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.

A new electron diffraction approach for structure refinement applied to Ca3Mn2O7

The digital large-angle convergent-beam electron diffraction (D-LACBED) technique is applied to Ca3Mn2O7 for a range of temperatures. Bloch-wave simulations are used to examine the effects that changes in different parameters have on the intensity in D-LACBED patterns, and atomic coordinates, thermal atomic displacement parameters and apparent occupancy are refined to achieve a good fit between simulation and experiment. The sensitivity of the technique to subtle changes in structure is demonstrated. Refined structures are in good agreement with previous determinations of Ca3Mn2O7 and show the decay of anti-phase oxygen octahedral tilts perpendicular to the c axis of the A21am unit cell with increasing temperature, as well as the robustness of oxygen octahedral tilts about the c axis up to ∼400°C. The technique samples only the zero-order Laue zone and is therefore insensitive to atom displacements along the electron-beam direction. For this reason it is not possible to distinguish between in-phase and anti-phase oxygen octahedral tilting about the c axis using the [110] data collected in this study.

Holographic reconstruction of the interlayer distance of bilayer two-dimensional crystal samples from their convergent beam electron diffraction patterns

The convergent beam electron diffraction (CBED) patterns of twisted bilayer samples exhibit interference patterns in their CBED spots. Such interference patterns can be treated as off-axis holograms and the phase of the scattered waves, meaning the interlayer distance can be reconstructed. A detailed protocol of the reconstruction procedure is provided in this study. In addition, we derive an exact formula for reconstructing the interlayer distance from the recovered phase distribution, which takes into account the different chemical compositions of the individual monolayers. It is shown that one interference fringe in a CBED spot is sufficient to reconstruct the distance between the layers, which can be practical for imaging samples with a relatively small twist angle or when probing small sample regions. The quality of the reconstructed interlayer distance is studied as a function of the twist angle. At smaller twist angles, the reconstructed interlayer distance distribution is more precise and artefact free. At larger twist angles, artefacts due to the moiré structure appear in the reconstruction. A method for the reconstruction of the average interlayer distance is presented. As for resolution, the interlayer distance can be reconstructed by the holographic approach at an accuracy of ±0.5 Å, which is a few hundred times better than the intrinsic z-resolution of diffraction limited resolution, as expressed through the spread of the measured k-values. Moreover, we show that holographic CBED imaging can detect variations as small as 0.1 Å in the interlayer distance, though the quantitative reconstruction of such variations suffers from large errors.

The importance of temporal and spatial incoherence in quantitative interpretation of 4D-STEM

Recent developments in pixelated detectors, when combined with aberration correction of probe forming optics have greatly enhanced the field of scanning electron diffraction. Differential phase contrast is now routine and deep learning has been proposed as a method to extract maximum information from diffraction patterns. This work examines the effects of temporal and spatial incoherence on convergent beam electron diffraction patterns and demonstrates that simple center of mass measurements cannot be naively interpreted. The inclusion of incoherence in deep learning data sets is also discussed.

Comparative study on the specimen thickness measurement using EELS and CBED methods

Two thickness measurement methods using an electron energy loss spectroscopy (EELS) and 10a convergent beam electron diffraction (CBED) were compared in an Fe-18Mn-0.7C alloy. The thin foil specimen was firstly tilted to satisfy 10a two-beam condition. Low loss spectra of EELS and CBED patterns were acquired in scanning transmission electron microscopy (STEM) and TEM-CBED modes under the two-beam condition. The log-ratio method was used for measuring the thin foil thickness. Kossel-Möllenstedt (K-M) fringe of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbf{13}\overline{\mathbf{1}} $$\end{document}131¯ diffracted disk of austenite was analyzed to evaluate the thickness. The results prove the good coherency between both methods in the thickness range of 72 ~ 113 nm with a difference of less than 5%.

Thickness and Stacking Sequence Determination of Exfoliated Dichalcogenides (1T-TaS2, 2H-MoS2) Using Scanning Transmission Electron Microscopy

Layered transition metal dichalcogenides (TMDs) have attracted interest due to their promise for future electronic and optoelectronic technologies. As one approaches the two-dimensional (2D) limit, thickness and local topology can greatly influence the macroscopic properties of a material. To understand the unique behavior of TMDs it is therefore important to identify the number of atomic layers and their stacking in a sample. The goal of this work is to extract the thickness and stacking sequence of TMDs directly by matching experimentally recorded high-angle annular dark-field scanning transmission electron microscope images and convergent-beam electron diffraction (CBED) patterns to quantum mechanical, multislice scattering simulations. Advantageously, CBED approaches do not require a resolved lattice in real space and are capable of neglecting the thickness contribution of amorphous surface layers. Here we demonstrate the crystal thickness can be determined from CBED in exfoliated 1T-TaS2 and 2H-MoS2 to within a single layer for ultrathin ≲9 layers and ±1 atomic layer (or better) in thicker specimens while also revealing information about stacking order-even when the crystal structure is unresolved in real space.

Identification of Phase Boundaries and Electrical Properties in Ternary Potassium-Sodium Niobate-Based Ceramics

A large piezoelectric constant (d33) of ∼480 pC/N was attained in new ternary (1-x-y)K0.5Na0.5Nb0.96Sb0.04O3-xBaSnO3-yBi0.5Na0.5ZrO3 ceramics by forming rhombohedral-orthorhombic-tetragonal (R-O-T) phase boundary using the variations of x and y, and such a phase boundary was successfully confirmed by the convergent beam electron diffraction (CBED) patterns. For (1-x)K0.5Na0.5Nb0.96Sb0.04O3-xBaSnO3, the orthorhombic (O) phase is well-maintained for 0 ≤ x ≤ 0.015, and both the R and T phases can be introduced to (0.99-y)K0.5Na0.5Nb0.96Sb0.04O3-0.01BaSnO3-yBi0.5Na0.5ZrO3 with y = 0.025-0.04 by simultaneously tailoring their compositions (x and y); then, R-O-T multiphases can be well-established. The CBED patterns strongly support the existence of R-O-T multiphases in the ceramics with y = 0.035. When the phase transitions endure from O to R-O-T, their piezoelectric activity endures a leapfrog development from ∼165 to ∼480 pC/N. In the region of the R-O-T phase boundary, a large d33 of ∼480 pC/N was attained in the ceramics with x = 0.01 and y = 0.035. In addition, the ceramics with x = 0.01 and y = 0.04 possess a high strain of ∼0.274% due to the multiphases coexistence. According to the variations of dielectric and ferroelectric properties, the enhancement in εr and Pr plays a part in the improved d33 except for the R-O-T phase boundary. We believe that the (K, Na)NbO3 ternary systems can be used to promote piezoelectric activity by forming new phase boundaries.

Determination of three-dimensional strain state in crystals using self-interfered split HOLZ lines

An experimental method to measure the strain through the thickness of a crystal is demonstrated. This enables the full three-dimensional stress-strain state of a crystal at the nanoscale to be determined taking the current practice from two-dimensional strain state determination. Knowing the 3D strain state is desired by crystal growers in order to improve their crystal's quality. This method involves combining electron diffraction with electron interferometry in a transmission electron microscope. The electron diffraction uses a split higher order Laue zone (HOLZ) line and the electron interferometry uses an electron biprism.

Automated CBED processing: sample thickness estimation based on analysis of zone-axis CBED pattern

An automated processing of convergent beam electron diffraction (CBED) patterns is presented. The proposed methods are used in an automated tool for estimating the thickness of transmission electron microscopy (TEM) samples by matching an experimental zone-axis CBED pattern with a series of patterns simulated for known thicknesses. The proposed tool detects CBED disks, localizes a pattern in detected disks and unifies the coordinate system of the experimental pattern with the simulated one. The experimental pattern is then compared disk-by-disk with a series of simulated patterns each corresponding to different known thicknesses. The thickness of the most similar simulated pattern is then taken as the thickness estimate. The tool was tested on [0 1 1] Si, [0 1 0] α-Ti and [0 1 1] α-Ti samples prepared using different techniques. Results of the presented approach were compared with thickness estimates based on analysis of CBED patterns in two beam conditions. The mean difference between these two methods was 4.1% for the FIB-prepared silicon samples, 5.2% for the electro-chemically polished titanium and 7.9% for Ar(+) ion-polished titanium. The proposed techniques can also be employed in other established CBED analyses. Apart from the thickness estimation, it can potentially be used to quantify lattice deformation, structure factors, symmetry, defects or extinction distance.

Direct atomic structure determination by the inspection of structural phase

A century has passed since Bragg solved the first atomic structure using diffraction. As with this first structure, all atomic structures to date have been deduced from the measurement of many diffracted intensities using iterative and statistical methods. We show that centrosymmetric atomic structures can be determined without the need to measure or even record a diffracted intensity. Instead, atomic structures can be determined directly and quickly from the observation of crystallographic phases in electron diffraction patterns. Furthermore, only a few phases are required to achieve high resolution. This represents a paradigm shift in structure determination methods, which we demonstrate with the moderately complex α-Al2O3. We show that the observation of just nine phases enables the location of all atoms with a resolution of better than 0.1 Å. This level of certainty previously required the measurement of thousands of diffracted intensities.

Digital electron diffraction--seeing the whole picture

Computer control of beam tilt and image capture allows the collection of electron diffraction patterns over a large angular range, without any overlap in diffraction data and from a region limited only by the size of the electron beam. This results in a significant improvement in data volumes and ease of interpretation.

The advantages of convergent-beam electron diffraction for symmetry determination at the scale of a few nm are well known. In practice, the approach is often limited due to the restriction on the angular range of the electron beam imposed by the small Bragg angle for high-energy electron diffraction, i.e. a large convergence angle of the incident beam results in overlapping information in the diffraction pattern. Techniques have been generally available since the 1980s which overcome this restriction for individual diffracted beams, by making a compromise between illuminated area and beam convergence. Here a simple technique is described which overcomes all of these problems using computer control, giving electron diffraction data over a large angular range for many diffracted beams from the volume given by a focused electron beam (typically a few nm or less). The increase in the amount of information significantly improves the ease of interpretation and widens the applicability of the technique, particularly for thin materials or those with larger lattice parameters.