Graphene Formation using the PFC Model with a Vapor Phase

Graphene is a one-atom-thick allotrope, or form, of carbon. Within graphene, each carbon atom bonds with three neighboring carbon atoms. Hence, the crystal lattice geometry is honeycomb, where the atoms form the vertices of regular hexagons. Perhaps the strongest material on earth, graphene has very high electrical and thermal conductivity. Although the production of graphene is costly, it has many uses, including solar panels, semiconductors, and body armor. The benefits of graphene, along with its virtual two-dimensional nature, motivate our study. We use the phase field crystal (PFC) model to simulate graphene. The PFC model yields a probabilistic atomic density field and, thus, crystal geometry. Traditionally, the PFC model includes solid and liquid phases and one spatial frequency mode for the crystal structure. This single mode model results in triangular geometry. We use three modes to achieve the honeycomb geometry of graphene. Since graphene is typically manufactured using chemical vapor deposition (CVD), we also add a vapor phase field to the model. Using frequency domain analysis, we develop a new, more accurate approach for building the crystal honeycomb geometry. This provides greater stability and enables us to produce solid island growth. We study the surface energy resulting from the solid-vapor phase interface, and we provide new insight into the effects of the surface energy on nanocrystal (solid crystal region) formation. Finally, we present an original model for dual-layer graphene with a vapor phase.