Vacancy formation energies were calculated by using a first-principles pseudopotential approach and large super-cells. Although the interactions of the present defects were negligible for reasonably small unit cells, adequate sampling of the Brillouin zone was found to be essential; even for systems which contained more than 100 atoms per unit cell. Thus, the vacancy formation energy in Al at 108 atoms per cell had an incorrect sign if only the  point was sampled. When the volume and structural relaxations were treated consistently, heats of formation and solution (and relaxation volumes) were obtained which were in good agreement with available experimental data. The trends in the relaxations around impurities could be understood in term of the size of the impurities in comparison with those of the host atoms. Contrary to some models, the energetics of the impurities were found to be dominated by electronic rather than by elastic contributions.

N.Chetty, M.Weinert, T.S.Rahman, J.W.Davenport: Physical Review B, 1995, 52[9], 6313-26