Bi$_{2}$Te$_{3}$ ($C33$) Structure: A2B3_hR5_166_c_ac-001
| Prototype | Bi$_{2}$Te$_{3}$ |
| AFLOW prototype label | A2B3_hR5_166_c_ac-001 |
| Strukturbericht designation | $C33$ |
| ICSD | 15753 |
| Pearson symbol | hR5 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A2B3_hR5_166_c_ac-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}$ |
Other compounds with this structure
$\beta$-As$_{2}$Te$_{3}$, Bi$_{2}$Te$_{2}$S, Bi$_{2}$Se$_{3}$, Bi$_{2}$Te$_{2}$Se, Ga$_{2}$Te$_{5}$, In$_{2}$Te$_{3}$, Sb$_{2}$Te$_{3}$
- (Gottfried, 1937) assigns Bi$_{2}$Te$_{2}$S as the prototype for Strukturbericht symbol $C33$, but (Lange, 1939) shows that this is isostructural with Bi$_{2}$Te$_{3}$, the sulfur atom being replaced by a tellurium atom. We will therefore retain our original designation.
- 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) | Te 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 II |
| $\mathbf{B_{5}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- c x_{3} \,\mathbf{\hat{z}}$ | (2c) | Te II |
References
- P. W. Lange, Ein Vergleich zwischen Bi$_2$Te$_3$ und Bi$_2$Te$_2$S, Naturwissenschaften 27, 133–134 (1939), doi:10.1007/BF01490284.
- C. Gottfried and F. Schossberger, eds., Strukturbericht Band III 1933-1935 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
Prototype Generator
aflow --proto=A2B3_hR5_166_c_ac --params=$a,c/a,x_{2},x_{3}$