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Crystal Lab › Prototype structures › Trigonal

Tetradymite (Bi₂Te₂S, C33)

Trigonal · space group R-3m (No. 166) · Pearson hR5 · mineral: tetradymite

Symmetry elements and Wyckoff positions (interactive)

Tetradymite (Bi₂Te₂S, C33) in R-3m

Setting
Loading the group…
x = 0.10, y = 0.17, z = 0.08

Unit cell

Lattice constants
a = 4.316 Å, b = 4.316 Å, c = 30.013 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
484.3 ų
Atoms in the conventional cell
15 (S 3, Bi 6, Te 6)
Formula units Z
3
Pearson symbol
hR5 — hexagonal / trigonal, rhombohedral lattice, 5 atoms per conventional cell
Symmetry operations
36 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
S2S3a30.00000.00000.0000
Bi1Bi6c60.00000.00000.3920
Te3Te6c60.00000.00000.7880

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 15 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

A2BC2_hR5_166_c_a_c-002: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hR5, then the space-group number 166, then the Wyckoff letters occupied by each element in turn (S: 3a; Bi: 6c; Te: 6c). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Other compounds with this structure

Ag₂O₂Ni, As₂Sn₂Eu, Bi₂Te₂Se, Gd₂I₂Ge, La₂I₂Ge, La₂I₂Te, Sb₂Se₂Te, Sn₂As₂Na <!--beginning with an

Note: Tetradymite.

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A2BC2_hR5_166_c_a_c-002 (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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