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Crystal Symmetries is a timely account of the progress in the most diverse fields of crystallography. It presents a broad overview of the theory of symmetry and contains state of the art reports of its modern directions and applications to crystal physics and crystal properties. Geometry takes a special place in this treatise. Structural aspects of phase transitions, correlation of structure and properties, polytypism, modulated structures, and other topics are discussed. Applications of important techniques, such as X-ray crystallography, biophysical studies, EPR spectroscopy, crystal optics, and nuclear solid state physics, are represented. Contains 30 research and review papers.
The central theme of this monograph is that the cosine seminvariants are the key to crystal structures. The cosine seminvariants are the cosines of those linear combinations of the phases (the so-called structure seminvariants) whose values, for a given functional form for the geometric structure factor, are uniquely determined by the crystal structure alone and are there fore independent of the choice of permissible origin. It follows that the cosine seminvariants themselves are uniquely determined, in general, by the observed magnitudes of the normalized structure factors. The values of the cosine seminvariants in turn lead unambiguously to the values of the individual phases and thus to the crystal structure by means of the E-map (Fourier synthesis). It is this property of the cosine seminvariants, that they serve to link the observed magnitudes with the desired phases of the normalized structure factors, which accounts for their importance and explains the emphasis which is here placed on their role.
This volume summarises recent developments and possible future directions for small molecule X-ray crystallography. It reviews specific areas of crystallography which are rapidly developing and places them in a historical context. The interdisciplinary nature of the technique is emphasised throughout. It introduces and describes the chemical crystallographic and synchrotron facilities which have been at the cutting edge of the subject in recent decades. The introduction of new computer-based algorithms has proved to be very influential and stimulated and accelerated the growth of new areas of science. The challenges which will arise from the acquisition of ever larger databases are considered and the potential impact of artificial intelligence techniques stressed. Recent advances in the refinement and analysis of X-ray crystal structures are highlighted. In addition the recent developments in time resolved single crystal X-ray crystallography are discussed. Recent years have demonstrated how this technique has provided important mechanistic information on solid-state reactions and complements information from traditional spectroscopic measurements. The volume highlights how the prospect of being able to routinely “watch” chemical processes as they occur provides an exciting possibility for the future. Recent advances in X-ray sources and detectors that have also contributed to the possibility of dynamic single-crystal X-ray diffraction methods are presented. The coupling of crystallography and quantum chemical calculations provides detailed information about electron distributions in crystals and has resulted in a more detailed understanding of chemical bonding. The volume will be of interest to chemists and crystallographers with an interest in the synthesis, characterisation and physical and catalytic properties of solid-state materials. Postgraduate students entering the field will benefit from a historical introduction to the subject and a description of those techniques which are currently used. Since X-ray crystallography is used so widely in modern chemistry it will serve to alert senior chemists to those developments which will become routine in coming decades. It will also be of interest to the broad community of computational chemists who study chemical systems.
Direct methods of crystal structure determination are usually associated with techniques in which phases for a set of structure factors are determined from the corresponding experimental amplitudes by probabilistic calcula tions. It is thus implied that such ab initio phase calculations do not require a knowledge of atomic positions, and this basis distinguishes direct methods from other techniques for structure determination. An acceptably wider interpretation of the term direct methods leads to other important applica tions involving, inter alia, the use of heavy atoms, resolution-limited phase data for large molecules, rotation functions, and Fourier series. These topics are discussed in the later chapters of this book. Although some earlier theoretical investigations were made by Harker and Kaspar, direct methods may be considered to have begun around the year 1950. Important landmarks in the development of the subject include the book by Hauptmann and Karle, The Centrosymmetric Crystal (1953), the definitive paper by Karle and Karle in Acta Crystallographica (1966), and the recent (1978) sophisticated program package MULTAN 78 produced mainly by Germain, Main, and Woolfson. Woolfson's book, Direct Methods in Crystallography, was published in 1961, but because of the rapid progress in direct methods, much of it soon became outmoded. It is interesting to note that direct methods nearly came into being many years earlier. Certainly the E2 relationship was used implicitly by Lonsdale in 1928 in determining the crystal structure of hexamethylbenzene.
This authoritative text on electron diffraction and crystal structure analysis is the first to describe direct phasing techniques in electron crystallography. Written for electron diffractionists and electron microscopists, this fully illustrated volume presents methods for specimen preparation, data collection and structure analysis. Chapters feature numerous detailed examples of actual structure analyses and contain over 350 illustrations.
Advances in Electronics and Electron Physics
In recent years crystallographic techniques have found applications in a wide range of subjects, and these applications in turn have led to exciting developments in the field of crystallography itself. This completely revised text offers a rigorous treatment of the theory and describes experimental applications in many fields: crystal symmetry, crystallographic computing, X-ray diffraction, crystal structure solution, mineral and inorganic crystal chemistry, protein crystallography, crystallography of real crystals, and crystal physics. A set of pedagogical tools on CD-ROM has been added to this new edition.
The Advances in Chemical Physics series provides the chemical physics and physical chemistry fields with a forum for critical, authoritative evaluations of advances in every area of the discipline. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics.
X-ray crystallography provides us with the most accurate picture we can get of atomic and molecular structures in crystals. It provides a hard bedrock of structural results in chemistry and in mineralogy. In biology, where the structures are not fully crystalline, it can still provide valuable results and, indeed, the impact here has been revolutionary. It is still an immense field for young workers, and no doubt will provide yet more striking developments of a major character. It does, however, require a wide range of intellectual application, and a considerable ability in many fields. This book will provide much help. It is a very straightforward and thorough guide to every aspect of the subject. The authors are ex perienced both as research workers and as teachers of standing, and this is shown in their clarity of exposition. There are plenty of illustrations and worked examples to aid the student to obtain a real grasp of the subject. The practical side is encouraged by the very clarity of the theory.