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.

• Klíčová slova
• dynamical diffraction, orthopyroxene, precession electron diffraction, site occupancy,
• Publikační typ
• časopisecké články MeSH

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.

• Klíčová slova
• dynamical diffraction, electron crystallography, electron diffraction tomography, kaolinite, mayenite, orthopyroxene, precession,
• Publikační typ
• časopisecké články MeSH

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 system Jana2006.

• Klíčová slova
• dynamical diffraction, electron crystallography, electron diffraction tomography,
• Publikační typ
• časopisecké články MeSH

Electron diffraction tomography (EDT) data are in many ways similar to X-ray diffraction data. However, they also present certain specifics. One of the most noteworthy is the specific rocking curve observed for EDT data collected using the precession electron diffraction method. This double-peaked curve (dubbed `the camel') may be described with an approximation based on a circular integral of a pseudo-Voigt function and used for intensity extraction by profile fitting. Another specific aspect of electron diffraction data is the high likelihood of errors in the estimation of the crystal orientation, which may arise from the inaccuracies of the goniometer reading, crystal deformations or crystal movement during the data collection. A method for the refinement of crystal orientation for each frame individually is proposed based on the least-squares optimization of simulated diffraction patterns. This method provides typical angular accuracy of the frame orientations of less than 0.05°. These features were implemented in the computer program PETS 2.0. The implementation of the complete data processing workflow in the program PETS and the incorporation of the features specific for electron diffraction data is also described.

• Klíčová slova
• crystal orientation, electron diffraction tomography, precession electron diffraction, profile fitting, serial electron crystallography,
• Publikační typ
• časopisecké články MeSH

Determination of lattice parameters from 3D electron diffraction (3D ED) data measured in a transmission electron microscope is hampered by a number of effects that seriously limit the achievable accuracy. The distortion of the diffraction patterns by the optical elements of the microscope is often the most severe problem. A thorough analysis of a number of experimental datasets shows that, in addition to the well known distortions, namely barrel-pincushion, spiral and elliptical, an additional distortion, dubbed parabolic, may be observed in the data. In precession electron diffraction data, the parabolic distortion leads to excitation-error-dependent shift and splitting of reflections. All distortions except for the elliptical distortion can be determined together with lattice parameters from a single 3D ED data set. However, the parameters of the elliptical distortion cannot be determined uniquely due to correlations with the lattice parameters. They can be determined and corrected either by making use of the known Laue class of the crystal or by combining data from two or more crystals. The 3D ED data can yield lattice parameter ratios with an accuracy of about 0.1% and angles with an accuracy better than 0.03°.

• Klíčová slova
• 3D electron diffraction, distortions, lattice parameters, parabolic distortion, precession electron diffraction,
• Publikační typ
• časopisecké články MeSH

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 = [Formula: see text]a0 = 7.089(9) Å, c = c0 = 8.439(9) Å, α = β = γ = 90° and q = [Formula: see text]a* + γc*. At 100 K the model presents a pure 4-layer stacking sequence with γ = [Formula: see text] whereas at the ambient temperature, ordered stacking faults are introduced leading to γ < [Formula: see text]. 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.

• Publikační typ
• časopisecké články MeSH

The crystal structure of the U(iv)-phosphate mineral vyacheslavite has been solved from precession electron diffraction tomography (PEDT) data from the natural nano-crystal and further refined using density-functional theory (DFT) calculations. Vyacheslavite is orthorhombic, with the space group Cmca, with a ≈ 6.96 Å, b ≈ 9.07 Å and c ≈ 12.27 Å, V ≈ 775 Å3 (obtained from PEDT data at 100 K), Z = 8. Its structure is a complex heteropolyhedral framework consisting of sheets of UO7(OH) and PO4 polyhedra, running parallel to (001), interconnected by additional PO4 polyhedra. There is an (OH) group associated with the U(iv) polyhedron. The question of H2O presence within the small cavities of the framework has been addressed by the DFT calculations, which have proved that vyacheslavite does not contain any significant amount of H2O at room temperature.

• Publikační typ
• časopisecké články MeSH

Thin film processing methods used to fabricate ferroelectric hafnium zirconium oxide typically result in small-grained films with a mixture of ferroelectric and nonferroelectric crystal phases with various crystallographic orientations. Although reliable, rapid determination of grain phase and orientation from four-dimensional scanning transmission electron microscopy maps is critical for measuring increased ferroelectric response, an assessment of automated analysis methods is not available. Here, a comparison of results between commercially available software (NanoMEGAS ASTAR) and an open-source code (py4DSTEM) is presented. Typically, the lamella used for STEM characterization are thicker than the average hafnium zirconium oxide (HZO) grain size, resulting in 4D maps where dynamical diffraction from more than one grain occurs in a significant number of pixels. Thus, precession electron diffraction (PED) data was required for reliable automated template matching analysis. Reliably distinguishing between the different crystal phases of HZO is challenging due to the small difference in lattice constant between phases and the possible presence of multiple orthorhombic phases. The HZO films in this study were characterized using PED, and precession diffraction simulation capability was added to py4DSTEM. Correlation of automated phase mapping with electrical verification of the ferroelectric effect confirmed the identification of the noncentrosymmetric space group 29 orthorhombic phase of HZO.

• Klíčová slova
• ferroelectric, hafnium zirconium oxide, indexing, orientation, phase, template matching,
• Publikační typ
• časopisecké články MeSH

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.

• Publikační typ
• časopisecké články MeSH
• práce podpořená grantem MeSH

Dynamical refinement is a well established method for refining crystal structures against 3D electron diffraction (ED) data and its benefits have been discussed in the literature [Palatinus, Petříček & Corrêa, (2015). Acta Cryst. A71, 235-244; Palatinus, Corrêa et al. (2015). Acta Cryst. B71, 740-751]. However, until now, dynamical refinements have only been conducted using the independent atom model (IAM). Recent research has shown that a more accurate description can be achieved by applying the transferable aspherical atom model (TAAM), but this has been limited only to kinematical refinements [Gruza et al. (2020). Acta Cryst. A76, 92-109; Jha et al. (2021). J. Appl. Cryst. 54, 1234-1243]. In this study, we combine dynamical refinement with TAAM for the crystal structure of 1-methyluracil, using data from precession ED. Our results show that this approach improves the residual Fourier electrostatic potential and refinement figures of merit. Furthermore, it leads to systematic changes in the atomic displacement parameters of all atoms and the positions of hydrogen atoms. We found that the refinement results are sensitive to the parameters used in the TAAM modelling process. Though our results show that TAAM offers superior performance compared with IAM in all cases, they also show that TAAM parameters obtained by periodic DFT calculations on the refined structure are superior to the TAAM parameters from the UBDB/MATTS database. It appears that multipolar parameters transferred from the database may not be sufficiently accurate to provide a satisfactory description of all details of the electrostatic potential probed by the 3D ED experiment.

• Klíčová slova
• 3D electron diffraction, dynamical refinement, electron crystallography, microcrystal electron diffraction, multipolar scattering factors, quantum crystallography, transferable aspherical atom model,
• Publikační typ
• časopisecké články MeSH