/e . & o

NATIONAL BUREAU OF STANDARDS REPORT

THERMAL CONDUCTIVITY OF SEMICONDUCTIVE SOLIDS

METHOD FOR STEADY-STATE MEASUREMENTS ON

SMALL DISK REFERENCE SAMPLES

Interim Technical Report

Covering Period

April 1, 1961, to August 31? 1962

by

D. R. Flynn

Report to the

Bureau of Ships

Department of the Navy

Washington, D. C.

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

77^0
THE NATIONAL BUREAU OF STANDARDS

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end Technical Notes. A complete listing of the Bureau’s publications can be found in National Bureau of Standards Circular

460, Publications of the National Bureau of Standards, 1901 to June 1947 (SI. 25), and the Supplement to National Bureau of Standards Circular 460, July 1947 to June 1957 ($1.50), and Miscellaneous Publication 240,

July IS'57 to June 1960 (Includes Titles of Papers Published in Outside Journals 1950 to 1959) (|2. 25); available from the Superintendent of Documents, Government Printing Office, Washington 25, D. C.
NATIONAL BUREAU OF STANDARDS REPORT

NU PROJECT NBS REPORT

1006-20-10461 October 29, 1962 774.0

THERMAL CONDUCTIVITY OF SEMICONDUCTIVE SOLIDS;

METHOD FOR STEADY-STATE MEASUREMENTS ON

SMALL DISK REFERENCE SAMPLES

Interim Technical Report

Covering Period

April 1, 1961, to August 31? 1962

by

D. R. Flynn

Heat Transfer Section

Building Research Division

Report to the

Bureau of Ships

Department of the Navy

Washington, D. C.

INDEX NO. S-R007 12 01, Task No. 800

(BuShlps 1700S-716-62). Code 2781

NATIONAL BUREAU OF STA

Intended for use within the C to additional evaluation and re listing of this Report, either li the Office of the Director, Hat

however, by the Government i to reproduce additional copies

IMPORTANT NOTICE

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST)

on October 9, 2015.

ogress accounting documents

nally published It is subjected

eproduction, or open-literature on is obtained in writing from

Such permission is not needed,

repared If that agency wishes

<NBS>

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
it

k-
TABLE OF CONTENTS

Page

ABSTRACT.. 1

1. INTRODUCTION 1

2. DESCRIPTION OF ABSOLUTE CUT -BAR APPARATUS 2

2.1. Apparatus 2

2.2. Instrumentation 3

3. ANALYSIS OF METHOD . , 4

3.1* Determination of Heat Flow 4

3.2. Temperature Gradients . *...« 8

3.3 Minimization of Systematic Errors 8

4. RESULTS OBTAINED USING THE HIGH TEMPERATURE

ABSOLUTE CUT BAR APPARATUS . 11

4.1* Platinum-Rhodium Alloy*..*. 11

a. Description of Specimen . 11

• b. Test Procedure 11

c. Results of Thermal Conductivity Tests 12

d. Thermoelectric Power 12

4.2. Nickel-Chromium Alloy l4

a. Description of Specimen ............. l4

b. Test Procedure..... l4

c. Results of Thermal Conductivity Tests 15

d. Thermoelectric Power... 19

4.3. Microcrystalline Glass 19

a. Description of Specimen....... 20

b. Test Procedure 20

c. Results of Thermal Conductivity Tests 21

5. DISCUSSION 21
Page

28

TABLE OF CONTENTS (Cont'd)

6 e REFERENCES eeo.eo.e

LIST OF TABLES

Table 1. Thermal Conductivity of a Nickel -Chromium

Alloy (Inconel 702) by Several Independent

Methods at NBS.

Table 2. Chemical Compositions of Four Nickel-Chromium

Alloys

Table 3. Thermal Conductivity of Four Nickel-Chromium

Alloys • • . . . * . . Table 4. Maximum Error for Various Ranges of Specimen

Thermal Conductivity. . . . . .

j

1 LIST OF FIGURES

. '

|

.

’

• ... Figure 1. Schematic of high temperature absolute cutbar apparatus for determination of thermal

conductivity of small solids

Figure *2. Temperature distribution, radial temperature

gradient at surface of meter bars and

specimen, and fractional change in power

for a typical cut-bar apparatus

Figure 3® Thermal conductivity of a 60$ platinum-40$

rhodium alloy «.o..o.9«.....«...«.o«......o.e

• i

• Figure 4. Thermoelectric power of platinum-4o$ rhodium

and platinum-10$ rhodium against pure

p la t inum ........... .'o..o. ......... o... .....o

Figure 5. Thermal conductivity of solution-annealed

Inconel 702

Figure 6. Departures of the thermal conductivity data

for solution-annealed Inconel 702 from

a smooth curve.........

Figure 7<> Departures of the thermal conductivity data

for age -hardened Inconel 702 from a

smooth curve B

17

18

18

24

30

31

32

33

34

35

36
fage

TABLE OF CONTENTS (Cont’d)

List of Figures (Cont 8 d)j

Figure 8. Apparent difference between the thermal

conductivity of solution-annealed Inconel

702 and that of the age-hardened alloy, . .... 37

Figure 9» Smoothed values for the thermal conductivity

and thermal resistivity of Pyroceram 9606. . « 38

Figure 10. Departures of the thermal resistivity data

for Pyroceram 9606 from a smooth curve...,.* 39

Figure 11. Effect of specimen thermal conductivity on

the fractional power change in a comparative cut-bar apparatus 40

APPENDIX A

Abstract of Previous Interim Report 7135? dated

April 28, 1961.... kl

THERMAL CONDUCTIVITY’ OF SEMI CONDUCTIVE SOLIDS

METHOD FOR STEADY-STATE MEASUREMENTS ON

SMALL DISK REFERENCE SAMPLES

by

D. R. Flynn

ABSTRACT

An absolute cut-bar method of measuring the thermal conductivity of solids is described, suitable for

small specimens of semiconductive materials. Measurements have been made at temperatures from 200° to

1200°C on a nickel-chromium alloy (Inconel 702) and a

60% platinum-40# rhodium alloy. Measurements have been

made to 1000°C on a microcrystalline glass (Pyroceram

9606). Additional measurements are intended.

.1. INTRODUCTION

The thermal conductivity of thermoelectric materials is

of great importance in determining the performance of a thermoelectric device. If such a device is to have a high efficiency, the thermal conductivity of the thermoelectric elements must be as low as possible in the temperature range in

which they are to operate. Reliable thermal conductivity

data are required at temperatures ranging from below room

temperature to 2000°C, since it is advantageous to operate a

thermoelectric generator at as high a temperature as possible.

Reliable thermal conductivity data at elevated temperatures are not generally available, partly because of the difficulties of making such measurements. Many semiconductor

materials of interest are available only in small samples,

because of the difficulty of obtaining them with adequate

uniformity. Consequently, it is necessary that a method of

measuring the thermal conductivity of such materials be one

suitable for small specimens and capable of use at high temperatures . It is the purpose of this investigation to develop a

method and apparatus for steady-state thermal conductivity

measurements at temperatures to 800°C and above, and suitable

for solids in the form of small specimens (l/2-in. by 1-in.

diameter disks), with the objective of providing samples for
2

use by other laboratories as thermal conductivity reference

specimens in connection with their measurements on solid

semiconductors,,

A previous report [l]^gave a summary of the findings of

this investigation during the two-year period from February

23 , 1959 ? to March 31 , 1961 , For the convenience of the

reader, the abstract of this earlier report is reproduced in

Appendix A.

The present report describes the high temperature model

of the absolute cut -bar apparatus, the design of which was

based on experience gained using rhe modified prototype apparatus described in reference [lj. A summary is given of the

findings of this investigation to date.

2. DESCRIPTION OF ABSOLUTE CUT-BAR METHOD

2.1. Apparatus

The general assembly of the thermal conductivity apparatus is shown in figure 1. The 2.5^-cm diameter specimen was

interposed between a hot bar and a cold bar, which were fabricated from 60$ platinum-^0% rhodium alloy. These bars were

supported by an alumina tube from below and an alumina rod

from above. Surrounding the inner assembly and concentric

with it was an alumina guard cylinder, which was in turn surrounded by a stainless steel case. The space inside the lower

alumina support tube, that between the central assembly and

the guard cylinder, and that between the guard cylinder and

the outer case were filled with finely divided alumina powder

as thermal insulation.

The desired temperature distributions within the apparatus were attained with the aid of a number of heaters, each of

which were fabricated from 80% platinum-20^ rhodium alloy wire.

a. .-The cold bar was brought to a desired temperature by

meapLS of a small heater fabricated from 0 . 2

5

-mm

4, diameter wire wound in a helical groove around the

alumina bar immediately above the cold bar.

. b, The hot bar was raised to the desired temperature

- above the cold bar by means of a small disk-shaped

heater between the hot bar and the lower alumina < Tl Figures in brackets indicate the literature references at

the end of this report.
3

support tube. This heater was fabricated from

0 . 2

5

-mm diameter wire and had a resistance of

approximately 2 ohms (at room temperature).

c. In order to minimize heat losses down the support

tube from the hot bar heater, a small heater,

fabricated of 0.25-mm wire, was wound on the

support tube at a position about 4 cm below the

hot bar.

d. A helical groove on the outer surface of the guard

cylinder was wound with two separate heaters of

0.5 JHm wire. Between the heaters, the guard cylinder wall thickness was reduced to permit a longitudinal temperature distribution along the guard

cylinder corresponding to that along the inner

assembly. A tap divided each of these heaters

into two sections which could be controlled

separately.

Temperatures In the system were determined by means of

platinum-10^ rhodium: platinum thermocouples, which were fabricated from 0.38-mm (unless otherwise stated; reference grade

thermocouple wire that had been calibrated by the NBS

Temperature Physics Section. Thermocouple positions are shown

in figure 1. There were two thermocouple stations in the hot

bar and two in the cold bar. In the hot bar support tube

there vfere two thermocouple stations and one differential

thermocouple. Eight thermocouples were installed to define

the temperature distribution along the guard cylinder. The

number and location of specimen thermocouples were determined

by the nature and geometry of the specimen.

2.2. Instrumentation

Power for the two guard heaters and the cold bar heater

was supplied by variable voltage transformers, which in turn

were fed by a voltage regulating transformer. The cold bar

heater and the guard heater sections nearest the plane of the

specimen were individually regulated by thermocouple-actuated

controllers. The guard heater sections remote from the plane

of the specimen were manually adjusted.

The hot bar heater, which provided the power flowing

through the specimen, was powered by a 28-volt, 4-ampere

regulated d-c power supply with a small bank of power resistors

In series for adjusting to the desired hedter current.

The heater In the hot bar support tube had to be closely

regulated, in order to prevent heat gains or losses from the
4

hot bar heater along the support tube. Using a small d-c

potentiometer 5 a bias was placed on the signal from a multiple Junction differential thermocouple located in the hot

bar support tube. The resultant signal was amplified by a

breaker-type d-c amplifier and fed into a d-c recorder. The

error signal from the control slidewir.e in the recorder was

fed into a current-adjusting-type proportional controller

incorporating automatic reset control and rate control. The

output of this unit regulated a magnetic amplifier which fed

power to the heater. The operation of a control system of

this type has been described in detail by West and Ginnings [2].

The noble metal leads of the thermocouples were brought

to an isothermal zone box at room temperature. A thermocouple

with one junction in the zone box and one in an ice bath was

placed in series with a double-pole selector switch, so that

each measuring thermocouple was automatically referenced

against the ice bath [3]* The zone box was also wired to

enable determination of the emf developed between similar

leads of different thermocouples in the hot bar, in the specimen, and in the cold bar. For these determinations, a separate

doublet-pole selector switch with no ice bath in series was

used.

Thermocouple emfs were read on a calibrated precision

potentiometer, usually to 0.1 pv for thermocouples in the

specimen and the hot and cold bar, and to 1.0 pv for thermocouples in the guard cylinder. Power input to the hot bar

heater was determined by measuring the d-c current through

the heater and the voltage drop across potential taps located

midway between the differential thermocouple junctions in the

hot bar support. These measurements were made using calibrated shunt and volt boxes and measuring their output

voltages by means of the precision potentiometer.

3* ANALYSIS OF METHOD

3«1« Determination of Heat Flow

The heat generated in the hot bar heater could flow, if

permitted, in several directions (see figure 1).

a° up the hot bar, through the. specimen, and into the

cold bar,

b. down the hot bar support column,

,

r

* c. across the convex surfaces of the hot bar and the

- specimen.

Ideally., the heat should flow entirely through the specimen.

The heat flows b and c should therefore be minimized.
5

The heat flow up or down the hot bar support column was

minimized by keeping the platinum-10^ rhodium: platinum differential thermocouple located in the column as nearly as

possible at a zero reading. For tests in which the reading

of the differential thermocouple was not zero, a correction

was made for the slight heat flow through the support column.

The heat flow across the convex surface of the hot bar,

specimen, and cold bar was analyzed by solution for the heat

flow in rhe hollow cylinder of powder insulation with prescribed temperature boundary conditions. This analysis was

utilized to determine the net heat flow across the inner surface of the hollow cylinder, taking place up to various longitudinal positions of interest on the assembly (i.e., hot barspecimen-cold bar).

The proper analysis of heat exchanges between the bar

assembly and the surrounding powder insulation is essential.

Some insight into this problem can be achieved by consideration of a rather crude model. The hot bar, specimen, and

cold bar can be thought of as three thermal resistances in

series.; Shunting each of these resistances is a resistance

consisting of a portion of the surrounding powder insulation.

For the case in which the thermal conductivity of the specimen is different from that of the bars, there will be a corresponding change in the longitudinal temperature gradient in

the adjacent insulation. Since the thermal conductivity of

the insulation does not undergo such a change, the insulation

must exchange heat with the bars and specimen. In particular,

if the specimen has a lower conductivity than the bars, it is

necessary for the insulation to steal heat from the bars and

specimen on the hotter side and return this heat on the colder

side.

A schematic diagram of a cut-bar apparatus (not that

described in this report) is shown in the upper left hand corner of figure 2. (The nomenclature used in this diagram

refers to a comparative cut -bar apparatus, rather than to an

absolute type; the heat flow analysis is the same, however.)

The hot and cold bars (meter bars) and the specimen are equal

in' length; this length is equal to twice their diameter. The

radius of the guard has been chosen as 1.5 times that of the

bars. For numerical evaluation, the specimen and insulation

have been chosen to have, respectively, thermal conductivities

1/5 and 1/100 that of the meter bars.

The graph in the lower left-hand corner of figure 2

illustrates the dimensionless longitudinal temperature distribution that would exist along the meter bars and specimen in

the absence of heat exchanges with the insulation. The

vertical dashed lines indicate the positions of the interfaces
6

between the meter bars and the specimen. Since, in this case,

an exactly matched guard is being considered, the temperature

distribution shown is also that which exists along the guard.

The graph in the upper right-hand corner of figure 2

illustrates the dimensionless radial temperature gradient

which exists in the insulation at the convex surface of the

meter bars and specimen. In this particular case, the radial

gradient is substantially zero, except in the regions near the

interfaces. In this graph, the peaks at the interfaces have

arbitrarily been cut off at -1.0 and +1.0. The effect of such

a radial gradient distribution is shown in the graph in the

lower right-hand corner of figure 2. The fractional power

change is plotted versus dimensionless length. The quantity

plotted is the percentage change in power i lowing longitudinally through the meter bars and specimen. In this graph,

the power flowing in the first meter bar is seen to remain

constant until the interface is approached. The power drops

rapidly near the interface, then levels off in the specimen

to a constant value approximately 2.2 percent less than that

which was flowing in the first meter bar. Near the second

interface, the longitudinal heat flow increases so that its

rate is the same in the second meter bar as it was in the

first.

It is necessary to originally establish a longitudinal

gradient in the insulation near the hotter bar. In the case

where the bars are quite short, the longitudinal gradient may

not become established, so that heat exchanges occur along the

entire length of the system.. Even in the case where the

specimen and the bars have the same conductivity, there may

be heat interchanges along the entire system. In order to

study the parasitic heat flows mentioned, it is necessary to

perform a rather extensive analysis.

Although there may be both radial and longitudinal heat

flows in the powder insulation, it is the radial gradient at

the surface of the bars and specimen that is of particular

interest. In the ideal case, the radial gradient at this

surface would be zero. This is, however, not the case in

general, so that an analysis of the heat flow across this

surface must be made. The heat flow across this surface in

a longitudinal element of area will be

dp = 27rak(||)

r=a

dZ

, (1)

where a is the radius of the bars and specimen (cm),

k is the thermal conductivity of the powder insulation

(watt/cm deg C),

T is the temperature in the system (°C),
7

r is the radial coordinate (cm)

,

' z is the longitudinal coordinate (cm).

The net power flowing across the surface r=a between z=z±

and z-z 2 is

In order to evaluate this integral, it is necessary to

have a knowledge of the thermal conductivity of the powder

insulation and (9T/9r) r=a as a function of z. An exact treatment of the system requires solution of the four body composite system involving the two bars, the specimen, and the

powder insulation. This has recently been done by B. A. Peavy

of the NBS Heat Transfer Section. The resultant solution is

very complicated, however, and was not used for the investigation described in this report.

For this apparatus, (9T/9r) r =a was determined by analysis

of the hollow cylinder of powder insulation with its boundaries

at known temperatures. The measured surface temperatures along

the bars and the guard cylinders were used to establish functions representing the temperatures on the curved surfaces of

the region. The ends of the region were assumed to be closed

by logarithmic radial temperature distributions, which provide

temperature continuity. Axial symmetry was assumed. The analytical solution of the temperature distribution in the region

established by these boundary conditions was utilized to

evaluate (9T/9r) r =a in the integral in (2). The thermal conductivity of the powdered alumina insulation was measured in

another apparatus [*+].

Since the analytical solution of this problem is in the

form of an infinite Fourier series, it was necessary to use a

digital computer for numerical evaluation of the data. The

details of the mathematical development are not amenable to

brief treatment and, hence, have been excluded from this

report. An unpublished paper giving a fairly detailed analysis

of heat flow in the insulation of a simplified cut-bar apparatus was reproduced in an earlier report [ 5]. It is planned to

publish the mathematical analysis of heat flow in a cut -bar

thermal conductivity apparatus soon.

The total heat flow through the specimen was determined as

where Q is the total heat (per unit time) flowing in the

specimen (watt),

P- is the measured heat input (watt),

( 2 )

Q = P + Cb + p ( 3 )
8

C is the heat flow up or down the support column due to

a unit temperature difference (watt/deg C),

b is the temperature difference in the support column

as indicated by the differential thermocouple

(deg C), • p is the mean value of the total net heat interchange

with the surrounding insulation for a thermocouple

span in the specimen (watt) (see Eq.(2)).

The measured power input , P, was known very accurately.

The contribution from heat flow in the support column was

minimized by keeping 6 small (usually less than 0.1 deg C).

The heaters on the guard cylinder were adjusted to minimize p.

3.2. Temperature Gradients

Temperatures in the specimens were measured using noble

metal thermocouples, as described above. The particular method

of thermocouple installation varied somewhat with the specimen

being tested, and will be discussed in the appropriate sections

describing experimental results.

$ince temperature differences in the specimen were rather

small, it was essential that the conversion of thermocouple

emfs to temperature not introduce any additional uncertainties.

The equation

E = 16.826iV(j^q) - 10.30487(j^q) 2 + 7. 91246 (^g)

3

(4)

- 2.05305( t

^5

) 4 - 2.8537 5(1.0 - exp [^L] )

>

where T is temperature (°C) and E is emf (millivolts), was

found to fit the platinum-10^ rhodj urn s platinum thermocouple

calibration data quite closely over the temperature range 0°

to l450°C. This equation was used for conversion of all thermocouple voltages to temperature.

3«3° Minimization of Systematic Errors

j . For all tests, thermal conductivity values were computed

by simultaneous solution of two tests 2 1) an "isothermal”

test with no power input to the specimen heater, and 2) a

"gradient" test with sufficient power input to the specimen

heater to maintain the desired longitudinal temperature

gradient. This procedure tends to minimize the effect of certain systematic errors in temperature or heat flow measurements.

For > one-dimensional steady-state heat flow, the total

heat flow, Q, through the specimen is
9

Q = -kAg , (5)

where k is thermal conductivity,

A is the cross-sectional area of the specimen,

T is the temperature^

z is the longitudinal coordinate.

For moderate temperature ranges, the thermal conductivity of

the specimen is assumed to vary linearly with temperature;

then (5) becomes

Q = -k0 A{l + a(T-T0 )}f| , (6)

where ko is the thermal conductivity at an arbitrary reference

temperature, To, and a is its corresponding temperature coefficient.

Integration of (6) yields, assuming Q to be constant,

Q =* ^AT[1 + a(f-To)] , (7)

where

AT = Ti-T2

T = (Ti+T 2 )/2

( 8 )

Ti and T2 being the temperatures at two positions a distance

L apart.

Consider two tests at approximately the same mean temperature; let the heat flow in one test be given by (7) and

that in the other test by a similar expression. The difference between these heat flows will be

Q-Q' = ^[AT-AT' + a{AT(T-T0 ) - At' Ct' -To)}] , (9)

where the primed quantities designate one test and the unprimed

quantities designate the other. The expression in braces in

(6) can be set equal to zero by proper choice of the reference

temperature, Tq . _ _

_ ATT-AT' T ' nn s If io = AT-AT' ’ (' 10 ')

the thermal conductivity at the indicated reference temperature,

To, is given by

(Q-Q' )L

A(AT-AT' ) ( 11 )
10

Equation (11) gives thermal conductivity in terms of

the ’’true" values of heat flows , temperature differences,

and dimensions. Now let

Q=q-s • Q'=q'-s

Ti=ti -Si ^1

; = ti

; -ei (12)

T 2 ~t 2 -£ 2 T2 '=t 2 '=e 2 9 where the capital letters designate "true" values of the

parameters ; the lower case t*s and q*s are the measured

values for these parameters; and s, e*, and e 2 are the associated systematic errors. It is assumed that, for two tests

at about the same temperature, the systematic errors associated with a particular parameter are the same; experience 1 indicates that this is a good approximation.

From (11) and (12) the thermal conductivity is given by

5 ( 13 ) v =

(q-q' k° A (At -At' ) corresponding to the mean temperature

To = to + Eo 9 where

AtlT-At ' t

7

to = At -At

7

£ 0 =

e 2 (t 2 -t 2

/ )-£i (ti-ti/

)

At -At' “

At = ti-tg

t = (ti+t 2 )/2

( 14 )

( 15)

( 16 )

Equation (13) gives thermal conductivity in terms of the

measured values of the parameters, all systematic errors of

the type being discussed having been eliminated. The effective mean temperature will be in error by £o$ however, for

most materials the effect of a slight error in mean temperature is negligible 0 All thermal conductivity values were computed using (13). The use of this simultaneous solution for computing results

significant!y improved the precision of the test results and,

it is believed, the accuracy as well.
il

4 e RESULTS OBTAINED USING THE HIGH TEMPERATURE

ABSOLUTE CUT -BAR APPARATUS

^,Io Platinum-Rhodium Alloy

Measurements were made of the thermal conductivity of the

platinum-rhodium alloy from which the hot and cold bars in the

high temperature absolute cut-bar apparatus were to be fabricated,, It was considered desirable that this be done so that

the hot and cold bars could later serve as meter bars to provide a useful check on the heat flow through a specimen interposed between them.

a„ Description of Specimen

The specimen used for these determinations was in the

form of a right circular cylinder 2.539 cm in diameter and

7.5 cm long with recesses at either end. The solid portion

of the cylinder was 6.49 cm long. The geometry of this specimen may be envisaged by reference to figure 1. The specimen

was later cut into two pieces which were ground and optically

polished to form the hot and cold bars.

. The specimen was machined by the manufacturer into the

form described. An NBS chemical analysis indicated that the

material of the specimen was 60.0 percent platinum and 40.0

percent rhodium by weightThe specimen was annealed at

1000°C < prior to the tests described below.

b» Test Procedure

The temperature distribution along the platinum-rhodium

alloy specimen was determined by means of four 0 . 38 -mm buttwelded platinum-10^ rhodiums platinum thermocouples pressed

into 0„3“flM grooves in the convex surface of the bar. The

distance between the two extreme thermocouples was 3»94 cm.

Thermal conductivity measurements were made in increasing

order of temperature from 200° to 1200°C at 200-degree intervals, and then in decreasing order of temperature at 800° and

400°C. Each conductivity determination involved two tests

s

(1) an "isothermal1

® test, in which there was no power input

to the specimen heater $ (2) a "gradient" test with sufficient

power input to the specimen heater to maintain a longitudinal

temperature gradient in the specimen of about 2 deg C/cm.

2 0 NBS spectrochemical analysis indicated the following

impurity elements? Fe 0.01-0.1$$ Cu, Ir, Pd, Si, Zr

0.001-0.01$$ B, Ca less than 0.001$.
12

In all of the tests, the guards were adjusted so that there

was very little net heat exchange between the specimen bar

assembly and the surrounding insulation.

Cc Results of Thermal Conductivity Tests

The thermal conductivity of the platinum-rhodium alloy

as determined by simultaneous solution of the various pairs

Of tests is shown in figure 3* The points plotted are

weighted averages of the values obtained for the three thermocouple spans. Due to uncertainty in the effective distances

between thermocouples, there was some scatter in the individual

values obtained for each span. The average of the three values,

weighted according to the length of each span, retains only

about one-third of this uncertainty.

The circles shown in figure 3 represent measurements

made in increasing order of temperature^/, and the inverted

triangles those made in decreasing order of temperature. The

solid line shown is the quadratic equation of least-meansquares fit to all of the data points shown. This equation is

k = 0.465 + 0.1+24 (jgL) - 0.151 (j^o)

2

» (17)

where k is thermal conductivity expressed in watt/cm deg C

and T is temperature in °C. The dotted lines shown bound the

region plus and minus 2.2 percent of the conductivity, equivalent to twice the estimated standard deviation divided by the

mean conductivity.

d. Thermoelectric Power

When the 60$ platinum-4o$ rhodium alloy bar was purchased,

a 0.5-mm wire was drawn by the manufacturer from the same

material. A thermocouple fabricated from a length of this

wire and a length of 0.38-mm reference grade platinum wire was

calibrated by the NBS Temperature Physics Section over the

temperature range 0° to 1100°C. The equation

* = 13 * 25682 (j^q) - 2. 76979 ^)2 + 6 . 09233

(

3

^

5)

3

(18)

- 1-79519 (j^q)

4 ” 1 - 80269 ( 1.0 - exp^j^T])

3. Prior to the tests shown in figure 3, the specimen was

annealed in place at 1000°C? hence the designations

'"second heating” and ^second cooling.”
13

where E is emf (millivolts) and T is temperature (°C), was

found to fit the calibration data quite closely

.

Differentiation of equation (18) gives

§ = 13.257 - 5.540^) + 18 . 277(ife)

2

(19)

- 7.18K10qq

) 3 - 8.112 0xp[~j§oo_

as the thermoelectric power (pv/deg C) of 60$ platinum-4-0$

rho dium : p lat inum

Similarly, differentiation of (4-) gives

ff = 16.826 - 20.610 ( i^q) + 23.737(I^q ) 2

(2°)

- 8.212 (tq^q)

j ~ 11. ^15 0Xp[_ 1000]

as the thermoelectric power (pv/deg C) of 90% platinum-10^

rhodium: platinum*

The solid lines in figure 4- show the thermoelectric power

of 60% platinum-4-0$ rhodium, and 90% platinum-10^ rhodium

against platinum, as computed from (19) and (20), respectively*

From the ,f Law of Intermediate Metals” [6] it follows that the

thermoelectric power of 60% platinum-4-0$ rhodium versus 90%

platinum-10^ rhodium can be obtained by subtracting equation

(20) from (19)$ the thermoelectric power of this combination

is indicated by the dotted line in figure 4-.

For each of the tests presented in figure 3? for both the

upper and lower thermocouple spans of the specimen, emfs were

measured between the respective platinum wires of the two

thermocouples and between the respective platinum-10^ rhodium

wires. Thus, the 60% platinum-4-0$ rhodium bar served as the

central portion of four differential thermocouples. From the

emf outputs of these differential thermocouples and from the

temperature differences, as indicated by the four platinum10^ rhodium % plat inum thermocouples, the thermoelectric power

of the specimen against 90$ platinum-10$ rhodium and against

platinum was computed. The effects of systematic errors were

minimized by simultaneous solution of the "gradient” and

"isothermal” tests. In figure 4-, the plotted points give the

average values obtained for thermoelectric power as a function of temperature. The circles and triangles correspond to
the similar symbols in figure 3 at the same temperatures.

It can be seen that the measured values agree quite well with

the curves obtained from equations (19) and (20).

*+.2. Nickel-Chromium Alloy

Measurements were made of the thermal conductivity of a

nickel chromium alloy (Inconel 702) which previously had

been measured in two models of the NBS metals apparatus [7]*

in the NBS modified prototype absolute cut-bar apparatus L1J?

and in the NBS steam calorimeter apparatus [8]. Determinations

made on this specimen material served a dual purposes (1) since

the thermal conductivity of this alloy was already known over a

large temperature range, measurements on this material enabled

a scrutiny of the accuracy of the high temperature absolute

cut -bar apparatus | and (2) they provided additional measurements

to elevated temperatures on a metal which appears suitable for

use as a thermal conductivity reference material.

a. Description of Specimen

The specimen used for these determinations was in the

form of a cylindrical bar nearly identical in size and shape

to the platinum-rhodium, alloy specimen described above (^i.l.a).

The specimen was machined at NBS from, the same solutionannealed hot-rolled plate as were the specimens previously

measured in several other NBS apparatus. An NBS chemical

analysis indicated that the alloy was composed of Ni 79»3$j

Cr 17.0$, A1 2. 5$ 5 and several other constituents in quantities less than 1 percent (by weight). The detailed analysis

is given in Table 2, along with analyses of several similar

alloys which will be discussed later.

b. Test Procedure

Temperatures along the specimen were determined by means

of four thermocouples installed in a similar manner to those

in the platinum-rhodium alloy (4.1.b)

Thermal conductivity measurements were made at 200°C, in

increasing order of temperature at 100 degree intervals from

400° to 1200°C , and then in decreasing order of temperature at

900°, 600° , and 300°C. Following preliminary analysis of these

data, an additional series of tests was conducted in which

measurements were made in increasing order of temperature at

200°C and 300°C, at 50 degree intervals from 400° to 700°C,

at 100 degree intervals from 800° to 1200°C, and then in

decreasing order of temperature at 900° , 600°, and 300°C.
15

Each conductivity determination involved two tests? (1) an

"isothermal” test, and (2) a "gradient" test with sufficient

power input to the specimen heater to maintain a longitudinal temperature gradient in the specimen of about Mr or 5

deg C/cm.

c. Results of Thermal Conductivity Tests

.-The Inconel 702 alloy from which the specimen was fabricated was solution-annealed by the manufacturer prior to purchase by NBS. The reported solution treatment for this alloy

is to hold the material at 1975°F (1080°C) for one hour,

followed by rapid air cooling. If this alloy is held at temperatures in the range from about 650° to 900°C, age hardening will occur due to precipitation of gamma-prime particle

from the super-saturated solid solution. The size of the pre

cipitate is highly dependent on the aging temperature. After

900°C aging, the gamma-prime particles are quite coarse,

having a maximum diameter of several thousand A; if the

solution-annealed alloy is aged only at lower temperatures,

the precipitate is more abundant and finer in size and cannot

be resolved by the light microscope.

In the course of the thermal conductivity determinations

being discussed, the specimen was cycled twice between room

temperature and 1200°C. Since the microstructure of this

alloy is dependent on thermal history, the thermal conductivity of the specimen might also be expected to change somewhat,' due to heat treatment. At the onset of the measurements, the specimen was in the solution-annealed state, with

the gamma-prime phase in supersaturated solution. After the

specimen was heated above about 650°C, the gamma-prime phase

presumably began to precipitate. As the temperature was further increased, this precipitate became much coarser. Above

about 1000°C the precipitate again went into solution. After

completion of testing to 1200°C V the specimen was cooled to

900°C, at which time a coarse precipitation occurred. Thus,

for the first heating cycle, the specimen was in the solution

annealed' state up to about 650°C$ from 650° to 900°C, the

gamma-prime precipitate was fine at the lower temperatures

aiid became coarser as the temperature was increased} from

1000° to 1200°C, the gamma-prime phase was again in solution.

For all of the other tests (first cooling, second heating,

second cooling), there was a coarse precipitate at 900°C and

below. Since the exact temperatures corresponding to precipitation or solution are not known, the temperatures mentioned should be considered approximate.

The- thermal conductivity of the nickel-chromium alloy as

determined by simultaneous solution of the various pairs of
16

tests taken during the first heating cycle is shown in figure

5. The points plotted are weighted averages of the values

obtained in each pair of tests for the three thermocouple

spans . The solid line shown is the cubic equation of leastmean-squares fit to all the data points. This equation is

ks = 0.1198 + 0.07387(^5) + o. 1915(][555)

2 - o.o8265q^o) 3 (21)

where ks is thermal conductivity (watt/cm deg C) of the

solution-annealed alloy and T is temperature (°C). To enable

closer scrutiny of the deviations of individual determinations

from the curve, these are shown in figure 6 as percent departures from the smooth curve plotted against temperature. The

dotted lines bound the region plus and minus two standard

deviations (estimated) from the solid curve. The maximum

departure of any data point from the solid curve is 0.6 percent . The thermal conductivities obtained when the specimen was

in an age-hardened condition can be represented by the equation

ka = 0.1179 + 0.1149 (jq5q) + 0.1173(][555)

2 °- 050o8(T6oo )3 (22)

in the same units as above. This equation is that of leastmean-squares fit to the data points obtained during the second

heating and second cooling. The deviations of individual

determinations are shown in figure 7 as percent departures from

smooth curve (22) plotted against temperature. The dotted lines

again bound the region plus or minus two standard deviations

(estimated, using data from second heating and cooling tests

only)

.

The apparent difference between the thermal conductivity

of this alloy in the solution-annealed state and that in the

age-hardened state is shown in figure 8. The quantity plotted

is 100 (ks/ka-1), where ks and ka are given in equations (21)

and (22), respectively. Below 600°C, the alloy in the solutionannealed condition has a thermal conductivity 2 or 3 percent

less than that in the age-hardened condition. Above 1000°C,

there should be no significant difference between ks and ka | the apparent 1 percent increase of ks over ka in this range

is probably due to experimental uncertainty.

The smoothed results of these determinations are tabulated

in table x at 100 degree C intervals over the temperature range

200° to 1200°C. The results obtained for solution-annealed
17

Inconel 702 are given in the second column; those for the agehardened alloy are given In the third column. Results obtained

by several other methods on specimens cut from the same plate

of nickel- chromium, alloy are included in table 1 for comparison.

The data presented in the fourth column were obtained by means

of the modified prototype absolute cut-bar and are discussed

in a previous report [lj. The tabulated values are those from

the quadratic equation of least -mean- squares fit through data

points for peened thermocouples only (see [l]). The data in

the fifth column represent the manually smoothed data from

numerous runs on two specimens of the alloy in two models of

the NBS metals apparatus [ 7]

The sixth column presents data

obtained on a specimen six inches in diameter and .one inch

thick in the NBS steam calorimeter apparatus [8]—/. Indication is given in table 1 as to the probable condition of the

alloy (i.e. ? solution-annealed or age-hardened for each set of

data;

.

; TABLE 1

Thermal Conductivity of a Nickel-Chromium. Alloy

(Inconel 702) by Several Independent Methods at NBS

~~ Prototype

Temp.

j

This Absolute Metals Steam

°C Investigation Cut -Bar Apparatus Calorimeter

(solution- (age- (solution- (solution- (ageannealed) hardened) annealed) annealed) hardened)

-150

-100 . — —-

0

100 . ' 200 > 0.142

300 .157

400 • 175

500 • .194

600 .215

‘700 • .237

800 .259

900 .281

1000 • 303

1100 .323

1200 .341

0.145 0.142

.162 .159

.179 .177

.198 .197

.218 .21

.239 .238

.259 .260

.280

.300

.320

• 338

0.099

.103

.114

.127

.142

.158

.176

,196

.218 0.213

.235

.258

.280

.303

4*"

- Ihe data presented in Table 1 for the NBS steam calorimeter

are preliminary and may vary slightly from values to be given in the published paper.
18

Since all of the results presented in table 1 are from

this laboratory, results obtained on similar alloys by an

independent laboratory may also be of interest* Powell and

Tye of the National Physical Laboratory recently reported a

series of measurements on a group of nickel- chromium alloys

somewhat similar in composition to the alloy being investigated at NBS • The chemical composition of the NBS alloy is

presented in table 2 along with the composition of three of

the NPL alloys*

TABLE 2

Chemical Compositions of Four Nickel-Chromium Alloys

Composition, weighlb percent

Ni Cr A1 Ti Fe Si Cu Co Mn C

NBS Alloy

Nimonic 75

Nimonic 80*

Nimonic 90

79.3

77 • 9*

73 * 7**

58 . 9**

17.0

20.53

21.0

19.5

2*5

1.2

lA

0.59

.23

2.5

2.45 —

0.36

.12

.5

•4l

0.19

.79

.5

*65

0. A

*06

.A

0.08

16.5

0.04

.27

.6

.03

0.066

.126

.04

.06

* Nominal compos

By difference

it ion

Table 3 presents tabulated thermal conductivity values for

the NBS alloy as determined by this investigation and for the

NPL alloys as reported [9]« Inspection of table 3 reveals that

the thermal conductivity values for the four alloys have a

range, at any given temperature, of about 13 percent at the

lower temperatures and that the values converge at higher temperatures such that the range at 800°C is only 3 percent*

TABLE 3

Thermal Conductivity of Four Nickel-Chromium Alloys

Inconel 702

Temp * 9 °c(solutionannealed)

(agehardened)

NPL

Nimonic 75

NPL

Nimonic

NPL

80 Nimonic

200 0.142 0.145 0.157 0.138 0.146

300 .157 .162 .175 .155 .165

bOO .175 .179 .191 .168 .184

500 .194 .198 *210 .184 *200

600 .215 .218 .226 *210 .218

700 .237 .239 .243 .235 *237

800 .259 .259 0 260 .255 .253

900 .281 .280 .276
19

d. Thermoelectric Power

For each of the tests presented in figures 5* 6, and 7 ? emfs were measured between similar legs of the thermocouples

in the specimen (see ^-.l.d). Using these data, the thermoelectric power of the specimen against 90$ platinum-10$ rhodium and against platinum was computed. The analysis has not

yet been completed; preliminary results indicate that temperature differences were measured quite accurately. The

thermoelectric power of Inconel 702 appeared to be significantly different in the solution-annealed state from that in

the age-hardened condition, and may provide a means of ascertaining the condition of the alloy in the tests discussed.

4.3* Microcrystalline Glass

Measurements were made of the thermal conductivity of a

microcrystalline glass (Pyroceram 9606; product of Corning

Glass Works, Corning, New York) . This material was selected

with the hope that it would come close to meeting the following criteria:

1. It should have a thermal conductivity in the

range 0.01 to 0.05 watt/cm deg C, comparable

to thermal conductivities of thermoelectric

materials.

2.

' It should be homogeneous and isotropic so that

a variety of sizes and shapes of specimens can

be made up from one large stock of the material

with confidence that all will have the same

thermal values.

3® It should be stable up to 1200°C or higher.

It should be opaque to thermal radiation up

to at least 1200°C.

5® Its cost should not be excessive.

Microcrystalline glass is first formed as a homogeneous

glass (incorporating a nucleating agent) which is transparent,

so that any defects can be readily detected visually. By

suitable heat treatment, the glass is later converted (by

Corning) to a polycrystalline solid which is opaque as a

result of the large number of vary small crystals. The

properties of such materials have been described in the

literature [10,11]

.
20

Pyroceram 9606 appears to meet the above criteria

fairly well, the biggest uncertainty being its stability

in the range 800° to 1200°C. There appears to be a small

slow change in dimension at the high temperatures, but there

is a reasonable possibility that this may not affect significantly the thermal conductivity.

The thermal conductivity of Pyroceram 9606 was measured

in the prototype absolute cut-bar apparatus and the results

reported previously [l]. The present specimen was fabricated from one of a lot of 2-inch bars supplied by Corning

Glass Works to Dr. D. C. Ginnings for measurements of thermal diffusivity, which are under way in the NBS Heat Measurements Section, 3*02. A specimen was also prepared for

measurement of thermal conductivity in our metals apparatus [ 7 ]$

preliminary results have been obtained which agree reasonably

well with the data presented in this report.

a. Description of Specimen

The specimen used for these determinations was in the

form of a cylinder 2.5*+0 cm in diameter and 1.269 cm. in

length. The specimen was fabricated from the same bar used

to prepare the specimen for the NBS metals apparatus. The

density of the specimen material was 2.601 g/cm3 (value supplied by Corning). The ends of the specimen were optically

polished so as to be flat to within 1/10 light fringe (approx.

3xlO”6 cm)

.

b. Test Procedure

The specimen was placed between the platinum-rhodium, hot

and cold bars, as shown in figure 1. (The hot and cold bars

had been optically polished to be flat to within 1 light

fringe.) Temperatures along the Pyroceram specimen were determined by means of three 0.20-mm butt-welded platinum-10^ rhodiumsplatinum thermocouples pressed into 0.15 mm grooves in

the convex surface of the specimen. These grooves were equally

spaced, one being at the mid-plane of the specimen and the

others 0.50 cm above and below the mid-plane.

Thermal conductivity measurements were made in increasing

order of temperature from 200° to 500°C at 100-degree intervals. The specimen was then heated to 600°C, but no data were

taken (due to a break in the water mains which supplied the

cooling water); the specimen was then cooled to room temperature. On second heating, measurements were made at 300°C and

at 100 degree intervals from 600° to 1000°C. The specimen was

held at 1000°C for about 275 hours, several sets of data being
21

taken during this time. Measurements were then made in

decreasing order of temperature at 900°, 600°, and 300°C.

Each conductivity determination involved an ’’isothermal”

test and a ’’gradient” test.

c. Results of Thermal Conductivity Tests

The thermal conductivity and thermal resistivity of the

Pyroceram specimen, as determined hy simultaneous solution

of the various pairs of tests, are shown in figure 9- The

solid lines shown are given by

w = 1/k = 26.7 + 9. 7 ( 3

^5

) , ( 23 ) where w is thermal resistivity (cm deg C/watt), k is thermal

conductivity (watt/cm deg C), and T is temperature (°C).

Equation (23) is the linear equation of least-mean-squares fit

to the .thermal resistivity values obtained from the first and

second heating cycles. The percent deviations of the experimental resistivity values from the smooth curve are shown in

figure 10. The points connected by a line (or in close juxtaposition) represent the individual values obtained in each

pair of tests for the two thermocouple spans in the specimen.

The horizontal displacement of two connected points is indicative of the temperature gradient in the specimen; for most of

the tests this gradient was 30 to *+5 deg C/cm-^ .

' The dotted

lines in figure 10 bound the region plus or minus two standard

percent deviations (estimated; first and second heating only).

The data points obtained on second cooling are in substantial agreement with the data taken before the specimen

was held at 1000°C, thus indicating that no appreciable change

in the thermal conductivity of Pyroceram 96O6 occurred as a

result of this heat treatment.

5. DISCUSSION

The* results presented above indicate that the high t emperature absolute cut-bar apparatus is capable of very good

precision. Comparison of the thermal conductivity values

obtained for Inconel 702 with independent values obtained by

T. "Exceptions to this are as follows:

First heating - 200°C, 20 deg C/cm (both pairs);

300°C, 20 deg C/cm (one pair);

Second heating - 600°C, 60 deg C/cm (one pair);

600°C, 10 deg C/cm (one pair);

1000°C, 15 deg C/cm (two pairs);

1000°C, .70 deg C/cm (one pair).
22

other methods are indicative of the accuracy of the method,

at least for that material. Preliminary results for Pyroceram

obtained using the NBS metals apparatus are in good agreement

with the values presented in Section 4.3.c. Additional analysis of the data presented in Section 4 will be performed and

minor adjustments in the values will probably be made. However, it is felt that the data given are substantially correct.

The ultimate objective of this investigation is the provision of samples for use by other laboratories as thermal

conductivity reference specimens in connection with their

measurements on solid semi-conductors. Of equal importance,

it is felt, is the proper use of such standards.

The problems encountered in the design and operation of

the absolute cut-bar apparatus have pointed out some of the

difficulties arising in measurements of this type on small

samples. The two most serious difficulties are due to the

thermal resistances at the contacting surfaces of the specimen

and the extraneous exchange of heat with the surrounding insulation. In order to avoid the problem of attempting to

measure contact resistance, it is recommended that thermocouples be placed in the specimen not too near its contact

surfaces.

A detailed analysis of heat flow in the insulation of a

simplified cut-bar apparatus was presented by this author at

the Invitational Conference on Thermal Conductivity Methods

held at Battelle Memorial Institute, Columbus, Ohio, on

October 26-28, 1961. In view of the similarity of- this analysis to that used for the NBS absolute cut-bar apparatus, this

paper, "Thermal Guarding of Cut-Bar Apparatus," was reproduced at the end of a previous report [ 5] • Many laboratories are currently utilizing various forms

of a comparative cut-bar apparatus for their thermal conductivity measurements. A typical example would be the apparatus of Francl and Kingery [12]. It was shown by Laubitz [ 13

]

that this type of apparatus is very sensitive to the alignment of its components. As has been pointed out, shunting

heat flows through the insulation are also a serious problem

in an apparatus of this type if the specimen and meter bars

are of different conductivities.

It was shown in the paper at the end of reference [ 5]

that the fractional error due to shunting of heat through the

insulation is given quite closely by

•e = Ki(U- - U)D

Km KS

(2*0
23

for a comparative cut-bar apparatus with meter bars of conductivity Km , a specimen of conductivity Kg, insulation of

conductivity Kp, and where D is a geometrical factor. The

effect of varying specimen thermal conductivity for different

meter bars is shown in greater detail in figure 11. Here the

coefficient conductivity-term of equation (24),

Ki( 1

Km

- Jo

Ks

?

is plotted against Ks, the thermal conductivity of the specimen, for four values of Kjn, the thermal conductivity of the

meter bars. The thermal conductivity of the insulation is

held fixed at 0.001 w/cm-C. The quantity plotted goes through

zero at Ks=Kn], approaches - oo as Ks becomes quite small, and

asymptotically approaches Ki/Krrj as Ks becomes large.

A typical geometrical factor, D(j_i), would probably not

exceed a value of 2.5* If the vertical scale in figure 11

were multiplied by 2.5, each scale division, 0.02, would

become 0,05, or 5 percent. Hopefully, the geometrical factor

might be made as small as 0.5 or 1.0, so that each vertical

scale division would become 1 or 2 percent, respectively.

If both the specimen and the meter bars have at least

one hundred times the thermal conductivity of the insulation,

the choice of a particular meter bar is not critical. If the

specimen to be measured has a thermal conductivity on the order

of ten times that of the insulation, or less, the choice of a

suitable meter bar becomes quite important.

It can be seen from Figure 11 that the conductivity of

the meter bars should be near the lower end of the range to be

covered, if it is desired to measure a wide range of specimen

thermal conductivities, utilizing a single pair of meter bars.

If

y = ^(Ks^ax ^s^min

(Ks )jBax^ ^-Ks )min

(25)

where (Ks) IDax and (Ks)min are the maximum and minimum specimen

thermal conductivities to be measured, then the maximum error

to be expected within the range is

Ki , 1 e L(Ks)max TiciTminJ

D ( 26 )

For relatively large (Ks)Dax , equation (26) reduces to
24

* 2 Tk^D( ^(27)

It is of interest to investigate numerically the significances of equations (25) and (26). Table 4 gives several

ranges of thermal conductivity, the preferred meter bar conductivity for each range, and the maximum, error to be expected

for a given geometrical factor (1.0) and insulation thermal

conductivity (0.001 w/cm-C).

TABLE 4

Maximum Error for Various Ranges of Specimen

Thermal Conductivity

KS

minimum. maximum optimal Km

maximum,

error

in K<? range

w/cm-C w/cm-C w/cm-C ± $

0.005 0.01 0.0067 5.0

.01 .015 .0120 1.7

.01 .02 .0133

.01 .05 .0167 4.0

.01 .10 .0182 if. 5

.01 1.00 .0198 5.0

.05 .10 .0667 .50

.05 .50 .0909 .90

.10 .50 .167 .40

.10

.10 10.00

1.00

.198

.182 M

.50

1.00 10.00 1.82 .045

The value assumed above for the thermal conductivity of

the insulation (0.001 w/cm deg C) is probably a fairly typical value; at high temperatures, however, the value might be

considerably higher, thus causing a proportionately larger

error. The value assumed for the geometrical factor (1.0)

may also be low by a factor of two or more under some conditions. Thus, the maximum errors obtained in an actual case

could be much larger than those given in table 4. Note that

the errors are particularly large in the range of maximum

interest for thermoelectric devices (0.01 to 0.05 watt/cm. deg C).

The effects of these unwanted heat flows can be avoided

by means of a suitable calibration, if suitable thermal conductivity reference specimens can be made available. The best
25

use of such reference specimens is discussed in another paper

presented at the above mentioned conference. In his paper

"Current NBS Steady-State Thermal Conductivity Methods,"

H. E. Robinson, Chief of the NBS Heat Transfer Section, concluded by saying:

. "The idea of a thermal conductivity reference standard

is manifest. Nevertheless, such standards involve other

problems than merely those of selecting suitable materials

and determining their conductivity as accurately as possible.

"For example, the best use of a reference material is

to use it as a substitute specimen, as is done for instance

in precise determinations of electrical resistance. When

the reference is used in this way in a particular apparatus,

it is presumably subject to the same unwanted heat flows,

resulting from what might be termed the accessory conditions

of the apparatus, as would be a test specimen of equal conductivity. If the reference is thus used to calibrate a

metering device of some sort, as it would be in a comparative

type of testing apparatus, the calibration of the meter would

inherently contain the effects of these perturbations. This

consideration is of special importance in the case of heat

flow measuring equipment, because there is no perfect thermal

insulation or guarding to eliminate unwanted heat flows.

Such use of the reference as a substitute specimen carries

with it, however, the strict requirement that the accessory

conditions of the apparatus be duplicable in ordinary tests,

as in the calibrating tests. Thus, in this sense, the best

use of a reference standard involves the design of the apparatus to be calibrated with it, in regard to the precision

with which the accessory conditions can be controlled and

duplicated.

"As an illustration, it would not be the best use of a

reference material of known conductivity to employ it as the

heat flow meters in a series arrangement such as meterspecimen-meter o The better use would be to employ for the

metering bodies some suitable material, and obtain a calibration for them by using the reference in place of the specimen, If reference substitute specimens covering a range of

conductivities were used, and accessory conditions were adequately reproduced, it is probable that test measurements on

unknown specimens of conductivities within the range covered

by the references could be made with results not seriously

inferior in absolute value to those of the reference specimens O o 0 o”

In order to adequately calibrate a thermal conductivity

measuring device for use on thermoelectric materials, it
26

would appear desirable to have available at least three

reference substitute specimens: a) one having a thermal

resistivity near the upper end of the range found for thermoelectric materials, b; one near the lower end of this

range, and c) one somewhere near the middle of this range.

All such reference standards should be homogeneous and isotropic, stable in air at elevated temperatures, opaque to

thermal radiation, and should not be excessive in cost.

The nickel-chromium alloy, Inconel 702, for which

results were presented above, appears to be suitable as a

reference standard having a thermal conductivity near the

upper limit of that of most thermoelectric materials of

interest. The data presented in table 1 indicate that the

thermal conductivity of this material is well-known over the

temperature range from -150° to 1200°C. Samples of this

alloy (cut from the same plate as were the NBS specimens)

have been sent to Dr. R. ¥. Powell of the National Physical

Laboratory (Teddington, Middlesex, England), to Dr. M. J.

Laubitz of the National Research Council (Ottawa, Ontario,

Canada), and to Dr.-Ing. Karl-Heinz Bode of the PhysikalischTechnische Bundesanstalt (Braunschweig ,. West Germany). Samples have also been provided to a few selected laboratories

in this country. In conjunction with thermal conductivity

measurements, many of these ^laboratories will also conduct

electrical resistivity determinations.

The NBS Heat Transfer Section intends to measure the

electrical resistivity of Inconel 702 from. -195° to 1200°C

or higher with particular attention to the effects of heat

treatment. The thermoelectric power of this alloy will also

be measured over a wide temperature range. Photomicrographs

are being prepared of the solution-annealed alloy and of a

sample cut from the thermal conductivity specimen after completion of testing to 1200°C in the high temperature absolute

cut-bar apparatus. It is felt that samples of NBS Inconel

702 can soon be made available to interested laboratories for

use as reference specimens.

Microcrystalline glass, Pyroceram 9606, appears quite

promising for use as a reference standard having a thermal

conductivity similar to that of many thermoelectric materials.

Measurements on this material have been completed in the NBS

metals apparatus over the range 100° to 650°C. The data have

not been completely analyzed, but appear to be in substantial

agreement with the values obtained in the high temperature

absolute cut-bar apparatus. These measurements will be

extended to -150°C if analysis indicates such to be feasible.

Thermal diffusivity of Pyroceram 9606 is being determined by

the NBS Heat Measurements Section. In view of the promising
27

results obtained thus far with Pyroceram 9606, it is considered worthwhile to discuss with the manufacturer the possibility of obtaining an adequate stock from which, after the

necessary measurements, samples suitable for distribution to

other laboratories can be cut.

The selection of a suitable reference standard having a

thermal conductivity lower than that liable to be encountered

in thermoelectric materials poses a rather difficult problem.

It is quite desirable that any material selected be available

in a wide variety of sizes and shapes, so that thermal conductivity specimens can be prepared for test by conventional

methods. In principle, a lower thermal conductivity should be

attainable in an electrical insulator than in a semiconductor,

since there is no electronic component of thermal conductivity

in the former. Furthermore, an amorphous solid, in general,

will have a lower thermal conductivity than a crystalline

material possessing long-range order. Thus, one is led to the

conclusion that a glassy material would be a suitable reference standard for this range of thermal conductivity.

Fused silica (quartz) has been proposed as a thermal conductivity standard. While there is a great deal of discrepancy among some of the older data in the literature, some of

the more recent determinations [14,15,16] are in better agreement, indicating that the room temperature value for the thermal conductivity of fused silica is about 0.013 to 0.015

watt/cm deg C. Above about 400°C, in addition to heat transfer by vibrational modes, heat is transferred through silica

by thermal radiation. This radiative transfer -rapidly becomes

quite large [17 ? 18,19] so that at elevated temperatures the

thermal conductivity of fused silica becomes a rather ambiguous

property.

Pyrex glass (77^-0, Corning) has a thermal, conductivity

somewhat lower than that of fused silica. At room temperature the value is about 0.010 to 0.012 watt/cm deg C [1,16,

18,20,21,22]. Unfortunately, Pyrex also becomes transparent

to thermal radiation above about 400°C. In order to confirm

measurements made in the prototype absolute cut-bar apparatus

[ 1] , a specimen of Pyrex 77^-0 has been prepared for testing

in the high temperature absolute cut -bar apparatus. The

specimen is identical in size and shape to the Pyroceram

specimen described in Section ^f.3» The flat surfaces of this

specimen have been coated with gold, in order to minimize

radiative heat transfer.

Additional efforts are being directed toward the selection of a suitable reference material having a thermal conductivity similar to that of fused silica or Pyrex. Consideration

is being given to a glass containing colorants to increase

opacity.

USCOMM-NBS-DC
28

6. REFERENCES

1. D. R. Flynn and H. E. Robinson, Thermal conductivity of

semiconductive solids 5 method for steady-state measurements on small disc samples, NBS Interim Technical Report

7135? covering period Feb. 23, 1959? to Mar. 31? 1961*

2# E. D. West and D. C. Ginnings, Automatic temperature

regulation and recording in precision adiabatic calorimetry, Rev. of Sci. Instru. 28, 1070-1074 (1957)-

3* W. F. Roeser, Thermoelectric thermometry, J. Appl. Phys.

11 , 404-405 (1940) 5 also in Temperature, its Measurement

and Control in Science and Industry, 202 (Reinhold Publishing Corp., New York, New York, 1941).

4. D. R. Flynn, A radial flow apparatus for determining the

thermal conductivity of loose-fill insulations to high

temperatures (to be published)

.

5* D. R. Flynn, Thermal conductivity of semiconductive

solids; method for steady-state measurements on small

disk reference samples, NBS Technical Progress Report

7367 for period July 1 to Sept. 30, 1961.

6. W. F. Roeser, ob. cit., 389-390; 181-182.

7* T. *W. Watson and H. E. Robinson, Thermal conductivity of

some commerical iron-nickel alloys, ASME Jour, of Heat

Transfer, 403-4q8 (Nov. 1961).

8. D. R. Flynn, D. A. Didion, and C. I. Siu, A steam calorimeter apparatus for determination of the thermal conductivity of refractory solids (to be published)

.

9* R. W. Powell and R. P. Tye, Thermal and electrical conductivities of nickel-chromium (nimonic) alloys, The

Engineer, 729-732 (April 29, I960).

10o S. D. Stookey, Glass-ceramics, Chem. Eng. News 39, 116

(June 19, 1961).

11- S. D. Stookey, Glass-ceramics, Mech Eng. 82, 65 (Oct. I960).

12. J. Francl and W. D. Kingery, Thermal conductivity: IV,

apparatus for determining thermal conductivity by a

comparative method, J. Am. Ceram. Soc. 32, 80 (1954).

13 » M. J, Laubitz, On measurement of thermal conductivity at

high temperatures, Can. J. Phys. 32, 1029 (1961).
29

l^e E. H. Ratcliffe, Thermal conductivities of fused and

crystalline quartz, Brit. J. Appl. Phys. 10, 22 (1959)*

15. E. D. Devyamkova, A. V. Pemrov, I. A. Smirnov, and

B. Ya. Moizhes, Fused quartz as a model material in thermal conductivity measurements, Soviet Physics, Solid

State, 2, 68l (Oct. I960). (Translated from Fizika

Tverdogo Tela, 2, 738 (Apr. i960)).

16. W. D. Kingery, Thermal conductivity: XII, temperature

dependence of conductivity of single-phase ceramics,

J. Amer. Ceram. Soc. 38? 251 (1955)$ and Thermal conductivity: XIV, conductivity of multicomponent systems,

J. Amer. Ceram. Soc. ^f2, 617 (1959).

17. W. D. Kingery, Heat conductivity processes in glass,

J. Amer. Ceram. Soc. 302 (1961).

18. C. -F. Lucks, H. W. Deem, and W. D. Wood, Thermal properties of six glasses and two graphites, Amer. Ceram. Soc.

Bull. 32, 313 (I960).

19. K. L. Wray and T. J. Connolly, Thermal conductivity of

clear fused silica at high temperatures, J. Appl. Phys.

30, 1702 (1959).

20. R. W. B. Stephens, The temperature variation of the thermal

conductivity of Pyrex glass, Phil. Mag. 14 ? 897 (1932).

21. F. Birch and H. Clark, The thermal conductivity of rocks

and its dependence upon temperature and composition,

Amer. J. Sci. 238, 529 (1940).

22. A. R. Challoner, H. A. Gundry, and R. W. Powell, A radial

heat-flow appratus for liquid thermal conductivity determinations, Proc. Roy. Soc. A245. 259 (1958).
NOTE:

32

T

d

CO

6

Oo

UJO/M‘ AllAliOnaNOO 1VIAId3Hl

00

o

200

400

600

800

1000

1200

TEMPERATURE

,°C

Figure

3*

Thermal

conductivity

of

a

60$

platinum-^O^

rhodium

alloy.
THERMOELECTRIC

POWER

,

|a.v

/

deg

C

Figure 4. Thermoelectric power of platinum-^OJ? rhodium and platinum -10% rhodium against pure platini.im.
3^

U SCOMM-NDS-DC

Figure

5*

Thermal

conductivity

of

solution-annealed

Inconel

702.
35

o

ro

T

o

c\i

o

o

! ° o 1

0

D 1

O 1

1 o O

O

CD

! °

a> | O o Q O

CD

h-

<

LU

X

h-co

QT

li. O

O

rO

%‘SlNIOd !VlN3l/Mld3dX3 30 N0I1VIA3Q

200

400

600

800

1000

1200

TEMPERATURE

,°C

Figure

6.

Departures

of

the

thermal

conductivity

data

for

solution-annealed

Inconel

702

from

a

smooth

curve.
36

o

o

CM

O

oPo

0

„

CD

LlI cr3

£

cr

LlJ CL

O UJ

CD hO

O

O

C\J

Figure

7*

Departures

of

the

thermal

conductivity

data

for

age-hardened

Inconel

7

02

from

a

smooth

curve.
APPARENT

DIFFERENCE

,%=

100 x

37 oo

CVJ oooo o o 0 ^

00 . I LU

cr

iD

I-<

cr

LU

CL O ^ o LU

CD h- Oooo

CM

Figure

8.

Apparent

difference

between

the

thermal

conductivity

of

solutionannealed

Inconel

702

and

that

of

the

age-hardened

alloy.
ovo

UDM/o 69P-UJ0 ‘ AJLIAI1SIS3U 1VWU3H1

O^roi'Of'OrorooJoJ 00 t0 C\i O 00 <0

o

LlI a:3

h-

<

ir

LlI CL

LU

IFigure

9*

Smoothed

values

for

the

thermal

conductivity

and

thermal

resistivity

of

Pyroceram

9606.
39

o

o

OJ

O

O

O

CO

O

CD

O

O

M"

O

O

CM

o

LU

cc

Z>

h-

<

cr

LJ

CL

LJ

hctf

Figure

10.

Departures

of

the

thermal

resistivity

data

for

Pyrcceram

9606

from

smooth

curve.
0.04

Figure

11.

Effect

of

thermal

conductivity

on

the

fractional

power

change

ina

comparative

cut-bar

apparatus.
4l

APPENDIX A

THERMAL CONDUCTIVITY OF SEMI CONDUCTIVE SOLIDS;

METHOD FOR STEADY-STATE MEASUREMENTS ON

SMALL DISC REFERENCE SAMPLES

Interim Technical Report 7135

Covering Period

February 23, 1959, to March 31, 1961

by

D. R. Flynn and H. E. Robinson

ABSTRACT

An absolute cut-bar method of measuring the thermal conductivity of solids is described, suitable for small specimens

of semiconductive materials. Measurements have been made at

temperatures from 100° to 800°C on Pyrex. Pyroceram, and a

nickel-chrome alloy, and representative tentative results are

given. The data for the nickel-chrome alloy, over the common

temperature range 130° to 600°C, agree with the smoothed data

from measurements made on the same material by an independent

absolute method, with a standard deviation of 0.7 percent.

The data for Pyrex and Pyroceram may be subject to errors

because of the uncertainties introduced by thermal contact

resistance at the surfaces of the specimens.

It is shown that the use of a matched guard in a cut -bar

apparatus does not reduce extraneous heat exchanges between

the bars and specimen and the surrounding powder insulation to

the small magnitude desirable for good accuracy of measurement. A mathematical analysis of the system indicates a

superior guarding condition which greatly reduces these extraneous heat flows, and which was used in the measurements

mentioned.

Using the knowledge acquired by these investigations, a

final model of the apparatus is being built for measurements

on small specimens (l/2-in. by 1-in. diameter discs) at temperatures in excess of 1200°C.
.

•- 1 -
U. S. DEPARTMENT OF COMMERCE

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