The first-principles all-electron linearized augumented plane-wave (LAPW) method was used to perform self-consistent total-energy electronic structure calculations for the vacancy formation energy in aluminum in the super-cell approximation. The method made no uncontrolled approximations of the shape of the potential. Super-cells with 4, 8, 16 and 27 sites were used. When no relaxation was allowed, the formation energy was 0.87, 0.88, 0.89 and 0.86eV for the 4-, 8-, 16-, and 27-site super-cells, respectively. When some of the atoms were allowed to relax around the vacancy the formation energy was lowered by 0.05eV in the 16-site cell and 0.03eV in the 27-site cell. These results were in semi-quantitative agreement with the experimental formation energy of 0.66eV.

All-Electron First-Principles Supercell Total-Energy Calculation of the Vacancy Formation Energy in Aluminium. M.J.Mehl, B.M.Klein: Physica B, 1991, 172[1-2], 211-5