Fe3W3C ($E9_{3}$) Structure: AB3C3_cF112_227_c_de_f

Picture of Structure; Click for Big Picture
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 : $\mbox{Fd}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=AB3C3_cF112_227_c_de_f
--params=
$a$,$x_{3}$,$x_{4}$


  • Experimentally, the (48f) site is a random mixture of composition W2/3Fe1/3. We use W for this site in the pictures above.

Face-centered Cubic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{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) & \mbox{C} \\ \mathbf{B}_{2} & = &\frac12 \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}& \left(16c\right) & \mbox{C} \\ \mathbf{B}_{3} & = &\frac12 \mathbf{a}_{2}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{C} \\ \mathbf{B}_{4} & = &\frac12 \mathbf{a}_{1}& = &\frac14 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{W} \\ \end{array} \]

References

  • Q.–B. Yang and S. Andersson, Application of coincidence site lattices for crystal structure description. Part I: Sigma = 3, Acta Crystallogr. Sect. B Struct. Sci. 43, 1–14 (1987), doi:10.1107/S0108768187098380.

Geometry files


Prototype Generator

aflow --proto=AB3C3_cF112_227_c_de_f --params=

Species:

Running:

Output: