Solid Cubane (C8H8) Structure: AB_hR16_148_cf_cf
| Prototype | : | C8H8 |
| AFLOW prototype label | : | AB_hR16_148_cf_cf |
| Strukturbericht designation | : | None |
| Pearson symbol | : | hR16 |
| Space group number | : | 148 |
| Space group symbol | : | $\mbox{R}\bar{3}$ |
| AFLOW prototype command | : | aflow --proto=AB_hR16_148_cf_cf [--hex] --params=$a,c/a,x_{1},x_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4}$ |
- Hexagonal settings of this structure can be obtained with the option ––hex.
Rhombohedral primitive vectors:
\[
\begin{array}{ccc}
\mathbf{a}_1 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13
\, c \, \mathbf{\hat{z}} \\
\mathbf{a}_2 & = & \frac{1}{\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\
\mathbf{a}_3 & = & - \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13
\, c \, \mathbf{\hat{z}} \\
\end{array}
\]
Basis vectors:
\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = &x_{1} \, \mathbf{a}_{1}+ x_{1} \, \mathbf{a}_{2}+ x_{1} \, \mathbf{a}_{3}& =&x_{1} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{C I} \\ \mathbf{B}_{2} & = &- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}& =&- x_{1} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{C I} \\ \mathbf{B}_{3} & = &x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& =&x_{2} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{H I} \\ \mathbf{B}_{4} & = &- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& =&- x_{2} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{H I} \\ \mathbf{B}_{5} & =&x_{3} \, \mathbf{a}_{1}+ y_{3} \, \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{3} - z_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(2 y_{3} - z_{3} - x_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(x_{3} + y_{3} + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{C II} \\ \mathbf{B}_{6} & =&z_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}+ y_{3} \, \mathbf{a}_{3}& =&\frac12 \, \left(z_{3} - y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(2 x_{3} - y_{3} - z_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(x_{3} + y_{3} + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{C II} \\ \mathbf{B}_{7} & =&y_{3} \, \mathbf{a}_{1}+ z_{3} \, \mathbf{a}_{2}+ x_{3} \, \mathbf{a}_{3}& =&\frac12 \, \left(y_{3} - x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(2 z_{3} - x_{3} - y_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(x_{3} + y_{3} + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{C II} \\ \mathbf{B}_{8} & =&- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& =&\frac12 \, \left(z_{3} - x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(z_{3} + x_{3} - 2 y_{3}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(x_{3} + y_{3} + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{C II} \\ \mathbf{B}_{9} & =&- z_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}& =&\frac12 \, \left(y_{3} - z_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(y_{3} + z_{3} - 2 x_{3}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(x_{3} + y_{3} + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{C II} \\ \mathbf{B}_{10} & =&- y_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{3} - y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(x_{3} + y_{3} - 2 z_{3}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(x_{3} + y_{3} + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{C II} \\ \mathbf{B}_{11} & =&x_{4} \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{2}+ z_{4} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{4} - z_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(2 y_{4} - z_{4} - x_{4}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(x_{4} + y_{4} + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{H II} \\ \mathbf{B}_{12} & =&z_{4} \, \mathbf{a}_{1}+ x_{4} \, \mathbf{a}_{2}+ y_{4} \, \mathbf{a}_{3}& =&\frac12 \, \left(z_{4} - y_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(2 x_{4} - y_{4} - z_{4}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(x_{4} + y_{4} + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{H II} \\ \mathbf{B}_{13} & =&y_{4} \, \mathbf{a}_{1}+ z_{4} \, \mathbf{a}_{2}+ x_{4} \, \mathbf{a}_{3}& =&\frac12 \, \left(y_{4} - x_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(2 z_{4} - x_{4} - y_{4}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(x_{4} + y_{4} + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{H II} \\ \mathbf{B}_{14} & =&- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}& =&\frac12 \, \left(z_{4} - x_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(z_{4} + x_{4} - 2 y_{4}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(x_{4} + y_{4} + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{H II} \\ \mathbf{B}_{15} & =&- z_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}& =&\frac12 \, \left(y_{4} - z_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(y_{4} + z_{4} - 2 x_{4}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(x_{4} + y_{4} + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{H II} \\ \mathbf{B}_{16} & =&- y_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{4} - y_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(x_{4} + y_{4} - 2 z_{4}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(x_{4} + y_{4} + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{H II} \\ \end{array} \]References
- E. B. Fleischer, X–Ray Structure Determination of Cubane, J. Am. Chem. Soc. 86, 3889–3890 (1964), doi:10.1021/ja01072a069.