eMap and eSlice: a software package for crystallographic computing

EDIC intensity correction of electron diffraction

Transmission electron microscopy (TEM) has recently become indispensable in determining crystal structures. The location of atoms in crystals can be determined using electron diffraction (ED) intensity data series if the diffracted intensities are directly proportional to the square of the structure factor (|Fhkl|2). However, due to the crystal thickness, the used electron wavelength and the potential misalignment of the measured crystal the detected intensities differ from the ideal values. A method, Electron Diffraction Intensity Correction (EDIC), and a computer program have been developed to recover the ideal |Fhkl|2 proportional intensities from experimental data for kinematic scattering, for further structure studies.

Structure solution of the Al69.2Cu20Cr10.8 ϕ phase

The stable ϕ phase that forms below ∼923 K around the Al69.2Cu20.0Cr10.8 composition was found to be hexagonal [P63, a = 11.045 (2), c = 12.688 (2) Å] and isostructural to the earlier reported Al6.2Cu2Re X phase [Samuha, Grushko & Meshi (2016). J. Alloys Compd. 670, 18–24]. Using the structural model of the latter, a successful Rietveld refinement of the XRD data for Al69.5Cu20.0Cr10.5 was performed. Both ϕ and X were found to be structurally related to the Al72.6Cu11.0Cr16.4 ζ phase [P63/m, a = 17.714, c = 12.591 Å; Sugiyama, Saito & Hiraga (2002). J. Alloys Compd. 342, 148–152], with a close lattice parameter c and a τ-times-larger lattice parameter a (τ is the golden mean). The structural relationship between ζ and ϕ was established on the basis of the similarity of their layered structures and common features. Additionally, the strong-reflections approach was successfully applied for the modeling of the ϕ phase based on the structural model of the ζ phase. The latter and the experimental structural model (retrieved following Rietveld refinement) were found to be essentially identical.

Electron Crystallographic Investigation of Crystals on the Mesostructural Scale

The precise structural solution of crystals on a mesostructural scale is challenging due to the difficulties in obtaining electron diffraction and the complicated relationship between the crystal structure factors (CSFs) and the conventional underfocus phase-contrast transmission electron microscopy (TEM) images due to the large unit cell and the complex structures. Here, we present the structural investigation of mesostructured crystals via the combination of electron crystallographic Fourier synthesis and high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) that only relies on the mass-thickness contrast. The three-dimensional electrostatic potential is reconstructed from the amplitudes and phases extracted from the Fourier transforms of the corresponding HAADF-STEM images and merged into a set of CSFs. This method is verified on silica scaffolds following a shifted double-diamond surface network with space group I41/amd. The results indicate that electron crystallography reconstruction by HAADF-STEM images is more suitable and accurate in determining the structure in comparison with conventional TEM electron crystallography reconstruction. This approach transfers the contrast of mesostructured crystals to images more accurately and the relationship between the Fourier transforms of HAADF-STEM images and the CSFs is more intuitive. It shows great advantages for the structural solution of crystals on the mesostructural scale.

Adaptive response of a metal-organic framework through reversible disorder-disorder transitions

The ultrahigh porosity and varied functionalities of porous metal-organic frameworks make them excellent candidates for applications that range widely from gas storage and separation to catalysis and sensing. An interesting feature of some frameworks is the ability to open their pores to a specific guest, enabling highly selective separation. A prerequisite for this is bistability of the host structure, which enables the framework to breathe, that is, to switch between two stability minima in response to its environment. Here we describe a porous framework DUT-8(Ni)-which consists of nickel paddle wheel clusters and carboxylate linkers-that adopts a configurationally degenerate family of disordered states in the presence of specific guests. This disorder originates from the nonlinear linkers arranging the clusters in closed loops of different local symmetries that in turn propagate as complex tilings. Solvent exchange stimulates the formation of distinct disordered frameworks, as demonstrated by high-resolution transmission electron microscopy and diffraction techniques. Guest exchange was shown to stimulate repeatable switching transitions between distinct disorder states.

Crystallography at the nanoscale: planar defects in ZnO nanospikes

The examination of anisotropic nanostructures, such as wires, platelets or spikes, inside a transmission electron microscope is normally performed only in plan view. However, intrinsic defects such as growth twin interfaces could occasionally be concealed from direct observation for geometric reasons, leading to superposition. This article presents the shadow-focused ion-beam technique to prepare multiple electron-beam-transparent cross-section specimens of ZnO nanospikes, via a procedure which could be readily extended to other anisotropic structures. In contrast with plan-view data of the same nanospikes, here the viewing direction allows the examination of defects without superposition. By this method, the coexistence of two twin configurations inside the wurtzite-type structure is observed, namely and , which were not identified during the plan-view observations owing to superposition of the domains. The defect arrangement could be the result of coalescence twinning of crystalline nuclei formed on the partially molten Zn substrate during the flame-transport synthesis. Three-dimensional defect models of the twin interface structures have been derived and are correlated with the plan-view investigations by simulation.

Explanation of structural differences and similarities between the AT2Al10 phases (where A=actinide, lanthanide or rare earth element and T=transition metal)

In the current work we have studied the crystallographic relationship between the AT2Al10 phases (where A = actinide, lanthanide and rare earth element and T = transition metal). It is known that with this stoichiometry two structure types exist: tetragonal CaCr2Al10 and orthorhombic YbFe2Al10. It was found that both CaCr2Al10 and YbFe2Al10 types are structural derivatives of the ThMn12 type structure (which has more general formula of AT x Al12− x , with x > 2). CaCr2Al10 structure has a group-subgroup relationship with the ThMn12 structure, while the relationship of the YbFe2Al10 to the ThMn12 was proved applying the strong reflection approach, suggested initially for approximants of quasi-crystals. Proposed here relationship between the studied structures explains the small difference in total energies, calculated using Density Functional Theory. Understanding the connection between these phases allows regarding AT2Al10 composition as somewhat extension of the AT x Al12− x compositional range. Due to the unique magnetic properties of the AT x Al12− x phases, tunable as a function of crystallographic structure, study of structural stability and crystallographic relationships of related phases are of outmost importance.

An average structure model of the intermediate phase between sodalite and cancrinite

Powder samples of the intermediate phase between sodalite and cancrinite (INT) have been synthesized hydrothermally. The formation of the INT phase was proved by both PXRD and TGA analysis and its stoichiometric composition was found to be |Na6.95(1)(CO3)0.48(2) (H2O)6.18(6)|[AlSiO4]6. The comparison of the intensity ratios of PXRD data with a SCXRD measurement indicates the formation of a comparable phase with the typical strong stacking disorder. The hexagonal lattice parameters with a=1266.3(2) pm and c=1586(1) pm and the unit cell setting were determined by Pawley fits. The average lattice and the stacking disorder along c axis could be confirmed by the reconstruction of three-dimensional ADT data. The average structure of INT was modeled considering only the combination of naturally existing (zeolitic) cages, restricted by the actual number of layers per unit cell. The possible combinations were further reduced by considering the amount of incorporated species. Through the comparison of simulated electron diffraction pattern to measured data the modeled framework could be confirmed. Using relative positions of the incorporated species in the natural cages as well as electron densities calculated by using only the framework of INT the positions of these species could be described.

Hydrogen positions in single nanocrystals revealed by electron diffraction

The localization of hydrogen atoms is an essential part of crystal structure analysis, but it is difficult because of their small scattering power. We report the direct localization of hydrogen atoms in nanocrystalline materials, achieved using the recently developed approach of dynamical refinement of precession electron diffraction tomography data. We used this method to locate hydrogen atoms in both an organic (paracetamol) and an inorganic (framework cobalt aluminophosphate) material. The results demonstrate that the technique can reliably reveal fine structural details, including the positions of hydrogen atoms in single crystals with micro- to nanosized dimensions.

Electron crystallography for determining the handedness of a chiral zeolite nanocrystal

Chiral crystals can be exploited for applications in enantioselective separation and catalysis. However, the study of chirality at the atomic level in a sub-micrometre-sized crystal is difficult due to the lack of adequate characterization methods. Herein, we present two efficient and practical methods of characterization that are based on electron crystallography. These methods are successfully applied to reveal the handedness of a chiral, zeolite nanocrystal. The handedness is identified through either a comparison of two high-resolution transmission electron microscope images, taken from the same nanocrystal but along different zone axes by tilting it around its screw axis, or the intensity asymmetry of a Bijvoet pair of reflections in a single precession electron-diffraction pattern. These two approaches provide new ways to determine the handedness of small, chiral crystals.

Structure determination of a pseudo-decagonal quasicrystal approximant by the strong-reflections approach and rotation electron diffraction

The structure of a complicated pseudo-decagonal (PD) quasicrystal approximant in the Al–Co–Ni alloy system, denoted as PD1, was solved by the strong-reflections approach on three-dimensional rotation electron diffraction (RED) data, using the phases from the known PD2 structure. RED shows that the PD1 crystal is primitive and orthorhombic, with a = 37.3, b = 38.8, c = 8.2 Å. However, as with other approximants in the PD series, the superstructure reflections (corresponding to c = 8.2 Å) are much weaker than those of the main reflections (corresponding to c = 4.1 Å), so it was decided to solve the PD1 structure in the smaller primitive unit cell first, i.e. with unit-cell parameters a = 37.3, b = 38.8, c = 4.1 Å and space group Pnam. A density map of PD1 was calculated from only the 15 strongest unique reflections. It contained all 31 Co/Ni atoms and many weaker peaks corresponding to Al atoms. The structure obtained from the strong-reflections approach was confirmed by applying direct methods to the complete RED data set. Successive refinement using the RED data set resulted in 108 unique atoms (31 Co/Ni and 77 Al). This is one of the most complicated approximant structures ever solved by electron diffraction. As with other approximants in the PD series, PD1 is built of characteristic 2 nm wheel clusters with fivefold rotational symmetry, which agrees with results from high-resolution electron microscopy images. The simulated electron diffraction patterns for the structure model are in good agreement with the experimental electron diffraction patterns obtained by RED.

Closing the gap between electron and X-ray crystallography

The development of a proper refinement algorithm that takes into account dynamical scattering guarantees, for electron crystallography, results approaching X-rays in terms of precision, accuracy and reliability. The combination of such dynamical refinement and electron diffraction tomography establishes a complete pathway for the structure characterization of single sub-micrometric crystals.

Structure refinement using precession electron diffraction tomography and dynamical diffraction: tests on experimental data

The recently published method for the structure refinement from three-dimensional precession electron diffraction data using dynamical diffraction theory [Palatinus et al. (2015). Acta Cryst. A71, 235–244] has been applied to a set of experimental data sets from five different samples – Ni2Si, PrVO3, kaolinite, orthopyroxene and mayenite. The data were measured on different instruments and with variable precession angles. For each sample a reliable reference structure was available. A large series of tests revealed that the method provides structure models with an average error in atomic positions typically between 0.01 and 0.02 Å. The obtained structure models are significantly more accurate than models obtained by refinement using kinematical approximation for the calculation of model intensities. The method also allows a reliable determination of site occupancies and determination of absolute structure. Based on the extensive tests, an optimal set of the parameters for the method is proposed.

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

Accurate structure refinement from electron-diffraction data is not possible without taking the dynamical-diffraction effects into account. A complete three-dimensional model of the structure can be obtained only from a sufficiently complete three-dimensional data set. In this work a method is presented for crystal structure refinement from the data obtained by electron diffraction tomography, possibly combined with precession electron diffraction. The principle of the method is identical to that used in X-ray crystallography: data are collected in a series of small tilt steps around a rotation axis, then intensities are integrated and the structure is optimized by least-squares refinement against the integrated intensities. In the dynamical theory of diffraction, the reflection intensities exhibit a complicated relationship to the orientation and thickness of the crystal as well as to structure factors of other reflections. This complication requires the introduction of several special parameters in the procedure. The method was implemented in the freely available crystallographic computing systemJana2006.

3D reconstruction of atomic structures from high angle annular dark field (HAADF) STEM images and its application on zeolite silicalite-1

The 3D atomic structure of silicalite-1 has been reconstructed for the first time by combining three high resolution HAADF-STEM images.

Structure refinement from precession electron diffraction data

Electron diffraction is a unique tool for analysing the crystal structures of very small crystals. In particular, precession electron diffraction has been shown to be a useful method for ab initio structure solution. In this work it is demonstrated that precession electron diffraction data can also be successfully used for structure refinement, if the dynamical theory of diffraction is used for the calculation of diffracted intensities. The method is demonstrated on data from three materials - silicon, orthopyroxene (Mg,Fe)(2)Si(2)O(6) and gallium-indium tin oxide (Ga,In)(4)Sn(2)O(10). In particular, it is shown that atomic occupancies of mixed crystallographic sites can be refined to an accuracy approaching X-ray or neutron diffraction methods. In comparison with conventional electron diffraction data, the refinement against precession diffraction data yields significantly lower figures of merit, higher accuracy of refined parameters, much broader radii of convergence, especially for the thickness and orientation of the sample, and significantly reduced correlations between the structure parameters. The full dynamical refinement is compared with refinement using kinematical and two-beam approximations, and is shown to be superior to the latter two.

Structure solution with automated electron diffraction tomography data: different instrumental approaches

Over the past few years automated electron diffraction tomography has become an established technique for structure solution of nano-crystalline material. The intentional choice of an arbitrary tilt axis and thus, the use of nonoriented diffraction patterns (off-zone acquisition) together with fine equidistant sampling of the reciprocal space result in high quality intensity data sets. Coupling automated electron diffraction tomography with electron beam precession (Vincent & Midgley, 1994) enables sampling of intensities between the static slices of reciprocal space and therefore enhances the quality of intensity data further; relatively complex structures have been solved using 3D electron diffraction intensities extracted from automated electron diffraction tomography data. Automated electron diffraction tomography data was collected initially using a dedicated automated module. In this manuscript we demonstrate that electron diffraction data of comparable quality can be collected using manual technique that mimics the automated process. A rather difficult material, i.e. a low symmetric (triclinic) sodium tetratungstate (Na(2) W(4) O(13) ) including heavy and light scatterers, was selected for testing. In this paper we show, that all collected data sets - automatic and manual, with and without electron beam precession - were able to provide data slightly different but suitable for ab initio structure solution and refinement.