An analytical theory is presented for the damping of low-frequency adsorbate vibrations via resonant coupling to the substrate phonons. The system is treated classically, with the substrate modeled as a semi-infinite elastic continuum and the adsorbate overlayer modeled as an array of point masses connected to the surface by harmonic springs. The theory provides a simple expression for the relaxation rate in terms of fundamental parameters of the system: γ = mω 2 0 /AcρcT , where m is the adsorbate mass,ω0 is the measured frequency, Ac is the overlayer unit-cell area, and ρ and cT are the substrate mass density and transverse speed of sound, respectively. This expression is strongly coverage dependent, and predicts relaxation rates in excellent quantitative agreement with available experiments. For a half-monolayer of carbon monoxide on the copper (100) surface, the predicted damping rate of in-plane frustrated translations is 0.50 × 10 12 s −1 , as compared to the experimental value of (0.43 ± 0.07) × 10 12 s −1 . Furthermore it is shown that, for all coverages presently accessible to experiment, adsorbate motions exhibit collective effects which cannot be treated as stemming from isolated oscillators.

A simple, broadly applicable theory is developed to describe resonant vibrational coupling between adsorbates and a substrate lattice. This is one of the principal mechanisms governing the relaxation of adsorbate vibrations. This theory can be applied to widely varying surface coverages and arbitrary overlayer structures, and it correctly incorporates collective adsorbate motion, which has been shown to have a critical impact on the relaxation dynamics. Vibrational lifetimes predicted by this theory are in excellent quantitative agreement with experiments on adsorbate systems ranging from a diffuse, disordered overlayer to a dense, periodic overlayer. [S0031-9007(98)08012-0] PACS numbers: 82.20. Rp, 68.35.Ja, 68.45.Kg, 82.65.My A key factor in many surface chemical phenomena is the existence of low-energy molecular vibrations associated with fluctuations about the adsorption bond. These modes involve relative motion between the adsorbate molecule and substrate, and thus act as vibrational precursors to surface reactions, diffusion, and desorption [1]. Indeed, the systematic study of these modes through inelastic spectroscopic techniques has become the chief tool for characterizing the potential energy surface encountered by atoms and molecules in heterogeneous catalysis, epitaxial growth, and other complex surface phenomena [2].These low-energy excitations of the adlayer are not isolated from their surroundings; they can exchange energy and momentum with various propagating substrate excitations. At the surface of a metal, for example, the relevant bulk modes include propagating elastic waves, electronhole pair excitations, and various collective modes arising from electron-electron and electron-phonon interactions. These bulk excitations provide decay channels which govern the lifetimes of the adsorbate vibrational modes and, thus, play a critical role in determining the surface dynamics and reactivity [3,4].In this Letter, we develop a general theory for the relaxation dynamics of low-frequency adsorbate vibrations due to resonant coupling to substrate elastic waves [5][6][7][8][9]. This theory applies to adsorbate modes with frequencies in the acoustic range of the substrate phonon spectrum, and is relevant, for example, to the in-plane frustrated translation (FT) of adsorbates on metal surfaces. Two recent experiments examined the FT relaxation dynamics of carbon monoxide molecules on the Cu(100) surface under very different conditions of coverage. One considered an ordered half monolayer and measured a lifetime of 2.3 6 0.4 ps [10], whereas the other considered a disordered adlayer at 3% coverage and found an 8 6 1 ps lifetime [11]. Our theory shows conclusively that the vibrational relaxation is governed by bulk elastic coupling, even for these widely varying adlayer conditions. This conclusion contrasts with the results of an earlier theory due to Persson and Ryberg (PR) [6]. They also considered relaxation via phonon emission, but focused on the case of an isolated adsorbate. Since direct adsorbateadso...

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 when adsorbates form aggregates with high local coverage. Based upon our previously published theory, we derive formulas describing the damping rate of adsorbate vibrations for two cases of such aggregation: (i) adsorbates attached to step edges and (ii) adsorbates forming twodimensional 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 equal to the local coverage in the island. The second part of the paper is devoted to facilitating the evaluation of damping rates for a disordered overlayer. The formula describing the damping rate involves the parameter β which is related to the local density of phonon states at the substrate surface and does not allow a closed-form representation. For substrates of isotropic and cubic symmetries, we have developed a good analytical approximation to this parameter. For a vast majority of cubic substrates the difference between the analytical approximation and numerical calculation does not exceed 4%. 82.20.Rp, 68.35.Ja, 68.45.Kg