# Difference between revisions of "Limiting complex"

### From Online Dictionary of Crystallography

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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. | 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 | + | 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, 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]] | ||

− | * | + | *Chapter 3.4.1.4 of ''International Tables for Crystallography, Section A'', 6th edition |

[[Category:Fundamental crystallography]] | [[Category:Fundamental crystallography]] |

## Revision as of 15:28, 15 May 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 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 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.

## See also

- Lattice complex
- Chapter 3.4.1.4 of
*International Tables for Crystallography, Section A*, 6th edition