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(De)lithiation of spinel ferrites Fe3O4, MgFe2O4, and ZnFe2O4: a combined spectroscopic, diffraction and theory study
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Deep-Learning Electron Diffractive Imaging
Here, we report the development of deep-learning coherent electron diffractive imaging at subangstrom resolution using convolutional neural networks (CNNs) trained with only simulated data. We experimentally demonstrate this method by applying the trained CNNs to recover the phase images from electron diffraction patterns of twisted hexagonal boron nitride, monolayer graphene, and a gold nanoparticle with comparable quality to those reconstructed by a conventional ptychographic algorithm. Fourier ring correlation between the CNN and ptychographic images indicates the achievement of a resolution in the range of 0.70 and 0.55 Å. We further develop CNNs to recover the probe function from the experimental data. The ability to replace iterative algorithms with CNNs and perform real-time atomic imaging from coherent diffraction patterns is expected to find applications in the physical and biological sciences.
Takagi–Taupin dynamical X-ray diffraction simulations of asymmetric X-ray diffraction from crystals: the effects of surface undulations
Dynamical X-ray diffraction simulations from crystals with surface undulations are reported. The Takagi–Taupin equations are applied and used to derive results in good agreement with experimental data reported in a separate paper [Macrander, Pereira, Huang, Kasman, Qian, Wojcik & Assoufid (2020). J. Appl. Cryst. 53, 789–792]. The development of Uragami [J. Phys. Soc. Jpn, (1969), 27, 147–154] is followed. Although previous work by Olekhnovich & Olekhnovich [Acta. Cryst. (1980), A36, 22–27] treated a crystal in the shape of a round cylinder, there do not seem to be any reports of previous dynamical X-ray diffraction treatments specifically for surface undulations. The significance of the present work is that it bridges the diffraction treatment of more classical dynamical diffraction theory, which assumes a flat surface, and the simple kinematic diffraction theory. Finally, the kinematic theory has, to date, been the primary means of simulating X-ray diffraction from surfaces.
Energy dispersive X-ray diffraction (EDXRD) for operando materials characterization within batteries
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Microgravity crystallization of perdeuterated tryptophan synthase for neutron diffraction
Abstract Biologically active vitamin B 6 -derivative pyridoxal 5′-phosphate (PLP) is an essential cofactor in amino acid metabolic pathways. PLP-dependent enzymes catalyze a multitude of chemical reactions but, how reaction diversity of PLP-dependent enzymes is achieved is still not well understood. Such comprehension requires atomic-level structural studies of PLP-dependent enzymes. Neutron diffraction affords the ability to directly observe hydrogen positions and therefore assign protonation states to the PLP cofactor and key active site residues. The low fluxes of neutron beamlines require large crystals (≥0.5 mm 3 ). Tryptophan synthase (TS), a Fold Type II PLP-dependent enzyme, crystallizes in unit gravity with inclusions and high mosaicity, resulting in poor diffraction. Microgravity offers the opportunity to grow large, well-ordered crystals by reducing gravity-driven convection currents that impede crystal growth. We developed the Toledo Crystallization Box (TCB), a membrane-barrier capillary-dialysis device, to grow neutron diffraction-quality crystals of perdeuterated TS in microgravity. Here, we present the design of the TCB and its implementation on Center for Advancement of Science in Space (CASIS) supported International Space Station (ISS) Missions Protein Crystal Growth (PCG)-8 and PCG-15. The TCB demonstrated the ability to improve X-ray diffraction and mosaicity on PCG-8. In comparison to ground control crystals of the same size, microgravity-grown crystals from PCG-15 produced higher quality neutron diffraction data. Neutron diffraction data to a resolution of 2.1 Å has been collected using microgravity-grown perdeuterated TS crystals from PCG-15.
Implications of gnomonic distortion on electron backscatter diffraction and transmission Kikuchi diffraction
The effect of gnomonic distortion on orientation indexing of electron backscatter diffraction patterns is explored through simulation of electron diffraction patterns for sample-to-detector geometries associated with transmission Kikuchi diffraction (TKD) and electron backscatter diffraction (EBSD). Simulated data were analysed by computing a similarity index for both Hough transformed data and simulated patterns to determine the sensitivity of each method for detecting subtle differences in the effect of gnomonic distortions on electron diffraction patterns. These results indicate that the increased gnomonic distortions in electron diffraction patterns for a TKD geometry enhance the sensitivity for detecting subtle differences in interband angles. Additionally, the utilisation of a Hough transform-based indexing approach further enhances the sensitivity.
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.
Combining Laue diffraction with Bragg coherent diffraction imaging at 34-ID-C
Measurement modalities in Bragg coherent diffraction imaging (BCDI) rely on finding a signal from a single nanoscale crystal object which satisfies the Bragg condition among a large number of arbitrarily oriented nanocrystals. However, even when the signal from a single Bragg reflection with ( hkl ) Miller indices is found, the crystallographic axes on the retrieved three-dimensional (3D) image of the crystal remain unknown, and thus localizing in reciprocal space other Bragg reflections becomes time-consuming or requires good knowledge of the orientation of the crystal. Here, the commissioning of a movable double-bounce Si (111) monochromator at the 34-ID-C endstation of the Advanced Photon Source is reported, which aims at delivering multi-reflection BCDI as a standard tool in a single beamline instrument. The new instrument enables, through rapid switching from monochromatic to broadband (pink) beam, the use of Laue diffraction to determine crystal orientation. With a proper orientation matrix determined for the lattice, one can measure coherent diffraction patterns near multiple Bragg peaks, thus providing sufficient information to image the full strain tensor in 3D. The design, concept of operation, the developed procedures for indexing Laue patterns, and automated measuring of Bragg coherent diffraction data from multiple reflections of the same nanocrystal are discussed.
Mapping nanocrystal orientations via scanning Laue diffraction microscopy for multi-peak Bragg coherent diffraction imaging
The recent commissioning of a movable monochromator at the 34-ID-C endstation of the Advanced Photon Source has vastly simplified the collection of Bragg coherent diffraction imaging (BCDI) data from multiple Bragg peaks of sub-micrometre scale samples. Laue patterns arising from the scattering of a polychromatic beam by arbitrarily oriented nanocrystals permit their crystal orientations to be computed, which are then used for locating and collecting several non-co-linear Bragg reflections. The volumetric six-component strain tensor is then constructed by combining the projected displacement fields that are imaged using each of the measured reflections via iterative phase retrieval algorithms. Complications arise when the sample is heterogeneous in composition and/or when multiple grains of a given lattice structure are simultaneously illuminated by the polychromatic beam. Here, a workflow is established for orienting and mapping nanocrystals on a substrate of a different material using scanning Laue diffraction microscopy. The capabilities of the developed algorithms and procedures with both synthetic and experimental data are demonstrated. The robustness is verified by comparing experimental texture maps obtained with Laue diffraction microscopy at the beamline with maps obtained from electron back-scattering diffraction measurements on the same patch of gold nanocrystals. Such tools provide reliable indexing for both isolated and densely distributed nanocrystals, which are challenging to image in three dimensions with other techniques.
Boundary diffraction wave theory approach to corner diffraction
The scattering process of plane waves by a discontinuous edge contour is studied with the three dimensional boundary diffraction wave theory. The edge and corner diffracted fields are obtained from the stationary phase and edge point evaluations of the line integral. A new corner diffraction coefficient is derived. The behaviors of the uniform edge and corner diffracted waves are investigated numerically.
Visualizing lattice dynamic behavior by acquiring a single time-resolved MeV diffraction image
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Novel experimental setup for megahertz X-ray diffraction in a diamond anvil cell at the High Energy
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Electromagnetic diffraction by plane reflection diffraction gratings
A plane wave theory was developed to study electromagnetic diffraction by plane reflection diffraction gratings of infinite extent. A computer program was written to calculate the energy distribution in the various orders of diffraction for the cases when the electric or magnetic field vectors are parallel to the grating grooves. Within the region of validity of this theory, results were in excellent agreement with those in the literature. Energy conservation checks were also made to determine the region of validity of the plane wave theory. The computer program was flexible enough to analyze any grating profile that could be described by a single value function f(x). Within the region of validity the program could be used with confidence. The computer program was used to investigate the polarization and blaze properties of the diffraction grating.
Electromagnetic diffraction efficiencies for plane reflection diffraction gratings
Results are presented of research activities on holographic grating research. A large portion of this work was performed using rigorous vector diffraction theory, therefore, the necessary theory has been included in this report. The diffraction efficiency studies were continued using programs based on a rigorous theory. The simultaneous occurrence of high diffraction efficiencies and the phenomenon of double Wood's anomalies is demonstrated along with a graphic method for determining the necessary grating parameters. Also, an analytical solution for a grating profile that is perfectly blazed is obtained. The performance of the perfectly blazed grating profile is shown to be significantly better than grating profiles previously studied. Finally, a proposed method is described for the analysis of coarse echelle gratings using rigorous vector diffraction that is currently being developed.
Analytical inversions in remote sensing of particle size distributions. I - Multispectral extinctions in the anomalous diffraction approximation. II Angular and spectral scattering in diffraction approximations
Consideration is given to analytical inversions in the remote sensing of particle size distributions, noting multispectral extinctions in anomalous diffraction approximation and angular and spectral scattering in diffraction approximation. A closed-form analytical inverse solution is derived in order to reconstruct the size distribution of atmospheric aerosols. The anomalous diffraction approximation to Mie's solution is used to describe the particles. Experimental data yield the geometrical area of aerosol polydispersion. Size distribution is thus found from a set of multispectral extinction measurements. In terms of the angular and spectral scattering of light in a narrow forward cone, it is shown that an analytical inverse solution may also be found for the Fraunhofer approximation to the Kirchhoff diffraction, and for an improved expression of this approximation due to Penndorf (1962) and Shifrin-Punina (1968).
Streaking images that appear only in the plane of diffraction in undoped GaAs single crystals: Diffraction imaging (topography) by monochromatic synchrotron radiation
Streaking images restricted to the direction of the diffraction (scattering) vector have been observed on transmission through undoped GaAs. These disruption images (caused by the reduction of diffraction in the direction of observation) appear both in the forward and in Bragg diffracted directions in monochromatic synchrontron radiation diffraction imaging. This previously unobserved phenomenon can be explained in terms of planar defects (interfaces) or platelets which affects the absorption coefficient in anomalous transmission. Such regions of the crystal look perfect despite the presence of imperfections when the scattering vector is not perpendicular to the normal of the platelets. The observed crystallographic orientation of these interfaces strongly indicates that they are antiphase boundaries.
Time resolved X-ray diffraction using the FIDDLE diagnostic at NIF: Preliminary assessment of diffraction precision
The Flexible Imaging Diffraction Diagnostic for Laser Experiments (FIDDLE) is a new diagnostic at the National Ignition Facility (NIF) designed to observe in situ solid-solid phase changes at high pressures using time resolved X-ray diffraction. FIDDLE currently incorporates five Icarus Ultrafast X-ray Imager sensors that take 2 ns snapshots and can be tuned to collect X-rays for tens of ns. The platform utilizes the laser power at NIF for both the laser drive and the generation of 10 keV X-rays for ~10 ns using a Ge backlighter foil. We aim to use FIDDLE to observe diffraction at different times during compression to probe the kinetics of phase changes. Pb undergoes two solid-solid phase transitions during ramp compression: from FCC to HCP and HCP to BCC. Results will be reported on some of the first shots using the FIDDLE diagnostic at NIF on ramp compressed Pb to a peak pressure of ~110 GPa and a single undriven CeO2 calibration shot. A discussion of the uncertainties in the observed diffraction is included.