Crystal Lab › Prototype structures › Trigonal
MnBi₄Te₇
Trigonal · space group P-3m1 (No. 164) · Pearson hP12
Symmetry elements and Wyckoff positions (interactive)
MnBi₄Te₇ in P-3m1
SettingUnit cell
- Lattice constants
- a = 4.355 Å, b = 4.355 Å, c = 23.815 Å; α = 90.00°, β = 90.00°, γ = 120.00°
- Cell volume
- 391.2 ų
- Atoms in the conventional cell
- 12 (Mn 1, Te 7, Bi 4)
- Formula units Z
- 1
- Pearson symbol
- hP12 — hexagonal / trigonal, primitive lattice, 12 atoms per conventional cell
- Symmetry operations
- 12 per cell
Crystallographic sites
| Site | Element | Wyckoff | Multiplicity | x | y | z |
|---|---|---|---|---|---|---|
| Mn3 | Mn | 1a | 1 | 0.0000 | 0.0000 | 0.0000 |
| Te4 | Te | 1b | 1 | 0.0000 | 0.0000 | 0.5000 |
| Te5 | Te | 2c | 2 | 0.0000 | 0.0000 | 0.7645 |
| Bi1 | Bi | 2d | 2 | 0.3333 | 0.6667 | 0.5842 |
| Bi2 | Bi | 2d | 2 | 0.3333 | 0.6667 | 0.8446 |
| Te6 | Te | 2d | 2 | 0.3333 | 0.6667 | 0.3443 |
| Te7 | Te | 2d | 2 | 0.3333 | 0.6667 | 0.0645 |
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 12 atoms drawn above are these sites multiplied by all 12 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
A4BC7_hP12_164_2d_a_bc2d-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP12, then the space-group number 164, then the Wyckoff letters occupied by each element in turn (Mn: 1a; Te: 1b; Te: 2c; Bi: 2d; Bi: 2d; Te: 2d; Te: 2d). Two structures with the same label are the same arrangement with different cell parameters or coordinates.
Other compounds with this structure
GeAs₄Te₇, GeBi₄Te₇, GeSb₄Te₇, PbBi₄Te₇, SnBi₄Te₇ <!--beginning with an
Source
Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A4BC7_hP12_164_2d_a_bc2d-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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