Curie principle

The Curie principle is a symmetry principle of solid state physics formulated by Pierre Curie in 1894 . He developed it when describing crystals that are in an electric field. This principle says:

The symmetry that is characteristic of a physical appearance is the greatest possible symmetry that is compatible with the phenomenon.
A physical phenomenon can only exist in an environment that has its characteristic symmetry or a subset of its characteristic symmetry.

He drew 2 conclusions from this:

Since causes produce certain effects, the symmetry elements of the causes must be found in the effects.
If effects reveal a lowering of symmetry, then this must be reflected in the symmetry of the cause.

In this way, Pierre Curie extends Franz Ernst Neumann's considerations of symmetry to cases in which an external force acts on the crystal - this he generally calls the cause or physical phenomenon. This force can be an electric or magnetic field, but also a mechanical tension. Due to the effect of this force, the symmetry of the crystal can decrease. According to Neumann's principle , this can also result in changes in the physical properties of the crystal. The Curie principle is therefore an extension of Neumann's principle.

description

If the symmetry group of the free crystal is designated as G _K and the symmetry group of the acting force G _F , then the following applies to the symmetry group of the crystal under the action of this force G _KF :

{\ displaystyle G_ {KF} = G_ {F} \ cap G_ {k}}

For the application of the Neumann principle, the symmetry group G _{KF should} be used as the crystal symmetry . Thus, for the symmetry group of the physical properties of the crystal under the force G _EF :

{\ displaystyle G_ {EF} \ supseteq G_ {KF} = G_ {F} \ cap G_ {k}}

example

A homogeneous electric field has the symmetry . In particular, it is not centrosymmetric. If you bring a crystal which has a center of symmetry into an electric field, its symmetry is lowered according to the Curie principle: the crystal loses its center of symmetry in a homogeneous electric field. This can be proven by the fact that the crystal becomes piezoelectric in the electric field. ${\ displaystyle \ infty m}$

With the help of the Curie principle one can determine which physical properties of the crystal can be induced by an external field.

literature

Pierre Curie: Sur la symétrie dans les phénomènes physiques, symétrie d'un champ électrique et d'un champ magnétique . In: Journal de Physique Théorique et Appliquée / 3. Série , Vol. 3 (1894), pp. 393-415, ISSN 0368-3893 .
Will Kleber , Hans-Joachim Bautsch , Joachim Bohm , Detlef Klimm: Introduction to crystallography . 19th edition. Oldenbourg Wissenschaftsverlag, Munich 2010, ISBN 978-3-486-59075-3 .

Web links

Curie law