$\beta'$-LiFeO$_{2}$ Structure: ABC2_mC32_15_2e_2e_2f-002
| Prototype | FeLiO$_{2}$ |
| AFLOW prototype label | ABC2_mC32_15_2e_2e_2f-002 |
| ICSD | 174084 |
| Pearson symbol | mC32 |
| Space group number | 15 |
| Space group symbol | $C2/c$ |
| AFLOW prototype command |
aflow --proto=ABC2_mC32_15_2e_2e_2f-002
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak y_{1}, \allowbreak y_{2}, \allowbreak y_{3}, \allowbreak y_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}$ |
Other compounds with this structure
ErLiO$_{2}$, ErNaO$_{2}$
- FeLiO$_{2}$ exhibits a wide variety of structures, with the exact structure present depends on thermodynamic effects, preparation methods, and charge/discharge history.
- We follow the nomenclature of (Kanno, 1996), where appropriate, with modifications found in (Tabuchi, 1995) and (Abdel-Ghany, 2012). The following list of structures is no doubt incomplete:
- $\alpha$–LiFeO$_{2}$ is in the cubic rock salt ($B1$) structure, with lithium and iron randomly placed on the sodium site and oxygen on the chlorine site. It is synthesized at temperatures above 600°C.
- $\beta$–LiFeO$_{2}$ is a tetragonal distortion of $\alpha$–LiFeO$_{2}$ with the lithium and iron atoms still randomly placed on their sublattice.
- $\beta'$–LiFeO$_{2}$ (this structure) is monoclinic and transforms to $\gamma$–LiFeO$_{2}$ near room temperature. This is likely the phase (Kanno, 1996) refers to as $\beta$–LiFeO$_{2}$.
- $\gamma$–LiFeO$_{2}$ is created by low-temperature synthesis below 500°C and can be considered as an ordered version of $\alpha$–LiFeO$_{2}$, with a doubled unit cell.
- o-LiFeO$_{2}$ is orthorhombic, produced by an ion exchange interaction. It is (meta)-stable below 400°C, transforming to $\alpha$–LiFeO$_{2}$ above 600°C.
- As with $\alpha$- and $\beta$–LiFeO$_{2}$, so of the iron and lithium atoms in $\beta$'-LiFeO$_{2}$ are partially disordered. The Fe-I site is 56% iron and 46% lithium, while the Li-I site is 46% iron and 54% lithium. The Fe-II and Li-II sites are fully ordered.
- Some other sources use ErNaO$_{2}$ as the prototype. We choose $\beta'$–LiFeO$_{2}$ to highlight the connection with the other LiFeO$_{2}$ structures.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- y_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}+\frac{1}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | Fe I |
| $\mathbf{B_{2}}$ | = | $y_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}c \cos{\beta} \,\mathbf{\hat{x}}- b y_{1} \,\mathbf{\hat{y}}+\frac{3}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | Fe I |
| $\mathbf{B_{3}}$ | = | $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | Fe II |
| $\mathbf{B_{4}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}c \cos{\beta} \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | Fe II |
| $\mathbf{B_{5}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | Li I |
| $\mathbf{B_{6}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}c \cos{\beta} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | Li I |
| $\mathbf{B_{7}}$ | = | $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+\frac{1}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | Li II |
| $\mathbf{B_{8}}$ | = | $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}c \cos{\beta} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+\frac{3}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | Li II |
| $\mathbf{B_{9}}$ | = | $\left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O I |
| $\mathbf{B_{10}}$ | = | $- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{5} + c \left(z_{5} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O I |
| $\mathbf{B_{11}}$ | = | $- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- \left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}- c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O I |
| $\mathbf{B_{12}}$ | = | $\left(x_{5} + y_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c \left(z_{5} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O I |
| $\mathbf{B_{13}}$ | = | $\left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O II |
| $\mathbf{B_{14}}$ | = | $- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{6} + c \left(z_{6} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O II |
| $\mathbf{B_{15}}$ | = | $- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}- c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O II |
| $\mathbf{B_{16}}$ | = | $\left(x_{6} + y_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + c \left(z_{6} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O II |
References
- M. Barré and M. Catti, Neutron diffraction study of the β' and γ phases of LiFeO$_{2}$, J. Solid State Chem. 182, 2549–2554 (2009), doi:10.1016/j.jssc.2009.06.029.
- R. Kanno, T. Shirane, Y. Kawamoto, Y. Takeda, M. Takano, M. Ohashi, and Y. Yamaguchi, Synthesis, Structure, and Electrochemical Properties of a New Lithium Iron Oxide, LiFeO$_{2}$, with a Corrugated Layer Structure, J. Electrochem. Soc. 143, 2435–2442 (1996), doi:10.1149/1.1837027.
- A. E. Abdel-Ghany, A. Mauger, H. Groult, K. Zaghib, and C. M. Julien, Structural properties and electrochemistry of α-LiFeO$_{2}$, J. Power Sources 197, 285–291 (2012), doi:10.1016/j.jpowsour.2011.09.054.
- Y. S. Lee, S. Sato, Y. K. Sun, K. Kobayakawa, and Y.Sato, A new type of orthorhombic LiFeO$_{2}$ with advanced battery performance and its structural change during cycling}, J. Power Sources \textbf{119-121, 285–289 (2003), doi:10.1016/S0378-7753(03)00152-6.
- M. Tabuchi, K. Ado, H. Sakaebe, C. Masquelier, H. Kageyama, and O. Nakamura, Preparation of AFeO$_{2}$ (A = Li, Na) by hydrothermal method, Solid State Ionics 79, 220–226 (1995), doi:10.1016/0167-2738(95)00065-E.
Prototype Generator
aflow --proto=ABC2_mC32_15_2e_2e_2f --params=$a,b/a,c/a,\beta,y_{1},y_{2},y_{3},y_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6}$