Al$_{12}$W Structure: A12B_cI26_204_g_a-001
| Prototype | Al$_{12}$W |
| AFLOW prototype label | A12B_cI26_204_g_a-001 |
| ICSD | 58207 |
| Pearson symbol | cI26 |
| Space group number | 204 |
| Space group symbol | $Im\overline{3}$ |
| AFLOW prototype command |
aflow --proto=A12B_cI26_204_g_a-001
--params=$a, \allowbreak y_{2}, \allowbreak z_{2}$ |
Other compounds with this structure
Al$_{12}$Mo, Al$_{12}$Mn, Al$_{12}$Re, Al$_{12}$Te
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | W I |
| $\mathbf{B_{2}}$ | = | $\left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}+y_{2} \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{3}}$ | = | $- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{4}}$ | = | $\left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+y_{2} \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{y}}- a z_{2} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{5}}$ | = | $- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{y}}- a z_{2} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{6}}$ | = | $y_{2} \, \mathbf{a}_{1}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{7}}$ | = | $- y_{2} \, \mathbf{a}_{1}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{8}}$ | = | $y_{2} \, \mathbf{a}_{1}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $- a z_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{9}}$ | = | $- y_{2} \, \mathbf{a}_{1}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $- a z_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{z}}$ | (24g) | Al I |
| $\mathbf{B_{10}}$ | = | $z_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}$ | (24g) | Al I |
| $\mathbf{B_{11}}$ | = | $z_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}$ | (24g) | Al I |
| $\mathbf{B_{12}}$ | = | $- z_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}- a z_{2} \,\mathbf{\hat{y}}$ | (24g) | Al I |
| $\mathbf{B_{13}}$ | = | $- z_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}- a z_{2} \,\mathbf{\hat{y}}$ | (24g) | Al I |
References
- J. Adam and J. B. Rich, The crystal structure of WAl$_{12}$, MoAl$_{12}$ and (Mn, Cr)Al$_{12}$, Acta Cryst. 7, 813–816 (1954), doi:10.1107/S0365110X54002514.
Prototype Generator
aflow --proto=A12B_cI26_204_g_a --params=$a,y_{2},z_{2}$