Formation energy of vacancies in graphite crystals

Abstract

A theoretical discussion is given of some of the energy factors associated with single vacancies in an otherwise perfect graphite lattice, caused by neutron bombardment. First, the loss of r-electron energy is shown to be 2.76 + 0.05 β where β is the molecular-orbital resonance integral for a carbon-carbon bond. Secondly, a careful account is provided of the symmetries of the various electronic states that are possible if it is supposed that the three electrons of the atoms adjacent to the vacancy are allowed to interact and form a pseudo-molecule. The energies of these states are calculated, taking account of configuration interaction. It is shown that the lowest state for a neutral vacancy would be a doubly-degenerate state of symmetry 2 E' . This would lead to a Jahn -Teller equilibrium deformation. Such deformation would not be expected to be large, or to modify the numerical results to any great extent. Finally, the earlier numerical values are combined with the experimental heat of atomization of graphite, and lead to a value for the heat of formation of a vacancy equal to about 10.7 eV. This differs considerably from the observed value, which is of the order of 3.4 eV. It is concluded that the model of a vacancy used may possibly not be correct, and an alternative suggestion is put forward.