We extend the phase field crystal (PFC) framework to quantitative modeling of polycrystalline graphene. PFC modeling is a powerful multiscale method for finding the ground state configurations of large realistic samples that can be further used to study their mechanical, thermal or electronic properties. By fitting to quantum-mechanical density functional theory (DFT) calculations, we show that the PFC approach is able to predict realistic formation energies and defect structures of grain boundaries. We provide an in-depth comparison of the formation energies between PFC, DFT and molecular dynamics (MD) calculations. The DFT and MD calculations are initialized using atomic configurations extracted from PFC ground states. Finally, we use the PFC approach to explicitly construct large realistic polycrystalline samples and characterize their properties using MD relaxation to demonstrate their quality.

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 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.

This paper introduces a phase-field crystal (PFC) approach that couples the atomic-scale PFC density field to order parameters describing ferromagnetic and ferroelectric ordering, as well to a solute impurity field. This model extends the magnetic PFC model introduced by Faghihi et al.

We extend the three-point XPFC model of Seymour & Provatas (Seymour & Provatas 2016 , 035447 (doi:10.1103/PhysRevB.93.035447)) to two components to capture chemical vapour deposition-grown graphene, and adapt a previous two-point XPFC model of Greenwood (Greenwood 2011, 064104 (doi:10.1103/PhysRevB.84.064104)) into a simple model of two-component graphene. The equilibrium properties of these models are examined and the two models are compared and contrasted. The first model is used to study the possible roles of hydrogen in graphene grain boundaries. The second model is used to study the role of hydrogen in the dendritic growth morphologies of graphene. The latter results are compared with new experiments.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.

Micromagnetic modeling provides a realistic description of the magnetic switching behavior in electrodeposited Co thin films that are either uniform (untemplated) or templated with an array of sub-micron spheres. Quantitative agreement between experimental results and simulations based on the Landau-Lifshitz-Gilbert equations is achieved for both in-plane and perpendicular MH loops at two temperatures. By accounting for the sweep-rate dependence in coercivity values from simulated loops (with sweep rates 104–10−1 Oe/ns) and then extrapolating to the experimental regime (measurement times of 10–100 s), a self-consistent set of microscopic parameters is established to accommodate the complexity of the electrodeposited films.