Crystal Lab › Prototype structures › Trigonal
Li₇Pb₂
Trigonal · space group P-3m1 (No. 164) · Pearson hP9
Symmetry elements and Wyckoff positions (interactive)
Li₇Pb₂ in P-3m1
SettingUnit cell
- Lattice constants
- a = 4.710 Å, b = 4.710 Å, c = 8.589 Å; α = 90.00°, β = 90.00°, γ = 120.00°
- Cell volume
- 165.0 ų
- Atoms in the conventional cell
- 9 (Li 7, Pb 2)
- Formula units Z
- 1
- Pearson symbol
- hP9 — hexagonal / trigonal, primitive lattice, 9 atoms per conventional cell
- Symmetry operations
- 12 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Li1 | Li | 1a | 1 | 0.0000 | 1.0000 | 0.0000 |
| Li2 | Li | 2c | 2 | 0.0000 | 1.0000 | 0.3333 |
| Li3 | Li | 2d | 2 | 0.3333 | 0.6667 | 0.9167 |
| Li4 | Li | 2d | 2 | 0.3333 | 0.6667 | 0.5833 |
| Pb5 | Pb | 2d | 2 | 0.3333 | 0.6667 | 0.2500 |
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 9 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
A7B2_hP9_164_ac2d_d-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP9, then the space-group number 164, then the Wyckoff letters occupied by each element in turn (Li: 1a; Li: 2c; Li: 2d; Li: 2d; Pb: 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 A7B2_hP9_164_ac2d_d-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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