Model of Austenite Structure (cI32): AB12C3_cI32_229_a_h_b
| 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} \]