International Tables for Crystallography (2015). Vol. A. ch. 1.5, pp. 75-105
https://doi.org/10.1107/97809553602060000923 |
Chapter 1.5. Transformations of coordinate systems
Contents
- 1.5. Transformations of coordinate systems (pp. 75-105) | html | pdf | chapter contents |
- 1.5.1. Origin shift and change of the basis (pp. 75-83) | html | pdf |
- 1.5.2. Transformations of crystallographic quantities under coordinate transformations (pp. 83-87) | html | pdf |
- 1.5.2.1. Covariant and contravariant quantities (p. 83) | html | pdf |
- 1.5.2.2. Metric tensors of direct and reciprocal lattices (p. 84) | html | pdf |
- 1.5.2.3. Transformation of matrix–column pairs of symmetry operations (p. 84) | html | pdf |
- 1.5.2.4. Augmented-matrix formalism (pp. 84-86) | html | pdf |
- 1.5.2.5. Example: paraelectric-to-ferroelectric phase transition of GeTe (pp. 86-87) | html | pdf |
- 1.5.3. Transformations between different space-group descriptions (pp. 87-90) | html | pdf |
- 1.5.4. Synoptic tables of plane and space groups (pp. 91-106) | html | pdf |
- References | html | pdf |
- Figures
- Fig. 1.5.1.1. The coordinates of the points X (or Y) with respect to the old origin O are x (y), and with respect to the new origin they are (p. 75) | html | pdf |
- Fig. 1.5.1.2. Monoclinic centred lattice, projected along the unique axis (p. 80) | html | pdf |
- Fig. 1.5.1.3. Body-centred cell I with aI, bI, cI and a corresponding primitive cell P with aP, bP, cP (p. 80) | html | pdf |
- Fig. 1.5.1.4. Face-centred cell F with aF, bF, cF and a corresponding primitive cell P with aP, bP, cP (p. 80) | html | pdf |
- Fig. 1.5.1.5. Tetragonal lattices, projected along (p. 81) | html | pdf |
- Fig. 1.5.1.6. Unit cells in the rhombohedral lattice (p. 81) | html | pdf |
- Fig. 1.5.1.7. Hexagonal lattice projected along (p. 82) | html | pdf |
- Fig. 1.5.1.8. Hexagonal lattice projected along (p. 82) | html | pdf |
- Fig. 1.5.1.9. Rhombohedral lattice with a triple hexagonal unit cell a, b, c in obverse setting (p. 82) | html | pdf |
- Fig. 1.5.1.10. Rhombohedral lattice with primitive rhombohedral cell arh, brh, crh and the three centred monoclinic cells (p. 82) | html | pdf |
- Fig. 1.5.2.1. Illustration of the transformation of symmetry operations , also called a `mapping of mappings' (p. 84) | html | pdf |
- Fig. 1.5.3.1. Three possible cell choices for the monoclinic space group (14) with unique axis b (p. 87) | html | pdf |
- Fig. 1.5.3.2. Two possible origin choices for the orthorhombic space group Pban (50) (p. 88) | html | pdf |
- Fig. 1.5.3.3. General-position diagram of the space group R3m (160) showing the relation between the hexagonal and rhombohedral axes in the obverse setting: = , = , = (p. 88) | html | pdf |
- Fig. 1.5.4.1. Symmetry-element diagram for space group P23 (195) (p. 95) | html | pdf |
- Tables
- Table 1.5.1.1. Selected 3 × 3 transformation matrices and (pp. 77-80) | html | pdf |
- Table 1.5.3.1. Transformation of reflection-condition data for P121/c1 to P1121/a (p. 89) | html | pdf |
- Table 1.5.4.1. Additional symmetry operations and their locations if the translation vector t is inclined to the symmetry axis or symmetry plane (p. 93) | html | pdf |
- Table 1.5.4.2. Additional symmetry operations due to a centring vector t and their locations (p. 94) | html | pdf |
- Table 1.5.4.3. List of plane-group symbols (p. 96) | html | pdf |
- Table 1.5.4.4. List of space-group symbols for various settings and cells (pp. 97-105) | html | pdf |