Renormalization group approach to multiscale simulation of polycrystalline materials using the phase field crystal model

Abstract

We propose a computationally-efficient approach to multiscale simulation of polycrystalline materials, based on the phase field crystal (PFC) model. The order parameter describing the density profile at the nanoscale is reconstructed from its slowly-varying amplitude and phase, which satisfy rotationally-covariant equations derivable from the renormalization group. We validate the approach using the example of two-dimensional grain nucleation and growth.

New material added with quantitative comparisons of grain boundary energies and demonstrations of computational efficiency

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Cited by in corpus (58)

• Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
• Phase-field crystal study of grain-boundary premelting
• Derivation of the phase field crystal model for colloidal solidification
• Diffusive Atomistic Dynamics of Edge Dislocations in Two Dimensions
• Phase-field crystal modeling of equilibrium bcc-liquid interfaces
• Amplitude expansion of the binary 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
• Coarse-graining of cellular automata, emergence, and the predictability of complex systems
• Adaptive mesh computation of polycrystalline pattern formation using a renormalization-group reduction of the phase-field crystal model
• Phase Field Crystal Modeling as a Unified Atomistic Approach to Defect Dynamics
• Phase-field approach to polycrystalline solidification including heterogeneous and homogeneous nucleation
• Defect stability in phase-field crystal models: Stacking faults and partial dislocations
• A Multi-Component Phase Field Crystal Model for Structural Transformations in Metal Alloys
• Consistent Hydrodynamics for Phase Field Crystals
• Amplitude equations for polycrystalline materials with interaction between composition and stress
• Description of hard sphere crystals and crystal-fluid interfaces: a critical comparison between density functional approaches and a phase field crystal model
• Phase-field-crystal models and mechanical equilibrium
• A coarse-grained phase-field crystal model of plastic motion
• Bimodal grain-size scaling of thermal transport in polycrystalline graphene from large-scale molecular dynamics simulations
• 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
• Dynamical density functional theory for circle swimmers
• Complex order-parameter phase-field models derived from structural phase-field-crystal models
• 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
• Phase Field Crystal Model for Magneto-Elasticity in Isotropic Ferromagnetic Solids
• Morphological instability, evolution, and scaling in strained epitaxial films: An amplitude equation analysis of the phase field crystal model
• A phase-field-crystal approach to critical nuclei
• Jerky active matter: a phase field crystal model with translational and orientational memory
• Defects at grain boundaries: A coarse-grained, three-dimensional description by the amplitude expansion of the phase-field crystal model
• An efficient numerical framework for the amplitude expansion of the phase-field crystal model
• Mesoscale Defect Motion in Binary Systems: Effects of Compositional Strain and Cottrell Atmospheres
• Field Dislocation Mechanics and Phase Field Crystal models
• Scale coupling and interface pinning effects in the phase-field-crystal model
• Emergence of foams from the breakdown of the phase field crystal model
• A unified field theory of topological defects and non-linear local excitations
• Hydrodynamic phase field crystal approach to interfaces, dislocations, and multi-grain networks
• Self-consistent modeling of anisotropic interfaces and missing orientations: Derivation from phase-field crystal
• Statistics of grain growth: experiment versus the Phase-Field-Crystal and Mullins models
• Scaling of alloy interfacial properties under compositional strain
• Elastically-mediated interactions between grain boundaries and precipitates in two-phase coherent solids
• The elastic inclusion problem in the (amplitude) phase field crystal model
• Anomalous grain dynamics and grain locomotion of odd crystals
• Long wavelength properties of phase field crystal models with second order dynamics
• Amplitude expansion of the phase-field crystal model for complex crystal structures
• A discrete nonlinear mass transfer equation with applications in solid-state sintering of ceramic materials
• Magnetic APFC modeling and the influence of magneto-structural interactions on grain shrinkage
• Gradient elasticity in Swift-Hohenberg and phase-field crystal models
• Hybrid-PFC: coupling the phase-field crystal model and its amplitude-equation formulation
• A Non-Isothermal Phase-Field Crystal Model with Lattice Expansion: Analysis and Benchmarks
• Mesoscale Field Theory for Quasicrystals
• Mesoscale modeling of deformations and defects in thin crystalline sheets
• Explicit temperature coupling in phase-field crystal models of solidification