A direct method for obtaining effective pair interactions in binary alloys

Abstract

It is shown that effective pair interactions (EPI) in disordered binary alloys can be calculated accurately and reliably by direct averaging over a small number of randomly selected configurations within the framework of the recursion method. This approach is illustrated on a canonical tight-binding Hamiltonian and relies on the 'orbital peeling' technique to calculate energy differences directly, without large subtractive cancellations. The results are checked for convergence, both as a function of the number of configurations and the number of levels of the continued fraction, and are also compared with more elaborate calculations. The main advantages of such a real-space method are the computational simplicity and the possibility to treat deviations from lattice periodicity. The EPI are basis quantities to understand the phase formation and stability of substitutionally disordered solid solutions.