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Metric Tensor and Symmetry Operations in Crystallography

Germano Rigault

Istituto di Mineralogia, Università di Torino, Italy

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• Introduction
  • Metric tensor
  • Symmetry operations
  • Symmetry elements and their orientation
  • Rotations compatible with a lattice base system
  • Symmetry groups
• Derivation of the Crystallographic Point Groups
  • Groups containing only one rotation axis
  • Groups containing more than one rotation axis
  • Groups containing type II symmetry operations
• Appendix

Teaching Aims

To use the ideas of vector and matrix calculus to introduce the concepts of symmetry operations and symmetry elements and to derive the crystallographic point groups on this basis.

Level

This is a fairly high-level course which would be most appropriate to the later years of undergraduate study or to the early years of postgraduate research. It could be helpful in relating crystallography to other disciplines such as physical chemistry and physics provided that the mathematical background of the students is high enough.

Background Required

A familiarity with vector manipulation is needed and, for certain sections, an understanding of tensor calculus.

Practical Resources

No particular practical resources are required.

Time Required for Teaching

This is a meaty course and could well occupy 7-10 hours of teaching and discussion for full assimilation.

Copyright © 1980, 1998 International Union of Crystallography