Model of Austenite Structure (cI32): AB12C3_cI32_229_a_h_b

Picture of Structure; Click for Big Picture
Prototype : CrFe12Ni3
AFLOW prototype label : AB12C3_cI32_229_a_h_b
Strukturbericht designation : None
Pearson symbol : cI32
Space group number : 229
Space group symbol : $\mbox{Im}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=AB12C3_cI32_229_a_h_b
--params=
$a$,$y_{3}$


  • Austenitic steels are alloys of iron and other metals with an averaged face-centered cubic structure. This model is not meant to represent a real steel, and the selection of atom types for each Wyckoff position is arbitrary. If we set the $y_{3}=1/4$ then the atoms are on the sites of an fcc lattice.

Body-centered Cubic primitive vectors:

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

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(2a\right) & \mbox{Cr} \\ \mathbf{B}_{2} & = &\frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}& \left(6b\right) & \mbox{Ni} \\ \mathbf{B}_{3} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{y}}& \left(6b\right) & \mbox{Ni} \\ \mathbf{B}_{4} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& = &\frac12 \, a \, \mathbf{\hat{z}}& \left(6b\right) & \mbox{Ni} \\ \mathbf{B}_{5} & = &2 y_{3} \, \mathbf{a}_{1}+ y_{3} \, \mathbf{a}_{2}+ y_{3} \, \mathbf{a}_{3}& = &y_{3} \, a \, \mathbf{\hat{y}}+ y_{3} \, a \, \mathbf{\hat{z}}& \left(24h\right) & \mbox{Fe} \\ \mathbf{B}_{6} & = &y_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}& = &- y_{3} \, a \, \mathbf{\hat{y}}+ y_{3} \, a \, \mathbf{\hat{z}}& \left(24h\right) & \mbox{Fe} \\ \mathbf{B}_{7} & = &- y_{3} \, \mathbf{a}_{2}+ y_{3} \, \mathbf{a}_{3}& = &y_{3} \, a \, \mathbf{\hat{y}}- y_{3} \, a \, \mathbf{\hat{z}}& \left(24h\right) & \mbox{Fe} \\ \mathbf{B}_{8} & = &- 2 y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}& = &- y_{3} \, a \, \mathbf{\hat{y}}- y_{3} \, a \, \mathbf{\hat{z}}& \left(24h\right) & \mbox{Fe} \\ \mathbf{B}_{9} & = &y_{3} \, \mathbf{a}_{1}+ 2 y_{3} \, \mathbf{a}_{2}+ y_{3} \, \mathbf{a}_{3}& = &y_{3} \, a \, \mathbf{\hat{x}}+ y_{3} \, a \, \mathbf{\hat{z}}& \left(24h\right) & \mbox{Fe} \\ \mathbf{B}_{10} & = &- y_{3} \, \mathbf{a}_{1}+ y_{3} \, \mathbf{a}_{3}& = &y_{3} \, a \, \mathbf{\hat{x}}- y_{3} \, a \, \mathbf{\hat{z}}& \left(24h\right) & \mbox{Fe} \\ \mathbf{B}_{11} & = &y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{3}& = &- y_{3} \, a \, \mathbf{\hat{x}}+ y_{3} \, a \, \mathbf{\hat{z}}& \left(24h\right) & \mbox{Fe} \\ \mathbf{B}_{12} & = &- y_{3} \, \mathbf{a}_{1}- 2 y_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}& = &- y_{3} \, a \, \mathbf{\hat{x}}- y_{3} \, a \, \mathbf{\hat{z}}& \left(24h\right) & \mbox{Fe} \\ \mathbf{B}_{13} & = &y_{3} \, \mathbf{a}_{1}+ y_{3} \, \mathbf{a}_{2}+ 2 y_{3} \, \mathbf{a}_{3}& = &y_{3} \, a \, \mathbf{\hat{x}}+ y_{3} \, a \, \mathbf{\hat{y}}& \left(24h\right) & \mbox{Fe} \\ \mathbf{B}_{14} & = &y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}& = &- y_{3} \, a \, \mathbf{\hat{x}}+ y_{3} \, a \, \mathbf{\hat{y}}& \left(24h\right) & \mbox{Fe} \\ \mathbf{B}_{15} & = &- y_{3} \, \mathbf{a}_{1}+ y_{3} \, \mathbf{a}_{2}& = &y_{3} \, a \, \mathbf{\hat{x}}- y_{3} \, a \, \mathbf{\hat{y}}& \left(24h\right) & \mbox{Fe} \\ \mathbf{B}_{16} & = &- y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- 2 y_{3} \, \mathbf{a}_{3}& = &- y_{3} \, a \, \mathbf{\hat{x}}- y_{3} \, a \, \mathbf{\hat{y}}& \left(24h\right) & \mbox{Fe} \\ \end{array} \]

References

Geometry files


Prototype Generator

aflow --proto=AB12C3_cI32_229_a_h_b --params=

Species:

Running:

Output: