An electron statistical vacancy model for the noble metals

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Abstract
An atomistic monovacancy model, specially designed for variational calculations, is presented for an FCC metal crystal. The total electron distribution is given as a superposition of several, differently centred, spherically symmetrical densities. The formation energy EVF, expressed as a sum of electrostatic integrals and statistical approximations for exchange, correlation and kinetic energy is minimized by variation of the electron density function in the vacancy region. A simple method, based on series expansion of the densities involved, is suggested for the variational calculation. Restrictions on and span of the suggested method are discussed. Resulting formation energies, 1.21 eV for Cu and 1.09 eV for Ag, are in close agreement with experimental values. The resulting conduction electron density in the vacant cell is considerably lower than those values predicted by other electron theoretical vacancy models.