AFLOW Prototype: A3B_tI16_139_cde_e
Prototype | : | Al3Zr |
AFLOW prototype label | : | A3B_tI16_139_cde_e |
Strukturbericht designation | : | $D0_{23}$ |
Pearson symbol | : | tI16 |
Space group number | : | 139 |
Space group symbol | : | $\text{I4/mmm}$ |
AFLOW prototype command | : | aflow --proto=A3B_tI16_139_cde_e --params=$a$,$c/a$,$z_{3}$,$z_{4}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & =&\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{y}}& \left(4c\right) & \text{Al I} \\ \mathbf{B}_{2} & =&\frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}& \left(4c\right) & \text{Al I} \\ \mathbf{B}_{3} & =&\frac34 \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \text{Al II} \\ \mathbf{B}_{4} & =&\frac14 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \text{Al II} \\ \mathbf{B}_{5} & =&z_{3} \, \mathbf{a}_{1}+ z_{3} \, \mathbf{a}_{2}& =&+ z_{3} \, c \, \mathbf{\hat{z}}& \left(4e\right) & \text{Al III} \\ \mathbf{B}_{6} & =&- z_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}& =&- z_{3} \, c \, \mathbf{\hat{z}}& \left(4e\right) & \text{Al III} \\ \mathbf{B}_{7} & =&z_{4} \, \mathbf{a}_{1}+ z_{4} \, \mathbf{a}_{2}& =&+ z_{4} \, c \, \mathbf{\hat{z}}& \left(4e\right) & \text{Zr} \\ \mathbf{B}_{8} & =&- z_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}& =&- z_{4} \, c \, \mathbf{\hat{z}}& \left(4e\right) & \text{Zr} \\ \end{array} \]