Geometric Crystallography

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Geometric Crystallography

Author : P. Engel
Publisher : Springer Science & Business Media
ISBN 13 : 9400947607
Total Pages : 273 pages
Book Rating : 4.4/5 (9 download)

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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.

Fundamentals of Crystals

Author : Boris K. Vainshtein
Publisher : Springer Science & Business Media
ISBN 13 : 9783540565581
Total Pages : 520 pages
Book Rating : 4.5/5 (655 download)

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Book Synopsis Fundamentals of Crystals by : Boris K. Vainshtein

Download or read book Fundamentals of Crystals written by Boris K. Vainshtein and published by Springer Science & Business Media. This book was released on 1994 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Topological Crystallography

Author : Toshikazu Sunada
Publisher : Springer Science & Business Media
ISBN 13 : 4431541772
Total Pages : 236 pages
Book Rating : 4.4/5 (315 download)

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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.

Geometry of Crystallographic Groups

Author : Andrzej Szczepański
Publisher : World Scientific
ISBN 13 : 9814412252
Total Pages : 208 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Geometry of Crystallographic Groups by : Andrzej Szczepański

Download or read book Geometry of Crystallographic Groups written by Andrzej Szczepański and published by World Scientific. This book was released on 2012 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Crystallographic groups are groups which act in a nice way and via isometries on some n-dimensional Euclidean space. This book gives an example of the torsion free crystallographic group with a trivial center and a trivial outer automorphism group.

Crystallography

Author : Thomas Leonard Walker
Publisher :
ISBN 13 :
Total Pages : 238 pages
Book Rating : 4.A/5 ( download)

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Book Synopsis Crystallography by : Thomas Leonard Walker

Download or read book Crystallography written by Thomas Leonard Walker and published by . This book was released on 1914 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Elements of Crystallography

Author : Friedrich Christian Accum
Publisher :
ISBN 13 :
Total Pages : 484 pages
Book Rating : 4.A/5 ( download)

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Book Synopsis Elements of Crystallography by : Friedrich Christian Accum

Download or read book Elements of Crystallography written by Friedrich Christian Accum and published by . This book was released on 1813 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Crystallography

Author : Frank Hoffmann
Publisher : Springer Nature
ISBN 13 : 3030351106
Total Pages : 309 pages
Book Rating : 4.0/5 (33 download)

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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.

Symmetry in Crystallography

Author : Paolo Radaelli
Publisher : Oxford University Press, USA
ISBN 13 : 0199550654
Total Pages : 141 pages
Book Rating : 4.1/5 (995 download)

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Book Synopsis Symmetry in Crystallography by : Paolo Radaelli

Download or read book Symmetry in Crystallography written by Paolo Radaelli and published by Oxford University Press, USA. This book was released on 2011-09-22 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elementary Crystallography

Author : Martin Julian Buerger
Publisher : MIT Press (MA)
ISBN 13 : 9780262520485
Total Pages : 528 pages
Book Rating : 4.5/5 (24 download)

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Book Synopsis Elementary Crystallography by : Martin Julian Buerger

Download or read book Elementary Crystallography written by Martin Julian Buerger and published by MIT Press (MA). This book was released on 1963 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Discrete Geometry and Topology

Author : Boris Nikolaevich Delone
Publisher : American Mathematical Soc.
ISBN 13 : 9780821831472
Total Pages : 220 pages
Book Rating : 4.8/5 (314 download)

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Book Synopsis Discrete Geometry and Topology by : Boris Nikolaevich Delone

Download or read book Discrete Geometry and Topology written by Boris Nikolaevich Delone and published by American Mathematical Soc.. This book was released on 1993 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of papers honors the 100th anniversary of the birth of Boris Nikolaevich Delone, whose mathematical interests centered on the geometry of positive quadratic forms. After an initial paper presenting an account of Delone's life, including his scientific work, the book centers on discrete geometry and combinatorics. The book presents new methods that permit a description of the structure of some $L$-bodies and $L$-partitionings and that, in many cases, provide a definitive description. Also studied are combinatorial-topological problems arising in the statistical Ising model, the disposition of finite point sets in convex bodies of high dimension under certain conditions, and investigations of regular partitionings of spaces of constant curvature.

Handbook of Convex Geometry

Author : Bozzano G Luisa
Publisher : Elsevier
ISBN 13 : 0080934404
Total Pages : 769 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Handbook of Convex Geometry by : Bozzano G Luisa

Download or read book Handbook of Convex Geometry written by Bozzano G Luisa and published by Elsevier. This book was released on 2014-06-28 with total page 769 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Convex Geometry, Volume B offers a survey of convex geometry and its many ramifications and connections with other fields of mathematics, including convexity, lattices, crystallography, and convex functions. The selection first offers information on the geometry of numbers, lattice points, and packing and covering with convex sets. Discussions focus on packing in non-Euclidean spaces, problems in the Euclidean plane, general convex bodies, computational complexity of lattice point problem, centrally symmetric convex bodies, reduction theory, and lattices and the space of lattices. The text then examines finite packing and covering and tilings, including plane tilings, monohedral tilings, bin packing, and sausage problems. The manuscript takes a look at valuations and dissections, geometric crystallography, convexity and differential geometry, and convex functions. Topics include differentiability, inequalities, uniqueness theorems for convex hypersurfaces, mixed discriminants and mixed volumes, differential geometric characterization of convexity, reduction of quadratic forms, and finite groups of symmetry operations. The selection is a dependable source of data for mathematicians and researchers interested in convex geometry.

Geometrical and Structural Crystallography

Author : Joseph V. Smith
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 472 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Geometrical and Structural Crystallography by : Joseph V. Smith

Download or read book Geometrical and Structural Crystallography written by Joseph V. Smith and published by John Wiley & Sons. This book was released on 1982 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometric Structure of Chemistry-Relevant Graphs

Author : Michel-Marie Deza
Publisher : Springer
ISBN 13 : 8132224493
Total Pages : 220 pages
Book Rating : 4.1/5 (322 download)

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Book Synopsis Geometric Structure of Chemistry-Relevant Graphs by : Michel-Marie Deza

Download or read book Geometric Structure of Chemistry-Relevant Graphs written by Michel-Marie Deza and published by Springer. This book was released on 2015-05-26 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of the present book is zigzags and central-circuits of three- or four-regular plane graphs, which allow a double covering or covering of the edgeset to be obtained. The book presents zigzag and central circuit structures of geometric fullerenes and several other classes of graph of interest in the fields of chemistry and mathematics. It also discusses the symmetries, parameterization and the Goldberg–Coxeter construction for those graphs. It is the first book on this subject, presenting full structure theory of such graphs. While many previous publications only addressed particular questions about selected graphs, this book is based on numerous computations and presents extensive data (tables and figures), as well as algorithmic and computational information. It will be of interest to researchers and students of discrete geometry, mathematical chemistry and combinatorics, as well as to lay mathematicians.

Geometric Algebra with Applications in Science and Engineering

Author : Eduardo Bayro Corrochano
Publisher : Springer Science & Business Media
ISBN 13 : 1461201594
Total Pages : 607 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Geometric Algebra with Applications in Science and Engineering by : Eduardo Bayro Corrochano

Download or read book Geometric Algebra with Applications in Science and Engineering written by Eduardo Bayro Corrochano and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science, and engineer ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar ticles here was pioneered in the 1960s by David Hestenes. Later, together with Garret Sobczyk, he developed it into a unified language for math ematics and physics. Sobczyk first learned about the power of geometric algebra in classes in electrodynamics and relativity taught by Hestenes at Arizona State University from 1966 to 1967. He still vividly remembers a feeling of disbelief that the fundamental geometric product of vectors could have been left out of his undergraduate mathematics education. Geometric algebra provides a rich, general mathematical framework for the develop ment of multilinear algebra, projective and affine geometry, calculus on a manifold, the representation of Lie groups and Lie algebras, the use of the horosphere and many other areas. This book is addressed to a broad audience of applied mathematicians, physicists, computer scientists, and engineers.

Structure of Materials

Author : Marc De Graef
Publisher : Cambridge University Press
ISBN 13 : 1139560476
Total Pages : 773 pages
Book Rating : 4.1/5 (395 download)

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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.

Sacred Geometry

Author : Stephen Skinner
Publisher : Sterling Publishing Company, Inc.
ISBN 13 : 9781402765827
Total Pages : 164 pages
Book Rating : 4.7/5 (658 download)

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Book Synopsis Sacred Geometry by : Stephen Skinner

Download or read book Sacred Geometry written by Stephen Skinner and published by Sterling Publishing Company, Inc.. This book was released on 2009 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fascinating and inspirational look at the vital link between the hidden geometrical order of the universe, geometry in nature, and the geometry of the man-made world. The Da Vinci Code has awakened the public to the powerful and very ancient idea that religious truths and mathematical principles are intimately intertwined. Sacred Geometry offers an accessible way of understanding how that connection is revealed in nature and the arts. Over the centuries, temple builders have relied on magic numbers to shape sacred spaces, astronomers have used geometry to calculate holy seasons, and philosophers have observed the harmony of the universe in the numerical properties of music. By showing how the discoveries of mathematics are manifested over and over again in biology and physics, and how they have inspired the greatest works of art, this illuminating study reveals the universal principles that link us to the infinite.

Indexing of Crystal Diffraction Patterns

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Author : Adam Morawiec
Publisher : Springer Nature
ISBN 13 : 3031110773
Total Pages : 427 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Indexing of Crystal Diffraction Patterns by : Adam Morawiec

Download or read book Indexing of Crystal Diffraction Patterns written by Adam Morawiec and published by Springer Nature. This book was released on 2022-09-28 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed, self-contained description of automatic indexing of crystal diffraction patterns, considering both ab initio indexing and indexing of patterns originating from known structures. Introductory chapters equip the reader with the necessary basic knowledge of geometric crystallography, as well as kinematic and dynamic theories of crystal diffraction. Subsequent chapters delve and describe ab initio indexing of single crystal diffraction patterns and indexing of patterns for orientation determination. The book also reviews methods of indexing powder diffraction and electron spot-type patterns, as well the subject of multigrain indexing. Later chapters are devoted to diffraction by helical structures and quasicrystals, as well as some aspects of lattice parameter refinement and strain determination. The book is intended equally for materials scientists curious about ‘nuts and bolts’ of diffraction pattern indexing and orientation mapping systems, as well as interdisciplinary researchers from physics, chemistry, and biology involved in crystallographic computing. It provides a rigorous, yet accessible, treatment of the subject matter for graduate students interested in understanding the functioning of diffraction pattern indexing engines.