Limiting complex

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

• Lattice complex
• Section 3.4.1.4 of International Tables of Crystallography, Section A, 6^th edition