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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

End-to-End Automated Segmentation Framework for Four-Dimensional Scanning Transmission Electron Microscopy Data

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.

47 OTHER INSTRUMENTATION

Learning and Controlling Silicon Dopant Transitions in Graphene Using Scanning Transmission Electron Microscopy

A machine learning approach is introduced to determine the transition dynamics of silicon atoms on a single layer of carbon atoms, when stimulated by the electron beam of a scanning transmission electron microscope (STEM). This method is data-centric, leveraging data collected on a STEM. The data samples are processed and filtered to produce symbolic representations, which is used to train a neural network to predict transition probabilities. These learned transition dynamics are then leveraged to guide a single silicon atom throughout the lattice to pre-determined target destinations. Empirical analyses are presented that demonstrate the efficacy and generality of the approach.

36 MATERIALS SCIENCE

Tutorial on In Situ and Operando (Scanning) Transmission Electron Microscopy for Analysis of Nanoscale Structure–Property Relationships

In situ and operando (scanning) transmission electron microscopy [(S)TEM] is a powerful characterization technique that uses imaging, diffraction, and spectroscopy to gain nano-to-atomic scale insights into the structure–property relationships in materials. This technique is both customizable and complex because many factors impact the ability to collect structural, compositional, and bonding information from a sample during environmental exposure or under application of an external stimulus. In the past two decades, in situ and operando (S)TEM methods have diversified and grown to encompass additional capabilities, higher degrees of precision, dynamic tracking abilities, enhanced reproducibility, and improved analytical tools. Much of this growth has been shared through the community and within commercialized products that enable rapid adoption and training in this approach. This tutorial aims to serve as a guide for students, collaborators, and nonspecialists to learn the important factors that impact the success of in situ and operando (S)TEM experiments and assess the value of the results obtained. As this is not a step-by-step guide, readers are encouraged to seek out the many comprehensive resources available for gaining a deeper understanding of in situ and operando (S)TEM methods, property measurements, data acquisition, reproducibility, and data analytics.

(S)TEM

BEACON—automated aberration correction for scanning transmission electron microscopy using Bayesian optimization

Aberration correction is an important aspect of modern high-resolution scanning transmission electron microscopy. Most methods of aligning aberration correctors require specialized sample regions and are unsuitable for fine-tuning aberrations without interrupting on-going experiments. Here, we present an automated method of correcting first- and second-order aberrations called BEACON, which uses Bayesian optimization of the normalized image variance to efficiently determine the optimal corrector settings. We demonstrate its use on gold nanoparticles and a hafnium dioxide thin film showing its versatility in nano- and atomic-scale experiments. BEACON can correct all first- and second-order aberrations simultaneously to achieve an initial alignment and first- and second-order aberrations independently for fine alignment. Ptychographic reconstructions are used to demonstrate an improvement in probe shape and a reduction in the target aberration.

techniques and instrumentation

Scanning Transmission Electron Microscopy–Atom Probe Tomography Correlative Analysis for the Characterization of Solute-defect Interactions

Atom probe tomography (APT) and (scanning) transmission electron microscopy ((S)TEM) are complementary techniques that provide spatially resolved chemical and structural information at the atomic scale. Here, in this study, we employ two different STEM/APT correlative analysis methods to investigate Cr segregation at dislocation loops in ultra-high purity Fe–Cr alloys. APT needles for the correlative analysis were extracted either from bulk material or from thinned TEM lamellae. STEM analysis was used to determine the Burgers vectors of ion-irradiation-induced dislocation loops, while APT reconstruction of the same region revealed the Cr segregation to these loops. We extended the g•b = 0 invisibility criterion of dislocation loops from TEM mode in a lamella to STEM mode in a needle-shaped specimen. STEM and APT analysis on the same needle provide straightforward correlative analysis, although it is limited by a small observation volume. In contrast, iterative STEM analysis of TEM lamellae, followed by the selective extraction of specific regions of interest for APT analysis, expands the observation area by up to 100 times but requires additional time-consuming steps for APT needle extraction from the lamellae.

47 OTHER INSTRUMENTATION

Quantitative Structure Determination from Experimental Four-Dimensional Scanning Transmission Electron Microscopy via the Scattering Matrix

Considerable inroads have recently been made on algorithms to determine the sample potential from four-dimensional scanning transmission electron microscopy data from thick samples where multiple scattering cannot be neglected. This paper further develops the scattering matrix approach to such structure determination. Through simulation, we demonstrate how this approach can be modified to better handle partial spatial coherence, unknown probe defocus, and information from the dark field region. By combining these developments we reconstruct the electrostatic potential of a monolithic SrTiO 3 crystal showing good quantitative agreement with the expected structure.

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

Autonomous fabrication of tailored defect structures in 2D materials using machine learning-enabled scanning transmission electron microscopy

Materials with tailored quantum properties can be engineered from atomic-scale assembly techniques, but existing methods often lack the agility and accuracy to precisely and intelligently control the manufacturing process. Here, we demonstrate a fully autonomous approach for fabricating atomic-level defects using electron beams in scanning transmission electron microscopy (STEM) that combines advanced machine learning and automated beam control. As a proof of concept, we achieved controlled fabrication of MoS-nanowire (MoS-NW) edge structures by iterative and targeted exposure of MoS 2 monolayer to a focused electron beam to selectively eject sulfur atoms, utilizing high-angle annular dark-field (HAADF) imaging for feedback-controlled monitoring of structural evolution of defects. A machine learning framework combining a random forest model and a convolutional neural network (CNN) was developed to decode the HAADF image and accurately identify atomic positions and species. This atomic-level information was then integrated into an autonomous decision-making platform, which applied predefined fabrication strategies to instruct beam control about atomic sites to be ejected. The selected sites were subsequently exposed to a localized electron beam using an FPGA-controlled scan routine with precise control over beam positioning and duration. While the MoS-NW edge structures produced exhibit promising mechanical and electronic properties, the proposed methods to build the autonomous fabrication framework is material-agnostic and can be extended to other 2D materials for the creation of diverse defect structures and heterostructures beyond Mo S2 .

Engineering

Strain-driven oxygen vacancy ordering in LaNiO 3 thin films revealed by integrated differential phase contrast imaging in scanning transmission electron microscopy

Rare-earth nickelates, such as LaNiO 3 (LNO), exhibit complex electronic properties, with ordered oxygen vacancies (OOV) influencing conductivity and magnetic behavior. We investigate the structural stability of strain-induced OOV phases in LNO thin films grown on SrTiO 3 substrates and the impact of Ruddlesden–Popper (RP) faults. Using high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and integrated differential phase contrast (iDPC) STEM imaging, we conducted atomic-scale structural and compositional analyses of OOV. Geometric phase analysis (GPA) was employed to measure the strain in fault-free and RP fault regions, while density functional theory (DFT) calculations explored different OOV arrangements in the LNO phase. Simulated iDPC-STEM imaging of energy-stabilized structures was performed to correlate with experimental results. Here, our findings reveal superstructure modulation in the chemical composition and atomic-scale lattice structure in LNO, primarily due to the formation of the OOV in Ni–O layers of the LaNiO 2.5 phase. The out-of-plane compressive strain of about 2% stabilizes this phase, reducing the strain, diminishing OOV, and transforming them into LNO.

36 MATERIALS SCIENCE

Quantitative phase retrieval and characterization of magnetic nanostructures via Lorentz (scanning) transmission electron microscopy

Magnetic materials phase reconstruction using Lorentz transmission electron microscopy (LTEM) measurements have traditionally been achieved using longstanding methods such as off-axis holography (OAH) fast-Fourier transform technique and the transport-of-intensity equation (TIE). The increase in access to processing power alongside the development of advanced algorithms have allowed for phase retrieval of nanoscale magnetic materials with greater efficacy and resolution. Specifically, reverse-mode automatic differentiation (RMAD) and the extended electron ptychography iterative engine (ePIE) are two recent developments of phase retrieval that can be applied to analyzing micro-to-nano- scale magnetic materials. This work evaluates phase retrieval using TIE, RMAD, and ePIE in simulations of Permalloy (Ni 80 Fe 20 ) nanoscale islands, or nanomagnets. Extending beyond simulations, we demonstrate total phase retrieval and image reconstructions of a NiFe nanowire using OAH and RMAD in LTEM and ePIE in Lorentz-mode-4D scanning transmission electron microscopy experiments and determine the saturation magnetization through corroborations with micromagnetic modeling. Finally, we demonstrate the efficacy of these methods in retrieving the total phase and highlight its use in characterizing and analyzing the proximity effect of the magnetic nanostructures.

Lorentz transmission electron microscopy

The role of Ca-bridged organic matter in an alkaline soil, as revealed by multimodal chemical imaging

Mineral–organic matter (OM) studies have predominantly focused on acidic soils that are abundant in iron (Fe) oxides and aluminum (Al) oxides. We have probed mineral–OM interactions in an alkaline or calcareous soil of the Aridisols class. Unlike the role of Fe and Al, the role of Ca-minerals (particularly calcite), which are ubiquitous in alkaline soils, in OM sequestration is not well understood. Multiple recent model studies with aqueous Ca2+ or synthetic calcite and a suite of OM compounds have shown Ca-OM assemblages to be spatially correlated with calcite at the microscale. To study the chemical state of both Ca and Fe and their competing role in soil organic matter (SOM) stabilization, we performed laboratory characterization using x-ray diffraction, Mössbauer spectroscopy, x-ray photoelectron spectroscopy, scanning electron microscopy, and scanning transmission electron microscopy, alongside synchrotron-based microscale chemical imaging using scanning transmission x-ray microscopy combined with near-edge x-ray absorption fine structure. Ca mineral–organic associations were found to be ubiquitous in this system and are likely critical for understanding SOM stabilization/degradation in alkaline soils. From our findings on mineralogy, speciation, and the nature of Ca-OM bridging, we identified differences in C and Ca chemistry based on the relative location of OM to Ca minerals. The OM near the calcite crystal was enriched in lipid and protein moieties, Ca-OM next to Fe minerals displayed a strong contribution from aromatic compounds, while on the surface of microbes, the carbonate was believed to be of microbial in origin, as also suggested by preliminary works reporting on the formation of amorphous calcite or nano-calcite. In Ca-OM admixed with carbonate, it was difficult to distinguish Ca-associated OM from amorphous calcite or nano-calcite.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Revealing Phase Heterogeneity in Vertically Aligned Nanocomposites via Plan-View Electron Energy Loss Spectroscopy

Hydrogen utilization in clean energy technologies is challenged by limited storage and transport within materials, owing to the complex hydrogen kinetics at interfaces [1]. Understanding these interfacial mechanisms at the nanoscale is crucial for developing improved materials for hydrogen applications, particularly proton-conducting fuel cells (PCFCs). Vertically aligned nanocomposites (VANs) grown by pulsed laser deposition (PLD) offer a unique platform for investigating the interfacial effects on hydrogen transport due to their well-defined interfaces parallel to the direction of charge transport [2-4]. To investigate hydrogen transport, the two phases within the VANs were chosen as BaZr 0.9 Y 0.1 O 3-x (BZY), a known proton conductor, and Pr 0.1 Ce 0.9 O 2-x (PCO), a mixed ionic-electronic conductor [5]. This PCO-BZY VANs architecture allows the investigation of how the interface between a proton conductor and a mixed conductor influences hydrogen transport. However, because of the small size of hydrogen, it is difficult to discern the nature of its interactions with interfaces from bulk measurements at the macroscale, thus necessitating nanoscale measurements [6]. Electron energy loss spectroscopy (EELS) allows for nanometer-resolution probing of the local atomic structure and chemistry at the BZY/PCO interface. In this study, plan-view analysis of PCO-BZY VANs films was employed to characterize the structure and phase distribution of the VANs and investigate the interface between the nanostructures. The films were imaged using scanning electron microscopy (SEM) in the Hitachi S-4800 SEM, collecting secondary electron images using mixed upper and lower detectors. Then, plan-view transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM) EELS were employed using a JEOL ARM300 microscope operated at 300kV with a Gatan K3 GIF Continuum detector to study the distribution of the BZY and PCO phases through the film. As a result, spectrum images were acquired at a dispersion of 0.18eV per channel and denoised afterward by principal component analysis (PCA) method.

Griffin, Elizabeth [Northwestern University, Evans

Chemical and morphological evolution of hybrid conversion coatings in low-Earth orbit space environment

Understanding how protective coatings respond to the harsh low-Earth orbit (LEO) environment is essential for ensuring the safety, longevity, and cost-effectiveness of spacecraft. In particular, identifying environmentally friendly, non-chromate alternatives that can maintain performance under such conditions has both technological and regulatory significance. This study investigates the environmental stability of zirconium-based hybrid conversion coatings with Cu additives (Cu10 and Cu20) applied to cold-rolled steel, tested in the Materials International Space Station Experiment (MISSE) outside the International Space Station (ISS). Chemical and morphological analyses were carried out using a combination of electron microscopy and X-ray spectroscopy techniques, including scanning electron microscopy (SEM), scanning transmission electron microscopy with energy-dispersive X-ray spectroscopy (STEM-EDS), X-ray photoelectron spectroscopy (XPS), and X-ray absorption near-edge structure (XANES) spectroscopy. After exposure outside the ISS, all coatings remained structurally intact, with all exhibiting a uniform Zr-rich matrix and embedded Cu-rich clusters, while a thin Si-rich surface layer developed from interaction with space environments. Depth-resolved XPS showed a layered structure with CuO on the surface, Cu 2 O, and partial Zr(IV) reduction near Cu-rich sites, evidence of Atomic Oxygen (AO)-driven surface oxidation. These results demonstrate that Cu–Zr coatings maintain their chemical integrity and microstructure in harsh space environments, offering a non-chromate alternative for long-term aerospace protection. These insights provide valuable guidance for developing next-generation protective coatings that combine environmental sustainability with the reliability required for future aerospace and orbital applications.

36 MATERIALS SCIENCE

Microstructure-Based Understanding of High-Temperature Deformation Behaviors in Laser Powder Bed Fusion (LPBF) 316H Stainless Steel

This report presents the results of high-temperature mechanical property testing and microstructural analysis of laser powder bed fusion (LPBF) 316H stainless steel (SS) conducted during Fiscal Year 2025 (FY25) under the U.S. Department of Energy, Office of Nuclear Energy’s Advanced Materials and Manufacturing Technologies (AMMT) program. The study builds upon prior work by expanding the mechanical property test matrix and advancing a microstructure-based mechanistic understanding of LPBF 316H SS performance, with a focus on the solution annealed (SA, 1100°C for 1 hour) materials. High-temperature tension, creep, fatigue, and creep-fatigue tests were performed. Thermal aging studies were conducted. Advanced characterization techniques, including scanning electron microscopy (SEM), scanning transmission electron microscopy (STEM), and high-energy synchrotron X-ray diffraction, were employed to investigate the microstructural evolution during thermal aging and mechanical testing. It was discovered that the as-built (AB) LPBF 316H SS exhibited precipitation kinetics during thermal aging that are 10–100 times faster than its wrought counterpart due to the presence of high densities of preferred nucleation sites, while the precipitation kinetics in SA LPBF 316H was under investigation. The accelerated precipitation of embrittling phases such as sigma phase in LPBF 316H SS compared to its wrought counterpart led to significant impacts on creep ductility. The influence of laser printing parameters and build orientations on fatigue and creep-fatigue performance was observed. In assessing the creep-fatigue performance, it was discovered that the SA LPBF 316H samples failed in less than 200 cycles under 595°C, 0.5% (strain amplitude) with a 60-minute hold time. This work establishes a mechanistic framework for predicting the long-term behavior of LPBF 316H SS, supporting its rapid qualification under the ASME BPVC. The findings contribute to the broader goal of enabling the deployment of advanced materials in next-generation nuclear energy systems. An outlook for FY26 work, including continued aging studies, mechanical testing, and microstructural characterization, is provided.

36 MATERIALS SCIENCE

4D-STEM Mapping of Nanocrystal Reaction Dynamics and Heterogeneity in a Graphene Liquid Cell

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 mi

Scanning transmission election microscopy observations of twisted epitaxial gold nanodiscs in twisted molybdenum disulfide bilayers

Atomic scale, scanning transmission electron microscopy (STEM) analysis of the moiré structures in twisted epitaxial gold nanodiscs encapsulated in twisted bilayer molybdenum disulfide is presented. High angle annular dark field STEM imaging reveals that the period of the moiré patterns between gold and molybdenum disulfide varies with different twist angles of the bilayer molybdenum disulfide, ranging from 1.80 nm (epitaxial alignment of gold) to 1.53 nm (twisted epitaxial alignment of gold). Additionally, bright field STEM imaging reveals a faint, larger "moiré of moiré" structure in cases where the bilayer molybdenum disulfide twist angle is small (~6°), arising from the overlapping three-layers, which is not visible in conventional transmission electron microscopy images. In conclusion, our experiments indicate that scanning transmission electron microscopy as a suitable tool for moiré analysis of twisted multilayer planar heterostructures, complementary to information provided by conventional transmission electron microscopy and diffraction.

Au

Redistribution of Ru in Fe 2 O 3 –Ru Nanocatalysts through an Oxidative Pretreatment Improves Reverse Water–Gas Shift Activity

We have synthesized Fe–Ru nanoparticles via a solvothermal method to create catalysts for the reverse water–gas shift reaction and demonstrated the impact of reductive and oxidative pretreatments on both catalytic performance and structure. Catalytic testing showed improved activity after exposure to O 2 at 600 °C. In contrast, the activity became lower if then exposed to H 2 at 600 °C. Environmental scanning transmission electron microscopy and scanning electron microscopy showed that exposure to O 2 at 600 °C changes the morphology and completely oxidizes Fe into Fe 2 O 3 . Exposure to H 2 at elevated temperature caused Ru coalescence at the surface of the nanoparticle, forming clusters which decreased the optimization of Ru. Reoxidation of the particles exposed to H 2 , however, caused a redistribution of Ru that appears beneficial in maximizing Ru exposure and synergy with Fe oxide, with no major changes in the morphology and oxide structure. Furthermore, our diagnostics demonstrate the complex and reversible rearrangements possible in these multicomponent particles and the benefits of oxidative pretreatment to enhance or regenerate Fe–Ru catalysts in other important catalytic reactions such as Fischer–Tropsch synthesis.

Fe−Ru nanoparticles