Simulation of Polyhedral Crystal Growth Based on the Estimated Surface Energy of Crystallographic Planes

Abstract

Polyhedral shapes can be found in crystalline materials ranging from macroscopic natural mineral solids to microscopic or nanoscopic particles. These shapes originate from the crystallographic properties of the constituting material, and the outer shape depends on several unique habit planes. In this study, polyhedral crystal growth was simulated considering the surface energy and crystallographic characteristics. A series of polyhedrons, including cube, truncated hexahedron, cuboctahedron, truncated octahedron, and regular octahedron, was targeted. First, the polyhedron’s static surface energy and dynamic energy variation during crystal growth were computed. Then, the crystal-growth process was simulated based on the energy minimization policy. Interestingly, when the simulation began with truncated hexahedral nucleus, the shape changed to a cuboctahedron; however, a certain type of truncated octahedron was obtained when starting with different types of truncated octahedrons. In addition, once converged cuboctahedron abruptly changed the shape to a truncated octahedron as the crystal became larger. These results were supported by the static and dynamic energy curves. Furthermore, the method was applied to different materials by assuming virtual parameters, yielding various morphologies.