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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.
Strain is known to enhance the activity of the oxygen reduction reaction in catalytic platinum alloy nanoparticles, whose inactivity is the primary impediment to efficient fuel cells and metal–air batteries. Here, Bragg coherent diffraction imaging (BCDI) was employed to reveal the strain evolution during the voltammetric cycling in Pt–Ni alloy nanoparticles composed of Pt 2 Ni 3 , Pt 1 Ni 1 , and Pt 3 Ni 2 . Analysis of the 3D strain images using a core–shell model shows that the strain as large as 5% is induced on Pt-rich shells due to Ni dissolution. The composition dependency of the strain on the shells is in excellent agreement with that of the catalytic activity. The present study demonstrates that BCDI enables quantitative determination of the strain on alloy nanoparticles during electrochemical reactions, which provides a means to exploit surface strain to design a wide range of electrocatalysts.
Many important aspects of the dynamic thermo-mechanical response of materials occur at the mesoscale, i.e. a physical scale of interactions smaller than what can be adequately described by homogenous behaviors, yet larger than the scale of the atomic lattice. Concurrent advancements in computational power, continuum theory, and experimental diagnostics are enabling unprecedented understanding of such interactions. However, we cannot develop a sufficient level of confidence in such mesoscale capability until the constitutive description of the underlying constituents is reliably representative of their actual physical behavior. Therefore, there is a strong need to combine experimental, modeling, and data-science techniques to validate models of the thermomechanical response of individual single crystals. One experimental diagnostic with high potential impact to shock physics and materials science is in-situ x-ray diffraction. This paper is primarily focused on simulation of x-ray diffraction in shock physics, but with an aim toward quantifying parametric uncertainty of simulation models. Here, we develop and demonstrate a data-science and model-driven approach to constrain the parameterization of continuum models of crystal lattice deformation associated with the shock response of crystalline materials. The framework is built around the connection between continuum hydrodynamic simulations of lattice deformation and a new Bragg diffraction simulation code, BarberShop. The dynamic deformation of a crystal lattice is modeled using the DiscoFlux model within an arbitrary Lagrangian-Eulerian hydrodynamic code, FLAG. These detailed continuum simulations of lattice deformation can be computationally slow, thus a statistical model is used to emulate the evolution of lattice deformation fields in time and across the considered model parameter space. Emulated lattice deformation fields can then be generated rapidly for any combination of physics model parameters. In turn, these fields can be fed into BarberShop to realize a rapid prediction of Bragg diffraction patterns associated with particular values of physics model parameters. The framework enables parameterization of the single crystal model to obtain Bragg diffraction patterns that most closely resemble a corresponding measurement. Furthermore, the framework naturally provides sensitivities of the lattice deformation to the physics parameters. We highlight the utility of this framework through the application to a synthetic closed-loop inverse problem leading to the parameterization of a single crystal material model. As a model problem, we consider the dynamic response of the energetic molecular crystal, cyclotrimethylenetrinitramine (or RDX), under dynamic compression induced by simulated flyer plate impact experiments.
InGaAs quantum wells embedded in GaAs nanowires can serve as compact near-infrared emitters for direct integration onto Si complementary metal oxide semiconductor technology. While the core–shell geometry in principle allows for a greater tuning of composition and emission, especially farther into the infrared, the practical limits of elastic strain accommodation in quantum wells on multifaceted nanowires have not been established. One barrier to progress is the difficulty of directly comparing the emission characteristics and the precise microstructure of a single nanowire. Here, in this study, we report an approach to correlating quantum well morphology, strain, defects, and emission to understand the limits of elastic strain accommodation in nanowire quantum wells specific to their geometry. We realize full 3D Bragg coherent diffraction imaging (BCDI) of intact quantum wells on vertically oriented epitaxial nanowires, which enables direct correlation with single-nanowire photoluminescence. By growing In 0.2 Ga 0.8 As quantum wells of distinct thicknesses on different facets of the same nanowire, we identified the critical thickness at which defects are nucleated. A correlation with a traditional transmission electron microscopy analysis confirms that BCDI can image the extended structure of defects. Finite element simulations of electron and hole states explain the emission characteristics arising from strained and partially relaxed regions. This approach, imaging the 3D strain and microstructure of intact nanowire core–shell structures with application-relevant dimensions, can aid the development of predictive models that enable the design of new compact infrared emitters.
Of current importance for alloy design is controlling chemical ordering through processing routes to optimize an alloy's mechanical properties for a desired application. However, characterization of chemical ordering remains an ongoing challenge, particularly when nondestructive characterization is needed. Here, in this study, Bragg coherent diffraction imaging is used to reconstruct morphology and lattice displacement in model Cu 3 Au nanocrystals that have undergone different heat treatments to produce variation in chemical ordering. The magnitudes and distributions of the scattering amplitudes (proportional to electron density) and lattice strains within these crystals are then analyzed to correlate them to the expected amount of chemical ordering present. Nanocrystals with increased amounts of ordering are found to generally have less extreme strains present and reduced strain distribution widths. In addition, statistical correlations are found between the spatial arrangement of scattering amplitude and lattice strains.
Abstract The problem of phase retrieval underlies various imaging methods from astronomy to nanoscale imaging. Traditional phase retrieval methods are iterative and are therefore computationally expensive. Deep learning (DL) models have been developed to either provide learned priors or completely replace phase retrieval. However, such models require vast amounts of labeled data, which can only be obtained through simulation or performing computationally prohibitive phase retrieval on experimental datasets. Using 3D X-ray Bragg coherent diffraction imaging (BCDI) as a representative technique, we demonstrate AutoPhaseNN, a DL-based approach which learns to solve the phase problem without labeled data. By incorporating the imaging physics into the DL model during training, AutoPhaseNN learns to invert 3D BCDI data in a single shot without ever being shown real space images. Once trained, AutoPhaseNN can be effectively used in the 3D BCDI data inversion about 100× faster than iterative phase retrieval methods while providing comparable image quality.
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.
Due to complex degradation mechanisms, disparities between the theoretical and practical capacities of lithium-ion battery cathode materials persist. Specifically, Ni-rich chemistries such as LiNi 0.8 Mn 0.1 Co 0.1 O 2 (or NMC811) are one of the most promising choices for automotive applications; however, they continue to suffer severe degradation during operation that is poorly understood, thus challenging to mitigate. Here in this paper we use operando Bragg coherent diffraction imaging for 4D analysis of these mechanisms by inspecting the individual crystals within primary particles at various states of charge (SoC). Although some crystals were relatively homogeneous, we consistently observed non-uniform distributions of inter- and intracrystal strain at all measured SoC. Pristine structures may already possess heterogeneities capable of triggering crystal splitting and subsequently particle cracking. During low-voltage charging (2.7–3.5 V), crystal splitting may still occur even during minimal bulk deintercalation activity; and during discharging, rotational effects within parallel domains appear to be the precursor for the nucleation of screw dislocations at the crystal core. Ultimately, this discovery of the central role of crystal grain splitting in the charge/discharge dynamics may have ramifications across length scales that affect macroscopic performance loss during real-world battery operation.
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.
Room temperature data, under Argon atmosphere, on particle B-7. Comes with a hotpixels mask.
Data on particle II-A1, 450°C, under CO and Argon atmosphere, 002 reflection, 1.818 detector distance, Eiger detector.
Dynamically compressed materials in longitudinal waves are described by two physical models: hydrostatic pressure, with equal, normal, principal stresses or material uniaxially strained in the wave propagation direction. These models are disparate, so experimental comparisons and evaluations are important. Polycrystalline material in a state of hydrostatic pressure will have no eccentricity of x-ray-diffracted Debye–Scherrer rings. A general three-dimensional solution of Bragg diffracted x rays based on principal crystallographic strains in the compression wave was found. The distortion of x-ray diffraction beams has been used for strain measurements; the analysis developed incorporates a strained reciprocal lattice and the incident x-ray beam. Strain-distorted Polanyi surfaces form an annulus of compression with an ellipsoid of revolution in reciprocal space, which is intersected by Ewald's sphere for Bragg diffraction. The in situ measurements for strain describe nanosecond diffraction evaluated using two planes, (hkl) and (h′k′l′), both in the same crystallographic phase. Diffraction from Al, Ni, Na, and Invar quantifies the compression axial strains in these materials: The compression axial ratios are 0.65, 1.05, 0.88, and 1.58 at pressures of 291, 402, 409, and 367 GPa for the respective materials. Crystal structure transformations with homogeneous pressurized stresses, mandating equal normal strains, should not be anticipated to agree with heterogeneous, uniaxially strained, and sheared crystalline phases. Measurements support in-plane strains increasing with pressure, p , in fcc and hcp aluminum as ε 22 = −0.21 p /TPa.
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.
Wavefront-preserving X-ray diamond crystal optics are essential for numerous applications in X-ray science. Perfect crystals with flat Bragg planes are a prerequisite for wavefront preservation in Bragg diffraction. However, this condition is difficult to realize in practice because of inevitable crystal imperfections. Here, X-ray rocking curve imaging is used to study the smallest achievable Bragg-plane slope errors in the best presently available synthetic diamond crystals and how they compare with those of perfect silicon crystals. It is shown that the smallest specific slope errors in the best diamond crystals are about 0.08 (3) µrad mm -2 . These errors are only 50% larger than the 0.05 (2) µrad mm -2 specific slope errors measured in perfect silicon crystals. High-temperature annealing at 1450°C of almost flawless diamond crystals reduces the slope errors very close to those of silicon. Further investigations are in progress to establish the wavefront-preservation properties of these crystals.
We have developed and demonstrated an image super-resolution method—XR-UNLOC: X-Ray UNsupervised particle LOCalization—for hard x-rays measured with fast-frame-rate detectors that is an adaptation of the principle of photo-activated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM), which enabled biological fluorescence imaging at sub-optical-wavelength scales. We demonstrate the approach on experimental coherent Bragg diffraction data measured with 52 keV x-rays from a nanocrystalline sample. From this sample, we resolve the fine fringe detail of a high-energy x-ray Bragg coherent diffraction pattern to an upsampling factor of 16 of the native pixel pitch of 30 μ m of a charge-integrating fastCCD detector. This was accomplished by analysis of individual photon locations in a series of “nearly-dark” instances of the diffraction pattern that each contain only a handful of photons. Central to our approach was the adaptation of the UNLOC photon fitting routine for PALM/STORM to the hard x-ray regime to handle much smaller point spread functions, which required a different statistical test for photon detection and for sub-pixel localization. A comparison to a photon-localization strategy used in the x-ray community (“droplet analysis”) showed that XR-UNLOC provides significant improvement in super-resolution. We also developed a metric by which to estimate the limit of reliable upsampling with XR-UNLOC under a given set of experimental conditions in terms of the signal-to-noise ratio of a photon detection event and the size of the point spread function for guiding future x-ray experiments in many disciplines where detector pixelation limits must be overcome.
Multi-photon Bragg diffraction is a powerful method for fast, coherent momentum transfer of atom waves. However, laser noise, Doppler detunings, and cloud expansion limit its efficiency in large momentum transfer (LMT) pulse sequences. We present simulation studies of robust Bragg pulses developed through numerical quantum optimal control. Optimized pulse performance under noise and cloud inhomogeneities is analyzed and compared to analogous Gaussian and adiabatic rapid passage pulses in simulated LMT Mach–Zehnder interferometry sequences. The optimized pulses maintain robust population transfer and phase response over a broader range of noise, resulting in superior contrast in LMT sequences with thermal atom clouds and intensity inhomogeneities. Large optimized LMT sequences use lower pulse area than Gaussian pulses, making them less susceptible to spontaneous emission loss. The optimized sequences maintain over five times better contrast with tens of momentum separation and offer more improvement with greater LMT. Such pulses could allow operation of Bragg atom interferometers with unprecedented sensitivity, improved contrast, and hotter atom sources.
Diffraction gratings with large angular dispersion rates are central to obtaining high spectral resolution in grating spectrometers operating over a broad spectral range from infrared to soft X-ray domains. The greatest challenge is of course to achieve large dispersion rates in the short-wavelength X-ray domain. Here it is shown that crystals in non-coplanar asymmetric X-ray Bragg diffraction can function as high-reflectance broadband soft X-ray diffraction gratings with dispersion rates that are at least two orders of magnitude larger than those that are possible with state-of-the-art man-made gratings. Additionally, this opens new opportunities to design and implement soft X-ray resonant inelastic scattering (RIXS) spectrometers with spectral resolutions that are up to two orders of magnitude higher than what is currently possible, to further advance a very dynamic field of RIXS spectroscopy, and to make it competitive with inelastic neutron scattering. Examples of large-dispersion-rate crystal diffraction gratings operating near the 930 eV L 3 absorption edge in Cu and of the 2.838 keV L 3 -edge in Ru are presented.
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.