Lattice Thermal Conductivity of Impure Tin

Measurements of the normal- and superconducting-state thermal conductivities (Kⁿ and Kˢ) were made on seven cadmium-doped tin single crystals in the temperature range 1^∘K<T<4^∘K. Data from six specimens measured previously are also included in the analysis. Cadmium concentrations range from 0.04 to 0.97 at.%. The crystal orientations are grouped in the near perpendicular direction (direction of heat flow approximately perpendicular to the tin tetrad axis). The small fractional size of the normal-state lattice conductivity, Kg^_ⁿ, precludes its direct determination from the normal-state data alone. However, the superconducting-state thermal conductivity is employed in a "universal curve" type of analysis, from which we deduce for Kg^_ⁿ a T^2.21±0.04 dependence upon temperature and a ρ₀^_^-(0.21±0.04) dependence upon residual resistivity. As the solid solubility limit is approached we find an additional lattice resistivity varying as T^-1.4 and increasing in magnitude with increasing impurity concentration. This is ascribed to phonon scattering by point defects and boundaries, using adjustable parameters describing the distortion about the impurity and the mean free path for boundary scattering. The best fit to our data yields values for the strain field size that are in good agreement with the x-ray data of Lee and Raynor. The apparent boundary scattering mean free path is much less than the sample diameter; this indicates large clusters of impurities in the alloy.