Tunneling Determination of Phonon-Energy Uncertainties due to Force-Constant Disorders in the AlloyPb1−2xTlxBix

Superconducting tunneling measurements of the alloy system ${\mathrm{Pb}}_{1-2x}{\mathrm{Tl}}_x{\mathrm{Bi}}_x$ have been performed and a determination of the product function ${\alpha }^2\left(\omega \right)F\left(\omega \right)$ for these alloys is reported. It is found that with this system, Tl and Bi can be added at least up to $x=0.2\mathrm{}$ before a change of phase from the fcc structure results. Because the electron concentration remains fixed at 4 e/at. throughout this phase, the electron-phonon coupling is not severely changed and the superconducting properties remain relatively unchanged. Associated with a gradual shift to lower energies of the phonon modes is a slight upward trend in the measured energy gap of the alloys. It is also found that with higher alloy concentrations there is a smearing of the fine structure in the product function ${\alpha }^2\left(\omega \right)F\left(\omega \right)$ and this is associated with finite lifetimes of the phonon modes resulting in energy uncertainties. In a simple quantitative fashion we have attempted to attribute these smearings to force-constant disorders between ions, and we obtain numbers for the deviations of interatomic force constants from their mean values.