(De)lithiation of spinel ferrites Fe3O4, MgFe2O4, and ZnFe2O4: a combined spectroscopic, diffraction and theory study
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99 GENERAL AND MISCELLANEOUS↗
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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.
36 MATERIALS SCIENCE↗
Physical optics simulations for synchrotron radiation sources
Here we describe approaches to high-accuracy physical optics calculations used for the development of x-ray beamlines at synchrotron radiation sources, as well as simulation of experiments and processing of experimental data at some of these beamlines. We pay special attention to the treatment of the partial coherence of x rays, a topic of high practical importance for modern low-emittance high-brightness synchrotron radiation facilities. The approaches are based, to a large extent, on the works of Emil Wolf and co-authors, including the basic scalar diffraction theory and the coherent mode decomposition method. The presented simulation examples are related to the case of the novel Coherent Diffractive Imaging beamline that is currently under development at the National Synchrotron Light Source II at the Brookhaven National Laboratory.
36 MATERIALS SCIENCE↗
Effective field theory factorization for diffraction
We derive a factorization formula for coherent and incoherent ep diffraction using the soft collinear effective theory, utilizing multiple power expansion parameters to handle different kinematic regions. This goes beyond the known hard-collinear diffractive factorization to address the small-x Regge dynamics and Pomeron exchange from first principles. The effective field theory analysis also uncovers and factorizes an important irreducible incoherent background generated by color-nonsinglet exchange, dubbed “quasi-diffraction”, for which we calculate the associated Sudakov suppression. For unpolarized scattering we show that there are four diffractive structure functions at leading power, and point out the importance of studying ${F}_{3,4}^D$ through asymmetries, in addition to ${F}_{2,L}^D$. For the quasi-diffractive background, we make model independent predictions for ratios of the corresponding structure functions in a perturbative kinematic region. Our analysis also makes predictions for six leading-power spin-dependent structure functions. Finally, we provide connections to diffractive parton distributions, and assess the Ingelman-Schlein model. Our work lays a path for further QCD-based studies of diffraction.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Reducing heat load density with asymmetric and inclined double-crystal monochromators: principles and requirements revisited
Asymmetric double-crystal monochromators (aDCMs) and inclined DCMs (iDCMs) can significantly expand the X-ray beam footprint and consequently reduce the heat load density and gradient. Based on rigorous dynamical theory calculations, the major principles and properties of aDCMs and iDCMs are presented to guide their design and development, particularly for fourth-generation synchrotrons. In addition to the large beam footprint, aDCMs have very large bandwidths (up to ∼10 eV) and angular acceptance, but the narrow angular acceptance of the second crystal requires precise control of the relative orientations and strains. Based on Fourier coupled-wave diffraction theory calculations, it is rigorously proved that the iDCM has almost the same properties as the conventional symmetric DCM, including the efficiency, angular acceptance, bandwidth, tuning energy range and sensitivity to misalignment. The exception is that, for the extremely inclined geometry that can achieve very large footprint expansion, the iDCM has (beneficially) a larger bandwidth and wider angular acceptance. Inclined diffraction has the `rho-kick effect' that can be cancelled by the second reflection of the iDCM (even with misalignment), except that inhomogeneous strains may cause non-uniform rho-kick angles. At present, fabrication/mounting-induced strains pose low risk since they can be controlled to <0.5 µrad over large areas. The only uncertain challenge is the thermally induced strains, yet it is estimated that these strains are naturally lowered by the large footprint and may be further mitigated by optimized cryogenic cooling to the 1–2 µrad level. Overall, aDCMs and iDCMs have more stringent requirements than normal DCMs, but they are feasible schemes in practice.
asymmetric monochromator↗
Scalable freeform optimization of wide-aperture 3D metalenses by zoned discrete axisymmetry
We introduce a novel framework for design and optimization of 3D freeform metalenses that attains nearly linear scaling of computational cost with diameter, by breaking the lens into a sequence of radial “zones” with 𝑛-fold discrete axisymmetry, where 𝑛 increases with radius. This allows vastly more design freedom than imposing continuous axisymmetry, while avoiding the compromises of the locally periodic approximation (LPA) or scalar diffraction theory. Using a GPU-accelerated finite-difference time-domain (FDTD) solver in cylindrical coordinates, we perform full-wave simulation and topology optimization within each supra-wavelength zone. We validate our approach by designing millimeter and centimeter-scale, poly-achromatic, 3D freeform metalenses which outperform the state of the art. By demonstrating the scalability and resulting optical performance enabled by our “zoned discrete axisymmetry” (ZDA) and supra-wavelength domain decomposition, we highlight the potential of our framework to advance large-scale meta-optics and next-generation photonic technologies.
Sun, Mengdi [Wesleyan University]↗
Deep learning of interface structures from simulated 4D STEM data: cation intermixing vs. roughening ∗
Abstract Interface structures in complex oxides remain an active area of condensed matter physics research, largely enabled by recent advances in scanning transmission electron microscopy (STEM). Yet the nature of the STEM contrast in which the structure is projected along the given direction precludes separation of possible structural models. Here, we utilize deep convolutional neural networks (DCNN) trained on simulated 4D STEM datasets to predict structural descriptors of interfaces. We focus on the widely studied interface between LaAlO 3 and SrTiO 3 , using dynamical diffraction theory and leveraging high performance computing to simulate thousands of possible 4D STEM datasets to train the DCNN to learn properties of the underlying structures on which the simulations are based. We test the DCNN on simulated data and show that it is possible (with >95% accuracy) to identify a physically rough from a chemically diffuse interface and create a DCNN regression model to predict step positions. We quantify the applicability of the model to different thicknesses and the transferability of the approach. The method shown here is general and can be applied for any inverse imaging problem where forward models are present.
42 ENGINEERING↗
Large Angle Rocking Beam Electron Diffraction Utilizing Electron Direct Detector
Electron diffraction of a crystal is fundamentally a function of the potential of that crystal. The intensity of electron diffraction patterns is, as a result, sensitive to the charge density of atoms and bonding inside crystals. Experimentally, the traditional method to probe this information is quantitative Convergent Beam Electron Diffraction (CBED). Quantitative CBED or QCEBD is a method which uses dynamic diffraction theory to quantify CBED intensities and to extract information about crystal structure and bonding. The sensitivity of dynamical scattering is leveraged to measure crystal symmetry and crystal structure factors. At its limit, electron structure factors are measured at high accuracy allowing access to chemical bonding information, which corroborate theoretical calculations through multipole model refinements of the experimental charge density. The primary limit to QCBED is the requirement of a non-overlapping convergent beam. This subsequently limits QCBED to crystals with small unit cells which are stable under the focused probe.
Busch, Robert↗
FiXR : a framework to reconstruct fiber cross-sections from X-ray fiber diffraction experiments
Ab initio reconstruction methods have revolutionized the capabilities of small-angle X-ray scattering (SAXS), allowing the data-driven discovery of previously unknown molecular conformations, exploiting optimization heuristics and assumptions behind the composition of globular molecules. While these methods have been successful for the analysis of small particles, their impact on fibrillar assemblies has been more limited. The micrometre-range size of these assemblies and the complex interaction of their periodicities in their scattering profiles indicate that the discovery of fibril structures from SAXS measurements requires novel approaches beyond extending existing tools for molecular discovery. In this work, it is proposed to use SAXS measurements, together with diffraction theory, to infer the electron distribution of the average cross-section of a fiber. This cross-section is modeled as a discrete electron density with continuous support, allowing representations beyond binary distributions. Additional constraints, such as non-negativity or smoothness/connectedness, can also be added to the framework. The proposed approach is tested using simulated SAXS data from amyloid β fibril models and using measured data of Tobacco mosaic virus from SAXS experiments, recovering the geometry and density of the cross-sections in all cases. The approach is further tested by analyzing SAXS data from different amyloid β fibril assemblies, with results that are in agreement with previously proposed models from cryo-EM measurements. The limitations of the proposed method, together with an analysis of the robustness of the method and the combination with different experimental sources, are also discussed.
Biochemistry & Molecular Biology↗
Two-beam Bragg diffraction, filtering, and delays
We summarize transmission and reflection amplitudes of Bragg-crystals based on two-beam Bragg diffraction theory. Then, we consider a specific case of infinitely thick and symmetrical Bragg-crystal and its reflective properties in spectral and angular domain. We obtain analytical expressions for filtering width and respective delay amplitudes, temporal delay from spectral phase shift and spatial displacement from angular phase shift.
43 PARTICLE ACCELERATORS↗
A density functional theory and neutron diffraction study of the ambient condition properties of sub-stoichiometric yttrium hydride
Several mechanical and thermophysical properties are required as a function of non-stoichiometry for the successful implementation of YH 2-x for nuclear reactor moderator applications. Density functional theory calculations, in combination with neutron diffraction experiments, were used to study the structural and mechanical properties of YH 2-x . Point defect analysis indicated H occupation primarily at the tetrahedral site within an fcc Y sub-lattice, confirming a fluorite YH 2 structure. The small positive formation energy for H vacancies under Y-rich conditions predicted that hypo-stoichiometry is accommodated by Y+YH 2 at ambient conditions and by H vacancies in the YH 2-x single phase that is relevant to high temperatures. Neutron diffraction studies were used to confirm both the occupation of H on tetrahedral sites and the near-stoichiometric composition of the hydride phase in the two-phase Y+YH 2 region of the phase diagram that dominates at room temperature. Energy minimized special-quasirandom-structures of H vacancies were used to calculate lattice parameters, elastic constants, and several other properties as a function of composition for the single phase YH 2-x . The lattice parameter of YH 2-x decreased by only 0.004 Å with increasing H/Y for the range 1.31 ≤ H / Y ≤ 2.0 indicating a negligible effect on lattice parameters due to vacancy formation. In the two-phase region, however, calculations predicted the density of z Y + ( 1 - z ) Y H 2 - x to increase with decreasing H/Y at lower temperatures due to the increased fraction of high-density Y metal. Additionally, for the high temperature single phase, decreasing H/Y reduced the density as a consequence of the lattice expansion associated with vacancy formation. All elastic constants and moduli increased with increasing hydrogen content in single-phase YH 2-x .
36 MATERIALS SCIENCE↗
X-ray beam monitoring and wavelength calibration using four-beam diffraction
Rigorous dynamical theory calculations show that four-beam diffraction (4BD) can be activated only by a unique photon energy and a unique incidence direction. Thus, 4BD may be used to precisely calibrate X-ray photon energies and beam positions. Based on the principles that the forbidden-reflection 4BD pattern, which is typically an X-shaped cross, can be generated by instant imaging using the divergent beam from a point source without rocking the crystal, a detailed real-time high-resolution beam (and source) position monitoring scheme is illustrated for monitoring two-dimensional beam positions and directions of modern synchrotron light sources, X-ray free-electron lasers and nano-focused X-ray sources.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Characterizing crystalline defects in single nanoparticles from angular correlations of single-shot diffracted X-rays
Characterizing and controlling the uniformity of nanoparticles is crucial for their application in science and technology because crystalline defects in the nanoparticles strongly affect their unique properties. Recently, ultra-short and ultra-bright X-ray pulses provided by X-ray free-electron lasers (XFELs) opened up the possibility of structure determination of nanometre-scale matter with Å spatial resolution. However, it is often difficult to reconstruct the 3D structural information from single-shot X-ray diffraction patterns owing to the random orientation of the particles. This report proposes an analysis approach for characterizing defects in nanoparticles using wide-angle X-ray scattering (WAXS) data from free-flying single nanoparticles. The analysis method is based on the concept of correlated X-ray scattering, in which correlations of scattered X-ray are used to recover detailed structural information. WAXS experiments of xenon nanoparticles, or clusters, were conducted at an XFEL facility in Japan by using the SPring-8 Ångstrom compact free-electron laser (SACLA). Bragg spots in the recorded single-shot X-ray diffraction patterns showed clear angular correlations, which offered significant structural information on the nanoparticles. The experimental angular correlations were reproduced by numerical simulation in which kinematical theory of diffraction was combined with geometric calculations. We also explain the diffuse scattering intensity as being due to the stacking faults in the xenon clusters.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Room temperature sodium diffusion in sodium iron phosphate investigated with neutron scattering
Sodium iron phosphate, Na x FePO 4 , is currently one of the most promising cathode materials for sodium ion batteries. Here we employ a systematic approach using three neutron scattering techniques to investigate temperature dependent properties with a focus on the charge transfer processes. Two distinct Na + diffusive motions are observed with quasielastic neutron scattering, including room temperature motion. These processes correspond to rapid double jumps through extrinsic vacancy sites of ∼6 Å along with the more fundamental nearest neighbor jumps of 3.1 Å. Experimental observations of room temperature ionic diffusion are highly desirable, as the diffusion pathways are naturally well suited for efficient transport. Inelastic neutron scattering was used to probe the vibrational density of states that assist in the ionic and electronic (polaronic) transport processes, which are further supported with density functional theory. Neutron diffraction examines the disordering of the sodium sublattice upon transition to the solid-solution phase, which is believed to enhance the overall kinetics during sodium insertion/extraction. Finally, 57 Fe Mössbauer spectroscopy measurements probes polaron hopping and the local structural evolution that modifies the electron density surrounding the redox active iron sites. This study sheds light on the temperature induced atomic scale dynamics that occur in olivine Na x FePO 4 .
Novak, Eric [Swarthmore College, Swarthmore, PA (U↗
Controlled Synthesis of Transition Metal Phosphide Nanoparticles to Establish Composition-Dependent Trends in Electrocatalytic Activity
Not Available
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Revisiting the structures and phase transitions of Ba 2 NaNb 5 O 15
The room-temperature and low-temperature structure(s) of Ba 2 NaNb 5 O 15 (BNN) have been debated since the structure was proposed in the 1960s. This work revisits the structures and phase transitions of BNN, combining high-resolution X-ray and neutron powder diffraction with density functional theory calculations. Temperature-dependent high-resolution X-ray powder diffraction patterns are collected from 4 to 918 K, and sequential batch Rietveld refinement using a symmetry mode approach to describe the structure is used to extract the main structural changes as a function of temperature. The data show that the average structure of BNN is best described by the Ama2 space group, and no other structural phase transitions were observed below the ferroelastic transition. The symmetry mode analysis, combining results from diffraction and density functional theory, shows significant octahedral tilting and corrugations of both the A1 and A2 sites along the c direction. A strong correlation between the spontaneous strain and the octahedral tilting was observed, and a potential connection with emerging microstructure at low temperatures is proposed, all enabled by the symmetry mode approach used in this work.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗