Surface lattice dynamics of Cu(111).

Abstract

We present and analyze off-specular electron-energy-loss data which explore surface vibrations of Cu(111), along the line from \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{} to M\ifmmode\bar\else\textasciimacron\fi{} in the two-dimensional surface Brillouin zone. The dispersion relation of the Rayleigh surface phonon and the longitudinal resonance found in inelastic-He-scattering studies have been measured out to M\ifmmode\bar\else\textasciimacron\fi{}, thus extending the earlier He work. In addition, we obtain the frequency of a (high-frequency) surface phonon which exists at and near M\ifmmode\bar\else\textasciimacron\fi{}, in a gap in the projected bulk-phonon density of states. The data are analyzed within a simple model of surface lattice dynamics. We have also carried out extensive calculations of the energy variation of the various features observed in the electron-loss spectrum, using multiple-scattering theory. Very good agreement between theory and experiment is obtained within a model where the intraplanar force constant between surface atoms is softened by a modest amount, 15%. In our view, the results presented here raise questions about recent suggestions that a very large (70%) softening of the intraplanar surface force constant is present in the Cu(111) surface.