Direct methods are, at present, applied to a large variety of cases: X-ray, neutron or electron data; single crystal and powder data; small molecules and macromolecules. While direct methods solved in practice the phase problem for small molecules, their application to macromolecules is recent and still undergoing strong development. The fundamentals of the methods are described: in particular it is shown how the methods can be optimized for powder, neutron or electron data, and how they can be integrated with isomorphous replacement, molecular replacement and anomalous dispersion techniques. Maximum Entropy methods are also described and discussed. Sets of test structures are used to verify, throughout the various chapters, the mathematical techniques there described and to provide practical examples of applications. This book will appeal to a wide variety of readers - offering both a comprehensive description of direct methods in crystallography and an invaluable reference tool. The first three chapters can be considered as an introduction to the field, with sufficient material to constitute a university course and for allowing the expert use of most direct methods programs. Subsequent chapters are aimed at graduate students and working crystallographers. Basic results are described and discussed in the main body of the text, while the appendices compliment these with in depth mathematical details. The quoted literature is extremely wide and the interested reader can find suggestions for future work and further reading throughout the book.

This volume presents reviews of topical areas in structural determination and structural chemistry, edited from the Proceedings of the 8th Symposium on Organic Crystal Chemistry, held at Poznan-Rydzyna, Poland in 1992. In this volume the definition of organic crystallography is interpreted widely to include factors influencing conformation, packing arrangements, and intermolecular bonding, as well as the determination of the positions and motions of the constituent atoms in molecular structures. An opening chapter introduces the edited proceedings which cover some of the most active areas in the structural determination and structural chemistry of small organic molecules in the crystalline state. The final chapter examines the current concerns of the adherents of organic crystallography and the future role and status of organic crystallography in structural science. The volume is divided into four sections: collection and treatment of diffraction data; crystalline-state reactions; structure correlation and structure-activity relations; and conformation, packing, and bonding in molecular crystals.

Paul Ewald's 1916-1917 masterpiece "On the Foundations of Crystal Optics" described the self-consistent interaction of electromagnetic waves with crystals on a molecular level. While astonishing in its detailed predictions for X-ray diffraction, full appreciation of the theory and its utility had to await much later advances in measurement techniques and crystal growth. Today, concepts introduced in the theory--now known as the Ewald sphere, Ewald summation, and Ewald-Oseen extinction--have become mainstays in diverse areas of modern physics. This memorial volume, with contributions by leading figures in the field, is an affectionate survey of Ewald's life, scientific work, and leading role in the international crystallographic community. Historians of science, and particularly of solid state physics and crystallography, will find this volume a compelling and fascinating tribute to this important scientist.

The International School on Crystallographic Computing was held at the Bischenberg Congress Center, close to Strasbourg, in 1990. This was the twelfth such school organized since 1960 under the auspices of the IUCR Commission of crystallographic computing. The school was a satellite meeting to the XVth Congress of the International Union of Crystallography in Bordeaux, at which lecturers and tutors gave conferences and demonstrated their programs. In selecting the contents of the school, the program committee took into account the increasing emphasis on the study of macromolecules of biological interests, a natural progression of the clear success of crystallographic methodology in small molecule crystallography. Themes covered include synchrotron data collection, the potentiality of imaging plate technology coupled with efficient software, maximum entropy phasing methods, refinement using molecular dynamics, and map interpretation using structural databases. This is the latest volume in a series of highly regarded volumes based on lectures given at the International School of Computational Crystallography. Here, international contributors have collaborated to provide a unique record of the state-of-the-art in this important area of crystallography.

This book features the essential material for any graduate or advanced undergraduate course covering solid-state electrochemistry. It provides the reader with fundamental course notes and numerous solved exercises, making it an invaluable guide and compendium for students of the subject. The book places particular emphasis on enhancing the reader's expertise and comprehension of thermodynamics, the Kroeger-Vink notation, the variation in stoichiometry in ionic compounds, and of the different types of electrochemical measurements together with their technological applications. Containing almost 100 illustrations, a glossary and a bibliography, the book is particularly useful for Master and PhD students, industry engineers, university instructors, and researchers working with inorganic solids in general.

The pharmaceutical industry has become acutely aware of the importance of the solid state, but pharmaceutical scientists often lack specific training in topics related to solid-state structure and crystallography. This book provides needed support in this topical area. Taking an intuitive and informal approach to solid-state structure and crystallographic concepts, this book is written for anyone who needs a clear understanding of modern crystallography, with specific reference to small-molecule pharmaceutical solids. The author describes molecular crystals and crystal structures, symmetry, space groups, single-crystal and powder X-ray diffraction techniques and the analysis and interpretation of crystallographic data. Useful technical details are presented where necessary and case studies from the pharmaceutical literature put theory into a practical context. Written by an internationally leading figure and with its focus on molecular crystals, this book is equally applicable to chemists with a need to understand and apply X-ray crystal-structure determination.

This book invites you on a systematic tour through the fascinating world of crystals and their symmetries. The reader will gain an understanding of the symmetry of external crystal forms (morphology) and become acquainted with all the symmetry elements needed to classify and describe crystal structures. The book explains the context in a very vivid, non-mathematical way and captivates with clear, high-quality illustrations. Online materials accompany the book; including 3D models the reader can explore on screen to aid in the spatial understanding of the structure of crystals. After reading the book, you will not only know what a space group is and how to read the International Tables for Crystallography, but will also be able to interpret crystallographic specifications in specialist publications. If questions remain, you also have the opportunity to ask the author on the book's website.

This sixth edition of what was previously known as the Brief Teaching Edition of Volume A provides an introduction to the basic crystallographic data for space groups found in Volume A, for symmetry relations between space groups in Volume A1 and for subperiodic groups in Volume E of International Tables for Crystallography, to magnetic space groups and to the symmetry database that forms part of International Tables Online at https: //it.iucr.org. It is designed for graduate students and young researchers who are new to the field of crystallographic symmetry, and includes many illustrative examples to help readers to understand and use these different kinds of information. Selected tables of symmetry data from the full volumes in the series are also included, making this a handy aid for classroom teaching. References are also provided to further specialized sources for those who need to go deeper into the subject and to textbooks for those who need more background information.

This book shows how the fundamentals of electron paramagnetic resonance (EPR) spectroscopy are practically implemented and illustrates the diversity of current applications. The technique is used at various levels, and applications are presented in order of increasing difficulty, with reference to theoretically obtained results. This book features a diverse array of application examples, from fields such as ionizing radiation dosimetry, neurodegenerative diseases, structural transitions in proteins, and the origins of terrestrial life. The final chapter of this book highlights the principles and applications of the technique of ferromagnetic resonance spectroscopy, followed by a brief introduction to advanced EPR techniques such as electron spin echo envelope modulation (ESEEM), hyperfine sub-level correlation (HYSCORE), pulsed electron-electron double resonance (PELDOR), and continuous wave electron nuclear double resonance (ENDOR) experiments.

This second edition is fully updated to include new developments in the study of metamorphism as well as enhanced features to facilitate course teaching. It integrates a systematic account of the mineralogical changes accompanying metamorphism of the major rock types with discussion of the conditions and settings in which they formed. The use of textures to understand metamorphic history and links to rock deformation are also explored. Specific chapters are devoted to rates and timescales of metamorphism and to the tectonic settings in which metamorphic belts develop. These provide a strong connection to other parts of the geology curriculum. Key thermodynamic and chemical concepts are introduced through examples which demonstrate their application and relevance. Richly illustrated in colour and featuring end-of-chapter and online exercises, this textbook is a comprehensive introduction to metamorphic rocks and processes for undergraduate students of petrology, and provides a solid basis for advanced study and research.

Hydrogen bonding is crucial in many chemical and biochemical reactions, as well as in determining material properties. A good insight into the theoretical methods of treating hydrogen bonding is essential for those wishing to model its effects computationally in a wide range of fields involving hydrogen bonding, as well as those wishing to extract the maximal amount of information from experimental data. Theoretical Treatments of Hydrogen Bonding presents the reader with the state of the art of the key theoretical approaches to hydrogen bonding and considers the hydrogen bond from the various aspects. The first five chapters are devoted to the methods used for treating the electronic basis of hydrogen bonding, including a consideration of the electrostatic model, density functional theory and molecular orbital methods. Later chapters consider the dynamics of hydrogen bonds with particular attention to the treatment of proton transfer; manifestations of dynamics as reflected in infrared spectra and nuclear magnetic relaxation are also considered. Hydrogen bonding in liquids and solids such as ferroelectrics are included. The book concludes with an epilogue which discusses the likely development of hydrogen bond computations in very large chemical systems. Theoretical Treatments of Hydrogen Bonding offers the reader a comprehensive view of the current theoretical approaches to hydrogen bonding. It is a valuable presentation of theoretical tools useful to those looking for the most appropriate approach for treating a particular problem involving hydrogen bonding.

With a focus on portland cement, the book systematically illustrates the composition, properties, and applications of different kinds of cementitious materials, and presents their reaction during the hydration and hardening process. The production technique and applied technology are also discussed with examples. Exercises are added in each chapter, making the work an essential textbook for students.

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.

This comprehensive text covers the basic physics of the solid state starting at an elementary level suitable for undergraduates but then advancing, in stages, to a graduate and advanced graduate level. In addition to treating the fundamental elastic, electrical, thermal, magnetic, structural, electronic, transport, optical, mechanical and compositional properties, we also discuss topics like superfluidity and superconductivity along with special topics such as strongly correlated systems, high-temperature superconductors, the quantum Hall effects, and graphene. Particular emphasis is given to so-called first principles calculations utilizing modern density functional theory which for many systems now allow accurate calculations of the electronic, magnetic, and thermal properties.

Crystal Clear takes you behind the scenes in the life of one of the most prominent scientists of the twentieth century, William Lawrence Bragg (WLB) - an innovative genius, who together with his father, William Henry Bragg (WHB) founded and developed a whole new branch of science, X-ray Crystallography. The main body of the text contains the hitherto unpublished autobiographies of both WLB and his wife, Alice. Alice Bragg was a public figure in her own right. She was Mayor of Cambridge and National Chairman of the Marriage Guidance Council among other roles. She and WLB were as different as chalk and cheese. Their autobiographies complement each other to give a rounded picture of the real personalities behind their public appearance. They write of their travels, their family life, their friends and their joys and sorrows. They write most of all about each other. Their younger daughter, Patience Thomson, provides anecdotes and vignettes, bringing her parents to life. She has also included extracts from previously unpublished letters and from articles which Alice Bragg wrote for National newspapers. The result is an unusual insight into the lives of two distinguished people. The two accounts reveal a fascinating interaction between these two characters, neither of whom could have achieved on this scale without the other. There is an underlying love story here which humanises and transforms. This is a unique book, adopting an original viewpoint, which will take the reader far beyond the scope of a normal biography.

Foams and froths are an important feature of everyday life; one only has to think of shaving foam, foam upholstery, fire fighting foam, bread, bear head, and ice cream. Less obvious but equally important are the foams and foaming processes which are being exploited in ever more complex and imaginative ways in industry. However, the unusual nature of foams, the fact that they are neither solids or liquids, and their very fragility has prevented scientists from obtaining a thorough understanding of even the basic principles of foam formation and stability. This volume presents papers on the physics, chemistry, structure and ultrastructure of foams by contributors from a wide range of backgrounds and research disciplines. The aim of the book is to present a unique multi-disciplinary cross section of work currently being undertaken on the subject of foams.

Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The underlying mathematics, known as the theory of aperiodic order, is the subject of this comprehensive multi-volume series. This first volume provides a graduate-level introduction to the many facets of this relatively new area of mathematics. Special attention is given to methods from algebra, discrete geometry and harmonic analysis, while the main focus is on topics motivated by physics and crystallography. In particular, the authors provide a systematic exposition of the mathematical theory of kinematic diffraction. Numerous illustrations and worked-out examples help the reader to bridge the gap between theory and application. The authors also point to more advanced topics to show how the theory interacts with other areas of pure and applied mathematics.

Bridging the gap between theory and practice, this text provides the reader with a comprehensive overview of industrial crystallization. Newcomers will learn all of the most important topics in industrial crystallization, from key concepts and basic theory to industrial practices. Topics covered include the characterization of a crystalline product and the basic process design for crystallization, as well as batch crystallization, measurement techniques, and details on precipitation, melt crystallization and polymorphism. Each chapter begins with an introduction explaining the importance of the topic, and is supported by homework problems and worked examples. Real world case studies are also provided, as well as new industry-relevant information, making this is an ideal resource for industry practitioners, students, and researchers in the fields of industrial crystallization, separation processes, particle synthesis, and particle technology.

The renowned Oxford Chemistry Primers series, which provides focused introductions to a range of important topics in chemistry, has been refreshed and updated to suit the needs of today's students, lecturers, and postgraduate researchers. The rigorous, yet accessible, treatment of each subject area is ideal for those wanting a primer in a given topic to prepare them for more advanced study or research. Moreover, cutting-edge examples and applications throughout the texts show the relevance of the chemistry being described to current research and industry. Learning features provided in the primers, including questions at the end of every chapter and interactive online MCQs, encourage active learning and promote understanding. Furthermore, frequent diagrams, margin notes, further reading, and glossary definitions all help to enhance a student's understanding of these essential areas of chemistry. This primer provides a succinct account of the technique of X-ray crystallography for determining structure in the solid state. Engaging examples of practical applications are described throughout, emphasising the importance of this field to modern research and industry. Furthermore, end of chapter exercises and online multiple choice questions enable students to test their own understanding of the subject. Online Resource Centre The Online Resource Centre to accompany X-Ray Crystallography features: For registered adopters of the text: * Figures from the book available to download For students: * Downloadable CIF data files * Multiple-choice questions for self-directed learning * Full worked solutions to the end-of-chapter exercises

This book gives a thorough treatment of the rapidly-expanding field of coherent X-ray optics, which has recently experienced something of a renaissance with the availability of third-generation synchrotron sources. It is the first book of its kind. The author begins with a treatment of the fundamentals of X-ray diffraction for both coherent and partially coherent radiation, together with the interactions of X-rays with matter. X-ray sources, optical elements and detectors are then discussed, with an emphasis on their role in coherent X-ray optics. Various facets of coherent X-ray imaging are then discussed, including holography, interferometry, self imaging, phase contrast and phase retrieval. Lastly, the foundations of the new field of singular X-ray optics are examined. Most topics are developed from first principles, with numerous references given to the contemporary research literature. This book will be useful to X-ray physicists and students, together with optical physicists and engineers who wish to learn more about the fascinating subject of coherent X-ray optics.

2012 marked the centenary of one of the most significant discoveries of the early twentieth century, the discovery of X-ray diffraction (March 1912, by Laue, Friedrich, and Knipping) and of Bragg's law (November 1912). The discovery of X-ray diffraction confirmed the wave nature of X-rays and the space-lattice hypothesis. It had two major consequences: the analysis of the structure of atoms, and the determination of the atomic structure of materials. The momentous impact of the discovery in the fields of chemistry, physics, mineralogy, material science, biochemistry and biotechnology has been recognized by the General Assembly of the United Nations by establishing 2014 as the International Year of Crystallography. This book relates the discovery itself, the early days of X-ray crystallography, and the way the news of the discovery spread round the world. It explains how the first crystal structures were determined, and recounts which were the early applications of X-ray crystallography. It also tells how the concept of space lattice has developed since ancient times, and how our understanding of the nature of light has changed over time. The contributions of the main actors of the story, prior to the discovery, at the time of the discovery and immediately afterwards, are described through their writings and are put into the context of the time, accompanied by brief biographical details.

This book is divided in two parts. Part I provides a brief but accurate summary of all the basic ideas, theories, methods, and conspicuous results of structure analysis and molecular modelling of the condensed phases of organic compounds: quantum chemistry, the intermolecular potential, force field and molecular dynamics methods, structural correlation, and thermodynamics. This Part is written in simple and intuitive form, so that the reader may easily find there the essential background for the discussions in the second part. Part II exposes the present status of studies in the analysis, categorization, prediction and control, at a molecular level, of intermolecular interactions in liquids, solutions, mesophases, and crystals. The main focus is here on the links between energies, structures, and chemical or physical properties.

In crystal chemistry and crystal physics, the relations between the symmetry groups (space groups) of crystalline solids are of special importance. Part 1 of this book presents the necessary mathematical foundations and tools: the fundamentals of crystallography with special emphasis on symmetry, the theory of the crystallographic groups, and the formalisms of the needed crystallographic computations. Part 2 gives an insight into applications to problems in crystal chemistry. With the aid of numerous examples, it is shown how crystallographic group theory can be used to make evident relationships between crystal structures, to set up a systematic order in the huge amount of known crystal structures, to predict crystal structures, to analyse phase transitions and topotactic reactions in the solid state, to understand the formation of domains and twins in crystals, and to avoid errors in crystal structure determinations. A broad range of end-of-chapter exercises offers the possibility to apply the learned material. Worked-out solutions to the exercises can be found at the end of the book.