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DOE OSTI2024

Long-range three-dimensional magnetic structures of the spin S =1 hexamer cluster fedotovite-like A 2 Cu 3 O ( SO 4 ) 3 ( A 2 = K 2 , NaK, Na 2 ): A neutron diffraction study

The crystal and magnetic structures of the spin S = 1 hexamer cluster fedotovite-like A 2 Cu 3 O(SO 4 ) 3 (A 2 = K 2 , NaK, Na 2 ) were studied by neutron powder diffraction at temperatures 1.6–290 K. The crystal structures in all compounds are well refined in the monoclinic space group C2/c. The basic magnetic units of the compounds are copper hexamers, which are coupled by weak superexchange interactions giving rise to three-dimensional long-range magnetic order below 3.0 < T N < 4.7 K. We have found that for A 2 = K 2 and NaK the propagation vector of the magnetic structure is k = [0,0,0], and the coupling of the Cu hexamers is ferromagnetic (FM) along the ab diagonal and antiferromagnetic along the bc diagonal. In contrast, for A = Na the propagation vector is k = [0,1,0], and the Cu hexamers are coupled antiferromagnetically (AFM) along the ab diagonal. Further, the hexamers are formed by three Cu pairs arranged along the b axis. The calculated spin expectation values $\langle s \rangle$ for the simplest symmetric spin Hamiltonian (obtained from inelastic neutron spectroscopy) of the isolated hexamers in the mean field amounted to $\langle s \rangle$ = 3/8 for the side spins Cu1 and Cu2 and $\langle s \rangle$ = 1/4 for Cu3 in the middle. The Cu spins are FM coupled in pairs and AFM between neighboring pairs. The experimental magnetic moments of the Cu 2+ ions turn out to be not completely collinear due to spin frustrations within the weak interhexamer interactions. The sizes of magnetic moments of Cu in the hexamers determined from the diffraction data are in fair agreement with the calculated values.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Identification of Phase Transitions and Metastability in Dynamically Compressed Antimony Using Ultrafast X-Ray Diffraction

Ultrafast x-ray diffraction at the LCLS x-ray free electron laser has been used to resolve the structural behavior of antimony under shock compression to 59 GPa. Antimony is seen to transform to the incommensurate, host-guest phase Sb-II at ~11 GPa, which forms on nanosecond timescales with ordered guest-atom chains. The high-pressure bcc phase Sb-III is observed above ~15 GPa, some 8 GPa lower than in static compression studies, and mixed Sb-III/liquid diffraction are obtained between 38 and 59 GPa. An additional phase which does not exist under static compression, Sb–I', is also observed between 8 and 12 GPa, beyond the normal stability field of Sb-I, and resembles Sb-I with a resolved Peierls distortion. In conclusion, the incommensurate Sb-II high-pressure phase can be recovered metastably on release to ambient pressure, where it is stable for more than 10 ns.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2018

Grating-based holographic diffraction methods for X-rays and neutrons: phase object approximation and dynamical theory

A method dubbed grating-based holography was recently used to determine the structure of colloidal fluids in the rectangular grooves of a diffraction grating from X-ray scattering measurements. Similar grating-based measurements have also been recently made with neutrons using a technique called spin-echo small-angle neutron scattering. The analysis of the X-ray diffraction data was done using an approximation that treats the X-ray phase change caused by the colloidal structure as a small perturbation to the overall phase pattern generated by the grating. In this paper, the adequacy of this weak phase approximation is explored for both X-ray and neutron grating holography. Additionally, it is found that there are several approximations hidden within the weak phase approximation that can lead to incorrect conclusions from experiments. In particular, the phase contrast for the empty grating is a critical parameter. Finally, while the approximation is found to be perfectly adequate for X-ray grating holography experiments performed to date, it cannot be applied to similar neutron experiments because the latter technique requires much deeper grating channels.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Correct interpretation of diffraction properties of quartz crystals for X-ray optics applications

Quartz has hundreds of strong Bragg reflections that may offer a great number of choices for making fixed-angle X-ray analyzers and polarizers at virtually any hard X-ray energies with selectable resolution. However, quartz crystals, unlike silicon and germanium, are chiral and may thus appear in two different forms of handedness that are mirror images. Furthermore, because of the threefold rotational symmetry along the c axis, the { h 1 h 2 h 3 L } and { h 2 h 1 h 3 L } Bragg reflections may have quite different Darwin bandwidth, reflectivity and angular acceptance, although they have the same Bragg angle. The design of X-ray optics from quartz crystals therefore requires unambiguous determination of the orientation, handedness and polarity of the crystals. The Laue method and single-axis diffraction technique can provide such information, but the variety of conventions used in the literature to describe quartz structures has caused widespread confusion. The current studies give detailed guidelines for design and fabrication of quartz X-ray optics, with special emphasis on the correct interpretation of Laue patterns in terms of the crystallography and diffraction properties of quartz. Furthermore, the quartz crystals examined were confirmed by X-ray topography to have acceptably low densities of dislocations and other defects, which is the foundation for developing high-resolution quartz-based X-ray optics.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Synthesizing pseudo-Kossel lines from neutron transmission data. II. Validation with neutron diffraction data

A new method to recover the orientation matrix of a single crystal with a known unit cell by analyzing synthesized pseudo-Kossel lines from time-of-flight neutron transmission data has been outlined in a companion article [Dessieux et al. (2023). J. Appl. Cryst. 56, https://dx.doi.org/10.1107/S1600576723001346; referred to here as Article I]. In this work, validation of this new technique is presented by employing experimental neutron transmission and diffraction measurements performed on two copper single-crystal specimens. Time-of-flight spectra were recorded during rotation (ω) of the single crystals about a vertical axis perpendicular to the incident neutron beam. The λ–ω maps recorded in transmission are utilized to determine the crystal orientation with respect to the neutron beam, following the procedure presented in Article I. Further, to validate the indexing procedure, the crystal orientations are compared with those obtained via conventional methods using the diffraction data. The resulting pseudo-Kossel lines across the 2D detectors are also observed for the first time.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Oblique diffraction geometry for the observation of several non-coplanar Bragg reflections under identical illumination

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.

Chemistry↗

DOE OSTI2026

Machine learning approaches for crystallographic classification from synthetic 2D X-ray diffraction data

Crystallographic structure identification is crucial for understanding material properties; however, current methodologies often depend on labor-intensive and time-consuming analyses of 2D X-ray diffraction (XRD) patterns. To address these limitations, this study employs synthetic 2D XRD patterns combined with deep learning (DL) techniques to enable automated and high-throughput classification of the seven crystal systems and 230 space groups. We introduce the novel Auto Diffraction Pipeline, designed to generate synthetic 2D XRD spot patterns from crystallographic information files under diverse conditions, including varying zone axes, atomic substitution, atomic depletion and mechanical loading. These conditions enhance the realism of synthetic data, mitigating the scarcity of experimental datasets and enabling the creation of large representative training sets. Convolutional neural networks were trained and validated on these synthetic datasets to classify crystallographic structures across multiple scenarios. Our results demonstrate that integrating synthetic 2D XRD patterns with DL facilitates rapid, accurate and automated crystallographic classification, promoting the wider adoption of data-driven approaches in materials science.

Shahnazari, Ayoub [Univ. of Rochester, NY (United ↗

DOE OSTI2023

A MHz X-ray diffraction set-up for dynamic compression experiments in the diamond anvil cell

An experimental platform for dynamic diamond anvil cell (dDAC) research has been developed at the High Energy Density (HED) Instrument at the European X-ray Free Electron Laser (European XFEL). Advantage was taken of the high repetition rate of the European XFEL (up to 4.5 MHz) to collect pulse-resolved MHz X-ray diffraction data from samples as they are dynamically compressed at intermediate strain rates (≤10 3 s −1 ), where up to 352 diffraction images can be collected from a single pulse train. The set-up employs piezo-driven dDACs capable of compressing samples in ≥340 µs, compatible with the maximum length of the pulse train (550 µs). Results from rapid compression experiments on a wide range of sample systems with different X-ray scattering powers are presented. A maximum compression rate of 87 TPa s −1 was observed during the fast compression of Au, while a strain rate of ∼1100 s −1 was achieved during the rapid compression of N 2 at 23 TPa s −1 .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2017

Merging single-shot XFEL diffraction data from inorganic nanoparticles: a new approach to size and orientation determination

X-ray free-electron lasers (XFELs) provide new opportunities for structure determination of biomolecules, viruses and nanomaterials. With unprecedented peak brilliance and ultra-short pulse duration, XFELs can tolerate higher X-ray doses by exploiting the femtosecond-scale exposure time, and can thus go beyond the resolution limits achieved with conventional X-ray diffraction imaging techniques. Using XFELs, it is possible to collect scattering information from single particles at high resolution, however particle heterogeneity and unknown orientations complicate data merging in three-dimensional space. Using the Linac Coherent Light Source (LCLS), synthetic inorganic nanocrystals with a core–shell architecture were used as a model system for proof-of-principle coherent diffractive single-particle imaging experiments. To deal with the heterogeneity of the core–shell particles, new computational methods have been developed to extract the particle size and orientation from the scattering data to assist data merging. The size distribution agrees with that obtained by electron microscopy and the merged data support a model with a core–shell architecture.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Solving protein structure from sparse serial microcrystal diffraction data at a storage-ring synchrotron source

In recent years, the success of serial femtosecond crystallography and the paucity of beamtime at X-ray free-electron lasers have motivated the development of serial microcrystallography experiments at storage-ring synchrotron sources. However, especially at storage-ring sources, if a crystal is too small it will have suffered significant radiation damage before diffracting a sufficient number of X-rays into Bragg peaks for peak-indexing software to determine the crystal orientation. As a consequence, the data frames of small crystals often cannot be indexed and are discarded. Introduced here is a method based on the expand–maximize–compress (EMC) algorithm to solve protein structures, specifically from data frames for which indexing methods fail because too few X-rays are diffracted into Bragg peaks. The method is demonstrated on a real serial microcrystallography data set whose signals are too weak to be indexed by conventional methods. In spite of the daunting background scatter from the sample-delivery medium, it was still possible to solve the protein structure at 2.1 Å resolution. The ability of the EMC algorithm to analyze weak data frames will help to reduce sample consumption. Furthermore, it will also allow serial microcrystallography to be performed with crystals that are otherwise too small to be feasibly analyzed at storage-ring sources.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2018

Inflexible stoichiometry in bulk pyrite FeS 2 as viewed by in situ and high-resolution X-ray diffraction

Non-stoichiometry is considered to be one of the main problems limiting iron pyrite, FeS 2 , as a photovoltaic absorber material. Although some historical diffraction experiments have implied a large solubility range of FeS 2-δ with δ up to 0.25, the current consensus based on calculated formation energies of intrinsic defects has lent support to line-compound behavior. Here it is shown that pyrite stoichiometry is relatively inflexible in both reductive conditions and in autogenous sulfur partial pressure, which produces samples with precise stoichiometry of FeS 2 even at different Fe/S ratios. By properly standardizing in situ gas-flow X-ray diffraction measurements, no significant changes in the lattice parameter of FeS 2 can be resolved, which portrays iron pyrite as prone to forming sulfur-deficient compounds, but not intrinsic defects in the manner of NiS 2-δ .

McAuliffe, Rebecca D.↗

DOE OSTI2018

Undistorted linear Bi chains with hypervalent bonding in La 3 TiBi 5 from single-crystal X-ray diffraction

The crystal structure of the lanthanum titanium bismuthide La 3 TiBi 5 (Pearson code hP18, Wyckoff sequence b d g2) has been established from single-crystal X-ray diffraction data and analyzed in detail using first-principles calculations. There are no anomalies pertaining to the atomic displacement parameter of the Ti site, previously reported based on a powder X-ray diffraction analysis of this compound. The anionic substructure contains columns of face-sharing TiBi 6 octahedra and linear Bi chains. Due to a significant La(5d) and Bi(6p) orbital mixing, a perfectly one-dimensional character of the Bi chains is not realised, while a three-dimensional electronic structure is established instead. The latter fact explains the stability of the polyanionic pnictide units against Peierls distortions. The hypervalent bonding in the Bi chains is reflected in a rather long Bi—Bi distance of 3.2264 (4) Å and a typical pattern of bonding and antibonding interactions, as revealed by electronic structure calculations.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Dicarbonyl[10,10-dimethyl-5,15-bis(pentafluorophenyl)biladiene]ruthenium(II): discovery of the first ruthenium tetrapyrrole cis -dicarbonyl complex by X-ray and electron diffraction

Dicarbonyl[10,10-dimethyl-5,15-bis(pentafluorophenyl)biladiene]ruthenium(II), [Ru(C 33 H 16 F 10 N 4 )(CO) 2 ] or Ru(CO) 2 [DMBil1], is the first reported ruthenium(II) cis-dicarbonyl tetrapyrrole complex. The neutral complex sports two carbonyls and an oligotetrapyrrolic biladiene ligand. Notably, the biladiene adopts a coordination geometry that is well distorted from square planar and much more closely approximates a seesaw arrangement. Accordingly, Ru(CO) 2 [DMBil1] is not only the first ruthenium cis-dicarbonyl with a tetrapyrrole ligand, but also the first metal biladiene complex in which the tetrapyrrole does not adopt a (pseudo-)square-planar coordination geometry. Ru(CO) 2 [DMBil1] is weakly luminescent, displaying λ em = 552 nm upon excitation at λ ex = 500 nm, supports two reversible 1 e – reductions at –1.45 and –1.73 V (versus Fc + /Fc), and has significant absorption features at 481 and 531 nm, suggesting suitability for photocatalytic and photosensitization applications. While the structure of Ru(CO) 2 [DMBil1] was initially determined by X-ray diffraction, a traditionally acceptable quality structure could not be obtained (despite multiple attempts) because of consistently poor crystal quality. Furthermore, an independent structure obtained from electron diffraction experiments corroborates the structure of this unusual biladiene complex.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Preliminary results of neutron and X-ray diffraction data collection on a lytic polysaccharide monooxygenase under reduced and acidic conditions

Lytic polysaccharide monooxygenases (LPMOs) are copper-center enzymes that are involved in the oxidative cleavage of the glycosidic bond in crystalline cellulose and other polysaccharides. The LPMO reaction is initiated by the addition of a reductant and oxygen to ultimately form an unknown activated copper–oxygen species that is responsible for polysaccharide-substrate H-atom abstraction. Given the sensitivity of metalloproteins to radiation damage, neutron protein crystallography provides a nondestructive technique for structural characterization while also informing on the positions of H atoms. Neutron cryo-crystallography permits the trapping of catalytic intermediates, thereby providing insight into the protonation states and chemical nature of otherwise short-lived species in the reaction mechanism. Here, to characterize the reaction-mechanism intermediates of LPMO9D from Neurospora crassa, a cryo-neutron diffraction data set was collected from an ascorbate-reduced crystal. A second neutron diffraction data set was collected at room temperature from an LPMO9D crystal exposed to low-pH conditions to probe the protonation states of ionizable groups involved in catalysis under acidic conditions.

Neurospora crassa↗

DOE OSTI2020

The crystal structures of Fe-bearing MgCO 3 sp 2 - and sp 3 -carbonates at 98 GPa from single-crystal X-ray diffraction using synchrotron radiation

The crystal structure of MgCO 3 -II has long been discussed in the literature where DFT-based model calculations predict a pressure-induced transition of the carbon atom from the sp 2 to the sp 3 type of bonding. We have now determined the crystal structure of iron-bearing MgCO 3 -II based on single-crystal X-ray diffraction measurements using synchrotron radiation. We laser-heated a synthetic (Mg 0.85 Fe 0.15 )CO 3 single crystal at 2500 K and 98 GPa and observed the formation of a monoclinic phase with composition (Mg 2.53 Fe 0.47 )C 3 O 9 in the space group C 2/ m that contains tetrahedrally coordinated carbon, where CO 4 4- tetrahedra are linked by corner-sharing oxygen atoms to form three-membered C 3 O 9 6- ring anions. The crystal structure of (Mg 0.85 Fe 0.15 )CO 3 (magnesium iron carbonate) at 98 GPa and 300 K is reported here as well. In comparison with previous structure-prediction calculations and powder X-ray diffraction data, our structural data provide reliable information from experiments regarding atomic positions, bond lengths, and bond angles.

Chariton, Stella (ORCID:0000000155220498)↗

DOE OSTI2020

Towards the spatial resolution of metalloprotein charge states by detailed modeling of XFEL crystallographic diffraction

Oxidation states of individual metal atoms within a metalloprotein can be assigned by examining X-ray absorption edges, which shift to higher energy for progressively more positive valence numbers. Indeed, X-ray crystallography is well suited for such a measurement, owing to its ability to spatially resolve the scattering contributions of individual metal atoms that have distinct electronic environments contributing to protein function. However, as the magnitude of the shift is quite small, about +2 eV per valence state for iron, it has only been possible to measure the effect when performed with monochromated X-ray sources at synchrotron facilities with energy resolutions in the range 2–3 × 10 −4 (Δ E / E ). This paper tests whether X-ray free-electron laser (XFEL) pulses, which have a broader bandpass (Δ E / E = 3 × 10 −3 ) when used without a monochromator, might also be useful for such studies. The program nanoBragg is used to simulate serial femtosecond crystallography (SFX) diffraction images with sufficient granularity to model the XFEL spectrum, the crystal mosaicity and the wavelength-dependent anomalous scattering factors contributed by two differently charged iron centers in the 110-amino-acid protein, ferredoxin. Bayesian methods are then used to deduce, from the simulated data, the most likely X-ray absorption curves for each metal atom in the protein, which agree well with the curves chosen for the simulation. The data analysis relies critically on the ability to measure the incident spectrum for each pulse, and also on the nanoBragg simulator to predict the size, shape and intensity profile of Bragg spots based on an underlying physical model that includes the absorption curves, which are then modified to produce the best agreement with the simulated data. This inference methodology potentially enables the use of SFX diffraction for the study of metalloenzyme mechanisms and, in general, offers a more detailed approach to Bragg spot data reduction.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

A simple technique to classify diffraction data from dynamic proteins according to individual polymorphs

One often observes small but measurable differences in the diffraction data measured from different crystals of a single protein. These differences might reflect structural differences in the protein and may reveal the natural dynamism of the molecule in solution. Partitioning these mixed-state data into single-state clusters is a critical step that could extract information about the dynamic behavior of proteins from hundreds or thousands of single-crystal data sets. Mixed-state data can be obtained deliberately (through intentional perturbation) or inadvertently (while attempting to measure highly redundant single-crystal data). To the extent that different states adopt different molecular structures, one expects to observe differences in the crystals; each of the polystates will create a polymorph of the crystals. After mixed-state diffraction data have been measured, deliberately or inadvertently, the challenge is to sort the data into clusters that may represent relevant biological polystates. Here, this problem is addressed using a simple multi-factor clustering approach that classifies each data set using independent observables, thereby assigning each data set to the correct location in conformational space. This procedure is illustrated using two independent observables, unit-cell parameters and intensities, to cluster mixed-state data from chymotrypsinogen (ChTg) crystals. It is observed that the data populate an arc of the reaction trajectory as ChTg is converted into chymotrypsin.

36 MATERIALS SCIENCE↗

DOE OSTI2020

In situ characterization of residual stress evolution during heat treatment of SiC/SiC ceramic matrix composites using high-energy X-ray diffraction

Volumetric strains were measured in silicon carbide/silicon carbide melt-infiltrated ceramic matrix composites (CMCs) at ambient and high temperatures using high-energy synchrotron X-ray diffraction (XRD). Both silicon and silicon carbide constituents were interrogated utilizing a broad spectrum of diffracting planes that would be largely inaccessible to common laboratory XRD equipment. Residual room-temperature principal strains in the melt-infiltrated silicon phase were found to be approximately 1100 mu epsilon in compression, corresponding to stresses of approximately 300 MPa using simplifying constitutive assumptions. Residual room-temperature principal strains in silicon carbide particles found throughout the matrix were approximately 500 mu epsilon in tension, corresponding to approximately 300 MPa. Residual strains were found to decrease considerably as temperatures increased from ambient temperature to 1250 degrees C. Additionally, residual strains returned to approximately preheat treatment values after cool-down to ambient temperature. Strain measurements in the silicon phase were found to be significantly affected by dissolved boron dopant levels causing contraction of the silicon lattice. This contraction must be accounted for in high-temperature experiments for accurate calculation of stresses in the silicon phase.

36 MATERIALS SCIENCE↗