[SY-N2] Symposium N-2

[SY-N2] The Phase Field Method: Crystal Structures and Facets

^○Peter Voorhees¹, Eli Alster¹, Nana Ofuri-Opoku^1,3, David Montiel², Katsuyo Thornton², James Warren³ (1.Northwestern University, United States of America, 2.University of Michigan, United States of America, 3.National Institute for Standards and Technology, United States of America)

Phase field crystal (PFC) method allows the atomic scale motion and defect formation to be determined on diffusive timescales. A major challenge with the method is to devise free energy functions that can yield complicated crystal structures. 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. This approach successfully yields energetically stable simple cubic, diamond cubic, simple hexagonal, graphene layers, and CaF2 crystals, as well as the particularly complex and technologically important perovskite crystal structure. Highly anisotropic interfaces play an important role in the development of material microstructure. We examine the capability of the PFC model to quantitatively describe faceted interfaces by coarse graining the PFC model to attain both its complex amplitude formulation, and its corresponding phase field limit. Using this formulation, we find that the model yields Wulff shapes with missing orientations, the transition to missing orientations, and facet formation. We demonstrate, in two dimensions, how the resultant model can be used to study the growth of crystals with varying degrees of anisotropy in the phase-field limit.