Adsorbate aggregation and relaxation of low-frequency vibrations

We present a study of resonant vibrational coupling between adsorbates and an elastic substrate at low macroscopic coverages. In the first part of the paper we consider the situation in which adsorbates form aggregates with h igh local coverage. Based upon our previously published theory, we derive f ormulas describing the damping rate of adsorbate vibrations for two cases o f such aggregation: (i) adsorbates attached to step edges and (ii) adsorbat es forming two-dimensional islands. We have shown that damping is governed by local coverage. Particularly, for a wide range of resonant frequencies, the damping rate of adsorbates forming well-separated islands is described by the damping rate formula for a periodic overlayer with the coverage equa l to the local coverage in the island. The second part of the paper is devo ted to facilitating the evaluation of damping rates for a disordered overla yer. The formula describing the damping rate involves the parameter beta, w hich is related to the local density of phonon states at the substrate surf ace and does not allow a closed-form representation. For substrates of isot ropic and cubic symmetries, we have developed a good analytical approximati on to this parameter. For a vast majority of cubic substrates the differenc e between the analytical approximation and numerical calculation does not e xceed 4%. (C) 2000 American Institute of Physics. [S0021-9606(00)70846-4].