Actions

Difference between revisions of "Superstructure"

From Online Dictionary of Crystallography

(category)
m (Minor typos and style changes)
Line 8: Line 8:
 
*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]]
+
[[Image:basic structure.png|right|thumb|A structure S composed of a single crystallographic orbit]]
 
[[Image:superstructure.png|right|thumb|A structure S' obtained from S by reducing its translational symmetry. 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 '''superstructure''' of S.  Vertical lines expanding beyond the horizontal boundaries of the unit cell indicate the translations along the ''b'' direction that are lost in the superstructure.]]
 
[[Image:superstructure.png|right|thumb|A structure S' obtained from S by reducing its translational symmetry. 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 '''superstructure''' of S.  Vertical lines expanding beyond the horizontal boundaries of the unit cell indicate the translations along the ''b'' direction that are lost in the superstructure.]]
  
Line 14: Line 14:
 
*[[Derivative structure]]
 
*[[Derivative structure]]
 
*[[Substructure]]
 
*[[Substructure]]
*Martin J. Buerger: ''Journal of Chemical Physics'' '''15''' (1947) 1-16.
+
*Buerger, Martin J. (1947). ''J. Chem. Phys.'' '''15''', 1-16.
  
 
[[Category:Crystal chemistry]]
 
[[Category:Crystal chemistry]]
 
[[Category:Fundamental crystallography]]
 
[[Category:Fundamental crystallography]]

Revision as of 13:33, 15 July 2021

Surstructure (Fr). Superstruttura (It). 超構造 (Ja).


A superstructure 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 subgroup T(G’) of S’ is a subgroup of translation subgroup T(G) of S, i.e. the unit cell of S’ is a supercell of the unit cell of S and the lattice of S’ is sublattice of the lattice of S;
  • the point group of P’ of S’ may either coincide with the point group P of S or be a subgroup of it;
  • 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 translational symmetry. 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 superstructure of S. Vertical lines expanding beyond the horizontal boundaries of the unit cell indicate the translations along the b direction that are lost in the superstructure.

See also