Bi$_{4}$Te$_{3}$ Structure: A4B3_hR7_166_2c_ac-002
| Prototype | Bi$_{4}$Te$_{3}$ |
| AFLOW prototype label | A4B3_hR7_166_2c_ac-002 |
| ICSD | 30526 |
| Pearson symbol | hR7 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A4B3_hR7_166_2c_ac-002
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}$ |
Other compounds with this structure
Bi$_{4}$Se$_{3}$
- (Villars, 2016) lists Bi$_{4}$Se$_{3}$ as the prototype for this structure, but the data for Bi$_{4}$Te$_{3}$ is much more accessible, so we use that instead.
- Al$_{4}$C$_{3}$ ($D7_{1}$) and Bi$_{4}$Te$_{3}$ have the same AFLOW prototype label, A4B3_hR7_166_2c_ac. They are generated by the same symmetry operations with different sets of parameters (
--params) specified in their corresponding CIF files. - 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) | Bi 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) | Bi II |
| $\mathbf{B_{6}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $c x_{4} \,\mathbf{\hat{z}}$ | (2c) | Te II |
| $\mathbf{B_{7}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- c x_{4} \,\mathbf{\hat{z}}$ | (2c) | Te II |
References
- K. Yamana, K. Kihara, and T. Matsumoto, Bismuth Tellurides: BiTe and Bi$_{4}$Te$_{3}$, Acta Crystallogr. Sect. B 35, 147–149 (1979), doi:10.1107/S0567740879002788.
- P. Villars, Bi$_{4}$Se$_{3}$ Crystal Structure (2016). PAULING FILE in: Inorganic Solid Phases, SpringerMaterials (online database), Springer, Heidelberg (ed.) SpringerMaterials.
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=A4B3_hR7_166_2c_ac --params=$a,c/a,x_{2},x_{3},x_{4}$