Cu(111) and Ag(111) surface-phonon spectrum: The importance of avoided crossings

Embedded-atom method (EAM) calculations of the phonon energies, polarizations, and first- and second-neighbor interatomic-force-constant tensors of the clean Cu(111) and Ag(111) surfaces are presented. Using embedded-atom parameters fit to bulk properties, we find that the EAM provides an accurate and detailed description of the lattice dynamics of these surfaces, in good agreement with the measured surface vibrational spectra. We find only modest 1015 % changes in the surface force constants for both Cu and Ag from their bulk values. Our calculations also suggest an explanation for the anomalous softening of the longitudinal resonance mode along the M symmetry line in terms of an avoided crossing of first- and second-layer sagittal-plane modes. © 1989 The American Physical Society.