Cr23C6 ($D8_{4}$) Structure: A6B23_cF116_225_e_acfh

Picture of Structure; Click for Big Picture
Prototype : Cr23C6
AFLOW prototype label : A6B23_cF116_225_e_acfh
Strukturbericht designation : $D8_{4}$
Pearson symbol : cF116
Space group number : 225
Space group symbol : $\mbox{Fm}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=A6B23_cF116_225_e_acfh
--params=
$a$,$x_{3}$,$x_{4}$,$y_{5}$


Other compounds with this structure

  • The general structure of this compound is M23X6 where M=Fe, Cr, Ni, Mn, V, W, …, or combinations thereof, and X = C or B.

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(4a\right) & \mbox{Cr I} \\ \mathbf{B}_{2} & = &\frac14 \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cr II} \\ \mathbf{B}_{3} & = &\frac34 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac34 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \frac34 \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cr II} \\ \mathbf{B}_{4} & = &- x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}+ x_{3} \, \mathbf{a}_{3}& = &x_{3} \, a \, \mathbf{\hat{x}}& \left(24e\right) & \mbox{C} \\ \mathbf{B}_{5} & = &x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+ x_{3} \, \mathbf{a}_{3}& = &x_{3} \, a \, \mathbf{\hat{y}}& \left(24e\right) & \mbox{C} \\ \mathbf{B}_{6} & = &x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}& = &x_{3} \, a \, \mathbf{\hat{z}}& \left(24e\right) & \mbox{C} \\ \mathbf{B}_{7} & = &x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}& = &- x_{3} \, a \, \mathbf{\hat{x}}& \left(24e\right) & \mbox{C} \\ \mathbf{B}_{8} & = &- x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}& = &- x_{3} \, a \, \mathbf{\hat{y}}& \left(24e\right) & \mbox{C} \\ \mathbf{B}_{9} & = &- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+ x_{3} \, \mathbf{a}_{3}& = &- x_{3} \, a \, \mathbf{\hat{z}}& \left(24e\right) & \mbox{C} \\ \mathbf{B}_{10} & = &x_{4} \, \mathbf{a}_{1}+ x_{4} \, \mathbf{a}_{2}+ x_{4} \, \mathbf{a}_{3}& = &x_{4} \, a \, \mathbf{\hat{x}}+ x_{4} \, a \, \mathbf{\hat{y}}+ x_{4} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Cr III} \\ \mathbf{B}_{11} & = &x_{4} \, \mathbf{a}_{1}+ x_{4} \, \mathbf{a}_{2}- 3 \, x_{4} \, \mathbf{a}_{3}& = &- x_{4} \, a \, \mathbf{\hat{x}}- x_{4} \, a \, \mathbf{\hat{y}}+ x_{4} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Cr III} \\ \mathbf{B}_{12} & = &x_{4} \, \mathbf{a}_{1}- 3 \, x_{4} \, \mathbf{a}_{2}+ x_{4} \, \mathbf{a}_{3}& = &- x_{4} \, a \, \mathbf{\hat{x}}+ x_{4} \, a \, \mathbf{\hat{y}}- x_{4} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Cr III} \\ \mathbf{B}_{13} & = &- 3 \, x_{4} \, \mathbf{a}_{1}+ x_{4} \, \mathbf{a}_{2}+ x_{4} \, \mathbf{a}_{3}& = &x_{4} \, a \, \mathbf{\hat{x}}- x_{4} \, a \, \mathbf{\hat{y}}- x_{4} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Cr III} \\ \mathbf{B}_{14} & = &- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+ 3 \, x_{4} \, \mathbf{a}_{3}& = &x_{4} \, a \, \mathbf{\hat{x}}+ x_{4} \, a \, \mathbf{\hat{y}}- x_{4} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Cr III} \\ \mathbf{B}_{15} & = &- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}& = &- x_{4} \, a \, \mathbf{\hat{x}}- x_{4} \, a \, \mathbf{\hat{y}}- x_{4} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Cr III} \\ \mathbf{B}_{16} & = &- x_{4} \, \mathbf{a}_{1}+ 3 \, x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}& = &x_{4} \, a \, \mathbf{\hat{x}}- x_{4} \, a \, \mathbf{\hat{y}}+ x_{4} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Cr III} \\ \mathbf{B}_{17} & = &3 \, x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}& = &- x_{4} \, a \, \mathbf{\hat{x}}+ x_{4} \, a \, \mathbf{\hat{y}}+ x_{4} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Cr III} \\ \mathbf{B}_{18} & = &2 \, y_{5} \, \mathbf{a}_{1}& = &y_{5} \, a \, \mathbf{\hat{y}}+ y_{5} \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Cr IV} \\ \mathbf{B}_{19} & = &2 \, y_{5} \, \mathbf{a}_{2}- 2 \, y_{5} \, \mathbf{a}_{3}& = &- y_{5} \, a \, \mathbf{\hat{y}}+ y_{5} \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Cr IV} \\ \mathbf{B}_{20} & = &- 2 \, y_{5} \, \mathbf{a}_{2}+ 2 \, y_{5} \, \mathbf{a}_{3}& = &y_{5} \, a \, \mathbf{\hat{y}}- y_{5} \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Cr IV} \\ \mathbf{B}_{21} & = &- 2 \, y_{5} \, \mathbf{a}_{1}& = &- y_{5} \, a \, \mathbf{\hat{y}}- y_{5} \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Cr IV} \\ \mathbf{B}_{22} & = &2 \, y_{5} \, \mathbf{a}_{2}& = &y_{5} \, a \, \mathbf{\hat{x}}+ y_{5} \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Cr IV} \\ \mathbf{B}_{23} & = &- 2 \, y_{5} \, \mathbf{a}_{1}+ 2 \, y_{5} \, \mathbf{a}_{3}& = &y_{5} \, a \, \mathbf{\hat{x}}- y_{5} \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Cr IV} \\ \mathbf{B}_{24} & = &2 \, y_{5} \, \mathbf{a}_{1}- 2 \, y_{5} \, \mathbf{a}_{3}& = &- y_{5} \, a \, \mathbf{\hat{x}}+ y_{5} \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Cr IV} \\ \mathbf{B}_{25} & = &- 2 \, y_{5} \, \mathbf{a}_{2}& = &- y_{5} \, a \, \mathbf{\hat{x}}- y_{5} \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Cr IV} \\ \mathbf{B}_{26} & = &2 \, y_{5} \, \mathbf{a}_{3}& = &y_{5} \, a \, \mathbf{\hat{x}}+ y_{5} \, a \, \mathbf{\hat{y}}& \left(48h\right) & \mbox{Cr IV} \\ \mathbf{B}_{27} & = &2 \, y_{5} \, \mathbf{a}_{1}- 2 \, y_{5} \, \mathbf{a}_{2}& = &- y_{5} \, a \, \mathbf{\hat{x}}+ y_{5} \, a \, \mathbf{\hat{y}}& \left(48h\right) & \mbox{Cr IV} \\ \mathbf{B}_{28} & = &- 2 \, y_{5} \, \mathbf{a}_{1}+ 2 \, y_{5} \, \mathbf{a}_{2}& = &y_{5} \, a \, \mathbf{\hat{x}}- y_{5} \, a \, \mathbf{\hat{y}}& \left(48h\right) & \mbox{Cr IV} \\ \mathbf{B}_{29} & = &- 2 \, y_{5} \, \mathbf{a}_{3}& = &- y_{5} \, a \, \mathbf{\hat{x}}- y_{5} \, a \, \mathbf{\hat{y}}& \left(48h\right) & \mbox{Cr IV} \\ \end{array} \]

References

  • A. L. Bowman, G. P. Arnold, E. K. Storms, and N. G. Nereson, The crystal structure of Cr23C6, Acta Crystallogr. Sect. B Struct. Sci. 28, 3102–3103 (1972), doi:10.1107/S0567740872007526.

Geometry files


Prototype Generator

aflow --proto=A6B23_cF116_225_e_acfh --params=

Species:

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Output: