Simulating complex crystal structures using the phase-field crystal model

We introduce a phase-field crystal model that creates an array of complex three- and two-dimensional crystal structures via a numerically tractable three-point correlation function. The three-point correlation function is designed in order to energetically favor the principal interplanar angles of a target crystal structure. This is achieved via an analysis performed by examining the crystal's structure factor. This approach successfully yields energetically stable simple cubic, diamond cubic, simple hexagonal, graphene layers, and CaF$_2$ crystals. To illustrate the ability of the method to yield a particularly complex and technologically important crystal structure, we show how this three-point correlation function method can be used to generate perovskite crystals.