An Incommensurately Modulated Structure of η′-Phase of Cu3+xSi Determined by Quantitative Electron Diffraction Tomography

Molybdenum Disorder in Hydrated Sedovite, Ideally U(MoO4)2·nH2O, a Microporous Nanocrystalline Mineral Characterized by Three-Dimensional Electron Diffraction, Density Functional Theory Computations, and Complexity Analysis

Sedovite, U⁴⁺(Mo⁶⁺O₄)₂·nH₂O, is reported as being one of the earliest supergene minerals formed of the secondary zone. The difficulty of isolating enough pure material limits studies to techniques that can access the nanoscale combined with theoretical analyses. The crystal structure of sedovite has been solved and refined using the dynamical approach from three-dimensional electron diffraction data collected on natural nanocrystals found among iriginite. At 100 K, sedovite is monoclinic a ≈ 6.96 Å, b ≈ 9.07 Å, c ≈ 12.27 Å, and V ≈ 775 ų with space group C2/c. The microporous structure presents a characteristic framework built from uranium polyhedra and disordered Mo pyramids creating pore hosting water molecules. To confirm the formula U⁴⁺(Mo⁶⁺O₄)₂·nH₂O, the possible presence of a hydroxyl group that would promote Mo⁵⁺ was tested with density functional theory (DFT) computations at the ambient temperature. DFT predicts that sedovite is a ferromagnetic insulator with a fundamental bandgap of E_g ∼ 1.7 eV with its chemical and physical properties dominated by U⁴⁺ rather than Mo⁶⁺. The structural complexity, I_G,tot, of sedovite was evaluated in order to get indirect information about the missing formation conditions.

Exotic Compositional Ordering in Manganese–Nickel–Arsenic (Mn‐Ni‐As) Intermetallics

In this work we benefited from recent advances in tools for crystal‐structure analysis that enabled us to describe an exotic nanoscale phenomenon in structural chemistry. The Mn_0.60Ni_0.40As sample of the Mn_1−xNi_xAs solid solution, exhibits an incommensurate compositional modulation intimately coupled with positional modulations. The average structure is of the simple NiAs type, but in contrast to a normal solid solution, we observe that manganese and nickel segregate periodically at the nano‐level into ordered MnAs and NiAs layers with thickness of 2–4 face‐shared octahedra. The detailed description was obtained by combination of 3D electron diffraction, scanning transmission electron microscopy, and neutron diffraction. The distribution of the manganese and nickel layers is perfectly described by a modulation vector q=0.360(3) c*. Displacive modulations are observed for all elements as a consequence of the occupational modulation, and as a means to achieve acceptable Ni–As and Mn–As distances. This modulated evolution of magnetic MnAs and non‐magnetic NiAs‐layers with periodicity at approximately 10 Å level, may provide an avenue for spintronics.

Pure and RE3+-Doped La7O6(VO4)3 (RE = Eu, Sm): Polymorphism Stability and Luminescence Properties of a New Oxyvanadate Matrix

Two polytypes of the new oxyvanadate matrix La₇O₆(VO₄)₃ were identified and deeply characterized. The crystal structure of the α-polytype was solved using a combination of precession electron diffraction and powder X-ray diffraction (XRD) techniques. It crystallizes in a monoclinic unit cell with space group P2₁, a = 13.0148(3) Å, b = 19.1566(5) Å, c = 7.0764(17) Å, and β = 99.87(1)°. Its structure is built upon [La₇O₆]⁹⁺ polycationic units at the origin of a porous 3D network, evidencing rectangular channels filled by isolated VO₄ tetrahedra. An in situ high-temperature XRD study highlights a number of complex phase transitions assorted with the existence of a β-polytype also refined in a monoclinic unit cell, space group P2₁/n, a = 13.0713(4) Å, b = 18.1835(6) Å, c = 7.1382(2) Å, and β = 97.31(1)°. Thus, during the transitions, while the polycationic networks are almost identical, the vanadate's geometry is largely modified. The use of Eu³⁺ and Sm³⁺ at different concentrations in the host lattice is possible using solid-state techniques. The photoluminescence (PL), PL excitation (PLE) spectra, and luminescence decay times were recorded and discussed. The phosphors present an emission light, being bright and reddish orange after excitation under UV. This is mainly due to the V-O band and f-f transitions. Whatever the studied polytype, the final luminescence properties are retained during the heating/cooling process.

Entropy-Driven Incommensurability: Chemical Pressure-Guided Polymorphism in PdBi and the Origins of Lock-In Phenomena in Modulated Systems

Incommensurate order, in which two or more mismatched periodic patterns combine to make a long-range ordered yet aperiodic structure, is emerging as a general phenomenon impacting the crystal structures of compounds ranging from alloys and nominally simple salts to organic molecules and proteins. The origins of incommensurability in these systems are often unclear, but it is commonly associated with relatively weak interactions that become apparent only at low temperatures. In this article, we elucidate an incommensurate modulation in the intermetallic compound PdBi that arises from a different mechanism: the controlled increase of entropy at higher temperatures. Following the synthesis of PdBi, we structurally characterize two low-temperature polymorphs of the TlI-type structure with single crystal synchrotron X-ray diffraction. At room temperature, we find a simple commensurate superstructure of the TlI-type structure (comm-PdBi), in which the Pd sublattice distorts to form a 2D pattern of short and long Pd-Pd contacts. Upon heating, the structure converts to an incommensurate variant (incomm-PdBi) corresponding to the insertion of thin slabs of the original TlI type into the superstructure. Theoretical bonding analysis suggests that comm-PdBi is driven by the formation of isolobal Pd-Pd bonds along shortened contacts in the distorted Pd network, which is qualitatively in accord with the 18-n rule but partially frustrated by the population of competing Bi-Bi bonding states. The emergence of incomm-PdBi upon heating is rationalized with the DFT-Cemical Pressure (CP) method: the insertion of TlI-type slabs result in regions of higher vibrational freedom that are entropically favored at higher temperatures. High-temperature incommensurability may be encountered in other materials when bond formation is weakened by competing electronic states, and there is a path for accommodating defects in the CP scheme.

3D Electron Diffraction: The Nanocrystallography Revolution

Crystallography of nanocrystalline materials has witnessed a true revolution in the past 10 years, thanks to the introduction of protocols for 3D acquisition and analysis of electron diffraction data. This method provides single-crystal data of structure solution and refinement quality, allowing the atomic structure determination of those materials that remained hitherto unknown because of their limited crystallinity. Several experimental protocols exist, which share the common idea of sampling a sequence of diffraction patterns while the crystal is tilted around a noncrystallographic axis, namely, the goniometer axis of the transmission electron microscope sample stage. This Outlook reviews most important 3D electron diffraction applications for different kinds of samples and problematics, related with both materials and life sciences. Structure refinement including dynamical scattering is also briefly discussed.

Structure analysis of materials at the order–disorder borderline using three-dimensional electron diffraction

Diffuse scattering, observed as intensity distribution between the Bragg peaks, is associated with deviations from the average crystal structure, generally referred to as disorder. In many cases crystal defects are seen as unwanted perturbations of the periodic structure and therefore they are often ignored. Yet, when it comes to the structure analysis of nano-volumes, what electron crystallography is designed for, the significance of defects increases. Twinning and polytypic sequences are other perturbations from ideal crystal structure that are also commonly observed in nanocrystals. Here we present an overview of defect types and review some of the most prominent studies published on the analysis of defective nanocrystalline structures by means of three-dimensional electron diffraction.

3D electron diffraction techniques

3D electron diffraction is an emerging technique for the structural analysis of nanocrystals. The challenges that 3D electron diffraction has to face for providing reliable data for structure solution and the different ways of overcoming these challenges are described. The route from zone axis patterns towards 3D electron diffraction techniques such as precession-assisted electron diffraction tomography, rotation electron diffraction and continuous rotation is also discussed. Finally, the advantages of the new hybrid detectors with high sensitivity and fast readout are demonstrated with a proof of concept experiment of continuous rotation electron diffraction on a natrolite nanocrystal.

A New Method Based on Electron Diffraction for Detecting Nanoparticles in Injectable Medicines

A new method for detecting and characterizing nanoparticles in an injectable pharmaceutical solution is presented. The method is based on the simultaneous use, on those nanoparticles that are crystalline, of three-dimensional electron diffraction tomography and energy dispersive X-ray spectrometry. With three-dimensional electron diffraction tomography, the unit cell and the crystal symmetry of the nanoparticles are determined, while with energy dispersive X-ray spectrometry, the chemical composition is derived. With these data, through an inspection of a crystallographic database, it is possible to determine the crystal phase of the nanoparticles. The knowledge of the crystal phase is a valuable element for understanding the provenance and the formation of the nanoparticles, helping the researcher in solving any quality control issue related to the presence of nanoparticles in an injectable solution.

Daliranite, PbHgAs2S5: determination of the incommensurately modulated structure and revision of the chemical formula

The incommensurately modulated crystal structure of the mineral daliranite has been determined using 3D electron diffraction data obtained on nanocrystalline domains. Daliranite is orthorhombic with a = 21, b = 4.3, c = 9.5 Å and shows modulation satellites along c. The solution of the average structure in the Pnma space group together with energy-dispersive X-ray spectroscopy data obtained on the same domains indicate a chemical formula of PbHgAs2S5, which has one S fewer than previously reported. The crystal structure of daliranite is built from columns of face-sharing PbS8 bicapped trigonal prisms laterally connected by [2+4]Hg polyhedra and (As3+ 2S5)4− groups. The excellent quality of the electron diffraction data allows a structural model to be built for the modulated structure in superspace, which shows that the modulation is due to an alternated occupancy of a split As site.

Stacking sequence variations in vaterite resolved by precession electron diffraction tomography using a unified superspace model

As a metastable phase, vaterite is involved in the first step of crystallization of several carbonate-forming systems including the two stable polymorphs calcite and aragonite. Its complete structural determination would consequently shed important light to understand scaling formation and biomineralization processes. While vaterite’s hexagonal substructure (a₀ ~ 4.1 Å and c₀ ~ 8.5 Å) and the organization of the carbonate groups within a single layer is known, conflicting interpretations regarding the stacking sequence remain and preclude the complete understanding of the structure. To resolve the ambiguities, we performed precession electron diffraction tomography (PEDT) to collect single crystal data from 100 K to the ambient temperature. The structure was solved ab initio and described over all the temperature range using a unified modulated structure model in the superspace group C12/c1(α0γ)00 with a = a₀ = 4.086(3) Å, b = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{{\bf{3}}}$$\end{document}3a₀ = 7.089(9) Å, c = c₀ = 8.439(9) Å, α = β = γ = 90° and q = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tfrac{{\bf{2}}}{{\bf{3}}}$$\end{document}23a* + γc*. At 100 K the model presents a pure 4-layer stacking sequence with γ = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tfrac{{\bf{1}}}{{\bf{2}}}$$\end{document}12 whereas at the ambient temperature, ordered stacking faults are introduced leading to γ < \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tfrac{{\bf{1}}}{{\bf{2}}}$$\end{document}12. The model was refined against PEDT data using the dynamical refinement procedure including modulation and twinning as well as against x-ray powder data by the Rietveld refinement.

Precession electron diffraction tomography on twinned crystals: application to CaTiO3 thin films

Strain engineering via epitaxial thin-film synthesis is an efficient way to modify the crystal structure of a material in order to induce new features or improve existing properties. One of the challenges in this approach is to quantify structural changes occurring in these films. While X-ray diffraction is the most widely used technique for obtaining accurate structural information from bulk materials, severe limitations appear in the case of epitaxial thin films. This past decade, precession electron diffraction tomography has emerged as a relevant technique for the structural characterization of nano-sized materials. While its usefulness has already been demonstrated for solving the unknown structure of materials deposited in the form of thin films, the frequent existence of orientation variants within the film introduces a severe bias in the structure refinement, even when using the dynamical diffraction theory to calculate diffracted intensities. This is illustrated here using CaTiO3 films deposited on SrTiO3 substrates as a case study. By taking into account twinning in the structural analysis, it is shown that the structure of the CaTiO3 films can be refined with an accuracy comparable to that obtained by dynamical refinement from non-twinned data. The introduction of the possibility to handle twin data sets is undoubtedly a valuable add-on and, notably, paves the way for a successful use of precession electron diffraction tomography for accurate structural analyses of thin films.

In Situ Electron Diffraction Tomography Using a Liquid-Electrochemical Transmission Electron Microscopy Cell for Crystal Structure Determination of Cathode Materials for Li-Ion batteries

We demonstrate that changes in the unit cell structure of lithium battery cathode materials during electrochemical cycling in liquid electrolyte can be determined for particles of just a few hundred nanometers in size using in situ transmission electron microscopy (TEM). The atomic coordinates, site occupancies (including lithium occupancy), and cell parameters of the materials can all be reliably quantified. This was achieved using electron diffraction tomography (EDT) in a sealed electrochemical cell with conventional liquid electrolyte (LP30) and LiFePO₄ crystals, which have a well-documented charged structure to use as reference. In situ EDT in a liquid environment cell provides a viable alternative to in situ X-ray and neutron diffraction experiments due to the more local character of TEM, allowing for single crystal diffraction data to be obtained from multiphased powder samples and from submicrometer- to nanometer-sized particles. EDT is the first in situ TEM technique to provide information at the unit cell level in the liquid environment of a commercial TEM electrochemical cell. Its application to a wide range of electrochemical experiments in liquid environment cells and diverse types of crystalline materials can be envisaged.

Characterization of Atomic Structures of Nanosized Intermetallic Compounds Using Electron Diffraction Methods

In metallurgy, many intermetallic compounds crystallize as nanosized particles in metallic matrices. These particles influence dramatically the physical properties of engineering materials such as alloys and steels. Since properties and crystal structure are intimately linked, characterization of the atomic model of these intermetallides is crucial for the development of new alloys. However, this structural information usually cannot be attained using traditional X-ray diffraction methods, limited by the small volume and size of the precipitates. In these cases, electron diffraction (ED) is the most suitable method. In the last few decades, ED has experienced a tremendous leap forward. Many structures, including intermetallides, are solved using these methods. The class of intermetallides should be discussed independently since these phases do not comprise regular polyhedrals; moreover, the interatomic distances and angles vary drastically even in the same compositional system. These facts point to difficulties that have to be overcome during the solution path. Furthermore, intermetallic compounds can be of high complexity-possessing hundreds of atoms in the unit cell. Here, this topic is expanded with an emphasis on novel developments in the field.

Stairlike Aurivillius Phases in the Pseudobinary Bi5Nb3O15-ABi2Nb2O9 (A = Ba and Sr) System: A Comprehensive Analysis Using Superspace Group Formalism

We report the possibility of extending the so-called stairlike Aurivilius phases in the pseudobinary Bi₅Nb₃O₁₅-ABi₂Nb₂O₉ (A = Ba and Sr) over a wide range of compositions. These phases are characterized by a discontinuous stacking of [Bi₂O₂] slabs and perovskite blocks, leading to long-period intergrowths stabilized as a single phase. When analyses from precession electron diffraction tomography and X-ray and neutron powder diffraction are combined, the monoclinic incommensurately modulated structure with q = αa* + γc* previously proposed for the ABi₇Nb₅O₂₄ composition could be generalized to the Bi₅Nb₃O₁₅-ABi₂Nb₂O₉ (A = Ba and Sr) compounds. Considering the compositions expressed as (A,Bi)_{1- x}Nb _xO_{3-3 x}, the stacking sequence associated with compositions ranging from x = ²/₅ to ³/₈ is governed by the component γ of the modulation vector and can be predicted following a Farey tree hierarchy independently to the A cation. The length of the steps, characteristic of the stairlike nature, is controlled by the α component and depends on the substitution ratio A/Bi and the nature of A (A = Ba and Sr). This study highlights the compositional flexibility of stairlike Aurivillius phases.

Single-crystal analysis of nanodomains by electron diffraction tomography: mineralogy at the order-disorder borderline

Electron diffraction tomography is a powerful emerging method for the structure characterization of materials available only as sub-micrometric grains. This technique can in fact deliver complete 3D information from a single crystal of few hundreds or few tens of nanometers, allowing the analysis of polyphasic or polytypic mixtures that generally cannot be fully addressed by X-ray methods. In this paper, we report and discuss three mineralogy-related study cases where electron diffraction tomography was the only way for achieving a proper description of the sample, by the identification and the structure determination of all the phases or all the polytypes within. We also show how electron diffraction tomography and dynamical refinement can be combined for finding accurate atomic positions and localizing hydrogen atoms at room conditions. Finally, we stress the future potential of this method in the fields of mineralogy and experimental petrology, where till now many samples cannot be properly described because nanocrystalline, polyphasic or disordered. Electron diffraction tomography can be used for detecting unexpected or unknown phases in high-pressure synthetic yields or for the characterization of fine rocks formed under extreme conditions, like impactites or meteorites. Eventually, this method allows the structure characterization of single domains that are ordered only at the scale of few cell repetitions, and therefore it makes possible investigating those materials at the borderline between crystalline and amorphous matter and delivers crucial and unique elements for the understanding of the first stages of solid matter organization.

Novel Layered Supercell Structure from Bi2AlMnO6 for Multifunctionalities

Layered materials, e.g., graphene and transition metal (di)chalcogenides, holding great promises in nanoscale device applications have been extensively studied in fundamental chemistry, solid state physics and materials research areas. In parallel, layered oxides (e.g., Aurivillius and Ruddlesden-Popper phases) present an attractive class of materials both because of their rich physics behind and potential device applications. In this work, we report a novel layered oxide material with self-assembled layered supercell structure consisting of two mismatch-layered sublattices of [Bi₃O_3+δ] and [MO₂]_1.84 (M = Al/Mn, simply named BAMO), i.e., alternative layered stacking of two mutually incommensurate sublattices made of a three-layer-thick Bi-O slab and a one-layer-thick Al/Mn-O octahedra slab in the out-of-plane direction. Strong room-temperature ferromagnetic and piezoelectric responses as well as anisotropic optical property have been demonstrated with great potentials in various device applications. The realization of the novel BAMO layered supercell structure in this work has paved an avenue toward exploring and designing new materials with multifunctionalities.

Crystal structures of η''-Cu3+xSi and η'''-Cu3+xSi

The binary phase diagram of Cu-Si is unexpectedly complex in the vicinity of Cu_3+xSi. The low-temperature region contains three closely related incommensurately modulated phases denoted, in order of increasing temperature of stability, η''', η'' and η'. The structure analysis of η' has been reported previously [Palatinus et al. (2011). Inorg. Chem. 50, 3743]. Here the structure model for the phases η'' and η''' is reported. The structures could be solved in superspace, but no superspace structure model could be constructed due to the complexity of the modulation functions. Therefore, the structures were described in a supercell approximation, which involved a 4 × 4 × 3 supercell for the η'' phase and a 14 × 14 × 3 supercell for the η''' phase. Both structures are very similar and differ only by a subtle symmetry lowering from η'' to η'''. A comparison of the structure models of η'' and η''' with the reported structure of η' suggests that the reported structure model of η' contains an incorrect assignment of atomic types.

Unusual Relaxor Ferroelectric Behavior in Stairlike Aurivillius Phases

New ferroelectric layered materials were found in the pseudobinary system Bi5Nb3O15-ABi2Nb2O9 (A= Ba, Sr and Pb). Preliminary observations made by transmission electron microscopy indicate that these compounds exhibit a complex incommensurately modulated structure. A (3 + 1)D structural model is obtained using ab initio phasing by charge flipping based on the analysis of precession electron diffraction tomography data. The (3 + 1)D structure is further validated by a refinement against neutron powder diffraction. These materials possess a layered structure with discontinuous [Bi2O2] slabs and perovskite blocks. While these structural units are characteristics of Aurivillius phases, the existence of periodic crystallographic shear planes offers strong similarities with collapsed or stairlike structures known in high-Tc superconductors and related compounds. Using dielectric spectroscopy, we study the phase transitions of these new layered materials. For A = Ba and Sr, a Vögel-Fulcher-like behavior characteristic of the so-called relaxor ferroelectrics is observed and compared to "canonical" relaxors. For A = Sr, the absence of a Burns temperature separated from the freezing temperature appears as a rather unusual behavior.

A Rutile Chevron Modulation in Delafossite-Like Ga3-xIn3TixO9+x/2

The structure solution of the modulated, delafossite-related, orthorhombic Ga3-xIn3TixO9+x/2 for x = 1.5 is reported here in conjunction with a model describing the modulation as a function of x for the entire system. Previously reported structures in the related A3-xIn3TixO9+x/2 (A = Al, Cr, or Fe) systems use X-ray diffraction to determine that the anion lattice is the source of modulation. Neutron diffraction, with its enhanced sensitivity to light atoms, offers a route to solving the modulation and is used here, in combination with precession electron diffraction tomography (PEDT), to solve the structure of Ga1.5In3Ti1.5O9.75. We construct a model that describes the anion modulation through the formation of rutile chevrons as a function of x. This model accommodates the orthorhombic phase (1.5 ≤ x ≤ 2.1) in the Ga3-xIn3TixO9+x/2 system, which transitions to a biphasic mixture (2.2 ≤ x ≤ 2.3) with a monoclinic, delafossite-related phase (2.4 ≤ x ≤ 2.5). The optical band gaps of this system are determined, and are stable at ∼3.4 eV before a ∼0.4 eV decrease between x = 1.9 and 2.0. After this decrease, stability resumes at ∼3.0 eV. Resistance to oxidation and reduction is also presented.

Structure determination of modulated structures by powder X-ray diffraction and electron diffraction

The combination of PXRD and ED is applied to determine modulated structures which resist solution by more conventional methods.

Structural analysis of strained LaVO3 thin films

While structure refinement is routinely achieved for simple bulk materials, the accurate structural determination still poses challenges for thin films due on the one hand to the small amount of material deposited on the thicker substrate and, on the other hand, to the intricate epitaxial relationships that substantially complicate standard x-ray diffraction analysis. Using both electron and x-ray diffraction, we analyze the crystal structure of epitaxial LaVO3 thin films grown on (1 0 0)-oriented SrTiO3. Transmission electron microscopy study reveals that the thin films are epitaxially grown on SrTiO3 and points to the presence of 90° oriented domains. The mapping of the reciprocal space obtained by high resolution x-ray diffraction permits refinement of the lattice parameters. We finally deduce that strain accommodation imposes a monoclinic structure onto the LaVO3 film. The reciprocal space maps are numerically processed and the extracted data computed to refine the atomic positions, which are compared to those obtained using precession electron diffraction tomography.

Fast electron diffraction tomography

A fast and fully automatic procedure for collecting electron diffraction tomography data is presented. In the case of a very stable goniometer it is demonstrated how, by variation of the tilting speed and the CCD detector parameters, it is possible to obtain fully automatic precession-assisted electron diffraction tomography data collections, rotation electron diffraction tomography data collections or new integrated electron diffraction tomography data collections, in which the missing wedge of the reciprocal space between the patterns is recorded by longer exposures during the crystal tilt. It is shown how automatic data collection of limited tilt range can be used to determine the unit-cell parameters, while data of larger tilt range are suitable to solve the crystal structureabinitiowith direct methods. The crystal structure of monoclinic MgMoO4has been solved in this way as a test structure. In the case where the goniometer is not stable enough to guarantee a steady position of the crystal over large tilt ranges, an automatic method for tracking the crystal during continuous rotation of the sample is proposed.

Synergy between transmission electron microscopy and powder diffraction: application to modulated structures

The crystal structure solution of modulated compounds is often very challenging, even using the well established methodology of single-crystal X-ray crystallography. This task becomes even more difficult for materials that cannot be prepared in a single-crystal form, so that only polycrystalline powders are available. This paper illustrates that the combined application of transmission electron microscopy (TEM) and powder diffraction is a possible solution to the problem. Using examples of anion-deficient perovskites modulated by periodic crystallographic shear planes, it is demonstrated what kind of local structural information can be obtained using various TEM techniques and how this information can be implemented in the crystal structure refinement against the powder diffraction data. The following TEM methods are discussed: electron diffraction (selected area electron diffraction, precession electron diffraction), imaging (conventional high-resolution TEM imaging, high-angle annular dark-field and annular bright-field scanning transmission electron microscopy) and state-of-the-art spectroscopic techniques (atomic resolution mapping using energy-dispersive X-ray analysis and electron energy loss spectroscopy).

Three-dimensional electron diffraction as a complementary technique to powder X-ray diffraction for phase identification and structure solution of powders

Phase identification and structure determination are important and widely used techniques in chemistry, physics and materials science. Recently, two methods for automated three-dimensional electron diffraction (ED) data collection, namely automated diffraction tomography (ADT) and rotation electron diffraction (RED), have been developed. Compared with X-ray diffraction (XRD) and two-dimensional zonal ED, three-dimensional ED methods have many advantages in identifying phases and determining unknown structures. Almost complete three-dimensional ED data can be collected using the ADT and RED methods. Since each ED pattern is usually measured off the zone axes by three-dimensional ED methods, dynamic effects are much reduced compared with zonal ED patterns. Data collection is easy and fast, and can start at any arbitrary orientation of the crystal, which facilitates automation. Three-dimensional ED is a powerful technique for structure identification and structure solution from individual nano- or micron-sized particles, while powder X-ray diffraction (PXRD) provides information from all phases present in a sample. ED suffers from dynamic scattering, while PXRD data are kinematic. Three-dimensional ED methods and PXRD are complementary and their combinations are promising for studying multiphase samples and complicated crystal structures. Here, two three-dimensional ED methods, ADT and RED, are described. Examples are given of combinations of three-dimensional ED methods and PXRD for phase identification and structure determination over a large number of different materials, from Ni-Se-O-Cl crystals, zeolites, germanates, metal-organic frameworks and organic compounds to intermetallics with modulated structures. It is shown that three-dimensional ED is now as feasible as X-ray diffraction for phase identification and structure solution, but still needs further development in order to be as accurate as X-ray diffraction. It is expected that three-dimensional ED methods will become crucially important in the near future.

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.

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.

Equivalence of superspace groups

An algorithm is presented which determines the equivalence of two settings of a (3 + d)-dimensional superspace group (d = 1, 2, 3). The algorithm has been implemented as a web tool findssg on SSG(3+d)D, providing the transformation of any user-given superspace group to the standard setting of this superspace group in SSG(3+d)D. It is shown how the standard setting of a superspace group can be directly obtained by an appropriate transformation of the external-space lattice vectors (the basic structure unit cell) and a transformation of the internal-space lattice vectors (new modulation wavevectors are linear combinations of old modulation wavevectors plus a three-dimensional reciprocal-lattice vector). The need for non-standard settings in some cases and the desirability of employing standard settings of superspace groups in other cases are illustrated by an analysis of the symmetries of a series of compounds, comparing published and standard settings and the transformations between them. A compilation is provided of standard settings of compounds with two- and three-dimensional modulations. The problem of settings of superspace groups is discussed for incommensurate composite crystals and for chiral superspace groups.

Ab Initio structure determination of vaterite by automated electron diffraction

"This is a mineral about which there has been much discussion" is a typical statement about vaterite in older standard textbooks of inorganic chemistry. This polymorph of CaCO(3) was first mentioned by H. Vater in 1897, plays key roles in weathering and biomineralization processes, but occurs only in the form of nanosized crystals, unsuitable for structure determination. Its structure could now be solved by automated electron diffraction tomography from 50 nm sized nanocrystals.

Structure of the new mineral sarrabusite, Pb5CuCl4(SeO3)4, solved by manual electron-diffraction tomography

The new mineral sarrabusite Pb5CuCl4(SeO3)4 has been discovered in the Sardinian mine of Baccu Locci, near Villaputzu. It occurs as small lemon–yellow spherical aggregates of tabular crystals (< 10 µm) of less than 100 µm in diameter. The crystal structure has been solved from and refined against electron diffraction of a microcrystal. Data sets have been measured by both a manual and an automated version of the new electron-diffraction tomography technique combined with the precession of the electron beam. The sarrabusite structure is monoclinic and consists of (010) layers of straight chains formed by alternating edge-sharing CuO4Cl2 and PbO8 polyhedra parallel to the c axis, which share corners laterally with two zigzag corner-sharing chains of PbO6Cl2 and PbO4Cl4 bicapped trigonal prisms. These blocks are linked together by SeO_3^{2-} flat-pyramidal groups.