α-LiIO$_{3}$ Structure: ABC3_hP10_173_b_a_c-001
| Prototype | ILiO$_{3}$ |
| AFLOW prototype label | ABC3_hP10_173_b_a_c-001 |
| ICSD | 14377 |
| Pearson symbol | hP10 |
| Space group number | 173 |
| Space group symbol | $P6_3$ |
| AFLOW prototype command |
aflow --proto=ABC3_hP10_173_b_a_c-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
- 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 $E2_{3}$.
- (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. (this structure)
- $\beta$–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 uses a = 5.485Å rather than the value 5.1815Å found in (Rosenzweig, 1966). This is perhaps influenced bo (De Boer, 1966) (ICSD 14344) and the original work of (Zachariasen, 1931), who both found values nearer 5.48Å. For now we will continue to use 5.1815Å.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (2a) | Li I |
| $\mathbf{B_{2}}$ | = | $\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Li I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (2b) | I I |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | I I |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} + y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{3} - y_{3}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (6c) | O I |
| $\mathbf{B_{6}}$ | = | $- y_{3} \, \mathbf{a}_{1}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - 2 y_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (6c) | O I |
| $\mathbf{B_{7}}$ | = | $- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{3} - y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (6c) | O I |
| $\mathbf{B_{8}}$ | = | $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{3} + y_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{3} - y_{3}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | O I |
| $\mathbf{B_{9}}$ | = | $y_{3} \, \mathbf{a}_{1}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{3} + 2 y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | O I |
| $\mathbf{B_{10}}$ | = | $\left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{3} - y_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | O I |
References
- A. Rosenzweig and B. Morosin, A reinvestigation of the crystal structure of LiIO$_{3}$, Acta Cryst. 20, 758–761 (1966), doi:10.1107/S0365110X66001804.
- 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).
- J. L. D. Boer, F. van Bolhuis, and R. V. Olthof-Hazekamp, Re-investigation of the crystal structure of lithium iodate, Acta Crystallographica 21, 841–843 (1966), doi:10.1107/S0365110X66004031.
Prototype Generator
aflow --proto=ABC3_hP10_173_b_a_c --params=$a,c/a,z_{1},z_{2},x_{3},y_{3},z_{3}$