Superstructure - Revision history

BrianMcMahon at 13:34, 15 July 2021

2021-07-15T13:34:02Z

BrianMcMahon: Minor typos and style changes

2021-07-15T13:33:03Z

Minor typos and style changes

MassimoNespolo: category

2019-02-17T09:24:07Z

MassimoNespolo: Created page with "Surstructure (''Fr''). Superstruttura (''It''). 超構造 (''Ja''). A '''superstructure''' i..."

2019-02-17T08:57:42Z

Created page with "Surstructure (''Fr''). Superstruttura (''It''). 超構造 (''Ja''). A '''superstructure''' i..."

New page

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 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: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.]]

== See also ==
*[[Derivative structure]]
*[[Substructure]]
*Martin J. Buerger: ''Journal of Chemical Physics'' '''15''' (1947) 1-16.

← Older revision		Revision as of 09:24, 17 February 2019
Line 15:		Line 15:
	*[[Substructure]]		*[[Substructure]]
	*Martin J. Buerger: ''Journal of Chemical Physics'' '''15''' (1947) 1-16.		*Martin J. Buerger: ''Journal of Chemical Physics'' '''15''' (1947) 1-16.
		+
		+	[[Category:Crystal chemistry]]
		+	[[Category:Fundamental crystallography]]

@@ Line 4: / Line 4: @@
 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 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 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.

@@ 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.
-[[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.]]
@@ Line 14: / Line 14: @@
 *[[Derivative structure]]
 *[[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:Fundamental crystallography]]