SURFACE LATTICE-DYNAMICS OF NEARLY INCOMMENSURATE OVERLAYERS

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 mean-square 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. © 1990 The American Physical Society.