AFLOW Prototype: AB3_mC16_12_g_ij
Prototype | : | AlCl3 |
AFLOW prototype label | : | AB3_mC16_12_g_ij |
Strukturbericht designation | : | None |
Pearson symbol | : | mC16 |
Space group number | : | 12 |
Space group symbol | : | $\text{C2/m}$ |
AFLOW prototype command | : | aflow --proto=AB3_mC16_12_g_ij --params=$a$,$b/a$,$c/a$,$\beta$,$y_{1}$,$x_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & =& - y_{1} \, \mathbf{a}_{1} + y_{1} \, \mathbf{a}_{2}& =& y_{1} \, b \, \mathbf{\hat{y}}& \left(4g\right) & \text{Al} \\ \mathbf{B}_{2} & =& y_{1} \, \mathbf{a}_{1} - y_{1} \, \mathbf{a}_{2}& =& - y_{1} \, b \, \mathbf{\hat{y}}& \left(4g\right) & \text{Al} \\ \mathbf{B}_{3} & =& x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3}& =& \left(x_{2} \, a + z_{2} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ z_{2} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4i\right) & \text{Cl I} \\ \mathbf{B}_{4} & =& - x_{2} \, \mathbf{a}_{1} - x_{2} \, \mathbf{a}_{2} - z_{2} \, \mathbf{a}_{3}& =& - \left(x_{2} \, a + z_2 \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- z_2 \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4i\right) & \text{Cl I} \\ \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(8j\right) & \text{Cl II} \\ \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(8j\right) & \text{Cl II} \\ \mathbf{B}_{7} & =& \left(y_{3} - x_{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(8j\right) & \text{Cl II} \\ \mathbf{B}_{8} & =& \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(8j\right) & \text{Cl II} \\ \end{array} \]