$\gamma$–Brass (Cu5Zn8, $D8_{2}$) Structure: A5B8_cI52_217_ce_cg

Picture of Structure; Click for Big Picture
Prototype : Cu5Zn8
AFLOW prototype label : A5B8_cI52_217_ce_cg
Strukturbericht designation : $D8_{2}$
Pearson symbol : cI52
Space group number : 217
Space group symbol : $\mbox{I}\bar{4}\mbox{3m}$
AFLOW prototype command : aflow --proto=A5B8_cI52_217_ce_cg
--params=
$a$,$x_{1}$,$x_{2}$,$x_{3}$,$x_{4}$,$z_{4}$


Other compounds with this structure

  • CuxZn1–x, CuxCd1–x, FexZn1–x

  • $\gamma$–Brass comes in a variety of compositions. We use the data from (Gourdon, 2007) for Cu5.00Zn8.00. At this composition the authors state that the sites are fully occupied as given below.

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

References

  • O. Gourdon, D. Gout, D. J. Williams, T. Proffen, S. Hobbs, and G. J. Miller, Atomic Distributions in the gamma–Brass Structure of the Cu–Zn System: A Structural and Theoretical Study, Inorg. Chem. 46, 251–260 (2007), doi:10.1021/ic0616380.

Geometry files


Prototype Generator

aflow --proto=A5B8_cI52_217_ce_cg --params=

Species:

Running:

Output: