Phase retrieval methods for surface crystallography

The key to understanding, and perhaps more importantly predicting, the detailed properties of materials and surfaces is an accurate model of the atomic structure of the surface. Everything from the flow of current through a transistor in an integrated circuit, to the function of the catalyst in a car's catalytic converter depends on the atomic structure of the surface under consideration.;Determination of the structures of surfaces on an atomic scale is carried out through several experimental methods. In the case of crystal surfaces, diffraction methods are frequently employed. These methods exploit the long-range periodicity of a crystal and the predictable interference of scattered waves due to this periodicity to detect the atomic structure of the material. In these techniques the intensities of the scattered radiation (electromagnetic or particle) are measured although it is in the relative phases of the scattered waves where much of the structural information is contained. Unfortunately the loss of the mostly immeasurable phases leads to time consuming and tedious methods for analysis of diffraction data which depend on models proposed by the investigator. The work presented here is a method by which this phase information can be recovered given just the measured intensities and the presumed known, bulk crystalline structure to enable the model-independent determination of the atomic-scale structure of the surface.;This work has been carried out for two different diffraction methods with surface sensitivity. The first is surface x-ray diffraction (SXRD) for which the method will be described in detail. The second is the case of low energy electron diffraction (LEED) to which the method developed in the first case will be applied through identification of justifiable analogies between the two techniques. Results from simulated data are presented from several different classes of surface structures.