AFLOW Prototype: A_hR12_166_2h
Prototype | : | $\alpha$–B |
AFLOW prototype label | : | A_hR12_166_2h |
Strukturbericht designation | : | None |
Pearson symbol | : | hR12 |
Space group number | : | 166 |
Space group symbol | : | $\text{R}\bar{3}\text{m}$ |
AFLOW prototype command | : | aflow --proto=A_hR12_166_2h [--hex] --params=$a$,$c/a$,$x_{1}$,$z_{1}$,$x_{2}$,$z_{2}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & =&x_{1} \, \mathbf{a}_{1}+ x_{1} \, \mathbf{a}_{2}+ z_{1} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{1} - z_{1}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \left(x_{1} - z_{1}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(2 x_{1} + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \text{B I} \\ \mathbf{B}_{2} & =&z_{1} \, \mathbf{a}_{1}+ x_{1} \, \mathbf{a}_{2}+ x_{1} \, \mathbf{a}_{3}& =&\frac12 \, \left(z_{1} - x_{1}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \left(x_{1} - z_{1}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(2 x_{1} + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \text{B I} \\ \mathbf{B}_{3} & =&x_{1} \, \mathbf{a}_{1}+ z_{1} \, \mathbf{a}_{2}+ x_{1} \, \mathbf{a}_{3}& =&\frac1{\sqrt3} \left(z_{1} - x_{1}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(2 x_{1} + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \text{B I} \\ \mathbf{B}_{4} & =&- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}& =&\frac12 \, \left(z_{1} - x_{1}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \left(z_{1} - x_{1}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(2 x_{1} + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \text{B I} \\ \mathbf{B}_{5} & =&- z_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{1} - z_{1}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \left(z_{1} - x_{1}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(2 x_{1} + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \text{B I} \\ \mathbf{B}_{6} & =&- x_{1} \, \mathbf{a}_{1}- z_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}& =&\frac1{\sqrt3} \left(x_{1} - z_{1}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(2 x_{1} + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \text{B I} \\ \mathbf{B}_{7} & =&x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{2} - z_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \left(x_{2} - z_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(2 x_{2} + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \text{B II} \\ \mathbf{B}_{8} & =&z_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& =&\frac12 \, \left(z_{2} - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \left(x_{2} - z_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(2 x_{2} + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \text{B II} \\ \mathbf{B}_{9} & =&x_{2} \, \mathbf{a}_{1}+ z_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& =&\frac1{\sqrt3} \left(z_{2} - x_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(2 x_{2} + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \text{B II} \\ \mathbf{B}_{10} & =&- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& =&\frac12 \, \left(z_{2} - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \left(z_{2} - x_{2}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(2 x_{2} + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \text{B II} \\ \mathbf{B}_{11} & =&- z_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{2} - z_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \left(z_{2} - x_{2}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(2 x_{2} + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \text{B II} \\ \mathbf{B}_{12} & =&- x_{2} \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& =&\frac1{\sqrt3} \left(x_{2} - z_{2}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(2 x_{2} + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \text{B II} \\ \end{array} \]