Strong long-range relaxations of structural defects in graphene simulated using a new semi-empirical potential

TL;DR

This paper introduces a new semi-empirical potential for graphene that captures long-range out-of-plane relaxations caused by defects, revealing significant effects on defect energies and structural behavior.

Contribution

A novel semi-empirical potential for graphene including out-of-plane terms, enabling large-scale simulations of long-range defect relaxations.

Findings

Buckling from defects extends hundreds of nanometers.

Long-range relaxations significantly lower defect formation energies.

Energy divergence behavior differs between flat and buckled graphene.

Abstract

We present a new semi-empirical potential for graphene, which includes also an out-of-plane energy term. This novel potential is developed from density functional theory (DFT) calculations for small numbers of atoms, and can be used for configurations with millions of atoms. Our simulations show that buckling caused by typical defects such as the Stone-Wales (SW) defect extends to hundreds of nanometers. Surprisingly, this long-range relaxation lowers the defect formation energy dramatically - by a factor of $2$ or $3$ - implying that previously published DFT-calculated defect formation energies suffer from large systematic errors. We also show the applicability of the novel potential to other long-range defects including line dislocations and grain boundaries, all of which exhibit pronounced out-of-plane relaxations. We show that the energy as a function of dislocation separation diverges logarithmically for flat graphene, but converges to a constant for free standing buckled graphene. A potential in which the atoms are attracted to the 2D plane restores the logarithmic behaviour of the energy. Future simulations employing this potential will elucidate the influence of the typical long-range buckling and rippling on the physical properties of graphene.