$E2_{3}$ (LiIO$_{3}$) Structure (Obsolete): ABC3_hP10_182_c_b_g-001
| Prototype | ILiO$_{3}$ |
| AFLOW prototype label | ABC3_hP10_182_c_b_g-001 |
| Strukturbericht designation | $E2_{3}$ |
| ICSD | 20012 |
| Pearson symbol | hP10 |
| Space group number | 182 |
| Space group symbol | $P6_322$ |
| AFLOW prototype command |
aflow --proto=ABC3_hP10_182_c_b_g-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}$ |
- LiIO$_{3}$ is known to exist in three forms:
- $\alpha$–LiIO$_{3}$, stable below 470K:
- (Zachariasen, 1931) originally determined that the structure of $\alpha$–LiIO$_{3}$ was in space group $P6_{3}22$ #182, which (Hermann, 1937) designated Strukturbericht $E2_{3}$. (this structure)
- (Rosenzweig, 1966) subsequently determined that this structure was incorrect because of the small sample size, and determined that the true structure was in space group $P6_{3}$ #173.
- $\beta$–LiIO$_{3}$, stable from 573K up to the melting point at 708K.
- $\gamma$–LiIO$_{3}$, stable between the $\alpha$- and $\beta$-phases, with an orthorhombic structure in space group $Pna2_{1}$ #33.
- The ICSD entry is from (Butolin, 1975). If we can obtain a copy we will report on their research into this structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2b) | Li I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2b) | 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) | I I |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2c) | I I |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}$ | = | $\frac{1}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}$ | (6g) | O I |
| $\mathbf{B_{6}}$ | = | $x_{3} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}$ | (6g) | O I |
| $\mathbf{B_{7}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}$ | (6g) | O I |
| $\mathbf{B_{8}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (6g) | O I |
| $\mathbf{B_{9}}$ | = | $- x_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (6g) | O I |
| $\mathbf{B_{10}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (6g) | O I |
References
- W. H. Zachariasen and F. A. Barta, Crystal Structure of Lithium Iodate, Phys. Rev. 37, 1626–1630 (1931), doi:10.1103/PhysRev.37.1626.
- C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928-1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
- S. A. Butolin, L. F. Belova, R. N. Samoylova, O. M. Kotenko, I. M. Dokuchaeva, and N. M. Ivanova, Optical and physico-chemical properties of αLiIO$_{3}$ monocrystal, Izvestiya Akademii Nauk SSSR, Neorganicheskie Materialy 11, 862–865 (1975).
Found in
- A. Rosenzweig and B. Morosin, A reinvestigation of the crystal structure of LiIO$_{3}$, Acta Cryst. 20, 758–761 (1966), doi:10.1107/S0365110X66001804.
Prototype Generator
aflow --proto=ABC3_hP10_182_c_b_g --params=$a,c/a,x_{3}$