KB$_{6}$H$_{6}$ Structure: A6B6C_cF104_202_h_h_c-001
| Prototype | B$_{6}$H$_{6}$K |
| AFLOW prototype label | A6B6C_cF104_202_h_h_c-001 |
| ICSD | 36148 |
| Pearson symbol | cF104 |
| Space group number | 202 |
| Space group symbol | $Fm\overline{3}$ |
| AFLOW prototype command |
aflow --proto=A6B6C_cF104_202_h_h_c-001
--params=$a, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak y_{3}, \allowbreak z_{3}$ |
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8c) | K I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (8c) | K I |
| $\mathbf{B_{3}}$ | = | $\left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (48h) | B I |
| $\mathbf{B_{4}}$ | = | $- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (48h) | B I |
| $\mathbf{B_{5}}$ | = | $\left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{y}}- a z_{2} \,\mathbf{\hat{z}}$ | (48h) | B I |
| $\mathbf{B_{6}}$ | = | $- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{y}}- a z_{2} \,\mathbf{\hat{z}}$ | (48h) | B I |
| $\mathbf{B_{7}}$ | = | $\left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{z}}$ | (48h) | B I |
| $\mathbf{B_{8}}$ | = | $- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{z}}$ | (48h) | B I |
| $\mathbf{B_{9}}$ | = | $\left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{z}}$ | (48h) | B I |
| $\mathbf{B_{10}}$ | = | $- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{z}}$ | (48h) | B I |
| $\mathbf{B_{11}}$ | = | $- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}$ | (48h) | B I |
| $\mathbf{B_{12}}$ | = | $\left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}$ | (48h) | B I |
| $\mathbf{B_{13}}$ | = | $- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}- a z_{2} \,\mathbf{\hat{y}}$ | (48h) | B I |
| $\mathbf{B_{14}}$ | = | $\left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}- a z_{2} \,\mathbf{\hat{y}}$ | (48h) | B I |
| $\mathbf{B_{15}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (48h) | H I |
| $\mathbf{B_{16}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (48h) | H I |
| $\mathbf{B_{17}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (48h) | H I |
| $\mathbf{B_{18}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (48h) | H I |
| $\mathbf{B_{19}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{z}}$ | (48h) | H I |
| $\mathbf{B_{20}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{z}}$ | (48h) | H I |
| $\mathbf{B_{21}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{z}}$ | (48h) | H I |
| $\mathbf{B_{22}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{z}}$ | (48h) | H I |
| $\mathbf{B_{23}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}$ | (48h) | H I |
| $\mathbf{B_{24}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}$ | (48h) | H I |
| $\mathbf{B_{25}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}$ | (48h) | H I |
| $\mathbf{B_{26}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}$ | (48h) | H I |
References
- J. A. Wunderlich and W. N. Lipscomb, Structure of B$_{12}$H$_{12}^{-2}$ Ion, J. Am. Chem. Soc. 82, 4427–4428 (1960), doi:10.1021/ja01501a076.
Found in
- P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds (2013). ASM International.
Prototype Generator
aflow --proto=A6B6C_cF104_202_h_h_c --params=$a,y_{2},z_{2},y_{3},z_{3}$