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Precession Electron Diffraction – a Topical Review ISSN 2052-2525 Paul A

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Precession Electron Diffraction – a Topical Review ISSN 2052-2525 Paul A topical reviews IUCrJ Precession electron diffraction – a topical review ISSN 2052-2525 Paul A. Midgley* and Alexander S. Eggeman PHYSICSjFELS Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, England. *Correspondence e-mail: [email protected] Received 20 August 2014 In the 20 years since precession electron diffraction (PED) was introduced, it Accepted 9 October 2014 has grown from a little-known niche technique to one that is seen as a cornerstone of electron crystallography. It is now used primarily in two ways. The first is to determine crystal structures, to identify lattice parameters and Edited by I. Robinson, UCL, UK symmetry, and ultimately to solve the atomic structure ab initio. The second is, † through connection with the microscope scanning system, to map the local orientation of the specimen to investigate crystal texture, rotation and strain at the nanometre scale. This topical review brings the reader up to date, highlighting recent successes using PED and providing some pointers to the Keywords: precession electron diffraction (PED); future in terms of method development and how the technique can meet some of electron crystallography; electron techniques; electron-based structure analysis the needs of the X-ray crystallography community. Complementary electron techniques are also discussed, together with how a synergy of methods may provide the best approach to electron-based structure analysis. 1. Introduction A modern (scanning) transmission electron microscope, or (S)TEM, is a remarkably versatile and powerful instrument. With the advent of aberration correctors, monochromators and computer control, the electron microscope is able to form not only ultra-high resolution images but also two- and three- dimensional maps of composition [using electron energy-loss spectroscopy (EELS) and energy-dispersive X-ray spectro- metry (EDS)] and of electromagnetic fields (through electron holography), and can follow time-resolved phenomena at the sub-picosecond timescale (Midgley & Thomas, 2014). Electron diffraction patterns are easily formed by making the final image plane conjugate with the back focal plane of the objective lens using post-specimen lenses. The strong Coulombic interaction between the electron beam (typically with energies 80–300 keV) and the electrostatic potential of the sample leads to diffraction intensities that are, in general, exquisitely sensitive to the underlying crystal symmetry and the thickness of the specimen. For typical samples and thick- nesses studied, this strong interaction leads to a high prob- ability of multiple (or dynamic) scattering and thus diffracted intensities that cannot, in general, be interpreted within a simple kinematic framework. For structure solution this is problematic, as all standard solution algorithms rely on the fact that the recorded intensities are proportional to the (square of the) structure factor for that reflection and, just as importantly, that the intensity of one reflection does not depend on the structure factor of other reflections. For many years, using electron diffraction intensities to ‘solve’ crystal structures relied on being able first to guess, or to have prior knowledge of, a likely model structure and then to refine that structure (and often the sample thickness), 126 doi:10.1107/S2052252514022283 IUCrJ (2015). 2, 126–136 topical reviews Figure 1 (a) A schematic ray diagram for precession electron diffraction (PED), illustrating the rocking/de-rocking action of the beam before and after the specimen. (b)–(e) Illustrations of how precession alters the recorded diffracted intensities, here from the [001] zone axis of Er2Ge2O7:(b) without precession, (c) with a precession angle of 20 mrad, (d) with a precession angle of 47 mrad. The pattern of diffracted intensities seen in (d) is similar to that seen in the kinematic simulation shown in part (e). taking dynamic effects into account, to best match computed used (with care) to determine structures ab initio using diffracted intensities with experimental ones. Whilst this led to conventional X-ray phasing methods and structure solution many successful refinements, including not only atomic posi- programs. At first this seems surprising, given the inherent tions (Vincent et al., 1984) but also refinements of charge dynamic effects in any electron diffraction pattern. However, bonding densities (Midgley & Saunders, 1996; Zuo et al., as will be discussed further below, even though individual 1999), ab initio structure determination was problematic. intensities are not kinematic, the ensemble of intensities in a To tackle that problem, precession electron diffraction PED pattern behaves in a ‘kinematic-like’ fashion, at least (PED) was introduced 20 years ago as a way of recording sufficiently so to enable successful structure solution. electron diffraction intensities more suited to structure solu- The use of PED has grown within the electron microscopy tion than those acquired with conventional methods (Vincent community and, importantly, is now seen as a method that & Midgley, 1994). As shown in Fig. 1, the electron beam is complements those of X-ray diffraction, especially when rocked in a hollow cone (at a fixed angle to the optic axis) examining multi-phase samples, disordered crystals or other above the sample and then de-rocked below the sample, the systems that, for whatever reason, may not be amenable to net effect being equivalent to precessing the sample about a conventional X-ray crystallographic analysis. fixed electron beam parallel to the optic axis. The resultant In this topical review, we focus on developments in the pattern is composed of many more reflections than would be understanding of why PED enables structure solution, on the the case for an unprecessed beam, and these PED reflections best use of the technique and on its application across a wide have intensities that are determined by integrating through range of specimens and structures. Since its inception 20 years the Bragg condition of each reflection. In early papers ago, PED has become an invaluable tool, not only for the (Vincent & Midgley, 1994), the high-order Laue zone (HOLZ) determination of unknown crystal structures but also in aiding reflections were used to determine (conditional) Patterson the analysis of local microstructure, particularly through a maps and then atomic positions, but it was soon realised that combination of PED and beam scanning to map relative even the zero-order Laue zone (ZOLZ) reflections could be crystal orientation, texture, strain etc. The brevity and topical IUCrJ (2015). 2, 126–136 Midgley and Eggeman PED 127 topical reviews focus of the review preclude a detailed exposition of the history of PED and how it complements other electron diffraction methods, but an interested reader may wish to consult a longer paper published by the authors two years ago (Eggeman & Midgley, 2012b). 2. Recent developments for structure solution Throughout the past ten years or so there has been a steady stream of papers using PED to solve structures that could not be solved through conventional X-ray (or neutron) methods. In parallel, there has been a great deal of work undertaken to try to establish the best conditions for PED, especially in terms of precession angle. However, almost uniformly across all the PED structure solutions has been the fact that, whilst the structures first solved, and then refined, are plausible, the R factors used to ascertain the quality of the structure have remained high (typically 0.20–0.30), far higher than most equivalent X-ray refinements. Figure 2 Early PED work suggested that the use of ZOLZ reflections The weighted residual value wR2 as a function of tilt angle away from the was nearly always going to lead to poor refinements because of ideal zone-axis orientation for Si h110i and as a function of precession inherent dynamic effects, prevalent in low-order reflections angle from 0 (green) to 3 (mauve), indicating the reduced sensitivity of but less so in the HOLZ. More detailed analysis of the PED data to small misalignments. Reproduced from Palatinus et al. (2013). behaviour of ZOLZ reflections showed that, whilst individual reflections could deviate a great deal from their kinematic value, for sufficiently high precession angles their intensities tend to increase monotonically over a relatively wide thick- 2013): in tests on known structures, the R factors dropped ness range, and the variations from reflection to reflection from 0.20–0.30 using a simple kinematic refinement to 0.05– seen in the PED pattern remain relatively constant (Eggeman 0.08 using a full dynamic treatment. Work in the 1990s and & Midgley, 2012b). In other words, broadly speaking, strong later, using convergent beam electron diffraction (CBED) reflections remain strong, weak reflections remain weak. This data to determine, for example, charge bonding density, was constancy leads to valid structure solutions, but comparison of able to reach R factors of just a few per cent, but accurate individual intensities (as performed in conventional refine- values of orientation and thickness were essential for such ment) will lead to large R values. high-quality refinements. Inaccurate refinement of thickness The integration across the Bragg condition, which lies at the could lead to spurious results. With PED, it is clear that the heart of the PED technique, has led some to use a two-beam pattern of intensities across the ensemble of reflections is, in dynamic
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