Physics of lattice relaxation at surfaces of simple metals

The physics of the inward or outward relaxation of the first plane of ions at a metal surface is explored by means of semi-self-consistent calculations for Al, Mg, and Na. The adiabatic screening response of the electron density to a shift of the first lattice plane drastically reduces the curvature of the potential in which this plane sits, and thus cannot be ignored in any qualitatively correct theory of the equilibrium lattice configuration at the surface. Because the electronic screening is nearly perfect, the calculated face-dependent surface energies and work functions are nearly independent of small displacements of the first lattice plane. Just as in the calculation of the bulk-longitudinal-phonon frequencies, there is a delicate cancellation between Madelung forces which are treated exactly and electronic forces which are approximated. Indeed a quantitatively correct theory of the surface interplanar spacing must also be detailed enough to predict the correct bulk-phonon frequencies.