Model of Austenite Structure (cP32): AB27CD3_cP32_221_a_dij_b_c-001
| Prototype | CrFe$_{27}$MoNi$_{3}$ |
| AFLOW prototype label | AB27CD3_cP32_221_a_dij_b_c-001 |
| ICSD | none |
| Pearson symbol | cP32 |
| Space group number | 221 |
| Space group symbol | $Pm\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=AB27CD3_cP32_221_a_dij_b_c-001
--params=$a, \allowbreak y_{5}, \allowbreak y_{6}$ |
- Austenitic steels are alloys of iron and other metals with an averaged face-centered cubic structure. This model represents one approximation for an austenite steel. It is not meant to represent a real steel, and the selection of atom types for each Wyckoff position is arbitrary. When $y_{5}=y_{6}=1/4$ all the atoms are on sites of a bcc lattice.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Cr I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (1b) | Mo I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (3c) | Ni I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (3c) | Ni I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (3c) | Ni I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}$ | (3d) | Fe I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}$ | (3d) | Fe I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{z}}$ | (3d) | Fe I |
| $\mathbf{B_{9}}$ | = | $y_{5} \, \mathbf{a}_{2}+y_{5} \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (12i) | Fe II |
| $\mathbf{B_{10}}$ | = | $- y_{5} \, \mathbf{a}_{2}+y_{5} \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (12i) | Fe II |
| $\mathbf{B_{11}}$ | = | $y_{5} \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (12i) | Fe II |
| $\mathbf{B_{12}}$ | = | $- y_{5} \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (12i) | Fe II |
| $\mathbf{B_{13}}$ | = | $y_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{z}}$ | (12i) | Fe II |
| $\mathbf{B_{14}}$ | = | $y_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{z}}$ | (12i) | Fe II |
| $\mathbf{B_{15}}$ | = | $- y_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{z}}$ | (12i) | Fe II |
| $\mathbf{B_{16}}$ | = | $- y_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{z}}$ | (12i) | Fe II |
| $\mathbf{B_{17}}$ | = | $y_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}$ | (12i) | Fe II |
| $\mathbf{B_{18}}$ | = | $- y_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}$ | (12i) | Fe II |
| $\mathbf{B_{19}}$ | = | $y_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}$ | (12i) | Fe II |
| $\mathbf{B_{20}}$ | = | $- y_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}$ | (12i) | Fe II |
| $\mathbf{B_{21}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ | (12j) | Fe III |
| $\mathbf{B_{22}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ | (12j) | Fe III |
| $\mathbf{B_{23}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ | (12j) | Fe III |
| $\mathbf{B_{24}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ | (12j) | Fe III |
| $\mathbf{B_{25}}$ | = | $y_{6} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ | (12j) | Fe III |
| $\mathbf{B_{26}}$ | = | $y_{6} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ | (12j) | Fe III |
| $\mathbf{B_{27}}$ | = | $- y_{6} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ | (12j) | Fe III |
| $\mathbf{B_{28}}$ | = | $- y_{6} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ | (12j) | Fe III |
| $\mathbf{B_{29}}$ | = | $y_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12j) | Fe III |
| $\mathbf{B_{30}}$ | = | $- y_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12j) | Fe III |
| $\mathbf{B_{31}}$ | = | $y_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12j) | Fe III |
| $\mathbf{B_{32}}$ | = | $- y_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12j) | Fe III |
References
- M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. Hart, and S. Curtarolo, The AFLOW library of crystallographic prototypes: part 1, Comput. Mater. Sci. 136, S1–S828 (2017), doi:10.1016/j.commatsci.2017.01.017.
Prototype Generator
aflow --proto=AB27CD3_cP32_221_a_dij_b_c --params=$a,y_{5},y_{6}$