Hydrodynamic phase field crystal approach to interfaces, dislocations, and multi-grain networks

Abstract

We derive a phase field crystal model that couples the diffusive evolution of a microscopic structure with the fast dynamics of a macroscopic velocity field, explicitly accounting for the relaxation of elastic excitations. This model captures better than previous formulations the dynamics of complex interfaces and dislocations in single crystals as well as grain boundary migration in poly-crystals where the long-range elastic field is properly relaxed. The proposed model features a diffusivity that depends non-linearly on the local phase. It induces more localized interfaces between a disordered phase (liquid-like) and an ordered phase, e.g., stripes or crystal lattices. For stripes, the interface dynamics are shown to be strongly anisotropic. We also show that the model is able to evolve the classical PFC at mechanical equilibrium. However, in contrast to previous approaches, it is not restricted to a single-crystal configuration or small distortions from a fixed reference lattice. To showcase the capabilities of this approach, we consider a few examples, from the annihilation of dislocation loops in a single crystal at mechanical equilibrium to the relaxation of a microstructure including crystalline domains with different orientations and grain boundaries. During the self-annihilation of a mixed type dislocation loop (i.e., not shear or prismatic), long-range elastic effects cause the loop to move out of plane before the annihilation event.

References in corpus (22)

• Modeling Elasticity in Crystal Growth
• Modeling Elastic and Plastic Deformations in Non-Equilibrium Processing Using Phase Field Crystals
• Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
• Phase-field Crystals with Elastic Interactions
• Free energy functionals for efficient phase field crystal modeling of structural phase transformations
• Emergence of active nematic behaviour in monolayers of isotropic cells
• Renormalization group approach to multiscale simulation of polycrystalline materials using the phase field crystal model
• Renormalization group theory for the phase field crystal equation
• Exploring the complex world of two-dimensional ordering with three modes
• Multiscale modeling of polycrystalline graphene: A comparison of structure and defect energies of realistic samples from phase field crystal models
• Consistent Hydrodynamics for Phase Field Crystals
• Amplitude equations for polycrystalline materials with interaction between composition and stress
• Dislocation dynamics and crystal plasticity in the phase field crystal model
• Mesoscale model of dislocation motion and crystal plasticity
• Phase-field-crystal models and mechanical equilibrium
• A coarse-grained phase-field crystal model of plastic motion
• An Atomistic Study of Diffusion-Mediated Plasticity and Creep using Phase Field Crystal Methods
• Closing the gap between atomic-scale lattice deformations and continuum elasticity
• A phase field crystal theory of the kinematics of dislocation lines
• Multiphase field models for collective cell migration
• Revisiting Phase Diagrams of Two-Mode Phase-Field Crystal Models
• Stress in ordered systems: Ginzburg-Landau type density field theory

Cited by in corpus (7)

• A unified field theory of topological defects and non-linear local excitations
• Amplitude expansion of the phase-field crystal model for complex crystal structures
• 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 modeling of deformations and defects in thin crystalline sheets
• Mechanics of incompatible asymmetric grain boundary migration