Modeling Elastic and Plastic Deformations in Non-Equilibrium Processing Using Phase Field Crystals

Abstract

A continuum field theory approach is presented for modeling elastic and plastic deformation, free surfaces and multiple crystal orientations in non-equilibrium processing phenomena. Many basic properties of the model are calculated analytically and numerical simulations are presented for a number of important applications including, epitaxial growth, material hardness, grain growth, reconstructive phase transitions and crack propagation.

arXiv comment20 pages, 26 figures

References in corpus (8)

• Theory of Phase Ordering Kinetics
• Modeling Elasticity in Crystal Growth
• Atomic-scale modeling of the deformation of nanocrystalline metals
• Sharp interface limits of phase-field models
• Spiral surface growth without desorption
• Model of surface instabilities induced by stress
• Weakly nonlinear theory of grain boundary motion in patterns with crystalline symmetry
• A Phase-Field Model of Spiral Dendritic Growth

Cited by in corpus (195)

• Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
• Phase-field Crystals with Elastic Interactions
• Tuned, driven, and active soft matter
• Phase-field crystal study of grain-boundary premelting
• Classical dynamical density functional theory: from fundamentals to applications
• Derivation of the phase field crystal model for colloidal solidification
• How crystals form: A theory of nucleation pathways
• Diffusive Atomistic Dynamics of Edge Dislocations in Two Dimensions
• Free energy functionals for efficient phase field crystal modeling of structural phase transformations
• Improving the Accuracy and Consistency of the Scalar Auxiliary Variable (SAV) Method with Relaxation
• Phase-field crystal modeling of equilibrium bcc-liquid interfaces
• Phase-field-crystal model for fcc ordering
• Phase field modeling of crack propagation
• Energy Stable and Efficient Finite-Difference Nonlinear Multigrid Schemes for the Modified Phase Field Crystal Equation
• 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
• Melting at dislocations and grain boundaries: A Phase Field Crystal study
• Traveling and resting crystals in active systems
• An Energy Stable BDF2 Fourier Pseudo-Spectral Numerical Scheme for the Square Phase Field Crystal Equation
• Interfacial layering in the electric double layer of ionic liquids
• Amplitude expansion of the binary phase field crystal model
• Polymorphism, crystal nucleation and growth in the phase-field crystal model in 2d and 3d
• An adaptive BDF2 implicit time-stepping method for the phase field crystal model
• 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
• Exploring the complex world of two-dimensional ordering with three modes
• Phase-field-crystal study of grain boundary premelting and shearing in bcc iron
• Multiscale modeling of polycrystalline graphene: A comparison of structure and defect energies of realistic samples from phase field crystal models
• Active crystals and their stability
• Adaptive mesh computation of polycrystalline pattern formation using a renormalization-group reduction of the phase-field crystal model
• An energy-stable convex splitting for the phase-field crystal equation
• Growth modes of quasicrystals
• Arbitrarily High-order Unconditionally Energy Stable Schemes for Thermodynamically Consistent Gradient Flow Models
• Kapitza thermal resistance across individual grain boundaries in graphene
• Preconditioned Steepest Descent Methods for some Nonlinear Elliptic Equations Involving p-Laplacian Terms
• Phase Field Crystal Modeling as a Unified Atomistic Approach to Defect Dynamics
• Phase-field crystal modelling of crystal nucleation, heteroepitaxy and patterning
• Phase-field approach to polycrystalline solidification including heterogeneous and homogeneous nucleation
• A New Structural Phase Field Crystal Approach for Modelling Graphene
• Defect stability in phase-field crystal models: Stacking faults and partial dislocations
• Remarks on some open problems in phase-field modelling of solidification
• 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
• Solidification fronts in supercooled liquids: how rapid fronts can lead to disordered glassy solids
• Amplitude equations for polycrystalline materials with interaction between composition and stress
• Computing optimal interfacial structure of modulated phases
• Grain Boundary Structures and Collective Dynamics of Inversion Domains in Binary Two-Dimensional Materials
• Phase-field-crystal model for liquid crystals
• Dislocation dynamics and crystal plasticity in the phase field crystal model
• Description of hard sphere crystals and crystal-fluid interfaces: a critical comparison between density functional approaches and a 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
• Numerical Bifurcation Analysis of Marine Ice Sheet Models
• Dynamical Crystallites of Active Chiral Particles
• Continuation for thin film hydrodynamics and related scalar problems
• Mesoscale model of dislocation motion and crystal plasticity
• Phase-field-crystal models and mechanical equilibrium
• Controlling crystal symmetries in phase-field crystal models
• Modeling multiple time scales during glass formation with phase-field crystals
• A coarse-grained phase-field crystal model of plastic motion
• Resting and Traveling Localized States in an Active Phase-Field-Crystal Model
• Unified Theoretical Framework for Polycrystalline Pattern Evolution
• Microscopic Treatment of Solute Trapping and Drag
• Dynamical transitions and sliding friction of the phase-field-crystal model with pinning
• Phase Field Crystals as a Coarse-Graining in Time of Molecular Dynamics
• Bimodal grain-size scaling of thermal transport in polycrystalline graphene from large-scale molecular dynamics simulations
• Heat transport in pristine and polycrystalline single-layer hexagonal boron nitride
• An Atomistic Study of Diffusion-Mediated Plasticity and Creep using Phase Field Crystal Methods
• Modelling fluids and crystals using a two-component modified phase field crystal model
• A mesoscopic field theoretical approach for active systems
• Closing the gap between atomic-scale lattice deformations and continuum elasticity
• Ginzburg-Landau theory of the bcc-liquid interface kinetic coefficient
• A phase field crystal theory of the kinematics of dislocation lines
• Complex order-parameter phase-field models derived from structural phase-field-crystal models
• Dynamical density functional theory for circle swimmers
• A Navier Stokes Phase Field Crystal Model for Colloidal Suspensions
• 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
• First order phase transitions and the thermodynamic limit
• Properties of pattern formation and selection processes in nonequilibrium systems with external fluctuations
• Phase-Field Crystal Model with a Vapor Phase
• Polar liquid crystals in two spatial dimensions: the bridge from microscopic to macroscopic modeling
• Controlling grain boundaries by magnetic fields
• Morphological instability, evolution, and scaling in strained epitaxial films: An amplitude equation analysis of the phase field crystal model
• Eighth-order phase-field-crystal model for two-dimensional crystallization
• Phase Field Crystal Model for Magneto-Elasticity in Isotropic Ferromagnetic Solids
• Quantum hydrodynamics for supersolid crystals and quasicrystals
• Spatially Localized Quasicrystals
• Nonlinear Driven Response of a Phase-Field Crystal in a Periodic Pinning Potential
• Revisiting Phase Diagrams of Two-Mode Phase-Field Crystal Models
• Jerky active matter: a phase field crystal model with translational and orientational memory
• Phase ordering, transformation, and grain growth of two-dimensional binary colloidal crystals: A phase field crystal modeling
• Two-dimensional localized states in an active phase-field-crystal model
• A microscopic field theoretical approach for binary mixtures of active and passive particles
• Structural short-range forces between solid-melt interfaces
• Stability of liquid crystalline phases in the phase-field-crystal model
• Development and Analysis of a Block-Preconditioner for the Phase-Field Crystal Equation
• Thermal fluctuations and phase diagrams of the phase field crystal model with pinning
• Defects at grain boundaries: A coarse-grained, three-dimensional description by the amplitude expansion of the phase-field crystal model
• Non-linear elastic effects in phase field crystal and amplitude equations: Comparison to ab initio simulations of bcc metals and graphene
• Simulating complex crystal structures using the phase-field crystal model
• Mesoscale Defect Motion in Binary Systems: Effects of Compositional Strain and Cottrell Atmospheres
• An efficient numerical framework for the amplitude expansion of the phase-field crystal model
• DDFT calibration and investigation of an anisotropic phase-field crystal model
• Combining phase field crystal methods with a Cahn-Hilliard model for binary alloys
• Controlling the accuracy of unconditionally stable algorithms in Cahn-Hilliard Equation
• Atomic structure of grain boundaries in iron modeled using the atomic density function
• Ab Initio Generalized Langevin Equation
• Properties of spatial arrangement of V-type defects in irradiated materials: 3D-modelling
• Li-diffusion accelerates grain growth in intercalation electrodes: a phase-field study
• Localized states in passive and active phase-field-crystal models
• $L^2$ norm error estimates of BDF methods up to fifth-order for the phase field crystal model
• Heat transport across graphene/hexagonal-BN tilted grain boundaries from phase-field crystal model and molecular dynamics simulations
• Combining $2D$ synchrosqueezed wave packet transform with optimization for crystal image analysis
• Mechanical relaxation and fracture of phase field crystals
• Vacancy diffusion in colloidal crystals as determined by dynamical density-functional theory and the phase-field-crystal model
• Scale coupling and interface pinning effects in the phase-field-crystal model
• Emergence of foams from the breakdown of the phase field crystal model
• Stress in ordered systems: Ginzburg-Landau type density field theory
• Elastic constants of stressed and unstressed materials in the phase field crystal model
• A unified field theory of topological defects and non-linear local excitations
• Phase field crystal model for heterostructures
• Angle-adjustable density field formulation for modeling crystalline microstructures
• Intermittent dislocation density fluctuations in crystal plasticity from a phase-field crystal model
• Thermo-Density Coupling in PFC Type Models for the Study of Rapid Crystallization
• Machine learning based data-driven discovery of nonlinear phase-field dynamics
• Hydrodynamic phase field crystal approach to interfaces, dislocations, and multi-grain networks
• Glassy phases and driven response of the phase-field-crystal model with random pinning
• Phase-field crystal description of active crystallites: elastic and inelastic collisions
• Benchmark computations of the phase field crystal and functionalized Cahn-Hilliard equations via fully implicit, Nesterov accelerated schemes
• Relaxation of curvature induced elastic stress by the Asaro-Tiller-Grinfeld instability
• Self-consistent modeling of anisotropic interfaces and missing orientations: Derivation from phase-field crystal
• Time scales of inertial motion in the collective dynamics of underdamped active phase field crystal systems
• Efficient calculation of phase coexistence and phase diagrams: application to a binary phase-field crystal model
• Energy Stable Multigrid Method for Local and Non-local Hydrodynamic Models for Freezing
• Derivation and analysis of a phase field crystal model for a mixture of active and passive particles
• Mean field approach of dynamical pattern formation in underdamped active matter with short-ranged alignment and distant anti-alignment interactions
• Hydrodynamic theory of freezing: Nucleation and polycrystalline growth
• Phase-field collagen fibrils: Coupling chirality and density modulations
• Modeling of grain boundary dynamics using amplitude equations
• Grain rotation and coupled grain boundary motion in two-dimensional binary hexagonal materials
• Classical nucleation theory in the phase-field crystal model
• Effect of the orientational relaxation on the collective motion of patterns formed by self-propelled particles
• Liquid to solid nucleation via onion structure droplets
• Minimal phase-field crystal modeling of vapor-liquid-solid coexistence and transitions
• Yielding and jerky plasticity of tilt grain boundaries in high-temperature graphene
• Bayesian Modelling of Pattern Formation from One Snapshot of Pattern
• The elastic inclusion problem in the (amplitude) phase field crystal model
• Theory of Microphase Separation in Elastomers
• Elastically-mediated interactions between grain boundaries and precipitates in two-phase coherent solids
• Long wavelength properties of phase field crystal models with second order dynamics
• Incorporating density jumps and species-conserving dynamics in XPFC binary alloys
• Amplitude expansion of the phase-field crystal model for complex crystal structures
• Phase-field-crystal modeling of the (2x1)-(1x1) phase-transitions of Si(001) and Ge(001) surfaces
• Transition pathways in Cylinder-Gyroid interface
• Control of phase ordering and elastic properties in phase field crystals through three-point direct correlation
• Magnetically induced/enhanced coarsening in thin films
• Rotation-limited growth of three dimensional body-centered cubic crystals
• Exploring Bifurcations in Bose-Einstein Condensates via Phase Field Crystal Models
• Magnetic APFC modeling and the influence of magneto-structural interactions on grain shrinkage
• Thermodynamics, formation dynamics and structural correlations in the bulk amorphous phase of the phase-field crystal model
• Stability and Error estimates of the SAV Fourier-spectral method for the Phase Field Crystal Equation
• Gradient elasticity in Swift-Hohenberg and phase-field crystal models
• Hybrid-PFC: coupling the phase-field crystal model and its amplitude-equation formulation
• Grain extraction and microstructural analysis method for two-dimensional poly and quasicrystalline solids
• Substrate curvature governs texture orientation in thin films of smectic block copolymers
• Improved time integration for phase-field crystal models of solidification
• A Non-Isothermal Phase-Field Crystal Model with Lattice Expansion: Analysis and Benchmarks
• Computational and analytical studies of a new nonlocal phase-field crystal model in two dimensions
• Quantized plastic deformation
• Stripe patterns orientation resulting from nonuniform forcings and other competitive effects in the Swift-Hohenberg dynamics
• Numerical scheme for solving the nonuniformly forced cubic and quintic Swift-Hohenberg equations strictly respecting the Lyapunov functional
• Uncovering liquid-substrate fluctuation effects on crystal growth and disordered hyperuniformity of two-dimensional materials
• Structural phase-field crystal model for Lennard-Jones pair interaction potential
• Mesoscale modeling of deformations and defects in thin crystalline sheets
• Efficient Linear and Unconditionally Energy Stable Schemes for the Modified Phase Field Crystal Equation
• A second order accurate scalar auxiliary variable (SAV) numerical method for the square phase field crystal equation
• Density and concentration field description of nonperiodic structures
• A Thermodynamically-Consistent Phase Field Crystal Model of Solidification with Heat Flux
• Explicit temperature coupling in phase-field crystal models of solidification
• Liquid crystalline growth within a phase-field crystal model
• Error analysis of SAV finite element method to phase field crystal model
• Mass transport of adsorbates near a discontinuous structural phase transition
• Linear Second Order Energy Stable Schemes of Phase Field Model with Nonlocal Constraints for Crystal Growth
• Noise induced effects at nano-structured thin films growth during deposition in plasma-condensate devices
• Anisotropy in interface stress at the BCC-iron solid-melt interface: molecular dynamics and phase field crystal modelling
• Phase Field Crystal model for particles with n-fold rotational symmetry in two dimensions
• A Phase Field Crystal Method for Multilayer Graphene Structure
• Fcc -> bcc phase transition kinetics in an immiscible binary system: atomistic evidence of the twinning mechanism of transformation
• Highly efficient and energy dissipative schemes for the time fractional Allen-Cahn equation
• A measure theoretical approach to non-uniform phases of matter with no long-range spatial order
• Crystallization and order-disorder transition of colloidal particles in a drying suspension: a phase field crystal approach
• SymPhas --General purpose software for phase-field, phase-field crystal and reaction-diffusion simulations
• Two Approaches to Dislocation Nucleation in the Supported Heteroepitaxial Equilibrium Islanding Phenomenon