AFLOW Prototype: A2BC4_tI14_82_bc_a_g
Prototype | : | CdAl2S4 |
AFLOW prototype label | : | A2BC4_tI14_82_bc_a_g |
Strukturbericht designation | : | $E3$ |
Pearson symbol | : | tI14 |
Space group number | : | 82 |
Space group symbol | : | $\text{I}\bar{4}$ |
AFLOW prototype command | : | aflow --proto=A2BC4_tI14_82_bc_a_g --params=$a$,$c/a$,$x_{4}$,$y_{4}$,$z_{4}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B_1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(2a\right) & \text{Cd} \\ \mathbf{B_2} & =& \frac12 \, \mathbf{a}_{1} + \frac12 \, \mathbf{a}_{2}& = & \frac12 \, c \, \mathbf{\hat{z}} & \left(2b\right) & \text{Al I} \\ \mathbf{B_3} & =& \frac34 \, \mathbf{a}_{1} + \frac14 \, \mathbf{a}_{2} + \frac12 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{y}} + \frac14 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \text{Al II} \\ \mathbf{B}_{4} & =& \left(y_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(z_{4}+x_{4}\right) \, \mathbf{a}_{2} + \left(x_{4}+y_{4}\right) \, \mathbf{a}_{3}& =& x_{4} \, a \, \mathbf{\hat{x}} + y_{4} \, a \, \mathbf{\hat{y}} + z_{4} \, c \, \mathbf{\hat{z}}& \left(8g\right) & \text{S} \\ \mathbf{B_5} & =& \left(z_{4}-y_{4}\right) \, \mathbf{a}_{1} + \left(z_{4}-x_{4}\right) \, \mathbf{a}_{2} - \left(x_{4}+y_{4}\right) \, \mathbf{a}_{3}& =& - x_{4} \, a \, \mathbf{\hat{x}} - y_{4} \, a \, \mathbf{\hat{y}} + z_{4} \, c \, \mathbf{\hat{z}}& \left(8g\right) & \text{S} \\ \mathbf{B_6} & =& - \left(z_{4}+x_{4}\right) \, \mathbf{a}_{1} + \left(y_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(y_{4}-x_{4}\right) \, \mathbf{a}_{3}& =& y_{4} \, a \, \mathbf{\hat{x}} - x_{4} \, a \, \mathbf{\hat{y}} - z_{4} \, c \, \mathbf{\hat{z}}& \left(8g\right) & \text{S} \\ \mathbf{B_7} & =& \left(x_{4}-z_{4}\right) \, \mathbf{a}_{1} - \left(y_{4}+z_{4}\right) \, \mathbf{a}_{2} + \left(x_{4}-y_{4}\right) \, \mathbf{a}_{3}& =& - y_{4} \, a \, \mathbf{\hat{x}} + x_{4} \, a \, \mathbf{\hat{y}} - z_{4} \, c \, \mathbf{\hat{z}}& \left(8g\right) & \text{S} \\ \end{array} \]