EVOLUTION OF EQUILIBRIUM FORMS OF A 2-DIMENSIONAL KOSSEL CRYSTAL IN A VAPOR DIFFUSION FIELD - A MONTE-CARLO SIMULATION

We introduce a Monte Carlo model for the evolution of equilibrium interface morphologies from initially fully faceted (straight) forms. The two-dimensional model integrates the stochastic occupation of surface sites and the diffusive exchange of particles with the surrounding vapor phase, other surface sites and the underlying bulk solid. Neither lattice gas nor solid-on-solid (SOS) restrictions are imposed. The exchange processes are associated with energy barriers, the absence of which is shown to result, in particular at low temperatures, in physically unrealistic transition probabilities. For medium-sized model crystals, the averaged shapes obtained through time averaging over a large number of instantaneous configurations agree well with equilibrium shapes resulting from analytical models. The interface widths are considerably larger than those resulting from SOS models, without significant increase in the surface roughness. Crystal-size-dependent collective motions of solid particles in the interfacial region are observed. On larger crystals the surface shape fluctuations have the character of capillary waves. These results provide a new link between the macroscopic, thermodynamic shape of the interface and the microscopic origin of interface roughness.