Unusual strain dependence of T/sub c/ and related effects for high-temperature (A-15-structure) superconductors: sound velocity at the superconducting phase transition

The sound velocities (elastic moduli) of V₃Ge and V₃Si 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 will lower T_c for cubic V₃Si and raise T_c for V₃Ge. 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 V₃Si: (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 V₃Si.. 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.