AFLOW Prototype: A2B_tP12_92_b_a
Prototype | : | SiO2 |
AFLOW prototype label | : | A2B_tP12_92_b_a |
Strukturbericht designation | : | $C30$ |
Pearson symbol | : | tP12 |
Space group number | : | 92 |
Space group symbol | : | $\text{P4}_{1}\text{2}_{1}\text{2}$ |
AFLOW prototype command | : | aflow --proto=A2B_tP12_92_b_a --params=$a$,$c/a$,$x_{1}$,$x_{2}$,$y_{2}$,$z_{2}$ |
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}& =&x_{1} \, a \, \mathbf{\hat{x}}+ x_{1} \, a \, \mathbf{\hat{y}}& \left(4a\right) & \text{Si} \\ \mathbf{B}_{2} & =&- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&- x_{1} \, a \, \mathbf{\hat{x}}- x_{1} \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \text{Si} \\ \mathbf{B}_{3} & =&\left(\frac12 - x_{1}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{1}\right) \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&\left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \text{Si} \\ \mathbf{B}_{4} & =&\left(\frac12 + x_{1}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{1}\right) \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&\left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \text{Si} \\ \mathbf{B}_{5} & =&x_{2} \, \mathbf{a}_{1}+ y_{2} \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& =&x_{2} \, a \, \mathbf{\hat{x}}+ y_{2} \, a \, \mathbf{\hat{y}}+ z_{2} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{O} \\ \mathbf{B}_{6} & =&- x_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+ \left(\frac12 + z_{2}\right) \, \mathbf{a}_{3}& =&- x_{2} \, a \, \mathbf{\hat{x}}- y_{2} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{O} \\ \mathbf{B}_{7} & =&\left(\frac12 - y_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac14 + z_{2}\right) \, \mathbf{a}_{3}& =&\left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{O} \\ \mathbf{B}_{8} & =&\left(\frac12 + y_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac34 + z_{2}\right) \, \mathbf{a}_{3}& =&\left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac34 + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{O} \\ \mathbf{B}_{9} & =&\left(\frac12 - x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 + y_{2}\right) \, \mathbf{a}_{2}+ \left(\frac14 - z_{2}\right) \, \mathbf{a}_{3}& =&\left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 - z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{O} \\ \mathbf{B}_{10} & =&\left(\frac12 + x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 - y_{2}\right) \, \mathbf{a}_{2}+ \left(\frac34 - z_{2}\right) \, \mathbf{a}_{3}& =&\left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac34 - z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{O} \\ \mathbf{B}_{11} & =&y_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& =&y_{2} \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}- z_{2} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{O} \\ \mathbf{B}_{12} & =&- y_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ \left(\frac12 - z_{2}\right) \, \mathbf{a}_{3}& =&- y_{2} \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{O} \\ \end{array} \]