KHF$_{2}$ ($F5_{2}$) Structure: A2BC_tI16_140_h_d_a-001
| Prototype | F$_{2}$HK |
| AFLOW prototype label | A2BC_tI16_140_h_d_a-001 |
| Strukturbericht designation | $F5_{2}$ |
| ICSD | 18094 |
| Pearson symbol | tI16 |
| Space group number | 140 |
| Space group symbol | $I4/mcm$ |
| AFLOW prototype command |
aflow --proto=A2BC_tI16_140_h_d_a-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}$ |
Other compounds with this structure
KN$_{3}$, CsN$_{3}$
- (Bozorth, 1923) originally determined the lattice constants of KHF$_{2}$ along with the positions of the potassium and fluorine atoms. He also assumed that the hydrogen atoms were on the (4d) Wyckoff sites. Both (Peterson, 1952) and (Ibers, 1964) confirmed his data. All three papers point out that it is possible that the hydrogen atoms are on half-filled (8h) sites, which would reduce to the (4d) site as the $x$ coordinate approached zero. In KN$_{3}$ and CsN$_{3}$ the nitrogen atoms occupy the (4d) and (8h) Wyckoff sites, while the cation occupies the (4a) site.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | K I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}$ | = | $\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4a) | K I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}$ | (4d) | H I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}$ | (4d) | H I |
| $\mathbf{B_{5}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\left(2 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (8h) | F I |
| $\mathbf{B_{6}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- \left(2 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (8h) | F I |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}$ | (8h) | F I |
| $\mathbf{B_{8}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}$ | (8h) | F I |
References
- J. A. Ibers, Refinement of Peterson and Levy's Neutron Diffraction Data on KHF$_{2}$, J. Chem. Phys. 40, 402–404 (1964), doi:10.1063/1.1725126.
- S. W. Peterson and H. A. Levy, A Single Crystal Neutron Diffraction Determination of the Hydrogen Position in Potassium Bifluoride, J. Chem. Phys. 20, 704–707 (1952), doi:10.1063/1.1700520.
- R. M. Bozorth, The crystal structure of potassium hydrogen fluoride, J. Am. Chem. Soc. 45, 2128–2132 (1923), doi:10.1021/ja01662a013.
Prototype Generator
aflow --proto=A2BC_tI16_140_h_d_a --params=$a,c/a,x_{3}$