γ-Bi$_{2}$O$_{3}$ Structure: A13B20_cI66_197_af_2cf-001
| Prototype | Bi$_{2}$O$_{3}$ |
| AFLOW prototype label | A13B20_cI66_197_af_2cf-001 |
| ICSD | 2376 |
| Pearson symbol | cI66 |
| Space group number | 197 |
| Space group symbol | $I23$ |
| AFLOW prototype command |
aflow --proto=A13B20_cI66_197_af_2cf-001
--params=$a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}$ |
Other compounds with this structure
Bi$_{12}$GeO$_{20}$, Bi$_{38}$ZnO$_{60}$
- 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$^\circ$C,
- body-centered cubic $\gamma$–Bi$_{2}$O$_{3}$, another metastable phase observed at 639$^\circ$C (this structure),
- face-centered cubic $\delta$–Bi$_{2}$O$_{3}$, the stable phase from 729$^\circ$ up to the melting point at 824$^\circ$C,
- a high-pressure HP-Bi$_{2}$O$_{3}$, and
- a second
non-quenchable
high-pressure structure, HPC-Bi$_{2}$O$_{3}$.
- The Bi-I (2a) site is 97.5% occupied, making the actual composition of this structure Bi$_{1.95}$O$_{3}$. The Bi-I site may be occupied by germanium or zinc atoms, e.g. Bi$_{12}$GeO$_{20}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Bi I |
| $\mathbf{B_{2}}$ | = | $2 x_{2} \, \mathbf{a}_{1}+2 x_{2} \, \mathbf{a}_{2}+2 x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (8c) | O I |
| $\mathbf{B_{3}}$ | = | $- 2 x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (8c) | O I |
| $\mathbf{B_{4}}$ | = | $- 2 x_{2} \, \mathbf{a}_{2}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (8c) | O I |
| $\mathbf{B_{5}}$ | = | $- 2 x_{2} \, \mathbf{a}_{1}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (8c) | O I |
| $\mathbf{B_{6}}$ | = | $2 x_{3} \, \mathbf{a}_{1}+2 x_{3} \, \mathbf{a}_{2}+2 x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (8c) | O II |
| $\mathbf{B_{7}}$ | = | $- 2 x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (8c) | O II |
| $\mathbf{B_{8}}$ | = | $- 2 x_{3} \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (8c) | O II |
| $\mathbf{B_{9}}$ | = | $- 2 x_{3} \, \mathbf{a}_{1}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (8c) | O II |
| $\mathbf{B_{10}}$ | = | $\left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (24f) | Bi II |
| $\mathbf{B_{11}}$ | = | $- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (24f) | Bi II |
| $\mathbf{B_{12}}$ | = | $\left(y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (24f) | Bi II |
| $\mathbf{B_{13}}$ | = | $- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (24f) | Bi II |
| $\mathbf{B_{14}}$ | = | $\left(x_{4} + y_{4}\right) \, \mathbf{a}_{1}+\left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (24f) | Bi II |
| $\mathbf{B_{15}}$ | = | $- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{1}- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (24f) | Bi II |
| $\mathbf{B_{16}}$ | = | $- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}+\left(y_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (24f) | Bi II |
| $\mathbf{B_{17}}$ | = | $\left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (24f) | Bi II |
| $\mathbf{B_{18}}$ | = | $\left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{2}+\left(y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (24f) | Bi II |
| $\mathbf{B_{19}}$ | = | $- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{2}- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (24f) | Bi II |
| $\mathbf{B_{20}}$ | = | $- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+\left(y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (24f) | Bi II |
| $\mathbf{B_{21}}$ | = | $\left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (24f) | Bi II |
| $\mathbf{B_{22}}$ | = | $\left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{23}}$ | = | $- \left(y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{24}}$ | = | $\left(y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{25}}$ | = | $- \left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{26}}$ | = | $\left(x_{5} + y_{5}\right) \, \mathbf{a}_{1}+\left(y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{27}}$ | = | $- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{1}- \left(y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{28}}$ | = | $- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}+\left(y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{29}}$ | = | $\left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}- \left(y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{30}}$ | = | $\left(x_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{2}+\left(y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{31}}$ | = | $- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{2}- \left(y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{32}}$ | = | $- \left(x_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\left(y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{33}}$ | = | $\left(x_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}- \left(y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (24f) | O III |
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=A13B20_cI66_197_af_2cf --params=$a,x_{2},x_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5}$