LiO Structure: AB_hP8_194_ac_f-003
| Prototype | LiO |
| AFLOW prototype label | AB_hP8_194_ac_f-003 |
| ICSD | 25530 |
| Pearson symbol | hP8 |
| Space group number | 194 |
| Space group symbol | $P6_3/mmc$ |
| AFLOW prototype command |
aflow --proto=AB_hP8_194_ac_f-003
--params=$a, \allowbreak c/a, \allowbreak z_{3}$ |
Other compounds with this structure
$\beta$-KTe, $\beta$-NaS, $\beta$-NaTe
- (Fehér, 1953) and (Föppl, 1957) presented competing structures for LiO, both in space group $P\overline{6}$ #174. First-principles calculation by (Cota, 2005) and (Chen, 2011) suggest that the Föppl structure is correct, but show that the proper space group is $P6_{3}/mmc$ #194. This is generally held to be the correct structure, e.g. (Jain, 2013). We use the symmetrization of Föppl's original data made by (Cota, 2005).
- The ICSD entry is from Föppl, 1957), updated to make the space group $P6_{3}/mmc$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Li I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2a) | Li I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2c) | Li II |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2c) | Li II |
| $\mathbf{B_{5}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4f) | O I |
| $\mathbf{B_{6}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4f) | O I |
| $\mathbf{B_{7}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (4f) | O I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4f) | O I |
References
- L. G. Cota and P. de la Mora, On the structure of lithium peroxide, Li$_{2}$O$_{2}$, Acta Crystallogr. Sect. B 61, 133–136 (2005), doi:10.1107/S0108768105003629.
- F. Fehér, I. von Wilucki, and G. Dost, Beiträge zur Kenntnis des Wasserstoffperoxyds und seiner Derivate, VII. Mitteil.: Über die Kristallstruktur des Lithiumperoxyds, Li$_{2}$O$_{2}$, Chem. Ber. 86, 1429–1437 (1953), doi:10.1002/cber.19530861111.
- H. Föppl, Die Kristallstrukturen der Alkaliperoxyde, Z. Anorganische und Allgemeine Chemie 291, 12–50 (1957), doi:10.1002/zaac.19572910104.
- A. Jain, S. Ping, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, and K. A. Persson, Commentary: The Materials Project: A materials genome approach to accelerating materials innovation, APL Materials 1, 011002 (2013), doi:10.1063/1.4812323.
Found in
- M. K. Y. Chan, E. L. Shirley, N. K. Karan, M. Balasubramanian, Y. Ren, J. P. Greeley, and T. T. Fister, Structure of Lithium Peroxide, J. Phys. Chem. Lett. 2, 2483–2486 (2011), doi:10.1021/jz201072b.
Prototype Generator
aflow --proto=AB_hP8_194_ac_f --params=$a,c/a,z_{3}$