γ-Brass (Cu$_{5}$Zn$_{8}$, $D8_{2}$) Structure: A5B8_cI52_217_ce_cg-001
| Prototype | Cu$_{5}$Zn$_{8}$ |
| AFLOW prototype label | A5B8_cI52_217_ce_cg-001 |
| Strukturbericht designation | $D8_{2}$ |
| Mineral name | γ-brass |
| ICSD | 240667 |
| Pearson symbol | cI52 |
| Space group number | 217 |
| Space group symbol | $I\overline{4}3m$ |
| AFLOW prototype command |
aflow --proto=A5B8_cI52_217_ce_cg-001
--params=$a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak z_{4}$ |
Other compounds with this structure
Cu$_{x}$Zn$_{1-x}$, Cu$_{x}$Cd$_{1-x}$, Fe$_{x}$Zn$_{1-x}$
- $\gamma$-brass comes in a variety of compositions. See the $D8_{1}$ and $D8_{3}$ structure pages for more information.
- We use the data from (Gourdon, 2007) for Cu$_{5.00}$Zn$_{8.00}$. At this composition the authors state that the sites are fully occupied.
- (Mizutani, 2010) classifies this as a
I-cell
$\gamma$-brass.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $2 x_{1} \, \mathbf{a}_{1}+2 x_{1} \, \mathbf{a}_{2}+2 x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}+a x_{1} \,\mathbf{\hat{z}}$ | (8c) | Cu I |
| $\mathbf{B_{2}}$ | = | $- 2 x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}+a x_{1} \,\mathbf{\hat{z}}$ | (8c) | Cu I |
| $\mathbf{B_{3}}$ | = | $- 2 x_{1} \, \mathbf{a}_{2}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}- a x_{1} \,\mathbf{\hat{z}}$ | (8c) | Cu I |
| $\mathbf{B_{4}}$ | = | $- 2 x_{1} \, \mathbf{a}_{1}$ | = | $a x_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}- a x_{1} \,\mathbf{\hat{z}}$ | (8c) | Cu I |
| $\mathbf{B_{5}}$ | = | $2 x_{2} \, \mathbf{a}_{1}+2 x_{2} \, \mathbf{a}_{2}+2 x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Zn I |
| $\mathbf{B_{6}}$ | = | $- 2 x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Zn I |
| $\mathbf{B_{7}}$ | = | $- 2 x_{2} \, \mathbf{a}_{2}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Zn I |
| $\mathbf{B_{8}}$ | = | $- 2 x_{2} \, \mathbf{a}_{1}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Zn I |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}$ | (12e) | Cu II |
| $\mathbf{B_{10}}$ | = | $- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}$ | (12e) | Cu II |
| $\mathbf{B_{11}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{y}}$ | (12e) | Cu II |
| $\mathbf{B_{12}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{y}}$ | (12e) | Cu II |
| $\mathbf{B_{13}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}$ | = | $a x_{3} \,\mathbf{\hat{z}}$ | (12e) | Cu II |
| $\mathbf{B_{14}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{z}}$ | (12e) | Cu II |
| $\mathbf{B_{15}}$ | = | $\left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+2 x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (24g) | Zn II |
| $\mathbf{B_{16}}$ | = | $- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- 2 x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (24g) | Zn II |
| $\mathbf{B_{17}}$ | = | $\left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (24g) | Zn II |
| $\mathbf{B_{18}}$ | = | $- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (24g) | Zn II |
| $\mathbf{B_{19}}$ | = | $2 x_{4} \, \mathbf{a}_{1}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (24g) | Zn II |
| $\mathbf{B_{20}}$ | = | $- 2 x_{4} \, \mathbf{a}_{1}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (24g) | Zn II |
| $\mathbf{B_{21}}$ | = | $\left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (24g) | Zn II |
| $\mathbf{B_{22}}$ | = | $- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (24g) | Zn II |
| $\mathbf{B_{23}}$ | = | $\left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+2 x_{4} \, \mathbf{a}_{2}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (24g) | Zn II |
| $\mathbf{B_{24}}$ | = | $- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- 2 x_{4} \, \mathbf{a}_{2}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (24g) | Zn II |
| $\mathbf{B_{25}}$ | = | $- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (24g) | Zn II |
| $\mathbf{B_{26}}$ | = | $\left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (24g) | Zn II |
References
- O. Gourdon, D. Gout, D. J. Williams, T. Proffen, S. Hobbs, and G. J. Miller, Atomic Distributions in the γ-Brass Structure of the Cu-Zn System: A Structural and Theoretical Study}, Inorg. Chem. 46, 251–260 (2007), doi:10.1021/ic0616380. \bibitem{Mizutani_Hume-Rothery_2010U. Mizutani, Hume-Rothery Rules for Structurally Complex Alloy Phases} (CRC Press, Boca Raton, London, New York, 2010).\bibAnnoteFile{Mizutani_Hume-Rothery_2010
Prototype Generator
aflow --proto=A5B8_cI52_217_ce_cg --params=$a,x_{1},x_{2},x_{3},x_{4},z_{4}$