High Temperature K$_{2}$LiAlF$_{6}$ Structure: AB6C2D_hR20_166_ab_2h_2c_c-001
| Prototype | AlF$_{6}$K$_{2}$Li |
| AFLOW prototype label | AB6C2D_hR20_166_ab_2h_2c_c-001 |
| ICSD | 48149 |
| Pearson symbol | hR20 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=AB6C2D_hR20_166_ab_2h_2c_c-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak z_{7}$ |
Other compounds with this structure
Ba$_{2}$MnTeO$_{6}$, Cs$_{2}$NaCrF$_{6}$
- This is the high temperature phase of K$_{2}$LiAlF$_{6}$, stable above 650°C (Tressaud, 1984). The low-temperature structure is hexagonal, but its exact space group is uncertain.
- Hexagonal settings of this structure can be obtained with the option
--hex.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | Al II |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $c x_{3} \,\mathbf{\hat{z}}$ | (2c) | K I |
| $\mathbf{B_{4}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- c x_{3} \,\mathbf{\hat{z}}$ | (2c) | K I |
| $\mathbf{B_{5}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $c x_{4} \,\mathbf{\hat{z}}$ | (2c) | K II |
| $\mathbf{B_{6}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- c x_{4} \,\mathbf{\hat{z}}$ | (2c) | K II |
| $\mathbf{B_{7}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $c x_{5} \,\mathbf{\hat{z}}$ | (2c) | Li I |
| $\mathbf{B_{8}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- c x_{5} \,\mathbf{\hat{z}}$ | (2c) | Li I |
| $\mathbf{B_{9}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6h) | F I |
| $\mathbf{B_{10}}$ | = | $z_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6h) | F I |
| $\mathbf{B_{11}}$ | = | $x_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6h) | F I |
| $\mathbf{B_{12}}$ | = | $- z_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6h) | F I |
| $\mathbf{B_{13}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6h) | F I |
| $\mathbf{B_{14}}$ | = | $- x_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{\sqrt{3}}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6h) | F I |
| $\mathbf{B_{15}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6h) | F II |
| $\mathbf{B_{16}}$ | = | $z_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6h) | F II |
| $\mathbf{B_{17}}$ | = | $x_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6h) | F II |
| $\mathbf{B_{18}}$ | = | $- z_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6h) | F II |
| $\mathbf{B_{19}}$ | = | $- x_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6h) | F II |
| $\mathbf{B_{20}}$ | = | $- x_{7} \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{\sqrt{3}}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6h) | F II |
References
- A. Tressaud, J. Darriet, P. Lagassié, J. Grannec, and P. Hagenmuller, On new K$_{2}$LiMF$_{6}$ phases (M = d-element, Al, Ga, In): Crystal structure of the rhombohedral high-temperature from of K$_{2}$LiAlF$_{6}$, Mater. Res. Bull. 19, 983–988 (1984), doi:10.1016/0025-5408(84)90211-3.
Prototype Generator
aflow --proto=AB6C2D_hR20_166_ab_2h_2c_c --params=$a,c/a,x_{3},x_{4},x_{5},x_{6},z_{6},x_{7},z_{7}$