K$_{2}$RbSc(PO$_{4}$)$_{2}$ Structure: A2B8C2DE_hP14_164_d_di_d_a_b-001
| Prototype | K$_{2}$O$_{8}$P$_{2}$RbSc |
| AFLOW prototype label | A2B8C2DE_hP14_164_d_di_d_a_b-001 |
| ICSD | 148290 |
| CCDC | 2261864 |
| Pearson symbol | hP14 |
| Space group number | 164 |
| Space group symbol | $P\overline{3}m1$ |
| AFLOW prototype command |
aflow --proto=A2B8C2DE_hP14_164_d_di_d_a_b-001
--params=$a, \allowbreak c/a, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}$ |
Other compounds with this structure
K$_{2}$CsYb(PO$_{4}$)$_{2}$, Rb$_{3}$Er(PO$_{4}$)$_{2}$, Rb$_{3}$Lu(PO$_{4}$)$_{2}$, Rb$_{3}$Yb(PO$_{4}$)$_{2}$
- The ICSD lists KAl(MoO$_{4}$)$_{2}$ as the structure type for these compounds, but the addition of an additional atomic species on a new (2d) site requires a new AFLOW prototype. We arbitrarily chose K$_{2}$RbSc(PO$_{4}$)$_{2}$ as the representative compound.
- K$_{2}$RbSc(PO$_{4}$)$_{2}$ and Na$_{2}$BaMn(VO$_{4}$)$_{2}$ occupy the same Wyckoff positions in space grop $P\overline{3}m1$ #164, but their AFLOW mismatch (Hicks, 2018) is sufficiently large (0.35) that we place them in two different prototypes. The structures are generated by the same symmetry operations with different sets of parameters (
--params) specified in their corresponding CIF files.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Rb I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | Sc I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (2d) | K I |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (2d) | K I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (2d) | O I |
| $\mathbf{B_{6}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (2d) | O I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (2d) | P I |
| $\mathbf{B_{8}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (2d) | P I |
| $\mathbf{B_{9}}$ | = | $x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (6i) | O II |
| $\mathbf{B_{10}}$ | = | $x_{6} \, \mathbf{a}_{1}+2 x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (6i) | O II |
| $\mathbf{B_{11}}$ | = | $- 2 x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (6i) | O II |
| $\mathbf{B_{12}}$ | = | $- x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (6i) | O II |
| $\mathbf{B_{13}}$ | = | $2 x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{6} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (6i) | O II |
| $\mathbf{B_{14}}$ | = | $- x_{6} \, \mathbf{a}_{1}- 2 x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{6} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (6i) | O II |
References
- J. Zhou, P. Gong, M. Xia, and Q. Wu, Co-substitution design: a new glaserite-type rare-earth phosphate K$_{2}$RbSc(PO$_{4}$)$_{2}$ with high structural tolerance, Dalton Trans. 52, 15807–15814 (2023), doi:10.1039/D3DT02494F.
- D. Hicks, C. Oses, E. Gossett, G. Gomez, R. H. Taylor, C. Toher, M. J. Mehl, O. Levy, and S. Curtarolo, AFLOW-SYM: platform for the complete, automatic and self-consistent symmetry analysis of crystals, Acta Crystallogr. Sect. A 74, 184–203 (2018), doi:10.1107/S2053273318003066.
Found in
- Inorganic Crystal Structure Database. Entry 148290 [K2RbSc(PoO4)2].
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=A2B8C2DE_hP14_164_d_di_d_a_b --params=$a,c/a,z_{3},z_{4},z_{5},x_{6},z_{6}$