A Review of Quantitative Phase-Field Crystal Modeling of Solid-Liquid Structures

Phase-field crystal (PFC) is a model with atomistic-scale details acting on diffusive time scales. PFC uses the density field as its order parameter, which takes a constant value in the liquid phase and a periodic function in the solid phase. PFC naturally takes into account elasticity, solid-liquid interface free energy, surface anisotropy, and grain boundary free energy by using this single-order parameter in modeling of coexisting solid-liquid structures. In this article, the recent advancements in PFC modeling of materials nanostructures are reviewed, which includes an overview of different PFC models and their applications, and the numerical algorithms developed for solving the PFC governing equations. A special focus is given to PFC models that simulate coexisting solid-liquid structures. The quantitative PFC models for solid-liquid structures are reviewed, and the methods for determining PFC model parameters for specific materials are described in detail. The accuracy of different PFC models in calculating the solid-liquid interface properties is discussed