Dynamical theory of low-energy-electron diffraction from disordered overlayers. I. Quasicrystalline analysis

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Abstract
A dynamical theory is developed for the elastic diffraction of low-energy electrons from disordered monolayers adsorbed on ordered substrates. The quasicrystalline approximation is adapted to treat multiple scattering from the adsorbate. Multiple scattering within the periodic substrate is analyzed without approximation in the context of the inelastic-collision model. Multiple scattering between adsorbate and substrate is considered in two distinct manners, namely in (a) a reorganization of the quasicrystalline description and (b) a more restricted version of this reorganization. Expressions for the cross sections, suitable for numerical evaluation, are calculated for an isotropic-scatterer model of the elastic electron-ion-core interaction. These expressions are functionals of only two statistical quantities: the adsorbate coverage and the pair correlations between adatoms. A lattice-gas model is used to describe the thermodynamic properties of the overlayer thus providing an adequate basis for the consideration of effects on electron scattering associated with the degree of both short- and long-range order in the adsorbate. The expressions for the cross-sections predict characteristic dynamical structure in the intensity and beam profiles associated with the degree of order in the overlayer.