Related papers: On the Read-Shockley energy for grain boundaries i…
In this note we consider a two-dimensional semi-discrete dislocation energy and propose a simple and physically motivated construction for the grain boundary between two crystal grains with a small orientation difference. In the case of a…
We present a phase-field approximation of sharp-interface energies defined on partitions, designed for modeling grain boundaries in polycrystals. The independent variable takes values in the orthogonal group $\mathrm{O}(d)$ modulo a lattice…
The grain boundary (GB) energy is a quantity of fundamental importance for understanding several key properties of graphene. Here we present a comprehensive theoretical and numerical study of the entire space of symmetric and asymmetric…
We investigate the formation of polycrystalline structures in a class of particle systems. The atomistic energy is modeled as a sum of particle energies that favor atoms being locally isometric to a reference lattice. The discrete frame…
In this paper we show the emergence of polycrystalline structures as a result of elastic energy minimisation. For this purpose, we introduce a variational model for two-dimensional systems of edge dislocations, within the so-called core…
We study an energy minimization problem $\sum_{i \neq j} W(z_i - z_j)$ for $N$ points $\left\{z_1, \dots, z_N\right\}$ with applications in dislocation theory. The $N$ points lie in the two-dimensional domain $\mathbb{R} \times [-\pi,…
The success of grain boundary (GB) plane orientation fundamental zone (FZ) has connected GB structures across multiple crystallographic characters with their properties in a unique insight, but quantitative understandings of the…
We propose a two dimensional frame-invariant phase field model of grain impingement and coarsening. One dimensional analytical solutions for a stable grain boundary in a bicrystal are obtained, and equilibrium energies are computed. We are…
In the limit of vanishing lattice spacing we provide a rigorous variational coarse-graining result for a next-to-nearest neighbor lattice model of a simple crystal. We show that the $\Gamma$-limit of suitable scaled versions of the model…
In this paper a we derive by means of $\Gamma$-convergence a macroscopic strain-gradient plasticity from a semi-discrete model for dislocations in an infinite cylindrical crystal. In contrast to existing work, we consider an energy with…
We investigate the emergence of rigid polycrystalline structures from atomistic particle systems. The atomic interaction is governed by a suitably normalized pair interaction energy, where the `sticky disk' interaction potential models the…
This paper studies how solute segregation and its relationship to grain boundary energy in binary alloys is captured in the phase field crystal (PFC) formalism, a continuum method that incorporates atomic scale elasto-plastic effects on…
In this paper we introduce Peierls-Nabarro type models for edge dislocations at semi-coherent interfaces between two heterogeneous crystals, and prove the optimality of uniformly distributed edge dislocations. Specifically, we show that the…
We predict the structural interaction of crystalline solid-melt interfaces using amplitude equations which are derived from classical density functional theory or phase-field-crystal modeling. The solid ordering decays exponentially on the…
We analyze a two-dimensional phase field model designed to describe the dynamics of crystalline grains. The phenomenological free energy is a functional of two order parameters. The first one reflects the orientational order while the…
The presence of interfaces and grain boundaries significantly impacts the mechanical properties of materials, particularly when dealing with micro- or nano-scale samples. Distinct interactions between dislocations and grain boundaries can…
Models of grain boundary energy are essential for predicting the behavior of polycrystalline materials. Typical models represent the minimum boundary energy as a function of macroscopic boundary parameters. An energy model may allow for…
We consider a discrete model of planar elasticity where the particles, in the reference configuration, sit on a regular triangular lattice and interact through nearest neighbor pairwise potentials, with bonds modeled as linearized elastic…
In light of the race towards macroscale superlubricity of graphitic contacts, the effect of grain boundaries on their frictional properties becomes of central importance. Here, we elucidate the unique frictional mechanisms characterizing…
We present a continuum model to determine the dislocation structure and energy of low angle grain boundaries in three dimensions. The equilibrium dislocation structure is obtained by minimizing the grain boundary energy that is associated…