Li$_{2}$Mn$_{3}$O$_{7}$ Structure: ABC2_hR4_166_a_b_c-011
| Prototype | Li$_{2}$Mn$_{3}$O$_{7}$ |
| AFLOW prototype label | ABC2_hR4_166_a_b_c-011 |
| ICSD | 92859 |
| CCDC | 1652340 |
| Pearson symbol | hR4 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=ABC2_hR4_166_a_b_c-011
--params=$a, \allowbreak c/a, \allowbreak x_{3}$ |
- The given stoichiometry is approximate, the lithium site is only 48% occupied and the manganese site 89%, so the true stoichiometry is Li$_{1.62}$Mn$_{3}$O$_{6.74}$.
- (Raekelboom, 2001) label Li as being on the (3a) site and Mn on the (3b) site, but give the coordinates for (1b) and (1a) respectively. The ICSD uses the coordinates, not the labels, and we follow them.
- However, the AFLOW Label standard shifts the origin of the z-axis by 1/2 c, putting the lithium and manganese atoms on the (1a) and (1b) site and shifting $z_{3}$ from 0.2646 to 0.7646.
- The ICSD assigns this to the NaFeO$_{2}$ structure type, but we feel the vacancies warrant putting it into its own AFLOW prototype.
- $\alpha$–NaFeO$_{2}$, rhombohedral delafossite, CuFeO$_{2}$, caswellsilverite ($F5_{1}$), LiNiO$_{2}$ and Li$_{2}$Mn$_{3}$O$_{7}$ have the same prototype label, ABC2_hR4_166_a_b_c. The structures are generated by the same symmetry operations with different sets of parameters (
--params) specified in their corresponding CIF files. - Hexagonal settings of this structure can be obtained with the option
--hex.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Li I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | Mn I |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $c x_{3} \,\mathbf{\hat{z}}$ | (2c) | O I |
| $\mathbf{B_{4}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- c x_{3} \,\mathbf{\hat{z}}$ | (2c) | O I |
References
- E. A. Raekelboom, A. L. Hector, J. Owen, G. Vitins, and M. T. Weller, Syntheses, Structures, and Preliminary Electrochemistry of the Layered Lithium and Sodium Manganese(IV) Oxides, A$_{2}$Mn$_{3}$O$_{7}$, Chem. of Mater. 13, 4618–4623 (2001), doi:10.1021/cm011105j.
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=ABC2_hR4_166_a_b_c --params=$a,c/a,x_{3}$