AFLOW Prototype: A_cI58_217_ac2g
Prototype | : | $\alpha$–Mn |
AFLOW prototype label | : | A_cI58_217_ac2g |
Strukturbericht designation | : | $A12$ |
Pearson symbol | : | cI58 |
Space group number | : | 217 |
Space group symbol | : | $\text{I}\bar{4}\text{3m}$ |
AFLOW prototype command | : | aflow --proto=A_cI58_217_ac2g --params=$a$,$x_{2}$,$x_{3}$,$z_{3}$,$x_{4}$,$z_{4}$ |
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{Mn I} \\ \mathbf{B}_{2} & = &2 x_{2} \, \mathbf{a}_{1}+ 2 x_{2} \, \mathbf{a}_{2}+ 2 x_{2} \, \mathbf{a}_{3}& = &x_{2} \, \, a \, \mathbf{\hat{x}}+ x_{2} \, \, a \, \mathbf{\hat{y}}+ x_{2} \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \text{Mn II} \\ \mathbf{B}_{3} & = &- 2 x_{2} \, \mathbf{a}_{3}& = &- x_{2} \, \, a \, \mathbf{\hat{x}}- x_{2} \, \, a \, \mathbf{\hat{y}}+ x_{2} \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \text{Mn II} \\ \mathbf{B}_{4} & = &- 2 x_{2} \, \mathbf{a}_{2}& = &- x_{2} \, \, a \, \mathbf{\hat{x}}+ x_{2} \, \, a \, \mathbf{\hat{y}}- x_{2} \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \text{Mn II} \\ \mathbf{B}_{5} & = &- 2 x_{2} \, \mathbf{a}_{1}& = &x_{2} \, \, a \, \mathbf{\hat{x}}- x_{2} \, \, a \, \mathbf{\hat{y}}- x_{2} \, \, a \, \mathbf{\hat{z}}& \left(8c\right) & \text{Mn II} \\ \mathbf{B}_{6} & = &\left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+ \left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+ 2 x_{3} \, \mathbf{a}_{3}& = &x_{3} \, \, a \, \mathbf{\hat{x}}+ x_{3} \, \, a \, \mathbf{\hat{y}}+ z_{3} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn III} \\ \mathbf{B}_{7} & = &\left(z_{3} - x_{3}\right) \, \mathbf{a}_{1}+ \left(z_{3} - x_{3}\right) \, \mathbf{a}_{2}- 2 x_{3} \, \mathbf{a}_{3}& = &- x_{3} \, \, a \, \mathbf{\hat{x}}- x_{3} \, \, a \, \mathbf{\hat{y}}+ z_{3} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn III} \\ \mathbf{B}_{8} & = &\left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}& = &- x_{3} \, \, a \, \mathbf{\hat{x}}+ x_{3} \, \, a \, \mathbf{\hat{y}}- z_{3} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn III} \\ \mathbf{B}_{9} & = &- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+ \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}& = &x_{3} \, \, a \, \mathbf{\hat{x}}- x_{3} \, \, a \, \mathbf{\hat{y}}- z_{3} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn III} \\ \mathbf{B}_{10} & = &2 x_{3} \, \mathbf{a}_{1}+ \left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+ \left(x_{3} + z_{3}\right) \, \mathbf{a}_{3}& = &z_{3} \, \, a \, \mathbf{\hat{x}}+ x_{3} \, \, a \, \mathbf{\hat{y}}+ x_{3} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn III} \\ \mathbf{B}_{11} & = &- 2 x_{3} \, \mathbf{a}_{1}+ \left(z_{3} - x_{3}\right) \, \mathbf{a}_{2}+ \left(z_{3} - x_{3}\right) \, \mathbf{a}_{3}& = &z_{3} \, \, a \, \mathbf{\hat{x}}- x_{3} \, \, a \, \mathbf{\hat{y}}- x_{3} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn III} \\ \mathbf{B}_{12} & = &\left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{3}& = &- z_{3} \, \, a \, \mathbf{\hat{x}}- x_{3} \, \, a \, \mathbf{\hat{y}}+ x_{3} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn III} \\ \mathbf{B}_{13} & = &- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+ \left(x_{3} - z_{3}\right) \, \mathbf{a}_{3}& = &- z_{3} \, \, a \, \mathbf{\hat{x}}+ x_{3} \, \, a \, \mathbf{\hat{y}}- x_{3} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn III} \\ \mathbf{B}_{14} & = &\left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+ 2 x_{3} \, \mathbf{a}_{2}+ \left(x_{3} + z_{3}\right) \, \mathbf{a}_{3}& = &x_{3} \, \, a \, \mathbf{\hat{x}}+ z_{3} \, \, a \, \mathbf{\hat{y}}+ x_{3} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn III} \\ \mathbf{B}_{15} & = &\left(z_{3} - x_{3}\right) \, \mathbf{a}_{1}- 2 x_{3} \, \mathbf{a}_{2}+ \left(z_{3} - x_{3}\right) \, \mathbf{a}_{3}& = &- x_{3} \, \, a \, \mathbf{\hat{x}}+ z_{3} \, \, a \, \mathbf{\hat{y}}- x_{3} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn III} \\ \mathbf{B}_{16} & = &- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+ \left(x_{3} - z_{3}\right) \, \mathbf{a}_{3}& = &x_{3} \, \, a \, \mathbf{\hat{x}}- z_{3} \, \, a \, \mathbf{\hat{y}}- x_{3} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn III} \\ \mathbf{B}_{17} & = &\left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{3}& = &- x_{3} \, \, a \, \mathbf{\hat{x}}- z_{3} \, \, a \, \mathbf{\hat{y}}+ x_{3} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn III} \\ \mathbf{B}_{18} & = &\left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+ \left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+ 2 x_{4} \, \mathbf{a}_{3}& = &x_{4} \, \, a \, \mathbf{\hat{x}}+ x_{4} \, \, a \, \mathbf{\hat{y}}+ z_{4} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn IV} \\ \mathbf{B}_{19} & = &\left(z_{4} - x_{4}\right) \, \mathbf{a}_{1}+ \left(z_{4} - x_{4}\right) \, \mathbf{a}_{2}- 2 x_{4} \, \mathbf{a}_{3}& = &- x_{4} \, \, a \, \mathbf{\hat{x}}- x_{4} \, \, a \, \mathbf{\hat{y}}+ z_{4} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn IV} \\ \mathbf{B}_{20} & = &\left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}& = &- x_{4} \, \, a \, \mathbf{\hat{x}}+ x_{4} \, \, a \, \mathbf{\hat{y}}- z_{4} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn IV} \\ \mathbf{B}_{21} & = &- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+ \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}& = &x_{4} \, \, a \, \mathbf{\hat{x}}- x_{4} \, \, a \, \mathbf{\hat{y}}- z_{4} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn IV} \\ \mathbf{B}_{22} & = &2 x_{4} \, \mathbf{a}_{1}+ \left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+ \left(x_{4} + z_{4}\right) \, \mathbf{a}_{3}& = &z_{4} \, \, a \, \mathbf{\hat{x}}+ x_{4} \, \, a \, \mathbf{\hat{y}}+ x_{4} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn IV} \\ \mathbf{B}_{23} & = &- 2 x_{4} \, \mathbf{a}_{1}+ \left(z_{4} - x_{4}\right) \, \mathbf{a}_{2}+ \left(z_{4} - x_{4}\right) \, \mathbf{a}_{3}& = &z_{4} \, \, a \, \mathbf{\hat{x}}- x_{4} \, \, a \, \mathbf{\hat{y}}- x_{4} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn IV} \\ \mathbf{B}_{24} & = &\left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{3}& = &- z_{4} \, \, a \, \mathbf{\hat{x}}- x_{4} \, \, a \, \mathbf{\hat{y}}+ x_{4} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn IV} \\ \mathbf{B}_{25} & = &- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+ \left(x_{4} - z_{4}\right) \, \mathbf{a}_{3}& = &- z_{4} \, \, a \, \mathbf{\hat{x}}+ x_{4} \, \, a \, \mathbf{\hat{y}}- x_{4} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn IV} \\ \mathbf{B}_{26} & = &\left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+ 2 x_{4} \, \mathbf{a}_{2}+ \left(x_{4} + z_{4}\right) \, \mathbf{a}_{3}& = &x_{4} \, \, a \, \mathbf{\hat{x}}+ z_{4} \, \, a \, \mathbf{\hat{y}}+ x_{4} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn IV} \\ \mathbf{B}_{27} & = &\left(z_{4} - x_{4}\right) \, \mathbf{a}_{1}- 2 x_{4} \, \mathbf{a}_{2}+ \left(z_{4} - x_{4}\right) \, \mathbf{a}_{3}& = &- x_{4} \, \, a \, \mathbf{\hat{x}}+ z_{4} \, \, a \, \mathbf{\hat{y}}- x_{4} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn IV} \\ \mathbf{B}_{28} & = &- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+ \left(x_{4} - z_{4}\right) \, \mathbf{a}_{3}& = &x_{4} \, \, a \, \mathbf{\hat{x}}- z_{4} \, \, a \, \mathbf{\hat{y}}- x_{4} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn IV} \\ \mathbf{B}_{29} & = &\left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{3}& = &- x_{4} \, \, a \, \mathbf{\hat{x}}- z_{4} \, \, a \, \mathbf{\hat{y}}+ x_{4} \, \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Mn IV} \\ \end{array} \]