A monolayer adsorbed on a crystal surface may form an overlayer whose unit-cell dimension in one or both principal directions is very long compared with the substrate lattice constant (5 -15 lattice constants, for example). We refer to such overlayers as nearly incommensurate.In this paper, we explore the lattice vibrations of such overlayers, within a model where the substrate is viewed as rigid, providing a corrugated potential well within which the adsorbates reside. We first find the static equilibrium configuration of the adlayer, and then calculate the phonon spectrum and meansquare displacements within harmonic lattice dynamics. For small corrugation amplitudes, we find very large mean-square displacements parallel to the surface. There is a smooth transition to a regime where the overlayer is locked to the substrate tightly; the transition occurs within a rather narrow range of corrugation strengths. This and other systematic aspects of the vibrational properties of such overlayers are explored in the paper.
We consider the resonant scattering of an electron from a localized object, in the presence of coupling to a spectrum of phonons. The discussion is carried out within the framework of the Friedel model of a virtual level; the electron couples to the phonons while it resides in this level. Within a certain approximation (the residence time of the electron in the virtual level is short compared to the period of vibration motion in the lattice), we obtain an expression for the cross section for elastic scattering off the center in the presence of electron-phonon coupling, and for scattering off the center with multiphonon emission. The results are compared with an earlier analysis of the problem by the present author, based on a semiclassical picture.
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