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 …

We review how phase-field models contributed to the understanding of various aspects of
crystal nucleation, including homogeneous and heterogeneous processes, and their role in …

The evolution mechanisms of grain boundaries and dislocations, including grain
morphology, grain boundary structure, and dislocation motion during plastic deformation in …

We propose a new numerical technique to deal with nonlinear terms in gradient flows. By
introducing a scalar auxiliary variable (SAV), we construct efficient and robust energy stable …

We construct unconditionally stable, unconditionally uniquely solvable, and second-order
accurate (in time) schemes for gradient flows with energy of the form \int_Ω(F(∇ϕ(\bfx))+ϵ …

Over the last decade, exsolution has emerged as a powerful new method for decorating
oxide supports with uniformly dispersed nanoparticles for energy and catalytic applications …

We present an unconditionally energy stable finite-difference scheme for the phase field
crystal equation. The method is based on a convex splitting of a discrete energy and is semi …

New perspectives on the phase field approach in modeling deformation and fracture at the
fundamental defect level are reviewed. When applied at sub-angstrom length scales the …

In this paper, we develop a series of linear, unconditionally energy stable numerical
schemes for solving the classical phase field crystal model. The temporal discretizations are …

In this paper we present and compare two unconditionally energy stable finite-difference
schemes for the phase field crystal equation. The first is a one-step scheme based on a …