Influence of Force-Constant Changes on the Superconducting Properties of High-Concentration Substitutional Alloys

We apply the self-consistent theory of lattice vibrations to calculate ${\alpha }^{2}F$, which is of central importance in the theory of strong-coupling superconductors. Neglecting the effects of alloying on the electron states and the electron-phonon interaction, it is found that the low-frequency dependence of ${\alpha }^{2}F$ changes from ${\omega }^2$ in the mass-defect case to $\omega$ if one includes force-constant fluctuations. Numerical results for ${\alpha }^{2}F$ show a shift in weight from the longitudinal to the transverse peak in qualitative agreement with experiment.