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Difference between revisions of "Limiting complex"

From Online Dictionary of Crystallography

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*[[Lattice complex]]
 
*[[Lattice complex]]
*Chapter 14 of [http://it.iucr.org/A/ ''International Tables of Crystallography, Section A'']
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*Section 3.4.1.4 of [http://it.iucr.org/A/ ''International Tables of Crystallography, Section A'', 6<sup>th</sup> edition]
  
 
[[Category:Fundamental crystallography]]
 
[[Category:Fundamental crystallography]]

Revision as of 16:17, 10 April 2017

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 specialisation 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