A phase field crystal theory of the kinematics of dislocation lines

Abstract

We introduce a dislocation density tensor and derive its kinematic evolution law from a phase field description of crystal deformations in three dimensions. The phase field crystal (PFC) model is used to define the lattice distortion, including topological singularities, and the associated configurational stresses. We derive an exact expression for the velocity of dislocation line determined by the phase field evolution, and show that dislocation motion in the PFC is driven by a Peach-Koehler force. As is well known from earlier PFC model studies, the configurational stress is not divergence free for a general field configuration. Therefore, we also present a method (PFCMEq) to constrain the diffusive dynamics to mechanical equilibrium by adding an independent and integrable distortion so that the total resulting stress is divergence free. In the PFCMEq model, the far-field stress agrees very well with the predictions from continuum elasticity, while the near-field stress around the dislocation core is regularized by the smooth nature of the phase-field. We apply this framework to study the rate of shrinkage of an dislocation loop seeded in its glide plane.

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Cited by in corpus (12)

• Perspective: New directions in dynamical density functional theory
• A unified field theory of topological defects and non-linear local excitations
• Kinematics and dynamics of disclination lines in three-dimensional nematics
• Hydrodynamic phase field crystal approach to interfaces, dislocations, and multi-grain networks
• Elasticity versus phase field driven motion in the phase field crystal model
• Analytical model for the motion and interaction of two-dimensional active nematic defects
• Hybrid-PFC: coupling the phase-field crystal model and its amplitude-equation formulation
• Gradient elasticity in Swift-Hohenberg and phase-field crystal models
• 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
• Modeling dislocations in quasicrystals through amplitude equations