Contribution to the Theory of Disordered Alloys

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.