The present book is an accessible, comprehensive guide to diffuse neutron scattering, an important technique for studying structural disorder in materials. The text takes the reader through theoretical, computational and experimental developments in the subject and describes in detail its application to a number of structural disorder problems. These include the more traditional subjects of substitutional disorder in alloys and orientational disorder in molecular systems as well as the more recent studies of superionic and framework materials. Particular emphasis is placed on recent refinement methods for data interpretation which are compared with established computer simulation techniques and analytical approaches. The book collects disparate themes into one unique volume, written as an introduction to the method for graduate scientists. It will be a valuable reference text for any crystallographer keen to understand and apply modern interpretative techniques to diffuse scattering data.

The mathematical modelling of changing structures in materials is of increasing importance to industry where applications of the theory are found in subjects as diverse as aerospace and medicine. This book deals with aspects of the nonlinear dynamics of deformable ordered solids (known as
elastic crystals) where the nonlinear effects combine or compete with each other. Physical and mathematical models are discused and computational aspects are also included. Different models are considered - on discrete as well as continuum scales - applying heat, electricity, or magnetism to the
crystal structure and these are analysed using the equations of rational mechanics. Students are introduced to the important equations of nonlinear science that describe shock waves, solitons and chaos and also the non-exactly integrable systems or partial differential equations. A large number of
problems and examples are included, many taken from recent research and involving both one-dimensional and two-dimensional problems as well as some coupled degress of freedom.

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

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 book gives the complete theory of the irreducible representations of the crystallographic point groups and space groups. This is important in the quantum-mechanical study of a particle or quasi-particle in a molecule or crystalline solid because the eigenvalues and eigenfunctions of a system belong to the irreducible representations of the group of symmetry operations of that system. The theory is applied to give complete tables of these representations for all the 32 point groups and 230 space groups, including the double-valued representations. For the space groups, the group of the symmetry operations of the k vector and its irreducible representations are given for all the special points of symmetry, lines of symmetry and planes of symmetry in the Brillouin zone. Applications occur in the electronic band structure, phonon dispersion relations and selection rules for particle-quasiparticle interactions in solids. The theory is extended to the corepresentations of the Shubnikov (black and white) point groups and space groups.

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.

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.

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.

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.

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.

* This extension to Volume A presents a systematic treatment of the maximal subgroups and minimal supergroups of the crystallographic plane groups and space groups * The second edition contains new chapters on building trees of group-subgroup relations for crystal structures that can be derived from an aristotype and on the Bilbao Crystallographic Server, and a detailed discussion of the listed supergroup data * Essential for those interested in phase transitions, the systematic compilation of crystal structures and twinning phenomena

This textbook presents an extensive manual of crystallography, including geometric crystallography, crystallochemistry, and crystallophysics. Illustrated with a wealth of figures and diagrams, it offers a thorough introduction to crystals for undergraduate and graduate students interested in learning the essentials and advanced concepts of crystallography. The book begins with basic concepts such as the geometry, morphology and symmetry of lattices, allowing readers to approach the subject from a mathematical point of view, abstracting it from its material content. In turn, the second part focuses on crystallochemistry and explains the differences between ideal and real crystals, and between static and dynamic ones. The third part of the textbook concerns crystallophysics and addresses the electrical, magnetic, mechanical, elastic and optical properties of crystals, as well as the fundamental laws and methods of X-ray diffraction.

This textbook provides students with a complete working knowledge of the properties of imperfections in crystalline solids. Readers will learn how to apply the fundamental principles of mechanics and thermodynamics to defect properties in materials science, gaining all the knowledge and tools needed to put this into practice in their own research. Beginning with an introduction to defects and a brief review of basic elasticity theory and statistical thermodynamics, the authors go on to guide the reader in a step-by-step way through point, line, and planar defects, with an emphasis on their structural, thermodynamic, and kinetic properties. Numerous end-of-chapter exercises enable students to put their knowledge into practice, and with solutions for instructors and MATLAB (R) programs available online, this is an essential text for advanced undergraduate and introductory graduate courses in crystal defects, as well as being ideal for self-study.

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.

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.

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.

Crystal structures and their associated electronic features play an enormous role in chemistry, constituting the most fundamental basis for analyzing and predicting properties of solid-state materials. In Crystal Structure: Properties, Characterization and Determination, the authors begin by discussing some of the refining models and X-ray data treatments for single-crystals containing heavy atoms, such as transition metals or lanthanides.Valuable information on crystal structures and microstructures may be obtained from the observation of high-resolution images if conditions associated iwth crystal thickness and defocus values are satisfied. These images include information not only on accurate atomic coordinates of cations but also on the ordered arrangements of oxygen atoms and oxygen vacancies.In the concluding study, measurements of the heat capacity of Y3-xErxAl5O12 (x=0,0.6,1.1,3), and mixed Er3-xTmx Al5O12, (x=0,1,2,3) and Er2HoAl5O12 solid solutions were carried out in the temperature range of 1.9 to 220 K in magnetic fields up to 9T. The findings suggest that heat capacity variations at low temperatures were impacted by Schottky anomalies.

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.

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.