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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.
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.
Although the basic idea may be traced back to the earlier X-ray diffraction studies of Sir W. L. Bragg, the holographic method as we know it was invented by D. Gabor in 1948 as a two-step lensless imaging technique to enhance the resolution of electron microscopy, for which he received the 1971 Nobel Prize in physics. The distinctive feature of holography is the recording of the object phase variations that carry the depth information, which is lost in conventional photography where only the intensity (= squared amplitude) distribution of an object is captured. Since all photosensitive media necessarily respond to the intensity incident upon them, an ingenious way had to be found to convert object phase into intensity variations, and Gabor achieved this by introducing a coherent reference wave along with the object wave during exposure. Gabor's in-line recording scheme, however, required the object in question to be largely transmissive, and could provide only marginal image quality due to unwanted terms simultaneously reconstructed along with the desired wavefront. Further handicapped by the lack of a strong coherent light source, optical holography thus seemed fated to remain just another scientific curiosity, until the field was revolutionized in the early 1960s by some major breakthroughs: the proposition and demonstration of the laser principle, the introduction of off-axis holography, and the invention of volume holography. Consequently, the remainder of that decade saw an exponential growth in research on theory, practice, and applications of holography. Today, holography not only boasts a wide variety of scientific and technical applications (e.g., holographic interferometry for strain, vibration, and flow analysis, microscopy and high-resolution imagery, imaging through distorting media, optical interconnects, holographic optical elements, optical neural networks, three-dimensional displays, data storage, etc.), but has become a prominent am advertising, and security medium as well. The evolution of holographic optical memories has followed a path not altogether different from holography itself, with several cycles of alternating interest over the past four decades. P. J. van Heerden is widely credited for being the first to elucidate the principles behind holographic data storage in a 1963 paper, predicting bit storage densities on the order of 1/lambda(sup 3) with source wavelength lambda - a fantastic capacity of nearly 1 TB/cu cm for visible light! The science and engineering of such a storage paradigm was heavily pursued thereafter, resulting in many novel hologram multiplexing techniques for dense data storage, as well as important advances in holographic recording materials. Ultimately, however, the lack of such enabling technologies as compact laser sources and high performance optical data I/O devices dampened the hopes for the development of a commercial product. After a period of relative dormancy, successful applications of holography in other arenas sparked a renewed interest in holographic data storage in the late 1980s and the early 1990s. Currently, with most of the critical optoelectronic device technologies in place and the quest for an ideal holographic recording medium intensified, holography is once again considered as one of several future data storage paradigms that may answer our constantly growing need for higher-capacity and faster-access memories.
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.
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.
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
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.
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.
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.
Real-space Bragg coherent x-ray-diffractive imaging unveils the formation of bubble and stripe antiferromagnetic (AFM) phase domains on the surface of Ni 2 CoTeO 6 single crystal. The stripe domains exhibit dislocation-type topological defects. The defects typically form as defect-antidefect pairs and can be created or annihilated by temperature changes and local heating. Thermal fluctuations of the AFM domain walls are observed near the Néel temperature. Topological defect pairs dynamically form and disappear in the fluctuating state. These observations provide a real-space perspective on the dynamics of the AFM phase transition in a helical antiferromagnet. Finally, the remarkable tunability of AFM domain walls in a helical antiferromagnet underscores their potential for AFM spintronics applications.