Interplay of order-disorder phenomena and diffusion in rigid binary alloys: Monte Carlo simulations of the two-dimensional ABV model

TL;DR

This study uses Monte Carlo simulations to explore how order-disorder transitions influence diffusion in a 2D binary alloy model, revealing complex relations between self-diffusion and interdiffusion coefficients.

Contribution

It provides a detailed simulation-based analysis of diffusion and phase transition phenomena in a 2D ABV alloy model, highlighting the limitations of mean field theory.

Findings

Phase transition belongs to 2D Ising universality class.

Self-diffusion and interdiffusion are not simply related.

Interdiffusion cannot be accurately described by mean field theory.

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 $\Gamma_A (\Gamma_B)$ in the case where the nearest neighbor attractive energy $\epsilon_{AB}$ is negligible in comparison with the thermal energy $k_BT$ in the system. This model exhibits a continuous order-disorder transition for concentrations $c_A,c_B=1-c_A-c_V$ in the range $c_{A,1}^{crit}\leq c_A \leq c_{A,2}^{crit}$, with $c_{A,1}^{crit}=(1-m^*-c_V)/2$, $c_{A,2}^{crit} =(1+m^*-c_V)/2$, $m* \approx 0.25$, the maximum critical temperature occurring for $c*=c_A=c_B=(1-c_V)/2$, 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 allow 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.