J

NBS SPECIAL PUBLICATION 260-46

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

d Reference Materials:

THERMAL CONDUCTIVITY

AND ELECTRICAL RESISTIVITY

ANDARD REFERENCE MATERIALS:

AUSTENITIC STAINLESS STEEL,

SRM's 735 AND 798, FROM 4 TO 1200 K
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards ' was established by an act of Congress March 3, 1901.

TTie Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology,

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* Part of the Center for Building Technology.

Maryland, unless otherwise noted; mailing address
Bureau of Standards

f S"?

^^0"'^^ ^^^^^^^^ Reference Materials:

'''^^ Thermal Conductivity and Electrical Resistivity ^ Standard Reference Materials: Austenitic Stainless

Steel, SRM's 735 and 798, from 4 to 1200 K

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, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

Issued March 1975
Library of Congress Cataloging in Publication Data

Hust, Jerome G. Thermal conductivity and electrical resistivity standard

reference materials. (Standard Reference Materials) (National Bureau of Standards Special Publication; 260-46) Includes bibliographical references.

Supt. of Docs. No.: C 13.10:260-46

1. Steel, Stainless- - Thermal properties.

2. Steel, Stainless -- 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; 260-46. QC100.U57 No. 260-46 (TA479.S7) 389'.08s (620.r7'96)

75-619013

National Bureau of Standards Special Publication 260-46

Nat. Bur. Stand. (U.S.), Spec. Publ. 260-46, 42 pages (March 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 (Order by SD Catalog No. C13.10:260-46). Price $1.00
PREFACE

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

National Bureau of Standards are "well-characterized materials, produced in quantity, that calibrate a measurement

system to assure compatibility of measurement in th'e 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 Cali, Chief

Office of Standard Reference Materials

iii
OTHER NBS PUBLICATIONS IN THIS SERIES

NBS Spec. Publ. 260, Standard Reference Materials: 1973 Catalog, April 1973, $1.25.*

NBS Misc. Publ. 260-1, Standard Reference Materials: Preparation of NBS White Cast Iron

Spectrochemical Standards, June 1964. COM

74-11061.**

NBS Misc. Publ. 260-2, Standard Reference Materials: Preparation of NBS Copper-Base

Spectrochemical Standards, October 1964.

COM 74-11063.**

NBS Misc. Publ. 260-3, Standard Reference Materials: MetaUographic Characterization of an NBS Spectrometric Low-AUoy Steel Standard, October 1964. COM 74-11060.**

NBS Misc. Publ. 260-4, Standard Reference Materials: Sources of Information on Standard

Reference Materials, February 1965. COM

74-11059.**

NBS Misc. Publ. 260-5, Standard Reference Materials: Accuracy of Solution X-Ray Spectrometric Analysis of Copper-Base Alloys,

March 1965. 25 cents. (Out of print).

NBS Misc. Publ. 260-6, Standard Reference Materials: Methods for the Chemical Analysis of

White Cast Iron Standards, July 1965. COM

74-11068.**

NBS Misc. Publ. 260-7, Standard Reference Materials: Methods for the Chemical Analysis of

NBS Copper-Base Spectrochemical' Standards, October 1965. COM 74-11067.**

NBS Misc. Publ. 260-8, Standard Reference Materials: Analysis of Uranium Concentrates at the National Bureau of Standards, December

1965. COM 74-11066.**

NBS Misc. Publ. 260-9, Standard Reference Materials: Half Lives of Materials Used in the

Preparation of Standard Reference Materials

of Nineteen Radioactive Nuclides Issued by

the National Bureau of Standards, November

1965. COM 74-11065.**

NBS Misc. Publ. 260-10, Standard Reference

Materials: Homogeneity Characterization on NBS Spectrometric Standards II: Cartridge

Brass and Low-AUoy Steel, December 1965.

COM 74-11064.**

NBS Misc. Publ. 260-11, Standard Reference

Materials: Viscosity of a Standard Lead-Silica

Glass, November 1966. NBS Misc. Publ.

260-10.**

NBS Misc. Publ. 260-12, Standard Reference

Materials: Homogeneity Characterization of

NBS .Spectrometric Standards III: White Cast

Iron and Stainless Steel Powder Compact,

September 1966. NBS Misc. Publ. 260-12.**

NBS Misc. Publ. 260-13, Standard Reference

Materials: Mossbauer Spectroscopy Standard

for the Chemical Shift of Iron Compounds,

July 1967. NBS Misc. Publ. 260-13.**

NBS Misc. Publ. 260-14, Standard Reference

Materials: Determination of Oxygen in Fer- rous Materials - SRM 1090, 1091, and 1092,

September 1966. NBS Misc. Publ. 260-14.**

NBS Misc. Publ. 260-15, Standard Reference

Materials: Recommended Method of Use of

Standard Light -Sensitive Paper for Calibrating Carbon Arcs Used in Testing Textiles for

Colorfastness to Light, June 1967. (Replaced

by Spec. Publ. 260-41.)

NBS Spec. Publ. 260-16, Standard Reference

Materials: Homogeneity Characterization of

NBS Spectrometric Standards IV: Preparation and Microprobe Characterization of

W-20% Mo Alloy Fabricated by Powder Metallurgical Methods, January 1969. COM

74-11062.**

NBS Spec. Publ. 260-17, Standard Reference

Materials: Boric Acid; Isotopic and Assay

Standard Reference Materials, February

1970. 65 cents.*

NBS Spec. Publ. 260-18, Standard Reference

Materials: Calibration of NBS Secondary

Standard Magnetic Tape (Computer Amplitude Reference) Using the Reference Tape

Amplitude Measurement "Process A," November 1969. (See Spec. Publ. 260-29.)

NBS Spec. Publ. 260-19, Standard Reference

Materials: Analysis of Interlaboratory Measurements on the Vapor Pressure of Gold

(Certification of Standard Reference Material

745), January 1970. PB 190071.**

NBS Spec. Publ. 260-21, Standard Reference

Materials: Analysis of Interlaboratory Measurements on the Vapor Pressures of Cadmium and Silver, January 1971. COM

74-11359.**

NBS Spec. Publ. 260-22, Standard Reference

Materials: Homogeneity Characterization of

Fe-3Si Alloy, February 1971. COM

74-11357**

iv
NBS Spec. Publ. 260-23, Standard Reference

Materials: Viscosity of a Standard Borosilicate Glass, December 1970. 25 cents.*

NBS Spec. Publ. 260-24, Standard Reference

Materials: Comparison of Redox Standards,

January 1972. $1.*

NBS Spec. Publ. 260-25, Standard Reference

Materials: A standard Reference Material

Containing Nominally Four Percent Austenite, February 1971. COM 74-11356.**

NBS Spec. Publ. 260-26, Standard Reference

Materials: National Bureau of Standards-U.S.

Steel Corporation Joint Program for Determining Oxygen and Nitrogen in Steel, February 1971. 50 cents.*

NBS Spec. Publ. 260-27, Standard Reference

Materials: Uranium Isotopic Standard Reference Materials, April 1971. COM

74-11358.**

NBS Spec. Publ. 260-28, Standard Reference

Materials: Preparation and Evaluation of

SRM's 481 and 482 Gold-SHver and GoldCopper AUoys for Microanalysis, August

1971. COM 71-50365.**

NBS Spec. Publ. 260-29, Standard Reference

Materials: Calibration of NBS Secondary

Standard Magnetic Tape (Computer Amplitude Reference) Using the Reference Tape

Amplitude Measurement "Process A-Model

2," June 1971. COM 71-50282.**

NBS Spec. Publ. 260-30, ' Standard Reference

Materials: Standard Samples Issued in the

USSR (A Translation from the Russian),

June 1971. COM 71-50283.**

NBS Spec. Publ. 260-31, Standard Reference

Materials: Thermal Conductivity of Electrolytic Iron SRM 734 from 4 to 300 K, November 1971. COM 71-50563.**

NBS Spec. Publ. 260-32,' Standard Reference

Materials: Standard Quartz Cuvettes For

High Accuracy Spectrophotometry. December 1973. 55 cents.*

NBS Spec. Publ. 260-33, Standard Reference

Materials: Comparison of Original and Supplemental SRM 705, Narrow Molecular

Weight Distribution Polystyrene, H. L. Wagner, May 1972. COM 72-50526.**

NBS Spec. Publ. 260-34, Standard Reference

Materials: Thermoelectric Voltage, April

1972. COM 72-50371.**

NBS Spec. Publ. 260-35, Standard Reference

Materials: Thermal Conductivity of

Austeniric Stainless Steel, SRM 735 from 5

to 280 K, April 1972. 35 cents.*

NBS Spec. Publ. 260-36, Standard Reference

Materials: A Referee Method for the Determination of Calcium in Serum. SRM 915,

May 1972. COM 72-50527.**

NBS Spec. Publ. 260-37, Standard Reference

Materials: Methods of Analysis of NBS Clay

Standards, June 1972. COM 72-50692.**

NBS Spec. Publ. 260-38, Standard Reference

Materials: Preparation and Calibration of

Standards of Spectral Specular Reflectance,

May 1972. 60 cents.*

NBS Spec. Publ. 260-39, Standard Reference

Materials: The Eddy Current Decay Method

for Resistivity Characterization of HighPurity Metals, May 1972. 55 cents.*

NBS Spec. Publ. 260-40, Standard Reference

Materials: Selection of Thermal Analysis

Temperature Standards Through a Cooperative Study (SRM 758, 759, 760), August

1972. 65 cents.*

NBS Spec. Publ. 260-41, Standard Reference

Materials: Use of Standard Light-Sensitive

Paper for Calibrating Carbon Arcs used in

Testing Textiles for Colorfastness to Light,

August 1972. COM 72-50775.**

NBS Spec. Publ. 260-42, Standard Reference

Materials: The Characterization of Linear

Polyethylene, SRM 1475, September 1972.

45 cents.*

NBS Spec. Publ. 260-43, Standard Reference

Materials: Preparation and Homogeneity

Characterization of an Austenitic Iron- Chromium-Nickel Alloy, November 1972.

45 cents.*

NBS Spec. Publ. 260-44, Standard Reference

Materials: Preparation and Use of Superconductive Fixed Point Devices, SRM 767, December 1972. 75 cents.*

NBS Spec. Publ. 260-45, Standard Reference

Materials: Powdered Lead-Based Paint, SRM

1579, March 1973. COM 73-50226.**

NBS Spec. Publ. 260-46, Standard Reference

Materials: Thermal Conductivity and Electrical Resistivity Standar-d Reference Materials:

Austenitic Stainless Steel, SRM's 735 and

798, from 4 to 1200 K. (In press)

V
NBS Spec. Publ. 26047, Standard Reference

Materials: Electrical Resistivity of Electrolytic Iron, SRM 797, and Austenitic Stainless

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

1974. 55 cents.*

NBS Spec. Publ. 260-48, Standard Reference

Materials: Description and Use of Precision

Thermometers for the Clinical Laboratory,

SRM 933 and SRM 934, May 1974. 60

cents.*

NBS Spec. Publ. 26049, Standard Reference

Materials: Calibrated Glass Standards for Fission Track Use, November 1974. 75 cents.*

*Send order with remittance to: Superintendent of Documents, U.S. Government Printing Office,

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

**May be ordered from: National Technical Information Services (NTIS), Springfield, Virginia

22151.

vi
CONTENTS

Page

1. Introduction 2

2. His£orical Review 4

2.1 Early Efforts 4

2.2 Iron 4

2.3 NBS, Washington Efforts 5

2.4 NBS, Boulder Efforts 5

2.5 AFML-AGARD Project 5

3. SRM Selection Criteria 6

4. Material Characterization 7 4.1 Material Acquisition and Fabrication 7 4.2 Composition 8

4.3 Electrical Resistivity Characterization 9

4.4 Other Characterization Data 12

5. Apparatus and Measurements 15

5.1 Low-Temperature (below ambient) 15

5.2 High-Temperature (above ambient) .... 16

6. Data Analysis (Selection of Best Values) 17

6.1 Electrical Resistivity 17

6.2 Thermal Conductivity 21

7. Discussion 26

8. Summary „ 27

9. Acknowledgements 28

10. References 29

Appendix I 31

Vii
LIST OF TABLES

Table Page

1. Characterization data of austenitic stainless steel, lot 1, as determined by Spyra - AGARD participant No. 7, and re- ported by Fitzer 8

2a. Electrical resistivity of austenitic stainless steel

(lot 1, as-received condition) 10

2b. Electrical resistivity of austenic stainless steel

(lot 2, as-received condition) 10

2c. Electrical resistivity of austenitic stainless steel

(lot 2, after hot swaging and annealing) 11

2d. Electrical resistivity of austenitic stainless steel

(lot 2, heat treatment effects) 11

2e. Hardness, grain size, and density of austenitic

stainless steel 12

3. Average low-temperature thermopower of three specimens

of austenitic stainless steel 13

4. Recommended values of electrical resistivity for

SRM 798, austenitic stainless steel 18

5. Recommended values of thermal conductivity for

SRM 735, austenitic stainless steel 23

LIST OF FIGURES

Figure Page

1. Low- temperature thermopower deviations among three

specimens of austenitic stainless steel 14

2. Deviations of electrical resistivity data for SRM

798 from equation 1 (parameters fitted to data above

273 K) . 19

3. Deviations of low- temperature electrical resistivity

data for SRM 798 from recommended values 20

viii
LIST OF FIGURES (continued)

Figure Page

4. Deviations of thermal conductivity data for SRM 735

above 200 K from equation 2 22

5a. Deviations of thermal conductivity data for SRM 735

from recommended values at temperatures from 5 to 40 K . 24

5b. Deviations of thermal conductivity data for SRM 735

from recommended values at temperatures from 40 to

280 K 25

ix

Thermal Conductivity and Electrical Resistivity

Standard Reference Materials: Austenitic

Stainless Steel, SRM's 735 and 798, from

4 to 1200 K

J. G. Hust and P. J. Giarratano

Cryogenics Division, NBS Institute for

Basic Standards, Boulder, Colorado 80302

A historical review of the development of selected thermophysical

Standard Reference Materials, SRM's, is given and selection criteria for

those SRM's are listed. Thermal conductivity and electrical resistivity

data for austenitic stainless steel, SRM's 735 and 798, are critically

evaluated. Recommended values are presented for the temperature range

4 to 1200 K. Material variability studies, including the effects of heat

treatment, have been performed at low temperatures. No irreversible

transformations are observed up to temperatures of 1200 K. Based on the

results of several types of characterization measurements, effects of

material variability are believed to be less than 1% in electrical re- sistivity and not significantly more in thermal conductivity. The uncertainty of the recommended electrical resistivity data is estimated at 1%

at low temperatures and 2% at higher temperatures. The corresponding

uncertainty for thermal conductivity is 2% below 100 K, increasing to 3%

at 300 K, and 5% at higher temperatures.

Key Words: Austenitic stainless steel, electrical resistivity, high

temperature, low temperature, standard reference materials, thermal

conductivity.

1
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., usually they are 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 ascertain 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 may indeed be possible but 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-of-the-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 virtually impossible. 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 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 some specimens change spontaneously with time, aging effects, and are

also dependent on their thermal and mechanical histories. These effects are especially significant at low temperatures especially for highly

* 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.

2
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 type measurements used by standardizing laboratories for state-of-the-art apparatus intercomparisons (see, for

example, Laubitz and McElroy [1]). Category (2) is considered to be the

most cost-effective 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 conductivity metal SRM's with conductivities ranging from

pure metals (high conductivity) to structural materials (low conductivity)

Plans are being foirmulated to extend this program to insulating materials

and dielectric solids as well. The current effort will result in two

additional reports: one on tungsten (high conductivity, 4 to 3000 K)

and another on electrolytic iron (medium- to-high conductivity, 4 to 1000 K)

The material reported on here, austenitic stainless steel, is in the low

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 austenitic stainless steel as electrical resistivity and thermal con- ductivity SRM's 798 and 735, respectively. As discussed later, thermal

conductivity and electrical resistivity data have been obtained to certify

these SRM's over the range 4 to 1200 K to well within engineering accuracy.

This material appears to have the qualities of an excellent 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 officially 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 lost. Not because the data are lost, but rather, because the stock of

material, on which the research was performed, is lost. This consideration also points out the significance of continuity in SRM projects.

3
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.

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 which has been the subject of the most extensive investigations

is ingot iron. Renewed interest in this material was spurred by the

round-robint 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 12" 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.

* 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.

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 consistent with the literature on ingot

iron.

4
2.3 NBS, Washington Efforts

D. R. Flynn of NBS, Washington began a study of potential thermal

conductivity SRM's during the early 1960's. He examined several ceramics*

and alloyst . 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 [8] re- ported 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 [9]

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 60'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 lowtemperature (4 to 280* K) SRM's of electrical resistivity and thermal con- ductivity. Current efforts are directed toward the extension of these to

higher temperature and to establish graphite and tungsten 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 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

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

t Inconel 702 (trade name of International Nickel Company, Inc.),

lead, and 60% platinum - 40% rhodium alloy.

5
this study. The results were reported in reference [10]. 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 [11]. Minges has also summarized some of the results on AFMLAGARD programs [12], 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 physical 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, be

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.

* 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.

6
5. The material should be useful over a wide temperature range.

The austenitic steel described in this report satisfies these criteria

reasonably well.

4. Material Characterization

Austenitic stainless steel was established as a low-temperature

(5 to 280 K) thermal conductivity Standard Reference Material (SRM 735)

in 1972 by Hust and Sparks [13]. In 1974 this material was established

as an" electrical resistivity Standard Reference Material (SRM 798) over

the same temperature range by Hust [14]. This steel was originally prepared and distributed for study as a high-temperature reference material

of thermophysical properties by AGAKD, NATO [11]. Several specimens of

the AGARD austenitic steel were measured over the low-temperature range

at this laboratory in advance of the completion of the AGARD program.

Because of its excellent low-temperature behavior it was established as an

SRM prior to the completion of the high-temperature AGARD work.

The high-temperature AGARD program has now been completed and the

results indicate that this austenitic stainless steel will be a useful

SRM of thermal conductivity and electrical resistivity up to temperatures

of about 1200 K. The purpose of this special publication is to present

an analysis of the AGARD and NBS data, to select best values, and to

indicate the uncertainty of these values. The characterization data,

described in the following sections, and the accord of the measurements

performed at low and high temperatures is sufficient to document the

data on this material for use as an SRM of electrical resistivity and

thermal conductivity.

4.1 Material Acquisition and Fabrication

Initially, AGARD supplied NBS with four 12" long rods for characterization and measurement. Two of these rods were 6 mm diameter and two were

10 mm diameter. The smaller diameter rods were used for fixed-point electrical resistivity measurements, while the larger two were machined for

measurement in the multi-property apparatus (thermal conductivity, electrical resistivity, and thermopower) . The larger diameter rods were also used

for grain size, hardness, and density measurements. No heat treatment was given these rods after machining. This material, referred to as lot 1, is

composed of melts A and B (See table 1)

.

These preliminary measurements indicated this material to be an excellent low- temperature SRM candidate. Therefore, another lot of this material

was purchased from the German manufacturer that produced lot 1. Twelve

rods, each 35 mm in diameter and 1 meter long, were obtained, fabricated

to appropriate size, and placed in NBS, OSRM stock. This material is

referred to as lot 2. Five cm long pieces were cut from the ends of six

of these rods for electrical resistivity and other characterization measurements. No heat treatment was given these rods after quartering and

7
machining to 6.25 nrni diameter rods. The characterization measurements

showed that lot 2 is indistinguishable from lot 1.

The next step was to prepare SRM specimens from the 35 mm diameter

rods of lot 2. Because of the high specimen preparation costs and ex- cessive material waste, that would result if the specimens were machined

to size, we decided to hot-swage the 35 mm diameter rods to the desirpd

size. This, of course, raises the question whether the material properties remain unchanged after swaging and reannealing. We performed

additional characterization measurements on several specimens prepared

in this manner by the U.S. Bureau of Mines, Albany, Oregon. The final

anneal was the same as that given in table 1. The results of these

measurements indicate again that the resulting specimens are indistinguishable from the specimens prepared originally from lots 1 and 2.

4.2 Composition

The aim composition and actual compositions of lot 1 (two melts)

were reported by Fitzer in his 1969 progress report [11] . These data

along with density values are listed in table 1. The reports by Fitzer

also contain data on thermal expansion, specific heat, thermal conductivity, and electrical resisitivity at temperatures from 20 to 900°C.

No other characterization data are presented.

Table 1 - Characterization data of austenitic

stainless steel, lot 1, as determined

by Spyra - AGARD participant No. 7, and reported by Fitzer

Composition in Weight %

Element Aim Melt Melt

Composition A B

Ni 20.0 - 20.5 19.90 20.48

Cr 16.0 - 16.5 16.41 15.98

Mh 1.0 - 1.2 1.20 1.22

Si 0.2 - 0.3 0.27 0.28

Nb 8 - 12 X C 0.10 0.09

Mo < 0.2 < 0.01 < 0.02

C < 0.02 0.009 0.008

P < 0.015 0.005 < 0.005

s < 0.015 0.006 0.004

N < 0.01 0.009 0.001

Fe bal 62.1 61.9

Heat treatment - 20 minutes at 1050 °C, quenched in water and 5 hours

at 900°C, cooled in air.

3 Density at 20°C - melt A = 8.007 g/cm

melt B = 8.011 g/cm"^

8
4.3 Electrical Resistivity Characterization

Electrical resistivity measurements are used extensively to characterize the variability of metals. For pure metals, the correlation of

thermal conductivity and electrical resistivity variability is excellent.

The theoretical basis for such a correlation in alloys is less rigorous,

but empirically we find if electrical resistivity is nearly invariant,

thermal conductivity variation will likely be small. The connection

between thermal conductivity and electrical resistivity is further discussed in Appendix I.

The ice-point and liquid helium temperature electrical resistivities

of ten specimens from lot 1 were measured and are listed in table 2a.

Nine specimens from lot 2 in the as-received condition were measured; the

results are listed in table 2b. The specimen identifications given in

these tables serve only to indicate that these were distinctly different

specimens. Six specimens were similarly measured from lot 2 after hotswaging and annealing. These results are listed in table 2c.

The effect of various heat treatments was also investigated. This

includes time-at-temperature as well as cooling rate effects. These data

are listed in table 2d.

The results listed in tables 2a-2d indicate a remarkable insensitivity of electrical resistivity on mechanical and thermal treatments for

this steel. The mean values of resistivity for each of these sets of data

are the same to within the uncertainty of the measurements (0.5%). The

range of each set is similarly within the uncertainty of the measurements.

Thus all of the specimens are indistinguishable on the basis of electrical

resistivity. Based on the earlier discussion, it is likely that thermal

conductivity variations for these specimens are not significantly larger

than ± 1%.

9
Table 2a - Electrical resistivity of austenitic

stainless steel (lot 1, as-received condition)

Specimen p(273.15 K) p(4 K)

(tJii cm) (|Jia cm)

1 (i/4" dia.) 78.8 . 59.4

2 (1/4" dia.) 79.2 59.9

1 (1/2" dia.) 78.6 59.5

2 (1/2" dia.) 78.7 59.6

X (1/4" dia.) 78.6

X (1/4" dia.) 78.7 59.3

1-1 (1/4" dia.)* 78.4 59.0

1-2 (1/4" dia.)* 78.6 59.0

1-3 (1/4" dia.)* 78.6 59.0

1-4 (1/4" dia.)* 78.6 59.1

Mean 78.7 59.3

Std. dev. 0.2 (0.3%) 0.3 (0.5%)

Range 78.4 to 79.2 59.0 to 59.9

* These specimens were measured by three other laboratories with a range

of ±0.5%.

Table 2b - Electrical resistivity of austenitic

stainless steel (lot 2, as-received condition)

Specimen p (273. 15 K) p (4 K)

(mH cm) (.\Jtfl cm)

Rl/Ql 78.5 59.0

R3/Q1 78.6 59.0

R2/Q1 78.6 58.9

R4/Q1 78.5 59.0

R5/Q1 78.7 59.2

R6/Q1 78.6 59.1

R1/Q4 -78.6 59.1

R1/Q2 78.6 59.1

R1/Q3 78.5 59.0

Mean 78.6 59.0

Std. dev. 0.1 (0.1%) 0.1 (0.2%)

Range 78.5 to 78.7 58.9 to 59

10
Table 2c - Electrical resistivity of austenitic

stainless steel (lot 2, after hot-swaging and annealing)

Specimen p (273.15 K) p (4 K)

cm) ([iQ cm)

1-0 79.1 59.2

1-1 78.8 59.0

2-0 78.7 58.8

2-1 78.9 59.0

3-0 78.6 58.9

4-0 78.6 59.1

Mean 78.8 59.0

Std. dev. 0.2 (0.3%) 0.1 (0.2%)

Range 78.6 to 79.1 58.8 to 59.2

Table 2d - Electrical res'istivity of austenitic

stainless steel (lot 2, heat treatment effects)

Specimen Heat Treatment p (273.15)

i\Jifl cm)

1-0 600°C in air for 1 hour 78.1

2-0 600°C in air for 1 hour 78.1

4-2 600°C in air for 2 hours 78.6

1-2 600°C in air for 2 hours 78.6

3-2 600°C in air for 4 hours 78.4

4-3 600°C in air for 4 hours 78.3

2-3 600°C in air for 8 hours 78.6

3-3 600°C in air for 8 hours 78.3

4-4 600°C in air for 16 hours 78.7

1-3 600°C in air for 16 hours 78.7

1-4 800°C in vacuum for 16 hours 78.3

4-4 800°C in vacuum for 16 hours 78.3

1-0 1000 °C in vacuum for 2 hours 78.3

2-0 1000°C in vacuum for 2 hours 78.4

1-4 1000° C in air for 1 hour,

water quench 78.1

4-4 1000°C in air for 1 hour,

water quench 78.2

1-0 1000°C in vacuum for 48 hours 78.5

2-0 1000°C in vacuum for 48 hours 78.4

Mean = 78.4

Std. dev. = 0.2 (0.3%)

11
4.4 Other Characterization Data

Other characterization data which support the thesis that thermal

conductivity variability is small are as follows: Hardness*, grain size,

and density variations, table 2e, are undetectable within the uncertainties of the measurements. Actual thermal conductivity measurements,

described in a later section, on three different specimens from both lots

1 and 2 confirm this conclusion.

This steel was also examined for low-temperature austenite-tomartensite transformation. Such a transformation would be undesirable

because of its effect on thermal conductivity and electrical resistivity.

Magnetization measurements were performed on specimens, which had been

cooled to liquid helium temperature for extended periods, to detect the

amount of the ferromagnetic martensitic phase. None was observed to

below the 0.1% level.

Table 2e - Hardness, grain size, and density of austenitic

stainless steel

Lot // 1

Lot # 2 as received

Lot # 2 after

hot swaging and

annealing

Hardness

(Rockwell B)

45 ± 2

48 ± 2

46 ± 2

Grain size

(mm)

0.04 ± 0.02

0.04 ± 0.02

0.07 ± 0.02

Density

(g/cm"^)

8.003 ± 0.004

8.009 ± 0.004

8.006 ± 0.004

The absolute thermopower was determined for three specimens of this

austenitic stainless steel at temperatures from 4 to 300 K. Two of the

specimens were from lot 1 and one from lot 2. One specimen from lot 1

is designated by WH because it was slightly bent during fabrication and

may have been work hardened. These data may serve as additional useful

characterization of this material. The conversion of the experimental

data, based on normal-silver wire, to the absolute scale, was performed

using the data of Borelius et al. [15]. The average thermopower of the

three specimens are listed in table 3. The deviations among the three

data sets are illustrated in figure 1. These measurements were performed

with the multi-property apparatus described in the next section.

The hardness of lot 2 after swaging and annealing appears larger

than the "as- received" lot 2 and lot 1; however, the uncertainty

shown is such that this conclusion is not justified.

12
Although the thermopower differences among the three specimens,

illustrated in figure 1, are within the total uncertainty of the measurements, part of the differences shown are attributed to real specimen

differences. This is due to the fact that a^major part of the uncertainty in these data is due to systematic error which is essentially

the same for all specimens. The estimated specimen-to-specimen component

of the uncertainty (imprecision) is about 0.02 ^iV/K above 80 K. Thus,

more than half of the deviation shown in figure 1 is attributed to real

specimen differences. This difference is equivalent to about 1% in

specimen-to-specimen thermopower variation.

Table 3 - Average low- temperature thermopower

of three specimens of austenitic stainless steel

Temp Thermopower Temp Thermopower

(K) (kiV/K) (K) (HV/K)

6 0.05 (0.05)* 60 -0.44 ( 0-.03)

8 0.09 (0.03) 70 -0.59 ( 0.03)

10 0.12 (0.02) 80 -0.71 ( 0.03)

12 0.18 (0.01) 90 -0.81 ( 0.03)

14 0.23 (0.01) 100 -0.89 ( 0.04)

16 0.27 (0.01) 120 -1.02 ( 0.04)

18 0.28 (0.02) 140 -1.12 ( 0.04)

20 0.28 (0.02) 160 -1.21 ( 0.04)

25 0.22 (0.02) 180 -1.28 ( 0.04)

30 0.14 (0.03) 200 -1.36 ( 0.03)

35 0.04 (0.03) 220 -1.44 ( 0.03)

40 -0.06 (0.03) 240 -1.51 ( 0.03)

45 -0.16 (0.03) 260 -1.59 ( 0.03)

50 -0.27 (0.03) 280 -1.66 ( 0.03)

* Numbers in ( ) are standard deviations.

13
/l I I I lJ \

I I I M I

\ u_

6 8 10 20 40 60 80 100 200 300

TEMPERATURE, K

FIGURE 1: Low- temperature thermopower deviations among three

specimens of austenitic stainless steel.

14
5. Apparatus and Measurements

5.1 Low-Temperature (Below Ambient)

Thermal conductivity and electrical resistivity measurements were

performed with a multiproperty apparatus based on the axial one-dimensional heat flow (longitudinal) method. This apparatus also yielded

the previously presented thermopower characterization data. The specimen

is 11,3 mm in diameter and 23 cm long with an electric heater at one end

and a temperature controlled heat sink at the other. The specimen is

surrounded by glass fiber and a temperature controlled shield. Eight

thermocouples are mounted at equally spaced points along the length of

the specimen to determine temperature gradients in the range 4 to 300 K.

A detailed description of this apparatus and an error analysis are presented by Hust et al. The estimated uncertainties (with 95% confidence) are as follows

Thermal conductivity: 2.5% at 300 K decreasing to 0.7% at 200 K,

0.7% from 200 K to 50 K, and increasing to 1.5% at 4 K.

Electrical resistivity: 0.25%

Thermopower: 0.2 [iV/K at 4 K, decreasing to 0.03 [XV/K at 80 K

and above.

Three specimens were measured in the low-temperature apparatus, two

from lot # 1 and one from lot # 2, over the range 4 to 280 K. The data

for each specimen were smoothed using conventional linear least-squares

methods with the following equations

n . , «n X = S a. r«n T]^

i=l

^

p = S b. [2n T]^"-^

i=l ^

S = E c^ [Cn T' ]^/T' ; T' = Jq

+ ^ 1=1

where X = thermal conductivity, p = electrical resistivity, and S = absolute thermopower. Temperatures are based on the IPTS-68 scale above

20 K and on the NBS P2-20 (1965) scale below 20 K. These functions have

no theoretical significance, but are chosen from past experience on the

basis of their usefulness for smoothing similar data. The optimum number of parameters is selected by utilizing orthogonal fitting analysis

15
to avoid either underfitting or overfitting the data. In the first case,

excessive oscillations, or wiggles, may be introduced in the temperature

dependence. These equations are used primarily for data analysis and

smoothing to within the accuracy of the data. Because of the form of the raw experimental data, the extensive number of data points, and the com- plexity ^of the data analysis, the experimental data are not presented

here. They are, however, printed in informal NBS reports [16,17] which

may be obtained from the author. No other data sources exist for temperatures below ambient.

5.2 High-Temperature (Above Ambient)

High-temperature thermal and electrical measurements were performed

by several participants of the AGARD, NATO project. These data are tabulated by Fitzer fll]. Participants 5 and 7 used a comparative (longitudinal heat flow) method to determine thermal conductivity above 400 K.

Participant 34 used an absolute (longitudinal heat flow) method as did

participant 7 below 400 K.

Thermal diffusivity values, which can be readily converted to thermal

conductivity data, were also measured on the AGARD, NATO program. These

data, also reported by Fitzer [11], were obtained as follows: participants 15 and 27 used a modulated electron beam technique, participants

22 and 24 used the angstrom technique, and participants 23, 30, and 5 used a laser flash method. To convert thermal diffusivity to thermal

conductivity one needs specific heat and density data. Participant 7 measured specific heat with an adiabatic calorimeter over the range 300

to 1100 K. These are the only specific heat values available for this

austenitic steel alloy. Densities were calculated from ambient density

and linear thermal expansion data as compiled by Fitzer.

In the next section, we describe the selection of "best values" of

thermal conductivity and electrical resistivity. This is done by the

method of weighted averaging; where the weight is assigned according to

the inverse square of the uncertainty. Thus it is imperative to obtain

reasonable estimates of the true uncertainty of each data set. It is

difficult, at best, to assess the true uncertainty of one's own data; and even more difficult to assess the validity of anothers' data. First, one must consider the published claims of the authors, second, one can make

data and theoretical intercomparisons . In making data intercomparisons

(from several sources) one runs the risk of confusing differences

caused by apparatus measurement errors and true specimen differences.

Based on the previously described characterization data, we believe that

specimen-to-specimen property variations caused by material inhomogeneities are not significantly larger than ± 1%. Since the differences in

reported experimental thermal conductivity and thermal diffusivity values

are appreciably greater than 1%, they are assumed to be caused primarily by

measurement errors. Note: above about 1200 K an irreversible transformation has been reported and may be a partial cause of larger reported variations. Our data show no such effects below 1200 K and, thus, no further

16
consideration is given to data above 1200 K. If this transformation does

in fact exist, one of the previously described desireable qualities of an

SRM is lacking and the use of this material should be limited to below

this temperature.

The uncertainty of the NBS thermal conductivity data near ambient

is taken as 2.5%, as previously reported by Hust and Sparks [16,17]. The

thermal conductivity data reported by the two AGARD participants 5 and 7 agree within 1-2% near ambient temperatures and within 4-5% at temperatures near 900 K. The agreement near ambient appears fortuitus considering the combined minimum uncertainties of their apparatus, the degree of

data scatter at only slightly higher temperatures, potential material

variability of their ingot iron standards (comparative methods were used

above 400 K) , and the disagreement of participant 5 from the data of other

participants on different materials on the AGARD, NATO project (see

Fitzer fll]). In view of this and other data presented by Fitzer fll],

the uncertainty for the high temperature thermal conductivity measurements

will be estimated as ± 5%.

The reported thermal diffusivity data of seven participants for a total

of ten specimens exhibit a scatter of about ± 40% at ambient temperature.

If one data source is omitted (participant 5) the range is reduced to

± 10%. At temperatures near 1200 K the range is about ± 15%. The un- certainty in the mean of this entire data set as converted to thermal con- ductivity values is estimated as ± 5%.

6. Data Analysis (Selection of best values)

No new thermal conductivity or electrical resistivity low-temperature data are reported. Therefore, the electrical resistivity data previously presented by Hust f 14] and the thermal conductivity data presented

by Hust and Sparks [13] are selected for the low temperature range. At

temperatures near ambient, joining of the low-temperature and high-temperature data sets necessitates slight changes in the previously recommended values, however. These changes are consistent with the previously

estimated uncertainty for each data set.

At temperatures above ambient, recommended values are based solely

on the data obtained from the AGARD, NATO project. Again, joining the

high-temperature and low-temperature data sets near ambient will alter

this somewhat, but not beyond the uncertainty of the data. Although,

other data exist in the literature for similar steels, characterization

of these steels is insufficient to warrant intercomparisons at the ± 5%

level.

6.1 Electrical Resistivity

Preliminary data analysis indicated that the electrical resistivity

data above 200 K varied as a constant power of temperature. Therefore,

17
the parameters of

p = aT + c (1) were fitted to the high-temperature data using an iterative' non-linear

least-squares method. Because of the numerous measurements performed on many specimens at 273.15 K, equation (1) was forced to yield the average

ice point value from table 2 (78.6 cm). The values of the constants

obtained are:

a = 154.1

b = 0.0997

c = -191.0

with p in cm and T in Kelvin. The maximum deviations of the experimental data from this equation are near 1%, consistent with the combined

material variability and measurement uncertainties. A systematic trend

of ± 0.5% occurs in the high .temperature deviations but this is believed

consistent with systematic measurement uncertainties. The deviations of

the data from equation 1 are shown in figure 2.. Equation 1 connects with

the low-temperature data of Hust fl4] at 273 K. Note that below 273 K

equation 1 does not have the correct form to represent the low temperature

data of Hust [14] . Above 273 K, equation 1 was used to obtain values of

electrical resistivity for SRM 798. Table 4 lists these values above

273 K and the existing low-temperature data from Hust [14]. The deviations

of the low-temperature data from the recommended values are illustrated in

figure 3.

Table 4 - Recommended values of electrical resistivity

for SRM 798, austenitic stainless steel

Temp Electrical Temp Electric.

(K) Resistivity (K) Resistiv

(pQ cm) (pO cm)

5 59.3 250 76.8

10 59.3 300 81.1

15 59.3 350 85.3

20 59.3 400 89.0

25 59.3 450 92.3

30 59.4 500 95.3

40 59.7 600 100.6

50 60.1 700 105.1

60 60.7 800 109.1

70 61.3 900 112.6

80 62.1 1000 115.8

100 63.8 1100 118.8

120 65.6 1200 121.4

140 67.4

160 69.2

180 71.0

200 72.7

18
3.6 T 1

\—

2.8

2.0

o

Q. O

o

1.2

cr

O

CL

Average of ice-point data (Table 2)

A Hust • Agard data

,

* *

-0.4 -

1.2 1 I I I 200 400 600 800

TEMPERATURE, K

1000 2000

FIGURE 2: Deviations of electrical resistivity data for SRM 798

from equation 1 (parameters fitted to data above 273K)

19
0.6

0.4 -

0.2 -

o

Q. O

o

J3O

Q. 0.2

0.4 -

-0.6

1 — —

1 1 —\

1 1 A bpecimen

1 1

1 1

i , Lot d Specimen 1, Lot 1 - T

Specimen WH, Lot 1 —

—

- T

T

A A

A

A

1

I 11 1 1 0 80 160

TEMPERATURE, K

240 320

FIGURE 3: Deviations of 1 ow- tempera ture electrical resistivity

data for SRM 798 from recommended values.

20
The uncertainty of the electrical resistivity data for SRM 798, including material variability, is estimated as 1% at low temperatures and 2%

at high temperatures.

6.2 Thermal Conductivity

Preliminary analysis of the thermal conductivity data for this

austenitic steel indicated that above 200 K the data varied as a constant

power of temperature. This prompted us to fit the equation

k = aT^ (2)

by non-linear least-squares methods to the data above 200 K. The data

were weighted according to the inverse square of the previously specified

uncertainties. The resultant values of the constants are

a = 1.22

b = 0.432,

the maximum deviations of the thermal conductivity and converted thermal

diffusivity data are 8%, slightly larger, but not unreasonably so, than

the estimated uncertainties of these data, 5%. The deviations of the

experimental data from those calculated with equation 2 are presented in

figure 4. The values calculated from equation 2 agreed with the NBS lowtemperature data at 230 K. Thus, the recommended values below 230 K are

those given by Hust [13] and above 230 K those obtained from equation 2.

These recommended values are tabulated in table 5. The deviations of

the NBS low-temperature data from the previously recommended values are shown in figures 5a and 5b. The currently recommended values between

230 K and 280 K differ slightly from the previously recommended values

in order to achieve a smooth transition at ambient temperature. The

maximum difference is 1% at 280 K, decreasing to zero at 230 K. The

estimated uncertainty of the recommended thermal conductivity data,

including material variability, is 2% up to 100 K, increasing to 3% at

300 K, and 5% at higher temperatures.

21
10

6

2

1

1

1

1 1 1 1 r # , A , Hus t —

- & A, 0,n Agard -

° o

- o

o ^

o

o

n

A

-

— O—

ir a

A n

A

B • t

T

O O A°

A A A

1 1 1

1 o o

1 1 1 1 200 400 600 800 1000 2000

TEMPERATURE, K

FIGURE 4: Deviations of Thermal Conductivity Data for SRM 735

above 200K from equation 2.

22
Table 5 - Recommended values of thermal conductivity

for SRM 735, austenitic stainless steel

Temp Thermal

(K) Conductivity

(W/m K)

5 0.466

6 0.565

7 0.676

8 0.796

9 0.921

10 1.05

12 1.32

14 1.58

16 1.86

18 2.13

20 2.40

25 3.07

30 3.72

35 4.34

40 4.92

45 5.47

50 5.98

55 6.45

60 6.88

65 7.28

70 7.64

75 7.97

80 8.27

85 8.55

90 8.80

95 9.04

Temp Thermal

(K) Conductivity

(W/m K)

100 9.25

110 9.65

120 9.99

130 10.3

140 10.6

150 10.9

160 11.1

170 11.4

180 11.6

190, 11.9

200 12.1

250 13.2

300 14.3

350 15.3

400 16.2

450 17.1

500 17.9

600 19.3

700 20.6

800 21.9

900 23.0

1000 24.1

1100 25.1

1200 26.1

23
T _0 05pecimen2,Lot2

q-| Specimen WH, Lot 1 ~^ ^ Specimen 1, Lot 1

I

O

4 12 20 28 36 44

TEMPERATURE, K

FIGURE 5a: Deviations of Thermal Conductivity Data for

SRM 735 from recommended values at temperatures

from 5 to 40K.

24
O Specimen 2, Lot 2

Specimen WH, Lot 1 A Specimen 1, Lot 1

0 80 160 240 320

TEMPERATURE, K

FIGURE 5b: Deviations of Thermal Conductivity Data for

SRM 735 from recommended values at temperatures

from 40 to 280K.

25
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

round-robin type measurements by standards laboratories 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 for 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

suggest that the effects of material variability in this austenitic

steel are not significantly larger than 1%. The results of thermal con- ductivity, electrical resistivity, and thermopower measurements on

three specimens of this steel over the temperature range 5 to 280 K

are also presented. These results are in accord with maximum material

variability effects of near 1%. The correlation of the deviations of

these properties for these three specimens may shed additional light

on the true specimen differences. As pointed out earlier, although the

measured differences between specimens are in all cases nearly as large

as the experimental uncertainties specimen differences somewhat below

the measurement uncertainty can be detected. This is so because the

imprecision of the measurements is about one-half the total uncertainty.

It is observed from figures 1, 3, and 5 that the specimen from

lot 2 has a slightly more positive (smaller in absolute magnitude)

thermopower, lower electrical resistivity, and an almost imperceptibly

larger thermal conductivity than the other two specimens. In the

absence of concomitant opposing effects these changes are consistent with

the indicated larger grain size of the specimen from lot 2. A larger

26
grain size results in less grain boundary scattering increasing the

electrical and thermal conductivity. It is more difficult to predict

the effect on thermopower, but, recent unpublished work on thermocouple

materials [18] suggests that the absolute value of thermopower decreases

with increasing grain size. This is in agreement with the observed

change.

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 would-be improved with additional measurements. This is especially true at temperatures above ambient where

the estimated uncertainty is ± 5% in thermal conductivity. Through its use as an SKM this material will be measured by other laboratories.

These data will be compiled and when sufficient reduction in uncertainty

is achievable, the recommended values will be updated. Anyone measuring this material with an absolute method is urged to make the data

available to the first author.

The electrical resistivity and thermal conductivity data has been

compiled and analyzed for an austenitic stainless steel. Recommended

values are tabulated for temperatures from 5 to 1200 K and form the

basis of SRM's 798 (electrical resistivity) and 735 (thermal conductivity).

Electrical resistivity values are estimated uncertain by 1% below ambient

and 2% above ambient. Thermal conductivity uncertainties are 2% below

100 K, increasing to 3% at ambient temperature, and 5% above ambient.

Material variability effects, included in the above uncertainties, are estimated to be near 1%.

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.

8 . Summary

SRM 735-S

SRM 735-Ml

SRM 735-M2

SRM 735-Ll

SRM 735-L2

SRM 798-1

SRM 798-2

SRM 798-3

0.64 cm diameter,

1.25 cm diameter,

1.25 cm diameter,

3.4 cm diameter,

3.4 cm diameter,

0.64 cm diameter,

0.64 cm diameter,

0.64 cm diameter.

30

15

30

5

10

5

10

15

cm

cmcm

cm

cm

cm

cm

cm

long

long

long

long

long

long

long

long.

Longer continuous lengths can be obtained by special order.

27
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. Larry L. Sparks assisted in the

measurement of thermal conductivity with the multiproperty apparatus.

E. Fitzer was very cooperative in the procurement of the stock of

material from the German manufacturer. He also supplied the AGARD

program results and the original specimens for measurement. We wish

to thank the personnel of the U.S. Bureau of Mines, Albany, Oregon,

especially Steve O'Hare, for fabricating the final rod sizes for these

SRM's. Last, but not least, we wish to thank R. E. Michaelis of NBS,

OSRM for supporting this work and many helpful discussions.

28
10. References

1. M. J. Laubitz and D. L. McElroy, Precise Measurements of Thermal

Conductivity at High Temperatures (100 - 1200 K) , Metrologia 7^, 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. Shelton, 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.

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. M. J. Laubitz and K. D. Cotnam, Thermal and Electrical Properties

of Inconel 702 at High Temperatures, Can. J. Phys. 42, 131-152

(1964) .

9. 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).

10. 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.

11. E. Fitzer, Thermophysical Properties of Solid Materials, Advisory

Report 12 (1967), Advisory Report 38 (1972); Report 606 (1972),

AGAKD, NATO, France.

29
12. M. L. Minges, Evaluation of Selected Refractories as High Temperature Thermophysical Property Calibration Materials, AFML Technical

Report TR-73-278 (1974); Int'l. J. Heat and Mass Transfer, Pergamon

Press, London, (to be published in 1974)

'13. J. G. Hust and L. L. Sparks, Thermal Conductivity of Austenitic

Stainless Steel, SRM 735, from 5 to 280 K, Nat. Bur. Stand. Special

Publication 260-35 (1972).

14. J. G. Hust, Electrical Resistivity of Electrolytic Iron, SRM 797,

and Austenitic Stainless Steel, SRM 798, from 5 to 280 K, Nat. Bur.

Stand. Special Publication 260-47 (1974).

15. G. Borelius, W. H. Keesom, C. H. Johansson, and J. 0. Linde,

Establishment of an Absolute Scale for the Thermometric Force,

Proc. Kon. Akad. Amsterdam 35, 10 (1932).

16. J. G. Hust and L. L. Sparks, Thermal Conductivity Standard Reference

Materials from- 4 to 300 K: III AGARD Stainless Steel, unpublished

NBS Report (1971)

17. J. G. Hust and L. L. Sparks, Thermal Conductivity Standard Reference

Materials from 4 to 300 K: V AGARD Stainless Steel, unpublished

NBS Report (1971)

18. Noel Burley (private communication).

30
Appendix I. Discussion of electrical resistivity and

thermal conductivity variability

The electrical resistivity, p, and thermal conductivity, A,, of

metals are intimately related, especially for pure metals, but also 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, X , and the lattice. A, , (the German

word for lattice is Gitter) components.

A, = A. + X . (1) e g

In most pure metals A,^ is small compared to X^, but in transition metals

A, may be as large as 20% of A, , and in some alloys A, is much larger

g e ' g

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:

^ = L = 2. 443 X

10"^ vV^, (2)

T o where is the Sommerfeld value of pA,/T and T is the temperature. At

intermediate temperatures, large deviations from the WFL law are observed.

For, our purposes the ice point is a sufficiently high temperature and

liquid helium is a sufficiently low temperature to satisfy the WFL

law. In complex alloys such as steel, equation (2) does not hold,

but it has been observed that the value of the Lorenz function, pA,/T,

is reasonably independent of material within a given class of alloys

such as austenitic stainless steel (Fe-18Cr-8Ni alloys) . This indicates

a close but unexplained relationship between p and X even though A, is small compared to A, . g

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.

31
p(T) = + P^CT). (3)

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

good approximation for our purposes. For steels, the residual resistivity

is a significant part of the total resistivity, even at room temperature;

thus, values of either room temperature resistivity or residual resistivity can be used as indicators of material variability. This differs

from pure metals in that is much smaller than p(293 K) for pure metals;

therefore, p(293 K) is not an indicator of purity. The variability in

resistivity for various specimens in a given lot of material is an indication of the variability in chemical composition and physical imperfection

concentration in the lot. These material variations also cause thermal

conductivity variations as indicated by the Lorenz function for a given

class of alloys. Therefore, a determination of resistivity variability

will usually approximate the thermal conductivity variability in alloys.

The determination of electrical resistivity is considerably easier than

the determination of X.
NBS-1 14A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS-SP 260-462, Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE STANDARD REFERENCE MATERIALS:

Thermal Conductivity and Electrical Resistivity Standard

R efer enc e Materials : Austenitic Stainless Steel, SRM s 735

and 798, from 4 to 1200 K.

5. Publication Date March 1975

6. Performing Organization Code

7. AUTHOR(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

Gaithersburg, Maryland

13. Type of Report 8c Period Covered Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 75-61903

16. ABSTRACT (A 200-word or less [actual summary of most si0\ilicant information. If document includes a significant

bibliography or literature survey, mention it here.)

A historical review of the development of selected thermophysical

Standard Reference Materials, SRM's, is given and selection criteria for

those SRM's are listed. Thermal conductivity and electrical resistivity

data for austenitic stainless steel, SRM's 735 and 798, are critically

evaluated. Recommended values are presented for the temperature range

4 to 1200 K. Material variability studies, including the effects of heat

treatment, have been performed at low temperatures. No irreversible

transformations are observed up to temperatures of 1200 K. Based on the

results of several types of characterization measurements, effects of

material variability are believed to be less than 1% in electrical re- sistivity and not significantly more in thermal conductivity. The uncertainty of the recommended electrical resistivity data is estimated at 1%

at low temperatures and 2% at higher temperatures. The corresponding

uncertainty for thermal conductivity is 2% below 100 K, increasing to 3%

at 300 K, and 5% at higher temperatures.

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

Austenitic stainless steel; electrical resistivity; high temperature; low temperature;

standard reference materials; thermal conductivity.

18. AVAILABILITY [x^ Unlimited

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