Roughness of the Crystal-Vapor Interface

Abstract

The equilibrium structure of the interface between a Kossel crystal and its vapor has been investigated by Monte Carlo simulation techniques, and by statistical mechanical analysis in zeroth‐ and first‐order approximation. The interface structure depends on L/kT_e, where L is the latent heat, k is the Boltzmann constant, and T_e is the equilibrium temperature. The results differ significantly from earlier calculations based on single level models of the interface or on simpler statistical models of the interface. The roughness of the surface R, which is defined as the energy of the surface relative to the energy of a smooth boundary, was found to increase with kT_e/L and to be almost the same for each model. The extent of the surface S defined as the number of surface molecules per unit area also increases with kT_e/L and is also almost independent of the model. The distribution of atoms amongst the various energy levels has been calculated, and again is similar for the three models. The interface profile is similar for all three models for large and small values of L/kT_e, but the Monte Carlo calculations differ from the other two models for intermediate values of L/kT_e. Calculations using the zeroth‐order model for (110) and (111) faces shows that the surfaces are somewhat rougher than the (100) surface and also have greater extent.