AFLOW Prototype: A2B_mP12_3_bc3e_2e
Prototype | : | SiO2 |
AFLOW prototype label | : | A2B_mP12_3_bc3e_2e |
Strukturbericht designation | : | None |
Pearson symbol | : | mP12 |
Space group number | : | 3 |
Space group symbol | : | $\text{P2}$ |
AFLOW prototype command | : | aflow --proto=A2B_mP12_3_bc3e_2e --params=$a$,$b/a$,$c/a$,$\beta$,$y_{1}$,$y_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & =& y_{1} \, \mathbf{a}_{2} + \frac12 \, \mathbf{a}_{3}& =& \frac12 \, c \, \cos\beta \, \mathbf{\hat{x}}+ y_{1} b \, \mathbf{\hat{y}}+ \frac12 \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(1b\right) & \text{O I} \\ \mathbf{B}_{2} & =& \frac12 \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2}& =& \frac12 \, a \, \mathbf{\hat{x}}+ y_{2} b \, \mathbf{\hat{y}}& \left(1c\right) & \text{O II} \\ \mathbf{B}_{3} & =& x_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3}& =& \left(x_{3} \, a + z_{3} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{3} \, b \, \mathbf{\hat{y}}+ z_{3} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \text{O III} \\ \mathbf{B}_{4} & =& - x_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} - z_{3} \, \mathbf{a}_{3}& =& - \left(x_{3} \, a + z_{3} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{3} \, b \, \mathbf{\hat{y}}- z_{3} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \text{O III} \\ \mathbf{B}_{5} & =& x_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3}& =& \left(x_{4} \, a + z_{4} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{4} \, b \, \mathbf{\hat{y}}+ z_{4} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \text{O IV} \\ \mathbf{B}_{6} & =& - x_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} - z_{4} \, \mathbf{a}_{3}& =& - \left(x_{4} \, a + z_{4} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{4} \, b \, \mathbf{\hat{y}}- z_{4} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \text{O IV} \\ \mathbf{B}_{7} & =& x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3}& =& \left(x_{5} \, a + z_{5} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{5} \, b \, \mathbf{\hat{y}}+ z_{5} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \text{O V} \\ \mathbf{B}_{8} & =& - x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} - z_{5} \, \mathbf{a}_{3}& =& - \left(x_{5} \, a + z_{5} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{5} \, b \, \mathbf{\hat{y}}- z_{5} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \text{O V} \\ \mathbf{B}_{9} & =& x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3}& =& \left(x_{6} \, a + z_{6} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{6} \, b \, \mathbf{\hat{y}}+ z_{6} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \text{Si I} \\ \mathbf{B}_{10} & =& - x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} - z_{6} \, \mathbf{a}_{3}& =& - \left(x_{6} \, a + z_{6} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{6} \, b \, \mathbf{\hat{y}}- z_{6} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \text{Si I} \\ \mathbf{B}_{11} & =& x_{7} \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3}& =& \left(x_{7} \, a + z_{7} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{7} \, b \, \mathbf{\hat{y}}+ z_{7} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \text{Si II} \\ \mathbf{B}_{12} & =& - x_{7} \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} - z_{7} \, \mathbf{a}_{3}& =& - \left(x_{7} \, a + z_{7} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{7} \, b \, \mathbf{\hat{y}}- z_{7} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \text{Si II} \\ \end{array} \]