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^∘{}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 ρ(T) for pure tin was determined. ρII(T)ρ_⊥(T) is found to be 1.53±{}0.01 at 373^∘{}K, 1.555±{}0.009 at 273^∘{}K, and 1.684±{}0.010 at 77^∘{}K. ρ_⊥(T) is 13.25±{}0.05, 9.05±{}0.03, and 1.772±{}0.006 {μ}{Ω}-cm at 373, 272, and 77^∘{}K respectively. The anisotropy of the residual resistivity ρ₀ for cadmium impurity was determined at 4.2^∘{}K by two different experimental methods in different regions of impurity concentration x. ρ0IIρ_0⊥ is found to be 1.6±{}0.1 in both regions. The residual resistivity for any specific crystal orientation is found to vary linearly with x (ρ_0⊥x=1.39 {μ}{Ω} cm/at.%). Deviations from Matthiessen's rule are found to vary linearly [ρ(T)ᵢₘₚᵤᵣₑ-ρ(T)ₚᵤᵣₑ=0.16ρ_0⊥] with impurity concentration and appear to be temperature-independent for 77^∘K≤T≤373^∘K. The general features of the data relating the change in superconducting transition temperature (Tc) with doping are in good agreement with the data of Lynton, Serin, and Zucker. However, there is evidence for anomalous Tc behavior in the region of composition (x≈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 ρ_0⊥ versus x, however. The theory of Markowitz and Kadanoff is applied to the data relating Tc to impurity concentration. Reasonable agreement between the theory and experiment is found. The mean-squared relative anisotropy of the superconducting energy gap parameter 〈a²〉, 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 〈a²〉 obtained from our data employing Clem's equations is 0.022, in good agreement with the value obtained from the Tc 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 〈a²〉 with doping as given by Clem's theoretical treatment.