AFLOW Prototype: AB4_oC20_41_a_2b
Prototype | : | PtSn4 |
AFLOW prototype label | : | AB4_oC20_41_a_2b |
Strukturbericht designation | : | $D1_{c}$ |
Pearson symbol | : | oC20 |
Space group number | : | 41 |
Space group symbol | : | $\text{Aba2}$ |
AFLOW prototype command | : | aflow --proto=AB4_oC20_41_a_2b --params=$a$,$b/a$,$c/a$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & =& - z_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3}& =& z_{1} \, c \, \mathbf{\hat{z}}& \left(4a\right) & \text{Pt} \\ \mathbf{B}_{2} & =& \frac12 \, \mathbf{a}_{1} + \left(\frac12 - z_{1}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{1}\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}} + z_{1} \, c \, \mathbf{\hat{z}}& \left(4a\right) & \text{Pt} \\ \mathbf{B}_{3} & =& x_{2} \, \mathbf{a}_{1} + \left(y_{2} - z_{2}\right) \, \mathbf{a}_{2} + \left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}& =& x_{2} \, a \, \mathbf{\hat{x}} + y_{2} \, b \, \mathbf{\hat{y}} + z_{2} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{Sn I} \\ \mathbf{B}_{4} & =& - x_{2} \, \mathbf{a}_{1} - \left(y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(z_{2} - y_{2}\right) \, \mathbf{a}_{3}& =& - x_{2} \, a \, \mathbf{\hat{x}} - y_{2} \, b \, \mathbf{\hat{y}} + z_{2} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{Sn I} \\ \mathbf{B}_{5} & =& \left(\frac12 + x_{2}\right) \, \mathbf{a}_{1} +\left(\frac12 - y_{2} - z_{2}\right) \,\mathbf{a}_{2} + \left(\frac12 - y_{2} + z_{2}\right) \, \mathbf{a}_{3}& =& \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{x}} + \left(\frac12 - y_{2}\right) \, b \, \mathbf{\hat{y}} + z_{2} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{Sn I} \\ \mathbf{B}_{6} & =& \left(\frac12 - x_{2}\right) \, \mathbf{a}_{1} +\left(\frac12 + y_{2} - z_{2}\right) \,\mathbf{a}_{2} + \left(\frac12 + y_{2} + z_{2}\right) \, \mathbf{a}_{3}& =& \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{x}} + \left(\frac12 + y_{2}\right) \, b \, \mathbf{\hat{y}} + z_{2} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{Sn I} \\ \mathbf{B}_{7} & =& x_{3} \, \mathbf{a}_{1} + \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}& =& x_{3} \, a \, \mathbf{\hat{x}} + y_{3} \, b \, \mathbf{\hat{y}} + z_{3} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{Sn II} \\ \mathbf{B}_{8} & =& - x_{3} \, \mathbf{a}_{1} - \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(z_{3} - y_{3}\right) \, \mathbf{a}_{3}& =& - x_{3} \, a \, \mathbf{\hat{x}} - y_{3} \, b \, \mathbf{\hat{y}} + z_{3} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{Sn II} \\ \mathbf{B}_{9} & =& \left(\frac12 + x_{3}\right) \, \mathbf{a}_{1} +\left(\frac12 - y_{3} - z_{3}\right) \,\mathbf{a}_{2} + \left(\frac12 - y_{3} + z_{3}\right) \, \mathbf{a}_{3}& =& \left(\frac12 + x_{3}\right) \, a \, \mathbf{\hat{x}} + \left(\frac12 - y_{3}\right) \, b \, \mathbf{\hat{y}} + z_{3} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{Sn II} \\ \mathbf{B}_{10} & =& \left(\frac12 - x_{3}\right) \, \mathbf{a}_{1} +\left(\frac12 + y_{3} - z_{3}\right) \,\mathbf{a}_{2} + \left(\frac12 + y_{3} + z_{3}\right) \, \mathbf{a}_{3}& =& \left(\frac12 - x_{3}\right) \, a \, \mathbf{\hat{x}} + \left(\frac12 + y_{3}\right) \, b \, \mathbf{\hat{y}} + z_{3} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{Sn II} \\ \end{array} \]