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Continuum Elastic Theory of Adsorbate Vibrational Relaxation

Steven P. Lewis·M. V. Pykhtin·E. J. Mele·Andrew M. Rappe
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Abstract

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: $γ= m\barω_0^2/A_c ρc_T$, where $m$ is the adsorbate mass, $\barω_0$ is the measured frequency, $A_c$ is the overlayer unit-cell area, and $ρ$ and $c_T$ 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 $0.50\times 10^{12}$~s$^{-1}$, as compared to the experimental value of $(0.43\pm0.07)\times 10^{12}$ 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.

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Steven P. Lewis, M. V. Pykhtin, E. J. Mele, Andrew M. Rappe. 1997-09-30. Continuum Elastic Theory of Adsorbate Vibrational Relaxation. https://doi.org/10.1063/1.475478

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