Difference between revisions of "Crystal pattern"
From Online Dictionary of Crystallography
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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'') | + | <Font color="blue">Motif cristallin </Font>(''Fr''). <Font color="black">Motivo cristallino</Font>(''It''). <Font color="purple"> 結晶模様 </Font>(''Ja''). |
| − | 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: | + | 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: |
| − | # there are ''n'' translations, the translation vectors '''t'''<sub>1</sub>, ... , '''t'''<sub>n</sub> of which are linearly independent; | + | # 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. | + | # 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 | + | 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]] | ||
*[[Noncrystallographic symmetry]] | *[[Noncrystallographic symmetry]] | ||
| − | *''International Tables | + | *''International Tables for Crystallography, Volumes A'' and ''A1'' |
[[Category:Fundamental crystallography]] | [[Category:Fundamental crystallography]] | ||
Revision as of 11:07, 13 May 2017
Motif cristallin (Fr). Motivo cristallino(It). 結晶模様 (Ja).
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:
- there are n translations, the translation vectors t1, ... , tn 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 or abstract, in any dimension, which obeys the conditions of periodicity and discreteness expressed above.
See also
- Point space
- Noncrystallographic symmetry
- International Tables for Crystallography, Volumes A and A1