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Ultrafast Bragg coherent diffraction imaging of epitaxial thin films using deep complex-valued neural networks

Abstract Domain wall structures form spontaneously due to epitaxial misfit during thin film growth. Imaging the dynamics of domains and domain walls at ultrafast timescales can provide fundamental clues to features that impact electrical transport in electronic devices. Recently, deep learning based methods showed promising phase retrieval (PR) performance, allowing intensity-only measurements to be transformed into snapshot real space images. While the Fourier imaging model involves complex-valued quantities, most existing deep learning based methods solve the PR problem with real-valued based models, where the connection between amplitude and phase is ignored. To this end, we involve complex numbers operation in the neural network to preserve the amplitude and phase connection. Therefore, we employ the complex-valued neural network for solving the PR problem and evaluate it on Bragg coherent diffraction data streams collected from an epitaxial La 2-x Sr x CuO 4 (LSCO) thin film using an X-ray Free Electron Laser (XFEL). Our proposed complex-valued neural network based approach outperforms the traditional real-valued neural network methods in both supervised and unsupervised learning manner. Phase domains are also observed from the LSCO thin film at an ultrafast timescale using the complex-valued neural network.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Adaptive Machine Learning for Bragg Coherent Diffraction Imaging (BCDI) of 3D Electron Density Maps with Application to La 2-x Ba x CuO 4 (LBCO) High Temperature Superconductor Studies [PowerPoint]

Understanding mesoscale heterogeneity is important for evaluating fatigue and failure of structural materials and for manufacturing processes. Data-driven tools can facilitate in guiding effort investment (measurements and computations) at various stages of the materials development. Our 3D reconstruction approach is to find a set of coefficients which define a bounding surface of the electron density. Data for training the 3D CNN was generated by sampling coefficients from uniform distributions. Test vs. prediction values are shown for the 28 even-valued coefficients for 1000 test structures, with the best and worst performers highlighted. The adaptive part of this work utilized a model independent extremum seeking (ES). The predictions of the CNN were used as the starting point for the ES algorithm. The convergence of the ES algorithm for 3 different structures is illustrated, and the robustness of the adaptive ML approach was demonstrated on experimentally measured 3D crystal from high energy diffraction microscopy. Reconstruction of a non-uniform density volume with different levels of Poisson noise is also shown. Preliminary attempts at reconstructing measured La 2-x Ba x CuO 4 diffraction patterns have so far failed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Modeling and experimental validation of dynamical effects in Bragg coherent x-ray diffractive imaging of finite crystals

Bragg coherent diffractive imaging (BCDI) is a noninvasive microscopy technique that can visualize the shape and internal lattice deviations of crystals with nanoscale spatial resolution and picometer deformation sensitivity. Its strain imaging capability relies on Fourier transform–based iterative phase retrieval algorithms, which are mostly developed under the kinematical approximation. Such approximation prohibits the application of BCDI on larger crystals, which are commonly seen in most emerging functional materials. Understanding the dynamical effect in BCDI, as well as developing a validated method for modeling BCDI at the dynamical diffraction limit, is crucial for applying BCDI to hierarchical systems that contain micron-sized crystals and grains. Thus we report a comparative study on the impact of dynamical diffraction effects by comparing the reconstruction results from two measurements of the same crystal. Forward simulation is implemented to show subtle changes of interference fringes in the diffraction pattern due to the dynamical diffraction, and is compared directly with the experimental data.

36 MATERIALS SCIENCE↗

Three-dimensional strain imaging of irradiated chromium using multi-reflection Bragg coherent diffraction

Abstract Radiation-induced materials degradation is a key concern in limiting the performance of nuclear materials. The formation of nanoscale void and gas bubble superlattices in metals and alloys under radiation environments can effectively mitigate radiation-induced damage, such as swelling and aid the development of next generation radiation tolerant materials. To effectively manage radiation-induced damage via superlattice formation, it is critical to understand the microstructural changes and strain induced by such superlattices. We utilize multi-reflection Bragg coherent diffraction imaging to quantify the full strain tensor induced by void superlattices in iron irradiated chromium substrate. Our approach provides a quantitative estimation of radiation-induced three-dimensional (3D) strain generated at the microscopic level and predicts the number density of defects with a high degree of sensitivity. Such quantitative evaluation of 3D strain in nuclear materials can have a major impact on predicting materials behavior in radiation environments and can revolutionize design of radiation tolerant materials.

36 MATERIALS SCIENCE↗

Structural Explanation of the Dielectric Enhancement of Barium Titanate Nanoparticles Grown under Hydrothermal Conditions

Abstract When synthesized under certain conditions, barium titanate (BaTiO 3 , BTO) nanoparticles are found to have the non‐thermodynamic cubic structure at room temperature. These particles also have a several‐fold enhanced dielectric constant, sometimes exceeding 6000, and are widely used in thin‐layer capacitors. A hydrothermal approach is used to synthesize BTO nanocrystals, which are characterized by a range of methods, including X‐ray Rietveld refinement and the Williamson–Hall approach, revealing the presence of significant inhomogeneous strain associated with the cubic phase. However, X‐ray pair distribution function measurements clearly show the local structure is lower symmetry than cubic. This apparent inconsistency is resolved by examining 3D Bragg coherent diffraction images of selected nanocrystals, which show the existence of ≈50 nm‐sized domains, which are interpreted as tetragonal twins, and yet cause the average crystalline structure to appear cubic. The ability of these twin boundaries to migrate under the influence of electric fields explains the dielectric anomaly for the nanocrystalline phase.

36 MATERIALS SCIENCE↗

Multiwavelength anomalous X-ray diffraction for combined imaging of atomic displacement and strain

The X-ray Bragg coherent diffractive imaging (CDI) technique assumes that the structure factor holds constant over the measured crystal. This approximation breaks down for materials exhibiting variations in the unit-cell configuration, such as piezo- and ferroelectrics. In that case, the strain field cannot be reliably determined from the reconstruction because the lattice deformation and the structure factor contribute concomitantly. Proposed here is a solution to this problem achieved by combining Bragg CDI and the multiwavelength anomalous diffraction approach that measures a Friedel pair of reflections at two different photon energies near an absorption edge. Comparing the obtained reconstructions with a parametric model that includes calculating the scattering amplitude as a function of wavelength and the unit-cell configuration, the contributions of the lattice deformation and the structure factor are separated. Simulations of the ferroelectric material BaTiO 3 demonstrate the possibility of simultaneous probing of the strain and displacement of the Ti atoms. The proposed method opens up an opportunity to apply coherent X-ray diffraction for nanoscale-resolved 3D mapping of polarization domains in micro- and nanocrystals.

lattice deformation↗

In Situ Strain Evolution on Pt Nanoparticles during Hydrogen Peroxide Decomposition

Fundamental understanding of structural changes during catalytic reactions is crucial to understanding the underlying mechanisms and optimizing efficiencies. Surface energy and related catalytic mechanisms are widely studied. However, the catalyst lattice deformation induced by catalytic processes is not well understood. Here, we study the strain in an individual platinum (Pt) nanoparticle (NP) using Bragg coherent diffraction imaging under in situ oxidation and reduction reactions. When Pt NPs are exposed to H 2 O 2 , a typical oxidizer and an intermediate during the oxygen reduction reaction process, alternating overall strain distribution near the surface and inside the NP is observed at the (111) Bragg reflection. In contrast, relatively insignificant changes appear in the (200) reflection. Density functional theory calculations are employed to rationalize the anisotropic lattice strain in terms of induced stress by H 2 O 2 adsorption and decomposition on the Pt NP surface. Our study provides deeper insight into the activity-structure relationship in this system.

3D imaging↗

Bragg Coherent Imaging of Fluctuating Domains

This review presents two examples of domain dynamics in crystalline solid state samples which were imaged recently with synchrotron X-rays by Bragg Coherent Diffraction methods. Domains are associated with sub-atomic phase shifts in the structure which are revealed by the strong phase contrast associated with Bragg diffraction. At low temperatures, La2-xSrxNiO4 has an antiferromagnetic spin-ordered phase with correlation lengths of 200 nm; its domains are imaged with magnetic Bragg Ptychography to visualize their slow fluctuations. Hydrothermally synthesized nanocrystalline BaTiO3 is found to be made up of ~50 nm domains using Bragg Coherent Diffraction Imaging; electric field induced movement of its internal domain walls is a likely explanation of the nano-material's anomalously large dielectric constant, which is used in the manufacture of multilayer ceramic capacitors

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Visualizing the Internal Nanocrystallinity of Calcite Due to Nonclassical Crystallization by 3D Coherent X–Ray Diffraction Imaging

The internal crystallinity of calcite is investigated for samples synthesized using two approaches: precipitation from solution and the ammonium carbonate diffusion method. Scanning electron microscopy (SEM) analyses reveal that the calcite products precipitated using both approaches have a well–defined rhombohedron shape, consistent with the euhedral crystal habit of the mineral. The internal structure of these calcite crystals is characterized using Bragg coherent diffraction imaging (BCDI) to determine the 3D electron density and the atomic displacement field. BCDI reconstructions for crystals synthesized using the ammonium carbonate diffusion approach have the expected euhedral shape, with internal strain fields and few internal defects. In contrast, the crystals synthesized by precipitation from solution have very complex external shapes and defective internal structures, presenting null electron density regions and pronounced displacement field distributions. These heterogeneities are interpreted as multiple crystalline domains, created by a nonclassical crystallization mechanism, where smaller nanoparticles coalescence into the final euhedral particles. The combined use of SEM, X–ray diffraction (XRD), and BCDI allows for structurally differentiating calcite crystals grown with different approaches, opening new opportunities to understand how grain boundaries and internal defects alter calcite reactivity.

36 MATERIALS SCIENCE↗

Coherent diffractive imaging with twisted X-rays: Principles, applications, and outlook

Recent technological breakthroughs in synchrotron and x-ray free electron laser facilities have revolutionized nanoscale structural and dynamic analyses in condensed matter systems. This review provides a comprehensive overview of the advancements in coherent scattering and diffractive imaging techniques, which are now at the forefront of exploring materials science complexities. These techniques, notably Bragg coherent diffractive imaging and x-ray photon correlation spectroscopy, x-ray magnetic dichroism, and x-ray correlation analysis leverage beam coherence to achieve volumetric three-dimensional imaging at unprecedented sub-nanometer resolutions and explore dynamic phenomena within sub-millisecond timeframes. Such capabilities are critical in understanding and developing advanced materials and technologies. Simultaneously, the emergence of chiral crystals—characterized by their unique absence of standard inversion, mirror, or other roto-inversion symmetries—presents both challenges and opportunities. These materials exhibit distinctive interactions with light, leading to phenomena such as molecular optical activity, chiral photonic waveguides, and valley-specific light emissions, which are pivotal in the burgeoning fields of photonic and spintronic devices. This review elucidates how novel x-ray probes can be leveraged to unravel these properties and their implications for future technological applications. A significant focus of this review is the exploration of new avenues in research, particularly the shift from conventional methods to more innovative approaches in studying these chiral materials. Inspired by structured optical beams, the potential of coherent scattering techniques utilizing twisted x-ray beams is examined. This promising direction not only offers higher spatial resolution but also opens the door to previously unattainable insights in materials science. By contextualizing these advancements within the broader scientific landscape and highlighting their practical applications, this review aims to chart a course for future research in this rapidly evolving field.

Physics↗

2022 AI Testbed Expeditions Report

By exploiting the coherent properties of a light source, coherent diffraction imaging (CDI) is able to obtain the sample image at a nanoscale resolution using the measured diffraction pattern. Bragg Coherent Diffraction Imaging (BCDI) has become valuable for recovering the displacement and strain field of crystals, providing a valuable tool in material science and solid-state physics. X-ray ptychography is another emerging CDI technique that can produce a high-resolution image of the extended sample and has become popular in many research areas (e.g., materials science, biology, electronics, and optics characterization). CDI including BCDI and ptychography has become an established technique in Synchrotron Facilities including the Advanced Photon Source (APS) and will greatly benefit from the 100x coherent flux increase of the upcoming APS Upgrade (APSU). The current image formation process in CDI employs iterative phase retrieval algorithms, which is a time-consuming and computationally expensive process. Especially after APSU, the traditional iterative methods will not be able to match the experimental data acquisition speed. We employ deep learning (DL) approach to replace the iterative approaches, therefore allowing hundreds of times faster recovery of the object. We developed AutoPhaseNN, a DL-based approach which learns to solve the inverse problem without labeled data. Taking 3D BCDI as a representative technique, AutoPhaseNN has been demonstrated to be one hundred times faster than traditional iterative phase retrieval methods while providing comparable image quality. The current network is trained with 64 x 64 x 64 data size, to achieve higher resolution imaging, we will need to scale the network to input and train/infer 3D arrays of size 256 x 256 x 256 (today) and of size 2560x2560x2560 (APSU). However, the scalability of the network is restricted due to the memory-intensive training process. To perform the training for a 256 x 256 x 256 data size, the required memory exceeds the capacity of the current machine. In this project, we explore using Sambanova system to train the network for the direct data inversion for CDI.

36 MATERIALS SCIENCE↗

X-ray Nanoimaging of Crystal Defects in Single Grains of Solid-State Electrolyte Li 7–3x Al x La 3 Zr 2 O 12

All-solid-state lithium batteries promise significant improvements in energy density and safety over traditional liquid electrolyte batteries. The Al-doped Li 7 La 3 Zr 2 O 12 (LLZO) solid-state electrolyte shows excellent potential given its high ionic conductivity and good thermal, chemical, and electrochemical stability. Nevertheless, further improvements on electrochemical and mechanical properties of LLZO call for an in-depth understanding of its local microstructure. Here, we employ Bragg coherent diffractive imaging to investigate the atomic displacements inside single grains of LLZO with various Al-doping concentrations, resulting in cubic, tetragonal, and cubic-tetragonal mixed structures. We observe coexisting domains of different crystallographic orientations in the tetragonal structure. We further show that Al doping leads to crystal defects such as dislocations and phase boundaries in the mixed- and cubic-phase grain. This study addresses the effect of Al doping on the nanoscale structure within individual grains of LLZO, which is informative for the future development of solid-state batteries.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

High-energy micrometre-scale pixel direct conversion X-ray detector

The objective of this work was to fabricate and characterize a new X-ray imaging detector with micrometre-scale pixel dimensions (7.8 µm) and high detection efficiency for hard X-ray energies above 20 keV. A key technology component consists of a monolithic hybrid detector built by direct deposition of an amorphous selenium film on a custom designed CMOS readout integrated circuit. Characterization was carried out at the synchrotron beamline 1-BM-B at the Advanced Photon Source of Argonne National Laboratory. The direct conversion detector demonstrated micrometre-scale spatial resolution with a 63 keV modulation transfer function of 10% at Nyquist frequency. In addition, spatial resolving power down to 8 µm was determined by imaging a transmission bar target at 21 keV. X-ray signal linearity, responsivity and lag were also characterized in the same energy range. Finally, phase contrast edge enhancement was observed in a phase object placed in the beam path. This amorphous selenium/CMOS detector technology can address gaps in commercially available X-ray detectors which limit their usefulness for existing synchrotron applications at energies greater than 50 keV; for example, phase contrast tomography and high-resolution imaging of nanoscale lattice distortions in bulk crystalline materials using Bragg coherent diffraction imaging. Here, the technology will also facilitate the creation of novel synchrotron imaging applications for X-ray energies at or above 20 keV.

36 MATERIALS SCIENCE↗

Unveiling nano-scale crystal deformation using coherent X-ray dynamical diffraction

Visualization of internal deformation fields in crystalline materials helps bridge the gap between theoretical models and practical applications. Applying Bragg coherent diffraction imaging under X-ray dynamical diffraction conditions provides a promising approach to the longstanding challenge of investigating the deformation fields in micron-sized crystals. Here, we present an automatic differentiation-based reconstruction method that integrates dynamical scattering theory to accurately reconstruct deformation fields in large crystals. Using this forward model, our simulated and experimental results demonstrate that three-dimensional local strain information inside a large crystal can be accurately reconstructed under coherent X-ray dynamical diffraction conditions with Bragg coherent X-ray diffraction imaging. These findings open an avenue for extending the investigation of local deformation fields to microscale crystals while maintaining nanoscale resolution, leveraging the enhanced coherence and brightness of advanced X-ray sources.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

High-Energy Coherent X-Ray Dffraction Microscopy of Polycrystal Grains: First Steps Towards a Multi-Scale Approach

Here, we present proof-of-concept imaging measurements of a polycrystalline material that integrate the elements of conventional high-energy x-ray diffraction microscopy with coherent diffraction-imaging techniques, and that can enable in situ strain-sensitive imaging of lattice structure in ensembles of deeply embedded crystals over five decades of length scale upon full realization. We demonstrate that the combination of these two characterization methods enables a more complete picture of the crystal-lattice strain than either method is capable of providing individually. Such complementary imaging capabilities are critical to addressing questions in a variety of research areas such as materials science and engineering, chemistry, and solid-state physics. Towards this eventual goal, the following key aspects are demonstrated: (1) high-energy Bragg coherent diffraction imaging (HE BCDI) of submicron-scale crystallites at 52 keV at current third-generation synchrotron light sources, (2) HE BCDI performed in conjunction with far-field high-energy diffraction microscopy (FF HEDM) on the grains of a polycrystalline sample in a smoothly integrated manner, and (3) the orientation information of an ensemble of grains obtained via FF HEDM used to perform complementary HE BCDI on multiple Bragg reflections of a single targeted grain. The imaged structures are seen to be 477 ± 50 nm or smaller in size, with an estimated strain resolution of 2.5 x 10 -4 . These steps lay the foundation for integration of HE BCDI, which typically provides a spatial resolution tens of nanometers, into a broad suite of well-established HEDM methods, extending HEDM beyond the few-micrometer resolution bound and into the nanoscale, and positioning the approach to take full advantage of the orders-of-magnitude improvement of x-ray coherence expected at fourth-generation light sources presently being built and commissioned worldwide.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Refinements for Bragg coherent X-ray diffraction imaging: electron backscatter diffraction alignment and strain field computation

Bragg coherent X-ray diffraction imaging (BCDI) allows the 3D measurement of lattice strain along the scattering vector for specific microcrystals. If at least three linearly independent reflections are measured, the 3D variation of the full lattice strain tensor within the microcrystal can be recovered. However, this requires knowledge of the crystal orientation, which is typically attained via estimates based on crystal geometry or synchrotron microbeam Laue diffraction measurements. Presented here is an alternative method to determine the crystal orientation for BCDI measurements using electron backscatter diffraction (EBSD) to align Fe–Ni and Co–Fe alloy microcrystals on three different substrates. The orientation matrix is calculated from EBSD Euler angles and compared with the orientation determined using microbeam Laue diffraction. The average angular mismatch between the orientation matrices is less than ∼6°, which is reasonable for the search for Bragg reflections. The use of an orientation matrix derived from EBSD is demonstrated to align and measure five reflections for a single Fe–Ni microcrystal via multi-reflection BCDI. Using this data set, a refined strain field computation based on the gradient of the complex exponential of the phase is developed. This approach is shown to increase accuracy, especially in the presence of dislocations. The results demonstrate the feasibility of using EBSD to pre-align BCDI samples and the application of more efficient approaches to determine the full lattice strain tensor with greater accuracy.

42 ENGINEERING↗

Imaging the Phase Transformation in Single Particles of Lithium Titanate Anode for Lithium-ion Batteries

Lithium uptake and release in lithium titanate (LTO) anode materials during a discharge and charge cycle is one of the fundamental processes of a Lithium-ion battery (LIB), still not fully understood at the microscopic level.During discharge cycle, LTO undergoes a phase transformation between Li 4 Ti 5 O 12 and Li 7 Ti 5 O 12 states within a cubic crystal lattice. To reveal the details of the microscopic mechanism,it is necessary to track the sequence of phase transformation sat different discharge/charge states under operating conditions.Here we use in-situ Bragg Coherent Diffraction Imaging (BCDI) and in-situ X-ray diffraction (XRD) experiments to examine the lithium insertion-induced materials phase transformation within a single LTO particle anda bulk battery analogue,respectively. BCDI analysis from (111) Bragg peak, shows the two-phase transformation manifesting as a distinct image phase modulation within a single LTO nanoparticle occurring in the middle of the discharge region then subsiding towards the end of the discharge cycle. We observe the biggest phase variation at the two-phase stage,indicating the formation of phase domains of 200 nm in size during the discharge process. Additionally, we also observe a lattice contraction of >0.2% in a single LTO nanoparticle at the (400) Bragg peak measurement, larger than that in the corresponding bulk material. Our observation of this phase transformation at a single particle level has implications for the understanding of the microscopic/mesoscale picture of the phase transformation in anode and cathode LIBs materials.

25 ENERGY STORAGE↗