$\beta_{1}$-K$_{2}$UF$_{6}$ Structure: A6B2C_hP9_189_fg_c_b-001
| Prototype | F$_{6}$K$_{2}$U |
| AFLOW prototype label | A6B2C_hP9_189_fg_c_b-001 |
| ICSD | 26193 |
| Pearson symbol | hP9 |
| Space group number | 189 |
| Space group symbol | $P\overline{6}2m$ |
| AFLOW prototype command |
aflow --proto=A6B2C_hP9_189_fg_c_b-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}$ |
Other compounds with this structure
K$_{2}$CeF$_{6}$, K$_{2}$ThF$_{6}$, $\delta$-Na$_{2}$UF$_{6}$
- $\alpha$–K$_{2}$UF$_{6}$ is in the cubic fluorite ($C1$, CaF$_{2}$) structure, with the potassium and uranium atoms placed randomly on the calcium sites.
- $\beta_{2}$-K$_{2}$UF$_{6}$ takes on the trigonal $\beta$–Na$_{2}$ThF$_{6}$ structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | U I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}$ | (2c) | K I |
| $\mathbf{B_{3}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}$ | (2c) | K I |
| $\mathbf{B_{4}}$ | = | $x_{3} \, \mathbf{a}_{1}$ | = | $\frac{1}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}$ | (3f) | F I |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}$ | (3f) | F I |
| $\mathbf{B_{6}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}$ | (3f) | F I |
| $\mathbf{B_{7}}$ | = | $x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{4} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | F II |
| $\mathbf{B_{8}}$ | = | $x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{4} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | F II |
| $\mathbf{B_{9}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | F II |
References
- G. Brunton, Refinement of the crystal structure of $\beta_{1}$-K$_{2}$UF$_{6}$, Acta Crystallogr. Sect. B 25, 2163–2164 (1969), doi:10.1107/S0567740869005310.
Found in
- A. Grzechnik, C. C. Underwood, J. W. Kolis, and K. Friese, Crystal structures and stability of K$_{2}$ThF$_{6}$ and K$_{7}$Th$_{6}$F$_{31}$ on compression, J. Fluor. Chem. 150, 8–13 (2013), doi:10.1016/j.jfluchem.2013.02.024.
Prototype Generator
aflow --proto=A6B2C_hP9_189_fg_c_b --params=$a,c/a,x_{3},x_{4}$