Mode damping in a commensurate monolayer solid

The normal modes of a commensurate monolayer solid may be damped by mixing with elastic waves of the substrate. This was shown by Hall, Mills, and Black [Phys. Rev. B 32, 4932 (1985)], for perpendicular adsorbate vibrations in the presence of an isotropic elastic medium. That work is generalized with an elastic-continuum theory of the response of modes of either parallel or perpendicular polarization for a spherical adsorbate on a hexagonal substrate. The results are applied to the discussion of computer simulations and inelastic atomic-scattering experiments for adsorbates on graphite. The extreme anisotropy of the elastic behavior of the graphite leads to quite different wave-vector dependence of the damping for modes polarized perpendicular and parallel to the substrate. A phenomenological extension of the elasticity theory of the graphite to include bond-bending energies improves the description of substrate modes with strong anomalous dispersion, and enables a semiquantitative account of observed avoided crossings of the adlayer perpendicular vibration mode and the substrate Rayleigh mode.