Tetradymite (Bi$_{2}$Te$_{2}$S, $C33$) Structure: A2BC2_hR5_166_c_a_c-002
| Prototype | Bi$_{2}$STe$_{2}$ |
| AFLOW prototype label | A2BC2_hR5_166_c_a_c-002 |
| Mineral name | tetradymite |
| ICSD | 26720 |
| CCDC | 1602106 |
| Pearson symbol | hR5 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A2BC2_hR5_166_c_a_c-002
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}$ |
Other compounds with this structure
Ag$_{2}$O$_{2}$Ni, As$_{2}$Sn$_{2}$Eu, Bi$_{2}$Te$_{2}$Se, Gd$_{2}$I$_{2}$Ge, La$_{2}$I$_{2}$Ge, La$_{2}$I$_{2}$Te, Sb$_{2}$Se$_{2}$Te, Sn$_{2}$As$_{2}$Na
- This is the ternary form of Bi$_{2}$Te$_{3}$, Strukturbericht symbol $C33$. It was the original $C33$ structure assigned by (Gottfried, 1937), but we decided to use the binary form as the designated structure.
- Hexagonal settings for rhombohedral structures can be obtained with the option
--hex.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | S I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $c x_{2} \,\mathbf{\hat{z}}$ | (2c) | Bi I |
| $\mathbf{B_{3}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- c x_{2} \,\mathbf{\hat{z}}$ | (2c) | Bi I |
| $\mathbf{B_{4}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $c x_{3} \,\mathbf{\hat{z}}$ | (2c) | Te I |
| $\mathbf{B_{5}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- c x_{3} \,\mathbf{\hat{z}}$ | (2c) | Te I |
References
- D. Harker, The Crystal Structure of the Mineral Tetradymite, Bi$_{2}$Te$_{2}$S 89, 175–181 (1934), doi:10.1524/zkri.1934.89.1.175.
Found in
- C. Gottfried and F. Schossberger, eds., Strukturbericht Band III 1933-1935 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=A2BC2_hR5_166_c_a_c --params=$a,c/a,x_{2},x_{3}$