Electronic structure and superconductivity in Pd-Ag-H and Pd-Rh-H alloys

Using the augmented-plane-wave method we have calculated the energy bands and the densities of states (DOS) of RhH, PdH, and AgH. We have also calculated the DOS for the nonstoichiometric hydrides ${\mathrm{Pd}}_{1-y}{\mathrm{Ag}}_y{\mathrm{H}}_x$ and ${\mathrm{Pd}}_{1-y}{\mathrm{Rh}}_y{\mathrm{H}}_x$ within the virtual-crystal approximation (VCA) and the rigid-band approximation (RBA). We present evidence from coherent-potential-approximation calculations that our DOS values in the vicinity of the Fermi level are reliable. The DOS decomposed per site and angular-momentum component are used to calculate the electron-phonon interaction and the superconducting transition temperature, $T_c$, for various compositions of the above alloys. Our results are in good agreement with experiment and provide a satisfactory understanding of the variation of $T_c$ with $x$ and $y$ and also of the isotope effect in these systems.