Unusual Strain Dependence ofTcand Related Effects for High-Temperature (A−15-Structure) Superconductors: Sound Velocity at the Superconducting Phase Transition

Abstract

The sound velocities (elastic moduli) of ${\mathrm{V}}_3$Ge and ${\mathrm{V}}_3$Si are found to have very large discontinuities in their temperature derivatives at the superconducting transition. A thermodynamic treatment of these data (with the specific-heat behavior) for a second-order phase transition is shown to yield a general dependence of $T_c$ on strain. It is found that all strains greater than roughly ${10}^{-3\mathrm{}}$ will lower $T_c$ for cubic ${\mathrm{V}}_3$Si and raise $T_c$ for ${\mathrm{V}}_3$Ge. The results show that these strain dependences are very large, mainly quadratic, and directly responsible for some of the anomalous behavior of the superconductors. They predict, quantitatively for ${\mathrm{V}}_3$Si: (a) the reduction in $T_c$ which results from the structural transformation, (b) the arrest of the structural phase transformation at $T_c$ (c) the strain dependence of the specific-heat discontinuity at $T_c$ (d) the strain dependence of the structural-transformation temperature, and (e) the anisotropic stress dependence of $T_c$. The predicted dependence of $T_c$ upon the lattice parameter is a major factor in accounting for the different $T_c$'s among the $A-15$-structure compounds. The microscopic source of this large strain dependence is discussed in terms of the Labbe-Friedel (density-of-states peak) model. It is a surprising result that this model does not predict the large strain dependence of $T_c$ for ${\mathrm{V}}_3$Si.. Finally, the "approximate" nature of the sound velocity data at a phase transition is discussed and the general thermodynamic form for the corrections to the nonideal case is given.