Rinneite (K$_{3}$NaFeCl$_{6}$) Structure: A6BC3D_hR22_167_f_b_e_a-001
| Prototype | Cl$_{6}$FeK$_{3}$Na |
| AFLOW prototype label | A6BC3D_hR22_167_f_b_e_a-001 |
| Mineral name | rinneite |
| ICSD | 170745 |
| Pearson symbol | hR22 |
| Space group number | 167 |
| Space group symbol | $R\overline{3}c$ |
| AFLOW prototype command |
aflow --proto=A6BC3D_hR22_167_f_b_e_a-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}$ |
Other compounds with this structure
Ca$_{3}$LiOsO$_{6}$, Ca$_{3}$LiRuO$_{6}$, Sr$_{3}$NiIrO$_{6}$, K$_{4}$CdCl$_{6}$
- We use the data taken at 293K.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2a) | Na I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2a) | Na I |
| $\mathbf{B_{3}}$ | = | $0$ | = | $0$ | (2b) | Fe I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | Fe I |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \left(4 x_{3} - 1\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{8}a \left(4 x_{3} - 1\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6e) | K I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \left(4 x_{3} - 1\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{8}a \left(4 x_{3} - 1\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6e) | K I |
| $\mathbf{B_{7}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6e) | K I |
| $\mathbf{B_{8}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \left(4 x_{3} + 3\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{24}a \left(12 x_{3} + 1\right) \,\mathbf{\hat{y}}+\frac{5}{12}c \,\mathbf{\hat{z}}$ | (6e) | K I |
| $\mathbf{B_{9}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \left(4 x_{3} - 1\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{24}a \left(12 x_{3} + 5\right) \,\mathbf{\hat{y}}+\frac{5}{12}c \,\mathbf{\hat{z}}$ | (6e) | K I |
| $\mathbf{B_{10}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{5}{12}c \,\mathbf{\hat{z}}$ | (6e) | K I |
| $\mathbf{B_{11}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{4} - 2 y_{4} + z_{4}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{4} + y_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (12f) | Cl I |
| $\mathbf{B_{12}}$ | = | $z_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{4} - z_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{4} - y_{4} - z_{4}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{4} + y_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (12f) | Cl I |
| $\mathbf{B_{13}}$ | = | $y_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{4} - y_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{4} + y_{4} - 2 z_{4}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{4} + y_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (12f) | Cl I |
| $\mathbf{B_{14}}$ | = | $- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{4} - 2 y_{4} + z_{4}\right) \,\mathbf{\hat{y}}- \frac{1}{6}c \left(2 x_{4} + 2 y_{4} + 2 z_{4} - 3\right) \,\mathbf{\hat{z}}$ | (12f) | Cl I |
| $\mathbf{B_{15}}$ | = | $- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{4} - z_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{4} - y_{4} - z_{4}\right) \,\mathbf{\hat{y}}- \frac{1}{6}c \left(2 x_{4} + 2 y_{4} + 2 z_{4} - 3\right) \,\mathbf{\hat{z}}$ | (12f) | Cl I |
| $\mathbf{B_{16}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{4} - y_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{4} + y_{4} - 2 z_{4}\right) \,\mathbf{\hat{y}}- \frac{1}{6}c \left(2 x_{4} + 2 y_{4} + 2 z_{4} - 3\right) \,\mathbf{\hat{z}}$ | (12f) | Cl I |
| $\mathbf{B_{17}}$ | = | $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{4} - 2 y_{4} + z_{4}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{4} + y_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (12f) | Cl I |
| $\mathbf{B_{18}}$ | = | $- z_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{4} - z_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{4} - y_{4} - z_{4}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{4} + y_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (12f) | Cl I |
| $\mathbf{B_{19}}$ | = | $- y_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} - y_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{4} + y_{4} - 2 z_{4}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{4} + y_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (12f) | Cl I |
| $\mathbf{B_{20}}$ | = | $\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{4} - 2 y_{4} + z_{4}\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \left(2 x_{4} + 2 y_{4} + 2 z_{4} + 3\right) \,\mathbf{\hat{z}}$ | (12f) | Cl I |
| $\mathbf{B_{21}}$ | = | $\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{4} - z_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{4} - y_{4} - z_{4}\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \left(2 x_{4} + 2 y_{4} + 2 z_{4} + 3\right) \,\mathbf{\hat{z}}$ | (12f) | Cl I |
| $\mathbf{B_{22}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} - y_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{4} + y_{4} - 2 z_{4}\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \left(2 x_{4} + 2 y_{4} + 2 z_{4} + 3\right) \,\mathbf{\hat{z}}$ | (12f) | Cl I |
References
- B. N. Figgis, A. N. Sobolev, E. S. Kucharski, and V. Broughton, Rinneite, K$_{3}$Na[FeCl$_{6}$], at 293, 84 and 9.5K, Acta Crystallogr. Sect. C 56, e228–e229 (2000), doi:10.1107/S0108270100006053.
Prototype Generator
aflow --proto=A6BC3D_hR22_167_f_b_e_a --params=$a,c/a,x_{3},x_{4},y_{4},z_{4}$