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Geometric Crystallography

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Geometric Crystallography

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Author : P. Engel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Geometric Crystallography written by P. Engel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

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.

Fundamentals Of Crystals

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Author : Boris K. Vainshtein
language : en
Publisher: Springer Science & Business Media
Release Date : 1994

Fundamentals Of Crystals written by Boris K. Vainshtein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Juvenile Nonfiction categories.

From the reviews: "[...] an excellent reference book. I have no doubt it will become a much-thumbed resource for students and researchers in mineralogy and crystallography." Geological Magazine

Crystallography

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Author : Thomas Leonard Walker
language : en
Publisher:
Release Date : 1914

Crystallography written by Thomas Leonard Walker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1914 with Crystallography categories.

Introduction To Crystal Geometry

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Author : Martin Julian Buerger
language : en
Publisher:
Release Date : 1971

Introduction To Crystal Geometry written by Martin Julian Buerger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Science categories.

Topological Crystallography

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Author : Toshikazu Sunada
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-23

Topological Crystallography written by Toshikazu Sunada and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-23 with Mathematics categories.

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.

Geometry Of Crystals Polycrystals And Phase Transformations

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Author : Harshad K. D. H. Bhadeshia
language : en
Publisher: CRC Press
Release Date : 2017-09-05

Geometry Of Crystals Polycrystals And Phase Transformations written by Harshad K. D. H. Bhadeshia and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-05 with Science categories.

Organized into a two-part structure aimed at readers of differing experience levels, Geometry of Crystals, Polycrystals, and Phase Transformations is accessible to both newcomers and advanced researchers within the field of crystallography. The first part of the text covers what any reader in the material sciences, physics, chemistry, earth sciences and natural sciences in general should know about crystallography. It is intentionally concise and covers sufficient material to form a firm foundation. The second part is aimed at researchers and discusses phase transformations, deformations, and interface crystallography in depth. The phase transformations are limited to those dominated by crystallography. The entire book contains worked examples and uniquely deals not just with crystals but aggregates of crystals and solid-state transformations between crystals.

Symmetry In Crystallography

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Author : Paolo Radaelli
language : en
Publisher: Oxford University Press
Release Date : 2011-09-22

Symmetry In Crystallography written by Paolo Radaelli and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-22 with Mathematics categories.

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.