β-KYb$_{2}$F$_{7}$ Structure: A7BC2_mP10_3_a3e_b_e-001
| Prototype | F$_{7}$KYb$_{2}$ |
| AFLOW prototype label | A7BC2_mP10_3_a3e_b_e-001 |
| ICSD | 16350 |
| CCDC | 1596935 |
| Pearson symbol | mP10 |
| Space group number | 3 |
| Space group symbol | $P2$ |
| AFLOW prototype command |
aflow --proto=A7BC2_mP10_3_a3e_b_e-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak y_{1}, \allowbreak y_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}$ |
- (Khaidukov, 1993) list KYb$_{2}$F$_{7}$ as occurring in space groups $P2$ #3 and $Pna2_{1}$ #33. Presumably this later structure is related to $\beta$–KEr$_{2}$F$_{7}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $y_{1} \, \mathbf{a}_{2}$ | = | $b y_{1} \,\mathbf{\hat{y}}$ | (1a) | F I |
| $\mathbf{B_{2}}$ | = | $y_{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (1b) | K I |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | F II |
| $\mathbf{B_{4}}$ | = | $- x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- \left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}- c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | F II |
| $\mathbf{B_{5}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | F III |
| $\mathbf{B_{6}}$ | = | $- x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- \left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}- c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | F III |
| $\mathbf{B_{7}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | F IV |
| $\mathbf{B_{8}}$ | = | $- x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- \left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}- c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | F IV |
| $\mathbf{B_{9}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Yb I |
| $\mathbf{B_{10}}$ | = | $- x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}- c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Yb I |
References
- Y. L. Fur, S. Aléonard, M. F. Gorius, and M. T. Roux, Structure cristalline de la phase β-KYb$_{2}$F$_{7}$, J. Solid State Chem. 35, 29–33 (1980), doi:10.1016/0022-4596(80)90459-4.
- N. M. Khaidukov, T. G. Filatov, M. B. Ikrami, P. P. Fedorov, M. B. Ikrami, and P. P. Fedorov, Morphotropy in lanthanide fluoride series, Inorg. Mater. 29, 873–876 (1993). Translated from Neorganicheskie Materialy 29(7) 992-996 (1993).
Found in
- Inorganic Crystal Structure Database. Entry 16350 (beta-KYb2F7).
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=A7BC2_mP10_3_a3e_b_e --params=$a,b/a,c/a,\beta,y_{1},y_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6}$