The Separation of the Semi-infinite Model and the Calculation of the Surface Parameters for the Three-Dimensional body at T = 0 K (Regula Falsi of Surface Theory)

Abstract

It is demonstrated, how the different ideas “surface energy” and “surface stress” come out from the energy band approximation of a crystalline solid used by Kronig and Penney and from the electronic surface states predicted by Tamm. If the potential energy is separable, we obtain for the chemical potential per particle in the three-dimensional system ζ and the chemical potentials in the subsystems ζ _i the relation ζ = ζ ₁ + ζ ₂ + ζ ₃. By a combination of three one-dimensional models for a solid to a three-dimensional one we obtain with a “regula falsi” (RF) approximate results for the surface charge density q ^ESB,RF, the surface energy φ ^ESB,RF, and the surface stress σ ^ESB,RF _ii . The superfix “^ESB” means that we consider here the results for the electrons in the surface bands.