Monte Carlo simulations were made of the effect of diffusing vacancies upon antiphase domain growth in a binary alloy, after quenching through an order-disorder transformation. The problem was modelled by means of a Blume-Emery-Griffiths Hamiltonian whose bi-quadratic coupling parameter, K, controlled the microscopic interactions between vacancies. The asymmetrical term was taken to be zero. The ordering dynamics were studied, at very low temperatures, as a function of K/J values of between 0.5 and 1.40; where J was the ordering energy. It was found that the system evolved according to Kawasaki dynamics, so that the alloy concentration was conserved while the order parameter was not. The simulations were performed on a 2-dimensional square lattice, and the concentration was chosen so that the system corresponded to a stoichiometric alloy which comprised a small concentration of vacancies. It was found that that, regardless of K, the vacancies exhibited a tendency to collect at antiphase boundaries. This effect gave rise, via vacancy-vacancy interactions, to an effective interaction between bulk diffusing vacancies and moving interfaces. This markedly affected the domain-growth process. Three different behaviors could be distinguished. When K/J was less than unity, the growth of ordered domains was anisotropic and could be described by power-laws with effective exponents that were less than ½. When K/J was equal to unity, the usual Allen-Cahn growth resulted. When K/J was greater than unity it was found that, although the motion of the interface was curvature-driven, a repulsive effective interaction between vacancies in the bulk and those at the interfaces tended to slow the growth.

Effect of the Vacancy Interaction on Antiphase Domain Growth in a Two-Dimensional Binary Alloy M.Porta, C.Frontera, E.Vives, T.Castán: Physical Review B, 1997, 56[9], 5261-70