Periodized discrete elasticity models for defects in graphene

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.

24 pages, 7 figures; comment on model with 3 slip directions, calculation of defect energies, typos corrected

References in corpus (13)

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• Two Dimensional Atomic Crystals
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• Electronic Properties of Disordered Two-Dimensional Carbon
• Effects of topological defects and local curvature on the electronic properties of planar graphene
• Adatoms and nanoengineering of carbon
• Dislocations in graphene
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• Edge dislocations in crystal structures considered as traveling waves of discrete models
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• Homogeneous nucleation of dislocations as bifurcations in a periodized discrete elasticity model
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Cited by in corpus (12)

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• Model of ripples in graphene
• Ripples in a string coupled to Glauber spins
• Ripples in a graphene membrane coupled to Glauber spins
• Ripples in hexagonal lattices of atoms coupled to Glauber spins
• Measuring strain and rotation fields at the dislocation core in graphene
• Theory of defect dynamics in graphene: defect groupings and their stability
• Thermo-electromechanical effects in relaxed shape graphene and bandstructures of graphene quantum dots
• A numerical study of the rippling instability driven by electron-phonon coupling in graphene
• Toy nanoindentation model and incipient plasticity