Actions

Difference between revisions of "Limiting complex"

From Online Dictionary of Crystallography

m (See also: 6th edition of ITA)
(Added German translation (U. Mueller))
 
(One intermediate revision by the same user not shown)
Line 1: Line 1:
 +
<font color="red">Grenzform </font> (''Ge'').
 +
 +
 
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.  
  
Line 8: Line 11:
 
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.  
 
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 ==
 
== See also ==
  
 
*[[Lattice complex]]
 
*[[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]]
 
[[Category:Fundamental crystallography]]

Latest revision as of 18:05, 14 November 2017

Grenzform (Ge).


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.

Example

The Wyckoff position 4l in the space-group type P4/mmm, with site-symmetry m2m., generates a lattice complex L1 that corresponds to point configurations consisting of squares in fixed orientation around the origin, with coordinates x00, -x00, 0x0 and 0-x0.

The Wyckoff position 4j in the space-group type P4/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 xy0, -x-y0, -yx0 and y-x0.

Among all the point configurations of L2 there is one, obtained by choosing y = 0, that corresponds to L1. The coordinates x00 in P4/m still correspond to Wyckoff position 4j, i.e. the specialization of the y coordinate does not change the Wyckoff position.

L1, occurring in P4/mmm, is found also in P4/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
  • Chapter 3.4.1.4 of International Tables for Crystallography, Section A, 6th edition