Phase-field crystal study of grain-boundary premelting

Abstract

We study the phenomenon of grain-boundary premelting for temperatures below the melting point in the phase-field crystal model of a pure material with hexagonal ordering in two dimensions. We investigate the structures of symmetric tilt boundaries as a function of misorientation for two different inclinations and compute in the grand canonical ensemble the disjoining potential V(w) that governs the fundamental interaction between crystal-melt interfaces as a function of the premelted layer width w. The results reveal qualitatively different behaviors for high-angle grain boundaries that are uniformly wetted, with w diverging logarithmically as the melting point is approached from below, and low-angle boundaries that are punctuated by liquid pools surrounding dislocations, separated by solid bridges. This qualitative difference between high and low angle boundaries is reflected in the w-dependence of the disjoining potential that is purely repulsive (V'(w)<0 for all w) above a critical misorientation, but switches from repulsive at small w to attractive at large w for low angles. In the latter case, V(w) has a minimum that corresponds to a premelted boundary of finite width at the melting point. Furthermore, we find that the standard wetting condition (the grain boundary energy is equal to twice the solid-liquid free energy) gives a much too low estimate of the critical misorientation when a low-temperature value of the grain boundary energy is used. In contrast, a reasonable estimate is obtained if the grain boundary energy is extrapolated to the melting point, taking into account both the elastic softening of the material at high temperature and local melting around dislocations.

24 pages, 13 figures, some figure files with reduced resolution because of submission size limitations. In the 2nd version, some parts (and figures) have been modified, especially in Sec. V (discussion)

References in corpus (10)

• Modeling Elasticity in Crystal Growth
• Modeling Elastic and Plastic Deformations in Non-Equilibrium Processing Using Phase Field Crystals
• Phase-field Crystals with Elastic Interactions
• Diffusive Atomistic Dynamics of Edge Dislocations in Two Dimensions
• Phase-field crystal modeling of equilibrium bcc-liquid interfaces
• Renormalization group approach to multiscale simulation of polycrystalline materials using the phase field crystal model
• Melting at dislocations and grain boundaries: A Phase Field Crystal study
• Ginzburg-Landau theory of crystalline anisotropy for bcc-liquid interfaces
• Phase field model of premelting of grain boundaries
• The superheated Melting of Grain Boundary

Cited by in corpus (54)

• Ice structures, patterns, and processes: A view across the ice-fields
• Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
• Free energy functionals for efficient phase field crystal modeling of structural phase transformations
• Phase-field-crystal model for fcc ordering
• Energy Stable and Efficient Finite-Difference Nonlinear Multigrid Schemes for the Modified Phase Field Crystal Equation
• 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
• Localized states in the conserved Swift-Hohenberg equation with cubic nonlinearity
• Phase-field-crystal study of grain boundary premelting and shearing in bcc iron
• Solid-liquid interfacial premelting
• Phase Field Crystal Modeling as a Unified Atomistic Approach to Defect Dynamics
• Phase-field crystal modelling of crystal nucleation, heteroepitaxy and patterning
• A New Structural Phase Field Crystal Approach for Modelling Graphene
• Defect stability in phase-field crystal models: Stacking faults and partial dislocations
• Derivation of a three-dimensional phase-field-crystal model for liquid crystals from density functional theory
• Amplitude equations for polycrystalline materials with interaction between composition and stress
• Solidification fronts in supercooled liquids: how rapid fronts can lead to disordered glassy solids
• New density functional approach for solid-liquid-vapor transitions in pure materials
• Structural disjoining potential for grain boundary premelting and grain coalescence from molecular-dynamics simulations
• Grain Boundary Structures and Collective Dynamics of Inversion Domains in Binary Two-Dimensional Materials
• Phase-field-crystal model for liquid crystals
• Method for Computing Short-Range Forces between Solid-Liquid Interfaces Driving Grain Boundary Premelting
• Phase-field-crystal models and mechanical equilibrium
• Controlling crystal symmetries in phase-field crystal models
• Microscopic Treatment of Solute Trapping and Drag
• Phase-field crystal model for ordered crystals
• Particles on curved surfaces - a dynamic approach by a phase field crystal model
• Grain boundary melting in ice
• Modelling fluids and crystals using a two-component modified phase field crystal model
• An orientation-field model for polycristalline solidification with a singular coupling between order and orientation
• Polar liquid crystals in two spatial dimensions: the bridge from microscopic to macroscopic modeling
• Morphological instability, evolution, and scaling in strained epitaxial films: An amplitude equation analysis of the phase field crystal model
• Phase field modelling of grain boundary premelting using obstacle potentials
• 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
• Simulating complex crystal structures using the phase-field crystal model
• Multi-phase-field analysis of short-range forces between diffuse interfaces
• Combining phase field crystal methods with a Cahn-Hilliard model for binary alloys
• Rotation induced grain growth and stagnation in phase field crystal models
• Vacancy diffusion in colloidal crystals as determined by dynamical density-functional theory and the phase-field-crystal model
• Emergence of foams from the breakdown of the phase field crystal model
• Elastic constants of stressed and unstressed materials in the phase field crystal model
• Self-consistent modeling of anisotropic interfaces and missing orientations: Derivation from phase-field crystal
• Modeling Heterogeneous Melting in Phase Change Memory Devices
• Self-similar diffuse boundary method for phase boundary driven flow
• The influence of short range forces on melting along grain boundaries
• Statistical Mechanics of Low Angle Grain Boundaries in Two Dimensions
• Substrate curvature governs texture orientation in thin films of smectic block copolymers
• Efficient and quantitative phase field simulations of polycrystalline solidification using a vector order parameter
• Hybrid-PFC: coupling the phase-field crystal model and its amplitude-equation formulation
• Grain Boundary Premelting of Monolayer Ices in 2D Nano-channels
• Linear Second Order Energy Stable Schemes of Phase Field Model with Nonlocal Constraints for Crystal Growth