Crystal Lab › Prototype structures › Trigonal
Li₁₃Sn₅
Trigonal · space group P-3m1 (No. 164) · Pearson hP18
Symmetry elements and Wyckoff positions (interactive)
Li₁₃Sn₅ in P-3m1
SettingUnit cell
- Lattice constants
- a = 4.700 Å, b = 4.700 Å, c = 17.120 Å; α = 90.00°, β = 90.00°, γ = 120.00°
- Cell volume
- 327.5 ų
- Atoms in the conventional cell
- 18 (Li 13, Sn 5)
- Formula units Z
- 1
- Pearson symbol
- hP18 — hexagonal / trigonal, primitive lattice, 18 atoms per conventional cell
- Symmetry operations
- 12 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Li1 | Li | 1a | 1 | 0.0000 | 0.0000 | 0.0000 |
| Sn8 | Sn | 1b | 1 | 0.0000 | 0.0000 | 0.5000 |
| Li2 | Li | 2c | 2 | 0.0000 | 0.0000 | 0.6640 |
| Li3 | Li | 2c | 2 | 0.0000 | 0.0000 | 0.1680 |
| Li4 | Li | 2d | 2 | 0.3333 | 0.6667 | 0.4430 |
| Li5 | Li | 2d | 2 | 0.3333 | 0.6667 | 0.9450 |
| Li6 | Li | 2d | 2 | 0.3333 | 0.6667 | 0.7840 |
| Li7 | Li | 2d | 2 | 0.3333 | 0.6667 | 0.6170 |
| Sn10 | Sn | 2d | 2 | 0.3333 | 0.6667 | 0.1091 |
| Sn9 | Sn | 2d | 2 | 0.3333 | 0.6667 | 0.2764 |
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 18 atoms drawn above are these sites multiplied by all 12 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
A13B5_hP18_164_a2c4d_b2d-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP18, then the space-group number 164, then the Wyckoff letters occupied by each element in turn (Li: 1a; Sn: 1b; Li: 2c; Li: 2c; Li: 2d; Li: 2d; Li: 2d; Li: 2d; Sn: 2d; Sn: 2d). 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 A13B5_hP18_164_a2c4d_b2d-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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