γ-Ga$_{2}$O$_{3}$ Structure: A11B4_cF120_227_acdf_e-001
| Prototype | Ga$_{2}$O$_{3}$ |
| AFLOW prototype label | A11B4_cF120_227_acdf_e-001 |
| ICSD | 236276 |
| Pearson symbol | cF120 |
| Space group number | 227 |
| Space group symbol | $Fd\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A11B4_cF120_227_acdf_e-001
--params=$a, \allowbreak x_{4}, \allowbreak x_{5}$ |
- Ga$_{2}$O$_{3}$ exhibits a variety of structures:
- $\alpha$Ga$_{2}$O$_{3}$, which has the corundum ($D5_{1}$) structure ,
- $\beta$Ga$_{2}$O$_{3}$,
- $\gamma$Ga$_{2}$O$_{3}$, this structure, and
- $\epsilon$Ga$_{2}$O$_{3}$, a structure with many vacancies which can be approximated by the $\kappa$ alumina structure.
- In $\gamma$Ga$_{2}$O$_{3}$ none of the gallium sites have full occupancy. Ga-I and Ga-II are 74.1% occupied, Ga-III is 6.6% occupied, and Ga-IV is only 2.4% occupied.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (8a) | Ga I |
| $\mathbf{B_{2}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $\frac{7}{8}a \,\mathbf{\hat{x}}+\frac{7}{8}a \,\mathbf{\hat{y}}+\frac{7}{8}a \,\mathbf{\hat{z}}$ | (8a) | Ga I |
| $\mathbf{B_{3}}$ | = | $0$ | = | $0$ | (16c) | Ga II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (16c) | Ga II |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16c) | Ga II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16c) | Ga II |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (16d) | Ga III |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (16d) | Ga III |
| $\mathbf{B_{9}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16d) | Ga III |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16d) | Ga III |
| $\mathbf{B_{11}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{12}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- \left(3 x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{13}}$ | = | $x_{4} \, \mathbf{a}_{1}- \left(3 x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{14}}$ | = | $- \left(3 x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{15}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(3 x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{16}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{17}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\left(3 x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{18}}$ | = | $\left(3 x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{19}}$ | = | $- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | Ga IV |
| $\mathbf{B_{20}}$ | = | $x_{5} \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | Ga IV |
| $\mathbf{B_{21}}$ | = | $x_{5} \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | Ga IV |
| $\mathbf{B_{22}}$ | = | $- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | Ga IV |
| $\mathbf{B_{23}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (48f) | Ga IV |
| $\mathbf{B_{24}}$ | = | $- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48f) | Ga IV |
| $\mathbf{B_{25}}$ | = | $\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | Ga IV |
| $\mathbf{B_{26}}$ | = | $- x_{5} \, \mathbf{a}_{1}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | Ga IV |
| $\mathbf{B_{27}}$ | = | $- x_{5} \, \mathbf{a}_{1}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | Ga IV |
| $\mathbf{B_{28}}$ | = | $\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | Ga IV |
| $\mathbf{B_{29}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (48f) | Ga IV |
| $\mathbf{B_{30}}$ | = | $\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (48f) | Ga IV |
References
- H. Y. Playford, A. C. Hannon, E. R. Barney, and R. I. Walton, Structures of Uncharacterised Polymorphs of Gallium Oxide from Total Neutron Diffraction, Chem. Euro. J. 19, 2803–2813 (2013), doi:10.1002/chem.201203359.
Prototype Generator
aflow --proto=A11B4_cF120_227_acdf_e --params=$a,x_{4},x_{5}$