Cylindrical system
From Online Dictionary of Crystallography
Système cylindrique (Fr). Zylindrisches System (Ge). Sistema cilindrico (It). Sistema cilíndrico (Sp).
Definition
The cylindrical system contains non-crystallographic point groups with one axis of revolution (or isotropy axis). There are five groups in the spherical system:
Hermann-Mauguin symbol | Short Hermann-Mauguin symbol | Schönflies symbol | Order of the group | General form |
---|---|---|---|---|
[math] A_\infty[/math] | [math]\infty[/math] | [math]C_\infty [/math] | [math] \infty[/math] | rotating cone |
[math] {A_\infty \over M}C[/math] | [math] {\bar \infty}[/math] | [math]C_{\infty h} \equiv S_{\infty} \equiv C_{\infty i}[/math] | [math] \infty[/math] | rotating finite cylinder |
[math] A_\infty \infty A_2[/math] | [math] \infty 2[/math] | [math]D_{\infty }[/math] | [math] \infty[/math] | finite cylinder submitted to equal and opposite torques |
[math] A_\infty M[/math] | [math]\infty m[/math] | [math]C_{\infty v}[/math] | [math] \infty[/math] | stationary cone |
[math] {A_\infty \over M} {\infty A_2 \over \infty M} C[/math] | [math] {\bar \infty}m \equiv {\bar \infty} {2\over m}[/math] | [math]D_{\infty h} \equiv D_{\infty d}[/math] | [math] \infty[/math] | stationary finite cylinder |
Note that [math] A_\infty M[/math] represents the symmetry of a force, or of an electric field, and that [math] {A_\infty \over M}C[/math] represents the symmetry of a magnetic field (Curie, 1894), while [math] {A_\infty \over M} {\infty A_2 \over \infty M} C[/math] represents the symmetry of a uniaxial compression.
History
The groups containing isotropy axes were introduced by P. Curie (1859-1906) in order to describe the symmetry of physical systems [Curie, P. (1884). Bull. Soc. Fr. Minéral. 7, 89-110. Sur les questions d'ordre: répétitions; Curie, P. (1894). J. Phys. (Paris), 3, 393-415. Sur la symétrie dans les phénomènes physiques, symétrie d’un champ électrique et d’un champ magnétique].
See also
- Curie laws
- Spherical system
- Chapter 3.2.1.4 of International Tables for Crystallography, Volume A, 6th edition
- Chapter 1.1.4 of International Tables for Crystallography, Volume D