Crystal Lab › Prototype structures › Trigonal
MnBi₆Te₁₀
Trigonal · space group R-3m (No. 166) · Pearson hR17
Symmetry elements and Wyckoff positions (interactive)
MnBi₆Te₁₀ in R-3m
SettingUnit cell
- Lattice constants
- a = 4.375 Å, b = 4.375 Å, c = 101.985 Å; α = 90.00°, β = 90.00°, γ = 120.00°
- Cell volume
- 1690.1 ų
- Atoms in the conventional cell
- 51 (Mn 3, Bi 18, Te 30)
- Formula units Z
- 3
- Pearson symbol
- hR17 — hexagonal / trigonal, rhombohedral lattice, 17 atoms per conventional cell
- Symmetry operations
- 36 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Mn4 | Mn | 3a | 3 | 0.0000 | 0.0000 | 0.0000 |
| Bi1 | Bi | 6c | 6 | 0.0000 | 0.0000 | 0.2367 |
| Bi2 | Bi | 6c | 6 | 0.0000 | 0.0000 | 0.2957 |
| Bi3 | Bi | 6c | 6 | 0.0000 | 0.0000 | 0.4702 |
| Te5 | Te | 6c | 6 | 0.0000 | 0.0000 | 0.0536 |
| Te6 | Te | 6c | 6 | 0.0000 | 0.0000 | 0.1173 |
| Te7 | Te | 6c | 6 | 0.0000 | 0.0000 | 0.1791 |
| Te8 | Te | 6c | 6 | 0.0000 | 0.0000 | 0.3492 |
| Te9 | Te | 6c | 6 | 0.0000 | 0.0000 | 0.4145 |
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 51 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
A6BC10_hR17_166_3c_a_5c-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR17, then the space-group number 166, then the Wyckoff letters occupied by each element in turn (Mn: 3a; Bi: 6c; Bi: 6c; Bi: 6c; Te: 6c; Te: 6c; Te: 6c; Te: 6c; Te: 6c). 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 A6BC10_hR17_166_3c_a_5c-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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