Symmetry elements and Wyckoff positions (interactive)
Ce₆Cd₃₇ in Pn-3
SettingUnit cell
- Lattice constants
- a = 15.808 Å, b = 15.808 Å, c = 15.808 Å; α = 90.00°, β = 90.00°, γ = 90.00°
- Cell volume
- 3950.3 ų
- Atoms in the conventional cell
- 188 (Cd 164, Ce 24)
- Formula units Z
- 4
- Pearson symbol
- cP188 — cubic, primitive lattice, 188 atoms per conventional cell
- Symmetry operations
- 24 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Cd1 | Cd | 4b | 4 | 0.0000 | 0.0000 | 0.0000 |
| Cd2 | Cd | 8e | 8 | 0.5811 | 0.5811 | 0.5811 |
| Cd3 | Cd | 8e | 8 | 0.8885 | 0.8885 | 0.8885 |
| Cd4 | Cd | 12f | 12 | 0.8436 | 0.2500 | 0.2500 |
| Cd5 | Cd | 12g | 12 | 0.0546 | 0.7500 | 0.2500 |
| Cd10 | Cd | 24h | 24 | 0.6648 | 0.6877 | 0.7058 |
| Cd6 | Cd | 24h | 24 | 0.9932 | 0.7445 | 0.8411 |
| Cd7 | Cd | 24h | 24 | 0.1558 | 0.7472 | 0.1007 |
| Cd8 | Cd | 24h | 24 | 0.8563 | 0.9452 | 0.0964 |
| Cd9 | Cd | 24h | 24 | 0.6316 | 0.5500 | 0.4067 |
| Ce11 | Ce | 24h | 24 | 0.9413 | 0.7552 | 0.0474 |
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 188 atoms drawn above are these sites multiplied by all 24 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
A41B6_cP188_201_b2efg5h_h-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol cP188, then the space-group number 201, then the Wyckoff letters occupied by each element in turn (Cd: 4b; Cd: 8e; Cd: 8e; Cd: 12f; Cd: 12g; Cd: 24h; Cd: 24h; Cd: 24h; Cd: 24h; Cd: 24h; Ce: 24h). 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 A41B6_cP188_201_b2efg5h_h-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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