THERMAL CONDUCTIVITY OF

ALUMINUM, COPPER, IRON, AND

TUNGSTEN FOR TEMPERATURES FROM

1 K TO THE MELTING POINT

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

June 1984

QC

100

,1156

84-3007

1984

NBSIR 84-3007

THERMAL CONDUCTIVITY OF

ALUMINUM, COPPER, IRON, AND

TUNGSTEN FOR TEMPERATURES FROM

1 K TO THE MELTING POINT

J. G. Hust

A. B. Lankford

Chemical Engineering Science Division

National Engineering Laboratory

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

June 1984

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

COMTENTS

Page

Abstract 1

1. Introduction . , , 1

1.1 Thermal Conductivity 4

1.2 Electrical Resistivity ........ 7

1.3 Wiedemann-Franz-Lorenz (WFL) Law 8

1.4 Literature Review 10

1.5 Analysis , , . 11

1.6 Thermal Expansion Corrections , . ~ . 13

1.7 Acknowledgments 13

1.8 References , ...... 14

2. Copper 15

2.1 General . , 15

2.2 Deviations From Recoirmended Equation . 16

2.2.1 Physical Defect Effects 17

2.2.2 Size Effects 20

2.2.3 Magnetic Field Effects ....... 21

2.3 Electrical Resistivity and Lorenz Ratio 21

2.4 Summary for Copper ....

2.5 Format for Annotated Bibliography for Copper 62

3. Aluminum

3.1 General

3.2 Deviations From Recommended Equation

3.2.1 Physical Defect Effects

3.2.2 Size Effects

3.2.3 Magnetic Field Effects

iii
Page

3.3 Electrical Resistivity and Lorenz Ratio .......... 91

3.4 Summary for Aluminum , , . , 93

3.5 Format for Annotated Bibliography for Aluminum 122

4. Iron ...... . , , 141

4.1 General 141

4.2 Deviations From Recommended Equation 142

4.2.1 Physical Defect Effects , , . . 143

4.2.2 Size Effects 144

4.2.3 Magnetic Field Effects ........ 144

4.3 Electrical Resistivity and Lorenz Ratio . 145

4.4 Summary for Iron 146

4.5 Format for Annotated Bibliography for Iron 176

5. Tungsten 199

5.1 General . . 199

5.2 Deviations From Recommended Equation 200

5.2.1 Physical Defect Effects 201

5.2.2 Size Effects 202

5.2.3 Magnetic Field Effects ...... 203

5.3 Electrical Resistivity and Lorenz Ratio 204

5.4 Summary for Tungsten .................... 205

5.5 Format for Annotated Bibliography for Tungsten 235

IV
THERMAL CONDUCTIVITY OF ALUMINUM, COPPER, IRON, AMO TUNGSTEN FOR TEMPERATURES

FROM 1 K TO THE MELTING POINT

J. G. Hust and A. B. Lankford

Chemical Engineering Science Division

National Bureau of Standards

Boulder, Colorado 80303

Literature data on the thermal conductivity of commercially Dure aluminum, copper, iron, and tunqsten specimens have been collected, coded,

critically analyzed, and correlated with analytical techniques based on theoretical and empirical equations. The resulting functions are presented and

used to qenerate tables and graphs of thermal conductivity as a function of

temperature and residual resistivity ratio (RRR). An annotated biblioqraphy of references is included. Discussions are included on the variations

in thermal conductivity caused by chemical impurities, physical defects,

size effects, and maqnetic fields. Smoothed values are presented for temperatures from 1 K to near the melting point and for a large ranqe of RRR

val ues.

I Keywords: aluminum; cooper; electrical resistivity; iron; Lorenz ratio;

residual resistivity ratio; thermal conductivity; tungsten

1. Introduction

The growth of modern technology has increased the need for and use of thermophysical properties reference data on materials, often by engineers not totally

familiar with the physical phenomena that influence the properties or the conditions under which the data are valid. Such a lack of understanding can lead to

serious design errors, especially for low- temperature transport properties, such

as thermal conductivity, that are strongly dependent on detailed material characteristics as well as environmental conditions. The data explosion appearing in

the literature may be a drawback rather than an asset to the non-specialist, who

needs ready access to critically evaluated, correlated, and smoothed data with a

clear indication of their range of application. Center for Information and Numerical Data Analysis and Synthesis (CINDAS) (at Purdue University), the editors

of Landol t-Bornstein, the Office of Standard Reference Data of the National

Rureau of Standards, and others have made efforts to perf orm this service. These

1
efforts generally encompass such a wide range of materials and properties that

the results are lacking in detail desirable for re ference data. For example, example, when recommended values are presented, it is not always clear how well

they agree with the original data. In cases where recommended values are not

qiven, the user must exercise considerable effort to obtain such values. This

paper presents both the literature thermal conductivity data as well as recommended values for a few metals (aluminum, copper, iron, and tungsten 1 alonq with

a clear indication of the agreement of the recommended values and the experimental data.

The objective of this work is to present reference data for selected metals

including the most pure research materials and the more commonly produced commercially pure materials. Generally soeakinq this includes impurities up to about

the 1 % level. The reference data are based on a critical analysis and correlation of the best experimental data. Only two variables (temperature and residual

electrical resistivity) are used to correlate the selected experimental data.

There are numerous factors that complicate the establishment of the uncertainty

of this correlation. First, there is the direct thermal conductivity measurement

uncertainty. It has been found that 5-10% uncertainties are common and occasionally data are found in error by as much as 50%. Second, literature data are frequently found for inadequately characterized specimens, i.e., the investigator

did not report such factors as residual resistivity, purity, anneal condition,

and specimen size. In addition, these factors are freauently not determined for

the exact specimen measured. Third, there are uncertainties introduced by extracting literature data by reading small qraphs and sometimes from extrapolated

equations. Finally, the uncertainty of the reference data is dependent on the

validity of the correlation equation used. Therefore, the reference data presented here, for a wide range of purities, are probably not as accurate as those

that can be obtained from the accurate measurement of a single specimen; hut they

2
do represent the best available data tor the entire family of specimens considered.

The reference data are most accurate for all specimens measured at hiqh temperatures where impurity effects are small and for the most pure specimens measured at low temperatures where the impurity effects are dramatic. A secondary

objective was to include as wide a ranqe of impurities as possible with a single

equation. Because of this the uncertainty tends to increase at the hiqher impurity levels. However, specimen size effects and increased experimental uncertainties tend to increase at low temperatures and low impurity levels, therefore

the total uncertainty at low temperatures is considerably larqer than at hiqh

temperatures. Each major section of this report discusses details of the deviations.

This work was performed under the auspices of the Committee on DATA for

Science and Technology of the International Council of Scientific Unions (CODATA)

which seeks to ".... improve the quality, reliability, and accessibility of data

of importance to science and technology ....". Therefore, its Task Group on

Thermophysical Properties has embarked on preparation of critically evaluated and

recommended values of a limited set of properties on materials often used for

calibration or reference. The properties are thermal conductivity, electrical

resistivity, heat capacity, thermal diffusivity, absolute thermopower, and

thermal expansion. Materials include aluminum, alumina, copper, iron, silicon,

and tungsten.

The above properties are similar in that at temperatures , T, well below the

Debye characteristic temperature, q, they vary rapidly with T in a complex

manner according to the degree of excitation of the thermal vibrations (phonons)

and the electrons in some cases. The properties are dissimilar as far as their

dependence on purity is concerned. The transport properties (cher.:l condi'ptivity, thermal diffusivity, and electrical resistivity) are dominated bv nos'
lattice imperfections as temperature approaches absolute zero, whereas specific

heat and thermal expansion depend primarily on the host lattice characteri sties

and are practically insensitive to lattice imperfections.

Thermal conductivity and electrical resistivity of pure metals are closely

associated with the same conduction source and limiting (scattering) mechanisms.

This correlation is expressed by the Wiedemann-Franz-Lorenz Ratio. Because of

this correlation between thermal and electrical resistivity and because the impurity effect is primarily additive in resistivity, the residual resistivity (or

the residual resistivity ratio) is a useful parameter to characterize these properties for a given specimen. A brief discussion of these properties is given

below.

1.1. Thermal Conductivity

The thermal conductivity, x, of a metal or alloy usually is considered to be

the sum of the electronic, A e , and lattice, A

g

, components:

X-Xg + Xg (l.l.l)

There are other mechanisms of heat transport; however, they generally are not applicable for metals. The electronic term designates the thermal energy carried

by the electrons, while the lattice term designates the energy carried by the

quantized lattice vibrations (phonons). In pure metals the lattice term is small

(frequently less than 5 and almost always less than 20 percent). Although theory

provides a guide for the dependencies of the lattice conductivity and its order

of magnitude, it is generally not sufficient for reference data purposes. Theory

does provide an adequate formulation for the 1 ow-temperature electronic term.

For these reasons, the formulation provided here is based on the theoretical form

of the electronic term. Modifications of this form to account for the lattice

contribution and higher temperature dependencies are based on the experimental

data.

4
Theory shows that at low temperatures the electronic thermal conductivity

component is limited mainly by two mechanisms, a) the interaction of the electrons with phonons, and b) the interaction of the electrons with physical and

chemical imperfections. The interaction of electrons with phonons leads to a

resistive term approximately proportional to T^. The proportionality constant,

a, is characteristic of the generic type of metal, i.e., it is an intrinsic property of the base metal. The interaction of electrons with lattice defects leads

to a thermal resistivity which is inversely proportional to temperature. The

proportionality constant, a, is determined by the type and concentration of the

lattice imperfections. This approximation of low-temperature electronic thermal

conductivity is written as

X = (W + W.)"1 = (0/T + cjV1 where n = 2 (1.1.2)

and where W0 represents the electron-defect interaction and W-j is the

electron-phonon interaction. Cezairliyan and Touloukian [1]* presented a revised

form of this theoretical equation to account for observed deviations. This revised form, reviewed in reference [2], is based on experimental data that show

a) n is usually larger than 2, and b) a is weakly dependent on lattice imperfections. The modified equation is valid only for temperatures up to about 1.5

times the temperature at which the maximum in thermal conductivity occurs. For

the metals of interest here, this limit occurs at about 40 K. At higher temperatures, thermal conductivity decreases more slowly with increasing temperature

than predicted by this equation. Theory predicts that at high temperatures

,

thermal conductivity of metals should approach a constant. To account for this

high temperature behavior, the form presented by Cezairliyan and Touloukian [1]

has been further modified-. Finally, evidence has been presented that indicates

*The references shown in [ ] are listed in Section 1.8.

5
the presence of an interaction term between W0 and W-j . It is denoted by

W-j 0. The base equation selected to represent the predominant thermal conductivity behavior of these metals is therefore.

A, = (W + w. + w. r

1 b

v o i io' (1.1.3)

where W = g/T

o (1.1.4)

P (p +p ) p W

i = PjT 2

/(l + P

1 P3

T

2 4 exp(-(P

5

/T)

6

)) + W

c (1.1.5)

W

io

= P

7 W

i W

o/(W

i + V (1-1-6)

where the P-j's are parameters determined by least squares fit of the experimental data. The quantity W

c is a temperature dependent term (defined later

for each metal) that accounts for mathematical residual deviations in W-j. This

equation is intended to describe the thermal conductivity of annealed bulk specimens of these metals. Thus it describes the intrinsic thermal conductivity and

the limiting effect of the presence of chemical impurities in each metal. The

reader should be aware, however, of the existence of other limiting mechanisms,

such as physical defects, size effects, and magnetic field effects. Brief discussions of these effects are presented for each metal.

Both thermal conductivity and electrical resistivity of a pure metal are

strongly dependent on the concentration of lattice imperfections. Indeed, they

are both influenced to the same degree by the imperfections at very low temperatures. The resulting correlation is referred to as the Wiedemann-Franz-Lorenz

Law, discussed in Section 1.3. Since electrical resistivity is much easier to

measure accurately than thermal conductivity, it is often used to determine imperfection concentrations, and therefore thermal conductivity. The following

discussions on electrical resistivity and the Wiedemann-Franz-Lorenz Law are included for that reason.

6
1.2. Electrical Resistivity

For discussion purposes the electrical resistivity is described adequately

by Matthiessen's rule (MR). This rule, (1.2.1) states that the electrical resis

tivity, p, of a metal is the sum of two parts: the intrinsic resistivity, p-j,

which is characteri zed by electrons interacting with phonons only, and the residual resistivity, p 0 , which is characterized by electrons interacting with

the chemical and physical imperfections of the metal.

p(T) = P0 + Pi (T) (1.2.1)

The residual resistivity is temperature independent, while the intrinsic resistivity increases rapidly with temperature. The specific temperature dependence

varies widely both with temperature and base material. Nevertheless, p-j is not

dependent significantly upon composition changes for a given base metal. Thus,

if one knows p-j(T) for a given base metal, p(T) for any composition of that

metal can be approximated from (1.2.1) after measuring only p Q. The value of

p 0 is obtained by measuring p at low temperatures , where p-j is negligible

(liquid helium temperatures generally are adequate). For several reasons, the

ratio of the resistivity at the ice point to the residual resistivity is frequently used to characterize the purity of a metal. This ratio is called the re

sidual resistivity ratio and is denoted by RRR.

Within the limitations of MR, RRR can be written as,

RRR = -1—

+ 1 (1.2.2)

Po

Although, deviations from MR cause (1.2.2) to be slightly in error, we hav

adopted it for conversion between p0 and RRR in this report. This conversiois necessary because some authors use p 0 for characterization while others use

7
RRR. In either case, the authors frequently do not report the value of pTM

It was convenient in this study of thermal conductivity to develop a simple analytical approximation for electrical resistivity. The base function chosen and

fitted to selected resistivity data for each metal is

where

p = p + p . + p

.

H MoH io

pQ

= residual electrical resistivity

(1.2.3)

(1.2.4)

P (P +P ) P P

n

- = PjT 2

/(l + PjPjT 2 4 exp(-(P

5

/T)

6

)) + p

c (1.2.5)

p io

= P

7 p

i p o/(pi + p o> (1.2.6)

Note the similarity to Eqs. 1.1.3 through 1.1.6. The pj 0 term accounts for

observed deviations from MR. The quantity p c is designed to account for the

mathematical residual deviations in p^ . It should be noted that Eq. 1.2.3 does

not assume the validity of MR as does Eq. 1.2.2. Section 1.5 describes how this

apparent contradiction was circumvented.

1.3 Wiedemann-Franz-Lorenz (WFL) Law

In 1853 Wiedemann and Franz formulated an empirical law relating the thermal

and electrical conductivities of metals, namely, that the ratio of the electrical

and thermal conductivities (WF ratio) at a given temperature is the same for all

metals. In 1872 Lorenz discovered that the WF ratio is proportional to temperature. The result was the Wiedemann-Franz-Lorenz (WFL) law:

£

= Xp = LT (1.3.1)

where a = electrical conductivity, L = Lorenz number, and T = absolute temperature.

8
data evaluation process. Graphical illustrations of the dependencies of A, p,

and L are given in the latter section of this report.

1.4. Literature Review

The existing principal compilations and reviews [2,3] were used as a starting point for this compilation. The resulting list of references was updated by

searching current literature, abstracting services, and computerized data banks,

as well as the reference lists of the most recent publications. The initial emphasis was directed toward temperatures below 300 K. Later the scope was extended to include temperatures up to near the melting point of each metal. The

high temperature compilation was directed toward obtaining the most significant

publications rather than a complete listing.

Since the principal interest is the dependence of thermal conductivity on

temperature and electrical resistivity for relatively pure metals, not all of the

literature data for a given base metal is referenced here. For example, numerous

publications on the measurement of thermal conductivity at a single temperature

have been excluded. Also, all measurements on specimens with more than 1% total

impurity concentration were excluded.

Each of the selected sources was coded for content, and the data were extracted for computer analysis. When the literature data were presented in

graphical form, the graphs were enlarged and read as accurately as possible. The

resulting data were then smoothed to reproduce the original curves. Each set of

data for a given measured specimen was characterized with values of residual resistivity, RRR, chemical impurity concentrations, and thermal /mechanical history.

Other details regarding the experimental procedure, purpose of the work, and

analysis of data are also coded in the annotated bibliography for the convenient.-

of the reader.

10
Drude gave a theoretical derivation of the WFL law in 1900 and obtained a

value of 2.228 x 10-8 v2/k 2 for L. Sommerfeld calculated the first order

approximation of L from the free electron theory of metals. His value, 2.443 x

1 q-8\/2/k2 commonly is designated L 0. It should be pointed out that the

theoretically calculated value of L is based on the electron component of thermal

conductivity, A e. Electron Lorenz numbers, p\e/T, other than the Sommerfeld

value are designated by Le to distinguish them from total Lorenz numbers, L

= pA/T.

For many pure metals the experimentally determined values of L fall between

2.2 and 3.0 x 10'^V^/K^ at room temperature and only slightly higher at

100 °C. At very low temperatures (liquid helium) the experimental values are

near the Sommerfeld value. Thus 3 as defined in Eq. 1.1.4 is equal to p0/Lq

.

For intermediate temperatures the agreement of L and L0 vanishes. At intermediate temperatures, Le and L are strong functions of purity and temperature,

with the decrease from L0 greatest for the most pure metals and at about 15 K

to 40 K.

Deviations of L from L0 at high temperatures are often attributed to the

presence of lattice conductivity; however, as pointed out by Touloukian, Powell,

Ho, and Klemens [2], the actual electronic Lorenz number may also deviate from

L 0 , even in the absence of lattice conductivity.

For the interested reader, detailed theoretical treatments can be found in

numerous sources. A few of these are listed in the references [2-13].

The principal reason for consideration of the WFL law in this report is because of its utility in examining experimental data for unusual behavior. The

functions used to represent A and p were used to calculate the Lorenz ratio as a

function of temperature and RRR. The resulting plots were examined to aid the

9
establish values of p 0 and RRR for each reported thermal conductivity measurement in the literature:

1 . The value of p 0 that produces the best agreement of Eq. 1.1.3 and the

reported thermal conductivity data at low temperatures was selected. The

corresponding residual resistivity ratio, RRR, was calculated from

Eq. 1 . 2 . 2 . In addition, at this stage of the analysis, the Sommerfeld value

of the Lorenz ratio, L0

= 2.443 x 10"8

, was assumed to be valid to obtain the corresponding value of p = p0 /L0

.

The values of p ^-/2 used i n Eq. 1.2.2 for the four metals investigated

are given below.

Metal Pi 273

(bfl*m)

Copper 15.4

A1 uminum 24.8

Iron 87.0

Tungsten 48.4

The values listed in this table are our best estimates based on literature values

and a variety of published and unpublished measurements performed at this laboratory over a period of 25 years.

2. Upon completion of the data fits and comparisons, plots were made of RRR

(selected) versus RRR (reported) for each metal. These plots were used to

determine the Lorenz ratio adjustment necessary for each metal and the range

of RRR for which Eq. 1.1.3 is valid. Recommended values as a function of T

and RRR are given in the form of equations, tables, and graphs for each

metal

.

12
1.5. Analysis

Selected data sets (primary data) were used to establish best values over

the entire range of temperature and p0 or RRR. The primary data were chosen on

the basis of proven laboratory techniques, as applied to pure and annealed specimens. These data are believed to be accurate to within 5 to 10%. The primary

data were then used to optimize the parameters in the selected equation for each

metal. The p 0 or RRR value assigned to each data set was not necessarily that

reported by the author. The values were selected to minimize the thermal conductivity deviations in the low temperature range, i.e., the range below the peak in

the curve. If data did not exist below the peak in the \ vs. T curve, the

author's value of RRR (or p0 ) was used. If a value of RRR (or p0

) was not

reported for a high temperature data set, it was estimated by considering purity

and anneal conditions. The relationship of the selected values of RRR (or p0 )

and reported values are shown in each of the following major sections. The

fitted equation was then compared to other data sets, including those for the

less pure and unannealed specimens. The comparisons were examined for deviations

varying systemati cal ly with RRR and temperature. The results of this analysis

are described in the section for each metal (Sections 2 through 5).

As briefly discussed in Section 1.2, the relationship between RRR and p0

is not uniquely defined for a given specimen in the absence of other measurements. For very pure metals RRR is frequently reported because the determination

of RRR can be done without a knowledge of the form factor, s,/ A, i.e., the length

to cross-sectional area ratio of the specimen. Such specimens are frequently

very thin; and consequently, the accurate determination of i/k and p0 is difficult. In the absence of MR deviations, Eq. 1.2.2 may be used to define the relationship between p 0 and RRR. However, MR deviations are known to exist and,

thus Eq. 1.2.2 is also inexact. We have chosen the following procedure to

11
1.6 Thermal Expansion Corrections

It would be desirable to specify that the recommended values in this report

are based on the actual dimensions of the specimens at any given temperature,

i.e., they are corrected for thermal expansion. However, only a small fraction

of the authors indicated whether their reported data are corrected or uncorrected

for thermal expansion. Therefore, the reported data were not modified for

thermal expansion effects. This, although an undesirable situation, is not

serious in view of the relatively large measurement uncertainties. It is also

noted that, although a linear correction is usually appropriate, the proper correction depends on the nature of the measurement method employed.

For the convenience of the reader, estimates of the magnitude of the thermal

expansion correction are given here. Room temperature is used as the basis for

this correction since specimen dimensions are normally determined at room temperature. The four metals discussed have positive thermal expansion coefficients, thus the thermal conductivity values corrected for thermal expansion are

smaller than the uncorrected values at temperatures above room temperature, and

larger at temperatures below room temperature.

1.7 Acknowledgments

This work began several years ago and has progressed at a low level of effort. It was funded in part by the Air Force Office of Scientific Research.

During these several years numerous NBS staff members have contributed to the

tasks involved. In particular, we wish to acknowledge the assistance of

Dr. Nancy Simon, Mr. Bruce Howry, and Mr. Jeff Wood. We also express appreciation to Dr. M. L. Minges (USAF-AFML), Dr. G. K. White (CSIRO-Austral ia) and other

members of the CODATA Task Group on Thermophysical Properties for their helpful

suggestions and reviews of this manuscript.

13
1.8 References

1. Cezairliyan, A. and Touloukian, Y. S. , Correlation and prediction of thermal

conductivity of metals through the application of the principle of corres- ponding states, in Advances in Thermophysical Properties at Extreme Temperatures and Pressures, Third Symposium on Thermoohysical Properties, ASME

(1965), 301-313.

2. Touloukian, Y. S. , Powell, R. W. , Ho, C. Y. , and Klemens, P. G. , Thermophysical properties of matter, Vol . 1, Thermal Conductivity (Metallic elements and alloys), Plenum Press, N.Y. (1970), 1469 pp.

3. Childs, G. E., Ericks, L. J., and Powell, R. L., Thermal conductivity of

solids at room temperature and below (A review and compilation of the literature), National Bureau of Standards, Monograph No. 131 (1973), 608 pp.

4. Parrott, J. E. and Stukes, A. D. , Thermal conductivity of solids, J. W. Arrowsmith Ltd., Bristol, England (1975), 157 pp.

5. Berman, R. , Thermal conduction in solids, Clarendon Press, Oxford, England

(1976), 193 pp.

6. Klemens, P. D. , Theory of the thermal conductivity of solids, in Thermal

Conductivity, Vol. 1, R. P. Tye, Editor, Academic Press, N.Y. (1969), 1-68.

7. Ziman, J. M. , Electrons and Phonons (The theory of transport phenomena in

solids). Clarendon Press, Oxford, England (1960), 554 pp.

8. Wilson, A. H. , The theory of metals, Cambridge Press, England (1958),

346 pp.

9. Klemens, P. G. , Thermal conductivity of solids at low temperatures , in Handbuch der Physik, S. Flugge, Editor, Vol. 14, Spri nger-Verl ag, Berlin ( 1956),

198-281.

10. Klemens, P. G. , Thermal conductivity and lattice vibrational modes, in Solid

State Physics, Vol. 7, Academic Press, N.Y. (1958), 1-99.

11. Mendelssohn, K. and Rosenberg, H. M. , The thermal conductivity of metals at

low temperatures, in Solid State Physics, Vol. 12, Academic Press, N.Y.

(1961), 223-274.

12. Mott, N. F. and Jones, H. , Theory of the properties of metals and alloys.

Clarendon Press, Oxford, England (1936), 326 pp.

13. Peierls, R. E. , Quantum theory of solids. Clarendon Press, Oxford, England

(1955), 229 pp.

14
2. Copper

2.1 General

Copper is discussed first because it is the most extensively measured metal.

A total of 44 references were selected for inclusion in the annotated bibliography. The following references from the annotated bibliography (Section 2.5)

represent the primary data sets: 4, 7, 8, 14, 16, 18, 19, 21, 23, 24, 26, 27,

28, 29, 30, 33, 34, 35, 38, 41, 42, and 43.

The primary data cover a range of temperatures from 0.2 to 1250 K, and a

range of RRR from 20 to 1800. These data are illustrated in Figs. 2.1.1 through

2.1.6. These data are illustrated seven sets to a figure to avoid figures that

are overly crowded and to aid in identifying the source of each data set. For

additional convenience a composite of all data is also given. Fig. 2.1.6, but

without source identification. For comparison, the electrically purest copper

ever produced has an RRR of about 50,000. These high RRR values are not indicative of the actual impurity content. They were produced by oxygen anneal of high

purity copper. The impurity content under these conditions remains unchanged,

but the impurities (especially iron) chemically combine with oxygen to form less

effective scattering centers. The RRR of typical commercially pure copper wire

is in the range of 50 to 500. Very high purity copper, produced routinely, may

have an RRR as high as 2000.

Equation 1.1.3 was fitted to represent the primary copper data over the entire temperature range.

The values of the parameters , P-j ,i = 1, 2, ..., 7, obtained by nonlinear

least squares fit are

15
p 1.754 x 10

-8

1

P 22.763 P6

1.765

P

3 = 1102 P

7 = 0.838/B^*

1661

P 4

= -0.165

where 3 r

= e/0.0003. All units are SI.

The data at high RRR were examined for systematic residuals as a function of

temperature. These residuals were represented by the W

c term in Eq. 1.1.5.

The result is

where W

c and T are in SI units.

2.2 Deviations From Recommended Equation

The deviations of the primary data from Eq. 1.1.3 are illustrated in

Figs. 2.2.1 through 2.2.6. Figure 2.2.6 is a composite of all deviations without

data source identification. Five data sets exhibit differences of greater than

+10%. In most of these cases, the deviations are significantly higher than the

stated or implied uncertainty of the source document. It is not clear if these

deviations are the result of underestimated uncertainties or the result of real

differences between specimens. Although temperature dependent deviations do

exist for individual data sets, the overall pattern is random in nature. No systematic trends with RRR were identified.

The primary data were selected from the literature data on relatively large,

well annealed specimens. Therefore, the deviations exhibited in Figs. 2.2.1

W

c = -0.00012 £n(T/420) exp(-(£n(T/470)/0.7) 2

)

-0.00016 £n(T/73) exp(-Un(T/87/0.45) 2

)

-0.00002 £n(T/18) exp(-Un(T/21)/0.5) 2

)

16
through 2.2.6 are indicative of the combined effect of (a) experimental measurement errors and (b) the inability of Eq. 1.1.3 to account for the effects of

chemical impurity variations. The effects of physical defect variations, small

specimen size variations, and magnetic fields are exhibited, in part, by the deviations of the secondary data. The thermal conductivity variations, caused by

other than chemical impurity variations, are not expected to be represented as

well by Eq. 1.1.3. However, the RRR (or p0 ) correlating parameter does account

for an appreciable part of these variations. Some users may find this to be an

adequate representation and, therefore, discussions of these comparisons are included for completeness.

The deviations of the secondary data sets (other than the primary sets) are

illustrated in Figs. 2.2.7 through 2.2.16. These plots are divided into two

groups, according to the magnitudes of the deviations. Figures 2.2.7 through

2.2.12 and Figs. 2.2.13 through 2.2.16. Figures 2.2.12 and 2.2.16 are composite

graphs for each group, respecti vely.

Finally, it was of interest to compare the values calculated from Eq. 1.1.3

to the most widely used references (13,39) of recommended thermal conductivity

values. Figure 2.2.17 shows this comparison. Within the combined uncertainties

of this work and references 13,39 the differences are not significant. It should

be noted however that references 13,39 give values only for a single value of RRR

(approximately 1800), while Eq. 1.1.3 covers a wide range of RRR.

2.2.1 Physical Defect Effects

Investigations of physical defects in copper have produced several noteworthy references 5,10,12,15,22,26,33,41,44. We shall discuss each of them

bel ow.

Reference 10 shows the effects of mechanical deformation. The peak value of

the thermal conductivity of the unstrained specimen was 2750 W*m-1 *K_1

. After

17
a 30.8% elongation, the value at the peak was 1050 W-irT^K"1

. The deviations from Eq. 1.1.3 for the unstrained condition were within +4%.

Reference 22 reports the effects of mechanical deformation on two specimens

of different purities. For the 99.9% pure Cu specimen, the unstrained peak value

of the thermal conductivity was 2700 W*m_1

*K _1

, and after a 30.8%

elongation, the peak value was 1100 W'nT^K" 1

. For the 99.99% Cu specimen, the unstrained peak value was 5800 W-m -1

*K

-1

, and after a 28.4%

elongation, the peak value was 1300 W*m_1 *K _1

. The deviations from

Eq. 1.1.3 for the 99.9% copper specimen are within +12% (unstrained condition).

Similarly, the deviations for the 99.99% copper specimen are within +3%

(unstrained condition). The strained conditions were not compared.

Another study of the effect of mechanical deformation is given in reference 15 in which a specimen was torsi onally deformed (nd/£ = 1.29, where n is the

number of turns on the specimen). The specimen was 99.55% copper and had

strained thermal conductivity values of 24 W'lrT-^K"-'- at 20 K, and

50 W

, m"l*K -

-'- at 40 K. After these measurements were taken, the specimen

was annealed in helium at 450 °C for three hours and measurements were taken

again. After the anneal, the values were 36 W*m“^*K _1 at 20 K and

60 W*m"-'-*K'-*- at 40 K. The thermal conductivities of a control specimen

were also measured. The deviations from Eq. 1.1.3 for the control specimen were

within +16%. The deviations for the deformed specimen were within +26%, while

for the annealed specimen, the deviations were within +_20%. A possible

explanation for these large deviations may be that the specimen's RRR is close to

the lower validity limit of Eq. 1.1.3.

References 26 and 33 demonstrate the effect on thermal conductivity of

annealing a specimen, then drawing it. The specimen was annealed in vacuum and

the thermal conductivity was determined. A similar specimen was cold -drawn 26%

18
and its thermal conductivity was measured. The maximum thermal conductivity for

the annealed specimen was 14000 WtfT-'-’K” 1

, while for the drawn specimen

it was 2500 W'nT^IC 1

. The deviations from Eq. 1.1.3 for the annealed

specimen were within +_9%, while for the cold-drawn specimen, the deviations were

within +6%.

Reference 41 reports the differences in thermal conductivity of a specimen

in the "as-drawn" state and in the annealed state. The peak value of the thermal

conductivity for the drawn condition was 1540 WttT-’K" 1

, and that for the

annealed condition was 5300 W*nT^*!C"l. The deviations from Eq. 1.1.3 for

the as-drawn state were within +7%, while for the annealed state, they were within

+ 10%.

Reference 12 investigated the effects on thermal conductivity of different

annealing conditions and sizes. For an oxygen anneal, the peak conductivity was

found to be 56500 WtitI'K"! for a specimen of 12.5 ym thickness, and

55300 W'm'^K' 1 for a specimen of 125 ym. After a high vacuum anneal,

these peaks are 15500 W*nT^*K

_

- and 5000 , respectively. The deviations from Eq. 1.1.3 for the smaller specimen were within j+30%

for the oxygen anneal, +35% for the high vacuum anneal. Those for the larger

specimen were within +30% for the oxygen anneal, +120% for the high vacuun anneal. A possible explanation for these very large deviations may be that size

corrections applied to the data were too large.

Reference 44 showed the effect on thermal conductivity of a specimen in an

unannealed (as fabricated) state and in an annealed state. The peak conduct:.':,

in the unannealed state was 390 WttT-^K"! , while for the annealed state,

it was 570 W*m“l.«-l t The deviations from Eq. 1.1.3 for both the unar,-

nealed and annealed specimens were within +5%.

19
Reference 5 reported the effect of neutron irradiation on thermal conductivity. Neutron irradiation produces physical defects within the lattice. The

neutrons had energies up to 10^ eV while the specimens had a maximum exposure

of 6.5 x 1()23 neutrons per square meter. The damage, as measured by thermal

resistivity, was linear with neutron exposure. The maximum thermal conductivity

for the unirradiated specimen was 16700 W*m_1 *K

_ ^, while for the maximum

exposure specimen, it was 1700 W*m_1 *K_1

. The deviations from Eq. 1.1.3

for the unirradiated specimen were within +35%, while those for the maximum exposure were within +20%. The nature of the deviations for these specimens are

not understood.

Although the temperature dependence of physical defect scattering mechanism

is different from that due to impurity scattering, Eq. 1.1.3 generally represents

the unannealed specimen data quite well (within +20%). This indicates that the

residual electrical resistivity characterizes both types of scattering for the

range of RRR included here.

2.2.2 Size Effects

Nath* showed that the thermal conductivity was a strong function of specimen

thickness below about 0.1 pm while it is nearly independent of thickness for

specimens larger than 0.4 pm. The variation of the thermal conductivity with

thickness was studied for temperatures above 80 K and was found to be significant

even at 500 K. A 50% reduction in thermal conductivity below that of bulk copper

was observed for a film of 0.01 pm thickness.

Reference 12 contains thermal conductivity data that has al ready been corrected for size effects on two copper crystals of 12.5, 125 pm thickness.

^Nath, P. and Chopra, K, L. , Thermal Conductivity of Copper Films, Thin Solid

Films, 20, 53-62 (1974).

20
2.2.3 Magnetic Field Effects

Although magnetic field effects on thermal conductivity were not studied explicitly, reference 24 showed that a 6 T field increases the thermal resistivity

by 33% at 3 K, decreasing to 18% at 31 K for the same field. The increase in

thermal resistivity changes linearly with the field while the slope decreases

with increasing temperature.

Sparks^ measured the effect of magnetic fields up to 8 T on two specimens

of copper of differing purities. The magnetothermal resistivity introduced into

the high conductivity specimen exhibited a strong temperature dependence below a

field of 2 T. Above this value, the temperature dependence was much less. The

value of the magnetothermal resistivity at high fields was about

0.0004 m*K*W-1 near 4 K. Up to 8 T, the lower conductivity specimen exhibited a more uniform behavior, and the magnetothermal resistivity introduced

near 4 K was appreciably higher, 0.002 nrK'W 1

. The relative change in

thermal resistivity, however, is greater for the high purity specimen at a given

field. Fevrier and Morize^ reported measurement on two specimens of pure

copper at fields up to 5 T at 4.2 K. The maximum field induced a factor of four

increase in resistivity. Nevertheless, the ratio of the thermal and electrical

conductivities was reported to be a constant for both longitudinal and transverse

magnetic fields.

2.3 Electrical Resistivity and Lorenz Ratio

During this investigation it was frequently helpful to examine the Lorenz

ratio as a function of temperature and RRR. However, to do this we needed values

^Sparks, L. L. , Magnetothermal Conductivity of Selected Pure Metals and Alloys,

Semi-Annual Technical Report on Materials Research in Support of Superconducting

Machinery- IV , NBSIR 75-828 (1975).

^Fevrier, A. and Morize, D. , The effect of Magnetic Field on the Thermal Conductivity and Electrical Resistivity of Different Materials, Cryogenics, _n,

603-6 (1973.

21
of electrical resistivity. Therefore, we selected those data sources from the

primary data set that contained electrical resistivity data. The electrical

resistivity data used is shown in Figs. 2.3.1 through 2.3.3. Figure 2.3.3 is a

composite of all data. The parameters for Eq. 1.2.3 are:

P

x = 0.1171 x 10" 16

P

2

= 4.49

P

3 = 3.841 x 10

10

P4

= 1.14

P

5 = 50

P 6 = 6.428

P

7 = 0.4531

All units are SI.

The deviations of the experimental data from this equation are illustrated

in Figs. 2.3.4 through 2.3.6. It is clear that in the midrange of the £nT plots

(10 to 100 K) there is a fairly large uncertainty in the representation (+10 to

15%). Smooth curves of p vs. T at selected RRR values are plotted in Fig. 2.3.7.

From the p(T,RRR) and x(T,RRR) equations values of L(T,RRR) were calculated and

plotted in Fig. 2.3.8. Irregul arities are greatly magnified on this plot (+10%

equals about 1 cm on the L scale). It is noted that the bumps in the curves in

the vicinity of 30 to 80 K correspond to the region of greatest uncertainty in

both the p(T,RRR) and x(T,RRR) representati ons. However, it is also noted that

the bumps correspond to less than _+10% irregularity in L from what is normally

expected and this corresponds to the combined irregularity of the p and X representations.

In Section 1.5 we discuss the procedure for selecting values of p 0 and

calculating RRR for each thermal conductivity data set. These values of p 0

22
along with the Sommerfeld value of Lorenz ratio were used to best fit each low

temperature data set. The resulting values of RRR obtained by this procedure are

compared to the values reported in the references in Fig. 2.3.9 and are listed in

Table 2.3.1. Figure 2.3.9 shows values of RRR (calc), those values from the

above procedure, versus RRR (obs), those values reported in the references listed

in the annotated bibliography. Also shown in this figure is the line that represents RRR (calc) = RRR (obs). Systematic deviations from this line indicate

ranges in which the derived Eq. 1.1.3 is invalid. Figure 2.3.9 indicates that

the fitted equation becomes progressi vely less valid below RRR values of 20.

Four points in the region 200 to 1600 lie appreciably (20%) from the line. Discussions with these authors suggest that large uncertainties were present in the

p 0 measurements for these specimens. In addition, the data listed in

Table 2.3.1 confirm the validity of using the Sommerfeld value of the Lorenz

ratio for copper.

2.4 Summary for Copper

Equation 1.1.3 represents the primary copper data to within +15% of the experimental values. Deviations for unannealed specimens (i.e., those containing

physical defects) are within 20%.

Based on the deviations illustrated in Figs. 2.2.1 through 2.2.16 and the

large changes that occur in thermal conductivity due to the introduction of

chemical defects, physical defects, size effect, and magnetic fields, it is clear

that a large proportion of these effects is reflected by the residual electrical

resistivity. The incorporati on of RRR (or p 0 ) in Eq. 1.1.3 produces an equation that represents the data for a wide range of copper specimens and environments .

Equation 1.1.3 with the parameters listed here was used to generate the^a,

conductivity values for selected temperatures and values of RRR. These vain'

are listed in Table 2.4.1 and plotted in Fig. 2.4.1.

23
List of Tables and Figures for Copper

Tables

Page

Table 2.3.1 Comparison of Calculated and Observed RRR Values

for Copper 27

Table 2.4.1 Thermal Conductivity Values for Copper Calculated

From Eq. 1.1.3 at Selected Temperatures and RRR

Values 28

Figures

Page

Figure 2.1.1 Experimental thermal conductivity data selected from

the following primary references in the copper annotated

bibliography: (4,7,8,14,16,18) 29

Figure 2.1.2 Experimental thermal conductivity data selected from

the following primary references in the copper annotated

bibliography: (19,20,21,23,24,27) 30

Figure 2.1.3 Experimental thermal conductivity data selected from

the following primary references in the copper annotated

bibliography: (26,27,28,29,30,33) 31

Figure 2.1.4 Experimental thermal conductivity data selected from

the following primary references in the copper annotated

bibliography: (35,38,41,43) 32

Figure 2.1.5 Experimental thermal conductivity data selected from

the following primary reference in the copper annotated

bibliography: (42) 33

Figure 2.1.6 Composite of the data in Figs. 2.1.1 through 2.1.5 .... 34

Figure 2.2.1 Thermal conductivity deviations of the copper data from

the following primary references compared to Eq. 1.1.3:

(4,7,8,14,16,18) 35

Figure 2.2.2 Thermal conductivity deviations of the copper data from

the following primary references compared to Eq. 1.1.3:

(19,20,21,23,24,27) 36

Figure 2.2.3 Thermal conductivity deviations of the copper data from

the following primary references compared to Eq. 1.1.3:

(26,27,28,29,30,33) 37

Figure 2.2.4 Thermal conductivity deviations of the copper data from

the following primary references compared to Eq. 1.1.3:

(35,38,41,43) 38

24
Page

Figure 2.2.5 Thermal conductivity deviations of the copper data from

the following primary reference compared to Eq. 1.1.3:

(42) 39

Figure 2.2.6 - Composite of the deviations in Figs. 2.2.1 through

2.2.5 40

Figure 2.2.7 Thermal conductivity deviations of the copper data from

the following secondary references compared to

Eq. 1.1.3: (1,2, 3, 6, 9) 41

Figure 2.2.8 Thermal conductivity deviations of the copper data from

the following secondary references compared to

Eq. 1.1.3: (10,15,17,22,25) 42

Figure 2.2.9 Thermal conductivity deviations of the copper data from

the following secondary references compared to

Eq. 1.1.3: (26,31,32,33,37) 43

Figure 2.2.10 Thermal conductivity deviations of the copper data from

the following secondary reference compared to

Eq. 1.1.3: (37) 44

Figure 2.2.11 Thermal conductivity deviations of the copper data from

the following secondary references compared to

Eq. 1.1.3: (40,43,44) 45

Figure 2.2.12 Composite of the deviations in Figs. 2.2.7 through

2.2.11 46

Figure 2.2.13 Thermal conductivity deviations of the copper data from

the following secondary references compared to

Eq. 1.1.3: (5,7,12) 47

Figure 2.2.14 Thermal conductivity deviations of the copper data from

the following secondary references compared to

Eq. 1.1.3: (11,12,15,27,36) 48

Figure 2.2.15 Thermal conductivity deviations of the copper data from

the following secondary references compared to

Eq. 1.1.3: (36,44) 49

Fiqure 2.2.16 Composite of the deviations in Figs. 2.2.13 through

2.2.15 50

Figure 2.2.17 Comparison of Eq. 1.1.3 to the values recommended

for copper in the following references: (13,39) 51

Figure 2.3.1 Experimental electrical resistivity data for copper

selected from the following references in the copper

annotated bibliography: (4,14,21,23,24,26,29) 52

25
Page

Figure 2.3.2 Experimental electrical resistivity data for copper

selected from the following references in the copper

annotated bibliography: (33,38,43) .... 53

Figure 2.3.3 Composite of the electrical resistivity data in

Figs. 2.3.1 and 2.3.2 54

Figure 2.3.4 Electrical resistivity deviations of the copper data

from the following references compared to Eq. 1.2.3:

(4,14,21,23,24,26,29) .... 55

Figure 2.3.5 Electrical resistivity deviations of the copper data

from the following references compared to Eq. 1.2.3:

(33,38,43) 56

Figure 2.3.6 Composite of the electrical resistivity deviations

shown in Figs. 2.3.4 and 2.3.5 57

Figure 2.3.7 Electrical resistivity for copper as a function of

temperature calculated from Eq. 1.2.3 at selected

values of RRR 58

Figure 2.3.8 Lorenz ratio for copper as a function of temperature

calculated from Eq. 1.2.3 and Eq. 1.1.3 at selected

values of RRR 59

Figure 2.3.9 RRR values calculated as per Section 1.5, RRR(CALC) versus reported RRR values, RRR(OBS), for copper 60

Figure 2.4.1 Thermal conductivity for copper as a function of

temperature calculated from Eq. 1.1.3 at selected

values of RRR 61

26
14

16

18

23

24

26

33

33

42

43

43

19

10

15

15

15

26

33

36

36

36

37

37

37

37

37

37

37

37

37

37

37

Comparison of Calculated and Observed RRR Values for Copper.

RRR (obs.) RRR (calc.)

Primary Data

274.0

45.5

214.0

900.0

270.0

900.0

49.2

1530.0

1450.0

400.0

1780.0

19.5

38.8

271.0

44.3

216.0

900.0

190.0

900.0

51.5

1070.0

1060.0

306.0

1800.0

20.5

42.8

Secondary Data

29.0

2.5

140.0

1.6

1.6

1.6

115.0

350.0

870.0

1390.0

2680.0

1.9

2.1

2.5

2.5

3.2

3.1

3.9

3.6

3.8

4.2

4.5

38.0

3.4

120.0

2.0

1.9

1.6

102.0

102.0

880.0

1350.0

2630.0

2.6

3.0

3.1

3.3

4.0

4.4

4.5

4.6

5.0

5.5

5.9

27
Table 2.4.1. Thermal Conductivity Values for Copper Calculated from Eq. 1.1.3

at Selected Temperatures and RRR Values.

X( W*m

-1

•K

-

'*'

)

(K) RRR = 30 RRR = 100 RRR = 300 RRR = 1000 RRR = 3000

1 46 156 471 1574 4726

2 91 312 942 3147 9434

3 137 468 1413 4710 14044

4 183 624 1880 6243 18380

5 228 779 2343 7715 22170

6 274 933 2796 9075 25084

7 319 1085 3232 10260 26834

8 365 1235 3642 11197 27328

9 409 1380 4015 11836 26756

10 454 1520 4343 12172 25496

12 541 1778 4844 12127 22264

14 624 2002 5144 11544 19150

16 703 2186 5267 10725 16398

18 777 2324 5231 9771 13924

20 843 2408 5054 8727 11683

25 960 2381 4215 6135 7271

30 999 2119 3245 4151 4573

35 970 1784 2436 2859 3028

40 900 1467 1841 2047 2122

45 814 1205 1423 1531 1568

50 731 1002 1135 1196 1216

60 597 740 799 824 832

70 513 601 634 647 651

80 465 526 549 557 560

90 437 485 502 508 510

100 421 461 475 480 482

150 396 419 426 429 430

200 391 407 413 414 415

250 388 401 405 407 407

300 386 397 400 401 402

400 383 391 393 394 394

500 379 385 387 388 388

600 374 379 381 381 381

700 368 372 374 374 374

800 362 365 367 367 367

900 356 359 360 360 360

1000 350 352 353 353 354

1100 344 347 347 348 348

1200 339 341 342 342 342

1300 335 337 337 338 338

28
THERMRL

CONDUCT

I

VITY,W/m.

Figure 2.1.1 Experimental thermal conductivity data selected f rom

the following primary ref erences In the copper annotated

bibliography : (4,7,8,14,16,181

O- (43, A- (7), - 17 ), V- (83,

O- (143, +- (16), X- (18)

29
THERMRL

CONDUCTIVITY,

H/m.

0.3 1 3 10 30 100 300 1000

TEMPERATURE,

K

Figure 2.1.2 Experimental thermal conductivity data selected from

the following primary references In the copper annotated

bibliography : (19,20,21,23,24,27)

O- (19), A- (20), - (21), V- (23),

O- (24), +- (27), X- (27)

30
THERMRL

CONDUCTIVITY,

W/m.

Figure 2.1.3 Experimental thermal conductivity data selected f rom

the following primary references In the copper annotated

bibliography : (26,27,28,23,30,33)

O- (27), A- (28), - (26), V- (29),

O- (30), +- (33), X- (33)

31
THERMRL

CONDUCTIVITY,

W/m.

Figure 2.1.4 Experimental thermal conductivity data selected from

the following primary references In the copper annotated

bibliography: (35,38,41,431

O- (351, A- (38), - (41), V- (41),

O- (41), +- (43), X- (43)

32
THERMRL

CONDUCTIVITY,W/m.

0.3 1 3 10 30 100 300 1000

TEMPERATURE,

K

Figure 2.1.5 Experimental thermal conductivity data selected from

the following primary reference In the copper annotated

bibliography: (42)
THERMAL

CONDUCTIVITY,W/m.

0.3 1 3 10 30 100 300 1000

TEMPERRTURE,K

Figure 2.1.6 Composite of the data In figs. 2.1.1 through 2.1.5
Figure 2.2.1 Thermal conductivity deviations of the copper data ' the following primary references compared to eq.

(4,7,8,14, 16,18)

O- (4), A- (7), - (7), V- (8),

O- (14), +- (16), X- (18)

35
0.3 1 3 10 30 100 300 1000

TEMPERRTURE,K

Figure 2.2.2 Thermal conductivity deviations of the copper data from

the following primary references compared to eq. (1.1.3):

(19,20,21,23,24,27)

O - (19), A- (20), - (21), V” (23),

O- (24), + - (27), X- (27)

36
Figure 2.2.3 Thermal conductivity deviations of the copper data from

the following primary references compared to eq. (1.1.3):

(26,27,28,29,30,33)

O- (27), A- (28), - (26), V- (29),

O- (30), +- (33), X- (33)

37
Figure 2.2.4 Thermal conductivity deviations of the copper data from

the following primary ref erences compared to eq. (1.1.3):

(35,38,41 ,43)

O- (35), A- (38),

“

(41), V- (41),

O- (41), +- (43), X- (43)

38
0.3 1 3 10 30 100 300 1000

TEMPERATURE,

K

Figure 2.2.5 Thermal conductivity deviations of the copper data from

the following primary reference compared to eq. (1.1.3):

(42)

O- (42)

39
0.3 3 10 30 100 300 1000

TEMPERATURE,

K

Figure 2.2.6 Composite of the deviations In figs. 2.2.1 through

2.2.5

40
Figure 2.2.7 Thermal conductivity deviations of the copper data

from the following secondaru references compared to

eq. (1.1.3):(1,2,3,6,9)

O- [1), A - (2), - (3), V- (63,

O- (63 , +- (63 , X- (9)

41
0.3 1 3 10 30 100 300

TEMPERATURE,

K

figure 2.2.8 Thermal conductivity deviations of the copper data

from the following secondary references compared to

eg. (1. 1. 3) : (10,15,17,22,25)

O - (101, A- (15), - (15), V- (17),

O- (22), +- (22), X- (25)

42
Figure 2.2.9 Thermal conductivity deviations of the copper data

from the following secondcry references compared to

eq. ( 1 . 1 .3) : (26,31 ,32,33,37)

O- (26), A- (31), - (32), V- (33),

O- (37), +- (37), X- (37)

43
Figure 2.2.10 Thermal conductivity deviations of the copper data

from the following secondary reference compared to

eq. (1.1.3) s C37)

O- (37), A- (37), - (37), V- (37),

O- (37), +- (37), X- (37)

44
Figure 2.2.11 Thermal conductivity deviations of the copper data

f rom the following secondary references compared to

eq. (1.1.3) : (40,43,44)

O- (40), A- (40), - (43), V- (44),

O- (44)

45
Figure 2.2.12 Composite of the deviations In figs. 2. 2.

7

through 2.2.11

46
100 f ! r i i

' i i i i |

i

i

i i m 1 i I r

50 - O

_J

CC0

1 CO

CDO

0 0 0 00

-50 -

-K>ocP

“7&-

QJO

E-h O

Q_

-100 -

-150 -

-200

0.2 0.4 2 4 10 20

TEMPERRTURE,K

40

Figure 2.2.13 Thermal conductivity deviations of the copper data

from the following secondary references compared to

eq. (1.1.3) : (5,7,12)

O- (5), A- (5), - (5), V- (5),

O- (7), +- (12), X- (12)

47
PCT.

DEV.

(OBS.-CRLC.

0.2 0.4 1 2 4 10 20 40

TEMPERRTURE,K

Figure 2.2.14 Thermal conductivity deviations of the copper data

from the following secondary references compared to

eq. (1.1.3) : (11,12,15,27,36)

O- (12), A- (12), - (ID, V- (11),

O- (15), +- (27), X- (36)

48
Figure 2.2.15 Thermal conductivity deviations of the copper data

from the following secondary references compared to

eq. (1.1.3): (36,441

O- (36), A- (36), - (44)

49
PCI

.

DEV.

(OBS.-CRLC.

Figure 2.2. 16 Composite of the deviations In figs. 2.2.13

through 2.2.15

50
PCT.

DEV.

(OBS.-CALC.

Figure 2.2.17 Comparison of eq. (1.1.31 to the values recommended

for copper In the following references :( 13,39

)

O- (39), A- (13)

51
ELECTRICAL

RESISTIVITY,

nil

.

TEMPERATURE,

K

Figure 2.3.1 Experimental electrical resistivity data for

copper selected from the following references In

the copper annotated bibliography: (4,14,21,23,24,26,291

O- (41, A- (141,

O- (241, +- (261,

- (21 1 , V- (231,

X- (291

52
ELECTRICAL

RESISTIVITY,

nfi.

I 'I

1 "T 1 'I I T T rrrf

-

30

10

V o

V V V V VVV v V W

o o oo ooooooo^

0.3 -

0.1 - A O

A A

0.03 -

0.01 * ® 1 |Q| 1 1 1 1 1 1 i i i . i 10 20 40 100

TEMPERATURE,

K

200

Figure 2.3.2 Experimental electrical resistivity data for

copper selected from the following references In

the copper annotated bibliography: (33,38,43)

O- (33), A- (33), - (38), V- (43),

O- (43)

xUJl.1 I I 400

53
ELECTRICAL

RESISTI

VITY,nC

.

Figure 2.3.3 Composite of the electrical resistivity data In

figs. 2.3.1 and 2.3.2

54
1 2 4 10 20 40 100 200 400

TEMPERRTURE,K

Figure 2.3.4 Electrical resistivity deviations of the copper

data from the following references compared to

eq

.

(1.2.3) :(4, 14, 21, 23, 24, 26

O- 14), A- (14), - (21)

O- (24), + - (26), X- (29)

29)

V- (23) /

55
1 2 4 10 20 40 100 200 400

temperature:, k

figure 2.3.5 Electrical resistivity deviations of the copper

data from the following references compared to

eq. (1.2.3) : (33,38,43)

O- (33), A- (33), - (38), V- (43),

O- (43)

56
1 2 4 10 20 40 100 200 400

TEMPERRTURC^K

Figure 2.3.6 Composite of the electrical resistivity deviations

shown In figs. 2.3.4 and 2.3.5

57
ELECTRICRL

RESISTIVITY,

nfi.

TEMPERRTURE,K

Figure 2.3.7 Electrical resistivity for copper as a function

of temperature calculated from eq. (1.2.3) at

selected values of RRR.

58
LORENZ

RATIO,

10

V

/K

TEMPERATURE,

K

Figure 2.3.8 Lorenz ratio for copper as a function of temperature

calculated f rom eq. (1.2.3) and eq. (1.1.3) at selected

values of RRR.

59
RRR(CflLC)

Figure 2.3.9 RRR values calculated as per Section 1.5, RRR(CflLC),

versus reported RRR values, RRR(OBS), for copper.

O “ Primary, A" Secondary,

~ Secondary

60
THERMAL

CONDUCTIVITY,

W/m.

TEMPERATURE,

K

Figure 2.4.1 Thermal conductivity for copper as a function of

temperature calculated from eq. (1.1.3) at selected

values of RRR.

61
V

2.5 FORMAT FOR ANNOTATED BIBLIOGRAPHY OF COPPER

REFERENCE

AUTHOR, TITLE, CITATION

ANNOTATION

PURPOSE

SPECIMEN

a) Dimensions/Shape; b) Crystal Status; c) Thermal ,/Mech. History;

d) Purity Specification; e) RRR; f) p 0 ; g) Other Characteri zation Data

APPARATUS

a) Type; b) Thermometry/Cal ibration/Anchoring; c) Thermal Isolation;

d) Other (Q meas.

)

DATA

a) Temperature Range/Difference; b) Content of Tables, Figures and

Equations/Data Extraction; c) Uncertainty/ Impreci sion ; d) Disputable

Corrections to Measurements by Authors; e) Errata (by Author or Reviewer)

ANALYSIS

a) Comparisons; b) Conclusions

1 ty

62
[1] Allen, J. F. and Mendoza, E. , Thermal Conductivity of Copper and German

Silver at Liquid Helium Temperatures, Proc. Cambridge Philos. Soc., 4j4, 280-3

(1948)

PURPOSE

To describe a longitudinal apparatus and perform x measurements on copper

and German silver.

SPECIMEN

a) /rod; c) annealed in air/machined before and after annealing; d) 0.003% Ag,

0.003% Ni , 0.003% Pb, 02 free; f) po = 5.5 x 10“ 8 q*crn; g) source: Johnson,

Matthey and Co., No. 1562.

APPARATUS

a) longitudinal; b) phosphor-bronze thermometers/cal ibrated in terms of

vapor pressure of He bath using 1932 scale/thermometer leads thermally

grounded to can; c) radiation shield, vacuum insulation.

DATA

a) 1.8 to 4.1 K/0.01 K maximum; b) figure 2 - X; c) uncertainty: ±2%.

ANALYSIS

b) in agreement with Makinson's theory.

[2] Andrews, F. A., Webber, R. T., and Spohr, D. A., Thermal Conductivity of

Copper, Aluminum and Tin at Helium Temperatures , ASTI A AD No. 147716; Contract

No. AF 33(616) -56-8

PURPOSE

To measure X for Cu, A1 , Sn and for Sn in low magnetic field, and

determine an emperical relationship.

SPECIMEN

a) /rod; b) polycrystal 1 i ne ; d) 99.998% Cu; g) source: Johnson, Matthey

and Co.

APPARATUS

a ) longitudinal ; b) gas thermometers; c) radiation shield, vacuum

insul ation.

DATA

a) 2.5 to 4.6 K; b) figure 2 - X; c) uncertainty: ±4% at T < 4.5 K, > 4%

at T > 4.5 K; d) corrections for second virial coefficient and oil volume

change for gas thermometry.

ANALYSIS

b) results in agreement with Allen, J. F. and Mendoza, E. , Proc. Cambridge

Philos. Soc. , 44, 280 (1948).

63
[3] Balcerek, K. , Lipinski, L. , Mucha, J., Rafalowicz, J., Wlosewicz, D.,

Grosse, G. and Hegenbarth, E., Thermal Conductivity of Copper in Temperature

Range 15 to 60 K, Acta Phys. Pol. A, 4-9, 417-20 (1976)

PURPOSE

To verify the CINDAS X equation for pure polycrystal 1 ine Cu.

SPECIMEN

a) 3.05 mm dia./rod; b) polycrystal 1 ine; c) /mechanically worked;

d) 99.999% Al; g) 6 = 1.33 cm-K ?- W-l.

APPARATUS

a) longitudinal; b) Cu-Au + 0.03 at. % Fe low temperature thermocouples of

alloy and Cu wi res//thermocoupl es glued to specimen surface.

DATA

a) 14.5 to 58 K; b) figure 1 - x/data points taken from private

communication with Rafalowicz, J.; c) uncertainty: larger than ±10%.

ANALYSIS

b) K

e

= (a'Tn + b/T)" 1

, n = 2.21, m = 2.63, B = 0.0237 cm.K 2 .W"l, a"

= 0.0423 x 10~ 4 cm-K( n_m-mn+^ )/( n+ l ) . W“1 ; CINDAS equation verified in the

range of maximum X.

[4] Berman, R. , MacDonald, D. K. C. , The Thermal and Electrical Conductivity

of Copper at Low Temperatures, Proc. Roy. Soc. London, Ser. A, 211, 122-8

(1952)

PURPOSE

To measure x and p at low temperatures for Cu.

SPECIMEN

a) 1.12 mm, 0.45 mm dia./rods; c) drawn, annealed 6 h in He at 450 °C;

d) 0.0005% Ag, < 0.0003% Ni , < 0.0004% Pb; f) P4.2 = 5.5 nfi-cm;

g) source: Johnson, Matthey and Co., No. 4234.

APPARATUS

a) longitudinal; b) gas thermometers ; c) radiation shield.

DATA

a) 3 to 90 K; b) figure 1 - X, figure 2 - p; c) uncertainty: ±2%; d) data

corrected for conduction through glass thermometers.

ANALYSIS

b) W(cm K W-l) = 0.212/T + 2.55 x 10- 5 T

2 for 12 < T < 30 K, 1/p

(10“ 6 n-cm) = 1/189.6 + 2.64 x 10“1°T 5 for 30 > T > 12; the Weidemann

Franz Law is not strictly obeyed at temperatures < 4 K, minimum of X given

in Makinson's theory not found.

64
[5] Bowman, H. F. , Ziebold, T. D. , Smith, J. L. , Jr., Low Temperature Thermal

Conductivity of Copper Irradiated with Reactor Neutrons, Proceedings of the

Eighth Thermal Conductivity Conf . , 175-84 (Oct 7-10, 1968)

PURPOSE

To measure x for radiated and irradiated Cu samples.

SPECIMEN

a) 2.00 in. (5.08 cm) long, 0.120 in. (0.305 cm) square/bar;

d) 99.999 + % Cu.

APPARATUS

a ) longitudinal ; b) precision Ge thermometers/instrument leads thermally

anchored to reference heat sink, Ge sensors anchored to pick-up shoes.

DATA

a) 5 to 100 K/0.4 K at 5 K, 4 K at 100 K; b) figure 4 - X; c) uncertainty:

±3%.

ANALYSIS

b) the influence of each neutron collision is roughly 10 to 30 times

greater than the influence of each impurity atom.

[6] Davey, G. and Mendelssohn, K., Heat Conductivity of Pure Metals Below 1 K,

Phys. Lett., 1(3), 183-4 (1963)

PURPOSE

To measure X for Cu, Au, Ti , Fe below 1 K.

SPECIMEN

a) /wire; b) polycrystalline; c) Cu 3 annealed for 3 h at 625 °C; d) Cu 1:

commercial wire, Cu 2, Cu 3: 99.999% Cu.

APPARATUS

a) not given.

DATA

a) 0.4 to 1.0 K; b) figure 1 - X.

ANALYSIS

a) Phillips, N. , Phys. Rev., 100, 1719 (1955), Jericho, M. H. , Thesis,

Cambridge (1963); b) anomalous deviations from T

1 for x.

65
T7] Dupre, A., Van Itterbeek, A., and Michiels, L. , Heat Conductivity of

Copper Below 1 K, Phys. Lett., 8(2), 99-100 (1964)

PURPOSE

To measure X of Cu samples from 0.2 K to 0.7 K.

SPECIMEN

a) 3 mm dia./rods; d) Cu 1: <10 ppm; Cu 3: 1 ppm Co, 2 ppm Fe, 0.5 ppm Mn,

1 ppm Ni , 2 ppm Si; Cu 5: 97 ppm Co, 110 ppm Fe, 130 ppm Mn , 140 ppm Ni

,

160 ppm Si; g) sources: Cu 1: Metallurgical Society of Hoboken

(Belgium); Cu 3: Johnson, Matthey and Co., CB 8; Cu 5: Johnson, Matthey

and Co. CB 2; Cu 1 : 3

= 0.075 cm-K^W"1

; Cu 3 : 3 = 1.73 cm.K 2 W"l; Cu 5:

3 = 17.3 cm*

K

2W~1

.

APPARATUS

a) not given.

DATA

a) 0.2 to 0.7 K; b) figure 1 - x(Cu 1), figure 2 - \(Cu 3, Cu 5).

ANALYSIS

a) Davey, G. and Mendelssohn, K., Phys. Lett., _7> 183 (1963); b) results

verify x = T/3; no anomalies found as in Davey, G. and Mendelssohn, K.

[8] Fletcher, R. , The Nernst-Etti nghausen Coefficient and the Kondo Effect in

Copper and Gold, Philos. Mag., 25(1), 87-95 (1972)

PURPOSE

To measure the isothermal Nernst-Etti nghausen coefficient over a wide

temperature range.

SPECIMEN

a) cut from 7 x 5 x 0.025 cm/plate; c) annealed for 6 hr. at 950 °C;

d) spectroscopical ly pure; e) RRR = 45.5; g) source: Johnson, Matthey and

Co.

APPARATUS

a ) 1 ongitudi nal ; d) Q

1 measured.

DATA

a) 5 to 42 K; b) figure 2 - X (zero field).

66
[9] Garber, M. , Scott, B. W. , and Blatt, F. J., Thermal Conductivity of Dilute

Copper Alloys, Phys. Rev., 130 (6) , 2188-92 (1963)

PURPOSE

To measure x of Cu and find its lattice component.

SPECIMEN

a) 0.25 cm

swaged; d)

for

di a. , 5-10 cm specimen 14 = specimen supplied by

long/rod; c) annealed at

0.23% Cd, 0.76% In; f)

American Smelting and

600 °C for 3 h, then

= 1.06 uft’crn; g) Cu

Re?ini ng Co.

APPARATUS

a )1 ongi tudi nal ; b) 2 Au 2.1% Co vs. Ag 37% Au thermocoupl es/cal ibrated

against Pt resistance thermometer/sol dered to small Cu fittings placed along

specimen ci rcumference.

DATA

a) 12.5 to 93 K; b) figure 2 - X (total)..

ANALYSIS

b) below 20 K, the lattice component is reduced relative to the residual

electrical resistivity, in agreement with Pippard's theory.

[10] Gladun, C. H. R. and Holzhauser, W. , Work on Thermal Conductivity at Low

Temperatures , Monatsber. Dtsch. Akad. Wiss. Berl in , 6_(1 ) , 311-3 (1961)

PURPOSE

To measure X and p of metal specimens from 17 to 100 K.

SPECIMEN

a) rod; d) electrolytic Cu; f) pn = 1.1 x 10" 8 f2 *cm; g) mechanical

deformation ranges from 0 to 30.8%.

APPARATUS

a) longitudi nal ; b) Pb resistance thermometers ; c) radiation shield, vacuum

i nsul ation.

DATA

a) 19 to 83 K; b) figure 1 - X (no deformation)

.

ANALYSIS

b) measurements show a strong lowering of the maximum x and a corresponding increase in residual resistance for increasing deformation.

67
[11] Groger, V. and Stangler, F. , Der Warmewiderstand infolge Elektron - Phononstreuung in Ideal -Rei nem Kupfer, Acta Phys. Austriaca, 40, 145-9 (1974)

PURPOSE

To determine W-j of high purity Cu due to electron-phonon interactions.

SPECIMEN

a) specimen 1: 12.5 ym thick, specimen 2: 125. ym thick/foil; c) annealed

for 4 h at 950 °C; d) specimen 1=3 ppm Fe, specimen 2 = 99.999% Cu.

APPARATUS

a) longitudinal; b) carbon resistance thermometer.

DATA

a) 8 to 37 K; b) figure 1 - X; c) uncertainty: less than ±5%.

ANALYSIS

b) Wi = aT2 - 98

.

[12] Groger, V. and Stangler, F. , Verbesserung der Warmelei tfahigkeit von Reinstkupfer durch G1 uhbehandl ung unter geringem sauerstoffparti aldruck, Z.

Metal Ikd. , 65(5), 333-6 (1974)

PURPOSE

To investigate the effect of different annealing conditions on x of high

purity Cu.

SPECIMEN

a) specimen 1: 12.5 ym thick, specimen 2: 0.125 ym thick/foil; c) three

states of anneal for each specimen: O2 anneal , high vacuum anneal, unan- nealed; d) ultrahigh purity (see Table 3).

APPARATUS

a) longitudinal ; b) carbon resistance thermometers.

DATA

a) 5 to 70 K; b) figure 1 - X (specimen 1), figure 2 - X (specimen 2);

c) uncertainty: less than ±5%; d) size effect, lattice conductivity corrections.

ANALYSIS

a) Anderson, H. H. and Nielsen, M. , Riso, Rep. No. 77; b) Lorenz number 15%

higher after high vacuum anneal than Lo for small Fe content; for large Fe

content, L is 22% higher than Lo.

68
[13] Ho, C. Y., Powell, R. W. , Li ley, P. E. , Thermal Conductivity of the Elements: A Comprehensive Review, J. Phys. Chem. Ref. Data, 3_, Supplement No. 1,

342-257 (1974)

PURPOSE

To provide a comprehensive listing of data on x of the elements.

SPECIMEN

d) high purity; f) p 0 = 5.79 x 10 “-*-^ ^’cm for T below 100 K.

APPARATUS

a) not given.

DATA

a) 0 to 8500 K; b) Table 48 - X, recommended values; c) uncertainty: ±2%

near room temperatue, ±4% at low and high temperatures, and ±15% for the

molten phase up to 2000 K. The values above 2000 K are provisional.

[14] Hust, J. G. and Giarratano, P. J., Semi-Annual Report on Materials Research

in Support of Superconducting Machinery: Thermal Conductivity, NB SIR 74-393, 1-35

(1974)

PURPOSE

To measure x for materials for use in superconducting machinery.

SPECIMEN

a) 23 cm long, 3.26 mm dia./rod; c) swaged, vacuum annealed at 650 °C for

1 h; e) RRR = 14; g) 0FHC.

APPARATUS

a) longitudinal ; b) thermocouples/cal ibrated by Pt + Ge resistance

thermometers; c) sample surrounded by insulation and radiation shield.

DATA

a) 8 to 300 K; b) Table 2 - X, p, L; c) uncertainty in X: from 4 to 20 K: ±2%; from 20 to 200 K: ±1%; from 200 to 300: ±2%; uncertainty in p:

±0 . 2%.

ANALYSIS

a) data within 10% of predicted values found in previous report

( NBSIR 74-359).

59
[15] Kemp, W. R. G. , Klemens, P. G. , and Tainsh, R. J., The Thermal

Conductivity of Copper Alloys: Effect of Plastic Deformation and Annealing,

Philos. Mag., 4(43), 845-57 (1959)

PURPOSE

To study the lattice component of a as a function of torsional deformation.

SPECIMEN

a) 8 cm long, 3.25 mm dia./rods; c) drawn, annealed at 450 °C; No. 0:

control specimen, No. 1: torsionally deformed to 1.29 with no anneal.

No. 4: No. 1 annealed at 450 °C in He; d) 99.55% Cu, 0.35% As, 0.05% P; f) No. 0 (p 0

= 2.71 yQ • cm ) , No. 1 (p 0= 2.79 yft*cm), No. 4 (p 0

= 2.77 yft*cm).

APPARATUS

a) longitudinal; b) He thermometers ; c) radiation shield, insulation.

DATA

a) 7 to 92 K; b) figure 1 - X, Table 1 - p0

.

ANALYSIS

b) the observed change in Ag due to removal of dislocations during

recrystal 1 i zation.

[16] Laubitz, M. J., Transport Properties of Pure Metals at High Temperatures,

Can. J. Phys., 45, 3677-96 (1967)

PURPOSE

To report measurements of high-temperature properties of monovalent

metal s.

SPECIMEN

a) 1.9 cm dia., 20 cm long/rod; c) annealed for 2 h at 700 K/machined from

1 in. dia. x 15 in. bar; d) 99.999 + % Cu; e) RRR = 900.

APPARATUS

a) modified Forbes Bar method; b) Pt/Pt-10% Rh thermocouples/calibrated at

NRC/peened into specimen; c) several radiation shields, argon atmosphere

of 10-25 cm Hg.

DATA

a ) 300 to 1200 K; b) equation 4 - A; c) uncertainty: ±0.9% at 300 K to

±1.5% at 1200 K.

ANALYSIS

a) Schofield, F. H. , Proc. Roy. Soc. London, Ser. A, 107 , 206 (1925),

Midryukov, V. E., Vestn. Mosk. Univ., Ser. Mat., Mekh., Astron., Fiz.,

Khim., 12, 57 (1957); b) A = 4.182(7) - 0.631(6) x 10“ 3 T; results agree

with Mikryukov to within combined experimental error.

70
17] Lees, C. H. , the Effects of Temperature and Pressure on the Thermal Conductivities of Solids - Part II: The Effects of Low Temperatures on the Thermal and

vlectrical Conductivities of Certain Approximately Pure Metals and Alloys,

Philos. Trans. Roy. Soc. London, Ser. A, 208, 381-443 (1908)

PURPOSE

To measure x and p of several materials from 107 to 299 K.

SPECIMEN

a) 7 cm long, 0.585 cm dia./rod; c) /soft-drawn, turned.

APPARATUS

a) longitudinal ; b) Pt resistance thermometer.

DATA

a ) 107 to 299 K; b) Table (pp. 406-7) - X, Table (p. 432) - p; c) uncertainty: less than ±5%; d) corrections for heat leaks.

ANALYSIS

b) x increases with increasing temperature.

[18] Lindenfeld, P., Lynton, E. A., and Soulen, R., Metallic Heat Conductivity

Below 1 K, Phys. Lett., 19(4), 265 (1965)

PURPOSE

To measure X of Cu below 1 K.

SPECIMEN

a) 0.05 cm thick/foil; c) annealed for 3 h at 530 °C; e) RRR = 270; g) electrolytic tough pitch from Chase Brass and Copper Co.

APPARATUS

a) longitudi nal ; b) carbon resi stors/cal ibrated against the vapor pressure

(above 1.2 K), susceptibility of ruby probe, germanium resistance thermometers (below 1.2 K).

DATA

a ) 0.4 to 1.5 K; b) figure 1 - X/T vs. T; c) uncertainty: less than ±14.

ANALYSIS

b) no anomaly found as in Davey, G. and Mendelssohn, K. , Phys. Lett., 7

_ (1963).

71
[19]

Lucks, C. F. and Deem, H. W. , Thermal Properties of Thirteen Metals, Am.

Soc. Test. Mater., Spec. Tech. Publ . , No. 227, 1-29 (1958)

PURPOSE

To report high temperature data on several metals.

SPECIMEN

a) 3/4 in. dia. x 6 in. /rod; c) cold drawn/electrolytic tough pitch; g) federal specification QQ-C-502; source: Revere Copper and Brass, Inc.

APPARATUS

a) longitudinal; b) specimen soldered to heater block, Fe standard; c) guard

tubes, insulation.

DATA

a) 366 to 1255 K; b) Table VI - X.

ANALYSIS

b) Smith, C. S. and Palmer, E. W. , Am. Inst. Min. Metal 1. Pet. Eng. , 124

(1937); Schofield, F. H., Proc. Roy. Soc. London, Ser. A, 107 (1925).

[20]

Mendelssohn, K. and Rosenberg, H. M. , The Thermal Conductivity of Metals at

Low Temperatures. I. The Elements of Groups 1, 2, and 3, Proc. Phys. Soc.,

London, Sect. A, 6_5, 385 (1952); see Rosenberg, H. M. , The Thermal Conductivity

of Metals at Low Temperatures , Philos. Trans. Roy. Soc. London, 247 , 441-497

(Mar 1955)

[21]

Mikryukov, V. E. , Vestn. Mosk. Univ., Ser. Mat., Mekh., Astron., Fiz.,

Khim. , jl(2) , 53-70 (1956)

PURPOSE

To measure X and p of Cu.

SPECIMEN

b) polycrystal 1 i ne ; d) 99.99% Cu.

APPARATUS

a) not given.

DATA

a) 320 to 773 K; b) Table 1 - X, p; c) uncertainty: ±3%.

72
[22] Misiorek, H. , Zakrzewski , T. , and Rafalowicz, J., Influence of Plastic

Deformation on the Thermal Conductivity Maximum of Copper and Aluminum in the

Temperature Range 4.2 to 70 K, Phys. Status Sol i d i A, _47, K137 (1978)

PURPOSE

To determine the effect of increasing deformation on the thermal

conductivity maximum.

SPECIMEN

a) /rod; c) deformed, undeformed specimens; d) 99.9%, 99.99% Cu.

APPARATUS

a) longitudinal.

DATA

a) 15 to 65 K (undeformed); b) figures 3,4; e) captions for all figures

switched: figure 1 should be labeled as 4, figure 2 as 3, figure 3 as 1,

figure 4 as 2.

ANALYSIS

b) with increasing deformation, the maximum decreases in value and is

shifted toward higher temperatures.

[23] Moore, J. P. , McElroy, D. L. , and Graves, R. S. , Thermal Conductivity and

Electrical Resistivity of High-Purity Copper from 78 to 400 K, Can. J. Phys.,

45, 3849-65 (1967)

PURPOSE

To compare measurements of a guarded longitudinal technique with other

data.

SPECIMEN

a) /rods; b) polycrystal 1 ine ; d) 99.999% Cu; e) RRR = 900; g) average

grain size: 574 ym, hardness of 40 (DPH) with 0.1 kg load.

APPARATUS

a) longitudinal ; b) Chromel-P, constantan thermocouples/cal ibrated

spool s/electrical ly insulating epoxy; c) Au plated radiation shield, spun

A1 2 O

3 placed between polished specimen and shield.

DATA

a) 85 to 400 K; b) Table 2 - X, p (both smoothed); c) uncertainty:

± 1 . 86 %; d) x, p uncorrected for thermal expansion.

ANALYSIS

a) Laubitz, M. J., Can. J. Phys., 45^, 3677 (1967); b) x(W cm-ik" 1

) = 4.1631 - 5.904 x 10

' 4 T + 7.0872 x 10 5 T

" 3 300 < T < 1200.

73
[24] Nelson, W. E. and Hoffman, A. R. , Measurements of Temperatures and Magnetic Field Dependence of Electrical Resistivity and Thermal Conductivity in

QFHC Copper, Proceedings of the Fourteenth Thermal Conductivity Conf., 73-80

(Jun 2-4, 1975)

PURPOSE

To measure X and p on Cu in a longitudinal magnetic field.

SPECIMEN

a) 2.5 cm long; c) soldered at T = 160 °C/machined from 0.5 in. rod;

d) commercial grade OFHC, 3 ppm P, 1 ppm Zn , 10 ppm each Pb, 0, Te, 10 ppm

total As, Bi , Mn, Sb, Sn; f) (p 0

= 3.15 x 10~8 ft. cm); g) source: Admiral

Brass and Copper Co., Alloy 101.

APPARATUS

a) longitudinal; b) carbon resistor thermocouples/cal ibrated against com- mercial Ge resistance thermometer and fit to a modified resistance vs. temperature expression (Clemment, J. R. and Quinnell, E. H. , Rev. Sci

.

Instr. , 24 (1952) 213).

DATA

a) 4.05 to 34.9 K; b) Table 1 - X, p, L; c) uncertainty in X: ±5%, uncer- tainty in p: ±1.5%.

ANALYSIS

b) X- 1 (0 field) = aT2 + eT” 1

, p (0 field) = a + bT4 - 42 .

[25] Nicol, J. and Tseng, T. P., Thermal Conductivity of Copper between 0.25

and 4.2 K, Phys. Rev., 92(4), 1062-3 (Nov 15, 1953)

PURPOSE

To measure low temperature x for Cu.

SPECIMEN

a) 27.2 cm long, 0.025 cm dia./wi re; b) polycrystal 1 ine; d) commercial

grade high-purity magnet wire; g) source: General Electric Co.

APPARATUS

a) longitudinal; b) T < 1 K: Cr-K-al urn paramagnetic thermometry, ac bridge. T > 1 K: carbon thermometers//T < 1 K: contact between salts

and mounting by high pressure salt molding.

DATA

a) 0.25 to 4.2 K; b) figure 1 - X.

ANALYSIS

b) x = aT: a(W-cm”l *K“ 2

) = 1.76; the observed linear dependence of X on temperature indicates X is electronic in character.

74
[26] Powell, R. L. , Roder, H. M. , and Hall, W. J., Low-Temperature Transport

Properties of Copper and Its Dilute Alloys: Pure Copper, Annealed and

Cold-Drawn, Phys. Rev., 115 (2) , 314-23 (Jul 15, 1959)

PURPOSE

To measure x, p and therinoel ectric power of two high purity Cu specimens.

SPECIMEN

a) specimen 1: 0.07 in. (0.18 cm) dia., specimen 2: 0.0816 in. (0.207 cm)

dia./rod; c) specimens 1,2 swaged and drawn from 3/8 in. (0.95 cm)

rod/specimens 1,2: annealed in vacuum at 400 °C, 2 h, after swaging and

before drawing. Specimen 1 annealed at 400 °C, 2 h, after drawing;

d) specimens 1,2: 99.999% Cu; e) specimen 1 (RRR = 1530), specimen 2 (RRR

= 115); f) specimen 1 (p 0

= 1.01 x 10" 9 ft*cm), specimen 2 (p 0= 1.30

x 10"° ft*cm); g) source: CRL of American Smelting and Refining Co.

APPARATUS

a) longitudinal ; b) Au-Co vs. Cu thermocouples, Pt resistance

thermometer.

DATA

a) 4 to 105 K; b) Table 1 - X, Table 2 - p n and RRR, figure 4 - p,

figure 8 - L. ANALYSIS

a) experimental results agree qualitatively with theory and previous work;

b) observed p deviation from Matthiessen 's rule; L curve flattens out

considerably below Sommerfeld valve when extrapolated to 0 K.

[27] Powell, R. L., Roder, H. M., and Rogers, W. M., Low Temperature Thermal

Conductivity of Some Commercial Copper, J. Appl . Phys., 28(11), 1282-8

(Nov 1957) —

PURPOSE

To measure X for some commercial coppers.

SPECIMEN

a) all specimens 0.144 in. (0.366 cm) dia./rod: c) all specimens ground

from 0.25 in. (0.64 cm) to 0.144 in. (0.366 cm); d) coalesced: 99.98% Cu;

Electrolytic Tough Pitch: 99.98% Cu; Tellurium Cu: 99.4% Cu; Phosphorus

Deoxidized Cu: 99.62% Cu; g) more detailed characteri zation given in

Table 1.

APPARATUS

a) longitudinal ; b) 8 Au-Co vs. Cu thermocouples/cal ibrated from 4 to 300 K in separate apparatus; c) temperature controlled radiation shield and vacuum insulation.

DATA

a ) 5 to 37 K, 4 to 33 K, 6 to 84 K, 5 to 80 K for coalesced, electrolytic , free cutting, phosphorized respecti vely/1 to 60 K; b) figure 2 - X. ANALYSIS

b') K/ r = (1/6) + (T/D), B(cm.K2. w-l) = 54(±2), 190(±10), D(cm.|<3.w"l)

= 7(±1) x 10°, 2.2(±0.5) x 10^ for phosphorized and free cutting

respectively; X of work hardened Cu-alloys is predominantly electronic

thermal conduction as limited by the imperfection scattering.

75
[28] Powell, R. L. , Rogers, W. M. , and Coffin, D. 0., An Apparatus for Measurement of Thermal Conductivity of Solids at Low Temperatures , J. Res. Nat. Bur.

Stand., 59(5), 349-55 (Nov 1957)

PURPOSE

To describe an apparatus for X measurements of solids between 4 and 300 K.

SPECIMEN

a) 23.2 cm long, 0.367 cm dia./rod; c) annealed in He for 4 h, 400 °C,

cooled to 200 °C for 8 h; d) 13 ppm 0o> 8 ppm Pb, 7 ppm Ni , Fe < 5 ppm;

g) density = 8.90 g/cnP, hardness on Vickers diamond point with 10 kg

weight: 54.1 - longitudinal, 48.8 - transverse, source: Phelps Dodge

Copper Products Corp.

APPARATUS

a) longitudinal; b) Au-Co vs. Cu thermocouples, Pt resistance reference

thermometer/Pt resistance thermometer calibrated down to 12 K by Temperature Measurements Section of NBS; c) vacuum insulation.

DATA

a) 9 to 142 K; b) figure 8 - X; c) uncertainty: ±5% (maximum).

[29] Powell, R. W. and Tye, R. P., New Measurements on Thermal Conductivity

Reference Materials, Internat. J. Heat and Mass Transfer , _H)(5) , 581-95

(1967)

PURPOSE

To provide information on x and p of possible reference materials.

SPECIMEN

a) 15 cm long, 7 mm dia./rod; c) heat treated to 900 °C; d) 0FHC;

g) source: Johnson, Matthey and Co. No. 4351.

APPARATUS

a) longitudinal

.

DATA

a) 293 to 1173 K; b) Table 1 - X; c) uncertainty: not given.

ANALYSIS

a) see Table 2 for data comparison at 50 °C; b) present data agree well

with the two highest values of Kannuluik, W. G. and Laby, T. H., Proc.

Roy. Soc., A121 , 640 (1928); Mikryukov, V. E. , Mosk. Gos. Univ., Ser.

Mat., Mekh. Astron. Fiz. i Khim. _U(2), 53 (1956).

76
[30] Powers, R. W. , Schwartz, D. , and Johnston, H. L. , The Thermal Conductivity

of Metals and Alloys at Low Temperatures. I. Apparatus for Measurements Between

2 5 and 300 K, USAF TR-264-5, Cryogenic Lab., Dept, of Chem. , O.S.U., Columbus,

Ohio (1950)

PURPOSE

To describe an apparatus for measuring x for metals from 25 to 300 K in

small temperature increments.

SPECIMEN

a) 20 in. (51 cm) long, 0.5 in. (1.3 cm) dia./rod; d) 0FHC; g) source:

American Brass Co.

APPARATUS

a ) longitudi nal ; b) Cu-constantan thermocoules/cal ibrated against a He gas

thermometer; c) 3 monel radiation shields.

DATA

a) 23 to 245 K; b) Table 4 - X; c) uncertainty: ±0.7% from 100 to 250 K,

±1.9% at 30 K,

[31] Quick, R. W. , Child, C. D. , and Lanphear, B. S. , Thermal Conductivity of

Copper. II. Conductivity at Low Temperatures, Phys. Rev., 3(1), 1-20 (1895)

PURPOSE

To extend observations of X from 219 to 260 K.

SPECIMEN

d) electrolytic Cu.

APPARATUS

a) Forbes bar method.

DATA

aT~219 to 260 K; b) Table 10 - X.

ANALYSIS

b) An increase in T corresponds to an increase in x over the temperature

range measured.

77
[32] Rhodes, B. L. , Moeller, C. E. , and Saver, H. J., An Apparatus for

Determining Thermal Conductivity of Solids From 20 to 600 K, Cryogenics, 5_(1),

17-20 (1965)

PURPOSE

To discuss a X apparatus with which a large temperature gradient is not

required over the specimen.

SPECIMEN

a) 10 cm long, 6 mm dia./rod; d) 99.999% Cu.

APPARATUS

a) longitudinal ; b] Cu-constantan thermocouples; c) radiation shield, 2

x 10 -5 mm (3 x 10“^ Pa) insulation.

DATA

a) 98 to 573 K; b) Table 2 - average X; c) uncertainty: ±3% (maximum) for

T > 48, ±12% at 20 K.

ANALYSIS

a) Roder, Powell, and Hall, Phys. Rev., 115 , 314 (1959); White, Aust. J.

Phys., _6 , 397 (1953); Berman and MacDonald, Proc. Roy. Soc. London,

Ser. A, 211 , 122 (1952); b) data agree to within ±6% of reference data.

[33] Roder, H. M. , Powell, R. L., and Hall, W. .J., Thermal and Electrical

Conductivity of Pure Copper, Low Temperature Physics and Chemistry, 364-6

(Aug 1958)

PURPOSE

To measure X and p for pure Cu.

SPECIMEN

a) /rod ; c) specimens 1,2: annealed, specimen 3: not annealed/

specimen 3: drawn to 25% less cross sectional area; d) specimens 1,3:

99.999% Cu, specimen 2: 343 ppm Ag; e) specimen 1 ( RRR = 1450),

specimen 2 (RRR = 400), specimen 3 (RRR > 350); g) source: American

Smelting and Refining Co.

APPARATUS

a) not given, but probably longitudinal.

DATA

a) specimen 1: 4 to 86 K, specimen 2: 4 to 64 K, specimen 3: 5 to 30 K; b) figure 1 - X, figure 2 - p, figure 3 - L.

ANALYSIS

b) W = ATn + B/T.

78
[34] Rosenberg, H. M. , The Thermal Conductivity of Metals at Low Temperatures , Philos. Trans. Roy. Soc. London, 247 , 441-97 (Mar 1955); see also

Mendel ssohn , K., and Rosenberg, H. M. , Proc. Phys. Soc., London, Sect. A, 5J5,

385 (1952)

PURPOSE

To measure x for many metals at low temperatures.

SPECIMEN

a) 2.99 cm long, 2.99 mm dia./rod; b) polycrystal 1 i ne ; c) vacuum annealed,

800 °C for several h/turned down from 3.02 mm dia.; d) 99.999% Cu;

g) P 293 /P 20

= 85.3, source: Johnson, Matthey and Co., No. 4234.

APPARATUS

a) longitudinal ; b) gas thermometers/cal ibrated at liquid He and H

2 temperatures/thermometer capillaries anchored to liquefier top and vacuum jacket; c) Cu radiation shield, vacuum insulation.

DATA

a) 2.5 to 41 K; b) figure 4 - X; c) uncertainty: ±3% (maximum).

ANALYSIS

a) Berman and MacDonald (1952) curve of Cu from same batch agrees for temperatures above the maximum and a = 2.5 x 10" 5 also agrees;

b) Matthiessen 1 s rule is not strictly valid in the region of x maximum; 1/x

= aT2 - 3/T.

[35] Schofield, F. H. , The Thermal and Electrical Conductivities of Some Pure

Metals, Proc. Roy. Soc. (London), 107 , 206-27 (1924)

PURPOSE

To measure x and p of several metals.

SPECIMEN

a) 3/4 in. (1.905 cm) dia./rod; c) hot rolled to 1 in. dia., drawn to

7/8 in. dia., machined and polished to 3/4 in. dia., then annealed;

d) 99.9%; g) source: T. Bolton and Sons, Ltd., Oakmoor.

APPARATUS

a) Forbes bar method; b) Pt/10%Ir-Pt thermocouples; c) insulation between

specimen and guard ring.

DATA

a) 369 to 898 K; b) Appendix II - X, p; c) uncertainty: not given.

ANALYSIS

a) Lees (1908); Jaeger and Diesselhorst (1900).

79
[36] Schriempf, J. T. , Deviations from Matthiessen 1 s Rule in the Low

Temperature Thermal and Electrical Resistivities of Very Pure Copper,

Proceedings of the Seventh Thermal Conductivity Conf., 249-52 (Nov 13-16, 1967)

PURPOSE

To use x and p data to show the deviation of Matthiessen 1 s rule at low

temperatures.

SPECIMEN

a) Cu 1: 0.119 in. (0.302 cm) dia., Cu 2 and Cu 2-0: 0.076 in. (0.19 cm)

dia./rods; c) Cu 1 : annealed 12 h at 1000 °C in air, 10" 3 mm (0.1 Pa),

Cu 2: annealed 3 h at 530 °C, 10~6 mm (10 -4 Pa), Cu 2-0: Cu 2 annealed

22 h at 1000 °C in air, 5 x 10“4 mm (7 x 10 -3 Pa)/Cu 1: swaged from 3/8

(0.95 cm) to 0.125 in. (0.318 cm) dia., annealed, etched, Cu 2: swaged to

0.080 in. (0.20 cm) dia., etched, annealed; d) Cu 1: 100 ppm Mn, Cu 2 and

Cu 2-0; Mn < 10 ppm; f) Cu 1 (p 0

= 1,73 x 10 -11 f2*m), Cu 2 (p 0

= 0.579

x 10“ 1J- £2 *m), Cu 2-0 (p 0

= 1.12 x 10 -11 fMm); g) source: American

Smelting and Refining Co.

APPARATUS

a) longitudinal; b) thermocouple difference thermometer/referenced by Ge

thermometer.

DATA

a) 2 to 20 K; b) figure 1 - X; c) uncertainty: ±3%.

ANALYSIS

b) results agree with White, G. K. and Tainsh, R. J., Phys. Rev., 119 , 1869 (1960), but disagree with Powell, R. L., Roder, H. M., and Hall,

W. J., Phys. Rev., 115, 314 (1959).

80
[37] Scott, B. W. , Transport Properties of Dilute Copper Alloys, Ph.D. Thesis,

Michigan State Univ. (1962), University Microfilms Inc., Ann Arbor, Michigan

PURPOSE

To measure x, p and thermoel ectri c power of dilute Cu alloys and compare

with existing theory.

SPECIMEN

a) all specimens 5 to 10 cm long, 0.25 cm dia./rods; c) all specimens cast

into 3/16 x 2 in. (0.48 x 5 cm) slugs from 99.999% Cu, homogenized at

600 °C for six days and annealed in sealed vycor capsules, each step in

2/3 atm. (6.8 x 10^ Pa) He (specimen 8 high vacuum). Specimen 3 annealed

at 600 °C for 5 h, 750 °C for 1 h, specimens 14, 15, 17 annealed at 600 °C

for 3 h, remaining annealed at 750 °C for 2 h/all swaged between homogeniza

tion and annealing, and given acid etch before casting and annealing;

d) specimen 8: 0.61% Sn, specimen 14: 0.225% Cd, 0.762% In, specimen 15:

0.104% Cd, 0.389% In, specimen 17: 0.477% Cd, 0.294% In, specimen 101:

0.47% Zn, 0.294% In, specimen 102: 0.49% Zn, 0.77% In, specimen 103:

0.416% In, 0.995% Zn, specimen 104: 0.331% Zn, 0.35% Ga, specimen 105:

0.34% Zn, 0.805% Ga , specimen 106: 0.856% Zn, 0.37% Ga; f) specimen 8 (p 0

= 1.75 x 10" 6 ft*cm), specimen 14 (p~ = 1.061 x 10"® Q*cm),

specimen 15 (p 0

= 0.549 x 10"® ft*cm], specimen 101 (p 0= 0.481

x 10"® ft* cm) , specimen 102 (pp = 1.03 x 10"® ft*cm), specimen 103

(p 0

= 0.73 x 10"® ft*cm), specimen 104 (p 0

= 0.585 x 10"® ft*cm),

specimen 105 (pp = 1.418 x 10"® ft*cm), specimen 106 (p 0

= 0.718

x 10"® ft*cm); g) source: American Smelting and Refining Co.

APPARATUS

a) longitudinal; b) Au - 2.1 at. % Cu vs. Ag - 37 at. % Au thermocouples/

calibrated against Pt resistance thermometer certified by NBS; c) vacuum in

sul ation.

DATA

a) 7 to 100 K/l to 5 K; b) Tables on pp. 142-149, 162-164, 166-170 - X and

p, all specimens; c) uncertainty: ±3% at 20 K, ±7% at 50 K.

ANALYSIS

b) low temperature lattice conductivity of dilute alloys is explained by

Pippard's theory. At higher temperatures the anisobaric effect is apparently masked by scattering.

81
[38] Siu, M. C. I., Carroll, W. L. , and Watson, T. W. , Thermal Conductivity and

Electrical Resistivity of Six Copper-Base Alloys, NBSIR 76-1003, 1-18 (1976)

PURPOSE

To measure A and p at high temperatures.

SPECIMEN

a) 37 cm long, 0.64 cm dia./rod; c) extruded at 1233 K and aged at 693 K in cracked natural gas atmosphere; d) 0.002% Fe, 0.662% Ni , 0.20% Zr.

APPARATUS

a) longitudinal; b) Pt/Pt - 10% Rh; c) heaterguard, vacuum, alumina powder

surrounds specimen and guard.

DATA

a) 373 to 923 K; b) Table 4 - X, Table 5 - p; c) uncertainty: ±2%.

ANALYSIS

b) the measured values of A, p conform to the Smith-Palmer equation to

within 10%.

[39] Touloukian, Y. S. , Powell, R. W. , Ho, C. Y., and Klemens, P. G. , Thermophysical Properties of Matter, Volume 1: Thermal Conductivity, Metallic Elements and Alloys, 68-81 (1970)

PURPOSE

To provide an extensive list of data for x of the metallic elements and

al 1 oys.

SPECIMEN

d) 99.999%; f) p0

= 8.51 x lO' 10

si- cm.

APPARATUS

a) not given.

DATA

a) 0 to 1356 K; b) Figure and Table 12R - X, recommended values; c) uncer- tainty: ±3% near room temperature, ±3 to 5% at other temperatures ; e) the

values below 1.5 Tm are calculated to fit the experimental data by using

n = 2.40, a = 0.19, m = 2.59, a" = 4.16 x 10~ 6

, and 3 = 0.0348.

82
[40] Tseng, Tse-Pei , Properties of Matter at Very Low Temperatures , Ph.D.

Thesis, Ohio State Univ. (1954)

PURPOSE

To provide x data on commercial grade Cu.

SPECIMEN

a) 0.025 cm dia./wire; d) commercial grade; g) source: General Electric

Co.

APPARATUS

a) longitudinal; b) C resistance thermometers/resi stance extrapolated to zero power of measuring current for calibration; c) 10"

6 mm (10"4 Pa)

insul ation.

DATA

a) 1.4 to 4.2 K; b) Table 2 - X; d) corrections for thermometer and heater

lead conduction.

ANALYSIS

b) results are comparable to Mendelssohn, K. and Rosenberg, H. M. , Proc.

Phys. Soc., London, Sect. A, 65_, 385 (1952).

[41] White, G. K., The Thermal and Electrical Conductivity of Copper at Low

Temperatures, Aust. J. Phys., 6^(4), 397-404 (1953)

PURPOSE

To measure X and p for pure Cu.

SPECIMEN

a) Cu 1, 2: 2 mm dia., Cu 3: 1 mm di a . , al 1 5 cm long/ rods; c) Cu 2 is

Cu 1 after vacuum annealing at 550 °C for 3 h/Cu 1 , 3 in "as drawn"

condition; d) all specimens, 0.0005% Ag, < 0.0003% Ni , 0.0004% Pb, trace

of Ga, Fe; e) Cu 1 (p 0

= 0.051 yn*cm); Cu 2 (p 0= 0.0576 yfl»cm); Cu 3

(p0

= 0.00458 pQ*cm); g) source: Johnson, Matthey and Co., No. JM4272.

APPARATUS

a) longitudinal ; b) gas thermometers ; c) vacuum insulation.

DATA

aT~Cu 1: 2.5 to 116 K, Cu 2: 5 to 58 K, Cu 3: 2.03 to 160 K; b) figure 2 - X; c) uncertainty: ±4% from 5 to 15 K, ±1% for all others;

d) correction for radiative heat loss at higher temperatures.

ANALYSIS

b) results in agreement with Berman, R. and MacDonald, D. K. C. , sample of

pure annealed Cu; measurements support theory of non-additivity of

impurity and ideal resistances.

S3
T42] Whits, G. K. and Tainsh, R. J., Lorenz Number for High Purity Copper, Phys.

Rev., 119(6), 1869-71 (Sep 1960)

PURPOSE

To investigate L for very pure copper.

SPECIMEN

a) 0.03 in. (0.08 cm) dia., 8 cm long/wire; c) annealed at 530 °C in vacuo/

rolled and drawn from 0.75 in. (1.9 cm) dia.; d) < 0.0001% Fe, Sb, Se each,

< 0.0002% Te, As each; f) pg

= 0.87 x 10"^ ft.cm; g) source:

American Smelting and Refining Co.

APPARATUS

a) longitudinal; b) He gas thermometers.

DATA

a) 2 to 55 K; b) figure 1 - X; c) uncertainty: ±4% for 2 < T < 15; ±1% T

> 15.

ANALYSIS

b) X = A/T + BTn

: A = 0.035 cm«K W" 1 compared to 0.059 for Powell, R. L.

,

Roder, H. M., and Hall, W. J., Phys. Rev., 115, 314 (1959).

[43] White, G. K. and Woods, S. B. , Thermal and Electrical Conductivities of

Solids at Low Temperatures, Can. J. Phys., 33, 58-73 (1955); The Lattice Thermal

Conductivity of Dilute Copper Alloys, Philos. Mag., 45, 1343-5 (1954)

PURPOSE

To describe an apparatus for measuring X and p of solids between 2 and

300 K.

SPECIMEN

a) 1 to 2 mm dia., 6 cm long/rods; c) Cu 1, 2, 3 annealed at 700 °C for

2 h/drawn; d) Cu 1: 0.02% Ge, Cu 2: 0.056% Fe. Cu 3: 0.0043% Fe; f) Cu 1 (p 0 =0.084 x 10

- 6

ft. cm), Cu 2 (p 0

= 0.53 x 10"° ft.cm), Cu 3 (p 0= 0.041

x I0“ 6 ft. cm).

APPARATUS

a) longitudinal; b) gas thermometers//al 1 leads to specimen are anchored to

Cu pillars; c) temperature controlled radiation shield.

DATA

a) 1 .5 to 142 K; b) figure 2 - p, figure 3 - X, Table 1 - p 0 ; c) uncer- tainty: ±5% for high X specimens from 4 to 15 K, all others: ±1%; d) cor- rection for radiation.

ANALYSIS

b) X = AT" 1 + B T

2 - 4 .

84
[44] Zavaritskii, N. V. and Zel'dovich, A. G. , Thermal Conductivity of Technical

Materials at Low Temperatures, Sov. Phys. Tech. Phys. , _1, 1970-4 (1956)

PURPOSE

To describe an apparatus for measuring x for solid materials.

SPECIMEN

a) 20 and 6 mm long, 10 and 6 mm dia./rods; c) M-3-anneal ed: annealed at

800 °C/M-3-anneal ed : cut from tube; d) M-3-annealed and unannealed: Bi

< 0.003, Sb < 0.05, As <_ 0.05, Fe 0.05, Ni _< 0.20, Pb _< 0.05, Sn <_ 0.05, S

_< 0.01, 0 _< 0.1%, Cupalloy: 0.61% Cr, 0.18% Ag.

APPARATUS

a) longitudinal ; b) carbon resistance thermometers/cal ibrated from 2 to

4.2 K and from 14 to 20 K from vapor pressures of He and H

2 respectively

and from 20 to 110 K from standard Pt resistance thermometer; c) radiation

shield and vacuum insulation.

DATA

a) 2 to 100 K; b) figure 2 - X; c) uncertainty: ±5%.

ANALYSIS

b) results agree with White, G. K. and Woods, S. B. , Can. J. Phys., 33., 58

(1955).

85

3. Aluminum

3.1 General

Aluminum has also been measured extensively but not as completely as copper

A total of 35 publications are included in the annotated bibliography (Section 3.5). The following of these data sets were selected as primary data: 1,

9, 11, 12, 17, 25, 26, 29, and 33.

The primary data contain only annealed specimens, and covers a range of tern

perature from 2 to 873 K, and a range of RRR from 13 to 16800. Thermal conductivity values from these sources are shown in Figs. 3.1.1 through 3.1.3, where

the last graph is a composite of the data. Although the RRR of the most electrically pure aluminum ever produced is comparable to that for copper (50,000),

aluminum with RRR values in the range of 10,000 to 20,000 is more readily obtai ned.

Equation 1.1.3 was fitted to the primary data set over the entire temperature range. The values of the parameters, P-j , i = 1,2 ... 7 obtained by nonlinear least squares fit are:

= 4.716 x 10"8

P

5 = 130.9

P 2 = 2.446 P 6 = 2.5

P 3

= 623.6 P

? = 0.8168

P4

= -0.16

with all units in SI.

The data at high RRR were then examined for systematic residual deviations

as a function of temperature. These residuals were represented by the W

c term

in Eq. 1.1.5. The resulting equation for W

c is:

87
W = -0.0005 £n( T/330) exp(-(£n(T/380)/0.6) 2

)

-0.0013 £n(T/110) exp(-Un(T/94)/0.5) 2

),

where W

c and T are in SI units.

3.2 Deviations from Recommended Equation

Equation 1.1.3 represented the overall primary aluminum data to yield random

deviations. Again some of the individual data sets exhibit systematic trends.

The deviations of these data from Eq. 1.1.3 are shown in Figs. 3.2.1, 3.2.2, and

3.2.3. Although temperature dependent deviations exist for individual data sets,

the overall pattern is random in nature. No systematic trends with RRR were

noted.

The primary data were selected from the literature data on relatively large,

well annealed specimens. Therefore, the deviations exhibited in Figs. 3.2.1

through 3.2.3 are indicative of the combined effect of a) experimental measurement errors and b) the inability of Eq. 1.1.3 to account for the effects of

chemical impurity variations. The effects of physical defect variations, small

specimen size variations, and magnetic fields are exhibited, in part, by the deviations of the secondary data. The thermal conductivity variations caused by

other than chemical impurity variations are not expected to be represented as

well by Eq. 1.1.3. However, the RRR (or p 0 ) correlating parameter does account

for an appreciable part of these variations. Some users may find this to be an

adequate representation and, therefore, discussions of these comparisons are included for completeness.

The deviations of the secondary data sets are illustrated in Figs. 3.2.4

through 3.2.10. Figures 3.2.7 and 3.2.10 are composite deviation plots.

Eq. 1.1.3 is compared to the most commonly used sources of reference data by

Ho and Touloukian, references 14A,32A, respecti vely, in Fig. 3.2.11. The agreement

88
is within the combined uncertainties except in the region around 60 K. In this

region data by Cook, reference 5, were published after both data sets and is the

reason for the large differences.

3.2.1 Physical Defect Effects

Investigations of physical defects in aluminum have produced only a few references 21,25. Each of these references will be discussed below.

Changes in thermal conductivity due to elongation are studied in reference 21. The conclusion is that increasing deformation lowers the thermal conductivity maximum and shifts it to a higher temperature. Unfortunatel y , it appears that the figure captions do not correspond to the proper figures; caption 3

belongs to Fig. 2 and caption 4 to Fig. 1. Note that in Fig. 2, the nondeformed

specimen has the wrong temperature dependence above the temperature of the maximum thermal conductivity. The deviations from Eq. 1.1.3 for this specimen were

within +_60%. The deviations from Eq. 1.1.3 for the specimens in Fig. 1 were

within +10% for the undeformed specimen. The deformed specimens were not compared.

Reference 25 showed the effects on the thermal conductivity of an "as fabricated" specimen and an annealed specimen of the same stock. Also included was a

high purity specimen. The peak value of the thermal conductivity for this specimen was about 1580 W*m- ^ -IC 1

, for the "as fabricated" specimen,

389 W*m“l*K"l, and for the annealed specimen, the peak value was

332 The authors comment on the effect of the anneal , indicating that the decrease in peak value of the annealed specimen it is due to

the large amount of impurities present in the original stock. The deviations

from Eq. 1.1.3 for the high purity specimen were within +7% as were those for the

annealed specimen. The deviations for the "as fabricated" specimen were within

+8%.

89
Although the temperature dependence of physical defect scattering mechanisms

is different from that due to impurity scattering. Eg. 1.1.3 represents the unannealed specimen data to within _+10% . This indicates that the residual electrical

resistivity characteri zes both types of scattering for the range of RRR included

here.

3.2.2 Size Effects

Amundsen and Olsen^ studied the size effects of several aluminum specimens. As the specimen size decreases, the peak value of the resistivity increases. Notice that magnetic fields were used to find the thermal resistivity

of each specimen. The ratio of the thermal and electrical resistivities was

shown to be constant, except at the highest fields, where the thermal resistivity

increased faster than the electrical resistivity.

Although not specifically studied, we can make some general comments regarding the thermal conductivity of several specimens at low temperatures as a function of specimen size. The peak thermal conductivity is shifted toward lower

temperatures for the larger specimens. The justification of this effect resides

in its observation in other metals.

3.2.3 Magnetic Field Effects

Although magnetic field effects on thermal conductivity were not studied explicitly, reference 14 showed that the peak conductivity value in a 0.5 T magnetic field was 5400 W*nT**K"l, while in a zero field, the value was

10500 W*m_1

*K _1

. It is interesting to notice that this peak disappears

completely for a field somewhere between 0.5 and 1 T.

1 Amundsen, T. and Olsen, T. , Size Dependent Thermal conductivity in Aluminum

Films, Phil. Mag., _U, 564-74 (1965).

90
Reference 31 reported that the peak conductivity value in a 1 T field was

3800 while in a zero field the value was

5800 W’iW'K - 1. This study supports the statement that the peak in

thermal conductivity disappears between 0.5 and 1 T.

Reference 32 reported low temoerature thermal conductivity data for fields

uo t.o 5 T. At zero field and a temperature of 20 K, the specimen had a conductivity value of 6500 W'm -1

‘K" 1

. At a field of 5 T, the conductivity

of the same specimen dropped to about 1800 W*m

_

^*K"-*-. This report

indicates that the peak in thermal conductivity disappears for a field between 1

and 2 T. Amundsen and Souik^ reported measurements on two single crystal

specimens of pure aluminum in fields up to 1.3 T and temperatures below 4 K. The

increase in thermal resistivity was linear in both specimens above 0.3 T, falling

sharply off below this field. A maximum increase in resistivity of 1.5 times was

induced by the magnetic field, but the ratio of thermal resistivity to electrical

resistivity was essentially independent of the field (less than 10% variation).

Sparks^ reported measurements on two specimens with similar thermal histories from 5 to 20 K. There were large differences in RRR and in thermal conductivity values due to different impurity concentrations. At 6 K, and zero

field, a factor of two difference is found in the thermal conductivities. For a

field of 8 T, he found a decrease of 29% at 5 K, and a 50% decrease at 20 K.

3.3 Electrical Resistivity and Lorenz Ratio

It was desirable to examine the Lorenz ratio of aluminum during the course

of this investigation. Therefore, an approximation of electrical resistivity was

^Amundsen, T and Souik. R. P. , Measurements of the Thermal Magnetoresi stance of

Aluminum, J. Low Temp. Phys., 2jl), 121-9 (1970).

^Sparks, L. L. , Magnetic Field Effect on Thermal Conductivity of Selected

Metals, Advances in Cryogenic Engineering, 24, 224-31, Plenum Press (1977).

91
needed. To do this, we selected those sources from this thermal conductivity

compilation that also contained electrical resistivity data and fitted Eq. 1.2.3

to the data. The electrical resistivity data used is shown in Figs. 3.3.1 and

3.3.2 with a composite of the data in Fig. 3.3.3. The parameters for Eq. 1.2.3

are

P

l = 0.09052 x 10" 16

P

5 = 40.

P

2 = 4.551 P 6

= 13.64

P

3 = 5.173 x 10

10

P

7 = 0.7416

P4

= 1.26

All units are SI.

The deviations of the experimental data from this equation are illustrated

in Figs. 3.3.4 through 3.3.6. Again, as for copper, there is considerable spread

in the deviations in the range 10-80 K. It is recognized that this is partly due

to the large range of p values represented (several orders of magnitude) as well

as the inadequacy of the simple equation used for representation. Nevertheless,

it is felt that for this purpose the approximation is useful.

Smooth values of p and T at selected RRR values are plotted in Fig. 3.3.7.

From the p(T,RRR) and x(T,RRR) equations smooth values of L(T,RRR) are plotted in

Fig. 3.3.8. As for copper, the irregul arities in the shape of these curves from

that expected are within the combined uncertainties of the two equations used.

In Section 1.5, we discuss the procedure for selecting values of p 0 and

calculating RRR for each thermal conductivity data set. These values of p 0

along with the Sommerfeld value of Lorenz ratio were used to best fit each low

temperature data set. The resulting values of RRR obtained by this procedure are

compared to the values reported in the references in Fig. 3.3.9 and are listed in

Table 3.3.1. Figure 3.3.9 shows values of RRR (calc), those values from the

92
above procedure, versus RRR (obs), those values reported in the references listed

in the annotated bi bl iography. Also shown in this figure is the line that represents RRR (calc) = RRR (obs). Systematic deviations from this line indicate

ranges in which the derived Eq. 1.1.3 is invalid. With the exception of four

points from the secondary data sets, all of the points lie near the line. Equation 1.1.3 is thus valid for the low temperatures from RRR of 10 to 10,000. Inspection of Table 3.3.1 indicates that the calculated values of RRR are generally

smaller than the observed values. This suggests that the Lorenz ratio of

aluminum at low temperatures may be slightly smaller than the Sommerfeld value.

3.4 Summary for Aluminum

Equation 1.1.3 represents the thermal conductivity of an annealed specimen

of aluminum over the whole temperature range. The deviations from the primary

set are shown in Figs. 3. 2. 1-3. 2. 3. Deviations for specimens in which physical

defects are important (unannealed specimens) are within _+20%.

Based on the deviations illustrated in Figs. 3.2.1 through 3.2.10 and the

large range that occurs in low temperature thermal conductivity of aluminum

(nearly three orders of magnitude) due to the introduction of chemical impurities

and physical defects, it is clear that a large proportion of these effects is reflected by the residual electrical resistivity. The incorporat ion of RRR (or

p 0 ) in Eq. 1.1.3 produces an equation that represents the data for a wide range

of aluminum specimens.

Equation 1.1.3 with the parameters listed here was used to generate thermal

conductivity values for selected temperatures and values of RRR. These values

are listed in Table 3.4.1 and plotted in Fig. 3.4.1.

93
List of Tables and Figures for Aluminum

Tabl es Page

Table 3.3.1 Comparison of Calculated and Observed RRR Values

for Aluminum 96

Table 3.4.1 Thermal Conductivity Values for Aluminum Calculated

from Eq. 1.1.3 at Selected Temperatures and RRR

Values 97

Figures

Page

Figure 3.1.1 Experimental thermal conductivity data selected from

the following primary references in the aluminum

annotated bibliography: (1,5,9,11) 98

Figure 3.1.2 Experimental thermal conductivity data selected from

the following primary references in the aluminum

annotated bibl iography : (12,17,25,26,29,33) 99

Figure 3.1.3 Composite of the data in figures 3.1.1 and 3.1.2 100

Figure 3.2.1 Thermal conductivity deviations of the aluminum data

from the following primary references compared to

Eq. 1.1.3: (1,5,9,11) 101

Figure 3.2.2 Thermal conductivity deviations of the aluminum data

from the following primary references compared to

Eq. 1.1.3: (12,17,25,26,29,33) 102

Figure 3.2.3 Composite of the deviations in figures 3.2.1 and

3.2.2 103

Figure 3.2.4 Thermal conductivity deviations of the aluminum data

from the following secondary references compared to

Eq. 1.1.3: (2,3,6,7,10,14) 104

Figure 3.2.5 Thermal conductivity deviations of the aluminum data

from the following secondary references compared to

Eq. 1.1.3: (15,16,19,20,21,23) 105

Figure 3.2.6 Thermal conductivity deviations of the aluminum data

from the following secondary references compared to

Eq. 1.1.3: (23,25,26,27,28) 106

Figure 3.2.7 Composite of the deviations in figures 3.2.4 through

3.2.6 107

94
Page

Figure 3.2.8 Thermal conductivity deviations of the aluminum data

from the following secondary references compared to

Eq. 1.1.3: (3,13,18,21,22,24,30) 108

Figure 3.2.9 Thermal conductivity deviations of the aluminum data

from the following secondary references compared to

Eq. 1.1.3: (30,31,32) 109

Figure 3.2.10 Composite of the deviations in figures 3.2.8 and

3.2.9 110

Figure 3.2.11 Comparison of Eq. 1.1.3 to the values recommended for

aluminum in the following references : (14A,32A) Ill

Figure 3.3.1 Experimental electrical resistivity data for aluminum

selected from the following references in the aluminum

annotated bibliography: (4,9,11,25,26) 112

Figure 3.3.2 Experimental electrical resistivity data for aluminum

selected from the following reference in the aluminum

annotated bibl iography : (33) 113

Figure 3.3.3 Composite of the electrical resistivity data in

figures 3.3.1 and 3.3.2 114

Figure 3.3.4 Electrical resistivity deviations of the aluminum data

from the following references compared to Eq. 1.2.3:

(4,9,11,25,26) 115

Figure 3.3.5 Electrical resistivity deviations of the aluminum data

from the following reference compared to Eq. 1.1.3:

(33) . . . 116

Figure 3.3.6 Composite of the electrical resistivity deviations shown

in figures 3.3.4 and 3.3.5 . . 117

Figure 3.3.7 Electrical resistivity for aluminum as a function of

temperature calculated from Eq. 1.2.3 at selected

values of RRR 118

Figure 3.3.8 Lorenz ratio for aluminum as a function of temperature

calculated from Eq. 1.2.3 and Eq. 1.1.3 at selected

values of RRR 119

Figure 3.3.9 RRR values calculated as per Section 1.5, RRR(CALC),

versus reported RRR values, RRR(OBS), for aluminum .... 120

Figure 3.4.1 Thermal conductivity for aluminum as a function of

temperature calculated from Eq. 1.1.3 at selected

values of RRR 121

95
Table 3.3.1. Comparison of Calculated and Observed RRR Values for Aluminum.

Reference RRR (obs.) RRR (calc.)

Primary Data

1 467.0 420.0

1 676.0 605.0

1 840.0 720.0

5 11600.0 11600.0

11 2750.0 2700.0

11 4370.0 4100.0

25 12.8 12.8

25 97.0 91

Secondary Data

14 2800.0 1550.0

14 4500.0 1720.0

22 520.0 520.0

23 147.0 147.0

23 86.0 86.0

23 36.0 36.0

23 17.0 17.0

30 15000.0 11900.0

30 24000.0 18000.0

96
le 3.4.1. Thermal Conducti vity Val ues for Aluminum Cal cul ated from

Eq. 1.1 .3 at Selected Temperatures and RRR Values.

A(W-m" 1 "K”

1

) T(K) RRR = 30 RRR = 100 RRR = 300 RRR = 1000 RRR = 3000 RRR = 10000

1 29 98 295 984 2954 9842

2 57 195 589 1956 5892 19521

3 86 292 833 2941 8765 28499

4 114 390 1175 3897 11475 35887

5 143 487 1463 4817 13885 40840

6 171 583 1746 5577 15853 43072

7 200 678 2020 6452 17272 42980

8 228 772 2232 7116 18109 41300

9 256 864 2528 7651 18406 38717

10 284 953 2755 8044 18260 35708

12 338 1122 3133 3420 17095 29474

14 391 1272 3398 8340 15360 23801

16 442 1400 3544 7960 13478 19074

18 489 1500 3582 7418 11658 15308

20 532 1572 3534 6801 9997 12366

25 617 1628 3178 5227 6706 7527

30 662 1542 2666 3843 4492 4791

35 664 1373 2130 2756 3036 3151

40 631 1172 1652 1972 2096 2143

45 581 980 1274 1440 1497 1519

50 526 817 997 1087 1117 1128

60 430 588 664 696 706 710

70 361 454 492 507 512 513

80 312 372 394 403 405 406

90 278 320 334 340 341 342

100 255 286 297 300 301 302

150 223 239 244 245 246 246

200 222 234 237 238 239 239

250 224 233 235 236 237 237

300 226 234 236 237 237 237

400 231 237 239 239 239 239

500 230 235 237 237 237 237

600 226 230 231 231 231 231

700 220 229 224 224 224 224

800 214 217 217 218 218 218

900 209 212 212 212 212 212

97
THERMAL

CONDUCTIVITY,

W/m.

TEMPERATURE,

K

Figure 3.1.1 Experimental thermal conductivity data selected from

the following primary references In the aluminum annotated

bibliography: (1,5,9,11)

O- (1), A- (1), - (1), V- (5),

O- (9), +- (11), X- (11)

98
THERMAL

CONDUCTIVITY,

W/m

.

Figure 3.1.2 Experimental thermal conductivity data selected from

the following primary references In the aluminum annotated

bibliography : (12,17,25,26,29,33)

O- (12), A- (17), - (25), V- (25),

O- (26), +- (29), X- (33)

99
THERMRL

CONDUCTIVITY,W/m.

2 4 10 20 40 100 200 400

TEMPERRTURE,K

Figure 3.1.3 Composite of the data In figs. 3.1.1 and 3.1.2

100
Figure 3.2.1 Thermal conductivity deviations of the aluminum data f rom

the following primary references compared to eq. (1.1.3):

(1,5,9,11)

O- (1), A- (1), - (1), V- (5),

O- (9), + - (11), X- (11)

101
20 - 1 1 1 * .1 . i » j_ i i_i_i . -i . i, , i i 2 4 10 20 40 100 200 400

TEMPERRTURE,K

Figure 3.2.2 Thermal conductivity deviations of the aluminum data from

the following primary ref erences compared to eq. (1.1.3):

(12,17,25,26,29,33)

O- (12), A- (17), - (25), V- (25),

O- (26), +- (29), X- (33)

in?
2 4 10 20 40 100 200 400

TEMPERATURE ,K

Figure 3.2.3 Composite of the deviations In figs. 3.2.1 and

3.2.2

103
2 4 10 20 40 100 200 400

TEMPERRTURE,K

Figure 3.2.4 Thermal conductivity deviations of the aluminum data

from the following secondary references compared to

eq. (1.1.3): (2,3,6,7,10,14)

O- (2), A- (3), - (6), V- (7),

O- (10), +- (14), X- (14)

104
2 4 10 20 40 100 200 400

TEMPERATURE,

K

Figure 3.2.5 Thermal conductivity deviations of the aluminum data

f rom the following secondary references compared to

eq. (1.1.3): (15,16,19,20,21,23)

O- (15), A- (16), - (19), V- (20),

O- (21), +- (23), X- (23)

105
2 4 10 20 40 100 200 400

TEMPERRTURE,K

Figure 3.2.6 Thermal conductivity deviations of the aluminum data

from the following secondary references compared to

eq. ( 1 . 1 .3) : (23,25,26,27,28)

O- (23), A- (23), - (25), V- (26),

O- (26), +- (27), X- (28)

106
Figure 3.2.7 Composite of the deviations In figs. 3. 2.

4

through 3.2.6

107
Figure 3.2.8 Thermal conductivity deviations of the aluminum data

from the following secondary references compared to

eg. (1.1.3) : (3,13,18,21,22,24,30)

O- (3), A- (13), - (18), V- (21),

O- (22), +- (24), X- (30)

103
Figure 3.2.9 Thermal conductivity deviations of the aluminum data

from the following secondary references compared to

eq. (1.1.3) : (30,31,32)

O- (30), A- (31), - (32)

1C3
Figure 3.2.10 Composite of the deviations In figs. 3.2.8

and 3.2.9

110
Figure 3.2.11 Comparison of eq. (1.1.3) to the values recommended

for aluminum In the following references ! ( 14fl,32F!)

O- (HR), A- (32fi)

111
ELECTRICAL

RESISTIVITY,

nfi.

2 4 10 20 40 100 200 400

TEMPERATURE,

K

Figure 3.3.1 Experimental electrical resistivity data for

aluminum selected from the following references In

the aluminum annotated bibliography: (4,9,11,25,26)

O- (4), A- (9), - (ID,

O- (25), + - (25), X- (26)

V- (11),

112
ELECTRICAL

RESISTIVITY,

nQ.

Figure 3.3.2 Experimental electrical resistivity data for

aluminum selected from the following reference In

the aluminum annotated bibliography: (33)

O- (33)

113
ELECTRICRL

RESISTIVITY,

nfl.

2 4 10 20 40 100 200 400

TEMPERRTURE,K

Figure 3.3.3 Composite of the electrical resistivity data In

figs. 3.3.1 and 3.3.2
2 4 10 20 40 100 200 400

TEMPERATURE,

K

Figure 3.3.4 Electrical resistivity deviations of the aluminum

data from the following references compared to

eq. (1.2. 3)1(4,9,11, 25, 26)

O- ( 4 ) , A- (9), - (11), V- (11),

O- (25), +- (25), X- (26)

115
Figure 3.3.5 Electrical resistivity deviations of the aluminum

data from the following reference compared to

eq. ( 1 .2.3) s (33)

O- (33)

116
Figure 3.3.6 Composite of the electrical resistivity deviations

shown In figs. 3.3.4 and 3.3.5

117
TEMPERATURE,

K

Figure 3.3.7 Electrical resistivity for aluminum as a function

of temperature calculated from eq. (1.2.3) at

selected values of RRR.

118
LORENZ

RRTIO,

10

°VVK

TEMPERRTURE,K

Figure 3.3.8 Lorenz ratio for aluminum as a calculated from eq. (1.2.3) and

values of RRR.

f unction of temperature

eq. (1.1.3) at selected

119
RRR(CflLC)

Figure 3.3.9 RRR values calculated as per Section 1.5, RRR(CFILC),

versus reported RRR values, RRR(OBS), for aluminum.

O - Primary, A - Secondary,

- Secondary

120
THERMAL

CONDUCTIVITY,

W/m.

TEMPERATURE,

K

Figure 3.4.1 Thermal conductivity for aluminum as a function of

temperature calculated from eq. (1.1.3) at selected

values of RRR.

121
3.5 FORMAT FOR ANNOTATED BIBLIOGRAPHY OF ALUMINUM

REFERENCE

AUTHOR, TITLE, CITATION

ANNOTATION

PURPOSE

SPECIMEN

a) Dimensions/Shape; b) Crystal Status; c) Thermal /Mech. History;

d) Purity Specification; e) RRR; f) p 0 ; g) Other Characteri zation Data

APPARATUS

a) Type; b) Thermometry/Cal i brat i on/Anchoring; c) Thermal Isolation;

d) Other (Q meas.)

DATA

a) Temperature Range/Difference; b) Content of Tables, Figures and Equations/Data Extraction; c) Uncertainty/Imprecision; d) Disputable Corrections to

Measurements by Authors; e) Errata (by Author or Reviewer)

ANALYSIS

a) Comparisons; b) Conclusions

122
[1] Andrews, F. A., Webber, R. T. and Spohr, D. A., Thermal Conductivities of

Pure Metals at Low Temperatures. I. Aluminum, Phys. Rev., 84(5), 994-6, (1951)

PURPOSE

lo measure X for three high purity A1 specimens.

SPECIMEN

a) 4 in. (10 cm) long, 0.15 in. (0.38 cm) dia./rod; b) A1 1,2: single

crystals, A1 3: polycrystal 1 i ne; c) A1 3: annealed; d) A1 1,2:

0.001% Mg, 0.001% Si, 0.0006% Fe, 0.0004% Cu, 0.0004% Na. A1 3:

0.002% Mg, < 0.001% Si, < 0.0005% Fe. < 0.0005% Cu, faint trace of Na;

e) A1 1 (RRR = 840), A1 2 ( RRR = 676), A1 3 (RRR = 467); f) A1 1 (p 0

= 3.04 nft.cm), A1 2 (3.85 n«*cm), A1 3 (p 0

= 5.51 nq.cm).

APPARATUS

aj longitudinal ; b) gas thermometers ; c) 0.05 ym of Hg (6.7 x 10" J Pa) vacuum.

DATA

aTT to 27 K/0.03 K at 2 K, 0.15 K at 20 K; b) figure 1 - X/data points

are listed in TPRC data series; c) uncertainty: from 2 to 4.2 and 14.5 to

20.5 K: ±4%; from 4.2 to 14.5 K: ±10%; d) corrections due to departures

of the thermometer system from ideal behavior at liquid helium

temperatures were taken from Hulm, J. K. , Proc. Roy. Soc. London, Ser. A,

204 , 98 (1950).

ANALYSIS

b) X" 1 = (AT)’ 1 + BT2

.

[2] Bailey, L. C. , The Thermal Conductivities of Certain Approximately Pure

Metals and Alloys at High Temperatures, Proc. Roy. Soc. London, Ser. A, 134,

57-76 (1932)

PURPOSE

lo continue the work of C. H. Lees on the effect of temperatures between

-160 °C and 15 °C, on x of nine metals and six alloys.

SPECIMEN

a ) / to 8 cm long, 0.585 cm dia./rods; c) turned down from larger rods;

dj 99% A1 ; g) specimens same as Lees, C. H., Philos. Trans. Roy. Soc.

London, Ser. A, 208 , 381-443 (1908)/density = 2.7 g/crrr at 293 K. APPARATUS

If) longitudinal ; b) thermocouples (chromel -al umel )/hot junction calibrated

at: melting ice, steam, aniline vapor, benzophenone vapor, sulphur vapor.

Cold junction: 293 K. Main current balanced against standard cell;

c) powdered magnesia between guard tube and specimen, asbestos wool

between guard tube and vessel

.

DATA

aj^5 to 554 °C; b) Table 1 - X. ANALYSIS

a) Schofield, F. H. , Proc. Roy. Soc. London, Ser. A, 107 , 206 (1925);

Griffiths, E., Proc. Roy. Soc. London, Ser. A, 1_15, 2TJ5 ( 1 927 ) ; x reaches

a maximum at 225 °C.

123
[3] Bid we 11, C. C. and Hogan, C. L. , Thermal Conductivity of Aluminum; Solid and

Liquid States, J. Appl . Phys., 18, 775 , (Aug 1947)

PURPOSE

To investigate A for A1 up to the melting point and beyond, with a modified

Forbes bar method.

SPECIMEN

a) 25 cm long, 2.5 cm dia./rod; d) specimen 1 = 99.2% Al, 0.10% Si,

0.67% Fe, 0.01% Cu; Mn, Mg < 0.01%, specimen 2 = 99.95% Al ; g) source:

Aluminum Company of America.

APPARATUS

a) modified Forbes bar method; b) thermocouples; c) finely screened Sil-ocel insulation.

DATA

a) specimen 1, 25 to 590 °C, specimen 2, 25 to 900 °C; b) data points taken

from text p. 779; d) correction for temperature drift.

ANALYSIS

a) data on specimen 1 is in agreement with Konno, S. , Philos. Mag., 40, 542

(1920); b) the data are consistent with k/pC = K/t + K'.

[4] Cook, J . G. , Moore, J. P., Matsumura, T. , and Van der Meer, M. P., The

Thermal and Electrical Conductivity of Aluminum, Proceedings of the Fourteenth

Thermal Conductivity Conf. (Storrs, Conn., June 2-4, 1975) P. G. Klemens and

T. K. Chu, eds., Plenum Press, New York (1976) pp. 65-71

PURPOSE

To measure A, p, and the absolute Seebeck coefficient of pure Al from 80 to

400 K.

SPECIMEN

e) specimen A (RRR = 8500), specimen B (RRR = 11000), specimen C (RRR

= 950), specimen D (RRR = 17); f) specimen A ( pq = 2.8 x 10"^ uP*cm),

specimen B (p Q

= 2.1 x 10

-4 pn»cm), specimen C (p 0

= 2.5 x 10“4

jjfi*cm),

specimen D (p Q

= 0.14 uft*cm).

DATA

a) 20 to 400 K; b) Table 1 - specimen characteri zation , Table 2 - A; c) un- certainty: ±1.2%; d) correction for impurities and thermal expansion.

ANALYSIS

a) data does not agree with Seeberg. P. and Olsen, T. , Phys. Norv., 2, 197

(1967); b) A = A + BT‘ 4 + CT2 + DT" 1

; Ag 1 = T/17 + 5000 T' 2 .

124
[5] Cook, J. 6. , Moore, J. P. , Matsumura, T. , and Van der Meer, M. P. , The

Thermal and Electrical Conductivity of Aluminum, 0RNL-5079, (Sep 1975)

PURPOSE

To measure X, p, and the absolute Seebeck coefficient of pure A1 from 80

to 400 K.

SPECIMEN

e) specimen A ( RRR = 8500), specimen B ( RRR = 11000), specimen C (RRR

= 950), specimen D (RRR = 17); f) specimen A (pg = 2.8 x 10~4 ufi-crn),

specimen B (p 0

= 2.1 x 10~4 yfi»cm), specimen C (p 0

= 8.5 x 10“4 ufi*cm),

specimen D (p 0

= 0.14 |jf2 *cm).

DATA

a) 20 to 400 K; b) Table 1 - specimen characteri zation , Table 2 - X; c) uncertainty: ±1.2%; d) correction for impurities and thermal

expansion.

ANALYSIS

a) data does not agree with Seeberg. P., Olsen, T. , Phys. Norv., _2, 197

(1967); b) X = A + BT' 4 + CT2 + DT“1; Xg 1 = T/G + HT“ 2 .

COMMENT

The data set contained in Reference 22 was not used because of comments

made in this paper.

[6] De Nobel, J., Heat Conductivity of Steels and a Few Other Metals at Low

Temperatures, Physica (Utrecht) , 17(5) , 551-52 (May 1951)

PURPOSE

To measure X for A1 , Fe, Monel metal, Ni-Cr steel and Mn-Cr steel by two

methods and compare the results.

SPECIMEN

a) /rod; c) /rolled; g) Brinell hardness 17.

APPARATUS

a) longitudinal ; b) I gas thermometers, II resistance thermometers

;

c) vacuum insulation.

DATA

a) 16 to 87 K; b) Table II - X.

ANALYSIS

b) for pure metals (> 99.93%), X is proportional to T at very low

temperatures and a maximum occurs between 3 and 20 K.

125
[7] Der Nigohossian, G. , Optimization of Electrical Leads for Cryogenic

Apparatus, Commissariat a L'Energie Atomique, Saclay, France, Centre d'Etudes

Nucleaires de Saclay, Rep. No. CEA-R-3167 (Feb 1967) 120 pp

PURPOSE

To optimize the geometry of electrical leads to cryogenic containers so that heat leakage is minimized.

SPECIMEN

a) 30 mm; b) single crystal

.

APPARATUS

a) longitudinal; b) Au-Co vs. Cu thermocouples for 70 to 300 K, carbon

resistance thermometers for lower temperatures; c) vacuum insulation, gas

cooled shield.

DATA

a) 4 to 295 K; b) figure p. 75 - p, figure p. 76 - X; c) uncertainty:

±10% (measurements with carbon resistance thermometers)

.

ANALYSIS

a) x data agrees with Roder, Powell, and Hall, Conference of Low

Temperature Physics and Chemistry, Madison, Wise., 364-367 (1958).

[8] Donth, E. and Gladun, C. , Measurement of Thermal Conductivity at Low

Temperatures by a Non-Stationary Method, Cryogenics, 2 , 223-5 (Jun 1962)

PURPOSE

To present a method of non-stationary x measurement at low temperatures.

SPECIMEN

a) /rod; d) 99.5% A1

.

APPARATUS

a) longitudinal; b) lead resistance thermometers ; c) vacuum insulation,

radiation shield.

DATA

a) 22 to 90 K; b) figure 3 - X.

ANALYSIS

b) the method allows the determination, continuously and quickly (15-120

minutes), of x over a wide temperature range.

126
[9] Duggi'n, M. J., The Thermal Conductivities of Aluminum and Platinum,

J. Phys. D: Appl . Phys., 3^> L21-23 (1970)

PURPOSE

To measure x of A1 , Pt.

SPECIMEN

a) /slab; d) 99.99%.

APPARATUS

a) guarded axial heat flow.

DATA

a) 380 to 600 K; b) Table 2 - X, p, L; c) uncertainty: +2.5%.

ANALYSIS

a) results agree with recommended values from TPRC (Powell, et al .

,

1966).

[10] Erdman, C. A., A Dynamic Technique for Measuring Thermal Conductivity in

Cylindrical Geometry, Designed for Use in Radiation Damage Studies, Ph.D.

Thesis in nuclear engineering, Univ. of Illinois, Urbana-Champaign (1971)

PURPOSE

To develop a valid technique for measuring x which involves a small amount

of equipment at the sample location.

SPECIMEN

a) 6 in. long (15 cm), 0.625 in. (1.59 cm) dia./rod; b) single crystal ; c) /machined from 1.25 in. (3.18 cm) dia./rod; d) 99.995% Al

.

APPARATUS

a ) radial ; b) thermocouples anchored to brass holder; c) vacuum insulation and shield.

DATA

a) 100 to 300 K; b) Table 9 - X; c) uncertainty: ±6.6% at 296 K, ±8.9% at

105 K; d) corrections for radiation and conduction.

ANALYSIS

a) data agree with recommended values for high purity polycrystalline Al

from the Seventh Thermal Conductivity Conference (Gai thersburg, MD, 1967).

127
[11]

Fenton, E. W. , Rogers, J. S. , and Woods, S. 8., Lorenz Numbers of Pure

Aluminum, Silver and Gold at Low Temperatures , Can. J. Phys., 41_, 2026-33

(Jul 1963)

PURPOSE

To attain accurate values of L for A1 , Au, Ag and compare with the

Sommerfeld value.

SPECIMEN

a) length/area (cm-1

): specimen 1 - 3500, specimen 2 - 1500, specimens 1,2

6 cm long; c) specimens 1,2 acid etched and annealed at 550 °C in air for

10 mi n. /specimens cut from 0.010 in. (0.025 cm) sheet, rod specimens

rolled square and drawn once; d) 99.9999% A1 ; f) specimen 1 (p 0

= 9.03

x 10“ 10 fl*cm), specimen 2 (p 0

= 5.68 x 10" 10 n*cm); g) source:

Consolidated Mining and Smelting Co. of Canada.

APPARATUS

a ) longitudinal ; b) gas thermometers//al 1 leads to specimen are anchored

to Cu pillars; c) temperature controlled radiation shield.

DATA

a) 2 to 50 K; b) figure 4 - L, Table 2 - pQ

, p-j/X data points listed in

TPRC data series; c) uncertainty: ±1.5%.

ANALYSIS

b) results agree with theoretical Sommerfeld value to about 1 1/2%.

[12]

Flynn, D. R., private communication (1965)

DATA

a ) 120 to 720 K; b) /data points listed in TPRC data series.

[13]

Gladun, C. and Holzhauser, W., Studies of Heat Conductivity at Low

Temperatures , Monatsber. Dtsch. Akad. Wiss. Berl i

n

, 6_(4) , 310-3 (1964)

PURPOSE

To report development of an improved non-equilibrium apparatus and data

for Cu, A1 , and Ti .

SPECIMEN

d) 99.99% A1 .

APPARATUS

a) longitudinal.

DATA

a) 4 to 55 K; b) figure 4 - X.

ANALYSIS

b) X -v T

2

, p x T

5 for T < 30 K.

128
[14] Gostishcher, V. I. and Drozd, A. A., Heat Conductivity of Aluminum in

Strong Transverse Magnetic Fields, Phys. Met. Metal logr. (USSR) (Engl. Transl.),

39(6), 168-70 (1975), Transl. of Fiz. Met. Metalloved., 39(6), 1307 (1975)

PURPOSE

To investigate the effect of strong transverse magnetic fields on x for

high-purity aluminum, in view of its use as a sheath for superconductors .

SPECIMEN

a) 3.5 cm long, 0.15 cm dia., 0.3 cm dia. at thermocouple, thermometer

and heater locations/rod; b) polycryst«ll i ne; c) /extruded through a round die; e) run 1 (RRR = 2800), run 2 (RRR = 4500); f) run 1, (p 0

= 8.55 x 10-1° n*cm), run 2 (p 0

= 5.32 x 10”^ ft*cm); g) run 1, 15

days after extrusion, run 2, 3.5 months after extrusion.

APPARATUS

a ) longitudi nal ; b) carbon resistance thermometers and Cu-Ag thermocouples

c) radiation shield with maintained thermal gradient similar to specimen.

DATA

a) 6 to 48 K; b) figure 1 - X.

ANALYSIS

b) x in strong fields is independent of density of imperfections but

determined by topology of the Fermi surface.

[14A] Ho, C. Y. , Powell, R. W. , Liley, P. E. , Thermal Conductivity of the Elements: A Comprehensive Review, J. Phys. Chem. Ref. Data, ]3, Supplement No. 1,

242-257 (1974)

PURPOSE

To provide a comprehensive listing of data on x of the elements.

SPECIMEN

d) high purity; f) p 0

= 5.94 x 10“ 10 frcm for T below 150 K.

APPARATUS

a) not given.

DATA

a) 0 to 8500 K; b) Table 2 - X, recommended values; c) uncertainty: ±5%

below room temperature, ±3% above room temperature, and ±8% for the molten

phase up to 1273 K. The values above 1273 K are provisional.

129
[15] Hogan, C. L. , The Thermal Conductivity of Metals at High Temperature,

Lehigh Univ., Bethlehem, PA., Ph.D. Thesis, (1950) 42 pp.

PURPOSE

To measure X for metals and alloys in the temperature range 0 to 1000 °C.

SPECIMEN

a) 12 in. (30.5 cm) long, 0.25 in. (0.64 cm) bore/tube; d) 99.996% A1

;

g) source: Norton RA 98 material.

APPARATUS

a) Forbes bar method; b) Chromel -A1 umel thermocouples glued with Alundum;

c) Sil-o-cel insulation.

DATA

a) 0 to 790 °C ; b) /data points listed in TPRC data series; c) uncertainty:

±5%.

ANALYSIS

b) the basic theory of Wilson and Makinson is found to be valid.

[16] Lees, C. H., The Effects of Temperature and Pressure on the Thermal Conductivities of Solids. Part II, Philos. Trans. Roy. Soc. London, Ser. A, 208, 381

443 (1908)

PURPOSE

To measure x and p for certain metals and alloys, and compare the results

with electronic theories.

SPECIMEN

a) 7 to 8 cm long, 0.585 cm dia./rod; c) /specimen turned down from larger

rod; d) 99% A1 ; g) density at 20 °C = 2.70 g/cm^, source: Johnson, Matthey

and Co.

APPARATUS

a) longitudinal; b) Pt resistance thermometer - oil contact/cal ibrated at

boiling point of 0

2

, icepoint and boiling point of H

2 0.

DATA

a) -166 to 24 °C; b) Table on p. 413 - X, Graph on p. 432 - p; d) radiative

heat loss, resistance of thermometer leads, offset of Pt resistor

temperature from bar temperature.

ANALYSIS

a) Jager and Diesselhorst measurements , (Abh. Phys. Tech. Reichsanstal t , 3,

p. 269 (1900), compared at 18 °C; b) found little variation in x in

temperature range investigated.

130
[17] Mendelssohn, K. and Rosenberg, H. M. , The Thermal Conductivity of Metals

at Low Temperatures. I. The Elements of Groups 1, 2, 3, Proc. Phys. Soc.,

London, 65^(6), 385-8, (Jun 1952)

PURPOSE

To measure x for metals at low temperatures

.

SPECIMEN

a) 15 cm long; 1 to 2 mm dia./rod; b) polycrystal 1 ine; c) annealed;

d) 99.994% A1 ; g) source: Johnson, Matthey and Co.

APPARATUS

a ) longitudi nal ; b) gas thermometers.

DATA

a) 4 to 50 K; b) figure 4 - x/data points listed in TPRC data series;

c) uncertainty: ±3% (maximum).

ANALYSIS

a) results disagree with those of Webber, R. T.. Andrews, F. A., and

Spohr, D. A., Phys. Rev., 84, 994 (1951); b) X

- * = aT? + 3/ T.

[18] Merisov, B. A., Khotkevich, V. I., Zlobintsev, G. M., and Kozinets, V. V.

,

Thermal Conductivity of Some Metals and Alloys at 4.2 to 273 K, J. Eng. Phys.

(USSR) (Engl. Transl . ) , 12(5) , 364-6 (1967)

PURPOSE

To report a thermal potentiometer method of measuring x in which the

radiation correction is experimental ly determined.

SPECIMEN

d) 0.05% Cu, 0.03% Fe, 0.35% Si, 0.10% others.

APPARATUS

a) thermal potentiometer method; b) Ge resistance thermometer from 4.2 to

20 K, Cu-constantan thermocouple from 20 to 273 K.

DATA

a) 6 to 273 K; b) figure 2 - X/data points taken from Table in Merisov,

et al.. Thermophysical Properties of Substances at Low Temperatures,

First All-Union Meeting, Feb. 16-19, 1971, 85-88 (1972); c) uncertainty:

±5%; d) experimentally determined correction for radiation heat loss.

131
[19] Mikryukov, V. E. , Thermal and Electrical Properties of Cu, Ag, A1 , and

the Alloy System Cu-Be, .J. Moscow Univ. JJ?(6), 57-67 (1957), Vestn. Mosk.

'Jni v . , Ser. Mat., Mekh., Astron., Fiz., Khim., 12(6), 57-67 (1957 )

PURPOSE

To present data on \ and p for some metals.

SPECIMEN

d) 99.99% A1 .

APPARATUS

a) not given.

DATA

a) 65 to 523 °C; b) Table 4 - A and p.

ANALYSIS

b) the Wiedemann-Franz law is not valid in this temperature range.

[20] Mikryukov, V. E. and Karagezyan, A. G., Thermal and Electrical Properties

of Alloys of the Systems A1 -Mg and A1 -Cu , Inzh. Fiz. Zh., _4(12), 90-3 (1961 )

PURPOSE

To investigate the temperature dependence of X and p, using the

Wiedemann-Franz law for the systems Al-Cu and Al-Mg from room temperature

to melting point.

SPECIMEN

a) 300 mm long, 3 mm dia.; c) annealed in vacuum at 430 to 520 °C;

d) 99.9% A1

.

DATA

a) 60 to 480 °C; b) ,/data points listed in TPRC data series.

A NALYSIS

a) Wiedeman-Franz ratio in agreement with theoretical values; b) in the

investigated alloys, thermal transport is basically by electrons.

132
[21] Misiorek, H. , Zarrzewski , T. , and Rafalowicz, J., Influence of Plastic

Deformation on the Thermal Conductivity Maximum of Copper and Aluminum in the

Temperature Range 4.2 to 70 K, Phys. Status Solidi A, 47_, K137-40 (1978)

PURPOSE

To determine the effect of increasing plastic deformation on A maximum of

Cu and A1 in the range of 4.2 to 70 K.

SPECIMEN

c) both specimens annealed at 540 °C for 4 h in He atmosphere/deformed by

extension at 77 K; d) 99.999% and 99.99% A1

.

APPARATUS

a) longitudinal steady state.

DATA

a) 5 to 50 K; b) figures 3, 4 - X (undeformed); e) captions for all figures

switched: figure 1 should be labelled as 4, figure 2 as 3, figure 3 as 1,

figure 4 as 2.

ANALYSIS

b) with increasing deformation, maximum A decreases in value and is shifted

toward higher temperatures.

[22] Moore, J. P. , McElroy, D. L. , and Barisoni, M. , Thermal Conductivity Measurements Between 78 and 340 on Aluminum, Iron, Platinum, and Tungsten, Proceedings of the Sixth Thermal Conductivity Conf. (1966)

PURPOSE

To measure A, p and the Seebeck coefficient for A1 , Fe, Pt, and W between

78 and 340 K.

SPECIMEN

c) /machined from stock; d) 99.999% A1 ; e) RRR = 520; g) P 273 = 2.440 yft*cm, source: Reynolds Aluminum Co.

APPARATUS

a) longitudinal; b) Chromel-P and constantan thermocoupl es/cal ibrated

against Pt resistance thermometers/thermocouple wires thermally grounded on guard cylinder; c) guard cylinder.

DATA

a) 100 to 380 K; b) Table 3 - A.

ANALYSIS

a) A values reported by Powell, et al . (1965) agreed to within 1/4%; c' the

experimental A curve has a minimum which disagrees with the theoretical curve in magnitude and temperature.

COMMENT

This data set not used because of reported error in technique. See Coo1 , J. G., Moore, J. P., Matsumura, T, and Van der Meer, M. P. , The Ther d ar : Electrical Conductivity of Aluminum, 0RNL-5079 (1975).

133
[23] Mucha, J. and Rafalowicz, J., Thermal Conductivity Minimum of Aluminum,

Phys. Status Sol i di A, 48, 221-4 (1978)

PURPOSE

To measure X minima for six different pure aluminum specimens, and to test

Wilson's equation.

SPECIMEN

a ) 10.0 to 20.0 cm long, 0.8 cm dia./rod; b) polycrystal 1 ine; c) annealed

at 500 °C, 48 h cooldown; d) specimen HI: 99.861%, H2: 99.526%, R0:

99.9931%, R6 : 99.97%; e) specimen HI (RRR = 36), H2 (RRR = 17), R0 ( RRR

= 147), R6 (RRR = 86).

APPARATUS

a ) longitudinal ; b) constantan-mangani n thermocouples; c) 10"^ mm

(10-5 p a ) insulation, screen at specimen temperature.

DATA

a) 80 to 380 K; b) figure 1 - X.

ANALYSIS

b) deviation of 6 to 7% of experimental data for least squares fit of W

= e 0 /L 0 T + AT^ - BT^. The Wilson equation fails to describe the X curve in the minimum range.

[24] Mucha, J., Wlosowicz, D. , and Rafalowicz, J., Thermal Conductivity of Constructional Aluminum at Temperatures Ranging from 77 to 300 K, Chlodnictwo,

4(11), 7-8 (1974)

PURPOSE

To report X for 99.8% and 98.5% Aluminum (constructional) from 77 to

300 K.

SPECIMEN

d) 99.8% A1 , 0.07% Fe, 0.057% Si, 0.006% Cu, 0.001% Ti , 0.008% V,

0.004% Mn, 0.001% Zn, 0.007% Cr, 0.006% Mg.

APPARATUS

a) longitudinal; b) room to N

2 temperatures : Cu-constantan thermocouples; He temperatures : carbon resi stors/thermocouples scaled separately

for room and N£ temperatures with a Hg thermometer, carbon resistors.

DATA

a) 77 to 300 K; b) Graph p. 7 - X; c) uncertainty: ±5% (maximum).

134
[25] Powell, D . L. , Hall, W. J., and Roder, H. M. , Low Temperature Transport

Properties of Comercial v etals and Alloys. II. Aluminums, J. Appl . Phys.,

31(3), 496-503 (1960)

>'JRP0SE

'"o o^esent data ^or x, p, L, thermoel ectn'c force and thermoelectric

power from 4 to 120 K. SPECIMEN

a' specimen A, 3, C: 3.66 mm dia./rods; b) specimen A: single crystal;

specimen B, C: polycrystalline; c) specimen A: ground from 3.68 to

3.55 mm, annealed in vacuum at 400 °C for 2 h; specimen 3: turned a^d

d-awn from 0.5 in. '1.25 cm) sheet to 3.65 mm rod; specimen C: turned

and d

r awn from 0.5 in. '1.25 cm) sheet to 3.65 mr rod, annealed in vacuum

at 350 °C for 1 n; d) specimen A: 99.995% A1 ; specimen 3: 99.308%;

specimen C: 98.917%; g) other characteristics found in ^able 1.

APPARATUS

a) longitudinal; b) Au-Co vs. Cu thermocouples.

DATA

a) 4 to 120 K; b) Table II - X, figure 1 - p, figure 5 - L. ANALYSIS

b~j L for high x samples were considerably below the Sommerfeld value

while those for the low x samples were somewhat above it.

[25] Powell, R. W. , Tye, R. P. , and Woodman, M. J., 'Hie Thermal Conductivity

o* Pure and -.lloyed Aluminum. I. Solid Aluminum as a Reference Material,

-d.ances ^nermophysical Properties at Extreme Temperatures a^d "ressu r es , Tnird Sy^pos 1 ^ on ’’hermophysical Properties, ASME, 227-88 ' 1S55 ) PURPOSE

To investigate the suitability of high purity and other aluminums as a X reference standard.

SPECIMEN

Low temperature:

a) specimen S.P. 'super pure): 8 cm x 0.44 cm x 0.44 cm/bar;

d) specimen S.P.: 99.993% A1

.

High temperature:

a) specimen S.P.: 28.0 cm x 2.81 cm dia.; specimen C51 : 27.4 c^

x 3.17 an dia. /rods; d) specimen S.P.: 99.993% A1 ; specimen C51 : 99.6% A1

.

APPARATUS

a) longitudinal; b) Ni-Cr, constantan, 90% Pt, 10% 3 n themocouD'es.

DATA

Low temperature:

a) specimen S. D .: 123 to 323 K; b) Table III - X, p, and _; d) radiat'/e

heat loss correction.

High temperature:

a) specimen S.P., C51: 323 to 873 K; b) Tab<e III - x, p, and

d) radiative heat loss correction.

ANALYSIS

b") X = ATp + 8.

135
[27] Powers, R. W. , Schwartz, D., and Johnston, H. L. , The Thermal Conductivity

of Metals and Alloys at Low Temperatures, Ohio State Univ., Columbus, Rep.

No. TR 264-5 (Apr 1951) Contract No. W33-038-AC-14794 (16243) 23 pp.

PURPOSE

To describe an apparatus for x measurements and discuss the results for

pure A1 , Cu, and Ni from 25 to 300 K.

SPECIMEN

a ) 20 in. (51 cm) long, 0.5 in. (1.3 cm) di a . ; c) cold-drawn, 55% reduction; d) 99.99+% purity; g) source: Aluminum Company of America.

APPARATUS

a) longitudinal; b) Cu-constantan thermocoupl es/thermocoupl es calibrated

with a gas thermometer* c) 3 gold plated temperature controlled shields

and 10 _ 5 mm of Hg (10~3 Pa) insulation.

DATA

a) 25 to 238 K; b) Table II and Table III - X; c) uncertainty: ±0.6% at

250 K, ±0.7% at 100 K, ±1.8% at 30 K; d) corrections for radiation and con duction.

[28] Roberts, R. B. and Crisp, R. S. , Thermoel ectric Power and Thermal Conductivity an Integral Method - Aluminum, Philos. Mag., 36(1), 81-9 (1977)

PURPOSE

To develop and evaluate an apparatus for the simultaneous measurement of x and thermoel ectric power of metal wire using an integral method from 2 to

300 K.

SPECIMEN

a) 18 cm long, 0.25 and 0.50 mm dia., for T < 70 K and T > 70 K respectively/wire; c) annealed at 600 °C at 10-6 mm of Hg (10"4 Pa) 24 h,

slow cooled/1 mm wire drawn to 0.5 run and 0.25 mm dia. for two specimens;

d) 99.9999% A1

.

APPARATUS

a) integral method; b) carbon resistance thermometer, thermocouple/thermocouple calibrated against Pt thermometer calibrated by CSIR0 Sydney to the

IPTS 68, carbon resistor was calibrated against He x and boiling point and

against Pt thermometer at 15 K; c) thin-walled stainless steel tube heat

shield and A1 Mylar surrounded complete assembly.

DATA

a) 2 to 300 K; b) /data points supplied by author; c) uncertainty: less

than ±1.0%.

ANALYSIS

a) data agrees with TPRC recommended values for 100 to 300 K; b) the integral method was shown to be capable of yielding accurate measurements of X

136
[29] Rosenberg, H. M. , The Thermal Conductivity of Metals at Low Temperatures

,

Philos. Trans. Roy. Soc. London, Ser. A, 247 (933) , 441-97 (1955)

PURPOSE

To investigate and report on x for 32 metallic elements in the 2 to 40 or

90 K range, to give a general picture of X at low temperatures. Also to

measure p so the Wiedemann-Franz relation could be studied.

SPECIMEN

a) 2.97 cm long, 0.394 cm dia./rod; b) polycrystall i ne; c) annealed in

vacuum at 600 °C, several h; d) 99.994% A1 ; e) p 293/ p 20

= 279; g) source:

Johnson, Matthey and Co.

APPARATUS

a) longitudinal; b) gas thermoineters//thermal ly anchored to liquefier and vacuum jacket; c) 10~ 5 mm of Mg (10“ p Pa) insulation.

DATA

a) 2 to 42 K; b) figure 12 - X/data points listed in TPRC data series;

c) uncertainty: ±3%; d) corrections for external volume of gas thermometer.

ANALYSIS

a) compared to Andrews, Webber, and Spohr (1951); b) X“1 = aT^ + bT~1

;

W

Q seems to vary as T^*2 over large temperature range.

[30] Seeberg, P. and Olsen, T. , The Thermal Conductivity of Pure Aluminum at

Low Temperatures, Phys. Norv.,_2(3), 197-201 (1967)

PURPOSE

To measure x for super pure aluminum and determine how the phonon scattering term (W-j ) varies with purity.

SPECIMEN

a) specimens 1,2 - 102, 65 cm long, 2.98, 2.03 mm dia. respect i vel y/ rods

;

c) air annealed at 480 °C, 24 h/cold rolled, drawn, wound into helix;

d) zone refined high purity A1 ; e) specimen 1 (RRR = 24,000), specimen 2

(RRR = 15,000); f) specimen 1 (p 0

= 1.3 x 10"^ ft*cm), specimen 2 (p^

= 1.9 x 10“10 ft. cm); g) electron mean free path, specimen 1 (0.75 mm],

specimen 2 (0.4 mm)

.

APPARATUS

a) longitudinal; b) < 4 K: carbon resistors, > 4 K: Ge resistance thermometers/< 4 K: calibrated against He vapor pressure.

DATA

a) 2.5 to 33.5 K; b) figure 1 - X; c) uncertainty: ±2% (maximum), T < 4;

±5% (maximum), 5 < T < 30.

ANALYSIS

b) x_1 = aT^ + gT-1; Matthi essen ' s rule fails to provide a satisfactory

description of the electronic x in metals, and the deviation of A1 follows

a pattern similar to tin and indium.

137
[31] Sirota, N. N. , Drozd, A. A., and Gostishcher, V. I., Measurement of Electrical and Thermal Conductivity of Metals in Strong Magnetic Fields, Thermophysical Properties of Substances at Low Temperatures (Proceedings of the First

All-Union Meeting, Feb. 16-19, 1971) M. P. Orlova, ed., All-Union Scientific Research Institute of Physico-Technical and Radiotechnical Studies (Moscow, 1972)

pp. 149-58

PURPOSE

To measure x for aluminum in strong, perpendicular magnetic fields.

SPECIMEN

d) 99.999% A1

.

APPARATUS

a) longitudinal-stationary heat flow; b) carbon resistance thermometers/

calibrated in strong magnetic fields (both perpendicular and parallel);

c) temperature controlled shield.

DATA

a) 7 to 73 K; b) figure 6 - X, figures 5 and 7 p and L.

[32] Sirota, N. N., Gostishcher, V. I., and Drozd, A. A., Thermal Conductivity

of Aluminum in Strong Magnetic Fields at Low Temperatures , JETP Lett., 16(4)

,

170-2 (Aug 1972)

PURPOSE

To study x for metals in strong magnetic fields at low temperatures to

separate electronic and lattice components.

SPECIMEN

a) 60 x 3 x 3 mm/bar; b) single crystal; c) /cut from ingot; e) RRR

= 6000; f) P 0 = 1.2 x 10-10 s

. cm .

APPARATUS

a ) longitudinal ; b) resistance thermometers ; c) radiation shield with temperature gradient similar to specimen.

DATA

a) 6 to 57 K; b) figure 1 - x(H=0); c) uncertainty: ±2%; e) RRR = 6000 is

inconsistent with data, closer to 600.

ANALYSIS

b) temperature dependence of the lattice component of x in region of maximum: Xg = AT^e-S'. A transverse magnetic field exerts a strong influence

on x for high purity A1

.

138
[32A] Touloukian, Y. S. , Powell, R. W. , Ho, C. Y. , and Klemens, P. G. , Thermophysical Properties of Matter, Volume 1: Thermal Conductivity, Metallic Clements

and Alloys, 68-81 (1970)

PURPOSE

To provide an extensive list of data for A of the metallic elements and

al loys.

SPECIMEN

d) 99.9999%; f) p0

= 5.93 x lO" 10 a* cm.

APPARATUS

a) not given.

DATA

a) 0 to 8000 K; b) higure and Table 1R - A, recommended values; c) uncer- tainty: ± 3 % near room temperature, ±3 to 5% at other temperatures ; e) the

values below 1.5 Tm are calculated to fit the experimental data by using n

= 2.00, a = 0.61, m = 2.61, a

!1 = 4.87 x 10‘ 5

, and 6 = 0.0245.

[33] Wilkes, K. E., Thermal Conductivity Measurements Between 77 K and 373 K on

Iron, Cobalt, Aluminum, and Zinc, M.S. Thesis, Purdue University, (1968) 93 pp.

PURPOSE

To resolve discrepancies and fill gaps in the literature for A for Co, Al , and Zn.

SPECIMEN

a) 10.16 cm long, 1.225 cm dia./rod; b) polycrystalline; c) unannealed;

d) 0.5 ppm Cu, 0.5 ppm Si, and 0.1 ppm Mg; f) P 273 = 0.02425 pfl.m,

p 77 = 0.0021 pP*m; g) density = 2698 Kg/m“ 3 at 23 °C.

APPARATUS

a) longitudinal; b) Chrome! -constantan thermocoupl es/T < 273

brated with a resistance thermometer and tables from Powell,

Sparks, L. L. , MBS Report 9249, T > 273 K: rhodium thermocoupl e/al 1 thermocouple leads

K:

R. cal iL., and

rods; c) 5 x 10*5 mm of Hg (7 x 10 '^ pa) insulation.

calibrated against a platinurfrom specimen tied to support

DATA

a) 88 to 283 K; b) Table 4 - A, figure 13 - p/p data points generated from

equation of line on figure 13; d) corrections for radiation and conduction.

ANALYSIS

a) p curve is very close to Flynn; Powell, Tye, Woodman; and Moore,

McElroy, Barisoni but A curves differ; b) L is well below theoretical but

appears to approach theoretical value well above ''oom ter Denature

.

139

4. Iron

4.1 General

A total of 41 references on iron are included in the annotated bibliography

of Section 4.5. The following references represent the primary data sets: 3A,

8, 9, 11, 13, 15, 16, 18, 23, 25, 28, 29, 31, 33, and 34.

The primary data cover a range of temperatures from 1.5 to 1000 K, and a

range of RRR from 4 to 200. These data are illustrated in Figs. 4.1.1 through

4.1.3 with a composite of the data given in Fig. 4.1.4. Iron produced in bulk

form is generally of much lower electrical purity than either copper or aluminum.

RRR values above 550 are not reported.

Equation 1.1.3 was used to represent the iron data over the entire temperature range. The values for the parameters, P-j , i = 1, 2 ... 7, obtained by

nonlinear least squares fit are:

P

1 166.9 x 10"8

on

li 238.6

It

CM

CL 1.868 P

6 * 1.392

P

3

1.503 x 10

5

P? = 0.0

P

4

-1.22

with all units in SI.

The data at high RRR 'were examined for systematic residual deviations as a

function of temperature. The residuals were represented by the Wc term in

Eq. 1.1.5 with the following equation:

W

c

= -0.004 Jin(T/440) exp( - ( An ( T/650/0.8)

2

)

-0.002 £n(T/90) exp(-Un(t/90)/0.45) 2

)

where Wc and T are in SI units.

141
4.2 Deviations From Recommended Equation

The deviations of the primary data from Eq. 1.1.3 are illustrated in

Figs. 4.2.1 through 4.2.3 with a composite shown in Fig. 4.2.4. Only three data

sets exhibit differences of greater than +10%. Although deviations, systematic

with temperature, exist for individual data sets, the overall pattern is random

in nature. No systematic trends varying with RRR were identified.

The primary data were selected from the literature data on relatively large,

well annealed specimens. Therefore, the deviations exhibited in Figs. 4.2.1

through 4.2.4 are indicative of the combined effect of a) experimental measurement errors and b) the inability of Eq. 1.1.3 to account for the effects of

chemical impurity variations. The effects of physical defect variations, small

specimen size variations, and magnetic fields are exhibited, in part, by the

deviations of the secondary data. The thermal conductivity variations caused by

other than chemical impurity variations are not expected to be represented as

well by Eq. 1.1.3. However, the RRR (or p 0 ) correlating parameter does account

for an appreciable part of these variations. Some users may find this to be an

adequate representation and, therefore, discussions of these comparisons are included for completeness.

The deviations of the secondary data sets are divided into two groups according to the magnitude of the deviations. They are illustrated in Figs. 4.2.5

through 4.2.10.

The equation developed here is also compared to the reference data in the

following references 9A, 12, 20, and 32A in Fig. 4.2.11. The differences are

within the combined uncertainties of the sources. It is noted that we did not

include data within our primary set for RRR above 200. Therefore the comparison

to the data in references 9A, 32A are an extrapolation of our equation.

142
4.2.1 Physical Defect Effects

Investigations of physical defects in iron have produced only a few references 20, 29, 33. Each of these references will be discussed below.

Reference 33 reports the effects of annealing on thermal conductivity. The

peak value of the thermal conductivity of the unannealed specimen was

99 W*nf**K"*, while for the annealed specimen of the same Armco iron

stock, it was 112 W*m“^*K"^. The deviations from Eq. 1.1.3 for the

unannealed specimen were within +9%, while those for the annealed specimen were

within +8%.

Although not directly related to physical defects, references 20 and 29 report on the effects of impurities. Reference 20 states that as much as 7% varia

tion in thermal conductivity is possible at 298 K for a specimen of Armco iron.

This difference is caused by variations of impurity concentrations in the Armco

stock. Reference 29 reports that the peak conductivity of pure (99.99%) iron is

287 W*m_1

*K_i at 32 K, while for SAE 1020 steel 99.48% Fe, peak value

is 65 WttT-^K' 1 at 160 K. The deviations from Eq. 1.1.3 the pure

iron were within +4%, while those for the steel were within +5%.

Reference 20 also reports on the effect of ice-water quenching on thermal

conductivity. A 1% increase was reported for specimens of thickness greater tha

8 mm. For a specimen of less than this thickness, ice-water quenching should

produce a greater effect on the thermal conductivity. No thermal strain effect

was produced.

Although the temperature dependence of the physical defect scattering mechan

ism is different from that due to impurity scattering, Eq. 1.1.3 represents the

unannealed specimen data quite well (within +10%). This indicates that the residual electrical resistivity characteri zes both types of scattering for the

range of RRR included here.

143
4.2.2 Size Effects

No size effect studies were found in our literature on iron.

4.2.3 Magnetic Field Effects

Although magnetic field effects on thermal conductivity were not studied explicitly, some interesting changes occur for iron (and ferromagnetic metals in

general). We will discuss these effects below.

Reference 3 shows that the thermal resistivity of a single crystal , oriented

in the [111] direction, decreases as the magnetic field increases from 0 to

12 KOe. Fickett 1 reports that ferromagnetic metals can show a decrease in resistivity with increasing fields. This decrease in a pure ferromagnetic metal is

rather large. Note that the opposite behavior is seen in nonferromagnetic

metal s.

Takaki amd Igaki 2 report that the electrical resistivity decreases rapidly

when a magnetic field of less than 0.8 kA/m is applied. The resistivity reaches

a minimum at 32 and 40 kA/m in single crystal specimens whose orientations are

[111] and [Oil], respecti vely. This effect also occurs for polycrystal 1 i ne

specimens in longitudinal fields of 56 to 64 kA/m.

One of the conclusions drawn in this paper indicates that a modified residual

resistivity ratio, RRR^, should be used to characterize the purity of iron

(RRR h

= p

( 298

) /p^ where is the minimum value of p for a specimen in

a longitudinal magnetic field of 56-64 kA/m).

iFic.kett, F. R. , Electrical Properties of Materials and Their Measurement at

Low Temperatures , NBS Technical Note 1053, National Bureau of Standards,

Boulder, Colorado, p. 41 (1982).

2 Takaki , S. and Igaki , K, Electrical Resistivity of High Purity Iron at 4.2 K,

Trans. Jpn. Inst. Met. JJ7, 353-9 (1976).

144
Equation 1.1.3 is expected to represent the thermal conductivity of specimens

in a magnetic field reasonably ,vel 1 for temperatures above 30 X. 3ul ow this temperature, the deviations are expected to increase dramatical ly.

4.3 Electrical Resistivity and Lorenz Ratio

It was desirable to examine the Lorenz ratio of iron during the course of

this investigation. Therefore an approximation of electrical resistivity as a

function of temperature md RRR was required. To obtain an approximate equation

we selected those sources from the primary set that also reported electrical ''osistivity data and fitted Eqs. 1.2.3 to those data. The electrical resistivity

data used here are shown in Figs. 4.3.1 to 4.3.3. The parameters obtained for

this equation are:

?

1 = 41.47 x 10" 16

P

5 = 180.3

P 0= 3.241 P,- = 1.947

i o

P

3 = 7.638 x 10

U

?! = 0.1867

P4

= 1.95

The systematic residuals, p c

, obtained from this fit wera than represented by

-3 x 10"9

in (T/ 105 ) exp(-(in(T/120)/0.45) 2

)

All units are SI.

The deviations of the data fron this fit are shown in Figs. 4.3.4 to 4.3.6.

Again the spread in the mid-range (40 to 100 K) is relatively large with a correspondingly large uncertainty, however, for the purpose at hand this is considered adequate.
Smooth values of p vs. T at selected RRR values are plotted in Fig. 4.3.7.

From Eqs. 1.1.3 and 1.2.3 smooth values of L(T,RRR) are plotted in Fig. 4.3.8.

No unexpected irrejul unities appear in Fig. 4.3.8.

In Section 1.5 we discuss the procedure for selecting values of p 0 and calculating RRR for each thermal conductivity data set. These values of p 0 along

with the Sominerfel d value of Lorenz ratio were used to best fit each low temperature data set. The resulting values of RRR obtained by this procedure are compared to the values reported in the references in Fig. 4.3.9 and are listed in

Table 4.3.1. Figure 4.3.9 shows values of RRR (calc), those values from the

above procedure, versus RRR (obs), those values reported in the references listed

in the annotated bibl iography. Also shown in this figure is the line that represents RRR (calc) = RRR (obs). Systematic deviations from this line indicate

ranges in which the derived Eq. 1.1.3 is invalid. For iron, the calculated

values of RRR are within 10% of the observed values for the range 13 to 200.

Also, Table 4.3.1 indicates that the Sommerfeld value of the Lorenz ratio is

valid for iron.

4.4 Summary for Iron

Equation 1.1.3 represents the primary iron data to within _+10'% of the experimental value at a given temperature. Deviations for unannealed specimens (i.e.,

those containing physical defects) are within +10%.

Based on the deviations illustrated in Figs. 4.2.1 through 4.2.3 it is clear

that the use of RRR in Eq. 1.1.3 accounts for a large proportion of the impurity

effect in. iron. Equation 1.1.3 with the parameters listed here was used to generate smoothed values of thermal conductivity as a function of temperature and

selected values of RRR. These are listed in Table 4.4.1 and Fig. 4.4.1.

146
List of Tables and Figures for Iron

Tab! es Page

Table 4.3.1 Comparison of Calculated and Observed RRR Values

for Iron 149

Table 4.4.1 Thermal Conductivity Values for Iron Calculated

From Eq. 1.1.3 at Selected Temperatures and RRR

Values 150

Figures

Page

Figure 4.1.1 Experimental thermal conductivity data selected from

the following primary references in the iron annotated

bibliography: (8,9,11,13,15,16) 151

Figure 4.1.2 Experimental thermal conductivity data selected from

the following primary references in the iron annotated

bibliography: (3A, 18, 23, 25, 28) 152

Figure 4.1.3 Experimental thermal conductivity data selected from

the following primary references in the iron annotated

bibliography: (29,31,33,34) 153

Figure 4.1.4 Composite of the data in figures 4.1.1 through 4.1.3 . . . 154

Figure 4.2.1 Thermal conductivity deviations of the iron data from

the following primary references compared to Eq. 1.1.3:

(8,9,11,13,15,16) 155

Figure 4.2.2 Thermal conductivity deviations of the iron data from

the following primary references compared to Eq. 1.1.3:

(3A, 18, 23, 25, 28) 156

Figure 4.2.3 Thermal conductivity deviations of the iron data from

the following primary references compared to Eq. 1.1.3:

(29,31,33,34) 157

Figure 4.2.4 Composite of the deviations in figures 4.2.1 through

4.2.3 158

Figure 4.2.5 Thermal conductivity deviations of the iron data from

the following secondary references compared to

Eq. 1.1.3: (1,3,4,5,6,10) 159

Figure 4.2.6 Thermal conductivity deviations of the iron data from

the following secondary references compared to

Eq. 1.1.3: (11,12,14,17,19,22) 160

147
Page

Figure 4.2.7 Thermal conductivity deviations of the iron data from

the following secondary references compared to

Eq. 1.1.3: ( 21 ,22A,24 ,26 ,27 ,30 ,32 ) 161

Figure 4.2.8 Thermal conductivity deviations of the iron data from

the following secondary refeences compared to

Eq. 1.1.3: (33,34,35,36) 162

Figure 4.2.9 Composite of the deviations in figures 4.2.6 through

4.2.8 163

Figure 4.2.10 Thermal conductivity deviations of the iron data from

the following secondary references compared to

Eq. 1.1.3: (2,7,22B) 164

Figure 4.2.11 Comparison of Eq. 1.1.3 to the values recommended for

iron in the following references: (9A,12,20,32A) .... 165

Figure 4.3.1 Experimental electrical resistivity data for iron

selected from the following references in the iron

annotated bibliography: (3A, 8, 11 ,15,16,25) 166

Figure 4.3.2 Experimental electrical resistivity data for iron

selected from the following references in the iron

annotated bibl iography : (31,34) 167

Figure 4.3.3 Composite of the electrical resistivity data in

figures 4.3.1 and 4.3.2 168

Figure 4.3.4 Electrical resistivity deviations of the iron data from

the following references compared to Eq. 1.2.3:

(3A, 8, 11, 15, 16, 25) 169

Figure 4.3.5 Electrical resistivity deviations of the iron data from

the following references compared to Eq. 1.2.3:

(31,34) 170

Figure 4.3.6 Composite of the electrical resistivity deviations

shown in figures 4.3.4 and 4.3.5 171

Figure 4.3.7 Electrical resistivity for iron as a function of

temperature calculated from Eq. 1.2.3 at selected

values of RRR 172

Figure 4.3.8 Lorenz ratio for iron as a function of temperature

calculated from Eq. 1.2.3 and Eq. 1.1.3 at selected

values of RRR 173

Figure 4.3.9 RRR values calculated as per Section 1.5, RRR(CALC),

versus reported RRR values, RRR(OBS), for iron 174

Figure 4.4.1 Thermal conductivity for iron as a function of

temperature calculated from Eq. 1.1.3 at selected

values of RRR 175

148
le

en

3A

3A

3A

8

11

13

15

15

16

10

11

11

12

14

36

Comparison of Calculated and Observed RRR Values for Iron.

RRR (obs.) RRR (calc

Primary Data

20.89 20.89

21.24 21.24

21.55 21.55

23.0 23.0

13.0 12.7

23.33 24.1

98.0 90.0

95.0 103.0

40.3 40.3

Secondary Data

189.0 189.0

13.0 13.9

13.0 12.8

23.0 23.4

29.4 29.4

36.4 36.4

149
Table 4.4.1. Thermal Conductivity Values for Iron Calculated from Eq. 1.1.3 at

Selected Temperatures and RRR Values.

X( W'liT

1 •K~

1

) T

(K) RRR = 10 RRR = 30 RRR = 100 RRR = 300

1 2.5 8.1 28 84

2 5.1 16.3 56 168

3 7.6 24 83 251

4 10.1 32 111 333

5 12.6 41 138 414

6 15.2 49 166 492

7 17.7 57 192 567

8 20 65 218 637

9 23 73 244 702

10 25 81 269 761

12 30 96 315 858

14 35 111 357 925

16 40 125 393 961

18 45 139 422 970

20 49 152 445 957

25 61 179 471 863

30 71 198 462 735

35 79 208 429 609

40 86 210 384 500

45 91 204 336 410

50 94 194 292 340

60 96 170 225 247

70 94 150 183 195

80 92 133 156 164

90 89 122 138 144

100 87 114 126 130

150 81 94 100 102

200 78 88 91 92

250 76 82 85 85

300 72 77 79 79

400 64 67 68 69

500 58 60 60 61

600 52 53 54 54

700 46 47 47 47

800 41 41 42 42

900 36 37 37 37

1000 32 32 33 33

150
THERMAL

CONDUCTIVITY

,W/m

.

1 2 4 10 20 40 100 200 400

TEMPERATURE,

K

FLgure 4.1.1 Experimental thermal conductivity data selected from

the following primary ref erences In the Iron annotated

bibliography: (8,9,11,13,15,16)

0= (8), A- (9), - (11), V - (13),

O- (15), +- (15), X- (16)

151
THERMAL

CONDUCT

I

VI

TY

,

W/m

.

Figure 4.1.2 Experimental thermal conductivity data selected f rom

the following primary ref erences In the Iron annotated

bibliography: ( 3R , 1 8 , 23 , 25 , 28

)

O- (18), A- (3fl) , - (23), V- (25),

O- (3R) , +- (3fl), X» (28)

152
THERMRL

CONDUCTIVITY,

W/m.

Figure 4.1.3 Experimental thermal conductivity data selected f rom

the following primary ref erences In the Iron annotated

bibliography: (29,31,33,34)

O- (29), A- (29), - (31), V- (31),

O- (33), + - (34)

153
THERMAL

CONDUCTIVITY,

W/m.

1 2 4 10 20 40 100 200 400

TEMPERATURE,

K

Figure 4.1.4 Composite of the data In figs. 4.1.1 through 4.1.3

154
1 2 4 10 20 40 100 200 400

TEMPERATURE,

K

Figure 4.2.1 Thermal conductivity deviations of the Iron data from

the following primary references compared to eq. (1.1.3):

(8,9,11,13,15,16)

O- (8), A- (9), - (11), V- (13),

O- (15), +- (15), X- (16)

155
Figure 4.2.2 Thermal conductivity deviations of the Iron data from

the following primary references compared to eq. (1.1.3):

(3FI, 18,23,25,28)

O- (18), A- ( 3R ) , - (23), V- (25),

O - (3R) , +- (3fl), X- (28)

156
1 2 4 10 20 40 100 200 400

TEMPERRTURE,K

Figure 4.2.3 Thermal conductivity deviations of the Iron data f rom

the following primary ref erences compared to eq. (1.1.3):

(29,31 ,33,34)

O- (29), A- (29), - (31), V- (31),

O - (33), +- (34)

157
o

-_) cr01 CO

CDO

bJ

CD

E-* CD

Cl.

15

10 -

5

-

V

x" 7

+ +

^

7 ***\

+M

- o O °

*- srOBaa^^^y. £- r -<^-

-5 J-

-10 - x

-15 -

-20

XC33 ^ ^ A S *a

a

A aO

O +

10 20 40 100

TEMPERATURE,

K

200 400

Figure 4.2.4 Composite of the deviations In figs. 4.2.1 through

4.2.3

158
Figure 4.2.5 Thermal conductivity deviations of the Iron data

from the following secondary references compared to

eq. ( 1 . 1 .3) :( 1,3,4,5,6,10)

O- (1), A- (3), - (4), V- (5),

O- (6), +- (6), X- (10)

159
Figure 4.2.6 Thermal conductivity deviations of the Iron data

from the following secondary ref erences compared to

eg. U. 1. 3) : (11,12,14,17,19,22)

O- (11), A- dll, - (12), V - (14),

O- (17), + - (19), X- (22)

150
2 4 10 20 40 100 200 400 1000

TEMPERATURE,

K

Figure 4.2.7 Thermal conductivity deviations of the Iron data

f rom the following secondary ref erences compared to

eq. (1.1.3) : (21 ,22R,24,26,27,30,32

)

O- (21), A- (22R) , - (24), V- (26),

O " (27), +- (30), X- (32)

161
Figure 4.2.8 Thermal conductivity deviations of the Iron data

f rom the following secondary ref erences compared to

eg. (1.1.3) : (33,34,35,36)

O- (33), A- (33), - (34), V- (35),

<0- (36)

152
20 — i

1 i

• i i I i i

|

CD

_Jaz01 • CD

CDO

QJO

f-* CD

Q_

15

10

5

0

-5

-10

15 h

a a aa +

Z—*• A _

A

*

A O &0 A

tr =f

V

+

S

-k-—QA° <* q _ . o

l

-20

10 20 40 100 200

TEMPERATURE,

K

400 1000

Figure 4.2.9 Composite of the deviations In figs. 4. 2.

6

through 4.2.8

163
PCT.

DEV.

(OBS.-CPILC.

Figure 4.2.10 Thermal conductivity deviations of the Iron data

from the following secondary references compared to

eq. (1 . 1 .3) : (2,7,22B)

O- (2) , A - (2), - (2), V- (7 )

,

O- (22B)

164
Figure 4.2. 11 Comparison of eq. (1.1.3) to the values recommended

for Iron In the following references; (9fl, 12,20, 32FI)

O- (9m , A- (9fl) , - (12), V- (20),

O- (32R)

165
ELECTRICAL

RESISTIVITY,

nfl.

2 4 10 20 40 100 200 400

TEMPERATURE,

K

Figure 4.3.1 Experimental electrical resistivity data for

Iron selected from the following references In

the Iron annotated bibliography: (3fl,8, 1 1 , 15, 16,25)

O- (8),

O - (25),

A- (11),

+ - (3R)

,

- (15),

X- (30)

V- (16),

166
ELECTRICRL

RESISTIVITY,

nfi.

Figure 4.3.2 Experimental electrical resistivity data for

Iron selected from the following references In

the Iron annotated bibliography: (31,34)

O- (31), A- (34)

167
ELECTRICRl

RESISTIVITY,

nfl.

2 4 10 20 40 100 200 400

TEHPERRTURE,K

Figure 4.3.3 Composite of the electrical resistivity data In

figs. 4.3.1 and 4.3.2
2 4 10 20 40 100 200 400

TEMPERATURE,

K

Figure 4.3.4 Electrical resistivity deviations of the Iron

data f rom the following ref erences compared to

eq

.

(1.2.3) : (38,8,11,15,16,25)

o- (8)

,

A- (11), - (15), V- (16),

O- (25)

,

+ - (3fl)

,

X- (3R)

169
Figure 4.3.5 Electrical resistivity deviations of the Iron

data from the following references compared to

eg. (1.2.3) : (31,34)

O- (31), A- (34)

170
Figure 4.3.6 Composite of the electrical resistivity deviations

shown In figs. 4.3.4 and 4.3.5

171
ELECTRICAL

RESISTIVITY,

nfh

TEMPERATURES

Figure 4.3.7 Electrical resistivity for Iron as a function

of temperature calculated f rom eq. (1.2.3) at

selected values of RRR.

172

JLill

I

,>

1,

>l,i

hi

AiJLl—

l.i t

,U
LORENZ

RATIO,

10

°VVK

TEMPERATURE,

K

Figure 4.3.8 Lorenz ratio for Iron as a function of temperature

calculated f rom eq. (1.2.3) and eq. (1.1.3) at selected

values of RRR.

173
RRR(CRLC)

Figure 4.3.9 RRR values calculated as per Section 1.5, RRR(CRLC),

versus reported RRR values, RRR(0BS),for Iron.

O” Primary, A = Secondary,

” Secondary

174
THERMRL.

CONDUCTIVITY,W/m.

TEMPERflTURE,K

Figure 4.4.1 Thermal conductivity for Iron as a function of

temperature calculated from eq. (1.1.3) at selected

values of RRR.

175
4.5 FORMAT FOR ANNOTATED BIBLIOGRAPHY OF IRON

AUTHOR, TITLE, CITATION

REFERENCE

ANNOTATION

PURPOSE

SPECIMEN

a) Dimensions/Shape; b) Crystal Status; c) Thermal /Mech . History; d) Purity

Specification; e) RRR; f) p0 ; g) Other Characteri zation Data

APPARATUS

a) Type; b) Thermometry/Cal ibration/Anchoring; c) Thermal Isolation;

d) Other (Q meas.

)

DATA

a) Temperature Range/Difference; b) Content of Tables, Figures and Equations/Data Extraction; c) Uncertainty/Imprecision; d) Disputable Corrections to

Measurements by Authors; e) Errata (by Author or Reviewer)

ANALYSIS

a) Comparisons; b) Conclusions

176
[ 1 ] Androulakis, J. G. and Kosson, R. L. , Experimental Determination of the

Thermal Conductivity of Solids Between 90 and 200 K, 7th Conference on Thermal

Conductivity, Nat. Bur. Stand. (U.S.), Spec. Publ . No. 302, 337-348 (1968)

PURPOSE

To describe details of an apparatus for measuring A which can be used for

good and poor conductors by varying sample geometry.

SPECIMEN

c) /machined from bar; g) SAE 1020 steel.

APPARATUS

a) longitudinal; b) Cu-constantan thermocouples; c) feedback controlled

guard, radiation shields; 10*5 - 10*6 pa vacuum.

DATA

a) 78.8 to 154 K; b) figure 7 - A; c) uncertainty: ± 8% at 89 K, ±5% at

200 K.

ANALYSIS

a) results agree with Powell, R. L. and Blanpied, W. A., NBS, Circular 556 , and Scott, R. B., Cryogenic Engineering, D. Van Nostrand Co., New York

(1959).

[2] Arajs, S. , Oliver, B. F. , and Dunmyre, G. R. , Thermal Conductivity of HighPurity Iron at Low Temperatures , J. Appl . Phys., _36, No. 7, 2210-2 (1965)

PURPOSE

To study A of a high purity iron as a function of temperature and compare

the results with theory.

SPECIMEN

a) specimen A: 15 cm long, 1.75 cm dia./rod; b) specimen B: polycrystalline; c) specimen A: distilled and reduced to metal with H2 , electron

beam zone refined, annealed in Pd purified Ho, specimen B: annealed/

specimen A: swaged and cleaned with chemical polish before anneal;

d) specimen A: 99.997%, specimen B: 99.926%.

APPARATUS

a) longitudi nal

.

DATA

a) specimen A (run 1 ): 6 to 198 K, specimen A (run 2): 6 to 78.4 K, speci- men B: 5 to 193 K; b) figure 1 - A.

ANALYSIS

a) A maximum higher than those of Rosenberg, H. M. , Phil. Trans. R. Soc

.

(London), A247 , 441 (1955) and Kemp, W. R. G. , Klemens, P. G., and Tainsh,

R. J., Ann. Phys. (Leipzig), _5, 35 (1959).

177
[3] Beitchman, J. G. , Trussel , C. W. , and Coleman, R. V., Electron Transport and

Lorenz Number in Iron, Phys. Rev. Lett., 25(18), 1291-94 (Nov 1970)

PURPOSE

To measure p and W of Fe single crystals from 2 to 77 K with and without

magnetic fields and investigate theoretical predictions for L and electron

transport theory.

SPECIMEN

b) single crystal , <1 1 1 > axial orientation; e) 700 < RRR < 2000.

DATA

a) 2.2 to 20 K; b) figure 1 - W(H = 0, 95 A/m).

ANALYSIS

b) intrinsic temperature dependence of p is aT^, and behavior of single

domain state (with H / 0) is not too different from non-transition metals.

[3A] Berman, R. , Hardy, N. D. , Sahota, M. , Hust, J. G. , and Tainsh, R. J.,

Standard Reference Materials for Thermal Conductivity Below 100 K, Proceedings of

the Seventeenth Conference on Thermal Conductivity, Gai thersburg , MD, 105-16

(1983)

PURPOSE

To report results of a CODATA round-robin investigation involving standard

reference materials of stainless steel, tungsten, and electrolytic iron.

SPECIMEN from Leeds University

a) SRM 734; b) approximately 1/4 in. (dia.) x 2 in. (6 x 50 mm); c) RRR

= 21.24.

SPECIMEN from National Measurement Laboratory

a) SRM 734; b) approximately 1/4 in. (dia.) x 2 in. (6 x 50 mm); c) RRR

= 21.55.

APPARATUS

a) not described.

DATA from Leeds University

a) 3 to 100 K; b) Table - A/data made available by private communication.

DATA from CSIR0

a) 4 to 90 K; b) Table - A, p, L/data made available by private communication.

178
[4] Bideau, 0., Troadec , J. P. , Meury, J. L. , Rosse, G., and Dang Tran Quan, Simultaneous Measurements of Thermoel ectri c Power and Thermal Conductivity of Small

Samples from 100 to 300 K, Rev. Phys. Appl . , 13(8) , 415-8 (Aug 1978)

PURPOSE

To simultaneously measure thermoel ectric power and x on small samples from

100 to 300 K, and present evaluation of apparatus.

SPECIMEN

a) 6 mm long, 6.4 mm diam./rod; c) /faces polished; d) SRM 734 electrolytic

Fe.

APPARATUS

a) longitudinal ; b) Cu-constantan thermocouples//^

tempered specimen

insul ation.

leads; c) radiation shield, 10~6 mm

foil

of

for thermal contact

Hg (10-4 Pa),

DATA

a) 100 to 300 K; b) figure 6 - X; c) uncertainty: <±3%.

ANALYSIS

a) results deviate <3% from Hust, J. G. , Giarratano, P. J., Nat. Bur.

Stand. (U.S.), Spec. Publ . No. 260 (1975).

[5] Cason, J. L. , Jr., Thermal Conductivity Measurements of Eu 0 across the

Curie Point, S.D. School of Mines and Technol., Rapid City, Dept, of Physics,

Rept. No. TR-22 (Oct 1967), Contract No. NONR-2964 (01), 85 pp., M.S. Thesis

PURPOSE

To measure X of Fe as a standard for other measurements.

SPECIMEN

a) 19 mm long, 3 mm dia./rod; g) source: Battelle Memorial Institute;

Armco.

APPARATUS

a) absolute longitudinal; b) Cu-constantan thermocouples on specimen, GRT

on heat sink, PRT in bath; c) radiation shield, heater temperature monitor, vacuum insulation.

DATA

a) 76.6 to 160 K; b) figure 13 - X; c) total uncertainty: ±20% at 68 K,

±14% at 297 K.

ANALYSIS

b) results agree within 6% of Powell, R. W. , Progress in Internati onal Re - search on Thermodynamic and Transport Properties, Academic Press, New York

(1962).

179
[6] deNobel , J., Heat Conductivity of Steels and a Few Other Metals at Low Temperatures, Physica (Utrecht), 17, 551-62 (1951)

PURPOSE

To measure X for some metals and alloys used in cryostat construction.

SPECIMEN

c) specimen 6936: forged, specimen 1 1 66 A/4 : annealed at 800 °C, furnace

cooled; d) specimen 6936: 99.93% Fe, specimen 1 166 A/4 : 0.14% C, 0.08% Si,

0.07% Mn; g) source: Sir R. A. Hadfield, specimen 1 166 A/4 : mild steel, 104

hardness B., specimen 6936: 103 hardness 3.

APPARATUS

a ) longitudi nal ; b) gas thermometers/cal ibrated against Pt thermometer in

bath; c) 10"6 mm of Hg (10

_/

^ Pa) vacuum.

DATA

a) 16 to 93 K; b) Table 2 - X; d) correction for thermometry heat leak.

ANALYSIS

b) X is proportional to T at low temperatures.

[7] Fieldhouse, I. B., Hedge, J. C., and Lang, J. I., Measurements of Thermal

Properties, WADC Tech. Rep. 58-274, 20 pp; ASTIA 206892 (1958)

PURPOSE

To calibrate a x apparatus.

SPECIMEN

a) 0.625 in. (1.59 cm) I.D. x 3.0 in. (7.6 cm) 0.0. x 1.0 in. (2.5 cm)

thick/disks; g) source: Armco.

APPARATUS

a ) radial ; b) Pt vs. Pt + 10% Rh thermocouples; c) bubble alumina, end guard

heaters, water-cooled steel housing.

DATA

a) 208 to 2410 K; b) Table 1 - X; c) uncertainty: ±5%.

ANALYSIS

a) results agree with Powell, R. W. , Proc. Phys. Soc., London, 4(5, pp. 659-

74 (1934).

180
[8] Fulkerson, W. , Moore, J. P. , and McElroy, D. L. , Comparison of the Thermal

Conductivity, Electrical Resistivity and Seebeck Coefficient of a High-Purity

Iron and an Armco Iron to 1000 °C, J. Appl . Phys., 37_(7), 2639-53 (1966)

PURPOSE

To make a comparative investigation of ingot and high purity Fe for x, p,

and S up to 1000 °C

SPECIMEN

a) 3 in. (7.6 cm) dia., 1.13 to 1.45 in. (2.87-3.68 cm) thick, 9 in. (23 cm)

tall stack/disks; e) RRR = 9.6, 23.0; g) source: Armco.

APPARATUS

a) radial; b) Pt - 10% Rh vs. Pt annealed reference grade thermocouple;

c) guard disks.

DATA

a) 323 to 1273 K; b) Table III - x, Table IV - p; c) uncertainty in X: ±1.5%; uncertainty in p: ±0.3%.

ANALYSIS

a) results agree with previous measurements.

[9] Godfrey, T. G. , Fulkerson, W., Kollie, T. G., Moore, J. P., and McElroy,

D. L. , Thermal Conductivity of Uranium Dioxide and Armco Iron by an Improved

Radial Heat Flow Technique, U.S.A.E.C. Rep. 0RNL-3556, 1-67 (1964)

PURPOSE

To describe an improved apparatus (radial heat flow) for making measurements on solids from -57 to 1100 °C and report results and analysis on

UO 2 and ingot Fe.

SPECIMEN

a) 1.375 in. (3.493 cm) outer radius, 5/8 in. (1.59 cm) inner radius, 1 in.

(2.54 cm) thick; d) < 99.4%.

APPARATUS

a ) radi al ; b) Pt vs. Pt-10% Rh reference grade thermocouple; c) He atm, end

guard heaters, granular alumina, insulation.

DATA

a) 385 to 990 K; b) Table El - X/data points listed in TPRC data series;

c) uncertainty: ±1.5%.

ANALYSIS

a) over the temperature range 100 to 1000 °C, results agree to ±3% with

Powell, R. W., ASME, N.Y. (1962), Laubitz, M. J., Can. J. Phys. 38(7), 837

(1960), and Cody, G. D. , Abeles, B. , and Beers, D. S. , Trans. Metal 1 . Soc.

AIME , 221(2), 25 (1961).

181
[9A] Ho, C. Y., Powell, R. W. , and Li ley, P. E. , Thermal Conductivity of the

Elements: A Comprehensive Review, J. Phys. Chem. Ref. Data, 3_, Supplement No. 1,

242-257 (1974)

PURPOSE

To provide a comprehensive listing of data on x of the elements.

SPECIMEN

d) high purity; f) p 0

= 1.43 x 10" 8 n*cm for T below 200 K.

APPARATUS

a) not given.

DATA

a) 0 to 6500 K; b) Table 78 - x, recommended values; c) uncertainty: ±5%

below 100 K, ±3% from 100 K to room temperature, ±2% from room temperature

to about 1000 K, increasing to ±8% at 1600 K, and ±15% at the melting

point.

[10] Holder, T. K., Thermal Conductivity, Electrical Resistivity and Seebeck Coefficient of High Purity Iron and Selected Iron Alloys from 90 to 400 K,

O.R.N.L., Tenn., Metals and Ceramics Div., Rep. No. ORNL/TM-5539 , Contract No. W7405-Eng-26. Also M.S. Thesis, 110 pp. (Jun 1977)

PURPOSE

To report x, p, and S of pure Fe and some Fe alloys from 90 to 400 K, calculate xe and Xg and compare to theory.

SPECIMEN

a) 7.6 cm long, 0.65 cm dia./rod; d) 99.994%; e) RRR = 189; g) zone re- fined.

APPARATUS

a ) longitudinal ; b) chromel-P: constantan thermocoupl es//al 1 specimen

leads tempered; c) temperature controlled guard, vacuum insulation.

DATA

a) 90 to 300 K; b) Table 2 - X, p. Table 12 - L; c) uncertainty: ±1.2%;

d) isothermal corrections due to small thermocouple differences.

ANALYSIS

b ) all oys deviated from Matthiessen 1 s rule.

182
[11] Hust, J. G. , Thermal Conductivity Standard Reference Materials from 4 to

300 K. I. Armco Iron, National Bureau of Standards, Boulder, Colo., Report

No. 9740 (Aug 1969) 97 pp.

PURPOSE

To measure A, p, L and thermopower of several specimens of Armco Fe from 4

to 300 K to check usefulness as an SRM.

SPECIMEN

a) 23 cm long, 3.6 mm dia./rod; c) annealed at 870 °C in gas-heated air

muffle for 1/2 h then in 10“^ mm for 1.5 h at 875 °C, held at 150 °C

for 24 h and repeated/machined between anneals; d) 0.015% C, 0.028% Mn

,

0.005% P, 0.025% S, 0.003% Si, 0.04 Cu; e) RRR (mean) = 13; g) source:

Battelle Memorial Institute, hardness B: 37.1, grain size: 0.064 mm.

APPARATUS

a) longitudinal; b) 8 thermocouples; c) glass fiber around specimen, temperature controlled shield.

DATA

a) specimens 2, 2a, 4: 6 to 300 K; b) Tables 20, 21 , 22 - A, p, L; c) un- certainty: ±2.5% at 300 K, decreases as T^ to 200 K, 0.7% at 200 to 50 K increasing as 1/T to 1.5% at 4 K.

ANALYSIS

a) RRR mean values are 5.5% below values of Lucks, C. F. , rms deviation is

3.6% compared to Luck's 6.5%.

[12] Hust, J. G. and Giarratano, P. J., Thermal Conductivity and Electrical Resistivity Standard Reference Materials: Electrolytic Iron SRM's 734 and 797 from

4 to 1000 K, Nat. Bur. Stand. (U.S.), Spec. Publ . No. 260-50, 32 pp. (Jun 1975)

PURPOSE

To review development of SRM's, give selection criteria and compile and

compare data on A and p for electrolytic Fe and other similar specimens.

SPECIMEN

a) 23 cm long, 3.6 mm dia./rod; c) annealed at 1000 °C for 2 h, held at

800 °C for 2 h; d) 99.90%; e) mean RRR = 23; g) density = 7.867 g/cm^,

Rockwell hardness and grain size: B24, 0.05 mm respectively.

APPARATUS

a) longitudinal ; b) thermocouples; c) glass fiber, temperature controlled

shield, insulation.

DATA

a) 6 to 1000 K; b) Table 1 - A, p, L; c) uncertainty: 2.5% below 280 K, 3%

above 280 K.

183
[13] Hust, J. G. and Sparks, L. L. , Thermal Conductivity Standard Reference

Materials from 4 to 300 K. II. OSRM Iron-1265, National Bureau of Standards,

Boulder, Colo., Report No. 9771 (Oct 1970) 35 pp.

PURPOSE

To measure X, p, and L for OSRM Fe-1265 from 4 to 300 K and study the variability by RRR measurements.

SPECIMEN

a) 23 cm long, 3.6 mm dia./rod; c) annealed at 1000 °C in vacuum or He for

2 h; d) < 99.87%; e) RRR = 23.33 ±0.24; g) density: 7.867 g/cm^, hard- ness B: 23.5 Rockwell, Grain size: 0.0507 mm, OSRM Fe-1265.

APPARATUS

a) longitudinal; b) 8 thermocouples; c) glass fiber around specimen, temperature controlled shield.

DATA

a) 6 to 280 K; b) Table 8 - A, p, L; c) uncertainty: ±2.5% at 300 K, de- creases as T^ to ±0.7% at 200 K, ±0.7% from 200 to 50 K, increases inversely with T to ±1.5% at 4 K.

ANALYSIS

b) Mathiessen's rule application shows dependence of p-j on p 0

.

[14] Karweil, J. and Schafer, K. , The Thermal Conductivity of Some Poorly Conducting Alloys between 3 and 20 K, Ann. Phys. (Leipzig), 36.» 567-77 (1939)

PURPOSE

To determine X, p, and L for some important alloys from 3 to 20 K.

SPECIMEN

a) 2.54 mm dia., 12 cm long/rod; c) /drawn; d) electrolytic Fe; f) RRR

= 29.4.

APPARATUS

a) longitudinal; b) gas thermometers , thermocouples/thermocouples calibrated at L 02 /leads to specimen run through bath; c) radiation shield,

i nsul ation.

DATA

a) 4.9 to 82 K; b) graph p. 575 - X.

ANALYSIS

b) Lorenz ratio is reasonably constant at low temperatures.

184
[15] Kemp, W. R. G. , Klemens, P. G. , and Tainsh, R. J., Thermal and Electrical

Conductivities of Rhodium and Iron, Ann. Phys. (Leipzig), _5(7), 35-41 ( 1959)

PURPOSE

To measure cr and X for pure Fe and Rh specimens from 2 to 90 K.

SPECIMEN

a) specimen 1: 28 x 2.5 x 2.5 mm, specimen 2: 2.4 x 1.7 x 30 mm/bars;

c) specimens 1,2: annealed at 950 °C and reannealed/cut from a precipitated

plate, compressed between anneals, specimen 2 face ground; e) specimen 1 (p 0

= 0.09 pfl.cm), specimen 2 (p 0

= 0.092 yft*cm); g) similar

material as used by Griineisen, E., doubly refined electrolytic Fe.

APPARATUS

a ) longitudi nal ; b) gas thermometers ; c) vacuum, temperature controlled

shield, insulation.

DATA

a) specimen 1: 6.5 to 90 K, specimen 2: 7.7 to 91 K; b) figure 3 - X,

Tables 1,2 - p 0

, p, respecti vely.

ANALYSIS

a) results of p 0 /p 273 higher than Griineisen, E. and Goens, E.

,

Z. Phys. 44, 615 (1927).

[16] Kemp, W. R. G. , Klemens, P. G. , and White, G. K., Thermal and Electrical

Conductivities of Iron, Nickel, Titanium and Zirconium at Low Temperatures,

Aust. J. Phys., 9(2), 180-8 (1956)

PURPOSE

To measure x for several metals down to 2 K and determine Xg, X e and L.

SPECIMEN

a) 2 mm dia./rod; c) annealed in vacuum at 750 °C for 4 h; d) 99.995%;

e) RRR = 40.3; f) p0

= 0.248 yft.cm; g) source: Johnson Matthey.

APPARATUS

a) longitudinal ; b) gas thermometers ; c) temperature controlled shield, vacuum insulation.

DATA

a) 1.5 to 128 K; b) figures 1,2,4 - X, L, p, respecti vel y.

ANALYSIS

a) results agree with Rosenberg, R. M. , Philos. Trans. Roy. Soc. London,

Ser. A, 247, 441 (1955).

135
[17] Kohlhaas, R. and Kierspe, W. , The Thermal Conductivity of Pure Iron and

Some Ferritic and Austenitic Steels Between the Temperature of Liquid Air and

Room Temperature, Arch. Eisenhuettenwes. , 36(4), 301-9 (1965)

PURPOSE

To measure A and p of pure Fe and steels between liquid air and room temperature, determine Ae and Ag, estimate X from p and examine effect

of alloying elements on X. SPECIMEN

g) 0.5 cm dia, 15 cm long/rod; d) 99.93%.

APPARATUS

a) longitudinal; b) Fe-constantan thermocouples; c) vacuum.

DATA

a) 88 to 300 K; b) Tables 2, 3 - X, p; c) uncertainty: ±3.5%.

ANALYSIS

b) x e

, Xg are temperature dependent.

[18] Laubitz, M. J., Thermal and Electrical Properties of Armco Iron at High

Temperatures , Can. J. Phys., 38(7), 887-907 (1960)

PURPOSE

To accurately determine x, a and thermoel ectric power of Armco Fe from 0 to

1000 °C in an effort to solve discrepancies in the literature.

SPECIMEN

a) 7.156 cm long, 2.324 cm dia. /rod; c) annealed at 850 °C 1/2 h/specimen

cut from 12 in. (30.5 cm) long sect.; g) source: Battelle Memorial

Institute.

APPARATUS

a) longitudinal; b) 6 Pt/Pt - 10% Rh thermocouples//thermocouple leads

anchored to guard; c) radiation shields, alumina guard and powder, vacuum

i nsul ation

DATA

a) 303 to 973 K; b) Table 2 - X, Table 3 - p, L; c) uncertainty: ±2.5%:

d) non-uniform power distribution of heater, deviations from thermal

equilibrium, average correction: 0.06%.

ANA LYSIS

a) results agree with Powell, R. W. , Proc. Phys. Soc. 46_, 659 (1934), but

disagree with Hattori , D., Sci. Rep. Tohoku Univ. 2Q, 190 (1937), and

Maurer, E. , Arch. Ei senhuettenwes. , _10, 1945 (1936).

186
[19] Lees, C. H. , The Effects of Temperature and Pressure on the Thermal Conductivities of Solids - Part II. The Effects of Low Temperatures on the Thermal and

Electrical Conductivities of Certain Approximately Pure -fetal s and Alloys,

Philos. Trans. Roy. Soc. London, Ser. A, 208 , 381-443 (1908)

PURPOSE

To make measurements of x for metals and alloys below 0 °C and to determine

the variation with temperature.

SPECIMEN

a) 7-8 cm long, 0.585 cm dia./rod; c] /turned from bar; d) 99.99%, ("best

scrap Fe

M ); g) density = 7.74 gm/cm"^ at 21 °C.

APPARATUS

a) longitudinal ; b) Pt resist thermometers/cal ibrated at boiling point of

O

2

, ice point and boil ding point H

2 O.

DATA

a) 113 to 286 K; b) Table p. 416 - X, graph p. 425 - p; d) correction for

radiation heat loss, conduction and offset of Pt temperature from rod temperature.

ANALYSIS

a) Jager and Diesselhorst compared at 18 °C; b) little variation in x over temperature range investigated; L doesn't agree with theory.

[20] Lucks, C. F. , 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, 522-31 (1973)

PURPOSE

Evaluate published data on ingot iron to determine its continued use as a reference materi al

.

DATA

a) 73 to 1273 K (no new data).

ANALYSIS

Recomnends continued use of ingot iron as reference material.

187
[21] Lucks, C. F. and Deem, H. W. , Thermal Properties of Thirteen Metals, ASTM

Spec. Tech. Pub! . No. 227 (1958)

PURPOSE

To measure A of ingot Fe as a standard for other measurements.

SPECIMEN

a) 6 in. (15 cm) long, 3/4 in. (1.9 cm) dia./rod; c) /hot rolled;

g) source: U. S. Steel Co.

APPARATUS

a) comparative longitudinal; b) No. 36 B and S gage: (Cu-constantan)

,

(chromel -al umel ) , (Pt 6% Rh - Pt 30% Rh) or No. 30 B and S gage

Pt-Pt 10% Rh thermocouples/ingot Fe as reference; c) double-walled guard

tube, 5 x 10~5 mm (7 x 10"3 pa) vacuum.

DATA

a) specimen 1: 116 to 293 K; b) Table 12 - A.

ANALYSIS

a) results agree with Am. Mach. 8£, pp. 869-80 (1938).

[22] Lucks, C. F., Thompson, H. 8., Smith, A. R., Curry, F. P., Deem, H. W., and

Bing, G. F. , The Experimental Measurement of Thermal Conductivities, Specific

Heats and Densities of Metallic, Transparent and Protective Materials. Part I.,

USAF TR 6145-1, 1-127 (1951) [ATI 117 715]

PURPOSE

To survey literature and make experimental determinations of A, specific

heat and densities of metallic, transparent and protective materials used

in missiles and supersonic aircraft.

SPECIMEN

a) 15 cm long, 2 cm dia./rod; c) /hot rolled; d) 99.44%; g) SAE 1020 steel

from U.S. Steel Corp.

APPARATUS

a) comparative longitudinal; b) Cu-constantan thermocouples/cal ibrated to

ingot Fe standard on hot end of specimen; c) double guard tube, vacuum insul ation.

DATA

a) 111 to 265 K; b) Table 12 - A (experimental). Table 19 - A (interpo1 ated).

ANALYSIS

a) results agree with Armstrong, L. D. , and Dauphinee, T. M. , Can. J. Res.,

Sect. A, 25,' (Nov 1947) pp. 357-74, Shelton, S. M. , J. Res. Nat. Bur.

Stand., 12 (RP 669), (Apr 1934) pp. 441-50, Hattori , D., Sci. Rep. Tohoku

Imp. Univ., 26, (1937) pp. 190-205, and Kannuluik, W. G., Proc. Roy. Soc.

London, 141,71933) pp. 159-68.

188
[22A] Maurer, E. , Heat Conductivity of Chrome Steels at High Temperatures , Arch.

Ei senhlittenw, _10(4) , 145-54 (1936)

PURPOSE

SPECIMEN II a) 98.7%

APPARATUS

a) longitudi nal

DATA

a ) 300 to 970 K/data points taken from TPRC.

[22B] McDonald, W. J., Jr., The thermal and Electrical Conductivities of High

Purity Iron at Low Temperatures , M.S. Thesis, Univ. of Texas, Austin, Tex.

(1962)

PURPOSE

To report low temperature X and a for a sample of pol ycrystal 1 i ne Fe.

SPECIMEN

a) 0.062 x 0.062 x 1/5 in. (0.16 x 0.16 x 3.8 cm)/bar; b) polycrystall i ne;

c) zone refined/machined from ingot; g) Rengstorff and Goodwin, J. Met. _7,

647 (1955).

APPARATUS

a) longitudi nal ; b) Au-Co vs. manganin thermocoupl es/cal i brated in place/

specimen leads anchored to exchange gas chamber; c) radiation shield, vacuum insulation.

DATA

a) 6 to 107 K; b) figure 6 - X, figure 7 - p, figure 10 - L.

ANALYSIS

b) W

L = W - aT" 1

; X % T

3 for T < 10 K.

189
[23] Mendelssohn, K. and Rosenberg, H. M. , The Thermal Conductivity of Metals at

Low Temperatures. II. The Transition Elements, Proc. Phys. Soc., London,

Sect. A, 65, 388-94 (1952)

PURPOSE

To measure A for the transition elements from 2 to 40 K and determine their

temperature dependences.

SPECIMEN

a) 5 cm long, 1-2 mm dia./rod; c) annealed; d) 99.99% Fe; g) source:

Johnson Matthey.

APPARATUS

a) longitudinal ; b) gas thermometers

.

DATA

a) 2.3 to 32 K; b) figure 2 - A; c) uncertainty: ±3% maximum.

ANALYSIS

b) 1/A = aT2 + 0/T.

[24] Moak, D. P. , Thermal Energy Storage Supporting Research, Final Tech. Rep.

NASA-CR-80058 N67-12043, 1-300 (1966)

PURPOSE

To measure A of ingot Fe for comparative measurements of some potential

thermal energy storage materials for spacecraft.

SPECIMEN

a) 0.75 in. (1.9 cm) dia., 5.00 in. (12.7 cm) long/rod; d) 99.9% Fe;

g) source: Armco.

APPARATUS

a ) longitudinal ; b) chromel -al umel thermocouples; c) vacuum, guard shield

and bubbled alumina insulation.

DATA

a ) 107 to 280 K; b) Table G-8 - A; c) uncertainty: ±5%.

ANALYSIS

a) results agree with previous measurements and with Powell, R. W. , et al .

,

Armco Iron as a Thermal Conductivity Standard, Review of Published Data,

p. 454, ASME and Academic Press, New York (1962).

190
[25] Moore, J. P. , McElroy, D. L. , and Barisoni, M. , Thermal Conductivity Measurements Between 78 and 340 K on Aluminum, Iron, Platinum and Tungsten, Sixth

Thermal Conductivity Conference, Dayton, Ohio, (Oct 1966), Air Force Materials

Lab., Wri ght-Patterson AFB, Ohio, pp. 737-78

PURPOSE

To make X, p, and S measurements from 78 to 340 K for A1 , W, Pt , Fe, and

compare to theory of Makinson for electronic component.

SPECIMEN

e) RRR = 201: g) electron beam zone refined (3 passes), density

= 7.824 g/cm3

, source: Materials Research Corp.

APPARATUS

a ) longitudinal ; b) chromel-p vs. constantan thermocoupl es/from calibrated

spools/tempered to guard cylinder; c) temperature controlled guard

cylinder, Au plated 5 x 10"? mm of Hg (7 x 10 -3 Pa) vacuum.

DATA

a) 90 to 300 K; b) Table 5 - X, p; c) uncertainty: ±1.8%.

ANALYSIS

a) results agree with Richter, U. F. and Kohlhaas, R. , Z. Naturforsch.

,

Teil A, [19, (1964) p. 1632, and Powell, R. W., Hickman, M. J., Tye, R. P. , and Woodman, M. J., ASME (1962), pp. 466-73.

[26] National Physical Laboratory, The Thermal Conductivity of Iron, NPL,

England, Report for 1964, Basic Physics Division, 128-30 (1965)

PURPOSE

To show that the results of Lucks, Deem (1958) are inconsistant with

present and previous values at high temperatures.

SPECIMEN

a) 10.45 cm dia. with 1.27 cm dia. axial hole/disks; d) 99.97% Fe;

g) source: N.P.L. Metallurgy Division.

APPARATUS

a ) radial ; b) thermocouple; c) 2 x 10" 5 mm (3 x 10" 3 Pa) vacuum insulation, end guards

DATA

a) 373 to 973 K; b) Table 2 - x/data points listed in TPRC data series.

ANALYSIS

a) Powel 1 , R. W. , Proc. Phys. Soc., London,^, 407 (1939), Lucks, C. F.

,

and Deem, H. W. , Am. Soc. Test. Mater., Spec. Tech. Publ . No. 227 (1958),

Powell, R. W. , Hickman, M. J., Tye, R. P. , and Woodman, M. J., Progress in

Internati onal Research on Thermodynamic and Transport Properties , Academic

Press, 466 (1962), Laubitz, M. J., Can. J. Phys., 41, 1663 (1963).

191
[27] Powell, R. W. , Armco Iron as a Thermal Conductivity Standard, ASME 2nd Symposium of Thermophysical Properties, 454-65 (1962)

PURPOSE

To review published data on ingot iron to determine if it is useful as a thermal conductivity standard.

DATA

a) -180 to 1320 °C (no new data).

ANALYSIS

Conclude that ingot iron is a good standard up to 800 °C. Above 800 °C

data spread is large.

[28] Powell, R. W. , Hickman, M. J., Tye, R. P., and Woodman, M. J., Armco Iron

as a Thermal Conductivity Standard, 43 Mew Determinations at N.P.L., Progress in

International Research on Thermodynamic and Transport Properties , ASME 2nd Symposium on Thermophysical Properties, 466-73 (1962)

PURPOSE

To report new measurements on X and p for ingot iron, recommended values to

1000 °C for use as a standard

SPECIMEN

a) 10 cm long, 0.63 cm dia./rod; c) machined to specifications; d) 99.84%;

g) source: Battelle Memorial Institute.

APPARATUS

a) absolute longitudinal; b) 42 SWG Ni-Cr and constantan thermocouples;

c) radiation shield, insulating powder, vacuum insulation.

DATA

a) 73 to 1273 K; b) Table 4 - A, p, L; d) heat dissipation in heater wire

not connected to rod, heat transfer to or from connecting leads, radiated

heat.

ANALYSIS

a) agrees with Lucks, C. F. and Deem, H. W. , Am. Soc. Test. Mater., Spec.

Tech. Publ . No. 227 (1958); b) recommended for thermal conductivity

standard.

192
[29] Powers, R. W. , Ziegler, J. B. , and Johnston, H. L. , The Thermal Conductivity of Metals and Alloys at Low Temperatures : II Data on Iron and Several

Steels Between 25 and 300 K. Influence of Alloying Constituents, USAF TR 264-5,

20 pp. (1951) [ATI 105923]

PURPOSE

To provide x data on pure Fe and commercially important steels from 25 to

300 K.

SPECIMEN

a) specimens 1, 2: 20 in. (51 cm) long, 0.5 in. (1.3 cm) dia./rods;

d) specimen 1: 99.99%, specimen 2: 99.5%; g) specimen 1: pure Iron,

source: Johnston-MacKay , Ltd., specimen 2: SAE 1020, source: Carnegie

Illinois Steel Corp.

APPARATUS

a) longitudinal; b) Cu-constantan thermocouples; c) double radiation

shield, vacuum insulation

DATA

a) 26 to 300 K; b) Table 2 - specimen 1 - X, Table 3 - specimen 2 - X; c) uncertainty: ±1.9% at 30 K, ±1.1% at 100 K, ±1.0% at room temperature.

ANALYSIS

a) agrees with Armstrong, L. D. and Dauphinee, T. M. , Can. J. Res.,

Sect. A, 2_5, 356 (1947), Powell, R. W. , J. Iron Steel Inst., London, CLIV,

No. 2, 105 (1946).

[30] Richter, F. and Kohlhaas, R. , Thermal Conductivity of Pure Iron Between

-180 and 1000 °C with Special Regard to Phase Transformations, Arch.

Eisenhuettenwes. , 30_(11), 827-833 (1965)

PURPOSE

To describe a process for calculating the absolute value of X for T

> 300 °C, and report measurements for x and p for pure Fe from -180 to

1000 °C.

SPECIMEN

a) 10-30 mm thick, 63 mm dia./disk; c) vacuum melted; d) 99.94%.

APPARATUS

a) longitudinal ; b) Fe-constantan thermocouples.

DATA

a) 93 to 973 K; b) Equations 2,3, Table 2 - X, p, L; c) uncertainty:

±8.7%.

ANALYSIS

b) X = a + ST-1

T > 400 K.

193
[31] Rosenberg, H. M. , The Thermal Conductivity of Metals at Low Temperatures

,

Philos. Trans. Roy. Soc. London, Ser. A, 247 , 441-97 (1955)

PURPOSE

To investigate and report on X for 32 metals in the 2-40 or 90 K range, and

to measure p so that the Wiedemann-Franz Law could be studied.

SPECIMEN

a) 2.89 cm long, 0.202 cm dia./rod; b) polycrystal 1 i ne; c) annealed in vacuum for several hours; d) 99.78%; e) RRR = 63; g) source: JohnsonMatt hey, Co.

APPARATUS

a) longitudinal ; b) gas thermometers ; c) vacuum insulation

DATA

a) run 2: 2.0 to 93 K; b) figure 29/ taken from TPRC data series; c) uncer- tainty: ±3%; d) correction made for external volume of gas thermometer.

ANALYSIS

a) previous measurements not in agreement with present results; previous

measurements discarded; b) 1/x = aT^ + g/T.

[32] Silverman, L., Thermal Conductivity Data Presented for Various Metals and

Alloys up to 900 °C, J. Met., 5, 631-2 (1953)

PURPOSE

To present thermal conductivity data between room temperature and 900 °C

for various metals and alloys used in the electron tube industry.

SPECIMEN

a) dimensions not given/rod; c) annealed at 900 °C; d) 99.89%; g) source:

Svea Iron.

APPARATUS

a) comparative longitudinal; b) thermocouples/Pb was the primary standard

with advance (55 Cu-45 Ni) as the working standard; c) guard tube.

DATA

a ) 50 to 900 °C , ; b) Table 2 - X; c) uncertainty: ±2%.

ANALYSIS

b) X decreases with temperature.

194
[32A] Touloukian, Y. S. , Powell, R. W. , Ho, C. Y., and Klemens, P. G. , Thermophysical Properties of Matter, Volume 1: Thermal Conductivity, Metallic Elements

and Alloys, 68-81 (1970)

PURPOSE

To provide an extensive list of data for x of the metallic elements and

alloys.

SPECIMEN

d) 99.998%; f) p0= 3.27 x 10‘ 8 a-crn.

APPARATUS

a) not given.

DATA

a) 0 to 6500 K; b) c igure and Table 24R-1 - x, recommended values; c) uncer

tainty: ±3% near room temperature, ±3 to 8% at other temperatures ; e) the

values below 1.5 Tm are calculated to fit the experimental data by using n = 2.10, a = 0.37, m = 2.47, a" = 2.05 x 10' 5

, and & = 1.34.

[33] Vuillermoz, P. L. and Pinard, P. , Conductibil ite Thermique du fer a basse

temperature, C. R. .Acad. Sci . , Ser. B Paris, 277 , 493-5 (1973)

PURPOSE

To test the accuracy of an apparatus designed to measure the thermal conduc

tivity of small samples of semiconductors.

SPECIMEN

a) specimens 1, 2: 8.9 x 3.74 x 4.44 mm, specimen 3: 10.78 x 3.04

x 2.95 mm/bars; b) polycrystalline; c) specimen 1: annealed for 30 min at

870 °C, again for 90 min at 875 °C in vacuum, and 24 h at 150 °C in vacuum,

specimens 2, 3: no anneal; d) specimen 3: 99.78%; g) specimens 1, 2:

Armco.

APPARATUS

a) longitudinal

.

DATA

a) 4 to 210 K; b) Fig. 1 - X; c) uncertainty: ±6%.

ANALYSIS

a) Must, J. G. , Nat. Bur. Stand. Rep., private communication; b' conclude

that the apparatus is sufficiently precise.

195
[34] Watson, T. W. , Flynn, D. R. , Robinson, H. E. , Thermal Conductivity and

Electrical Resistivity of Armco Iron, J. Res. Nat. Bur. Stand., Sect. C, 71(4)

,

285-91 (1967)

PURPOSE

To present X and p data on samples of Armco Iron.

SPECIMEN

a) specimen 1: 37 cm long, 2.386 cm dia./rod; c) specimen 1: annealed for

1/2 h at 870 °C/specimen 2: cold worked; d) specimens 1 and 2: 99.67%;

g) specimen 1 source: Battel le round-robin program, specimen 2 source:

Redstone Arsenal

.

APPARATUS

a) longitudinal; b) chrome! P-al umel /cal ibrated at NBS; c) heat shield,

diatomaceous earth insulation.

DATA

a) specimen 1: -160 to 640 °C, specimen 2: -150 to 200 °C; b) speci- men 1: Table 2 - X, p, L, specimen 2: Table 3 - X, p, L; c) corrections

for heat exchange with surroundi ngs.

ANALYSIS

b) expected specimen 2 to have greater x values, lower p values, but found

the opposite to be true.

[35] Watson, T. W. , Robinson, H. E. , Thermal Conductivity of Some Commercial

Iron-Nickel Alloys, J. Heat Transfer, 83, 403-8 (1961)

PURPOSE

To present X data for some Fe-Ni alloys from -150 to 540 °C.

SPECIMEN

a) 37 cm long, 2.54 cm dia./rod; d) 99.15%; g) AISI 1015 steel supplied by

International Nickel Co.

APPARATUS

a) longitudinal; b) chrome! -al umel thermocouples; c) radiation shield,

diatomaceous earth insulation

DATA

iy~^150 to 540 °C ; b) Table 2 - X.

ANALYSIS

a ) agrees with Shelton, S. M. , J. Res. Nat. Bur. Stand., 12_(4), RP 669

(1934), Powell, R. W., Research, (London) , 7_(12) (1954), Powell, R. L. and

Blanpied, W. A., Nat. Bur. Stand. (U.S.), Circ. No. 556 (1954).

196
[36] Wilkes, K. E. , Thermal Conductivity Measurements between 77 K and 373 K on

Iron, Cobalt, Aluminum, and Zinc, M.S. Thesis, Purdue Univ. (1968)

PURPOSE

To measure pure Fe as a check on the accuracy of apparatus.

SPECIMEN

a) 10.44 cm long, 1.247 cm dia./rod; d) 99.96%; e) RRR = 36.4; g) density:

7.879 g/cm.

APPARATUS

a) longitudinal ; b) chrome! -constantan thermocoupl es/cal ibrated against Pt

resistance thermometer; c) vacuum insulation.

DATA

a) 82 to 372 K; b) Table 2 - X, p; c) uncertainty: ±1.6%; d) radiation,

gas conduction corrections.

ANALYSIS

a) agrees with Moore, J. P. , McElroy, D. L. , and Barisoni, K., Sixth Conf.

on Thermal Conductivity, 737 (1966), Richter, Kohlhaas (1964).

197
198
5. Tungsten

5.1 General

The annotated bibliography for tungsten (Section 5.5) includes 39 references.

The following data sets were selected as primary data: 4A, 26A, 11, 14, 20, 21,

22, 23, 25, 27, 29, 32, and 33.

The primary data ranges in temperature from 2 to 3000 K, and in RRR from 30

to 170. The primary data are shown in Figs. 5.1.1 through 5.1.4. As for the

other metals, the data are divided into groups of seven and the last figure shows

a composite of all data.

Because high purity, single crystal tungsten specimens exhibit unusual behavior at the lowest temperatures ; these data are not included in the primary

data set. As a consequence, the range of RRR included in the fit of the data is

more restricted than the total range of data.

Equation 1.1.3 was fitted to the primary data over the entire range of temperatures. The values of the parameters, P-j , i = 1, 2, ... 7, obtained by nonlinear least squares fit are

P

x = 31.70 x 10‘8

P

5 = 69.94

P

2

= 2.29 P

6 = 3.557

P

3 = 541.3 P

7 = 0.0

P4

= -0.22

with all units in SI.

The systematic residuals from this equation were then represented by the W

c term in Eq. 1.1.5. The result is

199
W

c

= -0.00035 £n( T/130) exp(-Un(T/230)/0.7) 2

)

+ 0.00015 exp(-(£n(T/35OO)/0.8) 2

)

+ 0.0006 2 n( T/90) exp(-Un(T/30)/0.4) 2

)

+ 0.0003 Jin(T/24) exp( - (£n( T/33)/0. 5)

2

)

where W

c and T are in SI units.

5.2 Deviations From Recommended Equation

The deviations of the primary data from Eq. 1.1.3 with these parameters are

illustrated in Figs. 5.2.1 through 5.2.4. No deviations exhibit differences

greater than + 1%. Although there are systematic trends with respect to temperature, the overall pattern is random in nature. No systematic trends varying with

RRR were identified.

The primary data were selected from the literature data on relatively large,

well annealed specimens. Therefore, the deviations exhibited in Figs. 5.2.1

through 5.2.4 are indicative of the combined effect of a) experimental measurement errors and b) the inability of Eq. 1.1.3 to account for the effects of

chemical impurity variations. The effects of physical defect variations, small

specimen size variations, and magnetic fields are exhibited, in part, by the deviations of the secondary data. The thermal conductivity variations caused by

other than chemical impurity variations are not expected to be represented as

well by Eq. 1.1.3. However, the RRR (or p 0

) correlating parameter does account

for an appreciable part of these variations. Some users may find this to be an

adequate representation and, therefore, discussions of these comparisons are included for completeness.

200
The deviations of the secondary data sets are illustrated in Figs. 5.2.5

through 5.2.10. These data are divided into two subgroups according to the magnitude of the deviations. The composite plots for each group are 5.2.7 and

5.2.10, respecti vely.

Again it was of interest to compare this equation to existing reference data.

The deviations of these data are illustrated in Fig. 5.2.11. The data from reference 15 are for Standard Reference Material (designated as SRM 730) at values

of RRR = 50, 75, and 100. The reference data from references 12A,27A are for an

RRR of 2850 and therefore represent an extrapolation of the equation as given

here. Note that the differences in deviations between references 12A and 27A are

about 30% between 10 and 20 K. The differences otherwise are within the combined

uncertai nties of the reference data.

5.2.1 Physical Defect Effects

Investigations of physical defects in tungsten have produced some interesting

references 3, 14, 22. Each of these references will be discussed below.

Reference 14 reports on the effects of annealing NBS sintered tungsten. The

peak conductivity for the unannealed condition was 399 W*nT 1 *K

_

1

, while annealing produced a peak value of 635 Wvrf^K" 1

. The deviations from Eq. 1.1.3 for

both conditions were within +3%.

Reference 3 shows the effects of surface condition on thermal conductivity.

A polished specimen was measured to have a conductivity of 23000 WvtT^K'* at 2 K

and 33000 at 4 K. The specimen was then etched, and the resulting

measurements were 25000 (at 2 K) and 35000 W*m-1

’K

-1 (at 4 K). The

specimen was repolished and measured to have conductivities of 30000 W’m'^'K

- *

at 2 K, 40000 WvrT-'-'K'*-'- at 4 K. The specimen was then sandblasted, and the

conductivities were found to be 33000 W*m-1

*K

-1 at 2 K, 42000 W’nT^K-1

at

4 K. Notice that the repolished specimen gave conductivities that were

201
comparable to the original condition, indicating that surface condition is approximately reversible.

Although not directly related to physical defects, reference 22 describes the

effects of purity on thermal conductivity. Three specimens were involved: a

high purity specimen, a "radial" specimen (99.8% W) and a W + 2% Ta specimen.

The maximum decrease of 10% occurs at 90 K between the high purity and "radial"

specimens. The W + 2 Ta specimen's conductivity was lowered by a factor of two

at 90 K relative to the high purity specimen. The deviations from Eq. 1.1.3 for

the high purity specimen were within +6%, while the "radial" specimen deviations

were within +2%. The W + 2 Ta specimen was not compared to Eq. 1.1.3 because of

our requirement that specimens must have less than 1% total impurities.

Although the temperature dependence of the physical defect scattering mechanism is different from that due to impurity scattering, Eq. 1.1.3 represents the

unannealed specimen data quite well (+5%). This indicates that the residual

electrical resistivity characterizes both types of scattering for the range of

RRR included here.

5.2.2 Size Effects

In reference 31, the authors demonstrate that specimen size can cause a

noticeable change in thermal conductivity values. For a specimen of 3.0 mm

diameter (specimen W-7) the peak conductivity was 73000 while

for one of 1.5 mm (W-5) the corresponding value was 36000 W'nT^K"*. For a

1.0 mm diameter specimen (W-4) the value decreased to 15000 W'm

- -*- •!<"*-. There

is a definite correlation between thermal conductivity and specimen size. The

deviations from Eq. 1.1.3 of the 3.0 mm specimen were within +28%, those for the

1.5 mm diameter specimen were within +4%. The deviations for the 1.0 mm diameter

specimen were within +12%.

202
Reference 4 shows a similar effect. For a 3.2 mm diameter specimen, the peak

conductivity was 86000 while for a 1.4 mm diameter specimen, the

value was 58000 For a 0.8 mm diameter specimen, the peak value was

42000 The deviations from Eq. 1.1.3 of the 3.2 mm specimen were

within +50%, while those for the 1.4 mm diameter specimen were within +48%. The

deviations for the 0.8 mm diameter specimen were within +36%.

The maximum deviations indicated above have some common characteri sties.

They are all positive, which implies that the calculated value of Eq. 1.1.3 is

much too small. The temperature range in which these deviations occur is between

5 and 25 K.

5.2.3 Magnetic Field Effects

Although magnetic field effects on thermal conductivity were not explicitly

studied, reference 8 shows that an increase in the field decreases the specimen

conductivity. For a zero field at 15 K, the conductivity was 8500 W*m”^*K“^,

while for a field of 2.58 T, the value at 15 K was 61 W'nf^'K”*. The authors

note that the field dependence increases towards lower temperatures. Reference 9 extends these measurements to higher magnetic fields. The conductivity of

the specimen field at 15 K in a field of 3.64 T was 38 W*m_1,

K

_1

.

Reference 30 also showed that there is a decrease in longitudinal magnetoresistance with increasing magnetic fields. The author states that for a field

of 1.3 T, the resistance at 4 K had increased by five orders of magnitude relative to its value in a zero field. Thermal conductivity values were reported for

specimens in the zero field. Reference 4 confirms that there are five orders of

magnitude difference between a zero and a 2.3 T field.

203
5.3 Electrical Resistivity and Lorenz Ratio

During this investigation, it was frequently helpful to examine the Lorenz

ratio as a function of RRR and temperature. For this reason it was necessary to

obtain an approximation of the electrical resistivity as a function of temperature and RRR. For this approximation, we selected those data sources from the

primary data that also contained electrical resistivity data. The data used is

illustrated in Figs. 5.3.1 through 5.3.3. Figure 5.3.3 is a composite for all of

the electrical resistivity data. These data were represented via a nonlinear

least squares fit of Eq. 1.2.3. The resulting parameters are

P. = 4.801 x 10" 16

P c = 55.63

1 5

P

9 = 3.839 P

6 = 2.391

P

3 = 1.88 x 10

10

P = 0.0

P4

= 1.22

where all units are SI.

The systematic residuals from this equation were subsequently represented by

the p c term in Eq. 1.2.4 as follows:

P

c = 0.7 x 10“ 8

£n( T/560) exp ( - ( an ( T/1000 ) /0 . 6)

2

)

The deviations of the experimental data from this equation are illustrated in

Figs. 5.3.4 through 5.3.6. Smooth curves are calculated and plotted in

Fig. 5.3.7 at RRR values of 30, 100, and 300. From the \(T,RRR) and p(T,RRR)

equations, values of L(T,RRR) were calculated at the same RRR values and are

plotted in Fig. 5.3.8. No unusual behavior in this plot is observed.

In Section 1.5 we discuss the procedure for selecting values of p 0 and calculating RRR for each thermal conductivity data set. These values of p 0 along

with the Sommerfeld value of Lorenz ratio were used to best fit each low

204
temperature data set. The resulting values of RRR obtained by this procedure are

compared to the values reported in the references in Fig. 5.3.9 and are listed in

Table 5.3.1. Figure 5.3.9 shows values of RRR (calc), those values from the

above procedure, versus RRR (obs), those values reported in the references listed

in the annotated bibl iography. Also shown in the figure is the line that represents RRR (calc) = RRR (obs). Systematic deviations from this line indicate

ranges in which the derived Eq. 1.1.3 is invalid. The primary data for tungsten

extend only from 30 to 400 in RRR. These values agree to within 10%. The

secondary data at RRR near 60,000 disagree from the line by as much as 30%.

Equation 1.1.3 is considered valid only from 30 to 400. In this range it appears

that the Sommerfeld value is valid for the Lorenz ratio of tungsten.

5.4 Summary for Tungsten

Equation 1.1.3 represents the primary tungsten data to within +10% of the

experimental value at a given temperature. Deviations for unannealed specimens

(i.e., those containing physical defects) are also in this range.

Based on the observed deviations of the primary data set, the uncertainty of

the recommended values is as follows. The uncertainty of the low temperature \

values is estimated to be +10% for RRR values from 30 to 300. At RRR values outside this range, the uncertainty is larger. At temperatures above 200 K, the uncertainty is smaller (+5%) and is expected to be valid for much larger RRR

val ues.

Equation 1.1.3, with the parameters listed, was used to calculate thermal

conductivity values for selected temperatures and RRR. These values are listed

in Table 5.4.1 and plotted in Fig. 5.4.1.

205
List of Tables and Figures for Tungsten

Tables

Page

Table 5.3.1 Comparison of Calculated and Observed RRR Values

for Tungsten 208

Table 5.4.1 Thermal Conductivity Values for Tungsten Calculated

From Eq. 1.1.3 at Selected Temperatures and RRR

Values 209

Figures

Page

Figure 5.1.1 Experimental thermal conductivity data selected from

the following primary references in the tungsten

annotated bibliography: (4A, 11 ,14,20,22) 210

Figure 5.1.2 Experimental thermal conductivity data selected from

the following primary references in the tungsten

annotated bibliography: (4A,21 ,22,23,25,26A) 211

Figure 5.1.3 Experimental thermal conductivity data selected from

the following primary references in the tungsten

annotated bibliography: (27,29,32,33) 212

Figure 5.1.4 Composite of the data in figures 5.1.1 through 5.1.3 . . . 213

Figure 5.2.1 Thermal conductivity deviations of the tungsten data

from the following primary references compared to

Eq. 1.1.3: (4A, 11 ,14,20,22) 214

Figure 5.2.2 Thermal conductivity deviations of the tungsten data

from the following primary references compared to

Eq. 1.1.3: (4A,21 ,22 ,23 ,25 ,26A) 215

Figure 5.2.3 Thermal conductivity deviations of the tungsten data

from the following primary references compared to

Eq. 1.1.3: (27,29,32,33) 216

Figure 5.2.4 Composite of the deviations in figures 5.2.1 through

5.2.3 217

Figure 5.2.5 Thermal conductivity deviations of the tungsten data

from the following secondary references compared to

Eq. 1.1.3: (1,2,5,7,8,10) 218

Figure 5.2.6 Thermal conductivity deviations of the tungsten data

from the following secondary references compared to

Eq. 1.1.3: (10,13,16,19,26) 219

206
Page

Figure 5.2.7 Composite of the deviations in figures 5.2.5 and 5.2.6 . . 220

Figure 5.2.8 Thermal conductivity deviations of the tungsten data

from the following secondary references compared to

Eq. 1.1.3: (3,4, 4B ,11 ,28) 221

Figure 5.2.9 Thermal conductivity deviations of the tungsten data

from the following secondary reference compared to

Eq. 1.1.3: (31) 222

Figure 5.2.10 Composite of the deviations in figures 5.2.8 and 5.2.9 . . 223

Figure 5.2.11 Comparison of Eq. 1.1.3 to the values recommended for

tungsten in the following references: (12A,15,27A) . . . 224

Figure 5.3.1 Experimental resistivity data for tungsten selected

from the following references in the tungsten annotated

bibliography: (5A, 11 ,14,22) 225

Figure 5.3.2 Experimental electrical resistivity data for tungsten

selected from the following references in the tungsten

annotated bibliography: (4A,21 ,23,25, 26A, 33) 226

Figure 5.3.3 Composite of the electrical resistivity data in

figures 5.3.1 and 5.3.2 227

Figure 5.3.4 Electrical resistivity deviations of the tungsten data

from the following references compared to Eq. 1.2.3:

(5A, 11, 14, 22) 228

Figure 5.3.5 Electrical resistivity deviations of the tungsten data

from the following references compared to Eq. 1.2.3:

(4A,21 ,23,25, 26A, 33) 229

Figure 5.3.6 Composite of the electrical resistivity deviations

shown in figures 5.3.4 and 5.3.5 230

Figure 5.3.7 Electrical resistivity for tungsten as a function of

temperature calculated from Eq. 1.2.3 at selected

values of RRR 231

Figure 5.3.8 Lorenz ratio for tungsten as a function of temperature

calculated from Eq. 1.2.3 and Eq. 1.1.3 at selected

values of RRR 232

Figure 5.3.9 RRR values calculated as per Section 1.5, RRR(CALC),

versus reported RRR values, RRR(OBS), for tungsten .... 233

Figure 5.4.1 Thermal conductivity for tungsten as a function of

temperature calculated from Eq. 1.1.3 at selected

values of RRR 234

207
Table 5.3.1. Comparison of Calculated and Observed RRR Values for Tungsten

Reference RRR (obs.) RRR (calc.)

Primary Data

4A 70.0 70.0

4A 75.4 75.4

4A 131.0 131.0

11 75.0 75.0

14 39.8 40.8

14 74.6 77.6

22 31.4 30.0

22 400.0 400.0

25 150.0 150.0

25A 75.0 75.0

29 46.6 46.6

33 155.0 155.0

Secondary Data

3 40300.0 30000.0

4 96000.0 86000.0

7 2780.0 4850.0

11 75.0 75.0

28 16300.0 16300.0

31 8460.0 8400.0

31 27200.0 26000.0

31 39300.0 36500.0

31 69600.0 56500.0

31 85500.0 71000.0
Table 5.4.1. Thermal Conducti vity Val ues for Tungsten Calculated from

Eq. 1.1.3 at Selected Temperatures and RRR Values.

x(W*m'V1

) T

(K) RRR = 30 RRR = 100 RRR = 300

1 14.6 50 151

2 29 100 302

3 44 150 452

4 59 200 602

5 73 249 749

6 88 299 894

7 102 347 1033

8 117 395 1166

9 131 442 1291

10 145 488 1404

12 173 574 1595

14 201 651 1730

16 227 718 1802

18 251 768 1803

20 273 799 1734

25 311 786 1378

30 325 692 1020

35 321 586 768

40 306 494 600

45 285 418 483

50 262 357 398

60 226 281 302

70 211 250 264

80 204 236 246

90 199 225 234

100 195 217 224

150 184 197 201

200 180 139 191

250 175 182 134

300 169 174 176

400 155 158 159

500 143 145 146

600 135 136 137

700 129 130 130

800 124 125 125

900 121 122 122

1000 118 119 119

1100 115 116 116

1200 113 114 114

1300 111 111 112

1400 109 110 110

1500 107 108 108

1600 106 106 106

1800 103 103 103

2000 100 101 101

2200 98 99 99

2400 95 97 97

2600 95 95 95

2800 93 93 93

3000 92 92 92

209
THERMAL

CONDUCTI

VITY,W/m

.

figure 5.1.1 Experimental thermal conductivity data selected from

the following primary references In the tungsten annotated

bibliography: (4fl, 1 1 ,14,20,22)

O- (11), A- (11), - (14), V- (14),

O - (4fl) , +- (20), X- (22)

210
THERMRL

CONDUCTIVITY,

W/m

.

Figure 5.1.2 Experimental thermal conductivity data selected from

the following primary references In the tungsten annotated

bibliography: (4R,21 ,22,23,25,26R)

O- (22) , A- (21) , - (4fl), V- (4fl),

O- (23), +- (25), X- (26R)

211
THERMAL

CONDUCTIVITY,

W/m

.

Figure 5.1.3 Experimental thermal conductivity data selected from

the following primary references In the tungsten annotated

bibliography: (27,29,32,33)

O- (27), A- (29), - (32), V- (33)

212
THERMAL

CONDUCTIVITY,

W/m.

1000 -

600 r

400

200 -

i

i

i i'i m ii ri' l T i'T"' " ,| T^7

, rn , » T> rnTri v

V V

v V

v V V

V v

V

V

V V

7 V

V V

V « V . + &

v a v +

+

^

7

V V

^

v+

D V

30 100 300

TEMPERATURE,

K

3000

Figure 5.1.4 Composite of the data In figs. 5.1.1 through 5.1.3

213
1 3 10 30 100 300 1000 3000

TEMPERRTURE,K

Figure 5.2.1 Thermal conductivity deviations of the tungsten data from

the following primary references compared to eq. (1.1.3):

(4R, 11, 14, 20, 22)

O- (11), A- (11), - (14), V- (14),

O- (4fl) , +- (20), X- (22)

214
Figure 5.2.2 Thermal conductivity deviations of the tungsten data from

the following primary references compared to eq. (1.1.3):

(4R,21,22,23,25,26R)

O- (22), A- (21), - (4R) , V- (4R),

O- (23), +- (25), X- (26R)

215
1 3 10 30 100 300 1000 3000

TEIiPERRTURE,K

Figure 5.2.3 Thermal conductivity deviations of the tungsten data from

the following prlmarg references compared to eq. (1.1.3)*

(27,29,32,33)

O- (27), A- (29), - (32), V- (33)

216
Figure 5.2.4 Composite of the deviations In figs. 5.2.1 through

5.2.3

217
0.3 1 3 10 30 100 300 1000

TEMPERATURE,

K

Figure 5.2.5 Thermal conductivity deviations of the tungsten data

from the following secondary references compared to

eq. (1.1.3): (1,2,5,7,8,10)

O- (1), A- (2) , - (5), V- (7),

O- (8) , + - (10), X- (10)

218
0.3 1 3 10 30 100 300 1000

TEMPERRTURE,K

Figure 5.2.6 Thermal conductivity deviations of the tungsten data

from the following secondary references compared to

eq. (1.1.3):(10,13,16,19,26)

O- (10), A- (13), - (16), V- (16),

O- (16), +- (19), X- (26)

219
0.3 1 3 10 30 100 300 1000

TEMPERRTURE,K

Figure 5.2.7 Composite of the deviations In figs. 5. 2.

5

and 5.2.6

220
13 10 30 100 300 1000

TEMPERATURE ,K

Figure 5.2.8 Thermal conductivity deviations of the tungsten data

from the following secondary references compared to

eq. (1.1.3):(3,4,4B,11,28)

O- (11), A- (3), - (4), V- (4),

O- (4), +- (4B) , X- (28)

221
Figure 5.2.9 Thermal conductivity deviations of the tungsten data

from the following secondary reference compared to

eq. (1.1.3) = (31)

O- (31), A- (31), - (31), V- (31),

O- (31), +- (31)
1 3 10 30 100 300 1000

TEMPERRTURE,K

Figure 5.2.10 Composite of the deviations In figs. 5.2.8

and 5.2.9

223
Figure 5.2.11 Comparison of eq. (1.1.3) to the values recommended

for tungsten In the following references! ( 12FI, 15, 27fl)

O- (15), A- (15), - (15), V- ( 27R )

,

O- (12R)

724
ELECTRICAL

RESISTIVITY,

nfl.

4 10 20 40 100 200 400 1000 2000

TEMPERATURE,

K

Figure 5.3.1 Experimental electrical resistivity data for

tungsten selected from the following references In

the tungsten annotated bibliography: (5R, 1 1 , 14,22)

O- (11), A- (11), - (5fl), V- (14),

<0- (14), + - (22), X- (22)

225
ELECTRICAL

RESISTIVITY,

nfl.

Figure 5.3.2 Experimental electrical resistivity data for

tungsten selected from the following references In

the tungsten annotated bibliography: (4R,21 ,23,25,26fi,33)

O- (21), A- (4R) , - (23), V- (25),

O- (26R) , + - (33)

226
ELECTRICAL

RESISTIVITY,

nil.

Figure 5.3.3 Composite of the electrical resistivity data In

figs. 5.3.1 and 5.3.2

?27
Figure 5.3.4 Electrical resistivity deviations of the tungsten

data from the following references compared to

eq. tl.2.3):(5fl,ll,14,22)

O- (11), A- (11), - (5fl), V- (14),

O- (14), +- (22), X- (22)

228
Figure 5.3.5 Electrical resistivity deviations of the tungsten

data from the following references compared to

eq. (1.2.3):(4fl,21,23,25,26fl,33)

O- (21), A- (4R), - (23), V- (25),

O- ( 26R ) +- (33)
Figure 5.3.6 Composite of the electrical resistivity deviations

shown In figs. 5.3.4 and 5.3.5
ELECTRICAL

RESISTIVITY,

nH.

1000

E

300

100

30

10

3

1

0.3

0.1 — l. i.,uu i,i,g i.n.l,,. ,. > !., t4i a 1 1 l.u

1 3 10 30 100 300 1000 3000

TEMPERATURE,

K

Figure 5.3.7 Electrical resistivity for tungsten as a function

of temperature calculated from eq. (1.2.3) at

selected values of RRR.

231

Uil
LORENZ

RATIO,

10

°YVK

TEMPERATURE,

K

Figure 5.3.8 Lorenz ratio for tungsten as a function of temperature

calculated from eq. (1.2.3) and eq. (1.1.3) at selected

values of RRR.

23 ?
RRR(CRLC)

Figure 5.3.9 RRR values calculated as per Section 1.5, RRR(CRLC),

versus reported RRR values, RRR ( OBS 3 , for tungsten.

O” Primary, A - Secondary,

~ Secondary

233
THERMAL

CONDUCTIVITY,

W/m.

TEMPERATURE,

K

Figure 5.4.1 Thermal conductivity for tungsten as a function of

temperature calculated from eq. (1.1.3) at selected

values of RRR.

234
5.5 FORMAT FOR ANNOTATED BIBLIOGRAPHY OF TUNGSTEN

REFERENCE

AUTHOR, TITLE, CITATION

ANNOTATION

PURPOSE

SPECIMEN

a) Dimensions/Shape; b) Crystal Status; c) Thermal /Mech . History; d) Purity

Specification; e) RRR; f) p0 ; g) Other Characteri zation Data

APPARATUS

a) Type; b) Thermometry/Cal i brat i on/Anchoring; c) Thermal Isolation;

d) Other (Q meas.)

DATA

a) Temperature Range/Difference; b) Content of Tables, Figures and

Equations/Data Extraction; c) Uncertai nty/Impreci sion; d) Disputable Corrections

to Measurements by Authors; e) Errata (by Author or Reviewer)

ANALYSIS

a) Comparisons; b) Conclusions

235
[1] Backlund, N. G. , Measurement and Analysis of the Thermal Conductivity of

Tungsten and Molybdenum at 100 to 400 K, Thermal Conductivity Conference,

National Physical Laboratory, Teddington, England, 15-17 July (1964)

PURPOSE

To measure X for W and Mo from 100 to 400 K.

SPECIMEN

a) 4 mm dia., 10 cm long/rod; g) source: Johnson, Matthey Co.

APPARATUS

a) longitudi nal ; b) Fe-constantan thermocouples soldered to specimen/calibrated with earlier measurements (Backlund, J. Phys. Chem. Solids 20

(1961)); c) German silver shielding, isolating bricks between can and base

plate, vacuum insulation.

DATA

a) 95.9 to 280 K; b) figures 3, 5 - p, X respectively; c) uncertainty: ±2%.

ANALYSIS

b) Xg is proportional to T.

[2] Backlund, N. G. , Measurement and Analysis of the Thermal Conductivity of

Tungsten and Molybdenum at 100 to 400 K, J. Phys. Chem. Solids, 28, 2219-23

(1967)

PURPOSE

To obtain information regarding the scattering processes of phonons and

electrons in W and Mo.

SPECIMEN

a) 10 cm long, 4 mm dia. /rod; f) p0

= 1.24 yft-cm; g) source: Johnson,

Matthey and Co.

APPARATUS

a) longitudinal; b) Fe-constantan thermocouples soldered to specimen;

c) German silver shielding, isolating bricks between can and base plate; vacuum insulation.

DATA

a) 87.3 to 282 K; b) figure 5 - X/data points listed in TPRC data series;

c) uncertainty: ±1.5%.

ANALYSIS

b) scattering by electrons is expected to be constant, while Umklapp

scattering is found only at higher temperatures.

236
[3] Baer, D. R. and Wagner, 0. K. , Effect of Surface Condition on the

Transport Properties of Tungsten, J. Low Temp. Phys., _13(5/6), 445-69 ( 1973)

PURPOSE

To determine the effect of surface condition on p, W and L.

SPECIMEN W-12G

a) 0.74 mm dia./rod; b) single crystal; c) el ectropol i shed ; f) p0

= 1.26

x 10* 10 a*cm; g) crystal oriented to [110], P

2gg/p 0

= 43000.

APPARATUS

a) longitudinal; b) C resistance thermometers/cal i brated against a standard Ge resistance thermometer; c) adsorbent in vacuum chamber to

adsorb residual He.

DATA

a) 1.46 to 5.31 K; b) figure 12 - 1/X; c) uncertainty: ±1%.

ANALYSIS

b) surface scattering is specular for the el ectropol i shed surface, while

diffuse for the el ectroetched and sandblasted surfaces.

[4] Batdalov, A. B. , Tamarchenko, V. I., and Shalyt, S. S. , Manifestation of

Hydrodynamic Effect in the Thermal Conductivity of Tungsten, JETP Lett. (USSR),

20(6), 171-3 (Sep 1974)

PURPOSE

To determine x of a compensated metal.

SPECIMEN

a) specimens 1, 2, 3: 3.2, 1.4, 0.8 mm dia. respective! y/rods; b) single

crystals; c) /electrical etching reduced specimen 1 into 2 and 3;

e) specimen 1 ( RRR = 86000).

DATA

a) specimen 1: 2 to 102 K, specimen 2: 2.15 to 12.4 K, specimen 3: 2.23

to 9.0 K; b) figure 1 - X.

ANALYSIS

b) the hydrodynamic contribution to the total thermal conductivity behaves

1 ike T"3*4.

237
[4A] Berman, R. , Hardy, N. D., Sahota, M. Hust, J. G. , and Tainsh, R. J., Standards Reference Materials for Thermal Conductivity Below 100 K, Proceedings of the

Seventeenth Conference on Thermal Conductivity, Gaithersburg , MD, 105-16 (1983)

PURPOSE

To report results of a CODATA round-robin investigation involving standard

reference materials of stainless steel, tungsten, and electrolytic iron.

SPECIMEN from Leeds University

a) SRM 730; b) approximately 1/4 in. (dia) x 2 in. (6 x 50 mm); c) RRR = 70.

SPECIMEN from National Measurement Laboratory

a) SRM 730; b) approximately 1/4 in. (dia) x 2 in. (6 x 50 mm); c) RRR

= 75.4, 131.

APPARATUS

a) not discussed

DATA from Leeds University

a) 1 to 95 K; b) Table - X/data made available by private communication.

DATA from National Measurement Laboratory, CSIR0

a) 2 to 90 K; b) Table - X/data made available by private communication.

[4B] Binkele, L., Zur Frage der Hochtemperatur-Lorenzzahl bei Wolfram-eine

Analyse neuer Messwerte der thermischen und elektrischen Leitfahi gkei f im Temperatubereich 300 bis 1300 K, submitted for publication in High Temperature-High

Pressure (1982)

PURPOSE

SPECIMEN

a) SRM 730

APPARATUS

a) Details not given.

DATA

iy~300 to 1300 K

238
[5] Bremmer, H. and DeHaas, W. J., On the Conduction of Heat by Some Metals at

Low Temperatures , Physica, 3 , 672 (1936)

PURPOSE

To determine \ for Pb, Cu and W.

SPECIMEN

a) RRR = 2174; g) source: N. V. Philips Lampworks Eindhoven.

APPARATUS

a) longitudi nal ; b) Pt resistance thermometers.

DATA

a) 1.55 to 21.8 K; b) Table 4 - W/data points listed in TPRC data series.

ANALYSIS

a) results disagree with Gruneisen, E. and Goens, E. , Z. Phys., 44, 615

(1927).

[5A] Cezairliyan, A. and McClure, J. L. , High Speed (Subsecond) Measurement of

Heat Capacity, Electrical Resistivity, and Thermal Radiation Properties of

Tungsten in the Range 2000 to 3600 K, J. Research NBS, 75A(4) (1971)

PURPOSE

To apply a high speed measurement technique on a tungsten specimen in the

temperature range 2000 to 3600 K.

SPECIMEN

a) 4 in. length (101 mm), outside dia. 0.25 in. (6.3 mm), wall thickness

0.02 in. (0.5 mmj/tube; c) specimen produced from rod by el ectroerosion , an nealed up to 3200 K; e) RRR = 41; g) polished outer surface, density at

293 K: 19.23 x 10 3 kg-m“ 3

.

APPARATUS

a) subsecond transient; b) photoelectric pyrometer/cal ibrated against W fil

ament standard lamp; c) 10“^ mm of Hg (10“ 3 Pa) vacuum.

DATA

a) 2000 to 3600 K; b) Table 2, Fig. 3 - p; c) uncertainty: ±1% between 2000

and 3600 K.

ANALYSIS

a) Results agree with Osborn (1941), Platunov (1964), Neimark (1968), Jones

(1926); b) p = 14.08 + 3.515 x 10"^ T where p is in units of 10“° nm

and T in K.

239
[6] Cox M. , Thermal and Electrical Conductivities of Tungsten and Tantalum,

Phys. Rev., 64, 241 (Oct 1943)

PURPOSE

To measure A and of pure W and Ta.

SPECIMEN

a) specimens 2,8: 0.10 in. (0.025 cm) dia., 40 cm long/rods; c) specimen 2:

aged 370 h at 2400, 2600 °C, specimen 8: aged 370 h at 2300 °C; g) source:

General Electric Co.

APPARATUS

a) direct current heating; Hg thermometer and barometer for boiling point of

N

2 > 02 , H2 O and ice bath.

DATA

a) 77.4 to 274 K; b) Table 3 - A, p, L/A data listed in TPRC data series.

ANALYSIS

a) p results agree with Hoi born, L. (1919), Henning, F. (1921), Geiss, W. (1923), Forsythe, W. E. (1925), Meissner, W. (1930), Barratt, T. (1914),

Weber, S. (1917), Griineisen, E. ( 1927), Kannuluik, W. G. (1933), and DeHaas,

W. J. (1938). A results disagree with Griineisen, E. (1927), Kannuluik,

W. G. (1933), and DeHaas, W. J. (1938).

[7] DeHaas, W. J. and Biermasz, T. H., Sur la Conductibi 1 ite Thermique aux Basses Temperatures , Rapports et Communications, No. 24, 7e, Congres International du Froid, Supplement No. 82b, 204 (1936)

PURPOSE

To determine A for several metals at low temperatures.

APPARATUS

a) longitudinal; b) Pt resistance thermometer.

DATA

a) 15.5 to 21.8 K; b) Table 8 - W, L/L data from Table 8, A data points

listed in TPRC data series.

240
[8] DeHaas, W. J. and deNobel, J., The Thermal and Electrical Resistance of a Tungsten Single Crystal at Low Temperatures and in Magnetic Fields, Physica, 5^

449 (1938)

PURPOSE

To separate x of W into xe and Xn at low temperatures in strong magnetic

fields.

SPECIMEN

a) 30 mm long/hexagonal rod; b) single crystal; e) RRR = 2780; g) source:

Philips Works, axis is in [111] direction.

APPARATUS

a) longitudinal; b) Pb thermorneters/cal ibrated against a Pt resistance ther

mometer in bath; c) < 5 x 10"^ mm of Mg (7 x 10“^ Pa) vacuum.

DATA

a) 15.3 to 88.4 K; b) Tables 1, 3 - X, p/p data from Table 3, X data points

listed in TPRC data series.

ANALYSIS

b) W-F-L holds for p and xe in magnetic fields.

[9] deNobel, J., Thermal and Electrical Resistance of a Tungsten Single Crystal

at Low Temperatures and in High Magnetic Fields, Physica, _15(5-6), 532-40

(Jul 1949)

PURPOSE

To investigate the relationship of the W-F-L law to p and x due to electrons.

SPECIMEN

a) 30 mm long/hexagonal rod; b) single crystal; e) RRR = 2780; g) source:

Philips Works, axis is in [111] direction, same specimen as used by DeHaas,

W. J. (1938).

APPARATUS

a) longitudinal; b) Pb thermometers.

DATA

a) 15 to 20 K; b) Table 1 - x/data points listed in TPRC data series, run 1 4: H = 0.82, 2.1, 2.6, 2,8 kA/m, perpendicul ar.

ANALYSIS

b) W-F-L is not valid in strong magnetic fields for a and xe

, and it is

not possible to separate Xg and xe

.

241
[10] deNobel , J., Thermal and Electrical Resistivity of Some Tungsten Single

Crystals at Low Temperatures and in Strong Magnetic Fields, Physica, 23^ 261

(1957)

PURPOSE

To gain information about Ae and Ag from the change in anisotropy with

increasing field strength.

SPECIMEN

b) single crystals, A oriented in [111] direction, 1-38 and B oriented in

[100] (±5°) direction; g) P2(/ p 273

= 26 x 10 -4

.

APPARATUS

a) longitudinal ; b) phosphor bronze resistance thermometers.

DATA

a) specimen A: 15.3 to 20.3 K, specimen B: 3.86 to 20.2 K, specimen 1-38:

3.38 to 75.9 K; b) Table 1 - A/data points listed in TPRC data series.

ANALYSIS

b) A and B anisotropy ratio: 1.13, 1.23 respectively.

242
[11] Fitzer, E. , Thermophysical Properties of Solid Materials. Project

Section II. Cooperative Measurements on Heat Transport Phenomena of Solid Materials at High Temperature, AGARD Report No. 606, 1973

PURPOSE

To improve the data base used in the design and fabrication of high temperature equipment and systems under development by the NATO countries.

SPECIMEN Participant 5 a) /wire; c) sintered.

SPECIMEN Participant 31

a) /wire; c) sintered.

SPECIMEN Participant 41

a) /wire; c) arc cast; d) 99.55% W; g) p(T).

APPARATUS Participant 5 a) comparative

APPARATUS Participant 31

a) direct electrical heating

APPARATUS Participant 41

a) direct electrical heating; b) pyrometer; d) argon environment.

DATA Participant 5 a) 300 to 900 K; b) Table 33 - X.

DATA Partaicipant 31

a) 2100 to 2800 K; b) Table 33 - X.

DATA Participant 41

a) 1500 to 2750 K; b) Table 35 - X, Table 51 - p; c) uncertainty: ±2%.

ANALYSIS Participant 5 b) TPRC Recommended curves (1970, 1972).

ANALYSIS Participant 41

b) Jun, et al . , High Temperature-Hi gh Pressure, 43 (1970); TPRC Recommended

Curves (1970, 1972).

243
[12] Griineisen, E. and Adenstedt, H. , Anisotropie der Warmeleitung und Thermokraft Regul arer Metal le (Wolfram) im Transversal en Magnetfeld bei 20 K, Ann.

Phys. (Leipzig) , 29, 597-604 (1937)

PURPOSE

To determine X and thermopower of W in a transverse magnetic field.

SPECIMEN

a) 0.106 cir^ x 7.0 cm; g) specimen axis 8° to the [110] direction.

APPARATUS

a) longitudinal* b) Const^ntan-mangani n thermocouples; c) 10"^ to 10"^ mm of

Hg (10"2 to 10"3 pa) vacuum.

DATA

a) 21.5 to 91.2 K; b) Tables 1,2- X/data points listed in TPRC data

series, H = 0.

ANALYSIS

a) agrees with Griineisen, E. and Goens, E. , Z. Phys., 44, 615 (1927).

[12A] Ho, C. Y., Powell, R. W. , Liley, P. E., Thermal Conductivity of the Elements: A Comprehensive Review, «J. Phys. Chem. Ref. Data, 3, Supplement No. 1,

242-257 (1974)

PURPOSE

To provide a comprehensive listing of data on x of the elements.

SPECIMEN

d) high purity; f) p 0

= 1.70 x 10“^ crcm for T below 200 K.

APPARATUS

a) not given.

DATA

a) 0 to 22273 K; b) Table 171 - X, recommended values; c) uncertainty: ±2% near room temperature, ±3% from 300 to 1500 K, ±5% from 100 to 300 K and

1500 to 3000 K, and ±10% below 100 K and above 3000 K. The values above

3660 K are provisional.

244
[13] Must, J. G. , Thermal Conductivity Reference Materials, Progress Report,

Proceedings of the Thirteenth Thermal Conductivity Conf . , 22-4 (Nov 5-7, 1973)

PURPOSE

To present low temperature X measurements for sintered W.

SPECIMEN

c) sintered.

APPARATUS

a) longitudinal ; b) vapor pressure of LHe for T < 20 K, Pt reference thermometer for T > 20 with differential thermocouples; b) controlled temperature glass fiber shield, vacuum insulation.

DATA

a) 10 to 250 K; b) Table 1 - X, p, L.

ANALYSIS

b) SRM 734 can be extended to 800 °C and SRM 735 to 1000 °C.

[14] Hust, J. G., Thermal Conductivity Standard Reference Materials from 6 to

280 K: VI. N.B.S. Sintered Tungsten, NBSIR 73-351 (Jan 1974)

PURPOSE

To present measurements on the transport properties of NBS sintered W.

SPECIMEN

a) 23 cm long, 3.1 mm dia./rod; c) one specimen annealed at 2020 °C for

1 h, one unannealed; e) annealed (RRR = 74.6), unannealed (RRR = 39.8);

f) annealed: p

? = 0.6493 nfi-m, unannealed: pc = 1.229 nn»m; g) density

= (19.23 ± 0.05) g/crn^, DPH hardness 1 kg = 405 and 514 for annealed and

unannealed respecti vely.

APPARATUS

a) longitudinal; b) vapor pressure of LHe for T < 20 K, Pt reference thermometer for T > 20 with differential thermocouples; c) controlled temperature glass fiber shield, vacuum insulation.

DATA

a) annealed: 7 to 90 K, unannealed: 6 to 280 K; b) Table 12 - unannealed:

X, p, L, Table 13 - annealed: X, p, L; c) uncertainty: X - 2.5% at 300 K,

decreasing as T^ to 0.70% at 200 K, 0.70% from 200 to 50 K, increasing

inversely with temperature to 1.5% at 4 K, p

- 0.5%.

ANALYSIS

b) X = 2^ a.[*nT] i+1.

i =1 1

245
[15] Hust, J. G. and Giarratano, P. J., Thermal Conductivity and Electrical Resistivity Standard Reference Materials: Tungsten SRM's 730 and 799, from 4 to

3000 K, Nat. Bur. Stand. Spec. Publ . No. 260-52, 37 pp. (Sep 1975)

PURPOSE

To compile, correlate, and analyze X and p data for arc cast and sintered W.

SPECIMEN

a) 0.51 to 1.27 cm dia./rods; c) W powder vacuum arc melted into billet, an- nealed at 1700 K for 1/2 h/billet machined into rod, acid etched and final

swage before anneal; d) < 99.956%; e) specimens 1-3 (RRR = 50, 75, 100 re- spectively); f) specimens 1-3 (p 0

= 0.97, 0.65. 0.49 nft.m respectively);

g) AFML arc cast density: (19.20 ± 0.05) g/cnr.

APPARATUS

a) longitudinal.

DATA

a) 4 to 3000 K; b) Tables 4, 5 - recommended values of p , X for AFML arc

cast and NBS sintered W, respecti vely ; c) uncertainty: in \ is 2.5% at

300 K, decreasing to 0.7% at 200 K, 0.7% from 200 to 50 K increasing inversely with temperature to 1.5% at 4 K; in p is 0.5%.

ANALYSIS

2

b) X = l/(c*T

n + sCyT) + AT/p [e'

01 T + Be

(6 2 /T) 2

J *

[16] Jun, C. K. and Hoch, M. , Thermal Conductivity of Tantalum, Tungsten,

Rhenium, Ta-lOW, Tin, ^222

»

W-25 Re in the Temperature Range 1500 to 2800 K,

Proceedings of the Sixth Thermal Conductivity Conference, 933-49 (Oct 19-21,

1966), Air Force Materials Lab., Wri ght-Patterson AFB, Ohio

PURPOSE

To report measurements on X for Ta, W, Re and Ta-lOW, T^, T222 anc* W-25

Re alloys.

SPECIMEN

a) specimens 1,2,3: 2.5339, 2.4785, 2.0801 cm dia., 0.2999, 0.2714,

0.2700 cm thick, respectively/disks; c) /specimen 2 machined from specimen 1, specimen 3 machined from specimen 2; d) 99.998%; g) source: Fansteel

Metallurgical Corp., density: specimens 1,2,3 = 18.89, 19.03, 19.23 g/cm3

, respecti vely.

APPARATUS

c) vacuum insulation.

DATA

a) specimen 1: 1513 to 1930 K, specimen 2: 1572 to 1905 K, specimen 3:

1836 to 2608 K; b) Table 7 - X.

246
[17] Kannuluik, W. G. , On the Thermal Conductivity of Some Metal Wires, Proc.

R. See. London, Ser. A, 131 , 320-35 (1931)

PURPOSE

To investigate x for metals and alloys by an electrical steady state method.

SPECIMEN

a) 0.1022 cm dia./wire; c) annealing - specimen 1: 220 °C, specimen 2:

1300 °C ; g) source: General Electric Co.

APPARATUS

a) direct electric heating; b) ice point, steambaths; c) 10" ^ mm of Hg

(10 -2 Pa) vacuum.

DATA

a) 273 to 286 K; b) Tables 4, 5 - x, L/L data from Table 5, X data points

listed in TPRC data series; c) uncertainty: ±2%.

ANALYSIS

a) results disagree with Weber, S. (1917), Barratt, Winter (1914).

[18] Kannuluik, W. G., Eddy, C. E., and Oddie, T. H., The Thermal and Electrical

Conductivities of Several Metals Between -18 °C and 100 °C, Proc. Roy. Soc.

London, Ser. A, 141, 159-68 (1933)

PURPOSE

To extend observations of \ for metals from -18 °C to 100 °C.

SPECIMEN

a) specimen 1 : 7.846 cm x 0.01053 cm2

, specimen 2: 7.940 cm

x 0.01022 cm 2 /rectangul ar , hexagonal bars respectively; b) single crystals; d) 0.001% Co, Cr, In and 0s, each; g) specimen 1: axis in [100] direction, specimen 2: axis in [111] direction.

APPARATUS

a) direct electrical heating; b) ice point, steambaths; c) 10‘ 4 mm of Hg

(10“ 2 Pa) vacuum.

DATA

a) 90.1 to 273 K; b) Table 2 - X, p/p data points from Table 2, X data

points listed in TPRC data series; d) correction for radiative heat loss.

ANALYSIS

a) results agree with Griineisen, E. and Goens, E. , Z. Phys., 44, 615 (1927).

247
[19] Langmuir, I. and Taylor, J. B. , The Heat Conductivity of Tungsten and the

Cooling Effects of Leads Upon Filaments at Low Temperatures , Phys. Rev., 50, 68-

87 (Jul 1, 1936)

PURPOSE

To obtain voltage and resistance measurements across a filament, thereby

calculating A and the temperature distribution along the wire.

SPECIMEN

a) specimens 1, 2, 3: 25.82, 12.86, 5.87 cm long respectively, all speci- mens 0.00499 cm dia. /wires; c) all tubes baked at 450 °C, filaments heated

to 2000 K for 2 min., 2400 K for 4 h and 2800 K for 30 s; d) thoriated W

fi 1 aments.

APPARATUS

a) direct electrical heating; b) N? bath; c) vacuum insulation.

DATA

a) 240 to 300 K; b) Table 8 - A/data points listed in TPRC data series.

ANALYSIS

a) results agree with Barratt, T. , Proc. Phys. Soc., London, 26, 347 (1914)

and Kannuluik, W. G. , Proc. Roy. Soc. London, Ser. A, 131 , 320 (1931) 141 , 159 (1933).

[20] Mendelssohn, K. and Rosenberg, H. M. , The Thermal Conductivity of Metals at

Low Temperatures. II. The Transition Elements, Proc. Phys. Soc., London, Sect. A,

65, 388-94 (1952)

PURPOSE

To measure A of transition elements at low temperatures.

SPECIMEN

a) 15 cm long; 1 to 2 mm dia. /rod; b) polycrystal 1 ine; c) annealed;

d) 99.99% W; g) source: Johnson, Matthey and Co.

APPARATUS

a) longitudinal; b) He gas thermometers.

DATA

a) 2 to 43 K; b) Fig. 2 - A/data taken from TPRC data series; c) uncer- tainty: ±3%.

ANALYSIS

a) results agree with Hu 1 in , J. K . , Proc. Roy. Soc. London, Ser. A, 204 , 98

(1950).

248
[21] Moore, J. P., Graves, R. S. , Fulkerson, W. , and McElroy, D. L. , The Thermal

Properties of Tungsten, Proceedings of the Fifth Thermal Conductivity Conference,

Univ. of Denver, Vol . 2, V-G-l - V-G-35 (1965)

PURPOSE

To present the temperature dependence of several physical properties of polycrystal 1 i ne tungsten.

SPECIMEN

a) 3 in. (7.6 cm) dia., 5/16 in. (0.79 cm) dia. hole/disk; c) /machined from

3.5 in. (8.9 cm) dia. pressed and sintered powder billet which had been hot

extruded at 1800 °C for 3 to 1 reduction; d) 99.98%; e) p^ nn /p d

= 35;

g) density: 19.077 g/cm^.

APPARATUS

a ) radial ; b) annealed Pt^^ Rh^ - Pt/cal ibrated at 3 standard melting points.

DATA

a) 323 to 1273 K; b) Table 2 - p, X; c) uncertainty: ±1.5% at 1000 °C.

ANALYSIS

a) results agree with Langmuir, I. and Taylor, J. B. , Phys. Rev. Z. , 50_, 68-

87 (1936) and Tye, R. P., Nb, Ta, Mo and W , A. G. Quarrel 1, Ed., Elsevier

Publishing Co., 169-79 (1961) between 300 and 600 K.

[22] Moore, J. P., McElroy, D. L. and Barisoni, M. , Thermal Conductivity Measurements Between 78 and 340 K on Aluminum, Iron, Platinum, and Tungsten, Proceedings

of the Sixth Thermal Conductivity Conference, Wri ght-Patterson AFB, Ohio, 737-78

(1966)

PURPOSE

To describe an apparatus which is capable of accurately measuring x, o, and S for metals between 78 and 340 K.

SPECIMEN

a) 5 to 8 cm long/rod; c) high purity: electron beam melted; d) 98%,

radial: 99.98% W; e) high purity (RRR > 400), radial (RRR = 31.4), 98% (RRR

= 4.11; f) radial (p 0

= 0.1593 yft*cm), 98% (p 0

= 1.560 yfi*cm); g) density

(g/cm3): high purity: 19.29, radial: 19.077, 98% = 19.19.

APPARATUS

a) longitudinal; b) chromel-P and constantan thermocoupl es/from calibrated

spools/thermocouples attached to specimen by discharge welding or epoxy,

leads thermally grounded to guard cylinder; c) guard cylinder, 5 x 10' mm of

Hg (7 x 10"5 pa) mm vacuum.

DATA

a) high purity: 80 to 300 K, radial: 100 to 300 K; b) Table 4 - p, x (smoothed values); c) uncertainty: ±1.8%.

249
[23] Osborn, R. H. , Thermal Conductivities of Tungsten and Molybdenum at Incandescent Temperatures , J. Opt. Soc. Am., _31 , 428 (1941)

PURPuot

To determine X of W, Mo in filament form.

SPECIMEN

a) (2.5 to 5.0) x 10" 3 rm dia./wire; c) annealed at 2700 K for 2 h.

APPARATUS

a) direct electrical heating; b) disappearing filament optical pyrometer;

c) vacuum sealed pyrex tube.

DATA

a) 1100 to 2000 K; b) Table 1 - X, Fig. 3 - p/data points listed in TPRC

data series.

ANALYSIS

a) results agree with Forsythe, W. E. , J. Opt. Soc. Am., 24, 114 (1934).

[24] Powell, R. L., Harden, J. L., and Gibson, E. F. , Low Temperature Transport

Properties of Commercial Metals and Alloys. IV. Reactor Grade Be, Mo, and W,

J. Appl. Phys., 31(7), 1221-4 (1960)

PURPOSE

To study the low temperature mechanical and transport properties of several

reactor materials.

SPECIMEN

a) 13 mm long; 3.67 mm dia./rod; d) 97.9%; f) p0

= 0.16 x 10"^ ft*m.

APPARATUS

a) longitudinal; b) Au-Co vs. Cu thermocouples; c) vacuum insulation.

DATA

a) 4 to 70 K; b) figure 1 - X, figure 2 - p, figure 3 - L; d) correction for

thermal contraction.

ANALYSIS

a) deNobel , J., Physica, 25, 261 ( 1957); 23, 349 (1957) values of Xg for

single crystal W are three times larger than these results and his values

below 20 K show no T

2 dependence as expected theoretically.

250
[25] Powell, R. W. and Tye, R. P. , New Measurements on Thermal Conductivity Ref- erence Materials, Int. J. Heat Transfer, _10_(5), 581-96 (1967)

PURPOSE

To provide further data on x and p of materials suggested for use as standard reference materials.

SPECIMEN

a) 10 cm long; 0.4 cm dia./rod; d) 99.99% W; e) RRR = 150; g) source:

Johnson Matthey and Co.

APPARATUS

a) longitudinal, ingot Fe standard used for energy outflow measurements.

DATA

a) run 1: 300 to 700 K, run 2: 450 to 760 K, run 3: 400 to 1000 K; b) figure 3, Table 6 (smoothed).

ANALYSIS

a) results agree with Laubitz, M. J., Can. J. Phys., 41 (1963) and Flynn,

D. R. and Robinson, H. E., private communication by Laubitz, M. J.

[26] Sharma, J. K. N. , Heat Conductivities Below 1 K I, Cryogenics, 7^(3), 141-56

(1967)

PURPOSE

To determine if the anomalies found in X below 1 K represent a general behavior of metals.

SPECIMEN

a) /wire; b) polycrystal 1 ine; g) p^/pj 5 Ltd.

= 30, source

:

Lamp and Metals

APPARATUS

a) longitudinal; b) carbon resi stors/cal ibrated against heat sink temperature for each run.

DATA

a) 0.5 to 1.0 K; b) figure 9 - X; c) uncertainty: ±2%; corrected for

thermomolecul ar pressure.

ANALYSIS

a) comparison with Davey, G. and Mendelssohn, K., Phys. Lett., _7» 183

(1963).
[26A] Taylor, R. E. , Thermal Properties of Tungsten SRM's 730 and 799. J. Heat

Transfer, 100(2), 330-3 (1978)

PURPOSE

To compare A results on sintered tungsten with previous results on arc-cast

tungsten.

SPECIMEN

a) SRM 730, 99.98%; b) sintered; c) RRR = 75, density: 19.23 +_ 0.05 g/cm®.

APPARATUS

a) longitudinal .

DATA

a) 1300 to 2600 K; b) Table 3 - A, p, L; c) corrected for thermal expansion;

f) uncertainty: +5% from 300 to 2000 K, +8% above 2000 K.

ANALYSIS

b) results lie between NBS, TPRC values;

d) A(w/m*K) = 0.144644 x 10"® T® + 0.08 from 1200 to 3000 K.

[27] Timrot, D. L. and Poletskii, E., Use of Heating by Electron Bombardment to

Investigate the Coefficient at Heat Conductivity in High Melting Point Alloys and

Compounds, High Temp. (USSR), 1_, 147 (1963)

PURPOSE

To study the thermophysical properties of solids at high temperatures.

SPECIMEN

a) /rod; d) 99.9+% W; g) 5 < length/dia. ratio < 6.

APPARATUS

a) electron bombardment; b) optical pyrometer; c) vacuum insulation.

DATA

a) 1200 to 3000 K; b) text (smoothed), figure 3 - A/data points listed in

TPRC data series; c) uncertainty: ±10%.

ANALYSIS

a) comparison with Powell, R. W. and Schofield, F. H. , Proc. Phys. Soc.,

London, 51^, 153 (1939); Worthing, A. G. , Phys. Rev., 4- , 6 (1914); Osborn,

R. H. , J. Opt. Soc. Am., _3I> 428 (1941); Gumenyuk, V. S. and Lebedev, V. V.,

Fiz. Met. Metal 1 oved. , _U, 1 (1961).

252
[27A] Touloukian, Y. S. , Powell, R. W. , Ho, C. Y. , and Klemens, P. G. , Thermophysical Properties of Matter, Volume 1: Thermal Conductivity, Metallic Elements

and Alloys, 68-81 (1970)

PURPOSE

To provide an extensive list of data for x of the metallic elements and

al 1 oys.

SPECIMEN

d) 99.99+%; f) p0

= 1.70 x 10" 9 n*cm.

APPARATUS

a) not given.

DATA

a ) 0 to 8500 K; b) Figure and Table 63R - X, recommended values; c) uncer- tainty: ±3% near room temperature, ±3 to 8% at other temperatures ; e) the

values below 1.5 Tm are calculated to fit the experimental data by using n = 2.40, a' = 2.06 x 10" 5

, and 3 = 0.0696.

[28] Trodahl , H. J., The Thermopower of Pure Tungsten Below 9 K, J. Phys. F, 3 , 1972-6 (1973)

PURPOSE

To make measurements of S on a pure W crystal in order to identify electronelectron scattering effects.

SPECIMEN

a) 3 cm long; 3 mm dia./rod; b) single crystal; e) RRR = 16300; g) [110]

axis along geometric axis, supplied by Materials Research Corp.

APPARATUS

a) longitudinal; b) matched Ge thermometers

.

DATA

a) 0 to 9 K; b) figure 1 - X.

ANALYSIS

a) comparison with Wagner, D. K. , Garland, J. C. and Bowers, R. , Phys.

Rev. B, 3, 3141 (1971), and White, G. K. and Woods, S. B., Can. J. Phys.,

35, 656 11957).

253
[29] Van Witzenburg, W. and Laubitz, M. J., Magnetoresistances and the Phonon

Conductivity of Metals, Can. J. Phys. , 46(17) , 1887-94 (1968)

PURPOSE

To measure the magnetoresi stances of Cu, Ag, Au, and W.

SPECIMEN

a) 1.6 mm dia./wire; b) annealed in vacuum at 1620 K for 2 h; d) 99.95% W;

e) RRR = 46.6; f) p0

= 0.11 y£2*cm; g) source: United Min. Chem. Corp.

APPARATUS

a) longitudinal ; b) Pt resistance thermometers ; c) radiation shield.

DATA

a) 80 to 150 K; b) Table 4 - X; c) uncertainty: ±3%; d) correction applied

to temperature derived from Pt thermometers.

ANALYSIS

a) compared with Fulkerson, W. , private communication (1968); b) concludes

that lattice conductivity accounts for 40% at x for the temperature range

i nvestigated.

[30] Wagner, D. K. , Lattice Thermal Conductivity and High-Field Electrical and

Thermal Magnetoconductivities of Tungsten, Phys. Rev. B, 5^, 3.36-47 (1972)

PURPOSE

To investigate the temperature dependence of and x for W in a strong magnetic field to provide further information about low temperature scattering

mechani sms.

SPECIMEN

c) specimen spark cut from zone-refined crystal; e) original crystal:

p 2 gg/p 0 63000; g) rod axis parallel to [110] direction.

APPARATUS

a) longitudinal , H oriented normal to rod axis along [001] direction;

b) matched carbon resi stors/cal ibrated against stardard Ge resistance thermometer; c) adsorbent, vacuum insulation.

DATA

a) 1.8 to 6.5 K; b) figures 1,2 - H

2 /pxx, H^/WxxT respectively/p, H (kG)

for runs 7-13 = 2.66, 5.32, 7.98, 10.6, 13.3, 16.0, 18.6.

ANALYSIS

a) results agree with Long, J. R. , Phys. Rev. B, 3 > 2476 (1971).

254
[31] Wagner, D. K. , Garland, J. C. , and Bowers, R. , Low Temperature Electrical

and Thermal Resistivities of Tungsten, Phys. Rev. B, 3 , 3141 (1971)

PURPOSE

To study the temperature dependence of p and WT in a number of high purity

W single crystals.

SPECIMEN

a) W-3 , W-5 , W-8: 1.5 mm dia., W-4: 1.0 mm dia., W-7: 3.0 mm dia. /rods;

b) single crystals; c) electron beam zone melted; f) p0 (W-3) = 1.231

x 10”^ ft*cm, p 0 (W-4) = 1.780 x.10"^ fl*cm, p 0

( W-5 ) = 5.724

x 10" 10 ft*cm, pp

(W-7) = 0.566 x 10"10 ft. cm, p 0 (W-8) = 0.695

x 10"10 ft*cm; g) all oriented to [110].

APPARATUS

a) longitudinal ; b) carbon resistance thermometers/cal i brated against standard Ge resistance thermometer; c) adsorbent, vacuum insulation.

DATA

a) 0 to 6 K/< 30 mK; b) figure 3 - (WT-p0 /L0 ), figure 2 - (p-p0 ) ; c) uncertainty: ±1% for 1.5 mm dia., ±8% for 3.0 mm dia.

ANALYSIS

a) L results agree with Bennett, A. J. and Rice, M. J., Phys. Rev., 185 , 968

(1969) and Rice, M. J., Phys. Rev. Lett.,^0, 1439 (1968), but are significantly below Herring, C.

[32] Wheeler, M. J., Thermal Diffusivity at Incandescent Temperatures by a Modulated Electron Beam Technique, Br. J. Appl . Phys., _16, 365 (1965)

PURPOSE

To assess the performance of an apparatus by means of measuring K and A of

Pt, Ta, Mo, W.

SPECIMEN

a) 1.5 mm thick/disk; c) /cut from swaged rod; d) 99.5% W; g) source: General Electric Co., Osram Lamp Works.

APPARATUS

a) periodic heat flow; b) optical pyrometer; c) vacuum insulation.

DATA

a) 1200 to 3000 K; b) Fig. 10/data points listed in TPRC data series; c) un- certainty: ±5%; d) corrected for losses in viewing window of pyrometer,

spectral emissivity of specimen.

ANALYSIS

a) A results agree with Vines, R. F. (1941), Malter, L. and Langmuir, D. B. , Phys. Rev., .55, 745 (1939), Worthing, A. G., Phys. Rev., 28, 190 (1926), and

Worthing, A. G. and Forsythe, W. E. , Astrophys. J., 61_, 147 (1925).

255
[33] White, G. K. and Woods, S. B., Low Temperature Resistivity of the Transition Elements: Cobalt, Tungsten, and Rhenium, Can. J. Phys., 315, 656 ( 1957)

PURPOSE

To report experimental values of p and W for Co, W, Rh.

SPECIMEN

a) Wlb: 4 mm dia./rod; c) annealed at 1350 °C for several hours in vacuum,

then kept at 600 °C for several more hours.; d) 0.01% Mo, traces Fe, SI, Cu

;

f) p 0

= 3.15 x 10"° ft*cm; g) source: Johnson, Matthey and Co.

APPARATUS

a) longitudinal; b) He gas thermometers ; c) radiation shield, thermometers

Au plated to reduce radiation transfer.

DATA

a) 2 to 127 K; b) figure 2 - A/data listed in TPRC data series; c) uncer- tainty: ±1%.

ANALYSIS

a) comparison with Rosenberg, H. M. , Philos. Trans. Roy. Soc. London, 247 , 441 (1955), DeHaas, W. J., and deNobel , J., Physica,J5, 449 (1938), and

Kannaluik, W. G. , Proc. Roy. Soc. London, Ser. A, 141 , 159 (1933).

256
U.S. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report No. 3. Publ icacion Date BIBLIOGRAPHIC DATA

SHEET (See instructions)

REPORT NO. NBSIR 84-3007 June 1984

4. TITLE AND SUBTITLE

THERMAL CONDUCTIVITY OF ALUMINUM, COPPER, IRON, AND TUNGSTEN FOR TEMPERATURES FROM

1 K TO THE MELTING POINT

5. AUTHOR(S)

J. G. Hust and A. B. Lankford

6. PERFORMING ORGANIZATION (If joint or other than NBS, see in struction s) 7. Contract/Grant No. national bureau of standards

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

10.

SUPPLEMENTARY NOTES

^ Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. I f document includes a significant

bibliography or literature survey, mention it here)

Literature data on the thermal conductivity of commercially pure aluminum,

copper, iron, and tungsten specimens have been collected, coded, critically

analyzed, and correlated with analytical techniques based on theoretical and

empirical equations. The resulting functions are presented and used to generate

tables and graphs of thermal conductivity as a function of temperature and

residual resistivity ratio (RRR). An annotated bibliography of references is

included. Discussions are included on the variations in thermal conductivity

caused by chemical impurities, physical defects, size effects, and magnetic

fields. Smoothed values are presented for temperatures from 1 K to near the

melting point and for a large range of RRR values.

12.

KEY WORDS ( Six to twelve entries; alphabetical order; capitalize on!y proper names; and separate key * or cs aluminum; copper; electrical resistivity; iron; Lorenz ratio; residual resistivity

ratio; thermal conductivity; tungsten

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u nlimited

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