Surface structures by direct transform of electron diffraction patterns

We find that electron diffraction patterns can be directly inverted to provide three-dimensional atomic structures for the system studied. Depending on the scattering process, either holography or a Patterson inversion scheme is used. For diffraction patterns which were generated from a localized emitter source or predominantly by an inelastic-scattering feature like low-energy Kikuchi electrons, holography inversion is needed. The information obtained from Kikuchi electron holography includes the building blocks on the surface and their relative position to the atoms below the surface layer. On the other hand, for diffraction patterns generated predominantly by an elastic-scattering feature like low-energy electron diffraction (LEED), a Patterson inversion is needed. The information obtained from the Patterson transform of the LEED I(E) curves is the relative positions of surface atoms to the atoms in underlying layers; no intra-layer information can be extracted with this method. High-fidelity and artifact-free three-dimensional atomic structures obtained by inversion of low-energy Kikuchi electron patterns and low-energy electron diffraction curves are presented. The results from the two inversion methods are complementary and can be used to construct or to discriminate the surface atomic structural models. The future of these direct methods by inverting diffraction patterns is discussed. (author)