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Vacancies below the (111) surface of Pd

Density functional theory is used to investigate vacancies at or below the (111) surface of palladium and in the bulk. An accurate nonlocal pseudopotential for Pd based on relativistic all-electron calculations is employed. The interaction of the vacancy, a point defect, with a surface, a planar defect, is investigated. Also studied is the interaction between electronic structure and lattice structure around the vacancy. The vacancy-formation energy increases with the depth of the vacancy and with decreasing vacancy concentration. The ions surrounding a vacancy relax slightly into it, and the amount of relaxation decreases as vacancy depth is increased or as vacancy concentration is decreased. The primary electronic effects of the vacancy are a spillout of electrons into it and a strengthening of the bonds between the neighboring atoms that accompanies the inward relaxation.