A New Structural Phase Field Crystal Approach for Modelling Graphene

Abstract

This paper introduces a new structural phase field crystal (PFC) type model that expands the PFC methodology to a wider class of structurally complex crystal structures than previously possible. Specifically, our new approach allows for stabilization of graphene, as well as its coexistence with a disordered phase. It also preserves the ability to model the usual triangular and square lattices previously reported in 2D PFC studies. Our approach is guided by the formalism of the classical field theory, wherein the the free energy functional is expanded to third order in PFC density correlations. It differs from previous PFC approaches in two main features. First, it utilizes a hard-sphere repulsion to describe two-point correlations. Second, and more important, is that it uses a rotationally invariant three-point correlation function that provides a unified way to control the formation of crystalline structures that can be described by a specific bond angle, such as graphene, triangular or square symmetries. Our new approach retains much of the computational simplicity of previous PFC models and allows for efficient simulation of nucleation and growth of polycrystalline 2D materials. In preparation for future applications, this paper details the mathematical derivation of the model and its equilibrium properties, and uses dynamical simulations to demonstrate defect structures produced by the model.

Updated figures, included comparison to experimental paper by Huang et al

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Cited by in corpus (21)

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• Multiscale modeling of polycrystalline graphene: A comparison of structure and defect energies of realistic samples from phase field crystal models
• Convergence Analysis for Second Order Accurate Convex Splitting Schemes for the Periodic Nonlocal Allen-Cahn and Cahn-Hilliard Equations
• Bimodal grain-size scaling of thermal transport in polycrystalline graphene from large-scale molecular dynamics simulations
• Phase-field crystal model for ordered crystals
• Non-linear elastic effects in phase field crystal and amplitude equations: Comparison to ab initio simulations of bcc metals and graphene
• Simulating complex crystal structures using the phase-field crystal model
• Combining phase field crystal methods with a Cahn-Hilliard model for binary alloys
• Angle-adjustable density field formulation for modeling crystalline microstructures
• Thermo-Density Coupling in PFC Type Models for the Study of Rapid Crystallization
• Self-consistent modeling of anisotropic interfaces and missing orientations: Derivation from phase-field crystal
• Yielding and jerky plasticity of tilt grain boundaries in high-temperature graphene
• Minimal phase-field crystal modeling of vapor-liquid-solid coexistence and transitions
• Atom Based Grain Extraction and Measurement of Geometric Properties
• Incorporating density jumps and species-conserving dynamics in XPFC binary alloys
• Control of phase ordering and elastic properties in phase field crystals through three-point direct correlation
• Microscopic Patterns in the 2D Phase-Field-Crystal Model
• Computational and analytical studies of a new nonlocal phase-field crystal model in two dimensions
• Structural phase-field crystal model for Lennard-Jones pair interaction potential
• Atomic ordering and phase separation in lateral heterostructures and multijunctions of ternary two-dimensional hexagonal materials
• A Phase Field Crystal Method for Multilayer Graphene Structure