Crystal Lab › Prototype structures › Hexagonal
K₂Ta₄O₉F₄
Hexagonal · space group P6 (No. 168) · Pearson hP57
Symmetry elements and Wyckoff positions (interactive)
K₂Ta₄O₉F₄ in P6
SettingUnit cell
- Lattice constants
- a = 15.936 Å, b = 15.936 Å, c = 3.892 Å; α = 90.00°, β = 90.00°, γ = 120.00°
- Cell volume
- 856.0 ų
- Atoms in the conventional cell
- 57 (O 39, K 6, Ta 12)
- Formula units Z
- 3
- Pearson symbol
- hP57 — hexagonal / trigonal, primitive lattice, 57 atoms per conventional cell
- Symmetry operations
- 6 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| O2 | O | 3c | 3 | 0.5000 | 0.0000 | 0.0000 |
| K1 | K | 6d | 6 | 0.4965 | 0.1790 | 0.5550 |
| O3 | O | 6d | 6 | 0.0350 | 0.1870 | 0.0070 |
| O4 | O | 6d | 6 | 0.3490 | 0.0340 | 0.0180 |
| O5 | O | 6d | 6 | 0.1680 | 0.3880 | 0.0100 |
| O6 | O | 6d | 6 | 0.1950 | 0.5690 | 0.0200 |
| O7 | O | 6d | 6 | 0.0930 | 0.4540 | 0.5390 |
| O8 | O | 6d | 6 | 0.2730 | 0.0950 | 0.5550 |
| Ta10 | Ta | 6d | 6 | 0.0789 | 0.4368 | 0.0710 |
| Ta9 | Ta | 6d | 6 | 0.2634 | 0.0900 | 0.0860 |
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 57 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
A2B13C4_hP57_168_d_c6d_2d-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP57, then the space-group number 168, then the Wyckoff letters occupied by each element in turn (O: 3c; K: 6d; O: 6d; O: 6d; O: 6d; O: 6d; O: 6d; O: 6d; Ta: 6d; Ta: 6d). 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 A2B13C4_hP57_168_d_c6d_2d-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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