International Union of Crystallography Monographs on Crystallography – serie

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.

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.

Defect and Microstructure Analysis by Diffraction is focused on extracting information on the real structure of materials from their diffraction patterns. The primary features of a powder diffraction pattern are determined by the "idealized" periodic nature of the crystal structure. With the advent of computer automation the techniques for carrying out qualitative, quantitative and structure analysis based on the primary pattern features rapidly matured. In general, the deviations of a particular specimen, from the ideal or perfect crystal structure, cause diffraction peak profiles to broaden and sometimes to become asymmetric. Thus, information on the real structure or microstructure of a specimen can be obtained from a careful study of the diffraction line profiles. The evolving techniques for microstructure analysis from diffraction patterns such as micro-strain, crystallite size, macro-strain and preferred orientation analysis require an ever more detailed understanding of the effects of crystallographic mistakes on peak assymmetry and the effect of the distribution of small crystallites on the tails of diffraction peaks. This book provides a comprehensive analysis of the fundamental theory and techniques for microstructure analysis from diffraction patterns and summarizes the current state of the art. This complete survey lays the foundation for the next and last major development in this field: the extraction of the full information in a powder pattern by the simulation of the full experimental pattern. The goal of this branch of science is to extract all of the information locked in the powder diffraction pattern including: the types and densities of stacking faults, the strain field produced by each, the anisotropic crystallite size and orientation, along with the size and strain distributions of each phase in a specimen. This book provides a complete summary of the developments of the twentieth century and points the way.

Polymorphism - the multiplicity of structures or forms - is a term that is used in many disciplines. In chemistry it refers to the existence of more than one crystal structure for a particular chemical substance. The properties of a substance are determined by its composition and by its structure. In the last two decades, there has been a sharp rise in the interest in polymorphic systems, as an intrinsically interesting phenomenon and as an increasingly important component in the development and marketing of a variety of materials based on organic molecules (e.g. pharmaceuticals, dyes and pigments, explosives, etc.). This book summarizes and brings up to date the current knowledge and understanding of polymorphism of molecular crystals, and concentrates it in one comprehensive source. The book will be an invaluable reference for students, researchers, and professionals in the field.

The weak or non-conventional hydrogen bond has been subject of intense scrutiny over recent years in several fields, in particular in structural chemistry, structural biology, and also in the pharmaceutical sciences. There is today a large body of experimental and theoretical evidence confirming that hydrogen bonds like C-H...O, N-H...pi, C-H...pi and even bonds like O-H...metal play distinctive roles in molecular recognition, guiding molecular association, and in determining molecular and supramolecular architectures. The relevant compound classes include organometallic complexes, organic and bio-organic systems, and also DNA and proteins. The book provides a comprehensive assessment of this interaction type, and is of interest to all those interested in structural and supramolecular science, including fields as crystal engineering and drug design.

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.

The dynamical theory of diffraction has witnessed exciting developments since the advent of synchroton radiation. This book provides an up-to-date account of the theory of diffraction and its applications. The first part serves as an introduction to the subject, presenting early developments and the basic results. It is followed by a detailed development of the diffraction and propagation properties of x-rays in perfect crystals and by an extension of the theory to the case of slightly and highly deformed crystals. The last part gives three applications of the theory: X-ray optics for synchroton radiation, locations of atoms at surfaces, and X-ray diffraction topography. The book is richly illustrated and contains a wide range of references to the literature. It will be a most useful reference work for graduate students, lecturers and researchers.

By considering the solid state packing of linear chain wax components, this book aims at understanding three things: firstly, which modifications of molecular components are allowed for maintaining stable solid solutions; secondly, what happens when stability conditions are traversed and fractionation begins and thirdly, the structure of fractionated arrays. The co-compatibility of molecular ingredients is considered in terms of their shapes and relative sizes, following an approach originally proposed by Kitaigorodskii. As demonstrated profusely by the crystal structures of pure component types (e. g. alkanes, fatty alcohols, fatty acids, long chain esters, cholesteryl esters) and insertion of functional groups (e. g. chain branches, unsaturation, heteroatoms), characteristic molecular packing arrays provide important geometric information for understanding the co-packing of different molecules in mixtures. Single crystal and spectroscopic data from polydisperse arrays can then be evaluated to arrive at plausible structures of solid solutions and fractionated systems. The resultant structures are not only relevant to the understanding of so-called waxes but also include certain classes of polymers. The ramifications of this work extend into any solid state array of polymethylene chains, including lipid foodstuffs.

Paul Ewald's 1916-1917 masterpiece `On the Foundations of Crystal Optics' describes the selfconsistent 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. 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 his life, scientific work, and role in the international crystallographic community.

Modern experimental and computational techniques are capable of determining bond lengths and angles with precisions of a few thousandths of an oangström and a few tenths of a degree. Such precisions are meaningful only if they are coupled with rigorous error analysis and careful evaluation of the physical meaning of the parameters.Here, internationally respected authors present all modern experimental and computational techniques for the determination of accurate molecular structures for the first time in one volume. They establish guidelines for accuracy requirements in answering broadly varying questions in current chemical research.

This two-volume work forms a comprehensive treatise on the theory and applications of electron-diffraction techniques, and has been organized under the auspices of the Electron Diffraction Commission of the International Union of Crystallography.All those embarking on research which involves the use of electron diffraction methods, including graduate students and more experienced researchers who wish to add electron diffraction to their array of research tools will find this an invaluable reference. Volume 1 contains introductory chapters and the sections on electron diffraction which are less dependent on considerations of imaging in electron microscopes. Volume 2 deals with those aspects where there is a stronger correlation of the diffraction phenomena with the electron microscope imaging.

Volume 2 deals with those aspects when there is a stronger correlation of the diffraction phenomena with the electron microscope imaging.

The Rietveld method is a powerful and relatively new method for extracting detailed crystal structural information from X-ray and neutron powder diffraction data. Since such structural details dictate much of the physical and chemical attributes of materials, knowledge of them is crucial to our understanding of those properties and our ability to manipulate them. Since most materials of technological interest are not available as single crystals but often are available only in polycrystalline or powder form, the Rietveld method has become very important and is now widely used in all branches of science that deal with materials at the atomic level. This book, a collaboration by many authorities in the field, has tutorial and advisory value for those who already have some experience with this important method, but an introductory chapter enables the book to be used as a first text for researchers starting in this area of science.

Modern structural applications of crystallography make extensive use of statistical methods, in particular the probability density function (pdf) of the magnitude of the structure factor. Similarly, direct methods of phase determination have been responsible for much of the success of crystallography - methods based on properties of joint pdfs. This monograph, from two authorities in the field of structure factor statics, presents a survey of techniques and theories in this field of research in a self-contained and consistent way, with an emphasis on the probabilistic principles involved.

This text provides an up-to-date overview of crystallographic instrumentation and methods of diffraction measurements used for crystal and molecular structure determination. The book provides a unique description of both principles and specific instruments, and methods for data collection, adjustment of instruments, and primary data processing and error correction.

The dynamical theory of diffraction has witnessed exciting developments since the advent of synchrotron radiation. The present book is an up-to-date account of the theory of diffraction and its applications. The first part serves as an introduction to the subject, presenting the early developments and the basic results. It is followed by a detailed development of the diffraction and propagation properties of x-rays in perfect crystals and by an extension of the theory to the case of slightly and highly deformed crystals. The last part gives three applications of the theory: X-ray optics for synchrotron radiation, locations of atoms at surfaces, and X-ray diffraction topography. The book is richly illustrated and contains a wide range of references to the literature. It will be a useful reference work for graduate students, lecturers, and researchers.

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.

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.

The fascinating world of intermetallics is largely unexplored. There are many exciting physical properties and important technological applications of intermetallics, from magnetism to superconductivity. The main focus of this book is on the statistics, topology and geometry of crystal structures and structure types of intermetallic phases. The underlying physics, in particular chemical bonding, is discussed whenever it helps understand the stability of structures and the origin of their physical properties. The authors' approach, based on the statistical analysis of more than twenty thousand intermetallic compounds in the data base Pearson's Crystal Data, uncovers important structural relationships and illustrates the relative simplicity of most of the general structural building principles. It also shows that a large variety of actual structures can be related to a rather small number of aristotypes. The text aims to be readable and beneficial in one way or another to everyone interested in intermetallic phases, from graduate students to experts in solid state chemistry and physics, and materials science. For that purpose it avoids the use of enigmatic abstract terminology for the classification of structures. Instead, it focuses on the statistical analysis of crystal structures and structure types in order to draw together a larger overview of intermetallics, and indicate the gaps in it - areas still to be explored, and potential sources of worthwhile research. The text should be read as a reference guide to the incredibly rich world of intermetallic phases.

The bond valence model, a description of acid-base bonding, is widely used for analysing and modelling the structures and properties of solids and liquids. Unlike other models of inorganic chemical bonding, the bond valence model is simple, intuitive, and predictive, and is accessible to anyone with a pocket calculator and a secondary school command of chemistry and physics. This new edition of 'The Chemical Bond in Inorganic Chemistry: The Bond Valence Model' shows how chemical properties arise naturally from the conflict between the constraints of chemistry and those of three-dimensional space. The book derives the rules of the bond valence model, as well as those of the traditional covalent, ionic and popular VSEPR models, by identifying the chemical bond with the electrostatic flux linking the bonded atoms. Most of the new edition is devoted to showing how to apply these ideas to real materials including crystals, liquids, glasses and surfaces. The work includes detailed examples of applications, and the final chapter explores the relationship between the flux and quantum theories of the bond.

Over the past several decades, aThis book deals with the characterisation of the structure, the structure determination and the study of the physical properties, especially dynamical and electronic properties of aperiodic crystals. The treatment is based on a description in a space with more dimensions than three, the so-called superspace. This allows us to generalise the standard crystallography and to look differently at the dynamics. The three main classes of aperiodic crystals, modulated phases, incommensurate composites and quasicrystals are treated from a unified point of view, which stresses similarities of the various systems. The book assumes as a prerequisite a knowledge of the fundamental techniques of crystallography and the theory of condensed matter, and covers the literature at the forefront of the field.Since the first edition of this book in 2007, the field of aperiodic crystals has developed considerably, with the discovery of new materials and new structures. Progress has been made in structure determination, in the interpretation and understanding of the structural characteristics and in the calculation of electrons and phonons. This new edition reflects these new developments, and it includes discussions of natural quasicrystals, incommensurate magnetic and multiferroic structures, photonic and mesoscopic quasicrystals. The second edition also includes a number of new exercises that give the reader an opportunityt to check their understanding of the material.

Diffuse X-ray scattering is a rich source of local structural information over and above that obtained by conventional crystal structure determination. The main aim of the book is to show how computer simulation of a model crystal provides a general method by which diffuse scattering of all kinds and from all types of materials can be interpreted and analysed. Since the first edition was published in 2004 there have been major improvements both in the experimental methods for recording diffuse scattering and in our ability to analyse it. The advent of new and better detectors means that fully 3-dimensional diffuse scattering data can be collected routinely for even quite small samples and computational power that is now available has continued its upward trend, meaning modelling calculations inconceivable in 2004 are now routine. The final part of the book traces these recent developments and outlines their future potential in the field.

Most people are familiar with the fact that diamond and graphite are both composed only of carbon; yet they have very different properties which result from the very different structures of the two solids - they are polymorphs of carbon. Understanding the relationship between the structures and the properties of materials is of fundamental importance in developing and producing new materials with improved or new properties. The existence of polymorphic systems allows the direct study of the connection between structures and properties. This book provides grounding on the fundamental structural and energetic basis for polymorphism, the preparation and characterization of polymorphic substances and its importance in the specific areas of pharmaceuticals, pigments and high energy (explosive) materials. The closing chapter describes the intellectual property implications and some of the precedent patent litigations in which polymorphism has played a central role. The book contains over 2500 references to provide a ready entry into the relevant literature.

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.

This book is the first book dealing with structural crystallography of inorganic oxysalts in general. A special emphasis is placed upon structural topology and methods of its description. The latter include graph theory, nets, 2-D and 3-D tilings, polyhedra, etc. The structures considered range from minerals to organically templated oxysalts, for all of which this book provides a unified approach to structure interpretation and classification. Most of the structures have been analysed from the proposed viewpoint for the first time and it has been shown that they possess the same topological genealogy and relationships, sometimes despite their obvious chemical differences. In order to expand the range of oxysalts considered, the book offers not only traditional schemes but also alternative approaches such as anion topologis, anion-centered polyhedra and cation arrays. As such, this book can be considered as a comprehensive introduction into the amazingly complex and diverse world of inorganic oxysalts.

The crystallization of proteins and nucleic acids and/or their complexes has become more highly automated but is still often a trial and error based approach. In parallel, a number of X-ray diffraction based techniques have been developed which explain the physical reasons limiting the resulting crystallographic data and thus show how that data may be improved. Crystal growth is also pivotal in neutron crystallography, which establishes the hydrogen and hydration aspects. Thus this book is aimed at addressing the science behind obtaining the best and most complete structural data possible for biological macromolecules, so that the detailed structural biology and chemistry of these important molecules emerge. Crystal imperfections such as twinning and lattice disorders, as well as multiple crystal situations, and their possible remedies, are also described. The small crystal frontier in micro-crystal crystallography, crystallites in powders and finally down to the proposed single molecule structure determination of X-ray lasers are covered. Overall this interdisciplinary book will interest crystal growers, X-ray and neutron physicists and the biological crystallographers, including graduate students.

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 r s6methods 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.

Polymorphism - the multiplicity of structures or forms - is a term that is used in many disciplines. In chemistry it refers to the existence of more than one crystal structure for a particular chemical substance. The properties of a substance are determined by its composition and by its structure. In the last two decades, there has been a sharp rise in the interest in polymorphic systems, as an intrinsically interesting phenomenon and as an increasingly important component in the development and marketing of a variety of materials based on organic molecules (e.g. pharmaceuticals, dyes and pigments, explosives, etc.). This book summarizes and brings up to date the current knowledge and understanding of polymorphism of molecular crystals, and concentrates it in one comprehensive source. The book will be an invaluable reference for students, researchers, and professionals in the field.

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.