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].