Derivative structure - Revision history

BrianMcMahon: Minor typos and style changes

2021-07-15T12:50:34Z

Minor typos and style changes

MassimoNespolo: category

2019-02-17T09:24:19Z

MassimoNespolo at 08:46, 17 February 2019

2019-02-17T08:46:43Z

MassimoNespolo: Created page with "Structure dérivative (''Fr''). Struttura derivativa (''It''). A '''derivative structure''' is a crystal structure S’..."

2019-02-17T08:46:21Z

Created page with "Structure dérivative (''Fr''). Struttura derivativa (''It''). A '''derivative structure''' is a crystal structure S’..."

New page

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

== See also ==
[[Substructure]]
[[Superstructure]]

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	*[[Substructure]]		*[[Substructure]]
	*[[Superstructure]]		*[[Superstructure]]
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@@ Line 5: / Line 5: @@
 *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 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);
+*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.
-[[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: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 ==
-The definition of derivative structure was introduced by Martin J. Buerger: ''Journal of Chemical Physics'' '''15''' (1947) 1-16.
+The definition of derivative structure was introduced by Martin J. Buerger (1947): ''Journal of Chemical Physics'', '''15''', 1-16.
 == See also ==

@@ Line 14: / Line 14: @@
 == See also ==
-[[Substructure]]
+*[[Substructure]]
-[[Superstructure]]
+*[[Superstructure]]