AFLOW Prototype: A4BC12_cI34_204_c_a_g
Prototype | : | Fe4LaP12 |
AFLOW prototype label | : | A4BC12_cI34_204_c_a_g |
Strukturbericht designation | : | None |
Pearson symbol | : | cI34 |
Space group number | : | 204 |
Space group symbol | : | $Im\bar{3}$ |
AFLOW prototype command | : | aflow --proto=A4BC12_cI34_204_c_a_g --params=$a$,$y_{3}$,$z_{3}$ |
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(2a\right) & \text{La} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(8c\right) & \text{Fe} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}}- \frac{1}{4}a \, \mathbf{\hat{z}} & \left(8c\right) & \text{Fe} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}}- \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(8c\right) & \text{Fe} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & - \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(8c\right) & \text{Fe} \\ \mathbf{B}_{6} & = & \left(y_{3}+z_{3}\right) \, \mathbf{a}_{1} + z_{3} \, \mathbf{a}_{2} + y_{3} \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{y}} + z_{3}a \, \mathbf{\hat{z}} & \left(24g\right) & \text{P} \\ \mathbf{B}_{7} & = & \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + z_{3} \, \mathbf{a}_{2}-y_{3} \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{y}} + z_{3}a \, \mathbf{\hat{z}} & \left(24g\right) & \text{P} \\ \mathbf{B}_{8} & = & \left(y_{3}-z_{3}\right) \, \mathbf{a}_{1}-z_{3} \, \mathbf{a}_{2} + y_{3} \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{y}}-z_{3}a \, \mathbf{\hat{z}} & \left(24g\right) & \text{P} \\ \mathbf{B}_{9} & = & \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{1}-z_{3} \, \mathbf{a}_{2}-y_{3} \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{y}}-z_{3}a \, \mathbf{\hat{z}} & \left(24g\right) & \text{P} \\ \mathbf{B}_{10} & = & y_{3} \, \mathbf{a}_{1} + \left(y_{3}+z_{3}\right) \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & z_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{z}} & \left(24g\right) & \text{P} \\ \mathbf{B}_{11} & = & -y_{3} \, \mathbf{a}_{1} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & z_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{z}} & \left(24g\right) & \text{P} \\ \mathbf{B}_{12} & = & y_{3} \, \mathbf{a}_{1} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & -z_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{z}} & \left(24g\right) & \text{P} \\ \mathbf{B}_{13} & = & -y_{3} \, \mathbf{a}_{1} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & -z_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{z}} & \left(24g\right) & \text{P} \\ \mathbf{B}_{14} & = & z_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + \left(y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}} + z_{3}a \, \mathbf{\hat{y}} & \left(24g\right) & \text{P} \\ \mathbf{B}_{15} & = & z_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}} + z_{3}a \, \mathbf{\hat{y}} & \left(24g\right) & \text{P} \\ \mathbf{B}_{16} & = & -z_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}}-z_{3}a \, \mathbf{\hat{y}} & \left(24g\right) & \text{P} \\ \mathbf{B}_{17} & = & -z_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}}-z_{3}a \, \mathbf{\hat{y}} & \left(24g\right) & \text{P} \\ \end{array} \]