Ab initio calculations were made of the formation energies and stability of different types of multi-vacancies in carbon nanotubes. It was demonstrated that, as in the case of graphene, the reconstruction of the defects had drastic effects on the energetics of the tubes. In particular, the formation of pentagons eliminated the dangling bonds thus lowering the formation energy. This competition led to vacancies having an even number of carbon atoms removed to be more stable. Finally the appearance of magic numbers indicating more stable defects could be represented by a model for the formation energies that was based on the number of dangling bonds of the unreconstructed system, the pentagons and the relaxation of the final form of the defect formed after the relaxation.

Energetics and Stability of Vacancies in Carbon Nanotubes. J.E.Padilha, R.G.Amorim, A.R.Rocha, A.J.R.da Silva, A.Fazzio: Solid State Communications, 2011, 151[6], 482-6