Specific Heats of Tin Alloys and Their Relation to the Superconducting Transition Temperature

The specific heat between 1.2° and 2.2°K of a number of alloys of tin was measured. The alloys studied were Sn+Bi, Sn+In, and Sn+(InSb). These measurements enabled us to deduce the effect of alloying on the Sommerfeld $\gamma$ and Debye $\Theta$ of tin. We find that the changes in the former are compatible with the simple rigid parabolic band model of alloying, and that the latter depends only on the electron per atom ratio. The expression for the superconducting transition temperature given by the Bardeen-Cooper-Schrieffer theory was then used to estimate the changes in $T_c$ to be expected from the measured changes in $\gamma$ and $\Theta$. This accounts for only a part of the observed changes in transition temperature and we conclude that the increase in $T_c$ at high solute concentrations is mainly due to effects of alloying on the mean electron-electron interaction energy, $V$, of the theory.