Difference between revisions of "Limiting complex"
From Online Dictionary of Crystallography
BrianMcMahon (talk | contribs) m |
|||
| Line 3: | Line 3: | ||
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 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.