Crystal Lab › Prototype structures › Trigonal
HP-Bi₂O₃
Trigonal · space group P31c (No. 159) · Pearson hP20
Symmetry elements and Wyckoff positions (interactive)
HP-Bi₂O₃ in P31c
SettingUnit cell
- Lattice constants
- a = 7.749 Å, b = 7.749 Å, c = 6.302 Å; α = 90.00°, β = 90.00°, γ = 120.00°
- Cell volume
- 327.7 ų
- Atoms in the conventional cell
- 20 (Bi 8, O 12)
- Formula units Z
- 4
- Pearson symbol
- hP20 — hexagonal / trigonal, primitive lattice, 20 atoms per conventional cell
- Symmetry operations
- 6 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Bi1 | Bi | 2b | 2 | 0.3333 | 0.6667 | 0.0000 |
| Bi2 | Bi | 6c | 6 | 0.3370 | 0.1540 | 0.0210 |
| O3 | O | 6c | 6 | 0.4510 | 0.0610 | 0.2870 |
| O4 | O | 6c | 6 | 0.1490 | 0.2820 | 0.0830 |
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 20 atoms drawn above are these sites multiplied by all 6 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
A2B3_hP20_159_bc_2c-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP20, then the space-group number 159, then the Wyckoff letters occupied by each element in turn (Bi: 2b; Bi: 6c; O: 6c; O: 6c). Two structures with the same label are the same arrangement with different cell parameters or coordinates.
Note: HP.
Source
Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A2B3_hP20_159_bc_2c-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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