Trigonal Na$_{2}$BaMn(VO$_{4}$)$_{2}$ Structure: ABC2D8E2_hP14_164_a_b_d_di_d-001
| Prototype | BaMnNa$_{2}$O$_{8}$V$_{4}$ |
| AFLOW prototype label | ABC2D8E2_hP14_164_a_b_d_di_d-001 |
| ICSD | 13390 |
| CCDC | 1859758 |
| Pearson symbol | hP14 |
| Space group number | 164 |
| Space group symbol | $P\overline{3}m1$ |
| AFLOW prototype command |
aflow --proto=ABC2D8E2_hP14_164_a_b_d_di_d-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$_{2}$BaCa(PO$_{4}$)$_{2}$, K$_{2}$BaMn(VO$_{4}$)$_{2}$, K$_{2}$RbGd(VO$_{4}$)$_{2}$, K$_{2}$RbTb(VO$_{4}$)$_{2}$, Na$_{2}$BaCo(PO$_{4}$)$_{2}$, Na$_{2}$BaCo(VO$_{4}$)$_{2}$, Na$_{2}$BaFe(VO$_{4}$)$_{2}$, Na$_{2}$BaMg(PO$_{4}$)$_{2}$, Na$_{2}$BaMn(PO$_{4}$)$_{2}$, Na$_{2}$BaMn(VO$_{4}$)$_{2}$, Na$_{2}$BaNi(PO$_{4}$)$_{2}$, Sr$_{2}$BaMg(SiO$_{4}$)$_{2}$
- This is a quinary form of K$_{3}$Na(SO$_{4}$)$_{2}$. The ICSD lists K$_{3}$Na(SO$_{4}$)$_{2}$ as the structure type. We arbitrarily chose Na$_{2}$BaMn(VO$_{4}$)$_{2}$ as the prototype structure for the five-element form.
- Na$_{2}$BaMn(VO$_{4}$)$_{2}$ can also be found in a monoclinic form (Sanjeewa, 2019).
- 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) | Ba I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | Mn 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) | Na 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) | Na 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) | V 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) | V 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
- L. D. Sanjeewa, V. O. Garlea, M. A. McGuire, C. D. McMillen, and J. W. Kolis, Magnetic Ground State Crossover in a Series of Glaserite Systems with Triangular Magnetic Lattices, Inorg. Chem. 58, 2813–2121 (2019), doi:10.1021/acs.inorgchem.8b03418.
- 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 13390 [Na2BaMn(VO4)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=ABC2D8E2_hP14_164_a_b_d_di_d --params=$a,c/a,z_{3},z_{4},z_{5},x_{6},z_{6}$