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An Introduction To Mathematical Crystallography
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Book Synopsis Introduction to Crystallography by : Donald E. Sands
Download or read book Introduction to Crystallography written by Donald E. Sands and published by Courier Corporation. This book was released on 2012-06-14 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clear, concise explanation of logical development of basic crystallographic concepts. Topics include crystals and lattices, symmetry, x-ray diffraction, and more. Problems, with answers. 114 illustrations. 1969 edition.
Book Synopsis Mathematical Techniques in Crystallography and Materials Science by : Edward Prince
Download or read book Mathematical Techniques in Crystallography and Materials Science written by Edward Prince and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This practical guide and reference serves as a unified source book for students and professionals, and it provides a solid basis for further studies in more specialized literature. Based Prince’s decades of practical experience, it can be recommended as an introduction for beginners in crystallography, as a refresher and handy guide for crystallographers working on specific problems, and as a reference for others seeking a dictionary of basic mathematical and crystallographic terms. The third edition further clarifies key points.
Book Synopsis Mathematical Crystallography by : Monte B. Boisen
Download or read book Mathematical Crystallography written by Monte B. Boisen and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-12-17 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 15 of Reviews in Mineralogy is written with two goals in mind. The first is to derive the 32 crystallographic point groups, the 14 Bravais lattice types and the 230 crystallographic space group types. The second is to develop the mathematical tools necessary for these derivations in such a manner as to lay the mathematical foundation needed to solve numerous basic problems in crystallography and to avoid extraneous discourses. To demonstrate how these tools can be employed, a large number of examples are solved and problems are given. The book is, by and large, self-contained. In particular, topics usually omitted from the traditional courses in mathematics that are essential to the study of crystallography are discussed. For example, the techniques needed to work in vector spaces with noncartesian bases are developed. Unlike the traditional group-theoretical approach, isomorphism is not the essential ingredient in crystallographic classification schemes. Because alternative classification schemes must be used, the notions of equivalence relations and classes which are fundamental to such schemes are defined, discussed and illustrated. For example, we will find that the classification of the crystallographic space groups into the traditional 230 types is defined in terms of their matrix representations. Therefore, the derivation of these groups from the point groups will be conducted using the 37 distinct matrix groups rather than the 32 point groups they represent.
Book Synopsis Introduction to Crystallography by : Frank Hoffmann
Download or read book Introduction to Crystallography written by Frank Hoffmann and published by Springer Nature. This book was released on 2020-07-31 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Crystallography by : Donald E. Sands
Download or read book Introduction to Crystallography written by Donald E. Sands and published by Courier Corporation. This book was released on 1993-01-01 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise explanation of the logical development of basic crystallographic concepts. Extensive discussion of crystals and lattices, symmetry, crystal systems and geometry, x-ray diffraction, determination of atomic positions, and more. Well-chosen selection of problems, with answers. Ideal for crystallography course or as supplement to physical chemistry courses. 114 illustrations. 1969 edition.
Book Synopsis An Introduction to Mathematical Crystallography by : Maurice Aaron Jaswon
Download or read book An Introduction to Mathematical Crystallography written by Maurice Aaron Jaswon and published by . This book was released on 1965 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Mathematical Crystallography by : Maurice Aaron Jaswon
Download or read book An Introduction to Mathematical Crystallography written by Maurice Aaron Jaswon and published by . This book was released on 1965 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Crystallography by : P. Engel
Download or read book Geometric Crystallography written by P. Engel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade mathematical crystallography has found increasing interest. Siginificant results have been obtained by algebraic, geometric, and group theoretic methods. Also classical crystallography in three-dimen sional Euclidean space has been extended to higher dimen sions in order to understand better the dimension independent crystallographic properties. The aim of this note is to introduce the reader to the fascinating and rich world of geometric crystallography. The prerequisites for reading it are elementary geometry and topological notations, and basic knowledge of group theory and linear algebra. Crystallography is geometric by its nature. In many cases, geometric arguments are the most appropriate and can thus best be understood. Thus the geometric point of view is emphasized here. The approach is axiomatic start ing from discrete point sets in Euclidean space. Symmetry comes in very soon and plays a central role. Each chapter starts with the necessary definitions and then the subject is treated in two- and three-dimensional space. Subsequent sections give an extension to higher dimensions. Short historical remarks added at the end of the chapters will show the development of the theory. The chapters are main ly self-contained. Frequent cross references, as well as an extended subject index, will help the reader who is only interested in a particular subject.
Book Synopsis Crystalline Symmetries, An Informal Mathematical Introduction by : Marjorie Senechal
Download or read book Crystalline Symmetries, An Informal Mathematical Introduction written by Marjorie Senechal and published by CRC Press. This book was released on 1990 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Crystalline Symmetries: an informal mathematical introduction is a guided tour through the maze of mathematical models and classifications that are used today to describe the symmetries of crystals. The mathematical basis of crystallography and the interpretation of The International Tables for X-ray Crystallography are explained in a heuristic and accessible way. In addition to discussing standard crystals, a special feature of this book is the chapter on generalised crystals and the Penrose tile model for the kinds of generalised crystals known as quasicrystals. This fruitful interaction between pure mathematics (symmetry, tilings) and physics should prove invaluable to final year undergraduate/graduate physicists and materials scientists; the reader gets a flavour of the powerful coherence of a group theoretical approach to crystallography. Mathematicians interested in applications of group theory to physical science will also find this book useful.
Book Synopsis Structure of Materials by : Marc De Graef
Download or read book Structure of Materials written by Marc De Graef and published by Cambridge University Press. This book was released on 2012-10-08 with total page 773 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Topological Crystallography by : Toshikazu Sunada
Download or read book Topological Crystallography written by Toshikazu Sunada and published by Springer Science & Business Media. This book was released on 2012-12-23 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid’s Elements. Since then, geometry has taken its own path and the study of crystals has not been a central theme in mathematics, with the exception of Kepler’s work on snowflakes. Only in the nineteenth century did mathematics begin to play a role in crystallography as group theory came to be applied to the morphology of crystals. This monograph follows the Greek tradition in seeking beautiful shapes such as regular convex polyhedra. The primary aim is to convey to the reader how algebraic topology is effectively used to explore the rich world of crystal structures. Graph theory, homology theory, and the theory of covering maps are employed to introduce the notion of the topological crystal which retains, in the abstract, all the information on the connectivity of atoms in the crystal. For that reason the title Topological Crystallography has been chosen. Topological crystals can be described as “living in the logical world, not in space,” leading to the question of how to place or realize them “canonically” in space. Proposed here is the notion of standard realizations of topological crystals in space, including as typical examples the crystal structures of diamond and lonsdaleite. A mathematical view of the standard realizations is also provided by relating them to asymptotic behaviors of random walks and harmonic maps. Furthermore, it can be seen that a discrete analogue of algebraic geometry is linked to the standard realizations. Applications of the discussions in this volume include not only a systematic enumeration of crystal structures, an area of considerable scientific interest for many years, but also the architectural design of lightweight rigid structures. The reader therefore can see the agreement of theory and practice.
Book Synopsis Symmetry Relationships Between Crystal Structures by : Ulrich Müller
Download or read book Symmetry Relationships Between Crystal Structures written by Ulrich Müller and published by Academic. This book was released on 2013-04-04 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometric Crystallography by : P. Engel
Download or read book Geometric Crystallography written by P. Engel and published by Springer. This book was released on 1986-10-31 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade mathematical crystallography has found increasing interest. Siginificant results have been obtained by algebraic, geometric, and group theoretic methods. Also classical crystallography in three-dimen sional Euclidean space has been extended to higher dimen sions in order to understand better the dimension independent crystallographic properties. The aim of this note is to introduce the reader to the fascinating and rich world of geometric crystallography. The prerequisites for reading it are elementary geometry and topological notations, and basic knowledge of group theory and linear algebra. Crystallography is geometric by its nature. In many cases, geometric arguments are the most appropriate and can thus best be understood. Thus the geometric point of view is emphasized here. The approach is axiomatic start ing from discrete point sets in Euclidean space. Symmetry comes in very soon and plays a central role. Each chapter starts with the necessary definitions and then the subject is treated in two- and three-dimensional space. Subsequent sections give an extension to higher dimensions. Short historical remarks added at the end of the chapters will show the development of the theory. The chapters are main ly self-contained. Frequent cross references, as well as an extended subject index, will help the reader who is only interested in a particular subject.
Book Synopsis Introduction to Crystallographic Statistics by : Uri Shmueli
Download or read book Introduction to Crystallographic Statistics written by Uri Shmueli and published by Oxford University Press. This book was released on 1995 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Crystallography and the Theory of Groups of Movements by : Harold Hilton
Download or read book Mathematical Crystallography and the Theory of Groups of Movements written by Harold Hilton and published by . This book was released on 1903 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Crystallography by : Walter Borchardt-Ott
Download or read book Crystallography written by Walter Borchardt-Ott and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a self-study guide, course primer or teaching aid, Bor- chardt-Ott's Crystallography is the perfect textbook for students and teachers alike. In fact, it can be used by chemists, mineralogists, physicists and geologists. Based on the author's more than 20 years of teaching experience, the book has numerous line drawings designed especially for the text and a large number of exercises - with solutions - at the end of each chapter. The fourth edition of the original German text has been translated into English for an international readership. The heart of the book is firmly fixed in geometrical crystallography. It is from the concept of the space lattice that symmetry operations, Bravais lattices, space groups and point groups are all developed. Molecular symmetry and crystal formsare treated. Much emphasis is placed on the correspondence between point groups and space groups. The sections on crystal chemistry and X-ray diffraction are intended as an introduction to these fields.
Book Synopsis Orientations and Rotations by : Adam Morawiec
Download or read book Orientations and Rotations written by Adam Morawiec and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essentially, Orientations and Rotations treats the mathematical and computational foundations of texture analysis. It contains an extensive and thorough introduction to parameterizations and geometry of the rotation space. Since the notions of orientations and rotations are of primary importance for science and engineering, the book can be useful for a very broad audience using rotations in other fields.
