SPHERICAL VOIDS IN THE STABILIZED JELLIUM MODEL - RIGOROUS THEOREMS AND PADE REPRESENTATION OF THE VOID-FORMATION ENERGY

We consider the energy needed to form a spherical hole or void in a si mple metal, modeled as ordinary jellium or stabilzed jellium. (Only th e latter model correctly predicts positive formation energies for void s in high-density metals.) First we present two Hellman-Feynman theore ms for the void-formation energy 4piR2sigma(R)nu(nBAR) as a function o f the void radius R and the positive-background density nBAR, which ma y be used to check the self-consistency of numerical calculations. The y are special cases of more-general relationships for partially emptie d or partially stabilized voids. The difference between these two theo rems has-an analog for spherical clusters. Next we link the small-R ex pansion of the void surface energy (from perturbation theory) with the large-R expansion (from the liquid drop model) by means of a Pade app roximant without adjustable parameters. For a range of sizes (includin g the monovacancy and its ''antiparticle,'' the atom), we compare void formation energies and cohesive energies calculated by the liquid dro p expansion (sum of volume, surface, and curvature energy terms), by t he Pade form, and by self-consistent Kohn-Sham calculations within the local-density approximation, against experimental values. Thus we con firm that the domain of validity of the liquid drop model extends down almost to the atomic scale of sizes. From the Pade formula, we estima te the next term of the liquid drop expansion beyond the curvature ene rgy term. The Pade form suggests a ''generalized liquid drop model,'' which we use to estimate the edge and step-formation energies on an Al (111) surface.