paper the authors correct for the width of some but

not all lines. And in evaluating lines due to polycharged ions they omit

corrections for the fact that the photoplate response increases linearly

with ion energy. Other authors omit corrections for the effect of mass

on photoplate response. It has been shown that these corrections are

large [5] and they must be considered even in semi-quantitative work

if the total errors are to be kept within factors of 2 or 3.
MASS SPECTROSCOPY

C. Ion Charge Distribution

381

Bourguillot and co-workers and Strock and Oblas point out that polycharged ions may constitute a significant portion of the total ion beam.

It is possible that for one element the singly charged ions may be 80%

of the ion yield while for another they may be only 50%. Errors that might result from this ion charge distribution are avoided by measuring

the lines of singly, doubly, and maybe even the triply charged ions and

summing to get the ion yield for each element.

IV. Computer Use in Calculations

In their paper Paulsen and Branch describe an electronic analog computer for measuring intensity areas on mass spectrographic plates.

Similar computers have appeared in the past few years with at least two

companies producing them commercially. They differ in the number

of corrections that we have discussed that the computer will make on

the photographic data. The computer described in this paper corrects

for the background, the non-linearity of the photoplate response, and

the line width or more exactly the line profile.

V. Molecules Found in Spark Spectra

The paper by Doan discusses the existence of metal carbide molecules

in the vapor state. While this paper does not deal with trace characterization in the sense of trace impurity analysis, some comments on the

theory presented on the spark discharge might be worthwhile at this time. Doan suggests that a quasi-steady state vaporization exists in the

spark, that a reasonably constant temperature for the specimen can be

maintained, and that the specimen continues to vaporize between each

spark.

These hypotheses are difficult to reconcile with the results of the time

resolved studies reported by Franzen [4]. It was shown that the more

volatile elements were ionized during the early part of each discharge

half cycle, and the less volatile elements were ionized later in the same

half cycle. This cycle of ionization was repeated for each discharge

half cycle indicating a repetitive, wide excursion of temperature. In other studies [6] light detectors put at the window of the mass spectrograph source chamber indicate the emitted light completely disappears

between each half cycle of the discharge. These results do not seem

consistent with the long term type of equilibrium Doan suggests.

However, some studies [7, 8, 9] can be interpreted as indicating the

existence of very short periods of quasi-equilibrium in the vapor phase

within each half cycle of the rf spark under certain conditions of operation. It seems very unlikely that at any time during the half cycle there

exists equilibrium between the solid and the vapor phases. I would

suggest that some attempt be made to reconcile these apparently contradictory theories.
382 TRACE CHARACTERIZATION

VI. Quantitative Mass Spectrography

I would like to discuss now some areas of development which I feel are most encouraging in the effort toward quantitative mass spectrography.

We have come to realize that the rf-spark ion source is both tedious

to operate and difficult to control to the degree that good reproducibility can be obtained. A pulsed dc arc discharge has been investigated as an ion source by Honig [10] and by Franzen [11]. They report that with

this new source good reproducibility is more easily and more consistently achieved. I would not be surprised to see this source replace the

rf spark, but today I know of only one instrument manufacturer that

offers it commercially.

Some investigators [12, 13] have reported considerable improvement

in precision when they rotate the electrodes continuously during the

sparking. A good part of this improvement could be due to the elimination of inhomogeniety effects by this constant introduction of new surface

into the spark gap. This is a technique used for years by emission

spectroscopists.

Another area of development has to do with the problem of standards.

It appears inescapable that for quantitative accuracy we must have

standards that match our samples in chemical composition and in physical form. The very smaU volume of the sample consumed in the ionizing

discharge imposes stringent requirements on the homogeneity of both

samples and standards. Therefore, it is understandable that it may be some time before our hosts, the National Bureau of Standards, can

supply us with standards having the homogeneity required. But I sug- gest that it is not necessary that we wait. Dr. NichoUs of the University of Manchester [14] has shown that by

grinding and decomposition in a flux, he can prepare very homogeneous

samples from inhomogeneous mineralogical specimens. And by this same technique he can prepare matching standards from reagent grade

chemicals. In this manner Dr. NichoUs has achieved relative standard

deviations of about 5% of the true value.

It seems to me that we should apply this technique to all of our samples, be they metals, semiconductors, or insulators. Those of us who

have done trace determinations by emission spectroscopy wiU remember

that some of the best quantitative results were obtained by applying this same approach to the preparation of samples and standards. It will require more work, and some sensitivity may be lost. But in this way, we should be able to overcome inhomogeniety and standardization

problems and move further along that road toward real quantitative mass spectroscopy.

VII. Comments from the Authors and Discussion from the Floor

Desjardin made some comments on the sensitivity coefficients found

in his paper and in the paper by Bourguillot et al. He stated that the
MASS SPECTROSCOPY 383

32% reproducibility of the sensitivity coefficients found for manganese

in a number of matrices constituted, in his opinion, quantitative results. Later experiments using more corrections on the photographic data

produced very similar values for these coefficients. He stated that the

additional corrections reduced the scatter but did not change the value

itself. Desjardin said he was very optimistic about the method and

predicted that by this method absolute analysis would some day be

possible.

Bourguillot said that because of the language difficulties he could not

reply immediately to the questions raised about his paper by the rap- porteur. He asked those interested to consult his pubUcations.

R. E. Michaehs (NBS) called attention to the NBS Miscellaneous

PubHcation 260 series containing reports of investigations of homogeneity on certain NBS standard materials. He said that the NBS Steel

Standard Material No. 461 had been found to be sufficiently homogeneous

to be used for any current analytical technique. Other materials have

also been investigated and the results reported in the 260 series. He

then called attention to the NBS OSRM Bulletin No. 6 deahng with the

needs for standard reference materials in spark source mass spectroscopy and invited comments from the participants.

Strock called attention to the very high results for potassium reported

in his paper. These results varied between 2 and 15 times the true concentration depending perhaps on the heat treatment the sample had

experienced. R. E. Honig (RCA) commented that he thought that these

high values were the results of thermal ionization. The boiling off of

elements of low ionization potential from a material of high work function (such as tungsten) could cause the results Strock reported. R. J. Conzemius of Iowa State University called attention to the advantages of using electrical detectors in place of the photographic plate.

They have achieved a precision of 1% in the analysis of the NBS 461

steel standard with electrical detection.

W. Renter (IBM) stated that he gets results that agree well with the

true values for a variety of materials. He asks then how can the varia- tions of sensitivity suggested by Dr. Ahearn and the rapporteur be

reconciled with his consistently good results. Concerning the variabihty of sensitivity coefficients, Desjardin re- ported that he obtained different values for the same samples on two

different instruments. He felt that an instrument factor must be used

with a general sensitivity coefficient. H. Kaiser (Dortmund) remarked that the problems we are discussing

today closely parallel the problems that confronted emission spectroscopists some years ago. He stated that, because of the complexity

of the problem and in particular the rf spark, he doubted that absolute

analysis would be possible. P. R. Kennecott (G.E.) stated that absolute values are not always

needed if the precision is good. Relative values are useful.

237-323 0-67—24
384 TRACE CHARACTERIZATION

Smales (AERE) expressed some disappointment that only spark dis- charges were discussed as ion sources and gave an example of some

excellent quantitative results achieved by an isotope dilution method

using a thermal ion source. The rapporteur replied that perhaps the reason for the emphasis on spark source was due to its relatively uni- form sensitivity for all elements. Kaiser stated that he too had gotten

good results with thermal ion sources. He then pointed out that the

method of standard additions is one way to get around the standards

problem.

Doan stated that some of the questions about his paper might be

explained by the fact that he operated the spark so as to get his elec- trodes very hot, instead of the usual mode of operation.

W. W. Meinke (NBS) remarked that as Michaehs has said, the NBS

has a program to develop standards for spark source mass spectroscopy.

But the NBS must know the needs of the people in this field in order to choose the most important material first. The rapporteur replied that the answer to the Bureau's questions depended greatly on the answer

to the question of interchangeability of sensitivity coefficients. If any

grouping of elements or matrices is possible, the task of standardization

is simplified somewhat. However, he believed that we do not have today

sufficient knowledge to answer this question.

VIII. References

[1] Addink, N. W. H., Z. Anal. Chem. 206, 81 (1964).

[2] Franzen, J., and Hintenberger, H., Z. Naturforsch. 18a, 397 (1963).

[3] Woolston, J. R., and Honig, R. E., presented at the 11th Annual Conference on Mass

Spectrometry and Alhed Topics, San Francisco, May 1963.

[4] Franzen, J., Z. Naturforsch. 18a, 410 (1963).

[5] Owens, E. B., in Mass Spectroscopy of Solids, Ahearn, A. J., ed., Elsevier, Amster- dam, 1966, pp. 56-110.

[6] Owens, E. B., and Giardino, N. A., Anal. Chem. 35, 1172.(1963).

[71 Franzen, J., Schuy, K. D., and Hintenberger, H., presented at the 12th Annual Conterence on Mass Spectrometry and Alhed Topics, MontrccJ, June 1964.

[8] Franzen, J., and Hintenberger, H., Z. Naturforsch. 16a, 535 (1961).

[9] Chupakhin, M. S., Sovrem. Metody Anahza, Metody Issled. Khim. Sostava i Stroeniya

Veshchestv, Akad. Nauk SSSR, Inst. Geokhim. i Analit. Khim (1965), 33.

[10] Honig, R. E., Glass, S. S., Woolston, J. R., Proceedings 6th International Conference on Ionization Phenomena in Gases, Paris, 1963. Vol. 2, pp. 209-216.

[11] Franzen, J., and Schuy, K. D., Z. Naturforsch. 20a, 176 (1965).

[12] Franzen, J., Max Planck Institute fur Chemie, Mainz, Germany, private communication

[13] Habfast, K., Atlas Mess-und Analysen Technik. GMBH, Bremen, Germany, private communication.

[14] NichoUs, G. D., Analysis of Geological Materials by Spark Source Mass Spectroscopy,

presented at Fourth National Meeting, Soc. Appl. Spectroscopy, Denver, Colo., Sept. 2, 1965.
PRECONCENTRATION IN TRACE ANALYSIS

JERZY MINCZEWSKI

Technical University of Warsaw,

Institute of Nuclear Research, Warsaw, Poland

I. Introduction

Methods currently at our disposal in modern analytical chemistry

for the determination of trace impurities do not always ensure, unfortunately, direct determination of these impurities in all high purity

materials. Influence of the main component of the sample, mutual

effects of the trace components involved, hmited sensitivity of methods,

and sometimes difficult access to costly apparatus are all in part re- sponsible for trace impurities in high purity materials still being very

widely determined indirectly after the traces have been isolated from

the sample by concentration and eventual separation.

The problem of the determination of trace components is not related

exclusively to that of high-purity materials. The former has been used

first of all in agrochemical, biochemical, biological, agrotechnical, and

oceanographic studies, where the idea of microcomponents has been

known for quite a long time, and where methods for their determination

have been developed even before the so-called high purity materials

became important.

Yoe and Koch [1] ^ have presented a remarkable report on this question with respect mainly to the requirement of natural sciences,

the report being published with the materials of a symposium on trace

analysis (New York, 1955).

Methods of measurement of trace constitutents have been discussed

in other papers. Problems to be considered here, in general, are pre- sented in Table 1. In the middle column all analytical operations are

listed to which the material tested is subjected and from which an av- erage laboratory sample is withdrawn, and the most important chemical

processes resulting in isolation, concentration, and separation of the

trace components to be determined.

In the left column are presented the agents which may directly or

indirectly influence the particular steps of the process discussed, the

composition of the withdrawn sample and the successive steps of its chemical processing, causing concentration changes in the micro-

^ Figures in brackets indicate the literature references at the end of this paper. 385
386

Table 1. TRACE CHARACTERIZATION

General scheme of the analysis of high purity materials.

Agents influencing Analytical operations Methods of deter- mination

Homogeneity

Storage

tools atmosphere

reagents

changes in composition

contamers

reagents

atmosphere

volatility

MATERIAL

to be tested

>l J' J' sampling

grinding

mixing

surface cleaning

laboratory sample

I sample solution

separation separation

of matrix of traces

concentration

I solution of traces separation

/ I \

individual trace components

nondestructive

methods

direct methods

(solids)

direct methods

(solutions)

simultaneous

determinations

of many components

determination

of individual

components

components to be determined and leading consequently to an erroneous chemical characterization of the analyzed material. In the right column are indicated the analytical methods which can

be applied in the individual steps of the process. Chemical problems of the processing of samples of high purity materials in order to isolate, concentrate, and separate trace impurities were the subject both of the plenary reports at the conferences of the

lUPAC in Lisbon [2], London [3], and Moscow [4], and of many reviews

[5-12].
PRECONCENTRATION 387

II. Preparation of Sample

A. The Analyzed Materials and Sampling

The high-purity materials that will be discussed later in this report can be divided into three groups, using the type of sample as the cri- terion: sohds, powdered materials, and liquids. Included in the first group are mainly metals of high purity and materials used in production

and processing of metals of high purity. To the second and third groups

belong in principle chemicals of high purity used as starting materials

for obtaining metals, auxiHary production materials, and reagents used

in trace analysis.

The most difficult to analyze undoubtedly are solid materials because

of their considerable lack of homogeneity. The segregation of components, known from metallurgical analysis, also appear in the case of high purity metals, quaUfied as 5 A^, 6 N, and higher. Figures 1 and 2 present autoradiograms of aluminum-copper (Al-Cu 4) and aluminumnickel (Al-Ni 0.3) ingots [13]. The observed unequal distribution of the admixture is very indicative of errors which can be brought about

by withdrawing for analysis a random part of the material portion.

As a proof of these inhomogeneities, application of the zone melting

method for concentration of traces can be mentioned.

Metallurgical methods can be applied to prepare a homogeneous

sample from a block. Repeated melting, mixing, and rapid crystallization

may possibly produce a fine-crystalline structure without segregation.

This procedure has the inherent danger, however, of introducing impurities in the process of melting and, in addition, is not easily carried

Figure 1. Autoradiogram of Al-Cu 4; ingot; X 3.
388 TRACE CHARACTERIZATION

Figure 2. Autoradiogram of Al-Ni 0.3; ingot; X 8.

out in an ordinary analytical laboratory. More suitable to the average

laboratory conditions is a fine shaving of the material or powdering of

brittle materials, mixing, eventually etching and washing. Samples,

carefully withdrawn from such a material, do not show inhomogeneity.

In Table 2. are listed the variances of the spectrochemical results from an analysis of four aluminum samples (3 g each) prepared in the

way outlined above from a block (200 g). The comparison of the cal- culated Fisher's factor with the value taken from the table indicates

satisfactory homogeneity [14]. The inhomogeneous distribution of admixtures in metals are evidently

related to the solubility of the trace component in the matrix metal.

The determination, for example, of lead in aluminum (insoluble component) has shown (table 2) an appreciably larger dispersion than the

determination of manganese (soluble component — larger probability

of equal distribution).

Obviously, it should be remembered that the analysis of an averaged

sample results in a mean content of impurities, but it gives no picture

of the degree of homogeneity.

Shaving of metals even as soft as aluminum always introduces con- tamination of metals from a turning tool. Figure 3 presents the auto- radiograms of an aluminum piece cut with an ordinary steel turning

tool (Fig. 3a) and with a turning tool made from tungsten carbide (Fig. 3b).

Both the mechanical treatment of solid materials and the etching

with acids to wash the secondary admixtures may change the structure
PRECONCENTRATION 389

Table 2. Comparison of normalized variances of trace determinations

in standard aluminum sample (Vst) and in a sample homogenized in laboratory (Vh). F = Fisher test value taken from the table for given freedom degrees number [14].

Fisher test value

Element calculated

Vst

table value

Fe 6.80 4.04 1.68 2.60

Si 6.92 11.71 0.59 2.60

Mg 2.76 5.12 0.54 2.60

Mn 2.51 1.76 1.43 2.60

Pb 8.99 4.64 1.94 2.60

and composition of the meted involved. In particular etching of fine- grained samples may cause appreciable washing of the individual components from the sample. For this reason crushing cannot be carried

too far. In summary it may be said that the problem of sampling metals of

high-purity is difficult to solve in a universal and satisfactory way.

Insufficient correlation between the physical properties of high purity

metals and the chemical composition determined analytically probably

Ues in the problem of sampling. An interesting discussion of a similar

problem, i.e., with homogeneity of semiconductor materials and their

Figure 3. Autoradiograms of aluminum block cut using: a) ordinary steel turning tool; b) turning tool made from tungsten carbide.
390 TRACE CHARACTERIZATION

surface and structure investigations has recently been reported by

Kane [15].

It is much easier to take representative samples of powdered materials,

but such powders can readily be contaminated in the course of eventual

grinding before dissolution.

It seems that in the case of hard materials, mortars from a corundum

monocrystal, tungsten carbide [16], or pure molybdenum [17] would be

preferable. Since grinding always is accompanied by contamination

of the sample, such mortars introduce to the latter only one definite component to be neglected in the determination.

No difficulties are encountered in withdrawing representative samples

of liquid materials. A serious problem is presented, however, by their

storage.

B. The Technique of Work

Burriel-Marti [2] has rightly stated that aU operations concerning the

determination of trace components require the preservation of ''chemically aseptic" conditions of the work. Indeed, already the determination of 10~^% quantities of universally dispersed elements such as sodium, potassium, calcium, magnesium, silicon, boron, and zinc pre- sents difficulties in any ordinary unconditioned laboratory. By going

to the determination of 10~^% quantities and lower, analogous difficulties arise with a number of other elements such as iron, copper, lead, alu- minum, and titanium. Factors directly influencing the final results of trace impurities are the following: laboratory air, laboratory vessels, water, and reagents.

These questions have widely been discussed by Thiers [18].

7. Hermedzation of Operations

The air of any analytical laboratory and the analyst himself (e.g. creams and other cosmetics contain the mineral components Al, Zn,

B, and Si) can be a serious source of secondary contamination of the

analyzed sample. The air is contaminated by ordinary dust and in addition by metallic parts of laboratory devices (burners, cocks, etc.) which undergo corrosion when in contact with the vapors of volatile acids. Lead in the atmosphere of towns originates from the combustion of lead tetraethyl [19]. Table 3 presents data on the determination of various impurities in silicon and nitric acid, the data being indicative of the important positive influence of the hermetization of analytical operations. Figure 4

shows the dispersion of results obtained in the spectrochemical deter- mination of impurities in high purity aluminum. The circles denote

the results obtained without hermetization; the crosses denote the

results when aU analytical operations were done in hermetic boxes [20].
PRECONCENTRATION 391

Table 3. The influence of laboratory atmosphere on the results of

trace determinations. All results in 10"^% [17].

Contaminations determined

Sample Conditions

Al Fe Ca Cu Mg Mn Ni

Silicon ^ A 10 10 10 0.4 10 <0.2 < 0.5

B 50 300 50 2 50 2 2

Nitric

All operations

hermetized

1 8 3 <0.1 5 0.1 <0.1

acid

All operations

in laboratory

atmosphere

50 30 50 5 30 0.6 0.7

^ The traces were enriched on graphite powder and the first part (A) was excited immediately after enrichment, the second (B) after 1 week storage in normal laboratory atmosphere.

Chow and McKinney [21] have determined lead from the air intro- duced into a 500 ml hydrochloric acid sample and evaporated during

a long time under varying conditions. From the data in Table 4 it is seen that hermetization in a purified air stream diminishes the lead

contamination of the sample by a factor ranging from 10 to 40. Hermetization of analytical operations can be readily accomplished

in glove-boxes made from plexiglass and adapted individually for the

operations intended. This enables separation of the particular actions

connected with studies of various materials. For example, there may

be separate boxes for the processing of boron samples, separate ones

for silicon, aluminum, etc., thus permitting the adaptation of the sizes and shapes of boxes to a given analytical operation. It is also possible

with such boxes to change quickly the range of work in the same laboratory area.

2. Laboratory Vessels and Containers

The main materials used for laboratory vessels and containers include

glass, quartz, platinum, and organic plastics such as polyethylene.
Table 4. Lead contamination from air [21].

Beaker Condition Laboratory Time Amount

of lead

days

Teflon Open ordinary 8 4.07

2.32

Nitrogen flushed container ordinary 8 L13

Open pure air 8 0.44

Nitrogen flushed container pure air 8 0.18

0.13 Nitrogen flushed container pure air 1 0.02

Borosilicate Nitrogen flushed container pure air 1 0.03

glass
PRECONCENTRATION 393

polypropylene, and fluorine derivatives. These materials, when in contact with a sample can influence the concentration of trace components in solution by the following three ways: (1) by the sorption of trace components they can diminish the concentration of the traces in the solution examined, (2) by leaching, the solution can be enriched

in mineral components, thereby increasing the concentration of traces,

(3) the components previously adsorbed by the walls of the vessel can

pass into the sample solution. Studies carried out on these effects permit the estabhshment of a

series of the apphcabiUty of the use of the above mentioned materials

in trace analysis: Teflon and other fluorine plastics > polyethylene

> quartz > platinum > glass. Obviously this is an average series of the appKcabihty of the materials. In individual cases appreciable deviations may occur. These eff'ects are such that on the average the

composition of solutions may be assumed to be unchanged within a hmiting concentration of up to 10~^%. However, changes in concentration are very hkely to occur in solutions of lower concentrations such

as of the order of 10~Wc.

The equilibria of sorption, dissolution, and desorption at the above

concentrations usually estabUsh very slowly. Therefore these effects are of considerably greater importance in considering the preservation

of standard solutions and reagents than in the course of ordinary short- time analytical operations. In the latter case prolonged dissolution

and evaporation at elevated temperatures are particularly undesirable.

Studies of sorption and desorption equilibria on surfaces of various

materials have been developed appreciably during the last years. In

the field of apphcation of radioisotopes this is connected with an acute problem of contamination and decontamination of materials in radiochemical laboratories. Although it is necessary to consider that radioisotopes, differing energetically from stable isotopes, can behave

differently in these processes than the ordinary isotopes, nevertheless use can be made of these studies in trace analysis.

Attempts have been made to formulate simple mathematical rela- tions [22] to express the concentration of the isotope adsorbed on the

surface of a vessel and in the solution as a function of the partition

coefficient, volume of the solution, and the contacting surface of the

vessel with the solution. It is worthy of notice that the latter parameters,

and in particular the ratio of volume of the solution to surface area of the

vessel, change by a factor of two when going from a beaker of 50 ml

capacity to a beaker (bottle) of 1000 ml capacity, in favor of the latter.

It should be emphasized that glass is entirely unsuitable for work

with traces. The components of glass readily pass into any solution,

the concentration of the passed components easily reaching 10~^%. A

watch glass used to cover a dish in which water was boiUng gave up to
394 TRACE CHARACTERIZATION

1 mg of Si02 during one hour, and 1.4 mg of Si02 in 30 min when an ammonia solution was boiled [23]. Even such trace components of

glass as lead are in quantities high enough to pass into the solution

analyzed. Chow and McKinney [21] have found that the latter impurity

may increase up to 0.1 /xg during the normal course of analysis.

So called heavy metals easily undergo adsorption on glass the surface

of which, particularly after prolonged contact with aqueous solutions,

becomes soft and then behave similarly to an ion exchanger.

Quartz possesses much better properties and is more chemically

resistant than glass. In connection with the production of semiconductor materials, quartz of high purity now is widely available for analytical work.

Platinum vessels also seem not to be quite safe for work with traces because they can cause considerable contamination of the solutions

examined. Vasilevskaya [17] has reported results of analyses of hydrofluoric, hydrochloric, and nitric acids after evaporation in dishes made

from Teflon, platinum, and from the ordinary quartz. It is seen from

Table 5 that after evaporation in a platinum dish the content of some

impurities increased by 0.5-1.0 order of magnitude. The acids evap- orated from the ordinary quartz exhibited a still higher degree of con- tamination.

Table 5. Results of spectrochemical analysis of HF, HCl, and HNO3

after evaporation in Teflon, platinum, and quartz dishes. All results

in 10-7% [17].

Elements determined

Acid Material

Al Fe Ca Cu Mg Mn Ni Pb Ti Cr Sn

HF Teflon 3 3 1 <0.04 < 3 0.1 < 0.4 <0.1 0.1 < 0.4 N.D.^ platinum 10 10 10 0.4 10 0.2 0.3 0.5' 1 0.5 N.D.«

HCl Teflon < 4 3 5 0.2 3 0.1 N.D« < 0.4 N.D.^ N.D.^ platinum 2 2 10 1 6 0.2 0.6 < 0.4 0.4 Tr.'' < 0.4 quartz 10 10 60 1 10 0.4 2 0.5 2 0.6 0.4

HNO, Teflon 2 8 4 < 0.01 7 0.1 N.D.« N.D.« Tr." N.D.« N.D.^ platinum 20 20 30 0.4 20 0.6 Tr.^' 1 0.8 N.D.^ N.D.^

quartz 20 20 60 0.1 20 0.6 N.D.^ 1 0.3 N.D.'^ N.D.«

^ N.D. = not detected.

''Tr. = traces, not evaluated quantitatively.
PRECONCENTRATION 395

Plastics, in particular polyethylene which has widely been introduced

as a package for reagents, and Teflon with other fluorine plastics, surely

are the most suitable materials for trace analysis. Here also, however,

solutions may be contaminated with metal traces. In the case of fluorine materials the eventual adsorption of traces should be taken into account; this may be brought about by the complexing ability of fluorine with respect to some metals. This however seems to play no major role in practice.

Of particular concern, when working with traces, is the washing of laboratory vessels. The traditional chromium mixture should not be

used since, for example, as Butler and Johnston [24] have found, the

adsorption of chromium on Pyrex glass amounted to 10 ng per cm^.

It has long been shown by Lang [25] that the washing away of chromium

traces with water is very difficult. Thiers [18] recommended for this purpose a mixture of concentrated sulphuric and nitric acids and

Haberh [26] a hot ammoniacal solution of EDTA, advising, however, even after this operation that the purity be checked by means of a dilute dithizone solution (in case the heavy metals are to be determined).

3. Reagents

The reagents used in the course of trace analysis are the most important source of contamination and their preparation in a state of

suitable purity frequently is a chemically more difficult problem and more

laborious than the trace determination itself. Although reagents of special purity are at present produced, for example, the so called

"transistor grade" (B.D.H.), "Suprapur" (Merck), etc., their selection

is rather poor and their purity (usually the content of the particular impurity is not better than 10~^10~^%) sometimes is unsatisfactory.

The required purity of the reagent used in the course of trace analysis

depends, of course, on the content of the impurity to be determined and

on the mutual weight ratio of the sample to the reagent. The content

of impurities in a reagent should, however, be lower by one order of magnitude than that to be determined in the sample.

In the course of analysis the most important reagents are: water of

high purity, acids (HCl, HF, HBr, H2SO4, HNO3, CH3COOH) bases

(NaOH, NH3 aq), buffer solutions, and solvents, the latter being used

in large quantities.

The purification of water by means of ion exchangers (mixed bed

columns) and by double distillation from quartz or platinum vessels now does not afford any difficulty.

For the removal of Si02 traces, Wickbold [27] proposes the use

of strongly basic anion exchangers (Permutite ES). The content of

Si02, after the water sample was passed through the above exchanger,

did not exceed 1.5 fJLg/1.
396 TRACE CHARACTERIZATION

Irving and Cox [28] have widely discussed the preparation of HCl

and NH3 solutions of highest purity by isopiestic distillation. They

obtained ~ 10 NH3 and ~ 5 A'^ HCl solutions the purity of which was

equal to that of water applied for the absorption. Similar results can

be obtained in the case of ammonia solutions by saturating the water

with gaseous NH3 from a bottle, the gas being passed, as suggested

by Haberli [26], through three washing bottles with an ammoniacal

solution of EDTA.

Greater difficulties are encountered with the purification of hydrogen

fluoride. The slow distillation method has been applied for that pur- pose in silver and palladium vessels, collecting the middle fraction (50%)

which demonstrated the highest degree of purity. In order to obtain

hydrogen fluoride without sihcon, Stegeman [29] suggested the passage

of gaseous hydrogen fluoride from a bottle in a nitrogen stream through

a polyethylene assembly consisting of five bottles connected in a series. The first bottle contained an aqueous layer with polyethylene pellets,

the second and the third contained polyethylene peUets and an aqueous

suspension of sodium fluoride (to combine fluorosilicic acid) the fourth

contained an air buffer, and the fifth contained pure water in which

absorption proceeded.

Solutions of many reagents can be freed from the heavy metals by means of dithizone. This method is unsuitable for the purification of

sodium hydroxide solutions. Such solutions, as proposed by Nazarenko

and Fliantikova [30] can be prepared, using sodium of special purity

(distilled), dissolved in high purity water.

III. Concentration and Separation of Traces

To isolate, concentrate, and separate trace impurities all the known

methods of partition are applied [31]. The methods are based on

precipitation, coprecipitation, and solvent extraction. They also include

chromatographic methods, electrolytic methods, based on the diff'erence

in volatiUty of substances, and other more specific methods which are appHed occasionally.

Two principally different procedures consist either in separating the

main component (the matrix) of the sample, the trace component remaining in the mother solution (macro-micro separation), or in separating

trace components, the matrix remaining in the solution (micro-macro

separation). In addition, some methods require the trace components

to be separated from each other (micro-micro separation).

When discussing particular groups of methods, the role of two fields of chemistry in their development must be emphasized. These are: complexing compounds and organic reagents applied in inorganic analysis. In the last twenty years the development of both these very closely

related fields has introduced to analytical chemistry in general, and to
PRECONCENTRATION 397

the separation methods in particular, a very great number of new organic

complexing reagents and a good deal of information on the mechanism

and kinetics of complexing reactions. A thorough knowledge of these

two fields makes possible the solution of very difficult separation problems of any mixture of ions in a wide range of concentration.

The basic data on the theory of complexing reactions with the purpose

of determining stability constants and of using complexing agents in analytical chemistry can be found in papers of Bjerrum, Schwarzenbach

and Sillen [32], Jacimirski and Vasil'ev [33], and Ringbom [34]. Schwarzenbach [35] in his studies gave an excellent generaUzation of the rela- tionship between the location of an element in the Periodic Table, i.e. between its electronic configuration, and the ability of the element to form complexes with different ligands. This is of particular importance

when looking for suitable complexing agents for complicated separation

processes.

In the course of concentration and separation of traces, particularly

with chemical methods, an important role is played by masking reactions.

For this reason these reactions will be discussed first.

A. Masking

An appropriate choice of a masking agent in micro-macro separations

makes isolation of trace components possible while the main component

remains in the solution. The choice permits the attainment of a better

selectivity or even specificity of the reaction in micro-micro separations.

A better understanding of the theory of complexing renders it possible

to derive theoretical principles of masking. Studies of Cheng [36] and

Hulanicki [37] gave the theoretical basis of application of masking agents

in analytical problems.

In Table 6 the possibilities of the application of twelve most important masking agents are presented. Taking into account the great

similarity, some complexing agents are considered jointly, e.g. oxygen

complexes (e.g. Mn04, WO4^) and hydroxylic complexes A1(0H)4,

Zn(0H)4^, cyanide and ammonia complexes, citrate and tartrate complexes (citrate complexes are, in general, more stable in acid solutions,

tartrate complexes in alkaline solutions).

The following are interesting examples of masking. Large quantities

of zinc, nickel, manganese, copper, silver, and other elements are held

in solution after being transformed into the complexes during the precipitating separation of traces of Ca and Mg (with carriers) as the phosphates

[38]. For the analysis of trace admixtures in uranium, sodium carbonate can

be used as the masking agent. The latter isolates a majority of the

traces involved in the form of hydroxides or carbonates, while transforming the uranium into a soluble carbonate complex.
398 TRACE CHARACTERIZATION

Table 6. Some masking agents [31].*

Be

aei Mg

deCa

de

SrdeBa

de

Sc

deY

deLa

de

Tiegh

Zregh

Hf

egh

V

ahj "Nb"

egh Ta

egh

Cr

aeg Mo

aeb w

aeb

Mn

aed

Re

aej

Fedeg

aej Os

aej

Co

cdj "rT

cje

Ircje

Ni

cdj Pd~

cej Ptcbf

Cu

cfd

cfAu

cf

Zn

cad Cd~

cdf h7

cf

B

ga

AlGa

ade

deg

Tl

fgj

SigaGe

bgj in"

abj Pb

aef

As

ab "Sb"

abe

Bidef

Se

Ce Th U

de edi ieh

a — oxygen- and hydroxide-complexes

b — sulphide-complexes

c — cyanides and ammonia-complexes

d— EDTA-complexes

e — citrate- and tartrate-complexes

f — thiocyanate-complexes

g — fluoride-complexes

h— peroxide-complexes

i —carbonate-complexes

j — oxalate-complexes

In tables 6, 7, 8, 9, 10, 12, 13 the lanthanides and actinides are represented by cerium, thorium and uranium only.

B. Precipitation and Coprecipitation

Precipitation methods based on the difference in the solubihty of the

reaction products — both the main and trace components — can be appHed

to all types of separation processes [31]. In macro-micro separations, contrary to the common opinion that the

main component, precipitated from a solution, always is accompanied by

appreciable adsorption of microcomponents, it proved possible in numerous studies to separate the main component without any loss of the traces involved. Recently published papers illustrate this possibility. In the analysis of high purity silver aiming at the determination

of copper, zinc, cadmium, nickel, and cobalt, Marczenko and Kasiura [39]

separated the silver fron a dilute nitric acid solution as the chloride. It was observed by these authors that the traces were not adsorbed on the

precipitate. Karabash et al. [40], when analyzing lead, removed the

main component from a nitric acid solution as the sulphate. Using

radioactive tracers they have shown that none of the twenty-four ex- amined trace components was coprecipitated. Degtiareva and Ostrov- skaya [41] have similarly found that there is a possibility of removing

lead as the lead chloride by saturating the solution with gaseous hydrogen

chloride. Similarly it was found that macroquantities of bismuth can

be separated from nitric acid solutions as a sparingly soluble precipitate
PRECONCENTRATION 399

of bismuth iodide [42] or as the basic nitrate, mercury after being reduced

in a nitric acid solution by means of formic acid [44], molybdenum as the

benzoinoximate [45], and zirconium as a salt of amygdahc acid [46]. Listed in Table 7 are the most important methods of removing the

main component in the form of difficultly soluble precipitates. The

largest group contains the elements which can be isolated from solutions

in the elemental form by means of reduction, the most frequently applied

being electrochemical reduction. Electrolytical isolation of a metal

from an acid solution at a stable cathode is limited to the noble metals

and the half-noble metals of lower, under given conditions, decomposition potential than hydrogen. The application of a mercury electrode

that possesses a high overvoltage potential for hydrogen allows one to isolate from solution the less noble metals: iron, nickel, copper, zinc,

and lead. The noble metals and some other elements, for example,

selenium and tellurium, can be precipitated from solution in the ele- mental form during the reduction by chemical means.

Coprecipitation of traces with macroquantities of a precipitate, the

phenomenon that is so unfavorable during the removal of microcomponents, is widely used to isolate microcomponents by their precipitation on carriers. Although the action mechanism of carriers, and the coprecipitation

process in general, have been the subjects of numerous papers, many

papers possess only an empirical character.

Table 7. Separation of matrix using precipitation [31].

LibNa

b

Sid K

b Cac Cr

a Mna Fea Co

a Ni

a Cu

ab Zn

a Ga

a Ge

a Se

a Rb

b

Sr

c Zr

d Nb

d Moa Ru

a Rh

a Pd

a Ag

ab Cd

a

In

a Sn

a Sb

a Tea Cs

b Bac Ta

d W

d Os

a

Tra Pt

a Au

a Hg

ab

Tlab Pb

cb

Biab

The elements are separated:

a — in elemental form

b — as halogenides

c — as sulphates

d— as oxygen compounds
400 TRACE CHARACTERIZATION

In Table 8, in a Periodic Table scheme, the elements are listed whose

traces can be concentrated by means of coprecipitation on carriers. The most important forms in which a given element can be isolated are marked.

The elements that can be isolated on carriers in the form of a hydroxide

are also well isolated by organic reagents of the R—OH type, e.g., 8- hydroxyquinoline and cupferron. The elements that form difficultly

soluble sulphides can be precipitated with carriers not only as the sul- phides but also as complexes with organic reagents of the R—SH type, as for example, dithiocarbamic acid derivatives, xantogenic acid derivatives, thionalide and others. For the group separation of traces some

mixtures of precipitating reagents can be used, e.g., 8-hydroxyquinoUne + tannin + thionalide [47]. The same set of reagents has been

used to precipitate traces of copper, cobalt, and molybdenum using

aluminum and indium as carriers. The completeness of precipitation was proved by means of suitable radioisotope tracers [48]. Beside the group separations mentioned in Table 8, fairly specific

forms of separation can be chosen for many elements. Palladium, for example, can be precipitated with a nickel carrier (and vice versa) by means of dimethylglyoxime [49]. Rare earths and thorium can be pre- cipitated as the difficulty soluble oxalates or fluorides, and molybdenum

Table 8. Separation of traces using coprecipitation [31].

Be

aMg

ae Al

ae

Si Ca

e Sc

ae Mn

ab Fe

abe Co

ab Cuab Znab Gaae As

b Se

da Br

f Sr

ce Zr

ae Nb

ae Mobe Ru Rh

bad Pdbad Agabd Cd

ab

Inabe Sn

abe Sb

abe, Te

da Ba

ce La

ae Hfae Taae Re

ba

Ir Ptda Au

ad Hg

ab

Tlabe Pb

abe, Bi Ra

c Ce Th U

ae ae ae

The traces are precipitated as: a — hydroxides or oxides b — sulphides

c — sulphates d — elements after reduction

e — 8-hydroxyquinolates

f —silver salts
PRECONCENTRATION 401

and tungsten using the benzoinoxime. The traces of sulphur mentioned

in Table 8 can be isolated in the form of sulphates together with dichromate ions precipitated jointly by barium.

It foUows from Table 8 that for the majority of elements convenient

and simple forms can be found for the isolation of their microquantities

from solutions on suitable carriers. Elements with properties similar to the trace elements but not inter- fering in the course of further analysis are most frequently chosen as

suitable carriers. For elements precipitated as hydroxides the following

elements can be used: iron (ill), aluminum, and titanium. The carrier

properties of lanthanum are noteworthy [50]. Lanthanum is a relatively rare element, exhibits no chromophoric properties and, as a rule, is not being determined in high purity materials.

When looking for an appropriate carrier for the coprecipitation of

silicon, Marczenko and Kasiura [51] have used niobium, taking into account the close chemical and physical properties of niobic and silicic acids. To the sample solution containing traces of silicon, niobium was

introduced as a solution of its oxalate complex. During evaporation

with perchloric acid the niobium complex is decomposed, the silicon is dehydrogenated and the niobic acid with traces of silica gel simultaneously precipitated.

The carrier need not always be similar to the trace substance to achieve quantitative isolation of the trace from solution. The direct

turbidimetric determination of chloride traces in samples dissolved in water frequently is impossible because of too low concentration of the

chlorides or because of the negative influence exerted by the main component of the sample on the chloride traces. It was found that for chloride ions good results could be obtained with barium sulphate as the

carrier [52]. To the sample dissolved in dilute nitric acid, sulphate ions were added followed by a solution of barium and silver nitrates. From

the combined precipitate of barium sulphate and the traces of silver chloride the latter undergoes complete leaching by ammonia due to the

formation of a soluble ammonia-silver complex.

The quantity of the carrier element introduced to the solution before precipitation must be large enough that the carrier element is precipitated quickly in a visible quantity convenient for separation

(by filtration or centrifugation) and washing. On the other hand the

quantity of the carrier should be small enough as to neglect the adsorption by the precipitate of these ions which should remain in the solu- tion tested. The carrier quantity should be chosen with respect to the volume of the precipitate formed. This quantity may be lower in the case of precipitating an element in the form of 8-hydroxyquinolate

than during precipitation of the element as the hydroxide. It has been

found experimentally that 1-3 mg of a carrier element is a suitable

quantity for a solution of 50-250 ml.
402 TRACE CHARACTERIZATION

Kusnietsov [53] and his coworkers for over ten years have been using

organic compounds to isolate trace quantities of inorganic ions. Their

methods can be used to enrich traces both in a group way and specifically.

The organic compounds appUed, of basic and acid character, are chosen

appropriately to the chemical character of the traces to be determined

with which they form compounds of the salt or ion-pair type, e.g. Me+R~,

R+MeOn,or R+MeCl~^ The organic substance is introduced as an aqueous solution of a suitable pH value or in an organic solvent, e.g. in ethanol. Under the precipitation conditions the solubihty of the organic

substance is decreased causing the onset of its precipitation together with

the traces of interest. One of the advantages that is demonstrated by

organic carriers is the fact that the carrier can easily be separated from

inorganic traces by simple ignition. The latter may, however, be accompanied by losses of nonvolatile trace elements due to the formation of

hght aerosols which can be lost from the ignition vessel by a weak ther- mal movement of the air. A systematic discussion of various kinds of organic carriers and ways

of their apphcation can be found in a recently pubhshed paper by

Miasoyedova [54]. C. Extraction

The extraction process, applied very frequently to the isolation of

both the main and trace components from a solution of the sample

examined, is based on the difference in the solubility of the substance

extracted in the organic and aqueous phases. If the partition coefficient

is high enough to afford a high percentage extraction then the process is useful for analytical purposes and enables one to extract quantitatively

the required components from aqueous solutions into organic solvents

or to reextract them from the organic phase into the aqueous one [55-61].

More information about complexing reactions has appreciably broadened on one hand the possibility of applying the extraction process for isolating and concentrating traces and on the other hand it revealed

that the extraction mechanism is very complex. This is taking place

particularly in analytical applications where almost always complicated

solutions of mixtures are encountered.

The inorganic ions to be extracted should be transformed into a form

that is soluble in the organic phase. Attention must be paid to the re- actions and interactions which occur between the ion extracted and the

complexing agent, solvent (diluent), and foreign species present in the

solution. The eventual dissociation and association should also be

taken into account. The effective rate of the extraction process is limited by the kinetics of the processes mentioned and by the rate of passing the extracting species into the organic phase. Thus only a full knowledge of all the partial processes occurring in both the phases makes

possible a forecast of the overall extraction process that is essential

from the analytical point of view.
PRECONCENTRATION 403

Theoretical studies of the extraction process, and particularly those

of the theory of electrolyte and nonelectrolyte solutions, have explained

a number of extraction principles. As a result both the synergistic and

antagonistic effects discovered are being applied in analytical chemistry

[62-64], Extraction studies have shown that the extraction process

may be accompanied by coextraction [65]. The facts hitherto found on coextraction do not yet give us a theoretical explanation of the

phenomenon. The small number of papers on coextraction seem to indicate that the phenomenon has no wider meaning.

The monograph by Morrison and Freiser [66] on the theoretical basis

of extraction and on various aspects of its application in analytical

chemistry excellently classifies the trends and possibihties of apphcation

of the process including the separation and concentration of traces. An element in an aqueous solution can be extracted into an organic

phase in the elemental form, in the form of a simple covalent compound,

as an inner chelate, or as an association complex with the element of

interest in its cation or anion forms. The extraction of elements in the elemental form is characteristic for some elements (see Table 9) and cannot be influenced by us. On the other hand owing to the great

number of known organic complexing agents, extraction of other chemical forms of elements can be accomplished and is widely applied.

The apphcation of extraction to the separation of the main component

or to the isolation of trace components, differs basically in the requirements with respect to the solubility of the extracting species in the

organic phase. In the case of separation of a macrocomponent the

solubility must be high, in the second case, low solubihties suffice. Considering the above, the extraction process can be divided into

two classes. The high solubility in the organic phase is a characteristic

feature of some elements, covalent compounds with simple inorganic

hgands, and of ion-association systems. On the other hand, the solu- bihty of inner chelates in organic solvents is low and these systems are mainly used for the extraction of traces. In Table 9 are hsted elements which can be extracted as the main

component. Bromine, iodine, and sulphur can be extracted and separated in the elemental form. The following elements can be extracted

as simple covalent halogen-compounds: germanium [67], arsenic (ill) as chlorides into carbon tetrachloride or benzene, mercury (ll) as iodide

into cyclohexanone [68], ruthenium and osmium as tetraoxides into carbon tetrachloride.

The extraction based on the oxonium mechanism is the most widely

apphed for the separation of a considerable number of metals in the

form of anion halogen-complexes, nitrates, and others into oxygen containing solvents. As a classic example the extraction of uranyl nitrate

into diethyl ether or tri-n-butyl phosphate can be mentioned, the extraction being conducted in order to determine traces in the residue [69]. 237-323 0-67—25
404 TRACE CHARACTERIZATION

Table 9. Separation of matrix using extraction [31].

Be

Nb

Cr

dMo

Fe

aRu

ad

Co

Rh

Ni

aPd

Cu

a Zn Ga

Cd In

a

Ge

a As

Sb

s

caSe

caTe

a Ta W Re

d Os

ad

Pt Au

ab Hg Tl Pb Bi

Ce Th U

b b b The elements are extracted as: a — halogen-compound s b — nitrates

c — elements d — oxygen-compounds In the ion-association systems attention should be paid to the extraction

by ahphatic amines which are relatively poorly applied in analytical

separations [70]. As examples of specific extractive separations, the isolation of macroquantities of beryllium in the form of a hydroxo-acetic complex into

chloroform [71] or a separation of chromium as a peroxide compound

into diethyl ether should be mentioned.

In Table 10 are listed more important extractive methods for the

isolation of trace elements. Beside the methods that have already

been mentioned and which are being applied also to the extraction of trace impurities, the main role is played by the extraction of inner

chelates. The most important are here organic reagents that form

inner chelates with metal ions, the chelates being soluble in chloroform,

carbon tetrachloride, and other organic solvents. Table 10 presents some examples of chelating agents. Dithizone and DDTC are given

as representatives of reagents in which the sulphur atom is the main

ligand atom. These reagents are used for the extraction of metals

forming difficultly soluble sulphides. Cupferron and oxine containing

oxygen as the main ligand atom are suitable for the extraction of metals

which are apt to react with hydroxylic groups. These reagents and their mixtures have been used for group separations of metals, e.g. dithizone has been used for the determination

of traces in antimony of high purity [72], and dithizone, oxine, and di- ethyldithiocarbamic acid for the separation of twenty-six trace elements

in aluminum, titanium, zirconium, and selenium of high purity [73].
PRECONCENTRATION 405

Table 10. Separation of traces using extraction [31].

Be

b

bCa

b

Srb

Sc

bY

bLa

b

Tibd

Zr

bHf

b

V

bcdj

edTa

ed

Cr

bdMo

deb W

edg

Mn

beTc

Re

e

Fe

bed Ru

bed Os

ed

Co

ace Ni

ac

"Pd"

acPt

ac

Cu

ac

acAu

ace

Zn

ac Cd"

abc Hg"

ac

B

eaT

bdGa

be

Inba "tT

ace

SigGe

e

cde Pb

ac

P

gAs

ceg Sb

edc

Biacd

Se

e

ce

Br

f

Ce Th U

bd bd bd The traces are extracted as: a — dithizonates b — 8-hydroxyquinolates

c — diethyldithiocarbamates

d — cupferronates

e — halogen-compounds

f —elements

g — heteropolyacids

Other chelating agents that have recently been used for group separation of traces are: benzoylphenylhydroxylamine [74], acetylacetone

[75], and 2-thenoyltrifluoroacetone [76]. These reagents are usually used for group separation of an appreciable number of trace elements, the main elements being eventually

masked with suitable masking agents. Thus, for example, in the deter- mination of heavy metal traces with dithizone or diethyldithiocarbamate,

iron, aluminum, and titanium can be masked with sulphosalicylic acid

[77, 78]. Sometimes very specific extraction systems are used. As an example,

the extraction of trace impurities from chlorosilanes of high purity

with concentrated sulphuric acid, as suggested by Everingham et al., [79, 80] can be mentioned.

The further application of extraction for the separation of traces from

each other consists of choosing more and more selective and specific

chelating agents in connection with proper masking agents and suitable

conditions of the reaction course. As an example of the possibihties which give us the joint extraction

and coprecipitation processes, the separation of Ga, Fe, Tl, In, Bi, Cu,

Pb and Cd in zinc sulphide of high purity is given in Table 11 [81].

It may be said that at present by applying coprecipitation and extraction methods, and by applying the procedure on a semimicro scale with
406 TRACE CHARACTERIZATION

Table 11. Separation and concentration of trace contaminants in zinc

sulphide [81].

Ga Fe Tl In Bi Cu Pb Cd + A1-^+ carrier precipitation nth NH:,: pH =

precipitate

Ga Fe Tl In Bi

6A^ HCI; ethyl ether

extraction

organic aqueous Ga Fe Tl In Bi + La-*+ carrier coprecipitation with NaOH

5A^ HBr isoprop. -ether extraction

organic

In

aqueous

Bi

precipitate solution Fe Tl betaphenantr.

extraction organic aqueous

Zn

solution Cu Pb Cd Zn + H2S: coprecipitation with Zn; pH — 3.5

Cu Pb Cd

HiDz extraction pH = 0.3

organic aqueous Pb Cd~|

precipitate

+ La'*+ carrier coprecipitation with NH,

solution Pb Cd

1 g of a high purity substance, a complete isolation and separation of a dozen or so impurities can be achieved, the determination being done

colorimetricaUy on an average level of 10"^%.

D. Chromatography

Chromatographic processes, consisting in the application of the

different behavior of the component to be determined in the system:

stationary phase — mobile phase, frequently are used in the course of

isolating and concentrating traces. For macro-micro and micro-macro separations, ion-exchange chromatography (the stationary phase is an ion-exchanger, the mobile liquid

phase are aqueous and nonaqueous solutions) and reversed-phase

partition chromatography (the stationary phase is a liquid complexing

agent adsorbed on a solid supporting material, the mobile phase is an
PRECONCENTRATION 40?

aqueous solution of suitable composition) are mainly used. The most

suitable .are such systems in which a column operates as a sieve, the

trace components being held, and the main component being passed

through.

In addition to both the separation methods mentioned above, other

chromatographic techniques are being used but they are of much less importance.

The characteristic feature of chromatographic methods, treated as a whole, is their universahty. If gas chromatography is included, the

methods cover almost aU the elements of the Periodic Table.

The most commonly used is ion-exchange chromatography. The

recently pubhshed monograph of TremiUon [82] widely discusses

separation methods based on ion-exchangers taking into account also the problem of traces. In connection with the latter the most frequently

used are anion-exchangers and cation-exchangers. Chelating ion- exchangers have also been investigated, as can be found in exhaustive

reviews of Bayer [83] and Schmuckler [84]. The same applies to inorganic exchangers which have been discussed by Rein [85]. To give an example one can mention the isolation of the main components in gaUium arsenide [86] for the successive determination of impurities, and an interesting application of a special technique called

"precipitation ion-exchange" [87], which allows for an easy isolation of the sum of trace impurities from chloride solutions, e.g. of the alkah

metals. By means of ion-exchangers a fairly specific isolation of particular trace components can be achieved, e.g. the isolation of cesium

traces from potassium and sodium salts [88], and the isolation of nickel

and copper traces from cadmium, zinc, and iron (ill) [89]. A classic example of the application of ion-exchangers for group

separation is reported by Kalinin et al., [90] who separated 25 trace ele- ments in a sample of semiconductor silicon in the course of determining

them by neutron activation. After the silicon had been distilled off as SiF4, the solution was separated entirely by means of cation and anion

exchangers, according to the scheme given in Table 12. The elements

in the groups obtained were determined by gamma-spectrometric meas- urements and needed no further separation.

Ion-exchange has also been applied in studies of the purity of rare earth concentrates [91]. The possibilities of ion-exchange for the enrichment of traces are best illustrated by Brooks [92], who, using a small anion exchanger

column, has isolated and determined 1.5 /xg of gold in a 250-1 portion

of sea water. The determinability was 10~^^% in this case. Reversed-phase partition chromatography is, in principle, an extraction process performed in a continuous and multistage way on a column.

The method can also be interpreted as chromatography on liquid anionexchangers. The main trends of application developed by Siekierski
408 TRACE CHARACTERIZATION

Table 12. Scheme of separation of semiconductor-silicon contaminants

[90].^'^

The solution of contaminants in HF + HNO,+ HCIO4

f

AB-17-CIOr resin IN (NH2)2CS

3N HCIO4 \ I Au

KU-2-H_" I 4yV HCl

jsyV HCIO4

Sb,Ta,Sn,Mo

0.57V HF

i

AB-17-C1- 8N HCl + IN HF

\

As,P,W

AB-17-C2; 8N HCl

AB-17-0H

HiO~

2N HCl

H2O

f

IN NH4OH

Cu,Co,Ga,In,Zn,Fe,Cd

SiVHCl

Mn,Ni,Cr,Ag

KU-2-NH;

27V NH4Cr

Na,K,Rb,Cs

0.17V EDTA

pH = 10

Ca,Sr,Ba

^AB-17 — anion exchange resin ^KU-2 — cation exchange resin and his coworkers include systems in which the organic stationary

phases were mainly acidic and neutral esters of phosphoric acids, and

amines. They have shown the usefulness of this process to numerous

radiochemical separations which often can directly be employed for the

isolation and separation of traces. For instance, columns with TBP

absorbed on siliconated kieselguhr were used to separate traces of

arsenic from germanium [93], and traces of scandium from calcium [94]. This same system has been used for analytical separation of traces of niobium from molybdenum [95]. Good results were obtained by

Siekierski and Fidelis [96, 97] in micro-micro separations, e.g. with

mixtures of rare earth elements. Smulek et al., using columns with

tri-n-octylamine separated traces of cobalt from nickel [98], and traces

of iron (ill) from manganese [99].

It seems that application of this method can be considerably widened,

expecially with the use of relatively highly dissociated agents, such as those mentioned above, as the organic phase.
PRECONCENTRATION

E. Volatility

409

Separation and isolation methods based on distillation make use of

the difference in the volatility of elements or their corresponding compounds. These methods can be applied in three variants. The frac- tional distillation is applied from a solution of a proper composition, or a solid sample is distilled making use of the difference in the volatiUty

of the sample components, or, finally, a solid sample is attacked with

reagents in the gaseous phase at suitably selected temperatures. The

latter procedure, consisting of the attack of the sample vs^ith such agents

as fluorine, chlorine, bromine, hydrogen fluoride, hydrogen chloride,

vapours of nitric acid, etc., although usually technically complicated

has the advantage that the reagents in gaseous phase carry with them

the smallest quantity of impurities; they give the smallest blank.

Direct distillation of the components of the tested sample, as a method

for the isolation of traces, has found its classical application in the

method of Scribner and MuUin [100], the so-called "carrier distilla- tion" in spectrography, in which traces are distilled off from a difficultly volatile matrix directly to the excitation zone, and in the method of

Mandelshtam et al. [101] and Zaidel et al. [102] who distilled traces from

a difficulty volatile matrix and condensed them at an auxiliary electrode

from which the traces were excited.

Direct distillation of a more volatile metal (the main component)

from a sample in a special (usually vacuum) apparatus has been per- formed. The less volatile components remained in the residue, afford- ing an appreciable degree of concentration (usually ~ 100 times). This

procedure has been applied for the concentration of impurities in zinc

[103] and cadmium [104]. The reversed operation — distillation of traces — has been used by Neeb for the separation of zinc traces in aluminum of high purity [105], and by Joungdahl and Deboer for the iso- lation of manganese from aluminum [106]. Volatilization either of the main component of a sample, or of trace impurities from a matrix, under the influence of gaseous reagent, may

involve, in principle, all the elements hsted in Tables 13 and 14. These

methods are technically complicated because they require manipulation

with gaseous substances which are strongly toxic and corrosive, especially at elevated temperatures. Therefore suitable construction materials,

that do not cause secondary contamination, and hermetization of the

process are needed. Despite these difficulties a number of such

methods are described in the literature. Fratkin and Shebunin [107]

used gaseous hydrogen fluoride at 350 °C to distill the main component

of the tested sample as the fluoride or oxyfluoride. They examined,

under these conditions, the distillation of boron, vanadium, tungsten,

germanium, silicon, molybdenum, selenium, antimony, tantalum, and

titanium. With respect to titanium Fratkin [108], using initially a 1 g
410 TRACE CHARACTERIZATION

Table 13. Volatilization of traces [31],

B

d C

b Ncb Fc Sid P

c S

cb

CI

a Zn

a Ge

da As

acd Se

d Bra Ru

bd

Cd

a

In

a Sn

d Sb

acd Te

d

Ia Re

bd Os

bd Hg

a Tl

a Pb

a

Bi

a

The traces are volatilized as: a — elements

b — oxygen-compounds

c — hydrogen-compounds

d — halogen-compounds

Table 14. Volatilization of matrix [31].

Be B

db C

be N

abc F

ac

Sid s

abc

CI

ac

Tid Cr

d Ni Ga Ge

d As

d Se

db

Br

ac Zr

d Ru

b Snd Sbd Ted

Iac 1 Re

b Osb Hg

ad

The elements are volatilized as: a — elements

b — oxygen-compounds

c — hydrogen-compounds

d — halogen-compounds
PRECONCENTRATION 411

sample determined spectrographicaUy the following elements: Mn, Mg,

Cu, Cr, Al, Fe, Pb, Ca, Ni, and Sn in the range from 1 X IQ-^- 1 X IQ-^ %.

Karabash et al. [109] have appUed chlorination for the removal of

titanium as the main component, the fourteen elements in the residue

being determined spectrally.

Geilmann and Neeb [110] have proposed and proved the isolation of ten elements from mineral samples by means of roasting in a hydrogen

atmosphere at 1000 °C. It may be assumed that this method could

be applied to some materials of high purity, e.g. Si02 and AI2O3.

In order to remove nickel, as the main component, Shvarts [111] has even appHed the action of carbon monoxide on a powdered sample in an autoclave (150 atm) at an elevated temperature, transforming the

nickel into a volatile nickel carbonyl.

Distillation of inner chelate compounds, many of which are fairly

volatile, has as yet been rarely appUed. Nazarenko et al. [30] have

used gaUium oxinate for the removal of gallium as the main component.

Baudin, Lorrain, and Platzer [112] have distilled beryllium as the

acetylacetonate.

Distillation from solutions mainly involves easily volatile elements

and those in which covalent bonds prevail (an analogy to extraction by

nonpolar solvents). The compounds involved include those of hydrogen,

oxygen, hahdes, and inner chelates, e.g. (AsHs, GeCU, OSO4, gallium

oxinate). These compounds may have sufficiently low boiUng temperature so that their distillation from solutions is feasible. A classic

example of isolating the main component by distillation from solution

is the distillation of germanium tetrachloride [113], or arsenic trichloride,

in the course of preparation of semiconductor germanium and gallium

arsenide for spectrochemical analysis. Also the analysis of boron of

high purity requires a previous isolation of the main component which

is achieved by distilling boron as methyl borate [114]. This way is suitable for the removal of chromium as chromyl chloride

[115, 116] in the case where spectrographic or colorimetric determination

of traces is to follow. The same applies to selenium removed as SeBr4

and Se02.

Finally, the ignition or wet oxidation of organic compounds should

be considered as the removal of the main component by volatiHzation.

During investigations of high purity materials this operation is fre- quently involved when examining the purity of organic reagents or

graphite. The course of ignition, when determination of traces is to be followed, also requires some precautions. For instance, carriers

sometimes must be used to prevent the losses of material due to convection [117-119].

A classic example of isolating traces in the form of volatile compounds

is the isolation of traces of arsenic as AsHs, according to the method of
412 TRACE CHARACTERIZATION

Gutzeit. This method, when combined with neutron activation, aUows

fully specific determination up to 10~^% of arsenic in semiconductor

materials [120]. The isolation of sulphur as H2S for its successive

colorimetric determination by the methylene blue method can also be

quoted as another example [121].

Classical methods for the determination of trace contents of gases

in metals are also based on volatility. After being removed by the

melting method in vacuum the gasses are then determined by different

methods.

If the main component of a sample can be removed due to its volatili- zation (distillation, sublimation), particularly with no additional reagents

added, or if it can be attacked by gaseous reagents, then an exceptionally

favorable concentration coefficient can be obtained, which may reach even a value of 1000 (i.e. from a 10 g sample a 10 mg portion of the con- centrate is obtained).

During the course of evaporation it should be remembered that microgram quantities of some components may undergo partial distillation in spite of their low volatility. For instance, an aqueous solution of microquantities of boric acid can be concentrated by evaporation ^without

appreciable losses of boron. However, a solution of traces of .the acid can be evaporated without losses only after the solution has been made

alkaline. During the determination of traces of boron in silicon, the

latter is removed as SiF4. To avoid the losses of BF3 by distillation,

the boron must be combined with mannite to form a nonvolatile

compound.

F. Zone Melting

Among the methods which do not belong to any of the above mentioned, zone melting should be mentioned [122]. During this process some impurities are concentrated at the end of a block of the tested substance. These impurities can then be directly determined. The method

is, no doubt, of real value because no reagents are added to contaminate

the sample. Automation of the apparatus used permits the concentration of traces automatically. The disadvantage of the method is a

different partition coefficient between the crystalline and liquid phases

of various elements, followed by difficulties in obtaining a high and full concentration (e.g. by a factor of 100) for a large number of impurities.

Also some secondary processes, as volatility or oxidation of the particular impurities may influence the course of the concentration process. Nevertheless the method has been applied successfully for concentration

purposes in' the analysis of high purity materials [123-125] and wider

and wider appUcation and new approaches seem to indicate that the

method is not as yet fuUy exploited. Recently Konovalow and Peyzulayev [126] have used the method for the determination of silver,

thalhum, and copper traces in bismuth and lead of high purity. These

authors in their extensive paper discuss all the factors influencing the
PRECONCENTRATION 413

course of the concentration process, taking the analysis of bismuth

as an example.

IV. Final Remarks

The methods discussed above for isolation, concentration, and separation of trace admixtures in high purity materials indicate that the

problem has to a significant degree been overcome. Thus, chemical lab- oratories can, in principle, separate trace impurities of any required

sample enabhng quantitative determination of the traces by one of the

known methods. Further development of these methods, however, is required for further progress and must include a better understanding of the chemical reactions on which the methods depend, coupled with the

introduction of new specific complexing agents, the development of

techniques for obtaining substances of high purity (reagents), and the

introduction of new materials into chemical laboratories.

One problem that is important in the analytical chemistry of traces

still needs some comment. This is the problem of accuracy and pre- cision of the discussed processes, the lower limit of traces that it is possible to isolate, and a general evaluation of the pre-concentration

methods.

By applying the method of radioactive tracers it is possible to verify

accurately whether the separation and concentration takes place quantitatively with a yield sufficiently close to 100%.

The hmiting factor of apphcation of the methods described above is, in general, the so called blank test, i.e. the amount of the component

to be determined that is introduced with the reagents, from the air from

the materials of containers, etc. to the sample during its processing.

The blank test determines the lower limit of concentrating the components to be isolated. The variation of the blank test Umits the precision of the obtained results after pre-concentration.

The final precision of the results is affected by the dominating effects of enrichment and separation of traces, taking into account an average

performance of analysis.

For this reason these methods need constant control which can rela- tively easily be ensured by a parallel analysis and identical treatment

of the sample and a blank to which known and comparable quantities of the components to be determined are added.

Certain disadvantages of preconcentration and separation processes

are that they are time-consuming, and require that processes be per- formed by significantly better educated personnel to be sure that the

particular operations are correctly performed. The personnel should

be able to modify the way of treatment, if the normal course of analysis

would be disturbed by an unexpected change, for example, in composition of the traces to be determined.

Despite these disadvantages, the pre-concentration methods, combined with appropriate instrumental determination methods, are of real
414 TRACE CHARACTERIZATION

value in industrial laboratories, and may be particularly useful in re- search laboratories which must analyze samples of different and variable

composition.

V. Acknowledgements

The author wishes to thank both the staff of the Department of Analytical Chemistry of Technical University of Warsaw and the staff of

the Analytical Department of the Institute of Nuclear Research for their

help in preparing this paper. The author in particular is deeply in- debted to Dr. Z. Marczenko, assistant professor of the Technical University of Warsaw, for valuable discussions and remarks.

VI. References

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[2] Burriel-Marti, F., Experientia Suppl. 5, 71 (1956).

[3] Alimarin, I. P., Pure Appl. Chem. 7, 455 (1963).

[4] Minczewski, J., ibid. 10, 567 (1965).

[5] Specker, H., Harthamp, H., Angew. Chem. 67, 173 (1955).

[6] Claassen, A., Chem. Weekbl. 58, 33 (1962).

[7] Specker, H., Z. Erzbergbau Metallhiittenwesen 17, 132 (1964).

[8] Ehrhch, G., Rexer, E., Wiss, Z., Techn. Hochsch. Chem. Leuna-Merseburg 6, 207

(1964).

[9] Minczewski, J., Chim. Anal. (France) 47, 401 (1965).

[10] Lipis, L. v., Usp. Fiz. Nauk. 68, 71 (1959).

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[12] Konovalov, E. E., Peyzulayev, Sh. I., Trudy Komm. Anal. Khim. 15, 375 (1965).

[13] Radwan, M., Freiberger Forschungshefte, Heft B 111, December 1965, p. 167.

[14] Strzyzewska B., Chem. Anal. (Warsaw) 11 (1966) in press.

[15] Kane, P. F., Anal. Chem. 38, No. 3, 29a (1966). [161 Ducret, L., Anal. Chim. Acta 17, 213 (1957).

[17] Vasilevskaya, L. S., Metody Anahza Veshchestv Vysokoi Chistoty, Nauka, Moskva

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[19] D'Ambrosio, A., Mikrochim. Acta 1961, 927.

[20] Strzyzewska, B., Radwan, Z., Chem. Anal. (Warsaw) 11 (1966) in press.

[21] Chow, T. J., McKinney, C. R., Anal. Chem. 30, 1499 (1958).

[22] Kokotov, Yu, A., Radiokhimicheskiye Metody Opredielenia Mikroelementov, Nauka,

Moskva 1965, p. 54.

[23] Knizek, M., Provaznik, J., Chem. Listy 55, 389 (1961).

[24] Butler, E. B., Johnson, W. H., Science 120, 543 (1954).

[25] Lang, E. P., Ind. Eng. Chem., Anal. Ed. 6, 111 (1934).

[26] Haberh, E., Z. Anal. Chem. 160, 15 (1958).

[27] Wickbold, R., ibid. 171, 81 (1959).

[28] Irving, H., Cox, J. J., Analyst 83, 526 (1958).

[29] Stegeman, H. Z. Anal. Chem. 157, 267 (1957).

[30] Nazarenko, V. A., FUantikova, G. V., Zavod. Lab., 24, 663 (1958).

[31] Marczenko, Z., Zeszyty Naukowe Politechniki Warszawskiej (Warsaw) 115, Chemia,

No. 3, 1965.

[32] Bjerrum, J., Schwarzenbach, G., Sillen, L. G., Stability Constants of Metal Complexes

with Solubility Products of Inorganic Substances. I. Organic Ligands, II. Inorganic

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[33] Jacimirski, K. W., Vasil'ev, W. P., Instabihty Constants of Complex Compounds,

Pergamon Press, Oxford 1960, transl. from Russian.
PRECONCENTRATION 415

[34] Ringbom, A., Complexation in Analytical Chemistry, J. Wiley & Sons, New York,

1963.

[35] Schwarzenbach, G., Experientia Suppl. 5, 162 (1956); Angew. Chem. 70, 451 (1958).

[36] Cheng, K. L., Anal. Chem. 33, 783 (1961).

[37] Hulanicki, A., Talanta 9, 549 (1962).

[38] Gorbach, G., Pohl, F., Mikrochemie 36)87, 486 (1951).

[39] Marczenko, Z., Kasiura, K., Chem. Anal. (Warsaw) 9, 87 (1964).

[40] Karabash, A. G., Bondarenko, L. S., Mozozova, G. G., Peyzulayev, Sh. I., Zh. Anal. Khim. 15, 623 (1960).

[41] Degtiareva, D. F., Ostrovskaya, M. F., ibid. 20, 814 (1965).

[42] Baronova, L. L., Solodovnik, S. M., ibid. 19, 588 (1964).

[43] Krauz, L. S., Karabash, A. G., Peyzulayev, Sh. I., Lipatova, V. M., Moleva, V. S., Trudy Komm. Anal. Khim. 12, 175 (1960).

[44] Mayer, J., Z. Anal. Chem. 219, 147 (1966).

[45] Karabash, A. G., Samsonova, Z. N., Smirnova-Averina, N. I., Peyzulayev, Sh. I., Trudy Komm. Anal. Khim. 12, 255 (1960).

[46] Sotnikova, N. P., Romanovich, L. S., Peyzulayev, Sh. I., Karabash A. G., ibid. 12,

151 (1960).

[47] Silvey, W. D., Brennan, R., Anal. Chem. 34, 784 (1962).

[48] Pickett, E. E., Hankins, B. E., ibid. 30, 47 (1958).

[49] Marczenko, Z., Krasiejko, M., Chem. Anal. (Warsaw) 9, 291 (1964).

[50] Marczenko, Z., Kasiura K., ibid. 10, 449 (1965).

[51] Marczenko, Z., Kasiura, K., ibid. 9, 321 (1964).

[52] Chwastowska, J., Marczenko, Z., Stolarczyk, U., ibid. 8, 517 (1963).

[53] Kusnietsov, V. I., Zh. Anal. Khim. 9, 199 (1954).

[54] Miasoyedova, G. V., ibid. 21, 598 (1966).

[55] Green, H., Metallurgia 70, 143, 201, 254, 299 (1964).

[56] Stary, J., Anal. Chim. Acta 28, 132 (1963).

[57] Stary, J., Hladky, E., ibid. 28, 227 (1963).

[58] Stary, J., Smizanska, J., ibid. 28, 545 (1963).

[59] Zolotov, Yu. A., Trudy Komm. Anal. Khim. 15, 3 (1965).

[60] West, T. S., Anal. Chim. Acta 25, 405 (1961).

[61] Babko, A. K., Zharovskii, F. G., Zavod. Lab. 28, 1287 (1962).

[62] Specker, H., Cremer, M., Jackwerth, E., Angew. Chem. 71, 492 (1959)

[63] Siekierski, S., Taube, M., Nukleonika (Warsaw) 6, 489 (1961).

[64] Walker, W. R., Li N. C, J. Inorg. Nucl. Chem. 27, 411 (1965).

[65] Alimarin, L R., Zolotov, Ju. A., Shakhova, N. V., Trudy Komm. Anal. Khim. 14, 24

(1963).

[66] Morrison, G. H., Preiser, H., Solvent Extraction in Analytical Chemistry, J. Wiley &

Sons Inc., New York, 1957.

[67] Green, D. E., Haslop, J. A. B., Whittey, J. E., Analyst 88, 522 (1963).

[68] Jackwerth, E., Z. Anal. Chem. 2 02, 81 (1964).

[69] Czakow, J., Kucharzewski, B., Chem. Anal. (Warsaw) 12 (1967), in press.

[70] Green, H., Talanta 11, 1561 (1964).

[71] Karabash, A. G., Peyzulayev, Sh. I., Slusarieva, P. L., Lipatova, V. M., Trudy Komm.

Anal. Khim. 12, 331 (1960).

[72] Haberh, E., Z. AnaL Chem. 160, 15 (1958).

[73] Koch, O. G., Mikrochim. Acta 1958, 92, 347.

[74] Chwastowska, J., Minczewski, J., Chem. Anal. (Warsaw), 8, 157 (1963), 9, 791 (1964).

[75] Shigematsu, T., Tabushi, M., BuU. Inst. Chem. Res. Kyoto Univ. 39, 35 (1961).

[76] Moore, F. L., A.S.T.M. Spec. Tech. Publ. No. 238, 13 (1959).

[77] Karczewska, B., Minczewski, J.. Marczenko, Z., Chem. Anal. (Warsaw) 6, 501 (1961).

[78] Minczewski, J., Chwastowska, J., Marczenko, Z., ibid. 6, 509 (1961).

[79] Haas, C. S., Pelhn, R. A., Everingham, M. R., Anal. Chem. 36, 245 (1964).
416 TRACE CHARACTERIZATION

[80] Lancaster, W. A., Everingham, M. R., ibid. 36, 246 (1964).

[81] Marczenko, Z., Kasiura. K., private communication.

[82] Tremillon, B., Les Separations par les Resines Exangeuse d'lons, Masson et Cie., Paris 1965.

[83] Bayer, E., Angew. Chem. 76, 76 (1964).

[84] Schumuckler, G., Talanta 12, 281 (1965).

[85] Rein, J. E., paper presented at 150th Meeting ACS., Atlantic City, N.J., 1965.

[86] Kataev, G. A., Otmakhova, Z. I., Zh. Anal. Khim. 18, 339 (1963).

[87] Tera, F., Ruch, R. R., Morrison, G. H., Anal. Chem. 37, 358 (1965).

[88] Dybczynski, R., Sterlinski, S., Proc. Anal. Chem. Conference, Budapest 1966, p. 398.

[89] Fritz, J. S., Abbink, J. E., Anal. Chem. 37, 1274 (1965).

[90] KaUnin, A. I., Kusnetsov, R. A., Moyssev, V. V., Radiokhimia 4, 575 (1962).

[91] Dybczynski, R., Minczewski, J., Chem. Anal. (Warsaw) 11 (1966), in press.

[92] Brooks, R. P., Analyst 85, 745 (1960).

[93] Fidehs, I., Gwozdz, R., Siekierski, S., Nukleonika (Warsaw) 8, 320 (1963).

[94] Siekierski, S., Sochacka, R. J., Institute for Nuclear Research, Warsaw, Report No. 262/V (1964).

[95] Minczewski, J., Rozycki, C, Chem. Anal. (Warsaw) 10, 965 (1965).

[96] Siekierski, S., Fidehs, I., J. Chromatog. 4, 60 (1960).

[97] Fidehs, I., Siekierski, S., ibid, 5, 161 (1961).

[98] Smulek, W., Zelenay, K., Institute for Nuclear Research, Warsaw, Report No.

677/V/XIII/, (1965).

[99] Smutek, W., Nukleonika (Warsaw) 11 (1966), in press.

[100] Scribner, B. F., MuIHn, H. R., J. Research NBS 37, 378 (1946). [101] Mandelshtam, S. L., Semenov, N. N., Turovtseva, Z. M., Zh. Anal. Khim. 11,9 (1956). [102] Zaidel, A. V., Kahteevski, N. S., Lipis. L. V., Chayka, M. B., Behaso, Yu., ibid. L. 1 1, 21 (1956). [103] Shvarts, D. M., Kaporskii, L. N., Zavod. Lab 23, 11 (1957). [104] Gerken, E. B., Sbornik Trudov Gintsvetmeta 19, 800 (1962). [105] Neeb, K. H., Z. Anal. Chem. 194, 255 (1963). [106] Joungdahl, C. A., Deboer, F. E., Nature 184, 54 (1959). [107] Fratkin, E. G., Shebunin, V. S., Trudy Komm. Anal. Khim. 15, 127 (1965). [108] Fratkin, E. G., Zavod. Lab. 30, 170 (1964). [109] Karabash, A. G., Peyzulayev, Sh. I., Sotnikova, N. P., Sazanova, S. K., Trudy Komm.

Anal. Khim., 12, 108 (1960). [110] Geilmann, W., Neeb, K. H., Z. Anal. Chem. 160, 410 (1958); 165, 251 (1959). [Ill] Shvarts, D. M., Zavod. Lab. 26, 966 (1960). [112] Baudin, G., Lorrain, S., Platzer, R., Travaux XXXV Congres Intern. Cbimie. Ind., Varsovie 1965.

[113] Rutkowski, W., Wasowicz S., Chem. Anal. (Warsaw) 11 (1966), in press.

[114] Marczenko, Z., ibid. 9, 1093 (1964). [115] Minczewski, J., Chwastowska, J., ibid. 6, 715 (1961). [116] Chwastowska, J., ibid. 7, 731 (1962). [117] Pijck, J., Hoste, J., GiUis, J., Proc. Intern. Symp. Microchem., Birmingham, 1958,

p. 48.

[118] Schulek, E., Laszlovsky, J., Microchim. Acta 1960, 485.

[119] Gorsuch, T. T., Analyst. 87, 112 (1962). [120] Foldzinska, A., Mahnowski, J., Nukleonika (Warsaw) 7, 153 (1962); 8, 233 (1963). [121] Marczenko, Z., Choluj-Lenarczyk, L., Chem. Anal. (Warsaw) 10, 729 (1965). [122] Pfann, W. G., Zone Melting, J. Wiley & Sons, New York, (1959). [123] Downarowicz, J., Chem. Anal. (Warsaw) 4, 643 (1959). [124] Pfann, W. G., Theuerer, H. C, Anal Chem. 32, 1574 (1960). [125] Konovalov, E. E., Peyzulayev, Sh. I., Emelyanov, V. P., Zh. Anal. Khim. 18, 1500

(1963). [126] Konovalov, E. E., Peyzulayev, Sh. I., Trudy Komm. Anal. Khim. 15, 375 (1965).
PRECONCENTRATION, SAMPLING, AND

REAGENTS

Contributed Papers and Discussion

GEORGE H. MORRISON

Cornell University, Ithaca, New York 14850

I. Introduction

Any symposium concerned with the techniques for trace characterization would be incomplete without a session on the chemical and/or

physical methods of pretreatment of samples. Although we have

heard much of the capabilities of the various instrumental techniques

for trace analysis, the full realization of their potentialities for the

compositional characterization of complex materials can, in many cases, be accomplished only by coupling the techniques with preconcentrations and separations to remove or minimize the ever-present possibility of interferences or to provide adequate microconstituent for the measure- ment to be employed.

The lecture by Professor Minczewski presented earher has reviewed

the various methods of concentration and separation of traces and the

problems of contamination associated with these methods. The contributed papers in this session describe some new developments in the field, as well as provide reviews of specific methods. Before dis- cussing this material, however, a few additional comments on the

general subject may provide a better perspective for their role in trace

analysis. All analytical methods can be divided into three component steps:

samphng, chemical and/or physical pretreatment, and instrumental

measurement. These steps are interrelated and require different degrees of emphasis depending upon the individual analytical situation. But, in all cases, one is interested in finally measuring a signal which

can be related to the concentration of a particular species in the original

sample. Therefore, in order to properly evaluate the requirements of preconcentration, separation, and sampling, it would be most meaningful

to start with an examination of the last component step of analysis, i.e., instrumental measurement.

The usefulness of the various measurement techniques to trace characterization is governed to a considerable extent by the detection limits that can be achieved for the elements of interest in a given system, i.e.,

417
418 TRACE CHARACTERIZATION

the smallest quantity or concentration that can be detected with a certain

stated confidence. Figure 1 [1] ^ graphically summarizes the detection

limits that can be experimentally achieved with a number of trace techniques under conditions of little or no interference by the matrix or by

other elements. The original reference should be consulted for details

for specific elements and experimental conditions. It can be seen that

in the absence of interferences all of the techniques included are generally applicable to the determination of most elements down to 100 ng. Although many of the techniques are applicable to a more

limited number of elements in the range of 0.01-100 ng, only spark- source mass spectrometry and activation analysis are generally applicable below this. These limits, therefore, represent the capabilities of the measurement steps for the various techniques. Failure to achieve them in the analysis of actual samples arises because of inter- ferences by the matrix or other trace elements or because of the diluting

effect of the matrix.

The specific requirements for preconcentration and separation are intimately related to the sample under consideration and the technique of measurement employed. There are two important terms in separations in trace analysis that should be defined at this point [2]. FLAME SPECTROPHOTOMETRY

ABSORPTION SPECTROPHOTOMETRY

ATOMIC ABSORPTION

FLUORESCENCE

SPARK SOURCE MASS SPECTROSCOPY

ACTIVATION ANALYSIS COPPER SPARK EMISSION SPECTROSCOPY

D.C. ARC EMISSION SPECTROSCOPY

GRAPHITE SPARK EMISSION SPECTROSCOPY

"Cl 100

UJ5 80

UJt

60

O

tr 40

UJm

^ 20

10^ 10^ 10 I 0.1 10"^ 10"^ 10" Figure 1. Summary of detection limits in nanograms, for a number of trace techniques under conditions of little or no interference by matrix or other elements.

* Figures in brackets indicate the literature references at the end of this paper.
PRECONCENTRATION 4I9

One is the recovery or yield (Ra) of a desired trace element A, and the

other is the separation factor (Sb/a) for an undesired constituent B with

respect to a desired trace element A. The definitions are as follows: Ra = Qa/Q1x100(%) (1)

Sb/a = (Qb/Qa)/(Q°b/Qa) (2) where Qa the quantity of A in the sample; Qg = the quantity of B in the sample; Qa = the quantity of A after the separation; Qb = the quantity

of B after the separation.

The reciprocal of Sb/a is called the concentration factor or the enrichment factor of A when B is the matrix. The ideal separation has a recovery of 100% and separation factors of zero. Actually, these two

factors depend on the nature of the sample as well as on the method of

separation. Knowing the Hmits of detection of the various methods of measurement, one can then select an adequate sized sample and a method of appropriate separation and recovery factors to achieve

adequate sensitivity and precision in the trace analysis. Time and

effort can usually be conserved by selecting methods which do not

require complete separation.

II. Preconcentration and Separation Methods

Professor Minczewski has surveyed the various methods of separation.

Because of the broad scope of the subject, only an abbreviated treatment was possible in the time allotted for presentation. Of particular value,

however, is the citing of numerous applications of the various methods,

principally from papers not readily accessible to the Western world.

The separation methods included in the treatment are precipitation

and coprecipitation, extraction, chromatography, volatilization, and

zone melting.

A number of the contributed papers in this session further illustrate the effectiveness of a few of these methods of preconcentration and

separation to the determination of trace elements. With regard to precipitation methods, the paper by Alvarez illustrates the value of

electrolytic methods of preconcentration. In this study submicrogram

amounts of silver have been isolated from macro amounts of zinc matrix

by electrodeposition on high purity graphite or pyrolytic graphite

cathodes followed by washing for eventual determination by graphitespark emission spectroscopy. Many preconcentration procedures

produce extremely dilute solutions of the trace elements, resulting in sorption losses; however, trace elements having suitable electrodeposition potentials can be deposited directly on the cathode from a concentrated solution of the matrix, thus virtually eliminating errors

of this type.

237-323 0-67—26
420 TRACE CHARACTERIZATION

Ion exchange methods hold considerable promise for preconcentration

of trace elements and Professor Minczewski has discussed a number of applications. Most appHcations in the past, however, use ion exchange

in a more or less conventional fashion taking advantage of the different

distribution coefficients of the species to be separated in a given system.

I would hke to take this opportunity to refer to a novel approach to preconcentration of multielement traces by ion exchange which was

developed in our laboratory and which we refer to as "precipitation ion

exchange" [3, 4], By combining precipitation and ion exchange simultaneously on the resin column useful separations are made possible. In this approach the matrix and trace elements are first sorbed on a cation exchange column, the matrix is then precipitated by an organichydrochloric acid eluent, followed by nonselective elution of the traces. The separation is based on the insolubility of the matrix and low selectivity of the traces in 70% p-dioxane-30% concentrated hydrochloric

acid (v/v). As many as 40 trace elements may be preconcentrated in greater than 90% yields, matrix-free or with only small amounts of matrix

from the following matrices: hthium, sodium, potassium, rubidium,

magnesium, calcium, strontium, barium, scandium, yttrium, and

lanthanum. Using 81% dioxane-10% ethanol-9% concentrated hydrochloric acid as eluent, matrices such as nickel, chromium, manganese,

lead, and aluminum demonstrate sufficient insolubility and delayed

column breakthrough, as well as favorable trace recovery, to be of value

in preconcentration.

The paper by Burnett et al., describes a novel paper disk anion ex- change column that shows promise for the rapid separation of radionucHdes in neutron activation analysis. Their study has been directed

towards the decontamination of complexes of radioactive traces from

sodium-24, based on the sorption on the paper disks of anion complexes

of these metals formed in hydrochloric acid media.

Again I would like to cite a recent study in our laboratory concerned

with a general approach for the rapid separation of radioactive species,

which has particular application to matrix removal in activation analysis

[5]. The method, which is called "isotopic ion exchange", can effect rapid multi-element trace separations from large amounts of a radioactive matrix element, thereby permitting gamma spectrometric meas- urement of the traces. The approach is applicable to a variety of

matrices, and separations can be achieved in a matter of minutes.

A novel volatilization method of preconcentration that may have considerable impact on the determination of trace elements in organic and

biological materials is presented in the paper by Bersin, HoUahan, and

Holland. Excited atomic and molecular oxygen produced in a radio

frequency discharge permit the low temperature ashing of the organic

matrix. The net effect is to provide a low temperature environment for removing oxidizable material from the sample without introducing con-
PRECONCENTRATION 421

taminants. Thereby, one avoids sintering, melting, volatilization and

other consequences of high temperature which can destroy crystallinity or other structural characteristics of the developed ash, or create loss of volatile elements. This low temperature ashing is accomplished at a rate practical for analytical requirements. The coupling of this approach with a variety of measurement techniques is possible, per- mitting both compositional and structural characterization.

Other separation methods described in papers for this session include

a review of the ring-oven technique by Mukherji, and the appHcation of

the zone-melting process to metal chelate systems by Kaneko, Kobayashi,

and Ueno.

The appHcation of a variety of conventional separation and preconcentration methods to the trace analysis of several important materials

is also presented in papers for this session. Thus, the determination

of parts per million and parts per biUion amounts of a number of impurities in very pure rare earth oxides and metals is described in the

paper by Banks et al., in which extraction chromatography and solvent

extraction, among other methods, are coupled with atomic absorption

and spectrophotometric methods of determination. These determinations permit the evaluation of more direct methods of trace analysis

such as emission spectroscopy and spark source mass spectrometry.

An excellent review of preconcentration methods for the determination of trace elements in sea water is provided in the paper by Joyner

et al., involving cocrystallization, coprecipitation, solvent extraction,

and chromatography.

Much emphasis in this session has been placed on separations for the trace analysis of soHd and liquid samples. Of particular importance

in materials research is the use of ultrapure gases, and Roboz describes

several preconcentration methods for trace elements in gas matrices

used in conjunction with mass spectrometric determinations. Included

is the removal of matrix hydrogen by diffusion through a palladium membrane, removal of matrix carbon dioxide by freeze-out, and removal of oxygen matrix using sodium-potassium alloy.

III. Reagents

Any discussion of the chemical preconcentration and separation of

trace elements at the nanogram level in aqueous systems would be meaningless unless the problem of contamination by reagents and/or container

material is objectively evaluated. In their paper Freeman and Kuehner

discuss the mechanisms of contamination, the principles of contaminant

separation, and specific studies of reagent purification. Attention has

been given to the purification of water which is broadly needed for reagent preparation, to hydrochloric acid which is one of the common

acid reagents, and to the comparative decontamination of silica gel.
422 TRACE CHARACTERIZATION

IV. Sampling and Sample Preparation

Finally I would like to discuss the first and perhaps most critical step

in an analytical method, namely sampling and sample preparation. One

of the most serious sources of error in analysis is that introduced by

improper sampling. The situation is particularly acute in the case of trace characterization in materials research where the trace elements

at the parts per million and parts per billion levels are almost invariably

distributed in the soHd state material in a heterogeneous fashion as has

been shown by Professor Minczewski.

The paper by Skogerboe and Morrison examines a number of the

problems in terms of sampling theory and shows their effect on various

trace analytical techniques. In view of the many factors influencing

sampHng errors, it is understandable why analysts encounter difficulties when they try to compare the analytical results obtained by different trace techniques. Table I presents generalized data to illustrate the

sampHng capabilities of some of these techniques. The data may be

regarded as typical since they represent the most common practice,

usage, and results, as determined from the general literature. It can be seen that the combined pretreatment and measurement errors for all methods hsted are in the same range of 1-5% depending upon the care taken in the analysis. All of these techniques involve either electronic

of photographic detection in the measurement step and relative standard

deviations of 1-5% are reasonable.

With regard to the total error involved in the various methods, it is readily apparent that techniques utilizing solutions consistently result in a reported overall error which is better than that observed for direct

techniques. It should be noted that solution techniques normally

utilize a relatively large sample with a resultant reduction in the sampling

error observed. Also, it is a common practice to make several measure- ments on the same homogenized solution and use these data to obtain a precision estimate. In reaUty this estimates the measurement precision

only and tends to place the technique in a more favorable, but false,

position when compared with other techniques.

A similarly misleading practice is encountered in publications involving the nondestructive techniques such as neutron activation and x-ray fluorescence. Either the square root of the observed count or the reproducibility of subsequent measurements on the same sample are fre- quently taken as representative of the total error. The first approach

estimates only the measurement precision, while the latter partially

estimates the combined pretreatment-measurement errors if neutron

or x-ray bombardment is considered as a part of the pretreatment stage.

Explicitly, these usages tend to delete sampling error by ignoring it or

to reduce it by using a large sample together with homogenization.

The overall reproducibihties of direct methods of analysis are fre- quently less favorable because the techniques use smaller samples
PRECONCENTRATION 423

Table 1. Distribution of errors of trace methods.

Technique

Typical

Sample

Size, Mg

Most Common

Mode of Sample

Pretreatment

Typical Relative

Standard Deviation, 9?

Pretreatment

and

Measurement

Total

Spectrophotometry

Absorption 100-1000 homogenization 1-5 1-5

by dissolution

Fluorescence 100-1000 homogenization 1-5 1-5

by dissolution

Flame 100-1000 homogenization 1-5 1-5

by dissolution

Atomic 100-1000 homogenization 1-5 1-5

absorption by dissolution

Neutron activation 10-1000 direct or homog- 1-5 1-15

enization by

dissolution

Emission 1-50 direct or homog- 1-5 5-30

spectrography enization by

dissolution

Spark source 0.1-10 direct 1-5 5-30 mass spec

Microprobe 0.01-1 direct 1-5 5-30

X-Ray 10-1000 direct or homog- 1-5 5-30

fluorescence enization by

dissolution or fusion

subject to greater sampling error. Also, these techniques are often not amenable to prehomogenization practices. While it is true that the lack

of control of dc arc or the spark in emission or mass spectrography contributes to the total error, these same "uncontrolled" sources are often

used on samples known to be homogeneous to obtain a total error equivalent to the combined pretreatment measurement errors. Such results are numerous in emission and mass spectrometry, and indicate that although these techniques do not provide the best estimate of the bulk
424 TRACE CHARACTERIZATION

concentration of heterogeneous samples, they should be very useful

in giving a good estimate of the localized concentrations in the fashion of

a probe. It should be apparent from this discussion that comparison

of the indicated reUabilities of analytical results obtained by independent

methods may be invalidated by the difference in the capabilities of the

methods with regard to the inference of heterogeneity and/or misrepresentation of the total error reported. In connection with sampling, the preparation of solids for further

study and characterization is a very important step, and the paper by Hill,

Morris, and Frazer describes a cathodic etching method that has been

developed to clean the surfaces of metal samples prior to oxygen deter- mination by vacuum fusion. The sample is made the cathode in a low

pressure argon-ion discharge. The argon ions bombard the surface of

the sample and remove the oxide film by an etching process. The oxy- gen content of metal samples such as high purity uranium and iron

cleaned by cathodic etching is consistently lower than that achieved

using acid etching or filing.

A somewhat related study by Yates and Madey describes the preparation of atomically clean surfaces. Details are presented on the production

and measurement of ultrahigh vacuums, the purification and handling

of gases for adsorption studies under these conditions, as well as the

production and characterization of clean surfaces.

Finally, an example of the problem of losses of trace elements in solu- tion samples by adsorption is treated in the paper by F. K. West and

P. W. West. A study is described to evaluate the adsorption of silver in potable water samples on various storage container materials and the use of ligands to complex the traces of silver to prevent losses. V. Discussion

Margoshes (NBS) agreed with the general feeling that separations and

preconcentrations at the nanogram level are to be avoided in general

analysis because of the dangers of contamination. There are, however,

situations where they are essential and he cited the situation discussed

in the paper by Alvarez where it was necessary to remove the matrix in order to accurately determine traces of elements in certified standard

samples of zinc. Here every effort must be made to provide very dependable certification. Grant of the University of New Hampshire commented on the problem

of sampling errors and cited the example of the original sampling of

biological systems where errors of ± 25% are not uncommon before the

analyst receives the laboratory sample.

Morrison raised the question of the validity of the designation of commercially available high-purity materials as 5-9's or 6-9's purity. In many cases emission spectroscopy is used to characterize these materials

and the presence of many impurities is missed because of the ineffec-
PRECONCENTRATION 425

tiveness of the method. Comments from the audience indicated that most analysts recognized these designations as being meaningless and

understood the necessity of analyzing these materials for the specific

appHcation at hand.

Honig of RCA raised the question of reporting analytical results in units of parts per million on a weight basis versus an atomic basis. It was concluded that the preferred units depended upon the particular

application involved. In any case, it is a simple matter to convert from

one form to the other. Considerable interest was expressed in a novel approach to reagent

purification described by Freeman of the NBS. The method includes

the storage of high purity reagents in their frozen state. Water, sulfuric

acid and sodium hydroxide are maintained at —25 °C and facilities are being constructed for the frozen storage of aqueous mineral acid

solutions. VI. References

[1] Morrison, G. H. and Skogerboe, R. K., "General Aspects of Trace Analysis", in Trace

Analysis: Physical Methods, G. H. Morrison, editor, Interscience Publishers, N.Y.,

1965, p. 16.

[2] Mizuike, A., "Separations and Preconcentrations", in Trace Analysis: Physical Methods, G. H. Morrison, editor, Interscience Pubhshers, N.Y., 1965, p. 104.

[3] Tera, F., Ruch, R. R., and Morrison, G. H., Anal. Chem. 37, 358 (1965).

[4] Ruch, R. R., Tera, F., and Morrison, G. H., Anal. Chem. 37, 1565 (1965).

[5] Tera, F., and Morrison, G. H., Anal. Chem. 38, 959 (1966).

THE STUDY OF CRYSTAL IMPERFECTIONS

BY MEANS OF OPTICAL METHODS AND BY

MEANS OF ELECTRON MICROSCOPY

AND ELECTRON DIFFRACTION

S. AMELINCKX'

Centre d'Etude Nucleaire, Mol, Donk, Belgium

I. Introduction

In this paper a survey will be given of optical and electron optical

methods for revealing dislocations and other crystal defects. In a first part we shall sketch the historical development of the so-called methods

for "direct observation" of crystal defects. By a "direct" method is meant a method which allows to localize the defect and to determine at least some of its geometrical characteristics. This is in contrast with

indirect methods for the study of dislocations such as X-ray line broadening, internal friction, etc. From what follows it will become clear that the term "direct" is somewhat relative because for most of the methods

which are termed direct one does in fact not see the dislocation or defect itself, but some more or less adequate image which may be a row of particles in the case of the decoration method or a fringe pattern

in the case of electron microscopy.

The second part is devoted to a brief discussion of some of the properties of dislocations, stacking faults and other lattice defects. Only

these properties will be mentioned which are relevant for our purpose,

for instance because one of the methods of studying dislocations is based on it. A brief description will be given also of some of the geo- metrical features which lend themselves easily to a study of direct

methods.

In a third part a systematic discussion is presented of the different

optical and electron optical methods for the study of lattice imperfections. In particular we shaU emphasize the techniques, rather than

the results obtained by them. Consequently neither is an attempt

made to give a complete survey of all results, nor is it possible to include

aU references to such work. Special attention will be paid to the

limitations of each of the methods and specific fields of appUcation shall be indicated.

' Also at: Laboratorium Fysika Vaste Stof, Rijksuniversitair Centrum, Middelheimlaan

1 Antwerpen.

427
428 TRACE CHARACTERIZATION

II. Historical Survey

The discovery of X-ray diffraction and of methods for structure determination has laid the emphasis on the perfect three dimensional

periodicity of crystals. However it was soon found that real crystals

show deviations from strict three dimensional periodicity. This follows

already from a comparison of the observed intensity of the X-rays dif- fracted by a crystal with that calculated for a perfect crystal. It is only

very recently that crystals have been found which behave as perfect

crystals should according to the dynamical theory of X-ray diffraction. The properties which are most sensitive to the presence of geo- metrical imperfections are however the mechanical properties such as

yield stress. It was in fact in an attempt to explain the slip process in crystals that dislocations were first introduced by Taylor [1] ^ and Burgers

[2]. The basic idea was a very simple one. The reason why the calculations based on the perfect crystal assumption failed in predicting the

strength of crystals was that in a perfect crystal one had to accept that a whole crystal plane of atoms slipped at once over a similar plane.

This process obviously requires a large force since all atoms have to go

simultaneously over the potential hills constituted by the other layer

of atoms. This "one shot" process can be replaced by a progressive

motion of a small number of atoms at any time if one assumes the pres- ence of a dislocation. It was this idea which lead the theoreticians to postulate possible models for linear defects so called dislocations,

which would be capable of performing the required atom movement on

propagating between two crystal planes.

For a long time the study of dislocations remained the privilege of theoreticians and large chapters of dislocation theory were written with- out even a single observation proving that dislocations really exist in crystals. This situation persisted until 1950, when, again on theoretical

grounds, it was predicted that dislocations should play an important role

in the growth of crystals [3]. The importance of the dislocation theory

of crystal growth lies in the fact that it predicted an unambiguously

defined and in principle easily observable surface feature: the growth

spiral. The observation of growth spirals provided a simple means for localizing the emergence points of dislocations in the surface of crystals.

The scale of these surface features was such that the optical microscope was quite adequate, especially if phase contrast is used, to improve the

visibility of surface steps. For this reason optical methods have played an important role in the direct observation of dislocations at least in the

initial stage.

The study of growth features requires for obvious reasons growth

faces. Furthermore the growth steps to be revealed are of the scale of

the unit cell, which means that almost atomically flat growth faces are

^Figures in brackets indicate the literature references at the end of this paper.
MICROSCOPY 429

required for the study of the growth spirals. For this reason it is clear

that the use of growth spirals as "indicators" for the emergence points

of dislocations can only be of -limited application.

The logical step forward was obviously to try whether the reverse phenomena of growth, i.e., dissolution, etching or evaporation would

also be sensitive to the presence of dislocations. On etching crystals

exhibiting growth spirals or growth hills it was found that pits were

produced at the centers of growth spirals or at the tops of growth hills proving clearly that etchpits are formed preferentially at the emergence

points of the same dislocations that gave rise to growth spirals [4]. Moreover it was discovered that pits were produced also at sites other

than those marked by the emergence points of screw dislocations. This

observation was in agreement with the fact that according to the dislocation theory of crystal growth not all dislocations give rise to spirals, but

only those for which b • n 0 (n = unit normal on crystal face under

observation, b = Burgers vector of the dislocation). The etch pitting

technique for revealing the emergence points of dislocations has now

been developed to the stage where it has become a standard method for the quasi-non-destructive determination of crystal perfection, mainly

in the semi-conductor field. Also evaporation has found application as a means of studying the

dislocation geometry. Since the scale of the phenomena is however at the limit of resolution of the optical microscope, it is more successfully

used in conjunction with electron microscopy [5] although the first observations were made with optical microscopy [6]. All the methods mentioned so far are surface methods and therefore

only reveal the emergence points. As a result only a limited amount of information can be obtained from them. The first method capable of

revealing dislocations along their length in the interior of transparent

crystals was the so called "decoration" method. It reveals the dislocations by causing particles of a second phase or of the stoichiometric excess of one of the constituents to separate out along them. The

method was discovered as a by-product of a study of the photographic

process by Hedges and Mitchell [7]. When subjecting crystals of silver bromide to the print out process they discovered that specks of photolytic silver were formed preferentially along dislocations. The method

was afterwards adapted and used intentionally for the study of dislo- cations in alkali halides [8], in silicon [9] and other crystals [10]. Comparing etchpits with internal decoration patterns it was found

as well for alkali hahdes as for silver bromide and for silicon, that the etchpits do form at the emergence points of dislocations in the

surface, proving the relation between the two methods [11]. Also the decoration technique has limitations. The most obvious one is that since optical microscopy is used for the observation, one is limited by the resolution of the optical microscope. However as we
430 TRACE CHARACTERIZATION

shall see below other factors limit the use of the method. The crystals

should furthermore be transparent either to visible light or to some other

easily detectable radiation (e.g., infra red) which limits practically the

application to non-metals. However it has been shown recently that use can be made of the fact that certain metals are transparent in the

ultra violet [12]. The decoration methods do not allow to see "bare" dislocations; the

presence of dislocations can only be inferred from the presence of

linear arrangements of fine precipitate particles which scatter light and

which are assumed to "decorate" the dislocations.

"Bare" dislocations can nevertheless be observed optically as a re- sult of stress birefringence [13]. Comparison between the etch pattern,

the decoration pattern and the birefringence pattern for the same dis- location arrangement in silicon has shown perfect one to one corre- spondence giving confidence in the three methods [14]. The most versatile method for the direct study of dislocations is undoubtedly electron microscopy in transmission. After some partly

successful attempts by Heidenreich [15] and Castaign [16], transmission

electron microscopy was shown to be a method capable of revealing

dislocations and other crystal defects by Hirsch and coworkers [17] and

independently by BoUmann [18]. The contrast is not due to absorption,

as in the case of replica, but instead it results from diffraction phenomena

at the deformed region of the crystal around the dislocation.

For a correct interpretation of the image produced in the electron

microscope at imperfections a fairly good knowledge of diffraction contrast theory is required. If one wishes to extract all the information

which is contained in an electron micrograph a complete knowledge of

the exact diffraction conditions is necessary. It is therefore useful to combine direct observation with electron diffraction and correlate the

information obtained from both.

Almost simultaneously Menter [19] showed that the periodic arrange- ment of molecules in certain organic crystals (Pt-phthalocyanine) could

be imaged directly in the electron microscope. From the local dis- turbance of the lattice rows one can then conclude to the presence

of dislocations.

Pashley, Menter and Bassett [20] also developed methods to produce

a "geometrical" magnification of crystal lattices so as to bring the

detailed structure of the resulting pattern within the resolving power

of the electron microscope. The method consists in superposing thin

films formed by metals with slightly different lattice parameters or with

a slightly different orientation. The so called "moire pattern" gives a magnified representation of the actual crystal lattice. A dislocation

in the lattice of one of the constituent crystals of the sandwich is re- vealed as a dislocation in the moire pattern.
MICROSCOPY 431

As well the formation of "lattice fringes" as the formation of "moire

fringes" is the result of a diffraction phenomena. Considerable care

is therefore needed in interpreting discontinuities and disturbances

of fringes in terms of lattice defects. Some of the difficulties are discussed below.

Pierhaps the ultimate technique for the study of dislocations and even

individual point defects is the field ion microscope developed by Miiller [21]. It allows to reveal patterns of individual atoms in the surface

of fine tips of refractory metals. The application of high electrostatic

fields allows to "peel off" monolayers of atoms and as a result it be- comes possible to explore the crystal in depth.

Parallel with the electron optical methods a number of X-ray methods

for mapping dislocations have been developed. A review of these is the subject of another paper and we shall therefore not discuss them.

III. Structural Defects

In this chapter we shall only give a very elementary survey of some

notions of dislocation theory which are required for an understanding of the remaining part of the paper. For a more complete treatment

of the theory we refer to the well known textbooks [21b].

A. Dislocations

1. Definition, Displacement Vector

First an intuitive definition of the concept of a dislocation will be

given. The definition merely states how a dislocation can be intro- duced into a perfect crystal. Consider the ideal crystal with a primitive lattice of Figure la. Imagine a cut along one of the cube planes.

Displace now the two parts I and II, underneath and above the cut, one with respect to the other, over a vector b. This can be done in three different ways without destroying the homogeneity of the crystal:

(1) by shearing in the ^c-direction (Figure lb); (2) by shearing in the y-direction (Fig. Id); (3) by pulhng the two parts apart in the 2-direction and

inserting a supplementary half plane (Fig. Ic). It is evident from

Figure 1 that the operations (1) and (3) lead to the same configuration,

which is termed an edge dislocation; operation (2) gives a different configuration called a screw dislocation. In all cases a line discontinuity

XY is created, which is in cases (1) and (3) the edge of a supplementary

half plane, and in case (2), the axis of the helicoidal surface formed by

the {xz) "planes". In cases (1) and (3) this line, called the dislocation

line, is the Hmit between the part of the crystal plane, {xy) in this case, where gUde has occurred, and the part that remained unaltered. This

plane is the glide plane and for the edge dislocation this is unambiguously determined, since it passes through the line and is perpendicular
432 TRACE CHARACTERIZATION

Figure 1. (a) Perfect crystal, (b) Crystal containing an edge dislocation XY introduced by shearing in the j^-direction along the plane XYV. (c) Crystal containing an edge

dislocation XY introduced by inserting a supplementary half plane (yz). (d) Crystal

containing a screw dislocation XY introduced by shearing in the y-direction.

to the supplementary half plane. The configuration (3) could also result from glide on a plane (zy) perpendicular to the inserted half plane. For the screw dislocation, every plane passing through the line could function as a glide plane (the configuration has axial symmetry

in an isotropic medium).

For an edge dislocation b is perpendicular to the line, whereas in the case of a screw dislocation, b is parallel to the line. In both cases

the glide plane contains the fine and b. The definitions introduced here are not very rigorous. The main

purpose is to demonstrate that one can distinguish only two differ- ent types of pure dislocations, differing only in the relative orientation

of the displacement vector b and the line. It is possible to consider

all intermediate orientations; this leads to dislocations of mixed

character.

2. Burgers Circuit —Burgers Vector More rigorous definitions can be formulated in a geometrical way,

without thinking of a deformation, by comparing the real crystal with an ideal crystal, and introducing the concept of corresponding paths.

Consider first an edge dislocation, which can be represented in two

dimensions. Let Figure 2a represent the crystal containing an edge

dislocation (perpendicular to the plane of the figure at D) and Figure 2b

an ideal crystal. One can now consider a path in the ideal crystal de-
MICROSCOPY 433

fined by a prescription of the following kind: x unit distances to the left, y downward, z to the right, etc. As long as one stays in "good" parts,

there is no difficulty in finding a path given by the same prescriptions

in the real crystal. These are corresponding paths.

Consider now a closed path in a real crystal, going all the way through

the good crystal but possibly surrounding dislocations, such a path is called a Burgers circuit. The corresponding path may either be closed

also (e.g. path 1) or it may fail to close (e.g. path 2); this depends upon

whether the Burgers circuit surrounds a dislocation or not. The closure

failure i.e., the vector A'B' = b is the Burgers vector of the dislocation

surrounded by the Burgers circuit, b is perpendicular to the dislocation

line. It is further evident that b is identical with the displacement

vector introduced in section III.A.l. For a pure screw dislocation the

Burgers vector is parallel to the dislocation line. When a Burgers cir- cuit surrounds more than one dislocation, the closure failure is the sum

of the Burgers vectors of all the individual dislocations surrounded by

the circuit.

It is clear that the definition of the Burgers vector as given here still depends on a number of arbitrary conventions. The set of conventions

which is usually adopted is the so called FS/RH rule. It consists in applying the following prescriptions:

(i) Choose an arbitrary positive sense along the dislocation.

(ii) Make a closed Burgers circuit in the deformed crystal.

(iii) The circuit should be right handed (RH) when viewed along the

positive sense of the dislocation.

(iv) The corresponding circuit is constructed in the perfect crystal.

(v) The closing vector, which is the Burgers vector of the dislocation,

connects the final point (F) with the starting point (S) of the circuit. Once a positive sense is chosen along the dislocation the Burgers

vector is unambiguously defined.

Both kinds of dislocations can be positive or negative. When the

edge dislocation of Figure lb with supplementary half plane above the

plane UV, is called positive, an edge dislocation with the supplementary

half plane under UV would be called negative. Positive and negative screw dislocations can be defined as the axis of right- and left-handed

helicoidal surfaces.

3. Dislocation Loops

For topological reasons a dislocation line either emerges with both

ends at the surface or it forms a closed loop. When the dislocation

line branches, the sum of the Burgers vectors of the three (or more)

components is zero : bi +b2 + bs = 0. This last relation implies that the positive sense of the dislocations is chosen away from the branching

point.
434 TRACE CHARACTERIZATION

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( b) Figure 2. Burgers circuit for an edge dislocation Z); 1 is a circuit not surrounding the

dislocation, the corresponding circuit 1' is closed; circuit 2 surrounds the edge dislocation, 2' is not closed, the closure failure is vector A'B'

.

A dislocation loop has the same Burgers vector along its whole length.

As a consequence the line changes its character (edge or screw) along

different parts of the loop.
MICROSCOPY 435

Consider e.g., the cut ABCD (Fig. 3) along a glide plane in a primitive lattice and displace the material contained in the parallelepiped

ABCDA'B'C'D' with respect to the surrounding material over a vector b

parallel to DC. The resulting situation is shown in Figure 4b. Figure

4a is a cut along XY. It is evident that the square dislocation loop so obtained consists of two edge parts EC and AD and two screw parts

AB and DC, both being of opposite sign. Such a loop is "glissile."

One could also compress the parallelepiped into the crystal over a vector b parallel to AA', creating a square step on the upper surface

and a square dislocation loop ABCD in the interior of the crystal. The

loop now has edge character along its whole length; this is shown in Figure 5 which represents an arbitrary cut. It is termed a prismatic

dislocation.

4. Displacement Fields

It is clear that in the vicinity of a dislocation the atoms are not at the

sites which they would occupy in a perfect crystal. One can describe

the displacements of the atoms around a dislocation by means of a

vector field represented by a displacement function R{r). For a screw

dislocation in an infinite medium all displacements are parallel to the

hne. If the screw dislocation is along the z-axis the components of/? are R^ = Ry = 0 R, = (6/277) arctg (ylz) For an edge dislocation along the z-axis and with a Burgers vector along the :r-axis, the supplementary half plane being along the positive

part of the y-axis, one finds for the displacement field

Ra: = (6/277) [arctg (ylx) + xyl2{l - v){x^ + y^)]

Figure 3. Cut in a perfect crystal leading to the formation of a dislocation loop.
436 TRACE CHARACTERIZATION

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to present a bump at the position of the dislocation.

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MICROSCOPY 437

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the superposition of the displacement fields of the edge and screw components.

Dislocations are seen in the electron microscope because of their

displacement fields. Pictorial views of the lattice deformations around

dislocations are given below (Figs. 32, 33).

5. Stress Fields — Cottrell Interaction

With the displacement field a stress field is associated. The stress

field around a screw dislocation in an infinite isotropic medium only

contains shear stresses on planes which are not perpendicular to the

dislocation Une. The stress field has axial symmetry.

On the other hand the stress field due to an edge dislocation is more

compHcated. It has dilatational and shear components. The dilata- tional stress is compressive on that side of the glide plane where the

supplementary half plane is situated; it has tensile character on the

other side of the glide plane. As a result of this oversized and undersized impurity atoms are attracted respectively to the regions of tensile

and compressive stress. This effect is called "Cottrell interaction"

and it plays an important role in decoration and etching.

The stress fields of all dislocations decrease as 1/r; where r is the

distance from the dislocation core.

6. Energy of a Dislocation

A certain amount of energy per unit length is associated with a dis- location. This energy has its origin partly in the distorted core, but

for the largest part in the elastic strain field in the region around the

dislocation. It can be shown that the energy per unit length is proportional to the square of the Burgers vector. This is reasonable since it cannot depend on the sign of b. It depends on the character of the

dislocation, being smallest for screw dislocations and largest for edge

dislocations, at least in an isotropic medium.
438 TRACE CHARACTERIZATION

Two meeting dislocations may form a single dislocation if this process

is accompanied by a decrease in energy. In such a reaction the Burgers

vector ba of the newly formed dislocation is equally the sum of the

Burgers vector of the reacting dislocations bi and b2 : bs = bi + b2. One can say as a rough approximation that the reaction will give rise

to energy gain provided 6| < ^i + ^f. Reactions of this kind are responsible for the formation of threefold nodes at the intersection points of two dislocations.

Since the total energy associated with a dislocation is proportional

to its length it will tend to shorten giving rise to a certain "Une tension."

7. Force on a Dislocation; Motion of Dislocations

A dislocation being only a configuration of atoms the concept of

"force on a dislocation" is of course quite different from the Newtonian

notion of force on a mass. In fact forces act on atoms and not on the

dislocation.

Figure 6a represents a crystal containing two edge dislocations of

opposite sign. Under the influence of the shear stresses S the forces on the atoms wiU cause the rearrangements as indicated by the arrows and as a result the dislocations move. It is clear that dislocations of

opposite sign move in the opposite sense. Where they reach the sur- face, they are eliminated and steps result (Fig. 6b). Inversion of the

stresses inverts the sense of the movement of the two dislocations.

When the two supplementary half planes come one above the other,

the two dislocations annihilate mutually if they are in the same gUde

plane. A pure edge dislocation moves in the direction of its Burgers

vector (i.e., perpendicular to its line). When a shear stress S is applied to a screw dislocation, it moves in a

direction normal to its Burgers vector. Hera again an inversion of the sense of the shear stresses changes the sense of the movement. When

the two dislocations are in the same glide plane, they will also annihilate mutually on meeting.

As a result of the movement of a dislocation under the influence of

the applied shear stresses the crystal yields i.e., one part of the crystal

is displaced with respect to the other over the Burgers vector and therefore work is done by the applied forces. Also the "force" acting on

the dislocation has performed work since the dislocation has been

displaced over the slip plane. Equating these two amounts of work

yields an expression for the force F on a dislocation. In the simplest case F = bor where cr is the shear stress on the glide plane.

The force always acts in a direction perpendicular to the dislocation

line.Consider now the square loop of Figure 4b. Under the appHed shear

stress S the two edges move outwards, as well as the two screws, and as a consequence the loop expands. Inversion of the stresses inverts
MICROSCOPY 439

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( b)

Figure 6. Movement of two edge dislocations of opposite sign. When the dislocations leave the crystal surface steps result. the movement of every component of the loop, which will thus contract and might finally disappear.

The case of the prismatic dislocation of Figure 5 is different as every

section is edge. Each dislocation now has a different glide plane,

defined by the fine itself and its Burgers vector. The loop is thus

237-323 0-67—27
440 TRACE CHARACTERIZATION

mobile only on the cylindrical surface defined by the square loop and

with generators parallel to b. By generahzing the previous considerations, one formulates the general rule: a dislocation is mobile on

the cylindrical surface that contains the line and its Burgers vector. Up till now only conservative motion, i.e., motion involving only

ghde, has been considered. Edges are, however, capable of a diffu- sive type of motion. The arrival or the departure of vacancies at or from the dislocation will shorten or lengthen the supplementary half plane, and this changes the glide plane of the dislocation. This phe- nomenon is called climb. Edge dislocations can thus act as sources

or sinks for vacancies. The removal or the absorption of vacancies

takes place at jogs, which as a consequence move sideways along the

line. A jog in an edge is a site at which the supplementary half plane

becomes one unit longer or shorter, i.e., where the line changes its glide plane. Jogs in screw dislocations can move in a conservative

way along the line.

8. Forces Between Dislocations

The stress field due to one dislocation causes a force on other dis- locations in its vicinity: they interact one with the other. The force

laws for dislocations show a large analogy with those between electrically

charged lines. For parallel dislocations with the same character

the force may be either repulsive or attractive depending on whether

the Burgers vectors have the same or opposite sign. The forces between parallel dislocations in the same glide plane vary as 1/r, the pro- portionality coefficient being a function of the magnitude of the Burgers

vector and of the elastic constants. If the Burgers vectors enclose an acute angle there is repulsion; otherwise there is attraction.

9. Multiplication of Dislocations

One can now describe a mechanism for the multiplication of dislo- cations, which is of fundamental importance. In practice, dislocations

will be curved and may not even be plane. As a consequence it is to be expected that some parts of a dislocation will satisfy the mobility

condition, others not. Consider the situation where only a part AB of

a dislocation line is mobile in the plane of the drawing, i.e., the glide

plane; suppose it is of the edge type (Fig. 7a). Under the influence of

the applied stress the dislocation line will successively adopt the shapes

1, 2, 3, . . . and finally (situation 4), two screws of opposite sign will annihilate, and an expanding loop of the kind discussed in section III. A.

3

will be formed. At the same time the original line AB wiU be reformed,

so that the process can start over again. The area within the loop

is hereby displaced in the direction and the sense indicated by b,

with respect to the outside. If at a point n loops have passed, the
displacement is ^b. It is theoretically possible to obtain an unlimited

amount of slip from a single "source" AB. In reality the dislocation

loops wiU not be square, but curved (Fig. 7b). They may adopt complicated shapes as a consequence of their interaction with other dislo- cations.

B. Stacking Faults. Partial Dislocations

If the displacement vector or Burgers vector of the dislocation is not a lattice vector the dislocation is called partial. The plane YXV of Figure 1, over which slip has occurred would then be a plane of misfit or a fault plane and the partial dislocation forms the edge of the

faulted region. Such a situation often occurs because slip usually

takes place between close packed planes. A simple experiment

with layers of hard spheres will show us how such slip motion can occur. Such a layer of spheres is represented in Figure 8. It presents

two kinds of hollows: A hollows and V hollows. A second layer of the same kind would fill completely one family of hollows only. In the f.c.c. structure all successive layers fill hollows of the same kind in the

underlying layer. The perfect dislocation which would perform

1
442 TRACE CHARACTERIZATION

Figure 8. Close packed planes of balls illustrating the concept of Shockley partials. Glide from A to B proceeds in two steps: Aa and aB.

slip between two such layers would have a Burgers vector of the type

AB. However it is clear that the slip process will become easier if

it is performed in two steps. The first step brings the layer from the

A hollow into the V hollow, i.e., in a faulted position. The second

step completes the slip motion and brings the layer from the V hol- low again into the A hollow. In dislocation language one describes

this two step process by saying that slip is performed by the passage

of an extended dislocation or dislocation ribbon. The ribbon consists

of two partial dislocations (so called Shockley partials) separated by

a stacking fault. The first partial with b = Acr causes on passing the

first slip motion creating a stacking fault. The second partial with

b — crB removes the stacking fault and completes the slip process. The perfect dislocation with b = AB is said to have dissociated according to the dislocation reaction AB = Ao-H-crB. The two vectors Act and crB enclose an acute angle (60°) as a result the two partials repel.

They are kept together by the stacking fault between them. In more

complicated structures the slip process may break up in more than two

steps giving rise to multiribbons. Examples of this are shown below.

Stacking faults may also result during growth or as a result of the

formation of point defect loops. This is discussed below.

A certain amount of energy is associated with a stacking fault. The

energy per unit area of fault is called the stacking fault energy.
MICROSCOPY 443

C. Arrays of Dislocations

The contact zone between two differently oriented crystallites is called a grain boundary. There is now convincing evidence that they can be described as arrays of dislocation lines, at least when the orientation difference is small. A general grain boundary is defined by means of five parameters: n the unit vector normal on the contact

plane, u the unit vector along the rotation axis, and 6 the rotation angle.

Two ideal cases are

(i) the pure tilt boundary: n • u = 0

(ii) the pure twist boundary: n X u = 0. Two examples of the first kind are shown in Figure 9 in the case of

a primitive lattice. Figure 9a represents the symmetrical pure tilt

(a) (b)

Figure 9. (a) Symmetrical type tilt boundary in primitive lattice, (b) Asymmetrical pure

tilt boundary.
444 TRACE CHARACTERIZATION

boundary. The contact plane is a symmetry plane for the bicrystal.

The model consists of a set of equidistant (separation D) parallel and

straight edge dislocations all having the same Burgers vector b, where

D=bie,

When the contact plane forms an angle (f) with the symmetry plane,

the boundary still consists of parallel edges but they have mutually

perpendicular Burgers vectors (Fig. 9b). The two kinds of dislocations are both at characteristic distances given by

Di = bie sin (/) D2 = bid cos (f).

Figure 10 represents a pure twist boundary in a primitive lattice. Vectors u and n are both normal to the simple lattice plane, which is in the

plane of the drawing. The scheme in (a) represents two undistorted

lattice planes on both sides of the contact plane; (b) shows the configuration after a small relaxation of the atoms towards equiUbrium.

There is now a crossed grid of screws, the mesh size being D = bl6. For more general grain boundaries the models become increasingly more comphcated and they can no longer be derived on a purely geo- metrical basis. For actual crystal lattices the described models become

sHghtly more comphcated. The pure twist boundary in a (111) plane

of a face centered cubic lattice will be a hexagonal net (Fig. 11); a

Figure 10. Pure twist boundary on cube plane in primitive lattice, (a) after twisting

(b) the atoms have relaxed.
MICROSCOPY 445

pure twist boundary in a (100) plane will be the simple square grid of Figure 10.

If the dislocations can dissociate twist boundaries situated in close

packed planes acquire a somewhat more complicated geometry. We

shall only consider face centered .cubic crystals. If the stacking fault energy is small, half or all of the nodes of hexagonal networks become

extended (Fig. 12): small triangular regions of stacking fault are formed.

The degree of extension is determined by the balance between the in- crease in energy that accompanies the creation of the stacking fault region, and the decrease in energy resulting from the shortening of the dislocations. The extended nodes contain alternatively intrinsic and

extrinsic faults (see paragraph V. C.l). If both have small energy all nodes will dissociate; if only one type of fault has low energy only one family of nodes dissociates. In silicon the first situation prevails; in face centered cubic alloys usually one family of nodes only

is dissociated. However recently it has been found that also in f.c.c. metal alloys both types of nodes may be visibly dissociated. D. POLYGONIZATION

Pure tilt boundaries can be introduced by bending a crystal about an axis lying in a glide plane, normal to the Burgers vector, followed

by annealing. The formation of these boundaries is known as polygonization because curved lattice planes become polygonal during this process (Fig. 13). The phenomenon consists in a rearrangement of dis- locations in their glide plane, as well as normal to it; this implies the oc- currence of "climb". The final stable configuration is one in which

Figure 11. Model for a hexagonal grid of screw dislocations in the (111) plane of a f.c.c. crystal, (a) after twisting about the [111] axis (b) after the atoms have relaxed.
446 TRACE CHARACTERIZATION

(d) (e) Figure 12. Generation of networks, (a) Interaction of two dislocation segments with

vector AB and BC, with formation of new segments, with vector AC.(b) Formation of hexagonal meshes from the intersection of 2 families of dislocations, (c) Net after one

family of nodes has become extended (d) If the stacking fault energy is very small the network consists of an alternation of faulted and unfaulted triangular regions, (e) If both the intrinsic and extrinsic faults have small energy doubly dissociated nets result.

(a) (b)

Figure 13. Polygonization. (a) Distribution of dislocations immediately after bending,

(b) Stable configuration of dislocations resulting from a rearrangement in the glide plane

as well as from cHmbing.

the dislocation walls (pure tilt boundaries) are normal to the active

glide planes.
MICROSCOPY 447

IV. Observation Methods

A. Surface Methods

1. Growth Spirals [21, b] As we have mentioned above the first phenomenon which was shown

to be directly related to the presence of dislocations was the occurrence

of growth spirals centered on the emergence points of dislocations of which the Burgers vector has a component normal to the crystal face

under consideration. We now summarize briefly the underlying theory

[3]. It is obvious that a perfect crystal could only grow by the addition

of complete layers of growth units. In order to start a new layer on a

close packed plane a two dimensional nucleus has to be formed. However the probabihty for the formation of a two dimensional nucleus of

the critical size or larger is negligibly smaU at the low supersaturations

where crystals are found to grow at observable rates. This difficulty can be removed by taking into account that crystals contain dislocations

emerging in the surface. For geometrical reasons a surface step of height h = h-n is attached to each dislocation with Burgers vector b

emerging in a crystal face with unit normal n. Under conditions where

growth occurs this step will tend to acquire growth units and thereby

it tends to move parallel to itself. However since the step is anchored

in P (Fig. 14), it can only adopt the shapes shown in Figure 14. On

further growth each part of the curved step is displaced further out- wards. As a result the step winds up into spiral shape, but it never

grows away as an ordinary surface step, not attached to a dislocation,

(a) (b) (c)

(d) (e)

Figure 14. fa) Step attached to the emergence point P of a dislocation with a Burgers

vector which is not parallel to the surface. The step height h = h • n where n is the unit normal on the surface, (b) Under the influence of a supersaturation the step in (a) winds up into a spiral centered on P. id and e).
448 TRACE CHARACTERIZATION

would do. On continued growth each part of the spiral is displaced

outwards and the spiral apparently rotates around its center maintaining a stationary shape. After the cessation of growth one thus expects

to find crystal faces exhibiting spirally shaped growth hills the centers

of which are the emergence point of a dislocation.

It is clear that one can exploit this phenomenon and use the growth

spirals as "indicators" for the emergence points of dislocations. Fur- thermore, the step height, which can be measured by multiple beam

interferometry, gives the component of b perpendicular to the crystal

face. Steps as small as 7.5 A can be observed by reflection phase

contrast microscopy and using sufficiently well developed spirals, stepheights of the same magnitude can be measured by means of multiple

beam interferometry (Fig. 15). On moving, a dislocation creates in its wake a surface step (a so called

slip step) of which the step height is again h = h • n. Such unit slip

steps can be observed in the same way as the spiral steps; they sometimes start at the centre of the growth spirals giving rise to characteristic step configurations from which the path of the moving dislocation can be inferred [22].

It is clear that only a limited amount of information can be obtained

from the observation of growth spirals:

Figure 15. Growth promoted by a number of spirals of the same sense originating in a group of dislocations with components perpendicular to the c-face of the same sign. The step heights are 13 A.
MICROSCOPY 449

(i) One can estimate the density of dislocations having a component

perpendicular to the crystal face under examination and one can measure

this component.

(ii) The sense of winding of the spirals depends on the sign of b • n,

i.e., on the sign of the dislocation. One can as a result determine the

relative densities of dislocations for which the normal component of b has a given sign.

(iii) Some information on the motion of dislocations can be obtained.

For instance the mutual annihilation on moving together of two dislocations of opposite sign could be deduced from growth patterns [23]. The method is obviously of very hmited use because very clear and

perfect growth faces are needed to make the observations possible.

Furthermore not all the dislocations are revealed and only the emergence

points are detectable.

2. Evaporation Spirals

The reverse phenomena, i.e., evaporation under conditions of low

undersaturation also produces spiral steps of which the center is now the

lowest point. These spirals can be used in exactly the same way as the

growth spirals. However it is difficult to create undersaturations low

enough so as to produce spiral depressions with widely spaced turns which can be resolved in the optical microscope. The method is therefore used with greater success, in conjunction with electron microscopy [5]. The technique as applied to alkaU halides, is as follows. After the

alkah halide crystal has been subjected to evaporation a very thin layer

of gold is evaporated onto the surface, which is kept at a temperature

of about 150-200 °C (for NaCl). Under these circumstances the gold

does not form a continuous layer but instead small gold particles nucleate epitaxially in a highly preferential way along surface steps. A

layer of carbon is then deposited on top of the gold layer. On dissolv- ing the alkali halide crystal the gold particles remain imbedded in the

carbon replica, which is then examined in the electron microscope.

In this way monoionic steps can be revealed with very high contrast

(Fig. 16). This technique has been developed to a high degree of per- fection by Betghe and coworkers [5]. Recently they succeeded in obtaining decoration whilst deforming the crystal. In order to introduce

the parameter 'time' into their experiments, they used the double decoration technique, which consists in evaporating two different metals

at different times during the deformation process. The main hmitation of the technique is obviously that again only

emergence points are observed. However it turns out that possibly

also dislocations which have a Burgers vector parallel to the crystal

face can be revealed; their presence can be inferred from the presence

of sequences of closed contours of monosteps nucleated apparently

at their emergence points.
450 TRACE CHARACTERIZATION

y :

Figure 16. Evaporation spirals observed on the cube plane of sodium chloride. The

steps are decorated by means of small gold particles. Note that the step height of the square spiral is twice that of the rounded double spiral. This is concluded from the way the steps fuse. Courtesy Betghe and coworkers.

The resolution of the method is determined not only by the resolution

of the electron microscope but mainly by the quality of the decoration, i.e., by the size of the decorating particles and the degree of preferential nucleation of these along steps. The main parameters which

determine the quality of the decoration are: the nature of the metal

used and the temperature of the crystal face during deposition of the

metal.

It is to be expected that this method can be adapted to other crystals.

The type of information that can be obtained by the use of this method

is of course similar to that obtainable from growth spirals. A big ad- vantage however is that no growth faces are required and that the high

resolution of the electron microscope can be used.

3. Etching

Etching as well as evaporation is essentially the reverse of growth.

It consists simply in dipping the crystal in a suitable medium mostly a

liquid but possibly also a gas or another solid. It is then found that small pits develop at the emergence points of the dislocations; the pits can be observed by means of reflection optical microscopy. Under

conditions of high undersaturation such as those prevailing during etching, no resolvable dissolution or evaporation spirals develop since the

distance between successive turns would be too small. Instead a pit
MICROSCOPY 451

results which is easily observable only if the slope of its side faces is sufficiently large. This slope is determined by the ratio Vi/vn, where

Vi is the lateral growth rate of the pit, whereas Vn is the depth growth

rate. For good etch pits Vi/vn should be smaller than about 10. The

ratio Vi/vn can be influenced by adding small amounts of impurities to the etchant.

The formation of etch pits at dislocations with a Burgers vector which

has a component normal to the etched crystal face can be considered

as resulting from the same process that generates growth spirals except

that the dissolution fronts move and are curved in the opposite sense

of the growth fronts [24]. As a result the center of the dissolution

spiral is lower than the original crystal face. On the basis of this view one expects etchpits at the centers of the growth spirals. This

is indeed the case as e.g., in Figure 17. However one also finds pits

at other sites: these are associated with the emergence points of dislo- cations for which b -0 = 0. This assumption is e.g., born out by observations on deformed alkali halide crystals where one can develop in a

controlled way sUp bands in which dislocations emerge for which

b -11 = 0 [25, 26], With the emergence points of such dislocations no

surface steps are associated. The previous considerations are therefore not of apphcation. It is now assumed that the gain in strain energy

Figure 17. Etch pattern on the c-face of silicon carbide. Pits located at the centers of growth spirals, as well as pits located elsewhere can be seen. The growth spirals have become visible as a consequence of preferential attack along the growth steps. Single

steps are only 7 A high.
452 TRACE CHARACTERIZATION

resulting from the dissolution of the disturbed region around the dislo- cation core is sufficient to cause preferential dissolution at the emer- gence point of the dislocation [24]. The same argument is of course vahd for dislocations for which b • n = 0. The formation of etchpits

is therefore a somewhat more complex phenomenon than the formation

of growth or evaporation spirals.

It is found that dislocations freshly introduced by deformation etch

usually differently from grown-in dislocations [25, 26]. This seems to suggest that the segregation of impurities at dislocations plays a role,

although not a vital one. This fact can be exploited to distinguish fresh

and old dislocations, which may be a desirable feature of the technique,

e.g., when studying dislocation motion.

The effect of impurities in the etching solution seems to be more

pronounced. The addition of suitable impurities slows down the lateral displacement rate of steps and as a result it increases the slope of the

sides of the pits and therefore increases their visibility. In the ex- treme case etch tunnels can be formed all along the dislocations [27]. Etching seems to work best on close packed and low index crystal

faces, e.g., {100} for alkali halides; {111} for calcium fluoride etc. This is not well understood at present.

An important question which naturally arises is whether or not aU

dislocations are revealed by etch pits. This question can be answered

for a particular crystal-etchant pair by performing a few simple tests. One can introduce known densities and configurations of dislocations

e.g., by bending a crystal to a given radius of curvature, and afterwards one can compare the obtained density and configuration of etchpits

with the theoretical configuration. An even simpler test is possible

for crystals which cleave such as the alkali halides. It is now possible

to compare the etch patterns on the matching faces of a cleaved crystal;

they should very approximately be mirror images [28] (Fig. 18). For

metal specimens successive attacks alternated with electropolishing

should consistently reveal almost the same pattern of pits.

Alkali halides are also particularly suitable for comparing pits due to edge dislocations with those due to screw dislocations. As a result of the particular glide geometry (slip vector a [100], slip plane (110))

the slip traces which are at an angle of 45° to the cube edge are generated predominantly by edge dislocations, whereas the dislocations that emerge along slip lines parallel to the cube edge have predominantly screw character [29]. The conclusion from such experiments is that there is evidence that some pits are not due to dislocations; precipitates may for instance cause etching, also fission tracks in ionic crystals can be etched. Some

caution is therefore needed in interpreting etch patterns in terms of

dislocations.
MICROSCOPY 453

Figure 18. The etch pattern on two matching halves of a cleaved lithium fluoride crystal. The patterns are mirror images, but on printing one image has been reversed so that they

become identical. Courtesy of Oilman and Johnston. We shall now discuss what type of information can be obtained from

etch patterns. Although etching is essentially a surface method we can obtain somewhat more than just the emergence points of dis- locations. When making the reasonable assumption that the pit is always centered on the instantaneous position of the dislocation, the

detailed shape of the etch pit can inform us on the general direction of the dislocation hne, as represented in Figure 19. When using alter- natively poHshing and etching we can explore the pattern of dislocations in depth. It is also possible to etch the crystal several times

without poUshing and reveal for instance the positions of dislocations

before and after application of stress or before and after heat treatment. Etch pits left behind by the dislocations that gave rise to them and

which subsequently moved away, will on further etching, develop a

flat bottom since the pits only extend laterally, but not in depth. In such a way the successive positions of a dislocation which moved

during etching can be revealed, as shown schematically in Figure 20. Using this technique the glide motion of dislocations can be studied.

Gilman and Johnston [30] used this technique to estabUsh the stress- velocity relationship for edge and screw dislocations. In some exceptional cases it is found that dislocations which are

parallel to the surface over some distance are revealed as etch grooves

[31]. Apparently the strain is sufficient to cause etching along that part of the dislocation where it is close to the surface.
454

I

I

I

TRACE CHARACTERIZATION

\ \

)— )—

(a) (b (c)

Figure 19. Asymmetry of etch pits due to the inchnation with respect to the surface of the dislocation Unes giving rise to them, (a) Parallel hnes perpendicular to the surface produce symmetrical pits, (b) Parallel Hnes inchned with respect to the surface, as in a tilt boundary, produce asymmetrical pits all oriented in the same way. (c) Pits formed

at the emergence points of a hexagonal grid of dislocation; the pits are asymmetrical and

successive pits are oriented differently.

Figure 20. Etch pits due to moving dislocations. The flat bottomed pits (1) and (2) corre- spond to intermediate positions of the dislocations. The final position of the dislocation

is marked by the centered pit (3). We shall now enumerate some typical problems which can successfully be studied by means of etch pits. It is clear that all problems

which involve the study of static configurations of dislocations can in principle be solved. Also problems where the successive positions

of the same dislocations are required can be tackled.

(i) Deformation problems: the distribution of dislocations in slip

planes (pile-ups); multiplication of dislocations in glide bands [32] [33]; the movement of single dislocations with the possibility of determining

the stress velocity relation for single edge and screw dislocations [30].

(ii) Equilibrium configurations of dislocations: the geometry of dis- locations in subboundaries [25], the arrangement and the evolution
MICROSCOPY 455

of the configuration of dislocations on polygonization after bending and

heat treatment.

(iii) Fracture problems. The relationship between the nucleation

and propagation of cracks and the pile up in glide bands [34].

(iv) Fission tracks [35]. The possibility to etch fission tracks as well as tracks caused by high energy heavy ions in materials such as mica, has led to appUcations in the field of particle detection and of trace analysis of fissionable nuclei. The method allows for instance

to detect energetic heavy particles in the presence of a background of

fight particles; only the former leave etchable tracks in mica. For

the trace analysis of uranium or other fissionable nuclei it is sufficient

to irradiate the specimen in contact with mica by means of thermal

neutrons, and then count the number of fission tracks [36]. From a knowledge of the cross sections one can then calculate the concentration of fissionable nuclei.

For a more complete summary of results obtained with the etch pitting technique we refer to [37] and [38]. We reproduce here a table of etchants (table I) which have been used in revealing dislocations. A

more extensive list can be found in ref. [38]. The great simplicity of the etching method, especially for determining

dislocation densities and dislocation distributions makes it an attractive method for routine checks. As such, and also as a research tool,

it will undoubtedly be used further in the future. Whereas electron

microscopy (see below) can yield much more detailed information on

individual defects, it is clear that the overall picture may be lost. Etch

pitting is then an excellent complementary technique for providing this overall picture. B. Bulk Methods

1. Decoration

The technique consists in treating a crystal in such a way as to cause

the formation of small, but visible particles, along the dislocation

lines. The particles should be small enough so as to draw with suffi- cient resolution the pattern of dislocations. However they should be

large enough to scatter enough light so as to become visible in dark

field optical microscopy or even in transmission microscopy.

The possibility to produce decoration is connected with the following

properties of dislocations. Cottrell interaction causes an elastic at- traction between the impurities and dislocations. Along dislocation

fines diffusion is enhanced, which favours the preferential nucleation

of particles there. Also the dislocations can act as sources of vacancies

and hence enable the precipitate to grow. Since the migration of

atoms over several atomic distances is involved, heat treatment is usually

required to cause decoration. Impurities which diffuse along interstitial sites usually migrate rapidly already at relatively low tempera237-323 0-67—28
456 TRACE CHARACTERIZATION

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tures where self-diffusion is still insignificant, they are therefore good

decorating agents. Also the solubility of the impurity should decrease

with decreasing temperature. The stoichiometric excess of one of the

constituents of the crystal may also function as a decorating agent,

this is e.g. the case in silver bromide where on illumination silver specks

form along the dislocations [40]. It is also possible to cause a chemical

reaction inside the crystal, the reaction product being insoluble and

hence precipitating; this is e.g., the case in CaF2 heat treated in moist

air [41]. The inherent limitations of the method are obviously that the heat

treatment presumably modifies the dislocation configurations and

further that the dislocations are pinned by the impurities and therefore

become immobile. The method is clearly well suited for the study of

annealing structures. Nevertheless, if using rapidly diffusing impurities in well chosen crystals it is possible to reveal deformation struc- tures as well. The best examples of Frank-Read sources were in fact found by using copper decoration in deformed silicon single crystals

[39] (Fig. 21). The method allows with very simple means (i.e., optical microscopy)

to study the spatial arrangements of dislocations. The resolution

limiting factor is the particle size of the decorating agent rather than

the resolution of the microscope. For many purposes the resolution

which can be achieved is sufficient to study crystals with moderately

high dislocation densities (lOVcm^). In some cases "double" decorai I

Figure 21. Double ended Frank-Read source in silicon made visible by copper decoration. Courtesy of W. Dash.
MICROSCOPY 465

tion can be achieved which means that successive positions of the same

dislocation can be imaged. In table II a number of decoration methods

for specific crystals has been summarized.

A short summary wiU finally be given of some typical applications of decoration methods.

(i) The geometry of subboundaries. This is perhaps the most ideally

suited problem to be studied by means of decoration techniques be- cause we are now interested in equilibrium configurations resulting

from heat treatments such as those used for the decoration process. Detailed studies have been made of networks of dislocations in the alkali halides [45]. Figure 22 shows an example of these.

{ii) Dislocation climb. The use of decoration techniques lead to the

discovery that screw dislocations, adopt helical shape when subject

to climb, i.e., to a supersaturation or an undersaturation of point defects. The phenomenon was first discovered in calcium fluoride, in

Figure 22. Dislocation network of a mixed type in potassium chloride (dark field image).

The decorating particles are silver. They result from an anneal in hydrogen of a silver doped crystal. Note the zig-zag shaped dislocation hnes.
466 TRACE CHARACTERIZATION

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MICROSCOPY 467

which the dislocations were decorated using the procedure summarized

in table II [41]. Also in siHcon the phenomenon could be demonstrated

and from the sense of winding of the helical dislocations it could be

concluded that interstitials were responsible for the climb process [53]. Harvey observed large prismatic loops due to cHmb in sodium chloride

doped with barium chloride and quenched from a high temperature

[53,b].

(iii) Deformation patterns. The most spectacular images of FrankRead sources were observed by Dash [39] in silicon crystals in which

the dislocations were made visible by copper decoration (Fig. 21). Deformation by prismatic punching was studied by Jones and Mitchell

[54] in silver chloride in which the dislocations were revealed by printing

out.

(iv) Dislocations in whiskers. The gold decoration technique re- ferred to in table II has been applied successfully to sodium chloride

whiskers [55]. It was found that some of the whiskers did contain the

theoretically predicted axial dislocation, but others contained many

parallel dislocations.

(v) Prismatic loops. Prismatic loops, presumably due to the precipitation of vacancies were revealed by silver decoration in potassium

chloride [38]. Similar loops, but presumably due to interstitials, were made visible by decoration in silicon. [56].

2. Birefringence

It is well known that isotropic crystals become birefringent when

stressed. This can e.g., be observed in deformed sodium chloride.

Since dislocations have a stress field around them one might expect to be able to reveal the birefringence due to single dislocations. Birefringence can easily be observed with polarizing microscopes, supplemented with an additional sensitive tint plate. Unfortunately it turns

out that the resolution of the method is poor. As a result it can only

be applied successfully to almost perfect crystals which moreover have

large strain-optic coefficients. Silicon turns out to satisfy both cri- teria and the first observations in this field were made by Bond and Andrus in this crystal [13]. Similar observations were made on rochelle

salt [57]. Birefringence associated with groups of dislocations in de- formation bands was studied in LiF by Kear and Pratt [58], who also correlated the birefringence bands with etch patterns.

Perhaps the most convincing observations were made on silicon by

Indenbohm and coworkers [59]. Some of their pictures are reproduced

in Figure 23; this figure provides at the same time a good comparison

of three different techniques applied to the same specimen: etching,

decoration and birefringence.
468 TRACE CHARACTERIZATION

Figure 23. Dislocations in silicon seen by stress birefringence and other methods. All pictures refer to the same area (a) Stress pattern around dislocation (a = 0°). (b) Stress pattern around dislocation (a = 45°) (c) Etch pits (d) Decorated dislocations seen end on

(e) Decorated dislocations seen at small inclinations (f) Stress pattern around decorated

dislocations. Courtesy of Indenbohm. V. Electron Microscopy and Electron Diffraction

A. Transmission Electron Microscopy

1. Introduction

In recent years electron microscopy has become an extremely useful

tool for the detailed study of individual crystal imperfections. Considerable progress has been made in the theory of contrast at defects

[60]. The results of these theories are of great importance if one wishes
MICROSCOPY 469

to extract all the information contained in an electron micrograph. It will be briefly shown what information can be obtained and how this can be applied to the study of defects. We shall only make use of in- tuitive pictures: for a more rigorous theoretical foundation we shall refer to the original papers. We shall first discuss briefly the various experimental techniques

used for the observation and the preparation of specimens and we shall

illustrate the interpretation of micrographs by specific examples. It is not intended to give an exhaustive review of the literature; for a more

complete review on the observation of lattice defects by means of trans- mission electron microscopy we refer to [38].

2. Principle of the Method

The technique is in fact extremely simple. The specimen is a thin

foil (^5000 A) transparent to electrons. Usually an acceleration

voltage of 100 kV is used to have high penetrating power. Recently

microscopes working under much higher voltages, e.g., 1 MeV, have

been built [61]. The specimen is mounted on a grid Hke a conventional

repHca. A diffraction pattern is obtained from a transparent region

and the aperture is put around the selected beam, usually the direct

beam. The image is then magnified to the desired level; it is in fact a representation of the intensity distribution in the selected beam.

If the direct beam is selected, the image is called a "bright field" image; if a diffracted beam is used, the image is called a "dark field" image (Fig. 24). Since dark field images are formed from nonaxial

beams they are usually slightly deformed and diffuse. This can be overcome by tilting the electron gun or by using a bias on deflector

plates.

Optimum contrast is achieved by choosing the correct tilting angle.

The simplest type of contrast is obtained if there is only one strongly

diffracted beam; the most intense spot is then responsible for the

contrast: such a situation is called a two beam case and most of the

theory is made on this assumption. The diffraction vector g which

is perpendicular to the diffracting planes, and which has a length

inversely proportional to the interplanar distance, connects the center

of the diffraction pattern with the diffraction spot. The knowledge

of the diffraction vector of the contrast producing reflection is of great

importance for the interpretation of the images. Dark field images

are of special interest since their use allows to be sure which beam is producing the contrast. Whereas the contrast in the direct beam

is "subtractive" it is "additive" in the dark field image. In very thin

samples the dark field image has usually better contrast. Specimen heating by the electron beam, especially in insulating

crystals, is often a problem. For metal specimens the temperature

rise is small (10-20 °C).
470 TRACE CHARACTERIZATION

(a) (b) Figure 24. The image formation in the electron microscope, (a) Bright field image

(b) dark field image.

Attachments for special purposes are available for most microscopes,

e.g., cooling and heating stages, straining devices, double tilting specimen holders, etc.

3. Specimen Preparation

o The thinning of specimens to a suitable thickness (500-5000 A)

depending on the nature of the material, is an important and sometimes difficult problem that arises in the application of this technique.

Metals are usually thinned in successive stages by rolling alternated

with annealing treatments and finally electro-polishing. Bulk speci- mens can first be reduced to thin plates by acid sawing or by spark

cutting. We refer to Kelly and Nutting for an excellent review of these

techniques [62]. Some layered crystals, e.g., graphite can be cleaved to thin foils [63]. Other crystals develop as sufficiently thin plates when grown by sublimation, e.g., zinc, cadmium, tin disulfide, chromium chloride, etc. Chemical thinning can be applied to uranium dioxide [64], magnesium

oxide [65], silicon, germanium [66], etc. Annealed beaten foils of gold

[67] and platinum [68] have been used in radiation damage studies.

Extensive use has also been made of very thin evaporated metal films [69]. Thin layers of fine grained oxides (such as TiO-i and Ta205) can often be

recrystallized in the microscope by electron beam heating [70, 71] which

produces large foils of uniform thickness.
MICROSCOPY

4. Electron Diffraction in Perfect Crystals

471

We shaU not develop the theory of electron diffraction. We only

summarize the fundamentals required for an understanding of the

technique. The condition for diffraction is usually expressed by

Bragg's "reflection" law

2dhki sin d = kk (1) where dhki (=l/g) (2) is the interplanar distance of the lattice planes

which "reflect," 0 is the Bragg angle, k is an integer and k is the wave

length of the radiation used. In the case of electrons A. = 0.04 A for 100 kV electrons, and the Bragg angles are very smaU (a few degrees),

so that sin 6^6.

Using the reciprocal lattice concept the diffraction condition can

be formulated as follows. Let 0 be the origin of the reciprocal lattice

(Fig. 25a). From 0 we draw a vector —ko where ko is the wave vector

of the incident beam. This gives the point C. With C as a centre, we construct a sphere with radius l/A.= |/c()|. If this sphere, called Ewald's sphere, passes through the node point N of the reciprocal lattice,

the diffracted beam will have the direction CN: its diffraction vector

is g = OA^. In electron diffraction the radius of the reflecting sphere

is large compared to the mesh size of the reciprocal lattice, which is of the order of one reciprocal Angstriim. For many practical pur- poses the reflecting sphere can therefore be considered as planar. In a thin foil Bragg's condition is considerably relaxed, i.e., the

angle over which reflection takes place is relatively large. This is de- scribed in terms of the reciprocal lattice, by saying that the reciprocal

lattice nodes are not points, but "regions" in reciprocal space corre- sponding to large diffracted intensities. For a thin foil these regions

are rods perpendicular to the foil surface. The rods intersect Ewald's

sphere over a certain angular range. The intensity of the diffracted wave depends on the exact point where the rod is intersected by Ewald's

sphere. The deviation from the exact Bragg position is described by

the vector s (Fig. 25b) called excitation error. The vector s goes from

the considered reciprocal lattice point to Ewald's sphere. It is counted

positive in the sense of the incident beam, i.e., s >0 when the reciprocal lattice point is inside Ewald's sphere.

For a perfect crystal the amplitude of the transmitted beam is given,

according to the two-beam dynamical theory, neglecting anomalous

absorption by

5 At = (cos ttctzo — i — sin 7rc7Zo)e'^'*^o (3)

O" where zo is the thickness of the crystal. The quantity cr is defined by

(Ttg=^/l^{stg)\ (4)
472 TRACE CHARACTERIZATION

(a) (b) Figure 25. Reciprocal lattice construction of the diffracted beam. O is the origin of the

reciprocal lattice. C is the center of Ewald's sphere. CN is the direction of the dif- fracted beam for a reflection with diffraction vector ON.

where tg is the extinction distance, tg has the dimensions of a length,

it is related directly to the Fourier coefficient of the lattice potential

which corresponds to the operating reflection. Anomalous absorption

is taken into account phenomenologically by making tg complex, i.e., by

making the substitution — + — [72], where Tg is the absorption

length. Usually Tg is 10-15 times the extinction distance tg. The amplitude of the scattered beam is similarly given by:

As = sin TTcrzoe^^^^ (5)

(Ttg and the intensity of the scattered beam is 7^= [IKo-tgf] sin2 TTcrzo (6) without absorption

It=1-Is. (7) This expression is represented in Figure 26(1) as a function of s. If anomalous absorption is taken into account the curve (rocking curve)

for the intensity of the transmitted beam It becomes as shown in Figure

26(2). The curve is now asymmetrical; for 5 > 0 the intensity is much

larger than for 5 < 0 (this is the Borrmann effect).

5. Kikuchi Lines — Determination ofs

For several problems it is of interest to know at least the sign of 5; the 'magnitude is usually not required. This information can easily
-3 -2 -I 0 12 3

-3-2-1 0 I 2 ^,3

Figure 26. Intensity of the transmitted and scattered beam for a perfect crystal, as a function of the excitation errors. (1) without anomalous absorption (a) transmitted, (b) scattered. (2) with anomalous absorption (a) transmitted (b) scattered.

be deduced from the pattern of Kikuchi lines which is usually observed

in relatively thick crystals. Kikuchi lines are due to Bragg reflection of inelastically scattered electrons, which are incident under all possible

angles. The geometrical locus of the Bragg reflected beams is a very

wide cone with an opening angle of 90° — ^. This cone intersects the

photographic plate along part of a hyperbola, which becomes in fact very nearly a straight line. If the crystal is in the exact reflecting position, the Kikuchi hne corresponding to a given set of lattice planes

passes through the diffraction spot corresponding to the same set of planes. If the foil is now rotated over a small angle the position of

the spot does not change appreciably, but the beam producing the

Kikuchi line rotates over the same angle Ld. The Kikuchi line is thus
474 TRACE CHARACTERIZATION

displaced with respect to the spot over some distance. This displacement is outwards if the reciprocal lattice point is rotated towards the

interior of Ewald's sphere, it is inwards for a rotation in the opposite

sense. When the sign convention adopted in section V.A.4 is used the

situation can be summarized by Figure 27.

6. Extinction Contours [73]

According to the two-beam dynamical theory, neglecting anomalous

absorption, the intensity of the transmitted beam is given by eqs (6) and

(7). The magnitude of tg depends on the operating reflection. In metals it is usually of the order of 2-400 A. From this formula it is clear that It depends on the specimen thickness zo in a periodic way.

It also depends in an oscillating way on 5 (Fig. 26). Most specimens used in transmission work are very thin and therefore deformed; moreover they have a non-uniform thickness. As a

result of this, dark bands become visible. They are the geometrical

loci for zo = constant (thickness contours) or for 5 = constant (inclination contours).

a. Thickness Contours. Along the lines where the crystal has a thickness given by ^'""'"^^ ^'g with tg = IIa the intensity of the transmitFigure 27. The relation between the position of a diffraction spot and that of the corre- sponding Kikuchi hne (K). S indicates the sense into which the lattice has to rotate in order to approach the exact Bragg position.
MICROSCOPY 475

ted beam is minimum and a black contour is observed in the bright field image. The positions of the contours of this type are not sensitive to the tilt of the specimen; their intensity of course is. Since tg changes

with the operating reflection the depth distance between contours changes with the diffraction vector. Knowing the extinction distance

the number of fringes gives an easy measure of the thickness. Figure

28 shows typical thickness contours in a wedge shaped crystal.

b. Inclination or Bend Contours. The points for which the Bragg

condition is satisfied, i.e., for which 5 — 0 form continuous curves, which are called bend contours. Along these lines the intensity of the

transmitted beam is minimum and a black line is observed in the bright

field image. These contours are very sensitive to changes in orientation of the specimen; ihey are observed to migrate on tilting. In nearly perfect foils the bent contours are very broad and hardly vis- ible; in metal specimens they are usually much sharper. In thick

foils the contours become very broad as a result of anomalous absorption. Along the main contours one has 5—0; on passing the contours, 5 changes sign.

Figure 28. Thickness contours in a wedge shaped sihcon foil.

237-323 0-67—29
476 TRACE CHARACTERIZATION

The fine structure described by eq (6) can sometimes be revealed

as secondary contours along which 5 = constant. From the fringe

spacing in this fine structure the foil thickness can be deduced.

Figure 29 is a dark field image of inclination contours.

Figure 29. Dark field image of inclination contours in a bent graphite foil.
MICROSCOPY 477

B. Contrast at Dislocations [74, 75, 76]

1. Origin of the Contrast

We shall only use the intuitive approach, which is sufficient for most purposes. Let us assume that the thin foil F contains an edge

dislocation parallel to the foil plane in E (Fig. 30). We further suppose

that the set of lattice planes represented in Figure 30 is near the re- flecting position. For a thin foil Bragg reflection takes place over an appreciable angular range. This is pictured in reciprocal space

by saying that points have become rods perpendicular to the foil plane. Let us assume that the center of gravity of the reciprocal lattice rod is outside the Ewald sphere. A rotation in the sense S indicated in Figure

27 is then required to bring the crystal into the Bragg position. In the

perfect region of the foil, part of the intensity is transmitted and another

part is diffracted: this is indicated by the relative thickness of the

lines in Figure 30. The bright field image is now formed by observing

the intensity distribution in the direct beam; the scattered beams being

intercepted by an aperture like in Figure 24,

To the left of E the deformation of the lattice planes due to the pres- ence of the dislocation is such that Bragg's condition is better satis- fied and hence the intensity of the scattered beam is locally larger. At

the other side of the dislocation the deformation is in the opposite sense and the intensity of the scattered beam is consequently less. As a result a lack of intensity will be noted in the bright field image, on

one side of the dislocation, and a black line will be observed. The same

F

Figure -30. Illustrating the image formation at an edge dislocation. The thickness of the lines is a measure for the intensity.
478 TRACE CHARACTERIZATION

type of reasoning is valid for a screw dislocation. Summarizing we

can say that for 5 7^0 and relatively large, the image side for a dis- location is that side for which the lattice rotation is such as to bring

the lattice planes into the Bragg position.

From this picture which is essentially a kinematical approach, it is clear that changing the sign of the edge dislocation changes the image

side for a given sign of 5. This is visualized in Figure 31. Changing

the sign of s or changing the sign of the diffraction vector changes the

image side. The same reasoning can be made for a screw dislocation;

the result is also shown in Figure 31. It is clear that the results of this paragraph can be used to determine the sign of a dislocation. We

shall describe the procedure further below. Although the picture

given here is certainly not correct quantitatively, it gives the right

qualitative answer, which is sufficient for most purposes.

(d)

Figure 31. Image formation at edge and screw dislocations of both signs. The images

(heavy hnes) are on opposite sides of the true positions of the dislocations for dislocations

of opposite sign, (a) and (b) edge dislocations (c) and (d) screw dislocations.
MICROSCOPY 479

2. Determination of the Direction of the Burgers Vector. Extinction

Conditions

Intuitively one can see that if the contrast-producing reflection

corresponds to a set of lattice planes which is not deformed by the pres- ence of the dislocation, the latter will remain invisible. This is shown

specifically for an edge dislocation in Figure 32. The planes with dif- fraction vector gi are deformed by the presence of the dislocation

and reflection by these planes does reveal the dislocation. On the other

hand the dislocation can be considered as resulting from the superposition of planar arrangements perpendicular to the vector gs. This

evidently shows that on reflection with a diffraction vector gs no contrast will be seen. The planes perpendicular to g2 (i.e., the planes

parallel to the ghde plane), are slightly deformed, the glide plane having a Httle bump at the position of the dislocation, and hence only

very weak contrast will be produced by reflection with a diffraction vector g2.

The same reasoning is shown for a screw^ in Figure 33. Planes inter- secting the axis of the screw^ are deformed, whilst planes passing through

the screw axis remain flat to a first approximation. If the end effects are taken into account for a screw intersecting the surface, these planes

are in fact transformed into hehcoidal surfaces.

One can summarize these considerations by the following rule: if n = g b = 0 the dislocation shows no contrast. The quantity n is an

integer in the case of a perfect dislocation, since g is a reciprocal lat- tice vector and b a lattice vector. For a partial dislocation b is no

b

gi. b * 0 gg. b = 0 93 . b = 0 Figure 32. Deformation of different families of lattice planes by the presence of an edge

dislocation. Only families of lattice planes which are deformed by the presence of the

dislocations give rise to contrast.
480 TRACE CHARACTERIZATION

g . b = o Figure 33. Deformation of different families of lattice planes by the presence of a screw

dislocation.

longer a lattice vector and n may become fractional. For n ^ 1/3 the dis- location is invisible [75, 76]. Some care is therefore required when using

the absence of contrast as a criterion to decide that 7i = 0. There is another case where special care is needed (Fig. 34a). If the

dislocation has a Burgers vector perpendicular to the foil plane, and if the foil plane is perpendicular to the incident beam, the only operating

reflections have diffraction vectors that satisfy the criterion ^ • b = 0. No contrast would therefore be expected. However, as pointed out

(0

Figure 34. Image formation at a prismatic loop. The displacements are radial. The

diffracting planes are parallel to the Une joining the segments of no contrast.
MICROSCOPY 481

already above, the planes parallel to the glide plane, are, for an edge

dislocation, slightly deformed. For a prismatic loop, parallel to the

foil plane a radial displacement is produced as a result of this (Fig. 34b).

This radial displacement is either inwards or outwards depending on the

sign of the Burgers vector. This deformation is sufficient to produce

contrast for smaU 5-values [77]. Contrast is however completely absent

for these segments of the dislocation loop where the displacement is perpendicular to the operating diffraction vector. As a result a prismatic loop with Burgers vector perpendicular to the loop plane will show contrast except for two segments. The diffracting lattice planes

are parallel to the line connecting these two segments (Fig. 34c).

If the Burgers vector is inclined with respect to the loop plane, whilst

the loop is in the foil plane, contrast will only be "residual" for the set of lattice planes parallel to this inclined vector. For other reflections

the whole loop exhibits contrast. An example of this is' represented

in Figure 35, which shows loops in the basal plane of coldworked zinc. Some show residual contrast; others are in fuU contrast.

It is now evident how the extinction conditions can be used to deter- mine the direction of the Burgers vector. If a perfect dislocation is

Figure 35. Loops in the basal plane of zinc. Two types of images are visible. The

Burgers vector of the loops is inclined with respect to the basal plane. The inset shows

stacking fault fringes for loops which are inclined with respect to the foil plane. Courtesy

Stals.
482 TRACE CHARACTERIZATION

out of contrast for two diffraction vectors, gi and g2, the Burgers vector

is parallel to gi X g2. An example of a complete Burgers vector deter- mination for a dislocation network in graphite is shown in Figure 36,

where use is made of the bright field image. The foil has been inclined

at different small angles with respect to the electron beam so as to bring the three families of partial dislocations successively out of

contrast. The bright field method is difficult to apply in thin crystals because

one cannot easily obtain the two beam situations required for extinction.

It is then advisable to use the dark field method which consists in making dark field images using the different low order diffraction vectors. This method has successfully been applied to the study of dislocation

/

1 b,

b

Br

C 1 i

\

Figure 36. Determination of the direction of the Burgers vectors for a network in graphite. The different families of dislocations go successively out of contrast.
MICROSCOPY 483

networks in extremely thin polyethylene single crystals [78]. Figure 37

reproduces one of the sequences of photographs obtained in this study,

whilst Figure 38 shows the resulting Burgers vector analysis of the net- work which turns out to contain partial dislocations.

For the loops in zinc, shown in Figure 35, it is possible to conclude

that the vector is inclined with respect to the basal plane because

otherwise the loops would always exhibit residual contrast, which is obviously not the case. In this case there is additional evidence that the Burgers vector is inclined: the loops also contain a stacking fault.

3. Determination of the Sign of the Dislocations {i.e., the Sense of the Burgers Vector) [79, 80]

We describe the procedure for the simple case where the dislocation

is in the foil plane. The following information is required:

(i) the image side,

(ii) the sign of 5,

(iii) the direction of the Burgers vector. The image side is determined by comparing photographs taken with

two different signs of s and the same g-vector or with two different signs

of the g-vector for 5-values of the same sign. The image side changes

in both cases, the true position of the dislocation is between the two

images. Since the best bright field images are obtained for positive

5-values, it is often easiest to produce images for -\- g and —g.

The sign of s is determined in the manner described in subsection

V.A.5. As already mentioned it is usually positive for good contrast. The direction of the Burgers vector is found by means of the procedure

outlined in subsection V.B.2.

In the light of these three pieces of information. Figure 31 tells us immediately the sign of the dislocation i.e., the sense of the Burgers

vector. The application of this procedure to small loops is discussed

below.

According to the dynamical theory and adopting the FS/RH convention, the image side in the bright field image is left if (g • b)5 > 0. This

relation can obviously also be used to determine the sign of b if g and

s are known and if the direction of b is known [81].

4. Determination of the Length of the Burgers Vector The image profile of a dislocation depends on the value of zi [74, 15, 76]. In particular the change in aspect of the profile on crossing extinction contours where the sign of 5 changes, is different for n = l and n = 2 [76]. The behaviour is shown schematically in Figure 39. This behaviour

follows from the fact for n=l the image is a symmetrical peak at the

position of the dislocation for 5 = 0 (i.e., in the contour). For n = 2 the

image is double peaked for 5 0: the center of the image has the same
484 TRACE CHARACTERIZATION
MICROSCOPY 485
486 TRACE CHARACTERIZATION

9[200]

(c)

f9[020]

(b) Figure 38. Lettering pattern of a network of dislocations such as in Fig. 37 with all seg- ments represented. The different diagrams represent the dark field patterns as imaged

by the different reflections. Dotted lines represent dislocations which are out of contrast; double lines represent double images. These diagrams are to be compared with

the DF image of Fig. 37.

extinction contour

image dislocation line

n = 1 n=2

Figure 39. Difference in behaviour on crossing an extinction contour for dislocation images

with n = 1 and n = 2. intensity as the background. By observing the change in profile for a given dislocation image it is therefore possible to determine whether

n is equcil to 1 or to 2. If we know already the direction of h for this particular dislocation and knowing g it is possible to determine the

length of h\ b = n/g • e^, where is the unit vector along b. In fact the knowledge of n is equivalent to knowing the length of the projection

of b onto g.
MICROSCOPY 487

5. Dislocations Inclined With Respect to the Foil; Oscillating

Contrast [76, 77]

The image profile of a dislocation parallel to the foil plane depends,

especially for small 5-values, on its distance from the surfaces. The

profile varies in a periodic way with the distance, the period being

t'y. Figure 40 shows the variation of the image profile as a function of depth, for a screw dislocation parallel to the foil plane [76]. Bright

and dark sides are seen to alternate periodically with depth. If the

dislocation is now inclined with respect to the surface, the image profile

changes periodically with depth. An example of such oscillating images

is visible in Figure 41. The phenomenon is of importance because it provides a depth scale which is otherwise completely lacking in the electron microscope, as a

result of the large depth of focus. It can for instance be used to esti- mate the distance from the surface of a segment of a dislocation line which intersects the surface [79]. It is sufficient to count the number of periods between the emergence point in the surface and the segment of

interest. The phenomenon can also be used to determine the foil thickness.

As a result of anomalous absorption, oscillating dislocation images

are similar at the top end of the foil, but pseudo-complementary at the

bottom end (cfr. stacking fault fringes section V.C.3). This remark

allows to distinguish both ends of the dislocation line. The oscillations disappear for sufficiently large values of 5. It is clear that only for such

values of the s the image side has a meaning and can be used to deter- mine the sign of b.

6. Dislocations Seen End on [38, 82, 83, 84]

The contrast due to the dislocations seen end on cannot be inter- preted by means of the simple image of section V.B.I. It. is therefore

considered separately here. For an edge dislocation seen end on the contrast may be considered

to arise from the difference in lattice parameter in the compressed and

expanded regions of the dislocation. If the Bragg condition is better

satisfied than in the perfect part provided the lattice parameter were

smaller the compressed region wiU show up black in the bright field image, whilst the expanded region will show up bright. The reverse wiU be true after a change of the sign of 5. The image therefore consists

of a black-white dot. It is clear that these considerations allow a deter- mination of the sign of the dislocation. The effects mentioned are small

and it is not sure whether edge dislocations of this type can be observed.

For a screw dislocation in an infinite medium, all displacements are

parallel to the axis of the screw. No contrast is therefore to be ex- pected for a screw dislocation perpendicular to the foil plane, i.e..
488 TRACE CHARACTERIZATION

(a) (h)

o-2i

05

075

1-25

14

175

20

2-25 IT

2-75

bright field

IT -4r

IT

^

dark field

0-25

0-75

10

1-25

1-75

20

2-25

2-5

IT

275 -^

bright field dark field Figure 40. The image profile for a screw dislocation as a function of its distance from the

surface. Courtesy Howie and Whelan. The sequence (a) refers to a foil of thickness

3 tg and the sequence (b) to the foil of thickness 3.5 tg.

parallel to the electron beam. However, as a result of surface relaxation

the planes parallel to the screw axis are transformed into helicoidal

surfaces and contrast arises (Fig. 42). Let us consider as in Figure 42

diffracting planes perpendicular to g. Behind the screw of Figure 42

(in C) the lattice planes are then rotated towards 5 > 0 whereas in front of it (in D) they are rotated towards 5 < 0. If in the perfect crystal part

5 < 0 it follows that behind the screw (in C) the crystal locally approaches

the Bragg position, whereas in front of the screw (in D) the crystal is locally turned away from the Bragg position. It then follows that in the

bright field image a dark dot will be seen behind the dislocation and a
MICROSCOPY 489

Figure 41. Oscillating contrast at dislocations approaching the surface in a tin disulfide single crystal, (a) Bright field image, (b) Dark field image.

bright one in front of the dislocation. This is reversed for a screw dis- location of the opposite sign (Fig. 42e). The line of no contrast is parallel

to the diffraction vector. It is again clear how the sign of the dislocation can be determined. The same rule can still be applied to dislocations

which are not quite perpendicular.

Images of this type are visible in Figure 43.
490 TRACE CHARACTERIZATION

(d) (e) Figure 42. Image formation at a screw dislocation seen end on.

In Figure 43c the dislocations are out of contrast in the central part

of the foil, but the ends are visible as a result of surface relaxation alone. C. Stacking Faults

1. Types of Stacking Faults

a. In f.c.c. Crystals. In face centered cubic crystals stacking

faults can be generated in at least two ways:

(i) by the passage of a partial dislocation, e.g., resulting from the

splitting of a perfect dislocation into Shockley partials on the (111) glide

planes.

(ii) by removing or inserting part of a (111) lattice plane.

The mechanism (ii) suggests that two different types of stacking faults can be considered. The fault resulting from the removal of a single

(111) layer can be described by the stacking symbol

abcabcacabc

'—hzzLJ

(8)
MICROSCOPY 491

Figure 43. (a) and (b): Dislocations seen end on in uranium dioxide. The images consist

of black-white dot pairs. The line of no contrast is pargJlel to the diffraction vector,

(a) Bright field image (b) Dark field image (c) Dislocations in platinum. The dislocations are out of contrast in the central part of the foil; the ends are visible as a result of surface

relaxation. Courtesy Ruedl.

It contains one lameUa which is hexagonaUy close-packed and is called

intrinsic. Another fauh can be generated by inserting a single (111)

layer: such a fault is characterized by the layer sequence

abcabcbabc... I 1 1 I (9)

It contains again two triplets, in the hexagonal arrangement, but they

are one layer further apart than for the intrinsic fault. Such a fault is called extrinsic. The intrinsic fault can be generated by the passage of a single partial of the Shockley type, i.e., with Burgers vector of the type ^

a [112]. After

glide between the indicated layers in the sequence

abcabcabcabc

T the layer sequence becomes

(10)

abcabcacabcabc...

T

(11)

237-323 0-67—30
492 TRACE CHARACTERIZATION

which is obviously equivalent to (8). This is not possible for the extrinsic fault, which may have lower energy however.

The edge of a faulted region is a partial dislocation which in the case

of a prismatic loop has a vector [111] or its negative. Such a dis- location is called a Frank sessile. For a stacking fault generated by

glide the boundary partial has a vector of the type [112]. The shear

vector of the stacking fault, characterizing the displacement that brings

the perfect crystal into the faulted position is alternatively ^a [111] or

1 . . - a [112]. Both formulations are equivalent since e.g., 6

|a[lll] + ia[112]^|a[110] (12)

which is a lattice vector. b. In h.c.p. Crystals. Also in hexagonal close packed crystals one can distinguish different types of stacking faults. The normal stacking can be represented by the symbol sequence: a b a b a b . . . . The

single fault is then described by a sequence which contains only one

infraction against the stacking rule, e.g. ...abababcbcbc...

Such a fault can for instance be generated during growth. The displacement vector is the sum of a vector associated with a Shockley partial

(p) and the vector c/2 in the direction of the c axis, i.e., R = p + -. The double fault is described by a sequence containing two violations of the normal stacking, i.e., ...abababcacaca...

Such a fault results on deformation by the passage of a Shockley partial,

its displacement vector is p. Finally one can imagine triple faults such as abababcababab...

The displacement vector is now - c.
MICROSCOPY 493

c. Antiphase Boundaries; Periodic Antiphase Boundaries

and Stacking FauUs. A particular type of stacking fault occurs in ordered alloys. When ordering starts simultaneously in different

parts of a disordered alloy it is to be expected that on meeting different

ordered domains may be "out of step." If this is the case the contact plane is called an "antiphase boundary." It is shown schematically in Figure 44(1) for the CuAu alloy. Antiphase boundaries are generated also when dislocations, which are perfect with respect

to the disordered structure, but partial with respect to the ordered

structure, move through the crystal (Fig. 44(2)). A strip of antiphase

boundary then connects two dislocations, very much like a strip of stack- ing fault connects two partial dislocations. In a number of alloys periodic arrangements of antiphase boundaries occur; they can be revealed directly in the image as a periodic

hne structure [85] (Fig. 45a).

The nonperiodic antiphase boundaries exhibit fringe contrast similar to stacking faults (Fig. 45b). However in ordered alloys the contrast is due to a superlattice reflection. Since these reflections have

usually long extinction distances only a smaU number of fringes is vis- ible [86].

It has been found recently that certain ordered alloys contain periodically arranged stacking faults giving rise to complicated regular

stacking sequences, with long periods. These long periods can be

resolved directly in the electron microscope [87].

2. Origin of the Contrast

With respect to diffraction a stacking fault is characterized by its displacement vector R describing the displacement of the exit part of

the foil, with respect to the entrance part. With R corresponds the

phase angle a = 2 ng - R. For a face centered cubic crystal only

reflections hkl for which the indices are either all ever or all odd have

a non-zero intensity. Taking the shear vector ^ a [112] one finds a = 27r- [hkl] •]a[112]=| 7r(/i + A: + 2/) = ± | 7r(mod 27r). (13) a o o 6

The result of the presence of a stacking fault is to cause a phase

shift of the amount a between waves diffracted by the part of the crystal

above the fault plane with respect to the waves diffracted by the part

below the fault plane. The resulting intensity at the back surface

of the foil depends in a periodic way on the fault position. If the fault

is parallel to the foil plane, a different intensity will in general be found

within the faulted area as compared to that in the perfect part. For

an inchned fault plane this results in the formation of a fringe pattern.

The detailed intensity distribution in this fringe pattern is studied in

ref. 87b. An example of stacking fault fringes in a copper gallium
494

(I) TRACE CHARACTERIZATION

• Cu atom o Au atom ^—P

P 9—-p P-—-^

^— -p—^.p

-f) /•/ o / o / o / o / o /•/•/•/•/•/ o / o / o /

agj I o

I •

I • I •I • I •I oI o i o j o

I o

I •I •I • l/^

t

..i 6 6-—^ —4—-4— Hi—-A20A 20A

domain

boundary

domain

boundary

domain

boundary

dislocation line (002) planes

Figure 44. (1) One unit cell of the ordered alloy CuAu II. Courtesy Johansson and Line.

(2) Illustrating the relation between dislocations and antiphase domain boundaries in the alloy CuAu I.

Figure 45(a). Periodic antiphase boundaries in CuAu II. Courtesy Pashley.
MICROSCOPY 495

Figure 45(b). Antiphase boundaries in Tealite (SnPbS2). Courtesy Marinkovic.

alloy of low stacking fault energy is reproduced in Figure 46. The

depth distance between successive fringes close to the surface is

t'^=tg/Vl+{st,r. (14)

If tg and 5 are known, the foil thickness can be deduced from the number of fringes. Inversely if the foil thickness is known tg can be

measured.
496 TRACE CHARACTERIZATION

Figure 46. Fringe patterns due to stacking faults in a copper gallium alloy of low stacking

fault energy. The fault is intrinsic. Courtesy Art.

3. Some Properties of Stacking Fault Fringes [88, 89, 90, 91]

Some important conclusions of the dynamical two beam theory of stacking fault fringes, taking into account anomalous absorption, are now mentioned ^first for fringes with a = ±^^^-j.

(i) The fringe pattern is symmetrical with respect to the foil centre

in the bright field image, but asymmetrical in the dark field image.

(ii) The front part of the pattern is similar in the bright field and the

dark field image, whereas the back part is pseudo-complementary.

(iii) The nature of the outer fringes only depends on the sign of a

and not on the foil thickness zo, provided the foil is sufficiently thick 2

(i.e., Zo ^ ^tg). If q: = ±- 77 the extreme fringes in the bright field image

2 are bright, whereas they are dark if a: = — - tt.

(iv) The fringes are parallel to the nearest surface; new fringes are generated in the centre of the pattern.

These properties are illustrated by Figure 46. They result essentially from the effect of the anomalous absorption. We shall show

below how they can be used to determine the type of stacking fault

in f.c.c. metals.

Fringes for which the phase angle a = 7r have very characteristic

properties which allow to recognize them almost immediately [92]. Some of their specific properties are:
MICROSCOPY 497

(i) For 5 = 0 the fringes are parallel to the central line of the foil, rather

277- than to the surface Uke for a = ±—. As a result new fringes are born

277

at the surface rather than in the centre of the foil like for =t—. Howo ever for large values of 5 the fringes become again parallel to the surfaces.

(ii) For 5 = 0 the depth spacing of the fringes is ¥2?^ and not tg as for ±—277 ^ . Irmges.

(iii) For 5 = 0 the bright and dark field images are complementary on

both ends of the pattern, even with anomalous absorption present.

(iv) In bent foils the fringes are always continuous, i.e., a bright fringe

in one part of the fault, continues as a bright fringe in the other part of the bend.

These properties are illustrated in the set of Figures 47, 48. They

can be used to decide that for a given diffraction vector the phase angle

a:=7r±2A:77 (/c: integer). This information is helpful in determining the

displacement vector (see next paragraph).

4. Displacement Vector Determination

The determination of the displacement vector R = [z/, v, w] of a stack- ing fault or antiphase boundary is similar to the Burgers vector deter- mination of a dislocation. There is an important difference however.

Whereas a dislocation goes out of contrast (to a first approximation)

if g • b = 0 the extinction criterion for a stacking fault is g • R = 0 or an

integer. In practice one looks for a number of diffraction vectors

giihikili) for which the fringes disappear. This leads to a set of equations hiU + kiV + liW = n where n is zero or an integer. It is further

possible that one may be able to identify a number of reflections for which a = 77 (using the criteria given in the previous paragraph). Such

observations lead to additional equations of the type

hjU-\- kjV-\- ljW = 1/2 ±n.

^^^^

One then tries to satisfy all these equations with the smallest possible

values of n, v, and w. This determines usually the displacement vector

to within a lattice vector of course. Examples of displacement vectors determination can be found in ref. [93] and [94].

5. Determination of the Type of Stacking Fault

a. In f.c.c. Crystals. The displacement vector of a stacking fault can also be taken as -^a [111]. In view of the relation (12) this does not change the value of a since the vector ^

a [1 10] only contributes an integer
498 TRACE CHARACTERIZATION

Figure 47. Comparison of fringe characteristics for 180° and 120° faults. Examples are taken from APB in rutile (180°) and stacking faults in Cu-Ga alloy, (a) Behaviour for varying foil thickness. Note that for a = 180° and s =0 the fringes are added at the out- side of the pattern whilst in the case a = 120° forking of the inner fringes is observed,

(b) Contrast at bends. Note that for 180° the fringes continue at the bend vvrhereas for 120° a shift between the two fringe systems is present, (c) and (d) Characteristics of bright (BF) and dark (DF) field images (c) a = 180° and 5 = 0, the dark field image is complementary to the bright field image and thus also symmetrical, (d) for single faults with a = 120° the dark field image is always similar to the BF at the front surface whereas

it is complementary at the bottom; this result is an asymmetrical DF image.

X 277. It is now easy to see that intrinsic and extrinsic faults correspond

to displacement vectors of the type -^a [111] which are opposite in sign

and hence give an opposite sign to a for the same g. It is therefore

possible in principle to distinguish between intrinsic and extrinsic

faults on the basis of the nature of the extreme fringes since from this the sign of a can be deduced. A practical method for doing this has

been worked out [90, 91]. The resulting rule is as follows. Orient the image in such a way that the operating diffraction vector

points to the right of the intersection line of the fault plane and the foil plane. This is always possible. One should make sure that the image

and the diffraction pattern have the correct relative orientation. If the

reflection belongs to class A, and if the diffraction vector points towards

the bright fringe in the dark field image the fault is intrinsic. The
MICROSCOPY 499

Figure 48. Bright and dark field images are complementary for a = 7T and 5 = 0.

reverse is true for reflections belonging to class B. Reflections of class A are 200 and 222, those of class B are 400, 220, and 111. Application

of this rule to Figure 46 leads to the conclusion that the fault is intrinsic. From this rule it is evident that the dark field image alone is sufficient to make the determination. If both bright and dark field images are avail- able, one can determine top and bottom end of the foil as well. At the
500 TRACE CHARACTERIZATION

top part the fringe patterns are similar, while they are pseudo-complementary at the exit face. The rule can be deduced from Figure 49 which shows all the logically

possible configurations and the corresponding bright and dark field images for class A and class B reflections. The displacement vector is taken as Z) = ±^a [111] since, apart from its sign, this vector in unambiguously defined in contrast to the shear vector [112]. This vector describes the displacement of the cross hatched back part with respect

to the front part; it is perpendicular to the fault plane. For a derivation

of the rule we refer to [90]. b. Hexagonal Close Packed Crystals. The triple fault can easily

be distinguished from single and double faults because different extinction criteria apply to it. However, single and double faults obey the same extinction criteria and they can therefore not be distinguished on such a basis. A method has been worked out based on the nature of

the outer fringes. For the derivation of the method we refer to the original paper [95]; but we shall give the practical rule. If the nature of the

Figure 49. Schematic representation of the fringe pattern for intrinsic and extrinsic stack- ing fauhs in f.c.c. metals. A full line represents the first fringe (at the top) and a dotted Une the last fringe. The nature of these fringes is indicated by B (bright) and D (dark).
MICROSCOPY 501

outer fringes is different for dark field images with / even and with / odd

but for the same h — k value, the fault is single. If the nature of the outer

fringes does not depend on whether / is odd or even, the fault is double.

An example of apphcation to faults in wurtzite is shown in Figure 50. The nature of the outer fringes is different, for the dark field images

taken with /=! and 1 = 2 and therefore one concludes that the faults are single.

6. The Measurement of Stacking Fault Energies [96, 38]

One of the typical appUcations where transmission electron microscopy has been particularly successful is the measurement of stacking

fault energies, y, i.e., the excess energy per unit area associated with

a stacking fault. Electron microscopy provided in fact the first direct

methods for such measurements. In principle one can make use of any equiHbrium configuration of partial dislocations which is observable

in the microscope and which lends itself to theoretical treatment. We

shall discuss some of these configurations.

a. Ribbons. By far the simplest one is the dislocation ribbon or extended dislocation. According to isotropic elasticity theory in an

infinite sohd the two partials in the ribbon repel each other following an inverse distance law

Figure 50. Dark field images of stacking faults in wurtzite (ZnS). The nature of the outer

fringes is different for g = (1011) and for g = (1012).
502 TRACE CHARACTERIZATION

where d : distance between partials

jjL : shear modulus

V : Poisson's ratio

bis and 62s : the screw components of the Burgers vectors of the

bie and b-ze are similarly the edge components.

On the other hand the two partials are kept together by the stacking

fault between them, which exerts a constant attractive force equal

numerically to y, the stacking fault energy. An equilibrium separation

therefore necessarily results (Fig. 51). The equilibrium distance, in the case of Shockley partials, is given by

where y is the angle between the total Burgers vector b = bi+b2 and

the direction of the ribbon. For a general ribbon this relation becomes

somewhat more complicated; it is given in ref. [78].

If the ratio y//x6 becomes too large the spacing between partials

becomes too small to be measured with any accuracy. The extended

node discussed below should then be used.

The ribbon formula can easily be extended to the case of multiple

ribbons. The triple ribbon resulting from the interaction of two single

ribbons is a particularly interesting configuration. It consists of three

dislocations with the same Burgers vector. A model for such ribbons

in hexagonal crystals is shown in Figure 52. The two halves of the symmetrical ribbon contain stacking faults with the same energy, since they

are crystallographically equivalent. Because of their large width triple

ribbons are more sensitive probes than single ribbons and therefore they

allow more accurate measurements [38, 97]. However one has to be aware of possible surface effects which may lead to too high values for y [98]. An example of a triple ribbon is shown in Figure 53. Such triple ribbons have now also been observed in face centered

cubic Ag-In alloys with low stacking fault energy. One half contains an intrinsic fault and the other half an extrinsic fault. The ratio of the

width of the two halves allows to determine the ratio of the two stacking

fault energies [97, 99]. In complex crystals such as talc [100] and the chromium halides [101]

ribbons consisting of four and six partials occur (Fig. 54). From the

spacings of the partials one can deduce the values of all different stacking

faults provided the elastic constants are known.

two partials

(17)

do =

^b' 2-v

87ry \ — V

(18)
MICROSCOPY 503

(b) Figure 51. (a) Model for ribbons of partial dislocations of the Shockley type. The angle between the direction of the ribbon and the Burgers vector is called <}>. (b) The repulsive

force between partials (curve 1) goes as 1/d whereas the force due to the stacking fault

is constant (curve 2). The intersection point gives the equilibrium separation deq. A (T (T b C A

c

ca

b c c b

b ab a a

(T B

A —a c \ b B

b a \ c a-bK 1 b b-

—a a a a —

b b b b —a a C (T 0" a a —

B

(a) (b) Figure 52. Arrangement of layers in threefold ribbons in the hexagonal structure, in particular in graphite; the 3 partials have parallel Burgers vectors (a) symmetrical (b) asymmetrical.
504 TRACE CHARACTERIZATION

A

1

\

a A

A

JiL

Figure 53. Dislocation pattern in graphite, (a) isolated extended node and threefold ribbon. All partials are in contrast, (b) the same region as (a) but with some of the lines out of contrast; particularly the threefold ribbon is out of contrast. The direction of the Burgers vector is indicated.

Figure 54. Sixfold ribbons in chromium chloride.

b. Extended Nodes. Isolated extended nodes are generated by

the reaction between two ribbons which have a common partial. This

dislocation reaction is shown in Figure 55. One can now measure either
MICROSCOPY 505

(c) (d) Figure 55. Fusion of two ribbons giving rise to an isolated extended node.

the radius of curvature (R) or the radius of the enscribed circle (3^0), the

latter measurement is in practice the more accurate one. The stacking fault energy is related to the radius of curvature of the

partials by the relation

This relation expresses the equilibrium curvature of an isolated partial,

under the influence on the one hand of the effective shear stress yjh

exerted by the stacking fault inside the node, and on the other hand of the "line tension" of the partial [102]. A more accurate solution of the node problem requires taking into account the interaction between the different partials in the node. An

analytical solution to this problem was given by Siems et al. [103], and

the result is summarized here. The stacking fault energy is now given by

y-/^i//o/roV3 (20) where K==^^ (21) for edge ribbons and K = ^^f^ (22) for screw ribbons. The dimensionless quantity 1//0 is the solution of the

following equation

In i//o = i//o-l-0.267(e//^) (23)
506 TRACE CHARACTERIZATION

€ is the line energy; one has elK = 8.95

^ _^ for edge ribbons and

2 elK = 8.9S 2_3^ screw ribbons.

For dislocations in the basal plane of hexagonal crystals the anisotropy can easily be taken into account as well as in formula (17) as in formula

(20) by using the appropriate expressions for jjL and v (see ref. [38, 103]).

Also for dislocations in the (111) plane of cubic crystals it is possible to give approximate expressions for the effective values of fjL and v [104]. More recently Siems [105] has improved this analytical treatment by

taking into account the orientation dependence of the line energy. Numerical solutions of the node problem have been given independently by Brown and Tholen [106] and by J0ssang, Stowell, Hirth and

Lothe [107]. The results of Brown and Tholen can be summarized in "empirical" formulae which are accurate to about 10%:

^=0.27-0.08 (t-^) cos 2a

IJib^ \l — v/ + |o. 104 (f^^)

+ 0.24 cos 2«| logio ^ (24)

g^^0.055(f5^)-0.06(^)cos2«

+ |o.018 (f^^) +0.036 cos 2a\ logio ^ (25)

where the meaning of the symbols is as follows: b: Burgers vector of the partial dislocation,

a: describes the character of the partial at the point of closest approach

to the node center (^'^~~^ edge nodes, a = 0 for screw nodes^,

e: arbitrary parameter related to the core radius.

With these formulae the stacking fault energies can be derived either

from the radius of curvature {R) or from the radius of the enscribed

circle (yo) provided the Burgers vector of the partials has been determined

so that a is known.

Extended nodes usually occur in networks of the type shown in Figure

56 and which are in fact twist boundaries. Such a network usually

contains extended and contracted nodes. However in silicon [104] and

in certain f.c.c. metal alloys [97, 99] it is found that all nodes are disso- ciated. Only one family of nodes say the A nodes then contains an

intrinsic fault, the other family say the V nodes, containing an extrinsic
Figure 56. Network of extended and contracted nodes in a copper-gallium alloy. Courtesy Art.

fault. From the geometry of both types of nodes one can deduce the

y-values for the two types of fauks.

The same methods can of course be used to measure antiphase boundary energies.

The methods described here allow to study problems such as the

variation with composition of the stacking fault energy in binary alloys.
508 TRACE CHARACTERIZATION

Also the variation with temperature can conveniently be studied [108]. Continued interest in the method is to be expected in the future.

c. Other Methods Based on Electron Microscopy. Theory

shows that the maximum size of a stacking fault tetrahedron (see para- graph V.E.2b) is a function of the stacking fault energy. Measuring

this maximum size thus allows to determine the stacking fault energy. Unfortunately it is difficult in practice to decide whether the tetrahedra

in a quenched foil have reached their maximum size or not. The method

was apphed to gold and to cobalt-nickel alloys [108a], and acceptable

values were obtained.

Another interesting method which is particularly suited for measuring

high stacking fault energies, has recently been proposed. It is based on

a measurement of the chmb rate of faulted loops. The stress exerted

by the stacking fault in the interior of the Frank sessile loops, constitutes

the main driving force inducing the loop to shrink by chmb at temperatures where self diffusion becomes appreciable. The climb rate is thus a

function of y [108b]. If one measures the climb rate of faulted and

unfaulted loops under the same circumstances; knowledge of the activation energy for self diffusion is not required [108c]. The method has

been apphed to aluminum [108b] aluminum alloy [108c] and to magnesium and zinc [108d], [108c].

D. Contrast at Slip Traces [76]

Dislocations moving in a thin foil, which is being examined in the

microscope, leave traces at the upper and lower surfaces of the foil. This phenomenon is seen in most metals, although the stability of the

contrast is larger in one metal than in the other. In aluminium the contrast disappears after a few minutes, in other metals it may be almost

permanent. This contrast effect has been attributed to dislocations left behind at the interface between an oxide layer and the metal itself. In some cases this dislocation can actually be observed. In others this is not so. The image profile calculated for a dislocation dipole having

the surface as a symmetry plane leads to results in agreement with

experiment [76]. From a comparison of bright and dark field images top and bottom of the foil can be determined. The images are again similar at the top and

complementary at the bottom end of the foil. The effect can be used to study the geometry of slip. Cross slip is revealed in a very striking way, as illustrated in Figure 57 which refers

to aluminium. If the slip planes in a given metal are known, e.g., (Ill)

planes^ in f.c.c. metals, the effect can be used to determine the foil thickness. This is an important parameter if one wishes to estimate

defect densities for instance.
MICROSCOPY 509

Figure 57. Cross slip pattern observed in quenched aluminum foil. From the slip traces the foil thickness can be computed. Anomalously wide images due to loops close to the surface can be observed also. Courtesy of R. Cotterill.

E. Point Defects and Dislocations

In recent years the electron microscope has greatly contributed to our understanding of the formation of point defect clusters and their relation
510 TRACE CHARACTERIZATION

to dislocations. Dislocation loops or other point defect clusters can be

introduced by the following processes:

(i) quenching,

(iil irradiation with energetic particles or with ionizing radiation,

(iii) deviations from stoichiometry,

(iv) cold work,

(v) prismatic punching.

We shall only discuss briefly some of these processes.

We first discuss some of the processes that lead to the formation of

point defect clusters. Afterwards we describe the nature of the resulting

clusters and dislocation configurations.

a. Quenching. At each temperature a certain concentration of

point defects is in thermal equilibrium. The concentration of vacancies

in a metal is for instance given by an expression of the form

where AS is the entropy of formation and £/f is the energy of formation

of a vacancy; AS is usually a few times k, whilst f/^ is of the order of 1 eV. As a consequence, at temperatures close to the melting point, Cv may

become of the order of 10 If the solid is cooled rapidly enough this concentration of vacancies may be frozen in, at least partly. Vacancies

may disappear at sinks such as grain boundaries and dislocations, the

rest may be trapped as isolated vacancies, or associated with impurity

atoms. A certain fraction form agglomerates of different size and shape,

depending mainly on the stacking fault energy of the metal considered

[109]. It is easy to see from simple arguments that from a certain size on it becomes energetically more favourable to form a dislocation loop

rather than a disc shaped cavity. The energy of a cavity with diameter

d is given by

where cr is the surface energy. The energy of the loop is, on the other

hand, given approximately by

1. Processes Giving Rise to Point Defect Clusters

(26)

Ec (27)

Ei = fJib^d-\-- nd^y

4

(28)

where cr is the shear modulus and y the stacking fault energy. This last term disappears if the loop does not contain a stacking fault. One

notices that Ec > E\ provided
MICROSCOPY 511

d>^fjLb^/[7r{2(T-y)l (29) The agglomerate is presumably more or less spherical in the initial stage.

On transforming into a dislocation loop it has to pass through the disc- shaped configuration, which has a higher energy, due to the increased

surface area. Some activation energy is required for this process. In substances with a large surface energy it is possible that small cavities remain. This is presumably the case in platinum [83] where small

cavities are found after quenching. The geometry of the loops depends

on the structure and on the stacking fault energy. We shall consider

different structures below.

b. Irradiation. The irradiation of crystalline solids with energetic

particles such as neutrons, a-particles, fission fragments, etc. produces

knocked on atoms, which give rise to displacement cascades with the

simultaneous creation of vacancies and interstitials. At temperatures

where these defects become mobile they may disappear by mutual annihilation, or by migrating to sinks or finally they may agglomerate and

form clusters such as those found on quenching. However, where as on quenching the defects are presumably always derived from vacancies

(at least in metals), we now expect clusters of two types and it becomes a meaningful problem to determine the nature of the individual clusters.

c. Plastic Deformation. As early as 1952, Seitz [110] suggested

that plastic deformation would lead to the formation of point defects as a

result of the intersection of dislocations. The original idea was inspired

by the experiments of Guylai and Hartly [111] on the influence of plastic

deformation on the ionic conductivity of alkali halides and by some

experiments by Molenaar and Aarts [112] on the increase of the residual

electrical resistance of metals after plastic deformation. Evidence from

direct observation methods, decoration, etching and electron microscopy,

has shown that indeed some defects are left behind by moving dislocations. Depending on the process responsible for their formation, these

defects should either be vacancies or interstitials or both [113]. It is therefore again of interest to determine the character of the clusters. d. Deviations From Stoichiometry. In some binary systems

which crystallize as layer structures it has been found that deviations

from stoichiometry can be accommodated under the form of large dislo- cation loops, lying in the layer plane. This is e.g. the case in Sb-zTes containing an excess of Sb [114] and in InSe containing an excess of In [115] (Fig. 58). In both systems this excess can be accommodated

either as interstitial loops of metal or as vacancy loops of nonmetal.

Again a determination of the loop character is necessary to settle this question. Such a determination for the InSe system leads to the conclusion that they are vacancy loops [115].

237-323 0-67—31
Figure 58. Loops in InSe due to non-stoichiometry. Three different contrasts allowing a

determination of the loop character. Courtesy Marinkovic.

2. Nature of the Defect Clusters

a. Dislocation Loops — i. Face Centered Cubic Metals. Vacancies as well as interstitials can precipitate in a single sheet presumably

on the (111) planes since these are the closest packed planes. If a cavity

so formed collapses, a sessile dislocation loop with a Burgers vector ^a [111] and surrounding an intrinsic stacking fault results. It can be

eliminated if the loop is swept by a partial with a Burgers vector of the

type 7a [111]. The resulting loop is then a perfect dislocation with

o Burgers vector |a[lll] +ia[112]^|[110] (25)

inclined with respect to the original loop plane. Such a loop can glide on a cylinder parallel to the Burgers vector. For an interstitial loop the

fault is of the extrinsic type, two partials have to sweep the loop in order

to remove the stacking fault, one in a glide plane just above the loop

plane the other in the (111) plane below the loop plane.

The condition for removing the stacking fault is roughly that the energy

of the perfect loop should be smaller than that of the faulted one. The

partial dislocation sweeping the loop has apparently to be nucleated at the edge of the loop. The shear stress available for doing this originates

from the energy of the stacking fault; the equivalent shear stress is ylb.

With a value of 7 ~ 100 erg/cm^ and 6 = 2X10~^ this becomes 50

kg/mm^.
MICROSCOPY 513

For vacancy loops in nominally pure aluminium removal of the stacking

fault by the process described above seems to take place [1161. The

loops do not contain a stacking fault, moreover they are found to be

ghssile. However, in hyperpure aluminium, most of the loops retain the

stacking fault, presumably because of the difficulty of nucleation of the

partial [117]. This last hypothesis is supported by the observation that some loops lose their fault whilst under observation in the microscope

(Fig. 59). In some aluminium-silver alloys the stacking fault energy seems to be too small to remove the fault; in this case faulted loops

remain [118].

ii. Hexagonal Metals. In quenched magnesium, large vacancy

loops are formed in the basal plane [120]. The loops contain a stacking

fault. Their Burgers vector is presumably of the type TA in the notation

of Berghezan et al. [119]. The activation energy of annealing found by

measuring the rate of shrinking of loops corresponds to the activation

energy for self diffusion [120]. Hi. Body Centered Metals. Quenched in vacancy loops have been

observed in molybdenum quenched from 2600 °C and annealed for 1 hour at 400 °C [120 b].

iv. Graphite [121, 122]. After a quench from 3000 °C followed by

an aging treatment at 1300 °C loops are formed in graphite. The

r

Figure 59. Faulted loops in quenched aluminum. Some have lost their fault. Courtesy CotteriU.
514 TRACE CHARACTERIZATION

Burgers vectors of these loops appears to be inclined and the loops

contain a stacking fault. Using the argument developed in subsection

V.F.5 it was concluded that these loops were vacancy loops.

b. Stacking Fault Tetrahedra. It has been shown by Silcox and

Hirsch [123] that in gold, quenched from 950 °C and aged for one hour

at 100-250 °C, the vacancies cluster into spatial defects. An analysis

of the contrast effects shows that the defect is a tetrahedron limited by

stacking faults on (111) planes. The edges are stair rod dislocations with

a Burgers vector of the type ^a [110]. An example is reproduced in Figure 60 whilst Figure 61 is a schematic view. Similar tetrahedra have

been observed in silver [124] and in quenched nickel-cobalt alloys [125]. Silcox and Hirsch [123] have given the following mechanism by which

the tetrahedra can be generated. Let us assume that originally the

vacancies form a triangular sessile loop with a ^ a [111] = /4q: vector'^ and on a (111) plane. The edges of the triangle are parallel to the [110],

V,. 'V- .r'" V.-.

r.^^. I W ^ >^ - 4^ J

^ ^

Figure 60. Quench tetrahedra in gold. The fauh fringes can easily be recognized for the tetrahedron in the inset. Courtesy Cotterill. Use is made of Thompson's notation for Burgers vectors in the f.c.c. lattice.
MICROSCOPY 515

[101], and [Oil] directions. The partials limiting the loop can now spHt on the different [111] planes according to the schemes:

oA^ a3-^ /3A (in the 6-plane)

olA-^ ay~\-yA (in the c-plane)

olA^ ab^^A {m the G?-plane). (29) The dissociation is accompanied by a gain in energy, according to the

"Burgers vector squared" criterion. The Shockley partials with vector

/3A, yA, and SA bow out in their respective (111) planes being repelled

by the stair rods with vectors a/3, ay, and aS. In this way they generate

stacking faults on these planes. Along the intersection lines of the (111)

(a)

(b)

(c)

Figure 61. The formation of a tetrahedron. Courtesy Silcox and Hirsch. a) Triangular

sessile loop in the (111) plane resulting from the collapse of a disc of vacancies, b) The

partials bordering the loop dissociate and the Shockley partials bow out in the other (111) planes, c) Final shape of the tetrahedron. The edges are stair rod dislocations. The

side faces contain stacking faults.
516 TRACE CHARACTERIZATION

planes the Shockley partials meet and react to form new stair rod

dislocations according to the reactions

yA-\-A8^y8 (30)

6^+^j8-^ 813. The tetrahedron is now complete. This formation mechanism is rep- resented in Figure 61. It can easily be shown that the total energy

associated with the tetrahedron is smaller than that associated with the

initial sessile loop Es for tetrahedra which are smaller than some critical dimension. For gold the critical dimension is ~ 430 A. The mechanism discussed here demonstrates clearly the geometry of

the defect, however there is no real evidence that the tetrahedra are generated in this way. It is also difficult to see how the tetrahedra grow.

A possible nucleation and growth mechanism which does not imply the

formation of an intermediate loop has been proposed by De Jong and

Koehler [126], and modified by Kimura et al. [127]. c. Cavities. There is accumulating evidence that on quenching

under certain conditions cavities are formed rather than dislocation

loops [128, 129]. In many cases the polyhydral shape of the cavities can be recognized. It is not always clear whether these cavities are reaUy empty or contain gas which stabilizes them. If they are empty

they can be used for the study of clean surfaces, in particular ratios of

the surface energies of different crystal faces can be deduced from the

equilibrium shape of the cavities [130]. The contrast at cavities is discussed in ref. [131]. d. Helices. On quenching dislocations act as sinks creating de- nuded zones in their vicinity. Screw dislocations are hereby driven

into helices [132, 133]. Such helices were first observed by means of

decoration techniques [134], but electron microscopy has demonstrated

their occurrence in many quenched alloys [135]. The reason why they

are apparently more easily formed in aUoys than in elemental metals,

is not completely clear. However a plausible explanation is that in alloys the interaction of the vacancies with solute atoms prevents clus- tering and makes it more favourable for vacancies to disappear at existing dislocations.

F. Methods to Determine the Character of the Loops

For many problems in relation with point defects it is of particular

interest to be able to distinguish between vacancy and interstitial loops.

Methods have been developed which are based on diffraction effects only; we shall summarize these.
MICROSCOPY 517

Vacancy and interstitial loops may differ by:

(i) the sign of their Burgers vector,

(ii) the type of stacking fault they contain,

(iii) the direction of their Burgers vector. The diffraction methods make use of one of these features. The first feature is the more general one and a number of methods have been

developed to determine the sense of the Burgers vector, in particular for loops. The theory of contrast formation predicts that for s different

from zero the image side for a dislocation is essentially determined by the

sign of the quantity (g • b)5 (ref. [76]). If (g • b)5 > 0 the image is left. Provided the FS/RH convention for defining b is adopted. Apparently

it is therefore required to know all three quantities involved. In practice one can often avoid a Burgers vector determination in the strict sense. We now discuss these methods.

1. The Geometrical Method

Probably the simplest to expose is the procedure outlined by Groves

and Kelly [136], by Siems et al. [79], and Ruedl et al. [137]. In subsection

V. A.5 it was shown how the sign of 5 can be determined from the relative position of the diffraction spot and the corresponding bright Kikuchi hne

with respect to the centre of the diffraction pattern. In many cases,

especially in thick foils, use is made of the phenomenon of easy trans- mission. In such cases loop contrast wiU be best for 5 positive. In platinum it was even found [138] that good pictures are practically only

obtained for positive values of s. In order to determine the image side,

it is therefore best to change the sign of g. The image side can also be

deduced from the asymmetry of the dislocation image; the profile is steepest at the side of the dislocation [139]. From the sign of s and from

the image side one can deduce the sign of g • b. The diffraction vector can readily be determined in two beam cases; it is sufficient to join the centre of the diffraction pattern and the only active spot. If the direction

of b is known its sign follows directly from the sign of the dot product.

However, here arises the main difficulty associated with the method; it is often difficult to determine the direction of the Burgers vector because

two extinctions are required for this. Even if the sign of b is known one

has still to go through a consistent system of arbitrary conventions to relate the sign of b with the loop character or with the dislocation geometry. Mazey, Barnes, and Howie [140] have described completely the

formaUsm used in this method. We refer to their work for a detailed account. Instead we will describe the more intuitive geometrical

method, which makes use of the loop plane rather than of the Burgers

vector and which is equivalent to the formal method. This geometrical

method is an extension of the one outlined for single straight dislocations

[137].
518 TRACE CHARACTERIZATION

Let s be different from zero and let us assume that the sense into which

the contrast producing lattice planes have to be rotated in order to approach the Bragg position is as indicated in Figure 31. Let us further assume that we have purely prismatic loops situated in inclined planes.

The four possibilities are shown in Figure 62. It is now easy to deduce

for each case whether the image will be inside or outside of the loop.

It is found e.g., that for a vacancy loop, in a plane sloping upwards to the

right and with a diffraction vector to the right, the image is outside

because the lattice rotations are in the right sense (S) outside. Similar

conclusions can be drawn for the other cases, the result is shown in Figure 62. It is evident how on inversing the reasoning the loop character can be deduced. The conclusion is clearly based on the assumption

that the loops are purely prismatic, i.e., that the direction of the Burgers

vector is known and perpendicular to the loop plane. Only in this case we can deduce the sign of b once the sign of g • b and that of g is known.

However, if the loop is not purely prismatic the conclusion is still valid

if the angle 0 between the normal to the loop plane and the direction of

b is small enough so as to make sure that g • b has the same sign as for

(c) (d) Figure 62. Determination of the loop character by the diffraction method. The four

possible configurations are shown. The true position of the loop is indicated by a dotted

line; the image is represented as a full line. S is the sense into which the lattice has to be rotated in order to bring it into the exact Bragg position.
MICROSCOPY 519

a purely prismatic loop whatever the position of b on the cone with angle

(/) around the loop normal. For instance for {012} loops in f.c.c. metals

4>=18°: for fauked loops in the basal plane of zinc 0 = 31°, for loops in graphite (J) = 22°. If in the case of zinc e.g., the loop plane makes an

angle of 45° with the electron beam and if the diffraction vector forms

an angle of at least 45° with the hne of intersection of the loop plane and

the plane normal to the beam, the procedure still works without

ambiguity.

One question remains to be answered. How do we know in which

plane the loop is lying? For loops in zinc [119] or in graphite [141] this

is the basal plane, but in face centered cubic metals, as a consequence

of the higher symmetry mo^e possibilities arise. In order to discriminate

between these, the foil is mounted once normal to the beam and once in an inclined position (e.g., 45° to the beam). The change in shape of the

loops will allow to determine the sense of sloping of the loop plane, as well as the indices of the loop plane. In order to put the foil in an inclined position the grid is mounted

between two wedge shaped rings [136]. If the loops are in the foil plane

as it is the case for layer structures or for hexagonal metals it is still required to mount the foil in an inclined position in order to apply the

procedure. The situation is shown in Figure 63. If mounted under 45°

the sign of g • b is the same for the six possible orientations of b, and for a suitable g-vector as pointed out above. In f.c.c. metals the assumption that the loops are purely prismatic, i.e., that (f) = 0 instead of 0 = 18° wiU lead to the correct result provided the loop plane is again sufficiently

inclined.

It may be worth while to remind the reader that the reasoning pre- sented above has to be made looking along the line of intersection of the

loop plane and the plane normal to the electron beam, with the g vector

to the right of this line. It is of course always possible to orient the

photograph this way. The intersection line which is equivalent to the

rotation axis, can be deduced by measuring distances between equivalent

points on pictures in the normal and in the inclined positions [137]. The

Figure 63. Loop in a foil mounted in an inclined position. The Burgers vector b lies on a cone which has the loop normal as its axis. For all possible positions of b on this cone

the sign of g • b is the same.

n
520 TRACE CHARACTERIZATION

largest shortening evidently occurs in the direction perpendicular to the rotation axis. Although the reasoning is made for loops lying in a plane parallel to the rotation axis, not too large a deviation from this does not influence

the result. Loops lying approximately in the foil plane are apparently

the best choice for all operations. Moreover such loops usually have

their Burgers vector nearly normal to the foil, which makes it easy to determine its direction. Although this information is not absolutely

required it is of great help to remove ambiguity.

2. The Tilting Method [142]

If a tilting device that allows rotation over a large angle is available,

the following method can be used. Suppose that we have a prismatic

loop in a plane almost parallel to the beam, the image is then very narrow. Let us further assume that the contrast producing reflection is to the

right of the rotation axis and that we rotate the crystal through the Bragg

position. As one turns the foil the loop becomes wider for purely geo- metrical reasons. As one approaches the reflecting position it is evi- dently positive and the image is inside for an interstitial loop and outside

for a vacancy loop (Fig. 64). On passing through the reflecting position

the image side changes i.e. the image becomes outside for the interstitial loop and inside for the vacancy loop. We can conclude that the image

of the interstitial loop grows continuously in size as we rotate the crystal

in the positive sense, whilst the image of the vacancy loop first grows

and temporarily shrinks on going through the reflecting position before

growing further for geometrical reasons. Before the next reflection

arrives the image side changes because we start for this next reflection

again with 5 > 0. However, in general the image of the interstitial loop will not shrink as a consequence of this because of the geometrical

eff'ect. The image of the vacancy loop in any case increases in size. The same type of reasoning can be made for a rotation in the other sense and for a reflection at the left; the conclusion is the same. Fig. 64 is made for a purely prismatic loop and for a rotation axis perpendicular

to the diffraction vector and parallel to the loop plane. In practice these

conditions are not so strict. However, in order to have a noticeable

geometrical effect one should start with a loop in a rather steeply inchned

plane.

3. Loops Seen Edge On

In this special case one can make use of a method due to Ashby and

Brown [143]. These authors made calculations for the contrast effects associated with coherent precipitates that are under positive or negative

hydrostatic pressure. An interstitial loop can be considered as a special case of a precipitate platelet that gives rise to outward lattice displacements whereas a vacancy loop does the reverse. From machine calcula-
MICROSCOPY 521

Diffraction

condition __>^

s>0

n s <0

Interstitial 0 0 0

Vacancy 0 0 0

(a) (b) (c) Figure 64. Determination of the loop character by the tilting method. The width of an

interstitial loop is seen to increase continuously whereas the width of a vacancy loop increases first and then decreases as one passes through the reflecting position. The

fuU hne represents the image; the dotted line is the true position of the loop.

tions based on the dynamical theory the authors conclude that the images

of loops seen edge on and which are close to the surface are "anomalously

wide" and asymmetrical. Examples are visible in Figure 57. One side

consists of a bright crescent, the other side of a dark one. The line of no contrast is perpendicular to the diffraction vector. In the bright field image this asymmetry is in the opposite sense near top and bottom sur- face. However, in the dark field image the asymmetry is in the same

sense near top and bottom of the foil as a consequence of anomalous

absorption. The asymmetry is such that in the dark field image the

white crescent is in the positive sense of the diffraction vector for a vacancy loop and in the opposite sense for an interstitial loop. Recently

it has been pointed out that considerable caution is required when applying this method to loops [144, 145, 146].

4. Stacking Fault Method

In f.c.c. metals the interstitial loops may contain an extrinsic stacking

fault provided the stacking fault energy is smaU enough. Under the same circumstances a vacancy loop would contain an intrinsic stacking
522 TRACE CHARACTERIZATION

fault. As we have pointed out it is possible to deduce the nature of

stacking faults in the face centered cubic metals from the nature of the

first fringe at the surface in the dark field image. In principle it is therefore possible to distinguish loops on this basis. However, the use of the

method is restricted by the fact that the loops have to be large enough

to contain at least a few fringes and secondly they have to intersect the

surface. Nevertheless Hirsch et al. [148], have shown in this way that proton irradiated copper contains interstitial loops.

As mentioned above it is also possible for some intermediate value of

the stacking fault energy that interstitial loops contain a stacking fault,

whereas it could be removed from vacancy loops. In such a material

the distinction would be immediate. It was suggested that this is the case in platinum [137]. It is possible that these circumstances are also realized for copper, where fault free loops have been observed in neutron

irradiated specimens [147], whereas faulted loops were found in protonirratiated material [148].

The nature of loops in hexagonal crystals can also be determined by

similar methods. In low stacking fault energy hexagonal metals or

alloys vacancy loops would contain single faults whereas interstitial loops would contain triple faults. The two types of loops can be dis- tinguished on the basis of a Burgers vector determination, or by noting

that the vacancy loops show fault contrast for certain reflections belonging to the zone [0001] whereas the interstitial loops do not.

If the stacking fault energy is high both loops contain single faults because the triple fault is removed by the passage of a partial; the remaining single fault cannot be removed however [119]. The loops have then

to be distinguished by determining the sign of the Burgers vector of

the bordering partials.

In low stacking fault energy hexagonal metals, as well as in graphite,

still another method is available to distinguish vacancy and interstitial loops. The stacking in such crystals can be represented by the letter sequence

5. The Burgers Vector Method [121, 122]

a b a b a b. (16)

If one layer is removed like in a vacancy loop a fault

(17)

would be generated. This has a very large energy and will be removed

by shear along the basal plane. The stacking sequence becomes
MICROSCOPY

a b a b c b c 523

(18)

or

a b a c a c a (19)

in either case a fault, with smaller energy remains. The fault cannot

be removed completely by glide. The Burgers vector of the loop has now become inclined with respect to the basal plane (Fig. 65). If on the

other hand a layer is inserted as for an interstitial loop this layer can go

in c-position, i.e., the stacking sequence could become

a b a c b a b. (20) T

If the stacking fault energy is small enough there is no shear movement

and the Burgers vector of the loop remains perpendicular (Fig. 65).

b 1 c 1 b a 1 ^

' a

b

^ b a

b ^^^^

a

b a a

b b b

Figure 65. Prismatic loop in graphite: Vacancy loop:the Burgers vector is inclined with

respect to the c-plane.

It is clear that the distinction can now be made on the basis of a deter- mination of the direction of the Burgers vector. This method was

applied to quenched graphite. The stacking fault energy in graphite

is very small : 0.7 erg/cm'^ [149]. Graphite was in fact the first material

for which the distinction could be made [121]. The situation is especially favourable since the loops are in the foil plane. Interstitial loops

would only show residual line contrast in the normal orientation of the

foil, whatever the operating reflection. On the other hand vacancy

loops would show stacking fault contrast for certain reflection (when the

fault is at the right depth in the foil) and line contrast for other reflections. The vacancy loops would go out of contrast for reflection against a set of planes parallel to the Burgers vector. By making dark field images

with these reflections [1120] it was found that certain loops only exhibited

residual contrast whereas others were in full line contrast, in accord

with the fact that the inclined Burgers vector can lie in three different

planes of this type. From this observation and also from the fact that

fault contrast is observed one can conclude that the loops are vacancy
524 TRACE CHARACTERIZATION

loops as one would expect in quenched graphite. It is perhaps worth

mentioning that due to the large anisotropy of graphite the residual contrast is very weak and the loop goes out of contrast completely.

G. Domain Boundaries

Ferromagnetic, anti-ferromagnetic, ferroelectric and anti-ferroelectric

crystals are usually broken up into domains. The interfaces between

such domains shall be called "domain boundaries".

1. Ferroelectric Domains

We shall discuss as a specific example the domain structure of barium

titanate. Above the ferroelectric transition temperature barium titanate

is cubic and it has the perovskite structure which consists essentially

in a close packed arrangement of oxygen ions, a fraction of the oxygen

ions being replaced by barium ions. The titanium ions occupy the centers of the oxygen octahedra (Fig. 66-l(a)). Below the ferroelectric

transition temperature (120 °C) the crystal becomes tetragonal, as a result of the fact that the titanium ions no longer occupy the centers of the

oxygen octahedra. They are displaced along one of the cube directions

which now becomes the c axis of the tetragonal form (Fig. 66-l(b)).

This displacement also causes the ferroelectric polarization. Since

there are three equivalent cube directions, and since furthermore the

c axis becomes a polar axis there are three possible orientations, each

having two senses for the c axis as referred to the cubic structure. On

cooling through the transition temperature polarization starts simultaneously in different parts of the crystal. In each part the c axis adopts

hereby one out of the six possibilities, thereby creating a domain structure. Also it can be shown that it is energetically more favourable for the cyrstal to break up into domains rather than to form a single domain.

As a consequence one can consider two kinds of domain boundaries:

(i) 90° boundaries : the c axis of the domains on both sides of the

boundary are mutually perpendicular.

(ii) 180° boundary : the c axis of the domains on both sides of the

boundary are anti-parallel.

For the first kind of interface, the 90° boundary, the lattice is twinned,

the twinning vector being very small. Figure 66-2(b) shows in a highly

exaggerated way the lattices on both sides of the boundary.

We shall now discuss how fringe contrast arises at such boundaries

and what information can be obtained from the fringe patterns. From

Figure 66-2 it is clear that since the lattices are slightly different on both

sides of the boundary, also the simultaneously operating diffraction vectors gi and g2 are slightly different. It can be shown that for a coherent twin boundary the vector Ag=g2 — gi, is perpendicular to the

boundary plane [150]. The main consequence of this is a difference in excitation error ^s = S\— Sz for the crystal parts on both sides of the
MICROSCOPY 525

(I)

Figure 66. (1) a) structure of barium titanate, b) Displacements of the titanium ions giving

rise to domain formation. (2) a) Schematic cross section of a foil containing a domain

wall in barium titanate. In part I the diffraction conditions are determined by Si, part

II by S2. In part I the c-axis is perpendicular to the foil, whereas it is parallel to the foil in part II; b) Cross section of the lattice of barium titanate perpendicular to the twin plane and containing the tetragonal axis. The tetragonal deformation is highly

exaggerated. ^ domain boundary, As being in length equal to the component of Ag, per- pendicular to the foil plane (5i and 52 are the excitation errors in part I and II of the crystal; part I is first met by the electrons). It can be shown

that a fringe pattern results if the boundary plane is inclined with respect

to the foil plane. These fringe patterns have been called 8-fringes [151],

they have properties which are quite different from those due to stacking

faults and it is therefore easy to distinguish between stacking faults and

domain boundaries. The main properties of 6-fringes are summarized

here (Fig. 67):

(i) In the bright field image the outer fringes have opposite nature;

in the dark field image they have the same nature.

(ii) The fringe spacing may be slightly different at the top and bottom

end of the fringe pattern, it is only equal in the "symmetrical" case, i.e.,
526 TRACE CHARACTERIZATION

Figure 67. Ferroelectric domain boundaries in barium titanate. The fringe patterns are due to boundaries inclined with respect to the foil plane. The first and last fringes are opposite in nature. In A and B domain walls are perpendicular to the foil plane. Notice

the closed loop of boundary in C.

(iii) The fringe system is similar in the bright and in the dark field image at the top end, but pseudo-complementary at the bottom end of the pattern. This property is common to all contrast effects in "thick

foils"; it results from anomalous absorption.

(iv) The first fringe in the bright field image is bright if As > 0; it is dark if As < 0.
MICROSCOPY

2. Anti-Ferromagnetic Domain Boundaries

527

Similar domain boundaries occur in anti-ferromagnetic crystals such

as nickel oxide and cobaltous oxide. Nickel oxide is cubic above the

Neel point (550 °C) and it has then the sodium chloride structure. Below this temperature the magnetic moments of the nickel ions order

into ferromagnetic sheets parallel to the (111) plane. The coupling

between successive ferromagnetic sheets is antiferromagnetic. As a

result of the spin ordering a contraction takes place along a [111] direction

of the cubic structure, causing in this way a rhombohedral deformation.

Since there are four possible [111] directions in the cubic structure, the

contraction can take place along different directions in different parts

of the crystal and a domain structure results. Again the lattices on

both sides of the domain boundaries are in a twin relationship and

6-fringes result [152]. In cobaltous oxide the lattice deformation as a result of spin ordering

is similar to that in barium titanate; the crystal becomes tetragonal the

c axis coinciding with one of the cube axes of the NaCl structure. Also

the anti-ferromagnetic domain structure is therefore analogous to the

ferro-electric domain structure in barium titanate [153]. Bright and dark field images due to domain boundaries in nickel oxide

are shown in Figure 68. It is easy to verify the properties of the 8-fringes

mentioned above.

3. Domains Due to Interstitial Ordering

The ordering of interstitial atoms or ions in body centered metals leads

to a domain structure as well [154]. The interstitials when occupying

for instance one family of octahedral interstices cause a tetragonal de- formation of the lattice, the c axis being along one of the cube directions.

Since there are three different families of octahedral interstices a tet- ragonal deformation can be caused along the three different cube direc- tions and therefore the formation of domains is again to be expected.

Domains have actually been observed in oxygen containing niobium

[154], in hydrogen loaded titanium [155] and in carbon containing tan- talum [156]. A detailed study of the fringe patterns, making use of the properties

mentioned above, allows to determine the complete geometrical characteristics of domian boundaries. Figure 69 summarizes for instance the

results of such a study for barium titanate [150]. Comparing the ob- served fringe patterns with this figure one can immediately determine the

orientation of the c axis in the two crystal parts, as well as the sense of sloping of the boundary plane. A similar analysis has been made for the

anti-ferromagnetic domain walls in nickel oxide [150].

237-323 0-67—32
528 TRACE CHARACTERIZATION

Figure 68. Bright (a) and dark field (b) image of the same boundary in nickel oxide. Notice that in the dark field image the outer fringes have both the same nature. The

contraction direction and the contact plane of the boundary have been determined, the resuh is shown by means of a stereographic projection. The black full dot represents

the contact plane and the open dot and cross the contraction direction [150, 151].

4. Ferromagnetic Domain Walls

Ferromagnetic domain walls can be revealed in the electron microscope as a result of "Lorentz contrast" [157]. The image consists of

either a bright or a dark line at the position of the wall (Fig. 70). It results from the "Lorentz force" exerted on the electrons by the magnetic field within the domains. Since the magnetic field changes sign at the domain

walls the sense of the deflection also changes and locally either con- vergence or divergence of the electron beam will result. If for a wall

causing convergence the focal plane of the microscope is located behind

the specimens an excess of electrons will be noted, i.e., one will observe

a bright line. If on the contrary the focal plane is located in front of the specimen an absence of electrons, i.e., a black fine will be noted.

The reverse will be true for a wall causing divergence. This mechanism

of contrast formation is shown schematically in Figure 71. Ferromagnetic domains can also be imaged by diffraction contrast. Due to the presence of the magnetic field within the domains the elec- trons are deflected and describe curved paths. The effect of this on the

intensities of the scattered and the transmitted beam is the same as if the crystal were deformed, the displacement being proportional to the

square of the distance from the entrance face [158], This equivalent
MICROSCOPY 529

GEOMETRY FRINGE PATTERN

(the diffraction vector is assumed

to be of the "right,, of XY )

• boundary nornnal plotted on upper hemisphere

direction of fourfold axis for port ® II II II II II II (m

Figure 69. Schematic representation of the fringe pattern in bright and dark field image

of a domain boundary in barium titanate. All possible configurations for {110} boundaries are considered. The top fringe is indicated as a full line and the bottom fringe by means of a dotted hne. The nature of these fringes is indicated by means of the letters B (bright) and D (dark). In all cases the diffraction vector is to the right of the hne XY. # Boundary normal plotted on upper hemisphere, Direction of fourfold axis for part I, Direction of fourfold axis for part II.

displacement is further of opposite sign for magnetic domains with

opposite magnetization. It was shown in [158] that this causes the rocking curve for the scattered beam to be different for beams passing

through domains with oppositely oriented magnetization vectors. The

rocking curves for the transmitted beam remain the same however.
530 TRACE CHARACTERIZATION

1MFigure 70. Sequence of ferromagnetic walls in cobalt. Stacking faults and dislocations are visible simultaneously. The domain walls are lying along the "easy" axis [0001]. Courtesy of Silcox.

Figure 71. Origin of black and white lines at magnetic domain walls, (a) In focus: no

contrast (b) Over focus: A is marked by a black hne, B by a white hne (c) Under focus: A is marked by a white line, B by a black line.
MICROSCOPY 531

As a result one finds that different domains show up with a different intensity in the dark field image, but not in the bright field image [158]. H. Other Planar Defects

The contrast effects due to more comphcated planar defects have

been studied as well. [159, 160, 161]. In crystals which exhibit polytypism the contact between two dif- ferent polytypes usually takes place along a planar interface parallel

to close packed planes. In zinc sulfide for instance the interfaces be- tween cubic (sphalerite) and hexagonal (wurtzite) parts and between

wurtzite and 4H regions have been studied [162]. Such interfaces are again revealed as fringe patterns with characteristic properties which

are different from those of stacking faults and of domain boundaries.

Very often planar interfaces overlap which gives rise to more comphcated fringe patterns. This is for instance the case for thin twin

lameUa. Methods have been worked out to distinguish thin twin lamella

from overlapping stacking faults [160]. The contrast effects associated

with overlapping domain waUs have been studied as well, both from the

theoretical and from the experimental point of view [161]. Such studies are necessary for a complete understanding of the sometimes very comphcated contrast effects observed in the electron microscope.

I. Direct Lattice Resolution

In a number of crystals the distances between planes of molecules

or atoms are large enough to be resolved in the electron microscope.

Menter [163] was the first to demonstrate this possibility with platinum

phthalocyanine crystals. In order to obtain an image of a periodic struc- ture it is necessary, by analogy to the Abbe theory of optical image

formation, that apart from the directly transmitted beam at least the

first order diffracted beam is allowed to pass through the selector aperture. It is the interference between these two beams which produces

the fringe pattern. The fringes are perpendicular to the diffraction vector of the diffracted beam used for imaging the lattice rows; they

have the same spacing as the corresponding lattice planes. It is easy

to demonstrate this experimentally by selecting only one beam; in this case the line pattern disappears. By admitting more high order dif- fracted beams a better resolution of the crystal lattice can theoretically

be achieved; usually however the contrast decreases.

The line pattern cannot be considered as just the projection of the

lattice rows. According to the dynamical two beam theory the inter- ference between the direct beam and the scattered beam produces

fringes which have the same spacing as the corresponding lattice planes,

however their position in space depends on the diffraction conditions,

and on the crystal thickness. The dark fringes therefore do not mark
532 TRACE CHARACTERIZATION

lines of maximum mass-thickness; there is a phase shift with respect

to such hues. This phase shift varies with s and with the crystal thick- ness. For a wedge shaped crystal with the fringes perpendicular to the edge of the wedge, one finds that black fringes change over into white fringes for a thickness change of 1/2 tg. In bent crystals where

the fringes are parallel to the axis of bending spacing anomalies occur. Also the fringe spacing is then different from the lattice spacing [164,

38, 165].

The resolution conditions for periodic structures seem to be less stringent than those for point to point resolution; it is therefore not completely fair to use lattice resolution as a test. With present day

microscopes even the (111) (2.35 A) and (200) (2.04 A) spacings of gold can be resolved as shown by Komoda [166].

It is clear that this technique opens the possibility for the direct

observation of the geometry of lattice planes around dislocations, in particular it becomes possible to reveal the presence of supplementary

half planes associated with dislocations. Figure 72 shows examples of such dislocations in tantalum pentoxide, where the fringes reveal the

superlattice spacing of about 35 A. The Burgers vector can in principle be determined directly as well in direction as in magnitude by imaging the dislocation using three different

families of lattice planes not belonging to the same zone. The deter- mination is based on the fact that the number of supplementary half

fringes associated with the dislocation is n=g-h. For a perfect dis- location n is an integer; this is not the case for a partial dislocation.

With three different non coplanar gj vectors one can determine the three

components nj — gj • b of the vector b. The sign of the dislocation is of course immediately evident. Stacking faults in planes intersecting the foil surface, as well as the fringe

system, are revealed by discontinuities in the fringes along a line seg- ment, the endpoints of which are the emergence points of the partial

dislocations. However considerable care should be taken not to inter- pret fringe anomalies resulting from buckling or from thickness changes

as being due to dislocations or stacking faults. With the constantly improving resolution of the electron microscopes

it is to be expected that this method will be extended to crystals with

smaller lattice spacing; the method will therefore presumably grow in importance.

J. Moire Patterns [167, 168]

r In cases where the lattice resolution becomes difficult to achieve,

because of the small interplanar distance involved, like in pure metals, one can in a sense artificially increase the spacing to be resolved by

making use of the "moire fringes" formed by two overlapping crystal

films.
Figure 72. Lattice fringes in tantalum pentoxide. Note the presence of dislocations and

sub-grain boundaries. Courtesy Spyridelis. The formation mechanism of moire fringes can be demonstrated by means of an optical analogue consisting of two superposed line gratings,

which differ either in spacing or in orientation [167]. Also both spacing

and orientation may be different. The moire pattern is in fact just the
534 TRACE CHARACTERIZATION

"coincidence" pattern of the two gratings. At regular intervals the

lines in the two gratings are in coincidence. The coincidence points

form again a line grating which has a larger spacing however and which

can therefore be resolved in the electron microscope (Fig. 73). For a moire pattern resulting from the superposition of two parallel

gratings (a so-called parallel "moire pattern") the fringe spacing Dp is given by

where di and dz are the line spacings of the superposed gratings.

For a moire pattern resulting from the superposition of two identical

gratings (i.e., di = d2 = d) differing only in orientation by an angle

(a so-called "rotation moire" pattern) the fringe spacing becomes

Dr = dl7}

For a general moire pattern where there is as well an orientation dif- ference as a spacing difference one finds for the moire spacing

D = dA{dr-d^2)^ld^ + i}^]-'l\

Also the orientation of the fringes is different in both cases. For a

parallel moire pattern the moire fringes are parallel to the lines of both

gratings; for a rotation moire pattern the moire fringes are perpendicular

to the average orientation of the lines in the two gratings.

Figure 73. Optical analog illustrating the formation of Moire fringes by superposition of two lattices. First row: parallel Moire pattern. Second row: rotation Moire pattern. Courtesy J. Menter.
MICROSCOPY 535

The moire fringes due to superposed crystals result from double

diffraction. The bright field image is formed by the interference be- tween the beam transmitted through both crystals and the beam scat- tered by both crystals. Let Ag = gi — g2 be the difference between the

operating diffraction vector in both crystal parts. In general Ag will be

parallel to the foil plane. For double diffraction to occur Ag must be

small. One can then show that there is a phase difference 27rAg • r between the doubly transmitted and the doubly diffracted beam (r is a position vector in the foil plane) [162].

It is obvious that this phase difference is position dependent. The

phase difference and hence the total transmitted intensity will be the same along lines for which Ag • r is constant. This equation represents

the fringes, which are straight lines perpendicular to Ag.

The spacing is further given by D= l/|Ag|. It is easy to verify that

this formula leads as well for the parallel moire as for the rotation moire

to the same expressions for the spacing as those given above and which were based on the optical analogue. From these formula we can con- clude that for a small difference in lattice parameter or for a small

rotation angle (in general for small Ag), the moire spacing may become

fairly large and easily resolvable in the electron microscope.

The first moire patterns were observed on sandwiches which were

generated by chance during the preparation of specimens of layer crystals. Bassett et al. [168], worked out a technique which allows to make

specimens in a reproducible way. The technique is based on the epi- taxial growth of metal films. A first metal film is epitaxially grown, e.g., on sodium chloride or on mica, a film of a second metal with a slightly different lattice parameter is grown epitaxially on the first metal film. The sandwich of metal films is then removed from the substrate and

used as a specimen. Such specimens produce parallel moire patterns.

Careful superposition of two films of the same metal leads to rotation

moire specimens. An example of such a moire pattern is shown in Figure 74; the sandwich consists of superposed layers of gold and

palladium.

A more recent approach consists in using a single crystal foil of a layer crystal (e.g., molybdenite or mica) prepared by cleavage, as a substrate for the epitaxial growth of metal films. Good systems are molybdenite with gold or silver. Usually the evaporation of the metal is performed in the microscope itself whilst the substrate is being ob- served [170]. Using the optical analogue one can readily show that an edge dislocation in one of the components of the sandwich will be imaged as an edge

dislocation in the moire pattern. In the case of a parallel moire the

supplementary halfplane in the moire pattern will be parallel to the

supplementary halfplane in the crystal as seen by the same diffraction vector. The reverse is not true however.

I
536 TRACE CHARACTERIZATION

Figure 74. Moire pattern from a sandwich of palladium-gold. The encircled areas contain dislocations. In this case two different operating reflections produce a two-dimensional dot pattern. Courtesy of Bassett, Menter and Pashley.

Ending moire fringes do not necessarily correspond to ending half- planes. Also screw dislocations will be imaged as terminating fringes.

The number of terminating fringes is, like in the case of lattice resolution, given by n=g • b. For a partial dislocation the fringes undergo

a phase shift at the intersection line of the associated fault plane and

the foil plane. The phase shift expressed as a fraction of the inter fringe

spacing is again given by g * b, where g • b is now fractional since b is not a lattice vector. It is clear that application of this remark allows

to determine the Burgers vector of dislocations in magnitude and in direction [168]. The determination becomes especially simple if one

uses multiple beam moire patterns imaging these different families of

lattice planes simultaneously.

Although very elegant and attractive, the technique is not generally

applicable because of the difficulty in specimen preparation. Also the

interpretation of moire patterns in terms of defects is not always obvious. More theoretical work is needed before the same level of inter- pretation, which is now possible in transmission electron microscopy,

will be reached.
MICROSCOPY 537

K. The Effect of the Presence of Defects on the Diffraction

Pattern

We shall only consider the effect of geometrical effects such as dis- locations, stacking faults and domain boundaries on the fine structure

of diffraction spots.

It was already reahzed by Hirsch and Whelan [171] that the presence

of even a single- stacking fault causes beam spHtting. More recently

the effect of single stacking faults, domain boundaries and dislocations on the fine structure of diffraction spots has been studied in detail both

from the experimental and from the theoretical point of view [172. 173].

For the planar defects the intensities and the geometry of the different sateUites were calculated for the two beam case taking into account

anomalous absorption [172], For stacking faults it was found that for small 5-values as well the transmitted as the scattered beam is split into three components, the main beam which remains at the same position

as in the perfect crystal, and a satellite beam on each side of it. For

large 5-values one of the two sateUites becomes much weaker than the

other so that effectively one satellite only will be observed. The s- dependence of the intensities and positions of the satellites are con- veniently represented in reciprocal space by means of the curves of Figure 75a and 75b. One of the asymptotes of these curves is perpendicular to the fault plane, the other one is asymmetrical with respect

to the normal on the foil plane. The positions of the satellite spots

around the scattered beam are found by intersecting the curve of Figure

75a. which has to be imagined centered on the reciprocal lattice node

point, by means of Ewald's sphere. The directions of the scattered

beams are then found by connecting the centre of Ewald's sphere with

the intersection points. The width of the shaded region around the curve is a measure for relative intensity of the three beams. From this curve we deduce that for large s-values apparently a rod of intensity

perpendicular to the fault plane is created.

One can use this remark to determine the sense of sloping of the fault plane from the relative position of the main spot and the sateUite with

respect to the center of the diffraction pattern. Once the sense of sloping is known one can determine the nature of stacking faults in face

centered cubic metals from the bright field image along [174]. For the transmitted beam one can similarly describe the beam splitting by means of the curve of Figure 75b which has to be thought around

the origin of reciprocal space. It is to be noted that both sateUites have now the same intensity independent of the value of s. It is clear that a close relationship exists between the fringe pattern

observed in the image and the fine structure of the diffraction spot. The

fringe pattern in the dark field image results in fact from the interference

between the different components of the scattered beam. Similarly
538 TRACE CHARACTERIZATION

ko

u

Figure 75. (a) Geometry and intensity of the satellites in the case of stacking faults. From this drawing the position and intensity of the satellites can be deduced as a function

of 5. The width of the cross hatched part along the hyperbola is a measure of the intensity variation as a function of 5, (b) Graphical representation for the positions of the

satellites around the transmitted beam. The widths of the cross hatched strip is a measure for the intensity variation.

the bright field image results from the interference between the different

components of the transmitted beams.

The effect of the presence of a domain boundary is to cause splitting of the scattered and the transmitted beams into four components. For

a discussion we refer to the original paper [172]. Finally the effect of dislocations is to cause fine streaking of the

diffraction spots in a direction perpendicular to the direction of the

dislocations [175]. Figure 76 illustrates some of the effects discussed here with observations made on single stacking faults. If many stacking faults are present in parallel planes their effect is to cause streaking along certain

reciprocal lattice rows perpendicular to the interfaces. Kinematical

theories have been developed for the X-ray case, assuming different types

of faults to be present. However these theories are inadequate for the

electron case because of dynamical effects. Much work remains to be done in this field before the streaking in electron diffraction patterns from faulted crystals can be interpreted

in detail. Combining the information derived from the different diffrac- tion patterns, with the results obtained from the image should be a fruitful approach capable of yielding a detailed description of the fault structure

of crystals. L. Discussion

Transmission electron microscopy has already acquired the status of a routine technique in materials science in general and in physical
539

Figure 76. Bright field image of stacking faults in steel (a) and the associated diffraction pattern (c). An enlargement of the selected area is given in (b). The diffraction pattern

(c) is in correct orientation with respect to (b). Insets 1, 2, 3 and 4 show enlargements

of the four spots. The two satellites at the transmitted and 'dynamical' spots are clearly seen in insets 2 and 3. In spot 1 and 4 only one satelhte is visible.

metallurgy research in particular. As further progress is made in the

interpretation of the contrast effects more and also more detailed in- formation can be gained. Like any other method it has obviously some

limitations. In the first place we have to be aware of the fact that we are working

with a thin foil and that as a consequence of this the results may not always be representative for bulk material. A striking example of this

is the difference in the habit of precipitates depending on whether the

precipitation takes place in the bulk or in a thin foil. Also the width of

dislocation ribbons depends on the foil thickness and when measuring

stacking fault energies this can introduce serious errors. With the use

of high voltage microscopes thicker specimens will be used and this drawback can be minimized. However the use of high voltage microscopes makes the application of two-beam dynamical theory more ques-
540 TRACE CHARACTERIZATION

tionable. The need for multiple beam calculations for a detailed

interpretation of the contrast becomes then more urgent.

Some materials are not stable under electron irradiation; such materials are obviously difficult to study by this technique. Here again

the situation may improve with the use of high voltage microscopes.

New developments, extending greatly the range of possible applications are being made at present: small angle electron scattering and

energy loss spectroscopy are two of them. This last technique may

become very useful for identification purposes. For the same purpose

X-ray fluorescence analysis can now be combined with transmission

electron microscopy to yield information of a chemical nature. One of the main advantages of the technique, its great resolution, turns out to be sometimes a drawback. One observes only small areas

of the specimen at a time, which may lead to "selected area interpretation". For this reason transmission electron microscopy is not a good technique to judge the quality of relatively perfect crystals. Here some of the X-ray mapping techniques, or even etching, is superior.

With improving resolution, methods based on direct imaging of the

lattice will presumably gain importance, also for the study of perfect

crystals.

VI. Acknowledgments

I would like to express my gratitude to those authors who supplied

me with photographs for use as illustrations in this article. In this connection special thanks are due to Dr. P. Delavignette who supplied

me with a large number of photographs.

I also wish to thank the Academic Press and North Holland Pubhshing

Company for their kind permission to reproduce illustrations.

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MICROSCOPY 541

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542 TRACE CHARACTERIZATION

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MICROSCOPY 543

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(1962).
544 TRACE CHARACTERIZATION

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MICROSCOPY 545

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ELECTRON AND OPTICAL MICROSCOPY

Contributed Papers and Discussion

HEINZ G. F. WILSDORF

Department of Materials Science

University of Virginia, Charlottesville, Virginia

L Introduction

My task, namely to discuss the contributed papers of this session,

has been made easy in that the contributions are very interesting and of excellent quahty. But before embarking on these discussions I would

hke to provide some focus on a few details related to the techniques

involved.

Three methods of analysis have been employed which singly or in combination have proven to give valuable results when applied to the

analysis of trace elements. They are : (i) microscopy, both light optical

and electron optical, (ii) x-ray and electron diffraction, and (iii) electron

probe analysis.

The usefulness of the light microscope is unchallenged and I rather

would like to dwell upon some features of the electron microscope.

Due to the properties of fast electrons this instrument has an inherent

theoretical resolving power of about 1 atomic distance as well as the

capability to enlarge an image to a size so that all the details can be

easily seen with the naked eye. R. D. Heidenreich reported recently [1] a resolution of two angstroms and his micrographs show indications of the atomic arrangements of carbon in the basal plane of graphite.

This result has been obtained by viewing the specimens in transmission. It should be remembered, however, that the observation of sur- faces by replica techniques will yield only a resolution of about 25 A. Obviously, then, preparation techniques for electron microscopy must

receive a great deal of attention in connection with our aim.

A case in point is the detection of small particles of a second phase

in a matrix. The image contrast in such a specimen can be caused

by the following effects: (1) mass-thickness effects, (2) diffraction contrast due to different reflections in matrix and particle, (3) phase changes

at the interface, (4) structure factor contrast, that is: different extinction

distances for the two substances, (5) production of Moire patterns due

' Figures in brackets indicate the literature references at the end of this paper. 547

237-323 0-67—33
548 TRACE CHARACTERIZATION

to geometrical effects at the interface, (6) strain contrast. Extensive

investigations have been carried out to determine the smallest particle

size visible, and the result indicates that the limit is about 40 A [2]. Now, I have to mention some features in electron microscopy which

have to be carefully taken into account when considering this method

for trace analysis. Firstly, I have to point out the interaction of beam

electrons with the substance to be analyzed. It is known that high speed

electrons lose about 10 eV when passing through matter due to electron

excitation and ionization. Although the energy provided by the elec- trons is too low for the displacement of atoms, it has been observed

that point defects in the specimen can be expected to move through

the lattice under the influence of the imaging beam. For our consideration this could mean a redistribution of point defects but no change in the overall impurity content. The above mentioned phenomenon will lead to two additional effects namely the heating of the specimen and the contamination of the speci- men. Due to the irradiation by electrons and the subsequent heating

effects, the decomposition of unstable solids can occur. The contamination of the specimen will occur because of the decomposition of hydrocarbons, which are available in the vacuum, so that the remaining carbon

will be deposited as a layer on the specimen.

I am proceeding now to the electron diffraction method and I will discuss a rather special case. The electron microscope also offers the opportunity to do electron diffraction after viewing the specimen

simply by changing the optical path of the electron beam in the instru- ment. This type of electron diffraction is referred to as "selected area diffraction." It is very helpful to utilize this technique for the

identification of the structure of the specimen which can be observed

at high magnifications in the instrument. However, due to the spherical

aberration of the lens system involved, slight changes of the area seen

in the microscope can occur for the electron diffraction study. Also

the distortion of the diffraction pattern is easily possible and while

the accuracy is suffering from one two-hundreds of a percent for small

orders of reflections, for high orders this error may amount to about 1%.

It is clear that this technique has to be employed with great care for precision measurements, and the standardization of the instrument

is mandatory.

Finally, I come to the electron microprobe. The actual instrument

will receive our attention in some of the contributed papers so that I would like to mention at this time only an attachment which can be

found already on one make of electron microscope. This microanalyzer

is based on the same scientific principle as the microprobe instrument

and allows the subsequent observation and analysis of the specimen

in the electron microscope. The range of analysis covers elements

with atomic numbers from 10-40 with the resolution of about two at
MICROSCOPY 549

an exposure time between 30-90 sec. The smallest area which can be

analyzed has approximately a diameter of 2 microns and the amount

of material to be detected is on the order of 10"^^ g. Of course, the

inherent resolution of the electron microscope is somewhat affected and

amounts to about 100 A.

II. Contributed Papers

The first contributed paper to be discussed is concerned with the

identification of defects in aluminum oxide which have been produced

by the bombardment of neutrons. The paper is offered by D. J. Barber

and N. J. Tighe of the National Bureau of Standards in Washington, D.C.

The analytical tool in this investigation was the electron microscope

using the transmission technique. The specimens, synthetic sapphire, were irradiated in the Oak Ridge Research reactor with a neutron dose

of 1.8 XlO^^ n.v.t. After cutting the specimens parallel to the basal

plane and chemical thinning, the discs were annealed in air for 6 hours

at temperatures ranging from 280 °C. to 1500 °C. Before turning to the discussion of the atomic defects, it is of interest to note the changes

of a bulk property with annealing time. The dependence of hardness

with annealing temperature for the neutron irradiated AI2O3 was deter- mined. It was shown that with increasing temperature the hardness

decreases until a temperature of 1350° has been reached and then the

hardness increases with further increase in temperature.

The as-irradiated specimens showed point defect clusters which with

increasing annealing temperatures condensed into voids and platelike

precipitates. Samples annealed at temperatures below 1200 °C. showed

vacancy and interstitial loops.

The strain caused by the point defect clusters and voids makes it possible for them to be seen by diffraction contrast in the electron microscope. After annealing the samples at temperatures of about 1300 °C,

dislocations started to climb but impurity pinning was also in evidence.

An interesting feature of the investigation was the observation of dis- location behavior when annealing specimens in the electron microscope.

The authors point out, however, that the behavior of specimens in the

hot stage is comphcated by the fact that point defects can be created

in the electron microscope through the electron beam at temperatures

of about 1500 °C. In summary one can state that the transmission technique of the elec- tron microscope is a powerful tool for observing minute defects caused

by neutron irradiation and that vacancy and interstitial clusters can be

distinguished from voids and precipitates. This information, of course,

is of importance when trying to interpret bulk properties as, for example,

the change of hardness with annealing temperature.

The next paper is an electron microprobe and electron diffraction analysis of surface replica extractions by W. B. Estill, M. M. Robertson,
550 TRACE CHARACTERIZATION

and G. H. Conrad of the Sandia Laboratory, Albuquerque, New Mexico.

Three techniques, the electron microprobe, electron diffraction and

electron microscopy are employed for the analysis of micro-contamination on surfaces and for sampling precipitates or particles in the matrix.

First we will discuss the sampling of micro-contamination on surfaces.

After selecting a suitable surface area using optical microscopy, a thin

plastic layer is cast onto this area and later on is stripped. The side of

the film which shows the extracted particles is then coated with carbon

by evaporation and subsequently, the plastic film is dissolved. After

suitable mounting the specimen is ready for analysis with the electron

microprobe. After the spectrum has been recorded with this instrument,

the identical area is viewed in the electron microscope and, following

this particular analysis, the electron diffraction analysis is made by the

selected area diffraction technique.

For sampling precipitates or particles which are contained in a matrix,

the usual extraction replica is taken and then scanned in the electron

microprobe. It is worthwhile to remember that during the scanning

of the electron beam a thin film of carbon is laid down on the specimen

surface. This film, of course, can be used as supporting film for the

electron microscope and electron diffraction study after the plastic film has been dissolved. In this way the contamination by the electron beam

during electron microprobe scanning can be converted into a beneficial

factor. The introduction of the electron microprobe study preceding an elec- tron microscope and electron diffraction investigation is of importance

since it provides information on the composition of the particles. The

combination of the chemical analysis as obtained by the electron microprobe plus the structure determination by electron diffraction and the

determination of the shape of the particles thus can yield a complete

analysis of the particles involved. This conclusion has been demonstrated in the paper by a number of typical examples, as for instance

the contamination of a surface by K2Cr207.

The paper by Charles Hays of the Franklin Institute Research Laboratories in Philadelphia, Pennsylvania and by Robert J. Gray of the

Oak Ridge National Laboratory, Oak Ridge, Tennessee, reports on some

methods for identification of microconstituents in metals and alloys

and the application of quantitative metallography. These methods

are of importance for determining the composition of phases in binary

alloys. Normally, the metallurgist uses a metallographic sample which

has been prepared by cutting, polishing, and etching. However, the

etching technique may introduce artifacts or change the individual

components of the alloy to some extent. Therefore, the authors pro- posed the following procedure.

Provided the secondary phase in the alloy can be attacked by chemical means, the analysis is aided by concentrating this phase through
MICROSCOPY 552

electrolytic extraction or chemical extraction or by mechanical extraction. Depending on the size of these microconstituents, different methods of direct analysis can be utilized. If the size of the particles

is less than 3 ^, electron microprobe instruments or efectron microscopy must be employed. For particle sizes between 4 and 25 /x hght

microscopy is useful and for particle sizes larger than 25 ijl Hght microscopic inspection and x-ray diffraction will be adequate. Table 1 Hsts

a number of additional characterization methods for this second phase.

Table 1. Methods of additional analysis for quantitative metallography.

1. Electron microprobe analysis

2. X-ray microscopy

3. X-ray fluorescence

4. Electrodeposition

5. Micro-radiography

6. Auto-radiography

7. Electron or x-ray diffraction

8. Spectroscopy.

Consequently, it is proposed that extraction techniques should be

utilized for concentrating a microscopic constituent following a suitable

selection of the analytical techniques. The authors have worked out equations which involve the observed area, the volume, and the density

of the microconstituents so that the weight percentage of one of the

components in the alloy mixture can be easily calculated.

As a special application they describe the characterization of carbide

inclusions in the nickel-molybdenum system. As their micrograph

illustrates, spheroidal inclusions are very frequent in this alloy and the

question was to determine whether these inclusions were MC, MeC,

M23C6, or some other complex. Using an extraction cell the carbide

inclusions were concentrated and subjected to an x-ray diffraction analysis. The results showed that the particles were carbides belonging to the structural type M^C. Following this, a spectrographic study was made which revealed the presence of molybdenum, iron, chromium and

vanadium. This suggested that molybdenum and iron were the prime

metallic components of these M^C carbides. K. F. J. Heinrich of the National Bureau of Standards, Washington,

D.C. gives a critical assessment of the determination of trace elements

by electron probe microanalysis. The author points out that the elec- tron microprobe is not a typical trace analysis technique but that it is a very powerful microanalytical technique. The use of the instrument for trace analysis will be successful if trace elements can be preconcentrated and a number of possibihties are listed. The questions which one would hke to ask when thinking of the elec- tron microprobe for the determination of trace elements are, for instance.
552 TRACE CHARACTERIZATION

which are the elements that can be detected, how large is the excited

specimen volume and what are the limits of detectability. The answers

provided are as follows: The elements that can be detected range from

boron to the transuranic elements. The excited specimen can have a volume from about one to ten cubic microns which means that the mass

of specimen analyzed is between 10~^*^ to 10~" g. The limits of detectability are given as 0.01-0.2%. This leads to the conclusion that for a

limit of detection of 0.01% an absolute amount of 10"^"^ to 10~^^ g can be

found. Finally it should be mentioned that the accuracy of the method

is from 2-10% of the amount present for major constituents.

It must be clear that in order to obtain results of such sensitivity, a considerable amount of work is needed for the preparation of samples.

The author observes that systematic investigations have not been undertaken as yet to optimize the experimental conditions for this type of

analysis.

The paper by W. C. McCrone, of McCrone Associates Inc., Chicago,

Illinois, also concentrates on one particular technique. The paper is entitled "Trace Analysis by Microscopy." In order to prevent confusion

between the terms microanalysis and trace analysis the author gives the

definition of these two terms at the beginning of his paper. Microanalysis involves the determination of the major component in a very

small sample, while trace analysis usually refers to the identification or determination of very small percentages of elements or compounds

in a relatively large sample. When using microscopy, it is important

to realize that the trace elements or trace constituents can exist in two

states of aggregation or, say, dispersion. Firstly, they can be uniformly

dispersed as a solid solution in a matrix or in a liquid, and secondly,

they can be dispersed as small discrete particles in a very large matrix.

If the trace elements are dispersed in a solid solution they ought to be

identified by detecting and measuring some chemical or physical properties of the molecules or ions. In general, a concentration procedure

has to be employed. For a dispersion of small discrete particles or

precipitates, of course, the actual characteristics of that phase can be

used for identification. When performing a trace analysis it is mostly required to determine

the percentage of the known trace constituent while the use of the

microscope often enables also the identification of the minute sample.

Hereby the microscope may be used only as the initial instrument and

additional techniques will have to be brought into play. The article deals first with the characterization and identification of subnanogram

samples. If one uses light microscopical methods subnanogram samples of ten microns down to two microns can be utilized. The weight

of these specimens is on the order of 10"^^ g. The electron microscope can make visible samples down to about 100 A and the samples then

have a weight of 10"^*^

g.

4
MICROSCOPY 553

The advantage of using the hght microscope is that a complete morphological analysis can be made and Table 2 lists the major features

Table 2. Observations by microscopy.

1. Shape

2. Surface Characteristics

3. Homogeneity

4. Transparency

5. Color

6. Birefringence

7. Refractive Index

that can be observed. Furthermore, the basic observations can be

complimented by the measurement of physical properties, such as the

measurement of density or melting point: other techniques for the

study of physical properties are x-ray diffraction, ultra-microspectrometry, x-ray fluorescence and microchemical tests; also microprobe

analysis and dispersion staining should be mentioned. Explanations

of all of these measurements are given in the paper and I will refrain

from giving a detailed account with one exception, namely, the dis- persion staining technique. This technique is suitable for small particles of any transparent substance. The method is based on the appearance

of very specific colors when the particles are dispersed in a particular

liquid of a certain refractive index. For this investigation the microscope is used in dark-field. The characterization and identification of dispersed trace constituents

involves first the concentration of a small sample of nearly pure material.

A great number of these techniques have been mentioned prior to this session and I will only refer to the author's account of some unusual

techniques such as ion exchange beads, electrophoresis on a single

fiber, or concentrations through biological procedures. For example,

the measurement of the growth rate of microorganisms as a function

of the amount of a required chemical substance in the diet can be used

for such a procedure.

Not always will it be necessary nor will it be possible to provide a concentration of the trace elements. In these cases, fluorescence and

radiography are two successful techniques which have been apphed

in the past. For radiography one distinguishes between auto- and in- duced radiography. Employing fluorescence techniques it is possible

to detect concentrations of I ppm. Using radiography, particles of nuclear debris one or two microns in diameter can be detected by an exposure on x-ray film. The paper shows convincingly that microscopy is indeed a very powerful technique for trace analysis, in particular, using the instruments in conjunction with other means of investigation.
554 TRACE CHARACTERIZATION

A paper entitled "Stacking Fault Studies in Silver Alloys" by A. W.

Ruff, Jr., of the National Bureau of Standards in Washington, D.C., dis- cussed measurements of the amount and energy of stacking faults in a face-centered-cubic material. The geometrical properties of stacking

faults were first reviewed. The importance of stacking faults rests primarily on the properties of (111) glide dislocations which extend to form two partial dislocations and a stacking fault ribbon. The motion

and interaction of dislocations may be greatly modified by this extended

configuration. It is, therefore, of fundamental importance in studying

the properties of dislocated materials to know accurately the stacking

fault energy y. For alloy materials it is established that y depends in general on solute concentration. Measurements of this variation in

silver-tin solid solution alloys are reported in this paper. Two different methods of measurement were employed. The most

direct method involved the technique of transmission electron microscopy where threefold extended dislocation nodes were directly observed

and measured. The second technique utilized the effect of stacking

faults on the x-ray diffraction pattern from the alloy materials. Using

both techniques, the absolute values of y and their dependence on solute concentration were determined and compared.

Figure 1 shows examples of dislocation nodes from four alloys as observed in the electron microscope. These samples were plastically

deformed a few percent before examination at 100 kV. The details of

.-i^ - ^ a \y* d

Figure 1. Faulted dislocation nodes observed by transmission electron microscopy in aUoys containing (a) 0, (b) 2, (c) 4, and (d) 6 at. % tin in silver. M = 130,000.
MICROSCOPY 555

the observation and correction procedures have been given elsewhere

[3]. It is seen that the amount of node extension (i.e., the size of the

central faulted region) increases with increasing solute concentration.

According to theory [4], the radius y of a circle inscribed within the

faulted region and the stacking fault energy y are related as yy= Gh^ifiv. a, e). Here G is the shear modulus, bp the partial dislocation Burgers vector,

and (/? is a function of variables of the dislocation problem. The stack- ing fault energy y was found to decrease as the amount of tin increases

in the alloys. The quantitative results are shown in Figure 2 by the curve marked Nodes, determined for six different alloy compositions. These

results were compared with those from other silver alloys and good

agreement was found. It was pointed out that each electron micrograph examines only about 10~^^ cm^ of material and the techniques

of sampling are crucial if large systematic errors are to be avoided.

The x-ray diffraction measurements were performed on the same alloys

but in different form. Two types of samples were studied: powders

obtained from filings produced at room temperature, and bulk bar

specimens that were plastically deformed in compression. The change

in the Bragg diffraction angle (A2^) that occurs after plastic deformation can be related to the stacking fault probability a according to theory

[5] as follows,

a=f(eukl)^2e.

Here the function f{6) contains variables of the diffraction problem.

The fauk probabiUty a can be interpreted physically as the reciprocal

of the interplanar spacing between completely faulted layers. Measurements on the silver-tin alloys [6] revealed that a increased smoothly

with solute concentration in both types of samples. It was also possible to determine the dislocation density in the samples by further

x-ray analysis or by direct electron microscope observation. An ex- ample of the observed microstructure is shown in "Figure 3 for the 6

at.% alloy. Then using a particular model of the diffracting defect,

the stacking fault energy y can be calculated as y = Kpla.

Here a is the fauk probabiUty, p the dislocation density, and K includes

various constants of the problem. Figure 2 shows the resuks obtained

in this way for the two types of x-ray samples. It was emphasized that ah three curves shown were determined independently in absolute value. The x-ray resuks for the filed samples agree fairly well wkh the dislo-
556 TRACE CHARACTERIZATION

I I I I I I I I I I I 0 2 4 6 8 10

Atomic Percent Tin Figure 2. The stacking fault energy determined for silver-tin alloys.

Figure 3. Transmission electron micrograph of dislocation structure in compressed x-ray specimen of 6 at. % tin. M = 200,000.

cation node results for low and high tin concentrations. The agreement

for intermediate values of solute concentration is not as good. The

results for the bulk compressed samples diverge considerably at low

tin concentrations; the reason for this difference is not yet clear. Further study using these and other measurement methods should improve

the knowledge of the stacking fault energy in these materials.

The last paper is concerned with the identification of defects in oxides

using transmission electron microscopy. The paper is by N. J. Tighe

and A. Hyman of the National Bureau of Standards, Washington, D.C.
MICROSCOPY 557

The substance investigated here is aluminum oxide, using two different

types of this material, the analysis of which is given in Table 3. The

specimens were cut up into discs 50-70 ^ in thickness, and finally

thinned by ionic bombardment.

Table 3. Analysis of two alumina samples.

AI2O3

Sample A: Purity 99.8%

Impurities: Mg 0.15%;

Si 0.03%; Ca 0.004%; Fe 0.002%

Sample B: Purity 99.7%

Impurities: Na20 0.10%;

Fe.Os 0.10%; SiO. 0.05%;

K2O 0.05%

Transmission electron microscopy yielded significant differences

between the alumina designated A and B. While for alumina A the

usual grain boundaries were observed and little or no evidence of impurity precipitation could be found, the grain boundaries in alumina B

were irregular, and impurity precipitates and voids within the grains were clearly visible. This investigation provides further evidence that transmission electron microscopy of alumina can easily reveal important

differences due to impurities between specimens.

III. Discussion

In opening the general discussion. Dr. Newkirk remarked that there were several contributed papers in which the term x-ray microscopy was used. This may introduce a little confusion unless x-ray topography is mentioned at the same time and the two terms are clearly dis- tinguished. To one school x-ray microscopy means projection x-ray microradiography. That is not a diffraction method at all. And to another school x-ray microscopy means diffraction topography in which

the original image is not really magnified at all so that it is not really

microscopy, yet the term has come to mean that occasionally. We

should distinguish between x-ray topography and x-ray microradiography

or x-ray microscopy.

J. B. Wachtman (NBS) asked Dr. Estill whether the technique that he

described appears to be one capable of handhng nanogram samples.

A speaker earlier in the conference had pointed out the great difficulty

in handling very small samples as opposed to the difficulty of analyzing

them. The technique which Dr. Estill described in the context of a particular application to surface contamination might, however, be a way of handling very small specimens in general. Dr. Estill indicated
558 TRACE CHARACTERIZATION

that he had not made any calculations on the sensitivity of the method

but that this method presumably would fall in the category of trace

analysis.

When asked to comment on the microprobe. Dr. Heinrich stated that

it has to be realized that electron microprobe analysis is not a single

method. So the limits, depending on the particular technique, are very

wide. However, the instrument can analyze in many instances a single

layer of atoms and, considering the amount of material that is contained

in one square micron of the single layer of atoms, this is indeed an ex- treme micro-method. Concerning the manipulation of instruments, one of the advantages of the method is that the sample can be analyzed

in situ. The rapporteur called upon W. C. McCrone to add any comments

on microscopy. Dr. McCrone emphasized the importance of the elec- tron microprobe and pointed out that it combines both trace analysis

and microanalysis. Actually a trace analysis can be made on an ultra- micro sample. In favorable circumstances when everything is lined up

beautifully, analyses can be made of single particles less than 1 fx in diameter for trace elements.

J. B. Wachtman noted that specimens have to be exceedingly thin to be used for transmission electron microscopy. He asked Dr. Amelinckx

to comment on this, and also on the question of what opportunity the new high voltage microscopes offer in the use of thicker specimens, and

whether this higher voltage carries with it the danger of damage to the

specimen.

Dr. Amelinckx commented as follows: First of all, as to the thickness

of the specimens, this depends solely on the type of specimen, specifically on the Z value of the element involved. With aluminum,

specimens of 1 /u thickness can be used with a 100 kV electron microscope. However, with uranium you are restricted to 400 to 500 A. Of course, the specimen thickness is important in that the technique

in certain cases has severe limitations. You have to be aware of the

fact that you are working with a thin specimen and sometimes the behavior of these specimens is not the same as that of the bulk specimens.

As a concrete example, precipitation phenomena appear to be different

in thin foils in comparison to bulk specimens. Also, surface effects become important. For instance, to measure stacking fault energy as shown by Dr. Ruff, you use dislocation ribbons. Then you have to be aware of the fact that, on account of the thin specimen, the repulsion

forces between these dislocations are not the same as they would be

in the bulk material. Consequently, if one does not correct for the

presence of the surface, an error will be made.

Dr. Amelinckx referred to the second question on how can the situa- tion be improved. One way of doing it is, of course, to use high voltage

microscopy, say at 1 MeV instead of 100 kV. There is a practical limit
MICROSCOPY 559

in the sense that whereas you still gain in resolution by going to 1 MeV,

this rapidly levels off and there is not much point in going beyond 1.5 MeV. Although one still gains in penetrating power there is again a

leveling off and a compromise will have to be made somewhere between

500 kV and 1 MeV. Another consequence of high voltages, of course,

is the fact that you create radiation damage. By calculation we can

easily see that for 1.1 MeV the threshold for the displacement of a metal

atom by electrons is reached, assuming about 25 eV as the displacement

energy. Radiation damage then limits again the high voltage that can

be used.

Moreover, the interpretation of the micrographs becomes more diffi- cult. Two beam situations are necessary if you want to analyze diffrac- tion contrast phenomena quantitatively. As you go to higher voltages

the Ewald sphere becomes flatter and flatter and it becomes increasingly more difficult to realize two beam situations. And so we are in need

of multiple beam calculations and these are more difficult to perform

than two beam calculations. These are a few advantages and drawbacks of using high voltage electron microscopy.

IV. References

[1] Heidenreich, R. D., The Bell System Technical Journal XLV, 651 (1966).

[2] Ashby, M. F., and Brown, L. M., Phil. Mag. 8, 1649 (1963).

[3] Ruff, A. W., Jr., Kves, L. K., Acta Met. (in press).

[4] Brown, L. M., and Tholen, A. R., Discussions Faraday Society 38,35 (1964).

[5] Paterson, M. S., J. Appl. Phys. 23, 805 (1952).

[6] Newton, C. J., and Ruff, A. W., Jr., J. Appl. Phys. 37, 3860 (1966).
r
APPENDIX 1. CONTRIBUTED PAPERS*

ELECTROCHEMICAL METHODS

BIEDERMANN, George, NEWMAN, Leonard, OHTAKI, Hitoshi. Determination of Traces of Protolytic Impurities. Department of Chemistry, The Royal Institute of Technology, Stockholm, Sweden. GIERST, L., NICOLAS, E., VANDENBERGHEN, L., BIRKE, R. L. Characteristics and Potentiahties of the Chlorite Catalytic Wave for Trace Analysis. Free University

of Brussels, Brussels, Belgium.

JOYCE, R. J.. WESTCOTT, C. C. Evaluation of Mercury Film Electrodes for Trace

Analysis of Reagent Grade Chemicals by Stripping Analysis. Beckman Instruments,

Inc., Fullerton, California. MARK, Harry B., Jr. Application of the Catalytic Polarographic Behavior of Certain Metal Complex Systems to Trace Analysis. Department of Chemistry, University of Michigan, Ann Arbor, Michigan.

MAIENTHAL, E. June, TAYLOR, John K. Apphcation of Cathode-Ray Polarography and Anodic Stripping Voltammetry to Trace and Micro Analysis. NBS Institute for Materials Research, National Bureau of Standards, Washington, D.C. PARRY, E. P., OSTERYOUNG, R. A. Apphcation of Pulse Polarography to Trace and

Micro Analyses. North American Aviation Science Center, Thousand Oaks, California. PHILLIPS, Sidney L. Adsorption Electroanalysis. IBM Corporation, Poughkeepsie, N.Y. RECHNITZ, G. A. Ion-Specific Electrodes as Tools for Trace Analysis. Department of Chemistry, State University of New York, Buffalo, New York. ELECTRICAL MEASUREMENTS

BULLIS, W. Murray. Use of the Hall Effect in Trace Analysis of Semiconductors.

Institute for Applied Technology, National Bureau of Standards, Washington, D.C. MOULDER, John C, CLARK, Alan F., GNIEWEK, John J. Measurement of Effective Electronic Purity by the Eddy Current Decay Method. Institute for Materials Research,

National Bureau of Standards, Boulder, Colorado. SMAKULA, A. Dielectric Properties and Defects in Single Crystals. Crystal Physics

Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts. SPARKS, L. L., POWELL, R. L. Metals Characterization by Low-Temperature Thermoelectric Methods. Institute for Materials Research, National Bureau of Standards,

Boulder, Colorado. OPTICAL AND X-RAY SPECTROSCOPY

ADAMS, P. B., NORTH, C. H. Definitions of Some Terms Pertinent to Trace Analysis.

Corning Glass Works, Corning, N.Y., and National Lead Company, South Amboy, N.J. ADAMS, P. B., PASSMORE, W. O., CAMPBELL, D. E. The Determination of Trace Elements in Glasses and Refractory Materials by Flame Emission and Atomic Absorption

Spectroscopy. Corning Glass Works, Corning, N.Y. *These papers were available for discussion at the Symposium but are not included in

this summary volume. Pubhcation rights remain with the authors who will make their own arrangements for pubhcation in the scientific literature. (See also Preface.) 561
562 APPENDIX

ABLER, Seymour J. The Determination of the Rare Earths in SoHd-State Laser Materials. RCA Laboratories, Princeton, N.J. CAMPBELL, Wilham J., SPANO, Ernest F., GREEN, Thomas E. Micro and Trace Analysis

Using Ion Exchange Resin-Loaded Papers and X-Ray Spectrography. U.S. Department

of the Interior, Bureau of Mines, College Park Metallurgy Research Center, College

Park, Maryland.

CHAPLENKO, G., LANDON, D. O. Microspark Spectroscopy in Trace Analysis. Spex

Industries, Inc., Metuchen, N.J. ELFERS, Lawrence A. Flame Photometric Determination of Stable Cesium in Environ- mental Media. Radiological Health Research Activities, Robert A. Taft Sanitary Engineering Center, Cincinnati, Ohio. FASSEL, Velmer A., GOLIGHTLY, Danold W. Detection Limits of the Elements in the Spectra of Premixed Oxy-Acetylene Flames. Institute for Atomic Research and Department of Chemistry, Iowa State University, Ames, Iowa. HOBBS, D. J., REES, Barbara J. Confident Trace Analysis Above and Below the "Limit

of Spectrographic Detection. Johnson, Matthey & Co. Limited, Wembley, Middlesex,

England.

RIGDON, Lester P. The Determination of Impurities in Elemental Boron by X-Ray

Fluorescence. Lawrence Radiation Laboratory, University of California, Livermore,

California. CUNNINGHAM, J. L., RYAN, J. R. Trace Characterization of Refractory Materials by

Laser Spectroscopy. Harbison-Walker Refractories Company, Garber Research

Center, Pittsburgh, Pa. SVOBODA, V. High Purity Material Analysis Using Optical Fluorescence Excited by a Continuum Radiation Source. Institute for Research, Production and UtiHzation of Radioisotopes, Prague, Czechoslovakia. VUKANOVIC, Vladimir M., GEORGIJEVIC, Vida M. The Use of External Magnetic

Fields in Spectroscopic Analysis of Traces in DC Arc. Institute of Physics, Belgrade,

Yugoslavia.

WALTERS, R. M., COSGROVE, J. F., BRACCO, D. J. X-Ray Excited Optical Fluores- cence in the Analysis of Trace Rare Earths. General Telephone and Electronics Laboratories, Inc., Bayside, N.Y. WINEFORDNER, J. D. Atomic Fluorescence Flame Spectrometry. University of

Florida, Gainesville, Florida. WINEFORDNER, J. D. Use of Signal-to-Noise Ratio Theory as a Simple Means of Optimizations of Experimental Conditions and Estimation of Limits of Detection in Flame Spectrometric Methods of Analysis. University of Florida, Gainesville, Florida. X-RAY DIFFRACTION

BURLEY, Gordon. Improved X-Ray Atomic Scattering Factors: Effect on the Detection

of Point Defects and Trace Quantities. Institute for Materials Research, National Bureau of Standards, Washington, D.C. DESLATTES, Richard D., PARETZKIN, Boris. Trace Characterization for Strain by

Double Crystal Topography. Institute for Materials Research, National Bureau of Standards, Washington, D.C. van GOOL, W. Materials Characterization by Means of Predominant Defect Situations.

Scientific Laboratory, Ford Motor Company, Dearborn, Michigan.

INOUYE, Tamon, NAGAMI, Hatsutaro. Application of Fourier Analysis to X-Ray Stress Measurement. Central Research Laboratory, Tokyo Shibaura Electric Co., Ltd., Kawasaki, Japan. PRICKETT, Robert L., VAHLDIEK, Fred W. A High Temperature Single Crystal X-Ray

Camera. Air Force Materials Laboratory, Wright Patterson AFB, Ohio.
APPENDIX

OPTICAL METHODS

563

BAKER. John A. Calibration of Impurities in Silicon by Infrared Spectroscopy. Dow

Corning Corporation, Hemlock, Michigan.

CHANG, Te-Tse. Electron Spin Resonance Absorption as an Analytical Tool Exemplified

by the Study of Several Ions in Rutile (Ti02). National Bureau of Standards, Washington. D.C. LORIMOR. O. G.. SPITZER. W. G.. WILLARDSON, R. K.. ALLRED. W. P. Characterization and Concentration Determination of Impurities in Semiconductors from Infrared Local Mode Absorption. University of Southern California, Los Angeles, Cahfornia and Bell and HoweU Research Center, Pasadena, California. CHEMICAL SPECTROPHOTOMETRY

BURRELL. D. C. Trace Elements in Marine Waters by Atomic Absorption Spectro- photometry. Institute of Marine Science. University of Alaska, College. Alaska. CHENG. K. L. Spectrophotometric Determination of Microgram and Submicrogram Amounts of Silver with Thio-Michler"s Ketone. Department of Chemistry, University

of Missouri at Kansas City, Kansas City, Missouri. DODSON. E. M. Some Problems in the Assessment of Trace Impurities in Highly

Refractory Electronic Materials with Particular Reference to Single Crystal Ruby and

Sapphire for Maser and Laser Use. National Physical Laboratory, Teddington, England.

LUDW ICK. J. D. Dual Atmospheric Tracers Utilizing the Fluorescence of Fluorescein and Calcium Acetylsalicylate. BatteUe Memorial Institute, Pacific Northwest Laboratory. Richland. Washington.

LUKE. C. L. Spectrophotometric Determination of Vanadium in Steel. Bell Telephone

Laboratories. Inc.. Murray Hill, N.J. MENIS. Oscar. BURKE. R. W., RAINS. T. C. Evaluation of Absorptiometric Methods

for the Determination of Nanogram Quantities of Elements in High-Purity Materials.

Institute for Materials Research, National Bureau of Standards. Washington, D.C. ROSS. H. H. Precision Photometric Analysis Using a ^-Excited Isotopic Light Source.

Analytical Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee. NUCLEAR METHODS

DEYRIS, M., REVEL, G., ALBERT, Ph. Le Dosage de I'Oxygene dans I'Aluminium

par Radioactivation. C.N.R.S., Centre d'Etudes de Chimie Metallurgique, \ itry. BLOURI. J.. CHAUDRON. Th.. ALBERT. Ph. Le Dosage par Radioactivation Neutroni- que du Soufre et de Quelques Elements Mineraux dans le Carbazole Purifie par Zone

Fondue. C.N.R.S. Centre d'Etudes de Chimie Metallurgique, Vitry et Centre d'Etudes

et de Recherches de Chimie Organique Appliquee, Thiais, France. ENGELMANN, Ch. Analyses de Tres Faibles Traces d'Elements Legers dans les Materiaux de Tres Haute Purete par Activation dans les Photons y et les Particules Charges. Centre d'Etudes Nucleaires de Saclay, France. ERICKSON. N. E., KRISHNAN. S. S.. PERKONS, A. K. Neutron Activation in Forensic

Investigations. The Attorney General's Laboratory, Province of Ontario, Toronto, Canada. FISHER. D. E., RANCITELLI, L., LAWRENCE, J. F., CURRIE. R. L.. BERKEY. E. Some Recent Work on Instrumental Activation Analysis of Meteorites. Cornell University, Ithaca, N.Y. HOLM. Dale M., SANDERS. Wm. Mort. Interference Reduction and Sensitivity Improve- ment in Activation Analysis. University of California. Los Alamos Scientific Laboratory. Los Alamos, New Mexico.

237-323 0-67—34
564 APPENDIX

KRAMER, Henry H., HAMPTON, W. J., MOLINSKI, Victor J., WAHL, Werner, H. Geographic Characterization of Chromium Ore Deposits by Elemental Analysis. Union

Carbide Corporation, Sterling Forest Research Center, Tuxedo, New York. KRAMER, Raymond A. Characterization of Trace Amounts of Carbon in Aluminum.

Aluminum Company of America, Alcoa Research Laboratories, New Kensington,

Pennsylvania.

KRUGERS, Jan. Thickness Measurement of Metal Coatings with Radioisotopes. Hewlett-Packard Company, Palo Alto, California. LANDGREBE, A. R., PELLA, P. A., MCCT ENDON, L. T., DE VOE, J. R. The Application of Substoichiometric Radioisotopic Dilution Principles to Control Potential Coulometry and Solvent Extraction. Institute for Materials Research, National Bureau of Standards, Washington, D.C. LEDDICOTTE, George W. Ultratrace Element Research in the Life Sciences Using

Activation Analysis. Research Reactor Facility, University of Missouri, Columbia,

Missouri. NAGY, L. G., GIBER, J. Adsorption Effects in the Neutron Activation Analysis of High

Purity Ge, Si and Ga for Trace Impurities. Polytechnical University Budapest, Budapest, Hungary.

PERRY, K., AUDE, G., LAVERLOCHERE, J. Improvement of the Sensitivity in 14 MeV Neutron Activation Analysis. CEA-Department des Radioelements, Centre

d'Etudes Nucleaires, Grenoble, France. PIERCE, T. B. Experience with Analytical Methods Based on the Measurement of Prompt

7-Radiation Emitted During Charged-Particle Irradiation. Atomic Energy Research

Establishment, Didcot, Berks, England.

PILLAY, K. K. S., MILLER, W. W. Characteristic X-Rays from (n, y) Products and

Their Utilization in Activation Analysis. The Pennsylvania State University, University

Park, Pennsylvania.

ROBERTSON, D. E., PERKINS, R. W. Trace Elements and '^'Cs in Sea Water by

Gamma-Ray Spectrometric Techniques. Batelle Memorial Institute, Pacific Northwest

Laboratory, Richland, Washington.

ROSENBAUM, H. S., ARMIJO, J. S. Fission Track Etching as an Analytical Metallo- graphic Tool. General Electric Company, Vallecitos Atomic Laboratory, Pleasanton,

California. SMITH, Gilbert W., BECKER, Donald A., LUTZ, George J., CURRIE, Lloyd A., DE VOE,

James R. Determination of Trace Elements in Standard Reference Materials by

Neutron Activation Analysis. Analytical Chemistry Division, National Bureau of Standards, Washington, D.C. STATNICK, R. M., SCHMIDT-BLEEK, F. Identification of Less Than 10« Molecules

Via Radio-Gaschromatography. Department of Chemistry, Purdue University,

Lafayette, Indiana. TOLGYESSY, J., KONECNY, J., BRAUN, T. Ion-Exchange Membranes in Radiochelatometric Titrations of Traces of Metals. Slovak Technical University, Bratislava, Czechoslovakia and L. Eetves University, Budapest, Hungary.

YULE, Herbert P. Instrumental Reactor Neutron Activation Analysis Studies on 72 Elements Per Sample. Texas A & M University, College Station, Texas. MASS SPECTROSCOPY

BOURGUILLOT, R., CAVARD, A., CORNU, A., STEFANI, R. Analysis of Traces in BeryUium and Uranium by Spark Source Mass Spectrometry. Commissariat a I'Energie

Atomique Centre d'Etudes Nucleaires de Grenoble, Grenoble (Isere), France. DESJARDINS, Michel. Trace Impurity Analysis by Spark Source Mass Spectrometry.

Corning Glass Works, Corning, New York.
APPENDIX 565

DOAN, Arthur S., Jr. Existence of Metal Carbide Molecules in Vapor State. Lewis Research Center, National Aeronautics and Space Administration, Cleveland, Ohio. OBLAS, D. W., BRACCO, D. J., YEE, D. Y. Trace Analysis in Oxidic Matrices by SoHds Mass Spectroscopy. General Telephone & Electronics Laboratories, Inc., Bayside, New York. PAULSEN, ?. J., BRANCH, P. E. Electronic Analog Computer for Measuring Intensity Areas on Mass Spectrographie Plates. Spectrochemical Analysis Section, National Bureau of Standards, Washington, D.C. STROCK, Lester W., OBLAS, Dan. Spark Source Mass Spectrometer Analysis of Refractory Metals. Sylvania Lighting Center, Danvers, Massachusetts, and General Telephone and Electronics Research Laboratory, Bayside, New York.

PRECONCENTRATION, SAMPLING, AND REAGENTS

ALVAREZ, Robert. Eiectrodeposition of Trace Constituents as a Preconcentration Technique for Optical Emission Spectroscopy: Deposition of Silver from Zinc Solution. Spectrochemical Analysis Section, National Bureau of Standards, Washington, D.C. BERSIN, Richard L., HOLLAHAN, John R., HOLLAND, Waher D. Apphcations of Excited Gases to Trace Characterization. Research and Development Department,

TRACERLAB/WEST, Richmond, California. BURNETT. Wilham T., GOOD, Glenn, CARROLL, Nuala, COHAN, Morton D. An

Evaluation of an Original, Plastic, Paper Disk Anion Column. Department of Chemistry,

The Lousiana State University, Baton Rouge, Louisiana. FREEMAN, David H., KUEHNER, Edwin C. Preparation of Ultra-Pure Reagents.

Institute for Materials Research, National Bureau of Standards, Washington, D.C. HILL, John H., MORRIS, C. J., FRAZER, Jack W. Cathodic Etching to Prepare Metals

for Oxygen Determination. Lawrence Radiation Laboratory, University of California, Livermore, California. / JOYNER, Timothy, HEALY, M. L., CHAKRAVARTI, D., KOYANAGI, T. Preconcentration for Trace Analysis of Sea Waters. Bureau of Commercial Fisheries, Biological Laboratory, Seattle, Washington.

KANEKO, Hisamitsu, KOBAYASHI, Hiroshi, UENO, Keihei. Application of Zone Melting Process to the Metal Chelate Systems. Department of Organic Synthesis, Faculty of Engineering, Kyushu University, Fukuoka, Japan. MUKHERJI, Anil K. The Ring Oven Technique in Microanalysis. Drexel Institute of Technology, Philadelphia, Pennsylvania.

O'LAUGHLIN, J. W., HANSEN, R. K., HOFER, R. J., BACHMAN, R. Z., BANKS, C. V. Determination of Trace Impurities in Pure Rare Earth Metals and Oxides by Spectro- photometric and Atomic Absorption Methods. Institute for Atomic Research and Department of Chemistry, Iowa State University, Ames, Iowa. ROBOZ, John. Preconcentration Techniques in the Mass Spectrometric Analysis of Trace Impurities in Inorganic Gases. Air Reduction Company, Inc., Central Research

Laboratories, Murray Hill, New Jersey. SKOGERBOE, R. K., MORRISON, G. H. The Role of Samphng in Trace Analysis. Cornell University, Ithaca, New York. WEST, Foymae Kelso, WEST, Philip W., IDDINGS, Frank A. Adsorption Characteristics of Traces of Silver on Container Surfaces. Coates Chemical Laboratories and

Nuclear Science Center, Louisiana State University, Baton Rouge, Louisiana. YATES, John T., Jr., MADEY, Theodore E. Chemisorption on Atomically Clean Surfaces. Institute for Basic Standards, National Bureau of Standards, Washington, D.C.
566 APPENDIX

ELECTRON AND OPTICAL MICROSCOPY

BARBER, D. J., TIGHE, N. J. Identification of Defects in Oxides by Transmission Electron Microscopy I. Radiation Damage in ALO.i. Institute for Materials Research,

National Bureau of Standards, Washington, D.C. ESTILL, W. B., ROBERTSON, M. M., CONRAD, G. H. Electron Microprobe and Electron Diffraction Analysis of Surface Replica Extractions. Sandia Laboratory, Albu- querque, New Mexico. HAYS, Charles, GRAY, Robert J. Some Methods for the Identification of Microconstituents in Metals and Alloys and the Application of Quantitative Metallography.

Franklin Institute Research Laboratories, Philadelphia, Pennsylvania and Oak Ridge

National Laboratory, Oak Ridge, Tennessee. HEINRICH, Kurt F. J. Electron Probe Microanalysis and the Determination of Traces. Spectrochemical Analysis Section, National Bureau of Standards, Washington, D.C. McCRONE, Walter C. Trace Analysis by Microscopy. McCrone Associates, Inc., Chicago, Illinois. RUFF, A. W., Jr. Stacking Fault Studies in Silver Alloys. Institute for Materials Research, National Bureau of Standards, Washington, D.C. TIGHE, N. J., HYMAN, A. Identification of Defects in Oxides by Transmission Electron Microscopy. II. Study of Polycrystalline ALOs. Institute for Materials Research,

National Bureau of Standards, Washington, D.C.
APPENDIX II. SYMPOSIUM COMMITTEES

TRACE CHARACTERIZATION

Chemical and Physical

W. Wayne Meinke, General Chairman

Roger G. Bates, Assistant General Chairman

Program Committee

Bourdon F. Scribner, Chairman

Harry C. Allen Marvin Margoshes

Richard D. Deslattes Oscar Menis James R. DeVoe Robert L. Parker Hans Frederikse Eho Passaglia David H. Freeman John K. Taylor John B. Wachtman, Jr. Arrangements Committee

John K. Taylor, Chairman

William D. Dorko Thomas J. Murphy

Rolf A. Paulson

Social Program Committee

David H. Freeman, Chairman

Robert Schaffer David K. Snediker Tours Committee

James R. DeVoe

Ladies' Hospitality Committee

Mrs. W. Wayne Meinke

^ ^ Honorary Hostesses

Mrs. Roger G. Bates

Harriet L. Frush, Chairman

Mrs. Joseph C. Richmond

Mrs. James I. Shultz Mrs. Jon J. Spijkerman

Mrs. Robert S. Tipson

Finance Committee

Roger G. Bates, Chairman

Thomas B. Hoover John K. Taylor

INDEX

A

Absorption, atomic {see Atomic

absorption)

Absorption spectrophotometry (see Spectrophotometry)

Absorptivity, molar. 231

Accelerator source, use of, 341

Acid, purification of, 396, 421

Acid, storage of. 425

Activation analysis, 307 accuracy and precision, 326 charged particle. 320. 344

computer- techniques in, 345

detection limits, 311, 315, 318, 319,

321, 339

errors in, 339

fast neutron, 316, 340

high energy photon, 317, 320. 342

instrumentation for, 325 prompt radiation, 322

slow neutron, 310, 337

steps in, 309

Activation energy, effect of impurity

on, 36

Activator, role of, 17 Adsorption, losses by, 424

role of surfaces in, 36

Air, contamination from, 390

Alizarin, complexes of, 225

Alkali halides. color centers in, 16

dislocation in. 429

etching on, 452

evaporation spirals on, 449

Alkaline earths, determination of, 256

Alloys, electrical measurements of, 74 Aluminum, cross slip in, 508 Aluminum grain growth, effect of impurities on. 29, 31 Aluminum oxide, electron diffraction study of, 549

identification of defects in, 556 Aluminum purification, resistivity in, 44 Aluminum silver alloys, stacking faults

in. 513 Ammonia, purification of, 396

Analysis, criteria for methods of, 121, 144

Anisotropic materials, dislocations in, 174 Anomalous x-ray transmission, impurity effect on, 193

intensity mapping, 171 Antiferromagnetic domain boundaries, 527 Antiphase boundaries, and stacking

fauhs, 493

Arc, detection limits in, 134

evaporation in, 133

excitation in, 130

ionization in, 132 Arsenate, determination of, 235

Ashing, low-temperature, 420

preconcentration by, 411 Atomic absorption, 266 assessment of, 280

atomizers for, 270 Beer-Lambert law in, 279

burners for, 275 compared to flame emission, 129 continuum sources in, 274

detection limits in, 164, 282

discharge lamps in, 274

flame in tube, 276

flames for, 268, 277

furnace for, 163, 267, 305

future of, 283

hollow cathode lamps for, 272, 278

hollow cathode sputtering in, 271

matrix effects in, 280 microwave sources for, 275

monitor for, 306 monochromators in, 273

vaporization for, 267, 271 wavelengths for, 279 Atomic fluorescence, 284, 295

burners for, 289 continuum sources for, 292

detection hmits in, 149, 293

discharge lamps for, 291

equations for, 287

future of, 297

instruments for, 289 microwave sources for, 291

selectivity of, 292

sources for, 291

types of, 286 569
570 INDEX

Atomic scattering factors, 206 Atomic substitution in crystal, 204

Atomizers, for atomic absorption, 270

Autoradiograms, to test homogeneity, 387 B

Background, in emission spectrometry, 150

in mass spectrometry, 351, 355 Barium titanate, domains in, 524, 527, 529 Beer-Lambert Law, 231, 279 Bend contour, 475

Berg-Barrett method, in x-ray intensity

mapping, 167 BerylHum, determination of impurities in, 377

ductiUty of, 24 BerylHum oxide, impurities in, 185

Biological materials, electrical measure- ments of, 74

Birefringence, 467 Boltzmann equilibrium (see Maxwell- Boltzmann equihbrium)

Boron, determination of, 345 Borrmann effect, 472

in x-ray intensity mapping, 171 Bragg angle transmission, 171 Bragg reflection law, 471 Bulk methods, role in dislocation observation, 455

Burgers circuit, 432

Burgers vector, 432

direction determination for, 479

length determination, 483

sense determination of, 433, 483

Burgers vector method, for loop character, 522 C

Cadmium sulfide, helical dislocation

in, 178 Moire patterns of, 190

impurity doped, 180

thermally stimulated current curves

for, 66

x-ray diffraction topograph of, 180 Calcein blue reagent, 256

Calcium, determination of, 222 Camera, x-ray single crystal, 205 Capacitance measurement, doublelayer, 105

Carrier distillation, 409

Cartesian Diver system, 208

Catalytic current polarography, 88, 113

Catalytic wave polarography, 112

Cavities, causes of, 516

Characterization, definition of, 5

for microconstituents, 550 importance of, 37 importance of defects in, 204

in situ, 211

types of, 6 Charged partical activation, 320

detection limits, 321 Chelate cage reagents, 222

Chelating agents {see Complexes)

Chemical equilibria, in flames, 124, 269 Chemical reactions in solids, 29 Chromatography {see also Ion-exchange)

separation by, 406, 407 Chromium chloride, stacking faults in, 503 Chronoamperometry, 90^ Chronocoulometry, 94 Chronopotentiometry, 90 Chmb dislocation, 465 Climb rate technique, for stacking

fault energy, 508

Co-activator, in phosphors, 18 Cobalt nickel aUoys, stacking faults in, 508

Cobaltous oxide, domains in, 527

Color centers, in alkali halides, 16 Complexes, clathrate, 222

eff'ect of pH on, 219

extraction with, 402

for fluorimetry, 254

in preconcentrations, 396 masking by, 397 mixed, 224

steric hindrance in, 221

ternary, 224 Computers, in activation analysis, 326, 345

Concentration method {see Separations)

Conductance, electrolytic, 104 Conductivity {see also Resistivity), 71 Conductometric titrations, high fre- quency, 104 Contamination, from air, 390 from electron irradiation, 548 from laboratory ware, 391, 394

in sampling, 388
INDEX 571

Continuum sources, in atomic absorption, 274

in atomic fluorescence, 292

Contrast, at dislocations, 477

at slip traces, 508

at stacking faults, 493 caused by planar defects, 531 from ferroelectric boundaries, 524

in x-ray diffraction topography, 171, 172, 174

Coordination number, of ions, 224 Copper decoration, 178

in silicon. 464

Copper, determination of, 229, 304

oxidation of, 30 Copper gallium alloy, nodes in, 506

stacking faults in, 493, 495, 496 Copper gold alloy, boundaries in, 494

Coprecipitation, reagents for, 400

separation by, 398

Corrosion reactions, 32, 37

Cottrell interaction, 437, 455

Coulometric titration, 93 Coulometry, 92

galvanic analysis, 95

of surface layers, 92

stripping analysis, 96

thin layer, 92

Coulostatic analysis, 95

Crystal chemical fit, of foreign atom, 205

Crystal defects {see also Point defects) electron microscopy of, 430, 431 methods of observation of, 427, 469 Moire pattern method, 430

Crystal distortion, by impurities, 194

effects on x-ray images, 173

Crystal growth, role of dislocations in, 428

Crystal striations, by x-ray topography, 187, 188

Crystals, decoration methods for, 455, 464-466

defects in, 204, 207, 427

diffusion in, 24, 25

effect of dislocations in, 21 Moire patterns from, 535

stacking faults in, 490, 492, 498

x-ray diffraction study of, 165

x-ray topographs of, 206

yield point of, 21 Cyclotron, in activation analysis, 321

D

Decoration, of dislocations, 175, 204, 429, 455

Defect chemistry, 207

Defect clusters, 512

detected by electron diffraction, 549

Defects, by optical phenomena, 212

effect on diffraction pattern, 537 importance in characterization, 204

in crystals, 204, 207, 427

in oxides, 556, 557

point, 381

types of, 6, 204, 205

visibility of, 174 Deformation, studied by decoration methods, 467

studied by etch pits, 452

Delta fringes, properties, of, 525

Density, Cartesian Diver system for, 208

reference material for, 208

Density-sensitive defect properties, 208

Derivative dilution technique, 331

Desorption, in storage of solutions, 393

Detection hmits, activation analysis, 311,

315, 317, 319, 321, 339

atomic absorption, 164, 282

atomic fluorescence, 149, 293

contrasted to "sensitivity", 158

definition of, 153, 154

effect of parameters on, 153, 154, 159, 160

electrochemical, 75

electron microprobe, 552

electron spin resonance, 214

emission spectroscopy, 134, 162, 163

fluorimetry, 259 improvement by replicate determinations, 156, 157

infrared spectroscopy, 212, 213

polarography, 76, 80, 88

spark source mass spectrometry, 351 spectrophotometry, 232

stripping analysis, 98

trace analysis methods, 418

x-ray diffraction, 185, 206

x-ray fluorescence, 143

Detector, electrical, in mass spec- trometry, 383

lithium drifted, 325 phase sensitive, 86

scintillation, 325
572 INDEX

Dielectric constant, measurement of, 71

Diffraction characterization, of stacking

faults, 493

Diffraction pattern, effect of defects on, 537

Diffusion, effects of dislocations in, 24-27

x-ray camera for studies of, 205 Discharge lamps, in atomic absorption, 274

for atomic fluorescence, 291

Dislocation densities, effect of, 21

Dislocation loops, causes of, 513

definition of, 433 energy of, 510

Dislocation theory, role in crystal growth, 428

survey of, 431

Dislocations, arrays of, 443 chmb, 465

decorated, 175

definition of, 431 energy of, 437

extended, 442

force on, 437

forces between, 440

grain boundary, 443

helix, 178 inchned, 487

in corrosion, 32

internal methods for, 429

in whiskers, 467 movement of, 438

multiplication of, 440

observation of, 450, 453, 455, 477, 538

one-dimensional, 204

partial, 441

point defect, 509, 510

postulation of, 428

ribbon, 442, 501

screw, 479

seen end on, 487

stacking faults in, 554

surface methods for, 429, 447

tilt and twist types, 443, 444

undercoated, 178

x-ray condition for disappearance of, 174 Displacement function., 435 Displacement vector, 431

determination of, 497

Distillation, from solution, 411

separation by, 409 Domain boundaries, 524, 527, 538

Double crystal method, in x-ray intensity mapping, 168

lattice variations by, 187

Ductility of metals, effect impurities on,

24, 25

Dust, contamination by, 390 E

Eddy-current method, for resistivity measurement, 57, 72 Edge dislocation, 431 Edge-on method, to determine loop character. 520 Edge ribbon stacking fault, energy for, 505

Electrical measurements, applications of, 42, 65, 66, 73, 74

characteristics of, 40 combined with other techniques, 48 fundamentals of, 50

role in trace characterization, 39, 42

types of, 70

Electrical properties, effect of impurities

on, 7, 40

effect of oxygen on, 74 Electrochemical methods, adsorption, 113

applicability of. 111 comparison of, 105

detection limits, 75

future of, 105

selectivity of, 119

Electrodes, for stripping analysis, 115

glass, 102, 103, 117

impurities in graphite, 136

in potentiometry, 101, 102 membrane, 103

specific ion, 103, 117, 119 Electroluminescence, impurity interactions in, 18

Electrolysis, separation by, 101, 399, 419

Electrolytic conductance, 104

Electron density map, 195 Electron diffraction, 469, 471, 548

analysis of surface contamination by, 550

effects of defects on, 537

Electron microprobe, 143, 551 amount of sample for, 558

detection limits, 552

Electron microscope, resolving power

of, 547
INDEX 573

Electron microscope-microanalyzer, 548

Electron microscopy, analysis of surface contamination, 550

contrast in, 508, 547

crystal defect studies, 430, 468

direct lattice resolution by, 531

dislocation study by, 430

effect of voltage in, 539, 558, 559

fringe interpretation in, 532

identification of defects in oxides by, 556, 557

in trace analysis, 548

limitations of, 539 Moire patterns in, 430, 532

radiation damage in, 559 specimen preparation for, 470

stacking faults by, 554

status of transmission, 538, 539, 547

study of crystal imperfections by, 468, 469

thickness of specimen in, 558

Electron spin resonance, detection

limits, 214

impurity measurement by, 213 Emission intensities {see Intensities) Emission spectroscopy, 121, 149

detection limits in, 134, 162, 163

in study of GaAs, 49

precision in, 145. 146

Errors, in sampling and analysis, 422 Etch patterns, information to be ob- tained from, 32, 453 Etch pit formation, compared to growth and evaporation spirals, 452

Etchants, for specific crystals, 455, 456

Etching, effect of solution impurities, 452

role in dislocation observation, 429, 450

Evaporation, role in dislocation geometry, 429

Evaporation spirals, resolution of, 450

role in dislocation observation, 449

Ewald's sphere, 471 Extended nodes, 504

Excitation error vector, 471

Extinction contour, in transmission elec- tron microscopy, 474

Extraction, separation by, 402, 421

Extraction techriiques, for microconstituents, 551

Extrinsic fault, 491

F

Ferroelectric domains, 524

Ferroelectric polarization, causes of, 524

Ferroelectric transition temperature, 524 Ferromagnetic domain walls, 528 Ferromagnetic resonance, effect of impurities on, 19

Field ion microscope, study of dislocation

bv. 431 Film growth on solids, 30

Fission tracks, studied by etch pits, 455 Flames, burners for, 275, 289 chemical equihbria in, 122, 123, 269 comparison of emission and absorption spectra in, 129

excitation in, 122, 123

for atomic absorption, 268, 276, 277

higher temperature, 129, 130

in tubes, 276

ionization in, 122, 123

nitrous oxide-acetylene, 278

vaporization in, 268

Fluorescence, atomic {see Atomic fluores- cence)

delayed, 245

effect of parameters on, 243-246

energy transfer in, 258

inner-filter effect in, 246

lifetimes in, 239 mechanism of, 239, 250 quantum efficiency of, 243 quenching of, 243, 244, 245

x-ray excited, 150

Fluoride, determination of, 225, 234

Fluorimetry, assessment of, 259 compared to spectrophotometry, 252

detection limits in, 259

future of, 266

instruments for, 247

reagents for, 252, 253, 256

with atmospheric tracers, 304

Fourier analysis, of powder diffraction line

profiles, 205

Fracture problems, studied by etch pits, 455 Frank sessile loops, 492 Frank-Read source, 440

in silicon, 464

Fringe contrast, due to ferroelectric boundaries, 524
574 INDEX

Fringe interpretation in electron microscopy, 532

Fringes, produced by stacking faults, 496 FS/RH rule, for Burgers vector conventions, 433 G

Gallium arsenide, detection limits in, 213

determination of purity of, 48 mass spectrum of, 353 Gallium phosphide, effect of impurities

in, 18 Gallium purification, resistivity in, 44

Galvanic analysis, 95 Gamma activation, 319, 320 Gamma ray spectra, resolution of, 325

Gases, analysis of, 421 Geometrical method, for loop character, 517 Germanium, determination of impurities

in, 213

dislocations in, 21, 192

effect of impurities in, 194

effect of oxygen on, 74

Hall effect measurement of, 62

impurity distribution in, 45-47

lithium doped, 192

precipitation of Cu in, 30

x-ray diffraction pattern from, 182

Glass electrodes, 102

specific ion, 102, 103, 117 Glassware, cleaning of, 395

contamination from, 391, 393

Glide plane, 431

Glissile loop, 435

Gold, resistivity of, 12, 13 stacking faults in, 508, 514

Grain boundaries, types of, 443

Grain growth, effect of impurities on, 29

Grinding, of powders, 390

Graphite, Burgers vector determination

in, 482

dislocation pattern, 503

impurities in, 136

loops in, 513, 519

stacking fault energy in, 523 Growth spirals, in crystals, 428

role in dislocation observation, 447 H

Halides, determination of, 104

Hall effect, 73 apparatus for, 60

application of, 62

description of, 52

in semiconductors, 61

in study of GaAs, 48

voltage measurements, 60

Helical dislocations, causes of, 516

Hermetization, of laboratory operations, 390 Hollow cathode lamps, for atomic absorption, 272, 278

multi-element, 273

of high intensity, 279

sputtering in, 271 Homogeneity {see also Inhomogeneity) methods for attaining, 387

of reference materials, 370

Hydrochloric acid, purification of, 396, 421

Hydrofluoric acid, purification of, 396

I

Ilkovic equation, 76 Image contrast, in electron microscopy, 547

in x-ray diffraction topography, 174 Image formation, at prismatic loop, 481

Imperfections, due to trace impurities, 179

types of, 6, 7 Impurities, as a cause of bulk stress, 188, 189

clustering, 193

effect on dislocations, 175

effect on electron density distribution, 195

effect on intensity of x-ray diffraction, 191

effect on phase stability, 198

effect on properties, 18. 19, 40, 347

effect on solid state reaction kinetics, 199

effect on x-ray diffraction, 165, 166

effect on x-ray transmission, 193

lattice variations from, 186

role in physical effects, 211, 212

Impurity distribution, by resistivity, 46

Impurity segregation, x-ray topography of, 182

Inclination contour, 475 Indium selenide, loops in, 511
INDEX 575

Infrared spectroscopy, detection limits in, 212, 213

trace analysis by, 212, 213 Inhomogeneity {see also Homogeneity)

effect on detection limit, 159

in solids, 387

Insulators, electrical measurements on,

51, 52, 65

Intensities, calculation of emission line, 123

effect of temperature on emission line, 125, 126

Intensity mapping, in x-ray diffraction topography, 166

Interstitial impurities, effect of, 19

in solids, 26

Interstitial ordering, domains due to, 527

Intrinsic fault, 491

Iodide, determination of, 232

Ion exchange {see also Chromatography) 420 membrane electrode, 103 Ion fluctuations, in spark source, 367, 370

Ionic conductivity, effect of point defects

on, 14

of KCl, 15

role of, 14

Ions, energy distribution in mass spec- trometry, 361

Iron, ductility of, 24

Irradiation, as a cause of point defect

clusters, 511 production of centers by, 34

Isotope derivative technique, 331

Isotope dilution, applications of, 330

in mass spectrometry, 384

in radiochemical analysis, 328

substoichiometric, 329

Isotope displacement technique, 332

Isotope measurement, in mass spec- trometry, 357

Isotopic methods, in mass spec- trometry, 384

in radiochemical analysis, 328, 420

Isotropic materials, dislocations in, 174 K

Kikuchi lines, determination of excitation error by, 473 L

Laser probe, analysis with, 150

Lattice expansion, caused by x-irradiation, 188

Lattice variations, double crystal method for, 187 from impurities, 186 Lead, effect of impurities in, 23

electrical measurements on, 73 Lead sulfide, defects in, 9 Ligands {see Complexes)

Light elements, determination of, 318, 321, 343

Lithium, dopant in germanium, 192 Lithium fluoride, birefringence in, 467

etch pattern on, 452

Loops, determination of character of, 516, 517-519

Lorentz force, contrast source in electron microscopy, 528 Luminescence, effect of impurities and

defects on, 17M

Magnesium, determination of, 223 Magnetic properties, effect of impurities

on, 18 Masking in preconcentration, 397 Mass spectrograph, double focusing, 349

transmission stability of, 359 Mass spectrometry {see Spark source mass spectrometry) Mass spectrum, molecular, 381

of gallium arsenide, 353

Materials sciences, growth of, 5 Maxwell-Boltzmann equilibrium, in flames, 123 Mechanical properties, effect of impurities

on, 19

effect of oxygen on, 22 Metal ions, specific electrodes for, 103, 117 Metallography, quantitative, 550

Metals, effects of impurities on, 10, 23

electrical phenomena in, 12

point defects in, 12

resistance ratios for, 59 Methods of analysis, criteria for, 121, 144

Microanalysis, defined, 551

with electron microprobe, 143

witi^ laser probe, 150

with spark, 150 Micro-contamination, analysis of, 550
576 INDEX

Microprobe {see Electron microprobe)

Microscopy {see also Electron microscopy,

Optical microscopy)

radiography and fluorescence techniques

for, 553

Microstrain measurements, 206 Microwave-powered lamps, 275, 291 Moire patterns, in electron microscopy,

430, 532

in x-ray diffraction topography, 189, 208 Molybdenum, transition temperatures of, 14 Mossbauer eff'ect, evaluation of, 320 N

Neocuproine, as spectrophotometric re- agent, 222 Neutron activation {see Activation analysis) Neutron generators, 316 Neutron irradiation effects, 549

Neutrons, fast, 316, 317

thermal, 310 Nickel-molybdenum, inclusions in, 551 Nickel oxide, domains in, 527 Niobium, domains in, 527

Nitrogen, determination of, 345

Noise, causes and effects of, 154 Nomenclature, in trace analysis, 152 Non-destructive methods, 211, 318 Nuclear methods, other than activation, 327, 346

types of, 307 Nuclear reactor, in activation analysis, 310 O

Optical methods, role in dislocation observation, 428

Optical microscopy, advantages of, 553

trace analysis by, 552

Optical phenomena, in trace characterization, 211

role of impurities in, 211

Optical properties, of solids, 15

Oscillatory contrast, in dislocation images, 487 Oxide layer, determination of, 92

Oxides, analysis of, 378

identification of defects in, 556 Oxygen, determination of, 322, 343, 344

effect on mechanical properties, 22

segregation in silicon, 182

P

Palladium-gold, Moire pattern of, 535

Partial dislocations, 441 Pendellosung method, 196, 207, 208

Permeability of iron, effect of nitrogen

on, 19, 21 Phase changes, effects on properties, 204 Phase sensitive detectors, in polarography, 86 Phase stability, influence of impurities

on, 198 Phenanthroline complex, 227

Phosphate, determination of, 233, 235 Phosphorescence, mechanism, of, 239

triplet states in, 242 Phosphorimetry, instruments for, 247 Phosphors, effects of impurities in, 17 Photographic emulsion, mass calibration

of, 360, 380 mass sensitivity of, 359

reciprocity of, 359

Photographic process, effect of chemical

impurities in, 33

Photograpjiy, reduction of fogging in, 355

Physical effects, role of impurities in, 211

Piezoelectric ettect, 71 Planar defects, 531

Plastic deformation, point defects by, 511

Plastic vessels, contamination from, 393 Platinum vessels, contamination from, 393

Point defects, 509-511

strain produced by, 549

study of, 12

x-ray detection limit for, 206

Poisons, in phosphors, 18 Polarography, adsorption effects in, 88

alternating current, 85

catalytic current, 88, 113

catalytic wave, 112 cathode ray, 114

classical, 76

derivative, 79

derivative pulse, 82

detection hmits, 76, 80, 88 elements determined by, 115

intermittant, 78

pulse, 80, 116

radiochemical, 86

radiofrequency, 84

square wave, 84

Tast, 78
INDEX 577

Polygonization. tilt boundan^ formation. 445

Potentiometry, direct. 101

null-point. 103

trace acidity by. 118 Powders, grinding of. 390

Precipitates, size determination of. 181

strain cross section of. 180

Precipitation, phenomena, 27

reagents for, 400, 402

separations by, 398

Preconcentration {see also Separations) methods for. 150

Prismatic dislocation. 435

Prismatic loops, 518

decoration methods, 467 image formation at, 481 Prompt radiation activation analysis, 323

Properties, effect of impurities on, 347

relation to composition. 7 Pulse height analyzer, use of. 326

Purification, of reagents. 395. 396

of water, 395

resistivity measurement in. 44

Purity, measure by resistivity. 12 Q

Quantum efficiency, of fluorescence. 243

Quartz, color centers in. 188

impurities in. 188 Quartz vessels, contamination from, 393 Quenching, for point defect clusters, 510 R

Radiation effects, in electron microscopy,

559

in sohds, 33 Radiochemical analysis (see also Activation analysis) non-isotopic. 331

separations in. 323

using tracers, 327 Radiofrequency polarography, 84

Radioisotopes, in study of contamination, 393 Radiometric titration, 333

Radiopolarography, 86 Radioreagent technique, 331

Radiorelease technique. 332 Rare earths, trace analysis of, 421

Reaction kinetics, influence of impurities

on, 199 Reagents, chelate cage, 222

for coprecipitation, 402

for fluorimetry, 252

for precipitation. 400

for preconcentration. 404

for spectrophotometry, 219, 220

purification of. 395, 421

storage of. 425

Reciprocal lattice. 471 Reference materials {see Standard refer- ence materials) Refractory metals, analysis of, 378

Relative sensitivity coefficient, 362

Residual resistivity, 44, 50

apparatus for, 57 Resistance ratios, of metals, 12, 59

Resistivity, effect of impurities on, 72 low temperature. 10. 11 of copper, 10. 11, 12

of gold, 12

of insulators, 51

of semiconductors. 50

of water, 43 temperature effect on, 71

Resistivity measurement, 45, 47, 71 AC method for, 55 apparatus for, 53 apphcation of, 43 by capacitive couphng, 55 by eddy-current, 57

Resistivity probe, 54, 55

Resistivity ratios, monitoring purity by, 59

of metals, 12

Resistivity scan procedure, 54

Resolution, improvement by Moire pat- terns. 534

in electron microscopy, 531, 532

in mass spectrometry, 356 Ribbon dislocation, 501 Ruby, analysis of, 304S

Saha equiUbrium, in flames, 124 Samphng, contamination in, 388

errors in, 422. 424

of inhomogeneous sohds, 387

Sapphire, analysis of, 304 Scanning transmission methods, in x-ray

intensity mapping, 169
578 INDEX

Screw dislocation, 431, 479 Screw ribbon, stacking fault energy for, 505

Selenium, determination of. 294

Semiconductors, characterization of, 9

effect of impurities in, 9

electrical measurements on, 51

electrical properties of, 7

Sensitivity, contrasted to "detection

limit", 158

Sensitivity coefficients, in mass

spectrometry, 362, 379

Separation methods, future of, 413

Separations (see also Preconcentration)

by chromatography, 406 by electrolysis, 101, 399, 419 by extraction, 402, 421 by ion-exchange, 420 by precipitation, 398 by volatihzation, 409, 420 by zone melting, 412

concentration factor of, 419 masking in, 397

radiochemical, 323

recoveries in, 419 Shockley partials, 442, 502

Silica gel, purification of, 421

Silicon, birefringence in, 467 copper decoration in, 464

detection of oxygen in, 181 determination of impurities in, 212

dislocation-free, 193

dislocations in, 429

donors and acceptors in, 8

effect of oxygen on, 22

Hall effect, measurements of, 62 oxygen banding in, 182

precipitation of Li in, 27

surface layers on, 35

thickness contours in, 475

x-ray topographs of, 175

Silicon carbide, etch pattern on, 451

Silver, determination of, 227, 303

sulfiding of, 30

Silver alloys, stacking faults in, 554

Silver bromide, dislocations in, 429

Silver-indium alloys, stacking faults in, 502

Slip traces, contrast at, 508 Sodium hydroxide, purification of, 396

storage of, 425

Sorption, in storage of solutions, 393

Spark, analysis with micro, 150

surface analysis by, 138 Spark source, ionization pattern in, 360

secondary products in. 352 Spark source mass spectra, molecular, 381 Spark source mass spectrometry, 348 accuracy of, 358, 377, 378 background in, 351, 355

capabilities of, 348 computer use in, 381

detection limits, 351

effect of gases in, 358

electrical detection in, 349, 383 emulsion calibration in, 360

energy distribution of ions in, 362

factors affecting, 351, 372

future of, 373

integration of intensity in, 360

ion charge distribution in, 381

ion fluctuations in, 370

ion samples in, 362

precision of ion measurements in, 366

quantitative, 358, 382

relative sensitivity in, 361

resolving power of, 356 sample handhng in, 378 sample homogeneity in, 366, 370 sample volatility in, 379

selective ion transmission in, 379

sensitivity coefficients for, 362, 382

standards in, 371 suppression of fogging in, 353

Specific ion electrodes, 102, 117, 119

Spectrofluorimetry (see Fluorimetry, Fluo- rescence) Spectrograph resolving power, effect of, 159 Spectrographic analysis (see Emission

'spectroscopy)

Spectrophotometry (see also Fluorimetry,

Fluorescence)

amplification reactions in, 232

applications of, 304

catalytic reactions in, 233 compared to fluorimetry, 252

detection limits in, 232

future of, 237

high-precision, 305 masking in, 230

radioactive Hght sources for, 305

reagents for, 219

selectivity of, 217
INDEX 579

sensitivity of reactions, 230

ternary complexes in, 224

Spin ordering, effect of, 527

Stacking fault energy, climb rate tech- nique for, 508

for tetrahedron technique, 508 measurement of, 501 Stacking fault fringes, 496

Stacking fault method, for loop character, 521 Stacking fauks, 441, 490

antiphase boundaries, 493

determination in crystals, 498, 554

effects on electron diffraction, 537

types of, 490

x-ray diffraction topography of, 179 Stacking fault tetrahedra, 514 Standard reference materials, homogeneity of, 363, 370, 382

in mass spectrometry, 362, 382 need for, 326, 371, 383

Statistics, tor "not detected" results, 157

Steel, determination of vanadium in, 304

Steric effects, in complexes, 221, 256

Storage of reagents, 425

Strain, caused by traces, 205

role in x-ray images, 173

Stress, caused by impurities, 188

Stress field, 437

Stripping analysis, 96

detection limits, 98

electrode for, 115

reverse electrolysis in, 100

Structural defects, survey of, 431

types of, 6 Structural interstices, 204

Structural transformation, 24

Structure determination, historical survey of, 428

Structure factors, determination by

Pendellosung fringes, 196 Subboundary geometry, decoration methods for, 465

Sulfuric acid, storage of, 425

Superconductors, effects of impurities

in, 14 Surface methods, in dislocation observation. 447

Surfaces, analysis of, 92, 138, 150, 550

cleaning of, 424

properties of, 35

T

Tantalum, domains in, 527 Tantalum pentoxide, lattice fringes in, 532 Tarnish reactions, 30

Tast polarography, 78 Teahte, boundaries in, 495

Tellurium, determination of, 294 Temperature, effect of flame, 126

Tensile strength, effect of impurities on, 23 Tetrahedron technique, for stacking fault energy, 508 Thermally stimulated currents, analysis

by. 63 Thermoelectric effect, 71 Thermoelectric power, apphcation of, 73 Thickness contour, 474

Tilting method, to determine loop character, 520

Tin disulfide, oscillatory contrast of, 487

Titanium, domains in, 527 Titanium dioxide, transition metals in, 214

Titration, coulometric, 93 Topographical methods, in x-ray diffraction, 166 Topography, two-crystal, 206 Trace analysis, defined, 152, 552

function of, 207 symposium on, 2 Trace analysis methods, detection hmits, 351 Trace characterization, books on, 2

definition of, 118 requirements for, 1, 69 Trace impurities, in highly perfect crystals, 180

relation to properties, 7 Tracer methods, evaluation of, 333

Tracers, radioactive, 327

use in research, 334

Transformation in solids, types of, 24-28

Transition probabilities, determination of, 131 Triga reactor, use of, 316 U

Uranium, determination of, 88

determination of impurities in, 377
580 INDEX

V

Vacancies, in solids, 26 Van de Graff generator, 321 Vanadium, determination of, 304

Vaporization, losses in, 412

Volatilization, in arc, 131 separations by, 409 Voltammetry, 88, 114W

Washing, of laboratory ware, 395 Water, analysis of, 303, 421

determination of iodine in, 331

purification of, 395, 421

purity of, 43

storage of, 425 Whiskers, dislocations in, 467

properties of, 21 Wurtzite, stacking faults in, 501 X

X-ray atomic scattering factors, 206

X-ray diffraction, camera for, 205

detection limits, 206

dislocation decoration in, 175 impurity effect on, 166, 193

relevance to trace characterization, 203

stacking faults by, 554

X-ray diffraction intensity, effect of impurities on, 191 X-ray diffraction topography, assets and

limitations of, 199

contrast in, 171, 182

crystal striations by, 188

detection hmits, 185, 206 images in, 173

intensity mapping in, 166 methods in, 165, 166 Moire patterns in, 189

stacking faults by, 179

stereo, 178

traverse (Lang) topographs, 171 X-ray fluorescence spectroscopy,

analytical curves in, 141 combined with electron microscopy, 540

detection hmits, 139 X-ray intensity measurements, 206, 208

X-ray microscopy, terms in, 557

X-ray spectra, theory of excitation, 139 Xylenol orange, as spectrophoto- metric reagent, 235 Y

Yield point, effect of impurities on, 21 Yttrium iron garnet, effect of impurities

in, 19 Z

Zinc, determination of copper in, 305

loops in, 481, 519

Zinc oxide crystal, electron density

map of, 195 Zinc sulfide, interfaces in, 531

stacking faults in, 501 Zone melting, separation by, 412 Zone refining, resistivity measurement

in, 45

• U.S. GOVERNMENT PRINTING OfFICE : 1967 OL—237-323