AFLOW Prototype: AB3_hR8_155_c_de
Prototype | : | AlF3 |
AFLOW prototype label | : | AB3_hR8_155_c_de |
Strukturbericht designation | : | $D0_{14}$ |
Pearson symbol | : | hR8 |
Space group number | : | 155 |
Space group symbol | : | $\text{R32}$ |
AFLOW prototype command | : | aflow --proto=AB3_hR8_155_c_de [--hex] --params=$a$,$c/a$,$x_{1}$,$y_{2}$,$y_{3}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = &x_{1} \, \mathbf{a}_{1}+ x_{1} \, \mathbf{a}_{2}+ x_{1} \, \mathbf{a}_{3}& = &x_{1} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \text{Al} \\ \mathbf{B}_{2} & = &- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}& = &- x_{1} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \text{Al} \\ \mathbf{B}_{3} & = &y_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}& = &\frac12 \, y_{2} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}2 \, y_{2} \, a \, \mathbf{\hat{y}}& \left(3d\right) & \text{F I} \\ \mathbf{B}_{4} & = &- y_{2} \, \mathbf{a}_{1}+ y_{2} \, \mathbf{a}_{3}& = &- y_{2} \, a \, \mathbf{\hat{x}}& \left(3d\right) & \text{F I} \\ \mathbf{B}_{5} & = &y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}& = &\frac12 \, y_{2} \, a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}2 \, y_{2} \, a \, \mathbf{\hat{y}}& \left(3d\right) & \text{F I} \\ \mathbf{B}_{6} & = &\frac12 \, \mathbf{a}_{1}+ y_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}& = &\frac14 \, \left(2 \, y_{3} + 1\right) \, a \, \mathbf{\hat{x}}+ \frac1{4 \sqrt{3}} \, \left(6 \, y_{3} - 1\right) \, a \, \mathbf{\hat{y}}+ \frac16 \, c \, \mathbf{\hat{z}}& \left(3e\right) & \text{F II} \\ \mathbf{B}_{7} & = &- y_{3} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ y_{3} \, \mathbf{a}_{3}& = &- y_{3} \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac16 \, c \, \mathbf{\hat{z}}& \left(3e\right) & \text{F II} \\ \mathbf{B}_{8} & = &y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac14 \, \left(2 \, y_{3} - 1\right) \, a \, \mathbf{\hat{x}}- \frac1{4\sqrt{3}} \, \left(6 \, y_{3} + 1\right) \, a \, \mathbf{\hat{y}}+ \frac16 \, c \, \mathbf{\hat{z}}& \left(3e\right) & \text{F II} \\ \end{array} \]