KNaSO$_{4}$ Structure: ABC4D_hP14_156_ac_bc_ab2d_ab-001
| Prototype | KNaO$_{4}$S |
| AFLOW prototype label | ABC4D_hP14_156_ac_bc_ab2d_ab-001 |
| ICSD | 133733 |
| Pearson symbol | hP14 |
| Space group number | 156 |
| Space group symbol | $P3m1$ |
| AFLOW prototype command |
aflow --proto=ABC4D_hP14_156_ac_bc_ab2d_ab-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak z_{7}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak z_{10}$ |
- We have shifted the origin so that the atom (Okada, 1980) label K(2) is at the origin. Note that space group $P3m1$ #156 allows an arbitrary origin for the $z$-axis. In addition, the origin can be shifted so that (1b) or (1c) atoms are moved to the origin.
- There is no ICSD for the (Okada, 1980) structure of KNaSO$_{4}$, although the ICSD has entries for K$_{3}$Na(SO$_{4}$)$_{2}$ from the same paper. We provide the ICSD entry from the later work of (Filatov, 2019), who named the mineral form belomarinaite.
- Belomarinaite has some mixture of sodium and potassium on the (1a) and (1c) sites that was not reported by (Okada, 1980).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (1a) | K I |
| $\mathbf{B_{2}}$ | = | $z_{2} \, \mathbf{a}_{3}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (1a) | O I |
| $\mathbf{B_{3}}$ | = | $z_{3} \, \mathbf{a}_{3}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (1a) | S I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (1b) | Na I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (1b) | O II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (1b) | S II |
| $\mathbf{B_{7}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (1c) | K II |
| $\mathbf{B_{8}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (1c) | Na II |
| $\mathbf{B_{9}}$ | = | $x_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (3d) | O III |
| $\mathbf{B_{10}}$ | = | $x_{9} \, \mathbf{a}_{1}+2 x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{9} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (3d) | O III |
| $\mathbf{B_{11}}$ | = | $- 2 x_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{9} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (3d) | O III |
| $\mathbf{B_{12}}$ | = | $x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (3d) | O IV |
| $\mathbf{B_{13}}$ | = | $x_{10} \, \mathbf{a}_{1}+2 x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{10} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (3d) | O IV |
| $\mathbf{B_{14}}$ | = | $- 2 x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{10} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (3d) | O IV |
References
- K. Okada and J. Ossaka, Structures of potassium sodium sulphate and tripotassium sodium disulphate, Acta Crystallogr. Sect. B 36, 919–921 (1980), doi:10.1107/S0567740880004852.
- S. K. Filatov, A. P. Shablinskii, L. P. Vergasova, O. U. Saprikina, R. S. Bubnova, S. V. Moskaleva, and A. B. Belousov, Belomarinaite KNa(SO$_{4}$): A new sulfate from 2012–2013 Tolbachik Fissure eruption, Kamchatka Peninsula, Russia, Mineral. Mag. 81, 569–578 (2019), doi:10.1180/mgm.2018.170.
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=ABC4D_hP14_156_ac_bc_ab2d_ab --params=$a,c/a,z_{1},z_{2},z_{3},z_{4},z_{5},z_{6},z_{7},z_{8},x_{9},z_{9},x_{10},z_{10}$