Crystal Lab › Prototype structures › Trigonal
Th₂Zn₁₇
Trigonal · space group R-3m (No. 166) · Pearson hR19
Symmetry elements and Wyckoff positions (interactive)
Th₂Zn₁₇ in R-3m
SettingUnit cell
- Lattice constants
- a = 9.030 Å, b = 9.030 Å, c = 13.200 Å; α = 90.00°, β = 90.00°, γ = 120.00°
- Cell volume
- 932.1 ų
- Atoms in the conventional cell
- 57 (Th 6, Zn 51)
- Formula units Z
- 3
- Pearson symbol
- hR19 — hexagonal / trigonal, rhombohedral lattice, 19 atoms per conventional cell
- Symmetry operations
- 36 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Th1 | Th | 6c | 6 | 0.0000 | 0.0000 | 0.3333 |
| Zn2 | Zn | 6c | 6 | 0.0000 | 0.0000 | 0.0970 |
| Zn3 | Zn | 9d | 9 | 0.5000 | 0.0000 | 0.5000 |
| Zn4 | Zn | 18f | 18 | 0.3333 | 0.0000 | 0.0000 |
| Zn5 | Zn | 18h | 18 | 0.1667 | 0.8333 | 0.5000 |
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 57 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
A2B17_hR19_166_c_cdfh-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR19, then the space-group number 166, then the Wyckoff letters occupied by each element in turn (Th: 6c; Zn: 6c; Zn: 9d; Zn: 18f; Zn: 18h). Two structures with the same label are the same arrangement with different cell parameters or coordinates.
Other compounds with this structure
Ba₂Mg₁₇, Ce₂Co₁₇, Ce₂Fe₁₇, Ce₂Zn₁₇, Dy₂Co₁₇, Dy₂Fe₁₇, Dy₂Zn₁₇, Er₂Zn₁₇, Gd₂Co₁₇, Gd₂Fe₁₇, Gd₂Zn₁₇, Hf₂Be₁₇, Ho₂Co₁₇, Ho₂Zn₁₇, La₂Zn₁₇, Lu₂Zn₁₇, Nb₂Be₁₇, Nd₂Co₁₇, Nd₂Fe₁₇, Nd₂Zn₁₇, Pr₂Co₁₇, Pr₂Fe₁₇, Pr₂Zn₁₇, Pu₂Zn₁₇, Sm₂Co₁₇, Sm₂Fe₁₇, Sm₂Zn₁₇, Ta₂Be₁₇, Tb₂Co₁₇, Tb₂Fe₁₇, Tb₂Zn₁₇, Th₂Co₁₇, Th₂Fe₁₇, Th₂Zn₁₇, Ti₂Be₁₇, Tm₂Zn₁₇, U₂Zn₁₇, Y₂Co₁₇, Y₂Fe₁₇, Y₂Zn₁₇, Yb₂Zn₁₇, Zr₂Be₁₇, Al₂Ce₂Co₁₅, Ce₂Mn₇Al₁₀ <!--beginning with an
Source
Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A2B17_hR19_166_c_cdfh-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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