δ-Bi$_{2}$O$_{3}$ Structure: AB8_cF36_225_a_f-001
| Prototype | Bi$_{2}$O$_{3}$ |
| AFLOW prototype label | AB8_cF36_225_a_f-001 |
| ICSD | 2375 |
| Pearson symbol | cF36 |
| Space group number | 225 |
| Space group symbol | $Fm\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=AB8_cF36_225_a_f-001
--params=$a, \allowbreak x_{2}$ |
Other compounds with this structure
$\alpha$-CuI, $\gamma$-CuI
- Bi$_{2}$O$_{3}$ can be found in at least six forms (Harwig, 1978; Locherer, 2011):
- monoclinic $\alpha$–Bi$_{2}$O$_{3}$, the ground state, stable up to 729°,
- tetragonal $\beta$–Bi$_{2}$O$_{3}$, $D5_{12}$, a metastable state observed at 650°C (this structure),
- body-centered cubic $\gamma$–Bi$_{2}$O$_{3}$, another metastable phase observed at 639°C,
- face-centered cubic $\delta$–Bi$_{2}$O$_{3}$, the stable phase from 729° up to the melting point at 824°C (this structure),
- a high-pressure HP-Bi$_{2}$O$_{3}$, and
- a second
nonquenchable
high-pressure structure, HPC-Bi$_{2}$O$_{3}$.
- The oxygen sites are occupied 18.75% of the time. If $z_{2} \rightarrow 1/4$, they coalesce on the (2c) Wyckoff position, and this becomes the fluorite ($C1$) structure.
- Other compounds with different stoichiometries have this structure. In copper(I) iodide both the high temperature $\alpha$–CuI and the ground state $\gamma$–CuI phases are in this structure, with the copper atoms occupying 1/8 of the (32f) sites. (Keen, 1995)
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Bi I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (32f) | O I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}- 3 x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (32f) | O I |
| $\mathbf{B_{4}}$ | = | $x_{2} \, \mathbf{a}_{1}- 3 x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (32f) | O I |
| $\mathbf{B_{5}}$ | = | $- 3 x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (32f) | O I |
| $\mathbf{B_{6}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+3 x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (32f) | O I |
| $\mathbf{B_{7}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (32f) | O I |
| $\mathbf{B_{8}}$ | = | $- x_{2} \, \mathbf{a}_{1}+3 x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (32f) | O I |
| $\mathbf{B_{9}}$ | = | $3 x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (32f) | O I |
References
- H. A. Harwig, On the Structure of Bismuthsesquioxide: The α, β, γ, and δ-phase, Z. Anorganische und Allgemeine Chemie 444, 151–166 (1978), doi:10.1002/zaac.19784440118.
- D. A. Keen and S. Hull, The high-temperature structural behaviour of copper(I) iodide, J. Phys.: Condens. Matter 7, 5793–5804 (1995), doi:10.1088/0953-8984/7/29/007.
- T. Locherer, D. L. V. K. Prasad, R. Dinnebier, U. Wedig, M. Jansen, G. Garbarino, and T. Hansen, High-pressure structural evolution of HP-Bi$_{2}$O$_{3}$, Phys. Rev. B 83, 214102 (2011), doi:10.1103/PhysRevB.83.214102.
Found in
- D. Risold, B. Hallstedt, L. J. Gauckler, H. L. Lukas, and S. G. Fries, The Bismuth-Oxygen System, J. Phase Eq 16, 223 (1995), doi:10.1007/BF02667306.
Prototype Generator
aflow --proto=AB8_cF36_225_a_f --params=$a,x_{2}$