E. Bengu

Surface phase diagrams for the Ag-Ge(111) and Au-Si(111) systems

Abstract Based on results from recent structural studies and an overview of the literature, we propose surface phase diagrams for the Au–Si(111) system in the supermonolayer regime and for the Ag–Ge(111) system in the submonolayer region. In addition, time–temperature–transformation (T–T–T) curves are proposed to represent the metastable structures present in surface phase systems.

Application of Direct Methods to Dynamical Electron Diffraction Data for Solving Bulk Crystal Structures

The crystal structures of two previously unknown bulk phases in the Ga-In-Sn-O system have recently been solved using direct methods applied to electron diffraction intensities. In both cases, phasing of dynamical diffraction intensities clearly indicated the positions of O atoms in the crystal structures. It is shown here that a correlation between the dynamical diffraction amplitudes and the Fourier components of |1 - ψ(r)| enables direct methods using dynamical intensities to restore structural information present in |1 - ψ(r)|. Both the presence of atom-like peaks in |1 - ψ(r)| as well as the emphasis of light atoms are explained using electron channeling theory. Similar results can be expected for any structure consisting of well resolved atomic columns parallel to the zone-axis direction for which data are recorded. With (Ga, In) 2 SnO 5 as a model structure, it is shown that the combination of strongly dynamical electron diffraction with direct methods is a powerful technique for detecting light-atom positions in bulk inorganic crystal structures without the need to grow single crystals.

DIRECT METHODS FOR SURFACES

This paper reviews recent progress in the application of Direct Methods to solve surface structures using surface X-ray or transmission electron diffraction data. The basic ideas of (crystallographic) Direct Methods are presented, as well as the additional problems posed by trying to apply them to surfaces and how they connect to the mathematical theory of projections. Surface crystallography notation is presented, which differs from the widely used LEED notation in that it emphasizes the surface symmetry. This is followed by a description of methods for structure completion and refinement, followed by applications to some experimental systems, both those where the structure was previously known (calibration tests) and a few where it was not, concluding with problems and limitations.

Surface Structures Solved by Direct Methods

For years Direct Methods (DM) have proven to be an invaluable tool for determining bulk crystal structures from diffraction data, and it would now appear that the same can be said for surface structures as well [1]. Surface structures can be determined from surface transmission electron (or X-ray) diffraction data by Maximum Entropy [2] or Minimum Relative Entropy [3] methods. The Minimum Entropy method is combined with a Genetic Algorithm [4,5,6] (GA) global search routine for determining possible solutions. Competition between exploration and optimization is strongly dependent upon how the GA probes the solution space, relying on factors such as mutation rate, population size, number of generated children and the form of the Figure of Merit. Atomic positions are generated using a heavy-atom holography [7] algorithm which includes minor refinement. Solutions are then discriminated based upon physical or chemical considerations, and final atomic positions refined using χ2 minimization.