Model of Ferrite Structure (cF128): A9B16C7_cF128_225_acd_2f_be

Picture of Structure; Click for Big Picture
Prototype : Cr9Fe16Ni7
AFLOW prototype label : A9B16C7_cF128_225_acd_2f_be
Strukturbericht designation : None
Pearson symbol : cF128
Space group number : 225
Space group symbol : $\mbox{Fm}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=A9B16C7_cF128_225_acd_2f_be
--params=
$a$,$x_{5}$,$x_{6}$,$x_{7}$


  • Ferrite is steel with a bcc structure. This structure represents one possible ordering which might be found in an Fe–Ni–Cr steel. Note that it is not meant to represent a real steel. If we use the special values $x_{5} = 1/4$, $x_{6} = 1/8$, and $x_{7} = 3/8$, and replace the Ni atoms by Cr, then this structure reverts to CsCl (B2) with aB2 = 1/4 a$. If we replace both the Ni and Cr atoms by Fe, then the structure becomes bcc, again with $a_{bcc} = 1/4 a$.

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} & = &\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(4b\right) & \mbox{Ni I} \\ \mathbf{B}_{3} & = &\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}_{4} & = &\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}_{5} & = &\frac12 \, \mathbf{a}_{1}& = &\frac14 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(24d\right) & \mbox{Cr III} \\ \mathbf{B}_{6} & = &\frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(24d\right) & \mbox{Cr III} \\ \mathbf{B}_{7} & = &\frac12 \, \mathbf{a}_{2}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(24d\right) & \mbox{Cr III} \\ \mathbf{B}_{8} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(24d\right) & \mbox{Cr III} \\ \mathbf{B}_{9} & = &\frac12 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}& \left(24d\right) & \mbox{Cr III} \\ \mathbf{B}_{10} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(24d\right) & \mbox{Cr III} \\ \mathbf{B}_{11} & = &- x_{5} \, \mathbf{a}_{1}+ x_{5} \, \mathbf{a}_{2}+ x_{5} \, \mathbf{a}_{3}& = &x_{5} \, a \, \mathbf{\hat{x}}& \left(24e\right) & \mbox{Ni II} \\ \mathbf{B}_{12} & = &x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+ x_{5} \, \mathbf{a}_{3}& = &x_{5} \, a \, \mathbf{\hat{y}}& \left(24e\right) & \mbox{Ni II} \\ \mathbf{B}_{13} & = &x_{5} \, \mathbf{a}_{1}+ x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}& = &x_{5} \, a \, \mathbf{\hat{z}}& \left(24e\right) & \mbox{Ni II} \\ \mathbf{B}_{14} & = &x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}& = &- x_{5} \, a \, \mathbf{\hat{x}}& \left(24e\right) & \mbox{Ni II} \\ \mathbf{B}_{15} & = &- x_{5} \, \mathbf{a}_{1}+ x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}& = &- x_{5} \, a \, \mathbf{\hat{y}}& \left(24e\right) & \mbox{Ni II} \\ \mathbf{B}_{16} & = &- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+ x_{5} \, \mathbf{a}_{3}& = &- x_{5} \, a \, \mathbf{\hat{z}}& \left(24e\right) & \mbox{Ni II} \\ \mathbf{B}_{17} & = &x_{6} \, \mathbf{a}_{1}+ x_{6} \, \mathbf{a}_{2}+ x_{6} \, \mathbf{a}_{3}& = &x_{6} \, a \, \mathbf{\hat{x}}+ x_{6} \, a \, \mathbf{\hat{y}}+ x_{6} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Fe I} \\ \mathbf{B}_{18} & = &x_{6} \, \mathbf{a}_{1}+ x_{6} \, \mathbf{a}_{2}- 3 \, x_{6} \, \mathbf{a}_{3}& = &- x_{6} \, a \, \mathbf{\hat{x}}- x_{6} \, a \, \mathbf{\hat{y}}+ x_{6} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Fe I} \\ \mathbf{B}_{19} & = &x_{6} \, \mathbf{a}_{1}- 3 \, x_{6} \, \mathbf{a}_{2}+ x_{6} \, \mathbf{a}_{3}& = &- x_{6} \, a \, \mathbf{\hat{x}}+ x_{6} \, a \, \mathbf{\hat{y}}- x_{6} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Fe I} \\ \mathbf{B}_{20} & = &- 3 \, x_{6} \, \mathbf{a}_{1}+ x_{6} \, \mathbf{a}_{2}+ x_{6} \, \mathbf{a}_{3}& = &x_{6} \, a \, \mathbf{\hat{x}}- x_{6} \, a \, \mathbf{\hat{y}}- x_{6} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Fe I} \\ \mathbf{B}_{21} & = &- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+ 3 \, x_{6} \, \mathbf{a}_{3}& = &x_{6} \, a \, \mathbf{\hat{x}}+ x_{6} \, a \, \mathbf{\hat{y}}- x_{6} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Fe I} \\ \mathbf{B}_{22} & = &- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}& = &- x_{6} \, a \, \mathbf{\hat{x}}- x_{6} \, a \, \mathbf{\hat{y}}- x_{6} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Fe I} \\ \mathbf{B}_{23} & = &- x_{6} \, \mathbf{a}_{1}+ 3 \, x_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}& = &x_{6} \, a \, \mathbf{\hat{x}}- x_{6} \, a \, \mathbf{\hat{y}}+ x_{6} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Fe I} \\ \mathbf{B}_{24} & = &3 \, x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}& = &- x_{6} \, a \, \mathbf{\hat{x}}+ x_{6} \, a \, \mathbf{\hat{y}}+ x_{6} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Fe I} \\ \mathbf{B}_{25} & = &x_{7} \, \mathbf{a}_{1}+ x_{7} \, \mathbf{a}_{2}+ x_{7} \, \mathbf{a}_{3}& = &x_{7} \, a \, \mathbf{\hat{x}}+ x_{7} \, a \, \mathbf{\hat{y}}+ x_{7} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Fe II} \\ \mathbf{B}_{26} & = &x_{7} \, \mathbf{a}_{1}+ x_{7} \, \mathbf{a}_{2}- 3 \, x_{7} \, \mathbf{a}_{3}& = &- x_{7} \, a \, \mathbf{\hat{x}}- x_{7} \, a \, \mathbf{\hat{y}}+ x_{7} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Fe II} \\ \mathbf{B}_{27} & = &x_{7} \, \mathbf{a}_{1}- 3 \, x_{7} \, \mathbf{a}_{2}+ x_{7} \, \mathbf{a}_{3}& = &- x_{7} \, a \, \mathbf{\hat{x}}+ x_{7} \, a \, \mathbf{\hat{y}}- x_{7} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Fe II} \\ \mathbf{B}_{28} & = &- 3 \, x_{7} \, \mathbf{a}_{1}+ x_{7} \, \mathbf{a}_{2}+ x_{7} \, \mathbf{a}_{3}& = &x_{7} \, a \, \mathbf{\hat{x}}- x_{7} \, a \, \mathbf{\hat{y}}- x_{7} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Fe II} \\ \mathbf{B}_{29} & = &- x_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+ 3 \, x_{7} \, \mathbf{a}_{3}& = &x_{7} \, a \, \mathbf{\hat{x}}+ x_{7} \, a \, \mathbf{\hat{y}}- x_{7} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Fe II} \\ \mathbf{B}_{30} & = &- x_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}& = &- x_{7} \, a \, \mathbf{\hat{x}}- x_{7} \, a \, \mathbf{\hat{y}}- x_{7} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Fe II} \\ \mathbf{B}_{31} & = &- x_{7} \, \mathbf{a}_{1}+ 3 \, x_{7} \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}& = &x_{7} \, a \, \mathbf{\hat{x}}- x_{7} \, a \, \mathbf{\hat{y}}+ x_{7} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Fe II} \\ \mathbf{B}_{32} & = &3 \, x_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}& = &- x_{7} \, a \, \mathbf{\hat{x}}+ x_{7} \, a \, \mathbf{\hat{y}}+ x_{7} \, a \, \mathbf{\hat{z}}& \left(32f\right) & \mbox{Fe II} \\ \end{array} \]

References

Geometry files


Prototype Generator

aflow --proto=A9B16C7_cF128_225_acd_2f_be --params=

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