The formation mechanism of multiple vacancies and amorphous graphene under electron irradiation

The evolution of multiple vacancies (Vns) in graphene under electron irradiation (EI) was explored systematically by long time non-equilibrium molecular dynamics simulations, with n varying from 4 to 40. The simulations showed that the Vns form haeckelites in the case with small n, while forming holes as n increases. The scale of the haeckelites, characterized by the number of pentagon-heptagon pairs, grows linearly with n. Such a linear relationship can be interpreted as a consequence of compensating the missing area, caused by the Vns, in order to maintain the area of the perfect sp(2) network by self-healing. Beyond that, the scale of the haeckelite vs. the density of missing atoms is predicted to be Sh ∼ 6Dn, where Sh and Dn are the percentage of non-hexagonal rings and missing atoms, respectively. This study provides an intuitive picture of the formation of amorphous graphene under EI and the quantitative understanding of the mechanism.