π-FeMg$_{3}$Al$_{8}$Si$_{6}$ ($E9_{b}$) Structure: A8BC3D6_hP18_189_agh_b_f_i-001
| Prototype | Al$_{8}$FeMg$_{3}$Si$_{6}$ |
| AFLOW prototype label | A8BC3D6_hP18_189_agh_b_f_i-001 |
| Strukturbericht designation | $E9_{b}$ |
| ICSD | 21740 |
| Pearson symbol | hP18 |
| Space group number | 189 |
| Space group symbol | $P\overline{6}2m$ |
| AFLOW prototype command |
aflow --proto=A8BC3D6_hP18_189_agh_b_f_i-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}$ |
- We have been unable to obtain a copy of (Perlitz, 1942), and use the data provided by (Brandes, 1992) and (Foss, 2003). Foss et al. argue that the actual composition of this phase should be FeMg$_{3}$Al$_{9}$Si$_{5}$. This requires a reordering of the atomic positions, as described in A9BC3D5_hP18_189_fi_a_g_bh.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | Fe I |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}$ | = | $\frac{1}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}$ | (3f) | Mg I |
| $\mathbf{B_{4}}$ | = | $x_{3} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}$ | (3f) | Mg I |
| $\mathbf{B_{5}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}$ | (3f) | Mg I |
| $\mathbf{B_{6}}$ | = | $x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{4} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | Al II |
| $\mathbf{B_{7}}$ | = | $x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{4} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | Al II |
| $\mathbf{B_{8}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | Al II |
| $\mathbf{B_{9}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (4h) | Al III |
| $\mathbf{B_{10}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (4h) | Al III |
| $\mathbf{B_{11}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (4h) | Al III |
| $\mathbf{B_{12}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (4h) | Al III |
| $\mathbf{B_{13}}$ | = | $x_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{6} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (6i) | Si I |
| $\mathbf{B_{14}}$ | = | $x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (6i) | Si I |
| $\mathbf{B_{15}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+c z_{6} \,\mathbf{\hat{z}}$ | (6i) | Si I |
| $\mathbf{B_{16}}$ | = | $x_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{6} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (6i) | Si I |
| $\mathbf{B_{17}}$ | = | $x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (6i) | Si I |
| $\mathbf{B_{18}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- c z_{6} \,\mathbf{\hat{z}}$ | (6i) | Si I |
References
- H. Perlitz and A. Westgren, The Crystal Structure of Al$_{8}$Si$_{6}$Mg_{3}$Fe, Ark. Kemi Mineral. Geol. 15B, 1–8 (1942).
- E. A. Brandes and G. B. Brook, eds., Smithells Metals Reference Book (Butterworth Heinemann, Oxford, Auckland, Boston, Johannesburg, Melbourne, New Delhi, 1992), chap. 6, pp. 6–60, seventh edn.
Found in
- S. Foss, A. Olsen, C. J. Simensen, and J. Tafto, Determination of the crystal structure of the $\pi$-AlFeMgSi phase using symmetry- and site-sensitive electron microscope techniques, Acta Crystallogr. Sect. B 59, 36–42 (2003), doi:10.1107/S0108768102022887.
Prototype Generator
aflow --proto=A8BC3D6_hP18_189_agh_b_f_i --params=$a,c/a,x_{3},x_{4},z_{5},x_{6},z_{6}$