Effect of the vacancy interaction on antiphase domain growth in a two-dimensional binary alloy

Abstract

We have performed a Monte Carlo simulation of the influence of diffusing vacancies on the antiphase domain growth process in a binary alloy after a quench through an order-disorder transition. The problem has been modeled by means of a Blume-Emery-Griffiths Hamiltonian whose biquadratic coupling parameter $K$ controls the microscopic interactions between vacancies. The asymmetric term $L$ has been taken as $L=0$ and the ordering dynamics has been studied at very low temperature as a function of $K$ inside the range $\ensuremath{-}0.5<~K/J<~1.40$ (with $J>0$ being the ordering energy). The system evolves according to the Kawasaki dynamics so that the alloy concentration is conserved while the order parameter is not. The simulations have been performed on a two-dimensional square lattice and the concentration has been taken so that the system corresponds to a stoichiometric alloy with a small concentration of vacancies. We find that, independently of $K$, the vacancies exhibit a tendency to concentrate at the antiphase boundaries. This effect gives rise, via the vacancy-vacancy interaction (described by $K)$, to an effective interaction between bulk diffusing vacancies and moving interfaces that turns out to strongly influence the domain growth process. One distinguishes three different behaviors: (i) For $K/J<1$ the growth process of ordered domains is anisotropic and can be described by algebraic laws with effective exponents lower than $1/2$; (ii) $K/J\ensuremath{\simeq}1$ corresponds to the standard Allen-Cahn growth; (iii) for $K/J>1$ we found that, although the motion of the interface is curvature driven, the repulsive effective interaction between both the vacancies in the bulk and those at the interfaces slows down the growth.