Vacancy-mediated disordering process in binary alloys at finite temperatures: Monte Carlo simulations

We have investigated the time evolution of the vacancy-mediated disordering process in binary alloys at finite temperatures. Qualitatively, we monitor the changes in the configurations by taking sequences of snapshots for various temperatures and comparing their morphologies. Quantitatively, we carry out Monte Carlo simulations to determine the time-dependent disorder parameter A(L,T;t) and the time-dependent structure factors S_k(t) for moderately low temperatures. This study differs from previous studies done at infinite temperature in that the vacancy here executes highly active walks, which are subjected to nonlinear feedbacks, instead of the random walks that take place in the limit of T → ∞. We find that the slope of the log-log plot of A(L,T;t) vs. t for finite temperatures follows the temperature dependence given by the Gompertz function and reaches a limiting value of 1/2 only as the temperature approaches infinity. For the structure factors, namely, S_k(t) vs. t, the overall features are similar to those found at infinite T. The two key differences between our results and those at infinite T are the saturated value and the intermediate region in which the portion of the graph whose slope is equal to one becomes smaller and is gradually replaced by a curve having a slope of 0.5. This last difference is especially evident at very low temperatures.