Work functions and surface double layer potentials of monovalent metals from a network model

Abstract

The model described in this paper uses an electronic wave function which is defined to be nonzero only along the lines connecting first nearest neighbors in the metallic lattice. The electrons are assumed to move freely along the lines between nearest neighbors. No electron-electron or electron-nucleus force is included in the model calculations (except for forces arising from the Pauli exclusion principle). The work function is defined as the amount of energy required to move an electron from a point slightly inside the crystal to a point slightly outside. The contribution of the electronic double layer is included in the calculation of the work function as well as the dependence of the double layer potential on the surface geometry. Surface states, where the electron is localized in the neighborhood of the face of the crystal, are found to have energies sufficiently above the Fermi level to eliminate the possibility that they make any contribution to the double layer potential for the case of the (100) crystal plane. Consequently, surface states have been ignored in all the calculations. The surface double layer is assumed to be caused by the presence of a finite potential barrier at the surface of the crystal. Bulk electronic wave functions can penetrate this barrier and decay exponentially outside the crystal. The only parameters required by the model are the nearest neighbor distance for the lattice and the height of the potential barrier at the surface. The former quantity is fixed by the lattice structure (body centered cubic for the alkali metals) and by the density, while the latter quantity can be adjusted to give the best agreement between the model calculations and experiment. For the alkali metals, lithium through sodium, the best value of the barrier height is about 50% of the sum of the ionization potential energy, the heat of vaporization, and the calculated Fermi level for the corresponding metal. In addition, the value of the double layer potential for sodium agrees very well with a more sophisticated calculation by Bardeen and is reasonably close to the experimental measurement.