Mathematical Crystallography: An Introduction to the Mathematical Foundations of Crystallography: 15 (Reviews in Mineralogy & Geochemistry, 15) - Softcover

Book 24 of 83: Reviews in Mineralogy & Geochemistry

Boisen; Monte B.; Gibbs; Gerald V.

 
9780939950195: Mathematical Crystallography: An Introduction to the Mathematical Foundations of Crystallography: 15 (Reviews in Mineralogy & Geochemistry, 15)
Softcover
ISBN 10: 0939950197 ISBN 13: 9780939950195
Publisher: De Gruyter, 2018

Synopsis

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.

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About the Author

M. B. Boisen, Jr. and Gerald V. Gibbs, Blacksburg, Virginia, USA.

"About this title" may belong to another edition of this title.

Publisher
De Gruyter
Publication date
2018
Language
English
ISBN 10 
0939950197
ISBN 13 
9780939950195
Binding
Perfect Paperback
Number of pages
460

Other Popular Editions of the Same Title

9780939950263: Mathematical Crystallography: 015 (Reviews in Mineralogy)

Featured Edition

ISBN 10:  093995026X ISBN 13:  9780939950263
Publisher: Mineralogical Society of Amer, 1990
Softcover