X Ray And Neutron Dynamical Diffraction

This volume collects the proceedings of the 23rd International Course of Crystallography, entitled "X-ray and Neutron Dynamical Diffraction, Theory and Applications," which took place in the fascinating setting of Erice in Sicily, Italy. It was run as a NATO Advanced Studies Institute with A. Authier (France) and S. Lagomarsino (Italy) as codirectors, and L. Riva di Sanseverino and P. Spadon (Italy) as local organizers, R. Colella (USA) and B. K. Tanner (UK) being the two other members of the organizing committee. It was attended by about one hundred participants from twenty four different countries. Two basic theories may be used to describe the diffraction of radiation by crystalline matter. The first one, the so-called geometrical, or kinematical theory, is approximate and is applicable to small, highly imperfect crystals. It is used for the determination of crystal structures and describes the diffraction of powders and polycrystalline materials. The other one, the so-called dynamical theory, is applicable to perfect or nearly perfect crystals. For that reason, dynamical diffraction of X-rays and neutrons constitutes the theoretical basis of a great variety of applications such as: • the techniques used for the characterization of nearly perfect high technology materials, semiconductors, piezoelectric, electrooptic, ferroelectric, magnetic crystals, • the X-ray optical devices used in all modem applications of Synchrotron Radiation (EXAFS, High Resolution X-ray Diffractometry, magnetic and nuclear resonant scattering, topography, etc. ), and • X-ray and neutron interferometry.

ways in which the magnetic interaction between neutrons and magnetic moments can yield information on the magnetization densities of thin ?lms and multilayers. I commend the organizers for having organized a group of expert lecturers to present this subject in a detailed but clear fashion, as the importance of the subject deserves. Argonne, IL S. K. Sinha Contents 1 The Interaction of X-Rays (and Neutrons) with Matter . . . . . . . . . . . . . . 1 F. de Bergevin 1. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 2 Generalities and De?nitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1. 3 From the Scattering by an Object to the Propagation in a Medium . 14 1. 4 X-Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1. 5 X-Rays: Anisotropic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 1. A Appendix: the Born Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . 54 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2 Statistical Aspects of Wave Scattering at Rough Surfaces . . . . . . . . . . . . 59 A. Sentenac and J. Daillant 2. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2. 2 Description of Randomly Rough Surfaces . . . . . . . . . . . . . . . . . . . . . 60 2. 3 Description of a Surface Scattering Experiment, Coherence Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2. 4 Statistical Formulation of the Diffraction Problem . . . . . . . . . . . . . . 72 2. 5 Statistical Formulation of the Scattered Intensity Under the Born Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3 Specular Re?ectivity from Smooth and Rough Surfaces . . . . . . . . . . . . . 85 A. Gibaud and G. Vignaud 3. 1 The Re?ected Intensity from an Ideally Flat Surface . . . . . . . . . . . . 85 3. 2 X-Ray Re?ectivity in Strati?ed Media . . . . . . . . . . . . . . . . . . . . . . . . 98 3. 3 From Dynamical to Kinematical Theory . . . . . . . . . . . . . . . . . . . . . . 107 3. 4 In?uence of the Roughness on the Matrix Coef?cients . . . . . . . . . . 111 3. A Appendix: The Treatment of Roughness in Specular Re?ectivity . . 113 3. B Appendix: Inversion of re?ectivity data . . . . . . . . . . . . . . . . . . . . . . .

Understanding and manipulating the properties of materials naturally occurring in our world and artificially produced by modern technologies requires detailed information on their properties on the atomic scale. This information is the basis for any kind of research in physics, chemistry, biology, engineering, metallurgy, and ceramics. Among the various experimental methods, neutron and photon scattering have become the key techniques of choice. This book provides an overview of the complementarity between neutron and synchrotron x-ray scattering. The most important topics are covered, including structure determination, magnetic correlations, polymer dynamics, thin films and multilayers, photoemission studies, etc; they are thoroughly introduced and discussed by experts from both the experimental and the theoretical side. Contents:Neutron- and Synchrotron X-Ray Scattering (The Theoretical Principles) (W E Fischer)Structure Determination by Powder Synchrotron X-Ray Diffraction (A N Fitch)Magnetic Neutron and Synchrotron X-Ray Scattering (W G Stirling)Magnetic Excitations Through the Eye of the Neutron (W J L Buyers)Topological Excitations in Low-Dimensional Magnets (H B Braun)Elastic and Inelastic X-Ray Scattering from Correlated Electrons: A Theoretical Perspective (M Altarelli)From Thin Films to Superlattices Studied with X-Rays and Neutrons (D F McMorrow)Small-Angle and Surface Scattering from Porous and Fractal Materials (S K Sinha)Hot Topics in Condensed Matter Physics (H R Ott)Neutron Beam Optics (P Böni)Synchrotron X-Ray Beam Optics (A Freund)Summary Lecture: Some Features of the Scattering and Absorption of Beams of Neutrons and Beams of X-Rays (S W Lovesey)and other papers Readership: Condensed matter and solid state physicists. Keywords:Photon Scattering;Structure Determination;Magnetic Correlations;Polymer Dynamics;Thin Films;Multilayers;Photoemission Studies;Synchrotron X-Ray;Optics;Neutrons

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 Mossbauer 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.

Diffraction and Imaging Techniques in Material Science reviews recent developments in diffraction and imaging techniques used in the study of materials. It discusses advances in high-voltage electron microscopy, low-energy electron diffraction (LEED), X-ray and neutron diffraction, X-ray topography, mirror electron microscopy, and field emission microscopy. Organized into five parts encompassing nine chapters, this volume begins with an overview of the dynamical theory of the diffraction of high-energy electrons in crystals and methodically introduces the reader to dynamical diffraction in perfect and imperfect crystals, inelastic scattering of electrons in crystals, and X-ray production. It then explores back scattering effects, the technical features of high-voltage electron microscopes, and surface characterization by LEED. Other chapters focus on the kinematical theory of X-ray diffraction, techniques and interpretation in X-ray topography, and interpretation of the contrast of the images of defects on X-ray topographs. The book also describes theory and applications of mirror electron microscopy, surface studies by field emission of electrons, field ionization and field evaporation, and gas-surface interactions before concluding with a discussion on lattice imperfections. Scientists and students taking courses on diffraction and solid-state electron microscopy will benefit from this book.

During the last few decades, crystallography has become a wide and economically important field of science with many interesting applications in materials research, in different branches of physics, chemistry, geology, pharmacology, biochemistry, electronics, in many technological processes, machinery, heavy industry, etc. Twenty Nobel prizes awarded for achieve ments belonging to this· field only underline its distinction. Crystallo graphy has become a commonly used term, but - like a whale - it is much easier to recognize than to describe because of an extreme diversity of sub jects involved which range from highly sophisticated theories to the develop ment of routine technological processes or testing of materials in produc tion. It is apparent that only some aspects of selected topics could be included on a single occasion. The conference "ADVANCED METHODS IN X-RAY AND NEUTRON STRUCTURE ANALYSIS OF MATERIALS" held in Karlovy Vary (Czechoslovakia) on October 5-9, 1987, was intended to cover the most important crystallographic aspects of ma terials science. The conference was attended by 250 people from 16 countries (Belgium,Bulgaria, China, Czechoslovakia, Finland, France, FRG, GDR, Hungary, Italy, The Netherlands, Poland, Sweden, USA, USSR and Yugoslavia).