Energetics of vacancy and substitutional impurities in aluminum bulk and clusters

We present a careful study of the energetics of vacancy and substitutional impurities in aluminum in both the bulk and small cluster environments. The calculations are done within the framework of the local-densityfunctional formalism and are based on the pseudopotential method with plane-wave expansion and periodic boundary conditions. Both the ionic and electronic degrees of freedom are fully relaxed. The electronic structure problem is treated with a preconditioned conjugate-gradient method that applies equally well to insulators and metals, and is suitable for parallel computing. We have considered up to 216 atoms in the supercell, and we show that reliable results can be obtained with 108-atom cells with proper k-point sampling. Vacancy-formation energy, heats of solution of the impurities and the relaxations near the defects are in good agreement with available experimental data. The energetics of substitution in small clusters was found to be rather different from bulk. @S0163-1829~97!07320-7#