α-NaFeO$_{2}$ Structure: ABC2_hR4_166_a_b_c-009
| Prototype | FeNaO$_{2}$ |
| AFLOW prototype label | ABC2_hR4_166_a_b_c-009 |
| ICSD | 187705 |
| 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-009
--params=$a, \allowbreak c/a, \allowbreak x_{3}$ |
Other compounds with this structure
CeRbO$_{2}$, CeRbS$_{2}$, CeRbSSe, CeRbSe$_{2}$, CeRbTe$_{2}$, CeRbTeSe$_{2}$, CsYbSe$_{2}$, KCeS$_{2}$, LiCoO$_{2}$, LiNi$_{2}$, NaCoO$_{2}$, NaYbO$_{2}$, NaYbS$_{2}$, NaYbSe$_{2}$
- This is also referred to as O3-NaFeO$_{2}$.
- This structure is related to O2-LiCoO$_{2}$, O4-LiCoO$_{2}$, and OP4-LiNaCo$_{2}$O$_{4}$.
- $\alpha$–NaFeO$_{2}$ has the same AFLOW Label, ABC2_hR4_166_a_b_c, as rhombohedral delafossite, CuFeO$_{2}$ and caswellsilverite ($F5_{1}$). The difference in the internal parameter $z_{3}$ causes a large change in the bonding of the crystals, so we present them as different structures.
- 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) | Fe 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) | Na 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
- N. Yabuuchi, H. Yoshida, and S. Komaba, Crystal Structures and Electrode Performance of Alpha-NaFeO$_{2}$ for Rechargeable Sodium Batteries, Electrochemistry 80, 716–719 (2012), doi:10.5796/electrochemistry.80.716.
Prototype Generator
aflow --proto=ABC2_hR4_166_a_b_c --params=$a,c/a,x_{3}$