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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

Antiphase boundaries in epitaxially grown beta-SiC

When the surface of beta-SiC, grown epitaxially on (001) silicon by chemical vapor deposition, is chemically etched, boundaries appear which may be observed by optical or scanning electron microscopy. Examination by plan-view and cross-sectional transmission electron microscopy shows boundaries in the film which exhibit line or fringe contrast. Convergent beam electron diffraction has been used to show that these boundaries separate domains that are in an antiphase relationship to each other. A model is presented which discusses the formation of these domains from independent nucleation on a stepped substrate surface.

Pirouz, P.

Formation of the lamellar structure in Group IA and IIID iron meteorites

Analytical EM, light microscopy, and electron microprobe analysis are used to study the lamellar plessite structure of Group IA and IIID iron meteorites. The alpha lamellae in IIID structures contained a compositional gradient from 6.1 + or - 0.7 wt pct Ni at the center of the alpha lamellae to 3.6 + or - 0.5 wt pct at the alpha/gamma interface. For the Group IA irons, compositions of 4 wt pct Ni in alpha and about 48 wt pct Ni in gamma are found. Convergent beam electron diffraction was used to characterize the orientation relations at the alpha/gamma interface in the lamellar regions of both Group IA and IIID. The phase transformations responsible for the observed lamellar structure in the IA and IIID chemical groups were also investigated.

Kowalik, J. A.

Nonequilibrium synthesis of NbAl3 and Nb-Al-V alloys by laser cladding. I - Microstructure evolution

The evolution of the microstructure in NbAl3 synthesized by a laser cladding technique (a rapid solidification process, with cooling rates up to 10 exp 6 C/sec) is investigated, and the phases are identified using convergent beam electron diffraction. Two new metastable phases were identified and characterized in detail. The effect of adding V on the final microstructure was also investigated, and the various phase chemistries and the partitioning of different elements into different phases were studied.

Sircar, S.

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

Advanced High Brilliance X-Ray Source

The possibility to dramatically increase the efficiency of laboratory based protein structure measurements through the use of polycapillary X-ray optics was investigated. This project initiated April 1, 1993 and concluded December 31, 1996 (including a no cost extension from June 31, 1996). This is a final report of the project. The basis for the project is the ability to collect X-rays from divergent electron bombardment laboratory X-ray sources and redirect them into quasiparallel or convergent (focused) beams. For example, a 0.1 radian (approx. 6 deg) portion of a divergent beam collected by a polycapillary collimator and transformed into a quasiparallel beam of 3 millradian (0.2 deg) could give a gain of 6(exp 2)/0.2(exp 2) x T for the intensity of a diffracted beam from a crystal with a 0.2 deg diffraction width. T is the transmission efficiency of the polycapillary diffraction optic, and for T=0.5, the gain would be 36/0.04 x O.5=45. In practice, the effective collection angle will depend on the source spot size, the input focal length of the optic (usually limited by the source spot-to-window distance on the x-ray tube) and the size of the crystal relative to the output diameter of the optic. The transmission efficiency, T, depends on the characteristics (fractional open area, surface roughness, shape and channel diameter) of the polycapillary optic and is typically in the range 0.2-0.4. These effects could substantially reduce the expected efficiency gain. During the course of this study, the possibility to use a weakly focused beam (0.5 deg convergence) was suggested which could give an additional 10-20 X efficiency gain for small samples . Weakly focused beams from double focusing mirrors are frequently used for macromolecular crystallography studies. Furthermore the crystals are typically oscillated by as much as 2 deg during each X-ray exposure in order to increase the reciprocal space (number of crystal planes) sampled and use of a slightly convergent beam could, in principle, provide a similar sampling benefit without oscillation. Although more problematic, because of complications in analyzing the diffraction patterns, it was also suggested that even more extreme beam convergence might be used to give another order of magnitude intensity gain and even smaller focused spot size which could make it possible to study smaller protein crystals than can be studied using standard laboratory based X-ray diffraction systems. This project represents the first systematic investigation of these possibilities. As initially proposed, the contract included requirements for design, purchase, evaluation and delivery of three polycapillary lenses to the Laboratory for Structural Biology at MSFC and demonstration of such optics at MSFC for selected protein crystal diffraction applications.

Gibson, Walter M.

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