Dynamical Theory Of X Ray Diffraction

Publisher Description

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.

X-ray diffraction technique have been using for a long time to understand the characteristics of various materials around the world. So it is important to understand the kinematics and dynamical theory and their applications in different cases. So dynamical theory of x-ray diffraction for both absorption and without absorption is developed and applied to thin, thick and intermediate thick CuZn alloy to obtain the diffraction patterns for both Bragg's and Laue's cases. The famous asymmetric curve is found when absorption is considered; the diffraction curve is symmetrical without absorption. It is found that the intensity increases but FWHM decreases for higher indices. Order-disorder transformation of CuZn binary alloy is also noticed for various temperatures. The atomic scattering factors of different elements are calculated to see the temperature effect. The temperature dependence of reflection lines are computed using Debye and Einstein approximation. Interestingly intensity of reflection lines decreases with the increase of temperature and indices for both cases. This book will be helpful for the student and researchers who want to understand and work on x-ray diffraction.

X-ray multiple-wave diffraction, sometimes called multiple diffraction or N-beam diffraction, results from the scattering of X-rays from periodic two or higher-dimensional structures, like 2-d and 3-d crystals and even quasi crystals. The interaction of the X-rays with the periodic arrangement of atoms usually provides structural information about the scatterer. Unlike the usual Bragg reflection, the so-called two-wave diffraction, the multiply diffracted intensities are sensitive to the phases of the structure factors in volved. This gives X-ray multiple-wave diffraction the chance to solve the X-ray phase problem. On the other hand, the condition for generating an X ray multiple-wave diffraction is much more strict than in two-wave cases. This makes X-ray multiple-wave diffraction a useful technique for precise measure ments of crystal lattice constants and the wavelength of radiation sources. Recent progress in the application of this particular diffraction technique to surfaces, thin films, and less ordered systems has demonstrated the diver sity and practicability of the technique for structural research in condensed matter physics, materials sciences, crystallography, and X-ray optics. The first book on this subject, Multiple Diffraction of X-Rays in Crystals, was published in 1984, and intended to give a contemporary review on the fundamental and application aspects of this diffraction.

(Historical Survey) The discovery of X-ray diffraction in crystals by LAUE, FRIDRICH and KNIPPING in 1912 [1.1] served as the starting pOint for the development of scientific research along a number of important lines. We shall discuss just a few of them. The above discovery convincingly demonstrated the wave properties of X-rays. This, together with the previously established electromagnetic nature of radiation, confirmed the hypothesis that X-rays form the short-wave part of the electromagnetic spectrum. Further, this discovery was the first and decisive experimental proof of the periodic structure of crystals. In fact, theoretical crystallography had already arrived at this conclusion, mainly as an outcome of the theory of the space groups of symmetry elaborated by FEDOROV [1.2] and SCHOENFLIES [1.3]. From the optics of visible light we know that the radiation of a wave length of the same order as, and preferably less than, the period of a grat ing suffers diffraction on periodic objects of the type of optical grating. Thus, the discovery proved that the wavelength of an X-ray must be of the order of interatomic distances. It became clear why the visible light of wavelengths exceeding the crystal lattice periods by about 500 to 1000 times failed to reveal the periodic structure of crystals in diffraction experi ments.

This book provides a concise survey of modern theoretical concepts of X-ray materials analysis. The principle features of the book are: basics of X-ray scattering, interaction between X-rays and matter and new theoretical concepts of X-ray scattering. The various X-ray techniques are considered in detail: high-resolution X-ray diffraction, X-ray reflectivity, grazing-incidence small-angle X-ray scattering and X-ray residual stress analysis. All the theoretical methods presented use the unified physical approach. This makes the book especially useful for readers learning and performing data analysis with different techniques. The theory is applicable to studies of bulk materials of all kinds, including single crystals and polycrystals as well as to surface studies under grazing incidence. The book appeals to researchers and graduate students alike.

The three-dimensional arrangement of atoms and molecules in crystals and the comparable magnitude of x-ray wavelengths and interatomic distances make it possible for crystals to have more than one set of atomic planes that satisfy Bragg's law and simultaneously diffract an incident x-ray beam - this is the so-called multiple diffraction. This type of diffraction should, in prin ciple, reflect three-dimensional information about the structure of the dif fracting material. Recent progress in understanding this diffraction phenome non and in utilizing this diffraction technique in solid-state and materials sciences reveals the diversity as well as the importance of multiple diffraction of x-rays in application. Unfortunately, there has been no single book written that gives a sys tematic review of this type of diffraction, encompasses its diverse applica tions, and foresees future trends gf development. It is for this purpose that this book is designed. It is hoped that its appearance may possibly turn more attention of condensed-matter physicists, chemists and material scientists toward this particular phenomenon, and that new methods of non-destructive analysis of matter using this diffraction technique may be developed in the future.

Rigorous graduate-level text stresses modern applications to nonstructural problems such as temperature vibration effects, order-disorder phenomena, crystal imperfections, more. Problems. Six Appendixes include tables of values. Bibliographies.