Cluster Bethe Lattice Approach to Chemically Disordered Alloys with Short Range Order

Abstract

One simple way to incorporate short range order effects within the Hamiltonian of a binary alloy A_xB_1-x can be achieved by parameterizing the Coherent Potential Approximation (CPA). According to this parameterization¹, a correlation parameter P_A/B is introduced to specify the probability a lattice site to be occupied by an atom of type A when a nearest lattice site is occupied by an atom of type B. The correlation parameter P_A/B appears as an independent parameter of the total energy, E_tot, of the system and therefore the energetically favored state of the A_xB_1-x alloy is associated with the minimum of the energy function E_tot = E_tot (P_A/B). This theory has been used^2–3 within the Bethe lattice approximation to binary alloys which exhibit only diagonal disorder.