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Integrated Bragg X ray scattering intensities for monatomic crystalline lattices, considering thermal diffuse component contribution
A method to determine the strain tensor and local lattice rotation with dark-field X-ray microscopy is presented. Using a set of at least three non-coplanar symmetry-equivalent Bragg reflections, the illuminated volume of the sample can be kept constant for all reflections, facilitating easy registration of the measured lattice variations. This requires an oblique diffraction geometry,i.e.the diffraction plane is neither horizontal nor vertical. We derive a closed analytical expression that allows determination of the strain and lattice rotation from the deviation of experimental observables (e.g.goniometer angles) from their nominal values for an unstrained lattice.
Abstract We carried out a short beamtime at the Pohang Accelerator Laboratory x-ray Free Electron Laser to perform a pump-probe (PP) laser excitation diffraction experiment on the silicon (222) forbidden Bragg peak. To limit the x-ray penetration, we used a “device layer” silicon film wafer bonded to a silicon substrate. The sample, specially fabricated by MEMC Electronic Materials, had a Si(100) substrate bonded to a 170 nm Si(100) film rotated at 45° for crystallographic isolation. A second sample was reactive-ion-etched down to 52 nm thickness. In the silicon lattice, the covalent bonds are seen exclusively at the 222 reflection. Upon laser excitation, these electrons are expected to be excited to the valence band on femtosecond electronic time scales. The Si(222) reflection is therefore expected to be extinguished on this fast time scale, while the electron–phonon coupled acoustic response is determined by the lattice dynamics. The latter is determined by the speed of sound over the device thickness, which is in the mid-picosecond range.
New higher-count-rate, integrating, large-area X-ray detectors with framing rates as high as 17400 images per second are beginning to be available. These will soon be used for specialized macromolecular crystallography experiments but will require optimal lossy compression algorithms to enable systems to keep up with data throughput. Some information may be lost. Can we minimize this loss with acceptable impact on structural information? To explore this question, we have considered several approaches: summing short sequences of images, binning to create the effect of larger pixels, use of JPEG-2000 lossy wavelet-based compression, and use of Hcompress, which is a Haar-wavelet-based lossy compression borrowed from astronomy. We also explore the effect of the combination of summing, binning, and Hcompress or JPEG-2000. In each of these last two methods one can specify approximately how much one wants the result to be compressed from the starting file size. These provide particularly effective lossy compressions that retain essential information for structure solution from Bragg reflections.
Bragg reflecting crystals for spectroscopy and polarimetry in X ray astronomy
Structure elucidation via single-crystal methods has historically lacked experimental access to real-space information, instead relying exclusively on diffraction-space measurements of Bragg reflections. Here we exploit the dual-space imaging power of 4D scanning transmission electron microscopy to meaningfully integrate real-space information into the crystallographic workflow. We show that virtual apertures assembled by segmentation of high-angle annular dark-field images enable i) pixel-by-pixel separation of coherent Bragg signal from clusters of closely spaced nanocrystals and ii) selective extraction of integrated intensities from thinner subregions of individual specimens, facilitating retroactive tuning of multiple scattering artifacts. This strategy empowers us to simply pick and choose whichever nanoscale regions of interest generate the highest-quality diffraction patterns, allowing us to solve several independent structures of the metal-organic framework UiO-66 from specimens whose agglomerated morphology proved intractable for conventional microcrystal electron diffraction. Our method is compatible with both rotational and serial approaches to data processing, ultimately divulging the first scanning nanobeam electron diffraction structures determined by direct methods at subangstrom resolution.
Bis(pyridyl) urea-based gelators, namely L2 and its isomeric mixture ( L1 + L2 ), are known to self-assemble into 1D architectures capable of inducing supramolecular gelation. Coordination with metal ions such as Ag( I ), Cu( II ), and Fe( III ) introduces structural reinforcement, enabling the formation of distinct 3D networks governed by metal-specific coordination geometries. Here, we present a comprehensive investigation into the temperature-responsive behavior (20–60 °C) of L2 and L1 + L2 , both in the absence and presence of Ag( I ), Dy( III ), Fe( III ), Cu( II ), and Ho( III ), using real-time small-angle neutron scattering (SANS). To probe long-term structural evolution/kinetics of self-assembly, real-time small-angle X-ray scattering (SAXS) was employed on L2 + Ag gels, complemented by differential scanning calorimetry (DSC) to evaluate thermal transitions. Our results reveal strikingly divergent gelation behaviors: L2 forms a highly rigid, covalent polymer-like network, while L1 + L2 exhibits remarkable thermal adaptability. Upon metal coordination, the assemblies exhibit pronounced crystallinity and exceptional thermal stability, as evidenced by persistent Bragg reflections and invariant d-spacings. Intriguingly, L2 : Fe (2 : 1) and L1 : L2 : Fe (0.5 : 0.5 : 1) in acetonitrile-d 3 (ACN-d 3 ) deviate from this trend, forming thermally labile amorphous gels. These systems show a complete loss of crystalline order, reduced Porod exponents—indicative of collapsed or branched fiber morphologies—and prominent melting and glass transition events in DSC. Fitting SANS and SAXS data to the correlation length model unveiled insightful nanostructural features. While most systems displayed minimal temperature-induced variation in mesh size or surface morphology, L2 : Ag in dimethyl sulfoxide-d 6 (DMSO-d 6 )/D 2 O and L2 : Fe (1 : 1) in ACN-d 3 exhibited a rare combination of thermally stable correlation lengths and increasing high- q exponents—strongly suggesting progressive fiber densification or surface smoothing within a robust gel framework. These findings highlight the tunability and structural resilience of supramolecular gels through precise control of ligand architecture, metal coordination, and temperature, offering valuable design principles for functional soft materials.
There is a growing understanding of the structural dynamics of biological molecules fueled by x-ray crystallography experiments. Time-resolved serial femtosecond crystallography (TR-SFX) with x-ray Free Electron Lasers allows the measurement of ultrafast structural changes in proteins. Nevertheless, this technique comes with some limitations. One major challenge is the quality of data from TR-SFX measurements, which often faces issues like data sparsity, partial recording of Bragg reflections, timing errors, and pixel noise. To overcome these difficulties, conventionally, large volumes of data are collected and grouped into a few temporal bins. The data in each bin are then averaged and paired with the mean of their corresponding jittered timestamps. This procedure provides one structure per bin, resulting in a limited number of averaged structures for the entire time interval spanned by the experiment. Therefore, the information on ultrafast structural dynamics at high temporal resolution is lost. This has initiated research for advanced methods of analyzing experimental TR-SFX data beyond the standard binning and averaging method. To address this problem, we use a machine learning algorithm called Nonlinear Laplacian Spectral Analysis (NLSA), which has emerged as a promising technique for studying the dynamics of complex systems. In this work, we demonstrate the power of this algorithm using synthetic x-ray diffraction snapshots from a protein with significant data incompleteness, timing uncertainties, and noise. Our study confirms that NLSA is a suitable approach that effectively mitigates the effects of these artifacts in TR-SFX data and recovers accurate structural dynamics information hidden in such data.
We report the results of synchrotron Bragg Coherent x-ray Diffraction Imaging (BCDI) experiments to investigate domain formation in a micron-sized magnetite crystal undergoing the Verwey transition at low temperature. A strong splitting of the measured 311 Bragg reflection was observed in the low-temperature phase, indicating the formation of domains. BCDI revealed pronounced strain distributions, characterized by a clear layered stripe domain structure in real-space. Stripes were seen only along the [001] crystallographic direction, normal to the substrate surface direction, breaking the symmetry of the cubic high-temperature phase. It is argued that other domain directions were suppressed by the sample mounting orientation. More surprisingly, only a single domain orientation was observed, suggesting an additional symmetry-breaking influence originating from the shape of the crystal. Gaining insight into how thermal effects induce the formation of layered or striped phases offers a valuable framework for understanding the development of mesoscopic domains and strain patterns in functional materials.
In this Letter, we present a robust method for generating custom-shaped, coherent hard x-ray pulses in regenerative amplifier free-electron lasers (RAFELs) using laser-induced energy modulation of the electron beam. A temporally shaped optical modulation imprints an optical-wavelength energy pattern on the beam, which interacts with the recirculated seed in the x-ray cavity to generate spectral sidebands. These sidebands lie outside the Bragg reflection bandwidth and are extracted as out-coupled radiation, while the seed is retained for continued amplification, enabling a novel mechanism for both output coupling and pulse shaping. Furthermore, this approach allows deterministic control over the spectral and temporal properties of the emitted x-rays, including multicolor generation, twin-pulse structures, pulse duration tuning, and complex temporal waveforms. Importantly, it does not require modification of the RAFEL cavity or optics and is fully compatible with high-repetition-rate operation, offering a practical pathway to deliver coherent, shaped, and on-demand x-ray pulses for advanced time-resolved and nonlinear x-ray science.
Almost every electron microscopy experiment is fundamentally limited by radiation damage. Nevertheless, little is known about the onset and progression of radiolysis in beam-sensitive materials. Here we apply ambient-temperature scanning nanobeam electron diffraction to record simultaneous dual-space movies of organic and organometallic nanocrystals at sequential stages of beam-induced radiolytic decay. We show that the underlying mosaic of coherently diffracting domains undergoes internal rearrangement as a function of accumulating electron fluence, causing the intensities of some associated Bragg reflections to fade nonmonotonically. Furthermore, we demonstrate that repeated irradiation at a single probe position leads to the isotropic propagation of delocalized radiolytic damage well beyond the direct footprint of the incident beam. We refer to these expanding tides of amorphization as “impact craters.”
Numerical diffuse scattering cross-section calculations are used to establish a rigorous basis for determining the concentration and size distribution of dislocation loops in irradiated single crystals from integral X-ray diffuse scattering (XRDS) measurements. Differential XRDS intensities for prismatic {111} type dislocation loops are numerically calculated as a function of loop radius R and wavevectors q relative to Bragg reflections in tungsten. The results show the well known 1/q 2 Huang scattering form at small q that transitions to a ∼1/q 4 dependence associated with the Stokes–Wilson approximation for q ≳ 1/R. More importantly, they show further that the 1/q 4 falloff is not the asymptotic large-q form of the diffuse scattering for small loops (R < 200 Å) as has often been assumed. Rather, for loop sizes as small as R ≃ 5 Å with strong curvature, the calculations show definitively that the scattering transitions to a robust 1/q 5 falloff at larger q that arises due to the local strains near the dislocation core defining the circumference of the dislocation loops. The presence of this 1/q 5 asymptotic form for both small and large loops is experimentally confirmed using an integral XRDS measurement around the 110 reflection on self-ion-irradiated tungsten combined with numerically calculated integral XRDS cross-sections. Accordingly, the historical two-region theoretical treatment of the cross-sections for integral XRDS is extended to a three-region model that has direct sensitivity to the (first-moment) dislocation line lengths of dislocation loops. In conclusion, these developments enable the use of both numerical and analytically modeled cross-sections to make accurate integral XRDS determinations of dislocation loop sizes and concentrations using modest-intensity laboratory X-ray sources.
We report the use of streaming data interfaces to perform fully online data processing for serial crystallography experiments, without storing intermediate data on disk. The system produces Bragg reflection intensity measurements suitable for scaling and merging, with a latency of less than 1 s per frame. Our system uses the CrystFEL software in combination with the ASAP::O data framework. In a series of user experiments at PETRA III, frames from a 16 megapixel Dectris EIGER2 X detector were searched for peaks, indexed and integrated at the maximum full-frame readout speed of 133 frames per second. The computational resources required depend on various factors, most significantly the fraction of non-blank frames ('hits'). The average single-thread processing time per frame was 242 ms for blank frames and 455 ms for hits, meaning that a single 96-core computing node was sufficient to keep up with the data, with ample headroom for unexpected throughput reductions. Further significant improvements are expected, for example by binning pixel intensities together to reduce the pixel count. We discuss the implications of real-time data processing on the `data deluge' problem from recent and future photon-science experiments, in particular on calibration requirements, computing access patterns and the need for the preservation of raw data.
The increase in neutron flux at the Oak Ridge National Laboratory (ORNL) Spallation Neutron Source (SNS), currently operating at 2.0 MW proton beam power, has created new opportunities for higher-throughput neutron scattering experiments while also increasing the importance of minimizing background scattering and optimizing sample-environment operations. To address these challenges on the Backscattering Silicon Spectrometer (BA-SIS), several upgrades were developed and evaluated, including boron carbide (B₄C) masking for flat-plate sample containers, multi-cell sample holders used with a vertically translating sample stick, and an automated helium pump and purge (HPP) system for closed-cycle refrigerators. Neutron diffraction measurements demonstrate that B₄C masks reduce background scattering by 49–67%, outperforming both borated aluminum and boron nitride masks while introducing no additional Bragg reflections within the instrument’s accessible Q-range. Commissioning tests of a double-cell flat-plate sample contain-er showed no measurable crosstalk between adjacent sample compartments and con-firmed stable thermal performance, enabling multiple samples to be measured without re-peated temperature cycling. In addition, the automated HPP system provided reproducible sample-space gas handling with approximately ±1 mbar precision while reducing the need for operator intervention and supporting remote operation. Together, these developments improve signal-to-noise performance, increase experimental throughput, and enhance operational efficiency at BASIS, supporting the instrument’s continued operation under higher neutron flux conditions.
A large-area high-sensitivity X-ray spectrometer has been constructed and used to measure the 1.8- to 5.3-A X-ray emission of the sun under quiescent conditions. The instrument utilizes Bragg reflection from mosaic graphite crystals. The data indicate that the X-ray emission can best be accounted for by a multitemperature model of the solar atmosphere in which both the overall corona and active regions contribute to the X-ray spectrum. Theoretical calculations of the X-ray flux of a hot, optically thin plasma have been used to estimate the solar conditions at the time when the measurements were made.
The OSO-8 satellite, launched on June 21, 1975 contains two X-ray polarimeters. These polarimeters use mosaic crystals of graphite to yield polarization-sensitive Bragg reflection of stellar X-rays. The crystals reflect a narrow energy bandwidth centered at 2.6 and 5.2 keV. The polarimeter background signal is minimized by mounting the crystals on parabolic surfaces which focus the diffracted X-rays onto small-area, beryllium-window proportional counters. This technique permits the observation of low-intensity X-ray sources and reduces the possibility of systematic background effects which could lead to a false signature of polarization. A description of the instrument is given, and the sensitivity to polarization, particularly in regard to binary sources, is discussed. Preliminary results for Cen X-3 and GX5-1 are presented.
Crystal spectrometric properties and the factors that affect their measurement are discussed. Theoretical and experimental results on KAP are summarized and theoretical results based on the dynamical theory of X-ray diffraction are given for the acid phthalates as well as for the commonly used planes of ADP, PET and EDDT. Anomalous dispersion is found to be important for understanding the details of crystal Bragg reflection properties at long X-ray wavelengths and some important effects are pointed out. The theory of anomalous dispersion is applied to explain the anomalous reflectivity exhibited by KAP at 23.3 A.
Results of the measurement of Bragg reflection properties of crystals suitable for use in X-ray astronomy are presented. Measurements with a double crystal spectrometer were performed on rubidium acid phthalate and thallium acid phthalate to yield values of the integrated reflectivity and diffraction width in the range 8-18 A, and measurements of integrated reflectivity were also performed on ammonium dihydrogen phosphate. The theory and design of an arc-minute range multigrid collimator to be flown on a rocket for solar X-ray studies are also described, along with a method for determining the collimator's X-ray axis.