Total and component densities of states in substitutional alloys

We consider the evaluation of the average electronic spectrum in a disordered binary alloy. The single-site approximation is reformulated in terms of restricted averages of the total scattering operator and equations relevant to the average-$t$-matrix (ATA) and coherent-potential (CPA) approximations are obtained. Specializing to the muffin-tin model of the alloy, we derive expressions for the average total and component densities of states. The results for the ATA are new and the implied numerical calculations appear to be tractable. We find that the Gyorffy-Stocks version of the muffin-tin CPA is equivalent to the earlier approach of Soven and also, that their mixed ATA-CPA scheme can be viewed as an approximation to just the average-$t$-matrix equations.