NBS SPECIAL PUBLICATION 260-52

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards
NATIONAL BUREAU OF STANDARDS

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NATIONAL BUREAU

OP STANDARDS

LIBRARY

AUG 4 1976

/{of o

Standard Reference Materials: 'QcTioo

Thermal Conductivity and Electrical Resistivity %7*5 '^^

Standard Reference Materials: Tungsten SRM's

730 and 799, from 4 to 3000K c s> P

J. G. Hust and P. J. Giarratano

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

U.S. DEPARTMENT OF COMMERCE, Rogers C. B. Morton, Secretary

\j ,5» , NATIONAL BUREAU OF STANDARDS^Ernest Ambler, Aciing Direcior'J

_ (^^Ac^ 6^ Tl^t^^'a' 0

Issued September 1 975 fU^i/O^t^ A<-6uU v v C j .
Library of Congress Cataloging in Publication Data

Hust, Jerome G

Thermal Conductivity and Electrical Resistivity.

(Standard Reference Materials) (National Bureau of Standards

Special Publication; 260-52)

Includes bibliographical references. Supt. of Docs. No.: €13.10:260-50

1. Tungsten—Thermal Properties. 2. Tungsten—Electric Properties. I. Giarratano. P. J., joint author. II. Title. III. Series: United States. National Bureau of Standards. Standard Reference

Materials. IV. Series: United States. National Bureau of Standards. Special Publication; 260-52. OC100.U57 No. 260-52 [TA480.T9] 389'.082

[.546'..536'.5416l 75-619234

National Bureau of Standards Special Publication 260-52

Nat. Bur. Stand. (U.S.), Spec. Publ. 260-52,47pages (Sept. 1975)

CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1975

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

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PREFACE

Standard Reference Materials (SRM's) as defined by the

National Bureau of Standards are "we 1 1- char ac t er i z ed materials, produced in quantity, that calibrate a measurement

system to assure compatibility of measurement in the nation."

SRM's are widely used as primary standards in many diverse

fields in science, industry, and technology, both within the

United States and throughout the world. In many industries

traceability of their quality control process to the national

measurement system is carried out through the mechanism and

use of SRM's. For many of the nation's scientists and technologists it is therefore of more than passing interest to

know the details of the measurements made at NBS in arriving

at the certified values of the SRM's produced. An NBS series

of papers, of which this publication is a member, called the

NBS Special Publication - 260 Series is reserved for this

purpose

.

This 260 Series is dedicated to the dissemination of

information on all phases of the preparation, measurement,

and certification of NBS-SRM's. In general, much more detail will be found in these papers than is generally allowed,

or desirable, in scientific journal articles. This enables

the user to assess the validity and accuracy of the measurement processes employed, to judge the statistical analysis,

and to learn details of techniques and methods utilized for

work entailing the greatest care and accuracy. It is also

hoped that these papers will provide sufficient additional

information not found on the certificate so that new applications in diverse fields not foreseen at the time the SRM

was originally issued will be sought and found.

Inquiries concerning the technical content of this

paper should be directed to the author(s). Other questions

concerned with the availability, delivery, price, and so

forth will receive prompt attention from:

Office of Standard Reference Materials

National Bureau of Standards

Washington, D.C. 20234

J. Paul Call, Chief

Office of Standard Reference Materia

iii
OTHER NBS PUBLICATIONS IN THIS SERIES

NBS Spec. Publ. 260, Standard Reference Mate- NBS Misc. Publ. 260-12, Standard Reference

rials: 1973 Catalog, April 1973, $ 1.25.* Materials: Homogeneity Characterization of

NBS Misc. Publ. 260-1, Standard Reference NBS Spectrometric Standards III: White Cast

Materials: Preparation of NBS White (^ast Iron and Stainless Steel Powder Compact,

Iron Spectrochemical Standards, June 1964. September 1966. NBS Misc. Publ. 260-12.**

COM 74-11061.** NBS Misc. Publ. 260-13, Standard Reference

NBS Misc. l\ibl. 260-2, Standard Reference Materials: Mossbauer Spectroscopy Standard

Materials: Preparation of NBS Copper-Base for the Chemical Shift of Iron Compounds,

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COM 74-11063.** NBS Misc. Publ. 260-14, Standard Reference

NBS Misc. Publ. 260-3, Standard Reference Materials: Determination of Oxygen in FerMaterials: Mo^tallographic Characterization of rous Niaterials - SRM 1090, 1091, and 1092, -an NBS Spectrometric Low-AUoy Steel September 1966. NBS Misc. Publ. 260-14.**

Standard, October 1964. COM 74-11060.** NBS Misc. Publ. 260-15, Standard Reference

NBS Misc. Publ. 2604, Standard Reference Mat(;rials: Recommended Method of Use of

Materials: Sources of Information on Stand- Standard Light-Sensitive Paper for Calibratard Reference Materials, February 1965. ing Carbon Arcs Used in Testing Textiles for

COM 74-1 1059.** Colorfastness to Light, June 1967. (Replaced

NBS Misc. Publ. 260-5, Standard Reference by Spec. Publ. 260-41.)

Materials: Accuracy of Solution X-Ray Spec^l^S Spec. Publ. 260-16, Standard Reference

trometric Analysis of Copper-Base Alloys, Materials: Homogeneity Charaeterizalion of

March 1965. 25 cents. (Out of print). NBS Spectrometric _ Standards IV: PreparaNBS Misc. Publ. 260-6, Standard Reference tjon and Microprob(; Characterization of

Materials: Methods for the Chemical Analysis W-20% Mo Alloy Fabricated by Powd(;r Metof White Cast Iron Standards, July 1965. alluracal Methods, January 1969. COM

COM 74-11068.** 74-11062.**

NBS Misc. Publ. 260-7, Standard Reference ^BS Spec. Publ. 260-17, Standard Reference

Materials: Methods for the Chemical Analysis Materials: Boric Acid; Isotopic and Assay

of NBS Copper-Base Spectrochemical Stand- Standard Reference Materials, February

ards, October 1965. COM 74-1 1067.** 197Q 55 cents.*

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Materials: Analysis of Uranium Concentrates Materials: Calibration of NBS Secondary

at the National Bureau of Standards, Decem- Standard Magnetic Tape (Computer Ampliber 1965. COM 74-11066.**

^^^^^^ Reference) Using the Reference Tape

NBS Misc. Publ. 260-9, Standard Reference Amplitude Measurement "Process A," NoMaterials: Hall Lives of Materials Used in the ^^^j^^^. ^959 ^See Spec. Publ. 260-29.)

Preparation of Standard Reference Materials ^[^g Spec. Publ. 260-19, Standard Reference

of Ninetcu^n Radioactive Nuchdes Issued by Materials: Analysis of Interlaboratory Meathe National Bureau of S tandards, November surements on the Vapor Pressure of Gold

1965. COM 74-1 1065.**

(Certification of Standard Reference Material

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Materials: Homogeneity Characterization on Spec. Publ. 260-21, Standard Reference

NBS Spectrometric Standards 11: Cartridge Materials: Analysis of Interlaboratory MeaBrass and Low-Alloy Steel, December 1965. surements on the Vapor Pressures of CadCOM 74-11064.** ^i^,^ SUver, January 1971. COM

NBS Misc. Publ. 260-11, Standard Reference 74-11359 **

Materials: Viscosity of a Standard Lead-Silica ^BS Spec. Publ. 260-22, Standard Reference

Glass, November 1966. NBS Misc. Publ. Materials: Homogeneity Characterization of

260-10.** Fe-3Si Alloy, February 1971. COM

74-11357**

XV
NliS S|HT. Publ. 260-23, Standard Rei'cTCdcc NHS Spec. Publ. 260-35, Standard Reference

Materials: Viscosilv of a Standard Boro- Materials: Thermal Conductivity of Austensilicate (ilass, December 1970. 25 cents.* Stainless Steel, SRM 735 from 5 to

NBS Spec. Publ. 260-24, Standard Reference 280 K, April 1 972. 35 cents.*

Materials: Comparison of Redox Standards, Spec. Publ. 260-36, Standard Reference

lanuary 1972.$!.* Materials: A Referee Method for the DeterINBS Spec. Publ. 260-25, Standard Reference mination of Calcium in Serum.. SRM 915,

Materials: A standard Reference Material May 1972. COM 72-50527.**

Conlainincr Nominally Four Percent Austen- ^BS Spec. Publ. 260-37, Standard Reference

ite, February 1971. COM 74-1 1356.** Materials: Me thods of Analysis of IN BS (]lay

NBS Spec. Publ. 260-26, Standard Reference Standards, June 1 972. COM 72-50692.**

Materials: National Bureau of Standards-U.S. ^BS Spec. Publ. 260-38, Standard Reference

Steel Corj)oration Joint Program for Deter- Materials: Preparation and Calibration of

mininji Ow^cn and Nitrogen in Steel, Feb- Standards of Spectral Specular Reilc'ctance,

ruary 197L 50 cents.* May 1972. 60 cents.*

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Materials: Uranium Isotopic Standard Refer- Materials: The Eddy Current Decay Method

ence Materials, April 1971. COM R^'sistivity Characterization of lligh74-1 1358 ** Purity Metals, May 1972. 55 cents.*

NBS Spec. Publ. 260-28, Standard Reference ^'^^ Spec. Publ. 260-40, Standard Reference

Materials: Preparation and Rvalnation of Materials: Selection of Thermal Analysis

SRM's 481 and 482 Cold-Silver and Cold- Temperature Standards Through a CooperaCopper Alloys for Microanalysis. Kugust tive Study (SRM 758, 759. 760), August

1971 . COM 71-5036.5.** "2. 65 ce nts.*

NBS Spec. Publ. 260-29, Standard K( Irrencc ^'^S Spec. Publ. 260-41, Standard Reference

Materials: Calibration of NBS Secondary Materials: Use of Standard Lighl-Sensitive

Standard Magnetic Tape (Computer Ampli- ^''W^ ^'^r ^calibrating Carbon Arcs used in

tude Reference) Using the Reference Tape Testing Textiles for Colorfastness to Light,

Amphtude Measurement ''Process A-Model August 1972. COM 72-50775.**

2," ]une 1 971 . COM 71-50282.** ^\iS Spec. Publ. 260-42, Standard Reference

NBs' Spec. Publ. 260-30, Standard Reference Materials: The Characterization of Linear

Materials: Standard Samples Issued in the Polyethylene, SRM 1475. Se|)tember 1972.

USSR (A Translation from the Russian), 45 cents.*

June 1971. COM 71-50283.** '^^S Spec. Publ. 260-43, Stajidard Reference

NBS Spec. Publ. 260-31, Standard Reference ^iaterials: Preparation and Homogeneity

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ber 1971.COM 71-50563.** ^.nc^c'""^""*., i, o ^ r. r NBS Sp(>c. Publ. 260-32, Standard Reference^ ^f^S Spec. Publ. 260-44, Standard Referoice

Materials: Standard Quartz Cuvettes For ^iat. rials: I reparation and Use of Supereo.illigh Accuracy Spectrophotometrv . Decem- '^I'^ V'''"

^'""'"'^ Devices, SRM 767, !)<-

b.T 1973. 55 cents.*

" '^^^2. 7o e<-nls.*

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Materials: Comparison of Original and Sup- Materials: Powdered Lead-Based Paint. SRM

plemental SRM 705, Narrow Molecular 1579, March 1973. COM 73-50226.**

Weight Distribution PoKstNrene, II. L. ^^^S Spec. Publ. 260-46, Standard Rderenee

\\a<nuT Ma\ 197'^ (^OM 7'^-505 Y) ** Materials: Thermal (>>nductivit\ and ElectriNBS \sp,r*. Publ. 260-34, SlTuidard Refercii. ( R<"sistivil\ Standard Reference Mat(Tials:

Mat<>rials: Thermoelectric \ oltage. \pril Austenilic Stainless Steel, SRM's 735 and

1972. COM 72-50371.** ^'•"'"^ ^ to 1200 K, March 1975. .$1.00.

V
NBS Spec. Publ. 260-47, Standard Rrfcre-.i(r

MatcTials: KIcclrical Ri^sistivily of Electrolytic Iron, SRM 797, and Austcnitic Stainless

Steel, SRM 798, from 5 to 280K, February

1974. 55 cents.*

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Mat(;rials: Description and Use of Precision

Thermometers for the Clinical Laboratory,

SRM 933 and SRM 934, May 1974. 60

cents.*

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Materials: Calibrated Glass Standards for Fission Track Use, Novemb(;r 1974. 75 cents.*

NBS Spec. Publ. 260-50, Standard Reference

Materials: Thermal (Conductivity and Electrical Resistivity Standard Reference Materials:

Electrolytic Iron, SRM's 734 and 797 from 4

to 1000 K, June 1975. $1.00

NBS Spec. Publ. 260-51, Standard Reference

Materials: Glass Filters As a Standard Reference Material for Spectrophotometry; Selection, Preparation, Certification, Use - SRM

930. (In press)

NBS Spec. Publ. 260-52, Standard Reference

Materials: Thermal Conductivity and Electrical Resistivity Standard Reference Materials

730 and 799, from 4 to 3000 K. (In press)

*Send order with remittance to: Su{)erintcndent of Documents, U.S. Government Printing Office,

Washington, D.C. 20402. Remittance from foreign countries should include an additional onefourth of the purchase price for postage.

**May be ordered from: National Technical Information Services (NTIS), S[)ringfield, Virginia

221 5i
Contents

Page

1. Introduction 1

2. Historical Review 2

2.1 Early Efforts 2

2.2 Iron 3

2.3 NBS, Washington Efforts 3

2.4 NBS, Boulder Efforts 3

2.5 AFML-AGARD Project 3

3. SRM Selection Criteria 4

4. Material Characterization 4

4.1 AFML Arc Cast Tungsten 6

4.2 Sintered Tungsten 6

5. Apparatus and Measurements 9

5.1 Low-Temperature (Below Ambient) Measurements 9

5.2 High-Temperature (Above Ambient) Measurements 11

6. Data Analysis (Selection of Best Values) 18

6.1 Electrical Resistivity 18

6.2 Thermal Conductivity 26

7. Discussion 29

8. Summary 35

9. Acknowledgements 36

10. References 36

vii
List of Tables

Table Page

1. Composition of AFML arc cast and NBS sintered tungsten 7

2. Electrical resistivity characterization of AFML arc cast

tungsten (anneal = 1700 K: 1/2 hour) 8

3. Residual resistivity ratio (.9^-,^„l 9 ,„) of NBS sintered tungsten 10

4. Recommended electrical resistivity values for AFML arc cast and

NBS sintered tungsten for several values of RRR 27

5. Recommended thermal conductivity values for AFML arc cast and NBS

sintered tungsten for several values of RRR 34

List of Figures

Figure Page

1. Thermal conductivity deviations for NBS sintered tungsten

(unannealed) 12

2. Thermal conductivity deviations for NBS sintered tungsten

(annealed) 12

3. Electrical resistivity deviations for NBS sintered tungsten ^ (unannealed) 13

4. Electrical resistivity deviations for NBS sintered tungsten

(annealed) 13

5. Thermovoltage deviations for NBS sintered tungsten (unannealed) 14

6. Thermovoltage deviations for NBS sintered tungsten (annealed) 14

7. Thermal conductivity of NBS sintered tungsten 15

8. Electrical resistivity of NBS sintered tungsten 15

9. Lorenz ratio of NBS sintered tungsten 16

10. Thermopower of NBS sintered tungsten 17

11. Primary electrical resistivity data [12,15-19] for arc cast and

sintered tungsten 19

12. Deviations of primary intrinsic electrical resistivity data for arc

cast and sintered tungsten from the eleven term power series

representation (equation 7) 20

13. Deviations of primary intrinsic electrical resistivity data for arc

cast and sintered tungsten from rational fraction representation

(equation 8) 22

14. High-temperature electrical resistivity of tungsten. Literature and

unpublished data. (Reprinted from Minges [13]) 23

15. Electrical resistivity deviations of tungsten. (Reprinted from

Minges [13]) 24

viii
List of Figures (continued)

Figure Page

16. Electrical resistivity deviations from ORNL results.

(Reprinted in part from Moore et al. [17]) 25

17. * Primary thermal conductivity data for AFML arc cast and NBS

sintered tungsten 28

18. Thermal conductivity deviations of primary data from equation 12 30

19. Lorenz ratio of tungsten as computed from recommended values of thermal

conductivity (equation 12) and electrical resistivity (equation 8) . . . . 31

20. High temperature thermal conductivity data as presented by

Mlnges [13] compared to values calculated from equation 12 32

21. High temperature thermal conductivity values obtained from

thermal diffusivity and electrical resistivity data as presented

by Minges [13] compared to values calculated from equation 12 33

ix

THERMAL CONDUCTIVITY AND ELECTRICAL RESISTIVITY

STANDARD REFERENCE MATERIALS: TUNGSTEN

SRM's 730 and 799, from 4 to 300 K

J. G. Hust and P. J. Giarratano

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado, 80302

Abstract

A historical review of the development of thermophysical Standard

Reference Materials, SRM's, is given and selection criteria of SRM's are

listed. Thermal conductivity and electrical resistivity data for arc cast

and sintered tungsten are compiled, analyzed, and correlated. Recommended

values of thermal conductivity (SRM 730) and electrical resistivity (SRM

799) for these lots of tungsten are presented for the range 4 to 3000 K.

These values are based on low temperature NBS measurements and higher

temperature measurements by participants of the AFML-AGARD project. The

uncertainty of the thermal conductivity values below ambient is 2% and

rises to 5% between ambient and 2000 K. Above 2000 K the uncertainty

rises to a maximum of about 8%. The uncertainty of the electrical re- sistivity values is 2% over the entire temperature range.

Key words: Electrical resistivity; high temperature; Lorenz ratio;

low temperature; Standard Reference Material; thermal conductivity;

thermopower; tungsten.

1. Introduction

Design and development engineers continually demand thermal and electrical property

data of technically important materials. Often these data are not in the published literature and immediate measurements must be performed. Since only a handful of laboratories

have the proven expertise to make such measurements, they are often performed by inexperienced personnel using unproven apparatus. The results, as can be seen from the literature,

exhibit excessive scatter; 50% differences are commonplace. In such situations. Standard

Reference Materials, SRM's, are invaluable to predetermine the accuracy of the engineering

measurements. Currently, an inaccuracy of 10% is allowable for most engineering thermal

property data, and therefore, SRM's for engineering applications need to be established

with an uncertainty no larger than about 5%.

A few research laboratories performing thermal and electrical measurements are obtaining data with uncertainties at the state-of-the-art level, 1% for thermal conductivity

and lower for electrical resistivity. SRM's for use at such laboratories must be correspondingly more accurate, and though they may indeed be possible, they have not yet been

established.

Considerable effort has been directed toward the development of suitable thermophysical SRM's*, over a period of many years, with limited success. This lack of success

may be due, in part, to the tacit assumption that SRM data must be accurate to state-ofthe-measurement-art to be useful. There are several reasons why the achievement of thermal

and electrical property SRM's with certified inaccuracies of less than 1% is extremely

difficult. The principal reason is that material variability, generally, causes property

variations of greater than 1%, even with the most up-to-date production control techniques.

The effects of material variability lead to the consideration of three categories of calibration materials and three concomitant certification inaccuracies: (1) A characterized

type of material, e.g., copper, gold, iron, etc. Based on past experience it appears

* The term SRM is used here in a broad sense to denote any material or specimen that is to serve as a calibration standard. The term, as coined by the Office of Standard Reference

Materials, generally implies a specific lot of material prepared under strict control and

subsequently characterized for chemical composition and homogeneity.

1
that inaccuracies of 5-10% can be expected. (2) A characterized specific lot of a given

type of material, e.g., austenitic stainless steel, SRM 735, or electrolytic iron, SRM 734.

Data uncertainties of one percent appear to be near the lower limit of current production

control techniques. (3) Characterized specimens of material. At first glance, it may be

thought that the latter SRM's would be invariant; but it is known that the thermal and

electrical properties of specimens are dependent on their thermal and mechanical histories,

and some specimens change spontaneously with time at ambient temperature. These effects

are most important at low temperatures, especially for highly purified materials.

Appropriately chosen well-characterized specimens, handled with care to avoid physical and

chemical changes, and frequently reexamined to detect changes, presently represent the only means to achieve accuracies in the state-of-the-measurement-art range. This is the basis

of round-robin measurements used by standardizing laboratories for state-of-the-art apparatus

intercomparisons (see, for example, Laubitz and McElroy fl]). Category (2) is considered to

be the most cost^.ef f ective to satisfy engineering needs and, to a lesser extent, the needs

of standards laboratories. It is also the philosophical basis of the Office of Standard

Reference Materials, National Bureau of Standards.

This report is a result of a program to establish several thermal and electrical con- ductivity metal SRM's with conductivities ranging from pure metals (high conductivity) to

structural materials (low conductivity) . Plans are being formulated to extend this program

to insulating materials and dielectric solids. The current effort has resulted in two additional reports: one on iron (medium-to-high conductivity, 4 to 1000 K) and another on austenitic stainless steel (low conductivity, 4 to 1200 K) . The material reported on here,

tungsten, is in the high conductivity range.

This paper reviews the historical development of thermal conductivity SRM's. A

listing is given of selection criteria for SRM's and a justification is presented for the

establishment of both engineering and standards laboratory SRM's. Data are compiled and

best values are selected to establish two lots of tungsten as electrical resistivity and

thermal conductivity SRM's, 799 and 730, respectively. As discussed later, thermal condilfctivity and electrical resistivity data have been obtained to certify these SRM's over

the range 4 to 3000 K to within engineering accuracy. This material appears to have the

qualities of a useful SRM. An adequate supply of this material exists to insure measurement compatibility among laboratories for about ten years.

The following historical review of SRM efforts is presented to indicate the relatively

large amount of research that has been conducted, compared to the few thermophysical SRM's

that have been established. It is this divergence between expended efforts and concrete

results that has prompted us to establish potentially useful SRM's, 'at what may seem to some as a premature phase of the work. Based on past experience, it appears that if this

is not done, a vast amount of research is essentially wasted because the stock of material,

on which the research was performed, is generally no longer available. This consideration

also points out the significance of continuity in SRM projects.

2. Historical Review

2.1 Early Efforts

Thermophysical property reference material investigations began, for all practical

purposes, in the 1930 's with the work of R. W. Powell at the National Physical Laboratory

(NPL) , Teddington, England [2] on iron and Van Dusen and Shelton at NBS [3] on lead. These

efforts were successful in that they resulted in frequently used reference materials of

thermal conductivity. Powell's work resulted in the establishment of ingot iron* (category

1) as a standard which is still being used today. Lucks [4] recently reviewed the massive

amount of work which has been done on this material and recommends the continued use of

ingot iron as a reference material. Van Dusen and Shelton 's work resulted in an unofficial

lead standard based on a well-characterized lot of pure lead (category 2) distributed by

NBS as a freezing point standard.

* The ingot iron used for this purpose is Armco iron produced by Armco Steel Corporation.

The use of trade names of specific products is essential to the proper understanding of

the work presented. Their use in no way implies any approval, endorsement, or recommendations by NBS.

2
2.2 Iron

Since the 1930's, reference material investigations have been sporadic with notable

efforts by researchers from the NBS (National Bureau of Standards, U.S.)> NPL (National

Physical Laboratory, England), ORNL (Oak Ridge National Laboratory, Tennessee), BMI

(Battelle Memorial Institute, Ohio), and AFML (Air Force Materials Laboratory, Ohio). The

material that has been the subject of the most extensive investigations is ingot iron.

Renewed interest in this material was spurred by the round-robin^ experiments initiated

by C. F. Lucks of Battelle Memorial Institute during 1959. Twenty-four laboratories

requested and received the round-robin material for measurements. Data from eight

laboratories were ultimately reported and compiled by Lucks [4]. These data are on specimens obtained from a single lot of ingot iron. The literature, however, contains data on

a total of eleven distinct lots of ingot iron. Lucks [4] has shown that ingot iron is an acceptable reference material at temperatures from about 100 K to 1000 K. In this range,

material variability affects thermal conductivity and electrical resistivity by about 5%.

At higher temperatures, reported variations increase. At lower temperatures, especially

at liquid helium temperatures, variations of 10% have been reported on a single 30 cm long

rod by Hust et al. [5,6]. Electrolytic iron, SRM 734, was established as a low-temperature

standard by Hust and Sparks [7] because it exhibits relatively small low-temperature

variability. Based on their high temperature study of ingot iron and a high purity iron,

Fulkerson et al. [8] also concluded that high purity iron is a more homogeneous and stable

SRM than ingot iron. The thermal conductivity and electrical resistivity SRM's of electrolytic iron have been extended to 1000 K by Hust and Giarratano (NBS Special Publication

260-50)

2.3 NBS, Washington Efforts

D. R. Flynn of NBS, Washington began a study of potential thermal conductivity SRM's

tt during the early 1960's. He examined several ceramics* and metals . None of these

materials has achieved the status of an SRM. Descriptions of these efforts appear in the

unpublished proceedings of the early thermal conductivity conferences. Laubitz and Cotnam

[9] reported that Inconel 702 exhibits transformation effects of several percent in thermal

conductivity and recommended against its use as a reference material.

At the 1963 Thermal Conductivity Conference, Robinson and Flynn flO] presented the

results of a survey of thermal conductivity SRM needs. SRM's with a data uncertainty of

3-5% were in greatest demand. The intended use of SRM's, most often stated, was to check

and calibrate apparatus. Needs were indicated for SRM's of conductivities from 0.01 W/mK

to 500 W/mK at temperatures from 4 to 3300 K.

2.4 NBS, Boulder Efforts

R. L. Powell of NBS, Boulder initiated a low-temperature SRM project during the early

1960's. This project has been continued by the first author since that time. Materials

studied include ingot iron, electrolytic iron, gold, tungsten, graphite, and stainless

steel. As a result of these studies, electrolytic iron and stainless steel have been

established as SRM's of electrical resistivity and thermal conductivity. Current efforts

are directed toward establishing graphite as SRM's at temperatures up to near 3000 K. It

is anticipated that this project will continue until a sufficiently wide range of conductivities and temperatures are included to satisfy existing demands for thermophysical SRM's.

2.5 AFML-AGARD Project

Minges [5th Thermal Conductivity Conference, 1965] reported on the initiation of an AFML sponsored high-temperature reference materials program. This program was divided

into two phases. Phase I included the preliminary selection and characterization of

materials as potential reference materials. Selection criteria were established, dozens

t The use of the term "round-robin" is different here from that used earlier where the use of a single specimen was implied; however, this double meaning is allowed to be con- sistent with the literature on ingot iron.

* Pyroceram 9606 and Pyrex 7740 (trade names of Corning Glass Works)

tt Inconel 702 (trade name of International Nickel Company, Inc.), lead, and 60% platinum - 40% rhodium alloy.

3
of materials screened, and about 15 were chosen for experimental evaluation. Phase II

included further measurements on those materials selected from Phase I studies. Arthur D. Little Corp. contracted with AFML to perform this study. The results were reported in

reference fll]. The materials of particular interest in Phase II of this program were

aluminum oxide, thorium oxide, tungsten, and graphite.

After partial completion of the AFML program, an international program, principally

high-temperature, was initiated under the auspices of the Advisory Group for Aerospace

Research and Development, NATO (AGARD) . E. Fitzer of Karlsruhe University, Germany,

directed this program in close cooperation with the AFML program. The establishment,

progress, and results of this program are described in a series of reports by Fitzer [12].

Minges has also summarized some of the results on AFML-AGARD programs [13]. The materials,

internationally distributed and measured by numerous laboratories, are: platinum, gold,

copper, austenitic steel alloy, tungsten (both sintered and arc-cast) , tantalum - 10%

tungsten alloy, alumina, and graphite.

3. SRM Selection Criteria

The criteria for screening and selecting potentially useful materials for thermophysical property SRM's are generally well-understood and accepted. These criteria are

not met absolutely by any material, but serve as a guide to determine which materials are

most suitable. Some of the more significant factors are:

1. The material should be homogeneous* and isotropic throughout a lot. The lot

should be large enough to be adequate for at least a decade and renewable with a minimum of effort.

2. Thermophysical properties should not vary with time and should be relatively

unaffected by the environment of the measurement apparatus. The material should have

chemical stability, thermal shock resistance, low vapor pressure, and insensitivity

to stress.

3. The material should be readily available, machinable, relatively inexpensive, and

have sufficient strength to be handled without causing damage.

4. The material should have characteristics similar to the material to be measured.

5. The material should be useful over a wide temperature range.

The two lots of tungsten described in this report satisfy these criteria reasonably well

above 90 K. Below 90 K, individual specimen characterization is required.

4. Material Characterization

Extensive reliance is placed on electrical resistivity variability as an indicator of

thermal conductivity variability for pure metals. The justification for this is presented

below.

The electrical resistivity, p, and thermal conductivity, X, are intimately related

for pure metals and for alloys to a lesser extent. This relationship exists because in a metal most of the heat is transported by the electrons. Some heat is also transported by

the lattice vibrations. The total thermal conductivity is the sum of the electronic, \ , and the lattice, X^, (the German word for lattice is Gitter) components.

A = A + A . (1)

e g

In most pure metals A^ is small compared to A^, but in transition metals A^ may be as large as 20% of A^, and in some alloys A^ is much larger than A^. For pure metals and

dilute alloys, the relationship between p and A at both high and low temperatures is

reasonably well described by the Wiedemann-Franz-Lorenz (WFL) law:

* The term homogeneous refers here to the uniformity of the thermophysical property in

question. Homogeneity of a thermophysical SRM implies not only chemical homogeneity, as

in chemical composition SRM's, but also homogeneity of physical characteristics of the

material. The parameters affecting physical property homogeneity are so numerous that

detailed characterization of each is prohibitive. Instead, one often reverts to aggregate

characterization methods, such as by electrical resistivity as discussed later.

4
^ = L = 2.443 X 10 ^ v\ ^, (2)

1 o where L is the Sommerfeld value of. pA/T and T is the temperature. At intermediate temperao tures, large deviations from the WFL law are observed. Generally the ice-point is a sufficiently high temperature and liquid helium is a sufficiently low temperature to approximately satisfy the WFL law.

In metals there are two mechanisms that account for most of the scattering of electrons: the interaction of electrons with chemical impurities and physical imperfections,

and the interaction of electrons with thermal vibrations of the atoms of the lattice. The

former mechanism is usually taken to be independent of temperature, while the latter

is temperature dependent. If we assume that each of these mechanisms is independent of

the other, we may assign a separate resistivity to each. The resistivity arising from

impurity and imperfection scattering is usually referred to as the residual resistivity,

p^, while the resistivity due to thermal scattering is called the intrinsic resistivity,

p^(T). The total resistivity, p(T), may be written as the sum of these two terms.

p(T) = Pq + P^CT) . (3)

This separation of the total resistivity into a constant term, p^, and temperature dependent term, p^(T), is known as Matthiessen ' s rule. Although Matthiessen's rule is not

strictly valid, it is a sufficient approximation to be useful for our purposes.

At ambient temperatures the residual resistivity is a negligibly small fraction

of the total resistivity; consequently, the total resistivity, p(T), is nearly equal to

the intrinsic resistivity, p^(T) , and therefore a characteristic of the metal itself. As

the temperature approaches absolute zero, however, the intrinsic resistivity becomes very

small and the total resistivity is essentially the value of p^. The temperature at which

p(T) becomes constant depends upon the purity of the sample, but for most materials available at the present time, the intrinsic resistivity will be negligible at 4 K (the boiling

point of helium) . For the tungsten studied here the total resistivity is temperature

independent within the accuracy of our measurements, below 15 K.

The residual resistivity, which is caused primarily by impurities and imperfections,

provides a good indication of a specimen's purity and freedom from strain. Rather than

using the residual resistivity itself for this purpose, a common procedure is to determine

a specimen's resistance at the ice-point, ^^273' ^^'^ ^ ^' ^^4' calculate the ratio

between these two, R^^^/R^. This is nearly equal to the ratio of the resistivities at the

same temperatures, as the geometric form factor nearly cancels in the ratio. The geometric

form factors are not quite the same because of thermal expansion, which is about 0.5%

between 273 K and 4 K. This ratio is called the residual resistivity ratio, RRR, and its

magnitude is an indication of the purity and physical perfection of the specimen. Since

the specimens measured here were generally in the annealed condition, the RRR value should

indicate the effective chemical purity (electrical purity)

.

To support the validity of this statement, we computed the residual resistivity based

on the measured chemical composition of these tungsten lots. The specific resistivity of

impurities in tungsten was estimated to average 3 lJf2'cm/at.% on the basis of Blatt's fl4]

table of specific resistivities for many other metals. (This is a crude estimate since no data are listed for tungsten.) We obtained a value of 0.6 nf2*m assuming that all impurities are in solution for the two lots of tungsten studied. The measured residual resistivities range from 0.5 to 0.8 nf^'m. This indicates reasonable agreement between directly

measured chemical purity and electrically measured purity.

Electrical resistivity variations are accompanied by thermal conductivity variations

of nearly equal and opposite sign as indicated by the WFL law. Therefore, the determination of relative residual resistivity variability will directly indicate thermal conductivity variability. The measurement of electrical resistivity is much easier than the

determination of thermal conductivity.

5
Other characterization data are useful to establish the nature of these particular

tungsten lots. Of these, composition is the most significant, but hardness, grain size,

density, and other physical properties are valuable aids in data analyses. These data are presented in the following sections for AFML arc cast and NBS sintered tungsten.

A.l AFML Arc Cast Tungsten

In an earlier section, the AFML-AGARD project was briefly described and it was indicated that both sintered and arc cast tungsten were distributed for measurements. The arc

cast tungsten discussed in this paper is from the lot originating with that study and

therefore is referred to as AFML arc cast tungsten. The raw material for the starting

billet was high purity tungsten powder. A billet was formed from the powder by vacuum arc melting to a bar approximately 25 cm in diameter and 46 cm in length. The billet was machined to 20 cm diameter and then extruded to a rod of 10.5 cm diameter. After an acid

etch the rod was swaged to 4 cm diameter. Portions of this rod were swaged to form smaller

diameter rods. These rods were dye penetrant inspected for defects and heat treated at

1700 K for 1/2 hour. The composition of these rods as determined by the supplier is

listed in table 1. A considerable portion of this arc cast tungsten was used in the AFMLAGARD program. Part of it was sent to the European Transuranium Institute, Karlsruhe,

Germany, in care of H. E. Schmidt. The remaining rods were supplied to NBS, OSRM for

future distribution.

The available diameters in cm are 0.51, 0.64, 0.83, 1.02, 1.27, 2.54, 3.18, and 4.06.

3 The measured density of these rods is 19.20 ± 0.05 g/cm . Each of the rod sizes of this

heat of arc cast tungsten was characterized with electrical resistivity measurements at

the ice point and at liquid helium temperature. The variability of electrical resistivity

at the ice-point indicates primarily the homogeneity of macro-physical defects, such as cracks and voids. The variability at liquid helium temperature indicates homogeneity of

the lot from the standpoint of both chemical impurities and physical defects as discussed

earlier.

Table 2 lists the observed resistivities at 4 K and 273.15 K and calculated values of

RRR and intrinsic resistivities for AFML arc cast tungsten specimens of various diameters.

The range of resistivities observed at the ice point is ± 0.7% from the mean indicating

that the macro-homogeneity and the high temperature electrical resistivity and thermal

conductivity variability are quite acceptable for SRM's. The values observed at 4 K range

from 0.5 to 0.8 nJ^*m, indicating a relatively large percentage variation in chemical purity.

This is not surprising since for pure materials, a small absolute variation in chemical

impurity can amount to a large percentage variation. The variation observed is diameter

dependent, indicating that impurity pickup is greater for the small diameter specimens,

probably because of the increased surface-to-volume ratio. The large variation in p, and

therefore X, at 4 K detracts from the apparent usefulness of this lot of material at low

temperatures. However, by a simple measurement of for each specimen, the entire range

of p and A can be predicted to within engineering accuracy, as is shown later. Above 90 K

the effect of p^ variations is strongly diminished and can often be neglected.

Measurements on specimens of arc cast tungsten from different heats resulted in RRR

values similar to those in table 2 when annealed at 1700 K. However, the RRR values

increased to above 100 with less variability when annealed at 2300 K and above. This

indicates that an anneal at 1700 K is too low to remove most of the physical defects and

therefore, much of the variability may be the result of defect variation rather than

composition variation. An anneal of 2300 K for one hour is recommended.

The intrinsic resistivity is characteristic of the pure, defect-free base metal and

its constancy in table 2 serves as a check on the accuracy and precision of the measurements. The range of values is ± 0.5% of the mean, which is consistent with our estimated

measurement uncertainty.

4.2 Sintered Tungsten

The AFML-AGARD project initially included sintered tungsten as candidate reference

material. This material was later rejected for use as a reference material because of its

inhomogeneity and instability at high temperatures. This instability was observed primarily with the larger diameter specimens. The larger diameter specimen densities were

lower than the small diameter specimens by more than 5%. The instability is, therefore,

believed to be caused by incomplete sintering and heat treatment. For this reason, a lot

6
Table 1. Composition of AFML Arc Cast

and NBS Sintered Tungsten

Element

Composition

AFML Arc Cast

in Weight PPM

NBS Sintered

Al < 10

Ca < 5 < 10

Si < 20 10-100

Mo 140 10-100

Fe 16 < 10

Cr < 10 < 10

Ni < 55 -

Cu < 1 < 10

Mn < 10 - Mg < 1 < 10

Sn < 20 -

Pb < 20 -

Ti < 5

V < 10

Zr < 10

Hz 14

28

C 26

02 36

7
Table 2. Electrical Resistivity Characterization of AFML

Arc Cast Tungsten (Anneal = 1700 K: 1/2 hour)

(cm)

Electrical Resistivity

(n Q»m)

R R R

'

^273 k/^4 K

273. 15 K 4 K 273. 15 K

( Intrinsic

)

0.51

left end 49.4 Oil 0 . 82

1

48.6 60.2 ±0.2

right end 49 3 0 759 48. 5 64.9 ±0.2

0.64

left end 49. 3 0 . 788 48.5 62. 5 ± 0. 2

right end 4Q 3 0 786 48 5 62. 7 ±0.2

0.83

left end 49. 0

f\ / a 0. 64 A C\ A 48.4 77 ± 1 right end 48 9 0 63 48 3 78 ± 1

1 . 02

left end 48.9 0.50 48.4 97 ± 1 right end 48.8 0.49 48. 3 100 ± 1

1.27

left end 48. 7 0. 53 48.2 92 ± 2

right end 48. 7 0.53 48.2 92 ±2

RRR = Residual resistivity ratio

8
of sintered tungsten stocked by NBS-OSRM was investigated for use as thermal and electri3 cal SRM's. Its density is 19.23 ± 0.05 g/cm , comparable to the small diameter specimens

previously studied and the same as the arc cast material. The composition of this sintered

tungsten, referred to as NBS sintered tungsten, is listed in table 1. No difference was

observed in the composition of the two available diameters, 0.64 cm and 0.32 cm. The

overall purity is determined as 99.98% tungsten. Hardness has been measured as 405 DPH

for a specimen annealed at 2020°C and 514 for an unannealed specimen.

As with the arc cast tungsten, electrical resistivity measurements have been performed

to characterize the homogeneity of NBS sintered tungsten. Specimens were selected at

random from the entire lot in both the 0.64 and 0.32 cm diameter rods. Electrical resistivity measurements were performed on specimens annealed for 60 hours at 1200°C and on specimens annealed for one hour at 2020°C. Similar to the arc cast tungsten, increasing

the anneal temperature increased the residual resistivity ratio and the apparent homogeneity. A specimen diameter dependence was again observed, indicating that the smaller

diameter specimens were slightly less pure. In this case, however, the mean electrical

resistivities of the 0.64 cm and 0.32 cm diameter were within 2a (a being the standard deviation). Thus, statistically it is difficult to make a clear and unambiguous distinction

between them.

The effect of high temperature cycling (2800 K) was also studied on three 0.32 cm specimens. These specimens were temperature cycled by R. E. Taylor of Purdue University

using electrical self heating. The RRR measurements were performed at NBS. The results

show no further increase in RRR over the specimens annealed at 2020°C and no physical

degradation. The above described RRR results are listed in table 3. The intrinsic ice

point resistivity as determined for three of the 0.32 cm diameter specimens is 48.5 ± 0.2 nfi'm, which is the same as that determined for arc cast tungsten as listed in table 2.

The conclusions drawn from these and earlier AFML characterization data are as follows.

Both AFML arc cast tungsten and NBS sintered tungsten are useful as SRM's of thermal

conductivity and electrical resistivity at temperatures up to at least 2800 K if annealed

before use at 2300 K for one hour. Below ambient the effects of material inhomogeneity

gradually became significant. At liquid helium temperature, the thermal and electrical

conductivities of NBS sintered tungsten vary from specimen-to-specimen by about ± 5%. The

corresponding variation for the arc cast tungsten may be larger primarily because of the

dependence on rod diameter. The effect of these variations can be determined and corrections applied by a relatively simple residual electrical resistivity measurement on each

specimen. The effect of inhomogeneity on electrical resistivity and thermal conductivity

decreases rapidly with increasing temperature. These variations are relatively small

above 90 K and essentially insignificant above 300 K. This is demonstrated in later

sections.

5. Apparatus and Measurements

Numerous thermal conductivity and electrical resistivity measurements have been

performed on sintered and arc cast tungsten. However, neither of these materials has been

measured at both cryogenic and elevated temperatures. The AFML arc cast tungsten has been

measured at temperatures above ambient by several participants of the AFML-AGARD project.

The NBS sintered tungsten has been measured at temperatures below ambient at NBS, Boulder.

A sintered tungsten was also measured at elevated temperatures as part of the AFML-AGARD

project. These data are discussed below according to whether they are principally below

or above ambient temperature.

5.1 Low-Temperature (Below Ambient) Measurements

The electrical resistivity, thermal conductivity, and thermopower of NBS sintered

tungsten were measured from 6 to 280 K by Rust [15] . These measurements were performed

simultaneously on a single specimen using a longitudinal heat-flow, multi-property apparatus. The specimen was 3.1 mm in diameter and 23 cm long. Eight thermocouples were mounted

at equally spaced positions along the length of the specimen to determine temperature

gradients in the range 4 to 300 K. An unannealed specimen was measured from 6 to 280 K and a specimen annealed at 2020°C for one hour was measured from 7 to 90 K. These data were

represented with the following equations for smoothing and analysis.

n

InX = T, a. f«,nT] (4)

i=l

^

9
Table 3. Residual Resistivity Ratio (P^ys

of NBS Sintered Tungsten

Specimen

1 RRR Specimen RRR Spe cimen RRR

Unannealed 2020°C, 1 hr;

0. 64 cm dia

.

2020"C, 1 hr;

0 . 32 cm dia .

14-7 QO 1 -

1

78. 0 10-2 73.6

1200°C, 60 hr

;

2-2 76. 1 11-2 79. 0

0 . 64 cm dia . 3-1 83.2 12-6 80. 1

1-1 66 2 4-2 93.5 13-1 75. 5

1-2 4: O

QO 5-1 82. 8 14-7 74.9

3-1 69 5 6-1 79. 0 15-7 81.3

2 -2 63 9 6-2(1) 79.9 16-4 79.4.

6-1 44 2 6-2(2) 83. 1 17-5(1) 69.8

3-2 65 4

6-2(3) 80.8 17-5(2) 71.2

mean = 59 6

6-2(4) 82. 3 17-5(3) 69.8

std. dev. = 9 2 6-2(5) 83. 1 17-5(4) 70.4

mean = 82.0 17-5(5) 70.8

1200 °C, 60 hr;

0. 32 cm dia.

std. dev. = 4. 5 17-8 71 . 5

10-2 56. 6

c,Di^D C

;

0 . 32 cm dia

.

18-6(1)

18-6(2)

76.8

75. 1 10-7 46. 6 10-2 mean - 74 .

6

14-2 43. 5 30 min. 71.0 std. dev. = 4.0

14-7 45. 2 12-6

18-2 61. 9 10 min.

18-7 62. 5 5 times 78.2

mean = 52. 7 11-2

std. dev. = 8. 6 10 min,

1 0 time s 78.4

10
p' = E b. [JlnT]'- ^ (5)

i=l

^

S = ^ c. [ilnT']^/T' ;T' = Iq

+1 (6)

i=l

where A = thermal conductivity, p = electrical resistivity, S = thermopower, and T = temperature. The deviations of the experimental data from values calculated with these

equations are illustrated in figures 1-6. The horizontal bars in figures 3-6 indicate the

temperature span of each run. Smoothed low-temperature values of thermal conductivity,

electrical resistivity, Lorenz ratio, and thermopower as calculated from equations 4-6 are' illustrated in figures 7-10. The RRR values for the annealed and unannealed specimens are

76 and 40, respectively. The estimated uncertainties of the smoothed values are:

thermal conductivity - 2.5% at 300 K, decreasing to 0.7% at 200 K,

0.7% from 200 K to 50 K, and increasing inversely with temperature to 1.5% at 4 K

electrical resistivity - 0.5%

thermopower - 0.2 yv/K at 4 K, decreasing to 0.03 yv/K at 80 K

and above.

Further details of the NBS measurement procedure and data analysis are given by Hust

et al. [6]

.

5.2 High-Temperature (Above Ambient) Measurements

Several participants of the AFML-AGARD project have measured thermal conductivity,

electrical resistivity, thermal diffusivity, specific heat and other thermophysical properties of tungsten at temperatures above ambient. These data have been presented by

Fitzer fl2] and reviewed by Minges fl3]. Various apparatus were used to obtain these

data. The general description of these apparatus and methods can be obtained from the

original papers. Our interest is concerned primarily with the accuracy of the resultant

data. The stated uncertainties of the thermal conductivity data are generally in the 5 to

10% range.

Six participants reported thermal diffusivity data for AGARD sintered tungsten. The

scatter between these data sets is about ± 10%. The scatter within each of the data sets

is about ± 5%. The effect of high temperature exposure (2846 K) as reported by one participant was to increase the thermal diffusivity by approximately 10%. Four participants

reported thermal diffusivity data for AFML-AGARD arc cast tungsten. These data agreed to

within about ± 5%. The effect of high temperature exposure was not reported. Two participants reported specific heat data for sintered tungsten. Although they do not overlap

in temperature range, the agreement at the common temperature is within about 1%. These

data agree with existing literature data for other tungsten to within about 2%.

Two participants reported thermal conductivity data for sintered tungsten. These are widely separated in temperature (one set ranges from 400 to 900 K and the other from 2300

to 2800 K) thus, no comparisons between them are possible. The high temperature data are appreciably below other tungsten data reported in the literature.

Only one participant reported thermal conductivity data for arc cast tungsten (from

1600 to 2800 K) . These data agree with literature data for other tungsten to within 10%.

One participant reported the electrical resistivity of sintered tungsten and another

reported the same for arc cast tungsten. These two sets of data overlap from 2000 K to

2700 K and agree with each other to within 1%. Minges [13] compared resistivity measurements on various forms of tungsten, including single crystal, arc cast, sintered, and

ultra high purity. All of these data agree to within about ± 2%. These and other intercomparisons are presented in the following section.

Moore et al. [16,17] measured electrical resistivity, thermopower, and thermal

conductivity of two specimens of tungsten from 100 to 1700 K. One of them was a sintered

specimen very similar in composition to the NBS sintered tungsten, although its density

3 (19.1 g/cm ) was slightly lower. Its RRR was 31. The other was a higher purity electron

beam melted specimen with an RRR of 400.

11
o

t—<I

T — 1 ... ^ ... —

1

. 1—

f- -

+ 4

-

t *

+ -r

+ +

* + + —3*——?— 1

- ^ ^ ^ ^ . *

+ +

* 4. *

t - -

*

*

+

1——»—1 > I 1 1 i e; TEMPERATURE (Kelvin)

Figure 1. Thermal conductivity deviations for NBS sintered

tungsten (unanneaLed).

5C;

20 40 SO TEMPERATURE (Kelvin)

eo

Figure 2. Thermal conductivity deviations for NBS sintered

tungsten (annealed).

12
o

I—

: 2 •

:.2 ••

TEMPERATURE (Kelvin)

Figure 3. Electrical resistivity deviations for NBS sintered

tungsten (unannealed).

TEMPERATURE (Kelvin)

Figure 4. Electrical resistivity deviations for NBS sintered

tungsten (annealed).

13
TEMPERATURE (Kelvin)

Figure 5. Thermovoltage deviations for NBS sintered

tungsten (unannealed).

TEMPERATURE (Kelvin)

Figure 6. Thermovoltage deviations for NBS sintered

tungsten (annealed).

14
1000

f 500

=>o

o

100

I'll "1 1 1—I I I I

Annealed

I I I I

I I

I I I l_L

10 50 100

TEMPERATURE, K

Figure 7. Thermal conductivity of NBS sintered tungsten

300

60

50

G 40

<^ 30 1—

I

UJ

c_>

20

10

T

—— Annealed specimen —— Unannealed specimen

T

80 160

TEMPERATURE, K

240 320

Figure 8. Electrical resistivity of NBS sintered tungsten.

15

1 1 1 1

1 1

I

- ——— Annealed specimen —

— —

0 80 160

TEMPERATURE, K

Figure 10. Thermopower of NBS sintered tungsten

240 320

/

17
6. Data Analysis (Selection of Best Values)

6.1 Electrical Resistivity

Because of the many data sources and the existing comparisons, it is difficult to

present a simple comparison of all of these data. Thus, it has been decided to present

several comparison graphs using a reference equation to facilitate comparison between

graphs. First, the previously described experimental electrical resistivity data sets are illustrated in figure 11. This figure includes 153 data points from nine sources. The

points are so closely spaced and self consistent on this graph that it is impractical to

delineate the various sources. The main purpose of this graph is to illustrate the primary

data sets [12,15-19] and the range of data involved in the analysis. It is clear from

figure 11 that only 2 data points are excessively discordant with the data set. These

data sets will be unambiguously defined and compared in the following deviation plots.

Our objective is to obtain and present best values of resistivity for two partici-.lar lots

of tungsten, arc cast and sintered; therefore, only the data on tungstens similar in

composition to these are considered primary data.

Figure 11 illustrates the effect of impurity and state of annea]*- on the low temperature resistivity of these specimens. Below about 100 K these variations are pronounced.

At 4 K the resistivity is determined almost entirely by these imperfections. Because of

these low temperature variations, the representation problem becomes essentially three

dimensional, i.e., resistivity as a function of temperature and residual resistivity. For

the range of residual resistivity to be studied, it was assumed that Matdthiessen' s rule

would be valid, i.e., the total resistivity function is separable into additive residual

and intrinsic resistivities, p(T) = p^(T) + p^. To confirm this hypotheisis, we

expressed P^CT) as a power series in Z.nT (equation 7) and fitted it to the data illustrated

in figure 11. The deviations of this fit are shown in figure 12. Since the deviations

shown in figure 12 do not differ from each other systematically with RRR, we conclude that,

for this range of residual resistivities, Matthiessen ' s rule is valid within the scatter of

the data.

n

p. = E a.(£nT)'-, (7) ^ i=l

^

The power series representation of electrical resistivity data over a wide temperature

range has several disadvantages. First, a relatively high order, eleven, is required to

obtain a good fit. Second, the number of significant digits that must be carried in the

calculations is too large to be asthetically satisfactory. Last, but not least, power

series representations have a tendency to introduce unreal oscillations within the range

of the fitted data and can generally not be extrapolated beyond the data set. For these

reasons, a less complex function was sought to represent these data. By analyzing the low

and high temperature data sets separately, the following rational function was formulated.

p = (aT^ + bT^)/(l + C/t'") + p^. (8)

Using an iterative non-linear least squares fitting technique, the best values of the

parameters were determined to be

a = .04535 -

b = -2.90 X 10"^

c = 3.442 X 10^

n = 1.2472

m = 2.98

with T in kelvin and p in nf^'m. The deviations of the experimental data, uncorrected for

thermal expansion, from this equation are illustrated in figure 13. Also shown are deviations of equation 7 and the oscillatory nature of a power series is clearly evident.

Although figure 13 suggests that small systematic deviations exist between equation 8 and

the real resistivity behavior of tungsten, the simplicity of this function and the elimination of the disadvantages of the power series representation make this equation more

18
5 10 100 1000 4000

TEMPERATURE, K

Figure 11. Primary electrical resistivity data [12,15-19] for arc cast

and sintered tungsten.

19
I I I I

1 1—I—I I I I I I r o AGARD participant 41 [l2] RRR = 75

. AGARD participant 44 [iz] RRR = 75 • Must [15] RRR = 76 • Must [15] RRR = 40 • Moore et al . [l6] RRR = 31 *

1—I I I I I I

Oa

o

o

toO

a

-4

-8

V

*

o

*

9 ,~

V

8%

* •

400

31

1 J. I ' I I I I I I

A Moore et al . [l6] RRR

a Moore et al . [l7] RRR

V Powell et al. [l8] RRR = 150

O White and Woods [l9] RRR = 165

I

I ' ' I I I I I

I

10 100 1000

TEMPERATURE, K

Fiqure 12. Deviations of primary intrinsic electrical resistivity data for

arc cast and sintered tungsten from the eleven term power series

representation (equation 7).

4000

20
desirable as the baseline equation. The numerator of this rational fraction predicts the

high temperature behavior while the denominator compensates for low temperature deviation

from the higher temperature behavior. Omitting the term C/T^ from the denominator produces

3 a change of less than 1% above 330 K. The bT term represents only a small correction to

the numerator, reaching a maximum of 8% at the upper temperature of 3000 K. Thus, the

high temperature resistivity of tungsten can be reasonably well represented with simply

aT^. The low temperature resistivity is reasonably represented by ^

p^"*^ + p^^e

transition region between low and high temperature behavior occurs in the vicinity of 100

K. Comparisons to other than the primary data set and other smoothing equations is

facilitated through the use of equation 8. Figure 14 is a plot of arc cast and sintered

tungsten data presented by Minges [13] (reprinted by permission). Superimposed on this

plot is a line as computed from equation 8 showing excellent agreement. Figure 15 is a deviation plot presented by Minges fl3]'and again calculated values from equation 8 have

been added for comparison.

The data presented by Minges are uncorrected for residual resistivity variation since

the residual resistivity was not known for each of the specimens. Since it is likely that

all of these specimens have RRR values above 30, such correction could be as large as 3%

at 0°C and 0.5% at 800°C. The omission of these corrections may account for the 2-3%

deviation between the high purity (RRR - 4900) and lower purity (RRR = 31) tungsten at

ambient temperature as shown in figure 15. Minges [13] compared data to the following

baseline equation:

p = 4.64 + 2.533 x lO^T + 3.162 x lO^T^

with p in yf^'cm and T in °C. This equation was for the range 20 to 1800°C. It is cor- rected linearly for thermal expansion. The correction is zero at 20°C and 0.7% at 1800°C.

The large deviation between equation 8 and Minges' equation in the vicinity of 300 K is

apparently caused by the fact that his equation extrapolates to a resistivity of 4.64

yfi* cm at the ice point, 0°C. Note that this is outside the range of validity of his

equation by 20°C, but our results indicate an ice point resistivity of about 4.94 y^2*cm for

both of these tungsten lots. Also note that the Minges equation should not be extrapolated

above the upper temperature, 1800°C, specified by him, as indicated by the strong divergence between his equation and equation 8. This is an example of the danger of extrapolating even a very simple power series, as mentioned earlier. Figure 16 is a deviation plot

presented by Moore et al. [17] with the addition of equation 8.

The above comparisons show that good agreement exists between the intrinsic resistivity of various forms of tungsten, including sintered, arc cast, single crystal, and very

high purity tungsten. Typical deviations among various data sources are ± 2% for temperatures from 4 to 3000 K.

Examination of the various comparisons illustrated in figures 12 through 16 has led

the authors to accept equation 8 for the prediction of best values of electrical resistivity for these lots of arc cast and sintered tungsten. It could be argued that equation 7 is a better least squares representation of the entire data set. However, consideration

of the existing material variability, the data uncertainties, and the previously discussed

disadvantages of power series, has strongly influenced the decision to adopt an inherently

smooth equation rather than one which follows the intricacies of each data set more exactly

The difference between the two equations of course is small as illustrated in figure 13;

and the power series representation contains what appear to be unreal oscillations as a function of temperature. Values of resistivity calculated from equation 8, for values of

spanning the range of these tungsten lots, are listed in table 4. For values of p^

other than those listed, it is a simple matter to form a new column by adding p^ to the p^

= 0 resistivities. The uncertainty in the tabulated values of electrical resistivity is

estimated at ± 2% for the entire temperature range. A paper published by Williams [23],

after the above work was completed, contains a thorough analysis of the high temperature

resistivity of zone-refined tungsten. He presents smoothed values of resistivity for the

range 1050 to 2500 K. These data agree with the values listed in table 4 for p^ = 0 to

within 1% below 2000 K (Williams values are larger); above 2000 K the differences increase

to 2% at 2500 K. oi
o AGARD participant 41 [l2] RRR = 75

AGARD participant 44 [l2] RRR = 75 • Hust [15] RRR = 76 • Hust [15] RRR = 40 • Moore et al . [l6] RRR =31

"rrr| 1 1—i i i i i 1

1

A Moore et al. [l6] RRR = 400

a Moore et al . [l7] RRR = 31

V Powell et al. [l8] RRR = 150

O White and Woods [l9] RRR = 165 —— Equation 7 (Power series)

1 1—I I I I I

I

J_Lll J I

I I I I I I I _L J I i J L

10 100

TEMPERATURE, K

1000 4000

Fiqure 13. Deviations of primary intrinsic electrical resistivity data for

arc cast and sintered tungsten from rational fraction representation.

(Equation 8)

.

22
o

ooo

uio.yrt 'd

oooooo

'AilAIiSISay 1V3iai3313

'23
900) 1^

LT) 00

t->

II ro

1

fy' ' - Ol ry o in ID ID cy o CO 00 oCO St

+-> +J +-> o fO

(T3 m II o

O) (1) O) -o

_1_ .J— _i_ 0<J CO /-V o

<c <U q:

(—1 eC CO <z II 3 q; <t

q: -l-> LU ra S- s_ u. ro q; E 1- 1— 4-> (T3 "3 (O -o o

CO CQ CQ CQ OJ (U 4-

s: >i

i. CQ c

T3 o +-) +J +-> +J -o c 4- OJ

1/1 l/l l/l to dJ o <U !-> 0) "3 (B ro S- s- 5- U

U O o +Jo OJ o U O o o c CD c OJ

s_ s_ S- -1- o s-

(/I < LU Q.

+-> O) o o

-(-> Ol o o

l/l CO I

CO CO >, >, O

OJ QJ ro ro O

« • O 4 <

o

CO

CDcnc

o

a

i.Q.

(/) CDc

:3

c

o

-Mn

>

13

P

10

•r-

(/I a>

so

scr o o

CO o o

CM

{TM^-^d - d)00I

:N0Il\/IA3a

o

I

24
1 \ r < «

< *

o o O

o o

unf r-H + o

+-> o ooCM

I o

Ln+

CMO OD O CM

.—I o oo

I I o o

CO

-Io cn

—I CM

I I o o 1—

I

t—

1

X X

Ln 00 oo ro o

OD vo

CM

II II

o o

Q. Q.

I/) o

CO

^ - oo

• O

• O

< * o

CM

o

<_) o

o

CO

oo

CDC >

•r- QJ

S- XI O O)

-a -D c c

to (O

SI 13 4-> >, >> C

(/) OJ

5- E

c

s-o

O 3 t/l Li_ O O

OJ

I/) c

-oc

fO

S-(U

(/I Olo

a:

00o

cr

o

ooCM < m * < 0«

00

I I 00

(001 X d-d

25
6.2 Thermal Conductivity

Again, because of the multiplicity of data sets, thermal conductivity intercomparisons are difficult to present without the aid of a reference, or baseline equation.

Considerable effort was expended to find such an equation for the range 4 to 3000 K. This

equation would need to not only represent a complex temperature dependence, but also,

describe the low temperature impurity variation as evidenced by variations in residual

electrical resistivity. Figure 17 shows the primary data [12, 15-18] to be represented.

Delineation of the separate sources will be given in later deviation plots.

Consideration was given to using a power series fit of these data, as in the case of

the electrical resistivity data, and using the thermal equivalent of Matthiessen's rule

to obtain the variation with p^. However, it was found that the thermal equivalent of

Matthiessen's rule was not adequate to obtain a representation accurate to within the

uncertainty of the data., A three dimensional power series equation, A = A (p^,T) , was not

seriously considered because undoubtedly it would need to be unnecessarily complex to represent the data.

We thus resorted to the formulation of an equation based in part on theory but primarily on empirical grounds. Cezairliyan and Touloukian [20] has shown that for pure

metals the low temperature thermal conductivity behavior can be reasonably well described

by

A = (9)

aT + 3/T

where 3 is taken as a linear function ofp, i.e.,3=6'p,ct may be a weak function

o o of p^, and n is near 2. This theoretically based equation is generally valid up to about

0.1 of the Debye temperature, or in this case, approximately 40 K. For the range of residual resistivities of interest here, we felt it would be possible to neglect the dependence

of a on p^. Thus, we performed an iterative nonlinear least squares fit of the data

below 40 K to determine best values of ct, n, and 6'. It was found that this fit represented

the data below 35 K to within their uncertainty. The deviations above 35 K increased very

rapidly since this function falls rapidly to zero, and the experimental data fall off much

more slowly. By examining the nature of the A deviation and the character of the Lorenz

ratio curve for tungsten, we empirically found that the additive term

A ^

EXP (- (G^/T)^) (10)

allowed us to represent the experimental data to 300 K within their uncertainty. Extrapolating this equation to higher temperatures resulted in relatively small deviations

with respect to the data which could be fitted with yet another exponential

A' ^ EXP (-(O^/T)^). (11)

Thus our final equation for the entire range 4 to 3000 K is

^ = + A [EXP (-(0 /T)^) + B EXP (-(0„/T)^)] ^ . (12)

aT'^+B'p /T

z P o An iterative nonlinear least squares fit of the parameters in this equation to the

primary data set resulted in the following best values:

26
Table 4. Recommended Electrical Resistivity Values for AFML Arc Cast and NBS

Sintered Tungsten for Several Values of RRR

Electrical Resistivity (nU-m)

RRR = 50 RRR = 75 RRR = 100 RRR = °° Temperature (K) Pq = 0.97 Pq = 0.65 Pq = 0.49 Po = 0

4 . 0.970 0.650 0.490 0.000

6 0.970 0.650 0.490 0.000

8 0.971 0.651 0.491 0.001

10 0.972 0.652 0.492 0.002

12 0.975 0.655 0.495 0.005

14 0.979 0.659 0.499 0.009

16 0.986 0.666 0.506 0.016

18 0.996 0.676 0.516 0.026

20 1.011 0.691 0.531 0.041

30 1.185 0.865 0.705 0,215

40 1.635 1.315 1.155 0.664

50 2.469 2.149 1.989 1.498

60 3. 713 3. 393 3,233 2. 740

70 5.31 4,986 4. 826 4. 333

80 7. 15 6.83 6.67 6.18

90 9.15 8,83 8,6'7 8. 18

100 11.25 10.93 10. 77 10.27

120 15. 54 15.22 15. 06 14. 57

140 19. 88 19.56 19.40 18,91

160 24.24 23.92 23. 76 23.26

180 28.61 28.29 28. 13 27.64

200 33.02 32.70 32. 54 32.05

250 44. 25 43. 93 43, 77 43 28

300 55. 8 55. 5 55. 4 54 8

350 67. 8 67. 5 67. 3 66 8

400 80. 1 79. 8 79. 6 79 1 450 92. 7 92 4 92. 2 91 7

500 105. 7 105. 3 105. 2 104 7

600 132 4 132 1 131. 9 131 4

700 160, 1 159. 8 159. 6 159 2

800 188. 7 188 4 188. 2 187 8

900 218. 1 217 8 217. 6 217 1 1000 248 1 247. 8 247, 6 247 2

1200 309.9 309.6 309.4 309.0

1400 373.5 373.2 373.0 372.6

1600 438.6 438.3 438.1 437.6

1800 505 504 504 504

2000 572 571 571 571

2200 639 638 638 638

2400 706 706 706 705

2600 774 773 773 773

2800 841 840 840 840

3000 907 907 907 906

27
800

600

400

200

100

80

TTT| \ 1—I I I I I I I

] 1

1 I I I I I I

• ^^^^ = 7^

- • • •

RRR - 40 ••

11} \ I I I I I I I I 1

1

\ L

6 10 100 1000 4000

TEMPERATURE, K

Figure 17. Primary thermal conductivity data for AFML arc cast and NBS sintered

tungsten

.

28
a = 2.705 X 10

6' = 0.03982

n 2.367

A = 35.06

B

= -0.1689

^1 = 89.62

®2

= 370.4

with A in W*m 'K , T in helium, and p and p in nfi'm. The deviations of the primary data

o [12,15,16,17] from this equation are illustrated in figure 18. Deviations with respect to

the TPRC recommended curve [22] are included in figure 18. The differences are within the

combined uncertainties of both sets of recommended va-lues. However, above 2000 K these

two curves are divergent. Further measurements are desirable to reduce the uncertainty in

this range. Minges [13] presented two graphs illustrating high temperature thermal con- ductivity data as obtained from various sources and several prediction methods. We have

added values as calculated from equation 12 to these graphs, figures 20 and 21, as a convenient method of illustrating further intercomparisons

.

No attempt has been made in this formulation to separate the conductivity of tungsten

into electronic and lattice conductivity components, and therefore, any effort to attribute the exponential terms to specific interaction mechanisms is not recommended. In the

formulation of this ai;id other potentially useful equations, we examined the possibility

of simplifying the representation problem by subtracting the lattice conductivity as predicted by Moore et al. [16,21] and others. This potentially heuristic approach,

although esoterically more satisfying, resulted in a more complicated rather than simplified function, and therefore this approach was abandoned.

We decided that equation 12 is the best representation of the arc cast and sintered

tungsten. Values of thermal conductivity based on this equation and several values of p^ are listed in table 5. Values of Lorenz ratio as computed from the recommended values of

p and A are illustrated in figure 19. The uncertainties of the thermal conductivity data are estimated as 2% from 4 to 300 K, increasing to 5% at 2000 K, and rising to a maximum

of 8% above 2000 K. Above 2000 K the deviations (figure 18) are larger than 8%, but it is

noted that these data are converted diffusivity results. The direct thermal conductivity

values are well within 8% of equation 12.

7. Discussion

The principal factors determining the validity of SRM data are measurement uncertainty and material variability. Measurement uncertainty is a highly speculative quantity,

as evidenced by the fact that most experimentalists present optimistically low uncertainties for their own work. The best way to obtain realistic uncertainties is through roundrobin type measurements using apparatus as basically different as possible. Such programs

are expensive, and therefore not often performed. It is essential for standardizing

laboratories to be involved in such programs because this forms the basis of essentially all

other measurements. SRM's resulting from measurements by these standards laboratories

make it possible for all other laboratories to perform measurements on a common basis.

Material variability is determined by the degree of control exercised during material

production and the sensitivity of property values to physical and chemical variations in

the material. As pointed out earlier, however, transport properties at low temperatures

are strongly dependent on the detailed nature of the microscopic material structure.

Because of this, it is necessary to make measurements to determine the property variability of a lot of material produced even under the best of conditions. The only truly

foolproof method of determining material variability effects is to measure the property of

interest on a random sampling of specimens from the entire lot of material. For a thermal

conductivity SRM, this is costly and one must resort to less expensive characterization

measurements and careful production record keeping to insure maximum benefit from a minimum number of measurements.

Fixed-point electrical resistivity, density, grain size, and hardness data have been

compared earlier in the text. These comparisons for AFML arc cast and NBS sintered tungsten

29
R AGARD participant 39 [l2] RRR « 50 • AGARD participant 26 [l2] RRR « 50 « AGARD participant 1 [l2j RRR « 50

# AGARD participant 5 [l2j RRR = 50

O AGARD participant 41 [l2] RRR = 75

o Moore et al . [l6] RRR = 31

A Moore et al . [l7] RRR = 31

D Hust [15] RRR = 40

V Hust [l5] RRR - 76

Calculated from

diffusivity measurements

T T I I I I I I I I T 1—I

I I I I I I 1—

r

— TPRC recommended curve [22]

o o

J I I I I I I I I

I I I I I I I I I J L

10 100

TEMPERATURE, K

1000 4000

Figure 18. Thermal conductivity deviations of primary data from equation 12.

30
o

CO CO OO C\J >—I r-t

OTX^_>|^A 'OIi\/y ZN3aoi

31
1_ L o o O o o o o o o o o

CO <> «o CO o o. CO d d d

)lo- |/\IO/M' \ 'AilAlianONOG lVIAIB3Hi

32
o

<

GC

(13

-l->

c

o

>^

C

-QO

CO

OJ3

DO

a;c

fVi

!-(

u

co

u

a

^(

OJ

o

o

u

cn

c

u

Si

Oil a

s

o

u

CDu

Mo- IAI3/M'X 'AllAllOnONOO IVIAIHBHi

33
Table 5. Recommended Thermal Conductivity Values for AFML Arc Cast and NBS

Sintered Tungsten for Several Values of RRR

Thermal Conductivity ("Wm-.^K"-^)

Temperatxire (K) RRR = 50 RRR = 75 RRR = 100

4 103 154 205

6 155 231 306

8 206 306 404

10 255 377 496

12 302 444 580

14 345 503 652

16 384 553 709

18 417 591 748

20 443 618 769

30 468 585 667

4 0 3 84 4 3 8 4 7 0

50 305 330 345

60 260 275 283

70 236 245 251

80 221 229 232

90 212 218 221

100 206 211 213

120 199 202 204

140 194 197 199

160 191 194 195

180 189 190 191

200 186 187 188

250 178 180 180

300 171 172 172

350 163 164 164

400 157 157 158

450 151 151 152

500 146 146 147

600 138 138 139

700 132 132 132

800 127 127 127

900 123 123 123

1000 120 120 120

1200 114 114 114

1400 110 110 110

1600 107 107 107

1800 105 105 105

2000 102 102 102

2200 101 101 101

2400 99 99 99

2600 98 98 98

2800 97 97 97

3000 97 97 97

34
show that significant material variability effects exist at low temperatures (below 90 K)

.

At higher temperatures, the effects of material variability are less well defined because

of the larger-than-desirable measurement uncertainty, especially above 2000 K. The present

analysis demonstrates that the effects of material variability can be accounted for by

residual resistivity characterization.

Minges [13] and Fitzer [12] have indicated that irreversible effects may occur due to

high temperature use of these SRM's (above 2000°C). This conclusion is based on measurements

using large diameter sintered tungsten specimens produced early in the AFML-AGARD program.

The evidence suggests that this occurred primarily due to the incomplete sintering of that

lot of sintered tungsten. This is not to say that irreversible effects are totally absent

in these lots of tungsten. It would be surprising if such changes did not occur; however,

we believe that they will be within the previously mentioned uncertainties.

Although the SRM's described in this paper are considered quite adequate for engineering use, improvement in the accuracy and credibility of the values presented could be

accomplished with additional measurements. Through its use as an SRM, this material will

be measured by other laboratories. The resulting data will be compiled and, when sufficient reduction in uncertainty is achieveable, the recommended values will be updated.

Anyone measuring this material with an absolute method is urged to make the data available

to the author.

8 . Summary

Recommended values of electrical resistivity and thermal conductivity for two specific

lots of tungsten, AFML arc cast and NBS sintered tungsten, have been presented for the

range 4 to 3000 K. These recommended values are based on an analysis and correlation of

various characterization data, primarily those of NBS and AFML-AGARD. The semi-empirical

functions chosen as the basis for the recommended values are inherently smooth, and therefore may be extrapolated somewhat without fear of strong divergence from true physical

behavior. Although, it is believed that these functions are applicable to a wide range of

commercially available tungsten, the intent is to represent only the two specific lots of

interest here. The data presented are for ambient dimensions, uncorrected for thermal

expansion.

With an anneal of 2000°C for one hour in vacuum and a residual resistivity measurement, the uncertainties of the recommended values are estimated as follows:

Thermal Conductivity Electrical Resistivity

4-300 K 2% 2%

300-2000 K 2%-5% 2%

Above 2000 K 5%-8% 2%

The above anneal and residual resisitivity measurement must be done after the specimen has

been machined to size and completely readied for use.

If the specimens are to be used only at high temperatures (above ambient) , the residual

resistivity measurement is unnecessary, at the expense of a slight increase in uncertainty.

An anneal of 2000°C for one hour will produce specimens of nominal RRR = 75 and the corres- ponding columns of tables 4 and 5 are used. These specimens are not recommended for use below 90 K without a residual resistivity determination.

These SRM's are available in the form of rods from the Office of Standard Reference

Materials, National Bureau of Standards, Washington, D.C. 20234. Available sizes are as follows:

Sintered tungsten:

SRM 730-SlS, 799-SlS

SRM 730-S2S, 799-S2S

SRM 730-S3S, 799-S3S

SRM 730-MlS, 799-MlS

SRM 730-M2S, 799-M2S

SRM 730-M3S, 799-M3S

(0.32 cm dia, 5 cm long)

(0.32 cm dia, 10 cm long)

(0.32 cm dia, 20 cm long)

(0.64 cm dia, 5 cm long)

(0.64 cm dia, 10 cm long)

(0.64 cm dia, 20 cm long)

35
Arc cast tungsten:

(0.64 cm dia, 5 cm long)

(0.64 cm dia, 10 cm long)

(0.64 cm dia, 20 cm long)

(0.83 cm dia, 5 cm long)

(1.02 cm dia, 5 cm long)

(1.27 cm dia, 5 cm long)

Multiple continuous lengths may be obtained by special order. The larger diameter arc cast

specimens are in relatively limited supply.

9. Acknowledgements

This work has been in progress for several years, and over this period of time many

people have assisted in various ways. R. L. Powell was instrumental in suggesting the

importance of the work and in formulating ' the preliminary program. We wish to thank R. E. Michaells of NBS, OSRM and M. Minges of AFML for supporting this work and for many helpful

discussions. The cooperation of R. E. Taylor of Purdue University, in performing the high

temperature cycling of the NBS sintered tungsten, is also acknowledged.

10. References

1. M. J. Laubltz and D. L. McElroy, Precise Measurements of Thermal Conductivity at High

Temperatures (100 - 1200 K) , Metrologia T_, No. 1, 1-15 (1971).

2. R. W. Powell, The Thermal and Electrical Conductivities of Metals and Alloys: Part'

I, Iron from 0° to 800°C, Proc. Phys. Soc. 46, 659-679 (1934).

3^ M. S, Van Dusen and S. M. She! ton. Apparatus for Measuring Thermal Conductivity of

Metals up to 600°C, Bur. Stand. J. Res. (USA) 12, 429-440 (1934).

4. C. F. Lucks, Armco Iron: New Concept and Broad-Data Base Justify Its Use as a Thermal

Conductivity Reference Material, J. of Testing and Evaluation, 1^, No. 5, 422-431

(1973).

5. J. G. Hust, Thermal Conductivity Standard Reference Materials from 4 to 300 K. I. Armco Iron, Proc. of the 9th Thermal Conductivity Conference, Iowa State Univ., Ames,

Oct. 6-8 (1969).

i 6. J. G. Hust, Robert L. Powell, and D. H. Weitzel, Thermal Conductivity Standard Reference

Materials from 4 to 300 K. I. Armco Iron: Including Apparatus Description and Error

Analysis, J. Res. Nat. Bur. Stand. 74A, No. 5, 673-690 (1970).

7. J. G. Hust and L. L. Sparks, Thermal Conductivity of Electrolytic Iron, SRM 734, from

4 to 300 K, Nat. Bur. Stand. Special Publication 260-31 (1971).

8. W. Fulkerson, J. P. Moore, and D. L. McElroy, Comparison of the Thermal Conductivity,

Electrical Resistivity, and Seebeck Coefficient of a High-purity Iron and an Armco

Iron to 1000°C, J. Appl. Phys. 37 No. 7, 2639-2653 (1966).

9. M. J. Laubitz and K. D. Cotnam, Thermal and Electrical Properties of Inconel 702 at

High Temperatures, Can. J. Phys. 42, 131-152 (1964).

10. H. E. Robinson and D. R. Flynn,' The Current Status of Thermal Conductivity Reference

Standards at the National Bureau of Standards, unpublished proceedings of the 3rd

Thermal Conductivity Conference, Oak Ridge National Laboratory, Oct. 16-18 (1963).

11. A. D. Little, Inc., Development of High Temperature Thermal Conductivity Standards,

Technical Reports AFML-TR-66-415 (1967); AFML-TR-69-2 (1969), Wright-Patterson Air

Force Base, Ohio.

SRM 730-SlA, 799-SlA

SRM 730-S2A, 799-S2A

SRM 730-S3A, 799-S3A

SRM 730-MA

SRM 730-LA

SRM 730-LXA

36
12. E. Fitzer, Thermophysical Properties of Solid Materials, Advisory Report 12 (1967),

Advisory Report 38 (1972); Report 606 (1972),- AGARD, NATO, France.

13. M. L. Minges, Evaluation of Selected Refractories as High Temperature Thermophysical

Property Calibration Materials, AFML Technical Report TR-73-278 (1974); Int. J. Heat and Mass Transfer 17, 1365-1382 (1974).

14. F. J. Blatt, Physics of Electronic Conduction in Solids, McGraw-Hill, New York (1968).

15. J. G. Hust, Thermal Conductivity Standard Reference Materials from 6 to 280 K: VI

NBS Sintered Tungsten, NBSIR 73-351 (1974).

'

16. J. P. Moore, D. L. McElroy, and M. Barisonl, Thermal Conductivity Measurements between

78 and 340 K on Aluminum, Iron, Platinum, and Tungsten, Proc. of the 6th Conference

on Thermal Conductivity, pp. 737-778 (1966).

17. J. P. Moore, R. S. Graves, W. Fulkerson, and D. L. McElroy, The Physical Properties

of Tungsten, Proc. of the 5th Conference on Thermal Conductivity, pp. V-G-1 to V-G-35

(1965)

.

18. R. W. Powell and R. P. Tye, New Measurements on Thermal Conductivity Reference Materials,

Int. J. Heat Mass Transfer 10, 581-596 (1967).

19. G. K. White and S. B. Woods, Electrical and Thermal Resistivity of the Transition

Elements at Low Temperatures, Phil. Trans. Roy. Soc. London A251 No. 995, 273-302

(1959).

20. A. Cezairliyan and Y. S. Touloukian, Correlation and Prediction of Thermal Conductivity of Metals Through the Application of the Principle of Corresponding States,

Advances in Thermophysical Properties at Extreme Temperatures and Pressures, Proc. of

3rd Symposium on Thermophysical Properties, pp. 301-313 (1965).

21. R. K. Williams and W. Fulkerson, Separation of the Electronic and Lattice Contributions to the Thermal Conductivity of Metals and Alloys, Proc. of the 8th Conference

on Thermal Conductivity, pp. 389-456 (1968)

.

22. C. Y. Ho, R. W. Powell and P. E. Liley, Thermal Conductivity of the Elements, J.

Phys. Chem. Ref. Data, 1, # 2 (1972).

23. R. K. Williams, A Study of the Electrical Resistivity of Zone-Refined Tungsten at

High Temperatures, J. Appl. Phys. 46 No. 2, 475-490 (1975).

37
NBS-114A (REV. 7-73)"

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLIC ATION OR RI-PORT NO.

SP 260-52

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLK AND SUHTlTl.li

THERMAL CONDUCTIVITY AND ELECTRICAL RESISTIVITY STANDARD

REFERENCE MATERIALS: TUNGSTEN SRM's 730 and 799, FROM 4 to

3000 K

5. Publication Date Septesnnber 1975

6. Performing Organization Code

7. AU rHOR(S)

J. G. Hust and P. J. Giarratano

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2750295

11. Contract /Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

NBS, OSRM, Washington, D.C.

13. Type of Report & Period

Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

Library of Congress Catalog Card No. 75-619234

16. ABSTRACT (A 200-word or less [actual summary of most signidcarjt information. If document includes a significant

bibliography or literature survey, mention it here.)

A historical review of the development of thermophysical Standard

Reference Materials, SRM's, is given and selection criteria of SRM's are

listed. Thermal conductivity and electrical resistivity data for arc cast

and sintered tungsten are compiled, analyzed, and correlated. Recommended

values of thermal conductivity (SRM 730) and electrical resistivity (SRM

799) for these lots of tungsten are presented for the range 4 to 3000 K.

These values are based on low temperature NBS measurements and higher

temperature measurements by participants of the AFML-AGARD project. The

uncertainty of the thermal conductivity values below ambient is 2% and

rises to 5% between ambient and 2000 K. Above 2000 K the uncertainty

rises to a maximum of about 8%. The uncertainty of the electrical' resistivity values is 2% over the entire temperature range.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Electrical resistivity; high temperature; Lorenz ratio;

low temperature; Standard Reference Materials; thermal conductivity; thermopower;

tungsten.

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