Crystal Lab › Prototype structures › Trigonal
P3 La₃BWO₉ BLi₃O₉W
Trigonal · space group P3 (No. 143) · Pearson hP28
Symmetry elements and Wyckoff positions (interactive)
P3 La₃BWO₉ in P3
SettingUnit cell
- Lattice constants
- a = 8.843 Å, b = 8.843 Å, c = 5.575 Å; α = 90.00°, β = 90.00°, γ = 120.00°
- Cell volume
- 377.6 ų
- Atoms in the conventional cell
- 28 (B 2, W 2, La 6, O 18)
- Formula units Z
- 2
- Pearson symbol
- hP28 — hexagonal / trigonal, primitive lattice, 28 atoms per conventional cell
- Symmetry operations
- 3 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| B1 | B | 1a | 1 | 0.0000 | 0.0000 | 0.3600 |
| B2 | B | 1a | 1 | 0.0000 | 0.0000 | 0.8400 |
| W11 | W | 1b | 1 | 0.3333 | 0.6667 | 0.2500 |
| W12 | W | 1c | 1 | 0.6667 | 0.3333 | 0.7700 |
| La3 | La | 3d | 3 | 0.3630 | 0.0840 | 0.2290 |
| La4 | La | 3d | 3 | 0.2780 | 0.3650 | 0.7370 |
| O10 | O | 3d | 3 | 0.6170 | 0.1430 | 0.9960 |
| O5 | O | 3d | 3 | 0.1720 | 0.0560 | 0.8390 |
| O6 | O | 3d | 3 | 0.1380 | 0.1690 | 0.4180 |
| O7 | O | 3d | 3 | 0.1810 | 0.4980 | 0.9830 |
| O8 | O | 3d | 3 | 0.7280 | 0.1980 | 0.5940 |
| O9 | O | 3d | 3 | 0.1340 | 0.5020 | 0.4270 |
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 28 atoms drawn above are these sites multiplied by all 3 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
AB3C9D_hP28_143_2a_2d_6d_bc-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP28, then the space-group number 143, then the Wyckoff letters occupied by each element in turn (B: 1a; B: 1a; W: 1b; W: 1c; La: 3d; La: 3d; O: 3d; O: 3d; O: 3d; O: 3d; O: 3d; O: 3d). Two structures with the same label are the same arrangement with different cell parameters or coordinates.
Note: Trigonal.
Source
Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry AB3C9D_hP28_143_2a_2d_6d_bc-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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