A variational formulation of multiple scattering in muffin-tin alloys

Abstract

The authors develop a method for the band calculation of muffin-tin alloys which is as simple as the Korringa-Kohn-Rostoker (KKR) method for pure crystals. They begin by postulating Bloch-like basis functions, minimise the energy and arrive at a secular matrix with a formal resemblance to the secular matrix of the average t-matrix approximation (ATA) method. The density of energy states is derived from an argument based on the number of orthogonal basis functions. Using a similar argument, they derive an expression for the energy variance of the Bloch-like states. The advantage of the method is its extreme simplicity: an alloy calculation actually becomes as simple as a band structure calculation for a pure crystal. The method is also extended to situations in which it is feasible to increase the precision of the calculation by working with unit cells with more than one atomic site. Finally, the method is applied to a unidimensional alloy and compared favourably to a CPA and to a Monte Carlo calculation.