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Symmetry exists in realms from crystals to patterns, in external shapes of living or non-living objects, as well as in the fundamental particles and the physical laws that govern them. In fact, the search for this symmetry is the driving force for the discovery of many fundamental particles and the formulation of many physical laws. While one can not imagine a world which is absolutely symmetrical nor can one a world which is absolutely asymmetrical. These two aspects of nature are intermingled with each other inseparably. This is the basis of the existence of aperiodicity manifested in the liquid crystals and also quasi-crystals also discussed in “Crystallography and the World of Symmetry”.
Site Symmetry in Crystals is the first comprehensive account of the group-theoretical aspects of the site (local) symmetry approach to the study of crystalline solids. The efficiency of this approach, which is based on the concepts of simple induced and band representations of space groups, is demonstrated by considering newly developed applications to electron surface states, point defects, symmetry analysis in lattice dynamics, the theory of second-order phase transitions, and magnetically ordered and non-rigid crystals. Tables of simple induced respresentations are given for the 24 most common space groups, allowing the rapid analysis of electron and phonon states in complex crystals with many atoms in the unit cell.
A fresh approach to teaching crystallographic symmetry. Rather than being swamped by heavy algebraic notation, the reader is taken through a series of simple and beautiful examples from the visual arts, and taught how to analyse them employing the 'pictorial' diagrams used in the International Tables of Crystallography.
The book presents the basic information needed to understand and to organize the huge amount of known structures of crystalline solids. Its basis is crystallographic group theory (space group theory), with special emphasis on the relations between the symmetry properties of crystals.
Crystals are everywhere, from natural crystals (minerals) through the semiconductors and magnetic materials in electronic devices and computers or piezoelectric resonators at the heart of our quartz watches to electro-optical devices. Understanding them in depth is essential both for pure research and for their applications. This book provides a clear, thorough presentation of their symmetry, both at the microscopic space-group level and the macroscopic point-group level. The implications of the symmetry of crystals for their physical properties are then presented, together with their mathematical description in terms of tensors. The conditions on the symmetry of a crystal for a given property to exist then become clear, as does the symmetry of the property. The geometrical representation of tensor quantities or properties is presented, and its use in determining important relationships emphasized. An original feature of this book is that most chapters include exercises with complete solutions. This allows readers to test and improve their understanding of the material. The intended readership includes undergraduate and graduate students in materials science and materials-related aspects of electrical and optical engineering; researchers involved in the investigation of the physical properties of crystals and the design of applications based on crystal properties such as piezoelectricity, electro-optics, optical activity and all those involved in the characterization of the structural properties of materials.
This book invites you on a systematic tour through the fascinating world of crystals and their symmetries. The reader will gain an understanding of the symmetry of external crystal forms (morphology) and become acquainted with all the symmetry elements needed to classify and describe crystal structures. The book explains the context in a very vivid, non-mathematical way and captivates with clear, high-quality illustrations. Online materials accompany the book; including 3D models the reader can explore on screen to aid in the spatial understanding of the structure of crystals. After reading the book, you will not only know what a space group is and how to read the International Tables for Crystallography, but will also be able to interpret crystallographic specifications in specialist publications. If questions remain, you also have the opportunity to ask the author on the book's website.
This highly readable, popular textbook for upper undergraduates and graduates comprehensively covers the fundamentals of crystallography and symmetry, applying these concepts to a large range of materials. New to this edition are more streamlined coverage of crystallography, additional coverage of magnetic point group symmetry and updated material on extraterrestrial minerals and rocks. New exercises at the end of chapters, plus over 500 additional exercises available online, allow students to check their understanding of key concepts and put into practice what they have learnt. Over 400 illustrations within the text help students visualise crystal structures and more abstract mathematical objects, supporting more difficult topics like point group symmetries. Historical and biographical sections add colour and interest by giving an insight into those who have contributed significantly to the field. Supplementary online material includes password-protected solutions, over 100 crystal structure data files, and Powerpoints of figures from the book.
Written in a clear and understandable manner, this book provides a comprehensive, yet non-mathematical, treatment of the topic, covering the basic principles of symmetry and the important spectroscopic techniques used to probe molecular structure. The chapters are extensively illustrated and deal with such topics as symmetry elements, operations and descriptors, symmetry guidelines, high-fidelity pseudosymmetry, crystallographic symmetry, molecular gears, and experimental techniques, including X-ray crystallography and NMR spectroscopy. As an additional feature, 3D animations of most of the structures and molecules covered are available online at wiley.com. As a result, chemists learn how to understand and predict molecular structures and reactivity. Authored by a renowned expert with numerous publications and an excellent track record in research and teaching, this is a useful source for graduate students and researchers working in the field of organic synthesis, physical chemistry, biochemistry, and crystallography, while equally serving as supplementary reading for courses on stereochemistry, organic synthesis, or crystallography.
Complete with reference tables and sample problems, this volume serves as a textbook or reference for solid-state physics and chemistry, materials science, and engineering. Chapters illustrate symmetry, and its role in determining solid properties, as well as a demonstration of group theory.
The four-volume treatment Modern Crystallography presents an encyclopaedic exposition of problems concerning the structure of crystals, their growth and their properties. Structure of Crystals deals with crystal structures in inorganic and organic compounds, polymers, liquid crystals, biological crystals and macromolecules.