AFLOW Prototype: A7B6_hR13_166_ah_3c
Prototype | : | Fe7W6 |
AFLOW prototype label | : | A7B6_hR13_166_ah_3c |
Strukturbericht designation | : | $D8_{5}$ |
Pearson symbol | : | hR13 |
Space group number | : | 166 |
Space group symbol | : | $\text{R}\bar{3}\text{m}$ |
AFLOW prototype command | : | aflow --proto=A7B6_hR13_166_ah_3c [--hex] --params=$a$,$c/a$,$x_{2}$,$x_{3}$,$x_{4}$,$x_{5}$,$z_{5}$ |
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(1a\right) & \text{Fe I} \\ \mathbf{B}_{2} & =&x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& =&x_{2} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \text{W I} \\ \mathbf{B}_{3} & =&- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& =&- x_{2} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \text{W I} \\ \mathbf{B}_{4} & =&x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}+ x_{3} \, \mathbf{a}_{3}& =&x_{3} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \text{W II} \\ \mathbf{B}_{5} & =&- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}& =&- x_{3} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \text{W II} \\ \mathbf{B}_{6} & =&x_{4} \, \mathbf{a}_{1}+ x_{4} \, \mathbf{a}_{2}+ x_{4} \, \mathbf{a}_{3}& =&x_{4} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \text{W III} \\ \mathbf{B}_{7} & =&- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}& =&- x_{4} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \text{W III} \\ \mathbf{B}_{8} & =&x_{5} \, \mathbf{a}_{1}+ x_{5} \, \mathbf{a}_{2}+ z_{5} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{5} - z_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \left(x_{5} - z_{5}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(2 x_{5} + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \text{Fe II} \\ \mathbf{B}_{9} & =&z_{5} \, \mathbf{a}_{1}+ x_{5} \, \mathbf{a}_{2}+ x_{5} \, \mathbf{a}_{3}& =&\frac12 \, \left(z_{5} - x_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \left(x_{5} - z_{5}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(2 x_{5} + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \text{Fe II} \\ \mathbf{B}_{10} & =&x_{5} \, \mathbf{a}_{1}+ z_{5} \, \mathbf{a}_{2}+ x_{5} \, \mathbf{a}_{3}& =&\frac1{\sqrt3} \left(z_{5} - x_{5}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(2 x_{5} + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \text{Fe II} \\ \mathbf{B}_{11} & =&- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}& =&\frac12 \, \left(z_{5} - x_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \left(z_{5} - x_{5}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(2 x_{5} + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \text{Fe II} \\ \mathbf{B}_{12} & =&- z_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{5} - z_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \left(z_{5} - x_{5}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(2 x_{5} + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \text{Fe II} \\ \mathbf{B}_{13} & =&- x_{5} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}& =&\frac1{\sqrt3} \left(x_{5} - z_{5}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(2 x_{5} + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \text{Fe II} \\ \end{array} \]