Structure refinement using precession electron diffraction tomography and dynamical diffraction: theory and implementation


Structure solution and refinement from single-crystal X-ray diffraction data has become a standard approach for determination of crystal structures. On the other hand, electron diffraction used to be applied for the same purpose much more rarely, although numerous successful solutions were reported (Vainshtein, 1964[Vainshtein, B. K. (1964). Electron Diffraction Structure Analysis. Oxford: Pergamon Press.]; Cowley, 1992[Cowley, J. M. (1992). Electron Diffraction Techniques, Vols 1 and 2. Oxford University Press.]; Dorset, 1995[Dorset, D. L. (1995). Structural Electron Crystallography. New York: Plenum Press.]). The situation has been changing rapidly in the past decade with the advent of electron diffraction tomography (EDT) methods (Kolb et al., 2007[Kolb, U., Gorelik, T., Kuebel, C., Otten, M. T. & Hubert, D. (2007). Ultramicroscopy, 107, 507-513.], 2008[Kolb, U., Gorelik, T. & Otten, M. T. (2008). Ultramicroscopy, 108, 763-772.]; Wan et al., 2013[Wan, W., Sun, J., Su, J., Hovmöller, S. & Zou, X. (2013). J. Appl. Cryst. 46, 1863-1873.]), possibly combined with precession electron diffraction (PED) (Vincent & Midgley, 1994[Vincent, R. & Midgley, P. A. (1994). Ultramicroscopy, 53, 271-282.]; Mugnaioli et al., 2009[Mugnaioli, E., Gorelik, T. & Kolb, U. (2009). Ultramicroscopy, 109, 758-765.]). With these methods, a large number of increasingly complex structures were solved and refined. However, all the structure refinements were performed using kinematical approximation for the calculation of model intensities. Kinematical approximation implies that diffracted intensity associated with diffraction vector [{\bf h}] is proportional to the amplitude squared of the corresponding structure factor [F_{\bf h}]. It is, however, well known that this approximation has only limited validity for electron-diffraction data. Measures have been taken to minimize the departure of the electron-diffraction data from the kinematical limit by integrating the diffracted intensities across several beam orientations (using precession electron diffraction or fine-step slicing in rotation electron diffraction). Despite these measures, the refinements using this approximation are difficult, and yield high figures of merit and low accuracy of the refined structure parameters.

An image of a nanotransfer of the Ni2Si from the transmission electron microscope with the indicated portion that was used for analysis. Atomic positions in the basic cell structure of this nanowire were determined by the new method with an accuracy better than 1 µm (10-12 m), ie about 0.5% of the interatomic distance. The nanowire diameter is 15 nm.