Theoretical study of vibrational contribution on cluster formation in a binary alloy system

Lattice vibrational effects in the process of precipitation in a binary alloy system has been studied theoretically. We derived a cancellation condition of vibrational free energy change due to cluster formation within the first order approximation, in terms of the nearest bond pair interaction. Vibrational contribution to the free energy is calculated for a specific example of cluster formation from isolated atoms, and it is almost perfectly vanished when the unlike atom potential is assumed to be the geometric mean of their constituent potentials.