Percolation mechanism of the diffusion of impurity atoms in dense surface layers

The molecular dynamics method is used to study the migration of an impurity atom on an unfilled square lattice. The calculations are performed on a lattice containing 2¹² × 2¹⁴ sites at various values of the ratio p of the frequencies of jumps impurity and lattice atoms and various relative concentrations of vacancies ? _V . In the limit of vanishingly small concentrations of vacancies, ? _V ? 1, the present simulation results are in agreement with our previous analytical results. With increasing ? _V , the diffusion coefficient of impurity atoms predicted by the simulations exceeds the result of the analytical theory, a behavior that can be explained by the growing influence of vacancy clusters, voids on the surface, in which the impurity atom can travel long distances. This is most clearly seen in the case of highly mobile impurity atoms (p ? 1), where within the characteristic time of displacement of impurity atoms, lattice atoms remain practically immobile, and the problem appears to be closely related to the percolation problem. In this case, up to ? _V ≈ 0.3, the diffusion coefficient is independent of p; then, such a dependence appears, and the diffusion coefficient increases sharply with ? _V .