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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

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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## Version française

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