$\beta$–Potassium Nitrate (KNO3) Structure : ABC6_hR8_166_a_b_h
| Prototype | : | KNO3 |
| AFLOW prototype label | : | ABC6_hR8_166_a_b_h |
| Strukturbericht designation | : | None |
| Pearson symbol | : | hR8 |
| Space group number | : | 166 |
| Space group symbol | : | $R\bar{3}m$ |
| AFLOW prototype command | : | aflow --proto=ABC6_hR8_166_a_b_h --params=$a$,$c/a$,$x_{3}$,$z_{3}$ |
- On heating, $\alpha$–KNO3 (either Structure I or Structure II) transforms into $\beta$–KNO3 at 128 °C. When heated above 200 °C and then cooled, the $\beta$ phase transforms into the metastable ferroelectric $\gamma$–KNO3 phase, which can remain down to room temperature.
- In the $\beta$–phase the oxygen ($6h$) sites are only 50% filled. Presumably only the $+z$ or $–z$ sites will be occupied around a given nitrogen atom.
- (Nimmo, 1976) give the data for $\beta$–KNO3 taken at 151 °C.
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} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(1a\right) & \text{K} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(1b\right) & \text{N} \\ \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(6h\right) & \text{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(6h\right) & \text{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(6h\right) & \text{O} \\ \mathbf{B}_{6} & = & -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(6h\right) & \text{O} \\ \mathbf{B}_{7} & = & -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(6h\right) & \text{O} \\ \mathbf{B}_{8} & = & -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(6h\right) & \text{O} \\ \end{array} \]References
- J. K. Nimmo and B. W. Lucas, The crystal structures of $\gamma$–and $\beta$–KNO3 and the $\alpha$–$\beta$–$\gamma$ phase transformations, Acta Crystallogr. Sect. B Struct. Sci. 32, 1968–1971 (1976), doi:10.1107/S0567740876006894.
Found in
- R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).