Crystal Lab › Prototype structures › Trigonal
Ba₄NbRu₃O₁₂
Trigonal · space group R-3m (No. 166) · Pearson hR20
Symmetry elements and Wyckoff positions (interactive)
Ba₄NbRu₃O₁₂ in R-3m
SettingUnit cell
- Lattice constants
- a = 5.757 Å, b = 5.757 Å, c = 28.587 Å; α = 90.00°, β = 90.00°, γ = 120.00°
- Cell volume
- 820.6 ų
- Atoms in the conventional cell
- 60 (Nb 3, Ru 9, Ba 12, O 36)
- Formula units Z
- 3
- Pearson symbol
- hR20 — hexagonal / trigonal, rhombohedral lattice, 20 atoms per conventional cell
- Symmetry operations
- 36 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Nb3 | Nb | 3a | 3 | 0.0000 | 0.0000 | 0.0000 |
| Ru6 | Ru | 3b | 3 | 0.0000 | 0.0000 | 0.5000 |
| Ba1 | Ba | 6c | 6 | 0.0000 | 0.0000 | 0.1293 |
| Ba2 | Ba | 6c | 6 | 0.0000 | 0.0000 | 0.2868 |
| Ru7 | Ru | 6c | 6 | 0.0000 | 0.0000 | 0.4122 |
| O4 | O | 18h | 18 | 0.4923 | 0.5077 | 0.1224 |
| O5 | O | 18h | 18 | 0.5055 | 0.4945 | 0.2933 |
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 60 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
A4BC12D3_hR20_166_2c_a_2h_bc-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR20, then the space-group number 166, then the Wyckoff letters occupied by each element in turn (Nb: 3a; Ru: 3b; Ba: 6c; Ba: 6c; Ru: 6c; O: 18h; O: 18h). Two structures with the same label are the same arrangement with different cell parameters or coordinates.
Other compounds with this structure
Ir₄NbRu₃O₁₂, Mn₄NbRu₃O₁₂, Rh₄NbRu₃O₁₂ <!--beginning with an
Source
Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A4BC12D3_hR20_166_2c_a_2h_bc-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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