Interplay of order-disorder phenomena and diffusion in rigid binary alloys in the presence of vacancies: Monte Carlo simulations

Abstract

Transport phenomena are studied for a binary $(AB)$ alloy on a rigid square lattice with nearest-neighbor attraction between unlike particles, assuming a small concentration ${c}_{v}$ of vacancies $V$ being present, to which $A$ $(B)$ particles can jump with rates ${\ensuremath{\Gamma}}_{A}$ $({\ensuremath{\Gamma}}_{B})$ in the case where the nearest-neighbor attractive energy ${ϵ}_{AB}$ is negligible in comparison with the thermal energy ${k}_{B}T$ in the system. This model exhibits a continuous order-disorder transition for concentrations ${c}_{A},{c}_{B}=1\ensuremath{-}{c}_{A}\ensuremath{-}{c}_{V}$ in the range ${c}_{A,1}^{\mathit{crit}}\ensuremath{\leqslant}{c}_{A}\ensuremath{\leqslant}{c}_{A,2}^{\mathit{crit}}$, with ${c}_{A,1}^{\mathit{crit}}=(1\ensuremath{-}{m}^{*}\ensuremath{-}{c}_{V})∕2$, ${c}_{A,2}^{\mathit{crit}}=(1+{m}^{*}\ensuremath{-}{c}_{V})∕2$, $m\ensuremath{\ast}\ensuremath{\approx}0.25$, the maximum critical temperature occurring for $c\ensuremath{\ast}={c}_{A}={c}_{B}=(1\ensuremath{-}{c}_{V})∕2$---i.e., ${m}^{*}=0$. This phase transition belongs to the $d=2$ Ising universality class, demonstrated by a finite-size scaling analysis. From a study of mean-square displacements of tagged particles, self-diffusion coefficients are deduced, while applying chemical potential gradients allows the estimation of Onsager coefficients. Analyzing finally the decay with time of sinusoidal concentration variations that were prepared as initial condition, also the interdiffusion coefficient is obtained as function of concentration and temperature. As in the random alloy case (i.e., a noninteracting $ABV$ model) no simple relation between self-diffusion and interdiffusion is found. Unlike this model mean-field theory cannot describe interdiffusion, however, even if the necessary Onsager coefficients are estimated via simulation.