Electron momentum densities in disordered muffin-tin alloys

Abstract

The application of average $t$-matrix (ATA) and coherent potential (CPA) approximations to the calculation of average electron momentum density $\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}})$ in random muffin-tin alloys ${A}_{x}{B}_{1\ensuremath{-}x}$ is considered. The necessary equations for the general matrix elements of the operators describing scattering by the CPA atom and also by an $A$ or $B$ atom embedded in the effective medium are derived. Various versions of the ATA for $\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}})$ are discussed. Several $\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}})$ curves calculated on the basis of the CPA and ATA in ${\mathrm{Cu}}_{x}{\mathrm{Ni}}_{1\ensuremath{-}x}$ are presented. These results are used to delineate the effects on $\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}})$ of self-consistency in the treatment of disorder.