AFLOW Prototype: A2B11_cP39_200_f_aghij
Prototype | : | Mg2Zn11 |
AFLOW prototype label | : | A2B11_cP39_200_f_aghij |
Strukturbericht designation | : | $D8_{c}$ |
Pearson symbol | : | cP39 |
Space group number | : | 200 |
Space group symbol | : | $Pm\bar{3}$ |
AFLOW prototype command | : | aflow --proto=A2B11_cP39_200_f_aghij --params=$a$,$x_{2}$,$x_{3}$,$x_{4}$,$x_{5}$,$y_{6}$,$z_{6}$ |
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(1a\right) & \text{Zn I} \\ \mathbf{B}_{2} & = & x_{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6f\right) & \text{Mg} \\ \mathbf{B}_{3} & = & -x_{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6f\right) & \text{Mg} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} & \left(6f\right) & \text{Mg} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} & \left(6f\right) & \text{Mg} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(6f\right) & \text{Mg} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{2}-x_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(6f\right) & \text{Mg} \\ \mathbf{B}_{8} & = & x_{3} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & x_{3}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} & \left(6g\right) & \text{Zn II} \\ \mathbf{B}_{9} & = & -x_{3} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & -x_{3}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} & \left(6g\right) & \text{Zn II} \\ \mathbf{B}_{10} & = & x_{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6g\right) & \text{Zn II} \\ \mathbf{B}_{11} & = & -x_{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6g\right) & \text{Zn II} \\ \mathbf{B}_{12} & = & \frac{1}{2} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{z}} & \left(6g\right) & \text{Zn II} \\ \mathbf{B}_{13} & = & \frac{1}{2} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{z}} & \left(6g\right) & \text{Zn II} \\ \mathbf{B}_{14} & = & x_{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6h\right) & \text{Zn III} \\ \mathbf{B}_{15} & = & -x_{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6h\right) & \text{Zn III} \\ \mathbf{B}_{16} & = & \frac{1}{2} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6h\right) & \text{Zn III} \\ \mathbf{B}_{17} & = & \frac{1}{2} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6h\right) & \text{Zn III} \\ \mathbf{B}_{18} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(6h\right) & \text{Zn III} \\ \mathbf{B}_{19} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(6h\right) & \text{Zn III} \\ \mathbf{B}_{20} & = & 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(8i\right) & \text{Zn IV} \\ \mathbf{B}_{21} & = & -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(8i\right) & \text{Zn IV} \\ \mathbf{B}_{22} & = & -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(8i\right) & \text{Zn IV} \\ \mathbf{B}_{23} & = & 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(8i\right) & \text{Zn IV} \\ \mathbf{B}_{24} & = & -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(8i\right) & \text{Zn IV} \\ \mathbf{B}_{25} & = & 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(8i\right) & \text{Zn IV} \\ \mathbf{B}_{26} & = & 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(8i\right) & \text{Zn IV} \\ \mathbf{B}_{27} & = & -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(8i\right) & \text{Zn IV} \\ \mathbf{B}_{28} & = & y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & y_{6}a \, \mathbf{\hat{y}} + z_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \text{Zn V} \\ \mathbf{B}_{29} & = & -y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & -y_{6}a \, \mathbf{\hat{y}} + z_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \text{Zn V} \\ \mathbf{B}_{30} & = & y_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & y_{6}a \, \mathbf{\hat{y}}-z_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \text{Zn V} \\ \mathbf{B}_{31} & = & -y_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & -y_{6}a \, \mathbf{\hat{y}}-z_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \text{Zn V} \\ \mathbf{B}_{32} & = & z_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{3} & = & z_{6}a \, \mathbf{\hat{x}} + y_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \text{Zn V} \\ \mathbf{B}_{33} & = & z_{6} \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{3} & = & z_{6}a \, \mathbf{\hat{x}}-y_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \text{Zn V} \\ \mathbf{B}_{34} & = & -z_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{3} & = & -z_{6}a \, \mathbf{\hat{x}} + y_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \text{Zn V} \\ \mathbf{B}_{35} & = & -z_{6} \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{3} & = & -z_{6}a \, \mathbf{\hat{x}}-y_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \text{Zn V} \\ \mathbf{B}_{36} & = & y_{6} \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} & = & y_{6}a \, \mathbf{\hat{x}} + z_{6}a \, \mathbf{\hat{y}} & \left(12j\right) & \text{Zn V} \\ \mathbf{B}_{37} & = & -y_{6} \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} & = & -y_{6}a \, \mathbf{\hat{x}} + z_{6}a \, \mathbf{\hat{y}} & \left(12j\right) & \text{Zn V} \\ \mathbf{B}_{38} & = & y_{6} \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2} & = & y_{6}a \, \mathbf{\hat{x}}-z_{6}a \, \mathbf{\hat{y}} & \left(12j\right) & \text{Zn V} \\ \mathbf{B}_{39} & = & -y_{6} \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2} & = & -y_{6}a \, \mathbf{\hat{x}}-z_{6}a \, \mathbf{\hat{y}} & \left(12j\right) & \text{Zn V} \\ \end{array} \]