Difference between revisions of "Cylindrical system"
From Online Dictionary of Crystallography
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| − | < | + | <font color="blue">Système cylindrique</font> (''Fr''). <font color="red">Zylindrisches System</font> (''Ge''). <font color="black">Sistema cilindrico</font> (''It''). <font color="green">Sistema cilíndrico</font> (''Sp''). |
== Definition == | == Definition == | ||
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<table border cellspacing=0 cellpadding=5 align=center> | <table border cellspacing=0 cellpadding=5 align=center> | ||
<tr> | <tr> | ||
| − | <th>Hermann-Mauguin symbol</th> <th> Short Hermann-Mauguin symbol </th> <th> | + | <th>Hermann-Mauguin symbol</th> <th> Short Hermann-Mauguin symbol </th> <th>Schönflies symbol </th> <th>Order of the group</th><th>General form</th> |
</tr> | </tr> | ||
<tr> | <tr> | ||
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[[Image:CylindricalSystem.gif|center]] | [[Image:CylindricalSystem.gif|center]] | ||
| − | 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. | + | 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 == | == History == | ||
The groups containing isotropy axes were introduced by P. Curie (1859-1906) in order to describe the symmetry of | The groups containing isotropy axes were introduced by P. Curie (1859-1906) in order to describe the symmetry of | ||
| − | physical systems | + | 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 == | == See also == | ||
| − | [[Curie laws]] | + | *[[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'' | |
| − | + | ||
| + | [[Category:Fundamental crystallography]] | ||
| + | [[Category:Physical properties of crystals]] | ||
Latest revision as of 13:18, 29 November 2017
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