Mg$_{17}$Al$_{12}$ Structure: A12B17_cI58_217_g_acg-001
| Prototype | Al$_{12}$Mg$_{17}$ |
| AFLOW prototype label | A12B17_cI58_217_g_acg-001 |
| ICSD | 23607 |
| Pearson symbol | cI58 |
| Space group number | 217 |
| Space group symbol | $I\overline{4}3m$ |
| AFLOW prototype command |
aflow --proto=A12B17_cI58_217_g_acg-001
--params=$a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}$ |
- This is a binary form of $\alpha$–Mn ($A12$).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Mg I |
| $\mathbf{B_{2}}$ | = | $2 x_{2} \, \mathbf{a}_{1}+2 x_{2} \, \mathbf{a}_{2}+2 x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Mg II |
| $\mathbf{B_{3}}$ | = | $- 2 x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Mg II |
| $\mathbf{B_{4}}$ | = | $- 2 x_{2} \, \mathbf{a}_{2}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Mg II |
| $\mathbf{B_{5}}$ | = | $- 2 x_{2} \, \mathbf{a}_{1}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Mg II |
| $\mathbf{B_{6}}$ | = | $\left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+2 x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{7}}$ | = | $- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- 2 x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{8}}$ | = | $\left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{9}}$ | = | $- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{10}}$ | = | $2 x_{3} \, \mathbf{a}_{1}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{11}}$ | = | $- 2 x_{3} \, \mathbf{a}_{1}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{12}}$ | = | $\left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{13}}$ | = | $- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{14}}$ | = | $\left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+2 x_{3} \, \mathbf{a}_{2}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{15}}$ | = | $- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}- 2 x_{3} \, \mathbf{a}_{2}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{16}}$ | = | $- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{17}}$ | = | $\left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{18}}$ | = | $\left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+2 x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (24g) | Mg III |
| $\mathbf{B_{19}}$ | = | $- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- 2 x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (24g) | Mg III |
| $\mathbf{B_{20}}$ | = | $\left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (24g) | Mg III |
| $\mathbf{B_{21}}$ | = | $- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (24g) | Mg III |
| $\mathbf{B_{22}}$ | = | $2 x_{4} \, \mathbf{a}_{1}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (24g) | Mg III |
| $\mathbf{B_{23}}$ | = | $- 2 x_{4} \, \mathbf{a}_{1}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (24g) | Mg III |
| $\mathbf{B_{24}}$ | = | $\left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (24g) | Mg III |
| $\mathbf{B_{25}}$ | = | $- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (24g) | Mg III |
| $\mathbf{B_{26}}$ | = | $\left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+2 x_{4} \, \mathbf{a}_{2}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (24g) | Mg III |
| $\mathbf{B_{27}}$ | = | $- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- 2 x_{4} \, \mathbf{a}_{2}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (24g) | Mg III |
| $\mathbf{B_{28}}$ | = | $- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (24g) | Mg III |
| $\mathbf{B_{29}}$ | = | $\left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (24g) | Mg III |
References
- P. Schobinger-Papamantellos and P. Fischer, Neutronenbeugungsuntersuchung der Atomverteilung von Mg$_{17}$Al$_{12}$, Naturwissenschaften 57, 128–129 (1970), doi:10.1007/BF00600053.
Found in
- P. Villars, H. Okamoto, and K. Cenzual, eds., ASM Alloy Phase Diagram Database (ASM International, 2018), chap. Aluminum-Magnesium Binary Phase Diagram (1998 Okamoto H.). Copyright © 2006-2018 ASM International.
Prototype Generator
aflow --proto=A12B17_cI58_217_g_acg --params=$a,x_{2},x_{3},z_{3},x_{4},z_{4}$