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Difference between revisions of "Cylindrical system"

From Online Dictionary of Crystallography

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<Font color="blue"> Système cylindrique </Font> (''Fr'') <Font color="black"> Sistema cilindrico </Font> (''It'').
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<Font color="blue"> Système cylindrique</Font> (''Fr''). <Font color="black">Sistema cilindrico </Font> (''It'').
  
 
== Definition ==
 
== Definition ==
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  <tr>
<th>Hermann-Mauguin symbol</th> <th> Short Hermann-Mauguin symbol </th> <th>Schönfliess symbol </th> <th> order of the group</th><th>general form</th>
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<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>
 
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</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.
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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 (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.).
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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]]<br>
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*[[Curie laws]]
[[spherical system]]<br>
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*[[Spherical system]]
Section 3.2.1.4 of ''International Tables of Crystallography, Volume A'', 6<sup>th</sup> edition<br>
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*Chapter 3.2.1.4 of ''International Tables for Crystallography, Volume A'', 6th edition
Section 1.1.4 of ''International Tables of Crystallography, Volume D''<br>
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*Chapter 1.1.4 of ''International Tables for Crystallography, Volume D''
  
[[Category:Fundamental crystallography]]<br>
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[[Category:Fundamental crystallography]]
[[Category:Physical properties of crystals]]<br>
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[[Category:Physical properties of crystals]]

Revision as of 11:31, 13 May 2017

Système cylindrique (Fr). Sistema cilindrico (It).

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 groupGeneral 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


CylindricalSystem.gif

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