Tensor Properties of Crystals

  • Richard C. PowellEmail author
Part of the Lecture Notes in Physics book series (LNP, volume 824)


Due to the spatial symmetry of crystals discussed in 1, many important physical properties of a crystalline material depend on the orientation of the sample with respect to some specifically defined coordinate directions. Examples of such properties are electrical conductivity, elasticity, the piezoelectric effect, and nonlinear optics. The last of these is treated in detail in. In this chapter the tensor operator formalism that uses symmetry for treating these properties is summarized, and some specific examples are presented. The discussion focuses on bulk, macroscopic properties of materials and does not include surface effects or microscopic phenomena. The concepts of group theory developed in 2 are useful in elucidating the qualitative characteristics of these physical properties in materials with different crystal structures. The quantitative values for these properties must be found by experimental measurement. The tensor operator approach to material properties summarized here was developed extensively by Nye and is presented in detail in his book on the topic [1]. It should be noted that not all physical properties can be represented as tensors. Examples of nontensor properties include dielectric strength and surface hardness.


Point Group Axial Vector Symmetry Operation Pyroelectric Effect Inversion Operation 
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  1. 1.
    J.F. Nye, Physical Properties of Crystals, Their Representations by Tensors and Matrices (Clarendon, Oxford, 1957)Google Scholar
  2. 2.
    S. Bhagavantam, Crystal Symmetry and Physicsl Properties (Academic, London, 1966)Google Scholar
  3. 3.
    M.E. Lines, A.M. Glass, Principles and Applications of Ferroelectrics and Related Materials (Clarendon, Oxford, 1977)Google Scholar
  4. 4.
    M. Lax, Symmetry Principles in Solid State and Molecular Physics (Wiley, New York, 1974)Google Scholar
  5. 5.
    A.S. Borovik-Romanov, H. Grimmer, in International Tables for Crystallography Volume D, Physical Properties of Crystals, ed. A. Authier (Kluwer, Dordrecht, 2003), p. 105Google Scholar

Copyright information

© Springer Science+Business Media LLC 2010

Authors and Affiliations

  1. 1.University of ArizonaTucsonUSA

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