Modeling Elasticity in Crystal Growth

Abstract

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to times scales much larger than conventional atomic methods. The model is shown to be consistent with the predictions of Read and Shockley for grain boundary energy, and Matthews and Blakeslee for misfit dislocations in epitaxial growth.

4 pages, 10 figures

Cited by in corpus (235)

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• Tuned, driven, and active soft matter
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• Diffusive Atomistic Dynamics of Edge Dislocations in Two Dimensions
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• Phase-field modeling of crystal nucleation in undercooled liquids -- A review
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• Collective Motion of Self-Propelled Particles with Memory
• Amplitude expansion of the binary phase field crystal model
• Polymorphism, crystal nucleation and growth in the phase-field crystal model in 2d and 3d
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• Exploring the complex world of two-dimensional ordering with three modes
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• Amorphous nucleation precursor in highly nonequilibrium fluids
• 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
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• Convergence Analysis for Second Order Accurate Convex Splitting Schemes for the Periodic Nonlocal Allen-Cahn and Cahn-Hilliard Equations
• Active crystals and their stability
• Adaptive mesh computation of polycrystalline pattern formation using a renormalization-group reduction of the phase-field crystal model
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• Arbitrarily High-order Unconditionally Energy Stable Schemes for Thermodynamically Consistent Gradient Flow Models
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• Phase Field Crystal Modeling as a Unified Atomistic Approach to Defect Dynamics
• Phase-field approach to polycrystalline solidification including heterogeneous and homogeneous nucleation
• Consistent multiphase-field theory for interface driven multidomain dynamics
• Defect stability in phase-field crystal models: Stacking faults and partial dislocations
• A New Structural Phase Field Crystal Approach for Modelling Graphene
• A Multi-Component Phase Field Crystal Model for Structural Transformations in Metal Alloys
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• Consistent Hydrodynamics for Phase Field Crystals
• 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
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• New density functional approach for solid-liquid-vapor transitions in pure materials
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• Dynamical Crystallites of Active Chiral Particles
• Mesoscale model of dislocation motion and crystal plasticity
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• Defect-Mediated Phase Transitions in Active Soft Matter
• Elastic Deformation of Polycrystals
• Controlling crystal symmetries in phase-field crystal models
• Highly efficient schemes for time fractional Allen-Cahn equation using extended SAV approach
• A coarse-grained phase-field crystal model of plastic motion
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• Microscopic Treatment of Solute Trapping and Drag
• Unified Theoretical Framework for Polycrystalline Pattern Evolution
• 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
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• Bimodal grain-size scaling of thermal transport in polycrystalline graphene from large-scale molecular dynamics simulations
• An Atomistic Study of Diffusion-Mediated Plasticity and Creep using Phase Field Crystal Methods
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• A new class of efficient and robust energy stable schemes for gradient flows
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• A Phase Field Crystal Study of Solute Trapping
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• A Navier Stokes Phase Field Crystal Model for Colloidal Suspensions
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• Eighth-order phase-field-crystal model for two-dimensional crystallization
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• Nonlinear Driven Response of a Phase-Field Crystal in a Periodic Pinning Potential
• Revisiting Phase Diagrams of Two-Mode Phase-Field Crystal Models
• Grain coarsening in two-dimensional phase-field models with an orientation field
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• Glassy phases and driven response of the phase-field-crystal model with random pinning
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• Mechanism of Local Lattice Distortion Effects on Vacancy Migration Barriers in FCC Alloys
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• Modeling of grain boundary dynamics using amplitude equations
• Hydrodynamic theory of freezing: Nucleation and polycrystalline growth
• Derivation and analysis of a phase field crystal model for a mixture of active and passive particles
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• Mean field approach of dynamical pattern formation in underdamped active matter with short-ranged alignment and distant anti-alignment interactions
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• Structure and dynamics of interfaces between two coexisting liquid crystalline phases
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• Minimal phase-field crystal modeling of vapor-liquid-solid coexistence and transitions
• Well-posedness and longtime behavior for the modified phase-field crystal equation
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• A general class of linear unconditionally energy stable schemes for the gradient flows
• The elastic inclusion problem in the (amplitude) phase field crystal model
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• Phase Field Crystal Study of Symmetric Tilt Grain Boundaries of Iron
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• Density and concentration field description of nonperiodic structures
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• A second order accurate scalar auxiliary variable (SAV) numerical method for the square phase field crystal equation
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• Linear Second Order Energy Stable Schemes of Phase Field Model with Nonlocal Constraints for Crystal Growth
• Highly efficient and energy dissipative schemes for the time fractional Allen-Cahn equation
• Anisotropy in interface stress at the BCC-iron solid-melt interface: molecular dynamics and phase field crystal modelling
• A Phase Field Crystal Method for Multilayer Graphene Structure
• 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
• A measure theoretical approach to non-uniform phases of matter with no long-range spatial order
• Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation
• 2D Phase Diagram for Minimizers of a Cahn-Hilliard Functional with Long-Range Interactions
• Phase Field Crystal model for particles with n-fold rotational symmetry in two dimensions
• Benchmarking of Massively Parallel Phase-Field Codes for Directional Solidification