5. Tensors

  1. Anthony Kelly and
  2. Kevin M. Knowles

Published Online: 30 JAN 2012

DOI: 10.1002/9781119961468.ch5

Crystallography and Crystal Defects, Second Edition

Crystallography and Crystal Defects, Second Edition

How to Cite

Kelly, A. and Knowles, K. M. (2012) Tensors, in Crystallography and Crystal Defects, Second Edition, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119961468.ch5

Author Information

  1. Department of Materials Science and Metallurgy, University of Cambridge, UK

Publication History

  1. Published Online: 30 JAN 2012
  2. Published Print: 13 JAN 2012

ISBN Information

Print ISBN: 9780470750155

Online ISBN: 9781119961468

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Keywords:

  • tensors, and tensor nature;
  • tensors of zero, first and second rank;
  • field tensors, with two second-rank tensors, important;
  • transformation of components of a vector;
  • tensor of the second rank;
  • crystal symmetry for second-rank tensors, and limitations;
  • tensors, representing physical properties of perfect single crystals;
  • representation quadric;
  • representation ellipsoid, and radius–normal property;
  • third- and fourth-rank tensors

Summary

This chapter contains sections titled:

  • Nature of a Tensor

  • Transformation of Components of a Vector

  • Dummy Suffix Notation

  • Transformation of Components of a Second-Rank Tensor

  • Definition of a Tensor of the Second Rank

  • Tensor of the Second Rank Referred to Principal Axes

  • Limitations Imposed by Crystal Symmetry for Second-Rank Tensors

  • Representation Quadric

  • Radius–Normal Property of the Representation Quadric

  • Third- and Fourth-Rank Tensors

  • Problems

  • Suggestions for Further Reading

  • References