γ-brass (Fe$_{3}$Zn$_{10}$, $D8_{1}$) Structure: A3B10_cI52_229_e_fh-001
| Prototype | Fe$_{3}$Zn$_{10}$ |
| AFLOW prototype label | A3B10_cI52_229_e_fh-001 |
| Strukturbericht designation | $D8_{1}$ |
| Mineral name | brass |
| ICSD | none |
| Pearson symbol | cI52 |
| Space group number | 229 |
| Space group symbol | $Im\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A3B10_cI52_229_e_fh-001
--params=$a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak y_{3}$ |
- Adding another atom at the origin changes this to the $L2_{2}$ structure.
- The $D8_{1}$ structure is defined in (Pearson, 1958) quoting (Schramm, 1938). More recent investigations such as (Johansson, 1968), (Brandon, 1974) and (Yu, 2005) find that $\gamma$–Fe$_{3}$Zn$_{10}$ forms in the $D8_{2}$ structure, with Fe atoms on one (8c) site, Zn atoms on the other (8e) site and the (24g) sites, and a 50-50 alloy of Fe and Zn on the other (8e) site.
- We use Brandon's data, mapping (12g) $\rightarrow$ (12e), (24g) $\rightarrow$ (24h), and averaging the two (8e) sites to produce the (12e) coordinate here.
- (Mizutani, 2010) classifies this as an
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 | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}$ | (12e) | Fe I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}$ | (12e) | Fe I |
| $\mathbf{B_{3}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{y}}$ | (12e) | Fe I |
| $\mathbf{B_{4}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{y}}$ | (12e) | Fe I |
| $\mathbf{B_{5}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}$ | = | $a x_{1} \,\mathbf{\hat{z}}$ | (12e) | Fe I |
| $\mathbf{B_{6}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}$ | = | $- a x_{1} \,\mathbf{\hat{z}}$ | (12e) | Fe I |
| $\mathbf{B_{7}}$ | = | $2 x_{2} \, \mathbf{a}_{1}+2 x_{2} \, \mathbf{a}_{2}+2 x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (16f) | Zn I |
| $\mathbf{B_{8}}$ | = | $- 2 x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (16f) | Zn I |
| $\mathbf{B_{9}}$ | = | $- 2 x_{2} \, \mathbf{a}_{2}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (16f) | Zn I |
| $\mathbf{B_{10}}$ | = | $- 2 x_{2} \, \mathbf{a}_{1}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (16f) | Zn I |
| $\mathbf{B_{11}}$ | = | $2 x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (16f) | Zn I |
| $\mathbf{B_{12}}$ | = | $- 2 x_{2} \, \mathbf{a}_{1}- 2 x_{2} \, \mathbf{a}_{2}- 2 x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (16f) | Zn I |
| $\mathbf{B_{13}}$ | = | $2 x_{2} \, \mathbf{a}_{2}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (16f) | Zn I |
| $\mathbf{B_{14}}$ | = | $2 x_{2} \, \mathbf{a}_{1}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (16f) | Zn I |
| $\mathbf{B_{15}}$ | = | $2 y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (24h) | Zn II |
| $\mathbf{B_{16}}$ | = | $y_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (24h) | Zn II |
| $\mathbf{B_{17}}$ | = | $- y_{3} \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (24h) | Zn II |
| $\mathbf{B_{18}}$ | = | $- 2 y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (24h) | Zn II |
| $\mathbf{B_{19}}$ | = | $y_{3} \, \mathbf{a}_{1}+2 y_{3} \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{z}}$ | (24h) | Zn II |
| $\mathbf{B_{20}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{z}}$ | (24h) | Zn II |
| $\mathbf{B_{21}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{z}}$ | (24h) | Zn II |
| $\mathbf{B_{22}}$ | = | $- y_{3} \, \mathbf{a}_{1}- 2 y_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{z}}$ | (24h) | Zn II |
| $\mathbf{B_{23}}$ | = | $y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+2 y_{3} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}$ | (24h) | Zn II |
| $\mathbf{B_{24}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}$ | (24h) | Zn II |
| $\mathbf{B_{25}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}$ | (24h) | Zn II |
| $\mathbf{B_{26}}$ | = | $- y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- 2 y_{3} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}$ | (24h) | Zn II |
References
- J. Schramm, X-Ray Investigation of Phases and Phase Limits of the Zn Alloy Systems with Fe, Co and Ni, Z. Metallkd. 30, 122–130 (1938).
- A. Johansson, H. Ljung, and S. Westman, X-Ray and Neutron Diffraction Studies on Gamma-Ni,Zn and Gamma-Fe,Zn, Acta Chem. Scand. 22, 2743–2753 (1968), doi:10.3891/acta.chem.scand.22-2743.
- J. K. Brandon, R. Y. Brizard, P. C. Chieh, R. K. McMillan, and W. B. Pearson, New refinements of the γ-brass type structures Cu$_{5}$Zn$_{8}$, Cu$_{5}$Cd$_{8}$ and Fe$_{3}$Zn$_{10}$ 30, 1412–1417 (1974), doi:10.1107/S0567740874004997.
- J. Yu, J. Liu, J. Zhang, and J. Wu, Electron Diffraction Study on Fe–Zn Γ intermetallic Phase of a Galvannealed IF Steel Sheet, Mater. Trans. 46, 1079–1082 (2005).
- U. Mizutani, Hume-Rothery Rules for Structurally Complex Alloy Phases (CRC Press, Boca Raton, London, New York, 2010).
Found in
- W. B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, International Series of Monographs on Metal Physics and Physical Metallurgy, vol. 4 (Pergamon Press, Oxford, London, Edinburgh, New York, Paris, Frankfort, 1958), 1964 reprint with corrections edn.
Prototype Generator
aflow --proto=A3B10_cI52_229_e_fh --params=$a,x_{1},x_{2},y_{3}$