Crystallography

This text is an updated English version of a class-tested textbook originally published in Chinese in 2006. Its contents are based on the lecture notes of several courses taught by the authors at The Chinese University of Hong Kong and Peking University. These courses include Chemical Bonding, Structure and Properties of Matter, Advanced Inorganic Chemistry, Quantum Chemistry, Group Theory, and Chemical Crystallography. This book consists of three parts. Part I reviews the basic theories of chemical bonding, with chapters on elementary quantum theory, atomic structure, bonding in molecules, bonding in solids, and computational chemistry. Part II introduces point groups and space groups, and their applications to the study of discrete molecules and crystals. A large number of worked examples are provided in order to illustrate the usefulness and elegance of the symmetry concept. Part III constitutes about half of the book and it gives a succinct description of the structural chemistry of the elements in the Periodic Table. The main-group elements are covered in seven chapters and three other chapters deal with the rare-earth elements, transition-metal clusters and supramolecular systems. The selected systems, many of them from recent literature, are used to elucidate various aspects of structure and bonding presented in Parts I and II, and to expound the current research trends in structural inorganic chemistry

Until the 1970s, all materials studied consisted of periodic arrays of unit cells, or were amorphous. In the last decades a new class of solid state matter, called aperiodic crystals, has been found. It is a long range ordered structure, but without lattice periodicity. It is found in a wide range of materials: organic and anorganic compounds, minerals (including a substantial portion of the earths crust), and metallic alloys, under various pressures and temperatures. Because of the lack of periodicity, the usual techniques for the study of structure and physical properties no longer work, and new techniques have to be developed. This book deals with the characterization 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 the similarities of the various systems.

The bond valence model, which is derived from the ionic model, is expressed through a number of rules and equations that determines which acid-base bond structures can exist. Chief among these rules is the bond valence sum rule, which states that the sum of bond valences around an ion is equal to its atomic valence. These rules can be used to understand many of the properties of inorganic structures, such as bond lengths, coordination numbers, their structures and their solution chemistry. The unusual geometries and properties of hydrogen bonds follow naturally from these rules. Because the model describes chemically ideal structures, it allows one to quantify the role of electronic anisotropies and steric strain in observed structures, the latter frequently leading to phase transitions in crystals. In favourable cases the model can be used for structure prediction by constructing the bond network ab initio and then mapping this onto a compatible space group. The model has applications in many fields ranging from earth sciences to biology.

This book presents a less mathematical approach to X-ray crystal structure determination than is given in some detailed texts and concentrates on practical aspects. The book provides the necessary conceptual framework for understanding and applying the techniques described, but also gives practical advice on topics such as growing crystals, solving and refining structures, and understanding and using the results. There are also plenty of worked examples and problems provided (with answers), to reinforce the material presented. The book is based on the intensive course run by the Chemical Crystallography Group of the British Crystallographic Association every two years, and the material is drawn from the 2007 and 2009 courses. Much of the material of the first edition in 2001 has been significantly updated and expanded, and some new topics have been added. The approach to several of the topics is somewhat different as a result of changes in the authorship and the course teaching team. These changes reflect developments in the subject.

This book covers advanced aspects of practical crystal structure refinement, focusing on practical problems in the everyday life of a crystallographer. After an introduction to SHELXL in the first chapter, the second chapter provides a brief survey of crystal structure refinement. The next few chapters 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 shorter chapters deal with structure validation. In most chapters, the book gives refinement examples, based on the program SHELXL, describing every problem in detail.

This book presents a rational classification of the vast amount of material in literature followed by a sketch of the historical background. The structures and properties of the various kinds of crystalline inclusion complexes are described in some detail, distinguishing among container-molecule hosts, such as the cyclodextrins, clathrates, linear tunnel inclusion complexes, and two-dimensional intercalation complexes. Together with material on packing complexes, this comprises the first half. The second half contains descriptions of molecular compounds based on localized and delocalized interactions between the two components. Localized interactions are found in binary compounds with hydrogen bonding and those with charge-transfer interactions. The final group consists of binary compounds linked by delocalized charge transfer interactions with separate discussion of mixed stack compounds and segregated stack complexes. The most emphasis is placed on the solid state arrangements, supplemented by thermodynamic data where available. Rational classification and comprehensive comparison of the various structure types is an important feature of the treatment.

This book provides a 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. 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 microscale, together with disorder, causes many problems to the determination of crystal structures. The book develops the theory of twinning with the inclusion of worked examples. In spite of the increasing use of the concepts of modular crystallography for characterizing, understanding, and tailoring technological crystalline materials, this book offers a unified treatment of the results, which are spread across many different journal and papers published over the last twenty years.

This book describes the solid state behaviour of organic materials based the polymethylene chain, i.e., the functional molecular component of polyethylenes, soaps, detergents, edible fats, lipids, oils, greases, and waxes. Along with chain unsaturation and branching, polydispersity, i.e., the aggregation of several polymethylene chain lengths, is shown to control various physical properties, including the preservation of metastable phases (polymorphic as well as ‘rotator’ forms). Using linear chain waxes as model materials, this book explores how solid solutions are stabilized and what structures are possible. Strictly linear molecules are compared to those functionalized with ‘head-groups’. The onset of fractionation, followed by formation of eutectic phases, is discussed, again describing the structures of favoured molecular assemblies. The rationale for polydisperse aggregation derives from the early work of A. I. Kitaigorodskii, demonstrating how certain homeomorphic parameters such as relative molecular shape and volume, as well as favoured crystalline polymorphs, lead to stable solid solutions. Relevant to high-molecular weight polymers, the influence of chain-folding is also discussed. A comprehensive review of known linear chain single crystal structures, including the alkanes, cycloalkanes, perfluoroalkanes, fatty alcohols, fatty acids, fatty acid esters, and cholesteryl esters, is presented to show how molecular shape, including chain branching, influences layer packing and co-solubility. Finally, a critique of previously suggested models for petroleum and natural wax assemblies is given, based on current crystallographic and spectroscopic information. This includes single crystal structures based on electron diffraction data. Although constrained to single chain molecules in the examples discussed, cited behaviour can be generalized to multiple chain-containing fats and lipids.

This book presents a complete account of the theory of the diffraction of X-rays by crystals with particular reference to the processes of determining the structures of protein molecules. The book develops from first principles all relevant mathematics, diffraction, and wave theory. The practical aspects of sample preparation and X-ray data collection using both laboratory and synchrotron sources are covered along with data analysis at both the theoretical and practical levels. The important role played by the Patterson function in structure analysis by both molecular replacement and experimental phasing approaches is covered, as are methods for improving the resulting electron density map. The theoretical basis of methods used in refinement of protein crystal structures are then covered in depth along with the crucial task of defining the binding sites of ligands and drug molecules. The complementary roles of other diffraction methods which reveal further detail of great functional importance in a crystal structure are outlined.

In recent years it has become apparent that merely knowing and understanding the average atomic structure is insufficient for comprehending material properties fully. Deviations from this average structure play an important role regarding these properties. To understand the defect or local structure one has to study diffuse scattering and go beyond the classic interpretation of Bragg intensities. Although there is an increasing interest in analysing disordered materials, as expressed by a number of recent text books, the practical aspects of this analysis are not yet widely known. A detailed step-by-step guide that explains how to simulate disordered materials has been missing. This book covers the full range; from basic steps such as how to build a computer model of the crystal to complex disorder models such as domains, stacking faults, and nanoparticles. It also explains how to use advanced refinement techniques to determine the parameters of a disordered structure. This book provides many examples of the simulation of disordered materials including the input files for DISCUS and explains the concepts and pitfalls encountered when simulating disordered materials.