Calculations of Densities of States for Nonrandom, Substitutionally Disordered Alloys

Abstract

Disordered systems have received a great deal of theoretical attention in the last fifteen years or so, and many advances in our understanding of such systems have been made. The greatest progress has been made in connection with substitutionally disordered alloys in which atoms of various species are randomly distributed over the sites of a regular lattice. The most satisfactory single-site theory for studying the properties of random substitutionally disordered alloys, in particular the one-particle properties such as the density of states (DOS), is the coherent potential approximation (CPA) [1,2]. In the CPA, one considers that the real disordered material is replaced by a self-consistently determined effective medium which is characterized by an energy-dependent site-diagonal selfenergy, and which preserves all symmetries of the lattice. The CPA yields unique and analytic results, i.e., yields DOS and spectral weight functions that are nonnegative and satisfy the fundamental sum rules. There exist several reviews of the CPA [3-5] both for systems describable by tight binding (TB) and by muffin-tin (MT) Hamiltonians.