Migration energy calculations for small vacancy clusters in copper

The migration energies of tri- and tetravacancies in copper are calculated to be 0.56 eV and 0.38 eV, respectively, using a new energy minimisation scheme and a first-principles interatomic potential. Comparison with the previously calculated single and divacancy migration energies of 0.82 and 0.55 eV, respectively, indicates that the tri- and tetravacancies are very mobile in copper. The calculated binding and migration energies were used in a rate equation model which predicts the concentrations of vacancy defects during quenching and electron-irradiation experiments. The predicted activation energy of the model follows the same general behaviour as that measured in annealing experiments. The maximum concentrations of tri- and tetravacancies predicted by the model are very low (less than 0.001 p.p.m.), which suggests that these defects many not be observable using experimental techniques.