Electrical Resistivity of Tungsten

M. C. Billone

May 27, 1996

The electrical properties of unirradiated tungsten vs. temperature (T in deg-C) are well established. No data were found on the electrical resistivity of irradiated tungsten. However, the primary transmutation products of tungsten are rhenium (Re) and osmium (Os). Given the electrical resistivities of these two elements and their production rates for the ARIES-RS design, the electrical resistivity of tungsten was estimated as a function or neutron damage (D in dpa) by the law of mixtures.

1. Properties of Unirradiated Elements

Values for the electrical resistivity of tungsten (Rw in n-ohm-m) are given in Ref. 1 from room temperature to 627 C. A parabolic fit to these values gives agreement to within 1%:

Rw = 48.0 (1 + 4.8297 x 10-3 T + 1.1663 x 10-6 T2)

Values for the electrical resistivity of Re (RRe in n-ohm-m) are given in Ref. 2 (page 789) from room temperature to 900 C. A parabolic fit to these values also gives agreement to within 1%:

RRe = 177 (1 + 4.5585 x 10-3 T - 1.2447 x 10-6 T2)

Reference 2 (page 780) also gives the room temperature electrical resistivity of Os (ROs in n-ohm-m) and the temperature coefficient from 0-100 C. A linear fit to these values gives:

ROs = 94.9 (1 + 4.4250 x 10-5 T)

2. Electrical resistivity of W-Re-Os

Let ARe and AOs be the atom fractions (in absolute units) of Re and Os produced in the W by transmutation. The electrical resistivity of W-Re-Os can be estimated by the law of mixtures to be:

R = (1 - ARe - AOs) Rw + ARe RRe + AOs ROs

In general, direct data are preferred to this expression. As W-Re alloys have been considered for space power applications, it is possible that data are available for W-Re.

3. Production Rates of Re and Os

Greenwood and Garner (Reference 3) give the production rates of Re and Os for W as a first-wall tile material in STARFIRE, as well as in a couple of experimental fission reactors. As STARFIRE has a lower dpa rate than ARIES-RS and a higher thermal neutron flux because of the water coolant and beryllium multiplier, the productions rates can be anticipated to be different. The ARIES-RS production rates for tungsten should be provided to you by the University of Wisconsin. The following, however, represents a sample calculation for the production rates in STARFIRE, as well as the resulting increase in electrical resistivity for W. Use the sample results only if no ARIES-RS production rates for W are available.

Based on Greenwood and Garner, the production of Re from W and Os from Re can be expressed as a function of D in the range of 0-100 dpa as:

ARe = 0.13 [1 - exp (-0.03675 D)]

and

AOs = 0.027 [ exp (0.0158 D) -1]

Using the above equations, the electrical resistivity of W can be estimated as a function of dpa. The results for 300 C and 600 C are shown in Fig. 1. The predicted increase in electrical resistivity is < 26% at 300 C and < 19% at 600 C for 0-100 dpa. Higher increases would be predicted if the increase in osmium resistivity is parabolic rather than linear. However, the data found included only a room temperature value and a temperature coefficient from 0-100 C.

References

1. CRC Handbook of Chemistry and Physics, 75th Edition, eds. D. R. Lide and H. P. R. Frederikse, CRC Press (1994-95) p. 12-41.

2. Metals Handbook, 9th Edition, Vol. 2, Properties and Selection: Nonferrous Alloys and Pure Metals, ASM, Metals Park, OH, P. 789 and P. 780.

3. L. R. Greenwood and F. A. Garner, "Transmutation of Mo, Re, W, Hf and V in Various test facilities and STARFIRE," J. Nucl. Mater. 212-215 (1994) 635-639.