Amplitude expansion of the binary phase field crystal model

Abstract

Amplitude representations of a binary phase field crystal model are developed for a two dimensional triangular lattice and three dimensional BCC and FCC crystal structures. The relationship between these amplitude equations and the standard phase field models for binary alloy solidification with elasticity are derived, providing an explicit connection between phase field crystal and phase field models. Sample simulations of solute migration at grain boundaries, eutectic solidification and quantum dot formation on nano-membranes are also presented.

11 pages, 8 figures

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• Phase-field-crystal study of grain boundary premelting and shearing in bcc iron
• A Multi-Component Phase Field Crystal Model for Structural Transformations in Metal Alloys
• Amplitude equations for polycrystalline materials with interaction between composition and stress
• Dislocation dynamics and crystal plasticity in the phase field crystal model
• Phase-field-crystal models and mechanical equilibrium
• A coarse-grained phase-field crystal model of plastic motion
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• A mesoscopic field theoretical approach for active systems
• A Phase Field Crystal Study of Solute Trapping
• Closing the gap between atomic-scale lattice deformations and continuum elasticity
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• A phase field crystal theory of the kinematics of dislocation lines
• Ginzburg-Landau theory of the bcc-liquid interface kinetic coefficient
• 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 with a Vapor Phase
• 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
• Defects at grain boundaries: A coarse-grained, three-dimensional description by the amplitude expansion of the phase-field crystal model
• Combining phase field crystal methods with a Cahn-Hilliard model for binary alloys
• Mesoscale Defect Motion in Binary Systems: Effects of Compositional Strain and Cottrell Atmospheres
• An efficient numerical framework for the amplitude expansion of the phase-field crystal model
• Field Dislocation Mechanics and Phase Field Crystal models
• Scale coupling and interface pinning effects in the phase-field-crystal model
• Elastic constants of stressed and unstressed materials in the phase field crystal model
• Phase field crystal model for heterostructures
• Scaling of alloy interfacial properties under compositional strain
• The elastic inclusion problem in the (amplitude) phase field crystal model
• Elastically-mediated interactions between grain boundaries and precipitates in two-phase coherent solids
• Nonlinear effects for island coarsening and stabilization during strained film heteroepitaxy
• Pattern formation of phase-separated lipid domains in bilayer membranes
• Anomalous grain dynamics and grain locomotion of odd crystals
• Amplitude expansion of the phase-field crystal model for complex crystal structures
• Magnetic APFC modeling and the influence of magneto-structural interactions on grain shrinkage
• Gradient elasticity in Swift-Hohenberg and phase-field crystal models
• Mesoscale modeling of deformations and defects in thin crystalline sheets
• Anisotropy in interface stress at the BCC-iron solid-melt interface: molecular dynamics and phase field crystal modelling