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

Abstract

The evolution of multiple vacancies (V_ns) 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 V_ns 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 V_ns, in order to maintain the area of the perfect sp² network by self-healing. Beyond that, the scale of the haeckelite vs. the density of missing atoms is predicted to be S_h ∼ 6D_n, where S_h and D_n 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.