Thermal Conductivity of Cadmium and Cadmium-Alloy Crystals

Abstract

The intrinsic thermal resistivities $W_i$ of pure Cd and of Cd-Zn single crystals with residual-resistance ratios in the range 5 × ${10}^4$ - 570 (Zn content up to 0.56 at.%) were determined for both hexagonal and basal orientations in the temperature range $3<T<\mathrm{}100\mathrm{}$ K. One Cd-Sn crystal (0.14 at.% Sn) was measured in the basal orientation. The data are represented by $W_i\propto T^n$. In the case of pure Cd, $n=2\mathrm{}$ for $T<\mathrm{}3.5\mathrm{}$ K, whereas for the most impure alloy, $n=2\mathrm{}$ for $T<\mathrm{}13\mathrm{}$ K. For temperatures above the $n=2\mathrm{}$ region, $n$ was found to be as large as 4.5 in the interval $4<T<\mathrm{}7\mathrm{}$ K in the case of the purest crystal. The known rapid change of the specific-heat Debye $\Theta$ does not explain the large $n$. This indicates a small to negligible interaction between the electrons and transverse phonons. The region where $n>\mathrm{}2\mathrm{}$ is, in general, in the temperature range where phonon scattering outweighs impurity scattering. It is suggested that because of the particular shape of the Fermi surface, umklapp processes may be important in and above the temperature range where $n$ is large.