A Three-Dimensional Phase-Field Crystal Model for 2D Materials

We introduce a Phase-Field Crystal (PFC) model to simulate the growth of 2D materials in three dimensions. Our approach employs a set of two- and three-point correlation terms in the free energy functional that are designed to energetically favor structures with periodicity along a plane but are localized in the direction perpendicular to that plane. We show how this method can be applied to stabilize several two-dimensional structures and to study three-dimensional effects, such as buckling due to defects. This will allow us to examine how specific defects such as vacancies and grain boundaries affect growth of the layer and the resulting mechanical properties. Finally, we present examples of how our model can be adapted to study monolayers and multilayers, as well as their interactions with a substrate.