Crystallographers have to apply many mathematical methods in their daily work. Mathematical Techniques in Crystallography and Materials Science brings together common and less familiar mathematical procedures used in studies of the structures and physical properties of solids. This practical guide and reference serves as a unified source book for students and professionals, and it provides a solid basis for further studies in more specialized literature. Based Prince s decades of practical experience, it can be recommended as an introduction for beginners in crystallography, as a refresher and handy guide for crystallographers working on specific problems, and as a reference for others seeking a dictionary of basic mathematical and crystallographic terms. The third edition further clarifies key points, as well as offers new sections on two topics: the projection matrix and the fast Fourier transform. "

This two-volume work forms a comprehensive treatise on the theory and applications of electron-diffraction techniques, and has been organized under the auspices of the Electron Diffraction Commission of the International Union of Crystallography. All those embarking on research which involves the use of electron diffraction methods, including graduate students and more experienced researchers who wish to add electron diffraction to their array of research tools will find this an invaluable reference. Volume 1 contains introductory chapters and the sections on electron diffraction which are less dependent on considerations of imaging in electron microscopes. Volume 2 deals with those aspects where there is a stronger correlation of the diffraction phenomena with the electron microscope imaging.

This is the first comprehensive book on the dynamical diffraction of X-rays since the development of synchrotron radiation. Up-to-date, with extensive references, it is required knowledge for x-ray optics and x-ray characterization of materials. An excellent reference book for graduate students and researchers.

The accurate determination of the structure of molecular systems provides information about the consequences of weak interactions both within and between molecules. These consequences impact the properties of the materials and the behaviour in interactions with other substances. The book presents modern experimental and computational techniques for the determination of molecular structure. It also highlights applications ranging from the simplest molecules to DNA and industrially significant materials.

Readership Graduate students and researchers in structural chemistry, computational chemistry, molecular spectroscopy, crystallography, supramolecular chemistry, solid state chemistry and physics, and materials science.

This book is structured by two-level presentation including a simple descriptive treatment and slightly more in-depth discussions of specific topics. The first-level treatment covers the notions, terminology and techniques that are required to use a synchrotron facility. The book is therefore an ideal first step for all those beginning to use synchrotron light for their work or are considering it. The treated topics include the basic functioning mechanisms of synchrotrons and free electron lasers a description of sychrotron-based techniques in x-ray imaging and radiology, spectroscopy, microscopy and spectromicroscopy, EXAFS, crystallography and scattering, and microfabrication.

There has been an explosion of interest in the study of molecular crystals, and their applications in optics and electronics. This advanced 1994 textbook describes their chemical and physical structure, their optical and electronic properties and the reactions between neighbouring molecules in crystals. The author has taken into account research areas which have undergone extremely rapid development since the first edition was published in 1987. For instance, this edition features the applications of molecular materials in high-technology devices. There is also an additional chapter on C60 and organic non-linear optic materials. The level of treatment is aimed at first-year postgraduates or workers in industrial research laboratories wishing to gain insights into organic solid state materials. Molecular Crystals is also suitable for special topics in final year undergraduate courses in chemistry, physics and electronic engineering.

This volume contains papers presented at the NATO Advanced Study Institute (ASI) Photonic Crystals and Light Localization held at the Creta Maris Hotel in Limin Hersonissou, Crete, June 18-30, 2000. Photonic crystals offer unique ways to tailor light and the propagation of electromagnetic waves (EM). In analogy to electrons in a crystal, EM waves propagating in a structure with a periodically modulated dielectric constant are organized into photonic bands, separated by gaps where propagating states are forbidden. There have been proposals for novel applications ofthese photonic band gap (PBG) crystals, with operating frequencies ranging from microwave to the optical regime, that include zero threshold lasers, low-loss resonators and cavities, and efficient microwave antennas. Spontaneous emission, suppressed for photons in the photonic band gap, offers novel approaches to manipulate the EM field and create high-efficiency light-emitting structures. Innovative ways to manipulate light can have a profound iofluence on science and technology."

This book is the only book on the subject written to explain the basics of synchrotron radiation for scientists including life sciences, chemistry, and medicine. It can also be used as a textbook at the undergraduate or graduate level.

The electron density of a non-degenerate ground state system determines essentially all physical properties of the system. This statement of the Hohenberg-Kohn theorem of Density Functional Theory plays an exceptionally important role among all the fundamental relations of Molecular Physics. In particular, the electron density distribution and the dynamic properties of this density determine both the local and global reactivities of molecules. High resolution experimental electron densities are increasingly becoming available for more and more molecules, including macromolecules such as proteins. Furthermore, many of the early difficulties with the determination of electron densities in the vicinity of light nuclei have been overcome. These electron densities provide detailed information that gives important insight into the fundamentals of molecular structure and a better understanding of chemical reactions. The results of electron density analysis are used in a variety of applied fields, such as pharmaceutical drug discovery and biotechnology. If the functional form of a molecular electron density is known, then various molecular properties affecting reactivity can be determined by quantum chemical computational techniques or alternative approximate methods.

The prime objective of the collection of lectures contained in this book is to formulate our current understanding of aperiodic solids with long range order, quasicrystals in particular. At the same time it provides a comprehensive insight into the most recent concepts and tools of condensed matter physics and gives a detailed discussion and interpretation of relevant experimental data. The deliberate pedagogical approach of the authors makes this book particularly useful for graduate students and experimentalists wishing to acquaint themselves with the fundamental concepts.

This book, together with its companion volume The Science of Crystallization: Microscopic Interfacial Phenomena, make up a complete course that will teach an advanced student how to understand and analyse scientifically any of the phenomena that are observed during natural or technological crystallization from any medium and via any technique. It is an advanced text that goes into considerable detail concerning the many elements of knowledge needed to understand both quantitatively and qualitatively a crystallization event. Both the present book and its companion volume are sufficiently broad to provide the scientific basis necessary to address any area of application. The book and its companion can be used independently of each other, and together they provide the basis for advanced courses on crystallization in departments of materials science, metallurgy, electrical engineering, geology, chemistry, chemical engineering and physics. In addition the books will be invaluable to scientists and engineers in the solid state electronics, optoelectronics, metallurgical and chemical industries involved in any form of crystallization and thin film formation.

Crystal engineering is an interdisciplinary area that cuts across the traditional subdivisions of chemistry. Fuelled by our increasingly precise understanding of the chemistry and properties of supramolecular systems, interest in the potential of the field has increased rapidly. The topics discussed in the 28 contributions in this book provide a state-of-the-art description of the field and offer new research ideas that, if pursued, will serve to strengthen the field at the interface between supramolecular chemistry and materials science.

The 10th edition of the World Directory of Crystallographers and of Other Scientists Employing Crystallographic Methods is a revised and up-to-date edition of the World Directory and contains the current addresses, academic status and research interests of over 8000 scientists in 74 countries. It is produced directly from the regularly updated electronic World Directory database, which is accessible via the World-Wide Web. Full details of the database are given in an Annex to the printed edition.

At the time of its original publication this reissued 'classic' text, co-written by the Nobel Laureate of 1954, Max Born, represented the final account of the subject and in many ways it still does. The book is divided into four sections. The first of these is very general in nature and deals with the general statistical mechanics of ideal lattices, leading to the electric polarizability and to the scattering of light. The second part deals with the properties of long lattice waves; the third with thermal properties and the fourth with optical properties.

Site Symmetry in Crystals is the first comprehensive account of the group-theoretical aspects of the site (local) symmetry approach to the study of crystalline solids. The efficiency of this approach, which is based on the concepts of simple induced and band representations of space groups, is demonstrated by considering newly developed applications to electron surface states, point defects, symmetry analysis in lattice dynamics, the theory of second-order phase transitions, and magnetically ordered and non-rigid crystals. Tables of simple induced respresentations are given for the 24 most common space groups, allowing the rapid analysis of electron and phonon states in complex crystals with many atoms in the unit cell.

A number of general-purpose, reasonably accurate and well-tested ab-initio codes for crystals are discussed in this book. The aim is to expand competence of their application in material sciences and solid-state physics. The book addresses particularly readers with a general knowledge in quantum chemistry and intends to give a deeper insight into the special algorithms and computational techniques in ab-initio computer codes for crystals. Three different programs which are available to all interested potential users on request are presented.

The application of neutron scattering to polymers has been extremely successful during the last two decades. This book presents, for the first time, both the theories and experimental examples which are needed to understand how these techniques can be applied. Now available in paperback for the first time this book is specifically written to introduce the newcomer and non-expert to the experimental techniques and the basic theory necessary to understand the results.

Electrooptic effects provide the basis for much liquid-crystal display technology. This book, by two of the leaders in liquid-crystal research in Russia, presents a complete and accessible treatment of virtually all known phenomena occurring in liquid crystals under the influence of electric fields.

This text describes the theory and practice of optical mineralogy in terms useful to all practitioners from the beginning student to the professional in field and laboratory geology and industrial and environmental mineralogy. The author's aim is to provide the simplest possible access to the most powerful techniques of optical crystal identification. The book emphasizes useful practical theoretical material and methods for studying both thin sections of rocks and immersion of mineral grains in refractive index liquids. It contains original research results found in no other text. A major goal of the text is to allow precise determination of refractive index and the essential composition of crystals belonging to important mineral groups such as olivine, feldspar, and pyroxene. New methods for achieving this are developed for both white light and colored light of variable wavelength. Among the book's unique features is the color fringe chart developed by Prof. Morse for estimating both the direction and degree of mismatch between the refraction index of a crystal and that of the surrounding liquid medium in the immersion method. Further, a new algebraic treatment of the dispersion method allows a high precision of match between crystal and liquid. An original classification of interference figures aids crystal identification. Worked examples of refractive index determination and crystal identification are given for each optical class of crystals. The optic orientation of optically biaxial crystals is illustrated with examples from each crystal system portrayed in stereographic projection. Principles and applications of crystal identification with the dispersion method are developed in aseparate chapter. The final chapter is a practical, step-by-step guide to crystal identification in thin section or immersion. An identification table for the most common asbestos minerals, including the dispersion staining method used by most environmental laboratories.

Modern structural applications of crystallography make extensive use of statistical methods, in particular the probability density function (pdf) of the magnitude of the structure factor. Similarly, direct methods of phase determination have been responsible for much of the success of crystallography - methods based on properties of joint pdfs. This monograph, from two authorities in the field of structure factor statics, presents a survey of techniques and theories in this field of research in a self-contained and consistent way, with an emphasis on the probabilistic principles involved.

This book is the collection of most of the written versions of the Courses given at the Winter School "Beyond Quasicrystals" in Les Houches (March 7-18, 1994). The School gathered lecturers and participants from all over the world and was prepared in the spirit of a general effort to promote theoretical and experimental interdisciplinary communication between mathematicians, theoretical and experimental physicists on the topic of the nature of geometric order in solids beyond standard periodicity and quasi periodicity. The overall structure of the book reflects the wish of the editors to pose this fundamental question of geometric order in solids from both the experimental and theoretical point of view. The first part is devoted more specifically to quasicrystals. These materials were the common starting point of most of the audience and present a first concrete example of a non-trivial geometric order. We chose to focus on a few fundamental aspects of quasicrystals related to hidden symmetries in solids which are not easily found in standard textbooks on the topic, not to reach an exhaustive survey which is already available elsewhere.

Modern experimental and computational techniques are capable of determining bond lengths and angles with precisions of a few thousandths of an angstrom and a few tenths of a degree. Such precisions are meaningful only if they are coupled with rigorous error analysis and careful evaluation of the physical meaning of the parameters. This book demonstrates the meaning and applicability of accurate structures and their variations following a rigorous exposure of the demands and caveats in their determination. It establishes guidelines for accuracy requirements in answering broadly varying questions in current chemical research. The 21 chapters by internationally recognized authors discuss the following topics: potential energy surfaces; microwave, infrared, and liquid crystal NMR spectroscopies; gas phase electron diffraction; X-ray and neutron crystallography; electron density studies; ab initio molecular orbital methods and molecular mechanics calculations; the use of structural databases; applications to organic inorganic and organometallic chemistry; studies of reaction pathways; effects of substitution and crystal environment on molecular structure.

Cellular growth, especially its pattern formation, has been studied both experimentally and numerically. In situ observations of faceted cellular growth have clearly revealed cellular interactions in the array of cells. For the first time, the true time-dependent faceted cellular array growth has been modelled properly. It has been found that pattern formation is determined by cellular interactions in the array. Readers of the book will obtain a general view of the field of pattern formation in crystal growth, and in-depth and up-to-date knowledge of faceted cellular array growth, which occurs in semiconductor crystals.