Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview

TL;DR

This review discusses the phase-field-crystal (PFC) method, a computational approach in materials science that models atomic-scale phenomena on diffusive time scales, highlighting its development, theoretical foundations, and applications in hard and soft matter physics.

Contribution

It provides a comprehensive overview of the PFC method's evolution, linking it to density functional theory and thermodynamics, and summarizes its current applications and future potential.

Findings

PFC effectively models atomic-scale dynamics on diffusive time scales.

The method has been linked to density functional theory and thermodynamics.

PFC shows promise for future research in materials science.

Abstract

Here, we review the basic concepts and applications of the phase-field-crystal (PFC) method, which is one of the latest simulation methodologies in materials science for problems, where atomic- and microscales are tightly coupled. The PFC method operates on atomic length and diffusive time scales, and thus constitutes a computationally efficient alternative to molecular simulation methods. Its intense development in materials science started fairly recently following the work by Elder et al. [Phys. Rev. Lett. 88 (2002), p. 245701]. Since these initial studies, dynamical density functional theory and thermodynamic concepts have been linked to the PFC approach to serve as further theoretical fundaments for the latter. In this review, we summarize these methodological development steps as well as the most important applications of the PFC method with a special focus on the interaction of development steps taken in hard and soft matter physics, respectively. Doing so, we hope to present today's state of the art in PFC modelling as well as the potential, which might still arise from this method in physics and materials science in the nearby future.