BiI$_{3}$ ($D0_{5}$) Structure: AB3_hR8_148_c_f-001
| Prototype | BiI$_{3}$ |
| AFLOW prototype label | AB3_hR8_148_c_f-001 |
| Strukturbericht designation | $D0_{5}$ |
| ICSD | 36182 |
| Pearson symbol | hR8 |
| Space group number | 148 |
| Space group symbol | $R\overline{3}$ |
| AFLOW prototype command |
aflow --proto=AB3_hR8_148_c_f-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}$ |
Other compounds with this structure
AsI$_{3}$, CrBr$_{3}$, CrCl$_{3}$, CrI$_{3}$, FeCl$_{3}$, RhBr$_{3}$, SbI$_{3}$, VCl$_{3}$, VI$_{3}$
- Hexagonal settings of this structure 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 | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $c x_{1} \,\mathbf{\hat{z}}$ | (2c) | Bi I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $- c x_{1} \,\mathbf{\hat{z}}$ | (2c) | Bi I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{2} - 2 y_{2} + z_{2}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{2} + y_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6f) | I I |
| $\mathbf{B_{4}}$ | = | $z_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+y_{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{2} - z_{2}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{2} - y_{2} - z_{2}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{2} + y_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6f) | I I |
| $\mathbf{B_{5}}$ | = | $y_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{2} - y_{2}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{2} + y_{2} - 2 z_{2}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{2} + y_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6f) | I I |
| $\mathbf{B_{6}}$ | = | $- x_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{2} - 2 y_{2} + z_{2}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{2} + y_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6f) | I I |
| $\mathbf{B_{7}}$ | = | $- z_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{2} - z_{2}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{2} - y_{2} - z_{2}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{2} + y_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6f) | I I |
| $\mathbf{B_{8}}$ | = | $- y_{2} \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{2} - y_{2}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{2} + y_{2} - 2 z_{2}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{2} + y_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6f) | I I |
References
- H. Br\aekken, IX. Die Kristallstruktur der Trijodide von Arsen, Antimon und Wismut, Z. Kristallogr. 74, 67–72 (1930), doi:10.1524/zkri.1930.74.1.67.
Found in
- C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928-1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
Prototype Generator
aflow --proto=AB3_hR8_148_c_f --params=$a,c/a,x_{1},x_{2},y_{2},z_{2}$