Amplitude equations for polycrystalline materials with interaction between composition and stress

Abstract

We investigate the ability of frame-invariant amplitude equations [G. H. Gunaratne, Q. Ouyang, and H. Swinney, Phys. Rev. E {\bf 50}, 2802 (1994)] to describe quantitatively the evolution of polycrystalline microstructures and we extend this approach to include the interaction between composition and stress. Validations for elemental materials include studies of the Asaro-Tiller-Grinfeld morphological instability of a stressed crystal surface, polycrystalline growth from the melt, grain boundary energies over a wide range of misorientation, and grain boundary motion coupled to shear deformation. Amplitude equations with accelerated strain relaxation in the solid are shown to model accurately the Asaro-Tiller-Grinfeld instability. Polycrystalline growth is also well described. However, the survey of grain boundary energies shows that the approach is only valid for a restricted range of misorientations as a direct consequence of an amplitude expansion. This range covers approximately half the complete range allowed by crystal symmetry for some fixed reference set of density waves used in the expansion. Over this range, coupled motion to shear is well described by known geometrical rules and a transition from coupling to sliding motion is also reproduced. Amplitude equations for alloys are derived phenomenologically in a Ginzburg-Landau spirit. Vegard's law is shown to be naturally described by seeking a gauge invariant form of those equations under a transformation that corresponds to a lattice expansion and deviations from Vegard's law can be easily incorporated. Those equations realistically describe the dilute alloy limit and have the same flexibility as conventional phase-field models for incorporating arbitrary free-energy/composition curves...

28 pages

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• Phase Field Crystal Modeling as a Unified Atomistic Approach to Defect Dynamics
• A New Structural Phase Field Crystal Approach for Modelling Graphene
• Defect stability in phase-field crystal models: Stacking faults and partial dislocations
• A coarse-grained phase-field crystal model of plastic motion
• An Atomistic Study of Diffusion-Mediated Plasticity and Creep using Phase Field Crystal Methods
• Phase-field crystal model for ordered crystals
• Closing the gap between atomic-scale lattice deformations and continuum elasticity
• Ginzburg-Landau theory of the bcc-liquid interface kinetic coefficient
• 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 modelling of grain boundary premelting using obstacle potentials
• Structural short-range forces between solid-melt interfaces
• Non-linear elastic effects in phase field crystal and amplitude equations: Comparison to ab initio simulations of bcc metals and graphene
• An efficient numerical framework for the amplitude expansion of the phase-field crystal model
• Scale coupling and interface pinning effects in the phase-field-crystal model
• Angle-adjustable density field formulation for modeling crystalline microstructures
• 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
• Modeling of grain boundary dynamics using amplitude equations
• The elastic inclusion problem in the (amplitude) phase field crystal model
• Elastically-mediated interactions between grain boundaries and precipitates in two-phase coherent solids
• The influence of short range forces on melting along grain boundaries
• Amplitude expansion of the phase-field crystal model for complex crystal structures
• Hybrid-PFC: coupling the phase-field crystal model and its amplitude-equation formulation
• Gradient elasticity in Swift-Hohenberg and phase-field crystal models
• Coupled motion of asymmetrical tilt grain boundaries: molecular dynamics and phase field crystal simulations
• Explicit temperature coupling in phase-field crystal models of solidification
• From wetting to melting along grain boundaries using phase field and sharp interface methods
• Elastic and plastic effects on heterogeneous nucleation and nanowire formation