Crystal Lab › Prototype structures › Trigonal
Zr₂₁Re₂₅
Trigonal · space group R-3c (No. 167) · Pearson hR92
Symmetry elements and Wyckoff positions (interactive)
Zr₂₁Re₂₅ in R-3c
SettingUnit cell
- Lattice constants
- a = 25.847 Å, b = 25.847 Å, c = 8.771 Å; α = 90.00°, β = 90.00°, γ = 120.00°
- Cell volume
- 5074.6 ų
- Atoms in the conventional cell
- 276 (Re 150, Zr 126)
- Formula units Z
- 6
- Pearson symbol
- hR92 — hexagonal / trigonal, rhombohedral lattice, 92 atoms per conventional cell
- Symmetry operations
- 36 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Re1 | Re | 6b | 6 | 0.0000 | 0.0000 | 0.0000 |
| Re2 | Re | 18e | 18 | 0.0610 | 0.0000 | 0.2500 |
| Re3 | Re | 18e | 18 | 0.4446 | 0.0000 | 0.2500 |
| Zr7 | Zr | 18e | 18 | 0.6943 | 0.0000 | 0.2500 |
| Re4 | Re | 36f | 36 | 0.1555 | 0.6085 | 0.4147 |
| Re5 | Re | 36f | 36 | 0.8246 | 0.7658 | 0.7477 |
| Re6 | Re | 36f | 36 | 0.8837 | 0.7650 | 0.5000 |
| Zr10 | Zr | 36f | 36 | 0.8916 | 0.6871 | 0.7481 |
| Zr8 | Zr | 36f | 36 | 0.1027 | 0.6646 | 0.2091 |
| Zr9 | Zr | 36f | 36 | 0.8836 | 0.8839 | 0.5659 |
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 276 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
A25B21_hR92_167_b2e3f_e3f-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR92, then the space-group number 167, then the Wyckoff letters occupied by each element in turn (Re: 6b; Re: 18e; Re: 18e; Zr: 18e; Re: 36f; Re: 36f; Re: 36f; Zr: 36f; Zr: 36f; Zr: 36f). Two structures with the same label are the same arrangement with different cell parameters or coordinates.
Other compounds with this structure
Hf₂₁Re₂₅, Mg₂₁Zn₂₅, Ti₂₁Mn₂₅, Ti₂₁Re₂₅ <!--beginning with an
Source
Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A25B21_hR92_167_b2e3f_e3f-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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