CrCl$_{3}$(H$_{2}$O)$_{6}$ ($J2_{2}$) Structure: A3BC6_hR20_167_e_b_f-001
| Prototype | CrCl$_{3}$(H$_{2}$O)$_{6}$ |
| AFLOW prototype label | A3BC6_hR20_167_e_b_f-001 |
| Strukturbericht designation | $J2_{2}$ |
| ICSD | 26138 |
| Pearson symbol | hR20 |
| Space group number | 167 |
| Space group symbol | $R\overline{3}c$ |
| AFLOW prototype command |
aflow --proto=A3BC6_hR20_167_e_b_f-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
Other compounds with this structure
AlCl$_{3}$(H$_{2}$O)$_{6}$
- The positions of the hydrogen atoms in the water molecules were not determined, so we only provide the positions of the oxygen atoms (labeled as H$_{2}$O).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2b) | Cr I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | Cr I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \left(4 x_{2} - 1\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{8}a \left(4 x_{2} - 1\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6e) | Cl I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \left(4 x_{2} - 1\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{8}a \left(4 x_{2} - 1\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6e) | Cl I |
| $\mathbf{B_{5}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6e) | Cl I |
| $\mathbf{B_{6}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \left(4 x_{2} + 3\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{24}a \left(12 x_{2} + 1\right) \,\mathbf{\hat{y}}+\frac{5}{12}c \,\mathbf{\hat{z}}$ | (6e) | Cl I |
| $\mathbf{B_{7}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \left(4 x_{2} - 1\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{24}a \left(12 x_{2} + 5\right) \,\mathbf{\hat{y}}+\frac{5}{12}c \,\mathbf{\hat{z}}$ | (6e) | Cl I |
| $\mathbf{B_{8}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{5}{12}c \,\mathbf{\hat{z}}$ | (6e) | Cl I |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{3} - 2 y_{3} + z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{3} + y_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (12f) | H I |
| $\mathbf{B_{10}}$ | = | $z_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{3} - z_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{3} - y_{3} - z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{3} + y_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (12f) | H I |
| $\mathbf{B_{11}}$ | = | $y_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{3} - y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{3} + y_{3} - 2 z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{3} + y_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (12f) | H I |
| $\mathbf{B_{12}}$ | = | $- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{3} - 2 y_{3} + z_{3}\right) \,\mathbf{\hat{y}}- \frac{1}{6}c \left(2 x_{3} + 2 y_{3} + 2 z_{3} - 3\right) \,\mathbf{\hat{z}}$ | (12f) | H I |
| $\mathbf{B_{13}}$ | = | $- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{3} - z_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{3} - y_{3} - z_{3}\right) \,\mathbf{\hat{y}}- \frac{1}{6}c \left(2 x_{3} + 2 y_{3} + 2 z_{3} - 3\right) \,\mathbf{\hat{z}}$ | (12f) | H I |
| $\mathbf{B_{14}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{3} - y_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{3} + y_{3} - 2 z_{3}\right) \,\mathbf{\hat{y}}- \frac{1}{6}c \left(2 x_{3} + 2 y_{3} + 2 z_{3} - 3\right) \,\mathbf{\hat{z}}$ | (12f) | H I |
| $\mathbf{B_{15}}$ | = | $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{3} - 2 y_{3} + z_{3}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{3} + y_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (12f) | H I |
| $\mathbf{B_{16}}$ | = | $- z_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{3} - z_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{3} - y_{3} - z_{3}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{3} + y_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (12f) | H I |
| $\mathbf{B_{17}}$ | = | $- y_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - y_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{3} + y_{3} - 2 z_{3}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{3} + y_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (12f) | H I |
| $\mathbf{B_{18}}$ | = | $\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{3} - 2 y_{3} + z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \left(2 x_{3} + 2 y_{3} + 2 z_{3} + 3\right) \,\mathbf{\hat{z}}$ | (12f) | H I |
| $\mathbf{B_{19}}$ | = | $\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{3} - z_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{3} - y_{3} - z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \left(2 x_{3} + 2 y_{3} + 2 z_{3} + 3\right) \,\mathbf{\hat{z}}$ | (12f) | H I |
| $\mathbf{B_{20}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{3} + y_{3} - 2 z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \left(2 x_{3} + 2 y_{3} + 2 z_{3} + 3\right) \,\mathbf{\hat{z}}$ | (12f) | H I |
References
- K. R. Andress and C. Carpenter, Die Struktur von Chromchlorid- und Aluminiumchloridhexahydrat, Z. Krystallogr. 87, 446–463 (1934), doi:10.1524/zkri.1934.87.1.446.
Found in
- C. Gottfried and F. Schossberger, eds., Strukturbericht Band III 1933-1935 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
Prototype Generator
aflow --proto=A3BC6_hR20_167_e_b_f --params=$a,c/a,x_{2},x_{3},y_{3},z_{3}$