Number of hours
- Lectures 10.0
- Tutorials 10.0
ECTS
ECTS 2.0
Goal(s)
Symmetries
Solution of physical problems from symmetry laws
Physical properties of a Crystal allowed by its symmetries.
Content(s)
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
Test
2h written exam
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