Symmetry elements and Wyckoff positions (interactive)
Li₂₂Si₅ in F23
SettingUnit cell
- Lattice constants
- a = 18.750 Å, b = 18.750 Å, c = 18.750 Å; α = 90.00°, β = 90.00°, γ = 90.00°
- Cell volume
- 6591.8 ų
- Atoms in the conventional cell
- 432 (Li 352, Si 80)
- Formula units Z
- 16
- Pearson symbol
- cF432 — cubic, face-centred lattice, 432 atoms per conventional cell
- Symmetry operations
- 48 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Li3 | Li | 4a | 4 | 0.0000 | 0.0000 | 0.0000 |
| Li4 | Li | 4b | 4 | 0.5000 | 0.5000 | 0.5000 |
| Li2 | Li | 4c | 4 | 0.2500 | 0.2500 | 0.2500 |
| Li1 | Li | 4d | 4 | 0.7500 | 0.7500 | 0.7500 |
| Li10 | Li | 16e | 16 | 0.5830 | 0.5830 | 0.5830 |
| Li5 | Li | 16e | 16 | 0.8300 | 0.8300 | 0.8300 |
| Li6 | Li | 16e | 16 | 0.9170 | 0.9170 | 0.9170 |
| Li7 | Li | 16e | 16 | 0.0800 | 0.0800 | 0.0800 |
| Li8 | Li | 16e | 16 | 0.1700 | 0.1700 | 0.1700 |
| Li9 | Li | 16e | 16 | 0.3330 | 0.3330 | 0.3330 |
| Si17 | Si | 16e | 16 | 0.6610 | 0.6610 | 0.6610 |
| Si18 | Si | 16e | 16 | 0.4150 | 0.4150 | 0.4150 |
| Li12 | Li | 24f | 24 | 0.3330 | 0.0000 | 0.0000 |
| Si20 | Si | 24f | 24 | 0.8220 | 0.0000 | 0.0000 |
| Li11 | Li | 24g | 24 | 0.9170 | 0.2500 | 0.2500 |
| Si19 | Si | 24g | 24 | 0.0720 | 0.2500 | 0.2500 |
| Li13 | Li | 48h | 48 | 0.0890 | 0.4170 | 0.7450 |
| Li14 | Li | 48h | 48 | 0.4080 | 0.9170 | 0.7470 |
| Li15 | Li | 48h | 48 | 0.0000 | 0.8370 | 0.8370 |
| Li16 | Li | 48h | 48 | 0.5000 | 0.8330 | 0.8330 |
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 432 atoms drawn above are these sites multiplied by all 48 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
A22B5_cF432_196_abcd6efg4h_2efg-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol cF432, then the space-group number 196, then the Wyckoff letters occupied by each element in turn (Li: 4a; Li: 4b; Li: 4c; Li: 4d; Li: 16e; Li: 16e; Li: 16e; Li: 16e; Li: 16e; Li: 16e; Si: 16e; Si: 16e; Li: 24f; Si: 24f; Li: 24g; Si: 24g; Li: 48h; Li: 48h; Li: 48h; Li: 48h). Two structures with the same label are the same arrangement with different cell parameters or coordinates.
Other compounds with this structure
Li₂₂Ge₅, Li₂₂Pb₅, Li₂₂Sn₅, Li₂₂Tl₅ <!--beginning with an
Source
Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A22B5_cF432_196_abcd6efg4h_2efg-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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