NBSIR 76-1003

Thermal Conductivity and

Electrical Resistivity of Six

Copper-Base Alloys

M. C. I. Siu, W. L. Carroll, and T. W. Watson

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

March 1976

Final

Prepared for

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, OH 44135

NBSIR 76-1003

THERMAL CONDUCTIVITY AND

ELECTRICAL RESISTIVITY OF SIX

COPPER-BASE ALLOYS

M. C. I. Siii, W. L. Carroll, and T. W. Watson

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

March 1976

Final

Prepared for

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, OH 44135

/ w %

U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson. Sacratary

James A. Baker, III. Undar Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Sdanca and Technology

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Acting Dkaetor

Thermal Conductivity and Electrical Resistivity

of Six Copper-Base Alloys*, +

M. C. I. Siu, W. L. Carroll, and T. W. Watson

Thermal Engineering Section

Center for Building Technology

National Bureau of Standards

Washington, D.C. 20234

ABSTRACT

Measurements of the thermal conductivity, x, and electrical resistivity, p, of oxygen free copper and six copper-base alloys in the temperature range 298 to 924 K are presented. Except for copper, the X and

p values of copper alloys having the same chemical composition as those

given in this paper have not been previously reported. The measured

-1-1

values of X (W»m" «K~ ) and p (s>m) were found to conform, within 10

percent, to the predictions of the Smith-Palmer equation, X = 2.39 x

10 T/p + 7,50 [W»m~ ], where T is the thermodynamic temperature

expressed in kelvins.

Key Words: Copper-base alloy properties; electrical resistivity; Smith-Palmer equation; thermal conductivity

*The work reported in this paper was partially supported by the National

Aeronautics and Space Administration.

i

1. Introduction

The thermal conductivity, x, of copper and a large number of copper

alloys have been previously measured [l] . In many instances, measurements were made at temperatures below 100 K.

It is known [2,3] that x of a copper alloy usually can be predicted

with sufficient accuracy for practical purposes from a measurement of its

electrical resistivity, p. Specifically, measured values of x and p of

many copper alloys between 293 and 473 K were observed [2,3] to obey the

Smith-Palmer equation, x = 2.39 x 10"8 T/p + 7.50 [W-m" 1 •K'

1 ]

, where T

is the thermodynamic temperature expressed in kelvins, to within 10-15

percent. In the present investigation, it was desired to know the thermal conductivity of a number of specific copper alloys over a larger

temperature range than that in which the Smith-Palmer equation is known

to hold accurately.

Results of the measurements of X and p of oxygen free copper and six

copper-base alloys from 298 to 924 K are presented in this paper. Samples for measurement were provided by the National Aeronautics and Space

Administration (NASA), Lewis Research Center, Cleveland, Ohio. Measured

values were compared with those obtained from the Smith-Palmer equation.

Except for oxygen free copper, x and p values of copper alloys having

the same chemical compositions as those found in this paper have not

been previously reported.

1
2. Specimens and Apparatus

The copper-base metals provided by NASA for these measurements were

in the form of either rectangular bars or right circular cylinders. Radiographs obtained from the exposure of these samples to the National Bureau of Standards cobalt-60 source (1.25 MeV gamma rays) showed that the

samples did not contain observable voids. Results of laboratory determination of the chemical composition, thermal history and mechanical

properties made on these copper alloys were supplied by NASA and are

given in Tables la, lb and 2.

Experimental data for calculating x and p of the copper alloys were

obtained using an apparatus which has been described in detail elsewhere

by Watson and Robinson [4]. This apparatus employs an electric heater

and a circulating water heat sink to maintain a steady-state longitudinal

thermal gradient closely approximating one-dimensional heat flow in a

rod-shaped specimen about 37 cm long and 0.64 cm in diameter. The specimen is mounted vertically and is coaxial ly surrounded by a stainless

steel cylinder equipped with its own heater which is made to function as

a thermal guard by adjusting its temperature profile to match, as closely

as possible, that of the specimen, thereby reducing radial heat flows

even further. A computerized analysis procedure is used to make final

corrections to compensate for the small remaining amount of extraneous

radial heat flow not eliminated by the apparatus. Alumina powder insulation surrounds both the specimen and the thermal guard.

Basically, x was determined from measured input power to the specimen heater and the specimen temperature gradient, which was in turn determined using calibrated Pt /Pt -10%Rh thermocouples at seven known

2
positions spaced 3.5 cm apart along the specimen, creating six measurement intervals, or spans. Calculated values of A were thus obtained at

six different mean temperatures for each level of power input to the

specimen heater (a "run").

While steady-state thermal conditions were being maintained for

each run, electrical resistivity was measured by passing a measured direct current through leads attached to the ends of the specimen and

measuring the voltage differences between adjacent platinum leads of the

thermocouples along the specimen. Thermoelectric effects were accounted

for by taking voltage measurements with current flowing in forward and

reversed directions. All values of x and p were computed using specimen

dimensions determined at room temperature.

Vacuum and gas handling systems were added to the apparatus in order

to make the particular measurements described in this paper in argon gas.

This permitted higher temperatures than could be attained in air without

encountering oxidation of the copper alloy specimens. All measurements

were conducted with the specimen chamber backfilled with argon at a pressure of one atmosphere.

Typically, three runs were made with each specimen, starting at the

lowest power input level to the specimen heater and increasing it for

each subsequent run. The highest mean temperature of a span during the

hottest run was about 925 K. After a complete set of measurements was

made on specimen R2, it was completely removed and subsequently replaced

in the apparatus. A second set of measurements was then obtained. Only

two runs each were made for specimens R3 and R4, which limited the highest span mean temperatures to about 625 K in those cases. Specimens

3
were tested in the order: R2, R2 (repeat test), R9, R5, R14, R4 and R3.

(For composition of the specimens, see Table 1.)

3. Results

Examination of the specimens after completion of measurements revealed that, except for oxygen free copper, R5, there was no significant

amount of oxidation of the specimens. In the case of oxygen free copper,

examination of the specimen after testing revealed that a crust about

0.01 cm thick and 7.6 cm long covered the hottest end of the specimen.

This layer was observed to be detached from the specimen. Qualitative

analysis made on a piece of crust material using an electron beam probe

analyzer revealed the presence of an abundant amount of oxygen and copper. Thus, it is most likely that the crust formation was an oxide of

copper. The maximum temperature range of the encrusted section of the

specimen during the hottest run was about 775 K to 975 K, sufficiently

high for the oxidation of copper. The change of cross-sectional area of

the specimen as a result of oxidation was taken into account in the calculation of X of R5.

Values of x and p calculated from measured data are shown as individual points in Figures 1 and 2, respectively. R2 data is included

from both sets of measurements made on the specimen. The curves shown

in these figures represent cubic polynomials fitted to the individual

specimen data points by the method of least squares, of the form

X = a

Q

+ a-jT + a

2

T

2 + o^T^W-m' 1

• K

_1

) and p = e + ^T + ^J2 + $3

T

3

(ft«m). For T in degrees Celsius, values of the coefficients of these

polynomials are given in Table 3. Numerical results, called "smoothed

4
values", calculated from the above equations at uniform temperature intervals, are presented in Tables 4 and 5.

Below 833 K values of X for specimen R2 obtained in the repeated

measurement were in agreement to within 0.5 percent to that of the initial run. Between 833 and 920 K, results of the two successive measurements were in agreement to within 1.5 percent. Values of A for oxygenfree copper obtained in this work agree within better than 3 percent

with the values recommended by Touloukian, et al [l] over the full

temperature range of the results obtained in the present effort, except

for the highest temperature point (about 925 K, Fig. 1). This point is

anomalously low and is most likely due to errors introduced because of

heavy oxidation of the hottest span, and relatively large extraneous

heat flows for which the computerized analysis could not completely compensate; it subsequently causes an anomalously large decreasing trend of

the fitted curve with increasing temperature, particularly in the range

of about 825 to 925 K.

The fitted curves for A and p each tend to cluster into two groups,

one with A (p) near that of oxygen-free copper and the other with A (p)

somewhat lower (higher). The reason for this separation is not known.

However, other measured data for both properties indicate such variation

is not unreasonable for dilute copper alloys [3]. In addition, a consistency check was made by calculating the Lorenz function for each

specimen from the smoothed data at even temperature intervals. Over the

whole range of the data, the Lorenz function was almost temperature

independent and close to the theoretical Lorenz number for all specimens

except R14. Although the Lorenz functions are not presented, comparison

5
between measured and predicted values for x using the Smith-Palmer equation are given in Table 6. The same conclusion about the consistency of

the results is obtained. It is thus felt that the clustering of the

r

curves into two groups is coincidental and has no other significance.

The results for specimen R14 are an exception to the above conclusion. In addition to an anomalously low calculated Lorenz function

(compared to the other specimens) and a significant lack of agreement

with predictions of the Smith-Palmer equation, there is also a large

scatter in the electrical resistivity data (Fig. 2). Either the results

for x or p, or both, must be anomalous. Fictitious electrical resistivity values calculated from the Smith-Palmer relation using measured

values of x closely approximated a linear function of temperature with

only a small amount of data scatter (about 2% standard deviation) and a

fitted straight line closely matches the results of the measured p data

of the other specimens both in slope and in magnitude. These facts lead

to the belief that the x results for R14 are probably valid, and thus

that the p results for R14 are probably mostly anomalous (although there

was close agreement between the fictitious calculated p values and most

of the actual measured p data points in the temperature range 373-573 K)

The accuracy of the smoothed values of x obtained with this apparatus was established from a comparison of results on round-robin specimens by NBS and other laboratories. It is estimated to be about + 2 to

3 percent [5-8]. Because of the use of thermocouples as potential taps

in the measurement of p, similar uncertainties exist in geometry and

thermoelectric effects. Since these are the dominant sources of error,

it is estimated that the accuracy of the smoothed values of p are about

6
the same as that for x.

4. Conclusion

Measured values of the thermal conductivity and electrical resistivity of oxygen -free copper and six copper-base alloys are presented.

With one exception, the measured x values of these materials and the X

values predicted by the Smith-Palmer equation using measured p values

agree to within about 3 percent. The exceptional case is believed to be

due to erroneous p data, and not due to limits of validity of the SmithPalmer equation.

5. Acknowledgment

The authors wish to thank Dr. G. Hal ford of Lewis Research Center,

NASA, for providing the samples and information on the chemical composition and mechanical properties of the metals, Mr. T. P. Loftus of the

National Bureau of Standards for preparing the radiographs used in this

study, and Mr. C. E. Fiori of the National Bureau of Standards for performing the elemental analysis using the electron beam probe analyzer.

6. References

fj] Y. S. Touloukian, R. W. Powell, C. Y. Ho and P. G. Klemens, Thermophysical Properties of Matter, Vol. 1, Plenum Publishing Corporation, New York, 1970.

[2] C. S. Smith and E. W. Palmer, Trans. Amer. Inst. Min. Metall. Engrs.

117 , 225 (1935).

[3] R. W. Powell, Int. J. Heat Mass Transfer, 8, 1033 (1965).

7
[4] T, W. Watson and H. E. Robinson, J. Heat Transfer, 8, 1033 (1961).

[5] T. W. Watson, D. R. Flynn and H. E. Robinson, J. Res. NBS 71C , 285

(1967).

[6] T. W. Watson and D. R. Flynn, Trans. Met. Soc. AIME 242, 844 (1968).

[7] M. J. Laubitz and K. D. Cotnam, Canad. J. Phys. 42, 131 (1964).

[8] R. W. Powell and R. P. Tye, Int. J. Heat Mass Transfer 1_0, 581 (1967).

USCOMM-NBS-DG

8
Figure Captions

Figure 1 Thermal Conductivity of Oxygen Free Copper and Six CopperBase Alloys

Figure 2 Electrical Resistivity of Oxygen Free Copper and Six CopperBase Alloys

9
10
n
Table la Chemical Composition of the Copper Samples*

Identification

Number

Chemical

Composition

Percent

Weight

R2 Pb . 0.000

Sn 0.000

Zn 0.00

Fe 0 . 002

Ni 0.002

Zr 0.20

Cu Balance

R3 P 0.005

Te 0.5.1

Cu 99.50

R4 Mg 0.00

Si 0.02

Cr 1.07/1.13

Cu Balance

R5

+

Oxygen Free Copper

R9 Mg 0 . 05

Zr 0.17

Cr 0.48

Cu Balance

R14 Pb, Sn 1 ppm

Bi <0.0001

Be <0.0002

Si <0.0001

Ca <0.0003

Mn <0.0003

Co <0.001

Ni <0.001

Zn <0.001

As <0.002

P <0.002

Sb < 0.002

Zr 0.49

Ag 2 . 74

Cu Balance

R15**

Information provided by Lewis Research Center, NASA, Cleveland, Ohio.

**

R15 was made to the same chemical composition as R14 but differs in

its heat treatment (shown in Table lb).

Chemical composition not supplied by NASA.

12
Table lb Thermal History of the Copper Samples"

Identification No. History of Heat Treatment

R2 Extruded at 1233 K and aged at 693 K in cracked

natural gas atmosphere

R3 Not provided by NASA

R4 Solution annealed at 1273 K, quenched and aged

at 773 K for 3 hours

R5 Hot rolled at 1051-1109 K and cold drawn

R9 Solution heat treated at 1331 K in neutral (barium chloride) salt, quenched in water, cold drawn

and aged at 773 K for 2 1/2 hours and drawn

R14 Centrifugally cast, hot forged at 940 to 1134 K,

solution treated at 1451 ± 8 K for 2 hours

R15 Conventionally cast, hot rolled at 1134 ± 8 K,

solution annealed at 1451 ± 8 K for 1 hour,

quenched in water, aged at 773 K for 3 hours and

air cooled

^'Information provided by Lewis Research Center, NASA, Cleveland, Ohio.

13
Table 2 Mechanical Properties of the Copper Samples*

Alloy T (K)

Strength

Yield

(MN/m

2

) Tensile**

Reduction

in Area (%)

R2 2 97 336 378 81.5

811 213 216 84

R3 2 97 355 360 37.5

811 24.8 74.2 28

R4 297 521 529 56.5

811 255 262 17.5

R5 297 309 317 82

811 23.5 70.3 65

R9 2 97 537 550 77

811 296 309 40.5

R14 297 82.4 295.1 53.8

811 63.4 125.5 61.5

R15 297 99.0 288.5 55

811 85.1 127.0 53.5

Information provided by Lewis Research Center, NASA, Cleveland, Ohio

* -3 -1

Tensile strain rate: 2 x 10 sec in all tests

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15
Table 4 Smoothed Values of the Thermal Conductivity (W«m~ 1 «K" 1

) of Oxygen Free Copper and Six Copper-Base Alloys

T (K) R2 R3 R4 R5 R9 R14 R15

373 376 360 361 385 312 279 310

423 376 363 366 384 319 281 311

473 375 364 367 383 324 287 315

§23 373 364 367 382 329 295 319

573 372 363 366 380 333 305 323

623 370 362 364 377 335 314 327

673 367 360 364 375 336 324 330

723 364 371 336 332 333

773 361 367 334 338 334

823 359 362 331 341 334

873 356 356 327 339 331

923 354 349 321 333 326

16
Table 5 Smoothed Values of the Electrical Resistivity (10~ 8 £?«oi)

of Oxygen-Free Copper and Six Copper-Base Alloys

T (K) R2 R3 R4 R5 R9 R14 R15

323 2.00 2.07 2.06 1.93 2.47 2.63 2.51

373 2.36 2.45 2.43 2.30 2.82 3.04 2.91

423 2.71 2.80 2.78 2.64 3.17 3.39 3.28

473 3.05 3.14 3.11 2.96 3.52 3.69 3.64

523 3.39 3.47 3.44 3.29 3.86 3.96 3.98

573 3.72 3.79 3.76 3.61 4.20 4.22 4.30

623 4.07 4.13 4.09 3.97 4.54 4.48 4.63

673 4.41 4.49 4.42 4.32 4.86 4.75 4.95

723 4.77 4.71 5.18 5.05 5.29

773 5.14 5.50 5.39 5.63

823 5.52 5.80 5.78 6.00

873 5.93 6.09 6.24 6.40

923 6.36 6.37 6.79 6.82

17
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NBS-1 14A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OK REPORT NO.

NBSIR 76-1003

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Thermal Conductivity and Electrical Resistivity of

Six Copper-Base Alloys

5. Publication Date

riarcn j.y/o

6. Performing Organization Code

7. AUTHORCS)

M.C.I. Siu, W. L. Carroll, & T. W. Watson

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 4624140

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, OH 44135

13. Type of Report & Period

Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

Measurements of the thermal conductivity, A , and electrical resistivi ty , p , of

oxygen free copper and six copper-base alloys in the temperature range 298 to

924 K are presented. Except for copper, theAand p values of copper alloys

having the same chemical composition as those given in this paper have not been

previously reported. The measured values of A (W-m-l-K-1

) and p

(fi-m) were found

to conform, within 10 percent, to the predictions of the Smith-Palmer equation,

\= 2.39 x 10-8 T/

p + 7.50 fw-nr 1

• |<-lj

, where T is the thermodynamic temperature

expressed in kelvins.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons

)

Copper-base alloy properties; electrical resistivity; Smith-Palmer equation;

thermal conductivity

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