What question did this study set out to answer?

This paper aims to explore the charge density and surface energy of metal surfaces using theoretical models.

June 15, 1970

Theory of Metal Surfaces: Charge Density and Surface Energy

Key Points

This paper aims to explore the charge density and surface energy of metal surfaces using theoretical models.
Utilized the jellium model for metal surface analysis.
Calculated self-consistent electron density distributions and surface energy corrections.
Compared theoretical results with surface-tension measurements for various metals.
Surface energy is negative for high densities with ${ }_{s} ext{ } extless 2.5$.
Identified two essential corrections to surface energy at higher densities (${r}_{s} ext{ } extless 4$).
The resulting surface energy aligns within 25% of measured values for eight metals but disagrees significantly for Pb.

Abstract

The first part of this paper deals with the jellium model of a metal surface. The theory of the inhomogeneous electron gas, with local exchange and correlation energies, is used. Self-consistent electron density distributions are obtained. The surface energy is found to be negative for high densities (rₒ2. 5). In the second part, two corrections to the surface energy are calculated which arise when the positive background model is replaced by a pseudopotential model of the ions. One correction is a cleavage energy of a classical neutralized lattice, the other an interaction energy of the pseudopotentials with the electrons. Both of these corrections are essential at higher densities (rₒ4). The resulting surface energy is in semiquantitative agreement with surface-tension measurements for eight simple metals (Li, Na, K, Rb, Cs, Mg, Zn, Al), typical errors being about 25%. For Pb there is a serious disagreement.

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