Phase-field crystal modeling of equilibrium bcc-liquid interfaces

Abstract

We investigate the equilibrium properties of bcc-liquid interfaces modeled with a continuum phase-field crystal (PFC) approach [K. R. Elder and M. Grant, Phys. Rev. E 70, 051605 (2004)]. A multiscale analysis of the PFC model is carried out which exploits the fact that the amplitudes of crystal density waves decay slowly into the liquid in the physically relevant limit where the freezing transition is weakly first order. This analysis yields a set of coupled equations for these amplitudes that is similar to the set of equations derived from Ginzburg-Landau (GL) theory [K.-A. Wu et al., Phys. Rev. E 73, 094101 (2006)]. The two sets only differ in the details of higher order nonlinear couplings between different density waves, which is determined by the form of the nonlinearity assumed in the PFC model and by the ansatz that all polygons with the same number of sides have equal weight in GL theory. Despite these differences, for parameters (liquid structure factor and solid density wave amplitude) of Fe determined from molecular dynamic (MD) simulations, the PFC and GL amplitude equations yield very similar predictions for the overall magnitude and anisotropy of the interfacial free-energy and density wave profiles. These predictions are compared with MD simulations as well as numerical solutions of the PFC model.

12 pages, 2 figures

References in corpus (12)

• Modeling Elasticity in Crystal Growth
• Modeling Elastic and Plastic Deformations in Non-Equilibrium Processing Using Phase Field Crystals
• Phase-field Crystals with Elastic Interactions
• Efficient Computation of Dendritic Microstructures using Adaptive Mesh Refinement
• Direct calculation of the hard-sphere crystal/melt interfacial free energy
• Numerical Simulation of Three-Dimensional Dendritic Growth
• Diffusive Atomistic Dynamics of Edge Dislocations in Two Dimensions
• Direct calculation of the crystal-melt interfacial free energies for continuous potentials: Application to the Lennard-Jones system
• Renormalization group approach to multiscale simulation of polycrystalline materials using the phase field crystal model
• Phase-Field Approach for Faceted Solidification
• Renormalization group theory for the phase field crystal equation
• Ginzburg-Landau theory of crystalline anisotropy for bcc-liquid interfaces

Cited by in corpus (46)

• 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
• Phase-field-crystal model for fcc ordering
• Phase-field modeling of crystal nucleation in undercooled liquids -- A review
• Amplitude expansion of the binary phase field crystal model
• Polymorphism, crystal nucleation and growth in the phase-field crystal model in 2d and 3d
• Phase field crystal dynamics for binary systems: Derivation from dynamical density functional theory, amplitude equation formalism, and applications to alloy heterostructures
• Phase-field-crystal study of grain boundary premelting and shearing in bcc iron
• An energy-stable convex splitting for the phase-field crystal equation
• Phase-field crystal modelling of crystal nucleation, heteroepitaxy and patterning
• A Multi-Component Phase Field Crystal Model for Structural Transformations in Metal Alloys
• Grain growth beyond the Mullins model, capturing the complex physics behind universal grain size distributions
• Amplitude equations for polycrystalline materials with interaction between composition and stress
• Deriving phase field crystal theory from dynamical density functional theory: consequences of the approximations
• Description of hard sphere crystals and crystal-fluid interfaces: a critical comparison between density functional approaches and a phase field crystal model
• Heterogeneous nucleation of/on nanoparticles: a density functional study using the phase-field crystal model
• Controlling crystal symmetries in phase-field crystal models
• Solidification in soft-core fluids: disordered solids from fast solidification fronts
• Solid phase properties and crystallization in simple model systems
• Phase-field crystal model for ordered crystals
• Complex order-parameter phase-field models derived from structural phase-field-crystal models
• Ginzburg-Landau theory of the bcc-liquid interface kinetic coefficient
• Phase-Field Crystal Model with a Vapor Phase
• Growth of different faces in a body centered cubic lattice: a case of the phase-field-crystal modeling
• Eighth-order phase-field-crystal model for two-dimensional crystallization
• Morphological instability, evolution, and scaling in strained epitaxial films: An amplitude equation analysis of the phase field crystal model
• Revisiting Phase Diagrams of Two-Mode Phase-Field Crystal Models
• A phase-field-crystal approach to critical nuclei
• Structural short-range forces between solid-melt interfaces
• Free energy of the bcc-liquid interface and the Wulff shape as predicted by the Phase-Field Crystal model
• Simulating complex crystal structures using the phase-field crystal model
• Non-linear elastic effects in phase field crystal and amplitude equations: Comparison to ab initio simulations of bcc metals and graphene
• DDFT calibration and investigation of an anisotropic phase-field crystal model
• Atomic structure of grain boundaries in iron modeled using the atomic density function
• Stress in ordered systems: Ginzburg-Landau type density field theory
• Elastic constants of stressed and unstressed materials in the phase field crystal model
• Thermo-Density Coupling in PFC Type Models for the Study of Rapid Crystallization
• Dislocation nucleation in the phase field crystal model
• Self-consistent modeling of anisotropic interfaces and missing orientations: Derivation from phase-field crystal
• Modeling of grain boundary dynamics using amplitude equations
• Scaling of alloy interfacial properties under compositional strain
• A Phase Field Crystal Model of Phase and Microstructural Stability in Driven Nanocrystalline Systems
• Control of phase ordering and elastic properties in phase field crystals through three-point direct correlation
• Structural phase-field crystal model for Lennard-Jones pair interaction potential
• Anisotropy in interface stress at the BCC-iron solid-melt interface: molecular dynamics and phase field crystal modelling