KPF$_{6}$ Structure: A24BC_cF104_209_j_a_b-001
| Prototype | F$_{6}$KP |
| AFLOW prototype label | A24BC_cF104_209_j_a_b-001 |
| ICSD | none |
| Pearson symbol | cF104 |
| Space group number | 209 |
| Space group symbol | $F432$ |
| AFLOW prototype command |
aflow --proto=A24BC_cF104_209_j_a_b-001
--params=$a, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
- The (96j) Wyckoff positions are decorated by F atoms with a site occupation of 0.25, hence the prototype material is KPF$_{6}$ rather than KPF$_{24}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | K I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (4b) | P I |
| $\mathbf{B_{3}}$ | = | $\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{4}}$ | = | $\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{5}}$ | = | $\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{6}}$ | = | $- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{7}}$ | = | $\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{8}}$ | = | $- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{9}}$ | = | $\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{10}}$ | = | $\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{11}}$ | = | $\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{12}}$ | = | $\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{13}}$ | = | $- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{14}}$ | = | $\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{15}}$ | = | $\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{16}}$ | = | $- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{17}}$ | = | $- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{18}}$ | = | $\left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{19}}$ | = | $- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{20}}$ | = | $\left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{21}}$ | = | $\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{22}}$ | = | $- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{23}}$ | = | $- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{24}}$ | = | $\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{25}}$ | = | $\left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
| $\mathbf{B_{26}}$ | = | $- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (96j) | F I |
References
- Y. P. Mascarenhas and S. H. Pulcinelli, A redetermination of the structure of α-potassium fluorophosphate, Acta Cryst. 37, C175 (1981), doi:10.1107/S0108767381094294.
Found in
- P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds (2013). ASM International.
Prototype Generator
aflow --proto=A24BC_cF104_209_j_a_b --params=$a,x_{3},y_{3},z_{3}$