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Neutron and X-Ray Spectroscopy NEUTRON AND X-RAY SPECTROSCOPY Grenoble Sciences Grenoble Sciences pursues a triple aim: ®to publish works responding to a clearly defined project, with no curriculum or vogue constraints, ®to guarantee the selected titles’ scientific and pedagogical qualities, ®to propose books at an affordable price to the widest scope of readers. Each project is selected with the help of anonymous referees, followed by a one- year (in average) interaction between the authors and a Readership Committee, whose members’ names figure in the front pages of the book. Publication is then confided to the most adequate publishing company by Grenoble Sciences. (Contact: Tél.: (33) 4 76 51 46 95 – Fax: (33) 4 76 51 45 79 E-mail: [email protected]) Scientific Director of Grenoble Sciences : Jean BORNAREL, Professor at the Joseph Fourier University, Grenoble 1, France Grenoble Sciences is supported by the French Ministry of Education and Research and the “Région Rhône-Alpes”. Front cover photo: harmonious composition based on figures extracted from the work: ®The body-centred tetragonal unit cell of the bilayer manganite by CURRAT (after ref. [38]) ®Methyl group in lithium acetate dihydrate and in aspirin by JOHNSON (from refs [19] and [49]) ®X-PEEM images of permalloy micro-structures and of carbon films by SCHNEIDER (from ref. [11] and taken from ref. [17]) ®Interference of outgoing and backscattered photoelectron wave by LENGELER. Neutron and X-ray Spectroscopy Edited by FRANÇOISE HIPPERT Institut National Physique, St. Martin d'Hères, France ERIK GEISSLER Université J. Fourier de Grenoble, St. Martin d'Hères, France JEAN LOUIS HODEAU Laboratoire de Cristallographie, CNRS, Grenoble, France EDDY LELIÈVRE-BERNA Institut Laue Langevin, Grenoble, France and JEAN-RENÉ REGNARD Université J. Fourier de Grenoble, St. Martin d'Hères, France A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN-10 1-4020-3336-2 (HB) ISBN-13 978-1-4020-3336-0 (HB) ISBN-10 1-4020-3337-0 (e-book) ISBN-13 978-1-4020-3337-7 (e-book) Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. www.springer.com Printed on acid-free paper All Rights Reserved © 2006 Springer No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed in the Netherlands. TABLE OF CONTENTS Contributors.........................................................................................................................XV Foreword.............................................................................................................................. XIX Introduction ....................................................................................................................... XXI X--RAY SPECTROSCOPY 1 - Fundamentals of X-ray absorption and dichroism: the multiplet approach F. de Groot - J. Vogel ..............................................................................................................3 1. Introduction...........................................................................................................................4 1.1. Interaction of X-rays with matter....................................................................................4 1.2. Basics of XAFS spectroscopy.........................................................................................6 1.3. Experimental aspects.......................................................................................................9 2. Multiplet effects ..................................................................................................................11 2.1. Atomic multiplets..........................................................................................................14 2.1.1. Term symbols..............................................................................................................14 2.1.2. Matrix elements ..........................................................................................................18 2.2. Atomic multiplet ground states of 3dn systems............................................................20 2.3. j - j coupling...................................................................................................................20 2.4. X-ray absorption spectra described with atomic multiplets.........................................21 2.4.1. Transition metal LII-III edge........................................................................................21 2.4.2. MIV-VV edges of rare earths..........................................................................................28 3. Crystal field theory.............................................................................................................31 3.1. The crystal field multiplet Hamiltonian........................................................................32 3.2. Cubic crystal fields........................................................................................................33 3.3. The energies of the 3dn configurations.........................................................................36 3.3.1. Symmetry effects in D4h symmetry .............................................................................40 3.3.2. The effect of the 3d spin-orbit coupling.....................................................................40 3.3.3. The effects on the X-ray absorption calculations......................................................42 3.3.4. 3d0 systems in octahedral symmetry..........................................................................42 3.3.5. 3d0 systems in lower symmetries ...............................................................................45 3.3.6. X-ray absorption spectra of 3dn systems ...................................................................46 4. Charge transfer effects.......................................................................................................47 4.1. Initial state effects .........................................................................................................47 4.2. Final state effects...........................................................................................................52 4.3. The X-ray absorption spectrum with charge transfer effects.......................................53 5. X-ray linear and circular dichroism ................................................................................59 References..................................................................................................................................64 V VI NEUTRON AND X-RAY SPECTROSCOPY 2 - Multiple scattering theory applied to X-ray absorption near-edge structure P. Sainctavit - V. Briois.................................................................................67 1. Introduction.........................................................................................................................67 2. MST for real space calculations........................................................................................70 2.1. The absorption cross-section.........................................................................................71 2.2. Calculation of the cross-section for three different potentials.....................................73 2.2.1. Free particle ...............................................................................................................73 2.2.2. Particle in a spherical potential ................................................................................75 2.2.3. Particle in a "muffin-tin" potential............................................................................78 3. Construction of the potential ............................................................................................83 3.1. X – a exchange potential...............................................................................................85 3.2. Dirac-Hara exchange potential .....................................................................................85 3.3. Complex Hedin-Lundqvist exchange and correlation potential..................................87 4. Application of the multiple scattering theory .................................................................89 4.1. Vanadium K edge cross-section for VO6 cluster..........................................................90 4.2. Iron K edge cross-section for FeO6 cluster...................................................................93 4.3. Cross-section calculations in distorted octahedra ........................................................94 II 5. Spin transition in Fe (o-phenantroline)2 (NCS) 2 followed at the iron K edge...........95 6. Conclusion ...........................................................................................................................97 ij ij Appendix - Expression for the propagators J LL' and H L L' .............................................97 Acknowledgments.....................................................................................................................99 References................................................................................................................................100
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