Studies of Vibrational Surface Modes. III. Effect of an Adsorbed Layer

Abstract

The vibrational modes of adsorbate-substrate systems have been studied for models in which the adsorbate is simulated by a light or heavy monolayer. The monolayer is assumed to have the same structure and potential parameters as the substrate, and to differ only in particle mass. These models are more nearly realistic than those used in most previous treatments of this problem in that the structure of the substrate is fcc rather than simple cubic and, more important, in that the condition of rotational invariance is not violated. The (100), (111), and (110) surfaces have been treated. For each of these surface orientations, the vibrational modes have been calculated for mass ratios $\frac{{M}_{L}}{M}=\frac{1}{4},\frac{1}{2},\frac{4}{5},\frac{5}{4},\frac{2}{1},\mathrm{and} \frac{4}{1}$, where ${M}_{L}$ and $M$ are, respectively, the masses of adsorbate and substrate particles. The surface-dispersion curves are shown for each of these 18 cases, and the shifts in the surface-mode spectra with changes in the mass ratio are discussed. For very light or very heavy adsorbed particles, there are three principal surface-mode branches associated with the adsorbed layer which exist over all (for light particles) or nearly all (for heavy particles) of the two-dimensional Brillouin zone. For mass ratios which are not extreme, the separation of the principal surface-mode branches is not complete; at small wave vectors, some or all of these branches in effect enter the bulk bands as mixed modes (pseudosurface modes). As one expects, the first-layer modes are greatly affected by changes in the mass ratios. Second-and third-layer modes ordinarily are not much affected by increases in the mass ratio (heavy layer), but ordinarily are greatly affected by decreases in the mass ratio (light layer). The effect of the adsorbed layer on the localization of the generalized Rayleigh waves is examined; for these waves, heavy adsorbed layers enhance localization at the surface and light layers have the opposite effect.