Crystal Lab › Prototype structures › Triclinic
Triclinic BiMn₇O₁₂
Triclinic · space group P1 (No. 1) · Pearson aP20
Symmetry elements and Wyckoff positions (interactive)
Triclinic BiMn₇O₁₂ in P1
SettingUnit cell
- Lattice constants
- a = 6.410 Å, b = 6.438 Å, c = 6.504 Å; α = 108.86°, β = 108.60°, γ = 110.37°
- Cell volume
- 208.1 ų
- Atoms in the conventional cell
- 20 (Bi 1, Mn 7, O 12)
- Formula units Z
- 1
- Pearson symbol
- aP20 — triclinic, primitive lattice, 20 atoms per conventional cell
- Symmetry operations
- 1 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Bi1 | Bi | 1a | 1 | 0.0000 | 0.0000 | 0.0000 |
| Mn2 | Mn | 1a | 1 | 0.5171 | 0.9595 | 0.5196 |
| Mn3 | Mn | 1a | 1 | 0.5029 | 0.4600 | 0.0185 |
| Mn4 | Mn | 1a | 1 | 0.0022 | 0.4513 | 0.5063 |
| Mn5 | Mn | 1a | 1 | 0.5210 | 0.4566 | 0.5220 |
| Mn6 | Mn | 1a | 1 | 0.0045 | 0.9576 | 0.5052 |
| Mn7 | Mn | 1a | 1 | 0.0136 | 0.4868 | 0.0247 |
| Mn8 | Mn | 1a | 1 | 0.4926 | 0.9481 | 0.0069 |
| O9 | O | 1a | 1 | 0.8300 | 0.2520 | 0.1359 |
| O10 | O | 1a | 1 | 0.1610 | 0.6290 | 0.8551 |
| O11 | O | 1a | 1 | 0.1780 | 0.2630 | 0.5028 |
| O12 | O | 1a | 1 | 0.8220 | 0.6410 | 0.4928 |
| O13 | O | 1a | 1 | 0.8640 | 0.1060 | 0.6840 |
| O14 | O | 1a | 1 | 0.5400 | 0.7770 | 0.7100 |
| O15 | O | 1a | 1 | 0.1666 | 0.8030 | 0.3696 |
| O16 | O | 1a | 1 | 0.5312 | 0.1470 | 0.3486 |
| O17 | O | 1a | 1 | 0.3030 | 0.4340 | 0.1851 |
| O18 | O | 1a | 1 | 0.6650 | 0.8205 | 0.1613 |
| O19 | O | 1a | 1 | 0.6925 | 0.4720 | 0.8658 |
| O20 | O | 1a | 1 | 0.3175 | 0.0740 | 0.8428 |
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 1 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
AB7C12_aP20_1_a_7a_12a-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol aP20, then the space-group number 1, then the Wyckoff letters occupied by each element in turn (Bi: 1a; Mn: 1a; Mn: 1a; Mn: 1a; Mn: 1a; Mn: 1a; Mn: 1a; Mn: 1a; O: 1a; O: 1a; O: 1a; O: 1a; O: 1a; O: 1a; O: 1a; O: 1a; O: 1a; O: 1a; O: 1a; O: 1a). 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 AB7C12_aP20_1_a_7a_12a-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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