All-electron first-principles supercell total-energy calculation of the vacancy formation energy in aluminium

Abstract

We use the first-principles all-electron linearized augumented plane-wave (LAPW) method to perform self-consistent total-energy electronic structure calculations for the vacancy formation energy in aluminum in the supercell approximation. The method makes no uncontrolled approximations for the shape of the potential. Supercells with 4, 8, 16 and 27 sites are used. When no relaxation is allowed, the formation energy is 0.87, 0.88, 0.89 and 0.86 eV for the 4-, 8-, 16-, and 27-site supercells, respectively. When some of the atoms are allowed to relax about the vacancy the formation energy is lowered by 0.05 eV in the 16-site cell and 0.03 eV in the 27-site cell. These results are in semiquantitative agreement with the experimental formation energy of 0.66 eV. The dependence of the formation energy on cell size is discussed.