First-principles calculations of the vacancy formation energy in transition and noble metals

The vacancy formation energy and the vacancy formation volume of the $3d,$ $4d,$ and $5d$ transition and noble metals have been calculated within the local-density approximation. The calculations employ the order-$N$ locally self-consistent Green's-function method in conjunction with a supercell approach and include electrostatic multipole corrections to the atomic sphere approximation. The results are in excellent agreement with available full-potential calculations and with the vacancy formation energies obtained in positron annihilation measurements. The variation of the vacancy formation energy through a transition-metal series and the effects of crystal and magnetic structure are investigated and discussed.