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# Symetry and physical properties - 4PMNSPP7

• #### 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: Crystal 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.
• CHAPTER II Symmetry and Crystal properties *
Crystal anisotropy
Tensorial representation of physical properties: effect of symetries on tensors
Application to optics, pyro- and piezo-electricity, elasticity
• CHAPTER III Physical symmetry *
Space orientation
Polar and axial variables
Anti-symmetry
Magnetic properties
Generalised symmetry principle
Symmetry breakage
Order-Disorder transitionTransition ordre-désordre
Landau theory, order parameter
• CHAPITRE IV 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 8

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