Thermal and Electrical Conductivity of Pure Tin from 4.5 to 77 °K

Abstract

The thermal and electrical conductivities of two pure single crystals of tin have been measured. The samples were oriented at 72\ifmmode^\circ\else\textdegree\fi{} and 6\ifmmode^\circ\else\textdegree\fi{} with respect to the tetragonal axis of tin. The thermal conductivity values for the two samples were fit to the relation ${(\ensuremath{\alpha}{T}^{n}+\frac{\ensuremath{\beta}}{T})}^{\ensuremath{-}1}$ from 4 to 12 \ifmmode^\circ\else\textdegree\fi{}K with $n$ approximately 3.2 for both samples. This large value is attributed to dispersion in the phonon spectrum which causes an approximate 4.2-power dependence with temperature of the specific heat over the same temperature range. The electrical-resistivity value of the two pure samples was found to obey the Bloch-Gr\"uneisen expression over a wide range with a Debye temperature of 125 \ifmmode^\circ\else\textdegree\fi{}K and with a small additional residual resistivity. The anisotropy of the thermal conductivity exhibits a slight maximum at 10 \ifmmode^\circ\else\textdegree\fi{}K, attributable to the relative effect of impurity scattering and an anisotropic band structure. The anisotropy of the electrical conductivities exhibits a more pronounced maximum around 20 \ifmmode^\circ\else\textdegree\fi{}K because of an additional effect of area differences of Brillouin-zone segments on the Fermi surface when small-angle scattering dominates. The ratio of electrical anisotropy to thermal anisotropy at the maximum was found to be approximately 1.27, which compares well with the theoretically predicted value of 1.26 from the area differences at the zone segments in the 90\ifmmode^\circ\else\textdegree\fi{} and 0\ifmmode^\circ\else\textdegree\fi{} orientations.