The contribution made by lattice vacancies to the Wigner effect in radiation-damaged graphite

Models for radiation damage in graphite are reviewed and compared, leading to a re-examination of the contribution made by vacancies to annealing processes. A method based on density functional theory, using large supercells with orthorhombic and hexagonal symmetry, is employed to calculate the properties and behaviour of lattice vacancies and displacement defects. It is concluded that annihilation of intimate Frenkel defects marks the onset of recovery in electrical resistivity, which occurs when the temperature exceeds about 160 K. The migration of isolated monovacancies is estimated to have an activation energy of E(a) ≈ 1.1 eV. Coalescence into divacancy defects occurs in several stages, with different barriers at each stage, depending on the path. The formation of pairs ultimately yields up to 8.9 eV energy, which is nearly 1.0 eV more than the formation energy for an isolated monovacancy. Processes resulting in vacancy coalescence and annihilation appear to be responsible for the main Wigner energy release peak in radiation-damaged graphite, occurring at about 475 K.