Vacancies and impurities in aluminum and magnesium

The vacancy formation energies and (Mg, Al, and Si) impurity heats of solution are calculated for Al and Mg using a first-principles pseudopotential approach and large supercells. While the interaction of the defects considered here are already negligible for reasonably small unit cells, adequate sampling of the Brillouin zone is found to be essential for these metallic systems, even for systems containing more than 100 atoms per unit cell; e.g., the vacancy formation energy of Al for 108 atoms per cell has the incorrect sign if only the Γ point is sampled. When the volume and structural relaxations are treated consistently, heats of formation and solution and relaxation volumes are obtained that are in good agreement with the available experimental data. Simple trends in the relaxations around the impurities in the various materials can be understood in terms of the size of the impurities compared with the host atoms. Contrary to some commonly used models, the energetics of the impurities are found to be dominated by electronic, rather than elastic, contributions. The defect-induced changes to the local electronic structure are also discussed.