Gwaihir: Jupyter Notebook graphical user interface for Bragg Coherent Diffraction Imaging
Room temperature data, under Argon atmosphere, on particle B-7. Comes with a hotpixels mask.
Bragg Coherent Diffraction Imaging↗
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Results for “Bragg coherent X-ray diffraction imaging”
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Gwaihir: Jupyter Notebook graphical user interface for Bragg Coherent Diffraction Imaging
Data on particle II-A1, 450°C, under CO and Argon atmosphere, 002 reflection, 1.818 detector distance, Eiger detector.
Bragg Coherent Diffraction Imaging↗
Diffractive Image Reconstruction Utilizing Molecular Dynamics Enabling Near Atomic Resolution
We present a new algorithm for coherent x-ray imaging that combines error minimization and molecular dynamics. We show reconstructed atomic positions from Bragg peaks off simulated 2D nanocrystals and how these converge with atomic resolution.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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↗
Atomic resolution coherent x-ray imaging with physics-based phase retrieval
Coherent x-ray imaging and scattering from accelerator based sources such as synchrotrons continue to impact biology, medicine, technology, and materials science. Many synchrotrons around the world are currently undergoing major upgrades to increase their available coherent x-ray flux by approximately two orders of magnitude. The improvement of synchrotrons may enable imaging of materials in operando at the atomic scale which may revolutionize battery and catalysis technologies. Current algorithms used for phase retrieval in coherent x-ray imaging are based on the projection onto sets method. These traditional iterative phase retrieval methods will become more computationally expensive as they push towards atomic resolution and may struggle to converge. Additionally, these methods do not incorporate physical information that may additionally constrain the solution. In this work, we present an algorithm which incorporates molecular dynamics into Bragg coherent diffraction imaging (BCDI). This algorithm, which we call PRAMMol (Phase Retrieval with Atomic Modeling and Molecular Dynamics) combines statistical techniques with molecular dynamics to solve the phase retrieval problem. We present several examples where our algorithm is applied to simulated coherent diffraction from 3D crystals and show convergence to the correct solution at the atomic scale.
47 OTHER INSTRUMENTATION↗
Imaging surface topography with coherent x-ray reflectivity: Theory, kinematics, and simulations
A theoretical formalism is described for understanding coherent x-ray reflectivity (CXR) from the surface of a semi-infinite crystal having a variable surface topography, described by the height profile ℎ(𝑥,𝑦). The surface topography is imaged as a complex “effective density,” obtained from the phasing and inversion of the coherent x-ray reflectivity data, measured through a rocking scan centered at a vertical momentum transfer 𝑄$^{0}_{𝑧}$ and a vertical range Δ𝑄 𝑧 . The formalism predicts that the effective density has an amplitude with a maximum located at the surface height for each position within the surface plane. The phase of the effective density has a lateral variation that is controlled by the surface height and a vertical variation that reflects a combination of the interfacial structure and specific choice of measurement conditions. This understanding enables direct observation of nanometer-scale interfacial topography, i.e., ℎ(𝑥,𝑦)𝑐 𝑠 (where 𝑐 𝑠 is the vertical substrate lattice parameter) with Å-scale sensitivity to surface height. Numerical simulations illustrate and confirm the theoretical results. These results show how the interpretation of the interfacial density phase obtained by CXR data inversion (i.e., surface topography with respect to a flat surface) is conceptually similar to that previously known for Bragg coherent diffraction imaging (BCDI) measurements of isolated nanoparticles (i.e., lattice displacements with respect to an ideal crystal lattice). This suggests that CXR can be thought of as a form of dark field imaging with respect to the bright field BCDI approach. An implication of these results is that interfacial imaging may bypass some of the significant challenges associated with BCDI imaging of multiple particles having different orientations.
X-ray imaging↗
Enabling dynamic 3D coherent diffraction imaging via adaptive latent space tuning of generative autoencoders
Abstract Coherent diffraction imaging (CDI) is an advanced non-destructive 3D X-ray imaging technique for measuring a sample’s electron density. The main challenge of CDI is loss of phase information in diffraction intensity measurements, resulting in lengthy iterative reconstruction processes that can return non-unique solutions, which pose challenges for experiments attempting to track dynamic sample evolution through multiple states. As the increased brightness of fourth-generation light sources enables faster sample measurements and drives operando experiments with Bragg CDI, there is a growing need for faster reconstruction techniques that can keep pace. We have developed an adaptive generative autoencoder approach for uniquely tracking a sample’s electron density as it dynamically evolves. Our approach adaptively tunes the low-dimensional latent embedding of a generative autoencoder, enabling a computationally efficient manner to account for time-varying shifting distributions in real-time. Analytic proof of convergence is provided as well as numerical demonstration of sample tracking with noisy measurements.
97 MATHEMATICS AND COMPUTING↗
X‑ray Coherent Diffractive Imaging of Large Helium Nanodroplets Doped with Small Molecules
We report the first X-ray coherent diffractive imaging experiment on molecule-doped helium nanodroplets. It complements previous work, where we reported single-shot X-ray coherent diffractive imaging studies of Xe dopant clusters formed in 4He and 3He droplets. These noble gas clusters were used to visualize the impact of rotational excitation of the droplets on the spatial distribution of atomic dopants within the droplets, and to study the differences and connections between quantum and classical droplet rotational motion. Here, we expand our studies to the molecular dopants CF4, CHF3, CH3CN, and SF6, imaged with 1.5 keV photons. We find multiple Bragg spots in the diffraction patterns of molecule-doped droplets with radii of approximately 600 nm, which provide evidence that molecules form elongated clusters with preferential alignment along the angular momentum axis of the 4He droplets, in agreement with our previous results on the aggregation of Xe clusters on quantum vortices. Real-space reconstructions of molecular dopant cluster density profiles are obtained for droplets with smaller radii of approximately 300 nm. The diffuse images suggest the formation of low-density, potentially porous, molecular clusters upon aggregation at T = 0.4 K in 4He droplets. In the normal fluid 3He droplets, molecules aggregate into loose clusters on the droplets' equator, similar to previous observations for Xe atoms. Time-of-flight mass spectra reveal that the doped helium nanodroplet moieties fragment extensively into constituent atomic ions, producing only a small fraction of molecular fragment ions. The findings are discussed in the context of previously proposed schemes to use He droplets as potential tamper materials for ultrafast X-ray imaging experiments.
Feinberg, AlexandraJ↗
Extending Bragg Coherent Diffraction Imaging to the Atomic Scale with Physics-Based Optimization
As upgrades to synchrotrons increase coherent flux, atomic resolution in Bragg Coherent Diffraction Imaging has become a distinct possibility. Here, we present a new method that shows the capability to achieve atomic resolution for small nanoparticles.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Experimental demonstration of coupled multi-peak Bragg coherent diffraction imaging with genetic algorithms
Bragg coherent diffraction imaging has the potential to provide significant insight into the structure-properties relationship for crystalline materials by imaging, with nanoscale resolution, three-dimensional strain fields within individual grains and nanoparticles. The capability of present-day synchrotrons to locate and measure a multiplicity of Bragg reflections from a single grain makes it possible to recover the full strain tensor with nanometer resolution. Recent methods for coupling reconstructions from several peaks to determine the strain tensor have been developed and applied to synthetic data, but have not been applied to experimental data. Here, using a coupled genetic reconstruction algorithm, we reconstruct an experimental data set and demonstrate improvements in the ability to resolve vector-valued displacement fields internal to the particle as compared to what is achieved with a noncoupled approach. The coupled approach developed in this work was also validated on simulated data sets. In both simulated and experimental data, reconstructions from our coupled Bragg peak algorithm show improvements over the noncoupled independent reconstruction method of 5% in terms of accuracy and 53% in terms of consistency.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
High-luminosity meV-resolution single-shot hard X-ray spectrograph for cavity-based X-ray free-electron lasers
Cavity-based X-ray free-electron lasers (CBXFELs) represent a possible realization of fully coherent hard X-ray sources having high spectral brilliance along with a narrow spectral bandwidth of ∼1–50 meV, a high repetition pulse rate of ∼1 MHz, and good stability. A diagnostic tool is required to measure CBXFEL spectra with meV resolution and high luminosity on a shot-to-shot basis. We have designed a high-luminosity single-shot hard X-ray spectrograph that images 9.831 keV X-rays in a ∼200 meV spectral window with a spectral resolution of a few meV. The spectrograph is designed around angular dispersion of X-rays in Bragg diffraction from crystals. It operates close to design specifications, exhibiting a linear dispersion rate of ∼1.4 µm meV −1 and a ∼200 meV window of high-fidelity spectral imaging. The experimentally demonstrated spectral resolution is ∼20 meV; this resolution is twice as low as expected from theory primarily because the spectrograph is highly sensitive to crystal angular instabilities. The experiment was performed at the bending magnet X-ray optics testing beamline 1-BM at the Advanced Photon Source.
Bragg diffraction↗
Three-dimensional coherent X-ray diffraction imaging via deep convolutional neural networks
Abstract As a critical component of coherent X-ray diffraction imaging (CDI), phase retrieval has been extensively applied in X-ray structural science to recover the 3D morphological information inside measured particles. Despite meeting all the oversampling requirements of Sayre and Shannon, current phase retrieval approaches still have trouble achieving a unique inversion of experimental data in the presence of noise. Here, we propose to overcome this limitation by incorporating a 3D Machine Learning (ML) model combining (optional) supervised learning with transfer learning. The trained ML model can rapidly provide an immediate result with high accuracy which could benefit real-time experiments, and the predicted result can be further refined with transfer learning. More significantly, the proposed ML model can be used without any prior training to learn the missing phases of an image based on minimization of an appropriate ‘loss function’ alone. We demonstrate significantly improved performance with experimental Bragg CDI data over traditional iterative phase retrieval algorithms.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Extending the Takagi-Taupin equations for x-ray nanobeam Bragg coherent diffraction
We present an approach for simulating x-ray nanobeam Bragg coherent diffraction patterns based on the Takagi-Taupin equations. Compared to conventional methods, the current approach can be universally applied to any weakly strained system including semi-infinite crystals that diffract dynamically. It addresses issues such as the curved wave front and redivergence of the focused incident beam. In conclusion, we show excellent agreement with experimental data for a strained La 0.7 Sr 0.3 MnO 3 thin film on a SrTiO 3 substrate and a path to extracting physical information using automatic differentiation.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Electric field driven domain wall dynamics in BaTiO 3 nanoparticles
We report a detailed investigation into the response of single BaTiO 3 (BTO) nanocrystals under applied electric fields (E-field) using Bragg coherent diffraction imaging. Our study reveals pronounced domain wall migration and expansion of a sample measure under applied electric field. The changes are most prominent at the surface of the nanocrystal, where the lack of external strain allows greater domain wall mobility. The observed domain shifts are correlated to the strength and orientation of the applied E-field, following a side-by-side domain model from Suzana []. Notably, we identified a critical electric field strength of 3 MV/m, which leads to irreversible structural changes, suggesting plastic deformation. The findings highlight how surface effects and intrinsic defects contribute to the enhanced dielectric properties of BTO at the nanoscale, in contrast to bulk materials, where strain limits domain mobility. These findings deepen our understanding of nanoscale dielectric behavior and inform the design of advanced nanoelectronic devices. Published by the American Physical Society 2025
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Probing Fundamental Mechanisms of Plastic Deformation with High Energy X-rays (Final Progress Report)
Overall, substantial progress was made on developing BCDI techniques in the direction of imaging defects in multi-crystal samples. Section 2.1 describes a new method to reconstruct the 3D atomic displacement field within a grain from multiple coherently resolved diffraction peaks. The key development is the ability to recover a best fit to the grain shape at the same time as the internal displacement (strain) variation with no prior knowledge of the microstructure. This is complemented by the development of a method, Sec. 2.2, to separate out sets of Laue reflections that belong to a single grain (and thus be able to index its orientation) in the commonly encountered situation in which the beam illuminates several grains in a given location. This is essential for enabling collection of coherent diffraction data (at APS 34-ID-C) from neighboring grains. All experiments depend on the quality of samples used. Although good progress has been made with thin film samples, we are working with a broader range of geometries. A new sample design uses a high-Z metal (e.g., Pt) deposited in a sub-micron trench in a low-Z metal (e.g., Al) so that the grain size is prevented from exceeding the current limit for BCDI. We also report in section 3.1 on successfully applying NF-HEDM to a fine-grain Mg sample that would normally be considered out of scope for the method. This represents progress towards being able to map out polycrystalline samples in 3D before performing BCDI on individual grains. We further report in section 3.2 on preliminary NF-HEDM characterization of a sample of UO2 that has sub-micron grains; the data imply the capability of mapping fine-grain polycrystals at 1-ID-E, again for the purposes of BCDI in the bulk. Lastly, our plan is to load grains in polycrystalline samples by inducing thermal stress. We also report the experimental measurements of the Ti- 6Al-4V alloy obtained at the European Synchrotron Radiation Facility (ESRF), which had been indexed and mapped via HEDM at APS in section 9. As discussed below, however, technique development pre-occupied the team throughout the project which meant that we did not make any significant progress towards answering the original hypotheses as stated in the proposal. In summary, we assert that we have made good progress in methods and samples and future work taking advantage of this progress is likely to obtain and analyze BCDI data from multiple adjacent grains in 3D polycrystals. Obtaining such data depends on re-gaining access to the Advanced Photon Source, which is anticipated in late summer or the Fall. In all cases, work has involved close collaboration with faculty, staff, postdocs and students from Brigham Young University (BYU), the Los Alamos National Laboratory and APS beamlines 1-ID and 34-ID.
36 MATERIALS SCIENCE↗
Mechanistic Insights into Defect-Mediated Crystallization Revealed by Lattice Strain Evolution
Structural defects and lattice strain are intrinsic to many crystalline materials, yet their roles in controlling chemical reaction mechanisms and directing crystallization pathways remain poorly understood. Here, in this study, we revealed the three-dimensional evolution of strain and dislocation defects at the nanoscale during the growth of heterogeneously nucleated barite (BaSO 4 ) and calcite (CaCO 3 ) crystals by using coherent X-ray scattering, electron microscopy, and molecular simulations. Unlike barite, which formed with minimal internal strain, calcite developed dislocation defects and exhibited spatially varying strain that increased during growth. During growth in Sr-rich solutions, calcite likely incorporates Sr 2+ into the defects, which further modulates the local lattice structure and increases both the compressive and tensile strain. These findings suggest that calcite crystallization was likely dominated by attachment of precursor phases, which gave rise to defect-enriched domain structures not predicted by classical growth models. By linking defect formation to ion incorporation and growth dynamics, this work provides fundamental insight into how lattice-level strain heterogeneity governs the chemical reactivity of ionic crystals.
Bragg coherent diffractive imaging↗
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↗
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↗