International
Tables for Crystallography Volume D Physical properties of crystals Edited by A. Authier © International Union of Crystallography 2013 |
International Tables for Crystallography (2013). Vol. D, ch. 1.1, p. 11
Section 1.1.4.2. Curie laws^{a}Institut de Minéralogie et de Physique des Milieux Condensés, 4 Place Jussieu, 75005 Paris, France |
The example given above shows that the symmetry of the property may possess a higher symmetry than the medium. The property is represented in that case by the indicatrix. The symmetry of an ellipsoid is [Axes are axes of revolution, or axes of isotropy, introduced by Curie (1884, 1894), cf. International Tables for Crystallography (2005), Vol. A, Table 10.1.4.2 .]
The symmetry of the indicatrix is identical to that of the medium if the crystal belongs to the orthorhombic holohedry and is higher in all other cases.
This remark is the basis of the generalization of the symmetry principle by P. Curie (1859–1906). He stated that (Curie, 1894):
and concludes that some symmetry elements may coexist with the phenomenon but that their presence is not necessary. On the contrary, what is necessary is the absence of certain symmetry elements: `asymmetry creates the phenomenon' (`C'est la dissymétrie qui crée le phénomène'; Curie, 1894, p. 400). Noting that physical phenomena usually express relations between a cause and an effect (an influence and a response), P. Curie restated the two above propositions in the following way, now known as Curie laws, although they are not, properly speaking, laws:
The application of the Curie laws enable one to determine the symmetry characteristic of a phenomenon. Let us consider the phenomenon first as an effect. If Φ is the symmetry of the phenomenon and C the symmetry of the cause that produces it,
Let us now consider the phenomenon as a cause producing a certain effect with symmetry E: We can therefore conclude that
If we choose among the various possible causes the most symmetric one, and among the various possible effects the one with the lowest symmetry, we can then determine the symmetry that characterizes the phenomenon.
As an example, let us determine the symmetry associated with a mechanical force. A force can be considered as the result of a traction effort, the symmetry of which is . If considered as a cause, its effect may be the motion of a sphere in a given direction (for example, a spherical ball falling under its own weight). Again, the symmetry is . The symmetries associated with the force considered as a cause and as an effect being the same, we may conclude that is its characteristic symmetry.
References
International Tables for Crystallography (2005). Vol. A, Space-Group Symmetry, edited by Th. Hahn. Heidelberg: Springer.Curie, P. (1884). Sur les questions d'ordre: répétitions. Bull. Soc. Fr. Minéral. 7, 89–110.
Curie, P. (1894). Sur la symétrie dans les phénomènes physiques, symétrie d'un champ électrique et d'un champ magnétique. J. Phys. (Paris), 3, 393–415.