The Influence of Edge Energy on Step Flow Instability for Crystals with Bravais Versus Non-Bravais Lattice Structures

We examine the meandering instability for prismatic lattices formed from triangles, 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 orientation favored 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 that this is due to a significant difference in the reconstructed/equilibrium versus the nonreconstructed edge energy for non-Bravais crystals. Surface/edge energy is typically modeled 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-Bravais lattice structure. In the case of a hexagonally structured lattice, our arguments indicate that the non-reconstructed edge energy can be viewed as both discontinuous and multi-valued for a subset of orientations that are commensurate with the crystal structure. We support these conclusions with density functional theory calculations that also reveal multivalued surface energies for the set of singular orientations.