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

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).

Mikhail Alexandrovich Krivoglaz died unexpectedly when he was preparing the English edition of his two-volume monograph on diffraction and diffuse scatter ing of X-rays and neutrons in imperfect crystals. His death was a heavy blow to all who knew him, who had worked with him and to the world science community as a whole. The application of the diffraction techniques for the study of imperfections of crystal structures was the major field of Krivoglaz' work throughout his career in science. He started working in the field in the mid-fifties and since then made fundamental contributions to the theory of real crystals. His results have largely determined the current level of knowledge in this field for more than thirty years. Until the very last days of his life, Krivoglaz continued active studies in the physics of diffraction effects in real crystals. His interest in the theory aided in the explanation of the rapidly advancing experimental studies. The milestones marking important stages of his work were the first mono graph on the theory of X-ray and neutron scattering in real crystals which was published in Russian in 1967 (a revised English edition in 1969), and the two volume monograph published in Russian in 1983-84 (this edition is the revised translation of the latter).