Modeling materials with phase field crystal models

The phase field crystal (PFC) model is a novel approach for modeling phenomena on atomistic length and diffusive time scales. In this dissertation, we present new advances in the methodology of the PFC model and describe applications to solidification and grain boundaries. We present an extended phase diagram for the original formulation of the PFC model that allows to model three dimensional hexagonal and cubic close-packed crystal structures. The original PFC model is also applied to study crystallization of different polymorphs in diffusion-controlled growth. We also study the connection between the PFC model and statistical mechanical density functional theory of classical systems. Based on these studies, we propose a new variant of the PFC model. We show that using our new formulation of the model, it is possible to reproduce certain static and dynamic properties of the density functional theory with significantly greater accuracy than with previously proposed PFC models without losing the numerical feasibility of the PFC model. The new PFC model is applied to study grain boundaries of body-centered cubic iron near its melting point.