Convergent Beam Electron Diffraction Patterns Research Articles

High-speed 4-dimensional scanning transmission electron microscopy using compressive sensing techniques.

Here we show that compressive sensing allows 4-dimensional (4-D) STEM data to be obtained and accurately reconstructed with both high-speed and reduced electron fluence. The methodology needed to achieve these results compared to conventional 4-D approaches requires only that a random subset of probe locations is acquired from the typical regular scanning grid, which immediately generates both higher speed and the lower fluence experimentally. We also consider downsampling of the detector, showing that oversampling is inherent within convergent beam electron diffraction (CBED) patterns and that detector downsampling does not reduce precision but allows faster experimental data acquisition. Analysis of an experimental atomic resolution yttrium silicide dataset shows that it is possible to recover over 25 dB peak signal-to-noise ratio in the recovered phase using 0.3% of the totaldata. Lay abstract: Four-dimensional scanning transmission electron microscopy (4-D STEM) is a powerful technique for characterizing complex nanoscale structures. In this method, a convergent beam electron diffraction pattern (CBED) is acquired at each probe location during the scan of the sample. This means that a 2-dimensional signal is acquired at each 2-D probe location, equating to a 4-D dataset. Despite the recent development of fast direct electron detectors, some capable of 100kHz frame rates, the limiting factor for 4-D STEM is acquisition times in the majority of cases, where cameras will typically operate on the order of 2kHz. This means that a raster scan containing 256^2 probe locations can take on the order of 30s, approximately 100-1000 times longer than a conventional STEM imaging technique using monolithic radial detectors. As a result, 4-D STEM acquisitions can be subject to adverse effects such as drift, beam damage, and sample contamination. Recent advances in computational imaging techniques for STEM have allowed for faster acquisition speeds by way of acquiring only a random subset of probe locations from the field of view. By doing this, the acquisition time is significantly reduced, in some cases by a factor of 10-100 times. The acquired data is then processed to fill-in or inpaint the missing data, taking advantage of the inherently low-complex signals which can be linearly combined to recover the information. In this work, similar methods are demonstrated for the acquisition of 4-D STEM data, where only a random subset of CBED patterns are acquired over the raster scan. We simulate the compressive sensing acquisition method for 4-D STEM and present our findings for a variety of analysis techniques such as ptychography and differential phase contrast. Our results show that acquisition times can be significantly reduced on the order of 100-300 times, therefore improving existing frame rates, as well as further reducing the electron fluence beyond just using a faster camera.

3D electron diffraction goes multipolar.

Over 30 years ago, it was shown that bonding between atoms has a noticeable effect on convergent beam electron diffraction patterns. The paper by Olech et al. [(2024). IUCrJ, 11, 309-324] demonstrates that its influence is also clearly present in 3D electron diffraction data, opening up new possibilities for quantum crystallography.

Observations of specimen morphology effects on near-zone-axis convergent-beam electron diffraction patterns.

This work presents observations of symmetry breakages in the intensity distributions of near-zone-axis convergent-beam electron diffraction (CBED) patterns that can only be explained by the symmetry of the specimen and not the symmetry of the unit cell describing the atomic structure of the material. The specimen is an aluminium-copper-tin alloy containing voids many tens of nanometres in size within continuous single crystals of the aluminium host matrix. Several CBED patterns where the incident beam enters and exits parallel void facets without the incident beam being perpendicular to these facets are examined. The symmetries in their intensity distributions are explained by the specimen morphology alone using a geometric argument based on the multislice theory. This work shows that it is possible to deduce nanoscale morphological information about the specimen in the direction of the electron beam - the elusive third dimension in transmission electron microscopy - from the inspection of CBED patterns.

Electronic and nanoscale structures of metal oxyhalide intergrowth photocatalysts

Multimetal oxyhalide intergrowths show promise for photocatalytic water splitting. However, the relationships between intergrowth stoichiometry and their electronic and nanoscale structures are yet to be identified. This study investigates Bi4TaO8Cl–Bi2GdO4Cl intergrowths and demonstrates that stoichiometry controls the tilting of [TaO6] octahedra, influencing the bandgap of the photocatalyst and its valence and conduction band positions. To determine how the [TaO6] octahedral tilting in the intergrowths manifests as a function of intergrowth stoichiometry, we investigated changes in crystal symmetry by analyzing features arising at the higher order Laue zone (HOLZ) of convergent-beam electron diffraction patterns. Higher Ta content intergrowths displayed a more intense outer HOLZ ring compared to lower Ta content intergrowths, indicating transformation from P21cn (orthorhombic) to P4/mmm (tetragonal). This finding suggests that more distortion occurs along the ⟨001⟩ directions of the crystal than the ⟨100⟩ and ⟨010⟩ directions. This variation directly impacts the electronic structure, affecting both conduction and valence band energy levels. By combining ultraviolet photoelectron spectroscopy, UV-visible diffuse reflectance spectroscopy, and electron energy loss spectroscopy, the absolute band positions of the intergrowths were determined. Agreement between the bandgaps obtained via ensemble and nanoscale measurements indicates nanoscale homogeneity of the electronic structure. Overall, the integrated approach establishes that the bandgap energy increases with increasing Ta content, which is correlated with the crystal symmetry and [TaO6] octahedral tilting. Broadly, the modular nature of intergrowths provides building block layers to tune octahedral tilting within perovskite layers for manipulation of optoelectronic properties.

Direct observation of rotation of polarization at 90-degree domain walls in BaTiO3

The rotation of polarization at 90-degree domain walls in tetragonal BaTiO3 was directly observed by the STEM-CBED method, which combines scanning transmission electron microscopy and convergent-beam electron diffraction (CBED). The CBED patterns in the domain wall region exhibit continuous changes in intensity distribution within disks and specific features corresponding to the direction of the rotation of polarization. Simulations were performed using hypothetical superstructures created by continuously connecting Ti displacement with a 90-degree rotation and showed good qualitative agreement with the experimental patterns. The quantitative evaluation of the mirror symmetries existing in the tetragonal structure in bulk form revealed the width of the domain wall is approximately 9 nm. While distorted regions with slightly broken symmetry in CBED disks were found to extend further on both sides of the domain wall region in 6–7 nm. This finding can explain the discrepancy in the domain wall widths reported in previous studies.

Phase Object Reconstruction for 4D-STEM using Deep Learning

Abstract In this study, we explore the possibility to use deep learning for the reconstruction of phase images from 4D scanning transmission electron microscopy (4D-STEM) data. The process can be divided into two main steps. First, the complex electron wave function is recovered for a convergent beam electron diffraction pattern (CBED) using a convolutional neural network (CNN). Subsequently, a corresponding patch of the phase object is recovered using the phase object approximation. Repeating this for each scan position in a 4D-STEM dataset and combining the patches by complex summation yields the full-phase object. Each patch is recovered from a kernel of 3×3 adjacent CBEDs only, which eliminates common, large memory requirements and enables live processing during an experiment. The machine learning pipeline, data generation, and the reconstruction algorithm are presented. We demonstrate that the CNN can retrieve phase information beyond the aperture angle, enabling super-resolution imaging. The image contrast formation is evaluated showing a dependence on the thickness and atomic column type. Columns containing light and heavy elements can be imaged simultaneously and are distinguishable. The combination of super-resolution, good noise robustness, and intuitive image contrast characteristics makes the approach unique among live imaging methods in 4D-STEM.

4D-STEM Ptychography for Electron-Beam-Sensitive Materials.

Recent advances in high-speed pixelated electron detectors have substantially facilitated the implementation of four-dimensional scanning transmission electron microscopy (4D-STEM). A critical application of 4D-STEM is electron ptychography, which reveals the atomic structure of a specimen by reconstructing its transmission function from redundant convergent-beam electron diffraction patterns. Although 4D-STEM ptychography offers many advantages over conventional imaging modes, this emerging technique has not been fully applied to materials highly sensitive to electron beams. In this Outlook, we introduce the fundamentals of 4D-STEM ptychography, focusing on data collection and processing methods, and present the current applications of 4D-STEM ptychography in various materials. Next, we discuss the potential advantages of imaging electron-beam-sensitive materials using 4D-STEM ptychography and explore its feasibility by performing simulations and experiments on a zeolite material. The preliminary results demonstrate that, at the low electron dose required to preserve the zeolite structure, 4D-STEM ptychography can reliably provide higher resolution and greater tolerance to the specimen thickness and probe defocus as compared to existing imaging techniques. In the final section, we discuss the challenges and possible strategies to further reduce the electron dose for 4D-STEM ptychography. If successful, it will be a game-changer for imaging extremely sensitive materials, such as metal-organic frameworks, hybrid halide perovskites, and supramolecular crystals.

Orbital angular momentum-resolved convergent-beam electron diffraction by the post-selected injection of electron beam.

Recent advances in the production of electron vortex beams carrying orbital angular momentum (OAM) offer unique opportunities to explore materials at the nanoscale level. We present a novel method for observing convergent-beam electron diffraction (CBED) patterns by using an electron vortex beam. In a transmission electron microscope, a series of electron vortex beams generated by a forked grating mask located above the specimen illuminate the specimen, and CBED patterns are imaged onto the observation plane of the microscope, selecting one of the electron vortex beams using an aperture located beneath the specimen. We demonstrate that the post-selection method yields the same OAM-resolved CBED patterns as when a single convergent electron beam is injected. The formation mechanism of the post-selected CBED is also discussed. This post-selection method is general and can be applied to electron energy-loss spectroscopy to probe multipole excitations using electron vortex beams.

Potentials of individual atoms by convergent beam electron diffraction

In convergent beam electron diffraction (CBED) on two-dimensional (2D) materials, the intensity distributions within the individual CBED spots map the local atomic arrangements within the probed region. In this study we demonstrate that the average intensities within the CBED spots essentially depend on the scattering parameters by a single atom, thus, offering the possibility of the direct measurement of such parameters. Scattering potential of an individual atom can be approximated by the Gaussian function and its parameters, the standard deviation and the maximal phase shift, can be recovered from the ratio of the intensities in the zero- and higher orders spots in CBED pattern. In order to demonstrate this, we simulated CBED patterns and extracted the atomic scattering parameters from such patterns. In the simulated examples, no weak phase object approximation is applied and the proposed method provides accurate results even for materials with large phase shifts up to 1.5 rad, as for example tungsten. The scattering parameters recovered from the experimental CBED patterns of graphene and twisted graphene-hBN structure show good agreement with the theoretically obtained values.

Imaging defects in two-dimensional crystals by convergent-beam electron diffraction

Convergent-beam electron diffraction (CBED), recently demonstrated on two-dimensional (2D) materials, offers a number of interesting applications such as imaging atomic in- and out-of plane shifts, interlayer distances, and individual adsorbates. In this study, we show how CBED allows for atomic-precision imaging of individual defects in 2D materials using one single-shot intensity measurement. In combination with structural calculations using density-functional theory, we present simulated CBED patterns for various defects in graphene, each of which exhibits a unique fingerprint distribution. We also show how atomic positions, including the individual atomic defects in graphene, can be reconstructed by iterative phase retrieval from a single CBED pattern.

Space group determination and first-principles structure optimization of the A -site ordered perovskite-type manganite NdBaMn2O6

Space groups and crystal structures of $A$-site ordered ${\mathrm{NdBaMn}}_{2}{\mathrm{O}}_{6}$ perovskite have been investigated by a combination of selected-area electron diffraction (SAED), convergent-beam electron diffraction (CBED), and first-principles methods at high-temperature (HT $\ensuremath{\approx}$ 450 K), room-temperature (RT $\ensuremath{\approx}$ 293 K), and low-temperature (LT $\ensuremath{\approx}$ 95 K) phases. By symmetry analysis of the CBED patterns, space groups of ${\mathrm{NdBaMn}}_{2}{\mathrm{O}}_{6}$ at HT, RT, and LT phases have been determined to be $P4/mmm$ (No. 123), $C2mm$ (No. 38), and $P{2}_{1}am$ (No. 26), respectively. The space groups and the optimized structures using first-principle calculations at the HT and RT phases allow a single crystallographic site for Mn atoms, indicating no charge ordering state. At the LT phase, the observed SAED and CBED patterns revealed the existence of fourfold periodicity along the $c$ axis compared with the pseudocubic unit cell. The optimized structure of the LT phase suggested four inequivalent Mn sites classified into two crystallographically different ${\mathrm{MnO}}_{2}$ layers. Moreover, the structure showed that the four distinct ${\mathrm{MnO}}_{6}$ octahedra are similarly compressed in the apical direction.

Polarization fluctuation of BaTiO3 at unit cell level mapped by four-dimensional scanning transmission electron microscopy

Diffraction analysis in four-dimensional scanning transmission electron microscopy now enables the mapping of local structures including symmetry, strain, and polarization of materials. However, measuring the distribution of these configurations at the unit cell level remains a challenge because most analysis methods require the diffraction disks to be separated, limiting the electron probe sizes to be larger than a unit cell. Here, we show improved spatial resolution in mapping the polarization displacement and phases of BaTiO3 sampled at a rate equivalent to the size of the projected unit cells using 4D-STEM. This improvement in spatial resolution is accomplished by masking out the overlapping regions in partially overlapped convergent beam electron diffraction patterns. By reducing the probe size to the order of single projected unit cells in size, the measurement shows local fluctuation within the nanosized rhombohedral domains in tetragonal phased BaTiO3, indicating the origin of phase transition and evolution across different length scales.

Machine learning calculation of large-angle convergent-beam electron diffraction patterns

Machine learning calculation of large-angle convergent-beam electron diffraction patterns

Electric-field response of polar nanodomains in BaTiO3

In this study, we have investigated the electric-field response of polar nanodomains in the ferroelectric tetragonal phase of BaTiO3. Polar nanodomains were observed by a combination of scanning transmission electron microscopy (STEM) and convergent-beam electron diffraction (CBED). By applying an electric-field, significant changes in the distributions of nanometer-size domains were observed, besides the changes in the configurations of mesoscopic 90° and 180° ferroelectric domains. The obtained CBED patterns are categorized into three. One has higher tetragonal symmetry, and the other two show a deviation from tetragonal symmetry and exhibit a left-right reversal relation with each other. We propose a structural model of the rhombohedral nanodomain redistribution to reproduce the observed CBED patterns. The model consists of a balanced change in volume and size of rhombohedral nanodomains.

Improvement of precision in refinements of structure factors using convergent-beam electron diffraction patterns taken at Bragg-excited conditions

A local structure analysis method based on convergent-beam electron diffraction (CBED) has been used for refining isotropic atomic displacement parameters and five low-order structure factors with sin θ/λ ≤ 0.28 Å-1 of potassium tantalate (KTaO3). Comparison between structure factors determined from CBED patterns taken at the zone-axis (ZA) and Bragg-excited conditions is made in order to discuss their precision and sensitivities. Bragg-excited CBED patterns showed higher precision in the refinement of structure factors than ZA patterns. Consistency between higher precision and sensitivity of the Bragg-excited CBED patterns has been found only for structure factors of the outer zeroth-order Laue-zone reflections with larger reciprocal-lattice vectors. Correlation coefficients among the refined structure factors in the refinement of Bragg-excited patterns are smaller than those of the ZA ones. Such smaller correlation coefficients lead to higher precision in the refinement of structure factors.

Bloch-wave interpretations of Gjønnes-Moodie lines in convergent-beam electron diffraction for non-symmorphic space-group crystals.

The contrast of Gjønnes-Moodie (GM) lines which appear in convergent-beam electron diffraction patterns for non-symmorphic space-group crystals is explained using Bloch waves. In the two-dimensional space groups p2mg and pg the Bloch waves for electron diffraction are described. In both space groups along the Δ line, Bloch waves are arranged as two different types, and it is shown that the two types of Bloch waves do not contribute to the intensity of forbidden reflections. Along the position where the forbidden reflection satisfies the Bragg condition, degeneracies of two Bloch waves are found and it is shown that the degenerated pair of Bloch waves do not contribute to the intensity. These Bloch-wave results provide a new perspective in the understanding of the contrast mechanism of GM lines previously described using scattering polynomials. They also advance the understanding of Bloch-wave behaviour in high-energy electron diffraction.

Local crystal symmetry and structure at CaTiO3 twin boundaries

The local crystal symmetry and crystal structure at CaTiO3 twin boundaries were examined using convergent-beam electron diffraction (CBED). CBED patterns obtained right at the twin boundaries exhibited one mirror symmetry not observed in the bulk form. Two types of crystal structures were identified at the boundaries on different boundary widths and symmetry breaking. Quantitative analysis using CBED patterns revealed atomic shifts of Ti and Ca. A distortion of oxygen octahedra was also produced, which was smaller than the corresponding distortion obtained in the bulk form. The refined crystal structure conforms to the polar structure expected only at CaTiO3 twin boundaries.

HOLOGRAPHIC CONVERGENT ELECTRON BEAM DIFFRACTION (CBED) IMAGING OF TWO-DIMENSIONAL CRYSTALS

Convergent beam electron diffraction (CBED) performed on two-dimensional (2D) materials recently emerged as a powerful tool to study structural and stacking defects, adsorbates, atomic 3D displacements in the layers, and the interlayer distances. The formation of the interference patterns in individual CBED spots of 2D crystals can be considered as a hologram, thus the CBED patterns can be directly reconstructed by conventional reconstruction methods adapted from holography. In this study, we review recent results applying CBED to 2D crystals and their heterostructures: holographic CBED on bilayers with the reconstruction of defects and the determination of interlayer distance, CBED on 2D crystal monolayers to reveal adsorbates, and CBED on multilayered van der Waals systems with moiré patterns for local structural determination.

In situ TEM observations of thickness effect on grain growth in pure titanium thin films

Ultrafine-grained materials have a strong tendency to transform into coarse-grained materials due to the high density of grain boundaries at elevated temperature. In this study, pure titanium was processed by high-pressure torsion for 10 turns to give an ultrafine-grained (UFG) structure with an average grain size of ~96 nm. The recrystallization behavior of the UFG Ti was investigated by in-situ transmission electron microscopy (TEM). It is found that the gradient microstructures with average grain size ranging from ~129 nm to ~655 nm are formed under in-situ TEM heating up to 800 °C for 30 min. The Kossel-Möllenstedt (K-M) fringes in a convergent-beam electron diffraction (CBED) pattern were used to provide an accurate measure of the sample thicknesses. The results demonstrate that grain growth is significantly suppressed in the UFG pure Ti thin film compared to bulk material. Mechanism analysis shows the combined effects of driving force and drag force on grain boundary migration is the primary cause of the grain growth inhibition in the UFG pure Ti thin film.

Evaluation of TEM specimen quality prepared by focused ion beam using symmetry breaking index of convergent-beam electron diffraction.

Degradation of the crystalline quality of transmission electron microscopy specimens in silicon prepared with different conditions has been examined using convergent-beam electron diffraction (CBED). The specimens are prepared using focused ion beam (FIB) with different accelerating voltages, Ar-ion milling and crushing method. Symmetry breaking of CBED patterns was quantitatively evaluated by symmetry breaking index S, which has been previously reported. The degradation and inhomogeneity of the FIB specimen were suppressed by decreasing the accelerating voltages of the FIB fabrication in the final process.