Difference between revisions of "Limiting complex"
From Online Dictionary of Crystallography
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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. | 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]] | ||
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