Predicted ζ-LiAlO$_{2}$ Structure: ABC2_mC24_12_ah_cg_ij-001
| Prototype | AlLiO$_{2}$ |
| AFLOW prototype label | ABC2_mC24_12_ah_cg_ij-001 |
| ICSD | none |
| Pearson symbol | mC24 |
| Space group number | 12 |
| Space group symbol | $C2/m$ |
| AFLOW prototype command |
aflow --proto=ABC2_mC24_12_ah_cg_ij-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak y_{3}, \allowbreak y_{4}, \allowbreak x_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}$ |
- LiAlO$_{2}$ exists in many different forms. We describe them using the notation of (Liu, 2018):
- $\alpha$, synthesized from Al$_{2}$O$_{3}$ and Li$_{2}$CO$_{3}$ at 600°C (Marezio, 1966) forms in the Caswellsilverite $F5_{1}$ structure, space group $R\overline{3}m$ #166.
- $\beta$ is the low temperature structure (Thery, 1961) forming in the LiGaO$_{2}$ structure, space group $Pna2_{1}$ #33.
- $\beta'$ is a high-pressure monoclinic phase formed at 1.8 GPa and 370°C, but there is not enough information provided to determine either the space group or occupied Wyckoff positions (Chang, 1968).
- $\gamma$ is the standard phase under ambient conditions. It is tetragonal (Marezio, 1965), space group $P4_{1}2_{1}2$ #92.
- $\delta$ is formed at high pressures (9 GPa) under shock compression and takes the $\gamma$–LiFeO$_{2}$ structure.
- $\epsilon$, formed from Al$_{2}$O$_{3}$ and LiH at 500°C, (Debray, 1960) is a cubic phase (space group $I4_{1}32$ #214) with 48 formula units in a cube 12.65Å on a side, but the atomic positions were not determined.
- $\zeta$ (this structure) is a predicted high-pressure monoclinic structure (Liu, 2018), (space group $C2/m$ #12). It is apparently not related to the $\beta'$ phase.
- The $\alpha$, $\beta'$ and $\delta$ phases are metastable under ambient conditions, but transform to $\gamma$–LiAlO$_{2}$ upon heating. (Liu, 2008)
- Data for $\zeta$–LiAlO$_{2}$ was taken from the calculations of (Liu, 2018) at 40 GPa.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (2c) | Li I |
| $\mathbf{B_{3}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}$ | = | $b y_{3} \,\mathbf{\hat{y}}$ | (4g) | Li II |
| $\mathbf{B_{4}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}$ | = | $- b y_{3} \,\mathbf{\hat{y}}$ | (4g) | Li II |
| $\mathbf{B_{5}}$ | = | $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4h) | Al II |
| $\mathbf{B_{6}}$ | = | $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4h) | Al II |
| $\mathbf{B_{7}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O I |
| $\mathbf{B_{8}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- \left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O I |
| $\mathbf{B_{9}}$ | = | $\left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O II |
| $\mathbf{B_{10}}$ | = | $- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}- c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O II |
| $\mathbf{B_{11}}$ | = | $- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}- c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O II |
| $\mathbf{B_{12}}$ | = | $\left(x_{6} + y_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}+c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O II |
References
- G. Liu and H. Liu, First principles study of LiAlO$_{2}$: new dense monoclinic phase under high pressure, J. Phys.: Condens. Matter 30, 115401 (2018), doi:10.1088/1361-648X/aaad23.
- L. Lei, D. He, Y. Zou, W. Zhang, Z. Wang, M. Jiang, and M. Du, J. Solid State Chem.}, Phase transitions of LiAlO$_{2$ at high pressure and high temperature 181, 1810–1815 (2008), doi:10.1016/j.jssc.2008.04.006.
- M. Marezio, The crystal structure and anomalous dispersion of γ-LiAlO$_{2}$, Acta Cryst. 19, 396–400 (1965), doi:10.1107/S0365110X65003511.
- J. Théry, A.-M. Lejus, D. Briançon, and R. Collongues, Sur la structure et les propriétés des aluminates alcalins, Bull. Soc. chim. Fr. pp. 973–975 (1961).
- L. Debray and A. Hardy, Contribution à l'étude structurale des aluminates de lithium, C. R. Hebd. Séances Acad. Sci. 251, 725–726 (1960).
Prototype Generator
aflow --proto=ABC2_mC24_12_ah_cg_ij --params=$a,b/a,c/a,\beta,y_{3},y_{4},x_{5},z_{5},x_{6},y_{6},z_{6}$