α-O$_{2}$ Structure: A_mC4_12_i-001
- 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).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\left(a x_{1} + c z_{1} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{1} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $- \left(a x_{1} + c z_{1} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{1} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | 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_mC4_12_i --params=$a,b/a,c/a,\beta,x_{1},z_{1}$