AFLOW Prototype: A2B_hP12_194_cg_f
Prototype | : | SiO2 |
AFLOW prototype label | : | A2B_hP12_194_cg_f |
Strukturbericht designation | : | $C10$ |
Pearson symbol | : | hP12 |
Space group number | : | 194 |
Space group symbol | : | $\text{P6}_{3}\text{/mmc}$ |
AFLOW prototype command | : | aflow --proto=A2B_hP12_194_cg_f --params=$a$,$c/a$,$z_{2}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \text{O I} \\ \mathbf{B}_{2}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \text{O I} \\ \mathbf{B}_{3}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+\frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ z_{2} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \text{Si} \\ \mathbf{B}_{4}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \left(\frac12 + z_{2}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(4f\right) & \text{Si} \\ \mathbf{B}_{5}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}- z_{2} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \text{Si} \\ \mathbf{B}_{6}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \left(\frac12 - z_{2}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(4f\right) & \text{Si} \\ \mathbf{B}_{7}& = &\frac12 \, \mathbf{a}_{1}& = &\frac14 \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}4 \, a \, \mathbf{\hat{y}}& \left(6g\right) & \text{O II} \\ \mathbf{B}_{8}& = &\frac12 \, \mathbf{a}_{2}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}4 \, a \, \mathbf{\hat{y}}& \left(6g\right) & \text{O II} \\ \mathbf{B}_{9}& = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& = &\frac12 \, a \, \mathbf{\hat{x}}& \left(6g\right) & \text{O II} \\ \mathbf{B}_{10}& = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}4 \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{O II} \\ \mathbf{B}_{11}& = &\frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}4 \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{O II} \\ \mathbf{B}_{12}& = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(6g\right) & \text{O II} \\ \end{array} \]