Calculations of Surface Energy for a Free-Electron Metal

The surface energy of a free-electron metal is calculated using a square-cut barrier placed so that there is no net charge on the surface. The result is nearly independent of barrier height but leads to a value for surface tension less than half that observed for most molten metals. For sodium a self-consistent surface barrier, first developed by Bardeen, is also used in numerical computation of surface energy. The value so obtained is about half that resulting from the use of the square-cut barrier. Previous theoretical treatments of this problem have generally predicted surface energies larger than observed. The opposite result in this case appears to result from the requirement that the surface be maintained electrically neutral.