Exploiting reciprocal space : Electron diffraction, textures and precession

Abstract: Electron crystallography emerges as a new tool for accurate structure determination of very small crystals. In order to exploit the full potential of electron diffraction, the methods for data acquisition and processing have to be developed towards the high standards of X-ray crystallography. Spot diffraction patterns give complete separation of reflections and provide two-dimensional data sets. Separation of reflections occurs also in texture patterns; the whole or almost whole reciprocal lattice is represented on them in two dimensions. In order to speed up texture pattern analysis and improve the accuracy, the program TexPat was developed for quantification of texture patterns. It introduces new approaches for automated detection of centre and symmetry axes and simplifies the process of indexing and estimating the intensities of all reflections.The precession technique, developed by Vincent and Midgley at the University of Bristol in 1994, has become available to the TEM users because of recent hardware implementations that allow data acquisition of sufficient quality for structure determination. Dynamical interactions can be effectively reduced using the precession method, and the intensity data can be treated within the kinematical approximation. However, a deeper understanding of the theory is necessary. A program eMap has been developed which performs kinematical and dynamical simulations of precession electron diffraction patterns. A set of algorithms was introduced for indexing of precession patterns with HOLZ present, estimation of three-dimensional lattice parameters and crystal symmetry deduction using both ZOLZ and HOLZ. All developed algorithms were implemented in the diffraction simulation program eMap and electron diffraction analysis program ELD. Both oblique texture and precession electron diffraction patterns provide intensities of high quality, which can be treated kinematically for further crystal structure solution.However, there is also the fundamental phase problem in crystallography. For quasicrystal approximants, the strong reflections approach allows overcoming this problem and deducing structural models from already known structures. In order to perform the analysis of quasicrystal approximant structures in real and reciprocal space, the eMap program was used. The operations included in the program allow the calculation of three-dimensional electron density or potential maps; peak search, calculation of theoretical structure factors both for X-rays and electrons (kinematical and dynamical); visualization of reciprocal space and phase values of reflections in specified colouring scheme.