For a range of crystalline materials, such as multi-phase powders, polymorphic systems and precipitates and inter-phase crystals, the ability of electron microscopy to identify individual sub-micron phases enables electron diffraction patterns using focussed probes to be recorded without overlap or ambiguity. This great advantage over x-ray or neutron techniques is coupled with the inherent problems of dynamical diffraction brought about by the strong interaction between the electron beam and the underlying crystal potential. Conventional electron diffraction patterns recorded at major zone axes are prone to strong dynamical effects and in general the diffracted intensities in such patterns cannot be used directly to solve crystal structures with conventional direct methods or other similar algorithms. Precession electron diffraction in which a focussed beam is rocked in a hollow cone both above and below the specimen allows zone axis patterns to be recorded whose intensities are less prone to dynamical effects; this is because the beam is never exactly at the zone axis and the intensities are integrated through the Bragg condition. In this paper, we will explore with a number of examples how precession intensities can be used to solve crystal structures, methods to optimise the precession angle and discuss a new charge-flipping algorithm that appears to be quite robust and allow reliable structure solutions to be obtained from precessed diffraction patterns.

Precession electron diffraction (PED) is an experimental approach to reducing the severity of dynamical effects in electron diffraction [1], towards obtaining more interpretable structure indications. By precession the beam in a cone about the zone axis orientation, the number of simultaneously excited beams is reduced as the pattern is averaged over off-axis orientations. PED has been used to successfully solve a large and increasing list of structures (too large to cite here). However, these successes depend on using suitably thin sample areas, for which one can treat intensities approximately as kinematical or quasi-2 beam. For thicknesses beyond this, dynamical perturbations introduce errors in structure indications via direct methods, as well as lowered confidence in refinements. It is thus of interest to devise improved approximations relating PED intensities to underlying crystallographic parameters. In this presentation, some characteristics of PED intensities will be explored using multislice and Bloch wave modeling. It will be shown that PED reduces the complexity of the intensities vs. thickness {I(g,t)}, in a formal statistical sense using principal component analysis. Specifically, the number of parameters necessary to describe all the variation within the set of {I(g,t)} for a given zone axis is reduced with respect to the direct zone axis orientation. Although the PED intensities provide data of reduced complexity compared to zone axis intensities, the degree of simplification does not extend to a simple dependence of I(g,t) on known crystallographic or experimental parameters such as the structure factor amplitude |U(g)| and the spatial frequency |g|. Rather, it will be shown that beams of roughly the same |g| and |U(g)| may exhibit starkly different behavior of the PED intensity vs. thickness. Thus, any simplified model relating I(g,t) to the underlying structure factor amplitudes {|U(g)|} will at least need to consider multiple beam effects, i.e. the entire set of {|U(g)|}. Another feature of PED intensities which will be presented is that precession I(g)'s are less sensitive to structure factor phases than are zone axis intensities obtained using a single zone axis orientation. This suggests the possibility of computing approximate PED patterns without full knowledge of the structure (amplitudes and phases of structure factors). By optimizing a set of structure factor amplitudes {|U(g)|} to fit experiment, the resulting {|U(g)|} might be used to obtain structure solutions by applying well-established direct methods approaches. The details of the phase insensitivity will be presented, including an assessment of which beams in a pattern are likely to be most insensitive to the phases. [1]. R. Vincent. and P. A. Midgely, Ultramicroscopy 53 (1994) 271.[2]. C. S. Own, Dissertation, Northwestern University 2005.[3]. W. Sinkler, C. S. Own and L. D. Marks, Ultramicroscopy 107 (2007] 543.

Crystals < 1μm3 are to small for collecting X-ray diffraction data, even on a synchrotron. However, electron diffraction can be obtained from crystals a million times smaller than this, i.e. down to 10x10x10 nm3. Until now, it has been very difficult to collect complete and high-quality diffraction data by electrons. The electron precession method provides high quality (near-kinematical) data, but is not well-suited for 3D data collection, since each zone axis has to be aligned manually in the TEM and then processed one by one.We are developing the electron rotation method, for collecting complete 3D electron diffraction data. In X-ray crystallography, the beam is fixed while the crystal is rotated 360 degrees about an axis perpendicular to the beam. In electron diffraction, we rotate the beam, while keeping the crystal fixed. A computer-controlled system allows the electron beam to be oscillated along a line (rather than in a circle as in precession) within limits that can be specified in the program. For example, we may collect a set of data in 6 pieces, ranging from -3 to -2, -2 to -1 … +2 to +3 degrees, by letting the electron beam oscillate +/- 0.5 degrees around the middle points of these intervals. The resulting data will be a complete collection of all diffraction spots in a 6 degree wedge of reciprocal space. In order to collect all the unique diffraction data, we need to collect 90 degrees for an orthorhombic crystal; less for crystals of higher symmetries and more for lower symmetries. The maximal width of such a wedge depends on the TEM and can be more or less than 6 degrees. If the data is collected on a CCD camera that can also be controlled by the same computer program, such a wedge of data can be collected in a few seconds. The crystal may then be rotated, using the specimen holder in the EM, and another wedge of data is collected.All the data has to be precessed by a program providing accurate orientation of the start- and end-points of each exposure, all reflection indices hkl must be determined and the integrated intensities measured. Finally, all the data from one crystal must be merged and scaled into one single 3D data set. If radiation damage is not a problem, all the data can be collected on a single crystal. For radiation-sensitive crystals, including proteins, the crystals may only survive for a single frame, making data collection and merging becomes more cumbersome. Such work is being pursued by Georgieva et al. using the precession technique.We hope that this technique will allow a semi-automatic collection of complete 3D electron diffraction data to high resolution (1Å or better for organic and inorganic crystals). With such data, it should be possible to solve unknown structures and refine the atomic co-ordinates to an accuracy similar to what we expect from X-ray diffraction, i.e. within 0.01 Ångström. ReferenceGeorgieva, Jiang, Zandbergen, and Abrahams (2008). Acta Cryst. D64 in press

Structure determination in order to understand physical properties of a material is traditionally done via X-ray diffraction, using single crystals or powder. Although electron diffraction data has advantages compared to X-ray diffraction, i.e. it allows sampling of much smaller crystals and often delivers diffraction information for materials appearing “amorphous” for X-rays, its use for structure determination is less frequent. So far no automated procedure had been implemented for data acquisition and processing, so intensive training was necessary to collect data for structure characterization and use available processing software packages. Recently, we presented a new module providing a quick and easy way to collect automated 3D electron diffraction data from single crystals - automated diffraction tomography (ADT) [1]. The module is set up entirely in STEM mode alternately acquiring µ-STEM images and diffraction patterns using a nano sized probe to access nano crystalline material even if agglomerated or embedded in a matrix. In contrast to the traditional approach, the automated diffraction data is acquired through sequentially tilting a selected crystal around an arbitrary crystallographic axis. Such a data set may miss main crystallographic zones, but as it includes a large number of high-index reflections, the overall number of collected reflections is typically higher than that achieved by manual electron diffraction data collection. Using the ADT module diffraction data is collected statically after each tilt loosing the precise information about the diffracted intensity distribution between the tilt steps. Through precession of the electron beam within an angle equal to the tilt step integrated volume data between the neighboring tilt positions can be obtained. Furthermore, PED data is known to have less dynamical artifacts. Therefore, we combined an electron beam precession unit [2] with the ADT data acquisition module.ADT tilt series were recorded from a variety of materials such as salt (BaSO4), small organic molecules (e.g. pharmaceuticals), MOFs and silicates with and without beam precession. Cell parameter determination and intensity extraction were performed with the self-developed automated diffraction analysis and processing package (ADAP). Subsequent application of direct methods and maximum entropy for “ab intio” structure solution and refinement turned out ot be successful.[1] U. Kolb, T. Gorelik, C. Kübel, M.T. Otten and D. Hubert, Ultramicroscopy 107 (2007) 507; U. Kolb, T. Gorelik, M. T. Otten, Ultramicroscopy 108 (2008) 763.[2] R. Vincent and P. A. Midgley, Ultramicroscopy 53 (1994) 271; C.S. Own, Ph.D. Dissertation, Northwestern University Evanston Illinois, (2005); A. Avilov, K. Kuligin, S. Nicolopoulos, M. Nickolskiy, K. Boulahya, J. Portillo, G. Lepeshov, B. Sobolev, J.P. Collette, N. Martin, A.C. Robins and P. Fischione, Ultramicroscopy 107 (2007) 431.

Oxides are a vast class of materials presenting various properties used in different technological applications. You can find these materials in batteries, fuel cells, high Tc superconductors, multiferroics, etc. Many of the new phases in this field are synthesised at high temperature (HT) and under high pressure (HP). Single crystals suitable for X-ray diffraction are therefore rarely available and powder X-ray diffraction suffers from severe peak overlap. Even in the rare cases where the powders contain only one phase this hinders cell parameter determination and inhibits structure solution. Electron crystallography is then a powerful alternative for solving these structures. In this contribution we give an overview over different structures we have solved by precession electron diffraction (PED). The phases include a simple hexagonal structure (AgCoO₂) synthesised for potential thermoelectric properties, a complex monoclinic structure (PbMnO_2.75) produced at HT/HP in search of new multiferroic materials and a tetragonal structure (Sr₃Bi_0.6Ni_1.4O_x) fabricated in order to enhance the performance of fuel cells. In the main part of this contribution we will, however, concentrate on a typical case of an oxide containing very light atoms.The sample with nominal composition LiTi_1.5Ni_0.5O₄ was synthesised by solid state reaction for use in Li-batteries. The majority phase in this powder containing 3 phases was determined by electron diffraction to be of trigonal symmetry with space group P3c1 or P-3c1 and cell parameters a = 0.505 nm, c = 3.25 nm (hexagonal setting). PED data were extracted from 10 different zone axes yielding 105 independent intensities. The structure solution obtained in the centrosymmetric space group P-3c1 is composed of layers of oxygen octahedra formed by 4 independent oxygen positions. There are 6 independent positions for Ti and Ni occupying the centres of some of the octahedra. Discrimination between Ti and Ni proved to be difficult from theses results. Two independent positions were found for the Li ions equally occupying oxygen octahedra. The solution is robust against changes in the process parameters always yielding the same positions including those for Li. Since crystal chemistry suggested either sites with a Ti/Ni disorder or a non centrosymmetric structure we also attempted a structure solution in the non centrosymmetric space group P3c1. Here the solution contained 12 independent Ni / Ti positions, 7 independent O positions and 4 independent Li positions. Comparing these positions to those obtained in the centrosymmetric case shows that they are identical even for the light Li ions. A high resolution synchrotron radiation diffraction experiment was carried out on the powder at the ESRF in Grenoble, France. The measured intensities were consistent with our results from PED. Due to the presence of the two impurity phases the solution could not be improved from the structure determined by electron crystallography.