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Results for “time-resolved x-ray diffraction”

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DOE OSTI2025

Atomic-scale insights into topotactic transformations in an extra-large-pore zeolite using time-resolved 3D electron diffraction

Understanding the atomic-scale structural dynamics of phase transformations is crucial for developing materials and tailoring their properties. However, many materials are obtained as polycrystalline powders with large unit cells and/or complex structures, making it challenging to investigate detailed structural changes using conventional X-ray diffraction techniques. Here we employ time-resolved three-dimensional electron diffraction to reveal the topotactic reactions and transformations that convert the extra-large-pore silicate zeolite ECNU-45 into ECNU-46. ECNU-45 features three-dimensional interconnecting 24 × 10 × 10-ring channels, while ECNU-46 consists of one-dimensional 24-ring channels connected to 10-ring pockets. ECNU-45 and ECNU-46 are both examples of pure silicate zeolites with pore openings larger than 22-ring. Our findings indicate changes at six distinct tetrahedral silicon sites, involving atom displacement, addition and removal of framework atoms through bond breakage and formation. This work presents the synthesis of zeolites and also provides atomic-level insights into the dynamic processes of topotactic reactions. Our results have implications for advancing materials engineering and understanding complex solid-state reactions at an atomic scale.

Inorganic chemistry↗

DOE OSTI2026

Nanoscale strain wave generation by a piezoelectric grating from polar vortices

Nanostructures formed by spontaneously broken symmetry have provided new ways to manipulate quantum states. Specifically, topological structures with periodic spatial ordering, such as polar vortices and skyrmions, can be ideal hosts for creating engineered responses in both spatial and frequency domains. So far, however, only a few examples of such hierarchical engineering have been reported in the literature. Here we demonstrate that the spatially modulated piezoelectric response of a polar vortex structure can create strain waves with a characteristic nanoscale wavefront. Using time-resolved pump–probe resonant X-ray scattering and diffraction measurements, coupled with dynamical phase-field simulations, we show that the piezoelectric modulation of the spontaneously formed polar vortex crystal functions as an acoustic diffraction grating. This system converts incoming laterally uniform strain waves into outgoing waves with a characteristic sub-terahertz frequency, driven by an intrinsic excitation of the polar vortex crystal. Moreover, our phase-field simulations suggest that the dynamic mechanical displacements exhibiting vortex textures are generated from both space- and time-varying piezoelectric responses. Our findings illustrate a new method for generating nanoscale strain waves with unique spatial textures by tuning the hierarchical order of polar topologies to engineer new collective modes, allowing for a wide range of control through the topological lattice.

ferroelectrics↗

DOE OSTI2026

Visualization of Thermal and Strain Dynamics in X-ray Optics by Time-Resolved Rocking Curve Imaging

The absorption of intense X-ray pulses from free-electron lasers by X-ray crystal optics triggers rapid thermal and mechanical responses, including lattice compression, expan- sion, and strain-wave propagation, which dynamically modify diffraction conditions and wavefront properties. These effects pose significant challenges for next-generation high- repetition-rate X-ray sources, particularly for crystal monochromators used in XFEL beam- lines and self-seeding. Here, we demonstrate time-resolved rocking curve imaging (TrRCI) of X-ray Bragg optics with high spatial resolution (6.4 μm) and sub-1-μrad angular resolu- tion, enabling direct visualization of lattice dynamics from nanoseconds to microseconds. By combining a high-flux beamline at SPring-8, a scintillator-coupled sCMOS detector, and a synchronized femtosecond laser system, we capture lattice dynamics induced by tran- sient laser heating with a strain sensitivity on the order of 10−6 . Our results reveal transient lattice deformation and the propagation of laser-induced strain waves over millimeter-scale distances. This approach provides experimental benchmarks for understanding heat-load effects in high-repetition-rate X-ray optics.

Source record↗

DOE OSTI2025

Understanding the Benefit of Hybrid Electrolytes towards Vanadium Dissolution Suppression and Improved Capacity Retention in Zinc‐Aqueous Batteries Using NaV 3 O 8 Cathodes

Vanadate cathodes used in aqueous Zn-ion batteries with ZnSO 4 are hindered by capacity loss from V dissolution into the electrolyte. However, studies pinpointing the onset of dissolution as a function of electrochemical redox state and quantifying the amount of associated active material are lacking. To prevent dissolution of the NaV 3 O 8 active material, Na + ions are introduced into the electrolyte. Specifically, a hybrid ZnSO 4 + Na 2 SO 4 electrolyte is investigated in concert with NaV 3 O 8 (NVO) cathodes of varied crystallinity to determine the resulting impacts on cathode dissolution and functional electrochemistry. The use of Na + -containing hybrid electrolyte shows no significant change in Zn 2+ diffusion coefficients yet improved capacity retention. Time-resolved quantitative optical emission spectroscopy demonstrates the suppression of V dissolution with the hybrid electrolyte in both pristine and cycled electrodes. Operando synchrotron X-ray diffraction and absorption provide mechanistic insights. Hydrated NVO with wider interplanar spacing exhibits much higher H + /Zn 2+ capacity, while the Na 2 SO 4 mitigates the formation of irreversible side products. Furthermore, this study demonstrates that the use of hybrid electrolytes and control of crystallite size in the parent material can significantly improve electrochemical behavior of layered V-based cathodes in Zn-ion batteries, providing a general strategy toward safe and resilient aqueous battery systems.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Synthesis and characterization of 5,15-bis(hydroxymethyl)porphyrins – simple compounds distantly inspired by the chlorosomal bacteriochlorophylls

A self-assembly paradigm is provided in green photosynthetic bacteria by the chlorin macrocycle bacteriochlorophyll (BChl) c, which contains a 3-(1-hydroxyethyl) substituent, central magnesium ion, and 13-keto group. The assembled BChl c structure is a powerful light-harvesting apparatus that can support life even under extreme low-light conditions. Here, inspired by the work of Balaban, two far simpler porphyrins have been synthesized, 5,15-bis(hydroxymethyl)-10,20-diphenylporphinatozinc(II) (Ph/CH 2 OH) and 5,15-bis(hydroxymethyl)porphinatozinc(II) (H/CH 2 OH), and analogues wherein ethyl replaces hydroxymethyl (Ph/Et and H/Et). Examination of Ph/CH 2 OH and H/CH 2 OH by time-resolved spectroscopy showed an ∼2-fold enhancement in the singlet excited-state lifetime compared to meso-tetraphenylporphinatozinc(II) (ZnTPP). The single-crystal X-ray diffraction revealed distinct packing patterns. Porphyrin Ph/CH 2 OH exhibited double staircases wherein (1) each zinc is pentacoordinate (by apical coordination of one hydroxymethyl group of a porphyrin in the same staircase), (2) the second hydroxymethyl group is hydrogen-bonded to an apically coordinated hydroxymethyl oxygen atom in the adjacent staircase, (3) the porphyrins in a given staircase are coplanar but cofacially offset with each other, and (4) the adjacent staircases are oriented approximately 72° relative to each other. Porphyrin H/CH 2 OH assembled wherein (1) each zinc is hexacoordinate by ligation of hydroxymethyl moieties, (2) each hydroxymethyl –OH is hydrogen-bonded with an acetonitrile solvent molecule in the lattice, and (3) the planes of the four nearest neighbor porphyrins are essentially perpendicular to a given porphyrin. Study of the solid-state packing patterns of sparsely substituted porphyrins enables insights into how the structural design of tetrapyrroles can guide their aggregate self-assembly.

Tran, Vy-Phuong [North Carolina State University, ↗

DOE OSTI2025

Time-resolved probing of laser-induced nanostructuring processes in liquids

Laser synthesis and processing of colloids (LSPC) in liquids has gained widespread applications in producing nanomaterials of different classes of solids. While the technical processes in different cases of ablation, fragmentation or colloidal fusion may look macroscopically different in each application, the underlying fundamental mechanisms are always the same cascade of laser interaction with matter, non-thermal or thermal energy deposition, phase transitions, and the subsequent structure formation processes. Disentangling these mechanisms represents a veritable challenge, as ultrafast and structurally sensitive experimental methods are required. This review presents a discussion of how state-of-the-art experimental protocols using ultrafast lasers and sensitive structural probes, such as electrons or X-rays are able to address this challenge. In particular, it is possible to investigate LSPC on single objects using single probe pulses and avoid accumulation effects in a heterogeneous sample. The presented results capture structure formation with femtosecond and atomic scale resolution. Ultrafast time-resolved probing approaches are key to revealing the transient states and pathways that govern material transformation in LSPC.

X-ray scattering↗

DOE OSTI2025

Low blaze angle grating for fully dispersive x-ray spectroscopy

We demonstrate fabrication of an ultra-low blaze angle (LBA) grating designed for time-resolved spectroscopy in the x-ray region. A blaze angle of 0.12° was achieved by the groove depth reduction process providing a perfect saw-tooth shape of the grooves. The 200 lines/mm LBA grating exhibited high diffraction efficiency at a photon energy of 8 KeV. Use in a spectrometer would open up dispersive x-ray absorption spectroscopy across a wide energy range including the K edges of 3d transition metals, with much greater efficiency than traditional crystal spectrometers.

Voronov, D. L.↗

DOE OSTI2025

Low Frequency Vibrational Modes of Two-Dimensional Lead-Free Metal Halide Double Perovskites

2D layered double perovskites of (S-MPA) 4 AgBiI 8 (MPA-AgBiI 8 ) and (S-MPA) 4 CuBiI 8 (MPA-CuBiI 8 ) (S-MPA, S-β-methylphenethylammonium) were synthesized with a hydrothermal method. The crystal structure of MPA-AgBiI 8 was determined using single-crystal X-ray diffraction (scXRD). Powder XRD (pXRD) data suggest that the crystal structure of MPA-CuBiI 8 is more complex than that of MPA-AgBiI 8 . UV-Vis electronic absorption spectra of these perovskites reveal a bandgap of 2.03 eV for both. Short exciton lifetime from time-resolved photoluminescence (TRPL) results and low PL intensity of the Cu-based perovskite suggest a high density of trap states within the bandgap. Low frequency Raman spectra of both materials show distinct peaks and a slightly higher frequency for the Cu-based perovskite than the Ag-based perovskite. Density functional theory (DFT) calculations were conducted to simulate the low frequency Raman spectra and help explain the different phonon modes, which are collective vibrations of metal halide bond bending and stretching within the Ag- and Cu-centered octahedra coupled with MPA libration and twisting within the inorganic layer. The DFT theory also quantified octahedral distortions in the two perovskites. Furthermore, this combined experimental and computational study provides new insights into the low frequency vibrations of 2D perovskites.

Halogens↗

DOE OSTI2025

Role of Ammonium Hydroxide on Glucose Oxidase Immobilized in Metal–Azolate Framework-7 Enzyme Activity

Enzymes are nature’s catalysts, but their instability outside native environments limits practical applications. Metal–organic frameworks (MOFs) offer a promising platform for enzyme immobilization, enhancing stability, and reusability through their tunable porosity and crystallinity. While ZIF-based MOFs have been extensively studied, metal azolate framework-7 (MAF-7) remains largely unexplored for biomimetic mineralization. Its hydrophilic character makes it a promising alternative for enzyme encapsulation; however, the role of essential basic modulators such as ammonium hydroxide (NH 4 OH) on enzyme structure and function has not been investigated. Here, in this study, we examine the NH 4 OH mediated synthesis of glucose oxidase within MAF-7 using powder X-ray diffraction (PXRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), cryogenic transmission electron microscopy (cryo-TEM), and enzyme assays. Our results show that NH 4 OH modulates crystal morphology, enzyme activity, and nucleation behavior, with higher concentrations leading to partial enzyme denaturation and reduced catalytic performance. By integrating time-resolved cryo-TEM with activity assays, we uncover how modulator concentration impacts early stage crystallization and enzyme folding, a mechanistic insight not previously demonstrated in MOF systems. These findings highlight modulator chemistry as a critical, underexplored variable in MOF synthesis, advancing rational design strategies for enzyme@MOFs (E@MOF) beyond ZIFs and toward more tunable, biocompatible frameworks like MAF-7.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Dynamics of nanoscale phase decomposition in laser ablation

Abstract Laser ablation is a process that bears both fundamental physics interest and has wide industrial applications. For decades, the lack of probes on the relevant time and length scales has prevented access to the highly nonequilibrium phase decomposition processes triggered by laser excitation. In this study, a close integration of time-resolved probing by intense femtosecond X-ray pulses with large-scale atomistic modeling has yielded unique insights into the ablation dynamics of thin gold films irradiated by femtosecond laser pulses. The emergence and growth of nanoscale density heterogeneities in the expanding ablation plume, predicted in the simulations, are mapped to the rapid evolution of distinct small angle diffraction features. This mapping enables identification of the characteristic signatures of different phase decomposition processes occurring simultaneously in the plume, which are driven by photomechanical and thermodynamic driving forces. Beyond the specific insights into the ablation phenomenon, this study demonstrates the power of joint X-ray probing and atomistic modeling of material dynamics under extreme conditions of thermal and mechanical nonequilibrium.

Sun, Yanwen (ORCID:0000000159266565)↗

DOE OSTI2026

Observation of room-temperature charge density wave correlations via coherent phonon spectroscopy in the Sn-doped kagome superconductor CsV 3 ⁢Sb 5

In this study, we perform ultrafast time-resolved reflectivity measurements to track the evolution of charge density wave (CDW) correlations in Sn-doped Kagome superconductor CsV 3⁢ Sb 5−𝑥 ⁢Sn 𝑥 . By extracting the coherent phonon spectrum, we evidence robust signatures of CDW correlations at temperature and doping ranges far beyond the phase boundary of long-range CDW order. Remarkably, we show that short-range CDW correlations survive up to room temperature in 𝑥 = 0.32 Sn-doped CsV 3 ⁢Sb 5 , supported by synchrotron x-ray diffraction measurements. We point out that the introduction of quenched disorder by Sn doping can pin the CDW and form static short-range CDW, which can explain the observed persistent CDW signatures. Our results thus corroborate the ubiquity and robustness of CDW correlations in Sn-doped CsV 3⁢ Sb 5 and provide new insights on the role of disorders on the CDW correlations in AV 3 ⁢Sb 5 family.

Charge density waves↗

DOE OSTI2025

A Flat Analyzer Polycapillary Spectrometer for X-ray Absorption Spectroscopy of Dilute Transition Metals at X-ray-Free Electron Lasers

X-ray absorption spectroscopy (XAS) coupled with highly intense pulses from an X-ray-free electron laser (XFEL) can be used to track ultrafast chemical dynamics. Nonetheless, measurements for dilute samples (≤1 mM) have been exceptionally challenging, as scattering background signals dominate over the sample’s X-ray fluorescence. We show that femtosecond time-resolved XAS measurements of sub-millimolar transition metal solutions are now possible at the Linac Coherent Light Source (LCLS) using a high-throughput polycapillary XAS spectrometer, designed, developed, and commissioned at LCLS and the Stanford Synchrotron Radiation Lightsource (SSRL). The instrument integrates three polycapillary optics that collect and collimate X-ray fluorescence emitted from the interaction point with a high solid angle. X-ray collimated fluorescence is then selectively diffracted by coupled graphite analyzer crystals. As a result, the contribution of scattered photons is suppressed. Experiments at the Pt L 3 -edge on 0.1 mM aqueous K 2 PtCl 6 (delivered via a 100 μm liquid jet) were successfully performed in the laser pump X-ray probe configuration at the LCLS XCS and XPP instruments. We report the transient spectra of hexachloroplatinate within the first 10 ps after a 266 nm photoexcitation. We observed a short-lived reduced intermediate (≈2 ps). The polycapillary X-ray spectrometer at LCLS now enables the efficient study of the dynamics of ultradilute transition metals in solution. This capability opens the door to investigating plasmonic systems, photocatalysts, enzymes, and other scarce and dilute samples.

LCLS↗

DOE OSTI2025

On Stability and Electrochemical Performance of 316 Stainless Steel in Wastewater: Implications for Resource Recovery

Electrochemical nutrient recovery systems rely on stable electrode materials capable of operating in chemically complex wastewater environments. We investigated corrosion resistance and interfacial electrochemical behavior of 316 stainless steel (SS316) in a synthetic wastewater matrix representative of centrate streams, a key knowledge gap in electrochemical phosphorus recovery. A comprehensive suite of electrochemical techniques (chronoamperometry, cyclic voltammetry, potentiodynamic polarization, and electrochemical impedance spectroscopy (EIS)) and surface characterization methods (scanning electron microscopy, X-ray diffraction) were employed. Results revealed that wastewater containing typical ionic constituents (such as PO 4 3- , NH 4 + , and divalent cations) exhibited enhanced cathodic activity and the formation of a more stable, protective surface film on SS316 that mitigated chloride-induced corrosion. In contrast, SS316 in the NaCl solution showed significant susceptibility to passive layer breakdown and localized corrosion. Time-resolved EIS further confirmed improved interfacial stability and restricted charge transfer in WW over time, in stark contrast to the progressive passive layer degradation in NaCl. Surface analyses corroborated these findings, showing limited surface attack in WW compared to distinct localized corrosion features in NaCl. These findings indicate that competing ionic species in WW effectively mitigate chloride aggressiveness, enhance SS316 stability, and demonstrate improved electrode longevity and reliability for sustainable wastewater-based electrochemical phosphorus recovery applications.

36 MATERIALS SCIENCE↗

DOE OSTI2025

X-ray Absorption Spectroscopy of Dilute Metalloenzymes at X-ray Free-Electron Lasers in a Shot-by-Shot Mode

X-ray absorption spectroscopy (XAS) of 3d transition metals provides important electronic structure information for many fields. However, X-ray-induced radiation damage under physiological temperature has prevented using this method to study dilute aqueous systems, such as metalloenzymes, as the catalytic reaction proceeds. Here we present a new approach to enable operando XAS of dilute biological samples and demonstrate its feasibility with K-edge XAS spectra from the Mn cluster in photosystem II and the Fe–S centers in photosystem I. This approach combines highly efficient sample delivery strategies and a robust signal normalization method with high-transmission Bragg diffraction-based spectrometers at X-ray free-electron lasers (XFELs) in a damage-free, shot-by-shot mode. These photon-out spectrometers have been optimized for discriminating the metal Mn/Fe Kα fluorescence signals from the overwhelming scattering background present on currently available detectors for XFELs that lack suitable energy discrimination. We quantify the enhanced performance metrics of the spectrometer and discuss its potential applications for acquiring time-resolved XAS spectra of biological samples during their reactions at XFELs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Anomalous lattice expansion of bcc Ta in helium-loaded diamond anvil cells

Anomalous lattice expansion of bcc Ta is observed in helium-loaded diamond anvil cell (DAC) experiments near 6 GPa and above 400 K, while co-loaded W, Mo, and Au exhibit normal thermal expansion. The Ta volume expansion increases with temperature, reaching ~14% near 650 K before plateauing, and is largely retained after recovery to ambient conditions. Time-resolved measurements at 500 K reveal progressive expansion over several hours, consistent with gradual, thermally activated He incorporation. The largely retained expansion during subsequent cooling and holding at 400 K indicates that the incorporated He is predominantly kinetically trapped. The data reveal two distinct regimes: below ~550 K, modest and spatially uniform expansion consistent with interstitial He trapping at isolated, randomly distributed vacancies; above ~550 K, He-vacancy cluster growth producing dramatically larger expansion, peak broadening, and a core–shell microstructure revealed by micron-resolution X-ray diffraction mapping. These results demonstrate that He is not always a passive pressure medium in DAC experiments and reveal a previously unrecognized regime of He-mediated lattice modification in Ta, complementing conventional ion-implantation studies relevant to nuclear and fusion structural materials.

Diamond anvil cell↗

DOE OSTI2026

Electron-Deficient Phenazines: Synthesis, Structures, Redox, and Optoelectronic Properties in the Gas Phase, in Solution, and in the Solid State

High-temperature gas-phase reactions of 1,4-C4F8I2 with phenazine (PHNZ) afforded new thermally- and air-stable derivatives with cyclo-C4F8 substituents, viz. 1,2-PHNZ(C4F8), 2,3-PHNZ(C4F8), 1,2:6,7-PHNZ(C4F8)2, 1,2:7,8-PHNZ(C4F8)2, and 1,2:8,9-PHNZ(C4F8)2. Reactions in the presence of Cu powder resulted in reductive-defluorination/aromatization of some of the cyclo-C4F8 substituents to produce 2,3-PHNZ(C4F4), 2,3-PHNZ(C4HF3), and 1,2:6,7-PHNZ(C4F8)(C4F4), which are formally tri- or tetrafluoro derivatives of benzo[a]phenazine. Single-crystal X-ray diffraction structures of these compounds demonstrate the planarity of 2,3-PHNZ(C4F4) and 2,3-PHNZ(C4HF3) and ordered p-stacking in 1,2-PHNZ(C4HF3), 1,2-PHNZ(C4F4), 1,2-PHNZ(C4F8), and 2,3-PHNZ(C4F8). Low-temperature gas-phase photoelectron spectra of the PHNZ(C4F8)1,2 compounds show that they are strong electron acceptors, with the three PHNZ(C4F8)2 isomers having electron affinities exceeding that of C60. Cyclic voltammetry in acetonitrile show that the five PHNZ(C4F8)1,2 compounds exhibit reversible one-electron reductions with large positive shifts in their reduction potentials relative to unsubstituted PHNZ. Spectroelectrochemical absorption and EPR spectra of PHNZ(C4F8)1,2- • anion radicals and extensive DFT calculations revealed the significant role that the different substitution patterns have on determining the optoelectronic properties of the PHNZ(C4F8)1,2 derivatives and PHNZ(C4F8)1,2- • anion radicals. Time-resolved microwave conductivity measurements and photoluminescence spectra of blends of the PHNZ(C4F8)1,2 derivatives with the donor poly(3-hexylthiophene) (P3HT) were recorded to assess the possible use of the new compounds in optoelectronic devices.

Balser, Sebastian↗

DOE OSTI2025

Effect of growth dynamics on the structural, photophysical and pseudocapacitance properties of famatinite copper antimony sulphide colloidal nanostructures (including nanosheets)

Facile phase selective synthesis of copper antimony sulphide (CAS) nanostructures is important because of their tunable photoconductive and electrochemical properties. In this study, off-stoichiometric famatinite phase CAS (fCAS) quasi-spherical and quasi-hexagonal colloidal nanostructures (including nanosheets) of sizes, 2.4–18.0 nm were grown under variable conditions of temperature (60–200 °C), time and oleylamine capping ligand concentration using copper(II) acetylacetonate and antimony(III) diethyldithiocarbamate precursors. Data from powder X-ray diffraction, Raman spectroscopy and high-resolution scanning/transmission electron microscopy confirm the tetragonal structure of the famatinite phase. X-ray photoelectron spectroscopy, transmission electron microscopy and scanning electron microscopy-energy dispersive X-ray spectroscopy data suggest a correlation of particle size, morphology and composition of the off-stoichiometric fCAS nanostructures with growth temperature and time, and oleylamine concentration. The off-stoichiometric Cu 3-a Sb 1+b S 4±c (a, b, c – mole fractions) nanostructures being severely copper-deficient and antimony-rich, exhibit shallow-lying acceptor copper vacancy states, deep-lying donor states of antimony interstitials, sulphur vacancies and antimony-copper antisites and shallow-lying acceptor surface trapping states. Further, these electronic states are likely implicated in tunable UV-visible absorption and bandgaps between 2.3 and 2.8 eV, and broad visible-NIR photoluminescence with fast recombination of radiative lifetimes between 0.2 and 6.2 ns, confirmed from absorption, steady-state and time-resolved photoluminescence spectroscopies. Additionally, cyclic voltammetry and electrochemical impedance spectroscopy confirm that electrodes of the fCAS nanostructures display slightly variable pseudocapacitance of charge-storage primarily via possible sodium ion intercalation with a high specific capacitance of ~84 F g -1 obtained at a scan rate of 5 mV s -1 . Overall, these results show the influence of composition, in particular point defects, phase quality and morphology on the optical and pseudocapacitance properties of fCAS nanostructures, suitable as solar absorbers or electrodes for energy storage devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Filling data analysis gaps in time-resolved crystallography by machine learning

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.

Trujillo, Justin (ORCID:0000000285505360)↗