Effect of lattice vibrations on the ordering tendencies in substitutional binary alloys

The effect of lattice vibrations on the ordering tendencies and phase stability of substitutional binary alloys is analyzed. The alloy Hamiltonian is cast onto an Ising-like Hamiltonian through a cluster expansion of the vibrational free energy computed in the harmonic approximation. The temperature dependence of the vibrational effective cluster interactions (VECI's) is found for a general d-dimensional alloy. Analytic results for the VECI's for d=1 are derived. It is argued that the vibrations can have pronounced effects on the phase diagram and on the short-range order at high temperatures.