Electron statistical model for cohesion and vacancy formation in copper

Abstract

A copper crystal model, based on realistic, extended ions and completely devoid of empirical parameters is presented. For a perfect crystal lattice, the crystal energy E _c, the Wigner–Seitz radius R, and the compressibility K are calculated. For an unrelaxed monovacancy geometry, the energy of formation E _f and the conduction electron density profile v _f(R) are determined. The terms E _c and E _f are composed of an electrostatic term and electron statistical approximations for exchange, correlation, and kinetic energy. It is therefore possible to express E _c and E _f as functionals of the conduction density which is varied until the energy minima are found. Resulting values of E _c, R, K, and E _f (1.21 eV) agree well with experiments. Furthermore, for a perfect lattice the model is found to satisfy the virial theorem. The resulting conduction density profile v _f(R) in the vacant cell is considerably lower than the profiles predicted by other electron theoretical models.