International
Tables for Crystallography Volume A Space-group symmetry Edited by Th. Hahn © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. A. ch. 14.2, pp. 870-871
Section 14.2.3.2. Invariant lattice complexes
a
Institut für Mineralogie, Petrologie und Kristallographie, Philipps-Universität, D-35032 Marburg, Germany |
Invariant lattice complexes in their characteristic Wyckoff position are represented by a capital letter eventually in combination with some superscript. The first column of Table 14.2.3.3 gives a complete list of these symbols in alphabetical order. The characteristic Wyckoff positions are shown in column 3. Lattice complexes from different crystal families but with the same coordinate description for their characteristic Wyckoff positions receive the same descriptive symbol. If necessary, the crystal family may be stated explicitly by a small letter (column 2) preceding the lattice-complex symbol: c cubic, t tetragonal, h hexagonal, o orthorhombic, m monoclinic, a anorthic (triclinic).
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Example
D is the descriptive symbol of the invariant cubic lattice complex a as well as of the orthorhombic lattice complex Fddd a. The cubic lattice complex cD contains – among others – the point configurations corresponding to the arrangement of carbon atoms in diamond and of silicon atoms in β-cristobalite. The orthorhombic complex oD is a comprehensive complex of cD. It consists of all those point configurations that may be produced by orthorhombic deformations of the point configurations of cD.
The descriptive symbol of a noncharacteristic Wyckoff position depends on the difference between the coordinate descriptions of the respective characteristic Wyckoff position and the position under consideration. Three cases may be distinguished, which may also occur in combinations.
In noncharacteristic Wyckoff positions, the descriptive symbol P may be replaced by C, I by F (tetragonal system), C by A or B (orthorhombic system), and C by A, B, I or F (monoclinic system). If the lattice complexes of rhombohedral space groups are described in rhombohedral coordinate systems, the symbols R, , M and of the hexagonal description are replaced by P, I, J and , respectively (preceded by the letter r, if necessary, to distinguish them from the analogous cubic invariant lattice complexes).