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2024 | OriginalPaper | Chapter

12. Symmetry Constraints on Properties

Author : Rick Ubic

Published in: Crystallography and Crystal Chemistry

Publisher: Springer International Publishing

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Abstract

This chapter introduces the distinction between isotropic and anisotropic properties as well as the application of coordinate transformations to solve problems involving anisotropic properties. Neumann’s Principle and the Curie Principle are also discussed.

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Appendix
Available only for authorised users
Footnotes
1
They are often called the Curie Laws although they are not, strictly speaking, laws and Curie himself spoke only of “les propositions” of symmetry.
 
2
For the more mathematically pedantic, a tensor is often thought of as a generalized matrix. While any rank-two tensor can be represented as a matrix, not every matrix is really a rank-two tensor. A matrix consists of the coefficients of a (1,1) tensor, but it is not a tensor itself.
 
3
In Einstein summation notation, a summation is implied over every subscript which appears twice on the same side of an equation (m, n, o, and p in this case).
 
Literature
1.
F. E. Neumann, Vorlesungen über die Theorie der Elastizität der festen Körper und des Lichtäthers, O. E. Meyer, Ed., Leipzig: B. G. Teubner-Verlag, 1885.
2.
P. Curie, “Sur la symétrie dans les phénomènes physiques, symétrie d’un champ électrique et d’un champ magnétique,” Journal de Physique Theorique et Appliquee, vol. 3, pp. 393–415, 1894.CrossRef
Metadata
Title
Symmetry Constraints on Properties
Author
Rick Ubic
Copyright Year
2024
Book
Crystallography and Crystal Chemistry

Print ISBN: 978-3-031-49751-3

Electronic ISBN: 978-3-031-49752-0

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-49752-0_12

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