Dislocation and pentagon-heptagon pair generation in vacancy-induced graphene layer

We investigate the mechanism of the generation of long range order defects in graphene layer by tight binding molecular dynamics simulations and first-principles total energy methods. It is found that the vacancies are diffused and coalesced to make the dislocation defect with the two 5-7 pair defects when more than a certain number of vacancies are present. We examine the magic number of the vacancy which gives dislocation defects in a graphene layer. STM simulation results related to the graphite lattice with the period of $\sqrt 3 \times \sqrt 3 $ in an STM topograph will be discussed.