Structure and energetics of the vacancy in graphite

We determine properties of the vacancy in graphite from first principles calculations. The ground-state structure is associated with a formation energy of 7.4 eV and arises through a combination of symmetric relaxation and symmetry-breaking Jahn-Teller distortion to one of three degenerate, symmetry-related structures. The distortion results in a weak reconstructed bond and small out-of-plane atomic displacements. Dynamic switching between degenerate structures is activated by a barrier of 0.1 eV and we interpret scanning tunneling microscopy observations on the basis of thermal averaging between structures. The calculated migration energy of 1.7 eV is lower than that widely accepted from experiment, and we propose that the discrepancy is explained by a revised picture of trapping during vacancy transport, dependent on concentration. We discuss the significance of these findings in understanding defect behavior in irradiated graphite and related graphitic materials, in particular single-walled nanotubes.