AFLOW Prototype: AB4C_tI12_82_c_g_a
Prototype | : | BPO4 |
AFLOW prototype label | : | AB4C_tI12_82_c_g_a |
Strukturbericht designation | : | $H0_{7}$ |
Pearson symbol | : | tI12 |
Space group number | : | 82 |
Space group symbol | : | $\text{I}\bar{4}$ |
AFLOW prototype command | : | aflow --proto=AB4C_tI12_82_c_g_a --params=$a$,$c/a$,$x_{3}$,$y_{3}$,$z_{3}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B_1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(2a\right) & \text{P} \\ \mathbf{B_2} & =& \frac34 \, \mathbf{a}_{1} + \frac14 \, \mathbf{a}_{2} + \frac12 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{y}} + \frac14 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \text{B} \\ \mathbf{B_3} & =& \left(y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(z_{3}+x_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}+y_{3}\right) \, \mathbf{a}_{3}& =& x_{3} \, a \, \mathbf{\hat{x}} + y_{3} \, a \, \mathbf{\hat{y}} + z_{3} \, c \, \mathbf{\hat{z}}& \left(8g\right) & \text{O} \\ \mathbf{B_4} & =& \left(z_{3}-y_{3}\right) \, \mathbf{a}_{1} + \left(z_{3}-x_{3}\right) \, \mathbf{a}_{2} - \left(x_{3}+y_{3}\right) \, \mathbf{a}_{3}& =& - x_{3} \, a \, \mathbf{\hat{x}} - y_{3} \, a \, \mathbf{\hat{y}} + z_{3} \, c \, \mathbf{\hat{z}}& \left(8g\right) & \text{O} \\ \mathbf{B_5} & =& - \left(z_{3}+x_{3}\right) \, \mathbf{a}_{1} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3}-x_{3}\right) \, \mathbf{a}_{3}& =& y_{3} \, a \, \mathbf{\hat{x}} -x_{3} \, a \, \mathbf{\hat{y}} - z_{3} \, c \, \mathbf{\hat{z}}& \left(8g\right) & \text{O} \\ \mathbf{B_6} & =& \left(x_{3}-z_{3}\right) \, \mathbf{a}_{1} - \left(y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}-y_{3}\right) \, \mathbf{a}_{3}& =& - y_{3} \, a \, \mathbf{\hat{x}} + x_{3} \, a \, \mathbf{\hat{y}} - z_{3} \, c \, \mathbf{\hat{z}}& \left(8g\right) & \text{O} \\ \end{array} \]