Contribution to the Theory of Disordered Alloys

TLDR

A simple model of a disordered substitutional alloy, akin to transition‑metal alloys, is examined under various approximations. The authors develop a Green’s‑function formalism expressed as an infinite perturbation series whose leading term is the coherent‑potential approximation, and they study how average and local state densities vary with concentration in a specific model. The study shows that corrections to the rigid‑band model can be substantial even for similar constituents, that the coherent‑potential approximation is generally adequate, and that local density of states varies strongly with environment but averages well under the coherent‑potential scheme.

Abstract

A simple model of a disordered substitutional alloy, similar in some respects to transition-metal alloys, is studied in several approximations. A formalism is presented in which the Green's function for the alloy is represented in the form of an infinite perturbation series, the lowest term of which is the coherent-potential approximation introduced earlier. The average density of states for several model alloys is investigated, and it is found that corrections to the rigid-band model can be significant even in situations in which the constitutents are not very dissimilar. Study of certain terms in the perturbation series suggests that the coherent-potential approximation is adequate in many situations. The density of states localized about a particular type of atom is shown to bear little resemblance to the average density of states. It can be a strong function of the environment, but if an average environment is taken, the coherent-potential scheme gives good results. The variation of average and local state densities as a function of concentration is studied for a particular model.