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 work deals with the effect of crystal symmetry in determining the tensor properties of crystals. Although this is a well-established subject, the author provides a fresh approach using group theory and, in particular, the method of symmetry coordinates, which has not been used in previous books. Using this approach, all tensors of a given rank and type can be handled together, even when they involve very different physical phenomena. Applications to technologically important phenomena as diverse as the electro-optic, piezoelectric, photoelastic, piezomagnetic, and piezoresistance effects, as well as magnetothermoelectric power and third-order elastic constants, are presented. Attention is also given to special magnetic properties - that is, those that require the concepts of time reversal and magnetic symmetry, an important subject not always covered in other books in this area. This book should be of interest to researchers in solid state physics and materials science, and should also be suitable as a text for graduate students in physics and engineering taking courses in solid state physics.

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.

Despite the fact that crystals make up an estimated 80% of chemical and pharmaceutical products, few resources exist that provide practical guidance on achieving precision control of their size and size distribution. Based on a model developed by the author and his colleagues, Precision Crystallization: Theory and Practice of Controlling Crystal Size presents scientists and product engineers with the tools to control crystal nucleation, enabling them to ultimately control crystal size and size distribution for batch and continuous crystallizations. At the cutting edge of crystallization science and technology, this volume presents information never before available. Introducing the Balanced Nucleation and Growth (BNG) model, the book demonstrates how the results of the nucleation process are quantitatively related to practical experimental control values such as: reaction addition rate crystal solubility temperature residence time (continuous crystallizations) the effect of ripening agents (crystal supersizing) during nucleation the effect of crystal growth restrainers (crystal nanosizing) during nucleation control of renucleation The author shows how the BNG theory predicts previously unknown phenomena and also how it corrects erroneous perceptions of the importance of reaction volume on the outcome of crystal nucleation. Going above and beyond classical nucleation theories which rely to a large extent on guesswork, the BNG model gives precise guidance to scientists working in a range of critical areas, leading to promising implications for research, quality control, product development, production processes, pilot plant operations, and manufacturing.

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.

This book presents a computational scheme for calculating the electronic properties of crystalline systems at an ab-ini tio Hartree-Fock level of approximation. The first chapter is devoted to discussing in general terms the limits and capabilities of this approximation in solid state studies, and to examining the various options that are open for its implementation. The second chapter illustrates in detail the algorithms adopted in one specific computer program, CRYSTAL, to be submitted to QCPE. Special care is given to illustrating the role and in: fluence of computational parameters, because a delicate compromise must always be reached between accuracy and costs. The third chapter describes a number of applications, in order to clarify the possible use of this kind of programs in solid state physics and chemistry. Appendices A, B, and C contain various standard expressions, formulae, and definitions that may be useful for reference purposes; appendix D is intended to facilitate the interpretations of symbols, conventions, and acronyms that occur in the book. Thanks are due to all those who have contributed to the implementation and test of the CRYSTAL program, especially to V.R. Saunders and M. Causal, and to F. Ricca, E. Ferrero, R. Or lando, E. Ermondi, G. Angonoa, P. Dellarole, G. Baracco

Providing the first comprehensive overview of the method of crystal growth in gels, Professor Henisch reviews the field, covering the underlying physics as well as the empirical experience of growth techniques accumulated over the past century. In addition, the book discusses the phenomenon of periodic precipitation, which often governs the distribution of crystal in laboratory growth systems. For the first time, computer techniques are brought to bear on the subject, the diffusion equations being solved numerically, in association with the conditions governing precipitations and crystal growth.

A brief historical account of the background leading to the publication of the first four editions of the World Directory of Crystallographers was presented by G. Boom in his preface to the Fourth Edition, published late in 1971. That edition was produced by traditional typesetting methods from compilations of biographical data prepared by national Sub-Editors. The major effort required to produce a directory by manual methods provided the impetus to use computer techniques for the Fifth Edition. The account of the production of the first computer assisted Directory was described by S.C. Abrahams in the preface of the Fifth Edition. Computer composition, which required a machine readable data base, offered several major advantages. The choice of typeface and range of characters was flexible. Corrections and additions to the data base were rapid and, once established, it was hoped updating for future editions would be simple and inexpensive. The data base was put to other Union uses, such as preparation of mailing labels and formulation of lists of crystallographers with specified common fields of interest. The Fifth Edition of the World Directory of Crystallographers was published in June of 1977, the Sixth in May of 1981. The Subject Indexes for the Fifth and Sixth Editions were printed in 1978 and 1981 respectively, both having a limited distribution.

In the last decade mathematical crystallography has found increasing interest. Siginificant results have been obtained by algebraic, geometric, and group theoretic methods. Also classical crystallography in three-dimen sional Euclidean space has been extended to higher dimen sions in order to understand better the dimension independent crystallographic properties. The aim of this note is to introduce the reader to the fascinating and rich world of geometric crystallography. The prerequisites for reading it are elementary geometry and topological notations, and basic knowledge of group theory and linear algebra. Crystallography is geometric by its nature. In many cases, geometric arguments are the most appropriate and can thus best be understood. Thus the geometric point of view is emphasized here. The approach is axiomatic start ing from discrete point sets in Euclidean space. Symmetry comes in very soon and plays a central role. Each chapter starts with the necessary definitions and then the subject is treated in two- and three-dimensional space. Subsequent sections give an extension to higher dimensions. Short historical remarks added at the end of the chapters will show the development of the theory. The chapters are main ly self-contained. Frequent cross references, as well as an extended subject index, will help the reader who is only interested in a particular subject."

Liquid crystal displays were discovered in the 1960s, and today we continue to enjoy the benefits of that fundamental discovery and its translation into a wide variety of products. Like liquid crystals, polymers are unusual materials, and have similarly enjoyed a great deal of research attention because of their vast applications and uses and complex fundamental properties. The combination of liquid crystal and polymer properties produces a broad array of new effects-spanning from densely crosslinked, rigid polymer networks to weakly crosslinked elastomers-that are not simply manifestations of either native liquid crystals or polymers alone. Cross-Linked Liquid Crystalline Systems brings together liquid crystal and polymer systems and their variations. The field, much like traditional liquid crystals, is one of an interdisciplinary nature with a broad spectrum, from the very fundamental questions of nature to a myriad of practical uses. There seems to be no shortage of unusual properties and far-reaching applications in densely crossed-linked liquid crystal systems and liquid crystal elastomers. These systems provide a rich new avenue for both fundamental and applied research and continue to fascinate scientists and engineers. Specifically, this book covers: Cross-linked networks created from reactive mesogen materials Manipulation of liquid crystalline by external constraints Advances in liquid crystal display screen technology Physical and electromagnetic properties of elastomers and magnetic gels Computer simulations and theory of liquid crystal polymeric networks and elastomers Side-on nematic liquid-crystalline elastomers for artificial muscle applications Liquid crystal display technology has driven much of the fundamental research in crosslinked liquid crystalline systems. The systems' ability to enforce three-di

This book introduces the growing problem of microplastics pollution in the soil and aquatic environment and its interaction with other chemical pollutants. Further, it provides a detailed review of existing analysis techniques for characterization, separation, and quantification of microplastics including their merits and demerits with possible suggestions. Additionally, the regulatory need and actions for improving the economic and quality of plastic recycling, curbing microplastic littering, and stakeholders, researchers, and recyclers challenges are reviewed comprehensively. Priorities are identified to bridge the knowledge gaps for appropriate management of existing challenges. Features: Provides a comprehensive description of the fate and environmental impact of microplastics, along with various characterization methods Overviews the interaction of microplastics with other toxic chemicals and further their transportation in environment Explains how microplastics enter in environment and its effect on biota and human health Analyses existing analytical techniques for characterization of microplastics Describes societal awareness related to use of plastic and discarding This book focusses on graduate students, researchers in environmental engineering, ecological engineering, chemical and biological engineering, plastics and material sciences/engineering, waste management. materials science.

Crystallography is one of the most multidisciplinary sciences, with roots in fields as varied as mathematics, physics, chemistry, biology, materials science, computation and earth and planetary science. The structural knowledge gained from crystallography has been instrumental in acquiring new levels of understanding in numerous scientific areas. Perspectives in Crystallography provides an overview of the current state of the field, reviews its historical origins and explains how crystallography contributes to the sustainability of life. This book resonates with the recent United Nations and UNESCO International Year of Crystallography, a celebration of its achievements and importance, undertaken with the International Union of Crystallography. The author of this book is the editor in chief of Crystallography Reviews, where some of the contents have been previously published. Here, subjects of interest to specialists and non-specialists have been brought together in a single source. The book opens with a description of the ways to explain crystallography to diverse general audiences. It also addresses various topics in crystallography, including: The evolution and importance of synchrotron radiation to crystallography The structural chemistry and biology of colouration in marine crustacea Predicting protonation states of proteins versus crystallographic experimentation The book then offers a projection of crystal structure analysis in the next 100 years and concludes by emphasizing the societal impacts of crystallography that allow for sustainability of life. Perspectives in Crystallography offers a threefold look into the past, present and long-term development and relevance of crystal structure analysis. It is concerned not only with the state of the field, but with its role in the perpetuation of life on earth. As such, it is a reference of vital interest to a bro