α-ReO$_{3}$ ($D0_{9}$) Structure: A3B_cP4_221_c_b-001
| Prototype | O$_{3}$Re |
| AFLOW prototype label | A3B_cP4_221_c_b-001 |
| Strukturbericht designation | $D0_{9}$ |
| ICSD | 16810 |
| Pearson symbol | cP4 |
| Space group number | 221 |
| Space group symbol | $Pm\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A3B_cP4_221_c_b-001
--params=$a$ |
Other compounds with this structure
AlF$_{3}$, HfF$_{3}$, MoF$_{3}$, NCu$_{3}$, NNa$_{3}$, NbF$_{3}$, PbI$_{3}$, ScF$_{3}$, TaF$_{3}$, UO$_{3}$, WO$_{3}$
- Placing an atom on the origin, or (1a) Wyckoff position, transforms this into the cubic perovskite ($E2_{1}$) structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (1b) | Re I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (3c) | O I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (3c) | O I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (3c) | O I |
References
- K. Meisel, Rheniumtrioxyd. III. Mitteilung. Über die Kristallstruktur des Rheniumtrioxyds, Z. Anorganische und Allgemeine Chemie 207, 121–128 (1932), doi:10.1002/zaac.19322070113.
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=A3B_cP4_221_c_b --params=$a$