Symmetry elements and Wyckoff positions (interactive)
γ-Bi₂O₃ in I23
SettingUnit cell
- Lattice constants
- a = 10.268 Å, b = 10.268 Å, c = 10.268 Å; α = 90.00°, β = 90.00°, γ = 90.00°
- Cell volume
- 1082.6 ų
- Atoms in the conventional cell
- 66 (Bi 26, O 40)
- Formula units Z
- 2
- Pearson symbol
- cI66 — cubic, body-centred lattice, 66 atoms per conventional cell
- Symmetry operations
- 24 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Bi1 | Bi | 2a | 2 | 0.0000 | 0.0000 | 0.0000 |
| O3 | O | 8c | 8 | 0.2160 | 0.2160 | 0.2160 |
| O4 | O | 8c | 8 | 0.1480 | 0.1480 | 0.1480 |
| Bi2 | Bi | 24f | 24 | 0.3580 | 0.1870 | 0.4720 |
| O5 | O | 24f | 24 | 0.4210 | 0.2380 | 0.0140 |
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 66 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
A13B20_cI66_197_af_2cf-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol cI66, then the space-group number 197, then the Wyckoff letters occupied by each element in turn (Bi: 2a; O: 8c; O: 8c; Bi: 24f; O: 24f). Two structures with the same label are the same arrangement with different cell parameters or coordinates.
Other compounds with this structure
Bi₁₂GeO₂₀, Bi₃₈ZnO₆₀ <!--beginning with an
Note: \gamma-Bi₂O₃.
Source
Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A13B20_cI66_197_af_2cf-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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