X-ray diffraction crystallography for powder samples is a well-established and widely used method. It is applied to materials characterization to reveal the atomic scale structure of various substances in a variety of states. The book deals with fundamental properties of X-rays, geometry analysis of crystals, X-ray scattering and diffraction in polycrystalline samples and its application to the determination of the crystal structure. The reciprocal lattice and integrated diffraction intensity from crystals and symmetry analysis of crystals are explained. To learn the method of X-ray diffraction crystallography well and to be able to cope with the given subject, a certain number of exercises is presented in the book to calculate specific values for typical examples. This is particularly important for beginners in X-ray diffraction crystallography. One aim of this book is to offer guidance to solving the problems of 90 typical substances. For further convenience, 100 supplementary exercises are also provided with solutions. Some essential points with basic equations are summarized in each chapter, together with some relevant physical constants and the atomic scattering factors of the elements.

Nuclear magnetic resonance spectroscopy, which has evolved only within the last 20 years, has become one of the very important tools in chemistry and physics. The literature on its theory and application has grown immensely and a comprehensive and adequate treatment of all branches by one author, or even by several, becomes increasingly difficult. This series is planned to present articles written by experts working in various fields of nuclear magnetic resonance spectroscopy, and will contain review articles as well as progress reports and original work, its main aim, however, is to fill a gap, existing in literature, by publishing articles written by specialists, which take the reader from the introductory stage to the latest development in the field. The editors are grateful to the authors for the time and effort spent in writing the articles, and for their invaluable cooperation. The Editors Contents P. Diehl and C. L. Khetrapal NMR Studies of Molecules Oriented in the Nematic Phase of Liquid Crystais......................................................... 1 R. G. Jones The Use of Symmetry in Nuclear Magnetic Resonance................. 97 NMR Studies of Molecules Oriented in the Nematic Phase of Liquid Crystals P. DIEHL and C. L. KHETRAPAL * Department of Physics, University of Basel, Switzerland Contents 1. Introduction . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2. Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . . . . . . . . . . . . . . 2.1. Classification of Liquid Crystal Phases . . . . . . . . . . . . . . . . . . . . . . . 4 2.2. Theories of the Liquid Crystalline State . . . . . . . . . . . . . . . . . . . . . . 5 2.3. Nematic Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3. Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1 4. Basic Theory (for I = I ). . . . . . . . . . . . . * . . . . . . . . . . . . . . . . . . . . . . . 7 . .

This book provides a comprehensive study of the symmetry and geometry of crystals and molecules, starting from first principles. The pre-knowledge assumed is mathematics and physical science to about A-level; additional mathematical topics are discussed in appendices. It is copiously illustrated, including many stereoviews, with instructions both for stereoviewing and for constructing a stereoviewer. Problems for each chapter are provided, with fully worked tutorial solutions. A suite of associated computer programs has been devised and placed on-line, for assisting both the study of the text and the solutions of the problems. The programs are easily executed, and instructions are provided in the text and on the monitor screen. The applicability of symmetry in everyday life as well as in science is stressed. Point groups and space groups are first discussed and derived in a semi-analytical manner, and later by use of group theory. The basic principles of group theory are discussed, together with applications to symmetry, chemical bonding and aspects of vibrations of molecules and crystals. The book is addressed to those studying the physical sciences and meeting the subject for the first time, and it brings the reader to a level of appreciation for the definitive works produced by the International Union of Crystallography, such as the International Tables for X-ray Crystallography, Vol 1 (1965) and the International Tables for Crystallography, Vol A (2006).

This work presents a snapshot of the state of the art of modern biomolecular crystallography, from crystallisation through structure determination and even interactive presentation on the web. Methods driving the latest automated structure determination pipelines are explained, as well as how to deal with problems such as crystal pathologies that still demand expert analysis. These methods are illustrated through their application to problems of great biological interest, such as the molecular machinery underlying the complement pathway, the mechanism of action of monoamine oxidase inhibitors, and the structure of the eukaryotic ribosome. Complementary approaches, such as neutron diffraction, small angle X-ray scattering, coherent diffraction and computational modelling, are also explored.

The advances in and applications of x-ray and neutron crystallography form the essence of this new edition of this classic textbook, while maintaining the overall plan of the book that has been well received in the academic community since the first edition in 1977. X-ray crystallography is a universal tool for studying molecular structure, and the complementary nature of neutron diffraction crystallography permits the location of atomic species in crystals which are not easily revealed by X-ray techniques alone, such as hydrogen atoms or other light atoms in the presence of heavier atoms. Thus, a chapter discussing the practice of neutron diffraction techniques, with examples, broadens the scope of the text in a highly desirable way. As with previous editions, the book contains problems to illustrate the work of each chapter, and detailed solutions are provided. Mathematical procedures related to the material of the main body of the book are not discussed in detail, but are quoted where needed with references to standard mathematical texts. To address the computational aspect of crystallography, the suite of computer programs from the fourth edition has been revised and expanded. The programs enable the reader to participate fully in many of the aspects of x-ray crystallography discussed in the book. In particular, the program system XRAY* is interactive, and enables the reader to follow through, at the monitor screen, the computational techniques involved in single-crystal structure determination, albeit in two dimensions, with the data sets provided. Exercises for students can be found in the book, and solutions are available to instructors.

The interest of describing the ground state properties of a system in terms of one electron density (or its two spin components) is obvious, in particular due to the simple physical significance of this function. Recent experimental progress in diffraction made the measurement of charge and magnetization densities in crystalline solids possible, with an accuracy at least as good as theoretical accuracy. Theoretical developments of the many-body problem have proved the extreme importance of the one electron density function and presently, accurate methods of band structure determination become available. Parallel to the diffraction techniques, other domains of research (inelastic scattering, resonance, molecular spectroscopy) deal with quantities directly related to the one particle density. But the two types of studies do not interfere enough and one should obviously gain more information by interpreting all experiments that are related to the density together. It became necessary to have an International School that reviews the status of the art in the domain of "ELECTRON AND MAGNETIZATION DENSITIES IN MOLECULES AND CRYSTALS." This was made possible through the generous effort of N.A.T.O. 's Scientific Affairs Division, and I would specially thank Dr. T. KESTER, the head of this Division, for his help and competence. An Advanced Study Institute was thus held in ARLES, south France, from the 16th to the 31st of August 1978.

This monograph is not confined to mechanical twinning in the narrow sense (lattice reorientation in re- sponse to mechanical stress); it deals also with many effects related to mechanical twinning. such as formation of reoriented regions in response to high temperatures (martensite transformations. recrystallization twins). elec- tric fields (ferroelectric domains). and magnetiC fields (magnetic domains). Mechanical reorientation is discussed for classical twinning and also for an inhomogeneous distribution of residual stresses (irrational twinning. kinking. and so on). Mechanical twinning in the narrow sense (regular. symmetrical lattice reorientation in response to me- chanical stress) was for many years a specialist topic for mineralogists. petrographers. and crystallographers. Mineralogists and crystallographers carried out the study of the basic geometrical relationships in twinning; the principal names here are MUgge, Niggli. Johnsen. Reusch. Baumhauer. Churchman. Wallerant. Evans. and FriedeL The laws of mechanical twinning are now widely used in mineral identification and in elucidating the conditions of formation of rocks from the minerals they contain. The distribution of the twin bands in rock- forming minerals enables one to establish the later processes that have occurred in the rock. Mechanical twinning is discussed by geOlogiSts and petrologists in the analYSis of flow effects. The importance of mechanical twinning in the plastic deformation and rupture of crystalline solids was W stressed by Academician V. I. Vernadskii in 1897 and by Kirpicheva ina paper entitled WFatigue in Metals in 1914.

It is nonnal for the preface to explain the motivation behind the writing of the book. Since many good books dealing with the general theory of crystal defects already exist, a new book has to be especially justified, and here its main justification lies in its treatment of crystal line interfaces. About 1961, the work of the author, essentially based on the fundamental work of Professor F. C. Frank, started to branch away from the main flow of thought in this field and eventually led to a general geometrical theory which is presented as a whole for the first time in this book. Although nearly all that is presented has already been published in different journals and symposia, it might be difficult for the reader to follow that literature, as a new terminology and new methods of analysis had to be developed. Special emphasis is given to discussion and many diagrams are included in order that a clear view of the basic concepts be obtained. Intennediate summaries try to bring out the main points of the chapters. Instead of specific exercises, general suggestions for them are given. The part up to chapter 9 is considered more or less as introductory, so that the book can be studied without specific knowledge of crystals and crystal defects. The presentation of that part developed out of lectures given by the author at the Swiss Federal Institute of Technology (ETH) in Zurich."

1. The ninth International Summer School on Crystal Growth. ISSCG IX A complete theory of crystal growth establishes the full dependence of crystal size, shape and structure on external parameters like temperature, pressure, composition, purity, growth rate and stirring of the mother phase, implicitly establishing how the corresponding fields vary in space and time. Such a theory does not exist, however. Therefore equipment to grow crystals is developed on the basis of partial knowledge. Skill, experience and creativity still are of central importance for the success o~ a crystal growth system. In this book we collected contributions from the teachers of the ninth International Summer School on Crystal Growth ISSCG IX, held 11-16 june 1995 at Papendal, the national sports centre of the Netherlands. These contributions were used during the lectures. The authors have tried to present their work in such a way that only basic physical knowledge is required to understand the papers. The book can be used as an introduction to various important sub disciplines of the science and technology of crystal growth. Since, however the information content considerably exceeds a lecture note level and touches the present limits of understanding, it is an up to date handbook as well.

The NATO Special Programme Panel on Condensed Systems of Low Dimensionality began its work in 1985 at a time of considerable activity in the field. The Panel has since funded many Advanced Research Workshops, Advanced Study Institutes, Cooperative Research Grants and Research Visits across the breadth of its remit, which stretches from self-organizing organic molecules to semiconductor structures having two, one and zero dimensions. The funded activities, especially the workshops, have allowed researchers from within NATO countries to exchange ideas and work together at a period of development of the field when such interactions are most valuable. Such timely support has undoubtedly assisted the development of national programs, particularly in the countries of the alliance wishing to strengthen their science base. A closing Workshop to mark the end of the Panel's activities was organized in Marmaris, Turkey from April 23-27, 1990, with the same title as the Panel: Condensed systems of Low Dimensionality. This volume contains papers presented at that meeting, which sought to bring together chemists, physicists and engineers from across the spectrum of the Panel's activities to discuss topics of current interest in their special fields and to exchange ideas about the effects of low dimensionality. As the following pages show, this is a topic of extraordinary interest and challenge which produces entirely new scientific phenomena, and at the same time offers the possibility of novel technological applications.

This book, a continuation of the series "Advances in Materials Research," is intended to provide the general basis of the science and technology of crystal growth of silicon for solar cells. In the face of the destruction of the global environment,the degradationofworld-widenaturalresourcesandtheexha- tion of energy sources in the twenty-?rst century, we all have a sincere desire for a better/safer world in the future. In these days, we strongly believe that it is important for us to rapidly developanewenvironment-friendlycleanenergyconversionsystemusingsolar energyastheultimatenaturalenergysource. Forinstance,mostofournatural resources and energy sources will be exhausted within the next 100 years. Speci?cally, the consumption of oil, natural gas, and uranium is a serious problem. Solar energy is the only ultimate natural energy source. Although 30% of total solar energy is re?ected at the earth's surface, 70% of total solar energy can be available for us to utilize. The available solar energy amounts to severalthousand times larger than the world's energy consumption in 2000 of about 9,000 Mtoe (M ton oil equivalent). To manage 10% of the world's energy consumption at 2050 by solar energy, we must manufacture 40 GW solar cells per year continuously for 40 years. The required silicon feedstock is about 400,000 ton per year. We believe that this is an attainable target, since it can be realized by increasing the world production of silicon feedstock by 12times asmuchasthe presentproductionat2005.

This volume is a collection of the contributions presented at the 42nd Erice Crystallographic Course whose main objective was to train the younger generation on advanced methods and techniques for examining structural and dynamic aspects of biological macromolecules. The papers review the techniques used to study protein assemblies and their dynamics, including X-ray diffraction and scattering, electron cryo-electron microscopy, electro nanospray mass spectrometry, NMR, protein docking and molecular dynamics. A key theme throughout the book is the dependence of modern structural science on multiple experimental and computational techniques, and it is the development of these techniques and their integration that will take us forward in the future.

The scientific work of Jean Mandel has been exceptionally rich in the area of the mechanics of solids; the subjects which he has treated have been extremely diverse, from the theory of plasticity, buckling, soil mechanics, visco-elasticity, the theory of reduced models, and thermo dynamics, to percolation in porous media. But throughout this com prehensive work Jean Mandel has always maintained his interest in forming connections between the properties of materials (strength, deformability, viscosity) and the properties of their basic constituents. What is sometimes referred to in materials science as the transition from the microscopic to the macroscopic has for him been a very constant direction of research, which he never ceased to encourage in the Laboratoire de Mecanique des Solides of which he was the director. It is known that in the plasticity of metals permanent deformations must be sought in intercrystalline slip and more generally in disloca tions and the various microstructural defects. Before deformation of polycrystals is tackled, it is necessary to understand the mechanisms which take place within the crystal: the different systems of slip which may be activated and also the elementary mechanisms of twinning. Jean Mandel has shown how to make the transition from the behaviour of the single crystal to that of the polycrystal and has given the relation ships between the overall permanent deformation of the polycrystal and the plastic deformation of the single crystal."

There is no doubt that in the development of the Physics and Chemistry of Solids during the last fifteen years, the very important place taken by low-dimensional compounds will be remembered as a major event. Dealing very widely at the beginning with two-dimensional structures and intercalation chemistry, this theme progressively evolved as the synthesis of one-dimensional conductors increased, along with the observation of their remarkable properties. Beyond the classical separation of the traditional disciplines, essential progress has stemmed each time from the concerted efforts of, and overlapping between, chemists, experimental physicists, and theoreticians. This book is a synthetic approach which aims to retrace these united efforts. The observation and characterization of charge density waves in their static or dynamic aspects have been the main points to attract the interest of researchers. Two broad categories of compounds have been the material basis of these observa tions: transition-metal polychalcogenides and either condensed-cluster phases or bronze-type compounds. These families are referred to throughout the various chapters of this book, thus illustrating the continuous progress of concepts in this domain and, at the same time, providing the first synthetic and exhaustive view of this group of materials."

With the development of diverse analytical chemistry techniques, the discovery of rich and numerous properties pertaining to bicontinuous liquid crystal structures has yielded beneficial applications in medicine, consumer products, materials science, and biotechnology. Presenting contributions from 24 experts worldwide, Bicontinuous Liquid Crystals presents a comprehensive overview of these structures with a practical approach to applying them in manufacturing and laboratory processes. This book considers the cubic, mesh, ribbon, and sponge equilibrium phases of bicontinuous structures. It begins with a historical perspective and a theoretical platform for study, followed by a detailed discussion of physical chemistry, properties, and structural characteristics of the different phases. The text interrelates the most useful analytical methods for the characterization of the behavior and stability of liquid crystalline phases based on structure, geometry, composition-dependent changes, temperature, dispersion, and other factors. These techniques include differential geometry, thermodynamics, local and global packing, and the study of conformational entropy. The book also highlights tools for mathematically visualizing bicontinuous systems. This provides an excellent foundation for the authors' examination of the latest studies and applications, such as controlled release, materials development, fabrication, processing, polymerization, protein crystallization, membrane fusion, and treatment of human skin. Bicontinuous Liquid Crystals represents current trends and innovative ideas in the study of bicontinuous liquid crystals. Divided into three sections, it provides a complete overview of theoretical and modeling aspects, physical chemistry and characterization, and applications in this active field of research.

This volume comprises papers presented at the 40th Erice Course "From Molecules to Medicine: Structure of Biological Macromolecules and Its Relevance in Combating New Diseases and Bioterrorism," May 29 to June 8, 2008. The papers span the breadth of material presented, which emp- size the practical aspects of modern macromolecular crystallography and its applications to medicine. Topics addressed span from the selection of targets, through to structure determination, interpretation and exploitation. A particular theme that emerges is the dependence of modern structural science on multiple experimental and computational techniques. It is both the development of these techniques and their integration that will take us forward in the future. The NATO ASI directors worked alongside, and offer deep gratitude to Prof. Sir Tom Blundell, Director of the International School of Crystal- graphy, Dr Colin Groom, Dr Neera Borkakoti, Dr John Irwin and Prof. Lodovico Riva di Sanseverino, who were in turn supported by a number of local facilitators. The course was financed by NATO as an Advanced Study Institute. Additional support was given by the European Crystallographic Association, the International Union of Biochemistry and Molecular Biology, the Int- national Union of Crystallography, the University of Bologna, AstraZeneca, Roche, Merck & Co., Boehringer Ingelheim, Bruker Corporation, Douglas Instruments, Informa UK, the Department of Pharmaceutical Chemistry, TTP Lab Tech, University of California at San Francisco. Joel L. Sussman and Paola Spadon

This is the first book to provide a comprehensive treatment of theories and applications in the rapidly expanding field of the crystallography of modular materials. Molecules are the natural modules from which molecular crystalline structures are built. Most inorganic structures, however, are infinite arrays of atoms and some kinds of surrogate modules, e.g. co-ordination polyhedra, are usually used to describe them. In recent years the attention has been focused on complex modules as the basis for a systematic description of polytypes and homologous/polysomatic series (modular structures). This representation is applied to the modelling of unknown structures and understanding nanoscale defects and intergrowths in materials. The Order/Disorder (OD) theory is fundamental to developing a systematic theory of polytypism, dealing with those structures based on both ordered and disordered stacking of one or more layers. Twinning at both unit-cell and micro-scale, together with disorder, causes many problems, "demons", for computer-based methods of crystal structure determination. This book develops the theory of twinning with the inclusion of worked examples, converting the "demons" into useful indicators for unravelling crystal structure. In spite of the increasing use of the concepts of modular crystallography for characterising, understanding and tailoring technological crystalline materials, this is the first book to offer a unified treatment of the results, which are spread across many different journals and original papers published over the last twenty years.

X-ray crystallography is the pre-eminent technique for visualizing the structures of macromolecules at atomic resolution. These structures are central to understanding the detailed mechanisms of biological processes, and to discovering novel therapeutics using a structure-based approach. As yet, structures are known for only a small fraction of the proteins encoded by human and pathogenic genomes. To counter the myriad modern threats of disease, there is an urgent need to determine the structures of the thousands of proteins whose structure and function remain unknown. This volume draws on the expertise of leaders in the field of macromolecular crystallography to illuminate the dramatic developments that are accelerating progress in structural biology. Their contributions span the range of techniques from crystallization through data collection, structure solution and analysis, and show how modern high-throughput methods are contributing to a deeper understanding of medical problems.

For many years it was believed that translational symmetry would be the fundamental property of crystal structures of natural and synthetic compounds. It is now recognised that many compounds crystallise without translational symmetry of their atomic structures. "Incommensurate Crystallography" gives a comprehensive account of the superspace theory for the description of crystal structures and symmetries of these incommensurately modulated crystals and incommensurate composite crystals. It thus provides the necessary background for quantitative analysis of incommensurate crystals by methods in Solid State Chemistry and Solid State Physics. The second half of "Incommensurate Crystallography" is devoted to crystallographic methods of structural analysis of incommensurate compounds. Thorough accounts are given of the diffraction by incommensurate crystals, the choice of parameters in structure refinements, and the use of superspace in analysing crystal structures. The presentation of methods of structure determination includes modern methods like the Maximum Entropy Method and Charge Flipping.

Part of a complete new edition on ferroelectrics, Landolt-B rnstein volume III/36, this sub-volume (III/36C) covers organic crystals, liquid crystals and polymers. The other two sub-volumes cover: oxides (III/36A) and inorganic substances other than oxides (III/36B). This sub-volume includes an accompanying CD-ROM, which contains all the compiled data.

The study of interfaces within and between materials is a central field which is relevant to almost all aspects of materials science. For example, interfaces play a role in many of the mechanical and electrical properties of materials, phase transformations, and microstructure of materials.This book is intended to serve as a graduate text consisting of four inter-related parts spanning the structure, thermodynamics, kinetics, and properties of interfaces in crystalline materials. Throughout the book emphasis is placed on the conceptual foundations of the subject through the exposition of simple models and descriptions of key experimental observations. In this way the reader is gradually taken to the forefront of the subject. The first four chapters deal with structural aspects of interfaces - interfacial geometry, dislocation models, interatomic forces, and atomic structure. There are three chapters dealing with thermodynamic aspects of interfaces; the thermodynamics of interfaces; interfacial phases and phase transitions, and segregation of solute atoms. The kinetics of interfaces are covered in three chapters concerned with diffusion, conservative motion, and non-conservative motion. Finally there are two chapters which cover the electrical and mechanical properties of interfaces. This book is a unique introduction to the field of interfaces in crystalline materials spanning the subject in a coherent and pedagogical style.

The art of solving a structure from powder diffraction data has developed rapidly over the last ten years to the point where numerous crystal structures, both organic and inorganic, have been solved directly from powder data. However, it is still an art and, in contrast to its single crystal equivalent, is far from routine. The art lies not only in the correct application of a specific experimental technique or computer program, but also in the selection of the optimal path for the problem at hand. Written and edited by experts active in the field, and covering both the fundamental and applied aspects of structure solution from powder diffraction data, this book guides both novices and experienced practitioners alike through the maze of possibilities.

Despite the tremendous advances in the techniques and equipment for carrying out high-pressure crystallography, the application or exploration of the high-pressure variable in detailed structural studies remains rare. The chapters in this book provide a set of lecture notes and supplementary material for a course on high pressure crystallography. The material comprises state-of-the-art reviews of high-pressure experiments using X-ray and neutron diffraction techniques at synchrotron and neutron facilities and in the laboratory, as well as complementary experimental high-pressure techniques and theoretical methods for investigating matter at elevated pressures. The materials studies range from elemental solids and liquids to inorganic compounds, minerals, organic compounds, clathrates and pharmaceutical compounds, to large biological molecules such as proteins and viruses.
The book provides a reference for workers in high-pressure science wishing to learn more about crystallography and for established crystallographers potentially interested in high pressure as a variable, as well as an introductory guide to new researchers in the field.

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. "