β-O$_{2}$ Structure: A_hR2_166_c-003
| Prototype | O |
| AFLOW prototype label | A_hR2_166_c-003 |
| ICSD | 173934 |
| CCDC | 1688831 |
| Pearson symbol | hR2 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A_hR2_166_c-003
--params=$a, \allowbreak c/a, \allowbreak x_{1}$ |
- Solid oxygen can be found in the $\alpha$–O$_{2}$ phase below 24K and in the $\beta$–O$_{2}$ phase between 24 and 44K, with $\gamma$–O$_{2}$, stable between 44 and 54K, in the $\beta$–F$_{2}$ structure (Meier, 1984).
- Data for $\beta$–O$_{2}$ was taken at 30K.
- $\alpha$–As ($A7$), rhombohedral graphite, and $\beta$–O have the same AFLOW prototype label, A_hR2_166_c. They are generated by the same symmetry operations with different sets of parameters (
--params) specified in their corresponding CIF files. Hexagonal settings of rhombohedral structures can be obtained with the option--hex.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $c x_{1} \,\mathbf{\hat{z}}$ | (2c) | O I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $- c x_{1} \,\mathbf{\hat{z}}$ | (2c) | O I |
References
- R. J. Meier and R. B. Helmholdt, Neutron-diffraction study of α- and β-oxygen, Phys. Rev. B 29, 1387–1393 (1984), doi:10.1103/PhysRevB.29.1387.
First cited in
- M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
Geometry files
Prototype Generator
aflow --proto=A_hR2_166_c --params=$a,c/a,x_{1}$