Statistical Mechanical Theory of the Facet Edge of a Crystal

Abstract

The facet edge of the crystal is investigated theoretically on the basis of the Terrace-Step-Kink (TSK) model. The statistical mechanics of this model is formulated in terms of the lattice Fermion approach. The analysis leads always to the Pokrovsky-Talapov-Gruber-Mullins transition. At the facet edge, the facet connects with the neighboring curved surface without discontinuity of the slope. In such model the lattice underlying the surface is assumed to be rigid without any deformation caused by emergence of the steps. We extend the TSK model to a more general model including relaxation of the lattice bonds caused by the steps. The lattice deformation increases the elastic energy but can decrease the step creation energy. We show that the extended model leads always to a sharp edge; there is a discontinuity of the slope at the facet edge.