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The normal modes of a commensurate monolayer solid may be damped by mixingwith elastic waves of the substrate. This was shown by B. Hall et al., Phys.Rev. B 32, 4932 (1985), for perpendicular adsorbate vibrations in the presenceof an isotropic elastic medium. That work is generalized with an elasticcontinuum theory of the response of modes of either parallel or perpendicularpolarization for a spherical adsorbate on a hexagonal substrate. The resultsare applied to the discussion of computer simulations and inelastic atomicscattering experiments for adsorbates on graphite. The extreme anisotropy ofthe elastic behavior of the graphite leads to quite different wave vectordependence of the damping for modes polarized perpendicular and parallel to thesubstrate. A phenomenological extension of the elasticity theory of thegraphite to include bond-bending energies improves the description of substratemodes with strong anomalous dispersion and enables a semi-quantitative accountof observed avoided crossings of the adlayer perpendicular vibration mode andthe substrate Rayleigh mode.Comment: Latex file n2dampf.tex of 24 pages, with 3 postcript figures include

Mode damping in a commensurate monolayer solid