Precession electron diffraction using a digital sampling method

A software-based method for collecting precession electron diffraction (PED) patterns is described. The PED patterns are obtained on a computer controlled transmission electron microscope. A series of electron diffraction (ED) patterns are collected as still ED frames at equal intervals, while the electron beam is precessed by one period (360°) around the optical axis. A PED pattern is obtained by combining the different ED frames, which resembles the sampling of a conventional PED pattern. Since intermediate ED frames are collected, it is possible to perform different post-processing strategies on the ED data. This can be used for geometric corrections to obtain accurate integrated intensities. The alignments and data collection are fully automated and controlled by software. The data quality is comparable to what can be achieved using specialized hardware for precession. The PED data can be used for structure solution and refinement with reasonably good R-values.     

A quantitative analysis of the cone-angle dependence in precession electron diffraction

Precession electron diffraction (PED) is a technique which is gaining increasing interest due to its ease of use and reduction of the dynamical scattering problem in electron diffraction. To further investigate the usefulness of this technique, we have performed a systematic study of the effect of precession angle on the mineral andalusite where the semiangle was varied from 6.5 to 32 mrad in five discrete steps. The purpose of this study was to determine the optimal conditions for the amelioration of kinematically forbidden reflections, and the measurement of valence charge density. We show that the intensities of kinematically forbidden reflections decay exponentially as the precession semiangle () is increased. We have also determined that charge density effects are best observed at moderately low angles (6.5–13 mrad) even though PED patterns become more kinematical in nature as the precession angle is increased further.     

Application of a 2-beam model for improving the structure factors from precession electron diffraction intensities

A 2-beam model is used to simulate precession electron diffraction (PED) intensities. It is shown that this model can be inverted with minimal knowledge of the underlying crystal structure, permitting structure factor amplitudes to be deduced directly from measured intensities within the 2-beam approximation. This approach may be used in conjunction with direct methods to obtain correct, kinematically interpretable structure indications for data sets from relatively thin crystals (less than approximately 400A), and an experimental example based on (Ga,In)(2)SnO(5) is presented. The failure of this approach at large thickness is illustrated by an additional data set for MFI zeolite. The 2-beam approximation provides a simple model for PED intensities, and inversion using this model shows advantages over a kinematical approximation. It is however too rough approximation to be of general use and ultimately it is to be hoped that more accurate models with similar ease of use can be derived to treat PED data.     

Aberration-compensated large-angle rocking-beam electron diffraction

The application of convergent beam electron diffraction (CBED) to determine symmetry, refine structure factors, and measure specimen thickness requires rather thick specimen and is very difficult or even impossible in the case of large unit cell materials. The large-angle rocking-beam electron diffraction (LARBED) technique introduced in this paper gives access to the kind of experimental data contained in CBED patterns but over a much larger angular range. In addition to symmetry determination and thickness measurement even for thin samples this technique also allows, in principle, very accurate measurements of structure factors. Similar to precession electron diffraction (PED), LARBED uses the illumination tilt coils to sequentially change the angle of incidence of the electron beam over a very large range. I will present results obtained by a recently developed self-calibrating acquisition software which compensates for aberration-induced probe shifts during the acquisition of LARBED patterns and keeps the probe within a few nm, while covering a tilt range from 0 to 100 mrad. This paper is dedicated to Prof. John C. H. Spence on the occasion of his 65th birthday.     

“Ab initio” structure solution from electron diffraction data obtained by a combination of automated diffraction tomography and precession technique

Using a combination of our recently developed automated diffraction tomography (ADT) module with precession electron technique (PED), quasi-kinematical 3D diffraction data sets of an inorganic salt (BaSO₄) were collected. The lattice cell parameters and their orientation within the data sets were found automatically. The extracted intensities were used for “ab initio” structure analysis by direct methods. The data set covered almost the complete set of possible symmetrically equivalent reflections for an orthorhombic structure. The structure solution in one step delivered all heavy (Ba, S) as well as light atoms (O). Results of the structure solution using direct methods, charge flipping and maximum entropy algorithms as well as structure refinement for three different 3D electron diffraction data sets were presented.     

Structure solution with three-dimensional sets of precessed electron diffraction intensities

The use of the precession technique for obtaining three-dimensional (3D) sets of electron diffraction intensities suitable for structure solution is discussed. The minerals uvarovite and ?kermanite have been used as testing structures. The electron diffraction data sets obtained on these samples retain an acceptable linear relation with calculated structure factor amplitudes. The quality of these data is suitable to solve both structures using direct methods opening the possibility to use 3D precession ED data for solving unknown mineral structures.     

Precession technique and electron diffractometry as new tools for crystal structure analysis and chemical bonding determination

We have developed a new fast electron diffractometer working with high dynamic range and linearity for crystal structure determinations. Electron diffraction (ED) patterns can be scanned serially in front of a Faraday cage detector; the total measurement time for several hundred ED reflections can be tens of seconds having high statistical accuracy for all measured intensities (1-2%). This new tool can be installed to any type of TEM without any column modification and is linked to a specially developed electron beam precession "Spinning Star" system. Precession of the electron beam (Vincent-Midgley technique) reduces dynamical effects allowing also use of accurate intensities for crystal structure analysis. We describe the technical characteristics of this new tool together with the first experimental results. Accurate measurement of electron diffraction intensities by electron diffractometer opens new possibilities not only for revealing unknown structures, but also for electrostatic potential determination and chemical bonding investigation. As an example, we present detailed atomic bonding information of CaF(2) as revealed for the first time by precise electron diffractometry.     

Orientation and phase mapping in the transmission electron microscope using precession‐assisted diffraction spot recognition: state‐of‐the‐art results

A recently developed technique based on the transmission electron microscope, which makes use of electron beam precession together with spot diffraction pattern recognition now offers the possibility to acquire reliable orientation/phase maps with a spatial resolution down to 2 nm on a field emission gun transmission electron microscope. The technique may be described as precession‐assisted crystal orientation mapping in the transmission electron microscope, precession‐assisted crystal orientation mapping technique–transmission electron microscope, also known by its product name, ASTAR, and consists in scanning the precessed electron beam in nanoprobe mode over the specimen area, thus producing a collection of precession electron diffraction spot patterns, to be thereafter indexed automatically through template matching. We present a review on several application examples relative to the characterization of microstructure/microtexture of nanocrystalline metals, ceramics, nanoparticles, minerals and organics. The strengths and limitations of the technique are also discussed using several application examples.     

An efficient approach to characterize pseudo-merohedral twins by precession electron diffraction: Application to the LaGaO3 perovskite

Pseudo-merohedral twins are frequently observed in crystals displaying pseudo-symmetry. In these crystals, many [u v w] zone axis electron diffraction patterns are very close and can only be distinguished from intensity considerations. On conventional diffraction patterns (selected-area electron diffraction or microdiffraction), a strong dynamical behaviour averages the diffracted intensities so that only the positions of the reflections on a pattern can be considered. On precession electron diffraction patterns, the diffracted beams display an integrated intensity and a “few-beam” or “systematic row” behaviour prevails which strongly reduces the dynamical interactions. Therefore the diffracted intensity can be taken into account. A procedure based on observation of the weak extra-reflections connected with the pseudo-symmetry is given to identify without ambiguity any zone axis. It is successfully applied to the identification and characterization of {1 2 1} reflection twins present in the LaGaO₃ perovskite.     

A precession electron diffraction study of α, β phases and Dauphiné twin in quartz

Precession electron diffraction is used to distinguish between the hexagonal β high-temperature and the trigonal α low-temperature phases of SiO₂ quartz. The structures just differ by a kink of the SiO₄ tetrahedra arranged along spiraling chains, which induces a loss of the two-fold axis and subsequent twinning in the low-temperature phase. Conventional selected-area electron diffraction (SAED) does not enable the phases distinction since only the intensity of reflections is different. It becomes possible with precession that reduces the dynamical interactions between reflections and makes their intensity very sensitive to small variations of the electron structure factors. Distinction between the twinned individuals in the low-temperature phase is then easily made and the twin law is characterized using stereographic projections. The actual symmetry of precessed zone axis patterns is also examined in detail. Using dynamical intensity simulations, it is shown that under certain thickness conditions, the diffraction class symmetry can be observed on selected area patterns that are to be used in the case of beam sensitive materials such as quartz.     

Consistent indexing of a (set of) single crystal SAED pattern(s) with the ProcessDiffraction program

A computer program called "ProcessDiffraction" helps indexing a set of single crystal selected area electron diffraction (SAED) patterns by determining which of the presumed structures can fit all the measured patterns simultaneously. Distances and angles are measured in the digitalized patterns with a graphical tool by clicking on the two shortest non-collinear vectors (spots), using user-supplied calibration data. Centers of the spots and center of the pattern are optionally refined by the program. Suggested individual indexing solutions (consistent with an assumed unit cell) are listed by the program for each pattern. Simulated patterns are also consulted to check if the shortest calculated distances coincide with measured ones. Common solutions for the set are selected by checking the angles between the suggested zone axes against the angles between the experimental goniometer settings. The indexing process is manually controlled by selecting the candidate structures (one-by-one) for indexing and by specifying the tolerances for d-values, plane angles and zone angles. Patterns of any crystal system can be indexed successfully. Although error bars are larger in electron diffraction than in X-ray diffraction (XRD), frequently, many unrelated indexings are possible for any one electron diffraction pattern (irrespective of the indexing method), a set of SAED patterns can generally be indexed unambiguously, i.e. the three-dimensional reciprocal space can be identified correctly. Two other tools also help planning tilting experiments: zones along a plane can be listed (with their angles extended from a pre-selected zone in that plane) and zones lying at a given angle (specified with a tolerance) from a zone can also be identified (as they are situated between two cones). Another tool searches the XRD database directly either for advice on possible structures for a composition or to help calibration.     

Contribution of electron precession to the study of perovskites displaying small symmetry departures from the ideal cubic ABO3 perovskite: applications to the LaGaO3 and LSGM perovskites

Electron microscopy and electron diffraction are well adapted to the study of the fine‐grained, faulted pure and doped LaGaO₃ and LSGM perovskites in which the latter is useful for fuel cell components. Because these perovskites display small symmetry departures from an ideal cubic ABO₃ perovskite, many conventional electron diffraction patterns look similar and cannot be indexed without ambiguity. Electron precession can easily overcome this difficulty mainly because the intensity of the diffracted beams on the precession patterns is integrated over a large deviation domain around the exact Bragg condition. This integrated intensity can be trusted and taken into account to identify the ‘ideal’ symmetry of the precession patterns (the symmetry which takes into account both the position and the intensity of the diffracted beams). In the present case of the LaGaO₃ and LSGM perovskites, the determination of the ‘ideal’ symmetry of the precession patterns is based on the observation of weak ‘superlattice’ reflections typical of the symmetry departures. It allows an easy and sure identification of any zone axes as well as the correct attribution of hkl indices to each of the diffracted beams. Examples of applications of this analysis to the characterizations of twins and to the identification of the space groups are given. This contribution of electron precession can be easily extended to any other perovskites or to any crystals displaying small symmetry departures.     

Direct electron crystallographic determination of zeolite zonal structures

The prospect for improving the success of ab initio zeolite structure investigations with electron diffraction data is evaluated. First of all, the quality of intensities obtained by precession electron diffraction at small hollow cone illumination angles is evaluated for seven representative materials: ITQ-1, ITQ-7, ITQ-29, ZSM-5, ZSM-10, mordenite, and MCM-68. It is clear that, for most examples, an appreciable fraction of a secondary scattering perturbation is removed by precession at small angles. In one case, ZSM-10, it can also be argued that precession diffraction produces a dramatically improved 'kinematical' data set. There seems to no real support for application of a Lorentz correction to these data and there is no reason to expect for any of these samples that a two-beam dynamical scattering relationship between structure factor amplitude and observed intensity should be valid. Removal of secondary scattering by the precession mode appears to facilitate ab initio structure analysis. Most zeolite structures investigated could be solved by maximum entropy and likelihood phasing via error-correcting codes when precession data were used. Examples include the projected structure of mordenite that could not be determined from selected area data alone. One anomaly is the case of ZSM-5, where the best structure determination in projection is made from selected area diffraction data. In a control study, the zonal structure of SSZ-48 could be determined from selected area diffraction data by either maximum entropy and likelihood or traditional direct methods. While the maximum entropy and likelihood approach enjoys some advantages over traditional direct methods (non-dependence on predicted phase invariant sums), some effort must be made to improve the figures of merit used to identify potential structure solutions.     

Is precession electron diffraction kinematical? Part II: A practical method to determine the optimum precession angle

A series of experiments was undertaken to investigate the kinematical nature of precession electron diffraction data and to gauge the optimum precession angle for a particular system. Kinematically forbidden reflections in silicon were used to show how a large precession angle is needed to minimise multi-beam conditions for specific reflections and so reduce the contribution from dynamical diffraction. Small precession angles were shown to be detrimental to the kinematical nature of some low-order reflections. By varying precession angles, precession electron diffraction data for erbium pyrogermanate were used to investigate the effect of dynamical diffraction on the output from structure solution algorithms. A good correlation was noted between the precession angle at which the rate of change of relative intensities is small and the angle at which the recovered structure factor phases matched the theoretical kinematical structure factor phases.     

Investigation of Si–Au vicinal surfaces using scanning tunnelling microscopy and reflection high-energy electron diffraction

Silicon vicinal surfaces can be successfully used as substrates for the preparation of one‐dimensional nanostructures. The quality of the structures prepared may be controlled using scanning tunnelling microscopy, as shown in this work. Additionally, it is possible to obtain valuable information using reflection high‐energy electron diffraction. A typical way of employing reflection high‐energy electron diffraction is to observe patterns of scattered electrons on a screen. However, it is possible to obtain more detailed information on the arrangement of atoms at the surface if azimuthal plots are collected. Azimuthal plots are measured by recording the intensity of specularly reflected electrons during the rotation of the sample around an axis perpendicular to its surface. So far, only flat surfaces have been examined in such a way. In this work, it is shown that such data, containing interesting features, can also be collected for vicinal surfaces.     

Precession electron diffraction: observed and calculated intensities

Theory and algorithms have been developed for performing kinematical and dynamical two-beam and multibeam dynamical simulations of precession electron diffraction patterns. Intensities in experimental precession patterns have been quantified and are shown to be less dynamical.     

Crystal structure solution via precession electron diffraction data: The BEA algorithm

The statistical features of the amplitudes obtained via precession electron diffraction have been studied, with particular concern with their effects on direct phasing procedures. A new algorithm, denoted by BEA, is described: according to it, the average amplitude of the symmetry equivalent reflections is used in the Direct Methods step. Once an even imperfect structural model is available, the best amplitude among the equivalent reflections is used to improve the model. It is shown that BEA is able to provide more complete structural models, to make the phasing process more straightforward and to end with crystallographic residual much better than those usually obtained by electron diffraction.     

Crystal structure solution via precession electron diffraction data: the BEA algorithm

The statistical features of the amplitudes obtained via precession electron diffraction have been studied, with particular concern with their effects on direct phasing procedures. A new algorithm, denoted by BEA, is described: according to it, the average amplitude of the symmetry equivalent reflections is used in the Direct Methods step. Once an even imperfect structural model is available, the best amplitude among the equivalent reflections is used to improve the model. It is shown that BEA is able to provide more complete structural models, to make the phasing process more straightforward and to end with crystallographic residual much better than those usually obtained by electron diffraction.     

Precession electron diffraction‐assisted crystal phase mapping of metastable c‐GaN films grown on (001) GaAs

The control growth of the cubic meta‐stable nitride phase is a challenge because of the crystalline nature of the nitrides to grow in the hexagonal phase, and accurately identifying the phases and crystal orientations in local areas of the nitride semiconductor films is important for device applications. In this study, we obtained phase and orientation maps of a metastable cubic GaN thin film using precession electron diffraction (PED) under scanning mode with a point‐to‐point 1 nm probe size beam. The phase maps revealed a cubic GaN thin film with hexagonal GaN inclusions of columnar shape. The orientation maps showed that the inclusions have nucleation sites at the cubic GaN {111} facets. Different growth orientations of the inclusions were observed due to the possibility of the hexagonal {0001} plane to grow on any different {111} cubic facet. However, the generation of the hexagonal GaN inclusions is not always due to a 60° rotation of a {111} plane. These findings show the advantage of using PED along with phase and orientation mapping, and the analysis can be extended to differently composed semiconductor thin films. Microsc. Res. Tech. 77:980–985, 2014. © 2014 Wiley Periodicals, Inc.