Application of Pseudopotentials to the Calculation of Vacancy Formation Energy and Volume for Alkali Metals

Abstract

Based on the pseudopotential formalism, a calculation for vacancy formation energy and formation volume in metals has been formulated. The calculation is carried out in three steps: First, the structural energy required to create the vacancy is calculated; then the latticestatics method is used to calculate the relaxed vacancy configuration and the energy; finally, the dilatation of the whole defect lattice is determined according to the equilibrium condition. When applying this calculation to alkali metals, it was found that (a) the contribution from the volume-dependent lattice energy to the vacancy formation energy is very large compared to that due to the relaxation around the vacancy. Therefore, such energy must be considered in calculating vacancy volume and energy. (b) The relaxed displacements near the vacancy are highly anisotropic and quite large but the related relaxation energy contributes only about 25% of the formation energy. A local potential and an optimized nonlocal potential were chosen as pseudopotentials in the calculation, both of which have corrections for the electron exchange and correlation interactions in the screening function. The results are in quantitative agreement with the available experimental data of alkali metals. Some general problems about defect calculations for metals are also discussed.