AFLOW Prototype: AB30C16D3_cF200_225_a_ej_2f_bc
Prototype | : | AlF6H12N3 |
AFLOW prototype label | : | AB30C16D3_cF200_225_a_ej_2f_bc |
Strukturbericht designation | : | $J2_{1}$ |
Pearson symbol | : | cF200 |
Space group number | : | 225 |
Space group symbol | : | $Fm\bar{3}m$ |
AFLOW prototype command | : | aflow --proto=AB30C16D3_cF200_225_a_ej_2f_bc --params=$a$,$x_{4}$,$x_{5}$,$x_{6}$,$y_{7}$,$z_{7}$ |
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{Al} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(4b\right) & \text{N I} \\ \mathbf{B}_{3} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \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{N II} \\ \mathbf{B}_{4} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(8c\right) & \text{N II} \\ \mathbf{B}_{5} & = & -x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} & \left(24e\right) & \text{F I} \\ \mathbf{B}_{6} & = & x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} & \left(24e\right) & \text{F I} \\ \mathbf{B}_{7} & = & x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{y}} & \left(24e\right) & \text{F I} \\ \mathbf{B}_{8} & = & -x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{y}} & \left(24e\right) & \text{F I} \\ \mathbf{B}_{9} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{z}} & \left(24e\right) & \text{F I} \\ \mathbf{B}_{10} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{z}} & \left(24e\right) & \text{F I} \\ \mathbf{B}_{11} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(32f\right) & \text{H I} \\ \mathbf{B}_{12} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2}-3x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(32f\right) & \text{H I} \\ \mathbf{B}_{13} & = & x_{5} \, \mathbf{a}_{1}-3x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(32f\right) & \text{H I} \\ \mathbf{B}_{14} & = & -3x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(32f\right) & \text{H I} \\ \mathbf{B}_{15} & = & -x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + 3x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(32f\right) & \text{H I} \\ \mathbf{B}_{16} & = & -x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(32f\right) & \text{H I} \\ \mathbf{B}_{17} & = & -x_{5} \, \mathbf{a}_{1} + 3x_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(32f\right) & \text{H I} \\ \mathbf{B}_{18} & = & 3x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(32f\right) & \text{H I} \\ \mathbf{B}_{19} & = & x_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(32f\right) & \text{H II} \\ \mathbf{B}_{20} & = & x_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2}-3x_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(32f\right) & \text{H II} \\ \mathbf{B}_{21} & = & x_{6} \, \mathbf{a}_{1}-3x_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(32f\right) & \text{H II} \\ \mathbf{B}_{22} & = & -3x_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(32f\right) & \text{H II} \\ \mathbf{B}_{23} & = & -x_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + 3x_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(32f\right) & \text{H II} \\ \mathbf{B}_{24} & = & -x_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(32f\right) & \text{H II} \\ \mathbf{B}_{25} & = & -x_{6} \, \mathbf{a}_{1} + 3x_{6} \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(32f\right) & \text{H II} \\ \mathbf{B}_{26} & = & 3x_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(32f\right) & \text{H II} \\ \mathbf{B}_{27} & = & \left(y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(y_{7}-z_{7}\right) \, \mathbf{a}_{3} & = & y_{7}a \, \mathbf{\hat{y}} + z_{7}a \, \mathbf{\hat{z}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{28} & = & \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(y_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{3} & = & -y_{7}a \, \mathbf{\hat{y}} + z_{7}a \, \mathbf{\hat{z}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{29} & = & \left(y_{7}-z_{7}\right) \, \mathbf{a}_{1} + \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & y_{7}a \, \mathbf{\hat{y}}-z_{7}a \, \mathbf{\hat{z}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{30} & = & \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{1} + \left(y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & -y_{7}a \, \mathbf{\hat{y}}-z_{7}a \, \mathbf{\hat{z}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{31} & = & \left(y_{7}-z_{7}\right) \, \mathbf{a}_{1} + \left(y_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & z_{7}a \, \mathbf{\hat{x}} + y_{7}a \, \mathbf{\hat{z}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{32} & = & \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{1} + \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & z_{7}a \, \mathbf{\hat{x}}-y_{7}a \, \mathbf{\hat{z}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{33} & = & \left(y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{3} & = & -z_{7}a \, \mathbf{\hat{x}} + y_{7}a \, \mathbf{\hat{z}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{34} & = & \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(y_{7}-z_{7}\right) \, \mathbf{a}_{3} & = & -z_{7}a \, \mathbf{\hat{x}}-y_{7}a \, \mathbf{\hat{z}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{35} & = & \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & y_{7}a \, \mathbf{\hat{x}} + z_{7}a \, \mathbf{\hat{y}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{36} & = & \left(y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & -y_{7}a \, \mathbf{\hat{x}} + z_{7}a \, \mathbf{\hat{y}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{37} & = & \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{1} + \left(y_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(y_{7}-z_{7}\right) \, \mathbf{a}_{3} & = & y_{7}a \, \mathbf{\hat{x}}-z_{7}a \, \mathbf{\hat{y}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{38} & = & \left(y_{7}-z_{7}\right) \, \mathbf{a}_{1} + \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{3} & = & -y_{7}a \, \mathbf{\hat{x}}-z_{7}a \, \mathbf{\hat{y}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{39} & = & \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{1} + \left(y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & y_{7}a \, \mathbf{\hat{x}}-z_{7}a \, \mathbf{\hat{z}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{40} & = & \left(y_{7}-z_{7}\right) \, \mathbf{a}_{1} + \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & -y_{7}a \, \mathbf{\hat{x}}-z_{7}a \, \mathbf{\hat{z}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{41} & = & \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(y_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(y_{7}-z_{7}\right) \, \mathbf{a}_{3} & = & y_{7}a \, \mathbf{\hat{x}} + z_{7}a \, \mathbf{\hat{z}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{42} & = & \left(y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{3} & = & -y_{7}a \, \mathbf{\hat{x}} + z_{7}a \, \mathbf{\hat{z}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{43} & = & \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & z_{7}a \, \mathbf{\hat{y}}-y_{7}a \, \mathbf{\hat{z}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{44} & = & \left(y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & z_{7}a \, \mathbf{\hat{y}} + y_{7}a \, \mathbf{\hat{z}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{45} & = & \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{1} + \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(y_{7}-z_{7}\right) \, \mathbf{a}_{3} & = & -z_{7}a \, \mathbf{\hat{y}}-y_{7}a \, \mathbf{\hat{z}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{46} & = & \left(y_{7}-z_{7}\right) \, \mathbf{a}_{1} + \left(y_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{3} & = & -z_{7}a \, \mathbf{\hat{y}} + y_{7}a \, \mathbf{\hat{z}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{47} & = & \left(y_{7}-z_{7}\right) \, \mathbf{a}_{1} + \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & z_{7}a \, \mathbf{\hat{x}} + y_{7}a \, \mathbf{\hat{y}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{48} & = & \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{1} + \left(y_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & z_{7}a \, \mathbf{\hat{x}}-y_{7}a \, \mathbf{\hat{y}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{49} & = & \left(y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(y_{7}-z_{7}\right) \, \mathbf{a}_{3} & = & -z_{7}a \, \mathbf{\hat{x}} + y_{7}a \, \mathbf{\hat{y}} & \left(96j\right) & \text{F II} \\ \mathbf{B}_{50} & = & \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{3} & = & -z_{7}a \, \mathbf{\hat{x}}-y_{7}a \, \mathbf{\hat{y}} & \left(96j\right) & \text{F II} \\ \end{array} \]