Crystal Lab › Prototype structures › Trigonal
Ce₄Ga₅Rh₉
Trigonal · space group R-3m (No. 166) · Pearson hR18
Symmetry elements and Wyckoff positions (interactive)
Ce₄Ga₅Rh₉ in R-3m
SettingUnit cell
- Lattice constants
- a = 5.572 Å, b = 5.572 Å, c = 35.031 Å; α = 90.00°, β = 90.00°, γ = 120.00°
- Cell volume
- 941.9 ų
- Atoms in the conventional cell
- 54 (Ga 15, Ce 12, Rh 27)
- Formula units Z
- 3
- Pearson symbol
- hR18 — hexagonal / trigonal, rhombohedral lattice, 18 atoms per conventional cell
- Symmetry operations
- 36 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Ga3 | Ga | 3a | 3 | 0.0000 | 0.0000 | 0.0000 |
| Ce1 | Ce | 6c | 6 | 0.0000 | 0.0000 | 0.5492 |
| Ce2 | Ce | 6c | 6 | 0.0000 | 0.0000 | 0.6463 |
| Ga4 | Ga | 6c | 6 | 0.0000 | 0.0000 | 0.7778 |
| Ga5 | Ga | 6c | 6 | 0.0000 | 0.0000 | 0.8892 |
| Rh6 | Rh | 9d | 9 | 0.5000 | 0.0000 | 0.5000 |
| Rh7 | Rh | 18h | 18 | 0.5021 | 0.4979 | 0.6113 |
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 54 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
A4B5C9_hR18_166_2c_a2c_dh-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR18, then the space-group number 166, then the Wyckoff letters occupied by each element in turn (Ga: 3a; Ce: 6c; Ce: 6c; Ga: 6c; Ga: 6c; Rh: 9d; Rh: 18h). Two structures with the same label are the same arrangement with different cell parameters or coordinates.
Other compounds with this structure
Gd₄Ga₅Rh₉ <!--beginning with an
Source
Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A4B5C9_hR18_166_2c_a2c_dh-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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