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Difference between revisions of "Crystal pattern"

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<Font color="blue">Motif cristallin </Font>(''Fr''). <Font color="black">Motivo cristallino</Font>(''It''). <Font color="purple"> 結晶模様 </Font>(''Ja'')
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<font color="blue">Motif cristallin</font> (''Fr''). <font color="red">Unendlicher Idealkristall</font> (''Ge''). <font color="black">Motivo cristallino</font>(''It''). <font color="purple">結晶模様</font> (''Ja''). <font color="green">Cristal ideal infinito</font> (''Sp'').
  
An object in the n-dimensional [[point space]] E<sup>n</sup> is called an n-dimensional '''crystallographic pattern''' or, for short, '''crystal pattern''' if among its symmetry operations:
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'''Synonym''': ''infinite ideal crystal''
# there are ''n'' translations, the translation vectors '''t'''<sub>1</sub>, ... , '''t'''<sub>n</sub> of which are linearly independent;
 
# all translation vectors, except the zero vector '''0''', have a length of at least d > 0.
 
  
When the crystal pattern consists of atoms, it takes the name of '''crystal structure'''. The crystal pattern is thus the generalization of a crystal structure to any pattern, concrete of abstract, in any dimension, which obeys the conditions of periodicity and discreteness expressed above.
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An object in the ''n''-dimensional [[point space]] ''E<sup>n</sup>'' is called an ''n''-dimensional '''crystallographic pattern''' or, for short, '''crystal pattern''' if among its symmetry operations:
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# there are ''n'' translations, the translation vectors '''t'''<sub>1</sub>, ... , '''t'''<sub>''n''</sub> of which are linearly independent;
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# all translation vectors, except the zero vector '''0''', have a length of at least ''d'' > 0.
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When the crystal pattern consists of atoms, it takes the name of '''[[crystal structure]]'''. The crystal pattern is thus the generalization of a crystal structure to any pattern, concrete or abstract, in any dimension, which obeys the conditions of periodicity and discreteness expressed above.
  
 
== See also ==
 
== See also ==
 
*[[Point space]]
 
*[[Point space]]
*''International Tables of Crystallography, Volumes A and A1''
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*[[Noncrystallographic symmetry]]
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*''International Tables for Crystallography, Volumes A'' and ''A1''
  
 
[[Category:Fundamental crystallography]]
 
[[Category:Fundamental crystallography]]

Latest revision as of 15:33, 16 November 2018

Motif cristallin (Fr). Unendlicher Idealkristall (Ge). Motivo cristallino(It). 結晶模様 (Ja). Cristal ideal infinito (Sp).

Synonym: infinite ideal crystal


An object in the n-dimensional point space En is called an n-dimensional crystallographic pattern or, for short, crystal pattern if among its symmetry operations:

  1. there are n translations, the translation vectors t1, ... , tn of which are linearly independent;
  2. all translation vectors, except the zero vector 0, have a length of at least d > 0.

When the crystal pattern consists of atoms, it takes the name of crystal structure. The crystal pattern is thus the generalization of a crystal structure to any pattern, concrete or abstract, in any dimension, which obeys the conditions of periodicity and discreteness expressed above.

See also