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The ABCs of phase retrieval: Connecting the acronyms of scanning transmission electron microscopy

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.

36 MATERIALS SCIENCE

Site-specific nanoscale characterization of zirconium hydrides in the hydride rim structure of hydrogen-charged zircaloy-4 cladding

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.

4D-STEM

Simplex‐based model for nanoparticle grain identification in four‐dimensional scanning transmission electron microscopy data

Grain identification in polycrystalline nanoparticles, for example, determining which crystal phases are present at each spatial location, is fundamental to materials characterisation. This is particularly challenging when grains overlap extensively, as commonly occurs in four-dimensional scanning transmission electron microscopy (4D-STEM) datasets. We propose a simplex-based model (SBM) in which each simplex vertex represents the diffraction pattern (DP) of a pure grain, and the simplex edges and interior represent overlapping grains. Our SBM grain identification algorithm operates on the Bragg disk (BD) data matrix distilled from the 4D-STEM data to identify the grain membership at each scan position, together with a BD feature matrix whose columns represent the DPs for each constituent grain, which is important for identifying the crystal structure of each grain. We solve the model using a two-stage algorithm. In Stage 1, we adapt a linear mixing algorithm to estimate an initial BD feature matrix whose columns represent DPs of potentially overlapping grains. Our Stage 2 algorithm incorporates sparsity considerations to transform the initial BD feature matrix so that its columns represent DPs of pure grains. Using simulated datasets with various grain configurations, we demonstrate that SBM recovers both the BD feature matrix and membership maps more accurately than existing methods, even when a grain lacks any pure region and completely overlaps with other grains.

4D-STEM segmentation

Valence Electron Distributions from Sub-Angstrom Convergent Beam Electron Diffraction

Modern aberration-corrected scanning transmission electron microscopes can acquire four-dimensional data sets (“4D STEM”) by recording convergent beam electron diffraction (CBED) patterns, using precisely positioned, sub-angstrom probes. Here, we demonstrate that these patterns can probe the site symmetry, atomic displacements, and valence electron distributions at individual atomic columns. To this end, 4D STEM CBED patterns were acquired from SrTiO 3 single crystals and compared with patterns calculated using scattering potentials derived from density functional theory. Here, we show that an aspherical valence electron charge build-up at the oxygen sites causes intensity asymmetries in the low-angle scattering portion of the patterns. Using strained SrTiO 3 films containing subtle polar displacements within nanometer-sized domains, it is shown that the high-angle scattering portion in each pattern is sensitive to atomic displacements.

36 MATERIALS SCIENCE

3D strain field reconstruction by inversion of dynamical scattering

Strain governs not only the mechanical response of materials but also their electronic, optical, and catalytic properties. For this reason, the measurement of the 3D strain field is crucial for a detailed understanding and for further development of material properties through strain engineering. However, measuring strain variations along the electron beam direction has remained a major challenge for (scanning-) transmission electron microscopy (S/TEM). In this article, we present a method for 3D strain field determination using 4D-STEM. The method is based on the inversion of dynamical diffraction effects, which occur at strain field variations along the beam direction. We test the method against simulated data with a known ground truth and demonstrate its application to an experimental 4D-STEM dataset from an inclined pseudomorphically grown Al0.47Ga0.53N layer.

Niermann, Laura

Improved Three-Dimensional Reconstructions in Electron Ptychography through Defocus Series Measurements

A detailed analysis of ptychography for three-dimensional (3D) phase reconstructions of thick specimens is performed. Here, we introduce multi-focus ptychography, which incorporates a 4D-STEM defocus series to enhance the quality of 3D reconstructions along the beam direction through a higher overdetermination ratio. This method is compared with established multi-slice ptychography techniques, such as conventional ptychography, regularized ptychography, and multi-mode ptychography. Additionally, we contrast multi-focus ptychography with an alternative method that uses virtual optical sectioning through a reconstructed scattering matrix (S-matrix), which offers more precise 3D structure information compared to conventional ptychography. Our findings from multiple 3D reconstructions based on simulated and experimental data demonstrate that multi-focus ptychography surpasses other techniques, particularly in accurately reconstructing the surfaces and interface regions of thick specimens.

3D reconstruction

Structural and Mechanical Analysis of Individual Mineralized Collagen Fibrils Using In Situ Transmission Electron Microscopy

Bone serves as an example of nature’s architectured material with its characteristic blend of strength and toughness, all at a lightweight design. Given the hierarchical nature of these materials, it is essential to understand the governing mechanisms and organization of their constituents across length scales for bioinspired structural design. Despite recent advances in transmission electron microscopy (TEM) that have allowed us to witness the hierarchical arrangement of bone at micro-down to the nanoscale, we are still missing the details about the structural organization and mechanical properties of the main building blocks of bone─mineralized collagen fibrils (MCFs). Here, we present a method to extract individual MCFs from nature’s model material, mineralized turkey leg tendon, using a dropcasting procedure. By isolating the MCFs onto TEM supporting grids, we visualized the arrangement of organic and mineral phases within individual MCFs at the nanoscale. Using a four-dimensional scanning transmission electron microscopy (4D-STEM) approach, the orientation of individual mineral crystals within the MCFs was examined. Furthermore, we conducted in situ tensile experiments, revealing exceptional tensile strains of at least 8%, demonstrating the intricate relationship between structural organization and the mechanical behavior of MCFs. These insights into the ultrastructure of mineralized tissue building blocks, as well as the proposed sample-extraction method compatible with in situ mechanical testing, provide a strong basis for research into nature-inspired material design.

4D-STEM

STEM Ptychographic Holography of Electric and Magnetic Potentials

The development of fast an efficient direct electron imaging detectors have enabled the advancement of phase-imaging techniques in STEM such as iterative ptychography. As beneficial as these techniques are to imaging phase objects, the information recorded in the raw data is due to phase gradients across the probe, so it can be challenging to reconstruct slowly varying phase at lower spatial frequencies such as those induced by electric or magnetic potentials within the specimen. STEM holography [1,2] is an interferometric 4D-STEM technique where electrons in the beam are coherently divided into a superposition of two or more spatially separated probes which are then scanned over the specimen. For example, in a two-beam superposition, the two probes form overlapping bright field discs at the detector which then interfere (left of Fig. 1). Furthermore, if one probe passes through vacuum while the other transmits through the specimen, the resulting relative phase shift can be measured by recording shifts in the interference pattern. STEM holography is thus directly sensitive to the phase of the probe relative to the reference beam, and this phase can be measured regardless of the convergence angle of the probe, unlike single beam ptychography.

Biological Sciences

Phase segregation dynamics in mixed-halide perovskites revealed by plunge-freeze cryo-electron microscopy

Mixed-halide lead perovskites, with photoexcited charge-carrier properties suitable for high-efficiency photovoltaics, hold significant promise for high-efficiency tandem solar cells. However, phase segregation under illumination, where an iodide-rich phase forms carrier trap states, remains a barrier to application. This study employs plunge-freeze cryoelectron microscopy to visualize nanoscale phase segregation dynamics in CsPb(Br x I 1–x ) 3 films. By rapidly freezing the illuminated samples, we preserve transient photoexcited ion distributions for high-resolution structural and compositional analysis at the nanoscale. Cryogenic scanning transmission electron microscopy (STEM) techniques (electron energy loss spectroscopy [EELS] and 4D-STEM) captured the dynamics of photo-induced iodine migration from grain boundaries to centers, identified the buildup of anisotropic strain, and captured the heterogeneous evolution of this process within a single grain. These findings provide insight into microscopic phase segregation mechanisms and their dynamics, enhancing our understanding of mixed-halide perovskite photostability.

42 ENGINEERING

Building workflows for an interactive human-in-the-loop automated experiment (hAE) in STEM-EELS

Exploring the structural, chemical, and physical properties of matter on the nano- and atomic scales has become possible with the recent advances in aberration-corrected electron energy-loss spectroscopy (EELS) in scanning transmission electron microscopy (STEM). However, the current paradigm of STEM-EELS relies on the classical rectangular grid sampling, in which all surface regions are assumed to be of equal a priori interest. However, this is typically not the case for real-world scenarios, where phenomena of interest are concentrated in a small number of spatial locations, such as interfaces, structural and topological defects, and multi-phase inclusions. One of the foundational problems is the discovery of nanometer- or atomic-scale structures having specific signatures in EELS spectra. Herein, we systematically explore the hyperparameters controlling deep kernel learning (DKL) discovery workflows for STEM-EELS and identify the role of the local structural descriptors and acquisition functions in experiment progression. In agreement with the actual experiment, we observe that for certain parameter combinations the experiment path can be trapped in the local minima. We demonstrate the approaches for monitoring the automated experiment in the real and feature space of the system and knowledge acquisition of the DKL model. Based on these, we construct intervention strategies defining the human-in-the-loop automated experiment (hAE). This approach can be further extended to other techniques including 4D STEM and other forms of spectroscopic imaging. The hAE library is available on Github at https://github.com/utkarshp1161/hAE/tree/main/hAE.

Pratiush, Utkarsh [Univ. of Tennessee, Knoxville,

Identifying the Role of Magnesium Content in Assessing the Electrochemical Performance of (CoCuMgNiZn)O

High-entropy oxides (HEOs) featuring 5 or more metals in approximately equimolar ratios, such as the prototypical rock-salt-structured (CoCuMgNiZn)O, have attracted interest for their potential to display material properties superior to oxides with combinations of 4 or fewer of the component metals. In particular, (CoCuMgNiZn)O has shown promise as an anode for lithium-ion batteries with a high specific capacity retention over extended cycling. Previous studies have suggested that magnesium, despite being electrochemically inert, provides a crucial contribution to the favorable performance of this HEO by stabilizing the crystal structure through repeated charge–discharge cycles. This paper probes the extent and mechanism of the magnesium effect by using a facile microwave-assisted hydrothermal synthesis method to vary the level of Mg content. Moreover, we extensively characterized the product with techniques such as 4D-STEM and ICP-OES, which have not previously been applied in combination with this material, in order to elucidate the relationships among chemical composition, nanostructure, and performance. Here, we show that the level of Mg incorporation is positively correlated with long-term stability and negatively correlated with rate capacity, and that the latter effect yields a stronger influence upon the overall performance, with the best-performing sample possessing a Mg quantity equivalent to ∼1/5 that of an equimolar concentration. This finding demonstrates not only that the variation of individual elemental levels offers a promising and relatively unexplored avenue to optimize the electrochemical performance of HEO materials but also that it should not be assumed that equimolar compositions of constituent elements are necessarily the best.

36 MATERIALS SCIENCE

Revealing the Crystalline Architecture of Semicrystalline Ion Exchange Membranes for the Design of Conductive and Durable Alkaline Anion Exchange Membranes

Alkaline anion exchange membrane (AAEM) fuel cells offer a cost-effective alternative to proton exchange membrane (PEM) fuel cells by eliminating the need for expensive precious metal catalysts. In both PEMs and AAEMs, semicrystalline polymers are a common choice, as the crystalline domains can act as mechanical reinforcements that limit swelling and promote mechanical durability in the material. However, spatially resolved characterization of crystalline organization in ion exchange membranes beyond ensemble-averaged X-ray scattering is underrepresented, likely in part due to ionization damage limitations in soft materials. Here, in this study, we resolve the nanometer-size crystallites in semicrystalline ion exchange membranes by applying cryogenic four-dimensional scanning transmission electron microscopy (cryo-4D-STEM) along with data-processing algorithms designed to optimize signals at a low dose to minimize radiation damage. We investigate the effects of synthesis components, including molecular weight and thermal treatment, on a model system of AAEMs in comparison to Nafion, the most commonly used and commercially successful PEM today. We find that excess water uptake in polymer membranes, a property directly associated with weak mechanical durability and with possible negative impacts on ion conductivity, can be reduced by over 30% by varying the polymer's crystalline morphology through changes in synthesis parameters such as molecular weight and thermal history. Our results indicate that this improvement is correlated with smaller crystalline domains with a more homogeneous distribution. More broadly, these results demonstrate how the crystalline architecture of polymer membranes can be tuned through their chemistry and thermal treatment in order to improve their conductivity and durability for commercial fuel cell performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Multimodal Nanoscale Mapping of Local Structure and CO 2 Adsorption in Metal–Organic Frameworks

Diamine functionalization of the metal−organic framework Mg 2 (dobpdc) (dobpdc 4− = 4,4′-dioxidobiphenyl-3,3′-dicarboxylate) significantly enhances its selectivity for CO 2 capture from flue gases and air. The structure and CO 2 capacity of such materials are typically assessed using bulk techniques that rely on averaging signal over large ensembles of unit cells, obscuring local heterogeneities, such as variations in CO 2 occupancy across individual nanocrystals. To resolve this limitation, we demonstrate a multimodal, nanoscale characterization of Mg 2 (dobpdc) appended with 1,3-diaminopropane. By employing recently developed characterization techniques at progressively smaller length scales, we uncover insights from correspondingly smaller populations of unit cells. First, we use parallel-beam 3D electron diffraction (3D ED) to identify a prominent expansion in lattice parameters upon desorption of CO 2 , as observed at the level of single nanocrystals. Second, we use convergent-probe 4D scanning transmission electron microscopy (4D-STEM) to quantify associated differences in lattice strain as a function of gas loading and diamine appending. These measurements sample small subvolumes within individual nanocrystals. Finally, we apply infrared scattering scanning near-field optical microscopy (IR s- SNOM) to confirm variable CO 2 chemisorption across adsorption sites at the surface of single nanocrystals. This multimodal, multiscale approach allows us to map heterogeneity within individual nanocrystals. Collectively, these findings emphasize the importance of local, nanoscale characterization of metal−organic frameworks in revealing previously unresolvable features that impact their performance.

Karstens, Sarah L. [University of California, Berk

Multi-modal characterization of nitrate reduction nano-catalysts with periodic strain distribution

Strain engineering serves as a pivotal strategy to optimize catalytic activity in electrocatalysis. However, the catalyst sizes under industrial conditions are usually large and even beyond nanometer regime. The critical methodological limitations on strain imaging of such catalysts with both large field of view and high spatial resolution obscure the mechanistic understanding of strain-performance correlations. Here, we present an optimized four-dimensional scanning transmission electron microscopy (4D-STEM) method to acquire strain mapping of both bulk and surface across particles up to 500 nm with 0.6 nm spatial resolution and 0.55% precision. We observe the ripple-like periodic strain coupled with elemental fluctuations inside a perovskite-type hydroxide CuCoSn(OH) 6 and find it correlated to electrocatalytic nitrate reduction (NO 3 – RR) absorption energy to achieve the 92.6% Faradaic efficiency and long-term test over 1000 h at membrane electrode assembly (MEA) for ammonia electrosynthesis. This universal framework design offers a practical method that not only develops an advanced measurement combining multi-modal characterization techniques but also reveals the intrinsic structure-property constitutive law of industry-level catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Superlattice reflection signatures of the insulator–metal transition in V 3 O 5 thin films

Nanoelectronic systems that are inspired by the brain are increasingly looking to insulator–metal transition (IMT) materials as they can mimic the response characteristics of neurons to temperature changes so that these can be used in robotic and computational applications. V 3 O 5 has an insulator–metal transition at ∼430 or ∼80 K higher than VO 2 and provides a unique high-temperature opportunity for these types of applications. Here, in this work, we track the structural evolution of V 3 O 5 thin films across the IMT through conventional selected-area electron diffraction (SAED) and four-dimensional scanning TEM (4D-STEM), correlated with temperature-dependent resistance measurements. SAED patterns show reversible evidence of superlattice reflections associated with the IMT—present below T IMT and absent above it—consistent with the accompanying drop in resistance. At room temperature, nanobeam electron diffraction patterns further reveal three local configurations: (i) type I regions with clean patterns lacking superlattice reflections and spot splitting; (ii) type II regions exhibiting rows of superlattice reflections and split spots indicative of crystallographic variants; and (iii) type III regions with negligible superlattice reflections but larger spot splitting suggestive of overlapping domains of insulating and conducting phases likely driven by local lattice distortions. Upon heating, the superlattice reflections disappear between 413 and 453 K, concurrent with the resistance drop at T IMT , consistent with the emergence of a conducting phase. The overall diffraction geometry remains essentially unchanged up to 573 K, implying that relative domain orientations persist through the transition. These observations reveal nanoscale structural heterogeneity in V 3 O 5 thin films across the IMT and inform operation in regimes where mixed-phase textures are expected. A plausible indexing framework rationalizing the observed geometries is presented in the Discussion section, alongside its limitations and alternative interpretations.

25 ENERGY STORAGE

Multi-slice electron ptychographic tomography for three-dimensional phase-contrast microscopy beyond the depth of focus limits

Electron ptychography is a powerful computational method for atomic-resolution imaging with high contrast for weakly and strongly scattering elements. Modern algorithms coupled with fast and efficient detectors allow imaging specimens with tens of nanometers thicknesses with sub-0.5 Ångstrom lateral resolution. However, the axial resolution in these approaches is currently limited to a few nanometers, limiting their ability to solve novel atomic structures ab initio. Here, we experimentally demonstrate multi-slice ptychographic electron tomography, which allows atomic resolution three-dimensional phase-contrast imaging in a volume surpassing the depth of field limits. We reconstruct tilt-series 4D-STEM measurements of a $\mathrm{Co_3O_4}$ nanocube, yielding 2 Å axial and 0.7 Å transverse resolution in a reconstructed volume of $\mathrm{(18.2\,nm)^3}$. Our results demonstrate a 13.5-fold improvement in axial resolution compared to multi-slice ptychography while retaining the atomic lateral resolution and the capability to image volumes beyond the depth of field limit. Multi-slice ptychographic electron tomography significantly expands the volume of materials accessible using high-resolution electron microscopy. We discuss further experimental and algorithmic improvements necessary to also resolve single weakly scattering atoms in 3D.

36 MATERIALS SCIENCE

TEM Approaches for Microstructure-Informed Prediction of Mechanical Properties in Structural Alloys

Predicting the mechanical performance of structural alloys from their evolving microstructure remains a major challenge in materials science, particularly for nuclear structural materials, where irradiation-induced defects span multiple types and length scales and interact through complex mechanisms. The dispersed barrier hardening (DBH) [1] and Friedel–Kroupa–Hirsch (FKH) [2,3] models have been widely used to evaluate the hardening contributions of individual obstacles and to estimate tensile strength from quantified microstructures; however, when multiple size-dependent obstacles coexist and evolve, predicting temperature-dependent tensile strength becomes significantly more complex, and a fully consistent hardening model is still lacking. Transmission electron microscopy (TEM) plays a central role in refining hardening models and enabling predictive assessments of tensile strength evolution by providing quantitative characterization of dislocations, irradiation-induced defects (e.g., dislocation loops and cavities), precipitates, and grain structure (Fig. 1.). These experimentally measured defect densities are incorporated into physically based hardening models with size- and shape- dependent obstacle strengths [4], using root-sum-square superposition for obstacles of comparable strength and linear superposition for dissimilar ones [5]. In addition, recent advances in TEM [6-8], including high-resolution imaging, 4D-STEM strain mapping, EDS/EELS elemental analysis, and flash-polishing-based TEM specimen preparation and extraction-replica methods (Fig. 2), further improve the accuracy of microstructural quantification. By comparison with prior studies as well as our own results, we show that when TEM-derived microstructural information is carefully integrated with physically grounded hardening models, yield strength (or irradiation-induced hardening) measured at room temperature can be predicted with good quantitative agreement across multiple alloy classes. In-situ TEM combined with high-temperature mechanical testing represents an important next step for refining hardening models by directly probing dislocation–obstacle interactions across varying irradiation doses and temperatures [9]. Because the barrier strength factor (α) depends on both temperature and obstacle size, it should not be treated as a constant fitting parameter; rather, it must be explicitly evaluated to achieve physically meaningful predictions of mechanical behaviour at operating temperatures. This presentation therefore discusses why all strengthening contributions (e.g., Peierls stress, solid-solution strengthening, voids, bubbles, dislocation loops, dislocation lines, and grain boundaries) must be considered collectively, why appropriate superposition methods are essential when obstacles possess different barrier strength factors, how hardness measurements can be meaningfully related to tensile properties, and how TEM-derived microstructural information can be systematically incorporated into hardening models. More broadly, it outlines a pathway toward microstructure-informed prediction of mechanical properties and supports the goal of establishing science-based tools for evaluating structural materials in extreme environments [10].

Lin, Yan-Ru [ORNL] (ORCID:0000000339991473)

Strain mapping of three-dimensionally structured two-dimensional materials

Strain plays a crucial role in tuning materials’ properties, influencing their optical, electrical, and chemical performances. In two-dimensional (2D) materials, applied stress often induces out-of-plane deformation, resulting in a more intricate three-dimensional (3D) topography, where mapping the strain remains a challenge due to the limitations of conventional characterization techniques. In this work, we introduce BRIGHT (Bragg-Rod Informed, Gradient-based Height-mapping Technique), an integrated method for reconstructing both the topography and planar strain profile of 3D-structured 2D materials using nanobeam four-dimensional scanning transmission electron microscopy (4D-STEM). We apply BRIGHT to a MoS2-MoSe2 transition metal dichalcogenide (TMD) lateral heterojunctions exhibiting built-in strain and out-of-plane ripples and show that varying heterojunction widths lead to distinct surface morphologies and corresponding changes in the planar strain distribution. These results establish a foundation for more effective strain engineering in 2D materials by accounting for out-of-plane structural features, thereby enabling more precise control of strain-dependent properties.

Mireles, Adan [Rice Univ., Houston, TX (United Sta