Crystal Lab › Prototype structures › Trigonal
BaPb₃
Trigonal · space group R-3m (No. 166) · Pearson hR12
Symmetry elements and Wyckoff positions (interactive)
BaPb₃ in R-3m
SettingUnit cell
- Lattice constants
- a = 7.287 Å, b = 7.287 Å, c = 25.770 Å; α = 90.00°, β = 90.00°, γ = 120.00°
- Cell volume
- 1185.1 ų
- Atoms in the conventional cell
- 36 (Ba 9, Pb 27)
- Formula units Z
- 9
- Pearson symbol
- hR12 — hexagonal / trigonal, rhombohedral lattice, 12 atoms per conventional cell
- Symmetry operations
- 36 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Ba1 | Ba | 3a | 3 | 0.0000 | 0.0000 | 0.0000 |
| Ba2 | Ba | 6c | 6 | 0.0000 | 0.0000 | 0.2222 |
| Pb3 | Pb | 9e | 9 | 0.5000 | 0.0000 | 0.0000 |
| Pb4 | Pb | 18h | 18 | 0.1667 | 0.8333 | 0.1111 |
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 36 atoms drawn above are these sites multiplied by all 36 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
AB3_hR12_166_ac_eh-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR12, then the space-group number 166, then the Wyckoff letters occupied by each element in turn (Ba: 3a; Ba: 6c; Pb: 9e; Pb: 18h). Two structures with the same label are the same arrangement with different cell parameters or coordinates.
Other compounds with this structure
GdAl₃, PuAl₃, TbAl₃, YAl₃ <!--beginning with an
Source
Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry AB3_hR12_166_ac_eh-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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