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Raw and Processed 4D-STEM datasets organized by particles appeared in each figure in the publication. 1. Figure 1. 2. Figure 2. 3. Figure 3. 4. Figure S7. 5. Readme.txt
Y2TiO5 belongs to the Ln2TiO5 (Ln = lanthanide or Y) family of ceramic materials and exhibits a range of desirable material properties such as radiation tolerance, frustrated magnetism, and large dielectric constant. However, understanding the complex crystal structure of Y2TiO5 remains elusive, given that Y2TiO5 can adopt multiple polymorphs such as cubic, orthorhombic, and hexagonal phases within the lattice. In this work, we report a detailed structural analysis of Y2TiO5 using four-dimensional scanning transmission electron microscopy coupled with unsupervised machine learning. The pyrochlore nanodomains, characterized by the ordered arrangement of yttrium cations on the A site of their A2BO5 structure, are present within the matrix of a predominantly fluorite-structured Y2TiO5 along with a third polymorph, the hexagonal phase. The pyrochlore phase is found to form 2 nm boundary regions around hexagonal phase stacking faults, highlighting the potential influence of the hexagonal phase on the occurrence and distribution of the pyrochlore phase. Lastly, we identify a unique pyrochlore phase with asymmetric arrangement of cation ordering along a single planar direction. Our findings provide invaluable insights into the possible mechanisms stabilizing pyrochlore nanodomains within the fluorite lattice of Y2TiO5.
Irradiation produces a distribution of defect sizes in materials, with the smallest defects often below one nanometer in size and approaching the scale of a single unit cell in metals. While high-resolution scanning transmission electron microscopy (STEM)-based imaging can directly image structures at this level, techniques such as four-dimensional STEM (4D-STEM) enable characterization of materials across large fields of view, capturing a more representative volume that can be valuable for quantifying defects, their distributions, and the associated strain fields. Here we present a combined HRSTEM and 4D-STEM approach to study the model system of He bubble implantation in an Au thin film. The present work is of general interest for the study of materials in extreme environments, as it demonstrates an effective way to characterize even the tiniest sub-nanometer sized He bubbles in addition to larger irradiation defects.
Four-dimensional Scanning Transmission Electron Microscopy (4D-STEM) is a powerful technique for high-resolution and high-precision materials characterization at multiple length scales, including the characterization of beam-sensitive materials. However, the field of view of 4D-STEM is relatively small, which in absence of live processing is limited by the data size required for storage. Furthermore, the rectilinear scan approach currently employed in 4D-STEM places a resolution- and signal-dependent dose limit for the study of beam sensitive materials. Improving 4D-STEM data and dose efficiency, by keeping the data size manageable while limiting the amount of electron dose, is thus critical for broader applications. Here we introduce a general method for reconstructing 4D-STEM data with subsampling in both real and reciprocal spaces at high fidelity. The approach is first tested on the subsampled datasets created from a full 4D-STEM dataset, and then demonstrated experimentally using random scan in real-space. The same reconstruction algorithm can also be used for compression of 4D-STEM datasets, leading to a large reduction (100 times or more) in data size, while retaining the fine features of 4D-STEM imaging, for crystalline samples.
Four-dimensional scanning transmission electron microscopy (4D-STEM) enables mapping of diffraction information with nanometer-scale spatial resolution, offering detailed insight into local structure, orientation, and strain. However, as data dimensionality and sampling density increase, particularly for in situ scanning diffraction experiments (5D-STEM), robust segmentation of structurally consistent behavior across sequential measurements becomes essential for efficient and physically meaningful analysis. Here, we introduce a clustering framework that identifies crystallographically distinct domains from 4D-STEM datasets. By using local diffraction-pattern similarity as a metric, the method extracts closed contours delineating spatially contiguous regions. This approach produces cluster-averaged diffraction patterns that improve signal quality while reducing data volume by orders of magnitude, enabling rapid and accurate orientation, phase, and strain mapping. We demonstrate the applicability of this approach to in situ liquid-cell 4D-STEM data of gold nanoparticle growth. Our method provides a scalable and generalizable route for spatially coherent segmentation, data compression, and quantitative structure–strain mapping across diverse 4D-STEM modalities. The full analysis code and example workflows are publicly available to support reproducibility and reuse.
Precession of a converged beam during acquisition of a 4D-STEM dataset improves strain, orientation, and phase mapping accuracy by averaging over continuous angles of illumination. Precession experiments usually rely on integrated systems, where automatic alignments lead to fast, high-quality results. The dependence of these experiments on specific hardware and software is evident even when switching to nonintegrated detectors on a precession tool, as experimental set-up becomes challenging and time-consuming. Here, we introduce multi-angle precession electron diffraction (MAPED): a method to perform electron diffraction by collecting sequential 4D-STEM scans at different incident beam tilts. The multiple diffraction datasets are averaged together postacquisition, resulting in a single dataset that minimizes the impact of the curvature and orientation of the Ewald sphere relative to the crystal under study. Our results demonstrate that even four additional tilts improved measurement of material properties, namely strain and orientation, as compared to single-tilt 4D-STEM experiments. We show the versatility and flexibility of our MAPED approach with data collected on a number of microscopes with different hardware configurations and a variety of detectors.
Silicon carbide (SiC) fiber-reinforced SiC matrix composites (SiCf-SiCm) are promising materials for accident-tolerant fuel (ATF) cladding in light water reactors. This paper, using four-dimensional scanning transmission electron microscopy (4D-STEM), studied the microstructure of SiCf-SiCm at nanoscale and provided grain statistics at the CVI/fiber region. Here, the results reveal that CVI region mainly contain irregular sub-micron grains (115 nm to 1800 nm) with a preferred orientation, while the fiber region has nano equiaxed grains (21 nm to 78 nm) with random orientations. Centered dark field imaging over the fiber regions verified the grain size measurement by 4D-STEM. Through 4D-STEM virtual dark field imaging and orientation mapping, intragranular propagation was identified as the fracture mechanism for a microcrack observed within the CVI region. The amorphous pyrolytic carbon layer was also shown to effectively arrest the microcrack.
The structural evolution of NiTi during the B2→B19’ martensitic phase transformation via thermal cycling is investigated using in situ four dimensional scanning transmission electron microscopy (4D-STEM). With 4D-STEM, we can directly visualize and quantify the nanoscale evolution of the martensitic structure on thermal cycling and also investigate the origin of diffuse scattering of NiTi in the pre-transitional state. Mapping of the martensite orientation and strain visualizes the progression of the transformation front and self-accommodation of the B19’ structure. Diffuse streaking and strain are measured in the pre-transitional austenite (B2) phase and demonstrate no localization or preferential directionality hinting that long-range homogeneous instability rather than nanoscale heterogeneities may be the origin of the pre-transitional anomalies in NiTi. Finally, it is revealed that NiTi does not reform the same martensite nanostructure on thermal cycling but does express similar features. This small variation is likely owing to transformation-induced dislocations.
Li- and Mn-rich (LMR) layered oxides are known to exhibit a thin surface reconstruction layer, which grows during electrochemical cycling in a manner that depends on exposed crystallographic facets, cycling conditions, and electrolyte chemistry. Direct characterization of this layer has traditionally relied on high-resolution electron microscopy, which is inherently limited to small fields of view. Here, we employ four-dimensional scanning transmission electron microscopy (4D-STEM) combined with unsupervised machine-learning clustering to quantitatively map phase distributions over large areas and track their evolution in LMR cathodes during electrochemical aging. Our results show that the surface reconstruction layer consists predominantly of a rocksalt phase, whose thickness varies across different facets following activation cycling and becomes substantially thicker and more uniform during calendar aging. In contrast, a spinel-like phase is observed within the particle bulk. Large-area phase mapping and correlative high-resolution imaging reveal that this spinel-like phase preferentially nucleates at bulk crystallographic defects, including boundaries between 60°-rotated layered domains and associated mixed-phase regions, rather than exclusively at the particle surface. Our findings establish a mechanistic distinction between surface-driven rocksalt formation and bulk-defect-mediated spinel nucleation while demonstrating the unique capability of 4D-STEM to provide statistically robust, mesoscale insight into complex phase-evolution processes in LMR cathodes.
In semi‐crystalline polymeric materials, the initial stages of nucleation and the growth path of crystalline domains can determine the final performance. Here, in this work, we used four‐dimensional scanning transmission electron microscopy (4D‐STEM) imaging to analyze the changes in lamellar orientation in high‐density polyethylene (HDPE) during heating and cooling. This method allowed us to quantitatively detect the formation of lamellae clusters with different in‐plane orientations, which are not visible with traditional methods. Our analysis provided detailed insights into the orientation and size changes of crystalline domains. Additionally, this technique enabled direct observation of lattice structures in hierarchical lamellae and the growth of crystals, confirming the local variability in lamellar orientation. This innovative approach significantly improves our understanding of polymer crystallization, linking changes in morphology and lattice structures at different length scales.
A two-dimensional van der Waals ferromagnet Fe 5–x GeTe 2 (F5GT) exhibits room-temperature magnetic transition and magnetic anisotropy. Studies have identified diverse magnetic states, including stripe domains, skyrmionic type-I and topologically trivial type-II bubbles, depending on the magnetic and thermal history. Yet, the underlying micromagnetic energetics driving these states remains unclear. Here, we establish the magnetic phase diagram of bulk F5GT using cryogenic Lorentz four-dimensional scanning transmission electron microscopy. We reveal that stripe domains spontaneously form upon zero-field cooling, while metastable magnetic bubbles are stabilized by external fields. Transitions from type-I to type-II bubbles are driven by an oblique external field. Micromagnetic simulations confirm that these transitions arise from the interplay of uniaxial anisotropy, dipolar interactions, and external fields, without requiring significant Dzyaloshinskii–Moriya Interaction (DMI). In conclusion, these findings clarify the micromagnetic origin of spin textures of F5GT and establish it as a tunable platform for nanoscale topological magnetism.
Structure elucidation via single-crystal methods has historically lacked experimental access to real-space information, instead relying exclusively on diffraction-space measurements of Bragg reflections. Here we exploit the dual-space imaging power of 4D scanning transmission electron microscopy to meaningfully integrate real-space information into the crystallographic workflow. We show that virtual apertures assembled by segmentation of high-angle annular dark-field images enable i) pixel-by-pixel separation of coherent Bragg signal from clusters of closely spaced nanocrystals and ii) selective extraction of integrated intensities from thinner subregions of individual specimens, facilitating retroactive tuning of multiple scattering artifacts. This strategy empowers us to simply pick and choose whichever nanoscale regions of interest generate the highest-quality diffraction patterns, allowing us to solve several independent structures of the metal-organic framework UiO-66 from specimens whose agglomerated morphology proved intractable for conventional microcrystal electron diffraction. Our method is compatible with both rotational and serial approaches to data processing, ultimately divulging the first scanning nanobeam electron diffraction structures determined by direct methods at subangstrom resolution.
Many members of the tetragonal tungsten bronze (TTB) family of oxides display an incommensurate periodic lattice distortion, the nature of which has been the subject of some controversy. Here we present a study of this structural modulation in the relaxor ferroelectric Ba 5 SmSn 3 Nb 7 O 30 (BSSN) by quantitative scanning transmission electron microscopy (STEM). Additionally, we characterize the modulation in BSSN by employing a fast, pixelated direct electron detector to perform high resolution phase contrast STEM imaging of the crystalline lattice. By quantitatively analyzing the images, we visualize the atomic structural correlations present in the material on both the cation and anion sublattices. This analysis reveals the incommensurate structure to have an octahedral tilting pattern and cooperative A2 site cation displacements, analogous to an Ama2 commensurate cell. Finally, we show that the modulation is composed of a structural motif with a period of 3 x $d_{1\bar{1}0}$ and modified by discommensurations, likely arise from frustrated octahedral tilting in the odd-valued periodicity.
Chemical reaction kinetics at the nanoscale are intertwined with heterogeneity in structure and composition. However, mapping such heterogeneity in a liquid environment is extremely challenging. Here, in this work, we integrate graphene liquid cell (GLC) transmission electron microscopy and four-dimensional scanning transmission electron microscopy to image the etching dynamics of gold nanorods in the reaction media. Critical to our experiment is the small liquid thickness in a GLC that allows the collection of high-quality electron diffraction patterns at low dose conditions. Machine learning-based data-mining of the diffraction patterns maps the three-dimensional nanocrystal orientation, groups spatial domains of various species in the GLC, and identifies newly generated nanocrystallites during reaction, offering a comprehensive understanding on the reaction mechanism inside a nanoenvironment. This work opens opportunities in probing the interplay of structural properties such as phase and strain with solution-phase reaction dynamics, which is important for applications in catalysis, energy storage, and self-assembly.
Four-dimensional scanning transmission electron microscopy (4D-STEM) is powerful for rapidly characterizing arrays of nanoparticles produced via high-throughput synthesis. However, such 4D-STEM datasets typically contain thousands of nanoparticles, each characterized by thousands of diffraction patterns spatially distributed across the nanoparticle, necessitating efficient and comprehensive analysis. We propose an end-to-end segmentation framework to automatically segment each nanoparticle into regions with distinct composition/orientation of crystal grains, using only the 4D-STEM data. Bragg disk information is extracted in a physics-informed manner from the diffraction patterns at each spatial location and combined with the real space coordinates to form feature vectors. These feature vectors are then used as inputs to a Gaussian mixture model (GMM) to segment the nanoparticle into distinct regions. We also develop two visualization tools based on the GMM outputs to infer the interface transition and the degree of superposition. Our framework comprehensively integrates machine learning tools and physics knowledge, and provides a basis for substantially compressing enormous 4D-STEM datasets, e.g., by replacing the full 4D-STEM dataset for each nanoparticle with only a single set of Bragg disk features for each distinct crystal grain identified in the nanoparticle. In this article, we demonstrate the power of our framework by presenting results for real, complex datasets.
Determining atomic structures in crystalline materials—where atoms are arranged in rigid, periodic lattices—has been highly successful using probes such as electrons, X-rays, and neutrons. In contrast, amorphous materials, despite their ubiquity and technological importance, remain far more challenging to characterize with comparable accuracy and precision. This review highlights existing, emerging, and potential (scanning) transmission electron microscopy ((S)TEM) techniques for probing short- and medium-range order in amorphous materials. Approaches ranging from high-resolution (S)TEM imaging and selected electron diffraction pattern to four-dimensional STEM (4D-STEM) based pair distribution function, fluctuation electron microscopy, tomography, ptychography, and spectroscopic methods are discussed, emphasizing their ability to provide complementary insights across multiple length scales—from sub-angstrom local environments to nanometer-scale correlations. Here, we further explore the promise of multimodal and correlative strategies, as well as the growing role of machine learning and physics-informed AI in enabling real-time, quantitative interpretation of complex structural signatures. Together, these advances point toward a future where electron microscopy not only reveals the hidden order in amorphous systems but also establishes robust structure–property relationships, paving the way for materials innovation in disordered matter.
High-resolution scanning transmission electron microscopy (S/TEM) is an indispensable tool for characterizing the structure and properties of materials down to the atomic scale. Conventional S/TEM imaging, however, is limited by the phase problem, whereby the phase of the electron exit wave is lost upon detection. Recent advances in diffractive imaging and 4D-STEM have enabled a range of phase-retrieval techniques that computationally reconstruct the missing information encoded in the phase of the transmission function. These approaches offer improved dose efficiency and enhanced sensitivity to weakly scattering signals, extending quantitative imaging to beam-sensitive materials composed of light elements. In this work, we introduce the phase problem in electron microscopy and survey the diverse landscape of phase-retrieval techniques used in the field. Despite their many acronyms and algorithmic variations, these techniques share a common physical and mathematical foundation. We present a unified framework that connects these seemingly distinct methods, from parallax imaging and tilt-corrected bright-field (tcBF-STEM), to aberration-corrected bright-field (acBF-STEM), optimum bright-field (OBF-STEM) and single-sideband (SSB) ptychography, as well as first-moment integrated center of mass techniques (iCOM) and iterative ptychographic algorithms. Based on these insights, we discuss the opportunities and practical limitations of applying these methods across different materials systems, detector designs, and microscope configurations.Graphical abstractRepresentative electron microscopy configurations used for phase retrieval and diffractive imaging in S/TEM: (a) Zernike phase-contrast transmission electron microscopy (TEM), (b) small-convergence-angle four-dimensional scanning transmission electron microscopy (4D-STEM) for nanobeam-based phase reconstruction methods, and (c) large-convergence-angle 4D-STEM for ptychographic and related diffractive imaging techniques reviewed in this work.
Zircaloy-4 cladding tubes were hydrogen-charged using a static pressure hydrogen charging method to experimentally produce a zirconium-hydride rim structure similar to that observed in Zircaloy-4 cladding tubes after operation in commercial light-water nuclear reactors. Detailed characterization was performed using electron energy loss spectroscopy (EELS) and four-dimensional scanning transmission electron microscopy (4D-STEM). By mapping the position of the plasmon peak in the low-loss EELS spectrum, it was determined that the zirconium hydrides formed were predominantly solid δ-phase zirconium hydrides. 4D-STEM was used to generate phase and strain maps at nanoscale. The interactions between two zirconium hydride platelets less than 200 nm apart leads to the localized lattice rotations and possible phase change, revealing a potential hydride growth mechanism.