Limiting complex - Revision history

BrianMcMahon: Added German translation (U. Mueller)

2017-11-14T18:05:53Z

Added German translation (U. Mueller)

BrianMcMahon: Style edits to align with printed edition

2017-05-15T15:28:19Z

Style edits to align with printed edition

MassimoNespolo: /* See also */ 6th edition of ITA

2017-04-10T16:17:14Z

‎See also: 6th edition of ITA

BrianMcMahon at 16:00, 6 February 2012

2012-02-06T16:00:46Z

MassimoNespolo at 18:46, 19 February 2009

2009-02-19T18:46:23Z

MassimoNespolo: Definition already given in lattice complex but an ad-hoc entry is useful to highlight terms in journals

2009-02-13T15:33:09Z

Definition already given in lattice complex but an ad-hoc entry is useful to highlight terms in journals

New page

A '''limiting complex''' is a [[lattice complex]] L1 which forms a true subset of a second lattice complex L2. Each [[point configuration]] of L1 also belongs to L2.

L2 is called a '''comprehensive complex''' of L1.

==See also==

*[[Lattice complex]]
*Chapter 14 of [http://it.iucr.org/A/ ''International Tables of Crystallography, Section A'']

[[Category:Fundamental crystallography]]

← Older revision		Revision as of 18:05, 14 November 2017
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		+	<font color="red">Grenzform </font> (''Ge'').
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	A '''limiting complex''' is a [[lattice complex]] L1 which forms a true subset of a second lattice complex L2. Each [[point configuration]] of L1 also belongs to L2.		A '''limiting complex''' is a [[lattice complex]] L1 which forms a true subset of a second lattice complex L2. Each [[point configuration]] of L1 also belongs to L2.

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 The Wyckoff position 4''j'' in the space-group type ''P''4/''m'', with site-symmetry ''m''.., generates a lattice complex L2 that corresponds to point configurations consisting of squares in any orientation around the origin, with coordinates ''xy''0, -''x-y''0, -''yx''0 and ''y-x''0.
-Among all the point configurations of L2 there is one, obtained by choosing ''y'' = 0, that corresponds to L1. The coordinates ''x''00 in ''P''4/''m'' still correspond to Wyckoff position 4''j'', ''i.e.'' the specialisation of the ''y'' coordinate does not change the Wyckoff position.
+Among all the point configurations of L2 there is one, obtained by choosing ''y'' = 0, that corresponds to L1. The coordinates ''x''00 in ''P''4/''m'' still correspond to Wyckoff position 4''j'', ''i.e.'' the specialization of the ''y'' coordinate does not change the Wyckoff position.
-L1, occurring in ''P''4/''mmm'', is found also in ''P''4/''m'' as a special case of L2 when ''y'' = 0: L1 is therefore a limiting complex of L2 and L2 is a comprehensive complex of L1.
+L1, occurring in ''P''4/''mmm'', is found also in ''P''4/''m'' as a special case of L2 when ''y'' = 0; L1 is therefore a limiting complex of L2 and L2 is a comprehensive complex of L1.
 == See also ==
 *[[Lattice complex]]
-*Section 3.4.1.4 of [http://it.iucr.org/A/ ''International Tables of Crystallography, Section A'', 6<sup>th</sup> edition]
+*Chapter 3.4.1.4 of ''International Tables for Crystallography, Section A'', 6th edition
 [[Category:Fundamental crystallography]]

@@ Line 3: / Line 3: @@
 L2 is called a '''comprehensive complex''' of L1.
-===Example===
+== Example ==
 The Wyckoff position 4''l'' in the space-group type ''P''4/''mmm'', with site-symmetry ''m''2''m''., generates a lattice complex L1 that corresponds to point configurations consisting of squares in fixed orientation around the origin, with coordinates ''x''00, -''x''00, 0''x''0 and 0-''x''0.
 The Wyckoff position 4''j'' in the space-group type ''P''4/''m'', with site-symmetry ''m''.., generates a lattice complex L2 that corresponds to point configurations consisting of squares in any orientation around the origin, with coordinates ''xy''0, -''x-y''0, -''yx''0 and ''y-x''0.
-Among all the point configurations of L2 there is one, obtained by chosing ''y'' = 0, that corresponds to L1. The coordinates ''x''00 in ''P''4/''m'' still corresponds to Wyckoff position 4''j'', ''i.e.'' the specialisation of the ''y'' coordinate does not change the Wyckoff position.
+Among all the point configurations of L2 there is one, obtained by choosing ''y'' = 0, that corresponds to L1. The coordinates ''x''00 in ''P''4/''m'' still correspond to Wyckoff position 4''j'', ''i.e.'' the specialisation of the ''y'' coordinate does not change the Wyckoff position.
 L1, occurring in ''P''4/''mmm'', is found also in ''P''4/''m'' as a special case of L2 when ''y'' = 0: L1 is therefore a limiting complex of L2 and L2 is a comprehensive complex of L1.
-==See also==
+== See also ==
 *[[Lattice complex]]

← Older revision		Revision as of 18:46, 19 February 2009
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	L2 is called a '''comprehensive complex''' of L1.		L2 is called a '''comprehensive complex''' of L1.
		+
		+	===Example===
		+	The Wyckoff position 4''l'' in the space-group type ''P''4/''mmm'', with site-symmetry ''m''2''m''., generates a lattice complex L1 that corresponds to point configurations consisting of squares in fixed orientation around the origin, with coordinates ''x''00, -''x''00, 0''x''0 and 0-''x''0.
		+
		+	The Wyckoff position 4''j'' in the space-group type ''P''4/''m'', with site-symmetry ''m''.., generates a lattice complex L2 that corresponds to point configurations consisting of squares in any orientation around the origin, with coordinates ''xy''0, -''x-y''0, -''yx''0 and ''y-x''0.
		+
		+	Among all the point configurations of L2 there is one, obtained by chosing ''y'' = 0, that corresponds to L1. The coordinates ''x''00 in ''P''4/''m'' still corresponds to Wyckoff position 4''j'', ''i.e.'' the specialisation of the ''y'' coordinate does not change the Wyckoff position.
		+
		+	L1, occurring in ''P''4/''mmm'', is found also in ''P''4/''m'' as a special case of L2 when ''y'' = 0: L1 is therefore a limiting complex of L2 and L2 is a comprehensive complex of L1.

	==See also==		==See also==