Simple Model for Cohesion in Metals

Abstract

A simple model for the binding energy of metals has been examined. The electrostatic energy for the ion—electron interaction is calculated classically, assuming a uniform density of valence electrons within a Wigner—Seitz sphere but outside a spherical core of arbitrary radius r_c. r_c is determined by matching the equilibrium volume to the experimental value. Several expressions are examined for the kinetic energy and for the energy due to the electron—electron interaction, and the results are compared with experimental data for alkali metals. It is found that the best results are obtained if the presence of the core is ignored completely in computing the energy of the electron—electron interaction. One then obtains not only good agreement for the binding energy (ΔE≲0.01 Ry), but also values for the compressibility which are typically within 10% of experimental values. The empirical values of r_c are comparable with the ionic radii. The pressure—volume curves agree with experiment to a degree comparable with the compressibility values. Modifications of the energy expressions from the optimum one yield moderately poorer agreement with experiment, except for a particular combination which has been used by Raich and Good. In that case, very poor values of r_c and compressibility are obtained; this is apparently caused partly by a pecularity in the mathematical behavior of the energy expression. Application of the model to polyvalent metals was found to yield progressively poorer results with increasing valence for the binding energy and compressibility. The values of r_c, however, generally remain comparable with the empirical ionic radii.