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.
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