Model of Austenite Structure (cF108): AB18C8_cF108_225_a_eh_f

Picture of Structure; Click for Big Picture
Prototype : CrFe18Ni8
AFLOW prototype label : AB18C8_cF108_225_a_eh_f
Strukturbericht designation : None
Pearson symbol : cF108
Space group number : 225
Space group symbol : $\mbox{Fm}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=AB18C8_cF108_225_a_eh_f
--params=
$a$,$x_{2}$,$x_{3}$,$y_{4}$


  • Austenitic steels are alloys of iron and other metals with an averaged face-centered cubic structure. If we set $x_{2}=1/3$, $x_{3}=2/3$, and $y_{4}=2/3$, the atoms are on the sites of an fcc lattice with lattice constant $a_{fcc}=1/3a$.

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

References

Geometry files


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aflow --proto=AB18C8_cF108_225_a_eh_f --params=

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