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Symetry and physical properties - 4PMNSPP2

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  • Number of hours

    • Lectures : 10.0
    • Tutorials : 10.0
    ECTS : 2.0

Goals

Symmetries
Solution of physical problems from symmetry laws
Physical properties of a Crystal allowed by its symmetries.

Contact Thierry DUFFAR

Content

CHAPTER I: More symmetry

  • Orientation symmetry, Euler theorem
  • 32 punctual groups. Holoedric and Meriedric classes
  • 14 Bravais lattices: mathematical and geometrical construction
  • Particular case of trigonal and hexagonal lattices.
  • Infinite symmetry groups

CHAPTER II Physics and symmetry

  • Space orientation
  • Polar and axial variables
  • Anti-symmetry
  • Physical symmetries (spatial, temporal, électrical)
  • Generalised symmetry principle
  • Symmetry breakage
  • Order-Disorder transitionTransition ordre-désordre
  • Landau theory, order parameter

CHAPTER III Symmetry and Crystal properties

  • Crystal anisotropy
  • Tensorial representation of physical properties: effect of symetries on tensors
  • Application to optics, pyro- and piezo-electricity, elasticity
  • Symmetry of magnetic materials.
  • Twins and domains. Meriedral and pseudo-meriedral twins
  • Introduction to quasi-crystals.

ANNEX Determination of Crystal structures

  • Position Symmetry
  • Symmetries with translation : mathematical determination
  • Space groups. Searching space groups from X-ray diffractograms. Use of "International Tables For X-ray Crystallography".


Prerequisites

basic lecture on crystallography and X-ray diffraction

Tests

2h written exam



Additional Information

Curriculum->PNS->Semester 4

Bibliography

Symétrie et propriétés physiques des cristaux, Cécile Malgrange, Christian Ricolleau, Françoise Lefaucheux , Les Ulis : EDP sciences ; Paris : CNRS éd., cop. 2011

Description de la symétrie : des groupes de symétrie aux structures fractales / Jean Sivardière. Les Ulis : EDP Sciences, DL 2004

Symétrie et propriétés physiques : du principe de Curie aux brisures de symétrie /
Jean Sivardière. Les Ulis : EDP Sciences, DL 2004

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Université Grenoble Alpes