Computational study of diffraction image formation from XFEL irradiated single ribosome molecule.

Single particle imaging at atomic resolution is perhaps one of the most desired goals for ultrafast X-ray science with X-ray free-electron lasers. Such a capability would create great opportunity within the biological sciences, as high-resolution structural information of biosamples that may not crystallize is essential for many research areas therein. In this paper, we report on a comprehensive computational study of diffraction image formation during single particle imaging of a macromolecule, containing over one hundred thousand non-hydrogen atoms. For this study, we use a dedicated simulation framework, SIMEX, available at the European XFEL facility. Our results demonstrate the full feasibility of computational single-particle imaging studies for biological samples of realistic size. This finding is important as it shows that the SIMEX platform can be used for simulations to inform relevant single-particle-imaging experiments and help to establish optimal parameters for these experiments. This will enable more focused and more efficient single-particle-imaging experiments at XFEL facilities, making the best use of the resource-intensive XFEL operation.

Ultrafast demagnetization in bulk nickel induced by X-ray photons tuned to Ni M3 and L3 absorption edges.

Studies of light-induced demagnetization started with the experiment performed by Beaupaire et al. on Ni. Here, we present theoretical predictions for X-ray induced demagnetization of nickel, with X-ray photon energies tuned to its [Formula: see text] and [Formula: see text] absorption edges. We show that the specific feature in the density of states in the d-band of Ni, i.e., a sharp peak located just above the Fermi level, strongly influences the change of the predicted magnetic signal, making it stronger than in the previously studied case of X-ray demagnetized cobalt. It impacts also the value of Curie temperature for Ni. We believe that this finding will inspire dedicated experiments investigating magnetic processes in X-ray irradiated nickel and cobalt.

Femtosecond Reduction of Atomic Scattering Factors Triggered by Intense X-Ray Pulse.

X-ray diffraction of silicon irradiated with tightly focused femtosecond x-ray pulses (photon energy, 11.5 keV; pulse duration, 6 fs) was measured at various x-ray intensities up to 4.6×10^{19} W/cm^{2}. The measurement reveals that the diffraction intensity is highly suppressed when the x-ray intensity reaches of the order of 10^{19} W/cm^{2}. With a dedicated simulation, we confirm that the observed reduction of the diffraction intensity can be attributed to the femtosecond change in individual atomic scattering factors due to the ultrafast creation of highly ionized atoms through photoionization, Auger decay, and subsequent collisional ionization. We anticipate that this ultrafast reduction of atomic scattering factor will be a basis for new x-ray nonlinear techniques, such as pulse shortening and contrast variation x-ray scattering.

Non-thermal structural transformation of diamond driven by x-rays.

Intense x-ray pulses can cause the non-thermal structural transformation of diamond. At the SACLA XFEL facility, pump x-ray pulses triggered this phase transition, and probe x-ray pulses produced diffraction patterns. Time delays were observed from 0 to 250 fs, and the x-ray dose varied from 0.9 to 8.0 eV/atom. The intensity of the (111), (220), and (311) diffraction peaks decreased with time, indicating a disordering of the crystal lattice. From a Debye-Waller analysis, the rms atomic displacements perpendicular to the (111) planes were observed to be significantly larger than those perpendicular to the (220) or (311) planes. At a long time delay of 33 ms, graphite (002) diffraction indicates that graphitization did occur above a threshold dose of 1.2 eV/atom. These experimental results are in qualitative agreement with XTANT+ simulations using a hybrid model based on density-functional tight-binding molecular dynamics.

Water layer and radiation damage effects on the orientation recovery of proteins in single-particle imaging at an X-ray free-electron laser.

The noise caused by sample heterogeneity (including sample solvent) has been identified as one of the determinant factors for a successful X-ray single-particle imaging experiment. It influences both the radiation damage process that occurs during illumination as well as the scattering patterns captured by the detector. Here, we investigate the impact of water layer thickness and radiation damage on orientation recovery from diffraction patterns of the nitrogenase iron protein. Orientation recovery is a critical step for single-particle imaging. It enables to sort a set of diffraction patterns scattered by identical particles placed at unknown orientations and assemble them into a 3D reciprocal space volume. The recovery quality is characterized by a "disconcurrence" metric. Our results show that while a water layer mitigates protein damage, the noise generated by the scattering from it can introduce challenges for orientation recovery and is anticipated to cause problems in the phase retrieval process to extract the desired protein structure. Compared to these disadvantageous effects due to the thick water layer, the effects of radiation damage on the orientation recovery are relatively small. Therefore, minimizing the amount of residual sample solvent should be considered a crucial step in improving the fidelity and resolution of X-ray single-particle imaging experiments.

Picosecond to microsecond dynamics of X-ray irradiated materials at MHz pulse repetition rate.

Modern X-ray free-electron lasers (XFELs) produce intense femtosecond X-ray pulses able to cause significant damage to irradiated targets. Energetic photoelectrons created upon X-ray absorption, and Auger electrons emitted after relaxation of core-hole states trigger secondary electron cascades, which contribute to the increasing transient free electron density on femtosecond timescales. Further evolution may involve energy and particle diffusion, creation of point defects, and lattice heating. This long-timescale (up to a microsecond) X-ray-induced dynamics is discussed on the example of silicon in two-dimensional geometry. For modeling, we apply an extended Two-Temperature model with electron density dynamics, nTTM, which describes relaxation of an irradiated sample between two successive X-ray pulses, emitted from XFEL at MHz pulse repetition rate. It takes into account ambipolar carrier diffusion, electronic and atomic heat conduction, as well as electron-ion coupling. To solve the nTTM system of equations in two dimensions, we developed a dedicated finite-difference integration algorithm based on Alternating Direction Implicit method with an additional predictor-corrector scheme. We show first results obtained with the model and discuss its possible applications for XFEL optics, detectors, and for diagnostics tools. In particular, the model can estimate the timescale of material relaxation relevant for beam diagnostic applications during MHz operation of contemporary and future XFELs.

Application of Boltzmann kinetic equations to model X-ray-created warm dense matter and plasma.

In this review, we describe the application of Boltzmann kinetic equations for modelling warm dense matter and plasma formed after irradiation of solid materials with intense femtosecond X-ray pulses. Classical Boltzmann kinetic equations are derived from the reduced N-particle Liouville equations. They include only single-particle densities of ions and free electrons present in the sample. The first version of the Boltzmann kinetic equation solver was completed in 2006. It could model non-equilibrium evolution of X-ray-irradiated finite-size atomic systems. In 2016, the code was adapted to study plasma created from X-ray-irradiated materials. Additional extension of the code was then also performed, enabling simulations in the hard X-ray irradiation regime. In order to avoid treatment of a very high number of active atomic configurations involved in the excitation and relaxation of X-ray-irradiated materials, an approach called 'predominant excitation and relaxation path' (PERP) was introduced. It limited the number of active atomic configurations by following the sample evolution only along most PERPs. The performance of the Boltzmann code is illustrated in the examples of X-ray-heated solid carbon and gold. Actual model limitations and further model developments are discussed. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.

Tree-Code Based Improvement of Computational Performance of the X-ray-Matter-Interaction Simulation Tool XMDYN.

In this work, we report on incorporating for the first time tree-algorithm based solvers into the molecular dynamics code, XMDYN. XMDYN was developed to describe the interaction of ultrafast X-ray pulses with atomic assemblies. It is also a part of the simulation platform, SIMEX, developed for computational single-particle imaging studies at the SPB/SFX instrument of the European XFEL facility. In order to improve the XMDYN performance, we incorporated the existing tree-algorithm based Coulomb solver, PEPC, into the code, and developed a dedicated tree-algorithm based secondary ionization solver, now also included in the XMDYN code. These extensions enable computationally efficient simulations of X-ray irradiated large atomic assemblies, e.g., large protein systems or viruses that are of strong interest for ultrafast X-ray science. The XMDYN-based preparatory simulations can now guide future single-particle-imaging experiments at the free-electron-laser facility, EuXFEL.

Delayed Onset and Directionality of X-Ray-Induced Atomic Displacements Observed on Subatomic Length Scales.

Transient structural changes of Al_{2}O_{3} on subatomic length scales following irradiation with an intense x-ray laser pulse (photon energy: 8.70 keV; pulse duration: 6 fs; fluence: 8×10^{2} J/cm^{2}) have been investigated by using an x-ray pump x-ray probe technique. The measurement reveals that aluminum and oxygen atoms remain in their original positions by ∼20 fs after the intensity maximum of the pump pulse, followed by directional atomic displacements at the fixed unit cell parameters. By comparing the experimental results and theoretical simulations, we interpret that electron excitation and relaxation triggered by the pump pulse modify the potential energy surface and drives the directional atomic displacements. Our results indicate that high-resolution x-ray structural analysis with the accuracy of 0.01 Å is feasible even with intense x-ray pulses by making the pulse duration shorter than the timescale needed to complete electron excitation and relaxation processes, which usually take up to a few tens of femtoseconds.

Density functional tight binding approach utilized to study X-ray-induced transitions in solid materials.

Intense X-ray pulses from free-electron lasers can trigger ultrafast electronic, structural and magnetic transitions in solid materials, within a material volume which can be precisely shaped through adjustment of X-ray beam parameters. This opens unique prospects for material processing with X rays. However, any fundamental and applicational studies are in need of computational tools, able to predict material response to X-ray radiation. Here we present a dedicated computational approach developed to study X-ray induced transitions in a broad range of solid materials, including those of high chemical complexity. The latter becomes possible due to the implementation of the versatile density functional tight binding code DFTB+ to follow band structure evolution in irradiated materials. The outstanding performance of the implementation is demonstrated with a comparative study of XUV induced graphitization in diamond.

Effects of radiation damage and inelastic scattering on single-particle imaging of hydrated proteins with an X-ray Free-Electron Laser.

We present a computational case study of X-ray single-particle imaging of hydrated proteins on an example of 2-Nitrogenase-Iron protein covered with water layers of various thickness, using a start-to-end simulation platform and experimental parameters of the SPB/SFX instrument at the European X-ray Free-Electron Laser facility. The simulations identify an optimal thickness of the water layer at which the effective resolution for imaging the hydrated sample becomes significantly higher than for the non-hydrated sample. This effect is lost when the water layer becomes too thick. Even though the detailed results presented pertain to the specific sample studied, the trends which we identify should also hold in a general case. We expect these findings will guide future single-particle imaging experiments using hydrated proteins.

Atomic-Scale Visualization of Ultrafast Bond Breaking in X-Ray-Excited Diamond.

Ultrafast changes of charge density distribution in diamond after irradiation with an intense x-ray pulse (photon energy, 7.8 keV; pulse duration, 6 fs; intensity, 3×10^{19} W/cm^{2}) have been visualized with the x-ray pump-x-ray probe technique. The measurement reveals that covalent bonds in diamond are broken and the electron distribution around each atom becomes almost isotropic within ∼5 fs after the intensity maximum of the x-ray pump pulse. The 15 fs time delay observed between the bond breaking and atomic disordering indicates nonisothermality of electron and lattice subsystems on this timescale. From these observations and simulation results, we interpret that the x-ray-induced change of the interatomic potential drives the ultrafast atomic disordering underway to the following nonthermal melting.

Effect of Auger recombination on transient optical properties in XUV and soft X-ray irradiated silicon nitride.

Spatially encoded measurements of transient optical transmissivity became a standard tool for temporal diagnostics of free-electron-laser (FEL) pulses, as well as for the arrival time measurements in X-ray pump and optical probe experiments. The modern experimental techniques can measure changes in optical coefficients with a temporal resolution better than 10 fs. This, in an ideal case, would imply a similar resolution for the temporal pulse properties and the arrival time jitter between the FEL and optical laser pulses. However, carrier transport within the material and out of its surface, as well as carrier recombination may, in addition, significantly decrease the number of carriers. This would strongly affect the transient optical properties, making the diagnostic measurement inaccurate. Below we analyze in detail the effects of those processes on the optical properties of XUV and soft X-ray irradiated Si[Formula: see text]N[Formula: see text], on sub-picosecond timescales. Si[Formula: see text]N[Formula: see text] is a wide-gap insulating material widely used for FEL pulse diagnostics. Theoretical predictions are compared with the published results of two experiments at FERMI and LCLS facilities, and with our own recent measurement. The comparison indicates that three body Auger recombination strongly affects the optical response of Si[Formula: see text]N[Formula: see text] after its collisional ionization stops. By deconvolving the contribution of Auger recombination, in future applications one could regain a high temporal resolution for the reconstruction of the FEL pulse properties measured with a Si[Formula: see text]N[Formula: see text]-based diagnostics tool.

Structural dynamics in proteins induced by and probed with X-ray free-electron laser pulses.

X-ray free-electron lasers (XFELs) enable crystallographic structure determination beyond the limitations imposed upon synchrotron measurements by radiation damage. The need for very short XFEL pulses is relieved through gating of Bragg diffraction by loss of crystalline order as damage progresses, but not if ionization events are spatially non-uniform due to underlying elemental distributions, as in biological samples. Indeed, correlated movements of iron and sulfur ions were observed in XFEL-irradiated ferredoxin microcrystals using unusually long pulses of 80 fs. Here, we report a femtosecond time-resolved X-ray pump/X-ray probe experiment on protein nanocrystals. We observe changes in the protein backbone and aromatic residues as well as disulfide bridges. Simulations show that the latter's correlated structural dynamics are much slower than expected for the predicted high atomic charge states due to significant impact of ion caging and plasma electron screening. This indicates that dense-environment effects can strongly affect local radiation damage-induced structural dynamics.

X-ray induced damage of B4C-coated bilayer materials under various irradiation conditions.

In this report, we analyse X-ray induced damage of B4C-coated bilayer materials under various irradiation geometries, following the conditions of our experiment performed at the free-electron-laser facility SACLA. We start with the discussion of structural damage in solids and damage threshold doses for the experimental system components: B4C, SiC, Mo and Si. Later, we analyze the irradiation of the experimentally tested coated bilayer systems under two different incidence conditions of a linearly polarized X-ray pulse: (i) grazing incidence, and (ii) normal incidence, in order to compare quantitatively the effect of the pulse incidence on the radiation tolerance of both systems. For that purpose, we propose a simple theoretical model utilizing properties of hard X-ray propagation and absorption in irradiated materials and of the following electron transport. With this model, we overcome the bottleneck problem of large spatial scales, inaccessible for any existing first-principle-based simulation tools due to their computational limitations for large systems. Predictions for damage thresholds obtained with the model agree well with the available experimental data. In particular, they confirm that two coatings tested: 15 nm B4C/20 nm Mo on silicon wafer and 15 nm B4C/50 nm SiC on silicon wafer can sustain X-ray irradiation at the fluences up to ~10 µJ/µm2, when exposed to linearly polarized 10 keV X-ray pulse at a grazing incidence angle of 3 mrad. Below we present the corresponding theoretical analysis. Potential applications of our approach for design and radiation tolerance tests of multilayer components within X-ray free-electron-laser optics are indicated.

Radiation-Induced Chemical Dynamics in Ar Clusters Exposed to Strong X-Ray Pulses.

We show that electron and ion spectroscopy reveals the details of the oligomer formation in Ar clusters exposed to an x-ray free electron laser (XFEL) pulse, i.e., chemical dynamics triggered by x rays. With guidance from a dedicated molecular dynamics simulation tool, we find that van der Waals bonding, the oligomer formation mechanism, and charge transfer among the cluster constituents significantly affect ionization dynamics induced by an XFEL pulse of moderate fluence. Our results clearly demonstrate that XFEL pulses can be used not only to "damage and destroy" molecular assemblies but also to modify and transform their molecular structure. The accuracy of the predictions obtained makes it possible to apply the cluster spectroscopy, in connection with the respective simulations, for estimation of the XFEL pulse fluence in the fluence regime below single-atom multiple-photon absorption, which is hardly accessible with other diagnostic tools.

Multistep transition of diamond to warm dense matter state revealed by femtosecond X-ray diffraction.

Diamond bulk irradiated with a free-electron laser pulse of 6100 eV photon energy, 5 fs duration, at the ~19-25 eV/atom absorbed doses, is studied theoretically on its way to warm dense matter state. Simulations with our hybrid code XTANT show disordering on sub-100 fs timescale, with the diffraction peak (220) vanishing faster than the peak (111). The warm dense matter formation proceeds as a nonthermal damage of diamond with the band gap collapse triggering atomic disordering. Short-living graphite-like state is identified during a few femtoseconds between the disappearance of (220) peak and the disappearance of (111) peak. The results obtained are compared with the data from the recent experiment at SACLA, showing qualitative agreement. Challenges remaining for the accurate modeling of the transition of solids to warm dense matter state and proposals for supplementary measurements are discussed in detail.

Kinetic Boltzmann approach adapted for modeling highly ionized matter created by x-ray irradiation of a solid.

We report on the kinetic Boltzmann approach adapted for simulations of highly ionized matter created from a solid by its x-ray irradiation. X rays can excite inner-shell electrons, which leads to the creation of deeply lying core holes. Their relaxation, especially in heavier elements, can take complicated paths, leading to a large number of active configurations. Their number can be so large that solving the set of respective evolution equations becomes computationally inefficient and another modeling approach should be used instead. To circumvent this complexity, the commonly used continuum models employ a superconfiguration scheme. Here, we propose an alternative approach which still uses "true" atomic configurations but limits their number by restricting the sample relaxation to the predominant relaxation paths. We test its reliability, performing respective calculations for a bulk material consisting of light atoms and comparing the results with a full calculation including all relaxation paths. Prospective application for heavy elements is discussed.

A comprehensive simulation framework for imaging single particles and biomolecules at the European X-ray Free-Electron Laser.

The advent of newer, brighter, and more coherent X-ray sources, such as X-ray Free-Electron Lasers (XFELs), represents a tremendous growth in the potential to apply coherent X-rays to determine the structure of materials from the micron-scale down to the Angstrom-scale. There is a significant need for a multi-physics simulation framework to perform source-to-detector simulations for a single particle imaging experiment, including (i) the multidimensional simulation of the X-ray source; (ii) simulation of the wave-optics propagation of the coherent XFEL beams; (iii) atomistic modelling of photon-material interactions; (iv) simulation of the time-dependent diffraction process, including incoherent scattering; (v) assembling noisy and incomplete diffraction intensities into a three-dimensional data set using the Expansion-Maximisation-Compression (EMC) algorithm and (vi) phase retrieval to obtain structural information. We demonstrate the framework by simulating a single-particle experiment for a nitrogenase iron protein using parameters of the SPB/SFX instrument of the European XFEL. This exercise demonstrably yields interpretable consequences for structure determination that are crucial yet currently unavailable for experiment design.

Time-resolved observation of band-gap shrinking and electron-lattice thermalization within X-ray excited gallium arsenide.

Femtosecond X-ray irradiation of solids excites energetic photoelectrons that thermalize on a timescale of a few hundred femtoseconds. The thermalized electrons exchange energy with the lattice and heat it up. Experiments with X-ray free-electron lasers have unveiled so far the details of the electronic thermalization. In this work we show that the data on transient optical reflectivity measured in GaAs irradiated with femtosecond X-ray pulses can be used to follow electron-lattice relaxation up to a few tens of picoseconds. With a dedicated theoretical framework, we explain the so far unexplained reflectivity overshooting as a result of band-gap shrinking. We also obtain predictions for a timescale of electron-lattice thermalization, initiated by conduction band electrons in the temperature regime of a few eVs. The conduction and valence band carriers were then strongly non-isothermal. The presented scheme is of general applicability and can stimulate further studies of relaxation within X-ray excited narrow band-gap semiconductors.