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.


Materials Science and Engineering

Research Center/Lab(s)

Center for High Performance Computing Research

Keywords and Phrases

Algorithms; Free energy; Grain boundaries; Liquids; Governing equations; Liquid structures; Numerical algorithms; Periodic function; Phase-field crystal models; Phase-field crystals; Specific materials; Surface anisotropy; Phase interfaces

International Standard Serial Number (ISSN)

1047-4838; 1543-1851

Document Type

Article - Journal

Document Version


File Type





© 2015 Minerals, Metals and Materials Society, All rights reserved.

Publication Date

01 Jan 2015