相关论文: Read--Shockley formula for a general Bravais latti…
In the 50's Read and Shockley proposed a formula for the energy of small angle grain boundaries in polycrystals based on linearised elasticity and an ansazt on the distribution of incompatibilities of the lattice at the interface. In this…
We previously observed that an intrinsic staking fault shrunk through a glide of a Shockley partial dislocation terminating its lower end in a hard-sphere crystal under gravity coherently grown in <001> by Monte Carlo simulations [Mori et…
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 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…
We propose a discrete lattice model of the energy of dislocations in three-dimensional crystals which properly accounts for lattice symmetry and geometry, arbitrary harmonic interatomic interactions, elastic deformations and discrete…
A family of equilibria corresponding to dislocation-dipole, with variable separation between the two dislocations of opposite sign, is constructed in a one dimensional lattice model. A suitable path connecting certain members of this family…
A continuum dislocation model of formation of grains whose boundaries have a non-vanishing thickness is proposed. For a single crystal deforming in simple shear the lamellar structure of grains with thin layers containing dislocations as…
Lattice defects are inevitably present in two-dimensional materials, with direct implications on their physical and chemical properties. We show that the formation energy of a lattice defect in buckled two-dimensional crystals is not…
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…
One of the major challenges towards understanding and further utilizing the properties and functional behaviors of grain boundaries (GB) is the complexity of general GBs with mixed tilt and twist characters. Here, we report the correlations…
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…
A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to times scales…
In this paper, a strain-gradient plasticity model is derived from a mesoscopic model for straight parallel edge dislocations in an infinite cylindrical crystal. The main difference to existing work is that in this work the well-separateness…
We investigate lattice energies for radially symmetric, spatially extended particles interacting via a radial potential and arranged on the sites of a two-dimensional Bravais lattice. We show the global minimality of the triangular lattice…
In seeking to understand at a microscopic level the response of dislocations to stress we have undertaken to study as completely as possible the simplest case: a single dislocation in a two dimensional crystal. The intention is that results…
We develop a continuum dislocation description of twist and stretch moire superlattices in 2D material bilayers. The continuum formulation is based on the topological constraints introduced by the periodic dislocation network associated…
A detailed analytical and numerical analysis for the dislocation cloud surrounding a disclination is presented. The analytical results show that the combined system behaves as a single disclination with an effective fractional charge which…
Strain and rotation fields of dislocations in monolayer graphene have been mapped in a recent experiment. These fields are finite everywhere and differ from those given by linear elasticity which does not consider rotation explicitly and…
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 present a unified framework for the calculation of defect energies for those defects that can be represented as a superposition of isolated dislocations, and obtain both self and interaction energies of combinations of grain boundaries…