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.     

X‐ray‐Raman‐scattering‐based EXAFS beyond the dipole limit

X‐ray Raman scattering (XRS) provides a bulk‐sensitive method of measuring the extended X‐ray absorption fine structure (EXAFS) of soft X‐ray absorption edges. Accurate measurements and data analysis procedures for the determination of XRS‐EXAFS of polycrystalline diamond are described. The contributions of various angular‐momentum components beyond the dipole limit to the atomic background and the EXAFS oscillations are incorporated using self‐consistent real‐space multiple‐scattering calculations. The properly extracted XRS‐EXAFS oscillations are in good agreement with calculations and earlier soft X‐ray EXAFS results. It is shown, however, that under certain conditions multiple‐scattering contributions to XRS‐EXAFS deviate from those in standard EXAFS, leading to noticeable changes in the real‐space signal at higher momentum transfers owing to non‐dipole contributions. These results pave the way for the accurate application of XRS‐EXAFS to previously inaccessible light‐element systems.     

A large‐solid‐angle X‐ray Raman scattering spectrometer at ID20 of the European Synchrotron Radiation Facility

An end‐station for X‐ray Raman scattering spectroscopy at beamline ID20 of the European Synchrotron Radiation Facility is described. This end‐station is dedicated to the study of shallow core electronic excitations using non‐resonant inelastic X‐ray scattering. The spectrometer has 72 spherically bent analyzer crystals arranged in six modular groups of 12 analyzer crystals each for a combined maximum flexibility and large solid angle of detection. Each of the six analyzer modules houses one pixelated area detector allowing for X‐ray Raman scattering based imaging and efficient separation of the desired signal from the sample and spurious scattering from the often used complicated sample environments. This new end‐station provides an unprecedented instrument for X‐ray Raman scattering, which is a spectroscopic tool of great interest for the study of low‐energy X‐ray absorption spectra in materials under in situ conditions, such as in operando batteries and fuel cells, in situ catalytic reactions, and extreme pressure and temperature conditions.     

A high‐energy‐resolution resonant inelastic X‐ray scattering spectrometer at ID20 of the European Synchrotron Radiation Facility

An end‐station for resonant inelastic X‐ray scattering and (resonant) X‐ray emission spectroscopy at beamline ID20 of ESRF – The European Synchrotron is presented. The spectrometer hosts five crystal analysers in Rowland geometry for large solid angle collection and is mounted on a rotatable arm for scattering in both the horizontal and vertical planes. The spectrometer is optimized for high‐energy‐resolution applications, including partial fluorescence yield or high‐energy‐resolution fluorescence detected X‐ray absorption spectroscopy and the study of elementary electronic excitations in solids. In addition, it can be used for non‐resonant inelastic X‐ray scattering measurements of valence electron excitations.     

Momentum‐resolved resonant inelastic X‐ray scattering on a single crystal under high pressure

A single‐crystal momentum‐resolved resonant inelastic X‐ray scattering (RIXS) experiment under high pressure using an originally designed diamond anvil cell (DAC) is reported. The diamond‐in/diamond‐out geometry was adopted with both the incident and scattered beams passing through a 1 mm‐thick diamond. This enabled us to cover wide momentum space keeping the scattering angle condition near 90°. Elastic and inelastic scattering from the diamond was drastically reduced using a pinhole placed after the DAC. Measurement of the momentum‐resolved RIXS spectra of Sr_2.5Ca_11.5Cu₂₄O₄₁ at the Cu K‐edge was thus successful. Though the inelastic intensity becomes weaker by two orders than the ambient pressure, RIXS spectra both at the center and the edge of the Brillouin zone were obtained at 3 GPa and low‐energy electronic excitations of the cuprate were found to change with pressure.     

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.     

Highly efficient beamline and spectrometer for inelastic soft X‐ray scattering at high resolution

The design, construction and commissioning of a beamline and spectrometer for inelastic soft X‐ray scattering at high resolution in a highly efficient system are presented. Based on the energy‐compensation principle of grating dispersion, the design of the monochromator–spectrometer system greatly enhances the efficiency of measurement of inelastic soft X‐rays scattering. Comprising two bendable gratings, the set‐up effectively diminishes the defocus and coma aberrations. At commissioning, this system showed results of spin‐flip, d–d and charge‐transfer excitations of NiO. These results are consistent with published results but exhibit improved spectral resolution and increased efficiency of measurement. The best energy resolution of the set‐up in terms of full width at half‐maximum is 108 meV at an incident photon energy tuned about the Ni L₃‐edge.     

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.     

A microfocus X‐ray fluorescence beamline at Indus‐2 synchrotron radiation facility

A microfocus X‐ray fluorescence spectroscopy beamline (BL‐16) at the Indian synchrotron radiation facility Indus‐2 has been constructed with an experimental emphasis on environmental, archaeological, biomedical and material science applications involving heavy metal speciation and their localization. The beamline offers a combination of different analytical probes, e.g. X‐ray fluorescence mapping, X‐ray microspectroscopy and total‐external‐reflection fluorescence characterization. The beamline is installed on a bending‐magnet source with a working X‐ray energy range of 4–20 keV, enabling it to excite K‐edges of all elements from S to Nb and L‐edges from Ag to U. The optics of the beamline comprises of a double‐crystal monochromator with Si(111) symmetric and asymmetric crystals and a pair of Kirkpatrick–Baez focusing mirrors. This paper describes the performance of the beamline and its capabilities with examples of measured results.     

A novel X‐ray diffractometer for studies of liquid–liquid interfaces

The study of liquid–liquid interfaces with X‐ray scattering methods requires special instrumental considerations. A dedicated liquid surface diffractometer employing a tilting double‐crystal monochromator in Bragg geometry has been designed. This diffractometer allows reflectivity and grazing‐incidence scattering measurements of an immobile mechanically completely decoupled liquid sample, providing high mechanical stability. The available energy range is from 6.4 to 29.4 keV, covering many important absorption edges. The instrument provides access in momentum space out to 2.54 Å^?1 in the surface normal and out to 14.8 Å^?1 in the in‐plane direction at 29.4 keV. Owing to its modular design the diffractometer is also suitable for heavy apparatus such as vacuum chambers. The instrument performance is described and examples of X‐ray reflectivity studies performed under in situ electrochemical control and on biochemical model systems are given.     

Real‐space multiple‐scattering Hubbard model calculations for d‐ and f‐state materials

Calculations are presented of the electronic structure and X‐ray spectra of materials with correlated d‐ and f‐electron states based on the Hubbard model, a real‐space multiple‐scattering formalism and a rotationally invariant local density approximation. Values of the Hubbard parameter are calculated ab initio using the constrained random‐phase approximation. The combination of the real‐space Green's function with Hubbard model corrections provides an efficient approach to describe localized correlated electron states in these systems, and their effect on core‐level X‐ray spectra. Results are presented for the projected density of states and X‐ray absorption spectra for transition metal‐ and lanthanide‐oxides. Results are found to be in good agreement with experiment.     

On the correlation between the X‐ray absorption chemical shift and the formal valence state in mixed‐valence manganites

Here the correlation between the chemical shift in X‐ray absorption spectroscopy, the geometrical structure and the formal valence state of the Mn atom in mixed‐valence manganites are discussed. It is shown that this empirical correlation can be reliably used to determine the formal valence of Mn, using either X‐ray absorption spectroscopy or resonant X‐ray scattering techniques. The difficulties in obtaining a reliable comparison between experimental XANES spectra and theoretical simulations on an absolute energy scale are revealed. It is concluded that the contributions from the electronic occupation and the local structure to the XANES spectra cannot be separated either experimentally or theoretically. In this way the geometrical and electronic structure of the Mn atom in mixed‐valence manganites cannot be described as a bimodal distribution of the formal integer Mn³⁺ and Mn⁴⁺ valence states corresponding to the undoped references.     

Collimating Montel mirror as part of a multi‐crystal analyzer system for resonant inelastic X‐ray scattering

Advances in resonant inelastic X‐ray scattering (RIXS) have come in lockstep with improvements in energy resolution. Currently, the best energy resolution at the Ir L₃‐edge stands at ～25 meV, which is achieved using a diced Si(844) spherical crystal analyzer. However, spherical analyzers are limited by their intrinsic reflection width. A novel analyzer system using multiple flat crystals provides a promising way to overcome this limitation. For the present design, an energy resolution at or below 10 meV was selected. Recognizing that the angular acceptance of flat crystals is severely limited, a collimating element is essential to achieve the necessary solid‐angle acceptance. For this purpose, a laterally graded, parabolic, multilayer Montel mirror was designed for use at the Ir L₃‐absorption edge. It provides an acceptance larger than 10 mrad, collimating the reflected X‐ray beam to smaller than 100 µrad, in both vertical and horizontal directions. The performance of this mirror was studied at beamline 27‐ID at the Advanced Photon Source. X‐rays from a diamond (111) monochromator illuminated a scattering source of diameter 5 µm, generating an incident beam on the mirror with a well determined divergence of 40 mrad. A flat Si(111) crystal after the mirror served as the divergence analyzer. From X‐ray measurements, ray‐tracing simulations and optical metrology results, it was established that the Montel mirror satisfied the specifications of angular acceptance and collimation quality necessary for a high‐resolution RIXS multi‐crystal analyzer system.     

Liquid X‐ray scattering with a pink‐spectrum undulator

X‐ray scattering from a liquid using the spectrum from the undulator fundamental is examined as a function of the bandwidth of the spectrum. The synchrotron‐generated X‐ray spectrum from an undulator is `pink', i.e. quasi‐monochromatic but having a saw‐tooth‐shaped spectrum with a bandwidth from 1 to 15%. It is shown that features in S(q) are slightly shifted and dampened compared with strictly monochromatic data. In return, the gain in intensity is 250–500 which makes pink beams very important for time‐resolved experiments. The undulator spectrum is described by a single exponential with a low‐energy tail. The tail shifts features in the scattering function towards high angles and generates a small reduction in amplitude. The theoretical conclusions are compared with experiments. The r‐resolved Fourier transformed signals are discussed next. Passing from q‐ to r‐space requires a sin‐Fourier transform. The Warren convergence factor is introduced in this calculation to suppress oscillatory artifacts from the finite q_M in the data. It is shown that the deformation of r‐resolved signals from the pink spectrum is small compared with that due to the Warren factor. The q‐resolved and the r‐resolved pink signals thus behave very differently.     

Image contrast in X‐ray reflection interface microscopy: comparison of data with model calculations and simulations

The contrast mechanism for imaging molecular‐scale features on solid surfaces is described for X‐ray reflection interface microscopy (XRIM) through comparison of experimental images with model calculations and simulated measurements. Images of elementary steps show that image contrast is controlled by changes in the incident angle of the X‐ray beam with respect to the sample surface. Systematic changes in the magnitude and sign of image contrast are asymmetric for angular deviations of the sample from the specular reflection condition. No changes in image contrast are observed when defocusing the condenser or objective lenses. These data are explained with model structure‐factor calculations that reproduce all of the qualitative features observed in the experimental data. These results provide new insights into the image contrast mechanism, including contrast reversal as a function of incident angle, the sensitivity of image contrast to step direction (i.e. up versus down), and the ability to maximize image contrast at almost any scattering condition defined by the vertical momentum transfer, Q_z. The full surface topography can then, in principle, be recovered by a series of images as a function of incident angle at fixed momentum transfer. Inclusion of relevant experimental details shows that the image contrast magnitude is controlled by the intersection of the reciprocal‐space resolution function (i.e. controlled by numerical aperture of the condenser and objective lenses) and the spatially resolved interfacial structure factor of the object being imaged. Together these factors reduce the nominal contrast for a step near the specular reflection condition to a value similar to that observed experimentally. This formalism demonstrates that the XRIM images derive from limited aperture contrast, and explains how non‐zero image contrast can be obtained when imaging a pure phase object corresponding to the interfacial topography.     

X‐ray Raman spectroscopy of lithium‐ion battery electrolyte solutions in a flow cell

The effects of varying LiPF₆ salt concentration and the presence of lithium bis(oxalate)borate additive on the electronic structure of commonly used lithium‐ion battery electrolyte solvents (ethylene carbonate–dimethyl carbonate and propylene carbonate) have been investigated. X‐ray Raman scattering spectroscopy (a non‐resonant inelastic X‐ray scattering method) was utilized together with a closed‐circle flow cell. Carbon and oxygen K‐edges provide characteristic information on the electronic structure of the electrolyte solutions, which are sensitive to local chemistry. Higher Li⁺ ion concentration in the solvent manifests itself as a blue‐shift of both the π* feature in the carbon edge and the carbonyl π* feature in the oxygen edge. While these oxygen K‐edge results agree with previous soft X‐ray absorption studies on LiBF₄ salt concentration in propylene carbonate, carbon K‐edge spectra reveal a shift in energy, which can be explained with differing ionic conductivities of the electrolyte solutions.     

Feasibility of in‐line instruments for high‐resolution inelastic X‐ray scattering

Inelastic X‐ray scattering instruments in operation at third‐generation synchrotron radiation facilities are based on backreflections from perfect silicon crystals. This concept reaches back to the very beginnings of high‐energy‐resolution X‐ray spectroscopy and has several advantages but also some inherent drawbacks. In this paper an alternate path is investigated using a different concept, the `M⁴ instrument'. It consists of a combination of two in‐line high‐resolution monochromators, focusing mirrors and collimating mirrors. Design choices and performance estimates in comparison with existing conventional inelastic X‐ray scattering instruments are presented.     

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.     

High‐energy‐resolution diced spherical quartz analyzers for resonant inelastic X‐ray scattering

A novel diced spherical quartz analyzer for use in resonant inelastic X‐ray scattering (RIXS) is introduced, achieving an unprecedented energy resolution of 10.53 meV at the Ir L₃ absorption edge (11.215 keV). In this work the fabrication process and the characterization of the analyzer are presented, and an example of a RIXS spectrum of magnetic excitations in a Sr₃Ir₂O₇ sample is shown.     

An X‐ray Raman spectrometer for EXAFS studies on minerals: bent Laue spectrometer with 20 keV X‐rays

An X‐ray Raman spectrometer for studies of local structures in minerals is discussed. Contrary to widely adopted back‐scattering spectrometers using ≤10 keV X‐rays, a spectrometer utilizing ～20 keV X‐rays and a bent Laue analyzer is proposed. The 20 keV photons penetrate mineral samples much more deeply than 10 keV photons, so that high intensity is obtained owing to an enhancement of the scattering volume. Furthermore, a bent Laue analyzer provides a wide band‐pass and a high reflectivity, leading to a much enhanced integrated intensity. A prototype spectrometer has been constructed and performance tests carried out. The oxygen K‐edge in SiO₂ glass and crystal (α‐quartz) has been measured with energy resolutions of 4 eV (EXAFS mode) and 1.3 eV (XANES mode). Unlike methods previously adopted, it is proposed to determine the pre‐edge curve based on a theoretical Compton profile and a Monte Carlo multiple‐scattering simulation before extracting EXAFS features. It is shown that the obtained EXAFS features are reproduced fairly well by a cluster model with a minimal set of fitting parameters. The spectrometer and the data processing proposed here are readily applicable to high‐pressure studies.