Phase-field crystal modeling: Integrating density functional theory, molecular dynamics, and phase-field modeling

This chapter describes phase-field crystal (PFC) modeling for bridging length scales between electrons and phases. Next, it presents a derivation of the governing equations of two PFC models for solid-liquid coexistence (namely, one-mode and two-mode). The chapter then discusses density functional theory (DFT). It describes a procedure for determining PFC model parameters from molecular dynamics (MD) simulations. The one-mode PFC model explained in the preceding subsection was only used to quantitatively study two-phase solid-liquid phenomenon of body-centered cubic (bcc) metals. While the one-mode PFC model calculates properties such as solid-liquid interface free energy and grain boundary free energy in fair agreement with experiments, it gives a much higher expansion in melting than experiment does. PFC is considered as an important part of the Integrated Computational Materials Engineering (ICME), which can fill the gap between DFT, MD, and phase-field modeling. The chapter finally presents the methodology to develop PFC models from DFT concepts