On the flow of thermal defects from the bulk to surfaces

This paper treats flow of defects between bulk and surface sites, as a crystal passes towards equilibrium, for some practical cases. These include the realistic but quite elaborate example in which vacancy flow from the bulk is coupled to surface step edges, acting as sinks, by reaction with adatoms that are believed to dominate transport on metal surfaces. It is shown how surface processes modify the defect flow from the bulk only at short times. Lacking accurate parameters (such as concentrations) for surface defects, a crude modeling of the theoretical results is offered in order to explore likely generic behavior. The model employs a recently described approximate universality of behavior, scaled to the melting temperature, relevant mainly to fcc (1 1 1) surfaces. Under a range of conditions it is the reaction of advacancies with adatoms that provides the important channel for bulk vacancy flow. Adatom flow onto the terraces from surface step edge sinks is the bottleneck to flow above a crossover temperature (depending on step spacing) and equilibrium recombination is the bottleneck below the crossover.