Abstract
A semi-empirical formalism is developed to account for the detailed dependence of the superconducting transition temperature of dilute alloys on solute concentration. A mismatch of solute and solvent ion sizes causes small strain fields in the regions surrounding the solute ions. The precise change in transition temperature, ΔT c , for a particular solute concentration, N ϵ, is derived by averaging the strain over the entire sample and reducing the strain field by a factor exp{ α− ξr −1 eff }, where α is a constant of order unity, ξ is the coherence distance, and r eff is the total length of the strained region within ξ. The length, r eff, is proportional to N 1 3 8 . It is found that the strain is proportional to Δ R, the difference in ionic radii. Previously reported data on the effects produced by various solutes in tin, indium, and aluminum are explained in terms of this model.
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