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NATIONAL BUREAU OF STANDARDS REPORT

7^66

THERMAL CONDUCTIVITY OF SEMICONDUCTIVE SOLIDS;

METHOD FOR STEADY-STATE MEASUREMENTS ON

SMALL DISK REFERENCE SAMPLES

Technical Progress Report

for Period

October 1 to December 31, 1961

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
THE NATIONAL BUREAU OF STANDARDS

Functions and Activities

The functions of the National Bureau of Standards are set forth in the Act of Congress, March 3, 1901, as amended by Congress in Public Law 619, 1950. These include the development and maintenance of the national standards of measurement and the provision of meanB and methods for making measurements consistent

with these standards; the determination of physical constants and properties of materials; the development of methods and instruments for testing materials, devices, and structures; advisory services to government agencies on scientific and technical problems; invention and development of devices to serve special needs of the Government; and the development of standard practices, codes, and specifications. The work includes basic

and applied research, development, engineering, instrumentation, testing, evaluation, calibration services,

and various consultation and information services. Research projects are also performed for other government

agencies when the work relates to and supplements the basic program of the Bureau or when the Bureau’s

unique competence is required. The scope of activities is suggested by the listing of divisions and sections on the inside of the back cover.

Publications

The results of the Bureau’s research are published either in the Bureau’s own series of publications or

in the journals of professional and scientific societies. The Bureau itself publishes three periodicals avail- able from the Government Printing Office: The Journal of Research, published in four separate sections,

presents complete scientific and technical papers; the Technical News Bulletin presents summary and pre- liminary reports on work in progress; and Basic Radio Propagation Predictions provides data for determining

the best frequencies to use for radio communications throughout the world. There are also five series of nonperiodical publications: Monographs, Applied Mathematics Series, Handbooks, Miscellaneous Publications,

and 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 ($1.25), and the Supplement to National Bureau of Standards Circular 460, July 1947 to June 1957 ($1.50), and Miscellaneous Publication 240,

July 1957 to June 1960 (Includes Titles of Papers Published in Outside Journals 1950 to 1959) ($2.25); avail- able from the Superintendent of Documents, Government Printing Office, Washington 25, D. C.
NATIONAL BUREAU OF STANDARDS REPORT

NBS PROJECT MBS REPORT

1006-20-109-61 March 22, 1962 7^66

THERMAL CONDUCTIVITY OF SEMICONDUCTIVE SOLIDS;

METHOD FOR STEADY-STATE MEASUREMENTS ON

SMALL DISK REFERENCE SAMPLES

Technical Progress Report

for Period

October 1 to December 31, 1961

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

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

IMPORTANT NOTICE

NATIONAL BUREAU OF STAN

intended for use within the Go

to additional evaluation and rev

listing of this Report, either in the Office of the Director, Natic however, by the Government ag

to reproduce additional copies

*ress accounting documents Approved for public release by the lliy pubiished is subjected

Directoi of the National Institute Ot •, j s obtained in writing from Standards and Technology (NIST) ch permission is not needed, on October 9, 2015. ;pared if that agency wishes

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

Thermal Conductivity of Semiconductive Solids;

Method for Steady-State Measurements on

Small Disk Reference Samples

Technical Progress Report

for Period

October 1 to December 31? 1961

by

D. R. Flynn

1.

ABSTRACT

Thermal conductivity measurements were conducted over

the temperature range 200° to 1200°C on a specimen of Inconel

702 (79*3$ Nl, 17$ Cr, 2.5$ Al) . t The results plot smoothly

from 0.142 w/cm C at 200°C to 0.3*+1 w/cm C at 1200°C and are

in excellent agreement with previous NBS determinations for

this material.

2.

STATEMENT OF PURPOSE

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 use by other laboratories as thermal conductivity reference specimens in connection with their

measurements on solid semiconductors.

3.

WORK PERFORMED IN REPORTING PERIOD

(October 1 to December 31? 1961)

During this quarter measurements were made of the thermal conductivity of a specimen of nickel-chromium alloy

(Inconel 702). The specimen was in the form of a right

cylinder 2.5*+ cm in diameter and 7.62 cm in length, which was

machined from the same solution-annealed hot-rolled plate as

were specimens previously measured in two models of the NBS

metals apparatus, in the NBS modified prototype absolute cutbar apparatus, and in the NBS steam calorimeter apparatus.

Since the thermal conductivity of this alloy is believed to

be well known (±2$) over a large temperature range, measurements on this material should enable confirmation of the

accuracy of the high temperature absolute cut -bar apparatus.

Measurements were made over the temperature range 200°

to 1200°C in the high temperature model of the absolute cutbar apparatus . (For a description of this equipment, see
2

NBS Report 7323.) The specimen was supported between the

alumina tube below and the alumina rod above. The thermal

insulation used throughout the apparatus was alumina powder.

The power generated in the specimen heater was determined by

current and potential drop measurements, using a calibrated

volt box and shunt box in conjunction with a precision potentiometer.

The temperature distribution along the nickel -chromium

specimen was determined by means of four butt-welded platinum:

platinum- 10# rhodium thermocouples, fabricated from, calibrated

O .38 mm reference grade wire, pressed into four transverse

0.3 mm grooves in the convex surface of the bar. Each of the

four specimen thermocouples could be read against an ice

junction, so that temperature gradients could be determined

by difference.

The insulated room-temperature zone box was wired to

enable determination of the emf developed between similar leads

of different thermocouples. The emf was measured between the

platinum wires of the lower two thermocouple junctions in the

specimen, the platinum wires of the upper two junctions, the

platinum-10# rhodium wires of the lower two junctions, and the

platinum-10# rhodium wires of the upper two junctions. Thus,

the nickel-chromium alloy bar served as the central portion of

four differential thermocouples. These measurements were used

as checks of the internal consistency of the platinum : platinum- 10# rhodium thermocouples. In addition, they enabled determination of the thermoelectric power of the nickel-chromium

alloy vs either platinum or platinum- 10# rhodium.

Thermal conductivity measurements were made at 200°C, and

in increasing order of temperature at 100 deg C intervals from

4- 00 ° to 1200°C, and then in decreasing order of temperature at

900°, 600°, and 300°C. Each conductivity determination

involved two tests. First, an "isothermal" test, in which

there was no power input to the specimen heater, was made to

determine variations between specimen thermocouples. This

test was followed by a "gradient" test with sufficient power

input to the specimen heater to maintain a longitudinal temperature gradient in the specimen of about 4 or 5 deg C/cra.

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

was little net heat exchange between the specimen bar assembly

and the surrounding insulation.

A program was developed to enable all data processing ' and calculations to be effected by means of the IBM 7090 computer facilities installed at NBS during this quarter. The

analysis carried out is basically that described in Appendices

A and B of the Interim Technical Report Covering Period

February 23, 1959 , to March 31 , 1961 (NBS Report 7135). The

major differences ares
3

a) In th8 evaluation of heat exchanges between the

specimen and the surrounding powder insulation, the analysis

has been extended so as to allow for a linear variation of

the thermal conductivity of the insulation with temperature.

b) A simultaneous solution of the "gradient" test and

the "isothermal" test is carried out by the computer. This

tends to minimize the effect of any systematic errors which

might be present either in temperature measurements or in

heat flow.

c) The thermoelectric power of the specimen vs platinum,

and vs platinum-10$ rhodium, is also computed. The results

obtained vs platinum~10$ rhodium, are adjusted, using the

known thermoelectric power of platinum-10^ rhodium vs platinum, to yield a separate value for the thermoelectric power

vs platinum.

Since temperature gradients in the specimen are rather

small, it is essential that the conversion of thermocouple

emfs to temperature does not introduce any additional uncertainties. The equation

E = 16. 82614

10. 30487 (nL)2

+ 7-912461(^3 - 2.053050 C^)4

- 2 . 8537^8 ( 1.0 “6 1000 ) ,

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

found to fit the platinum: platinum-10$ rhodium thermocouples 9 calibration data provided by the NBS High Temperature Measure

ments Laboratory quite closely over the temperature range 0°

to 1^50° C. This equation was incorporated into the computer

program, for conversion of all thermocouple voltages to temperature .

The thermal conductivity of the nickel-chromium alloy

as determined by simultaneous solution of the various pairs

of tests is shown in figure 1. The points plotted are

weighted averages of the values obtained in each pair of

tests 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.
4

The circles shown in figure 1 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 cubic equation of least-meansquares fit to all of the data points represented by circles.

This equation is

k=0. 1198+0. 07387 (tt^) +0.1915(t^) 2 -°-08 265(^^) 3

'1000 1000 ‘ 1000 '

where T is temperature (°C) and k is thermal conductivity.

To enable closer scrutiny of the deviation of individual

determinations from the curve, these are shown in figure 2 as

percent departures from the smooth curve plotted against temperature. The dotted lines bound the region plus and minus

two standard deviations from the solid line. The maximum

departure from the solid line of any point represented by a

circle is 0.6 percent. The inverted triangles depart significantly from, the solid line as the temperature decreases,

being high by 1.1 percent at 600°C and by 3.2 percent at

300°C. It is believed these two departures reflect an actual

change in the specimen conductivity rather than measurement

error. Inconel 702 is reported to age-harden if held for b

hours at temperatures around 730°C. It would not be surprising to detect a change in thermal conductivity at lower

temperatures after the specimen had passed slowly through

this temperature range, as it did in the decreasingtemperature tests.

The smoothed results of this determination are tabulated

in the second column of table 1 at 100 deg C intervals over

the temperature range 200° to 1200°C. 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 third column were obtained by means

of the modified prototype absolute cut-bar and are discussed

in detail in NBS Report 7135* The tabulated values are those

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

data points for peened thermocouples only. The data in the

fourth column represent the manually smoothed data from

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

the NBS metals apparatus [ l]

.

The fifth column presents data

obtained on a specimen six inches in diameter and one inch

thick in the NBS steam calorimeter apparatus. The tabulated

values correspond to the linear equation of least-mean-squares

fit to the calorimeter data available as of this date. With

the exception of one point (steam calorimeter at 600°C) the

thermal conductivity values tabulated in table 1 are within

±1 percent of their mean value at any given temperature.
5

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 3 presents tabulated thermal conductivity values for the NBS alloy as determined by this investigation and for the NPL alloys as reported [2], 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. The data acquired at NBS for

Inconel 702 show a slightly larger increase with temperature

than do the NPL results for Nimonie alloys. As noted above,

this may be partly due to different thermal histories.

The results of the tests made to date in the high temperature absolute cut-bar apparatus serve as an indication

of the precision and accuracy possible with this apparatus.

It is felt that measurements can scon begin on materials

having thermal conductivity similar to those of thermoelectric materials of interest.

k* FUTURE ACTIVITIES

Additional measurements will be made on the. specimen of

Inconel 702 to determine If the thermal conductivity at lower

temperatures was actually changed by heat treatment. Such

measurements are considered necessary to establish the

ability of the high temperature absolute cut-bar apparatus to

reproduce results after operation at high temperatures.

Initial measurements on lower conductivity material will

be -undertaken soon on a 1/2 -inch by 1-inch diameter disk of

Pyroceram 9606. Thermal conductivity measurements on Pyroceram. 9606 were made in the modified prototype absolute cutbar apparatus and are currently underway in the NBS metals

apparatus. Thermal diffusivity determinations are being made

at NBS by the Heat Measurements Section. This material was

chosen as having a thermal conductivity similar to that of

many thermoelectric materials. Preliminary results indicate

that it may be an excellent reference material.

A series of tests will be made with the Pyroceram 9606

specimen to evaluate the effects of heat exchanges with the

insulation and of thermal contact resistance. Following the

completion of tests on Pyroceram 9606, measurements will be

undertaken on selected thermal conductivity reference samples

provided by the Bureau of Ships.
Work will be begun soon on an annual report describing

activities since April 1. 1961. The report will present

much more technical detail concerning the high temperature

absolute cut-bar apparatus than has previously been given.

5. REFERENCES

[1]

« "Thermal Conductivity of Some Commercial Iron-Nickel

Alloys," by T. W. Watson and H. E. Robinson, Trans, of

the ASME Jour, of Heat Transfer, November 1961 , pp. 403-4o8.

[2]

, "Thermal and Electrical Conductivities of NickelChromium (Nimonic) Alloys," by R. W. Powell and R. P.

Tya, The Engineer, April 29 > I960, pp. 729-732.
7

TABLE 1

Thermal Conductivity of a Nickel-Chromium. Alloy (Indonel 702)

by Several Independent Methods at NBS

Temp * 9 °C

This

Investigation

Prototype

Absolute

Cut -Bar

Metals

Apparatus

Steam

Calorimeter

-100 —

----- 0.103 -----

0 —

--—

.114 -----

100 —

,127 —

200 Oelb-2 0 . lb2

,142 -----

300 .1 57 ,159 .158 . -----

4oo ,.175 .177 ,176

500 o±9b ,197 .196 -----

600 ,215 ,217 .218 0,213

700 ,237 .238 —-

.235 , 800 .259 o260 ,258

900 .281 ----- .280

1000 ,303 —

,303

1100 ,323 —

fe* O* ----- 1200 »34l te- AmS BU. «m>
0

TABLE 2

Chemical Compositions of Four

Nickel-Chromium Alloys

Composition, weight percent

Cr A1 Ti Fe Si Cu Co Mn C Ni

NBS Alloy 17.0 2.5 0.59 0.36 0.19 0.14 0.08 0.04 0.066 79.3

Nimonic 75 20.53 0.23 ,0.12 0.79 0.06 0.27 0.126 77.9**

Nimonic 80* 21.0 1.2 2.5 0.5 o.-5 — — 0.6 0.04 73.7**

Nimonic 90 19.5 1.40 2.45 0.4i 0.65 0.14 16.5 0.03 0.06 58.9**

^Nominal Composition

**By Difference

TABLE 3

Thermal Conductivity of Four

Nickel“Chromium Alloys

Temp.

,

°c

NBS

Inconel 702

NPL

Nimonic 75

NPL

Nimonic 80

NPL

Nimonic 90

200 0.142 0.157 0.138 0.146

300 .157 .175 .155 .165

4oq .175 .191 .168 .184

500 .194 .210 .184 .200

600 .215 .226 .210 .218

700 .237 .243 .235 .237

800 .259 .260 • 255 .253

900 .281 .276

USCOMM-NBS-DC
U SCOHM-NBS-DC

200

400

600

800

SOOO

1200

TEMPERATURE

,

°C

Fig.

1.

Thermal

conductivity

of

Inconel

702

as

determined

by

the

high

temperature

absolute

cut

-bar

apparatus.
~~~~\

\ ry n r ! !

i < Lft

| ° 1

i

1

I

J

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1

1

!

1

1

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1 - . [ o

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i

s ^ ! p I

1

*

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1

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!

!

I

1

3 ! -

1

1

1

1

1

s

!

I 0 ! - 1

• 1

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00 *

i

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o

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o

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CVi o

rO

Q

<NJ o

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1 ro

I %‘SlNI0d TviN3WIH3dX3 30 NOI1VIA30

Fig.

Departures

of

the

data

in

figure

1

from,

a

smooth

curve.
II. S. DEPARTMENT OF COMMERCE

Luther II. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director

THE NATIONAL BUREAU OF STANDARDS

The scope of activities of the National Bureau of Standards at its major laboratories in Washington, D.C., and

Boulder, (Colorado, is suggested in the following listing of the divisions and sections engaged in technical work.

In general, each section carries out specialized research, development, and engineering in the field indicated by

its title. A brief description of the activities, and of the resultant publications, appears on the inside of the

front cover.

WASHINGTON, B.C.

Electricity. Resistance and Reactance. Electrochemistry. Electrical Instruments. Magnetic Measurements,

f lielectrics. High Voltage.

Metrology. Photometry and Colorimetry. Refractometry. Photographic Research. Length. Engineering Metrology,

Mass and Scale. Volumetry and Oensimetry.

Heat. Temperature Physics. Heat Measurements. Cryogenic Physics. Equation of State. Statistical Physics.

Radiation Physics. X-ray. Radioactivity. Radiation Theory. High Energy Radiation. Radiological Equipment.

Nucleonic Instrumentation. Neutron Physics.

Analytical and Inorganic Chemistry. Pure Substances. Spectrochemistry. Solution Chemistry. Standard Refer- ence Materials. Applied Analytical Research.

Mechanics. Sound. Pressure and Vacuum. Fluid Mechanics. Engineering Mechanics. Rheology. Combustion

Controls. Organic and Fibrous Materials. Rubber. Textiles. Paper. Leather. Testing and Specifications. Polymer Structure. Plastics. Dental Research.

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Engineering Applications. Systems Analysis.

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Instrumentation. Engineering Electronics. Electron Devices. Electronic Instrumentation. Mechanical Instru- ments. Basic Instrumentation. Physical Chemistry. Thermochemistry. Surface Chemistry. Organic Chemistry. Molecular Spectroscopy. Molecular Kinetjcs. Mass Spectrometry.

Office of Weights and Measures. BOULDER, COLO.

Cryogenic Engineering. Cryogenic Equipment. Cryogenic Processes. Properties of Materials. Cryogenic Technical Services. Ionosphere Research and Propagation. Low Frequency and Very Low Frequency Research. Ionosphere Research.

Prediction Services. Sun-Earth Relationships. Field Engineering. Radio Warning Services. Vertical Soundings Research. Radio Propagation Engineering. Data Reduction Instrumentation. Radio Noise. Tropospheric Measurements.

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Hesearch. Antenna Research. Navigation Systems.

tipper Atmosphere and Space Physics. Upper Atmosphere and Plasma Physics. Ionosphere and Exosphere

Scatter. Airglow and Aurora, Ionospheric Radio Astronomy.