The traditional picture of a carbon nanotube as a rolled graphene sheet implied that the mechanisms of intra-layer atomic processes in the two systems should be qualitatively similar. Using density-functional theory and tight-binding methods, it was shown that the mechanism of single vacancy migration in nanotubes was different to that in graphite, as the curvature of the nanotube atomic network broke the trigonal symmetry of a perfect graphene sheet, making the diffusion anisotropic, and strongly influencing the migration barrier. It was also demonstrated that the formation energy of a double vacancy in nanotubes was smaller than that for a single vacancy, a behavior different from most monatomic solids, including graphite.

Bending the Rules: Contrasting Vacancy Energetics and Migration in Graphite and Carbon Nanotubes. Krasheninnikov, A.V., Lehtinen, P.O., Foster, A.S., Nieminen, R.M.: Chemical Physics Letters, 2006, 418[1-3], 132-6