Basic Concepts of X–Ray Diffraction

Authored by a university professor deeply involved in X–ray diffraction–related research, this textbook is based on his lectures given to graduate students for more than 20 years. It adopts a well–balanced approach, describing basic concepts and experimental techniques, which make X–ray diffraction an unsurpassed method for studying the structure of materials. Both dynamical and kinematic X–ray diffraction is considered from a unified viewpoint, in which the dynamical diffraction in single–scattering approximation serves as a bridge between these two parts. The text emphasizes the fundamental laws that govern the interaction of X–rays with matter, but also covers in detail classical and modern applications, e.g., line broadening, texture and strain/stress analyses, X–ray mapping in reciprocal space, high–resolution X–ray diffraction in the spatial and wave vector domains, X–ray focusing, inelastic and time–resolved X–ray scattering. This unique scope, in combination with otherwise hard–to–find information on analytic expressions for simulating X–ray diffraction profiles in thin–film heterostructures, X–ray interaction with phonons, coherent scattering of Mössbauer radiation, and energy–variable X–ray diffraction, makes the book indispensable for any serious user of X–ray diffraction techniques. Compact and self–contained, this textbook is suitable for students taking X–ray diffraction courses towards specialization in materials science, physics, chemistry, or biology. Numerous clear–cut illustrations, an easy–to–read style of writing, as well as rather short, easily digestible chapters all facilitate comprehension.

Preface XI Introduction 1 1 Diffraction Phenomena in Optics 5 2 Wave Propagation in Periodic Media 11 3 Dynamical Diffraction of Particles and Fields: General Considerations 21 3.1 The Two–Beam Approximation 23 3.2 Diffraction Profile: The Laue Scattering Geometry 33 3.3 Diffraction Profile: The Bragg Scattering Geometry 38 4 Dynamical X–Ray Diffraction: The Ewald–Laue Approach 45 4.1 Dynamical X–Ray Diffraction: Two–Beam Approximation 49 4.1.1 The Role of X–Ray Polarization 50 4.1.2 The Two–Branch Isoenergetic Dispersion Surface for X–Rays 52 4.1.3 Isoenergetic Dispersion Surface for Asymmetric Reflection 56 5 Dynamical Diffraction: The Darwin Approach 61 5.1 Scattering by a Single Electron 61 5.2 Atomic Scattering Factor 64 5.3 Structure Factor 66 5.4 Scattering Amplitude from an Individual Atomic Plane 68 5.5 Diffraction Intensity in the Bragg Scattering Geometry 71 6 Dynamical Diffraction in Nonhomogeneous Media: The Takagi–Taupin Approach 77 6.1 Takagi Equations 77 6.2 Taupin Equation 84 6.2.1 Taupin Equation: The Symmetric Laue Case 84 6.2.2 Taupin Equation: The Symmetric Bragg Case 86 6.2.3 Solution of the Taupin Equation for Multilayered Structures 88 7 X–Ray Absorption 91 8 Dynamical Diffraction in Single–Scattering Approximation: Simulation of High–Resolution X–Ray Diffraction in Heterostructures and Multilayers 97 8.1 Direct Wave Summation Method 103 9 Reciprocal Space Mapping and Strain Measurements in Heterostructures 121 10 X–Ray Diffraction in Kinematic Approximation 131 10.1 X–Ray Polarization Factor 133 10.2 Debye–Waller Factor 135 11 X–Ray Diffraction from Polycrystalline Materials 139 11.1 Ideal Mosaic Crystal 139 11.2 Powder Diffraction 141 12 Applications to Materials Science: Structure Analysis 145 13 Applications to Materials Science: Phase Analysis 155 13.1 Internal Standard Method 158 13.2 Rietveld Refinement 159 14 Applications to Materials Science: Preferred Orientation (Texture) Analysis 161 14.1 The March–Dollase Approach 165 15 Applications to Materials Science: Line Broadening Analysis 171 15.1 Line Broadening due to Finite Crystallite Size 174 15.1.1 The Scherrer Equation 175 15.1.2 Line Broadening in the Laue Scattering Geometry 178 15.2 Line Broadening due to Microstrain Fluctuations 180 15.3 Williamson–Hall Method 181 15.4 The Convolution Approach 183 15.5 Instrumental Broadening 184 15.6 Relation between Grain Size–Induced and Microstrain–Induced Broadenings of X–Ray Diffraction Profiles 186 16 Applications to Materials Science: Residual Strain/Stress Measurements 189 16.1 Strain Measurements in Single–Crystalline Systems 189 16.2 Residual Stress Measurements in Polycrystalline Materials 190 17 Impact of Lattice Defects on X–Ray Diffraction 193 18 X–Ray Diffraction Measurements in Polycrystals with High Spatial Resolution 203 18.1 The Theory of Energy–Variable Diffraction (EVD) 206 18.1.1 Homogeneous Materials 210 18.1.2 Inhomogeneous Materials 212 19 Inelastic Scattering 217 19.1 Inelastic Neutron Scattering 218 19.2 Inelastic X–Ray Scattering 221 20 Interaction of X–Rays with Acoustic Waves 225 20.1 Thermal Diffuse Scattering 228 20.2 Coherent Scattering by Externally Excited Phonons 230 21 Time–Resolved X–Ray Diffraction 237 22 X–Ray Sources 241 22.1 Synchrotron Radiation 250 23 X–Ray Focusing Optics 257 23.1 X–Ray Focusing: Geometrical Optics Approach 261 23.2 X–Ray Focusing: Diffraction Optics Approach 268 23.2.1 Bragg–Fresnel Lenses and Fresnel Zone Plates 268 23.2.2 Using Asymmetric Reflections 272 24 X–Ray Diffractometers 275 24.1 High–Resolution Diffractometers 275 24.2 Powder Diffractometers 280 References 285 Index 291

Emil Zolotoyabko is Professor in the Department of Materials Science and Engineering at the Technion – Israel Institute of Technology (Haifa). He is holder of the Abraham Tulin Academic Chair and recipient of the 2001 Henry Taub Prize for Academic Excellence. Emil Zolotoyabko has authored more than 160 scientific publications, three books, and four book chapters devoted to the development of new X–ray diffraction methods and their applications for studying the structure and dynamical characteristics of different materials systems.