SUPERCONDUCTING PROPERTIES AND ANISOTROPIC ELECTRICAL RESISTIVITIES OF PURE AND CADMIUM-DOPED TIN

Approximately 60 cylindrically shaped single crystals of pure and cadmium-doped (%1 Cd) tin in the tetragonal phase were prepared. Electrical-resistivity determinations were made at 373, 273, 77, and 4.2\ifmmode^\circ\else\textdegree\fi{}K. An investigation was made of the variation of the superconducting critical-field parameters with impurity content. The anisotropy of the temperature-dependent electrical resistivity $\ensuremath{\rho}(T)$ for pure tin was determined. $\frac{{\ensuremath{\rho}}_{\mathrm{II}}(T)}{{\ensuremath{\rho}}_{\ensuremath{\perp}}(T)}$ is found to be 1.53\ifmmode\pm\else\textpm\fi{}0.01 at 373\ifmmode^\circ\else\textdegree\fi{}K, 1.555\ifmmode\pm\else\textpm\fi{}0.009 at 273\ifmmode^\circ\else\textdegree\fi{}K, and 1.684\ifmmode\pm\else\textpm\fi{}0.010 at 77\ifmmode^\circ\else\textdegree\fi{}K. ${\ensuremath{\rho}}_{\ensuremath{\perp}}(T)$ is 13.25\ifmmode\pm\else\textpm\fi{}0.05, 9.05\ifmmode\pm\else\textpm\fi{}0.03, and 1.772\ifmmode\pm\else\textpm\fi{}0.006 \ensuremath{\mu}\ensuremath{\Omega}-cm at 373, 272, and 77\ifmmode^\circ\else\textdegree\fi{}K respectively. The anisotropy of the residual resistivity ${\ensuremath{\rho}}_{0}$ for cadmium impurity was determined at 4.2\ifmmode^\circ\else\textdegree\fi{}K by two different experimental methods in different regions of impurity concentration $x$. $\frac{{\ensuremath{\rho}}_{0\mathrm{II}}}{{\ensuremath{\rho}}_{0\ensuremath{\perp}}}$ is found to be 1.6\ifmmode\pm\else\textpm\fi{}0.1 in both regions. The residual resistivity for any specific crystal orientation is found to vary linearly with $x$ ($\frac{{\ensuremath{\rho}}_{0\ensuremath{\perp}}}{x}=1.39$ \ensuremath{\mu}\ensuremath{\Omega} cm/at.%). Deviations from Matthiessen's rule are found to vary linearly [$\ensuremath{\rho}{(T)}_{\mathrm{impure}}\ensuremath{-}\ensuremath{\rho}{(T)}_{\mathrm{pure}}=0.16{\ensuremath{\rho}}_{0\ensuremath{\perp}}$] with impurity concentration and appear to be temperature-independent for $77\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}\ensuremath{\le}T\ensuremath{\le}373\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}$. The general features of the data relating the change in superconducting transition temperature (${T}_{c}$) with doping are in good agreement with the data of Lynton, Serin, and Zucker. However, there is evidence for anomalous ${T}_{c}$ behavior in the region of composition ($x\ensuremath{\approx}0.3%$) at which a lattice-spacing anomaly was reported by Lee and Raynor. The development of vacant sites as reported by Lee and Raynor in this region is not observed in plots of ${\ensuremath{\rho}}_{0\ensuremath{\perp}}$ versus $x$, however. The theory of Markowitz and Kadanoff is applied to the data relating ${T}_{c}$ to impurity concentration. Reasonable agreement between the theory and experiment is found. The mean-squared relative anisotropy of the superconducting energy gap parameter $〈{a}^{2}〉$, is found from this analysis to be 0.023. A recent theoretical treatment due to Clem which describes the change in the critical-field parameters with doping is compared to our experimental results. The so-called "similarity conditions" are found not to be satisfied. The shape of the reduced critical-field curve is found to be a function of impurity concentration. The value of $〈{a}^{2}〉$ obtained from our data employing Clem's equations is 0.022, in good agreement with the value obtained from the ${T}_{c}$ data alone. The data describing the reduced critical-field curve of pure tin is in good agreement with the results od Shaw et al. The change in shape of the reduced critical-field curve can be understood both qualitatively and quantitatively in terms of the reduction of the effects of $〈{a}^{2}〉$ with doping as given by Clem's theoretical treatment.