AFLOW Prototype: A12B_cF52_225_i_a
Prototype | : | UB12 |
AFLOW prototype label | : | A12B_cF52_225_i_a |
Strukturbericht designation | : | $D2_{f}$ |
Pearson symbol | : | cF52 |
Space group number | : | 225 |
Space group symbol | : | $\text{Fm}\bar{3}\text{m}$ |
AFLOW prototype command | : | aflow --proto=A12B_cF52_225_i_a --params=$a$,$y_{2}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = &0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = &0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(4a\right) & \text{U} \\ \mathbf{B}_{2} & = &\left(\frac12 + 2 \, y_{2}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48i\right) & \text{B} \\ \mathbf{B}_{3} & = &\frac12 \, \mathbf{a}_{1}+ \left(\frac12 + 2 \, y_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 - 2 \, y_{2}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48i\right) & \text{B} \\ \mathbf{B}_{4} & = &\frac12 \, \mathbf{a}_{1}+ \left(\frac12 - 2 \, y_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 + 2 \, y_{2}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48i\right) & \text{B} \\ \mathbf{B}_{5} & = &\left(\frac12 - 2 \, y_{2}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48i\right) & \text{B} \\ \mathbf{B}_{6} & = &+ \frac12 \, \mathbf{a}_{1}+ \left(\frac12 + 2 \, y_{2}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48i\right) & \text{B} \\ \mathbf{B}_{7} & = &\left(\frac12 - 2 \, y_{2}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left(\frac12 + 2 \, y_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}\left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48i\right) & \text{B} \\ \mathbf{B}_{8} & = &\left(\frac12 + 2 \, y_{2}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left(\frac12 - 2 \, y_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48i\right) & \text{B} \\ \mathbf{B}_{9} & = &\frac12 \, \mathbf{a}_{1}+ \left(\frac12 - 2 \, y_{2}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}\left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48i\right) & \text{B} \\ \mathbf{B}_{10} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left(\frac12 + 2 \, y_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(48i\right) & \text{B} \\ \mathbf{B}_{11} & = &\left(\frac12 + 2 \, y_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 - 2 \, y_{2}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(48i\right) & \text{B} \\ \mathbf{B}_{12} & = &\left(\frac12 - 2 \, y_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 + 2 \, y_{2}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(48i\right) & \text{B} \\ \mathbf{B}_{13} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left(\frac12 - 2 \, y_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(48i\right) & \text{B} \\ \end{array} \]