AFLOW Prototype: A2B_aP6_2_2i_i
Prototype | : | P2I4 |
AFLOW prototype label | : | A2B_aP6_2_2i_i |
Strukturbericht designation | : | None |
Pearson symbol | : | aP6 |
Space group number | : | 2 |
Space group symbol | : | $\text{P}\bar{1}$ |
AFLOW prototype command | : | aflow --proto=A2B_aP6_2_2i_i --params=$a$,$b/a$,$c/a$,$\alpha$,$\beta$,$\gamma$,$x_{1}$,$y_{1}$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & =& x_{1} \, \mathbf{a}_{1} + y_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3}& =& \left(x_{1} \, a + y_{1} \, b \, \cos\gamma \, + z_{1} \, c_x\right)\, \mathbf{\hat{x}}+ \left(y_{1} \, b \, \sin\gamma + z_{1} \, c_y\right) \, \mathbf{\hat{y}}+ z_{1} \, c_z \, \mathbf{\hat{z}}& \left(2i\right) & \text{I I} \\ \mathbf{B}_{2} & =& - x_{1} \, \mathbf{a}_{1} - y_{1} \, \mathbf{a}_{2} - z_{1} \, \mathbf{a}_{3}& =& - \left(x_{1} \, a + y_{1} \, b \, \cos\gamma \, + z_{1} \, c_x\right)\, \mathbf{\hat{x}}- \left(y_{1} \, b \, \sin\gamma + z_{1} \, c_y\right) \, \mathbf{\hat{y}}- z_{1} \, c_z \, \mathbf{\hat{z}}& \left(2i\right) & \text{I I} \\ \mathbf{B}_{3} & =& x_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3}& =& \left(x_{2} \, a + y_{2} \, b \, \cos\gamma \, + z_{2} \, c_x\right)\, \mathbf{\hat{x}}+ \left(y_{2} \, b \, \sin\gamma + z_{2} \, c_y\right) \, \mathbf{\hat{y}}+ z_{2} \, c_z \, \mathbf{\hat{z}}& \left(2i\right) & \text{I II} \\ \mathbf{B}_{4} & =& - x_{2} \, \mathbf{a}_{1} - y_{2} \, \mathbf{a}_{2} - z_{2} \, \mathbf{a}_{3}& =& - \left(x_{2} \, a + y_{2} \, b \, \cos\gamma \, + z_{2} \, c_x\right)\, \mathbf{\hat{x}}- \left(y_{2} \, b \, \sin\gamma + z_{2} \, c_y\right) \, \mathbf{\hat{y}}- z_{2} \, c_z \, \mathbf{\hat{z}}& \left(2i\right) & \text{I II} \\ \mathbf{B}_{5} & =& x_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3}& =& \left(x_{3} \, a + y_{3} \, b \, \cos\gamma \, + z_{3} \, c_x\right)\, \mathbf{\hat{x}}+ \left(y_{3} \, b \, \sin\gamma + z_{3} \, c_y\right) \, \mathbf{\hat{y}}+ z_{3} \, c_z \, \mathbf{\hat{z}}& \left(2i\right) & \text{P} \\ \mathbf{B}_{6} & =& - x_{3} \, \mathbf{a}_{1} - y_{3} \, \mathbf{a}_{2} - z_{3} \, \mathbf{a}_{3}& =& - \left(x_{3} \, a + y_{3} \, b \, \cos\gamma \, + z_{3} \, c_x\right)\, \mathbf{\hat{x}}- \left(y_{3} \, b \, \sin\gamma + z_{3} \, c_y\right) \, \mathbf{\hat{y}}- z_{3} \, c_z \, \mathbf{\hat{z}}& \left(2i\right) & \text{P} \\ \end{array} \]