On the Surface Free Energy of Certain Metals

Abstract

For the purpose of calculating the surface energy and surface double layer for a number of monovalent metals, a simple and yet adequate model is proposed, which does not have the disadvantages of models employed by previous authors. In this the valence electrons are treated according to a simple Sommerfeld model, and the positive charge of the ions is distributed uniformly through the metal. It is shown that by a suitable combination of the methods of Thomas-Fermi and of direct wave mechanics, both the surface energy and the strength of the double layer can be calculated The surface double layers for the metals considered are found to be in the range 0.1-0.5 ev. The contribution to the surface energy from the electrostatic energy in the double layer is found to be very small. In estimating the surface energy, the electrons in a metal can be considered as moving in a box with finite potential walls of suitably determined height ϕ. A temperature-dependent term in the surface free energy due to the change in lattice vibrations caused by the free surface is also considered. The surface energies obtained from ϕ determined in two independent ways agree closely and are found to agree with the experimental values of the surface tension of the liquid metals to within a factor 1.5.