AFLOW Prototype: A_mC12_5_3c
Prototype | : | Po |
AFLOW prototype label | : | A_mC12_5_3c |
Strukturbericht designation | : | $A19$ |
Pearson symbol | : | mC12 |
Space group number | : | 5 |
Space group symbol | : | $\text{C2}$ |
AFLOW prototype command | : | aflow --proto=A_mC12_5_3c --params=$a$,$b/a$,$c/a$,$\beta$,$x_{1}$,$y_{1}$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & =&\left(x_{1} - y_{1}\right) \, \mathbf{a}_{1}+ \left(x_{1} + y_{1}\right) \, \mathbf{a}_{2}+ z_{1} \, \mathbf{a}_{3}& =&\left(x_{1} \, a + z_{1} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{1} \, b \, \mathbf{\hat{y}}+ z_{1} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4c\right) & \text{Po I} \\ \mathbf{B}_{2} & =&- \left(x_{1} + y_{1}\right) \, \mathbf{a}_{1}+ \left(y_{1} - x_{1}\right) \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}& =&- \left(x_{1} \, a + z_{1} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{1} \, b \, \mathbf{\hat{y}}- z_{1} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4c\right) & \text{Po I} \\ \mathbf{B}_{3} & =&\left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}+ \left(x_{2} + y_{2}\right) \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& =&\left(x_{2} \, a + z_{2} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{2} \, b \, \mathbf{\hat{y}}+ z_{2} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4c\right) & \text{Po II} \\ \mathbf{B}_{4} & =&- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{1}+ \left(y_{2} - x_{2}\right) \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& =&- \left(x_{2} \, a + z_{2} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{2} \, b \, \mathbf{\hat{y}}- z_{2} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4c\right) & \text{Po II} \\ \mathbf{B}_{5} & =&\left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}+ \left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& =&\left(x_{3} \, a + z_{3} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{3} \, b \, \mathbf{\hat{y}}+ z_{3} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4c\right) & \text{Po III} \\ \mathbf{B}_{6} & =&- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}+ \left(y_{3} - x_{3}\right) \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& =&- \left(x_{3} \, a + z_{3} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{3} \, b \, \mathbf{\hat{y}}- z_{3} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4c\right) & \text{Po III} \\ \end{array} \]