Accurate structure refinement from 3D electron diffraction data

Structure determination from electron diffraction data has seen an enormous progress over the past few years. At present, complex structures with hundreds of atoms in the unit cell can be solved from electron diffraction using the concept of electron diffraction tomography (EDT), possibly combined with precession electron diffraction (PED) [1]. Unfortunately, the initial model is typically optimized using the kinematical approximation to calculate model diffracted intensities. This approximation is quite inaccurate for electron diffraction and leads to high figures of merit and inaccurate results with unrealistically low standard uncertainties. The obvious remedy to the problem is the use of dynamical diffraction theory to calculate the model intensities in structure refinement. This technique has been known and used before, but it has not become very popular, because good fits could be obtained only for sufficiently perfect and sufficiently thin crystals. It has been shown recently on several zone-axis patterns [2] that the quality of the refinement can be improved by using precession electron diffraction. In the present contribution we demonstrate that the same approach can be successfully used to refine crystal structures against non-oriented patterns acquired by EDT combined with PED (PEDT in short). Because the PEDT technique provides three-dimensional diffraction information, it can be used for a complete structure refinement. Several test examples demonstrate that the dynamical structure refinement yields better figures of merit and more accurate results than the refinement using kinematical approximation.

Electron Diffraction vs aperiodic crystal: from indexation to structure solution

Can we solve aperiodic structures using intensities from electron diffraction? Yes! How? No mystery about it: the data analysis and the tools used for structure solution are essentially the same as the ones used in X-ray crystallography. The trick actually lies in new approaches used in electron crystallography. In analogy to X-ray diffraction, the so-called Electron Diffraction Tomography (EDT) [1] corresponds to a phi-scan data collection on a single crystal. There lies one major advantage of this technique: a powder sample is easily converted to infinitely large number of single crystals for electron diffraction. In case of aperiodic crystals this makes the difference over X-ray or neutron powder diffraction where, often, the lack of peaks clearly assignable to satellite reflections prevents any indexation and further analysis of the structure [2]. EDT allows for an accurate estimation of the modulation vector and a good guess of the super space group. These informations can be advantageously used as an input for X-ray or neutron powder diffraction. Not limited to indexation, EDT combined with Precession Electron Diffraction (PED) [3], offers a unique tool for solving modulated structures when crystals suitable for X-ray diffraction are missing. By limiting the paths for multiple scattering, PED makes the diffracted intensities closer to kinematical approximation so that they can be used efficiently for structure solution. Regarding aperiodic crystals, the superspace electron density map, generated as an output of the charge flipping algorithm used in Superflip, can be interpreted to obtain a structural model. This will be illustrated on a series of layered materials closely related to the Aurivillius phases belonging to the pseudo-binary Bi5Nb3O15-ABi2Nb2O9 (A=Pb, Sr, Ca, Ba). Limitations and possible combination with powder diffraction patterns will be discussed.