Kirkendall effect in the two-dimensional lattice-gas model

Customarily, the Kirkendall effect is associated with the vacancy-mediated balance of diffusion fluxes of atoms at the interface between two metals. Nowadays, this effect attracts appreciable attention due to its crucial role in the formation of various hollow nanoparticles via oxidation of metal nanocrystallites. The understanding of the physics behind this effect in general and especially in the case of nanoparticles is still incomplete due to abundant complicating factors. Herein, the Kirkendall effect is illustrated in detail at the generic level by performing two-dimensional (2D) lattice Monte Carlo simulations of diffusion of A and B monomers with attractive nearest-neighbor interaction for times up to 10^{7} Monte Carlo steps. Initially, A monomers are considered to form a close-packed array, while B monomers are in the 2D-gas state. The A-B interaction is assumed to be stronger compared to the other interactions, so that thermodynamically the c(2×2) A-B phase is preferable compared to the close-packed A phase (as in the case of metal oxidation). Depending on the relative rate of the diffusion jumps of A and B monomers, the patterns observed at the late stage of the formation of the mixed phase are shown to range from a single array without voids to those with appreciable disintegration of the initial array. In this way, the model predicts a single array with numerous small voids, a few moderate voids, or a single large void inside.