X-RAY DIFFRACTION Pan Stanford Series on Renewable Energy — Volume 2 X-RAY DIFFRACTION Modern Experimental Techniques editors Preben Maegaard edited by Anna Krenz Oliver H. Seeck Wolfgang Palz Bridget M. Murphy The Rise of Modern Wind Energy Wind Power for the World CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2014 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20150122 International Standard Book Number-13: 978-981-4303-60-6 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reason- able efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. 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CCC is a not-for-profit organiza- tion that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents Preface 1. Ov ervie w of X-Ray Scattering and Diffraction Theory xiii and Techniques 1 Oliver H. Seeck 1.1 Scattering at Single Electrons 2 1.2 Scattering in Bulk Matter 5 1.2.1 Scattering in Disordered Matter 6 1.2.2 Scattering in Crystalline Matter 7 1.2.3 Scattering at Powders of Crystalline Matter 10 1.3 Scattering at Surfaces 12 1.3.1 Scattering at Crystal Surfaces 14 1.3.2 Scattering at Surfaces with Density Profile 16 1.3.3 Scattering at Rough Surfaces 19 2. 1Sc.4a tterinSog maned D Dyinffarmacitciaoln S Bcaetatmerliinnegs T ahte Soyrnyc hrotron 22 Radiation Sources 29 Oliver H. Seeck 2.1 Synchrotron Radiation Sources 31 2.1.1 Bending Magnets 32 2.1.2 Wigglers 37 2.1.3 Undulators 38 2.1.4 Undulators at X-Ray Free Electron Lasers 43 2.2 Brilliance 45 3. 2M.3ic ro- aBneda Nmalinnoed Oifpfrtaicctsi on 4575 Christina Krywka and Martin Müller 3.1 Introduction 55 3.2 X-Ray Focusing Optics 56 vi Contents 3.2.1 Refractive Optics 58 3.2.1.1 Metal compound refractive lenses 58 3.2.1.2 Silicon nanofocusing refractive lenses 60 3.2.1.3 Diamond lenses 61 3.2.1.4 Polymer lenses 62 3.2.2 Diffractive Optics 62 3.2.2.1 Fresnel zone plates 62 3.2.3 Reflective Optics 65 3.2.3.1 Kirkpatrick–Baez mirror 65 3.2.3.2 Multilayer KB mirror 67 3.2.4 Beam Concentrating and Collimating Elements 67 3.2.4.1 Capillaries 67 3.2.4.2 Waveguides 69 3.3 Experiments 71 3.3.1 X-Ray Micro- and Nanodiffraction Instrumentation 72 3.3.2 Examples of Micro- and Nanodiffraction Experiments 74 3.3.2.1 Small beams and crystallographic parameters 75 3.3.2.2 µSAXS on single-cellulose fibers 77 3.3.2.3 2D microdiffraction scanning of the wood cell wall 78 3.3.2.4 In situ deformation of single wood cells 81 3.3.3 Beam Damage in Microdiffraction Experiments 82 4. 3Sm.4a ll-AnSuglme mX-aRrayy Scattering 8839 Ulla Vainio 4.1 Introduction 90 4.2 Experimental Setup 91 4.2.1 Sample Cells and Optimal Sample Thickness 93 4.2.2 Corrections to Experimental Data 94 Contents vii 4.2.3 Absolute Intensity Scale 96 4.3 Theory 97 4.3.1 Scattering Length Density 99 4.3.2 Power Laws 100 4.3.3 Porod Constant 102 4.3.4 Scattering from Particles 103 4.3.4.1 Guinier approximation 105 4.3.4.2 Form factor 106 4.3.4.3 Structure factor 107 4.3.4.4 Polydispersity 109 4.3.4.5 Distance distribution function 110 4.3.4.6 Kratky plot and Porod invariant 111 4.3.5 Scattering from Fluctuations 113 4.3.6 Generalized Scattering Functions 113 4.4 Radiation Damage 114 4.5 BioSAXS 115 4.6 GISAXS 115 5. 4Th.7e X-RaAyS AStXaSn ding Wave Technique: Fourier Analysis 118 with Chemical Sensitivity 129 Jörg Zegenhagen 5.1 Introduction 129 5.2 Formation of an XSW 132 5.3 XSW Analysis 133 5.4 XSW Structure Factor versus XRD Structure Factor 136 5.5 XSW Fourier Analysis: Imaging of Mn In GaAs 137 6. 5In.6el asticS uX-mRmaya Srcya ttering from Phonons 114415 Alexeï Bosak and Michael Krisch 6.1 Introduction 145 6.2 General Formalism 148 6.3 Experimental Technique 150 6.4 Mapping of Phonon Dispersion Surfaces 152 6.5 Combining IXS and TDS 154 viii Contents 6.5.1 Visualization of the Fermi Surface of Zinc 155 6.5.2 Giant Kohn Anomaly in ZrTe3 158 6.5.3 Diffuse Scattering and Correlated Disorder in Manganese Analogue of Prussian Blue 162 6.5.4 Powder Wide-Angle IXS 164 7. Magneti6c. 5X.-5R ay CSocantctleursiinogn s and Outlook 116785 S. P. Collins 7.1 Introduction 175 7.2 Is Magnetic X-Ray Scattering the Right Technique? 177 7.3 Strength of the Magnetic Resonance 180 L M 7.3.1 Strong Magnetic Resonances (3d/4d/5d 2,3; 4f/5f 4,5) 180 K L 7.3.2 Weak Magnetic Resonances (3d ; 4f 2,3) 181 7.3.3 Nonresonant Magnetic Scattering 182 7.4 Sample Material 182 7.5 FeBO3: Introduction 184 7.6 Nonresonant Magnetic X-Ray Calculation: FeBO3 185 7.7 Magnetic X-Ray Scattering Measurements: FeBO3 189 7.8 Discussion: FeBO3 193 7.9 Magnetic Scattering and Polarization 195 7.10 Resonant Scattering and Atomic Multipoles 197 8. 7N.u1c1le arF Ruetsuornea Dnitr Seccatitotenrsi ng of Synchrotron Radiation: 198 Applications in Magnetism 205 Ralf Röhlsberger 8.1 Introduction 205 8.2 Basic Principles of Nuclear Resonant Scattering 207 8.3 Imaging the Magnetic Spin Structure of Exchange-Spring Magnetic Layers 215 Contents ix 8.4 Antiferromagnetic Coupling in Fe/Cr Multilayers 218 8.5 Spatially Resolved Magnetic Reversal in an Exchange Bias Layer System 220 9. 8Re.6fl ectivCiotyn caltu Lsiiqouni da nIndt eOrufatcloeos k 222259 Bridget M. Murphy 9.1 Introduction 230 9.2 X-Ray Reflectivity 231 9.3 Fresnel Reflectiviy 231 9.4 Roughness at Liquid Surfaces 234 9.5 Kinematic Scattering Theory for Liquid Surfaces 237 9.5.1 Experimental Considerations 239 9.5.2 Bulk Scattering 240 9.6 Instrumentation 241 9.6.1 Single-Crystal Liquid Diffractometer 241 9.6.2 High-Energy Liquid Diffractometer 241 9.6.3 Double-Crystal Liquid Diffractometer 243 9.7 Examples 245 9.7.1 Reflectivity from Water 245 9.7.2 Reflectivity from Liquid Mercury 247 10. 9X-.8R ay DiSfufrmacmtiaorny a t Extreme Conditions: Today and 248 Tomorrow 255 Hanns-Peter Liermann 10.1 Introduction 255 10.1.1 Why X-Ray Diffraction at Extreme Conditions 257 10.1.1.1 Precise high-P and high-T equation of state studies 258 10.1.1.2 Studies on crystallographic properties 260 10.1.1.3 Phase stabilities studies 262 10.1.1.4 Elastic–plastic behavior of mantle minerals 263 10.1.2 LVP vs. DAC: Advantages and Disadvantages 266