GAPD: a GPU‐accelerated atom‐based polychromatic diffraction simulation code

GAPD, a graphics‐processing‐unit (GPU)‐accelerated atom‐based polychromatic diffraction simulation code for direct, kinematics‐based, simulations of X‐ray/electron diffraction of large‐scale atomic systems with mono‐/polychromatic beams and arbitrary plane detector geometries, is presented. This code implements GPU parallel computation via both real‐ and reciprocal‐space decompositions. With GAPD, direct simulations are performed of the reciprocal lattice node of ultralarge systems (～5 billion atoms) and diffraction patterns of single‐crystal and polycrystalline configurations with mono‐ and polychromatic X‐ray beams (including synchrotron undulator sources), and validation, benchmark and application cases are presented.     

Chemical speciation via X‐ray emission spectra

Since the early days of X‐ray spectrometry, X‐ray emission and fluorescence spectra have been used to investigate chemical speciation, e.g. the dependence on the formal oxidation state. Laboratory wavelength‐dispersive spectrometers have adequate resolution for these measurements. However, almost all studies have employed empirical methods to interpret the spectra. We aim to place such methods on a quantitative basis by means of efficient ab initio calculations of the X‐ray emission line shapes based on a self‐consistent, real‐space Green's function approach, as implemented in the X‐ray spectroscopy code FEFF8.2. Calculations are presented for the phosphorus K‐M_{2, 3}, and the chromium L‐series emission lines for a selection of simple compounds. These lines exhibit changes depending on the oxidation state and on the neighboring atoms in the compounds that can be observed with instruments available in many XRF laboratories. The calculated spectra, as modified by convolution with a model monochromator response function, are compared with measured spectra. Simulated and measured spectra are found to be in reasonable agreement, and show that the approach has the potential to yield quantitative information about the chemical state. Copyright © 2006 John Wiley & Sons, Ltd.     

Improved charge transfer multiplet method to simulate M‐ and L‐edge X‐ray absorption spectra of metal‐centered excited states

Charge transfer multiplet (CTM) theory is a computationally undemanding and highly mature method for simulating the soft X‐ray spectra of first‐row transition metal complexes. However, CTM theory has seldom been applied to the simulation of excited‐state spectra. In this article, the CTM4XAS software package is extended to simulate M_2,3‐ and L_2,3‐edge spectra for the excited states of first‐row transition metals and also interpret CTM eigenfunctions in terms of Russell–Saunders term symbols. These new programs are used to reinterpret the recently reported excited‐state M_2,3‐edge difference spectra of photogenerated ferrocenium cations and to propose alternative assignments for the electronic state of these cations responsible for the spectroscopic features. These new programs were also used to model the L_2,3‐edge spectra of Fe^II compounds during nuclear relaxation following photoinduced spin crossover and to propose spectroscopic signatures for their vibrationally hot states.     

Vanadium K‐edge XANES in vanadium‐bearing model compounds: a full multiple scattering study

A systematic study is presented on a set of vanadium‐bearing model compounds, representative of the most common V coordination geometries and oxidation states, analysed by means of vanadium K‐edge X‐ray absorption near‐edge spectroscopy calculations in the full multiple scattering (FMS) framework. Analysis and calibration of the free parameters of the theory under the muffin‐tin approximation (muffin‐tin overlap and interstitial potential) have been carried out by fitting the experimental spectra using the MXAN program. The analysis shows a correlation of the fit parameters with the V coordination geometry and oxidation state. By making use of this correlation it is possible to approach the study of unknown V‐bearing compounds with useful preliminary information.     

Synchrotron‐based spectroscopy of X‐ray channeling through hollow capillary microchannels inside glass plates

Here, soft X‐ray synchrotron radiation transmitted through microchannel plates is studied experimentally. Fine structures of reflection and XANES Si L‐edge spectra detected on the exit of silicon glass microcapillary structures under conditions of total X‐ray reflection are presented and analyzed. The phenomenon of the interaction of channeling radiation with unoccupied electronic states and propagation of X‐ray fluorescence excited in the microchannels is revealed. Investigations of the interaction of monochromatic radiation with the inner‐shell capillary surface and propagation of fluorescence radiation through hollow glass capillary waveguides contribute to the development of novel X‐ray focusing devices in the future.     

Soft X‐ray refractive index by reconciling total electron yield with specular reflection: experimental determination of the optical constants of graphite

The complex refractive index of many materials is poorly known in the soft X‐ray range across absorption edges. This is due to saturation effects that occur there in total‐electron‐yield and fluorescence‐yield spectroscopy and that are strongest at resonance energies. Aiming to obtain reliable optical constants, a procedure that reconciles electron‐yield measurements and reflection spectroscopy by correcting these saturation effects is presented. The procedure takes into account the energy‐ and polarization‐dependence of the photon penetration depth as well as the creation efficiency for secondary electrons and their escape length. From corrected electron‐yield spectra the absorption constants and the imaginary parts of the refractive index of the material are determined. The real parts of the index are subsequently obtained through a Kramers–Kronig transformation. These preliminary optical constants are refined by simulating reflection spectra and adapting them, so that measured reflection spectra are reproduced best. The efficacy of the new procedure is demonstrated for graphite. The optical constants that have been determined for linearly polarized synchrotron light incident with p‐ and s‐geometry provide a detailed and reliable representation of the complex refractive index of the material near π‐ and σ‐resonances. They are also suitable for allotropes of graphite such as graphene.     

Finite lifetime broadening of calculated X‐ray absorption spectra: possible artefacts close to the edge

X‐ray absorption spectra calculated within an effective one‐electron approach have to be broadened to account for the finite lifetime of the core hole. For methods based on Green's function this can be achieved either by adding a small imaginary part to the energy or by convoluting the spectra on the real axis with a Lorentzian. By analyzing the Fe K‐ and L_2,3‐edge spectra it is demonstrated that these procedures lead to identical results only for energies higher than a few core‐level widths above the absorption edge. For energies close to the edge, spurious spectral features may appear if too much weight is put on broadening via the imaginary energy component. Special care should be taken for dichroic spectra at edges which comprise several exchange‐split core levels, such as the L₃‐edge of 3d transition metals.     

Soft X‐ray absorption spectroscopy and resonant inelastic X‐ray scattering spectroscopy below 100 eV: probing first‐row transition‐metal M‐edges in chemical complexes

X‐ray absorption and scattering spectroscopies involving the 3d transition‐metal K‐ and L‐edges have a long history in studying inorganic and bioinorganic molecules. However, there have been very few studies using the M‐edges, which are below 100 eV. Synchrotron‐based X‐ray sources can have higher energy resolution at M‐edges. M‐edge X‐ray absorption spectroscopy (XAS) and resonant inelastic X‐ray scattering (RIXS) could therefore provide complementary information to K‐ and L‐edge spectroscopies. In this study, M_2,3‐edge XAS on several Co, Ni and Cu complexes are measured and their spectral information, such as chemical shifts and covalency effects, are analyzed and discussed. In addition, M_2,3‐edge RIXS on NiO, NiF₂ and two other covalent complexes have been performed and different d–d transition patterns have been observed. Although still preliminary, this work on 3d metal complexes demonstrates the potential to use M‐edge XAS and RIXS on more complicated 3d metal complexes in the future. The potential for using high‐sensitivity and high‐resolution superconducting tunnel junction X‐ray detectors below 100 eV is also illustrated and discussed.     

Simultaneous small‐ and wide‐angle scattering at high X‐ray energies

Combined small‐ and wide‐angle X‐ray scattering (SAXS/WAXS) is a powerful technique for the study of materials at length scales ranging from atomic/molecular sizes (a few angstroms) to the mesoscopic regime (～1 nm to ～1 µm). A set‐up to apply this technique at high X‐ray energies (E > 50 keV) has been developed. Hard X‐rays permit the execution of at least three classes of investigations that are significantly more difficult to perform at standard X‐ray energies (8–20 keV): (i) in situ strain analysis revealing anisotropic strain behaviour both at the atomic (WAXS) as well as at the mesoscopic (SAXS) length scales, (ii) acquisition of WAXS patterns to very large q (>20 Å^?1) thus allowing atomic pair distribution function analysis (SAXS/PDF) of micro‐ and nano‐structured materials, and (iii) utilization of complex sample environments involving thick X‐ray windows and/or samples that can be penetrated only by high‐energy X‐rays. Using the reported set‐up a time resolution of approximately two seconds was demonstrated. It is planned to further improve this time resolution in the near future.     

Retrieval of the atomic displacements in the crystal from the coherent X‐ray diffraction pattern

The retrieval of spatially resolved atomic displacements is investigated via the phases of the direct(real)‐space image reconstructed from the strained crystal's coherent X‐ray diffraction pattern. It is demonstrated that limiting the spatial variation of the first‐ and second‐order spatial displacement derivatives improves convergence of the iterative phase‐retrieval algorithm for displacements reconstructions to the true solution. This approach is exploited to retrieve the displacement in a periodic array of silicon lines isolated by silicon dioxide filled trenches.     

Transmission of an X‐ray beam through a two‐dimensional photonic crystal and the Talbot effect

Results of computer simulations of the transmission of an X‐ray beam through a two‐dimensional photonic crystal as well as the propagation of an X‐ray beam in free space behind the photonic crystal are reported. The photonic crystal consists of a square lattice of silicon cylinders of diameter 0.5 µm. The amount of matter in the path of the X‐ray beam rapidly decreases at the sides of the cylinder projections. Therefore the transmission is localized near the boundaries, and appears like a channeling effect. The iterative method of computer simulations is applied. This method is similar to the multi‐slice method that is widely used in electron microscopy. It allows a solution to be obtained with acceptable accuracy. A peculiarity in the intensity distribution inside the Talbot period z_T in free space was found when the intensity is approximately equal to the initial value at a distance 0.46z_T, and it is shifted by half a period at distance 0.5z_T. The reason for this effect is the existence of a periodic phase of the wavefunction of radiation inside the intensity peaks. Simulations with zero phase do not show this effect. Symmetry rules for the Talbot effect are discussed.     

Investigation of nanoparticulate silicon as printed layers using scanning electron microscopy,transmission electron microscopy,X‐ray absorption spectroscopy and X‐ray photoelectron spectroscopy

The presence of native oxide on the surface of silicon nanoparticles is known to inhibit charge transport on the surfaces. Scanning electron microscopy (SEM) studies reveal that the particles in the printed silicon network have a wide range of sizes and shapes. High‐resolution transmission electron microscopy reveals that the particle surfaces have mainly the (111)‐ and (100)‐oriented planes which stabilizes against further oxidation of the particles. X‐ray absorption spectroscopy (XANES) and X‐ray photoelectron spectroscopy (XPS) measurements at the O 1s‐edge have been utilized to study the oxidation and local atomic structure of printed layers of silicon nanoparticles which were milled for different times. XANES results reveal the presence of the +4 (SiO₂) oxidation state which tends towards the +2 (SiO) state for higher milling times. Si 2p XPS results indicate that the surfaces of the silicon nanoparticles in the printed layers are only partially oxidized and that all three sub‐oxide, +1 (Si₂O), +2 (SiO) and +3 (Si₂O₃), states are present. The analysis of the change in the sub‐oxide peaks of the silicon nanoparticles shows the dominance of the +4 state only for lower milling times.     

Effect of gamma irradiation on X‐ray absorption and photoelectron spectroscopy of Nd‐doped phosphate glass

X‐ray absorption near‐edge structure (XANES) and X‐ray photoelectron spectroscopy (XPS) of Nd‐doped phosphate glasses have been studied before and after gamma irradiation. The intensity and the location of the white line peak of the L₃‐edge XANES of Nd are found to be dependent on the ratio O/Nd in the glass matrix. Gamma irradiation changes the elemental concentration of atoms in the glass matrix, which affects the peak intensity of the white line due to changes in the covalence of the chemical bonds with Nd atoms in the glass (structural changes). Sharpening of the Nd 3d_5/2 peak profile in XPS spectra indicates a deficiency of oxygen in the glasses after gamma irradiation, which is supported by energy‐dispersive X‐ray spectroscopy measurements. The ratio of non‐bridging oxygen to total oxygen in the glass after gamma radiation has been found to be correlated to the concentration of defects in the glass samples, which are responsible for its radiation resistance as well as for its coloration.     

Characterization of X‐ray gas attenuator plasmas by optical emission and tunable laser absorption spectroscopies

X‐ray gas attenuators are used in high‐energy synchrotron beamlines as high‐pass filters to reduce the incident power on downstream optical elements. The absorption of the X‐ray beam ionizes and heats up the gas, creating plasma around the beam path and hence temperature and density gradients between the center and the walls of the attenuator vessel. The objective of this work is to demonstrate experimentally the generation of plasma by the X‐ray beam and to investigate its spatial distribution by measuring some of its parameters, simultaneously with the X‐ray power absorption. The gases used in this study were argon and krypton between 13 and 530 mbar. The distribution of the 2p excited states of both gases was measured using optical emission spectroscopy, and the density of argon metastable atoms in the 1s₅ state was deduced using tunable laser absorption spectroscopy. The amount of power absorbed was measured using calorimetry and X‐ray transmission. The results showed a plasma confined around the X‐ray beam path, its size determined mainly by the spatial dimensions of the X‐ray beam and not by the absorbed power or the gas pressure. In addition, the X‐ray absorption showed a hot central region at a temperature varying between 400 and 1100 K, depending on the incident beam power and on the gas used. The results show that the plasma generated by the X‐ray beam plays an essential role in the X‐ray absorption. Therefore, plasma processes must be taken into account in the design and modeling of gas attenuators.     

Variational approaches to the negative-U Hubbard model for arbitrary bandfillings

Results of several variational approaches to the negative-U Hubbard model away from halffilling are presented. The approaches include charge ordered and BCS variational states as well as the Gutzwiller approximation. No evidence for a charge density wave state has been observed.     

Multiple‐element spectrometer for non‐resonant inelastic X‐ray spectroscopy of electronic excitations

A multiple‐analyser‐crystal spectrometer for non‐resonant inelastic X‐ray scattering spectroscopy installed at beamline ID16 of the European Synchrotron Radiation Facility is presented. Nine analyser crystals with bending radii R = 1 m measure spectra for five different momentum transfer values simultaneously. Using a two‐dimensional detector, the spectra given by all analysers can be treated individually. The spectrometer is based on a Rowland circle design with fixed Bragg angles of about 88°. The energy resolution can be chosen between 30–2000 meV with typical incident‐photon energies of 6–13 keV. The spectrometer is optimized for studies of valence and core electron excitations resolving both energy and momentum transfer.     

Organic cyclic difluoramino‐nitramines: infrared and Raman spectroscopy of 3,3,7,7‐tetrakis(difluoramino)octahydro 1,5‐dinitro‐1,5‐diazocine (HNFX)

We present the first vibrational structure investigation of 3,3,7,7‐tetrakis(difluoramino)octahydro‐1,5‐dinitro‐ 1,5‐diazocine (HNFX)—and, more generally, of a member of the new class of gem‐bis(difluoramino)‐substituted heterocyclic nitramine energetic materials—using combined theoretical and experimental approaches. Optimized molecular structure and vibrational spectra of the Ci… symmetry conformer constituting the HNFX crystal were computed using density functional theory methods. Fourier transform infrared and Raman spectra of HNFX crystalline samples were also collected at ambient temperature and pressure. The average deviation of calculated structural parameters from X‐ray diffraction data is ∼1% at the B3LYP/6‐311 + + G(d,p) level of theory, suggesting the absence of significant molecular distortion induced by the crystal field. Very good agreement was found between simulated and measured spectra, allowing reliable assignment of the fundamental normal modes of vibration of the HNFX crystal. Detailed analysis of the normal modes of the C–(NF₂)₂ and N–NO₂ moieties was performed due to their critical importance in the initial steps of the molecular homolytic fragmentation process. Copyright © 2009 John Wiley & Sons, Ltd.     

Residual‐density mapping and site‐selective determination of anomalous scattering factors to examine the origin of the Fe K pre‐edge peak of magnetite

The electron‐density distribution and the contribution to anomalous scattering factors for Fe ions in magnetite have been analyzed by X‐ray resonant scattering at the pre‐edge of Fe K absorption. Synchrotron X‐ray experiments were carried out using a conventional four‐circle diffractometer in the right‐handed circular polarization. Difference‐Fourier synthesis was applied with a difference in structure factors measured on and off the pre‐edge (E_on = 7.1082 keV, E_off = 7.1051 keV). Electron‐density peaks due to X‐ray resonant scattering were clearly observed for both A and B sites. The real part of the anomalous scattering factor f′ has been determined site‐independently, based on the crystal‐structure refinements, to minimize the squared residuals at the Fe K pre‐edge. The f′ values obtained at E_on and E_off are ?7.063 and ?6.682 for the A site and ?6.971 and ?6.709 for the B site, which are significantly smaller than the values of ?6.206 and ?5.844, respectively, estimated from the Kramers–Kronig transform. The f′ values at E_on are reasonably smaller than those at E_off. Our results using a symmetry‐based consideration suggest that the origin of the pre‐edge peak is Fe ions occupying both A and B sites, where p–d mixing is needed with hybridized electrons of Fe in both sites overlapping the neighbouring O atoms.     

Sorting algorithms for single‐particle imaging experiments at X‐ray free‐electron lasers

Modern X‐ray free‐electron lasers (XFELs) operating at high repetition rates produce a tremendous amount of data. It is a great challenge to classify this information and reduce the initial data set to a manageable size for further analysis. Here an approach for classification of diffraction patterns measured in prototypical diffract‐and‐destroy single‐particle imaging experiments at XFELs is presented. It is proposed that the data are classified on the basis of a set of parameters that take into account the underlying diffraction physics and specific relations between the real‐space structure of a particle and its reciprocal‐space intensity distribution. The approach is demonstrated by applying principal component analysis and support vector machine algorithms to the simulated and measured X‐ray data sets.