Anisotropy of the Residual Resistivity of Tin with Sb, In, Zn, and Cd Impurities, and the Ideal Resistivities and Deviations from Matthiessen's Rule at 77 and 273°K

Abstract

Measurements have been made of the orientation and of the electrical resistivities at 4.2, 77, and 273\ifmmode^\circ\else\textdegree\fi{}K of single-crystal tin samples containing In, Sb, Zn, and Cd impurity up to 2.2 at.%. The superconducting transition temperature was used as a measure of impurity concentration. The anisotropy of the residual resistivity is found to be dependent on impurity type. Defining ${\mathrm{a}}_{0}$ as the ratio of residual resistivities parallel and perpendicular to the tin tetrad axis (${a}_{0}=\frac{{\ensuremath{\rho}}_{0\ensuremath{\parallel}}}{{\ensuremath{\rho}}_{0\ensuremath{\perp}}}$), it is found that ${a}_{0}=1.21\ifmmode\pm\else\textpm\fi{}0.05, 1.30\ifmmode\pm\else\textpm\fi{}0.07, 1.53\ifmmode\pm\else\textpm\fi{}0.07, \mathrm{and} 1.60\ifmmode\pm\else\textpm\fi{}0.07$ for In, Sb, Zn, and Cd impurities, respectively. These results indicate that impurity scattering in tin is not isotropic, and a qualitative discussion of these results is offered. It is found that ${\ensuremath{\rho}}_{0\ensuremath{\perp}}$ varies linearly with impurity content $x$ for indium and antimony impurity; we determine $(\frac{{\ensuremath{\rho}}_{0\ensuremath{\perp}}}{x})=0.54\ifmmode\pm\else\textpm\fi{}0.02 \mathrm{and} 0.63\ifmmode\pm\else\textpm\fi{}0.03$ \ensuremath{\mu}\ensuremath{\Omega} cm/at.% for these two impurities, respectively. For zinc impurity this quantity is estimated to be at least 0.82 \ensuremath{\mu}\ensuremath{\Omega} cm/at.%. For the $\ensuremath{\theta}={90}^{\ensuremath{\circ}}$ orientation, it is found that the deviations from Matthiessen's rule at 77 and 273\ifmmode^\circ\else\textdegree\fi{}K vary linearly with ${\ensuremath{\rho}}_{0\ensuremath{\perp}}$ and are, within experimental uncertainty, the same for Sb, In, and Zn impurity. At the ice point the deviation is approximately 1.7 times larger than at 77\ifmmode^\circ\else\textdegree\fi{}K where the deviation is (10\ifmmode\pm\else\textpm\fi{}1)% of ${\ensuremath{\rho}}_{0\ensuremath{\perp}}$. Determinations of the ideal resistivity at 77 and 273\ifmmode^\circ\else\textdegree\fi{}K are in good agreement with previous determinations made by Gueths.