Royal Society Publishing

Electrical and Thermal Resistivity of the Transition Elements at Low Temperatures

G. K. White, S. B. Woods

Abstract

The results of measurements on 20 transition elements are reported giving values for the thermal resistivity, W, from 2 to about 140 degrees K and for electrical resistivity, $\rho $, from 2 to about 300 degrees K. Values of the 'ideal' resistivities, W$_{i}$ and $\rho _{i}$ (due to scattering of the electrons by thermal vibrations), are deduced from these and tabulated for various temperatures. Comparisons are made with values for Cu, Ag, Au and Na and with the predictions of the 'standard' theory, i.e. solutions of the transport equation developed by Bloch, Gruneisen, Wilson, etc. Excepting Mn, $\rho _{i}$ follows a Bloch-Gruneisen function tolerably down to $\theta _{D}$/5, although slight anomalies are shown by V, Cr, Fe, Co and Ni; at low temperatures behaviour is varied but below 10 degrees K in Mn, Fe, Co, Ni, Pd, Pt and perhaps in W and Nb, $\rho _{i}$ appears to vary nearly as T$^{2}$. The parameter, $\rho _{i}$M$\theta _{D}^{2}\Omega ^{\frac{1}{3}}$ (at 273 degrees K) has rather similar values for different members of each group, e.g. for Ti, Zr and Hf of group IV A. The ideal thermal resistivity, W$_{i}$, can generally be approximated by the relation, W$_{i}$/W$_{\infty}$ = 2(T/$\theta $)$^{2}$ J$_{3}$($\theta $/T), although for many elements, W$_{i}$ falls more rapidly than T$^{2}$ below $\theta $/10. Measurements on the relatively poor conductors, e.g. Ti, Zr and Hf, suggest the presence of an appreciable lattice conductivity, which affects the confidence with which values can be deduced for W$_{i}$ in these elements.

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