AFLOW Prototype: A12B_tI26_139_fij_a
Prototype | : | Mn12Th |
AFLOW prototype label | : | A12B_tI26_139_fij_a |
Strukturbericht designation | : | $D2_{b}$ |
Pearson symbol | : | tI26 |
Space group number | : | 139 |
Space group symbol | : | $\text{I4/mmm}$ |
AFLOW prototype command | : | aflow --proto=A12B_tI26_139_fij_a --params=$a$,$c/a$,$x_{3}$,$x_{4}$ |
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{Th} \\ \mathbf{B}_{2} & =&\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(8f\right) & \text{Mn I} \\ \mathbf{B}_{3} & =&\frac12 \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(8f\right) & \text{Mn I} \\ \mathbf{B}_{4} & =&\frac12 \, \mathbf{a}_{1}& =&\frac34 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(8f\right) & \text{Mn I} \\ \mathbf{B}_{5} & =&\frac12 \, \mathbf{a}_{2}& =&\frac14 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(8f\right) & \text{Mn I} \\ \mathbf{B}_{6} & =&x_{3} \, \mathbf{a}_{2}+ x_{3} \, \mathbf{a}_{3}& =&x_{3} \, a \, \mathbf{\hat{x}}& \left(8i\right) & \text{Mn II} \\ \mathbf{B}_{7} & =&- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}& =&- x_{3} \, a \, \mathbf{\hat{x}}& \left(8i\right) & \text{Mn II} \\ \mathbf{B}_{8} & =&x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{3}& =&x_{3} \, a \, \mathbf{\hat{y}}& \left(8i\right) & \text{Mn II} \\ \mathbf{B}_{9} & =&- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{3}& =&- x_{3} \, a \, \mathbf{\hat{y}}& \left(8i\right) & \text{Mn II} \\ \mathbf{B}_{10} & =&\frac12 \, \mathbf{a}_{1}+ x_{4} \, \mathbf{a}_{2}+ \left(\frac12 + x_{4}\right) \, \mathbf{a}_{3}& =&x_{4} \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}& \left(8j\right) & \text{Mn III} \\ \mathbf{B}_{11} & =&\frac12 \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+ \left( \frac12 - x_{4} \right) \, \mathbf{a}_{3}& =&- x_{4} \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}& \left(8j\right) & \text{Mn III} \\ \mathbf{B}_{12} & =&x_{4} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left( \frac12 + x_{4} \right) \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ x_{4} \, a \, \mathbf{\hat{y}}& \left(8j\right) & \text{Mn III} \\ \mathbf{B}_{13} & =&- x_{4} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left( \frac12 - x_{4} \right) \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}- x_{4} \, a \, \mathbf{\hat{y}}& \left(8j\right) & \text{Mn III} \\ \end{array} \]