Continuum Elastic Theory of Adsorbate Vibrational Relaxation

TL;DR

This paper develops an analytical elastic continuum model to accurately predict the vibrational relaxation rates of adsorbates on surfaces, showing strong agreement with experimental data and highlighting collective effects in adsorbate motions.

Contribution

The paper introduces a simple, parameter-based analytical expression for adsorbate vibrational damping rates, incorporating coverage dependence and collective effects, validated against experimental results.

Findings

Predicted damping rate for CO on Cu(100) matches experimental data.

Relaxation rates depend strongly on adsorbate coverage.

Adsorbate motions exhibit collective behavior beyond isolated oscillators.

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: $\gamma = m\bar{\omega}_0^2/A_c \rho c_T$, where $m$ is the adsorbate mass, $\bar{\omega}_0$ is the measured frequency, $A_c$ is the overlayer unit-cell area, and $\rho$ 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.