Kinetic roughening of the Kossel (100) surface: comparison of classical criteria with Monte Carlo results

Kinetic roughening is not a phase transition and, as such, it lacks an exact definition. Many criteria are used to mark the onset of kinetic roughening. Criteria stemming from the classical two-dimensional nucleation theory are widely used. On the other hand, experimentalists observe a transition from flat to rounded crystal facets at certain driving forces. And measuring the growth rate as a function of driving force, a change from exponential to linear growth kinetics is frequently found. It is assumed that these experimental phenomena coincide with the onset of kinetic roughening. These experimental criteria, three classical criteria for kinetic roughening and statistical mechanical criteria based on the interface width and the surface roughness, are compared with each other by means of Monte Carlo simulations on a Kossel (100) SOS model. Surface diffusion is neglected, and only attachment/detachment kinetics is considered. The change from flat to rounded facets with increasing driving force turns out to be quite gradual. Nevertheless, this experimental criterion is made explicit by defining a critical driving force for which the curvature of a facet becomes visible by optical microscopy. The conditions for an experiment to detect kinetic roughening using this criterion are described. The different criteria for kinetic roughening yield different values for the critical driving force, although most of the criteria studied show a similar, almost linear, dependence of the critical driving force on the nearest neighbor bond strength. This again indicates that kinetic roughening is diffuse in nature, and shows that in discussions on kinetic roughening it is imperative to mention the criterion used. Some attention is also paid to the two-dimensional anisotropy of step motion on a Kossel (100) surface. An anisotropic step velocity is found far below thermal roughening. The anisotropy is reduced by increasing the driving force.