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Conditional diffusion machine-learning framework for mapping valence electron distribution from convergent beam electron diffraction

Quantitative convergent beam electron diffraction (CBED) enables determination of aspherical valence electron distributions through refinement of low-order structure factors, which are highly sensitive to chemical bonding and charge density variations. However, conventional quantitative CBED (QCBED) requires solving a highly nonlinear inverse problem with many coupled parameters, and computationally intensive dynamical diffraction calculations, making it time-consuming and difficult to apply to complex systems. More broadly, reconstructing charge density and orbital electron distribution from diffraction data has long been a central challenge in both x-ray and electron crystallography. Here, in this study, we introduce an artificial-intelligence (AI)-based framework that replaces traditional refinement with a data-driven inverse solver. Using a large synthetic CBED dataset generated by Bloch-wave simulations, we train a conditional diffusion model to directly infer crystal structural parameters and multipole density formalism parameters, and hence valence electron distributions, from CBED patterns alone. By learning from forward simulations across realistic parameter space, the model effectively solves the inverse problem. Compared with direct regression approaches, the diffusion-based framework provides posterior parameter distributions for rigorous uncertainty quantification while preserving quantitative fidelity and reducing analysis time by orders of magnitude. By eliminating the need for external single-crystal x-ray diffraction data and complex nonlinear refinement, this approach enables practical, high-throughput, and in situ quantitative CBED, enabling real-time mapping of valence electron distributions and their correlation with functional responses in quantum and energy materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

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

Multi-angle Precession Electron Diffraction (MAPED): A Versatile Approach to 4D-STEM Precession

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.

4D-STEM

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

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