Journal articles on the topic 'X-ray Raman scattering'

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1

Huotari, Simo. "X-ray Raman scattering spectroscopy." Acta Crystallographica Section A Foundations and Advances 70, a1 (August 5, 2014): C219. http://dx.doi.org/10.1107/s2053273314097800.

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For elements with low atomic number, or shallow absorption edges falling in the energy range below ~1 keV, x-ray absorption studies are often limited by surface sensitivity and the necessity of a vacuum environment, making bulk-sensitive measurements and for example studies of liquids difficult. An exciting alternative is provided by X-ray Raman scattering (XRS) spectroscopy. It is used to measure a photon-in-photon-out process, where a hard x-ray photon loses only part of its energy creating an excitation of an inner core electron. As such, it is the x-ray analogue of electron energy loss spectroscopy. The advantage of XRS is that the incident photon energy can be chosen freely and thus low-energy absorption edges can be studied with high-energy X-rays. Thus XRS is becoming increasingly popular since it allows for bulk-sensitive measurements of inner core spectra where the corresponding x-ray absorption threshold falls into the soft x-ray regime. This lifts all constraints on the sample environment inherent to soft x-ray studies, and offers access to bulk-sensitive information on solids, liquids and gases as well as systems in enclosed sample environments such as high-pressure cells. For example the microscopic structure of water within the supercritical regime has been recently studied using the oxygen K-edge excitation spectra measured by XRS, yielding new information on the hydrogen-bond network of water in extreme conditions [1]. Another important feature of XRS is that it allows for other than dipole transitions to be studied, thanks to an practically unlimited range of momentum transfer offered by hard x-rays. These higher order multipole excitations can yield novel information on the electronic structure, not accessible by many other spectroscopies [2]. The availability of XRS instruments at third-generation synchrotron radiation sources has made highly accurate XRS measurements possible. XRS can be even used as a contrast mechanism in three-dimensional X-ray imaging [3]. In this contribution, the capabilities of XRS and recent examples of novel studies allowed by it will be reviewed.
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2

Gel'mukhanov, Faris, and Hans Ågren. "Resonant X-ray Raman scattering." Physics Reports 312, no. 3-6 (May 1999): 87–330. http://dx.doi.org/10.1016/s0370-1573(99)00003-4.

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3

Gel’mukhanov, Faris, Paweł Sałek, Timofei Privalov, and Hans Ågren. "Duration of x-ray Raman scattering." Physical Review A 59, no. 1 (January 1, 1999): 380–89. http://dx.doi.org/10.1103/physreva.59.380.

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4

Tohji, Kazuyuki, and Yasuo Udagawa. "Observation of X-ray Raman scattering." Physica B: Condensed Matter 158, no. 1-3 (June 1989): 550–52. http://dx.doi.org/10.1016/0921-4526(89)90384-0.

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5

Huotari, S., Ch J. Sahle, Ch Henriquet, A. Al-Zein, K. Martel, L. Simonelli, R. Verbeni, et al. "A large-solid-angle X-ray Raman scattering spectrometer at ID20 of the European Synchrotron Radiation Facility." Journal of Synchrotron Radiation 24, no. 2 (February 16, 2017): 521–30. http://dx.doi.org/10.1107/s1600577516020579.

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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.
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6

Harada, Y., H. Ishii, M. Fujisawa, Y. Tezuka, S. Shin, M. Watanabe, Y. Kitajima, and A. Yagishita. "Spectrometer for polarized soft X-ray Raman scattering." Journal of Synchrotron Radiation 5, no. 3 (May 1, 1998): 1013–15. http://dx.doi.org/10.1107/s0909049597019481.

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An experimental system for polarized soft X-ray Raman scattering spectroscopy has been constructed. The soft X-ray spectrometer is based on the Rowland circle geometry with a holographic spherical grating. Three types of gratings are used to cover the energy range from 18 eV to 1200 eV. According to a ray-trace simulation, the resolution is expected to be 200 meV at 700 eV by using a 10 µm slit width. The polarized and depolarized soft X-ray Raman scattering spectra can be measured by rotating the soft X-ray spectrometer around the axis of the incident beam. Preliminary measurements of polarized and depolarized spectra were accomplished at undulator beamline BL-2C of the Photon Factory.
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7

Sałek, P., A. Baev, F. Gel'mukhanov, and H. Ågren. "Dynamical properties of X-ray Raman scattering." Phys. Chem. Chem. Phys. 5, no. 1 (2003): 1–11. http://dx.doi.org/10.1039/b209717f.

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8

Gel’mukhanov, Faris, Paweł Sałek, Anatoly Shalagin, and Hans Ågren. "X-ray Raman scattering under pulsed excitation." Journal of Chemical Physics 112, no. 13 (April 2000): 5593–603. http://dx.doi.org/10.1063/1.481134.

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9

Krisch, M. H., F. Sette, C. Masciovecchio, and R. Verbeni. "X-ray resonant Raman scattering from Gd3Fe5O12." Journal of Electron Spectroscopy and Related Phenomena 86, no. 1-3 (August 1997): 159–64. http://dx.doi.org/10.1016/s0368-2048(97)00062-5.

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10

Gel'mukhanov, F. K., and H. Ågren. "Nuclear dynamics in X-ray Raman scattering." Applied Physics A: Materials Science & Processing 65, no. 2 (August 1, 1997): 123–30. http://dx.doi.org/10.1007/s003390050553.

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11

Carra, Paolo, Michele Fabrizio, and B. T. Thole. "High Resolution X-Ray Resonant Raman Scattering." Physical Review Letters 74, no. 18 (May 1, 1995): 3700–3703. http://dx.doi.org/10.1103/physrevlett.74.3700.

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12

Gel'mukhanov, Faris, and Hans Agren. "ChemInform Abstract: Resonant X-Ray Raman Scattering." ChemInform 30, no. 35 (June 13, 2010): no. http://dx.doi.org/10.1002/chin.199935321.

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13

Rohringer, Nina. "X-ray Raman scattering: a building block for nonlinear spectroscopy." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, no. 2145 (April 2019): 20170471. http://dx.doi.org/10.1098/rsta.2017.0471.

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Ultraintense X-ray free-electron laser pulses of attosecond duration can enable new nonlinear X-ray spectroscopic techniques to observe coherent electronic motion. The simplest nonlinear X-ray spectroscopic concept is based on stimulated electronic X-ray Raman scattering. We present a snapshot of recent experimental achievements, paving the way towards the goal of realizing nonlinear X-ray spectroscopy. In particular, we review the first proof-of-principle experiments, demonstrating stimulated X-ray emission and scattering in atomic gases in the soft X-ray regime and first results of stimulated hard X-ray emission spectroscopy on transition metal complexes. We critically asses the challenges that have to be overcome for future successful implementation of nonlinear coherent X-ray Raman spectroscopy. This article is part of the theme issue ‘Measurement of ultrafast electronic and structural dynamics with X-rays’.
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14

KRISCH, MICHAEL, and FRANCESCO SETTE. "X-RAY RAMAN SCATTERING FROM LOW Z MATERIALS." Surface Review and Letters 09, no. 02 (April 2002): 969–76. http://dx.doi.org/10.1142/s0218625x02001689.

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X-ray Raman scattering from core electrons of low Z materials provides an alternative to soft X-ray absorption spectroscopy in cases where (i) exotic final states will be probed, (ii) the penetrating power of hard X rays is needed to study bulk properties, and (iii) when systems under high pressure are studied. The theoretical background and experimental requirements are discussed. The present capabilities of the technique are illustrated by two experiments, performed on the inelastic X ray scattering beamlines at the European Synchrotron Radiation Facility.
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15

Udagawa, Yasuo, and Kazuyuki Tohji. "X-ray raman scattering. A substitute for soft X-ray EXAFS." Bulletin of the Japan Institute of Metals 27, no. 11 (1988): 878–84. http://dx.doi.org/10.2320/materia1962.27.878.

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16

Hirose, Raita, Taiyo Yoshioka, Hiroko Yamamoto, Kummetha Raghunatha Reddy, Daisuke Tahara, Kensaku Hamada, and Kohji Tashiro. "In-house simultaneous collection of small-angle X-ray scattering, wide-angle X-ray diffraction and Raman scattering data from polymeric materials." Journal of Applied Crystallography 47, no. 3 (May 10, 2014): 922–30. http://dx.doi.org/10.1107/s1600576714006724.

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An in-house X-ray scattering system, which can simultaneously measure small-angle X-ray scattering (SAXS) and wide-angle X-ray diffraction (WAXD) data, as well Raman scattering data, has been developed to study the phase transitions of polymeric materials. To date, these types of measurements have been limited to synchrotron radiation. The present system is an in-house SAXS system combined with a WAXD detector and a Raman spectrometer. A rotating-anode X-ray generator and multilayer optic are employed to provide a high-flux X-ray beam. Two two-dimensional hybrid pixel detectors are utilized for the rapid-scan time-resolved SAXS and WAXD measurements. The Raman unit consists of a compact probe with a near-infrared excitation laser operating at a wavelength of 1064 nm. This long-wavelength laser produces less fluorescence than conventional excitation lasers with wavelengths of 532 or 785 nm. The performance of this system was tested by investigating the thermally induced ferroelectric phase transition of vinylidene fluoride–trifluoroethylene (VDF-TrFE) copolymers. It has been demonstrated that the combination of SAXS, WAXD and Raman techniques gives useful information for revealing the relationship between the structural change in the crystal lattice and the morphological change in the lamellar stacking mode in polymer samples of complicated hierarchical structure.
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17

Lehmkühler, Felix, Yury Forov, Thomas Büning, Christoph J. Sahle, Ingo Steinke, Karin Julius, Thomas Buslaps, Metin Tolan, Mikko Hakala, and Christian Sternemann. "Intramolecular structure and energetics in supercooled water down to 255 K." Physical Chemistry Chemical Physics 18, no. 9 (2016): 6925–30. http://dx.doi.org/10.1039/c5cp07721d.

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18

Weis, Christopher, Georg Spiekermann, Christian Sternemann, Manuel Harder, György Vankó, Valerio Cerantola, Christoph J. Sahle, et al. "Combining X-ray Kβ1,3, valence-to-core, and X-ray Raman spectroscopy for studying Earth materials at high pressure and temperature: the case of siderite." Journal of Analytical Atomic Spectrometry 34, no. 2 (2019): 384–93. http://dx.doi.org/10.1039/c8ja00247a.

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19

TOHJI, Kazuyuki, and Yasuo UDAGAWA. "Present aspects of X-ray Raman scattering measurement." Journal of the Spectroscopical Society of Japan 35, no. 1 (1986): 72–73. http://dx.doi.org/10.5111/bunkou.35.72.

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20

UDAGAWA, Yasuo. "Local structure analysis by X-ray raman scattering." Nihon Kessho Gakkaishi 31, no. 1 (1989): 24–26. http://dx.doi.org/10.5940/jcrsj.31.24.

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21

Gel'mukhanov, Faris, and Hans Ågren. "X-ray Raman scattering involving electronic continuum resonances." Journal of Physics B: Atomic, Molecular and Optical Physics 29, no. 13 (July 14, 1996): 2751–62. http://dx.doi.org/10.1088/0953-4075/29/13/012.

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22

Gel’mukhanov, Faris, Hans Ågren, and Paweł Sałek. "Doppler effects in resonant x-ray Raman scattering." Physical Review A 57, no. 4 (April 1, 1998): 2511–26. http://dx.doi.org/10.1103/physreva.57.2511.

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23

Hiraoka, N., and Y. Q. Cai. "High-Pressure Studies by X-ray Raman Scattering." Synchrotron Radiation News 23, no. 6 (November 30, 2010): 26–31. http://dx.doi.org/10.1080/08940886.2010.531679.

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24

Sahle, Christoph J. "X-ray Raman scattering spectroscopy at the ESRF." Acta Crystallographica Section A Foundations and Advances 73, a2 (December 1, 2017): C566. http://dx.doi.org/10.1107/s2053273317090076.

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25

Magnuson, M., S. M. Butorin, A. Agui, and J. Nordgren. "Resonant soft x-ray Raman scattering of NiO." Journal of Physics: Condensed Matter 14, no. 13 (March 22, 2002): 3669–76. http://dx.doi.org/10.1088/0953-8984/14/13/324.

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26

Galambosi, Szabolcs, Matti Knaapila, J. Aleksi Soininen, Kim Nygård, Simo Huotari, Frank Galbrecht, Ullrich Scherf, Andrew P. Monkman, and Keijo Hämäläinen. "X-ray Raman Scattering Study of Aligned Polyfluorene." Macromolecules 39, no. 26 (December 2006): 9261–66. http://dx.doi.org/10.1021/ma060823u.

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27

Higuchi, T., T. Tsukamoto, T. Hattori, Y. Taguchi, Y. Tokura, and S. Shin. "Soft-X-ray Raman scattering of La1−xSrxTiO3." Journal of Electron Spectroscopy and Related Phenomena 144-147 (June 2005): 853–56. http://dx.doi.org/10.1016/j.elspec.2005.01.226.

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28

Wang, Jingjing, Da Chen, Yan Xu, Qixin Liu, and Luyin Zhang. "Influence of the Crystal Texture on Raman Spectroscopy of the AlN Films Prepared by Pulse Laser Deposition." Journal of Spectroscopy 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/103602.

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We investigate the Raman scattering of the AlN films prepared by pulse laser deposition. The Raman spectrum and the X-ray diffraction (XRD) patterns of the AlN films were compared to find out the influence of the crystal texture on the Raman scattering. TheE2(high) andA1(TO) scattering modes were observed in Raman spectra. The results show that the orientation and the crystal quality of the AlN films have a great impact on these Raman scattering modes. The deterioration of (002) orientation and the appearance of other orientations in the XRD patterns lead to the weakening of theE2(high) mode and strengthening of theA1(TO) mode in the Raman spectrum. In addition, theE2(high) peak is broadened with the increasing of the width of the X-ray rocking curve. The broadening of the Raman peaks can be associated with degeneration in crystal quality. Furthermore, by combining the energy shift ofE2(high) mode with the measured residual stress in the films, the Raman-stress factor of the AlN films prepared by pulse laser deposition is −4.45 cm−1/GPa for theE2(high) mode.
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29

Huotari, Simo, Tuomas Pylkkänen, J. Aleksi Soininen, Joshua J. Kas, Keijo Hämäläinen, and Giulio Monaco. "X-ray-Raman-scattering-based EXAFS beyond the dipole limit." Journal of Synchrotron Radiation 19, no. 1 (November 25, 2011): 106–13. http://dx.doi.org/10.1107/s0909049511039422.

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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.
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30

NAKAI, S., T. WATANABE, K. SASAKI, T. IWASAKI, M. ODAKA, T. KASHIWAKURA, T. YAMAZAKI, and T. IWAZUMI. "RESONANT Lα X-RAY RAMAN SCATTERING SPECTRA OF CeF3, CeO2andCeB6." Surface Review and Letters 09, no. 02 (April 2002): 1059–64. http://dx.doi.org/10.1142/s0218625x02003342.

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Resonant Lα emission spectra of Ce compounds, CeF 3, CeO 2 and CeB 6, were measured around the LIII absorption threshold. As the energy of the incident photon is tuned at the pre-edge region and at the absorption peaks of the Ce LIII absorption spectrum, the Raman peaks are resonantly enhanced. Obtained spectra are decomposed into Raman and normal Lα emission peaks by line shape analysis. The results show that the Raman spectra provide more detailed information than the absorption spectra about the 4f configuration of Ce compounds.
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31

Kompan M.E., Malyshkin V.G., Boiko M.E., Sharkov M.D., Sapurina I.Yu., and Shishov M.A. "Crystals of the phenazine coordination polymer with the third order symmetry axis: formation, properties." Technical Physics 92, no. 6 (2022): 688. http://dx.doi.org/10.21883/tp.2022.06.54414.319-21.

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Unusual quasi-two-dimensional crystals of a regular triangular shape, self-formed in the process of obtaining a coordination polymer based on phenazine and silver, are described and studied. X-ray diffraction studies were carried out, the interplanar distance was determined, and the spectra of Raman scattering were obtained. A mechanism is proposed that can cause the appearance of triangular crystals from nuclei of hexagonal symmetry. Keywords: X-ray diffractometry, Raman scattering, phenazines - organic crystals.
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32

Bergmann, Uwe, Pieter Glatzel, and Stephen P. Cramer. "Bulk-sensitive XAS characterization of light elements: from X-ray Raman scattering to X-ray Raman spectroscopy." Microchemical Journal 71, no. 2-3 (April 2002): 221–30. http://dx.doi.org/10.1016/s0026-265x(02)00014-0.

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33

Xu, Qiang, Hua Yang Sun, Cheng Chen, Ling Yun Jang, E. Rusli, Suwan P. Mendis, Chin Che Tin, et al. "4H-SiC Wafers Studied by X-Ray Absorption and Raman Scattering." Materials Science Forum 717-720 (May 2012): 509–12. http://dx.doi.org/10.4028/www.scientific.net/msf.717-720.509.

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Synchrotron radiation X-ray absorption and UV 325 nm excitation Raman scattering- photoluminescence (PL) have been employed to investigate a series of 4H-SiC wafers, including bulk, epitaxial single or multiple layer structures by chemical vapor deposition. Significant results on the atomic bonding and PL-Raman properties are obtained from these comparative studies.
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34

ABASZADE, R. G., О. А. KAPUSH, and A. M. NABIEV. "PROPERTIES OF CARBON NANOTUBES DOPED WITH GADOLINIUM." Journal of Optoelectronic and Biomedical Materials 12, no. 3 (July 2020): 61–65. http://dx.doi.org/10.15251/jobm.2020.123.61.

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An analysis of some properties of carbon nanotubes using X-ray diffraction analysis, Raman scattering, and IR luminescence is given. After doping with gadolinium the peak intensities in X-ray and Raman spectra drastically increase. It was found that 15% doping with gadolinium strongly affects the physical properties of carbon nanotubes functionalized by a carboxyl group.
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35

Hudis, E., and A. E. Kaplan. "Ionization-front soliton in x-ray-stimulated Raman scattering." Optics Letters 19, no. 9 (May 1, 1994): 616. http://dx.doi.org/10.1364/ol.19.000616.

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36

Kanata, T., H. Murai, and K. Kubota. "Raman and x‐ray scattering from ultrafine semiconductor particles." Journal of Applied Physics 61, no. 3 (February 1987): 969–71. http://dx.doi.org/10.1063/1.338150.

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37

Hudis, E., P. L. Shkolnikov, and A. E. Kaplan. "X‐ray stimulated Raman scattering in Li and He." Applied Physics Letters 64, no. 7 (February 14, 1994): 818–20. http://dx.doi.org/10.1063/1.111024.

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38

Sahle, Ch J., A. Mirone, J. Niskanen, J. Inkinen, M. Krisch, and S. Huotari. "Planning, performing and analyzing X-ray Raman scattering experiments." Journal of Synchrotron Radiation 22, no. 2 (February 3, 2015): 400–409. http://dx.doi.org/10.1107/s1600577514027581.

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A compilation of procedures for planning and performing X-ray Raman scattering (XRS) experiments and analyzing data obtained from them is presented. In particular, it is demonstrated how to predict the overall shape of the spectra, estimate detection limits for dilute samples, and how to normalize the recorded spectra to absolute units. In addition, methods for processing data from multiple-crystal XRS spectrometers with imaging capability are presented, including a super-resolution method that can be used for direct tomography using XRS spectra as the contrast. An open-source software package with these procedures implemented is also made available.
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39

Tohji, Kazuyuki, Yasuo Udagawa, Tadashi Matsushita, Masaharu Nomura, and Tetsuya Ishikawa. "Anisotropic effects in x‐ray Raman scattering from graphite." Journal of Chemical Physics 92, no. 5 (March 1990): 3233–35. http://dx.doi.org/10.1063/1.457875.

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40

Nakashima, S., Y. Nakakura, and B. Palosz. "Raman scattering and X-ray diffraction of disordered CdI2." Journal of Physics C: Solid State Physics 21, no. 34 (December 10, 1988): 5707–17. http://dx.doi.org/10.1088/0022-3719/21/34/008.

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41

Gomonnai, A. V., I. M. Voynarovych, A. M. Solomon, Yu M. Azhniuk, A. A. Kikineshi, V. P. Pinzenik, M. Kis-Varga, L. Daroczy, and V. V. Lopushansky. "X-ray diffraction and Raman scattering in SbSI nanocrystals." Materials Research Bulletin 38, no. 13 (October 2003): 1767–72. http://dx.doi.org/10.1016/s0025-5408(03)00181-8.

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42

Iwazumi, T., K. Kobayashi, S. Kishimoto, T. Nakamura, S. Nanao, D. Ohsawa, R. Katano, and Y. Isozumi. "Magnetic resonance effect in x-ray resonant Raman scattering." Physical Review B 56, no. 22 (December 1, 1997): R14267—R14270. http://dx.doi.org/10.1103/physrevb.56.r14267.

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43

Marcano, G., C. Rincón, G. Marín, G. E. Delgado, A. J. Mora, J. L. Herrera-Pérez, J. G. Mendoza-Alvarez, and P. Rodríguez. "Raman scattering and X-ray diffraction study in Cu2GeSe3." Solid State Communications 146, no. 1-2 (April 2008): 65–68. http://dx.doi.org/10.1016/j.ssc.2008.01.018.

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44

Gel'mukhanov, Faris, and Hans A˚gren. "Dynamics and coherence of resonant X-ray Raman scattering." Journal of Electron Spectroscopy and Related Phenomena 88-91 (March 1998): 29–33. http://dx.doi.org/10.1016/s0368-2048(97)00263-6.

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45

Joly, Yves, Chiara Cavallari, Sergey A. Guda, and Christoph J. Sahle. "Full-Potential Simulation of X-ray Raman Scattering Spectroscopy." Journal of Chemical Theory and Computation 13, no. 5 (April 28, 2017): 2172–77. http://dx.doi.org/10.1021/acs.jctc.7b00203.

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46

HIRAOKA, Nozomu. "X-Ray Raman Scattering: Present Status and Future Prospect." Review of High Pressure Science and Technology 23, no. 3 (2013): 252–59. http://dx.doi.org/10.4131/jshpreview.23.252.

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47

van Veenendaal, Michel, Paolo Carra, and B. T. Thole. "X-ray resonant Raman scattering in the rare earths." Physical Review B 54, no. 22 (December 1, 1996): 16010–23. http://dx.doi.org/10.1103/physrevb.54.16010.

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48

Soininen, J. A., K. Hämäläinen, W. A. Caliebe, C.-C. Kao, and Eric L. Shirley. "Core-hole-electron interaction in x-ray Raman scattering." Journal of Physics: Condensed Matter 13, no. 35 (August 16, 2001): 8039–47. http://dx.doi.org/10.1088/0953-8984/13/35/311.

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49

Ruf, T. "Inelastic X-ray scattering: new possibilities for Raman spectroscopy." Applied Physics A: Materials Science & Processing 76, no. 1 (January 1, 2003): 21–26. http://dx.doi.org/10.1007/s003390201287.

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50

Papademitriou, D. K., and A. D. Zdetsis. "A note on X-ray raman scattering from Boron." Applied Physics A Solids and Surfaces 55, no. 3 (September 1992): 258–60. http://dx.doi.org/10.1007/bf00348394.

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