KBrO$_{3}$ ($G0_{7}$) Structure: ABC3_hR5_160_a_a_b-001
| Prototype | BrKO$_{3}$ |
| AFLOW prototype label | ABC3_hR5_160_a_a_b-001 |
| Strukturbericht designation | $G0_{7}$ |
| ICSD | 47173 |
| Pearson symbol | hR5 |
| Space group number | 160 |
| Space group symbol | $R3m$ |
| AFLOW prototype command |
aflow --proto=ABC3_hR5_160_a_a_b-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak z_{3}$ |
Other compounds with this structure
FeBiO$_{3}$, KNO$_{3}$, $\gamma$-KNO$_{3}$, RbNO$_{3}$
- $\gamma$–KNO$_{3}$ and KBrO$_{3}$ ($G0_{7}$) have the same AFLOW prototype label, ABC3_hR5_160_a_a_b. They are generated by the same symmetry operations with different sets of parameters (
--params) specified in their corresponding CIF files. - Hexagonal settings rhombohedral structures can be obtained with the option
--hex.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $c x_{1} \,\mathbf{\hat{z}}$ | (1a) | Br I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $c x_{2} \,\mathbf{\hat{z}}$ | (1a) | K I |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (3b) | O I |
| $\mathbf{B_{4}}$ | = | $z_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (3b) | O I |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (3b) | O I |
References
- D. H. Templeton and L. K. Templeton, Tensor X-ray optical properties of the bromate ion, Acta Crystallogr. Sect. A pp. 133–142 (1985), doi:10.1107/S0108767385000277.
Found in
- D. SantamarÃa-Pérez, R. Chulia-Jordan, P. RodrÃguez-Hernández, and A. M. {n}oz, Crystal behavior of potassium bromate under compression, Acta Crystallogr. Sect. B 71, 798–804 (2015), doi:10.1107/S2052520615018156.
Prototype Generator
aflow --proto=ABC3_hR5_160_a_a_b --params=$a,c/a,x_{1},x_{2},x_{3},z_{3}$