Model of Austenite Structure (cP32): AB27CD3_cP32_221_a_dij_b_c

Picture of Structure; Click for Big Picture
Prototype : CrFe27MoNi3
AFLOW prototype label : AB27CD3_cP32_221_a_dij_b_c
Strukturbericht designation : None
Pearson symbol : cP32
Space group number : 221
Space group symbol : $\mbox{Pm}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=AB27CD3_cP32_221_a_dij_b_c
--params=
$a$,$y_{5}$,$y_{6}$


  • 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. Note that when $y_{5}=y_{6}=1/4$ all the atoms are on sites of an fcc lattice.

Simple Cubic primitive vectors:

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

Basis vectors:

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

References

Geometry files


Prototype Generator

aflow --proto=AB27CD3_cP32_221_a_dij_b_c --params=

Species:

Running:

Output: