KBrO3 ($G0_{7}$) Structure : ABC3_hR5_160_a_a_b

Picture of Structure; Click for Big Picture
Prototype : BrKO3
AFLOW prototype label : ABC3_hR5_160_a_a_b
Strukturbericht designation : $G0_{7}$
Pearson symbol : hR5
Space group number : 160
Space group symbol : $R3m$
AFLOW prototype command : aflow --proto=ABC3_hR5_160_a_a_b
--params=
$a$,$c/a$,$x_{1}$,$x_{2}$,$x_{3}$,$z_{3}$


Other compounds with this structure

  • KNO3, $\gamma$–KNO3, and RbNO3

  • $\gamma$–KNO3 and KBrO3 ($G0_{7}$) 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 (\texttt––params) specified in their corresponding CIF files.

Rhombohedral primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac{1}{\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & - \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + x_{1} \, \mathbf{a}_{3} & = & x_{1}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Br} \\ \mathbf{B}_{2} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & x_{2}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{K} \\ \mathbf{B}_{3} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{3}-z_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{3}-z_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{3}+\frac{1}{3}z_{3}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{O} \\ \mathbf{B}_{4} & = & z_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{3}+z_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{3}-z_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{3}+\frac{1}{3}z_{3}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{O} \\ \mathbf{B}_{5} & = & x_{3} \, \mathbf{a}_{1} + z_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & \frac{1}{\sqrt{3}}\left(-x_{3}+z_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{3}+\frac{1}{3}z_{3}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{O} \\ \end{array} \]

References

  • D. H. Templeton and L. K. Templeton, Tensor X–ray optical properties of the bromate ion, Acta Crystallogr. Sect. A 133–142 (1985), doi:10.1107/S0108767385000277.

Found in

  • D. Santamaría–Pérez, R. Chulia–Jordan, P. Rodríguez–Hernández, and A. Mu noz, Crystal behavior of potassium bromate under compression, Acta Crystallogr. Sect. B Struct. Sci. 71, 798–804 (2015), doi:10.1107/S2052520615018156.

Geometry files


Prototype Generator

aflow --proto=ABC3_hR5_160_a_a_b --params=

Species:

Running:

Output: