β-F$_{2}$ Structure: A_cP8_223_ac-001
| Prototype | F$_{2}$ |
| AFLOW prototype label | A_cP8_223_ac-001 |
| ICSD | 15821 |
| CCDC | 1596505 |
| Pearson symbol | cP8 |
| Space group number | 223 |
| Space group symbol | $Pm\overline{3}n$ |
| AFLOW prototype command |
aflow --proto=A_cP8_223_ac-001
--params=$a$ |
Other compounds with this structure
γ-O$_{2}$
- Below 45.6K this transforms to the ordered monoclinic $\alpha$–F$_{2}$ structure (Ivlev, 2019). It melts at 53.53K.
- This is an approximate and somewhat misleading structure for $\beta$–F$_{2}$. Both fluorine sites are actually F$_{2}$ molecules which have random orientation. Thus there are actually 16 fluorine atoms in the unit cell.
- Treating the F$_{2}$ molecules as
atoms,
this is isostructural with the $A15$ structure. - (Ivlev, 2019) presents (CCDC 1874485) an alternative version of this structure, with partially occupied fixed points for all of the fluorine atoms. This structure does not add much to our understanding, so we will use the simpler version of (Jordan, 1964).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | F I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (2a) | F I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6c) | F II |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6c) | F II |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (6c) | F II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}$ | (6c) | F II |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (6c) | F II |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (6c) | F II |
References
- T. H. Jordan, W. D. Streib, H. W. Smith, and W. N. Lipscomb, Single-crystal studies of β-F$_{2}$ and γ-O$_{2}$, Acta Cryst. 17, 777–778 (1964), doi:10.1107/S0365110X6400202X.
- S. I. Ivlev, A. J. Karttunen, M. Hoelzel, M. Conrad, and F. Kraus, The Crystal Structures of α- and β-F$_{2}$ Revisited, Chem. Eur. J. 25, 3310–3317 (2019), doi:10.1002/chem.201805298.
Found in
- Y. A. Freiman and H. J. Jodl, Solid Oxygen, Phys. Rep. 401, 1–228 (2004), doi:10.1016/j.physrep.2004.06.002.
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=A_cP8_223_ac --params=$a$