The Influence of Edge Energy on Step Flow Instability for Crystals with Bravais Versus Non-Bravais Lattice Structures (Communications in Computational Physics, 2020)
We examine the meandering instability for prismatic lattices formed fromtriangles, squares and hexagons using a nearest neighbor kinetic Monte Carlo model.In the first two cases, which are Bravais lattices, we find that facets with the orientationfavored in the equilibrium shape of isolated islands are most prone to this instability,while the analogous facet for the hexagonal lattice is the least unstable. We argue thatthis is due to a significant difference in the reconstructed/equilibrium versus the non-reconstructed edge energy for non-Bravais crystals. Surface/edge energy is typicallymodeled as a single-valued function of orientation. We put forward a simple geometric argument that suggests this picture is inadequate for crystals with a non-Bravaislattice structure. In the case of a hexagonally structured lattice, our arguments indicate that the non-reconstructed edge energy can be viewed as both discontinuous andmulti-valued for a subset of orientations that are commensurate with the crystal structure. We support these conclusions with density functional theory calculations thatalso reveal multivalued surface energies for the set of singular orientations.