AFLOW Prototype: A3B_oP8_59_bf_a
Prototype | : | $\beta$–TiCu3 |
AFLOW prototype label | : | A3B_oP8_59_bf_a |
Strukturbericht designation | : | $D0_{a}$ |
Pearson symbol | : | oP8 |
Space group number | : | 59 |
Space group symbol | : | $\text{Pmmn}$ |
AFLOW prototype command | : | aflow --proto=A3B_oP8_59_bf_a --params=$a$,$b/a$,$c/a$,$z_{1}$,$z_{2}$,$x_{3}$,$z_{3}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & =&\frac14 \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ z_{1} \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{1} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \text{Ti} \\ \mathbf{B}_{2} & =&\frac34 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}& =&\frac34 \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{1} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \text{Ti} \\ \mathbf{B}_{3} & =&\frac14 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}+ z_{2} \, c \, \mathbf{\hat{z}}& \left(2b\right) & \text{Cu I} \\ \mathbf{B}_{4} & =&\frac34 \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& =&\frac34 \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}- z_{2} \, c \, \mathbf{\hat{z}}& \left(2b\right) & \text{Cu I} \\ \mathbf{B}_{5} & =&x_{3} \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& =&x_{3} \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \text{Cu II} \\ \mathbf{B}_{6} & =&\left(\frac12 - x_{3}\right) \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& =&\left(\frac12 - x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \text{Cu II} \\ \mathbf{B}_{7} & =&- x_{3} \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& =&- x_{3} \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \text{Cu II} \\ \mathbf{B}_{8} & =&\left(\frac12 + x_{3}\right) \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& =&\left(\frac12 + x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \text{Cu II} \\ \end{array} \]