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

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.

95 pages, 48 figures

References in corpus (26)

• Phase-field Crystals with Elastic Interactions
• Phase-field crystal study of grain-boundary premelting
• Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?
• Derivation of the phase field crystal model for colloidal solidification
• Phase-field crystal modeling of equilibrium bcc-liquid interfaces
• An Efficient Algorithm for Solving the Phase Field Crystal Model
• Dynamical density functional theory for molecular and colloidal fluids: a microscopic approach to fluid mechanics
• Melting at dislocations and grain boundaries: A Phase Field Crystal study
• Tension and stiffness of the hard sphere crystal-fluid interface
• Renormalization group theory for the phase field crystal equation
• The favoured cluster structures of model glass formers
• Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps
• Colloidal crystal growth at externally imposed nucleation clusters
• Dynamical density functional theory for dense atomic liquids
• Adaptive mesh computation of polycrystalline pattern formation using a renormalization-group reduction of the phase-field crystal model
• Exotic fluids and crystals of soft polymeric colloids
• A dynamic density functional theory for particles in a flowing solvent
• Phase-field approach to polycrystalline solidification including heterogeneous and homogeneous nucleation
• Phase Diagram and Commensurate-Incommensurate Transitions in the Phase Field Crystal Model with an External Pinning Potential
• Glassy Dislocation Dynamics in 2-D Colloidal Dimer Crystals
• Density functional theory of freezing for soft interactions in two dimensions
• Nonlinear Driven Response of a Phase-Field Crystal in a Periodic Pinning Potential
• Hydrodynamic Self-Consistent Field Theory for Inhomogeneous Polymer Melts
• Thermal fluctuations and phase diagrams of the phase field crystal model with pinning
• Ginzburg-Landau theory of the liquid-solid interface and nucleation for hard-spheres
• Molecular Dynamics on Diffusive Time Scales from the Phase Field Crystal Equation

Cited by in corpus (14)

• How crystals form: A theory of nucleation pathways
• Gradient dynamics models for liquid films with soluble surfactant
• New density functional approach for solid-liquid-vapor transitions in pure materials
• Grain Boundary Structures and Collective Dynamics of Inversion Domains in Binary Two-Dimensional Materials
• Heterogeneous nucleation of/on nanoparticles: a density functional study using the phase-field crystal model
• Solidification in soft-core fluids: disordered solids from fast solidification fronts
• Crystal growth from a supersaturated melt: relaxation of the solid-liquid dynamic stiffness
• Simulating complex crystal structures using the phase-field crystal model
• Free energy of the bcc-liquid interface and the Wulff shape as predicted by the Phase-Field Crystal model
• Intermittent dislocation density fluctuations in crystal plasticity from a phase-field crystal model
• Modeling of grain boundary dynamics using amplitude equations
• Effect of the orientational relaxation on the collective motion of patterns formed by self-propelled particles
• Dynamical density functional theory for the diffusion of injected Brownian particles
• Hard rectangles near curved hard walls: tuning the sign of the Tolman length