Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
arXiv:1207.0257 · doi:10.1080/00018732.2012.737555
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.
arXiv comment95 pages, 48 figures
References in corpus (80)
- Modeling Elasticity in Crystal Growth
- Modeling Elastic and Plastic Deformations in Non-Equilibrium Processing Using Phase Field Crystals
- Topological Defects and Interactions in Nematic Emulsions
- Dynamic Density Functional Theory of Fluids
- Effective interactions between electric double-layers
- Dynamical density functional theory and its application to spinodal decomposition
- An Exactly Solvable Phase-Field Theory of Dislocation Dynamics, Strain Hardening and Hysteresis in Ductile Single Crystals
- Phase-field Crystals with Elastic Interactions
- Exact Criterion for Determining Clustering vs. Reentrant Melting Behavior for Bounded Interaction Potentials
- Dynamic Fracture in Single Crystal Silicon
- Phase-field crystal study of grain-boundary premelting
- Phase-Field Model of Dendritic Sidebranching with Thermal Noise
- Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?
- Aggregation of self-propelled colloidal rods near confining walls
- Theoretical evidence for a dense fluid precursor to crystallization
- Derivation of the phase field crystal model for colloidal solidification
- Precursor-mediated crystallization process in suspensions of hard spheres
- Diffusive Atomistic Dynamics of Edge Dislocations in Two Dimensions
- Free energy functionals for efficient phase field crystal modeling of structural phase transformations
- Phase-field crystal modeling of equilibrium bcc-liquid interfaces
- Phase-field-crystal model for fcc ordering
- Renormalization group approach to multiscale simulation of polycrystalline materials using the phase field crystal model
- 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
- Novel Colloidal Crystalline States on Two Dimensional Periodic Substrates
- Amplitude expansion of the binary phase field crystal model
- Polymorphism, crystal nucleation and growth in the phase-field crystal model in 2d and 3d
- Columnar and lamellar phases in attractive colloidal systems
- Spinodal Decomposition in a Binary Polymer Mixture: Dynamic Self Consistent Field Theory and Monte Carlo Simulations
- Renormalization group theory for the phase field crystal equation
- Phase field crystal dynamics for binary systems: Derivation from dynamical density functional theory, amplitude equation formalism, and applications to alloy heterostructures
- Amorphous nucleation precursor in highly nonequilibrium fluids
- Effective potentials for polymers and colloids: Beyond the van der Waals picture of fluids?
- The favoured cluster structures of model glass formers
- Phase-field approach to heterogeneous nucleation
- 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
- Dynamical density functional theory for colloidal particles with arbitrary shape
- Dynamical density functional theory: binary phase-separating colloidal fluid in a cavity
- Exotic fluids and crystals of soft polymeric colloids
- Phase-field crystal modelling of crystal nucleation, heteroepitaxy and patterning
- A dynamic density functional theory for particles in a flowing solvent
- Phase-field approach to polycrystalline solidification including heterogeneous and homogeneous nucleation
- Dynamic density functional study of a driven colloidal particle in polymer solutions
- Remarks on some open problems in phase-field modelling of solidification
- Topological Defects in Nematic Droplets of Hard Spherocylinders
- Phase Diagram and Commensurate-Incommensurate Transitions in the Phase Field Crystal Model with an External Pinning Potential
- Derivation of a three-dimensional phase-field-crystal model for liquid crystals from density functional theory
- Amplitude equations for polycrystalline materials with interaction between composition and stress
- Phase-field-crystal model for liquid crystals
- Description of hard sphere crystals and crystal-fluid interfaces: a critical comparison between density functional approaches and a phase field crystal model
- Controlling crystal symmetries in phase-field crystal models
- Modeling multiple time scales during glass formation with phase-field crystals
- Dynamical transitions and sliding friction of the phase-field-crystal model with pinning
- Glassy Dislocation Dynamics in 2-D Colloidal Dimer Crystals
- Modelling fluids and crystals using a two-component modified phase field crystal model
- Diblock copolymer ordering induced by patterned surfaces
- Low-Temperature Orientation Dependence of Step Stiffness on {111} Surfaces
- Polar liquid crystals in two spatial dimensions: the bridge from microscopic to macroscopic modeling
- Morphological instability, evolution, and scaling in strained epitaxial films: An amplitude equation analysis of the phase field crystal model
- Dynamic density functional theory versus Kinetic theory of simple fluids
- Microscopic and macroscopic theories for the dynamics of polar liquid crystals
- Nonlinear Driven Response of a Phase-Field Crystal in a Periodic Pinning Potential
- Density functional theory of freezing for soft interactions in two dimensions
- A phase-field-crystal approach to critical nuclei
- Hydrodynamic Self-Consistent Field Theory for Inhomogeneous Polymer Melts
- Stability of liquid crystalline phases in the phase-field-crystal model
- First Principles Derivation of Effective Ginzburg-Landau Free Energy models for Crystalline Systems
- Thermal fluctuations and phase diagrams of the phase field crystal model with pinning
- DDFT calibration and investigation of an anisotropic phase-field crystal model
- Ginzburg-Landau theory of the liquid-solid interface and nucleation for hard-spheres
- Numerical Method for Hydrodynamic Transport of Inhomogeneous Polymer Melts
- Emergence of foams from the breakdown of the phase field crystal model
- Kinetics of Ordering in Fluctuation-Driven First-Order Transitions: Simulations and Dynamical Renormalization
- Polydomain growth at isotropic-nematic transitions in liquid crystalline polymers
- Molecular Dynamics on Diffusive Time Scales from the Phase Field Crystal Equation
Cited by in corpus (131)
- Classical dynamical density functional theory: from fundamentals to applications
- How crystals form: A theory of nucleation pathways
- Phase-field modeling of crystal nucleation in undercooled liquids -- A review
- Origin of similarity of phase diagrams in amphiphilic and colloidal systems with competing interactions
- Localized states in the conserved Swift-Hohenberg equation with cubic nonlinearity
- Exploring the complex world of two-dimensional ordering with three modes
- Quasicrystalline order and a crystal-liquid state in a soft-core fluid
- Phase-field-crystal study of grain boundary premelting and shearing in bcc iron
- Nonequilibrium dynamics of mixtures of active and passive colloidal particles
- Active crystals and their stability
- Gradient dynamics models for liquid films with soluble surfactant
- Consistent multiphase-field theory for interface driven multidomain dynamics
- Consistent Hydrodynamics for Phase Field Crystals
- New density functional approach for solid-liquid-vapor transitions in pure materials
- Three-dimensional Phase Field Quasicrystals
- 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
- Active crystals on a sphere
- Deriving phase field crystal theory from dynamical density functional theory: consequences of the approximations
- Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow
- Continuation for thin film hydrodynamics and related scalar problems
- Numerical Bifurcation Analysis of Marine Ice Sheet Models
- Mesoscale model of dislocation motion and crystal plasticity
- Solid phase properties and crystallization in simple model systems
- Solidification in soft-core fluids: disordered solids from fast solidification fronts
- A coarse-grained phase-field crystal model of plastic motion
- Resting and Traveling Localized States in an Active Phase-Field-Crystal Model
- Analytical approach to chiral active systems: suppressed phase separation of interacting Brownian circle swimmers
- An Atomistic Study of Diffusion-Mediated Plasticity and Creep using Phase Field Crystal Methods
- Classical density functional theory, unconstrained crystallization, and polymorphic behavior
- Predictive local field theory for interacting active Brownian spheres in two spatial dimensions
- Extended dynamical density functional theory for colloidal mixtures with temperature gradients
- Closing the gap between atomic-scale lattice deformations and continuum elasticity
- Crystal growth from a supersaturated melt: relaxation of the solid-liquid dynamic stiffness
- Collective dynamics of active Brownian particles in three spatial dimensions: a predictive field theory
- Differently Shaped Hard Body Colloids in Confinement: From passive to active particles
- A phase field crystal theory of the kinematics of dislocation lines
- Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal model
- Coarse-grained modeling of crystals by the amplitude expansion of the phase-field crystal model: an overview
- Instability, rupture and fluctuations in thin liquid films: Theory and computations
- First order phase transitions and the thermodynamic limit
- Controlling grain boundaries by magnetic fields
- Growth of different faces in a body centered cubic lattice: a case of the phase-field-crystal modeling
- Quantum hydrodynamics for supersolid crystals and quasicrystals
- Spatially Localized Quasicrystals
- Grain coarsening in two-dimensional phase-field models with an orientation field
- Two-dimensional localized states in an active phase-field-crystal model
- Jerky active matter: a phase field crystal model with translational and orientational memory
- Traveling band formation in feedback-driven colloids
- Perspective: New directions in dynamical density functional theory
- Emergence of the bifurcation structure of a Langmuir-Blodgett transfer model
- Development and Analysis of a Block-Preconditioner for the Phase-Field Crystal Equation
- Relations between angular and Cartesian orientational expansions
- Coarse-grained forms for equations describing the microscopic motion of particles in a fluid
- Confined colloidal crystals in and out of equilibrium
- Image Inversion and Uncertainty Quantification for Constitutive Laws of Pattern Formation
- Defects at grain boundaries: A coarse-grained, three-dimensional description by the amplitude expansion of the phase-field crystal model
- 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
- Combining phase field crystal methods with a Cahn-Hilliard model for binary alloys
- An efficient numerical framework for the amplitude expansion of the phase-field crystal model
- Field Dislocation Mechanics and Phase Field Crystal models
- Localized states in passive and active phase-field-crystal models
- Li-diffusion accelerates grain growth in intercalation electrodes: a phase-field study
- Rotation induced grain growth and stagnation in phase field crystal models
- Stress in ordered systems: Ginzburg-Landau type density field theory
- Vacancy diffusion in colloidal crystals as determined by dynamical density-functional theory and the phase-field-crystal model
- Elastic constants of stressed and unstressed materials in the phase field crystal model
- Stationary broken parity states in active matter models
- Phase field crystal model for heterostructures
- Quasicrystal formation in binary soft matter mixtures
- Crystallisation of soft matter under confinement at interfaces and in wedges
- Angle-adjustable density field formulation for modeling crystalline microstructures
- Thermo-Density Coupling in PFC Type Models for the Study of Rapid Crystallization
- Hydrodynamic phase field crystal approach to interfaces, dislocations, and multi-grain networks
- Intermittent dislocation density fluctuations in crystal plasticity from a phase-field crystal model
- Dislocation nucleation in the phase field crystal model
- Benchmark computations of the phase field crystal and functionalized Cahn-Hilliard equations via fully implicit, Nesterov accelerated schemes
- Microscopic approach to entropy production
- Relaxation of curvature induced elastic stress by the Asaro-Tiller-Grinfeld instability
- Phase-field crystal description of active crystallites: elastic and inelastic collisions
- Efficient calculation of phase coexistence and phase diagrams: application to a binary phase-field crystal model
- Hydrodynamic theory of freezing: Nucleation and polycrystalline growth
- Bifurcations of front motion in passive and active Allen-Cahn-type equations
- Mean field approach of dynamical pattern formation in underdamped active matter with short-ranged alignment and distant anti-alignment interactions
- Modeling of grain boundary dynamics using amplitude equations
- Statistics of grain growth: experiment versus the Phase-Field-Crystal and Mullins models
- Derivation and analysis of a phase field crystal model for a mixture of active and passive particles
- Effect of the orientational relaxation on the collective motion of patterns formed by self-propelled particles
- Structure and dynamics of interfaces between two coexisting liquid crystalline phases
- Classical nucleation theory in the phase-field crystal model
- Stable and metastable hard sphere crystals in Fundamental Measure Theory
- Well-posedness and longtime behavior for the modified phase-field crystal equation
- Periodic patterns displace active phase separation
- Dynamical density functional theory for the diffusion of injected Brownian particles
- Pattern formation of phase-separated lipid domains in bilayer membranes
- Scaling of alloy interfacial properties under compositional strain
- The elastic inclusion problem in the (amplitude) phase field crystal model
- Anomalous grain dynamics and grain locomotion of odd crystals
- Validated forward integration scheme for parabolic PDEs via Chebyshev series
- Long wavelength properties of phase field crystal models with second order dynamics
- Atom Based Grain Extraction and Measurement of Geometric Properties
- Amplitude expansion of the phase-field crystal model for complex crystal structures
- Elasticity versus phase field driven motion in the phase field crystal model
- Hard rectangles near curved hard walls: tuning the sign of the Tolman length
- Biaxial nematic order in fundamental measure theory
- Chirality and odd mechanics in active columnar phases
- Anamorphic Quasiperiodic Universes in Modified and Einstein Gravity with Loop Quantum Gravity Corrections
- Magnetic APFC modeling and the influence of magneto-structural interactions on grain shrinkage
- Exploring Bifurcations in Bose-Einstein Condensates via Phase Field Crystal Models
- Dynamical properties of heterogeneous nucleation of parallel hard squares
- Starobinsky Inflation and Dark Energy and Dark Matter Effects from Quasicrystal Like Spacetime Structures
- Thermodynamics, formation dynamics and structural correlations in the bulk amorphous phase of the phase-field crystal model
- Gradient elasticity in Swift-Hohenberg and phase-field crystal models
- Microscopic Patterns in the 2D Phase-Field-Crystal Model
- Surface melting and crystallisation driven by sedimentation: a particle resolved study
- Hybrid-PFC: coupling the phase-field crystal model and its amplitude-equation formulation
- Improved time integration for phase-field crystal models of solidification
- Atomic ordering and phase separation in lateral heterostructures and multijunctions of ternary two-dimensional hexagonal materials
- Perturbative Expansion in Reciprocal Space: Bridging Microscopic and Mesoscopic Descriptions of Molecular Interactions
- Computational and analytical studies of a new nonlocal phase-field crystal model in two dimensions
- A Non-Isothermal Phase-Field Crystal Model with Lattice Expansion: Analysis and Benchmarks
- Structural phase-field crystal model for Lennard-Jones pair interaction potential
- Ginzburg-Landau free energy for molecular fluids: determination and coarse-graining
- Pattern formation aspects of electrically charged tri-stable media with implications to bulk heterojunction in organic photovoltaics
- Motility-induced crystallization and rotating crystallites
- Dimension reduction and optimality of the uniform state in a Phase-Field-Crystal model involving a higher order functional
- Mesoscale modeling of deformations and defects in thin crystalline sheets
- Robust exponential attractors for the modified phase-field crystal equation
- Liquid crystalline growth within a phase-field crystal model
- Explicit temperature coupling in phase-field crystal models of solidification