International Union of Crystallography Texts on Crystallography – serie

In crystal chemistry and crystal physics, the relations between the symmetry groups (space groups) of crystalline solids are of particular importance. Part I 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 II 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 the 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 chemical reactions in the solid state, to understand the formation of domains and twins in crystals, and to avoid errors in crystal structure determinations. Part III delves further into some specific topics, namely the isomorphic subgroups of space groups, the theory of phase transitions, and computer programs dedicated to crystallographic group theory. In this new edition, several topics have been extended to cover the latest scientific findings, a new chapter has been added dealing with pertinent computer programs, and references have been updated.

This book deals with the electron density distribution in molecules and solids as obtained experimentally by X-ray diffraction. It is a comprehensive treatment of the methods involved, and the interpretation of the experimental results in terms of chemical bonding and intermolecular interactions. Inorganic and organic solids as well as metals are covered in the chapters dealing with specific systems. Encompassing a broad interface with other physical sciences this book will appeal to researchers in crystallography and chemical physics.

This text focuses on the practical aspects of crystal structure analysis, and provides the necessary conceptual framework for understanding and applying the technique. By choosing an approach that avoids undue emphasis on the mathematics involved, the book gives practical advice on topics such as growing crystals, solving and refining structures, and understanding and using the results. The technique described is a core experimental method in modern structural chemistry, and plays an ever more important role in the careers of final-year undergraduates, graduate students, postdoctoral and academic staff in chemistry.

Crystal Structure Refinement is a mixture of textbook and tutorial. As A Crystallographers Guide to SHELXL it covers advanced aspects of practical crystal structure refinement, which have not been much addressed by textbooks so far. After an introduction to SHELXL in the first chapter, a brief survey of crystal structure refinement is provided. Chapters three and higher address the various aspects of structure refinement, from the treatment of hydrogen atoms to the assignment of atom types, to disorder, to non-crystallographic symmetry and twinning. One chapter is dedicated to the refinement of macromolecular structures and two short chapters deal with structure validation (one for small molecule structures and one for macromolecules). In each of the chapters the book gives refinement examples, based on the program SHELXL, describing every problem in detail. It comes with a CD-ROM with all files necessary to reproduce the refinements.

This book provides a clear and very broadly based introduction to crystallography, light, X-ray and electron diffraction - a knowledge which is essential to students in a wide range of scientific disciplines but which is otherwise generally covered in subject-specific and more mathematically detailed texts. The text is also designed to appeal to the more general reader since it shows, by historical and biographical references, how the subject has developed from the work and insights of successive generations of crystallographers and scientists.The book shows how an understanding of crystal structures, both inorganic and organic may be built up from simple ideas of atomic and molecular packing. Beginning with (two dimensional) examples of patterns and tilings, the concepts of lattices, symmetry point and space groups are developed. 'Penrose' tilings and quasiperiodic structures are also included. The reciprocal lattice and its importance in understanding the geometry of light, X-ray and electron diffraction patterns is explained in simple terms, leading to Fourier analysis in diffraction, crystal structure determination, image formation and the diffraction-limited resolution in these techniques. Practical X-ray and electron diffraction techniques and their applications are described. A recurring theme is the common principles: the techniques are not treated in isolation.The fourth edition has been revised throughout, and includes new sections on Fourier analysis, Patterson maps, direct methods, charge flipping, group theory in crystallography, and a new chapter on the description of physical properties of crystals by tensors (Chapter 14).

This book provides a clear and very broadly based introduction to crystallography, light, X-ray and electron diffraction - a knowledge which is essential to students in a wide range of scientific disciplines but which is otherwise generally covered in subject-specific and more mathematically detailed texts. The text is also designed to appeal to the more general reader since it shows, by historical and biographical references, how the subject has developed from the work and insights of successive generations of crystallographers and scientists.The book shows how an understanding of crystal structures, both inorganic and organic may be built up from simple ideas of atomic and molecular packing. Beginning with (two dimensional) examples of patterns and tilings, the concepts of lattices, symmetry point and space groups are developed. 'Penrose' tilings and quasiperiodic structures are also included. The reciprocal lattice and its importance in understanding the geometry of light, X-ray and electron diffraction patterns is explained in simple terms, leading to Fourier analysis in diffraction, crystal structure determination, image formation and the diffraction-limited resolution in these techniques. Practical X-ray and electron diffraction techniques and their applications are described. A recurring theme is the common principles: the techniques are not treated in isolation.The fourth edition has been revised throughout, and includes new sections on Fourier analysis, Patterson maps, direct methods, charge flipping, group theory in crystallography, and a new chapter on the description of physical properties of crystals by tensors (Chapter 14).

This book presents the reader with a fresh and unconventional approach to teaching crystallographic symmetry. Whereas traditional crystallography textbooks make a heavy use of algebra and rapidly become very technical, this book adopts in the first few chapters a 'pictorial' approach based on the symmetry diagrams of the International Tables for Crystallography. Readers are led step-by-step through simple 'frieze' and 'wallpaper' patterns, with many examples from the visual arts. At the end of chapter 3 they should be able to identify and analyse all these simple symmetries and apply to them the nomenclature and symbols of the International Tables. Mathematical formalism is introduced later on in the book, and by that time the reader will have gained a solid intuitive grasp of the subject matter. This book will provide graduate students, advanced undergraduate students and practitioners in physics, chemistry, earth sciences and structural biology with a solid foundation to master the International Tables of Crystallography, and to understand the relevant literature.

In the modern world of ever smaller devices and nanotechnology, electron crystallography emerges as the most important method capable of determining the structure of minute objects down to the size of individual atoms. Crystals of only a few millionths of a millimetre are studied. This is the first textbook explaining how this is done. Great attention is given to symmetry in crystals and how it manifests itself in electron microscopy and electron diffraction, and how this symmetry can be determined and taken advantage of in achieving improved electron microscopy images and solving crystal structures from electron diffraction patterns.Theory and practice are combined; experimental images, diffraction patterns, formulae and numerical data are discussed in parallel, giving the reader a complete understanding of what goes on inside the "black boxes" of computer programs.This up-to-date textbook contains the newest techniques in electron crystallography, including detailed descriptions and explanations of the recent remarkable successes in determining the very complex structures of zeolites and intermetallics. The controversial issue of whether there is phase information present in electron micrsocopy images or not is also resolved once and for all. The extensive appendices include computer labs which have been used at various courses at Stockholm University and international schools in electron crystallography, with applications to the textbook. Students can download image processing programs and follow these lab instructions to get a hands-on experience of electron crystallography.

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.

Since the early 1990s the atomic pair distribution function (PDF) analysis of powder diffraction data has undergone something of a revolution in its ability to do just that: yield important structural information beyond the average crystal structure of a material. With the advent of advanced sources, computing and algorithms, it is now useful for studying the structure of nanocrystals, clusters and molecules in solution or otherwise disordered in space, nanoporous materials and things intercalated into them, and to look for local distortions and defects in crystals. It can be used in a time-resolved way to study structural changes taking place during synthesis and in operating devices, and to map heterogeneous systems.Although the experiments are somewhat straightforward, there can be a gap in knowledge when trying to use PDF to extract structural information by modelling. This book addresses this gap and guides the reader through a series of real life worked examples that gradually increase in complexity so the reader can have the independence and confidence to apply PDF methods to their own research and answer their own scientific questions. The book is intended for graduate students and other research scientists who are new to PDF and want to use the methods but are unsure how to take the next steps to get started.

Since the late 19th century, X-ray structural studies have forged ahead through technological progress and the creative ingenuity of researchers. As high intensity X-ray sources and increased speed and sensitivity of the detectors have emerged, it's now possible to image the atomic structure of complex bio-macromolecules, the orbital electron density of small molecules, and to even follow the dynamical behavior of bio-macromolecules. Textbooks from which junior researchers can grasp the current art have not kept pace with the technological developments and diversification of the field. X-ray studies of bio-macromolecules require a broad understanding of the theory and practical methodologies. A project can include isolating, crystalizing, and adjudicating suitable samples, obtaining and analysing the X-ray data, and finally publishing the results in a standard format. Early decisions in a project can become pitfalls that swallow the unwary. It is increasingly essential to become adept at managing both proteins and nucleic acids. Whereas software is available to help in the critical problem of resolving the phase, expedience often encourages treating such tools as a black-box. The aim here is to help navigate the researcher through these multifarious issues. The book is intended to serve as a "companion" to experimentalists. It is divided into a general overview of X-ray structural analysis techniques (chapters 1-2) and a detailed discussion (chapters 3-16) that begins with the preparation of proteins and (uniquely) nucleic acids and ends with publishing the results and is organized to lead the reader through the whole process.

Since the late 19th century, X-ray structural studies have forged ahead through technological progress and the creative ingenuity of researchers. As high intensity X-ray sources and increased speed and sensitivity of the detectors have emerged, it's now possible to image the atomic structure of complex bio-macromolecules, the orbital electron density of small molecules, and to even follow the dynamical behavior of bio-macromolecules. Textbooks from which junior researchers can grasp the current art have not kept pace with the technological developments and diversification of the field. X-ray studies of bio-macromolecules require a broad understanding of the theory and practical methodologies. A project can include isolating, crystalizing, and adjudicating suitable samples, obtaining and analysing the X-ray data, and finally publishing the results in a standard format. Early decisions in a project can become pitfalls that swallow the unwary. It is increasingly essential to become adept at managing both proteins and nucleic acids. Whereas software is available to help in the critical problem of resolving the phase, expedience often encourages treating such tools as a black-box. The aim here is to help navigate the researcher through these multifarious issues. The book is intended to serve as a "companion" to experimentalists. It is divided into a general overview of X-ray structural analysis techniques (chapters 1-2) and a detailed discussion (chapters 3-16) that begins with the preparation of proteins and (uniquely) nucleic acids and ends with publishing the results and is organized to lead the reader through the whole process.

Newcomers to the field of structural biology, which aims to understand life at the molecular level, see a vast number of existing results and are faced with a diverse range of experimental methods. These are used singly or in various combinations, however the uncertainties of the results found are unfortunately not fully assessed.Beginning with the basic physics of describing systematic and random errors, this book aims to explore these uncertainties, by examining the accuracy of each experimental method used to determine a 3D biological macromolecule structure and its dynamics, and their various possible combinations. The book also discusses the uncertainties in our determination of atomic positions in our static structures, and our analysis of the living cell. Aimed at graduate students from a wide range of science disciplines including physics, chemistry, biology, and mathematics, this book provides an overview of the topic of precision and accuracy in biological crystallography, diffraction, scattering, microscopies, and spectroscopies.

This concise book is for chemists, material scientists, and physicists who deal with description of crystalline matter and the determination of its structure, and would like to gain more understanding of the principles involved. The main purpose of the book is to introduce the reader to principles of crystallographic symmetry, to discuss some traditional, as well as modern, experimental techniques, to formulate the phase problem of crystallography, and present in some detail the methods for its indirect and direct solution which are indispensable for further work. The book also contains discussions of structure-factor statistics, of value for resolving space-group ambiguities, and atomic displacement parameters which form an inseparable part of the structure. A discussion of the refinement of structural parameters, conventional, constrained and restrained, concludes the book. Derivations are, as far as possible, self contained and wherever mathematical detail might disrupt the line of reasoning the reader is referred to one of four appendices present in the book. The book is of course valuable for students of crystallography at a graduate and upper undergraduate level. No previous course on crystallography is a prerequisite for graduates in the above fields.

This book is a revised and updated English edition of a textbook that has grown out of several years of teaching. The term "inorganic" is used in a broad sense as the book covers the structural chemistry of representative elements (including carbon) in the periodic table, organometallics, coordination polymers, host-guest systems and supramolecular assemblies. Part I of the book reviews the basic bonding theories, including a chapter on computational chemistry. Part II introduces point groups and space groups and their chemical applications. Part III comprises a succinct account of the structural chemistry of the elements in the periodic table. It presents structure and bonding, generalizations of structural trends, crystallographic data, as well as highlights from the recent literature.

This book is a revised and updated English edition of a textbook that has grown out of several years of teaching. The term "inorganic" is used in a broad sense as the book covers the structural chemistry of representative elements (including carbon) in the periodic table, organometallics, coordination polymers, host-guest systems and supramolecular assemblies. Part I of the book reviews the basic bonding theories, including a chapter on computational chemistry. Part II introduces point groups and space groups and their chemical applications. Part III comprises a succinct account of the structural chemistry of the elements in the periodic table. It presents structure and bonding, generalizations of structural trends, crystallographic data, as well as highlights from the recent literature.

This text focuses on the practical aspects of crystal structure analysis, and provides the necessary conceptual framework for understanding and applying the technique. By choosing an approach that does not put too much emphasis on the mathematics involved, the book gives practical advice on topics such as growing crystals, solving and refining structures, and understanding and using the results. The technique described is a core experimental method in modern structural chemistry, and plays an ever more important role in the careers of graduate students, postdoctoral and academic staff in chemistry, and final-year undergraduates.Much of the material of the first edition has been significantly updated and expanded, and some new topics have been added. The approach to several of the topics has changed, reflecting the book's new authorship, and recent developments in the subject.

This text focuses on the practical aspects of crystal structure analysis, and provides the necessary conceptual framework for understanding and applying the technique. By choosing an approach that does not put too much emphasis on the mathematics involved, the book gives practical advice on topics such as growing crystals, solving and refining structures, and understanding and using the results. The technique described is a core experimental method in modern structural chemistry, and plays an ever more important role in the careers of graduate students, postdoctoral and academic staff in chemistry, and final-year undergraduates.Much of the material of the first edition has been significantly updated and expanded, and some new topics have been added. The approach to several of the topics has changed, reflecting the book's new authorship, and recent developments in the subject.

In recent years it has become apparent that knowing the average atomic structure of materials is insufficient to understand their properties. Diffuse scattering in addition to the Bragg scattering holds the key to learning about defects in materials, the topic of many recent books. What has been missing is a detailed step-by-step guide how to simulate disordered materials. The DISCUS cook book fills this need covering simple topics such as building a computer crystal to complex topic such as domain structures, stacking faults or using advanced refinement techniques to adjust parameters on a disordered model. The reader is free to follow the principles behind simulating disordered materials or to get down into the details and run or modify the given examples.

This book presents the reader with a fresh and unconventional approach to teaching crystallographic symmetry. Whereas traditional crystallography textbooks make a heavy use of algebra and rapidly become very technical, this book adopts in the first few chapters a 'pictorial' approach based on the symmetry diagrams of the International Tables for Crystallography. Readers are led step-by-step through simple 'frieze' and 'wallpaper' patterns, with many examples from the visual arts. At the end of chapter 3 they should be able to identify and analyse all these simple symmetries and apply to them the nomenclature and symbols of the International Tables. Mathematical formalism is introduced later on in the book, and by that time the reader will have gained a solid intuitive grasp of the subject matter. This book will provide graduate students, advanced undergraduate students and practitioners in physics, chemistry, earth sciences and structural biology with a solid foundation to master the International Tables of Crystallography, and to understand the relevant literature.

Crystallography is an interdisciplinary science covering a wide area, from biology to earth sciences, mathematics and materials science. Its role is growing, owing to the contribution crystallography can offer to the understanding of such diverse fields as biological structures, high-temperature superconductors, mineral properties, and phase transitions. The book describes both the theoretical bases and applications of different areas interacting with crystallography. As with the first and second editions, it is organized as a collection of chapters written by recognized specialists, with all contributions being harmonized into a unified whole. The main text is devoted to the presentation of basics; the appendices deal with specialist aspects. In this third edition topics have been updated so as to document the present state of the art: emphasis is placed upon areas of current research. To facilitate learning and make teaching more effective, new illustrations have been introduced. As with the second edition, a software package is included via the book's OUP web site: modern graphics will help users to better understand the basics of this science via three-dimensional images, simulation of experiments, and exercises.

Crystallography is an interdisciplinary science covering a wide area, from biology to earth sciences, mathematics and materials science. Its role is growing, owing to the contribution crystallography can offer to the understanding of such diverse fields as biological structures, high-temperature superconductors, mineral properties, and phase transitions. The book describes both the theoretical bases and applications of different areas interacting with crystallography. As with the first and second editions, it is organized as a collection of chapters written by recognized specialists, with all contributions being harmonized into a unified whole. The main text is devoted to the presentation of basics; the appendices deal with specialist aspects. In this third edition topics have been updated so as to document the present state of the art: emphasis is placed upon areas of current research. To facilitate learning and make teaching more effective, new illustrations have been introduced. As with the second edition, a software package is included via the book's OUP web site: modern graphics will help users to better understand the basics of this science via three-dimensional images, simulation of experiments, and exercises.

This book aims to explain how and why the detailed three-dimensional architecture of molecules can be determined by an analysis of the diffraction patterns obtained when X rays or neutrons are scattered by the atoms in single crystals. Part 1 deals with the nature of the crystalline state, diffraction generally, and diffraction by crystals in particular, and, briefly, the experimental procedures that are used. Part II examines the problem of converting the experimentally obtained data into a model of the atomic arrangement that scattered these beams. Part III is concerned with the techniques for refining the approximate structure to the degree warranted by the experimental data. It also describes the many types of information that can be learned by modern crystal structure analysis. There is a glossary of terms used and several appendixes to which most of the mathematical details have been relegated.

This book aims to explain how and why the detailed three-dimensional architecture of molecules can be determined by an analysis of the diffraction patterns obtained when X rays or neutrons are scattered by the atoms in single crystals. Part 1 deals with the nature of the crystalline state, diffraction generally, and diffraction by crystals in particular, and, briefly, the experimental procedures that are used. Part II examines the problem of converting the experimentally obtained data into a model of the atomic arrangement that scattered these beams. Part III is concerned with the techniques for refining the approximate structure to the degree warranted by the experimental data. It also describes the many types of information that can be learned by modern crystal structure analysis. There is a glossary of terms used and several appendixes to which most of the mathematical details have been relegated.

In the modern world of ever smaller devices and nanotechnology, electron crystallography emerges as the most important method capable of determining the structure of minute objects down to the size of individual atoms. Crystals of only a few millionths of a millimetre are studied. This is the first textbook explaining how this is done. Great attention is given to symmetry in crystals and how it manifests itself in electron microscopy and electron diffraction, and how this symmetry can be determined and taken advantage of in achieving improved electron microscopy images and solving crystal structures from electron diffraction patterns.Theory and practice are combined; experimental images, diffraction patterns, formulae and numerical data are discussed in parallel, giving the reader a complete understanding of what goes on inside the "black boxes" of computer programs.This up-to-date textbook contains the newest techniques in electron crystallography, including detailed descriptions and explanations of the recent remarkable successes in determining the very complex structures of zeolites and intermetallics. The controversial issue of whether there is phase information present in electron micrsocopy images or not is also resolved once and for all. The extensive appendices include computer labs which have been used at various courses at Stockholm University and international schools in electron crystallography, with applications to the textbook. Students can download image processing programs and follow these lab instructions to get a hands-on experience of electron crystallography.

Small-angle scattering of X-rays (SAXS) and neutrons (SANS) is an established method for the structural characterization of biological objects in a broad size range from individual macromolecules (proteins, nucleic acids, lipids) to large macromolecular complexes. SAXS/SANS is complementary to the high resolution methods of X-ray crystallography and nuclear magnetic resonance, allowing for hybrid modeling and also accounting for available biophysical and biochemical data. Quantitative characterization of flexible macromolecular systems and mixtures has recently become possible. SAXS/SANS measurements can be easily performed in different conditions by adding ligands or binding partners, and by changing physical and/or chemical characteristics of the solvent to provide information on the structural responses. The technique provides kinetic information about processes like folding and assembly and also allows one to analyze macromolecular interactions. The major factors promoting the increasingly active use of SAXS/SANS are modern high brilliance X-ray and neutron sources, novel data analysis methods, and automation of the experiment, data processing and interpretation.In this book, following the presentation of the basics of scattering from isotropic macromolecular solutions, modern instrumentation, experimental practice and advanced analysis techniques are explained. Advantages of X-rays (rapid data collection, small sample volumes) and of neutrons (contrast variation by hydrogen/deuterium exchange) are specifically highlighted. Examples of applications of the technique to different macromolecular systems are considered with specific emphasis on the synergistic use of SAXS/SANS with other structural, biophysical and computational techniques.

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.