The concept of reciprocal space is over 100 years old, and has been of particular use by crystallographers in order to understand the patterns of spots when x-rays are diffracted by crystals. However, it has a much more general use, especially in the physics of the solid state. In order to understand what it is, how to construct it and how to make use of it, it is first necessary to start with the so-called real or direct space and then show how reciprocal space is related to it. Real space describes the objects we see around us, especially with regards to crystals, their physical shapes and symmetries and the arrangements of atoms within: the so-called crystal structure. Reciprocal space on the other hand deals with the crystals as seen through their diffraction images. Indeed, crystallographers are accustomed to working backwards from the diffraction images to the crystal structures, which we call crystal structure solution. In solid state physics, one usually works the other way, starting with reciprocal space to explain various solid-state properties, such as thermal and electrical phenomena. In this book, I start with the crystallographer's point of view of real and reciprocal space and then proceed to develop this in a form suitable for physics applications. Note that while for the crystallographer reciprocal space is a handy means of dealing with diffraction, for the solid-state physicist it is thought of as a way to describe the formation and motion of waves, in which case the physicist thinks of reciprocal space in terms of momentum or wave-vector k-space. This is because, for periodic structures, a characteristic of normal crystals, elementary quantum excitations, e.g. phonons and electrons, can be described both as particles and waves. The treatment given here, will be by necessity brief, but I would hope that this will suffice to lead the reader to build upon the concepts described. I have tried to write this book in a suitable form for both undergraduate and graduate students of what today we call "condensed matter physics".

There are more than 20 million chemicals in the literature, with new materials being synthesized each week. Most of these molecules are stable, and the 3-dimensional arrangement of the atoms in the molecules, in the various solids may be determined by routine x-ray crystallography. When this is done, it is found that this vast range of molecules, with varying sizes and shapes can be accommodated by only a handful of solid structures. This limited number of architectures for the packing of molecules of all shapes and sizes, to maximize attractive intermolecular forces and minimizing repulsive intermolecular forces, allows us to develop simple models of what holds the molecules together in the solid. In this volume we look at the origin of the molecular architecture of crystals; a topic that is becoming increasingly important and is often termed, crystal engineering. Such studies are a means of predicting crystal structures, and of designing crystals with particular properties by manipulating the structure and interaction of large molecules. That is, creating new crystal architectures with desired physical characteristics in which the molecules pack together in particular architectures; a subject of particular interest to the pharmaceutical industry.

Dendrimers are hyperbranched molecules with well-defined nanometer-scale dimensions. Important technological applications of these systems, both in biomedicine and materials science, have been recently proposed. Liquid crystal dendrimers are fascinating materials that combine the characteristics of dendrimers with the anisotropic physical behaviour and molecular self-organization typical of liquid crystals. This unique association of physical and chemical properties, together with the possibility of multi-selective functionalization put forward by dendrimers, opens new perspectives for applications. Nuclear magnetic resonance (NMR) is a powerful experimental technique applied in materials science and an important tool to the study of molecular organization and dynamics. This book presents an introduction to dendrimers properties with special insight into liquid crystal dendrimers and a detailed description of the NMR theory and experimental techniques used in the investigation of these materials. It also discusses recent NMR research results on liquid crystal dendrimers, with emphasis on molecular order and dynamics studies. This book introduces the properties of dendrimers, with special insight into liquid crystal dendrimers, and a detailed description of NMR theory and experimental techniques used in the investigation of these materials. It also discusses results of recent NMR research on liquid crystal dendrimers, with an emphasis on molecular order and dynamics studies. Advanced undergraduate and graduate students of physics, chemistry, and materials science and researchers in the fields of dendrimers, liquid crystals, and NMR will find the book extremely useful.

Zeitschrift fur Kristallographie. Supplement Volume 37 presents the complete Abstracts of all contributions to the 25th Annual Conference of the German Crystallographic Society in Karlsruhe (Germany) 2017: - Plenary Talks - Microsymposia - Poster Session Supplement Series of Zeitschrift fur Kristallographie publishes Abstracts of international conferences on the interdisciplinary field of crystallography.

X-ray scattering is a well-established technique in materials science. Several excellent textbooks exist in this field, but these texts are typically written by physicists who use mathematics to make things clear. Consequently these books appeal less to students and scientists in the field of soft matter (polymers, liquid crystals, colloids, self-assembled organic systems) who usually have a more chemical-oriented background with limited mathematics. Moreover, they need to know about the technique of x-ray scattering, but do not intend to become an expert. The aim of this book is to explain basic principles and applications of x-ray scattering in a simple way using many practical examples followed by more elaborate case studies. The book contains a separate chapter on the different types of order/disorder in soft matter that play such an important role in modern self-assembling systems. Finally the last chapter treats soft matter surfaces and thin film that are increasingly used in coatings and in many technological applications, such as liquid crystal displays and nanostructured block copolymer films. This book has been written for the large community of soft matter students and scientists.

Liquid crystals (LCs) were discovered over a century ago, but their profound impact was in the past four decades through their successful implementation into electronic devices that we are using every day. The research on liquid crystals actively continues in the 21st century and offers unlimited potential in various display or non-display applications. This book covers novel topics related to LCs and is intended for a wide range of researchers in both, academia and industry, from beginners to advanced level professionals in many scientific areas, viz. materials science and engineering, chemistry, physics, optics, photonics, nanotechnology, electrical engineering, and so on. The book contains topics on nematic and cholesteric LCs, in the form of films or particles, as well as modified LC behaviour with variety of dopants, micron and nano-sized particles, microencapsulation of LC particles and modelling of their behaviour under an externally applied field. Topics related to the effect on nanomaterials on LC behaviour, as well as structural and magnetic properties of different types of iron-containing liquid crystals (metallo-mesogens) are covered, as well. Finally, an overview of different alignment technologies for nematic liquid crystals such as mechanical rubbing of polymer films, obliquely-deposited inorganic films, photo-irradiated, IB-bombarded and patterned surfaces, are briefly reviewed along with several novel alignment concepts. The state of the art in respective fields related to LCs in each chapter is given by leading experts.

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).

Since the discovery of the first liquid crystal in 1888 by the Austrian biologist Friedrich Reinitzer with the considerable assistance of the German physicist Otto Lehman, who in that time had been universally recognised authority in the field of microscope technique, thousands and thousands of liquid crystals have been synthesised among them nematics, short-pitch cholesterics and various kinds of smectics such as smectic-A and smectic-C. The smectic-A or smectic-C phases grow from a nematic or unwinded large-pitch cholesteric oriented in the middle part of the cells and from strongly-deformed nematic or unwinded large-pitch cholesteric layer in the boundary regions of the liquid crystal cells.

An excellent book for professional crystallographers! In 2012 the crystallographic community celebrated 100 years of X-ray diffraction in honour of the pioneering experiment in 1912 by Max von Laue, Friedrich and Knipping. Experimental developments e.g. brilliant X-ray sources, area detection, and developments in computer hardware and software have led to increasing applications in X-ray analysis. This completely revised edition is a guide for practical work in X-ray analysis. An introduction to basic crystallography moves quickly to a practical and experimental treatment of structure analysis. Emphasis is placed on understanding results and avoiding pitfalls. Essential reading for researchers from the student to the professional level interested in understanding the structure of molecules.

The study of solids is one of the richest, most exciting, and most successful branches of physics. While the subject of solid state physics is often viewed as dry and tedious this new book presents the topic instead as an exciting exposition of fundamental principles and great intellectual breakthroughs. Beginning with a discussion of how the study of heat capacity of solids ushered in the quantum revolution, the author presents the key ideas of the field while emphasizing the deep underlying concepts. The book begins with a discussion of the Einstein/Debye model of specific heat, and the Drude/Sommerfeld theories of electrons in solids, which can all be understood without reference to any underlying crystal structure. The failures of these theories force a more serious investigation of microscopics. Many of the key ideas about waves in solids are then introduced using one dimensional models in order to convey concepts without getting bogged down with details. Only then does the book turn to consider real materials. Chemical bonding is introduced and then atoms can be bonded together to crystal structures and reciprocal space results. Diffraction experiments, as the central application of these ideas, are discussed in great detail. From there, the connection is made to electron wave diffraction in solids and how it results in electronic band structure. The natural culmination of this thread is the triumph of semiconductor physics and devices. The final section of the book considers magnetism in order to discuss a range of deeper concepts. The failures of band theory due to electron interaction, spontaneous magnetic orders, and mean field theories are presented well. Finally, the book gives a brief exposition of the Hubbard model that undergraduates can understand. The book presents all of this material in a clear fashion, dense with explanatory or just plain entertaining footnotes. This may be the best introductory book for learning solid state physics. It is certainly the most fun to read.

Plasticity of crystals in a microscopic viewpoint, especially on the basis of dislocation (linear defects in crystal) motion, is detailed from the data obtained mainly by the strain-rate cycling tests associated with ultrasonic oscillation for several kinds of alkali-halide single crystals at low temperatures. Topics discussed include process for thermal activated overcoming of the short-range obstacle by a dislocation; strain-rate cycling tests associated with ultrasonic oscillation; influence of state of impurities on the effective stress due to the impurities; effective stress and critical temperature of KCl doped with various divalent cations; and the Friedel relation and thermally activated flow parameters of KCl doped with various divalent cations.

This book is important because it is the first textbook in an area that has become very popular in recent times. There are around 250 research groups in crystal engineering worldwide today. The subject has been researched for around 40 years but there is still no textbook at the level of senior undergraduates and beginning PhD students. This book is expected to fill this gap.

The writing style is simple, with an adequate number of exercises and problems, and the diagrams are easy to understand. This book consists major areas of the subject, including organic crystals and co-ordination polymers, and can easily form the basis of a 30 to 40 lecture course for senior undergraduates.

Borate2008: Proceedings of the Sixth International Conference on Borate Glasses, Crystals and Melts: new techniques and practical applications held at Himeji, Japan on 18-22 August 2008 A collected volume of papers from the Sixth International Conference, the papers were originally published in Physics and Chemistry of Glasses: European Journal of Glass Science and Technology Part B: and Glass Technology: European Journal of Glass Science and Technology Part A: The Conference was dedicated to Professor Adrian C. Wright to honour his achievements in glass science, and in particular borate glasses and neutron diffraction.

This book consists of over 422 problems and their acceptable answers on structural inorganic chemistry at the senior undergraduate and beginning graduate level. The central theme running through these questions is symmetry, bonding and structure: molecular or crystalline. A wide variety of topics are covered, including Electronic States and Configurations of Atoms and Molecules, Introductory Quantum Chemistry, Atomic Orbitals, Hybrid Orbitals, Molecular Symmetry, Molecular Geometry and Bonding, Crystal Field Theory, Molecular Orbital Theory, Vibrational Spectroscopy, Crystal Structure, Transition Metal Chemistry, Metal Clusters: Bonding and Reactivity, and Bioinorganic Chemistry. The questions collected here originate from the examination papers and take-home assignments arising from the teaching of courses in Chemical Bonding, Elementary Quantum Chemistry, Advanced Inorganic Chemistry, and X-Ray Crystallography by the book's two senior authors over the past five decades. The questions have been tested by generations of students taking these courses. The questions in this volume cover essentially all the topics in a typical course in structural inorganic chemistry. The text may be used as a supplement for a variety of inorganic chemistry courses at the senior undergraduate level. It also serves as a problem text to accompany the book Advanced Structural Inorganic Chemistry, co-authored by W.-K. Li, G.-D. Zhou, and T. C. W. Mak (Oxford University Press, 2008).

The question of what is matter has fascinated the human race for thousands of years, and continues to fascinate us today: what is it made of, and how does it behave? Early in our history, the character of natural materials was of critical importance to us, and it is no accident that we date the prehistory of humanity by the materials with which our predecessors made their tools. Tools are one of the more enduring creations of our prehistoric ancestors, and are of particular historical significance as they document the increasing technological sophistication of the human race. From the Stone Age to the Bronze Age to the Iron Age, there was an increasing awareness of the diversity of natural materials, how they could be used, and eventually, how they could be processed in order to provide even more technologically effective materials for our use. This increasing reliance on rocks and minerals required that more and more people be conversant with these materials and their properties. The atomistic theory of the Greeks was a solely philosophical construct, and further development had to await a more sophisticated approach to Science. The first steps in this direction were taken by who else but Isaac Newton (1643-1727 AD). Although his ideas on action at a distance initially referred to planets, he also considered them as applying to atoms, and concluded from physical evidence involving surface tension and viscosity that there must be strong attractions between atoms. In what must be considered as insight of legendary proportions, Roger Joseph Boscovich (1711-1787), a Jesuit mathematician from Croatia, proposed that at very short distances, atoms repulse each other, the repulsion increasing indefinitely as the particles become closer together, whereas at longer distances apart, atoms oscillate between attraction and repulsion. Frank Hawthorne uses the republication of this set of landmark papers as a vehicle to focus on the development of key issues concerning structural connectivity in inorganic solids, of which minerals are a key component, and to look at where we are today in our understanding of crystal structure.

Protein crystallography has become vital to further understanding the structure and function of many complex biological systems. In recent years, structure determination has progressed tremendously however the quality of crystals and data sets can prevent the best results from being obtained. With contributions from world leading researchers whose software are used worldwide, this book provides a coherent approach on how to handle difficult crystallographic data and how to assess its quality. The chapters will cover all key aspects of protein crystallography, from instrumentation and data processing through to model building. This book also addresses challenges that protein crystallographers will face such as dealing with data from microcrystals and multi protein complexes. This book is ideal for both academics and researchers in industry looking for a comprehensive guide to protein crystallography.

Crystallography can be studied from two different view-points: one as a mathematical science with its applications both in the instrumental determination of crystal angles and in their mapping or projection; the other chiefly as an observational study with the application of some simple rules that will enable the student to determine the crystalline form with sufficient accuracy for practical purposes in the field or the laboratory. This book concerns itself with the latter, author presenting his notes in the form of lectures given in the Pennsylvania State College for the use of students. A fascinating and comprehensive treatise on the subject, this rare book will greatly appeal to those with a serious interest in Crystallography. This book has been elected for modern republication due to its immense educational value, and is proudly republished here with a new introduction to the subject.

Plaiting and braiding have a long history. They encompass decorating hair, weaving and basket-making as well as making knots. So it is surprising that John Gorham seems to have been the first person to have looked at the subject systematically. The main part of this book is a reprint of his 1888 work on plaiting crystal models has been an inspiration to many others working in this field, notably Robert Pargeter and Jean Pedersen. Along with Robert Pargeter and James Brunton's articles in the Mathematical Gazette Gorham's work is here reproduced. The ideas were extensively covered in Mathematical Models by Cundy and Rollett, also reprinted by Tarquin. It is through this book and Pargeter's article that Gorham's techniques have been kept alive. The book itself has been rare and most references to it are only as a result of Pargeter having quoted it as his source. Through this reprint the work can be more widely read and admired by mathematicians, plaiters and crystallographers, as well as historians of science and mathematics.

New Developments In Crystal Growth

This volume deals with the technologies of crystal fabrication, of crystal machining, and of epilayer production and is the first book on industrial and scientific aspects of crystal and layer production. Highest-quality crystals and epitaxical layers form the base for many of industries technological advances, including telecommunication, computer and electric energy technology, and those technologies based on lasers and nonlinear-optic crystals. Furthermore, automobile electronics, audiovisual equipment and infrared night-vision all depend on high-quality crystals and epilayers, as do novel technologies currently in development and planned for the future.

This book contains 29 contributions of leading crystal technologists covering the following topics: General aspects of crystal growth technology Silicon Compound semiconductors Oxides and halides Crystal machining Epitaxy and layer deposition

Scientific and technological problems of production and machining of industrial crystals are discussed by top experts, most of the m from the major growth industries and crystal growth centres.

It is anticipated that this volume will serve all scientists and engineers involved in crystal and epilayer fabrication. In addition, it will be useful for the users of crystals, for teachers and graduate students in materials sciences, in electronic and other functional materials, chemical and metallurgical engineering, micro-and optoelectronics including nanotechnology, mechanical engineering and precision-machining, microtechnology, and in solid-state sciences. Also consultants and specialists will profit from this book, as will those interested in crystals, epilayers, and their productionfor saving energy (GaN- and SiC-based high-power electronics and light-emitting diodes for illumination) and for renewable energy sources (economic high-efficiency solar cells and forthcoming laser-fusion energy).

Superb study begins with fundamentals of x-ray diffraction theory using Fourier transforms, then applies general results to various atomic structures, amorphous bodies, crystals and imperfect crystals. Elementary laws of X-ray diffraction on crystals follow as special case. Highly useful for solid-state physicists, metallographers, chemists and biologists. 1963 edition. 154 illustrations. Appendixes. Index.