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Chemical Applications of Inelastic X-Ray Scattering

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Chemical Applications of Inelastic X-Ray Scattering BNL- 68406 CHEMICAL APPLICATIONS OF INELASTIC X-RAY SCATTERING H. Hayashi and Y. Udagawa Research Institute for Scientific Measurements Tohoku University Sendai, 980-8577, Japan J.-M. Gillet Structures, Proprietes et Modelisation des Solides UMR8580 Ecole Centrale Paris, Grande Voie des Vignes, 92295 Chatenay-Malabry Cedex, France W.A. Caliebe and C.-C. Kao National Synchrotron Light Source Brookhaven National Laboratory Upton, New York, 11973-5000, USA August 2001 National Synchrotron Light Source Brookhaven National Laboratory Operated by Brookhaven Science Associates Upton, NY 11973 Under Contract with the United States Department of Energy Contract Number DE-AC02-98CH10886 DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy; completeness, or any third party’s use or the results of such use of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof or its contractors or subcontractors. Th.e views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. CHEMICAL APPLICATIONS OF INELASTIC X-RAY SCATTERING H. Hayashi*, Y. Udagawa Research Institute for Scientific Measurements, Tohoku University, Sendai, 980-8577, Japan J.-M. Gillet Structures, PropriCtCs et Modelisation des Solides, UMR8580 Ecole Centrale Paris, Grande Voie des Vignes, 92295 Chatenay-Malabry Cedex, France W.A. Caliebe, C.-C. Kao National Synchrotron Light Source, Brookhaven National Laboratory, Upton, New York 11973, U.S.A. I. INTRODUCTION . ....................~. 2 II. THEORETICAL BACKGROUND . ..~.3 III. EXPERIMENTAL CONFIGURATIONS . ..*......................... 5 Iv. APPLICATIONS . ................... 9 A. X-RAY RAMAN SCATTERING...................................................................................................................... .9 1. General description .....................................................................................................................................9 2. Excitations of inner shell electrons: X4NES, E;xAFS,polarization dependence...................................... 11 3. Excitations of valence electrons : Bethe su$aces and complete optical spectra of water.. ...................... 11 4. S(q;)and electron correlation effects......................................................................................................... 13 B. ‘RESONANTRAMAN AND RESONANTINELASTIC SCATTERING................................................................... 14 1. X-ray ResonantRaman Scattering.. ..........................................................................................................14 2. Many electron efsectsin XRRS.................................................................................................................. 16 3. Magnetic sensitivity in XRRS ....................................................................................................................16 4. X-ray ResonantInelastic Scattering.......................................................................................................... 17 5. Example: RlxS in NiO ..............................................................................................................................18 C. COMPTONSCATTERING. ............................................................................................................................ 19 1. Theoy and approximations. .....................................................................................................................19 2. Sharpfeature for valence electrons: relevance to chemical bonding...................................................... .21 3. Kinetic energy. ..........................................................................................................................................22 4. Technical issuesin the interpretation of ComptonproJi1e.s ...................................................................... .23 5. Examples and applications. ......................................................................................................................24 V. CONCLUSIONS . ................. 27 *Present address: National Synchrotron Light Source I. Introduction Inelastic x-ray scattering (IXS), complementary to other more established inelastic scattering probes, such as light scattering, electron scattering, and neutron scattering, is becoming an important experimental technique in the study of elementary excitations in condensed matters. Over the past decade, IXS with total energy resolution of few meV has been achieved, and is being used routinely in the study of phonon dispersions in solids and liquids as well as dynamics in disordered and biological systems. In the study of electronic excitations, IXS with total energy resolution on the order of 100 meV to 1 eV is gaining wider applications also. For example, IXS has been used to study collective excitations of valence electrons, single electron excitations of valence electrons, as well as core electron excitations. In comparison with the alternative scattering techniques mentioned above, IXS has several advantages. First, IXS probes the full momentum transfer range of the dielectric response of the sample, whereas light scattering is limited to very small momentum transfers, and electron scattering suffers the effects of multiple scattering at large momentum transfers. Second, since IXS measures the bulk properties of the sample it is not surface sensitive, therefore it does not require special preparation of the sample. The greater flexibility in sample conditions and environments makes IXS an ideal probe in the study of liquids and samples under extreme temperature, pressure, and magnetic field. Third, the tunability of synchrotron radiation sources enables IXS to exploit element specificity and resonant enhancement of scattering cross sections. Fourth, IXS is unique in the study of dynamics of liquids and amorphous solids because it can probe the particular region of energy-momentum transfer phase space, which is inaccessible to inelastic neutron scattering. On the other hand, the main disadvantages of IXS are the small cross sections and the strong absorption of x-rays in high Z elements. In the high momentum transfer limit, IXS evolves into the well-known Compton scattering regime. In this case, the inelastic scattering cross section, instead of providing information about excited states of the system, can be used to determine the ground state momentum distribution of the valence electrons. Compton profiles also provide rigorous tests on the accuracy of the wavefunctions obtained from advanced electronic structure calculations. With synchrotron sources, momentum resolution of 0.1 to 0.15 atomic unit (a.u.) can be achieved. Three dimensional momentum distributions of valence electrons of a number of solids have been reconstructed. Recently, momentum resolution of 0.01 a.u. has been demonstrated using lower energy x-rays. Although the relatively low photon energy limits the selection of samples to a few low Z elements, this unprecedented momentum resolution nevertheless provides a unique opportunity to the study of Fermi surfaces related features and electron correlation effects in Compton profiles. There have been several reviews of IXS in the literature. For meV resolution and the study of phonon with x-rays, there is the review by Burke1 in 199 1 [Burkel91]. For the latest developments, the readers should look into recent works by Sette’s group at European Synchrotron Radiation Facility [Sette]. For electronic excitations, there is the review by Schulke in Vol. 3 of Handbook on Synchrotron Radiation in 1991 [Schulkeg 11. And, for Compton 2 scattering, the interested readers are advised to consult the reviews by [Cooper851 and [Schulke91], as well as the monograph edited by [Williams77]. Due to the development of high flux and brightness insertion devices and the construction of several dedicated IXS beamlines at several synchrotron radiation facilities around the world, there has been a rapid growth in experimental activities. These experimental works, in turn, have stimulated many theoretical works. The advantages of IXS mentioned above have also been exploited to address important issues in a growing list of scientific disciplines. It is the purpose of this chapter to review these recent developments in IXS and their applications. In this chapter, we will focus on the study of electronic excitations in condensed matter with total energy resolution of 100 meV to 1.0 eV. We will also review Compton scattering with an emphasis on its applications to chemical physics. The rest of this chapter is organized as follows: the kinematics of IXS and the derivation of the double differential scattering cross section are given in section II. Experimental configurations for different types of IXS experiments are briefly summarized in section
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