conductivity variability in alloys. The determination of
electrical resistivity is considerably easier than the

determination of i.

Table 1. Characterization data of SRM 735

stainless steel.

Specimen Lot 1 Lot 2 Lot 2*
2273 x, em? 788 786 788
4 x, em? 596 590 590
RRR = 9273 x/P4 xt. 002 1.322 1.331 1.334
hardness, (Rockwell) +2 B45 B48 B46
grain size, (mm) +0.01 0.04 0.04 0.07
density, (g/m?) #0.004 8.004 8.009 8.006

*after hot-swaging and reannealing.

10


3. SPECIMEN CHARACTERIZATION

Initially, AGARD supplied four steel rods for character-
ization and measurement. Two rods were 6 mm diameter and
the other two were 10 mm diameter. The smaller rods were
used for electrical resistivity measurements while the larger
two were machined for thermal conductivity measurements.
These rods are referred to as lot 1 and measurements on them
suggested that this steel would be a useful standard of thermal
conductivity. A second lot of this material was purchased
for further measurements and for stocking. The 12 rods
from lot 2 were each 35 mm in diameter and 1 meter in length.
Six five-cm-long pieces were cut from the ends of six of
these rods for electrical resistivity characterization. These
Measurements showed that lot 2 is indistinguishable, within
1%, from lot 1.

Preparation of specimens by NBS-OSRM was then begun.
Because of high specimen preparation costs and the excessive
waste that would result from machining the 35-mm rods to
smaller size, we decided to hot swage the rods to the desired
diameters. However, this raised the question of whether the
specimens would remain unchanged after hot swaging and
reannealing. We performed additional characterization
measurements on six specimens prepared by this method.

The results, listed in table 1, show that specimens prepared
by this procedure are within 1% in resistivity of the
specimens from lots 1 and 2 as received. Based on a total
of 21 elctrical resistivity determinations, it is concluded
that the thermal conductivity variability of specimens

from these lots is less than 1%. A discussion of the
connection between electrical resistivity and thermal con-
ductivity variability is presented in Appendix I.


( robs . atc )100 robs

2.4 + +

t) 80 160 240
TK
Figure lb. Expermental thermal conductivity deviations

from mean values of three specimens from 40
to 300 K.

14

320


OTHER NBS PUBLICATIONS IN THIS SERIES

NBS Spec. Publ. 260, Catalog of Standard Reference Materials,

July 1970. 75 cents.* (Supersedes NBS Misc. Publ. 260,
January 1968 and NBS Misc. Publ. 241, March 1962.)

NBS Misc. Publ. 260-1, Standard Reference Materials:
Preparation of NBS White Cast Iron Spectrochemical
Standards, June 1964. 30 cents.*

NBS Misc. Publ. 260-2, Standard Reference Materials:
Preparation of NBS Copper-Base Spectrochemical
Standards, October 1964. 35 cents.*

NBS Misc. Publ. 260-3, Standard Reference Materials:
Metallographic Characterization of an NBS Spectrometric
Low-Alloy Steel Standard, Cctober 1964. 20 cents.

(Out of print).

NBS Misc. Publ. 260-4, Standard Reference Materials:
Sources of Information on Standard Reference Materials,
February 1965. 20 cents. (Out of print).

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).

WBS Misc. Publ. 260-6, Standard Reference Materials:
Methods for the Chemical Analysis of White Cast Iron
Standards, July 1965. 45 cents.*

NBS Misc. Publ. 260-7, Standard Reference Materials:
Methods for the Chemical Analysis of NBS Copper-Base
Spectrochemical Standards, October 1965. 60 cents.*

NBS Misc. Publ. 260-8, Standard Reference Materials:
Analysis of Uranium Concentrates at the National
Bureau of Standards, December 1965. 60 cents.
(Out of print).

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. 15 cents.*

NBS Misc. Publ. 260-10, Standard Reference Materials:
Homogeneity Characterization on NBS Spectrometric
Standards II: Cartridge Brass and Low-Alloy Steel,
December 1965. 30 cents.*

iv


Table 2. Parameters, ay of equation (4).

i ay
1 -4.85984600
2 6.59025067
3 -3.74701178
4 1.16265324
5 -2.05457295 x 1072
6 1.93981539 x 1072
7 -7.59098428 x 107+

11


obs

)100/\

Oops - reale

ic)
Og
4 4 7
, qa 8 8
é 9 0 A
; ate 0 pe. % ACE o4 9 @
6 oT haa a
4% ° oe, 9go6ng
0 4
tc)

-4

12

Figure la.

20

TK

28

36

4

Experimental thermal conductivity deviations

from mean values of three specimens from 5 to

40 K.


Appendix I. Discussion of electrical resistivity and
thermal conductivity variability.

The electrical resistivity, op, and thermal conductivity,
A, of metals are intimately related, especially for pure
metals, put also for alloys to a lesser extent. This
relationship exists because in a metal most of the heat
is transported by the elettrons. Some heat is also
transported by the lattice vibrations. The total thermal
conductivity is the sum of the electronic, Aer and the lattice,
Age (the German word for lattice is Gitter) components.

A=AL +ALL (1)

In most pure metals Ag is small compared to Aer but in
transition metals Ag May be as large as 20% of rer and in
some alloys g is much larger than rer For pure metals

and dilute alloys, the relationship between p and i at

both high and low temperatures is reasonably well described
by the Wiedemann-Franz-Lorenz (WFL) law:

= Ly = 2.443 x 1078 v?x-?, (2)

ae.
)

where Ly is the Sommerfeld value of p\/T and T is the temper-
ature. 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 this steel eq (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 relation-

ship between p and i even re is small compared to Age


LIST OF FIGURES

Figure No.
la. Experimental thermal conductivity
deviations from mean values of three
specimens from 5 to 40 K ...........2.e eens

lb. Experimental thermal conductivity
deviations from mean values of three
specimens from 40 to 300 K weceeeeesecoeeee

2. Thermal conductivity of SRM 735 ...........

PAGE

13

14

15


NBS Spec. Publ. 260-22, Standard Reference Materials:
Homogeneity Characterization of Fe-3Si Alloy,
February 1971. 35 cents.*

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. $1.00.*

NBS Spec. Publ. 260-25, Standard Reference Materials:
A Standard Reference Material Containing Nominally Four
Percent Austenite, February 1971. 30 cents.*

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. $1.25.*

NBS Spec. Fubl. 260-28, Standard Reference Materials:
Preparation and Evaluation of SRM's 481 and 482 Gold-Silver
and Gold-Copper Alloys for Microanalysis, August 1971.
$1.00.*

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. 60 cents.*

NBS Spec. Publ. 260-30, Standard Reference Materials:
Standard Samples Issued in the USSR (A Translation
from the Russian), June 1971. $1.00.*

NBS Spec. Publ. 260-31, Standard Reference Materials:
Thermal Conductivity of Electrolytic Iron SRM 734 from
4 to 300K, November 1971. 35 cents.*

NBS Spec. Publ. 260-32, Standard Reference Materials:
The Cooperative Study of Temperature Scale Standards
for DTA by ICTA and NBS. (In preparation)

NBS Spec. Publ. 260-33, Standard Reference Materials:
comparison of Original and Supplemental SRM 705,
arrow Molecular Weight Distribution Polystyrene,

L. Wagner. ‘In preparation).

vi


NBS Misc. Publ. 260-11, Standard Reference Materials:
Viscosity of a Standard Lead-Silica Glass, November
1966. 25 cents.*

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. 20 cents,*

NBS Misc. Publ. 260-13, Standard Reference Materials:
Mésssbauer Spectroscopy Standard for the Chemical Shift
of Iron Compounds, July 1967. 40 cents.*

NBS Misc. Publ. 260-14, Standard Reference Materials:
Determination of Oxygen in Ferrous Materials --
SRM 1090, 1091, and 1092, September 1966. 30 cents.*

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.

20 cents.*

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. 35 cents.*

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.
50 cents.*

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. 30 cents.*

NBS Spec. Publ. 260-20, Standard Reference Materials:
Preparation and Analysis of Trace Element Glass
Standards. (In preparation)

NBS Spec. Publ. 260-21, Standard Reference Materials:
Analysis of Interlaboratory Measurements on the Vapor
Pressures of Cadmium and Silver, January 1971. 35 cents.*

v


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, Por while the resistivity due
to thermal scattering is called the intrinsic resistivity,
0; (T). The total resistivity, p(T), may be written as the
sum of these two terms.

e(T) = p, + p,(T). (3)

This separation of the total resistivity into a constant
term (p,) and a temperature dependent term (0; (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; there-
fore, o(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 conduc-
tivity variations as indicated by the Lorenz function for a
given class of alloys. Therfore, a determination of resis-

tivity variability will usually approximate the thermal
9


TABLE OF

1. Introduction .......

2. Apparatus and Data Analysis

3. Specimen Characterization .

4. Results . 2. 2. 6 ee se eee

5S. Summary . - +--+ + + + + + ©

6. Footnotes and References. :

Appendix I ......-.

LIST OF

Table No.

CONTENTS

TABLES

1. Characterization data of SRM 735

stainless steel. ...

2. Parameters, a; of equation (4)

3. Thermal conductivity of austenitic

stainless steel (SRM 735) oe

ix

PAGE
. 2
. 3
. 4
. 5
- 6
. 7
. 8
PAGE
- 10
» ill
» (12


-1

K

-1

THERMAL CONDUCTIVITY, Wm

20

0.4

t+ + a +--+ +
4
4
8 10 20 ao 66 80 100 200
TK
Figure 2. Thermal conductivity of SRM 735

400


U.S.
DEPARTMENT
OF

COMMERCE
National
Bureau

of

Standards

NBS SPECIAL PUBLICATION 260-35

Standard Reference Materials:

THERMAL CONDUCTIVITY OF
AUSTENITIC STAINLESS STEEL,
SRM 735, FROM 5 to 280 K



1. INTRODUCTION

This report is a result of a program to establish
several thermal conductivity Standard Reference Materials
(SRM's). Measurements are planned for SRM's of high, medium
and low conductivity. An earlier report [1] describes the
establishment of SRM 734 material as a medium-high thermal
conductivity SRM. The material reported on here, stainless
steel SRM 735* [2], is in the low conductivity range.

Design and development engineers in the aerospace
industry continue to have urgent need for thermal and
mechanical property data for new materials. For most
materials, especially new or uncommon alloys, measured values
of thermal conductivity are not available and predictions
cannot be made with adequate confidence. To help satisfy
these needs, we have constructed an apparatus for the
simultaneous measurement of thermal conductivity, electrical
resistivity, and thermopower. We intend to measure several
specimens of materials that appear to be useful as standards.
SRM data are useful for intercomparison of existing ther-
mal conductivity apparatus, for debugging new apparatus, and
for calibration of comparative apparatus. The apparent large
differences (50% is not uncommon) among the results of various
investigators for a given material is evidence of the need
for reliable thermal conductivity SRM's.

* This steel was originally prepared and distributed for use
as a Standard Reference Material for high-temperature ther-
mophysical properties by the Advisory Group for Aerospace
Research and Development (AGARD) under the direction of NATO.
It was measured at this laboratory to establish a standard

at low temperatures as well. Temperatures from 5 to 280 K
are included in this work. Later, as data from other labora-
torys are reported, it will be possible to extend the range
to higher temperatures.


THERMAL CONDUCTIVITY OF AUSTENITIC STAINLESS
STEEL, SRM 735, FROM 5 TO 280 K*

J. G. Hust and L. L. Sparks
Cryogenics Division, NBS Institute for
Basic Standards, Boulder, Colorado 80302

Thermal conductivity data are presented for a well-
characterized austenitic stainless steel. Thermal conductivity
and electrical resistivity measurements were conducted on
two lots of this steel. Electrical resistivity measurements
were performed on the second lot both before and after the
material was hot-swaged and reannealed to a size 1/10 the
original diameter. These measurements indicate that this
steel can be swaged and reannealed without an appreciable
change in thermal conductivity. Electrical resistivity
Measurements as well as direct thermal conductivity measure-
ments on several specimens from both lots indicate a material
variability in these lots of less than 1% in thermal con-
ductivity.

Key words: Cryogenics; electrical resistivity; stainless
steel; Standard Reference Material; thermal conductivity.

*This work was carried out at the National Bureau of
Standards, Boulder, Colorado, under the sponsorship of NASA-
Space Nuclear Systems Office, Cleveland, Ohio, and the
National Bureau of Standards Office of Standard Reference
Materials (NBS-OSRM), Washington, D. C.


NBS Spec. Publ. 260-34, Standard Reference Materials:
Thermoelectric Voltage. (In preparation).

NBS Spec. Publ. 260-35, Standard Reference Materials:
Thermal Conductivity of Austenitic Stainless Steel,
SRM 735 from 5 to 280K*. (This publication).

*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.

vii


Table 3. Thermal conductivity of austenitic
stainless steel (SRM 735).

Thermal Thermal
Temperature Conductivity Temperature Conductivity
(K) (n> x7) (x) (wm? x7)
5 0.466 75 7.97
6 0.565 80 8.27
7 0.676 85 8.55
8 0.796 90 8.80
9 0.921 95 9.04
10 1.05 100 9.25
12 1.32 110 9.65
14 1.58 120 9.99
16 1.86 130 10.3
18 2.13 140 10.6
20 2.40 150 10.9
25 3.07 160 11.1
30 3.72 170 11.4
35 4.34 180 11.6
40 4.92 190 11.9
45 5.47 200 12.1
50 5.98
55 6.45 220 12.6
60 6.88 240 13.0
65 7.28 260 13.4
70 7.64 280 13.8

12


PREFACE

Standard Reference Materials (SRM's) as defined by the
National Bureau of Standards are "well-characterized mate-
rials,produced in quantity, that calibrate a measurement
system to assure compatability 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 tech-
nologists 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 de-
tail 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 measure-
ment 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 appli-
cations 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


The nominal composition of stainless steel SRM 735 is as
follows: (The composition of lot 1 as determined by the
supplier is given in parentheses)

Element Percent, by weight

Ni 20.0-20.5 (19.390)
cr 16.0-16.5 (16.41)
Mn 1.0- 1.2 (1.20)
Si 0.2- 0.3 ( 0.27)
Nb 8-12 x C (0.10)
Mo <0.2 ( 0.01)
c <0.02 (0.009)
N <0.01 (0.009)
P <0.015 ( 0.005)
s <0.015 ( 0.006)
Fe bal (bal)

4, RESULTS

The thermal conductivity of three specimens, two from
lot 1 and one from lot 2, was measured from 5 to 280 K.
uhese data were functionally represented with the following

equation:

n
&nd = xr a; nT]

i=l

itl
(4)

where A = thermal conductivity in wn tk7+ and T = temperature

in K. Temperatures are based on the IPTS-68 scale above 20
K and the NBS P2-20 (1965) scale below 20 K. ‘The parameters,
ay determined by least squares for the mean conductivity

of these three specimens, are presented in table 2. Further
details of the method of data analysis are given by Hust,

et al. [3]. The deviations of the experimental data from
this equation are given in figures la and lb. Calculated
values of thermal conductivity are presented in table 3 and

figure 2. 5


(1]

{2]

(3]

6. FOOTNOTES AND REFERENCES

Hust, J. G.,Sparks, L. L., Thermal Conductivity of
Electrolytic Iron, SRM 734, from 4 to 300 K, Nat. Bur.
of Stand. Spec. Pub. 260-31, 19 p. (Nov. 1971).

This SRM is available in the form of rods of three
diameters and may be ordered from the Office of
Standard Reference Materials, National Bureau of
Standards, Washington, D. C. 20234. SRM 735-S is
0.65 cm in diameter and 30 cm long. SRM's 735-Ml
and M2 are 1.25 cm in diameter and 15 and 30 cm
long, respectively. SRM's 735-L1l and f2 are 3.5
cm in diameter and 5 and 10 cm long, respectively.

Hust, J. G. Powell, R. L., and Weitzel, D. H.,

Thermal Conductivity Standard Reference Materials

from 4 to 300 K. I. Armco Iron: Including Apparatus
Description and Error Analysis, J. Res. Nat. Bur. Stand.
(U.S.), 74A (Phys. and Chem.) No. 5, 673-690 (1970).


Library of Congress Catalog Number: 72-600028

National Bureau of Standards Special Publication 260-35

Nat. Bur. Stand. (U.S.), Spec. Publ. 260-35, 22 pages (Apr. 1972)
CODEN: XNBSAV

Issued April 1972

For sale by the Superintendent of Documents, U.S. Government Printing Office
Washintgon, D.C. 20402 (Order by SD Catalog No. C 13.10:260-35). Price 35 cents.


Standard Reference Materials:

Thermal Conductivity of Austenitic Stainless Steel,
SRM 735, from 5 to 280 K

J. G. Hust and L. L. Sparks

Institute for Basic Standards
National Bureau of Standards
Boulder, Colorado 80302

nt OF
gnen Cy,

* a
hros «3

woe on,

S
a 3
‘Ureay of °

U.S. DEPARTMENT OF COMMERCE, Peter G. Peterson, Secretary
NATIONAL BUREAU OF STANDARDS, Lewis M. Branscomb, Director,

Issued April 1972



The availability of SRM's will result in more accurate and
more permanent transport property data for technically
important solids.

The basic characteristics of a thermal conductivity
SRM are that it be: (a) stable and reproducible under the
conditions of use, (b) uniform throughout a single specimen
and from specimen-to-specimen, (c) similar in thermal con-
ductivity to that of the materials to which it will be applied,
(d) readily machined and fabricated to appropriate size
and shape, (e) chemically inert with its environment, and
(£) usable over a wide temperature range. Stainless steel
SRM 735 satisfies these criteria reasonably well.

2. APPARATUS AND DATA ANALYSIS

The apparatus is based on the axial one-dimensional
heat flow method. The specimen is a cylindrical rod 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.

The experimental data are represented by arbitrary
functions over the entire range and smooth tables are
generated from these functions. The number of terms used
to represent each of the data sets is optimized, through the
use of orthonormal functions, so that none of the precision
of the data is lost by underfitting, nor are any unnecessary
oscillations introduced by overfitting. A detailed descrip-
tion of this apparatus and the methods of data anlaysis are
given by Hust, et al. [3].


A detailed error analysis for this system has been
presented previously by Hust, et al. [3]. Based on this
analysis of systematic and random errors, the uncertainty
estimates (with 95% confidence) are as follows:

2.5% at 300 K, decreasing as r4 to 0.70% at 200 K,
0.70% from 200 K to 50 K, increasing inversely with
temperature to 1.5% at 4 K.

5. SUMMARY

We have established low temperature thermal conductivity
standard reference data for stainless steel SRM 735. Thermal
conductivity measurements have been made on this steel from
4 to 300 K. These data were fitted to an empirical equation
that was used to generate tabular values. Material varia-
bility is estimated to be less than + 1% in thermal conduc-
tivity, and measurement uncertainty is less than 2.5%.

We wish to thank R. E. Michaelis of NBS-OSRM, for
assistance in specimens procurement and helpful discussions.
This measurement program has been carried out under the
helpful guidance of R. L. Powell.