Ab initio structure determination and quantitative disorder analysis on nanoparticles by electron diffraction tomography

Refining short-range order parameters from the three-dimensional diffuse scattering in single-crystal electron diffraction data

Our study compares short-range order parameters refined from the diffuse scattering in single-crystal X-ray and single-crystal electron diffraction data. Nb0.84CoSb was chosen as a reference material. The correlations between neighbouring vacancies and the displacements of Sb and Co atoms were refined from the diffuse scattering using a Monte Carlo refinement in DISCUS. The difference between the Sb and Co displacements refined from the diffuse scattering and the Sb and Co displacements refined from the Bragg reflections in single-crystal X-ray diffraction data is 0.012 (7) Å for the refinement on diffuse scattering in single-crystal X-ray diffraction data and 0.03 (2) Å for the refinement on the diffuse scattering in single-crystal electron diffraction data. As electron diffraction requires much smaller crystals than X-ray diffraction, this opens up the possibility of refining short-range order parameters in many technologically relevant materials for which no crystals large enough for single-crystal X-ray diffraction are available.

Quantitative three-dimensional local order analysis of nanomaterials through electron diffraction

Structure-property relationships in ordered materials have long been a core principle in materials design. However, the introduction of disorder into materials provides structural flexibility and thus access to material properties that are not attainable in conventional, ordered materials. To understand disorder-property relationships, the disorder - i.e., the local ordering principles - must be quantified. Local order can be probed experimentally by diffuse scattering. The analysis is notoriously difficult, especially if only powder samples are available. Here, we combine the advantages of three-dimensional electron diffraction - a method that allows single crystal diffraction measurements on sub-micron sized crystals - and three-dimensional difference pair distribution function analysis (3D-ΔPDF) to address this problem. In this work, we compare the 3D-ΔPDF from electron diffraction data with those obtained from neutron and x-ray experiments of yttria-stabilized zirconia (Zr0.82Y0.18O1.91) and demonstrate the reliability of the proposed approach.

Quantitative analysis of diffuse electron scattering in the lithium-ion battery cathode material Li1.2Ni0.13Mn0.54Co0.13O2

In contrast to perfectly periodic crystals, materials with short-range order produce diffraction patterns that contain both Bragg reflections and diffuse scattering. To understand the influence of short-range order on material properties, current research focuses increasingly on the analysis of diffuse scattering. This article verifies the possibility to refine the short-range order parameters in submicrometre-sized crystals from diffuse scattering in single-crystal electron diffraction data. The approach was demonstrated on Li_1.2Ni_0.13Mn_0.54Co_0.13O₂, which is a state-of-the-art cathode material for lithium-ion batteries. The intensity distribution of the 1D diffuse scattering in the electron diffraction patterns of Li_1.2Ni_0.13Mn_0.54Co_0.13O₂ depends on the number of stacking faults and twins in the crystal. A model of the disorder in Li_1.2Ni_0.13Mn_0.54Co_0.13O₂ was developed and both the stacking fault probability and the percentage of the different twins in the crystal were refined using an evolutionary algorithm in DISCUS. The approach was applied on reciprocal space sections reconstructed from 3D electron diffraction data since they exhibit less dynamical effects compared with in-zone electron diffraction patterns. A good agreement was achieved between the calculated and the experimental intensity distribution of the diffuse scattering. The short-range order parameters in submicrometre-sized crystals can thus successfully be refined from the diffuse scattering in single-crystal electron diffraction data using an evolutionary algorithm in DISCUS.

Determination of Spinel Content in Cycled Li1.2Ni0.13Mn0.54Co0.13O2 Using Three-Dimensional Electron Diffraction and Precession Electron Diffraction

Among lithium battery cathode materials, Li1.2Ni0.13Mn0.54Co0.13O2 (LR-NMC) has a high theoretical capacity, but suffers from voltage and capacity fade during cycling. This is partially ascribed to transition metal cation migration, which involves the local transformation of the honeycomb layered structure to spinel-like nano-domains. Determination of the honeycomb layered/spinel phase ratio from powder X-ray diffraction data is hindered by the nanoscale of the functional material and the domains, diverse types of twinning, stacking faults, and the possible presence of the rock salt phase. Determining the phase ratio from transmission electron microscopy imaging can only be done for thin regions near the surfaces of the crystals, and the intense beam that is needed for imaging induces the same transformation to spinel as cycling does. In this article, it is demonstrated that the low electron dose sufficient for electron diffraction allows the collection of data without inducing a phase transformation. Using calculated electron diffraction patterns, we demonstrate that it is possible to determine the volume ratio of the different phases in the particles using a pair-wise comparison of the intensities of the reflections. Using this method, the volume ratio of spinel structure to honeycomb layered structure is determined for a submicron sized crystal from experimental three-dimensional electron diffraction (3D ED) and precession electron diffraction (PED) data. Both twinning and the possible presence of the rock salt phase are taken into account. After 150 charge–discharge cycles, 4% of the volume in LR-NMC particles was transformed irreversibly from the honeycomb layered structure to the spinel structure. The proposed method would be applicable to other multi-phase materials as well.

Refinements on electron diffraction data of β-glycine in MoPro: a quest for an improved structure model

The advancement in 3D electron diffraction (3D ED) techniques that lead to a revolution in molecular structure determination using nano-sized crystals is now achieving atomic resolution. The structures can be obtained from 3D ED data with tools similar to those used for X-ray structure determination. In this context, the MoPro software, originally designed for structure and charge density refinements using X-ray diffraction data, has been adapted. Structure refinement on 3D ED data was achieved via implementation of electron scattering factors available in the literature and by application of the Mott–Bethe equation to X-ray scattering factors computed from the multipolar atom model. The multipolar model was parametrized using the transferable pseudoatom databanks ELMAM2 and UBDB. Applying the independent atom model (IAM), i.e. spherical neutral atom refinement, to 3D ED data on β-glycine in MoPro resulted in structure and refinement statistics comparable to those obtained from other well known software. Use of the transferred aspherical atom model (TAAM) led to improvement of the refinement statistics and a better fit of the model to the 3D ED data as compared with the spherical atom refinement. The anisotropic displacement parameters of non-H atoms appear underestimated by typically 0.003 Å2 for the non-H atoms in IAM refinement compared with TAAM. Thus, MoPro is shown to be an effective tool for crystal structure refinement on 3D ED data and allows use of a spherical or a multipolar atom model. Electron density databases can be readily transferred with no further modification needed when the Mott–Bethe equation is applied.

Three-dimensional electron diffraction for porous crystalline materials: structural determination and beyond

Porous crystalline materials such as zeolites, metal-organic frameworks (MOFs) and covalent organic frameworks (COFs) have attracted great interest due to their well-defined pore structures in molecular dimensions. Knowing the atomic structures of porous materials is crucial for understanding their properties and exploring their applications. Many porous materials are synthesized as polycrystalline powders, which are too small for structure determination by X-ray diffraction. Three-dimensional electron diffraction (3DED) has been developed for studying such materials. In this Minireview, we summarize the recent developments of 3DED methods and demonstrate how 3DED revolutionized structural analysis of zeolites, MOFs, and COFs. Zeolites and MOFs whose structures remained unknown for decades could be solved. New approaches for design and targeted synthesis of novel zeolites could be developed. Moreover, we discuss the advances of structural analysis by 3DED in revealing the unique structural features and properties, such as heteroatom distributions, mixed-metal frameworks, structural flexibility, guest-host interactions, and structure transformation.

New zeolite-like RUB-5 and its related hydrous layer silicate RUB-6 structurally characterized by electron microscopy

This study made use of a recently developed combination of advanced methods to reveal the atomic structure of a disordered nanocrystalline zeolite using exit wave reconstruction, automated diffraction tomography, disorder modelling and diffraction pattern simulation. By applying these methods, it was possible to determine the so far unknown structures of the hydrous layer silicate RUB-6 and the related zeolite-like material RUB-5. The structures of RUB-5 and RUB-6 contain the same dense layer-like building units (LLBUs). In the case of RUB-5, these building units are interconnected via additional SiO4/2 tetrahedra, giving rise to a framework structure with a 2D pore system consisting of intersecting 8-ring channels. In contrast, RUB-6 contains these LLBUs as separate silicate layers terminated by silanol/sil-oxy groups. Both RUB-6 and RUB-5 show stacking disorder with intergrowths of different polymorphs. The unique structure of RUB-6, together with the possibility for an interlayer expansion reaction to form RUB-5, make it a promising candidate for interlayer expansion with various metal sources to include catalytically active reaction centres.

Refinement of organic crystal structures with multipolar electron scattering factors

A revolution in resolution is occurring now in electron microscopy arising from the development of methods for imaging single particles at cryogenic temperatures and obtaining electron diffraction data from nanocrystals of small organic molecules or macromolecules. Near-atomic or even atomic resolution of molecular structures can be achieved. The basis of these methods is the scattering of an electron beam due to the electrostatic potential of the sample. To analyse these high-quality experimental data, it is necessary to use appropriate atomic scattering factors. The independent atom model (IAM) is commonly used although various more advanced models, already known from X-ray diffraction, can also be applied to enhance the analysis. In this study a comparison is presented of IAM and TAAM (transferable aspherical atom model), the latter with the parameters of the Hansen-Coppens multipole model transferred from the University at Buffalo Databank (UBDB). By this method, TAAM takes into account the fact that atoms in molecules are partially charged and are not spherical. Structure refinements were performed on a carbamazepine crystal using electron structure-factor amplitudes determined experimentally [Jones et al. (2018). ACS Cent. Sci. 4, 1587-1592] or modelled with theoretical quantum-mechanical methods. The results show the possibilities and limitations of the TAAM method when applied to electron diffraction. Among others, the method clearly improves model fitting statistics, when compared with IAM, and allows for reliable refinement of atomic thermal parameters. The improvements are more pronounced with poorer-resolution diffraction data.

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.

Automated electron diffraction tomography - development and applications

Electron diffraction tomography (EDT) has gained increasing interest, starting with the development of automated electron diffraction tomography (ADT) which enables the collection of three-dimensional electron diffraction data from nano-sized crystals suitable for ab initio structure analysis. A basic description of the ADT method, nowadays recognized as a reliable and established method, as well as its special features and general applicability to different transmission electron microscopes is provided. In addition, the usability of ADT for crystal structure analysis of single nano-sized crystals with and without special crystallographic features, such as twinning, modulations and disorder is demonstrated.

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.

Elucidation of correlated disorder in zeolite IM-18

Classical crystallography is based on the translational periodicity of crystals and the analysis of discrete Bragg reflections. However, it is inadequate for determining disordered structures, of which the diffuse scattering is vital to evaluate the disorder level. The correlated disorder of IM-18 presents as zigzag chains arranged in translational periodicity and the double four-ring units randomly distributed along two dimensions. Supercell models regulated by multiple probabilities were systematically built to simulate the single-crystal and powder X-ray diffraction patterns in order to ascertain the specific disorder configuration in the single-crystal or polycrystalline samples of IM-18. The presence of defects in the polycrystalline sample was proved by combining ²⁹Si magic angle spinning (MAS) NMR and ¹H-¹H double quantum MAS NMR spectra, and was quantitatively explored by the simulation method. The method could also elucidate other disordered structures in polycrystalline or single-crystal samples, despite the presence of defects or multidimensional disorder.