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UNITED STATES DEPARTMENT OF COMMERCE

Alexander B. Trowbridge, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Thermal Conductivity of

Selected Materials

Part 2

C. Y. Ho,* R. W. Powell,* fC and P. E. Liley'

*This report was prepared under contract at the

Thermophysical Properties Research Center

Purdue University, 2595 Yeager Road

West Lafayette, Indiana 47906

NSRDS-NBS 16

National Standard Reference Data SeriesNational Bureau of Standards—16

(Category 5—Thermodynamic and Transport Properties)

Issued February 1968

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 - Price $2
National Bureau of Standards

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Foreword

The National Standard Reference Data System is a government-wide effort to give to the

technical community of the United States optimum access to the quantitative data of physical

science, critically evaluated and compiled for convenience. This program was established in

1963 by the President’s Office of Science and Technology, acting upon the recommendation of

the Federal Council for Science and Technology. The National Bureau of Standards has been

assigned responsibility for administering the effort. The general objective of the System is to

coordinate and integrate existing data evaluation and compilation activities into a systematic,

comprehensive program, supplementing and expanding technical coverage when necessary,

establishing and maintaining standards for the output of the participating groups, and

providing mechanisms for the dissemination of the output as required.

The NSRDS is conducted as a decentralized operation of nation-wide scope with central

coordination by NBS. It comprises a complex of data centers and other activities, carried on

in government agencies, academic institutions, and nongovernmental laboratories. The independent operational status of existing critical data projects is maintained and encouraged.

Data centers that are components of the NSRDS produce compilations of critically evaluated

data, critical reviews of the state of quantitative knowledge in specialized areas, and

computations of useful functions derived from standard reference data. ' For operational purposes, NSRDS compilation activities are organized into seven

categories as listed below. The data publications of the NSRDS, which may consist of

monographs, looseleaf sheets, computer tapes, or any other useful product, will be classified as belonging to one or another of these categories. An additional “General” category of

NSRDS publications will include reports on detailed classification schemes, lists of compilations considered to be Standard Reference Data, status reports, and similar material. Thus,

NSRDS publications will appear in the following eight categories:

Category

12

3

4

5

6

7

8

Title

General

Nuclear Properties

Atomic and Molecular Properties

Solid State Properties

Thermodynamic and Transport Properties

Chemical Kinetics

Colloid and Surface Properties

Mechanical Properties of Materials

The present compilation is in category 5 of the above list. It constitutes the sixteenth

publication in a new NBS series known as the National Standard Reference Data Series.

A. V. Astin, Director.

in
PREFACE

This report was prepared under contract by the Thermophysical Properties Research Center (TPRC) of

Purdue University and forms a continuation of the work described in the first report NSRDS-NBS-8.

The work presented in this report comprises the critical evaluation, analysis, and synthesis of the available

thermal conductivity data and the generation of recommended values for twelve metallic elements, mainly for the

solid state, for a range of graphites, and for three fluids in the gaseous state. These are cadmium, chromium,

lead, magnesium, molybdenum, nickel, niobium, tantalum, tin, titanium, zinc, zirconium, Acheson graphite, ATJ

graphite, pyrolytic graphite, 875S graphite, 890S graphite, acetone, ammonia, and methane. For each of the materials recommended values are given over a wide range of temperature.

The senior staff engaged in this program consisted of the same personnel as for the first report. Dr. C. Y. Ho and Dr. R. W. Powell collaborated on the sections comprising the metallic elements and graphites and Dr.

P. E. Liley was responsible for the section on fluids. Dr. Y. S. Touloukian has served as adviser to the program.

The cooperation and assistance received from other TPRC staff is gratefully acknowledged.

This effort will continue into the third year, when it is hoped to complete the assessment of the data that are

available for the thermal conductivity for all elements and to include recommended values wherever possible.

In order to give a greater degree of confidence to the recommendations set forth in this work, following the same procedure as that for the first report, a preliminary version of the present report has been submitted internationally to some sixty expert workers in this field for their comments and criticisms. The authors wish to express their appreciation and gratitude to all who responded so generously. Particular acknowledgment is made

for the valuable contributions of the following individuals:

Prof. N. G. Backlund, The Royal Institute of Technology, Stockholm, Sweden,

Drs. B. L. Bailey and A. A. Cline, Great Lakes Carbon Corporation, Niagara Falls, New York,

Prof. C. F. Bonilla, Columbia University, New York, New York,

Dr. A. Cezairliyan, National Bureau of Standards, Washington, D. C.

,

Prof. E. Fitzer, Direktor der Institut fur Chemische Technik der Technischen Hochschule Karlsruhe, Karlsruhe,

W. Germany,

Mr. D. R. Flynn, National Bureau of Standards, Washington, D. C.

,

Prof. P. Grassmann, Eidg. Technische Hochschule Institut fiir Kalorische Apparate, Kaltetechnik und

Verfahrenstechnik, Zurich, Switzerland,

Prof. R. A. Greenhorn, Purdue University, W. Lafayette, Indiana,

Prof. M. Hoch, University of Cincinnati, Cincinnati, Ohio, Dr. D. T. Jamieson, National Engineering Laboratory, East Kilbride, Scotland, Dr. J. Kaspar, Aerospace Corporation, El Segundo, California,

Prof. J. Kestin, Brown University, Providence, Rhode Island,

Dr. C. A. Klein, Raytheon Company, Waltham, Massachusetts,

Dr. P. G. Klemens, Westinghouse Research Laboratories, Pittsburgh, Pennsylvania,

Dr. M. J. Laubitz, National Research Council, Ottawa, Canada,

Dr. W. W. Lozier, Carbon Products Division, Union Carbide Corporation, Cleveland, Ohio,

Mr. J. D. McClelland, Aerospace Corporation, El Segundo, California,

Dr. D. L. McElroy, Oak Ridge National Laboratory, Oak Ridge, Tennessee,

Dr. E. McLaughlin, Imperial College, London, England,

Prof. T. Makita, Kobe University, Kobe, Japan,

Mr. I. B. Mason, Atomic Energy Research Establishment, Harwell, England,

Mr. R. A. Meyer, General Atomics, San Diego, California, Dr. M. L. Minges, Air Force Materials Laboratory, Wright-Patterson A. F. Base, Ohio,

Prof. A. Missenard, Saint -Quentin, France,

Mr. C. D. Pears, Southern Research Institute, Birmingham, Alabama,

IV
Dr. R. L. Powell, National Bureau of Standards, Boulder, Colorado,

Dr. F. Richter, Thyssen Rohrenwerke Aktiengesellschaft, Dusseldorf, W. Germany,

Prof. B. H. Sage, California Institute of Technology, Pasadena, California, Dr. E. I. Shobert, Stackpole Carbon Company, St. Marys, Pennsylvania,

Prof. A. E. Sheindlin, Director of Scientific Research Institute of High Temperature, Moscow, U. S. S. R. , Dr. G. A. Slack, General Electric Research Laboratory, Schenectady, New York,

Mr. L. M. Swope, Chairman of ASTM Committee C-5 on Manufactured Carbon and Graphite Products, Aerojet

General Corporation. Sacramento, California, Dr. F. L. Shea, Great Lakes Research Corporation, Elizabethton, Tennessee,

Prof. N. B. Vargaftik, Moskovskii Aviatsionnyi Institut, Moscow, U. S. S. R.

It goes without saying that while the individuals mentioned above have read selected parts of the preliminary

version of this report and given helpful comments and criticisms, this in no way commits them to the views ex- pressed in this report for which the authors assume complete responsibility.

v
C ONTENTS

Page

FOREWORD iii PREFACE iv LIST OF FIGURES vii LIST OF TABLES viii ABSTRACT AND KEY WORDS ix

PART I - THERMAL CONDUCTIVITY OF METALLIC ELEMENTS 1

A. INTRODUCTION 2

B. THERMAL CONDUCTIVITY OF A GROUP OF

SELECTED METALLIC ELEMENTS 3

C. REFERENCES 77

PART II - THERMAL CONDUCTIVITY OF GRAPHITES 81

A. INTRODUCTION 82

B. THERMAL CONDUCTIVITY OF A GROUP OF

SELECTED GRAPHITES 88

C. REFERENCES 134

PART HI - THERMAL CONDUCTIVITY OF GASES 137

A. INTRODUCTION 138

B. THERMAL CONDUCTIVITY OF A GROUP OF

SELECTED GASES 138

vi
LIST OF FIGURES

Figure Page

1. Recommended Thermal Conductivity of Metallic Elements 17

2. Recommended Thermal Conductivity of Metallic Elements 18

3. Thermal Conductivity of Cadmium 22

4. Thermal Conductivity of Chromium 25

5. Thermal Conductivity of Lead 27

6. Thermal Conductivity of Magnesium 36

7. Thermal Conductivity of Molybdenum 39

8. Thermal Conductivity of Nickel 43

9. Thermal Conductivity of Niobium 48

10. Thermal Conductivity of Tantalum 53

11. Thermal Conductivity of Tin 57

12. Thermal Conductivity of Titanium 67

13. Thermal Conductivity of Zinc 69

14. Thermal Conductivity of Zirconium 74

15. Thermal Conductivity of Graphites 93

16. Recommended Thermal Conductivity of Graphites 125

17. Recommended Thermal Conductivity of Graphites 126

18. Thermal Conductivity of Acheson Graphite 129

19. Thermal Conductivity of ATJ Graphite 130

20. Thermal Conductivity of Pyrolytic Graphite 131

21. Thermal Conductivity of 875S Graphite 132

22. Thermal Conductivity of 890S Graphite 133

23. Departure Plot for Thermal Conductivity of Gaseous Acetone .... 141

24. Departure Plot for Thermal Conductivity of Gaseous Ammonia . . . 143

25. Departure Plot for Thermal Conductivity of Gaseous Methane . . . 145-146

vii
LIST OF TABLES

Table Page

1. Derived Values of /3 and Associated Constants and Parameters for

High-Purity Metallic Elements 16

2a. Recommended Thermal Conductivity of Metallic Elements at Low Temperatures (T in deg. K) 19

2b. Recommended Thermal Conductivity of Metallic Elements at Moderate and High Temperatures (T in deg. K) 20

2c. Recommended Thermal Conductivity of Metallic Elements at Moderate and High Temperatures (T in deg. C) 21

3. Specifications of the Specimens of Cadmium 23-24

4. Specifications of the Specimens of Chromium 26

5. Specifications of the Specimens of Lead 28-35

6. Specifications of the Specimens of Magnesium 37-38

7. Specifications of the Specimens of Molybdenum 40-42

8. Specifications of the Specimens of Nickel 44-47

9. Specifications of the Specimens of Niobium 49-52

10. Specifications of the Specimens of Tantalum 54-56

11. Specifications of the Specimens of Tin 58-66

12. Specifications of the Specimens of Titanium 68

13. Specifications of the Specimens of Zinc 70-73

14. Specifications of the Specimens of Zirconium 75-76

15. Specifications of the Specimens of Graphites 94-124

16a. Recommended Thermal Conductivity of Graphites (T in deg. K) . . 127

16b. Recommended Thermal Conductivity of Graphites (T in deg. C) . . 128

17. Thermal Conductivity of Gaseous Acetone 140

18. Thermal Conductivity of Gaseous Ammonia 142

19. Thermal Conductivity of Gaseous Methane 144
THERMAL CONDUCTIVITY OF

SELECTED MATERIALS

By

C. Y. Ho, R. W. Powell, and P. E. Liley

ABSTRACT

The work presented in this report comprises the critical evaluation, analysis, and synthesis of the

available thermal conductivity data and the generation of recommended values for twelve metallic elements, mainly

for the solid state, for a range of graphites, and for three fluids in the gaseous state. These are cadmium, chromium, lead, magnesium, molybdenum, nickel, niobium, tantalum, tin, titanium, zinc, zirconium, Acheson

graphite, ATJ graphite, pyrolytic graphite, 875S graphite, 890S graphite, acetone, ammonia, and methane. For

each of the materials recommended values are given over a wide range of temperature.

KEY WORDS

Thermal Conductivity

Metallic Elements

Metals

Graphites

Gases

Critical Evaluation

Recommended Values

Standard Reference Data

IX
.
PART I

THERMAL CONDUCTIVITY OF METALLIC ELEMENTS

1
PART I - THERMAL CONDUCTIVITY OF METALLIC ELEMENTS

A . Introduction

The metallic elements studied in this report consist of cadmium (solid and liquid states), chromium, lead

(solid and liquid states), magnesium (solid and liquid states), molybdenum, nickel, niobium, tantalum, tin (solid

and liquid states), titanium, zinc (solid and liquid states), and zirconium. Whereas the seven metallic elements

of the first report that were studied in the solid state have cubic crystal structures, of those now considered, only

chromium, lead, molybdenum, nickel, niobium, and tantalum have this symmetrical structure. The others can be expected to yield thermal conductivity values that are dependent on the crystal orientation and which may differ

for polycrystalline and single crystal samples. For non-cubic metals the recommended values are mainly for

randomly oriented polycrystalline samples of each metal, but whenever sufficient data are available for the main

crystal directions of single crystals, the thermal conductivities for these directions will also be given.

The general method of procedure has followed closely that adopted in the first report [l] . * The Thermophysical Properties Research Center (TPRC) data sheets for each material have been thoroughly updated, the

original papers have been critically re-examined and more complete specification tables have been prepared.

The method previously adopted for dealing with the thermal conductivity data for metallic elements at low

temperatures has again been followed [2-4]. For each metallic element the experimental curve yielding the highest thermal conductivity values in the region of the maximum has been accepted as representative of the values

for the sample of the highest purity so far examined. From these data a value of 0 , the impurity-imperfection

parameter, has been derived, as indicated previously, and this has been used to calculate thermal conductivity

values from 1 K to about 1. 5 Tm, where Tm is the temperature corresponding to the thermal conductivity maximum, by using the equation

k = lv'Tn

+ 0/T] _1

where

Oi' = O'" (0/Wi")

a'^ m + ^ (2)

Here a, m, n, and a" are constants for a metal whereas Oi' and 0 are dependent on the purity and perfection.

Theoretically,

j8 = Pfl /L0 (3) where p^

is the residual electrical resistivity and L0 is the theoretical value of the Lorenz function and equal to 2.443 x 10 -8 Volt2 T

-2

. Using the theoretical relationship as given by Equation (3), Equations (l) and (2) can be

written as

k = [a'Tn

+ p0 /L0 T]

-1 (4)

Oi' = Oi"(pJna"L0 ) a// ' m +

(5)

Equations (4) and (5) give explicitly the relationship between the thermal conductivity and the residual electrical

resistivity of a metallic element, though their application is more limited than Equations (l) and (2) due to the

limited applicability of Equation (3). As explained before, the thermal conductivity in this range of temperature is particularly sensitive to the

degree of purity and perfection of the sample, since 0 decreases as the purity and perfection increase. The

values that have been used for 0 in each instance are given in Table 1 together with the associated constants and

parameters. Due to the insufficiency of available low -temperature thermal conductivity data for these metallic

References appear under the heading REFERENCES.

2
elements it is hardly possible to determine the constants a,m,ando!" of Equation (2), and therefore only the values

of n and o?' of Equation (l) are determined from the available data. Here the values for a' are the average values,

and actually oc' varies from sample to sample and is a function of 0 depending upon sample purity and perfection. It can be seen in Table 1 that the values of 0 of column 9, derived from thermal conductivity data and used for subsequent calculations of the recommended values, are comparable with those of column 8 derived for the same sample from residual electrical resistivity measurements whenever available using Equation (3). For the latter o4> 2k

has been used as approximating to P()

. The values of the electrical resistivity ratio P295 ^/P4 2 Kc °lumn 6 relate

to the purest samples for which low-temperature thermal conductivity measurements have been reported, whereas

the values of this ratio given in the last column of Table 1 are the highest that have been reported so far. Comparison of the values in these two columns reveals large differences for most of the metallic elements. This indicates

that the much purer samples now becoming available will possess correspondingly lower values of 8 and higher

thermal conductivities. It is clear that in the low temperature region most of the thermal conductivity values now

given will need to be increased subsequently.

The recommended thermal conductivity values are reported collectively in Tables 2a, 2b, and 2c and plotted

in Figures 1 and 2. These recommended values are for fully annealed high-purity metals with purity and residual

electrical resistivity indicated in the Tables. The residual electrical resistivity characterization is very important

only at low temperatures below 100 K and is therefore not given in Tables 2b and 2c. Table 2a contains the recommended

values at temperatures below 100 K and Tables 2b and 2c contain those above 100 K. The temperatures given in Tables 2a

and 2b are in degree K and those in Table 2 c are in degree C. In the tables the third significant figure is given only for

internal comparison and for smoothness and is not indicative of the degree of accuracy.

In Figure 1 the thermal conductivity curves that are repi’oduced for those metallic elements that become superconducting above 1 K include values that have been obtained for both normal and superconducting states . The recommended values are, however, limited at present to the normal state of each metallic element. With lead and tin, since Tm is below the transition temperature at which the metal normally becomes superconducting, it is possible to determine Tm by

using measurements made in the presence of a magnetic field of sufficient strength for the sample to remain in the

normal state.

In order to make recommendations at higher temperatures the available experimental information for the thermal

conductivity of each metallic element has been plotted on a linear temperature scale as shown in Figures 3 to 14 . These

curves have been carefully examined in the light ofthe information given in the accompanying specification tables and from

other considerations. In the specification tables, the code designations used for the experimental methods are as follows:

C Comparative method

E Electrical method

F Forbes bar method

L Longitudinal heat flow method

P Periodic or transient heat flow method

R Radial heat flow method

T Thermoelectrical method

An attempt has been made in each figure to include a curve that seems likely to prove the most probable for each

metallic element and this is drawn to form a smooth continuation of the above mentioned low -temperature curve. Use is made of electrical resistivity (or conductivity) data whenever possible and this information and other pertinent comments regarding the treatment of the data for each metallic element are given in the following section.

B. Thermal Conductivity of a Group of Selected Metallic Elements

Cadmium

Four curves are available for the thermal conductivity of cadmium at low temperatures. That giving the

highest thermal conductivity is by Rosenberg [5] for a single crystal of 99. 995 percent Cd with the direction of heat flow inclined at 79 degrees to the hexagonal axis of the crystal. Only this one crystal direction

3
appears to have been investigated, but Mendelssohn and Rosenberg [6] obtained values for a cast polycrystalline

sample that was stated to be of 99.9999 percent purity. These values are so very much lower, that, if the purity

is as stated either the thermal conductivity of cadmium in the region of the maximum and below is very strongly

dependent on the crystal orientation, or the purer of these samples must be unannealed and in a highly strained

condition; alternatively this sample is less pure than stated.

The two curves published by Zavaritskii [7] relate mainly to the superconducting state, but do include a few values for the normal state. These are for two single crystals that appear to be of the same material but with

the heat flow direction respectively perpendicular and parallel to the hexagonal axis. At the transition temperature

(0.53 K given by Zavaritskii) these results indicate the thermal conductivity ratio k

± /k/7 to be 1.31. Zavaritskii's

paper contains a thermal conductivity value at this temperature for one other sample. This was also for the perpendicular direction and the value is about three times that of the plotted curve and is comparable with the higher curve of Rosenberg. This last value has been used for the derivation of /3 and the calculation of the low-temperature curve for cadmium in the normal state and to about 1. 5 Tm. Since this is for a sample that tends to approximate to the higher perpendicular direction, cori’esponding values have also been derived for the parallel direction

and for polycrystalline cadmium, assuming k

x /k =1.31 at 0. 53 K.

Further measurements are required in this temperature range, and the present values can only be re- garded as tentative.

At higher temperatures, Goens and Griineisen [8] give values in fair agreement for two single crystals

(curves 13 and 14) approximating to the perpendicular direction and for one (curve 12) approximating to the

parallel direction. These results indicate that over the range 21 to 293 K k^ /k

/7 increases from about 1.12 to about 1.25. It seems reasonable to raise the k^ value at 21 K to give the same ratio of 1.25, particularly as it then lies close to Rosenberg's curve.

The recommended low temperature curves have been smoothly extended to higher temperatures. That for the perpendicular direction at first approximates to curve 8, and then follows Goens and ©runei sen's derived

values for k to about 300 K. The curve for the parallel direction is derived from this on the basis of k

/7 = k^A.25

and for polycrystalline cadmium by assuming k = 1/3 (2k^ + k ). It is noted that on account of the effect of anisotropy the thermal conductivity of cadmium single crystals (and other single crystals of non-cubic crystal structure)

with different impurities will form many families of curves (instead of- one single family of curves). Each family

of curves corresponds to each crystal orientation. Within one family of curves (with the same orientation but with

different impurity) the curves are non-crossing whilst curves of different families might cross one another at temperatures above Tm.

Further extrapolation of these curves to the melting point is believed to be justified. Most of the available

data in this temperature range conform with these recommendations to within 5 percent. Only determinations by

Mikryukov and Rabotnov [9] for a single crystal and by Mikryukov, Tyapunina, and Cherpakov [10] for a polycrystalline sample at temperatures below 400 K seem noticeably high.

It is of interest that several workers who had included electrical resistivity measurements had obtained

Lorenz functions that agree to within a few percent with the theoretical value at temperatures near normal.

For liquid cadmium the only available thermal conductivity data are those of Brown [ 1 1 ] . Unfortunately

Brown's values for the solid state are seen to differ from most others in having a positive rather than a slight

negative coefficient. He made no electrical resistivity measurements, but when his data for the liquid phase are used with the electrical resistivity values of Matuyama [ 12] for temperatures near the melting point and 100 I< above, the resulting Lorenz functions are 2.50 x 10~a and 2.34 x 10~8 V2 K“2

, which seem reasonably acceptable.

Furthermore, use of these resistivity values in the equation proposed by Powell / 1 3 ] for liquid metals

Cadmium becomes electrically superconducting at and below 0. 53 K (more recent value given as 0.56 K). The

thermal conductivity of the superconducting state is not treated here.

4
k = 2. 32 x 10 -8 Tp -1 + 0.012 (6)

yields values for k that are only some 4 percent greater than those obtained by Brown. The recommended curve

has been drawn through the mean of his data. At the melting point the ratio of the recommended thermal conductivity values for the solid state k , kp0]y CIyS _ , k

f/ to that for the liquid state are, respectively, 2. 26,2.1, andl.8.

The recommended values are thought to be accurate to within ±4 percent of the true values at moderate temperatures, ±6 percent at high temperatures, ±10 percent for molten cadmium, and ±15 percent at low temperatures.

Chromium

Only two groups of workers, Lucks and Deem [l4]and Powell and Tye [15] have measured the thermal conductivity of chromium to temperatures appreciably above normal. The investigation of Powell and Tye was of

interest in that they commenced with an electrolytically deposited tube of the metal and followed the changes

brought about by heating to successively higher temperatures. After their final heating to 1410 C the thermal conductivity at 50 C was 3.66 times the initial value, and the density had increased from 6.975 to 7.15 g cm-3

. At

470 K the value of Lucks and Deem for a chemically pure ductile chromium is greater by 1.7 percent, at 1000 K,

the region of greatest difference, by 11 percent, and at 1270 K by 5 percent. In view of this good agreement for

two quite independent determinations, the most probable curve from 470 to 720 K has been drawn as a smooth curve

through the points of Lucks and Deem and from 720 to 1270 K through the mean values of Lucks and Deem and

Powell and Tye. This curve has been extended to both higher and lower temperatures and at temperatures of 320

and 345 K it passes two of the points obtained by McElroy et al. [16] . Just below, at 311 K, is the Neel temperature, where these workers found signs of an upward turn and promised further confirmatory measurements in this region.

The foregoing completes the information available for relatively pure chromium above the Neel temperature.

Whilst at the moment the agreement appears very good, this is for only two samples, so may be somewhat fortuitous, particularly as large values of the Lorenz function are indicated. The Lorenz function of Powell and Tye fell from 3.75 x 10

8 to 3.15 x 10 _8V2 K

_2 over the range 323 to 1273 K, indicating about one third of the heat conduction

at the lower temperature to be by phonons. With two different conducting mechanisms present in fairly comparable

proportions and with a Neel temperature included it is conceivable that the thermal conductivity may not be a simple function of chemical purity or temperature and that the cuiwe for a high-purity chromium may differ from

that now proposed.

At low temperatures, # has been derived from the experimental data of Harper, Kemp, Klemens, Tainsh,

and White [ 1 7] for a 99. 998 percent chromium with a residual electrical resistivity p(| = 0. 55 x 10 -7 ohm cm. This

yields a Tm of 23 K and the calculated curve in this instance agrees reasonably well with the experimental one up

to about 55 K. From 55 K to 311 K the curve has been continued smoothly through the uppermost values of Harper

et al. to 150 K and on for another 150 K or so for which no measurements have yet been made. The slope of the

recommended curve changes abruptly at the Neel point.

The properties of chromium in the normal temperature region could also be influenced under some conditions by a change of phase. At temperatures below 299 K it has been found possible to electrolytically deposited

chromium having the close-packed hexagonal structure [ 1 8 , 19]. The stable cubic form, to which the above

thermal conductivity curve applies, is obtained on heating. Chromium is certainly a metal for which measurements

on a further range of specimens would be of interest from about 100 K and upwards.

IVith the forgoing reservations, the recommended values are thought to be accurate to within ±3 percent of the true values at moderate temperatures, ±5 percent at temperatures below 40 K, and ±10 percent in the ranges

40 to 200 K and above 700 K.

Lead

There are 142 curves available for the thermal conductivity of lead.

5
In the low temperature region, curve 56 of Wolff [20] for an annealed pure single crystal enriched with

lead isotopes is the highest. The recommended values below 3 K were obtained by calculation using a value of j8 derived from this curve. From 3 to 7 K the recommended curve follows closely curve 56 and from 7 to 35 K lies close to curves 17 and 6. The former is by Mendelssohn and Rosenberg [6] for a 99. 998 percent pure single

crystal and the latter by DeHaas and Rademakers [21] for a high-purity single crystal.

At normal and higher temperatures the thermal conductivity of lead is of particular interest owing to its early use by Shelton and Swanger [22] (the same results were later published by Van Dusen and Shelton [23]). The

sample used was the NBS melting-point lead as available in the 1930's, having a freezing point of 327.4 C. *

The most recent publication on the thermal conductivity of lead is by Lucks [24] . He used a similar

comparative method to that just mentioned but with Armco iron as the standard material. It was Lucks who had

organized a round-robin investigation of the thermal conductivity of this same stock of Armco iron and he used the

mean values as reported by four other measuring laboratories. He has studied two NBS Pyrometric Standard

lead samples, one of their most recent, with a freezing point of 327. 417 C and an earlier grade with a freezing

point of 327. 31 C. The tabulated smooth values of Lucks and those of Van Dusen and Shelton agreed exactly over

the common range of 50 to 150 C for their two samples, and extrapolation leads to complete agreement from 0 to 300 C. For the purer sample, Lucks' value at 50 C is greater by about 1. 8 percent, and at 150 C by about 4.3

percent, whilst at 300 C the extrapolated difference is nearly 9 percent.

Lucks concludes "These data are believed significant and indicate the data of Van Dusen and Shelton should

not be used for NBS Pyrometric Standard lead having a freezing point 0. 1 C difference".

Support for Lucks' higher set of values is forthcoming from the recently published values of Dauphinee,

Armstrong, and Woods [25] . These workers had carried out their measurements several years previously by an

absolute longitudinal heat flow method on a very pure lead that was stated to be of 99. 999 percent or better purity.

Their temperature range was about -50 to 300 C. Two independent sets of measurements gave results that agreed

to within 1 percent but fitted straight lines of differing slope. Lucks' values at 50 C for the higher freezing point

sample are in close agreement and his extrapolated value at 300 C is greater than the mean value of Dauphinee

et al. by only 1.5 percent. Thus both of Lucks' curves receive independent support from other workers and the

recommended curve has been drawn to fit closely with these two recent determinations. The derived Lorenz

function is of the order of 2.5 x 10 -8 V

2 K

-2 and is thus in fairly good agreement with the earlier values of Lees [26]

and of Jaeger and Diesselhorst [27] . Nevertheless the divergence of the thermal conductivity curves with in- crease in temperature for these two grades of lead is sufficiently unusual to warrent further independent investigation. The 3 to 4 percent higher thermal conductivity values of Powell and Tye [28] were made on smaller and

less suitable samples and these values which were thought to have an uncertainty of ±3 percent, have been ignored

as likely to be too high. The many earlier determinations are considered low, probably due to use of less pui'e

lead.

The two sections of the recommended curve below 35 K and above room temperature were extrapolated to join smoothly together and the resulting curve in the subnormal temperature region lies above the curve of Lees

[26] by about 2 percent.

For molten lead there are eight curves available and the values differ by about 60 percent and in the sign of the temperature coefficient. The recommended values are derived from electrical resistivity and the theoretical

value of the Lorenz function and are seen to agree most closely with the data of Dutchak and Panasyuk [29j and of

Powell and Tye [30], whose specimen in the molten state was from the same supply as the specimen measured in the solid state. At the melting point the ratio of the recommended thermal conductivity for the solid lead to that for the molten lead is 2.01, which is close to the value of 1 . 94 obtained by Roll and Motz [31] for the corresponding electrical conductivity ratio.

The curve for superconducting lead from 1 to 7.19 K (the transition temperature) is also shown in Figure 1

,

The freezing point of this lead was quoted as 327. 3 C by Lucks [24].

6
but the values are not considered sufficiently well established to be recommended.

The recommended values are thought to be accurate to within ±3 percent of the true values at moderate

temperatures, ±5 percent at high temperatures, and ±10 percent at low temperatures and for molten lead.

Magnesium

There are 24 curves available for the thermal conductivity of magnesium. At low temperatures the purest

magnesium studied seems to be the annealed Johnson Matthey sample of 99. 98

+ percent magnesium content used by

Kemp, Sreedhar, and White [32] . The recommended values below 25 K were calculated using a 0 value derived

from their data for this specimen, and the continuation of the recommended curve from 25 to 150 K closely follows

their data. From 150 to 273 K and above 729 K no determinations appear to have been made for the thermal

conductivity of magnesium.

The majority of the workers that have made thermal conductivity determinations on magnesium in the range

273 to 729 K have included electrical resistivity values for the same samples. The resultant values of the Lorenz

function at about 373 K range from 2. 16 x 10~R to 2. 48 x 10 _8 V

2 K~2 and it seems significant that in only one work is the theoretical value exceeded. These highest values are due to Mannchen [33] , a worker whose data have been

criticized and are thought to be uncertain (see Kempf, Smith, and Taylor [34] and Powell [35]). The values

for the Lorenz function obtained by Schofield [36], Powell [35] , and Powell et al. [37] are in fair accord and

indicate that this quantity probably increases slowly with increase in temperature and has values of 2.27, 2.31,

2.33, 2.35, 2.36, 2.37, and 2.38 x 10 -8V

2

K~2 at temperatures of 273, 373, 473, 573, 673, 773, and 923 K,

respectively.

From these values and the electrical resistivity of pure magnesium the most probable thermal conductivity curve has been derived. The electrical resistivity at 273 K has been taken as 3. 95 x 10 -6 ohm cm with values of 5.61, 7.28, 9.00, 10.76, 12.51, and 15. 2 x 10~ 6 ohm cm at 373, 473, 573, 673, 773, and 923 K. Increasing uncertainty arises as the melting point, 923 K, is approached. The above value at 923 K is based on that of Roll and

Motz [31] of 15.4 x 10 -6 ohm cm for magnesium of 99.8 percent purity, but it should be noted that measurements

by Horn [38] indicate a strong upturn as the melting point is approached, his value being greater by about ten percent.

Since no thermal conductivity determinations have been made on molten magnesium, a provisional value can be evaluated from Equation (6) proposed by Powell [13]. Roll and Motz [31] have reported values for p which,

used with Equation (6), lead to thermal conductivity values at 923 K and 1173 K respectively of 0.79 and 0. 96 Watt

cm -1K

-1

. The recommended values are considered accurate to within ±3 percent of the true values at moderate temperatures, ±10 percent for low tempei’atures and as the melting point is approached, and ±15 percent for the liquid

state.

Molybdenum

But few thermal conductivity values have been reported for molybdenum at low temperatures and /3 has

been derived from the data of Rosenberg [5] for a 99. 95 percent sample of this metal. The maximum is about

35 K and the calculated curve has been extended to about 50 K where the agreement with Rosenberg's data is still good. This most probable curve approximately follows Rosenberg's to its upper limit (96 K) where it is some

4 percent above a very recent curve due to Backhand [39] . A smoothly falling curve can be drawn through

Backlund's experimental values and this tends to disprove the shallow minimum at about 200 K which had been

indicated by Kannuluik [40,41] . The recommended curve has accordingly been drawn some 2 percent above

Backlund's curve to merge into that due to Tye [42] for the range 323 to 473 K. This curve is continued smoothly

to the melting point. It falls at a steadily decreasing rate and in the high temperature range lies up to 10 percent

below the values of Rasor and McClelland [43], Timrot, Peletskii, and Voskresenskii [44], and those derived

from the thermal diffusivity data of Kraev and Stel'makh [45], and exceeds the derived values of Wheeler [46] by

7
about 10 percent and the thermal conductivity measurements of Lebedev [47] and of several other workers by still greater amounts.

The recommended curve gives a value of 0. 94 W cm -1K

-1 at 1723 K, which with Tye' s electrical resistivity

of 44. 7 pohm cm leads to a Lorenz function at 1723 K of 2. 44 x 10~8V

2K

-2

.

Further measurements are required to confirm the exact form of the thermal conductivity curve, particularly athigh temperatures. The low temperature curve is for a sample with the high p 0 of 0. 167 pohm cm and data are certainly required for a purer sample. The present values should be within some ±4 percent of that of highpurity molybdenum near normal temperatures, ±10 percent at low temperatures, and within ±15 percent as the

melting point is approached.

Nickel

In view of the technological importance of nickel, it appears that insufficient attention has been given to the thermal conductivity of this metal. This examination of the available data indicates both the need for further work

and the interest likely to be found in attempting to more fully understand the conducting processes involved. No

very firm recommendations can be made at present.

Only three curves are available at cryogenic temperatures, there is the customary dearth of values at temperatures just below normal, whilst at high temperatures the tendency, found for iron, for values to converge

with increase of temperature seems completely lacking.

The /3 value used to calculate the low temperature values for the range 1 to 30 K has been derived from the

highest available thermal conductivity values in this region, those of Kemp, Klemens, and White [48] for an annealed sample of 99. 99 + percent nickel. In attempting to fit these results with the form of curve usually adopted

and considered satisfactory, the first difficulty arises, and suggests the need for further measurements on nickel

at low temperatures. As the present results do not fit the curve of Equation (l), a compromise has been adopted

and a value used for /3 to give a curve that is some 6 percent too high in the region of the maximum and about the same amount low near 2 K.

At temperatures above normal the available values cover a wide band. Whilst those of Angell [49] and

Sager [50] can be discounted as of low accuracy, much of the spread is no doubt due to a strong dependence of the

thermal conductivity of nickel on purity. The sharp decrease in conductivity with increase in temperature that was

found with iron is again evident and again persists to the Curie temperature. With nickel, however, there is hardly

any tendency for the values to converge as the Curie temperature is approached, possibly because this temperature

is much lower than that with iron. Above the Curie temperature the thermal conductivity increases with temperature, and here again, the well separated individual curves remain roughly parallel to each other. A strong increase

in the electronic component of thermal conductivity, k

g

, can be expected from consideration of the Lorenz equation,

and the unusually high value of the constant term in the linear equation that approximates to the temperature variation of electrical resistivity, p. Assuming that p = mT + c (7) the Lorenz relationship gives

k

g = L0T(mT + c)

_1

(8) from which it follows that dk

= L0c(mT + c)"2 (9)

For most metals c is close to zero and k

g relatively constant, but for nickel and iron above their Curie

temperatures, c has large positive values and k

g increases strongly with T.
It has been usual to assume that L0 = 2.443 x 10 8 V

2 K 2 and then to derive the lattice thermal conductivity

component, kg, from

k = k - k = k - 2.443 x 10 -8 TP _1 (10)

g e For nickel in this high-temperature region the recent work of Powell, Tye, and Hickman [51] indicates

k„ as found in this way to be relatively large, to vary from sample to sample, and to increase with increase in otemperature whereas this quantity is usually expected to decrease according to T

-1

. Thus it seems probable that

the conducting mechanisms of nickel are not fully understood. Further support for this is suggested by the relatively high temperature to which a Lorenz function persists that is less than the theoretical value. This even seems to be the case with nickel at the Debye temperature (0 = 375 K), where the above procedure would yield a

quite unacceptable negative value for k . o Such considerations as the above indicate that the thermal conductivity of a sample of nickel cannot be predicted with any degree of certainty from an electrical resistivity determination and that further work is required

for nickel in both the experimental and theoretical fields. A reasonably good link for the immediate sub-normal temperature range has been provided by the recent measurements of Backlund and Langemar [39] over the range 87 to 374 K, and the curve at present regarded as most probable for the thermal conductivity of pure nickel follows their curve fairly closely to a location between

the curves of Shelton and Swanger [22] and the highest due to Powell et al. [51] . The mean course of these last mentioned curves is followed to the Curie temperature, where a sharp minimum is shown and the curve to about

1400 K is drawn as a straight line again fitting the highest values of Powell et al. The uncertainty of much of this curve is probably of the order of ±10 percent.

Niobium

Niobium becomes superconducting at a higher temperature than any other metal. This no doubt helps to account for the high proportion of thermal conductivity determinations on niobium that relate to the superconducting state. From the point of view of the present analysis, the highest values so far obtained in the superconducting

region are due to Kuhn [52] for a single crystal of about 99. 9 percent purity. By applying an appropriate magnetic

field he has obtained thermal conductivity values for the normal state over the temperature range of 1.3 to 9.4 K. His values are much higher than those of Mendelssohn [53, 54] for a zone-refined 99. 999 + percent pure single

crystal. The last-mentioned purity of the sample seems questionable. From Kuhn's data a 0 value has been derived and calculated values have been obtained to about 1.5 Tm «23 K. This is the curve for 0 = 3.991, and is at present assumed to represent the thermal conductivity of niobium at low temperatures. It is realized that this can

scarcely be regarded as satisfactory. Furthermore, niobium is a metal that readily takes up gaseous impurities

at high temperature, even from a relatively good vacuum, and improved preparation techniques will probably yield

samples for which this curve is too low.

Nor is the situation much better at higher temperatures, except that above room temperature all measurements show a steady increase in thermal conductivity.

From 94 to 273 K there are no values at all. Indeed, since the two sets of measurements of White and

Woods [55] and of Mendelssohn and Rosenberg [5, 6] made to about 90 K gave lower values than that used for deriving the low temperature curve and since the 99. 99 percent Nb sample of the latter yielded values much lower

than those of the 99. 9

+ percent Nb sample of the former, there is need for experimental data for pure niobium to be provided for the range from 1 to 273 K. A probable curve has been drawn in this region, but it is a very tentative line drawn to link on smoothly with another curve fitted to the available high temperature data. Until recently

the values in the range of approximately 323 to 873 K were limited to five sets of measurements that differed by

about 20 percent, with the lowest of these measurements continuing to 1910 K. Now, however, a sixth set of values

has been reported by Raag and Kowger [56] that tends to support the highest of those previously given. These

workers determined the thermal diffusivity of a 99. 95 percent rod of niobium over the range 345 to 1195 K. They

9
claimed an accuracy of ±2 percent and to derive thermal conductivity, made use of the specific heat data of Jaeger

and Veenstra [57] . This is certainly regarded as the most acceptable of the available specific heat data. Raag

and Kowger also measured the electrical resistivity and obtained values of the Lorenz function that increase from

2.73 x 10 -8V

2 K

-2 at 300 K to 2.77 x 10 -RV2 K

-2 at 1200 K, and for the lower two thirds of this range are in reasonable agreement with the data of Bell and Tottle [58, 59]. The recommended curve has been drawn as a straight

line through the thermal conductivity data so derived by Raag and Kowger.

At still higher temperatures, three sets of information are available. All are lower than the normal extension of the present curve, but this difference is probably associated with the reduced purity of the samples

studied. The radial heat flow thermal conductivity determinations of Fieldhouse, Hedge, and Lang [60] lie on a

linear curve which is about 14 percent below the recommended curve at 1200 K. Those of Voskresenskii,

Peletskii, and Timrot [61] are within 2 percent of the curve of Fieldhouse et al. , whilst the thermal conductivity

values deduced from the thermal diffusivity data of Kraev and Stel'makh [45] are lower than those of Fieldhouse

et al. by 6 percent at 1800 K. These no longer increase linearly with temperature but rise to a small maximum

at about 1900 K. In view of these results it seems reasonable to allow the curve at present recommended to continue its linear increase to about 1500 K and then to gradually decrease its slope. In this high temperature

region there is clearly need for more experimental work on pure material that remains pure under the test conditions.

The recommended values are thought to be accurate to within ±5 to ±10 percent at moderate temperatures

and ±15 percent at low and high temperatures. The curve for superconducting niobium from 1 to 9.13 K is also

shown in Figure 1, but the values are not considered sufficiently well established to be recommended.

Tantalum

At low temperatures the highest curve at present available is that of White and Woods [62] for a 99. 9 percent tantalum that had been annealed at 2500 C. The value of /3 derived from these measurements has been used

to give calculated values up to about 30 K. White and Woods' experimental curve has been followed up to about

65 K. From here to about 300 K is a region of uncertainty and lacking in experimental evidence.

Rosenberg [5] had obtained considerably lower values for a purer but unannealed sample, and had indicated a minimum in the region of 65 K but this occurred towards the upper limit of his method and appears unlikely. In the approximate temperature range of 323 to 400 K, however, thermal conductivity values due to Deverall [63],

Tye [42] , and Denman [64] agree to within about ±4 percent and all have small positive temperature coefficients. Hence, from about 65 K, the tentative recommended curve has been smoothly extrapolated to give a shallow minimum at about 250 K and then to pass through a point at 373 K which is the mean value obtained from

these three sets of data. This curve has been continued through the upper portion of Denman's curve approximately linearly to about 1300 K and then with gradually decreasing slope as the melting point is approached. In

this upper temperature range the proposed curve lies some 9 percent above the mean values of Rasor and

McClelland [43] and of Peletskii and Voskresenskii [65], and from 5 to 10 percent below the values derived by

Wheeler [46] from thermal diffusivity determinations . There are however, uncertainties associated with the

density and specific heat data required for deriving thermal conductivity values from thermal diffusivity measurements, and other available values of density and specific heat could bring Wheeler 1 s data into close agreement at the highest temperature. For similar reasons, it seems possible that the thermal diffusivity determinations of

Kraev and Stel'makh [45] could yield thermal conductivities having a negative temperature coefficient at these

high temperatures. This would support some of the measurements of Jun and Hoch [66] , but, these seem low.

since, if the l’ecent electrical resistivity data of Peletskii and Voskresenskii [65] of 108. 8 jUohm cm at 2900 I\ represents the value for pure tantalum, any thermal conductivity at this temperature that is lower than the recom- mended value by more than 2 percent would bring the Lorenz function below the theoretical value.

It is of interest to note that the 1914 measurements of Worthing [67] which must have been the first reported measurements for temperatures of the order of 2000 K are only from 16 to 29 percent above the proposed curve.

10
The uncertainty of the proposed curve is probably of the order of ±5 percent at room temperature, rising

to ±10 percent at the highest temperature. The curve for superconducting tantalum from 1 to 4.48 K is also shown

in Figure 1, but the values are not considered sufficiently well established to be recommended.

Tin

In this section it is only proposed to consider white tin. No thermal conductivity values are available for

the gray cubic form of tin to which the white tetragonal form transforms under certain conditions at about 13 C.

The majority of the thermal conductivity determinations on tin relate to the supperconducting state, and thus 114

of the available 133 curves are at temperatures below 5 K.

In this low-temperature region the highest thermal conductivity curve is that of Zavaritskii [68] for a highpurity single crystal in the normal state measured with heat flow perpendicular to the tetragonal axis. The residual electrical resistivity of this sample was reported to be (l ±0. 5) x 10“10 ohm cm. He also reported data from

2.6 to 4.6 K for two other single crystals measured with heat flow parallel to the tetragonal axis. All these three

crystals are apparently of the same material. These data indicate the thermal conductivity anisotropy ratio

k /k to be 1 . 44

.

± // An attempt was made to derive values of # from Zavaritskii 's data so as to complete his curves down to

0 K. However, preliminary calculations indicate that the values of Tm for his curves are below 1. 5 K. His data are therefore at temperatures above 1. 5 Tm and Equation (l) cannot be used to fit his thermal conductivity data.

Furthermore, # values cannot be accurately derived from his residual electrical resistivity data either, since

the latter have 50 percent uncertainty. Consequently no values below 3 K are given for tin.

The recommended curves for k and k from 3 to 5 K follow Zavaritskii 's data. The values for polycrystalline tin are calculated assuming ^p0^yCryS = 1/3 (2 k^ + k

/7 ). From 5 to 36 K the curves have been drawn

approximately parallel to that of Rosenberg [5] for a 99. 997 percent tin single crystal sample. There are no measurements from 36 to 99 K and only those of Lees [26] obtained from a rod of Kahlbaum pure polycrystalline

tin, from 99 K to normal temperature. Lees appears from general evidence to have been a careful worker, but

the purity of his sample may have been rather low, hence for polycrystalline tin a smooth curve has been drawn

from 36 K to lie some 2 percent above that of Lees. The continuation of this curve to the melting point conforms

reasonably well with most of the higher experimental values for polycrystalline tin in this temperature range. The

values of k^ and k

f/ from 36 K to the melting point are derived from values of ^p0jyCryS based on the assumption

that k /k

f/ - 1.44 is valid also in this temperature range. This anisotropy ratio is further supported by the

electrical resistivity measurements of Bridgman [69]. He obtained room-temperature values for p^ and p^ of

14. 3 and 9. 9 jLiohm cm, respectively, which gives

p^ /p

( = 1.44.

The curve of Mikryukov and Rabotnov [9] is displaced to much higher values, about 10 percent higher than

the recommended curve for k^ . Their measurements are reported as being made on a single crystal of tin. The

crystal direction in which the measurements were made is not stated, but from the reported electrical resistivity,

which ranges from 14.45 /iohm cm at 117. 2 C to 18.94 /i ohm cm at 187. 1 C, it seems likely that this was the high

conductivity direction. It is further noticed that over this temperature range their Lorenz function ranges from

2. 94 x 10~8 to 2. 98 x 10~8 V

2K

-2 and are probably some 15 to 20 percent too high, since those of Lees [26] and of Jaeger and Diesselhorst [27] are in fair agreement at 291 K with values of 2.47 x 10 -8 and 2.53 x 10 -8V

2 K~2

, respectively. Thus the high values of Mikryukov and Rabotnov appear to be capable of a reasonable explanation.

The seven sets of data available for the thermal conductivity of molten tin show closer agreement than for

many other metals. The proposed straight line for the thermal conductivity of tin in the liquid state has been

drawn through a mean value (0.317 W cm-1 K

-1

) at 573 K and a derived value at 973 K obtained from the equation

k = 2.443 x 10~8 Tp_I (ll)

when using the value of Roll and Motz [3l] of 59.6 jiiohm cm for the value of p. It is interesting to note that at 1473 K this line also conforms closely with the value derived from the p-value of 72.0 /lohm cm which Roll and

11
Motz obtained. Also that the thermal conductivity values of Nikolskii et al. [70] fit this line well up to 833 K. At

1300 K, however, the recommended thermal conductivity value is some 55 percent greater than the almost temperature independent value which Filippov [71] and Yurchak and Filippov [72] have given in separate papers as derived from thermal diffusivity measurements.

At the melting point the ratio of the values proposed for the solid state k^ , ^p0^y CryS » \to that for

the liquid state are, respectively, 2.18, 1.96, and 1.52.

The recommended values for polyciystalline tin are thought to be accurate to within ±3 percent of the true values at moderate temperatures, ±5 percent at high temperatures, and ±15 percent at low temperatures. The

values for k^ and k

/f of tin single crystal should be accurate to within ±6 percent at moderate temperatures, ±10

percent at high temperatures, and ±15 percent at low temperatures. For molten tin the values are probably good

to ±5 percent near the melting point, but an increasing uncertainty remains to be resolved at higher temperatures.

The curves for superconducting tin from 1 to 3.72 K are also shown in Figure 1, but the values are not considered

sufficiently well established to be recommended.

Titanium

The calculated curve for polycrystalline titanium at low temperatures has been based on the experimental curve of White and Woods [62] for a 99.99 percent titanium sample that had been annealed at 800 C for 60 hours.

The experimental and calculated curves agree closely over the range 7. 3 to 20 K. Beyond 20 K the calculated

values are higher, and at the maximum, which occurs at about 41 K, the difference has risen to the order of 10

percent. Well before 1.5 Tm is reached, however, the curves cross. Titanium has a relatively shallow maximum for the samples so far studied and it seems clear that the normal form of Equation (l), which is more applicable to the thermal conductivity of high -purity samples, does not apply well to this case. From just above Tm to the 293 K value of Powell and Tye [73] for a sample of very high purity with

P293K ~ 42.7 /uohm cm, a smooth curve with a gradually decreasing slope has been drawn.

Over the temperature range from about 300 to 900 K the 11 sets of thermal conductivity values that are

available cover a wide range, with the highest values some 50 percent greater than the lowest. With most metals,

the purer the sample, the higher is the thermal conductivity. In the present instance, however, the two highest curves are those of Loewen [74] for a commercially pure titanium, for which no analysis is given, and of Mikryukov [75] for a sample of 99. 6 percent purity. The situation is further complicated by the fact that

Mikryukov reported at the same time values for a sample of 99.9 percent purity which are mainly some 6 to 12

percent lower. For the less pure sample Mikryukov' s data indicate a higher Lorenz function and one that is increasing with increase in temperature, whereas the results for the purer sample are more in accord with the

Lorenz function found by Powell and Tye [73] and Deem, Wood, and Lucks [76] which gives mean values decreasing from 3. 24 x 10 at 323 K to 3. 06 x 10 -R V2 K

-2 at 773 K. Whilst admitting that complications might well

be associated with the high phonon conductivity component of this metal, a tentative curve from room temperature

upwards has been derived by assuming values of the Lorenz function of the order found by these three groups of

workers. The Lorenz function has been assumed to continue to fall steadily to 2.4 x 10 -8 V2 K“2 at 1673 K, and in the uppermost range use has been made of the electrical resistivity data compiled in [77]

.

A minimum thermal

conductivity is indicated at about 650 K. Over the range 750 to 1400 K the suggested curve shows no step at the

phase transition (1155 K) and lies some 30 to 3 percent above a curve deduced from the thermal diffusivity measurements made by Rudkin, Parker, and Jenkins [78] on a sample of titanium for which no details were given.

From 1417 to 1606 K similarly derived values lie on a reasonable continuation of the proposed curve.

The close-packed hexagonal crystalline form of this metal transforms into body-centered cubic form at about 1155 K. Any associated change in the thermal conductivity has yet to be experimentally investigated. The

curve derived from the measurements of Rudkin, Parker, and Jenkins has a gradual drop of about 8 percent in

12
this region, whereas according to the previously quoted electrical resistivity data [77], the electrical conductivity

increases by about 10 percent. Since these changes are about equal and opposite, no break has been introduced at

this stage in the proposed curve.

Quite apart from the importance of titanium in modem technology, facts such as the foregoing should en- courage further investigation to be undertaken of the thermal and electrical conductivities of titanium in the transformation region and above.

The values given by the proposed curve are thought to be accurate to within ±10 percent of the true values

at moderate temperatures, and ±15 percent at low and high temperatures.

Zinc

The low-temperature thermal conductivity measurements on zinc single crystals are found to involve a

difficulty that has not been met with the earlier metals treated. The curves for k^ and k

/f appear to cross both

above and below the temperature where the thermal conductivity is a maximum.

This behavior occurs with curves 22 and 23 of Table 13. Both relate to measurements made by Mendelssohn

and Rosenberg [6] on samples prepared from the same batch of 99.997 percent purity zinc. Sample No. 3 (curve

23) has the higher maximum, but lower values are shown for this below about 7 K and above 27 K. This sample was

a single crystal with the hexagonal axis at 13 degrees to the rod axis, and thus gave values approximating to k^

.

Sample No. 2 (curve 22), with the lower maximum was a single crystal with the hexagonal axis at 80 degrees to the

rod axis and so gave values that approximated to k . The data for another sample No. 4 (curve 34) with the hexagonal axis at 13 degrees to the rod axis measured by Rosenberg [5] agree well with those for sample No. 3.

Goens and Griineisen [8] had previously made measurements on four single crystals of zinc at temperatures

of 21.2, 83.2, and 293.2 K. From these measurements they derived values for k and at these temperatures.

Their values are given in the following table:

Values for Ideal Undeformed Zinc Crystals Parallel and Perpendicular

to the Hexagonal Axis as Extrapolated by Goens and Griineisen

T, K k± , Wcm *K 1 k„ , Wcm *K 1 kx A// px , Mohm cm p/y ,JUohm cm P///P±

21.2 5.65 7.09 0.797 0.0366 0.0440 1.202

83.2 1.372 1.316 1.043 1.155 1.293 1.119

293.2 1.242 1.242 1.00 5.83 6.05 1.038

These thermal conductivity values seem to be consistent with those of Mendelssohn and Rosenberg at temperatures above Tm. Whereas k

// >k^ at 21.2 K, k// < ki

at 83. 2 K and the two thermal conductivity values agree

at 293.2 K. The electrical resistivity values on the other hand show no similar cross-over. The electrical conductivity for the perpendicular direction exceeds that for the parallel direction at all three temperatures.

Zavaritskii [7] has made thermal conductivity determinations on zinc single crystals at lower temperatures. Zinc becomes superconducting at Tc = 0.825 K and he was mainly interested in the thermal conductivity of

the superconducting state. He found k > k

/f for the normal state at temperatures close to T c as well as for the

superconducting state. These findings are also in accord with Mendelssohn and Rosenberg's measurements.

The three sets of available measurements of the low temperature thermal conductivities of zinc crystals are

therefore self-consistent. They show a type of behaviour, however, that is quite incompatible with the treatment of

Cezairliyan and Touloukian [2-4] which has formed the basis of the evaluation of thermal conductivity values in this

low-temperature region. The use of different values for # yields a family of curves which never intersect at temperatures below Tm.

Whilst this unusual behaviour appears to be reasonably well established, it clearly requires explanation and

therefore calls for further experimental investigation. Since the resistivity data of Goens and Gi'uneisen show no

Given by Zavaritskii; recent information suggesting T = 0.875 K.

13
cross-over it seems likely that the explanation might be associated with a marked difference in the anisotropy of

the electronic and lattice components of the heat conduction. There seems no reason why other non-cubic metals

should not show similar departures from what has come to be regarded as normal behaviour.

Pending further information, it is considered ill-advisable to present any recommended curves for the

thermal conductivity of single crystals that cross one another, and, for the time being the recommendations for

zinc will relate only to the polycrystalline form. These will be derived at low temperature in the same manner that

has been used throughout this work.

The highest low -temperature value is a single observation at 0. 825 K reported by Zavaritskii [7] for a

single crystal of zinc having the hexagonal axis perpendicular to the direction of measurement. From this value

the corresponding thermal conductivity of a polycrystalline sample has been derived, using the ratio of k to k

f/ obtained by Zavaritskii at this temperature for two other samples. This has been used to evaluate j8 and to derive

the curve for polycrystalline zinc in the normal state and up to about 8 K. Beyond the maximum the curve continues to reach the value derived for polycrystalline zinc from the single crystal data of Goens and Gruneisen

around 83 K. It then continues with steadily falling conductivity and passes some 2 percent below the polycrystalline value derived in the same way at 293 K. From here to the melting point the proposed curve has about the

mean slope of the earlier values but is drawn in a rather higher position to compensate for the reduced purity of

these specimens. It is located about mid-way between the early measurements of Shelton and Swanger [22] and

the most recent values which are due to Mikryukov and Rabotnov [9]

.

A need clearly exists for new measurements on polycrystalline zinc of the high purity now available. A

more complete examination of the conducting properties of single crystals of zinc is also most desirable.

There is also a very strong case for a redetermination of the thermal conductivity of molten zinc, although

the position has been somewhat improved whilst this report was in progress by the recently reported measurements of Dutchak and Panasyuk [29] . Theirs is the third determination to be made of the thermal conductivity of molten zinc. The earlier measurements of Konno [79] and Bidwell [80] had agreed closely with each other but

posed problems when considered in the light of the electrical resistivity. Both workers obtained a negative temperature coefficient, whereas the thermal conductivity as derived by use of the theoretical value of the Lorenz

function should have a strong positive coefficient. Also, the ratio of the two conductivities, thermal and electrical, for the solid and liquid states are far from comparable. The present recommended curve gives a thermal

conductivity of 1. 0 W cm-1K

-1 for solid zinc at the melting point. In the liquid state, if a mean line is fitted to the

data of Konno and Bidwell, it yields a value at the same temperature of 0. 6 W cm -1 K

-1

. Hence the ratio kg/kL =

1. 67 and this may be compared with a value of 2. 2 as obtained by Roll and Motz [31] for the ratio Pp/PgThe recent values of Dutchak and Panasyuk [ 29] for the thermal conductivity of molten zinc in the range 713 to 873 K do show about the expected increase with increase in temperature, but are considered too high since they

give a ratio kg/k^ of 1.72.

The broken line shown in Figure 13 yields a ratio kg/k^ of about 2. 0 and is regarded as being a more

likely representation of the thermal conductivity of molten zinc. It is tentatively proposed, but clearly further

experimental investigation is required.

The recommended values are thought to be accurate to within ±3 percent of the true values at moderate

temperatures, ±5 percent at high temperatures, and ±15 percent at low temperatures and for molten zinc.

Zirconium

The -value has again been calculated from experimental data due to White and Woods [62], and, using

this /3 -value, the low -temperature section of the proposed curve has been derived to about 20 K. An extension of

this curve passes through the data of White and Woods near 90 K, but at higher temperatures considerable uncertainties arise. In the temperature range 94 to 297 K the only determination available is at 121 K. This is the

uppermost point due to White and Woods where radiation corrections could lead to some uncertainty. From 298 to

14
about 900 K several sets of values are available; these are consistent in indicating the thermal conductivity versus temperature curve to have a minimum within this range, but this is about the limit of their consistency. The minimum value ranges from about 0. 170 to 0. 245 W cm -1 K

-1

. Mikryukov [75] obtained this highest value for a 99. 9 percent sample of iodide zirconium which is seen to have an unusually low electrical resistivity. Indeed, the quoted

value of 36. 1 /iohm cm at 331 K (which extrapolates to about 26 pohm cm at 273 K) has to be compared with Treco'

s

273 K value of 38. 8 /iohm cm [81], which is the next lowest value reported for zirconium. Treco obtained his

value for an oxygen-free high -purity zirconium and found the 273 K resistivity to increase to 57. 7 pohm cm at 2.-

5

atomic percent of oxygen. As zirconium is a metal that readily combines with oxygen, this seems a factor which

could help in explaining some of the conductivity differences. Since zirconium has a hexagonal crystal structure below about 1135 K, another contributing factor could be the varying degrees of preferred orientation. No information appears to be available, however, regarding the anisotropy of the conductivity of zirconium.

At high temperatures the two sets of data available for the thermal conductivity again differ considerably.

That of Timrot and Peletskii [82] appears to be much too low in its lower temperature range, for, at 1200 K, use

of the electrical resistivity value of 117 /uohm cm selected by Touloukian [77] leads to a Lorenz function of only

2. 0 x 10“8V

2K"2

.

Over the range 331 to 898 K the mean Lorenz function reported by Mikryukov [75] from his measurements

on two samples decreases from 3. 42 x 10 -8 to 3. 11 x 10 -8V

2K~2 whilst that of Powell and Tye [83] for three samples at 323 K is 3. 10 x 10 -8V2K

-2

, decreasing to 2. 73 x 10 -8V2K

-2 at 823 K for two samples. Bing et al. [84] for

three samples reported mean values of 3. 14 x 10 -8V

2K

-2 at 323 K and 2. 84 x 10 -8V

2K

-2 at 523 K.

Zirconium is clearly a metal that requires considerably more experimental investigation before any very

firm recommendation about its thermal conductivity is possible.

For the present a smooth curve showing a steadily decreasing rate of fall of thermal conductivity has been

drawn from the value of 0. 35 W cm -1 K

_1 at 90 K to 0. 232 W cm -1 K-1 at 273 K, the latter value having been derived

from Treco' s electrical resistivity and a Lorenz function close to the mean value indicated by the three sets of measurements last mentioned. This value lies 4 percent above the lowest-temperature value of the smooth curve

obtained by Moss [85] for nominally high -purity zirconium, and the curve now proposed follows about this amount

above Moss' curve until it commences to cross the curve of Fieldhouse and Lang [86] and to lie some 3 percent

below this curve to the highest temperature.

As with titanium at about 1155 K, the true curve of thermal conductivity of zirconium versus temperature

could be expected to have a discontinuous change at about 1135 K where a phase transformation occurs. The electrical resistivity has been found to undergo a drop of about 14 percent in this region, but the only thermal conductivity measurements which extend above and below this region, those of Fieldhouse and Lang, shown no comparable

increase in thermal conductivity, but possibly a decrease in slope. Hence the proposed curve has been drawn with no discontinuity, but this is clearly another aspect of the thermal conductivity of zirconium that requires further

investigation.

The proposed curve may represent the thermal conductivity of very high-purity polycrystalline zirconium

to about ±10 percent at temperatures below 800 K, the uncertainty increasing to ±20 to ±25 percent as the melting

point is approached.

Predictions could be made with more certainty at high temperatures if the electrical resistivity determinations were extended to temperatures above the present upper limit of about 1280 K.

15
TABLE

1.

DERIVED

VALUES

OF0

AND

ASSOCIATED

CONSTANTS

AND

PARAMETERS

FOR

HIGH-PURITY

METALLIC

ELEMENTS

05

16 /

This

is

the

curve

number

in

the

respective

figure

and

table

of

the

metallic

element. '

The

value

ofp

at

4.

2K

is

used

approximately

aspQ. *

Information

not

available.
THERMAL

CONDUCTIVITY

,

Walt

cm"

i

17
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18

RECOMMENDED

THERMAL

CONDUCTIVITY

OF

METALLIC

ELEMENTS
TABLE

2a.

RECOMMENDED

THERMAL

CONDUCTIVITY

OF

METALLIC

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AT

LOW

TEMPERATURES*

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19

Residual

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resistivity

in

microhm

cm.
TABLE

2b.

RECOMMENDED

THERMAL

CONDUCTIVITY

OF

METALLIC

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MODERATE

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HIGH

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Thermal

Conductivity,

k,

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the

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See

TPRC

Data

Book

Vol.

1,

Chapter

1,

References

[95]
Cur.

Ref. v

Met'

d.

Range

Specimen

No.

No.

Author(s)

Year

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Designation

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Specifications,

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24

See

TPRC

Data

Book

Vol.

1,

Chapter

1,

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Vol.

1,

Chapter

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36
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38

See

TPRC

Data

Book

Vol.

1,

Chapter

1,

References
THERMAL

CONDUCTIVITY

,

Watt

cm"

39
Cur.

Ref. *

Met'd.

Temp.

Name

and

No.

No.

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Year

Used

Range

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Composition

(weight

percent),

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TABLE

7.

SPECIFICATIONS

OF

THE

SPECIMENS

OF

MOLYBDENUM

(continued)

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3) ri

W

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r-H <N| <N CO CO CO

(NNN (N (M 0 W W M w k K M ffi

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41

See

TPRC

Data

Book

Vol.

1,

Chapter

1,

References
SPECIFICATIONS

OF

THE

SPECIMENS

OF

MOLYBDENUM

(continued)

d

fl ft

ctf d oT o' £ < £ 3 £ 1

o

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THERMAL

CONDUCTIVITY

,

Watt

cm'

1

THERMAL CONDUCTIVITY OF

NICKEL

1500 TPRC FIG 8

Curie Temp 63i k

600 700 800 TEMPERATURE, K

43
Cur.

Ref.*

Met'd.

Temp.

Name

and

No.

No.

Author(s)

Year

Used

Range

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percent),

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(K)

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44
TABLE

8.

SPECIFICATIONS

OF

THE

SPECIMENS

OF

NICKEL

(continued)

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ta

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45

716

Berger,

L.

and

Rivier,

D.

1962 L

4.

18

Ni

5011(H)

Specimen

0.

19

cm

in

dia.

drawn

from a

cylindrical

sample

5.0

cm

long;

supplied

by

Messrs.

Johnson,

Matthey

Co.

Ltd. ;

annealed

for

10

hrs

at

1573 K

in

hydrogen

and

left

at

1573 K

ina

vacuum

of

10~ 2

mm

Hg

for 2

hrs;

electrical

resistivity

at

4.

18,

80.

5,

and

273.

15K

reported

respectively

as

0.

0213,

0.

60,

and

6.

35

jxohm

cm;

p(273K)/P(4.

2K) =
SPECIFICATIONS

OF

THE

SPECIMENS

OF

NICKEL

(continued)

00w

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Gs

<DGG0a

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55a"

ni :<si ^ B

47

See

TPRC

Data

Book

Vol.

1,

Chapter

1,

References

"Thermal

Conductivity

ofa

Specimen

of

Electroformed

Nickel",

NBS

unpublished

report,

April

30,

1964

Private

communication,

January,

24,

1967
TPRC

TEMPERATURE

THERMAL CONDUCTIVITY, Watt cm

-1 K"

1

I4B
Cur.

Ref. v

Met'd.

Temp.

Name

and

No.

No.

Author(s)

Year

Used

Range

Specimen

Composition

(weight

percent),

Specifications,

and

Remarks

(K)

Designation

'to

gs O CO 3 J : ® §

toJ § - d ii

O« g d ^ q q S ^ £ o >> o £ >

<5 2 d a £ 73 s ©

q cd d —- q

vjd

.© jg

u *—

d ^ II frco 3 2 * 5 1 V 3 > a s , O"

m i I 0 j 8 ! a o * | W b£> o3 I p H .3

-S3 ® § i T3 1 q £ • CQ CQ a d . '• di q < q 'O . • d ' a -a ^ | *"** tn ! T3 : od 1 ^ w < .

cd id >

*9 CQ CO Ctj 5 !> £

02

isr. , „ i—i co Tl t> q q co gp'C -

TO 4_> co £ g S

(0 ^ CO q „ q °2 rig's ° ^

T3d

d § | * V

d co : a S § —< q i 10 a > ! o 3 'g ; d d d - a ) o >£! "0 . © » d

*!d ,5 rSfl

>>

w -H (T) gj £

a> 3 S -

Cdd

q

q

bJD q

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cd rt ^ s a £* o c

to o o V ® ^ Ofl

r-t jo

a c- . c3 cO CM

,g

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ho to d ' -J

d o q ^

j? §

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cd

d

T3 ^ _ d q cd

cd

d T3

TJ- cd § g.

35 £ © 5 O q_4 CD O s q

q

•3doqdqadqd ^ 3 Id Id

-4»i +J

CO CO & E? q q Ioqdq§ N CO D

CVI <M* 00

rH CQ

co as

cq <m co

CO ^ CO ^

1-1 dl h4h4 hi hi ^

LO ID LO LO

as as as as as as

’—1 ^

(N ID CO CO D D D D

as as as as

00 00 00 oo D D D D

as as os as

dt«0" dq

bOIw

'dq

ffi§ f o o

CQ CP

CC CQ

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cj d

d

fx§ s s k

a

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a

d -S q d n g o 59 K a

a

a x)

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w

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co to co CO CO CO

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CO CQ CQ CQ

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49

20

389,676

Mendelssohn,

K.

1958 L

1.

0-4.4

Similar

to

the

above

specimen

but

13.

4%

strained.

21

389,676

Mendelssohn,

K.

1958 L

0.87-4.1

Similar

to

the

above

specimen

but

19.

5%

strained.
TABLE

9.

SPECIFICATIONS

OF

THE

SPECIMENS

OF

NIOBIUM

(continued) £ H "2 c3 cti m CQ £*3 O0 C

O is &

-a s

ip-d -50 3d

cS

O +-> -pH cq +»

fl aD 0) o° g o -S

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g> §

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d 3 -d 3 £ O C3 to g

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T3

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50

of

Armco

iron

as

comparative

standard.
TABLE

9

.

SPECIFICATIONS

OF

THE

SPECIMENS

OF

NIOBIUM

(continued)

oa

£

oa

o

0> T2 pa S

Q CU 0 ^

co ^ 0 $ d -E 3 0 Is

o O S

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Teplofiz.

Vysokikh

Temp.,

22(2),

302,

1964
THERMAL

CONDUCTIVITY,

Wott

crn

1.0

1.7

1.6

1.5

THERMAL CONDUCTIVITY OF

TANTALUM

1.4

1.3

1.2

I

I

I

I

I

TPRC TEMPERATURE, K FIG 10

53
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See

TPRC

Data

Book

Vol.

1,

Chapter

1,

References

Unpublished

data,

1966

Teplofiz.

Vysokikh

Temp., 2

(2),

302,

1964
THERMAL

CONDUCTIVITY,

Watt

cm"

57
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TPRC

Data

Book

Vol.

1,

Chapter

1,

References
TABLE

11.

SPECIFICATIONS

OF

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See

TPRC

Data

Book

Vol.

1,

Chapter

1,

References
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TPRC

Data

Book

Vol.

1,

Chapter

1,

References
Cur.

Ref.*

Met'd.

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Name

and

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No.

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63

See

TPRC

Data

Book

Vol.

1,

Chapter

1,

References
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65

See

TPRC

Data

Book

Vol.

1,

Chapter

1,

References
3

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66

See

TPRC

Data

Book

Vol.

1,

Chapter

1,

References
67
TABLE

12.

SPECIFICATIONS

OF

THE

SPECIMENS

OF

TITANIUM 3fHda0aco

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68
THERMAL

CONDUCTIVITY,

Watt

cm'

69
Met'd.

Temp.

Name

and

Author(s)

Year

Used

Range

Specimen

Composition

(weight

percent),

Specifications,

and

Remarks

(K)

Designation

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70

342

Mendelssohn,

K.

and

Rosenberg,

H.

M.1953 L

2.5

Zn4

Similar

to

the

above

specimen

but

rod

axis

at

13

degrees

with

the

hexagonal

axis;

measured

ina

transverse

magnetic

field

with

strength

ranging

from

0.

36

to

3.

59

kilooersteds.

342

Mendelssohn,

K.

and

Rosenberg,

H.

M.1953 L

2.5

Zn4

The

above

specimen

measured

ina

longitudinal

magnetic

field

with

strength

ranging

from

0.

36

to

3.

50

kilooersteds.
TABLE

13.

SPECIFICATIONS

OF

THE

SPECIMENS

OF

ZINC

(continued) oaSoO

<d

UJs

bJD d

•a

tod

CD

C 73

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255. 8C

being,

respectively,

8.

22,

9.

09,

9.

45,

10.

19,

11.

04,

11.

85,

12.

70,

and

13.

19

jiohm

cm.

S7

504

Parker,

W.

J.,

Jenkins,

R.

J.,

1961 P

295. 2

Pure;

specimen

size

1.9x

1.

16x

0.

282

cm;

density

(20 C)

7.

14g

cm

-3

taken

from

Smithsonian

Butler,

CP.

and A

bbott,

G.

L.

Physical

Table,

1954;

measured

specific

heat(22C)

0.088

calg

-1K

_1 .

See

TPRC

Data

Book

Vol.

1,

Chapter

1,

References
TABLE

13.

SPECIFICATIONS

OF

THE

SPECIMENS

OF

ZINC

(continued)

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m 0

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0

b£u

z

COTJC

CTJ

0X

CO

72

zinc

and

casting

in

graphite;

lead

used

as

the

comparative

standard

(value

taken

from

International

Critical

Table

Vol.

H:

0.

352

Watt

cm

-1C

-1

at0

C).

129

Shelton,

S.

M.

and

Sw

anger,

W.

H.

1933

C

313-596

Z.

S.

Similar

to

that

of

the

above

specimen

except

commercial

malleable

nickel

used

as

the

indirect

comparative

standard

(also

based

on

the

data

for

lead).
SPECIFICATIONS

OF

THE

SPECIMENS

OF

ZINC

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References
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1,

References
C. References

1. Powell, R.W., Ho, C.Y., and Liley, P. E., "Thermal Conductivity of Selected Materials", National Standard

Reference Data Series - National Bureau of Standards NSRDS-NBS 8, 1-168, 1966. This report deals with the

thermal conductivity of the following materials: the metals aluminum, copper, gold, Armco iron, iron, manganin, mercury, platinum, platinum (60%) + rhodium (40%) alloy, silver, tungsten; the nonmetallic solids

aluminum oxide, beryllium oxide, Corning code 7740 glass, diamond, magnesium oxide, Pyroceram brand

glass-ceramic code 9606, quartz (crystalline and fused), thorium dioxide, titanium dioxide; the liquids argon,

carbon tetrachloride, diphenyl, helium, nitrogen, m-terphenyl, p-terphenyl, toluene, water, and the gases

argon, carbon tetrachloride, diphenyl, helium, nitrogen, toluene, and water (steam).

2. Cezairliyan, A. , "Prediction of Thermal Conductivity of Metallic Elements and Their Dilute Alloys at Cryogenic Temperatures" Purdue University, Thermophysical Properties Research Center, TPRC Rept. 14,

1-140, 1962.

3. Cezairliyan A. , and Touloukian, Y. S. , "Generalization and Calculation of the Thermal Conductivity of Metals

by means of the Law of Corresponding States". High Temperature, £), 63-75, 1965; A translation of Teplofizika Vysokikh Temperature, 3, 75-85, 1965.

4. Cezairliyan, A., and Touloukian, Y.S. , "Correlation and Prediction of Thermal Conductivity of Metals

Through the Application of the Principle of Corresponding States", Advances in Thermophysical Properties

at Extreme Temperatures and Pressures , 3rd Symposium on Thermophysical Properties, A.S. M. E. , 301-313, 1965.

5. Rosenberg, H. M. , "The Thermal Conductivity of Metals at Low Temperatures" , Phil. Trans. Roy. Soc. London, A 247 , 441-97, 1955.

6. Mendelssohn, K. , and Rosenberg, H.M., "The Thermal Conductivity of Metals at Low Temperatures, I: The Elements of Groups 1, 2, and 3, II: The Transition Elements", Proc. Phys. Soc. (London), 65A, 385-94,

1952.

7. Zavaritskii, N. V. , "Measurement of Heat Conductive Anisotropy of Zn and Cd in the Superconducting State",

Zhur. Eksptl. i Teoret. Fiz. , 39, 1193-7, I960; Soviet Phys. JETP, 1_2(5), 831-3, 1961.

8. Goens, E. , and Gruneisen E. , "Electrical and Thermal Conductivities of Single Crystals of Zinc and

Cadmium", Ann. Physik, L4, 164-80, 1932.

9. Mikryukov, V. E. , and Rabotnov, S. N. , "Thermal and Electric Conductivities of Mono- and Polycrystalline

Substances from 100° to the Melting Point", Uchenyc, Zapiski, Moskov Ordina Lenina Gosudarst, Univ. M.V.

Lomonosova, Fizika, 74, 167-79, 1944.

10. Mikryukov, V. E. , Tyapunina, N.A. , and Cherpakov, V. P. , "Thermal Conductivity and Electrical Conductivity of Alloys of Bismuth with Cadmium", Vestnik Moskov Univ. , IT, Ser. Mat. , Mekli, Astron, Fiz. , Khim. , (1), 127-36, 1956.

11. Brown, W.B. "Thermal Conductivities of some Metals in the Solid and Liquid States" , Phys., Rev., 22,

171-9, 1923.

12. Matuyama, Y. , "On the Electrical Resistance of Molten Metals and Alloys", Sci, Repts. , Tohoku. Imp. Univ. , 16 (4), 447-74, 1927.

13. Powell, R.W. , "Correlation of Metallic Thermal and Electrical Conductivities for Both Solid and Liquid

Phases", Int. J. Heat Mass Transfer, 1033-45, 1965.

14. Lucks, C.F. , and Deem, H.W., "Thermal Conductivities, Heat Capacities, and Linear Thermal Expansion

of 5 Materials", WADC TR 55-496, 65, 1956. [AD 97 185]

15. Powell, R.W. , and Tye, R. P. , "The Influence of Heat Treatment on the Electrical Resistivity and the

Thermal Conductivity of Electrodeposited Chromium", J. Inst. Metals, 24, Pt 5, 185-92, 1957.

16. McElroy, D. L. , Kollie, T.G. , Fulkerson, W. , Moore, J. P. , and Graves, R.S., private communication,

1965.

17. Harper, A. F.A., Kemp, W.R.G., Klemens, P.G. , Tainsh, R.J. , and White, G.K., "The Thermal and

Electrical Conductivity of Chromium at Low Temperatures" , Phil. Mag., 8, 2, 577-83, 1957.

18. Wood, W. A. , Transition from Hexagonal to Cubic Electrodeposited Chromium", Phil. Mag., 7, 24(l6l),

511-8, 1937.

19. Sasaki, K. , and Sekito, S. "Three Crystalline Modifications of Electrolytic Chromium", Trans. Electrochem.

Soc. (America), 59, 437-60, 1931.

20. Wolff, C.L. , "Thermal Conductivity of Lead at Low Temperature", TR 1 on Experimental Research upon

Superconducting Metals, OOR Rept. No. 2771-2, 58, 1961. [AD 253117]

21. DeHaas, W. J. , and Rademakers, A. , "Thermal Conductivity of Lead in the Superconducting and the Normal

State", Physica, 7, 992-1002, 1940.

22. Shelton, S. M. , and Swanger, W.H.

,

"Thermal Conductivity of Irons and Steels and Some Other Metals in the

Temperature Range 0-600° ", Ti’ans. Am. Soc. Steel Treating, 21, 1061-77, 1933.

77
23. Van Dusen, M. S. and Shelton, S. M. , "Apparatus for Measuring Thermal Conductivity of Metals Up to 600 C",

NBS J. Research, 12, 429-440, 1934.

24. Lucks, C.F. , "Pyrometric Standard Lead As a Thermal Conductivity Reference Material", J. Appl. Phys. , 38(4), 1973-1974, 1967.

25. Dauphinee, T.M. , Armstrong, L.D. , and Woods, S.B. , "The Thermal Conductivity of Pure Lead", Can. J. Phys., 44, 2035-2039, 1966.

26. Lees, C. H. , "The Effects of Temperature and Pressure on the Thermal Conductivities of Solids. Part II. The Effects of Low Temperatures on Thermal and Electrical Conductivities of Certain Approximately Pure

Metals and Alloys" , Phil. Trans. Roy. Soc. London, A208 , 381-443, 1908.

27. Jaeger, W. , and Diesselhorst, H. , "Thermoconduction, Electrical Conduction, Specific Heat, and Thermoelectric Force of Several Metals", Wiss. Abhandl. Physik Techn Reichsanstalt, 3, 269-425, 1900.

28. Powell, R.W. , and Tye, R.P. , "New Measurements on Thermal Conductivity Reference Materials", Intern. J. Heat Mass Transfer, U)(5), 581-96, 1967.

29. Dutchak, Ya. I. and Panasyuk, P. V. , "Investigation of the Heat Conductivity of Certain Metals on Transition

From the Solid to the Liquid State", Fiz. Tverdogo Tela. , 8(9), 2805-2808, 1966; for English translation see

Soviet Physics-Solid State, 8(9), 2244-2246, 1967.

30. Powell, R.W. , and Tye, R.P. , "Experimental Determinations of the Thermal and Electric Conductivities of Molten Metals", Proc. Conf. Thermodynamic and Transport Properties Fluids, 182-7, 1957.

31. Roll, A. and Motz, H. , "The Electrical Resistance of Melts, I. Measuring Method and Electrical Resistance

of Molten Pure Metals", Z. Metallkde, 48(5), 272-80, 1957.

32. Kemp, W.R.G. , Sreedhar, A.K. , and White, G.K., "The Thermal Conductivity of Magnesium at Low Temperatures", Proc. Phys. Soc. , A66 (ll), 1077-1078, 1953.

33. Mannchen, W. , "Heat Conductivity, Electrical Conductivity and the Lorenz Number for a Few Light Metal

Alloys", Z. Metallkunde, 23, 193-6, 1931.

34. Kempf, L.W. , Smith, C.S. , and Taylor, C.S. , "Thermal and Electrical Conductivities of Aluminum Alloys",

Trans. AIMME, 124, 287-98, 1937.

35. Powell, R.W. , "The Thermal and Electrical Conductivities of Some Magnesium Alloys", Phil. Mag. , 7, 27 , 677-86, 1939.

36. Schofield, F. H. , "The Thermal and Electrical Conductivities of Some Pure Metals", Proc. Roy. Soc .( London),

A107 , 206-27, 1925.

37. Powell, R.W. , Hickman, M. J. , and Tye, R . P. , "The Thermal and Electrical Conductivity of Magnesium and

Some Magnesium Alloys", Metallurgia, 7])(420), 159-163, 1964.

38. Horn, F.H. , "The Change in Electrical Resistance of Magnesium on Melting", Phys. Rev. , 84(4), 855-6, 1951.

39. Backlund, N.G. , private communication, January 24, 1967.

40. Kannuluik, W.G. , "The Thermal and Electrical Conductivities of Several Metals between -183° and 100° C" , Proc. Roy. Soc. (London), A141 , 159-68, 1933.

41. Kannuluik, W.G., "On The Thermal Conductivity of Some Metal Wires", Proc. Roy. Soc. (London) A131, 320-

35, 1931.

42. Tye, R.P. , "Preliminary Measurements on the Thermal and Electrical Conductivities of Molybdenum,

Niobium, Tantalum and Tungsten", J. Less-Common Metals, 3(l), 13-18, 1961.

43. Rasor, N.S. , and McClelland, J.D. , "Thermal Properties of Materials Part I. Properties of Graphite,

Molybdenum and Tantalum to their Destruction Temperatures", WADC TR 56-400, I, 1-53, 1957. [AD 118144]

44. Timrot, D. L. , Peletskii, V. E. , and Voskresenskii, V. Yu. , "Experimental Investigation of Integral Hemispherical Degree of Blackness, Electrical Conductivity, and Coefficient of Thermal Conductivity of a Series of

Refractory Metals in the Temperature Range 1300 - 3000 K", Symposium on M.G.D. , in Salzburg, 1966, in press, (private communication from Prof. A.E. Sheindlin, Feb. 13, 1967.)

45. Kraev, O. A. andStel'makh, A. A. "Thermal Diffusivity of Tantalum , Molybdenum, and Niobium at Temperatures

Above 1800 K','TeplofIz. Vysok. Temp. ,2(2), 302, 1964 ;for English translation see High Temp. ,2(2), 270, 1964.

46. Wheeler, M. J. "Thermal Diffusivity at Incandescent Temperatures by a Modulated Electron Beam Technique",

Brit. J. Appl. Phys., 16, (3), 365-76, 1965.

47. Lebedev, V.V. , "Determination of the Thermal Conductivity of Metals at High Temperatures", Fiz. Metal, i Metalloved. , 10, 187-90, 1960; for English translation see Phys. Metals and Metallog. , USSR, 10(2), 31-34,

1960.

48. Kemp, W.R.G. , Klemens, P. G. , and White, G.K., "Thermal and Electrical Conductivities of Iron, Nickel,

Titanium and Zirconium at Low Temperatures", Austral. J. Phys., 9, 180-8, 1956.

49. Angel, M.F. , "Thermal Conductivity at High Temperatures", Phys. Rev., 1, 33, 421-32, 1911.

50. Sager, G. F. , "Investigation of the Thermal Conductivity of the System Copper-Nickel", Rensselaer Polytech.

Inst. Eng. & Sci. Ser. , (27), 3-48, 1930.

78
51. Powell, R.W. , Tye, R. P. , and Hickman, M. J. , "The Thermal Conductivity of Nickel", Intern. J. Heat Mass

Transfer, 8(5), 679-87, 1965.

52. Kuhn, G. , "Irreversible Magnetic Behavior of Superconductors", Comm. Energie At. (France), Rappt. CEAR 2808, 1-116, 1966.

53. Mendelssohn, K. , "Thermal Conductivity of Superconductors", Physica, 24, S53-S62, 1958.

54. Calverley, A. , Mendelssohn, K. , and Rowell, P. M. , "Some Thermal and Magnetic Properties of Tantalum,

Niobium, and Vanadium at Helium Temperatures", Cryogenics, 2, 26-33, 1961.

55. White, G.K. , and Woods, S.B., "Low Temperature Resistivity of Transition Elements: Vanadium, Niobium,

and Hafnium", Canad. J. Phys. , 35(8), 892-900, 1957.

56. Raag, V. , and Kowger, H. V. , "Thermoelectric Properties of Niobium in the Temperature Range 300° - 1200° K". J. Appl. Phys., 36(6), 2045-8, 1965.

57. Jaeger, F.M. , and Veenstra, W. A. , "The Exact Measurement of the Specific Heats of Solid Substances at High Temperatures. VT - The Specific Heats of Vanadium, Niobium, Tantalum and Molybdenum," Rec. Trav.

Chim. , 53, 677-87, 1934.

58. Bell, I.P. , "Fast Reactor: Physical Properties of Materials of Construction", UKAEA Rept. R & DB(C)

TN-127, 1-10, 1955.

59. Tottle, C.R. , "The Physical and Mechanical Properties of Niobium", J. Inst. Metals, 85, 375-378, 1957.

60. Fieldhouse, I.B. , Hedge, J.C. , and Lang, J.I. , "Measurements of Thermal Properties", WADC TR 58-274,

1-79, 1958.

61. Voskresenskii, V. Yu. , Peletskii, V.E., and Timrot, D. L. , "Thermal Conductivity and Emissivity of

Niobium", Teplofiz. Vysok. Temp., 4(l), 46-49, 1966; for English translation see High Temperature, 4(l),

39-42, 1966.

62. White, G.K. and Woods, S.B., "Electrical and Thermal Resistivity of Transition Elements at Low Temperatures", Phil. Trans. Roy. Soc. London, A25l(995), 273-302, 1959.

63. Deverall, J. E. , "The Thermal Conductivity of a Molten Pu-Fe Eutectic (9. 5a/o Fe)", USAEC Rept. LA-2269,

1-62, 1959.

64. Denman, G. L. , unpublished data, 1966.

65. Peletzskii, V. E. and Voskresenskii, V.Yu. , "Tantalum Thermophysical Properties at Temperatues Above

1000°K", Teplofiz. Vysok. Temp., 4(3), 336-342, 1966; for English translation see High Temperature, 4(3),

329-333, 1966.

66. Jun, C.K. and Hoch, M. , "Thermal Conductivity of Tantalum, Tungsten, Rhenium, Ta-lOW, Tm, T222 > W-25 Re in the Temperature Range 1500-2800 K", AFML-TR-66-367, 1-17, 1966.

67. Worthing , A.G., "The Thermal Conductivities of Tungsten, Tantalum, and Carbon at Incandescent Temperatures by an Optical Pyrometer Method", Phys. Rev. , 4, 535-543, 1914.

68. Zavaritskii, N. V. , "The Thermal Conductivity of High Purity Thallium and Tin" , J. Exptl. Theoret. Phys.

(USSR), 39, 1571-7, 1960.

69. Bridgman, P.W., "Certain Physical Properties of Single Crystals of Tungsten, Antimony, Bismuth, Tellurium, Cadmium, Zinc and Tin," Proc. Amer. Acad. Arts Sci. , 6C), (6) 303-449, 1925.

70. Nikol'skii, N. A. , Kalakutskaya, N. A. , Pchelkin, I.M., Klassen, T.V. , and Vel'tishcheva, V.A. , "Thermophysical Properties of a Number of Fused Metals and Alloys", Voprosy Teploobmena, Akad. Nauk SSSR,

Energet. Inst, im G. M. Krzhizhanovskogo, 11-45, 1959; for English translation see Problems of Heat

Transfer, Moscow, Acad, of Sci. SSSR, 11-45, 1959.

71. Filippov, L.P. , "Methods of Simultaneous Measurement of Heat Conductivity, Heat Capacity, and Thermal

Diffusivity of Solid and Liquid Metals at High Temperatures", Intern. J. Heat Mass Transfer, 9(7), 681-691,

1966.

72. Yurchak, R. P. and Filippov, L.P. , "Thermal Properties of Liquid Tin and Lead", Teplofiz. Vysok. Temp. , 3(2), 323-325, 1965; for English translation see High Temperature, 3(2), 290-291, 1965.

73. Powell, R.W. , and Tye, R.P. , "The Thermal and Electrical Conductivity of Titanium and Its Alloys", J. Less-Common Metals, 3, 226-33, 1961.

74. Loewen, E.G. , "Thermal Properties of Titanium Alloys and Selected Tool Materials", Trans. Am. Soc. Mech. Engrs., 78, 667-70, 1956.

75. Mikryukov, V. E. , "Temperature Dependence of the Heat Conductivity and Electrical Resistance of Ti, Zr, and

Zr Alloys", Vestnik Moskov Univ. , Ser. Mat. Mekh. Astron. Fiz. Khim. , 12(5), 73-80, 1957.

76. Deem, H.W. , Wood, W.D. , and Lucks, C. F. , "The Relationship between Electrical and Thermal Conductivities of Titanium Alloys", Trans. Met. Soc., Amer. Inst. Min. Met. Eng., 212(4), 520-3, 1958.

77. Touloukian, Y. S. (Editor), "Thermophysical Properties of High Temperature Solid Materials" , Vol. 1: Elements, MacMillan Company, 1967.

79
78. Rudkin, R.L., Parker, W.J., and Jenkins, R.J., "Thermal Diffusivity Measurements on Metals and Ceramics

at High Temperatures", ASD-TDR-62-24, 1-20, 1963.

79. Konno, S. , "On The Variation of Thermal Conductivity during the Fusion of Metals", Sci. Repts. Tohoku Imp.

Univ. , 8, 169-79, 1919.

80. Bidwell, C. C. , "A Precise Method of Measuring Thermal Conductivity Applicable to Either Molten or Solid

Metals. Thermal Conductivity of Zinc", Phys. Rev. , 56, 594-598, 1939.

81. Treco, R.M., "Some Properties of High Purity Zirconium and Dilute Alloys With Oxygen", Trans. Am. Soc. Metals, 45, 872-892, 1953.

82. Timrot, D. L. and Peletskii, V. E. , "The Thermal Conductivity and Integral Blackness of Zirconium",

Teplofiz. Vysok. Temp., 3(2), 223-227, 1965; for English translation see High Temperature, 3(2), 199-202,

1965.

83. Powell, R.W. and Tye, R.P., "The Thermal and Electrical Conductivities of Zirconium and of Some

Zirconium Alloys", J. Less -Common Metals, 3^, 202-15, 1961.

84. Bing, G. , Fink, F.W., and Thompson, H.B., "The Thermal and Electrical Conductivities of Zirconium and

Its Alloys", USAEC Rept. BMI-65, 1-19, 1951.

85. Moss, M. , "An Apparatus for Measuring the Thermal Conductivity of Metals in Vacuum at High Temperatures", Rev. Sci. Instr. , 26, 276-280, 1955.

86. Fieldhouse, I.B. and Lang, J.I. , "Measurement of Thermal Properties", Armour Research Foundation,

Chicago, 111., WADD TR 60-904, 1-119, 1961. [AD 268 304].

87. Drangel, I. and Murray, G.T. , "Parameters Pertinent to the Electron Beam Zone Refinement of Refractory

Metals", A1 ME Refractory Metal Symp. , New York, 1964, Gordon and Breach, New York, 1965.

88. Metallurgia Editor, "Ultra-Pure Nickel Prepared" (News Note), Metallurgia, 72(430), 85, 1965.

89. Albano, V.J. and Soden, R.R. , "The Preparation of Ultra- High-Purity Nickel Single Crystals" , J. Electrochem. Soc., 113 , 511, 1966.

90. Taylor, G. and Christian, J.W. , "The Effect of High Vacuum Purification on the Mechanical Properties of

Niobium Single Crystals", Acta Met. , LB, 1217, 1965.

91. Van Tome, L.I. , "The Electrical Transport and Mechanical Properties of Ta-Mo Alloy Single Crystals”,

Univ. Calif. (Berkeley), Ph.D. Thesis, 1965; also USAEC Rept. UCRL-11752, 1965.

92. Guenault, A.M. , "Thermal Conduction in Normal and Superconducting Tin and Indium”, Proc. Roy Soc. (London), A262 , 420-34, 1961.

93. Higgins, R.J., Marcus, J.A. , and Whitmore, D. H. , "Intermediate -Field DeHaas-Van Alphen Effect in Zinc",

Phys. Rev., 137A , A1172-81, 1965.

94. Betterton, J.O. , "Electronic Properties of Metals and Alloys", USAEC Rept. ORNL-3870, 27-37, 1965.

95. Touloukian, Y. S. , Thermophysical Properties Research Center Data Book, Volume I . Metallic Elements and

Their Alloys, Chapter 1. Thermal Conductivity, Dec. 1966. References with numbers above 777 given in Tables 3 to 14 of the present report are either included above, under appropriate authorship, or are listed below:

835. Walton, A. J. , "The Thermal and Electric Resistance of Tin in the Intermediate State", Proc. Roy. Soc. (London), A289( 1418), 377-401, 1966.

836. Boxer, A. S. , "The Thermal Conductivity of Impure Tin at Low Temperatures", Univ. of Connecticut,

Ph.D. Thesis, 1-74, 1958.

837. Pearson, G. J. , Ulbrich, C.W. , Gueths, J.E., Mitchell, M. A. , and Reynolds, C.A. , "Superconducting - and Normal- State Thermal Conductivity of Impure Tin", Phys. Rev. , 2, 154 (2), 329-37, 1967.

844. Pigalskaya, L.A. , Yurchak, R. P. , Makarenko, I. N. , and Filippov, L. , "Thermal Properties of Molybdenum at High Temperatures", Teplofiz. Vysok. Temp. , 4(1), 144-7, 1966.

845. Pigalskaya, L. A., Yurchak, R. P. , Makarenko, I. N. , and Filippov, L. , "Thermal Properties of Molybdenum at High Temperatures", High Temperature, 4(1), 135-7, 1966.

846. Jain, S. C. , Goel, T. C. , and Chandra, I., "Thermal and Electrical Conductivities and Spectral and Total

Emissivities of Nickel at High Temperatures", Phys. Letters, 24A(6), 320-1, 1967.

851. Wright, W.H. , "Thermal Conductivity of Metals and Alloys at Low Temperatures, Part I. A Survey of Existing Data, Part H. The Thermal Conductivity of a Yellow Brass and of Cadmium", Georgia Institute

of Technology, M. S. Thesis, 1-225, 1960.

80
PART II

THERMAL CONDUCTIVITY OF GRAPHITES

81
PART II - THERMAL CONDUCTIVITY OF GRAPHITES

A. Introduction

Since graphite is not a specific material but a large family of materials and since graphite crystal is highly

anisotropic due to its two-dimensional layer structure, the thermal conductivity of graphite covers a very wide

range. The available thermal conductivity data for graphite are shown in Figure 15 and the information on the test specimens corresponding to the respective curves in the figure is given in Table 15. For the sake of clarity, only

three-tenth of the 580 curves listed in Table 15 are plotted in the figure. For those curves not shown in the figure, one is referred to the TPRC Data Book, Volume 3, Chapter 1 [l]*, in which complete numerical data tables are

also given.

Graphite falls into two categories: Natural graphite and artificial graphite. Of the latter category pyrolytic

graphite distinguishes itself from pitch-bonded artificial graphite for its well-oriented crystal structure such that

the thermal conductivity of treated pyrolytic graphite measured both parallel and perpendicular to the layer planes

approaches the values for ideal graphite single crystal [2] . Due to the lack of sufficiently large single crystals of

graphite and the difficulty in handling them, information on graphite single crystals can best be obtained through

the study of pyrolytic graphite. Experimental evidences indicate that the anisotropy of the thermal conductivity of pyrolytic graphite is far greater than that of natural graphite. In Figure 15 the highest thermal conductivity curves

are for pyrolytic graphite in the direction parallel to the layer planes. At temperatures above 100 K they are high- er than the thermal conductivity of all known solids except diamond. In contrast, the thermal conductivity of pyrolytic graphite in the direction perpendicular to the layer planes is comparable with that of the insulators. In between these two extremes lie the whole family of curves of pitch -bonded graphite varieties and natural graphites,

the location of the curves depending upon the combined effect of various parameters such as impurity, imperfection

(defects), the orientation and the size and the degree of ordering of the grains and of the crystallites, the degree

of graphitization, i. e. , the ratio of the amount of the crystalline graphite to that of the cross-linking intercrystalline carbon, the nature of the raw material, porosity and the size, shape, number, and distribution of the pores,

and so forth.

In graphite at temperatures below about 2000 K, heat is conducted primarily by lattice vibrations (phonons)

.

This is evidenced by the fact that the Lorenz function of graphite is highly dependent on temperature and on the type

of graphite and at room temperature it is two hundred to several hundred times the value for good metallic conductors, that the thermal conductivity of graphite above room temperature varies approximately as T

_1

, which is typical for a nonmetallic crystal in which the phonon-phonon (Umklapp) scattering is predominant '7 and that the

low temperature dependence of the thermal conductivity of graphite is different from that of metals. At very high

temperatures (above 2000 K), however, the thermal conductivity of graphite varies much more slowly than T

_1

, and becomes nearly temperature independent at least up to 3000 K. This behavior has been explained by Kaspar[4]

in terms of ambipolar (electrons and holes) thermal conduction in graphite at very high temperatures. He showed

that, in this high temperature region, the Wiedemann- Franz law holds for graphite with a Lorenz number of about

9(K/e;2

, in consequence of the established ambipolar electrical conduction in graphite.

At low temperatures the phonons are scattered mainly by the boundaries of crystallites, and, according to Casimir's theory [5] , the thermal conductivity should be proportional to the average size of the crystallites and

to the specific heat. It has been experimentally verified that at low temperatures the thermal conductivity of

graphite is indeed roughly proportional to the crystallite size [see, for example, 6 and 7] . However, the thermal

conductivity of graphite at low temperatures does not have the same temperature dependence as the specific heat

(T2 dependence above 10 K), but rather varies more rapidly with temperature (as great as T

2 - 7 ) [see, for example.

6 , 8

— 10 ]

.

References appear under the heading REFERENCES.

**The general feature of the thermal conductivity of nonmetallic crystals has been briefly discussed in the

INTRODUCTION to Part II of the first report [3].

82
The specific heat of graphite was treated by Komatsu and Nagamiya [ 11 ] and Gurney [l 2] assuming that in the layer-type structure of graphite each layer can be treated separately as a two-dimensional crystal, thus yielding a T

2 dependence of the specific heat of graphite at low temperatures instead of the familiar T3 law for most

solids. From another approach, by employing a semirigorous analysis of the normal mode problem for the trans- verse vibrations, Krumhansl and Brooks [ 13] showed the T

2 dependence of the specific heat to be a consequence of

the elastic anisotropy of graphite. Experimentally this T2 dependence has been confirmed by the measurements of

DeSorbo and Tyler [ 14] in the temperature range from 13 to 54 K. Measurements by Keesom and Pearlman [l 5

]

also confirmed this T2 dependence for temperatures between 10 and 20 K, though both theory [ 16] and experiment

[15,17-19] showed that the T2 law does not hold below 10 K and that eventually the T3 law predominates.

This anomaly of the thermal conductivity of graphite, which increases with temperature faster than does the

specific heat at low temperatures (above 10 K), has been explained by Klemens [20] in terms of a mean free path

for waves in the hexagonal plane, which, as a consequence of the crystallite geometry, is considerably larger for

longitudinal than for transverse waves, resulting in an increased contribution of the former to the thermal conductivity. Another explanation for this anomaly was proposed by Hove and Smith [21] in terms of a two-medium

theory, which is based on their assumption that the pitch-bonded artificial graphite is comprised of two media: the

graphite particles (each of which is made up of many single crystallites) and the intergranular ungraphitized carbon

(pitch residue). They considered the thermal conductivity of graphite particles as having a T2 dependence while that

of the ungraphitized carbon, which is assumed to be an isotropic thermal conductor, is considered to have a T3 dependence, and the latter can be taken in series with the former to obtain the total conductivity. In this way, as they

claimed, the anomalous temperature dependence of the artificial graphite can be immediately explained.

This two-medium theory has, however, been criticized by Klein and Holland and their co-workers [22,23]

on the ground that, while magnetic susceptibility results [24] imply that there is little if any nongraphitic carbon in pyrolytic graphite, experimental results indicate that the thermal conductivity of pyrolytic graphite at low temperatures is not proportional to T2

, but rather varies more rapidly than T

2 also.

Klein and Holland [22] found that across the layer planes the thermal conductivity of turbostratic pyrolytic

graphite below 20 K is nearly proportional to T

2 - 3

. Slack [25] also reported a similar temperature variation for a sample of pyrolytic graphite deposited at 2250 C. It was concluded that heat transfer across the layer planes

proceeds entirely through the lattice vibrations.

Along the layer planes, Klein and Holland's results [22] indicate that the thermal conductivity of turbostratic pyrolytic graphite varies as T2 - 5 from about 10 to 80 K. On another sample of pyrolytic graphite that had

been heat-treated at 3250 C [23], their thermal conductivity data above 10 K exhibit a T

2 • 7 dependence that accords

with Berman's measurements on a natural graphite crystal [6].

At temperatures below 10 K the thermal conductivity of pyrolytic graphite along the layer plane falls much

less rapidly than it does above 10 K

‘

' , leading to the conclusion that electrons are involved in the layer-plane heat

transport at very low temperatures [27] . Thus the thermal conductivity along the layer planes of pyrolytic graphite below 10 K can be expressed [22] as a sum of two terms: aT + bTn

, where aT represents the electronic contribution, bTn

the phonon contribution, and n^2.6 as predicted from a long-wave-length treatment of the "effective"

phonon velocity, which shows that the in-plane modes of lattice vibrations are seriously enhanced relative to the

part they play in the lattice specific heat.

Because of the large anisotropy of graphite crystals , the over-all thermal conduction of conventional graphite will

be mainly determined by the basal-plane behavior. Therefore, to sum up the discussions on the low temperature region,

the thermal conductivity of graphite should varyas T2 - 5± 0-2 above 10 K and as aT +bT2 - 5± 0,2 below 10 K.

Pyrolytic graphite whose adjacent basal planes are randomly rotated with respect to one another and thus do not display evidence of three-dimensional ordering.

The thermal conductivity of pitch-bonded artificial graphite behaves also in the same manner, see, for example,

Deegan's curves [26] in Figure 15.

83
In Figure 15 it can be seen that in the low temperature region there seems to be a trend for the thermal conductivity of pitch -bonded graphite that the higher the curve the steeper is its slope. Probably this can be explained

as the direct result of the aforementioned fact that the thermal conductivity of graphite crystal along the basal

plane varies with temperature more rapidly than that across the basal plane, in addition to the difference in magnitude due to anisotropy.

In manufacturing the pitch-bonded artificial graphite [28, 29] , when the calcined petroleum coke is crushed

or milled to obtain the dry aggregate, the individual particles, although irregular in shape, tend to have one dimension larger than the other two. This results from the fact that, in the coking process, the aromatic molecules

tend to be oriented with the planes of the benzene rings parallel to the cellular walls of the coke. These walls

usually fracture so that the length of coke particles is in the direction of the layer planes of the ultimate graphite

crystalline structure. In the process of forming, the long axes of the particles tend to take a preferred orientation:

either parallel to the direction of extrusion or perpendicular to the direction of molding pressure. The final graphite product retains the same pattern of grain orientation. The with-the-grain direction is parallel to the direction

of extrusion in extruded graphite and perpendicular to the direction of molding pressure in the molded piece. The

across-the -grain direction is perpendicular to this. Therefore, it is apparent that the low -temperature thermal

conductivity of pitch-bonded graphite measured in the with-the-grain direction is not only higher (due to inherent

anisotrophy) than that measured in the across -the -grain direction but also varying more rapidly with temperature

(due to inherent difference in temperature dependence).

For a group of different graphite samples measured in the same direction, say, in the direction with-thegrain, it is also apparent that the higher the curve the steeper is its slope. Since, other things being equal, higher

thermal conductivity implies higher degree of ordering and better alignment of the axes, and therefore the contribution to the total heat flow from conduction in the basal -plane direction is higher.

In Figure 15 it is also observed that many of the maxima of the thermal conductivity curves seem to fall approximately on a straight line (in the logarithmic plot). There are, however, many exceptions, notably the curves for samples

of Canadian natural graphite [ 10, 30] and many of the lower curves. The information available for this correlation of thermal conductivity maxima is extremely sparse due to the termination near room temperature of almost all the low temperature curves of pitch-bonded graphite before reaching their maxima. It is therefore highly desirable to have systematic measurements extending from low to high temperatures for a set of selected graphite samples with thermal conductivity covering a wide range. While knowing that the thermal conductivity maxima falling on a straight line in logarithmic

plot is a characteristic feature of the thermal conductivity of a metallic element'' and therefore can hardly be true for

graphite , the following tentative equation has been derived for this line:

1^ = 4.64 x 1010 Tm

~

4 - 35 (l)

where Tm is the temperature corresponding to the thermal conductivity maximum km. This line (a curve in linear plot) is intended mainly for the pitch-bonded graphite varieties.

Pitch-bonded artificial graphite is a mixture of crystalline graphite and cross-linking intercrystalline

carbon which may have also been graphitized or partially graphitized, and is usually of high purity but low density,

with numerous pores distributed throughout. Its thermal conductivity (or thermal resistivity) is the result of contributions from all sources and is therefore affected by many factors. In order to understand some of the factors

affecting its thermal conductivity, the production process is here briefly reviewed [28,29]

.

In manufacturing the

pitch-bonded graphite, the raw material such as calcined petroleum coke is first crushed or milled to obtain fine

particles, which are then combined with coal tar pitch to make the plastic mix. This mixture is heated to assure homogeneity and is then formed into pieces by extrusion or molding. The formed pieces are then heated by gas to a temperature of 750 to 900 C in a kiln to coke the pitch binder in the pieces to develop an infusible carbon bond

See References [2-4] of Part I of this report.

84
(the so-called first bake). In order to improve the density and other properties of the final product, the baked

pieces are pitch-impregnated at this stage. Finally the impregnated pieces are heated in an electric furnace to a temperature in the 2600-3000 C range to convert carbon into graphite, known as graphitizing.

First of all, the thermal conductivity of pitch-bonded artificial graphite is affected by the nature of the

starting raw material. Cokes from different sources behave differently with respect to the shapes of the crushed

particles. Some yield longer and more splintery particles than others and each coke source tends to have a different particle eccentricity, which affects the degree of alignment on molding or extrusion. The other major

difference among petroleum cokes is the graphitic ity, or perfection attained by the graphite crystals after heating

to 2600 to 3000 C, which affects greatly the properties of the final products. Besides the difference in the attainable perfection of graphitization, some petroleum cokes are also graphitized more easily than the others and require lower graphitizing temperature. Thus the sensitivity of thermal conductivity to thermal history can vary

considerably with graphites of different coke sources. Therefore, graphite samples of the same composition and

manufactured under identical process conditions but from different coke sources might have different anisotropy

ratios and different thermal conductivities.

Purity of the sample is an important factor affecting thermal conductivity. The purity of artificial graphite

is usually high, higher than that of the natural graphite [31]. This is partly because, during the graphitization

process, a large fraction of the impurities, which are present in the original materials to the extent of about 1 percent, distill away, since the temperatures involved are higher than the boiling points of most of the impurity compounds.

Density (or porosity) is another important factor. Results on the variation of thermal conductivity of graphite with bulk density obtained by workers at Battelle Memorial Institute and reported by Caeciotti [32] showed that

the thermal conductivities of a series of samples of graphite measured parallel to the direction of extrusion with

densities 1.41, 1.55, 1.65, 1.70, and 1 . 75 g cm-3 are, respectively, 0.795, 1.21, 1.46, 1.88, and 2.34 Watt

cm^K'1

. The conductivity versus density curve is nearly linear in the density range from 1.41 to 1.65 g cm -3 and

also in the range from 1.65 to 1.75 g cm'3 with a gradual change of slope around 1.65 g cm -3

. Thus, in the

density range from 1.41 to 1.65 g cm'3

, samples with 1 percent difference in density would have about 5 percent

difference in thermal conductivity, while in the range 1.65 to 1.75 g cm'3

, 1 percent difference in density would

cause about 10 percent difference in thermal conductivity. It should be noted that besides the bulk density (or

total porosity), the size, shape, number, and the way of distribution of the pores also have effect on thermal conductivity. In the same graphite stock, thermal conductivity and density can vary not only from piece to piece but

also within a piece of graphite. In many cases in a large piece of graphite thermal conductivity and density are

the highest near the surface and are the lowest at the center of the piece, with intermediate values gradually decreasing from the surface to the central region. Consequently, specimens cut out of the same piece of graphite

may not have the same thermal conductivity and density.

As mentioned before, the thermal conductivity of graphite is roughly proportional to the size of the crystallites, which make up the grains (graphitic particles). Thus the crystallite size is a very important factor influencing thermal conductivity. Due to the large anisotropy of graphite crystals, thermal conductivity is affected also by

the degree of ordering of the crystallites. Another important factor is the crystal imperfection; the type and the concentration of defects are of important influence. The effect of lattice defects on the thermal conductivity of graphite

has been extensively studied [see, for example, 10, 26,33-40] by investigating the effects of irradiation damage on

thermal conductivity. The thermal conductivity of graphite is drastically reduced by irradiation, which produces lattice defects, and it can be recovered by annealing. Smith and Rasor [10] found that neutron irradiation causes the

thermal conductivity of graphite to decrease markedly at a rate that decreased with exposure time and also the

exponent of the temperature dependence decreases with exposure. Mason and Knibbs [37] found that when the

crystallite size of graphite is so small (<100 A) that the number of crystal layers per unit volume is greater than

the number of displaced atoms, clusters cannot form and the thermal resistivity is directly proportional to the

85
irradiation dose, and that when the crystallite size is large (>100 A), so that the diameter is greater than the dis- tance between clusters, the number of clusters is independent of crystallite size and the thermal resistivity varies

only as the square root of the dose. Unpublished work by Meyer [40] indicated that the irradiation effect on thermal conductivity is inversely proportional to the irradiation temperature from room temperature to 1400 C.

The thermal conductivity of graphite is affected by the size of the graphitic particles (grain size). However,

this effect is different with different type of graphites, and no general conclusion can therefore be drawn. As discussed in detail before, due to the planar shape of the calcined petroleum coke particles, in the forming process

the long axes of the particles tend to take a preferred orientation: either parallel to the direction of extrusion or

perpendicular to the direction of molding pressure, and the final graphite product retains the same pattern of

grain orientation. Therefore, the thermal conductivity is highly dependent on the grain orientation and also on the

degree of ordering of the grains.

The graphitizing temperature has a tremendous effect on thermal conductivity. During graphitization, the

thermal conductivity of the material can increase by a factor of the order of twenty-five [28] . This is due to the

increased perfection, growth, and rearrangement of the graphite crystallites, these being quite small and in ran- dom arrangement in the gas-baked carbon piece. The thermal conductivity of any piece of graphite is, therefore,

directly dependent upon the highest temperature reached in graphitization. The higher the graphitizing temperature,

the greater the temperature uniformity and the longer the graphitizing time, the higher is the thermal conductivity

of the end product. Consequently, the heat treatment associated with measurements on a sample of graphite made

at temperatures higher than its graphitizing temperature may increase its thermal conductivity. It should be noted, as mentioned before, that some petroleum cokes are graphitized more easily than others and therefore the

sensitivity of thermal conductivity to thermal history can vary considerably.

The thermal conductivity of graphite from room temperature to about 2000 K decreases gradually and monotonically with increasing temperature and varies roughly as T

_1

, in accord with the theory of phonon conduction.

Above 2000 K the thermal conductivity varies much more slowly than T

-1 and in fact becomes nearly independent

of temperature due to the contribution of ambipolar electronic thermal conduction, as discussed earlier. However,

at very high temperatures approaching the sublimation temperature of graphite, the thermal conductivity of pitchbonded graphite decreases abruptly, falling by about an order of magnitude in a relatively small temperature interval [41-43]. Euler [42] regarded this as being due to the loosening of the graphite structure at these very high

temperatures, and a consequent large irreversible drop in density. However, Rasor and McClelland i-4ll found no permanent change in density from their measurements. Since the specific heat of graphite measured by them has an

abrupt and large increase at about the same temperature at which the thermal conductivity has an abrupt and

large decrease, they explained this striking feature being due to the formation of thermally produced lattice defects - vacant lattice sites, and suggested a vacancy concentration of about 0. 5 atomic percent at the sublimation temperature and an energy of formation of 7.7 ±0.5 eV for the vacancies.

Golovina and Kotova [44] have demonstrated that when graphite is heated in a gaseous reagent such as carbon dioxide or oxygen at high temperatures above 2300 K, unsteady -state internal diffusion within the graphite

specimen occurs such that carbon atoms diffuse from within the solid to the surface on which the reaction with the

gas takes place. The density of the graphite decreases, and that of the surface layer reduces to about one half of the original density. With increase in temperature and reaction time the carbon atoms are removed from ever deeper layers of the graphite specimen and the depth of loosening increases. However, the density at the surface

changes only insignificantly and remains at about one half of the original density for a wide range of temperatures

and for various degrees of removal of graphite mass of 15 to 30 percent. The conditions of Golovina and Kotova

differed from those of Euler [42, 43] and of Rasor and McClelland [41], furthermore, Anacker and Mannkopff [67]

report experiments which yielded no marked drop in thermal conductivity, so more studies near the upper temperature limit of graphite are required.

A correlation between the thermal and electrical conductivities of graphite was first proposed by Powell in 1937 [45]. For Acheson graphite from room temperature to 1073 K he suggested the following equation for the

86
variation of the Lorenz function with temperature:

L = ko'~ 1 T

-1 = 0.123 T

_1,8 (2)

or

k = 0.123 ctT -0 - 8 (3)

where L is the Lorenz function, k the thermal conductivity in Watt cm-1 K

-1

, a the electrical conductivity in ohm-1 cm-1

, and T the temperature in K. Based upon further available data, Powell [46] later proposed the

equation

k = 2.2ctT _1 -3 + 0.18 (4)

for the Ceylon and Hilger and Acheson graphites and

k= 3.1CTT -1 - 3 + 0.25 (5)

for the Cumberland graphites.

Currie, Hamister, and MacPherson [28] derived an empirical relationship between the room -temperature

thermal conductivity and the room-temperature electrical resistivity of pitch-bonded artificial graphite based upon

the data of Powell [45] , Powell and Schofield [47], Johnson [48], Neubert [49],and of Micinski [50], They

claimed that the following equation would yield the thermal conductivity of graphite at 25 C accurate to within 5 percent:

k = 0. 0013p _1 (6)

where the thermal conductivity, k, is in Watt cm_1 K

_1 and the electrical resistivity, o, is in ohm cm and measured

at 25 C.

'

Mason and Knibbs [51] demonstrated that for a given graphite the thermal resistivity varies linearly with

electrical resistivity when either the orientation or the crystallinity varies. They attributed this correlation to the

fact that the flow of both heat and electricity is restricted essentially to the crystal layer planes and that in both cases the flow is controlled by scattering at crystal boundaries. They derived the following relationship, applicable at 20 C,

707 p + 0.0813 v '

which was shown to hold fairly well for over forty graded graphites, and enables the thermal conductivity to be

estimated from electrical measurements to within ±15 percent.

Although there are 580 curves listed in Table 15, yet most of the measurements are for low and/or moderate temperatures and many are for unidentified graphite specimens. It is found that no graphite has available

thermal conductivity data covering the full range of temperature.

The graphites studied in the following section include Acheson graphite

v

, ATJ graphite, pyrolytic graphite,

87 5S graphite, and 890S graphite. They are selected mainly because they seem to be the only graphites with

available thermal conductivity data covering a fairly wide range of temperature. This selection, therefore, does

not give a fair representation of all the graphites in common usage.

It is understood that most of the other pitch-bonded artificial graphites can also be called Acheson graphite.

Here this group is intended mainly for those early measurements in which the graphite specimens used were

known only as Acheson graphite.

87
There are many other important graphites for which, unfortunately, the available thermal conductivity data are not sufficient at the present time to include them in this study. It is hoped that due to the current great interest

in graphites many further measurements on thermal conductivity will be made over wide ranges of temperature and

that in the subsequent updating and revision of this work many other graphites can then be included. It is interesting to note that in the Directory of Graphite Availability [52] published in 1963, there are listed over 230 grades of graphites manufactured by 18 companies in the United States. For many of these graphites there are not any

published experimental thermal conductivity data available.

The available data for the five graphites being studied are separately plotted in Figures 18 t© 22. The

information on the specimens corresponding to the respective curves in the figures has been given in Table 15. Each figure includes two heavy broken lines which seem likely to represent the most probable curves for each

graphite. However, due to the lack of experimental data in low and/or high temperature regions for most of these

graphites, many sections of the recommended curves have been obtained by extensive extrapolations and are very

tentative and subject to modification and revision in the light of further work.

Tne recommended thermal conductivity values are reported collectively in Figures 16 and 17 and in Tables

16a and 16b. Table 16a gives temperatures in degree K while Table 16b gives temperatures in degree C. In the

tables, the third significant figure is given only for internal comparison and for smoothness and is not indicative

of tiie degree of accuracy. Some pertinent comments regarding the treatment of the data for each graphite are

given in the following section.

B. Thermal Conductivity of a Group of Selected Graphites

Ache son Graphite

Acheson graphite is generally referred to as the graphite manufactured by using the production process

invented by Dr. E. G. Acheson (1856-1931) [53]. Before the second world war and especially in Europe, the

commercially available artificial graphite was (mown only as Acheson graphite. Most of the thermal conductivity

data for this group are from early measurements and are therefore of historical interest also.

There are 20 curves available. As shown in Figure 18 , the available data for specimens measured along

the direction of extrusion cover the temperature range from 93 to 2000 K while those for specimens measured

perpendicular to the direction of extrusion are over the range 93 to 3048 K. Most of the data were produced by

Powell [45] and Powell and Schofield [47] for two different sets of specimens, and their data are in good agreement when taking the anisotropy of the specimens into account. Buerschaper's [54] data for the two principal

directions( curves 44 and 45) near room temperature are also in agreement with their data. However,

Buerschaper's data increase monotonically as the temperature decreases down to 93 K indicating that the thermal

conductivity maxima are at temperatures at least below 93 K, which is considered very unlikely. Although there

is no experimental information available for the locations of the thermal conductivity maxima, it is believed that

the maxima of the curves would not be at temperatures lower than 250 K.

The recommended curve from 300 to 3000 K for the direction perpendicular to the axis of extrusion follows

the curves of Powell and Schofield [47], while the curve for the direction parallel to the axis of extrusion from

300 to 1000 K passes through the mean of Powell's curves [45]. From these two sections of the recommended

curves so obtained, the anisotropy ratio is calculated and is equal to 1.375 at 300 K and 1.36 at 1000 K. Extrapolating these two values to higher temperatures gives 1.349 at 1500 K, 1.339 at 2000 K, 1.328 at 2500 K, and

1. 317 at 3000 K. Based upon these values for the anisotropy ratio, the curve for the direction parallel to the axis

of extrusion is extrapolated from 1000 to 3000 K.

Both recommended curves have been extensively extrapolated from 300 K down to 0 K according to the

general trend of the low -temperature curves of other graphites. This is intended mainly for indicating the trend

of the thermal conductivity values of this graphite at low temperatures.

88
The uncertainty of the recommended values that are derived from experimental data is probably of the

order of ±10 to ±20 percent, and that of the values obtained by extensive extrapolation is probably twice as great.

ATJ Graphite

ATJ graphite 5 - is a pitch-bonded petroleum -coke -base graphite, produced by the Carbon Products Division

of Union Carbide Corporation. It is a widely known premium grade graphite with very fine grains (0.006 inch

maximum) and is formed by molding into rectangular blocks, 9 x 20 x 24 inches in size. Nominal room-temperature properties [29] are: bulk density 1.73 g cm-3 with standard deviation 0.036 g cm'3(i.e, , 2. 1 percent), electrical resistivity 11.0 x 10 -4 ohm cm (with grain), 14.5 x 10 -4 ohm cm (across grain), and anisotropy in electrical

resistivity 1.32.

As shown in Figure 19, there are nineteen curves available for the thermal conductivity of this graphite.

The three curves 93, 111, and 120 for GBH graphite [41,55,56] have been included here. Since the two single data

points (curve numbers 344 and 345) at room temperature are believed to be calculated values [29], the experimental data cover the temperature range only from 484 to 3276 K.

For the direction perpendicular to the molding pressure, the data of Lucks and Deem(curve 93)[55]are in good agreement with those of Fieldhouse, Lang, and Blau (curve 21 7) [57] in the narrow temperature range 650 to 800 K. Above 800 K these two sets of data diverge, and at 1200 K they differ by about 35 percent. At these higher

temperatures Lucks and Deem's data (curve 93) appear to be high, which may probably be due to the uncertainty in the reference data at high temperatures in the early years for the Armco iron bar used as a comparative reference

material. On the other hand, the data of Fieldhouse et al. (curve 217) at temperatures above 1000 K are too low,

since their curve (217) decreases almost linearly to values at temperatures above 1420 K lower than their other curve (216), which is for a sample measured with heat flow parallel to the molding pressure. The recommended

curve from 484 to 1000 K follows curves 93 and 217, and is extended in the temperature range 1400 to 2000 K through the mean of curves 269 and 270 of workers at the Parma Research Laboratory of Union Carbide Corporation [58] and

in the range 2400 to 3273 K through the mean of curve 120 of Rasor and McClelland [41] . It is then extrapolated to 3800 K according to the general trend indicated by the data of Rasor and McClelland [41] for 875S graphite.

For the direction parallel to the molding pressure the recommended curve from 600 to 2000 K lies close to curve 216 of Fieldhouse, Lang, and Blau[57] and curve 271 of workers at Parma Research Laboratory [58], and

is then extrapolated to 3800 K.

The resultant recommended curves yield anisotropy ratio of 1 . 32 at 300 K, decreasing to 1.29 at 1000 K,

1.25 at 2000 K, and 1.19 at 3800 I\. Both curves have been extensively extrapolated from room temperature down

to absolute zero according to the general trend of the low-temperature curves of other graphites.

The uncertainty of the recommended values that are derived from experimental data is probably of the

order of ±10 to ±20 percent, and that of the values obtained by extensive extrapolation is probably twice as great.

Pyrolytic Graphite

Pyrolytic graphite is produced by the deposition of carbon from a gaseous hydrocarbon onto a heated surface

at high temperature of the order of 2000 C. As shown in Figure 20, there are 77 curves available for this graphite.

The general feature of the thermal conductivity of pyrolytic graphite has been briefly reviewed in the

INTRODUCTION. Figure 20 shows clearly the large anisotropy in the thermal conductivity. Since the thermal

conductivity of this graphite is highly sensitive to small sample variations, curves for the samples measured in the same direction spread also into a very wide band. It has been noted [22] that significant variations in thermal

conductivity can be encountered with pyrolytic graphites deposited at identical temperature. This effect is ascribed

to be a result of influencing factors in the manufacturing procedure other than temperature.

TT7 —

This graphite was previously designated in the development stage as GBH graphite.

89
The highest thermal conductivity curve (No. 491 ) for the direction parallel to the layer planes is that of De Combarieu [59] for a specimen deposited at 2100 C and annealed under a pressure of 200 bars for 10 to 15

minutes at 2800 C. The recommended curve follows Combarieu' s data to 300 K and is then extended to higher

temperatures according to the temperature dependency indicated by Taylor's [60] curve (No. 519), which is for a sample annealed at 3300 C. At high temperatures the recommended curve lies close to curve 514 of Johnson and

Watt [61] and nearly passes through a point (No. 558) obtained by Hoch and Vardi [62]. It is interesting to note that

at room temperature the thermal conductivity of highly-oriented and well-annealed pyrolytic graphite in the direction parallel to the layer planes is 4.7, 5.0, and 11.3 times higher than the thermal conductivity of silver, copper,

and tungsten, respectively, and is only slightly lower than that of Type Ha diamond. At 2000 K it is still 2. 5 times

higher than that of tungsten.

The recommended values for the direction perpendicular to the layer planes are derived from the values

for the direction parallel to the layer planes based upon the assumed anisotropy ratio given as a function of temperature. The anisotropy ratio in the thermal conductivity of pyrolytic graphite at temperatures below 1 K lies between 2 and 3 as reported by Slack [25], Its exact value is determined by the elastic constants and by the

ellipsoidal shape of the crystallites. In the liquid-helium temperature region Klein and Holland [22] found that the

ratio is close to 3, which remains the same for samples deposited at different temperatures, but rises rapidly with

temperature above 20 K. For highly-oriented and well-annealed sample, Hooker, Ubbelohde, and Young [2]

found that the ratio increases to about 100 at 90 K, 196 at 150 K, 215 at 200 K, 211 at 250 K, and 210 at 300 K. Taylor [60] also found that the anisotropy ratio for his samples is 210 at 300 K. From 300 to 900 K Taylor's data

indicate a nearly constant anisotropy ratio. Since the data of Taylor [60] and of Hooker et al. [2] are close to that

of De Combarieu [59] and since their samples are all similar, the above-mentioned values for the anisotropy

ratio at different temperatures are adopted for deriving the recommended values for the direction perpendicular

to the layer planes. The resulting curve has a maximum conductivity of 1. 55 Watt cm-1 K

_1 at about 30 K, and lies

close to the curves (No. 579, 498, and 499) of Hooker, Ubbelohde, and Young [63,2] in the temperature range

from 90 to 300 K. From 250 to 830 K it has the same temperature dependency as curve 520 of Taylor [60], It

is noted that the values are lower than the thermal conductivity of aluminum oxide by 3. 7 and 5 times at room

temperature and 2000 K, respectively.

The uncertainty of the recommended values for the direction parallel to the layer planes at temperatures

below 1500 K is probably of the order of ±10 to ±20 percent, and that at temperatures above 1500 K is probably

twice as great. The values for the direction perpendicular to the layer planes are intended only for indicating

the general trend.

875S Graphite

875S graphite* is a medium -grain (0. 032 inch maximum), pitch-bonded petroleum-coke-base graphite,

which is formed by extrusion into rods 20 or 24 inches in diameter and 72 inches long. It is produced by Speer

Carbon Co. , with typical density 1.67 g cm -3 and typical ash content 0.70 percent ;L 64] . As shown in Figure 21

,

there are six curves available for the thermal conductivity of this graphite over the temperature range from 433

to 3708 K.

For the direction perpendicular to the axis of extrusion, the data of Lucks and Deem (curve 94) [55] agree

well with the higher curves (117,114, and 115) of Rasor and McClelland [41] . Curve 117 is the result of measurements made after prolonged heating the specimen at temperatures greater than 2480 K and thus represents the

stable thermal conductivity values at high temperatures. Accordingly, the recommended curve from 433 to 3800 K

follows closely the curves 94, 117, 114, and 115.

For the direction parallel to the axis of extrusion, only the data of Fieldhouse, Hedge, and Waterman

(curve 112) [56] are available. If a smooth curve is drawn through their data, the resulting curve, together with

the recommended curve for the direction perpendicular to the axis of extrusion just obtained above, will give

*This graphite was previously designated in the development stage as 7087 graphite.

90
anisotropy ratios of 1. 64 at 800 K, 1.52 at 1400 K, and 1.49 at 1800 K. These values of the anisotropy ratio for

the thermal conductivity are much greater than the anisotropy ratio of 1. 19 for the electrical resistivity of this

graphite as reported by Rasor and McClelland [41], This is inconsistent with the statement of Rasor and

McClelland [41] that these two anisotropy ratios are approximately the same. Since the data of Lucks and Deem

[55] and of Rasor and McClelland [41] for the direction perpendicular to the axis of extrusion are in good agreement, curve 112 is suspected to be too high. This conclusion is further supported by the fact that, as shown in Figure 15, curve 112 is so high that it approaches or even exceeds some of the curves for the same temperature

and direction for pyrolytic graphite and hot-pressed graphites of much greater anisotropy. It is decided therefore

that the recommended curve will not follow curve 112.

It is noted that the anisotropy ratio of pitch-bonded graphite above room temperature is generally decreasing

with increase in temperature. To give a little weight to curve 112, it is assumed that the anisotropy ratio of this

graphite at 3800 K is 1.19, which is the anisotropy ratio of this graphite for the electrical resistivity as reported

by Rasor and McClelland [41] , and that the anisotropy ratio decreases by about 10 percent from room temperature

to 3800 K. The latter assumption is based upon the anisotropy ratio of ATJ graphite which is also 1.19 at 3800 K

as indicated by the derived recommended values and which decreases by about 10 percent from room temperature

to 3800 K. Thus the recommended values from room temperature to 3800 K for the direction parallel to the axis

of extrusion are calculated from the values for the direction perpendicular to the axis of extrusion according to the

assumed values of anisotropy ratio.

Both of the recommended curves have been extensively extrapolated down to 0 K to indicate the general

trend of the curves.

The uncertainty of the recommended values for the direction perpendicular to the axis of extrusion that are

derived from experimental data is probably of the order of ±10 to ±20 percent, and that of the values obtained by

extrapolation is probably twice as great. The values for the direction parallel to the axis of extrusion are intended

only for indicating the general trend.

890S Graphite

890S graphite* is a fine-grain (0.008 inch maximum), pitch-bonded petroleum -coke -base graphite, which is formed by extrusion into rods 2. 5 to 8 inches in diameter and 24 to 72 inches long. It is produced by Speer Carbon

Company, with typical density 1.63 g cm~3 and typical ash content 0 . 08 percent [65]. As shown in Figure 22 , there are six curves available for the thermal conductivity of this graphite over the temperature range from 798 to 3786 K.

For the direction perpendicular to the axis of extrusion, all the three available curves are of Rasor and

McClelland [41] . A curve passing through the mean of their data from 1000 to 3800 K serves as the recommended

curve.

For the direction parallel to the axis of extrusion, all the three curves, which cover the temperature range

798 to 1809 K, are of Fieldhouse, Hedge, Lang, Takada, and Waterman [66]. Of these three curves, curve 6, which is for the specimen heated only once, coincides with the curve of Rasor and McClelland, noting that they are

for different directions. Curve 7, which is for the specimen heated twice, is higher than curve 6 by about 20 percent, and curve 8, which is for the specimen heated three times, crosses all the curves and is higher than curve 6 by 30 percent at 800 K and lower than Rasor and McClelland's curve by 25 percent at 1800 K. Under this confusing

circumstance, a small section of the recommended curve has been drawn through the middle portion of curve 8, using as a guide the general trend of the other recommended curves. From these two sections of the recommended curves the anisotropy ratio can be calculated and is equal to 1.18 at 1000 K. By assuming that the anisotropy ratio above room temperature decreases linearly with increase

This graphite was previously designated in the development stage as 3474D graphite.

91
in temperature and that at 3800 K it is equal to 1. 08, which is the anisotropy ratio for the electrical resistivity of

this graphite as reported by Rasor and McClelland [41] , the recommended values from 1000 to 3800 K are obtained

by calculation based upon the recommended values already derived for the direction perpendicular to the axis of

extrusion.

Both recommended curves have been excessively extrapolated from 1000 K down to 0 K to indicate the

general trend of the curves.

The uncertainty of the recommended values above 1000 K that are derived from experimental data is probably of the order of ±10 to ±20 percent; and that of the values obtained by extensive extrapolation is probably

twice as great. The values below 1000 K are intended only for indicating the general trend.

92

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15.

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TABLE

15.

SPECIFICATIONS

OF

THE

SPECIMENS

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116

See

TPRC

Data

Book

Vol.

3,

Chapter

1,

References
Cur.

Ref.

Met’d.

Temp.

Name

and

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No.

Author(s)

Year

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Range

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298

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sound

velocity

4.7

x

10 5

cm

sec

-1

at

the

same

conditions

as

above;

heat

flow

perpendicular

to

c-axis.
TABLE

15.

SPECIFICATIONS

OF

THE

SPECIMENS

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127

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third

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internal

comparison

and

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smoothness

and

is

not

indicative

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the

degree

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accuracy.
TABLE

16b.

RECOMMENDED

THERMAL

CONDUCTIVITY

OF

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for

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is

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accuracy.
129

TPRC

TEMPERATURE,

K

—

FIG

18
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130
THERMAL

CONDUCTIVITY

,

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131
132

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TEMPERATURE,

K

—

FIG

21
133

TPRC

TEMPERATURE,

K

—

FIG

22
C. References

1. Touloukian, Y. S. , Thermophysical Properties Research Center Data Book, Vol. 3. Nonmetallic Elements,

Compounds and Mixtures (in Solid State atNTP), Chapter 1. Thermal Conductivity, Dec. 1966. References

with numbers above 369 given in Table 15 of the present report are listed at the end of this section.

2. Hooker, C.N. , Ubbelohde, A. R. , and Young, D.A., "Anisotropy of Thermal Conductance in Near-Ideal

Graphite", Proc. Royal Soc. (London), A284 (1396), 17-31, 1965.

3. Powell, R.W., Ho, C.Y. , and Liley, P. E. , "Thermal Conductivity of Selected Materials", National Standard

Reference Data Series -- National Bureau of Standards NSRDS-NBS 8, 65-6, 1966.

4. Kaspar, J. , "Thermal Propagation in Carbons and Graphites at Very High Temperatures", USAF Rept.

SSD-TR-67-56, Aerospace Corp. Rept. TR-1001 (9250-02)-l, 1-40, 1967.

5. Casimir, H. B. G. , "Note on the Conduction of Heat in Crystals", Physica, 5, 495-500, 1938; also Commun.

Kamerlingh Onnes Lab. , Univ. Leiden, Suppl. No. 85B, 1-6, 1938-42.

6. Berman, R. , "The Thermal Conductivity of Some Polycrystalline Solids at Low Temperatures", Proc. Phys.

Soc. (London), A65, (l2), 1029-40, 1952.

7. Jamieson, C.P. and Mrozowski, S. , "Thermal Conductivities of Polycrystalline Carbons and Graphites",

Proc. Conf. Carbon, Univ. Buffalo, 155-66, 1956.

8. Tyler, W.W. and Wilson, A.C., Jr., "Thermal Conductivity, Electrical Resistivity, and Thermoelectric

Power of Graphite" , Phys. Rev., 89(4), 870-5, 1953; also USAEC Rept. KAPL-789, 1-44, 1952.

9. Rasor, N.S. , "Low Temperature Thermal and Electrical Conductivity and Thermoelectric Power of Graphite",

USAEC Rept. NAA-SR-1061, 1-23, 1955.

10. Smith, A.W. and Rasor, N.S. , "Observed Dependence of the Low-Temperature Thermal and Electrical Conductivity of Graphite on Temperature, Type, Neutron Irradiation, and Bromination ", Phys. Rev. , 104(4), 885-91, 1956; also USAEC Rept. NAA-SR-1590, 1-25, 1956. [AD 106 065]

11. Komatsu, K. and Nagamiya, T., "Theory of the Specific Heat of Graphite", J. Phys. Soc. Japan, 6(6), 438-

44, 1951.

12. Gurney, R.W. , "Lattice Vibrations in Graphite", Phys. Rev. , _88(3), 465-6, 1952.

13. Krumhansl, J. and Brooks, H. , "The Lattice Vibration Specific Heat of Graphite", J. Chem. Phys., 2l(l0),

1663, 1953.

14. DeSorbo, W. and Tyler, W.W., "The Specific Heat of Graphite from 13 to 300 K", J. Chem. Phys., 2l(l0),

1660-3, 1953.

15. Keesom, P. H. and Pearlman, N. , "Atomic Heat of Graphite between 1 and 20 K", Phys. Rev., £9, 1119-24,

1955.

16. Komatsu, K. "Theory of the Specific Heat of Graphite", J. Phys. Soc. Japan, 1_0, 346-56, 1955.

17. Bergenlid, U. , Hill, R.W. , Webb, F.J., and Wilks, J. , "The Specific Heat of Gi’aphite below 90 K", Phil.

Mag., 45, 851-4, 1954.

18. DeSorbo, W. and Nichols, G. E. , "A Calorimeter for the Temperature Region 1 to 20 K - The Specific Heat

of Some Graphite Specimens" , J. Phys. Chem. Solids, 6(4), 352-66, 1958.

19. Van der Hoeven, B.J.C. and Keesom, P. H. , "Specific Heat of Various Graphites between 0. 4 and 2. 0 K". Phys. Rev., 130(4), 1318-21, 1963.

20. Klemens, P. G. , "The Specific Heat and Thermal Conductivity of Graphite", Australian J. Phys. , 6, 405-9,

1953.

21. Hove, J.E. and Smith, A.W., "Interpretation of Low-Temperature Thermal Conductivity of Graphite", Phys.

Rev., 104(4), 892-900, 1956.

22. Klein, C.A. and Holland, M.G., "Thermal Conductivity of Pyrolytic Graphite at Low Temperatures. I. Turbostratic Structures", Phys. Rev. , 136( 2A) , A575-90, 1964.

23. Holland, M. G. , Klein, C.A. , and Straub, W.D. , "The Lorenz Number of Graphite at Very Low Temperatures", J. Phys. Chem. Solids, 27(5), 903-6, 1966.

24. Fischbach, D.B., "The Magnetic Susceptibility of Pyrolytic Carbon", Proc. 5th Conf. Carbon, Univ. Park,

Penn., 1961, 2, 27-36, publ. 1963.

25. Slack, G.A. , "Anisotropic Thermal Conductivity of Pyrolytic Graphite" , Phys. Rev., 127 , 694-701, 1962.

26. Deegan, G.E. , "Thermal and Electrical Properties of Graphite Irradiated at Temperatures From 100 to 425 K", USAEC Rept. NAA-SR-1716, 1-77, 1956.

27. Klein, C.A. , "Simple Two-Band (STB) Model and Transport Properties of Pyrolytic Graphites", J. Appl.

Phys., 35(10), 2947-57, 1964.

28. Currie, L.M., Hamister, V.C., and MacPherson, II. G. , "The Production and Properties of Graphite for Reactors", Proc. Intern. Conf. Peaceful Uses Atomic Energy, 1-49, 1955.

134
29. Union Carbide Corporation, Carbon Products Division, "The Industrial Graphite Engineering Handbook", 1965.

30. Smith, A.W. , "Low Temperature Thermal Conductivity of a Canadian Natural Graphite", Phys. Rev. , 95,

1095-6, 1954.

31. Neubert, T. J. , Royal, J. , and Van Dyken, A. R. , "The Structure and Properties of Artificial and Natural

Graphite", USAEC Rept. ANL-5524, 1-44, 1956.

32. Cacciotti, J. J. , "Graphite and Its Properties", General Electric Co. , Flight Propulsion Laboratory Department, 1-63, 1958 (revised 1960).

33. Rasor, N.S. , "Technique for the Measurement of Changes in Thermal and Electrical Properties of Pulse - Annealed Irradiated Graphite" , USAEC Rept. NAA-SR-43, 1-36, 1950.

34. Durand, R. E. and Klein, D. J. , "The Effect of Reactor Irradiation at Temperatures between 400 and 700 C on

the Thermal Conductivity of Graphite", USAEC Rept. NAA-SR- 1520, 1-33, 1956.

35. Fletcher, J. F. and Snyder, W.A. , "Use of Graphite in the Atomic Energy Program", Am. Ceram. Soc. Bull.,

36(3), 101-4, 1957.

36. Schweitzer, D. and Singer, R. , "Thermal Conductivity of Radiation Damaged AGOT Graphite from the

Graphite Research Reactor", USAEC Rept. BNL-696 (S-59), 56-8, 1962.

37. Mason, I.B. and Knibbs, R.H. , "Influence of Crystallite Size on the Thermal Conductivity of Irradiated

Polycrystalline Graphite", Nature, 198 , 850-1, 1963.

38. Hooker, C.N. , Ubbelohde, A.R. , and Young, D.A., "Thermal Conductance of Graphite in Relation to its Defect Structure", Proc. Roy. Soc. (London), 276(1364) , 83-95, 1963.

39. Goggin, P.R. and Reynolds, W. N. , "The Annealing of Thermal Conductivity Changes in Electron-Irradiated

Graphite", Phil. Mag., 8, 265-72, 1963.

40. Meyer, R.A. , paper presented in the Carbon Conference 1965; private communication, February 6, 1967.

41. Rasor, N.S. and McClelland, J.D. , "Thermal Properties of Graphite, Molybdenum, .and Tantalum to Their

Destruction Temperatures" , J. Phys. Chem. Solids, L5, 17-26, 1960; also WADC TR 56-400, Parti, 1-53,

1957.

42. Euler, J. , "The Heat Conductivity of Artificial Graphite Rods at Temperatures between 3300 and 3700 K",

Naturwissenschaften, (39, 568-9, 1952.

43. Euler, J. , "The Axial Temperature Distribution on the Internal Anode of a Carbon Arc and the Thermal Conductivity of Graphite at High Temperatures", Ann. Physik, 6,_18, 345-69, 1956.

44. Golovina, E. S. and Kotova, L.L. , 'Relationships in the High-Temperature Reaction of Carbon", Doklady

Akademii Nauk SSSR, 169 (4 ) , 807-9, 1966; for English Translation see Soviet Phys. - Doklady, _M(8), 689-91,

1967.

45. Powell, R. W. , "The Thermal and Electrical Conductivities of a Sample of Acheson Graphite from 0 C to 800

C", Proc. Phys. Soc. (London), 49 (4), 419-25, 1937.

46. Powell, R. W. , "The Thermal Conductivities of Carbons and Graphites at High Temperatures", Proc. Conf.

Ind. Carbon and Graphite (London) , 1957,46 - 51, publ. 1958.

47. Powell, R. W. and Schofield, F.H. , "The Thermal and Electrical Conductivities of Carbon and Graphite to High Temperatures", Proc. Phys. Soc. (London), 51 (1), 153-72, 1939.

48. Johnson, H. V., Unpublished data, National Carbon Company, as quoted in Ref. 28. 49. Neubert, T. J. , Argonne National Laboratory, private communication as quoted in Ref. 28.

50. Micinski, E. , Unpublished data, National Carbon Company, as quoted in Ref. 28. 51. Mason, I. B. and Knibbs, R. H. , "The Thermal Conductivity of Artificial Graphites and Its Relationship to Electrical Resistivity", UKAEA Rept. AERE-R 3973, 1-22, 1962.

52. Glasser, J. and Few, W. E., "Directory of Graphite Availability", ASD-TDR-63-853, 1-266, 1963.

[AD 422700]

53. Acheson, E. G. , U.S. Patent 542 , 982, 1895.

54. Buerschaper, R. A. , "Thermal and Electrical Conductivity of Graphite and Carbon at Low Temperatures",

J. Appl. Phys., U5, 452-4, 1944.

55. Lucks, C. F. and Deem, H. W. , "Thermal Conductivities, Heat Capacities, and Linear Thermal Expansion of Five Materials", WADC TR 55-496, 1-65, 1956. [AD 97185]

56. Fieldhouse, I. B. , Hedge, J. C., and Waterman, T. E. , "Measurements of thermal Properties", WADC TR

55-495, Ptm, 1-10, 1956. [AD 110526]

57. Fieldhouse, I. B. , Lang, J. I., and Blau, H. H., "Investigation of Feasibility of Utilizing Available Heat

Resistant Materials for Hypersonic Leading Edge Applications, Vol. IV. Thermal Properties of Molybdenum

Alloy and Graphite", WADC TR 59-744 (Vol. 4), 1-78, 1960. [AD 249166]

58. Breckenridge, R. G. (Coordinator), "Thermoelectric Materials", Union Carbide Corp. Parma Research Lab.

Bi-Monthly Progress Report No. 4, 1-33, 1959. [AD 231650]

135
59. De Combarieu, A. , "The Effects of Irradiation on the Thermal Conductivity at Low Temperatures of PseudoMonocrystalline Graphite", Bull. Inst. Intern. Froid, Annexe 1965-2, 63-72, 1965.

60. Taylor, R. , "The Thermal Conductivity of Pyrolytic Graphite", Phil. Mag. , _8, 13(121), 157-66, 1966.

61. Johnson, W. and Watt, W. , "Thermal Conductivity of Pyrolytic Graphite", in Special Ceramics 1962 , Proc. Symp. Brit. Ceram. Res. Assoc. (England), 1962, 237-59, publ. 1963.

62. Hoch, M. and Vardi, J. , "Thermal Conductivity of Anisotropic Solids at High Temperatures. The Thermal

Conductivity of Molded and Pyrolytic Graphites. Part I. ", ASD-TDR-62-608 (Pt l), 1-19, 1962. [AD 292326]

63. Hooker, C.N. , Ubbelohde, A.R. , and Young, D. A. , "Thermal Conductance of Graphite in Relation to its Defect Structure", Proc. Roy. Soc. (London), A276 (l364), 83-95, 1963.

64. Speer Carbon Company, Inc. , Data Sheet "Characteristics of Speer Grade 875S", 1966.

65. Speer Carbon Company, Inc. , Data Sheet "Characteristics of Speer Grade 890S", 1966.

66. Fieldhouse, I. B. , Hedge, J. C. , Lang, J.I., Takata, A. N. , and Waterman, T.E., "Measurements of Thermal Properties", WADC TR 55-495 Pt I, 1-64, 1956. [AD 110404]

67. Anacker, W. F. and Mannkopff, R. , "The Thermal Conductivity of Graphite in the Vicinity of the Sublimation

Temperature", Naturwissenschaften, 4(3(6), 199-200, 1959.

References with numbers above 369 given in Table 15 of the present report, which are not yet listed in

Reference [l], are listed below:

391. Bocquet, M. and Micaud, G. , "Heat Conduction by Nuclear Graphite", Bull. Inform. Sci. Tech. (Paris),

(79), 83-96, 1964.

392. Schweitzer, D. and Singer, R. , "Thermal Conductivity of Radiation Damaged AGOT Graphite from the Graphite Research Reactor", USAEC Rept. BNL-696(S-59), 56-8, 1962.

393. Meyer, R. A. and Koyama, K. , "Method of Measuring the Thermal Conductivity of Graphite From 50 to 2200 C", USAEC Rept. GA-4621, 1-12, 1963.

394. Digesu, F. L. and Pears, C. D. , "The Determination of Design Criteria for Grade CFZ Graphite",

USAF Rept. AFML-TR -65-142, 1-279, 1965. [AD 471337]

395. Hooker, C. N. , Ubbelohde, A. R. , and Young, D. A. , "Thermal Conductance of Graphite in Relation to

its Defect Structure", Proc. Roy. Soc. (London), A276 (l364), 83-95, 1963.

396. Kaspar, J. , "Thermal Propagation in Carbons and Graphites at Very High Temperatures", USAF Rept.

SSD-TR -67-56, Aerospace Corp. Rept. TR-100l(9250-02)-l, 1-40, 1967.

397. Bortz, S.A. and Connors, C. L. , "Physical Properties of Refractory Materials", IIT Research Inst. Quarterly Rept. No. 6 for Contract AF 33(615)-3028, 1-67, 1966. [AD 804 035]

136
PART III

THERMAL CONDUCTIVITY OF GASES

137
PART El - THERMAL CONDUCTIVITY OF GASES

A. Introduction

Recent developments have resulted in more accurate experimental and theoretical methods of determining

the thermal conductivity of gases at high temperatures. Despite such developments, data obtained by older techniques for more moderate temperatures still, in some cases, differ by a significant amount. In the analyses which

follow, preference has been given to experimental data over theoretical values, or, where only theoretical values

exist, to those derived by the most reliable basis.

B. Thermal Conductivity of a Group of Selected Gases

Acetone

Most of the experimental data for the thermal conductivity of gaseous acetone are reported from two laboratories [254; 367, 368, 370]* while two other values [212] are available. In addition two correlations [223; 601,

602] have been made, the former with no source references and the latter based upon [254, 367, 368, 370].

In an analysis of these data, the Vargaftik method of plotting the logarithm of thermal conductivity as a function on the logarithm of absolute temperature was tested and the best curve through the available points was found

to differ insignificantly from a straight line. The recommended values were therefore obtained by assuming a

straight line relationship, the data of [367, 368, 370] being preferred over those of [254], The departure plot

shows that all the experimental data points except three values of [254] fall close to such a correlation and that the

average deviation is about one percent. The three data points of [254] are some four to six percent lower. More

experimental measurements are desirable to confirm the accuracy of the choice made above.

The accuracy of the recommended values can be assessed at within two percent for temperatures below 450

K and possibly as low as eight percent for the highest temperature tabulated.

Ammonia

Several measurements of the thermal conductivity of gaseous ammonia made over moderately large temperature ranges [51, 95, 96, 105, 568, 587-589], for smaller ranges or single temperatures [14, 59, 86, 187, 228] and

correlations [105, 187, 223, 521] have been compared with more recent experimental and correlated values [59,

644-647].

The trend with temperature of the Keyes [187] correlation appears to be erroneous above 400 K and was

ignored in the preparation of the recommended values. More difficult to explain are the published data of Ziebland et al. [646] which are higher than his preliminary values [589] and which, with the exception of two data

points [568, 644], are higher than all other values. The measurements of Baker and Brokaw [644], while parallelling the Ziebland values below 400 K, exhibit a trend at higher temperatures more in agreement with all other

work.

The recommended values were therefore chosen to fall near the average of all measurements for temperatures below 400 K and to approach the trend in the Geier and Schafer data [587] for the highest temperatures. The

conclusion which can be drawn from the departure plot is that the recommended values should be accurate to about

1. 5 percent for temperatures below 400 K and possibly ten percent for the highest temperature tabulated. More

precise estimation wall require more accurate measurements to be undertaken in order to resolve differences of up

to thirteen percent which exist between present data.

* Reference numbers used in the text and figures of Part in of this report refer to the references listed in the

section of References in TPRC Data Book Volume 2 , Chapter 1.

138
Methane

About twenty measurements of the thermal conductivity of gaseous methane at atmospheric pressure have

been reported, of which eleven [96, 168, 187, 305, 331, 587, 603, 645, 649, 650, 65 1J extend over appreciable

temperature ranges. A graphical plotting of all the data revealed reasonable agreement below about 300 K and

relatively poor agreement above 4 00 K. After a careful analysis of the differing data it was decided to base the

higher temperature values upon the measurements of Geier and Schafer [587 ] which, as can be ascertained from

the departure plots, fall almost exactly midway between the extremes of other measurements for temperatures

above about 525 K. Even the Geier and Schafer data appear somewhat uncertain in trend for temperatures above

800 K and this fact has limited the extent of the extrapolation of the values to higher temperatures.

The recommended values were obtained from a smooth curve drawn through all the data for temperatures

below 400 K and through the Geier and Schafer data for higher temperatures. The recommended values are considered accurate to within one percent for temperatures below 300 K, two percent for temperatures between 300

and 425 K and six percent for all other temperatures tabulated.

139
TABLE 17. THERMAL CONDUCTIVITY OF GASEOUS ACETONE (mW cm"1 KT1

)

T, K k

250 0. 0803

260 0. 0867

270 0. 0933

280 0. 1002

290 0. 1073

300 0. 1146

310 0. 1222

320 0. 1300

330 0. 1380

340 0. 1463

350 0. 1548

360 0. 1635

370 0. 1725

380 0. 1817

390 0. 1911

400 0. 2008

410 0. 2106

420 0. 2206

430 0. 2309

440 0. 2412

450 0. 252

460 0. 263

470 0. 275

480 0. 286

490 0. 298

500 0. 310

140
FIGURE

23.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

ACETONE

14 1

368
TABLE 18. THERMAL CONDUCTIVITY OF GASEOUS AMMONIA ( mW cm"1 K"1

)

T, K k T, K k

200 0. 153 550 0. 580

210 0. 162 560 0. 595

220 0. 171 570 0. 610

230 0. 180 580 0. 625

240 0. 188 590 0. 640

250 0. 197 600 0. 656

260 0. 206 610 0. 671

270 0. 215 620 0. 686

280 0. 225 630 0. 702

290 0. 235 640 0. 717

300 0. 246 650 0. 733

310 0. 256 660 0. 749

320 0. 207 670 0. 764

330 0. 279 680 0. 780

340 0. 290 690 0. 795

350 0. 302 700 0. 811

360 0. 314 710 0. 828

370 0. 327 720 0. 844

380 0. 339 730 0. 861

390 0. 352 740 0. 877

400 0. 364 750 0. 894

410 0. 377 760 0. 910

420 0. 390 770 0. 927

430 0.404 780 0. 944

440 0.418 790 0. 962

450 0.433 800 0. 979

460 0.447 810 0. 996

470 0. 462 820 1. 012

480 0.476 830 1. 029

490 0. 491 840 1. 046

500 0. 506 850 1. 063

510 0. 520 860 1. 080

520 0. 535 870 1. 096

530 0. 550 880 1. 113

540 0. 565 890 1. 130

900 1. 146

142
FIGURE

24.

DEPARTURE

PLOT

FOR

THERMAL

CONDUCTIVITY

OF

GASEOUS

AMMONIA

m.

to.

to.*

OJ—

.

CM

CM*

tn___ ro*

iN30d3d ‘3dn±avd3a

1

143

86

16

645

228

17

645

14

18

646

568

19

646

587

20

647
T, K

100

110

120

130

140

150

160

170

180

190

200

210

220

230

240

250

260

270

280

290

300

310

320

330

340

350

360

370

380

390

THERMAL CONDUCTIVITY OF GASEOUS METHANE (mW cm -1 K

-1

)

k T, K k T, K k

0. 106 400 0. 484 700 1. 041

0. 117 410 0. 501 710 1. 060

0. 128 420 0. 519 720 1. 079

0. 139 430 0. 537 730 1. 098

0. 150 440 0. 556 740 1. 117

0. 162 450 0. 574 750 1. 137

0. 173 460 0. 593 760 1. 157

0. 184 470 0. 613 770 1. 178

0. 195 480 0. 633 780 1. 199

0. 207 490 0. 652 790 1. 220

0. 218 500 0. 671 800 1. 241

0. 230 510 0. 690 810 1. 262

0. 242 520 0. 710 820 1. 283

0. 254 530 0. 729 830 1. 305

0. 266 540 0. 749 840 1. 326

0. 277 550 0. 767 850 1. 348

0. 289 560 0. 786 860 1. 370

0. 301 570 0. 804 870 1. 392

0. 314 580 0. 823 880 1. 415

0. 329 590 0. 840 890 1.438

0. 343 600 0. 858 900 1. 460

0. 357 610 0. 876 910 1.482

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0. 440 670 0. 985 970 1. 620

0. 455 680 1. 004 980 1. 643

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1000 1. 690

144
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146
THE NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards1 provides measurement and technical information services

essential to the efficiency and effectiveness of the work of the Nation’s scientists and engineers. The

Bureau serves also as a focal point in the Federal Government for assuring maximum application of

the physical and engineering sciences to the advancement of technology in industry and commerce. To

accomplish this mission, the Bureau is organized into three institutes covering broad program areas of

research and services:

THE INSTITUTE FOR BASIC STANDARDS . .

. provides the central basis within the United

States for a complete and consistent system of physical measurements, coordinates that system with the

measurement systems of other nations, and furnishes essential services leading to accurate and uniform

physical measurements throughout the Nation’s scientific community, industry, and commerce. This

Institute comprises a series of divisions, each serving a classical subject matter area: —Applied Mathematics—Electricity—Metrology—Mechanics—Heat—Atomic Physics—Physical

Chemistry—Radiation Physics—Laboratory Astrophysics2—Radio Standards Laboratory, 2 which

includes Radio Standards Physics and Radio Standards Engineering—Office of Standard Refer- ence Data.

THE INSTITUTE FOR MATERIALS RESEARCH . . . conducts materials research and provides

associated materials services including mainly reference materials and data on the properties of materials. Beyond its direct interest to the Nation’s scientists and engineers, this Institute yields services

which are essential to the advancement of technology in industry and commerce. This Institute is or- ganized primarily by technical fields: —Analytical Chemistry—Metallurgy—Reactor Radiations—Polymers—Inorganic Materials—Cryogenics 2—Office of Standard Reference Materials.

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principal elements of this Institute are: —Building Research—Electronic Instrumentation—Technical Analysis—Center for Computer Sci- ences and Technology—Textile and Apparel Technology Center—Office of Weights and Measures —Office of Engineering Standards Services—Office of Invention and Innovation—Office of Vehicle

Systems Research—Clearinghouse for Federal Scientific and Technical Information3—Materials

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2 Located at Boulder, Colorado, 80302.

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JOURNAL OF RESEARCH reports National Bureau of Standards research and development in physics, mathematics, chemistry, and

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.