electron crystallography

Since the pioneering work of W.L. Bragg, P.P. Ewald and M. v. Laue at the beginning of the 20th century structure determination of crystals is the domain of X-ray diffraction. During the past three decades neutron diffraction with its special possibilities to include hydrogen and to distinguish different isotopes has complemented structural analysis. Crystallography with X-ray and neutron diffraction is commonly performed on single crystals, where the intensity of specific reflections is gathered in three dimensions to refine atomic positions and occupancies at highest accuracy. The structure determination by diffraction methods yields all distances and angles between atoms in crystals and is nowadays virtually essential as proof of a new compound. However, prerequisite for all structural studies with the above mentioned methods is the production (crystal growth) or the availability of a good and sufficiently large crystal.
In principle, electron diffraction can be used for crystallographic studies as well. Different from the diffraction of X-rays or neutrons, the interaction of electrons with matter is some orders of magnitude stronger. A resulting advantage of electron diffraction is that only small volumes are required for the investigation. Hence electron crystallography becomes increasingly important, e.g. in solid state chemistry. Single crystal data of products that result as powders and also contain several phases can be obtained. And even so-called X-ray amorphous products with very small crystallites can be structurally characterised.

Since the beginning of scientific studies with the electron microscope in the forties of the 20th century electron diffraction - here: selected area diffraction - is applied to determine the geometry of the crystal lattice and the detection of symmetry elements. Together with convergent beam electron diffraction (CBED [1]) crystallographic point groups can be distinguished and the space group of a crystal can be unambiguously defined. The occupancy of lattice sites with atoms of differing scattering powers (different atomic numbers) can be clarified only by using the diffracted intensities. Until some years ago this was not possible for electrons due to technical reasons. Nowadays electron intensities can be recorded on digital cameras or imaging plates with a high dynamic range and good linearity. Computers, even the cheap ones, became sufficiently powerful to allow computations of the dynamic interaction of electrons with crystals. In 1998 a program package named ELSTRU [2] became available which is able to refine structures on the basis of "dynamic" electron diffraction calculations based on the multi-slice algorithm. With the help of these technical possibilities and the computational methods (hardware and software) quantitative electron crystallography has become feasible.

Structural research with electrons starts qualitatively with the determination of the space group from SAD and CBED images. For that task a sufficiently good knowledge about symmetry elements and the related extinction conditions in diffraction is required. Lattice images (HRTEM) in different zone axis together with principles of structural chemistry are the basis of a first guess of the crystal structure. By refining the atom positions of the proposed structure, the final structure is obtained with quantitative methods of electron crystallography (ELSTRU [2]).

Until now electron diffraction patterns were used which were generated under parallel illumination. Currently we develop a procedure on the basis of diffraction patterns recorded under coherent illumination. Intensities from areas within each diffraction disc are read out as function of the incidence direction and then the intensities are further treated as if they had been generated under parallel illumination. One of the advantages is that the diffraction data can be checked with respect to consistence and reliability: the intensities in certain areas of the discs are uniquely correlated with respect to their incidence direction, and this correlation must be reproduced by the refinement procedure. For convergent illumination, the following criteria can be used for the quality control of the diffraction data:

In case of convergent illumination, small regions with unique crystal thickness can be illuminated. Hence, the different data sets from one convergent beam diffraction pattern have to yield the same thickness in the refinement procedure.
After the parameter of the crystal thickness is fixed the convergent beam diffraction patterns can be simulated, and these can be quantitatively compared with the experimental patterns. The refined crystal thickness as well as the incidence direction of the convergent beam can be checked accurately.
The different incidence directions within one CBED pattern must produce the same resulting "centre of Laue circle".
Only if the refined values of thickness and incidence direction did yield self consistence results, the data are used for structure refinement. For that procedure diffraction data from principal zone axes and selected other zone axes at different crystal thicknesses are used. Thus, an over-determined parameterisation of the diffraction process can be exploited for consistency and reliability checks.

[1] B.F. Buxton, J.A. Eades, J.W. Steeds, G.M. Rackham: The symmetry of electron diffraction zone-axis patterns, Philos. Trans. R. Soc. Lond. 281 (1976) 171-194.
[2] J. Jansen, D. Tang, H. Zandbergen, H. Schenk: MSLS, a least-squares procedure for accurate crystal structure refinement from dynamical electron diffraction patterns, Acta Cryst. A54 (1998) 91-101.

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Electron diffraction patterns of (ZnO)2InGaO3 corresponding to (a) [0001], (c) [010] and (d) [110] zone axis and CBED pattern corresponding to (b) [0001] zone axis. The appearance of forbidden 000l (l = 2n+1) spots in (c) is the result of dynamic scattering effects.


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