Crystal Lab › Prototype structures › Orthorhombic
Bi₇(Fe,Ti)₆O₂₁ m = 6 Aurivillius
Orthorhombic · space group Fmm2 (No. 42) · Pearson oF136
Symmetry elements and Wyckoff positions (interactive)
Bi₇(Fe,Ti)₆O₂₁ m = 6 Aurivillius in Fmm2
SettingUnit cell
- Lattice constants
- a = 5.470 Å, b = 57.551 Å, c = 5.492 Å; α = 90.00°, β = 90.00°, γ = 90.00°
- Cell volume
- 1729.0 ų
- Atoms in the conventional cell
- 136 (Bi 28, O 84, Fe 24)
- Formula units Z
- 4
- Pearson symbol
- oF136 — orthorhombic, face-centred lattice, 136 atoms per conventional cell
- Symmetry operations
- 16 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Bi1 | Bi | 4a | 4 | 0.0000 | 0.0000 | 0.0000 |
| O8 | O | 4a | 4 | 0.0000 | 0.0000 | 0.6290 |
| O9 | O | 8b | 8 | 0.2500 | 0.2500 | 0.2340 |
| Bi2 | Bi | 8c | 8 | 0.0000 | 0.0737 | 0.9980 |
| Bi3 | Bi | 8c | 8 | 0.0000 | 0.1473 | 0.9870 |
| Bi4 | Bi | 8c | 8 | 0.0000 | 0.2251 | 0.9870 |
| Fe5 | Fe | 8c | 8 | 0.0000 | 0.3138 | 0.0210 |
| Fe6 | Fe | 8c | 8 | 0.0000 | 0.4671 | 0.0250 |
| Fe7 | Fe | 8c | 8 | 0.0000 | 0.3954 | 0.0530 |
| O10 | O | 8c | 8 | 0.0000 | 0.3560 | 0.0580 |
| O11 | O | 8c | 8 | 0.0000 | 0.7120 | 0.0540 |
| O12 | O | 8c | 8 | 0.0000 | 0.4340 | 0.1070 |
| O13 | O | 16e | 16 | 0.6990 | 0.9020 | 0.8280 |
| O14 | O | 16e | 16 | 0.7260 | 0.8120 | 0.7230 |
| O15 | O | 16e | 16 | 0.2940 | 0.9720 | 0.8050 |
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 136 atoms drawn above are these sites multiplied by all 16 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
A7B6C21_oF136_42_a3c_3c_ab3c3e-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol oF136, then the space-group number 42, then the Wyckoff letters occupied by each element in turn (Bi: 4a; O: 4a; O: 8b; Bi: 8c; Bi: 8c; Bi: 8c; Fe: 8c; Fe: 8c; Fe: 8c; O: 8c; O: 8c; O: 8c; O: 16e; O: 16e; O: 16e). Two structures with the same label are the same arrangement with different cell parameters or coordinates.
Note: m = 6 Aurivillius.
Source
Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A7B6C21_oF136_42_a3c_3c_ab3c3e-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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