$D0_{15}$ (AlCl$_{3}$) Structure (Obsolete): AB3_mC16_5_c_3c-001
| Prototype | AlCl$_{3}$ |
| AFLOW prototype label | AB3_mC16_5_c_3c-001 |
| Strukturbericht designation | $D0_{15}$ |
| ICSD | none |
| Pearson symbol | mC16 |
| Space group number | 5 |
| Space group symbol | $C2$ |
| AFLOW prototype command |
aflow --proto=AB3_mC16_5_c_3c-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}$ |
- This structure was suggested by (Ketelaar, 1935) and given the Strukturbericht designation $D0_{15}$ by (Gottfried, 1395) with no reference to the $D0_{13}$ structure of (Laschkarew, 1930) found in (Hermann, 1937).
- Ketelaar gave a description of the unit cell a hexagonal setting, but the atomic positions resolve into the body-centered monoclinic cell shown here. This structure, however, has a lower symmetry than the currently accepted structure, which we previously designated $D0_{15}$. The current accepted structure is body-centered orthorhombic, space group $C2/m$ #12.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\left(x_{1} - y_{1}\right) \, \mathbf{a}_{1}+\left(x_{1} + y_{1}\right) \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\left(a x_{1} + c z_{1} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}+c z_{1} \sin{\beta} \,\mathbf{\hat{z}}$ | (4c) | Al I |
| $\mathbf{B_{2}}$ | = | $- \left(x_{1} + y_{1}\right) \, \mathbf{a}_{1}- \left(x_{1} - y_{1}\right) \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $- \left(a x_{1} + c z_{1} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}- c z_{1} \sin{\beta} \,\mathbf{\hat{z}}$ | (4c) | Al I |
| $\mathbf{B_{3}}$ | = | $\left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ | (4c) | Cl I |
| $\mathbf{B_{4}}$ | = | $- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $- \left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}- c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ | (4c) | Cl I |
| $\mathbf{B_{5}}$ | = | $\left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (4c) | Cl II |
| $\mathbf{B_{6}}$ | = | $- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- \left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}- c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (4c) | Cl II |
| $\mathbf{B_{7}}$ | = | $\left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (4c) | Cl III |
| $\mathbf{B_{8}}$ | = | $- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- \left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}- c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (4c) | Cl III |
References
- J. A. A. Ketelaar, Die Kristallstruktur der Aluminiumhalogenide II, Z. Krystallogr. 90, 237–255 (1935), doi:10.1524/zkri.1935.90.1.237.
- W. E. Laschkarew, Zur Struktur AlCl$_{3}$, Z. Anorganische und Allgemeine Chemie 193, 270–276 (1930), doi:10.1002/zaac.19301930123.
- C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928-1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
Found in
- C. Gottfried and F. Schossberger, eds., Strukturbericht Band III 1933-1935 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
Prototype Generator
aflow --proto=AB3_mC16_5_c_3c --params=$a,b/a,c/a,\beta,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4}$