Determination of effective-pair interactions in random alloys by configurational averaging

A real-space method is presented for calculating effective-pair interactions (EPIs) in substitutionally disordered alloys, starting from electronic structure information for the constituting elements. The EPIs are obtained by averaging over a small number of randomly generated configurations. The electronic structure is calculated by tridiagonalizing a tight-binding Hamiltonian using the recursion method. Convergence, both as a function of the number of configurations and the number of recursion levels, is rapid, and the results compare very well with other calculations. The advantage of the present scheme is that deviations from lattice periodicity can be taken into account in a completely straightforward way. The EPI are essential ingredients in statistical methods for determining alloy phase diagrams.