# Difference between revisions of "Limiting complex"

### From Online Dictionary of Crystallography

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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''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. | 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 | + | 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. | 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]] |

## Revision as of 16:00, 6 February 2012

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 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.