Periodized discrete elasticity models for defects in graphene

TL;DR

This paper develops periodized discrete elasticity models to study defect cores in graphene, revealing stable and unstable configurations of dislocations and defects at zero temperature.

Contribution

It introduces a novel discretization method for linear elasticity on a hexagonal lattice, enabling detailed analysis of defect cores in graphene.

Findings

Stable dislocation cores include heptagon-pentagon pairs and octagons.

Vacancies and certain divacancies are dynamically stable.

Stone-Wales defects and asymmetric vacancies are unstable.

Abstract

The cores of edge dislocations, edge dislocation dipoles and edge dislocation loops in planar graphene have been studied by means of periodized discrete elasticity models. To build these models, we have found a way to discretize linear elasticity on a planar hexagonal lattice using combinations of difference operators that do not involve symmetrically all the neighbors of an atom. At zero temperature, dynamically stable cores of edge dislocations may be heptagon-pentagon pairs (glide dislocations) or octagons (shuffle dislocations) depending on the choice of initial configuration. Possible cores of edge dislocation dipoles are vacancies, pentagon-octagon-pentagon divacancies, Stone-Wales defects and 7-5-5-7 defects. While symmetric vacancies, divacancies and 7-5-5-7 defects are dynamically stable, asymmetric vacancies and 5-7-7-5 Stone-Wales defects seem to be unstable.