AFLOW Prototype: ABC2_aP16_1_4a_4a_8a
Prototype | : | AsKSe2 |
AFLOW prototype label | : | ABC2_aP16_1_4a_4a_8a |
Strukturbericht designation | : | None |
Pearson symbol | : | aP16 |
Space group number | : | 1 |
Space group symbol | : | $\text{P1}$ |
AFLOW prototype command | : | aflow --proto=ABC2_aP16_1_4a_4a_8a --params=$a$,$b/a$,$c/a$,$\alpha$,$\beta$,$\gamma$,$x_{1}$,$y_{1}$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$ y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$,$x_{8}$,$y_{8}$,$z_{8}$,$x_{9}$,$y_{9}$,$z_{9}$,$x_{10}$,$y_{10}$,$z_{10}$,$x_{11}$,$y_{11}$,$z_{11}$,$x_{12}$,$y_{12}$,$z_{12}$,$x_{13}$,$y_{13}$,$ z_{13}$,$x_{14}$,$y_{14}$,$z_{14}$,$x_{15}$,$y_{15}$,$z_{15}$,$x_{16}$,$y_{16}$,$z_{16}$ |
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(1a\right) & \text{As I} \\ \mathbf{B}_{2} & =& 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(1a\right) & \text{As II} \\ \mathbf{B}_{3} & =& 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(1a\right) & \text{As III} \\ \mathbf{B}_{4} & =& x_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3}& =& \left(x_{4} \, a + y_{4} \, b \, \cos\gamma \, + z_{4} \, c_x\right)\, \mathbf{\hat{x}}+ \left(y_{4} \, b \, \sin\gamma + z_{4} \, c_y\right) \, \mathbf{\hat{y}}+ z_{4} \, c_z \, \mathbf{\hat{z}}& \left(1a\right) & \text{As IV} \\ \mathbf{B}_{5} & =& x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3}& =& \left(x_{5} \, a + y_{5} \, b \, \cos\gamma \, + z_{5} \, c_x\right)\, \mathbf{\hat{x}}+ \left(y_{5} \, b \, \sin\gamma + z_{5} \, c_y\right) \, \mathbf{\hat{y}}+ z_{5} \, c_z \, \mathbf{\hat{z}}& \left(1a\right) & \text{K I} \\ \mathbf{B}_{6} & =& x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3}& =& \left(x_{6} \, a + y_{6} \, b \, \cos\gamma \, + z_{6} \, c_x\right)\, \mathbf{\hat{x}}+ \left(y_{6} \, b \, \sin\gamma + z_{6} \, c_y\right) \, \mathbf{\hat{y}}+ z_{6} \, c_z \, \mathbf{\hat{z}}& \left(1a\right) & \text{K II} \\ \mathbf{B}_{7} & =& x_{7} \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3}& =& \left(x_{7} \, a + y_{7} \, b \, \cos\gamma \, + z_{7} \, c_x\right)\, \mathbf{\hat{x}}+ \left(y_{7} \, b \, \sin\gamma + z_{7} \, c_y\right) \, \mathbf{\hat{y}}+ z_{7} \, c_z \, \mathbf{\hat{z}}& \left(1a\right) & \text{K III} \\ \mathbf{B}_{8} & =& x_{8} \, \mathbf{a}_{1} + y_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3}& =& \left(x_{8} \, a + y_{8} \, b \, \cos\gamma \, + z_{8} \, c_x\right)\, \mathbf{\hat{x}}+ \left(y_{8} \, b \, \sin\gamma + z_{8} \, c_y\right) \, \mathbf{\hat{y}}+ z_{8} \, c_z \, \mathbf{\hat{z}}& \left(1a\right) & \text{K IV} \\ \mathbf{B}_{9} & =& x_{9} \, \mathbf{a}_{1} + y_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3}& =& \left(x_{9} \, a + y_{9} \, b \, \cos\gamma \, + z_{9} \, c_x\right)\, \mathbf{\hat{x}}+ \left(y_{9} \, b \, \sin\gamma + z_{9} \, c_y\right) \, \mathbf{\hat{y}}+ z_{9} \, c_z \, \mathbf{\hat{z}}& \left(1a\right) & \text{Se I} \\ \mathbf{B}_{10} & =& x_{10} \, \mathbf{a}_{1} + y_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3}& =& \left(x_{10} \, a + y_{10} \, b \, \cos\gamma \, + z_{10} \, c_x\right)\, \mathbf{\hat{x}}+ \left(y_{10} \, b \, \sin\gamma + z_{10} \, c_y\right) \, \mathbf{\hat{y}}+ z_{10} \, c_z \, \mathbf{\hat{z}}& \left(1a\right) & \text{Se II} \\ \mathbf{B}_{11} & =& x_{11} \, \mathbf{a}_{1} + y_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3}& =& \left(x_{11} \, a + y_{11} \, b \, \cos\gamma \, + z_{11} \, c_x\right)\, \mathbf{\hat{x}}+ \left(y_{11} \, b \, \sin\gamma + z_{11} \, c_y\right) \, \mathbf{\hat{y}}+ z_{11} \, c_z \, \mathbf{\hat{z}}& \left(1a\right) & \text{Se III} \\ \mathbf{B}_{12} & =& x_{12} \, \mathbf{a}_{1} + y_{12} \, \mathbf{a}_{2} + z_{12} \, \mathbf{a}_{3}& =& \left(x_{12} \, a + y_{12} \, b \, \cos\gamma \, + z_{12} \, c_x\right)\, \mathbf{\hat{x}}+ \left(y_{12} \, b \, \sin\gamma + z_{12} \, c_y\right) \, \mathbf{\hat{y}}+ z_{12} \, c_z \, \mathbf{\hat{z}}& \left(1a\right) & \text{Se IV} \\ \mathbf{B}_{13} & =& x_{13} \, \mathbf{a}_{1} + y_{13} \, \mathbf{a}_{2} + z_{13} \, \mathbf{a}_{3}& =& \left(x_{13} \, a + y_{13} \, b \, \cos\gamma \, + z_{13} \, c_x\right)\, \mathbf{\hat{x}}+ \left(y_{13} \, b \, \sin\gamma + z_{13} \, c_y\right) \, \mathbf{\hat{y}}+ z_{13} \, c_z \, \mathbf{\hat{z}}& \left(1a\right) & \text{Se V} \\ \mathbf{B}_{14} & =& x_{14} \, \mathbf{a}_{1} + y_{14} \, \mathbf{a}_{2} + z_{14} \, \mathbf{a}_{3}& =& \left(x_{14} \, a + y_{14} \, b \, \cos\gamma \, + z_{14} \, c_x\right)\, \mathbf{\hat{x}}+ \left(y_{14} \, b \, \sin\gamma + z_{14} \, c_y\right) \, \mathbf{\hat{y}}+ z_{14} \, c_z \, \mathbf{\hat{z}}& \left(1a\right) & \text{Se VI} \\ \mathbf{B}_{15} & =& x_{15} \, \mathbf{a}_{1} + y_{15} \, \mathbf{a}_{2} + z_{15} \, \mathbf{a}_{3}& =& \left(x_{15} \, a + y_{15} \, b \, \cos\gamma \, + z_{15} \, c_x\right)\, \mathbf{\hat{x}}+ \left(y_{15} \, b \, \sin\gamma + z_{15} \, c_y\right) \, \mathbf{\hat{y}}+ z_{15} \, c_z \, \mathbf{\hat{z}}& \left(1a\right) & \text{Se VII} \\ \mathbf{B}_{16} & =& x_{16} \, \mathbf{a}_{1} + y_{16} \, \mathbf{a}_{2} + z_{16} \, \mathbf{a}_{3}& =& \left(x_{16} \, a + y_{16} \, b \, \cos\gamma \, + z_{16} \, c_x\right)\, \mathbf{\hat{x}}+ \left(y_{16} \, b \, \sin\gamma + z_{16} \, c_y\right) \, \mathbf{\hat{y}}+ z_{16} \, c_z \, \mathbf{\hat{z}}& \left(1a\right) & \text{Se VIII} \end{array} \]