AFLOW Prototype: AB3C3_cF112_227_c_de_f
Prototype | : | Fe3W3C |
AFLOW prototype label | : | AB3C3_cF112_227_c_de_f |
Strukturbericht designation | : | $E9_{3}$ |
Pearson symbol | : | cF112 |
Space group number | : | 227 |
Space group symbol | : | $\text{Fd}\bar{3}\text{m}$ |
AFLOW prototype command | : | aflow --proto=AB3C3_cF112_227_c_de_f --params=$a$,$x_{3}$,$x_{4}$ |
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(16c\right) & \text{C} \\ \mathbf{B}_{2} & = &\frac12 \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}& \left(16c\right) & \text{C} \\ \mathbf{B}_{3} & = &\frac12 \mathbf{a}_{2}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16c\right) & \text{C} \\ \mathbf{B}_{4} & = &\frac12 \mathbf{a}_{1}& = &\frac14 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16c\right) & \text{C} \\ \mathbf{B}_{5} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(16d\right) & \text{Fe I} \\ \mathbf{B}_{6} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(16d\right) & \text{Fe I} \\ \mathbf{B}_{7} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16d\right) & \text{Fe I} \\ \mathbf{B}_{8} & = &\frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16d\right) & \text{Fe I} \\ \mathbf{B}_{9} & = &x_{3} \mathbf{a}_{1}+ x_{3} \mathbf{a}_{2}+ x_{3} \mathbf{a}_{3}& = &x_{3} \, a \, \mathbf{\hat{x}}+ x_{3} \, a \, \mathbf{\hat{y}}+ x_{3} \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{Fe II} \\ \mathbf{B}_{10} & = &x_{3} \mathbf{a}_{1}+ x_{3} \mathbf{a}_{2}+ \left(\frac12 - 3 \, x_{3}\right) \mathbf{a}_{3}& = &\left(\frac14 - x_{3}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac14 - x_{3}\right) \, a \, \mathbf{\hat{y}}+ x_{3} \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{Fe II} \\ \mathbf{B}_{11} & = &x_{3} \mathbf{a}_{1}+ \left(\frac12 - 3 \, x_{3}\right) \mathbf{a}_{2}+ x_{3} \mathbf{a}_{3}& = &\left(\frac14 - x_{3}\right) \, a \, \mathbf{\hat{x}}+ x_{3} \, a \, \mathbf{\hat{y}}+ \left(\frac14 - x_{3}\right) \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{Fe II} \\ \mathbf{B}_{12} & = &\left(\frac12 - 3 \, x_{3}\right) \mathbf{a}_{1}+ x_{3} \mathbf{a}_{2}+ x_{3} \mathbf{a}_{3}& = &x_{3} \, a \, \mathbf{\hat{x}}+ \left(\frac14 - x_{3}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 - x_{3}\right) \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{Fe II} \\ \mathbf{B}_{13} & = &- x_{3} \mathbf{a}_{1}- x_{3} \mathbf{a}_{2}+ \left(\frac12 + 3 \, x_{3}\right) \mathbf{a}_{3}& = &\left(\frac14 + x_{3}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac14 + x_{3}\right) \, a \, \mathbf{\hat{y}}- x_{3} \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{Fe II} \\ \mathbf{B}_{14} & = &- x_{3} \mathbf{a}_{1}- x_{3} \mathbf{a}_{2}- x_{3} \mathbf{a}_{3}& = &- x_{3} \, a \, \mathbf{\hat{x}}- x_{3} \, a \, \mathbf{\hat{y}}- x_{3} \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{Fe II} \\ \mathbf{B}_{15} & = &- x_{3} \mathbf{a}_{1}+ \left(\frac12 + 3 \, x_{3}\right) \mathbf{a}_{2}- x_{3} \mathbf{a}_{3}& = &\left(\frac14 + x_{3}\right) \, a \, \mathbf{\hat{x}}- x_{3} \, a \, \mathbf{\hat{y}}+ \left(\frac14 + x_{3}\right) \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{Fe II} \\ \mathbf{B}_{16} & = &\left(\frac12 + 3 \, x_{3}\right) \mathbf{a}_{1}- x_{3} \mathbf{a}_{2}- x_{3} \mathbf{a}_{3}& = &- x_{3} \, a \, \mathbf{\hat{x}}+ \left(\frac14 + x_{3}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 + x_{3}\right) \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{Fe II} \\ \mathbf{B}_{17} & = &\left(\frac14 - x_{4}\right) \mathbf{a}_{1}+ x_{4} \mathbf{a}_{2}+ x_{4} \mathbf{a}_{3}& = &x_{4} \, a \, \mathbf{\hat{x}}+ \frac18 \, a \, \mathbf{\hat{y}}+ \frac18 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{W} \\ \mathbf{B}_{18} & = &x_{4} \mathbf{a}_{1}+ \left(\frac14 - x_{4}\right) \mathbf{a}_{2}+ \left(\frac14 - x_{4}\right) \mathbf{a}_{3}& = &\left(\frac14 - x_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac18 \, a \, \mathbf{\hat{y}}+ \frac18 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{W} \\ \mathbf{B}_{19} & = &x_{4} \mathbf{a}_{1}+ \left(\frac14 - x_{4}\right) \mathbf{a}_{2}+ x_{4} \mathbf{a}_{3}& = &\frac18 \, a \, \mathbf{\hat{x}}+ x_{4} \, a \, \mathbf{\hat{y}}+ \frac18 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{W} \\ \mathbf{B}_{20} & = &\left(\frac14 - x_{4}\right) \mathbf{a}_{1}+ x_{4} \mathbf{a}_{2}+ \left(\frac14 - x_{4}\right) \mathbf{a}_{3}& = &\frac18 \, a \, \mathbf{\hat{x}}+ \left(\frac14 - x_{4}\right) \, a \, \mathbf{\hat{y}}+ \frac18 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{W} \\ \mathbf{B}_{21} & = &x_{4} \mathbf{a}_{1}+ x_{4} \mathbf{a}_{2}+ \left(\frac14 - x_{4}\right) \mathbf{a}_{3}& = &\frac18 \, a \, \mathbf{\hat{x}}+ \frac18 \, a \, \mathbf{\hat{y}}+ x_{4} \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{W} \\ \mathbf{B}_{22} & = &\left(\frac14 - x_{4}\right) \mathbf{a}_{1}+ \left(\frac14 - x_{4}\right) \mathbf{a}_{2}+ x_{4} \mathbf{a}_{3}& = &\frac18 \, a \, \mathbf{\hat{x}}+ \frac18 \, a \, \mathbf{\hat{y}}+ \left(\frac14 - x_{4}\right) \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{W} \\ \mathbf{B}_{23} & = &\left(x_{4} + \frac34\right) \mathbf{a}_{1}- x_{4} \mathbf{a}_{2}+ \left(x_{4} + \frac34\right) \mathbf{a}_{3}& = &\frac38 \, a \, \mathbf{\hat{x}}+ \left(x_{4} + \frac34\right) \, a \, \mathbf{\hat{y}}+ \frac38 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{W} \\ \mathbf{B}_{24} & = &- x_{4} \mathbf{a}_{1}+ \left(x_{4} + \frac34\right) \mathbf{a}_{2}- x_{4} \mathbf{a}_{3}& = &\frac38 \, a \, \mathbf{\hat{x}}- x_{4} \, a \, \mathbf{\hat{y}}+ \frac38 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{W} \\ \mathbf{B}_{25} & = &- x_{4} \mathbf{a}_{1}+ \left(x_{4} + \frac34\right) \mathbf{a}_{2}+ \left(x_{4} + \frac34\right) \mathbf{a}_{3}& = &\left(x_{4} + \frac34\right) \, a \, \mathbf{\hat{x}}+ \frac38 \, a \, \mathbf{\hat{y}}+ \frac38 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{W} \\ \mathbf{B}_{26} & = &\left(x_{4} + \frac34\right) \mathbf{a}_{1}- x_{4} \mathbf{a}_{2}- x_{4} \mathbf{a}_{3}& = &- x_{4} \, a \, \mathbf{\hat{x}}+ \frac38 \, a \, \mathbf{\hat{y}}+ \frac38 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{W} \\ \mathbf{B}_{27} & = &- x_{4} \mathbf{a}_{1}- x_{4} \mathbf{a}_{2}+ \left(x_{4} + \frac34\right) \mathbf{a}_{3}& = &\frac38 \, a \, \mathbf{\hat{x}}+ \frac38 \, a \, \mathbf{\hat{y}}- x_{4} \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{W} \\ \mathbf{B}_{28} & = &+ \left(x_{4} + \frac34\right) \mathbf{a}_{1}+ \left(x_{4} + \frac34\right) \mathbf{a}_{2}- x_{4} \mathbf{a}_{3}& = &\frac38 \, a \, \mathbf{\hat{x}}+ \frac38 \, a \, \mathbf{\hat{y}}+ \left(x_{4} + \frac34\right) \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{W} \\ \end{array} \]