Advances in direct and diffraction methods for surface structural determination

Abstract

I describe recent advances in low-energy electron diffraction holography and photoelectron diffraction holography. These are direct methods for determining the surface structure. I show that for LEED and PD spectra taken in an energy and angular mesh, the relative phase between the reference wave and the scattered wave has a known geometric form if the spectra are always taken from within a small angular cone in the near backscattering direction. By using data in the backscattering small cone at each direction of interest, a simple algorithm is developed to invert the spectra and extract object atomic positions with no input of calculated dynamic factors. I also describe the use of a convergent iterative method of PD and LEED. The computation time of this method scales as N 2, where N is the dimension of the propagator matrix, rather than N 3 as in conventional Gaussian substitutional methods. Both the Rehr–Albers separable-propagator cluster approach and the slab-type non-separable approach can be cast in the new iterative form. With substantial savings in computational time and no loss in numerical accuracy, this method is very useful in applications of multiple scattering theory, particularly for systems involving either very large unit cells (>300 atoms) or where no long-range order is present.