Crystal Lab › Prototype structures › Trigonal
Ce₇Ga₁₁Rh₁₈
Trigonal · space group R-3m (No. 166) · Pearson hR36
Symmetry elements and Wyckoff positions (interactive)
Ce₇Ga₁₁Rh₁₈ in R-3m
SettingUnit cell
- Lattice constants
- a = 5.592 Å, b = 5.592 Å, c = 67.955 Å; α = 90.00°, β = 90.00°, γ = 120.00°
- Cell volume
- 1840.3 ų
- Atoms in the conventional cell
- 108 (Ce 21, Ga 33, Rh 54)
- Formula units Z
- 3
- Pearson symbol
- hR36 — hexagonal / trigonal, rhombohedral lattice, 36 atoms per conventional cell
- Symmetry operations
- 36 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Ce1 | Ce | 3a | 3 | 0.0000 | 0.0000 | 0.0000 |
| Ga5 | Ga | 3b | 3 | 0.0000 | 0.0000 | 0.5000 |
| Ce2 | Ce | 6c | 6 | 0.0000 | 0.0000 | 0.0524 |
| Ce3 | Ce | 6c | 6 | 0.0000 | 0.0000 | 0.1553 |
| Ce4 | Ce | 6c | 6 | 0.0000 | 0.0000 | 0.1046 |
| Ga6 | Ga | 6c | 6 | 0.0000 | 0.0000 | 0.4447 |
| Ga7 | Ga | 6c | 6 | 0.0000 | 0.0000 | 0.2778 |
| Ga8 | Ga | 6c | 6 | 0.0000 | 0.0000 | 0.3334 |
| Ga9 | Ga | 6c | 6 | 0.0000 | 0.0000 | 0.2223 |
| Ga10 | Ga | 6c | 6 | 0.0000 | 0.0000 | 0.3887 |
| Rh11 | Rh | 18h | 18 | 0.5028 | 0.4972 | 0.1391 |
| Rh12 | Rh | 18h | 18 | 0.4997 | 0.5003 | 0.0831 |
| Rh13 | Rh | 18h | 18 | 0.5002 | 0.4998 | 0.0276 |
The multiplicity and the Wyckoff letter say how many copies of the site the group makes in one cell and on which kind of symmetry element the site sits; the 108 atoms drawn above are these sites multiplied by all 36 operations. Press Wyckoff under Colour to see the sites, and tick a symmetry element on the left to see which atoms lie on it.
How to read the label
A7B11C18_hR36_166_a3c_b5c_3h-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR36, then the space-group number 166, then the Wyckoff letters occupied by each element in turn (Ce: 3a; Ga: 3b; Ce: 6c; Ce: 6c; Ce: 6c; Ga: 6c; Ga: 6c; Ga: 6c; Ga: 6c; Ga: 6c; Rh: 18h; Rh: 18h; Rh: 18h). Two structures with the same label are the same arrangement with different cell parameters or coordinates.
Source
Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A7B11C18_hR36_166_a3c_b5c_3h-001 (M. J. Mehl et al., Comput. Mater. Sci. 136, S1 (2017); D. Hicks et al., ibid. 161, S1 (2019) and 199, 110450 (2021); S. Eckert et al., ibid. 240, 112988 (2024)). Symmetry elements, Wyckoff assignment and the diagram are computed on this page from the group operations.
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