Discrete atomistic model to simulate etching of a crystalline solid

A discrete atomistic solid-on-solid model is proposed to describe dissolution of a crystalline solid by a liquid. The model is based on the simple assumption that the probability per unit time of a unit cell being removed is proportional to its exposed area. Numerical simulations in one dimension demonstrate that the model has very good scaling properties. After removal of only about 10(2) monolayers, independently of the substrate size, the etched surface shows almost time-independent short-range correlations and the receding surface presents the Family-Vicsek scaling behavior. The scaling parameters alpha=0.491+/-0.002 and beta=0.330+/-0.001 indicate that the system belongs to the Kardar-Parisi-Zhang universality class. The imposition of periodic boundary conditions on the simulations reduces the effective system size by a factor of 0.68 without changing the exponents alpha and beta. Surprisingly, the periodic condition changes drastically the statistics of the surface height fluctuations and the short-range correlations. Without periodic conditions, that statistics is, up to 3 standard deviations, an asymmetric Lévy distribution with mu=1.82+/-0.01, and outside this region the statistics is Gaussian. With periodic conditions, that statistics is Gaussian, except for large negative fluctuations.