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Difference between revisions of "Derivative structure"

From Online Dictionary of Crystallography

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*the space group G’ of S is a subgroup of the space group G of S;
 
*the space group G’ of S is a subgroup of the space group G of S;
 
*the translation lattice is preserved, ''i''.''e''. the translation subgroup T(G’) of S’ is the same as the translation subgroup T(G) of S;
 
*the translation lattice is preserved, ''i''.''e''. the translation subgroup T(G’) of S’ is the same as the translation subgroup T(G) of S;
*as a consequence,  the point group of P’ of S’ is a subgroup of the point group P of S (''i''.''e''. S’ belong to a lower-symmetric geometric crystal class with respect to S);
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*as a consequence,  the point group P’ of S’ is a subgroup of the point group P of S (''i''.''e''. S’ belong to a lower-symmetric geometric crystal class with respect to S);
 
*at least one of the [[Wyckoff position]]s of S is split into two or more independent Wyckoff positions of S’ and the corresponding [[crystallographic orbit]]s are occupied by chemically different atoms.
 
*at least one of the [[Wyckoff position]]s of S is split into two or more independent Wyckoff positions of S’ and the corresponding [[crystallographic orbit]]s are occupied by chemically different atoms.
  
[[Image:basic structure.png|right|thumb|A structure S composed by a single crystallographic orbit]]
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[[Image:basic structure.png|right|thumb|A structure S composed of a single crystallographic orbit]]
 
[[Image:derivative structure.png|right|thumb|A structure S' obtained from S by reducing its point symmetry while preserving its translation lattice. Atomic positions represented by a different colour are not equivalent in S' and are occupied by chemically different atoms. S is called a '''basic structure''', S' a '''derivative structure''' of S]]
 
[[Image:derivative structure.png|right|thumb|A structure S' obtained from S by reducing its point symmetry while preserving its translation lattice. Atomic positions represented by a different colour are not equivalent in S' and are occupied by chemically different atoms. S is called a '''basic structure''', S' a '''derivative structure''' of S]]
 
== Notes ==
 
== Notes ==
The definition of derivative structure was introduced by Martin J. Buerger: ''Journal of Chemical Physics'' '''15''' (1947) 1-16.
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The definition of derivative structure was introduced by Martin J. Buerger (1947): ''Journal of Chemical Physics'', '''15''', 1-16.
  
 
== See also ==
 
== See also ==
 
*[[Substructure]]
 
*[[Substructure]]
 
*[[Superstructure]]
 
*[[Superstructure]]
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[[Category:Crystal chemistry]]
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[[Category:Fundamental crystallography]]

Latest revision as of 12:50, 15 July 2021

Structure dérivative (Fr). Struttura derivativa (It).


A derivative structure is a crystal structure S’ obtained from another crystal structure (called a basic structure) S under the following conditions:

  • the space group G’ of S is a subgroup of the space group G of S;
  • the translation lattice is preserved, i.e. the translation subgroup T(G’) of S’ is the same as the translation subgroup T(G) of S;
  • as a consequence, the point group P’ of S’ is a subgroup of the point group P of S (i.e. S’ belong to a lower-symmetric geometric crystal class with respect to S);
  • at least one of the Wyckoff positions of S is split into two or more independent Wyckoff positions of S’ and the corresponding crystallographic orbits are occupied by chemically different atoms.
A structure S composed of a single crystallographic orbit
A structure S' obtained from S by reducing its point symmetry while preserving its translation lattice. Atomic positions represented by a different colour are not equivalent in S' and are occupied by chemically different atoms. S is called a basic structure, S' a derivative structure of S

Notes

The definition of derivative structure was introduced by Martin J. Buerger (1947): Journal of Chemical Physics, 15, 1-16.

See also