Invited ReviewEnergy dispersive inelastic X-ray scattering spectroscopy – A review
Graphical abstract
Introduction
When x-ray photons interact with atoms, scattering processes occur. Elastic scattering from a single isolated electron, usually named Thompson scattering, represents the simplest interaction and the theoretical equations for cross sections are of significant importance for other more complex scattering processes [1]. In the high-energy range, photons have a high probability of scatter inelastically with the external electrons; this process is the so-called Compton scattering [2]. On the other hand, at lower energies, photons interact elastically with the whole atom; this interaction is the so-called Rayleigh scattering [3]. It should be noted that the term Rayleigh scattering could have different meanings according to the context, see the discussion on this subject in [4]. In addition, elastic and inelastic scattering are frequently called coherent and incoherent scattering. Elastic or inelastic refer to preserving the energy of the incident and scattered photons. On the other hand, coherence makes reference to a more complex process, which implies amplitudes enhancement because of relative phases. In this way, some process can be elastic but not coherent [5].
A. H. Compton described an inelastic process with core (bound) electrons for the first time in 1924 [6]. Because of the similitude with the optical and UXV Raman effect, this inelastic process is frequently named X-Ray Raman scattering. X-Ray Raman scattering involves very small momentum transfer and thus mimics photoabsorption. In the non-resonant regime X-Ray Raman scattering has a very low probability. However, when the energy of the photons are close to an absorption edge, resonant conditions increase significantly the probability of occurrence. Resonant inelastic x-ray scattering (RIXS) has been also mentioned as resonant x-ray emission, resonant x-ray fluorescence, or more commonly X-ray resonant Raman scattering (RRS). Nevertheless, all these different names refer essentially the same process [7]. In this work, RIXS and RRS will be used.
RIXS can be used to establish spectroscopic techniques for the incident photon or/and the scattered photon. In particular, RIXS allows gathering information about energy, momentum, and polarization of the scattered photon. Energy, momentum, and polarization of the photons are closely related to the atomic environment due to the intrinsic excitations produced in the material under study. Most of these techniques and applications have been implemented using synchrotron sources and very high-resolution systems [8].
Immediate questions arise: Do RIXS effects affect everyday measurements? Can RIXS effects be observed in conventional systems using low-resolution devices, i.e., energy dispersive setups? Moreover, can RIXS techniques be used in this kind of experiments? This review will try to answer these questions.
As early as 1988, Jaklevic et al. [9] exposed the probable influence of resonant Raman scattering in the background of XRF spectra, as well as Karydas and Paradellis [10] later in 1998. However the most critical incident in a practical situation was reported by Pianetta et al. in 2000 [11] during TXRF analysis of metal contamination on silicon wafer surfaces. In these measurements, aluminum contaminations were determined by TXRF using tunable synchrotron radiation. The energy of the incident photons was set right above the aluminum K-edge but incidentally this energy was close below the silicon K-edge establishing a resonant condition for the Raman scattering and thus creating an unexpected background contribution below the aluminum Kα line.
In order to quantify the influence of RIXS in the XRF spectra, total RRS cross sections were needed. Theoretical cross sections can be calculated based on the theory of the inelastic scattering using the conventional algorithms, even a wave packet approach was presented by Salek in 2003 [12]. Nevertheless, experimental values were long overdue. The first report of experimental determination of RIXS cross sections was presented by Spark in 1974 [13]. Using a Cu and Mo x-ray tube and a graphite monochromator cross section of Ni, Cu, Zn, Ge and Ta were measured and compared with theoretical values. The same experimental configuration was used by Bannett et al. [14] in 1997 to obtain experimental values for Ni, Cu, Zn, and Ge. In 1979 Suortti [15] obtained theoretical and experimental absolute cross section of RRS for Cr, Mn, Fe, Ni, and Cu at energies 42 to 940 eV below the K absorption edge using a single bent graphite crystal and an x-ray tube.
The significant advantage that represent the use synchrotron radiation gave place to the determination of cross sections for more elements. Briand et al. in 1986 [16] reported measurements of Mn cross section in KMnO4 compounds at the LURE facility. Nickel cross section excited with photons down to 150 eV below the absorption K-edge were obtained by Manninen et al. [17] in 1986 at Lure. Determinations of cross sections for Cu, Zn and Ho were carried out by Hämäläinen et al. in 1989 [18] at the Daresbury storage ring using and excitation energy from 1 keV below the absorption edge to 300 eV above the absorption edge.
More recently in 1997 and 2002, there has been also reported measurements of K and L RRS cross sections with proton induced monochromatic x-ray beams by Karydas and collaborators [19,20]. In addition, a pioneer work of 2002, by Karydas et al., explored the possibility of variations in the RIXS peak centroid for different vanadium oxidation states [21].
Finally, monochromatic synchrotron radiation was used to study the RRS effect on pure samples of Mn, Fe, Cu and Zn by Sánchez et al. [22] in 2006 at the LNLS facility (Campinas Brazil). Energy scans were carried out in different ranges of energy near the absorption edge of the target elements. In this work for the first time an experimental parametrization of the RIXS cross section as a function of the incident energy was obtained. The same experimental configuration was used later in 2008 by Valentinuzzi et al. [23] to obtain a comparative analysis of the RRS cross sections of pure samples and oxides. In addition, during the last two decades, some other works have presented RIXS cross sections of several elements utilizing different sources as well [10,21,[24], [25], [26], [27], [28]].
A complete determination of the oxidation state by Energy-Dispersive Resonant-Raman Scattering Spectroscopy was reported in 2011 by Leani et al. [29] where pure samples of transition metals (Cu, Fe, Mn) and different oxides of them (CuO, Cu2O, Fe2O3, Mn2O3, MnO2) were irradiated with monochromatic synchrotron radiation below their absorption edges to inspect the RRS emissions. Later in the same year Leani et al. [30] presented first results of determination of the oxidation state of several Fe samples by means of resonant Raman scattering spectroscopy using monochromatic synchrotron radiation with an energy-dispersive system. Measurements of samples of Fe, FeO, Fe2O3 and Fe3O4 were carried out at the XRF station of the D09B-XRF beamline at Brazilian synchrotron facility (LNLS, Campinas, Brazil).
The availability of theoretical and experimental values of RIXS cross sections in a variety of elements and their parametrization in a wide range of energies below the absorption edges gave, finally, the possibility to estimate the influence of RIXS on XRF spectra and their consequences. It was done by Sánchez et al. [29] in 2012 reporting theoretical calculations of the influence of resonant Raman scattering on the quantification of XRF Analysis.
This review will present an overview of Energy Dispersive Inelastic X-ray Scattering (EDIXS) spectroscopy. A theoretical frame, a description of the utilized multivariate methods and a set of applications in a variety of experimental conditions are provided and discussed.
Due to the use of energy dispersive detection systems and the particular features of this spectroscopic tool (as fast acquisition, low self-absorption and the avoidance of any energy scan during the measurements) EDIXS offers the chance of studying electron density changes in a variety of samples at the nano- and micro-scale with high sensitivity, allowing a characterization difficult, or even impossible, to achieve by conventional X-ray techniques.
The possibilities of applying EDIXS beyond a synchrotron facility, for example with an X-ray tube in a conventional laboratory, portable XRF spectrometers for in-situ analysis and even pulsed X-ray sources are clear and considered as well.
Section snippets
Theoretical approach
Starting with the nonrelativistic limit, the coupling of the electromagnetic field to the scattering-electron system can be represented by the following Hamiltonian [31],where the summation is over the electrons of the scattering system, A is the vector potential of the electromagnetic field and p is the momentum operator of the scattering electrons. In addition, e and m represent, respectively, the charge and mass of the electron and c is the speed of light.
Taking into
Data/spectra analysis
As can be understood from the previous sections, the chemical state information is encrypted in the small damped oscillations of the low energy tail of the RIXS peak. Nevertheless, the task of extracting information from such small variations in a spectrum seems like a difficult one if considering of doing it so by simple observation. Some first attempts in extracting this information have been performed using Fast Fourier Transform based Algorithms [43], which have succeeded in the task, but
Experimental applications
Due to the versatility of spectroscopic techniques involving emission processes, EDIXS can be implemented in a variety of irradiation geometries and experimental setups commonly used by conventional techniques, as XRF.
It should be noticed that the absorption effect for the RIXS process is relatively weak compared with other spectroscopic techniques, since both the incident and emitted photon energies are below the K absorption edge of the element under study. In this way, the need of
Final remarks and perspectives
As can be seen, the existing patterns present in the fine structure of the RIXS peaks allow the discernment between the measured compounds of the studied elements. Since the first applications of this novel tool, the results suggested the possibility of structural characterization by means of RIXS using the several advantages of an energy dispersive system combined with synchrotron radiation. The addition of multivariate methods for the data examination allowed the implementation of a reliable
Acknowledgments
The authors would like to thank the National Scientific and Technical Research Council (CONICET) of Argentina and the National University of Córdoba of the same country.
References (74)
An Introduction to the Passage of Energetic Particles Through Matter
(2007)Compton Effect
(1958)The Atomic Nucleus
(1955)Rayleigh scattering
Phys. Today
(1982)A general quantum theory of the wave-length of scattered X-rays
Phys. Rev.
(1924)- et al.
Raman emission by X-ray scattering: proceedings of the international conference
(1996) - et al.
Resonant inelastic x-ray scattering studies of elementary excitations
Rev. Mod. Phys.
(2011) - et al.
Resonant Raman scattering as a source of increased background in synchrotron excited x-ray fluorescence
Anal. Chem.
(1988) - et al.
Proton induced monochromatic X-rays: a technique for solving interference problems in X-ray fluorescence analysis
AIP Press
(1998)
Application of synchrotron radiation to TXRF analysis of metal contamination on silicon wafer surfaces
Thin Solid Films
A wave-packet technique to simulate resonant X-ray scattering cross sections
Comput. Phys. Commun.
Inelastic resonance emission of x rays: anomalous scattering associated with anomalous dispersion
Phys. Rev. Lett.
Resonant X-ray Raman scattering and the infrared divergence of the Compton effect
Phys. Rev. A
Scattering of X-rays near the K absorption edge I. fluorescence and resonant Raman scattering in transition metals
Phys. Status Solidi B
X-Ray Raman and compton scattering in the vicinity of a deep atomic level
Phys. Rev. Lett.
X-ray resonant Raman cross section and yield in nickel
Phys. Rev. B
Resonant Raman scattering and inner-shell hole widths in Cu, Zn and Ho
J. Phys. Condens. Matter
Measurement of KL and LM resonant Raman scattering cross sections with a proton-induced x-ray beam
J. Phys. B Atomic Mol. Phys.
Proton induced monochromatic X-ray beams: a versatile source for resonant Raman scattering studies
Nucl. Instrum. Methods Phys. Res. Sect. B Beam Interact. Mater. At.
Chemical state speciation by resonant Raman scattering
J. Phys. Condens. Matter
X-ray resonant Raman scattering cross sections of Mn, Fe, Cu and Zn
J. Phys. B Atomic Mol. Phys.
Comparative analysis of the resonant Raman cross sections of pure samples and oxides
X-Ray Spectrom. Int. J.
High-resolution study of the x-ray resonant Raman scattering process around the 1 s absorption edge for aluminium, silicon, and their oxides
Phys. Rev. A
High-resolution study of x-ray resonant Raman scattering at the K edge of silicon
Phys. Rev. Lett.
Absolute determination of cross sections for resonant Raman scattering on silicon
Phys. Rev. A
X-ray resonant Raman scattering on Ni employing polarized and unpolarized exciting radiation
Spectrochim. Acta B
Resonant Raman scattering of polarized and unpolarized x-ray radiation from Mg, Al, and Si
Phys. Rev. A
Determination of the oxidation state by resonant-Raman scattering spectroscopy
J. Anal. Spectrom.
Chemical environment determination of iron oxides using RRS spectroscopy
X-Ray Spectrom.
Handbook of Synchrotron Radiation
Electronic excitations investigated by inelastic x-ray scattering spectroscopy
J. Phys. Condens. Matter
Resonant inelastic x-ray scattering spectra for electrons in solids
Rev. Mod. Phys.
Inelastic scattering by electronic excitations
Handb. Synchrotron Radiat.
Resonant x-ray Raman scattering studies using synchrotron radiation
Phys. Rev. B
X-Ray resonant Raman scattering: observation of characteristic radiation narrower than the lifetime width
Phys. Rev. Lett.
Statistical theory of electronic Raman resonance scattering by oriented atoms
J. Phys. B At. Mol. Phys.
Cited by (16)
Discriminating Chemical States of Rare Earth/heavy Elements by EDIXS spectroscopy through L-lines inspection
2023, Radiation Physics and ChemistryAdvanced scanning electron microscopy and microanalysis: Applications to nanomaterials
2023, Encyclopedia of NanomaterialsPossibilities of spatially-resolved energy dispersive inelastic X-ray scattering (EDIXS) spectroscopy for painting characterization
2022, Spectrochimica Acta - Part B Atomic SpectroscopyCitation Excerpt :The region of interest (ROI) for applying multivariate methods for the characterization procedure is also indicated. The criteria for a proper selection of the ROI is explained in previous works (see for example [22]), spreading from the channel of maximum amplitude (centroid of the RIXS peak) to a few hundreds eV toward lower energies. Regarding the painted crosses on paper, and with the aim of characterizing the chemical state of Cu in the intersection paint spots, a Machine Learning approach was applied on the tail of the RIXS spectra, being normalized before applying a k Nearest Neighbor (k−NN) algorithm [35].
Facile synthesis of reduced graphene oxide encapsulated selenium nanoparticles prepared by hydrothermal method for acetone gas sensors
2020, Chemical Physics LettersCitation Excerpt :Hence, chemical composition has been proved the existence of elements C, O, and Se. The atomic percentages were nearly 90.30%, 5.63%, and 4.07%, respectively, and the mass ratios are 72.26%, 6.22%, and 21.52%, respectively [48]. The EDS spectrums revealed that the as-prepared Se NPs and rGO-Se nanocomposite were successfully synthesized free from any other impurities.
Assessment of the physical properties, and the hydrogen, carbon, and oxygen content in plastics using energy-dispersive X-ray fluorescence spectrometry
2020, Spectrochimica Acta - Part B Atomic SpectroscopyCitation Excerpt :The authors of this work did not employ multivariate spectral processing, but they used the intensities of scattered Cu Kα and Pd Kα lines to assess the content of light elements. Some other interesting examples using scattered radiation signals on XRF can be found in the recent review by Leani et al. [9]. Further developments in this field are very interesting in order to broaden the number of XRF-detectable elements and to improve the performance capabilities of XRF spectrometry.