$E2_{3}$ (LiIO3) (obsolete) Structure : ABC3_hP10_182_c_b_g

Picture of Structure; Click for Big Picture
Prototype : ILiO3
AFLOW prototype label : ABC3_hP10_182_c_b_g
Strukturbericht designation : $E2_{3}$
Pearson symbol : hP10
Space group number : 182
Space group symbol : $P6_{3}22$
AFLOW prototype command : aflow --proto=ABC3_hP10_182_c_b_g
--params=
$a$,$c/a$,$x_{3}$


  • LiIO3 is known to exist in three forms:
    • $\alpha$–LiIO3, stable below 273 K: (Zachariasen, 1931) originally determined that this was the structure of $\alpha$–LiIO3, and (Hermann, 1937) designated it as 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.
    • $\beta$–LiIO3, stable from 573 K up to the melting point at 708 K.
    • $\gamma$–LiIO3, stable between the $\alpha$– and $\beta$–phases, with an orthorhombic structure.

Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{Li} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{Li} \\ \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{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{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{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{I} \\ \mathbf{B}_{5} & = & x_{3} \, \mathbf{a}_{1} & = & \frac{1}{2}x_{3}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} & \left(6g\right) & \mbox{O} \\ \mathbf{B}_{6} & = & x_{3} \, \mathbf{a}_{2} & = & \frac{1}{2}x_{3}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} & \left(6g\right) & \mbox{O} \\ \mathbf{B}_{7} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} & = & -x_{3}a \, \mathbf{\hat{x}} & \left(6g\right) & \mbox{O} \\ \mathbf{B}_{8} & = & -x_{3} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & -\frac{1}{2}x_{3}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{O} \\ \mathbf{B}_{9} & = & -x_{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -\frac{1}{2}x_{3}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{O} \\ \mathbf{B}_{10} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{O} \\ \end{array} \]

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).

Found in

  • A. Rosenzweig and B. Morosin, A reinvestigation of the crystal structure of LiIO3, Acta Cryst. 20, 758–761 (1966), doi:10.1107/S0365110X66001804.

Geometry files


Prototype Generator

aflow --proto=ABC3_hP10_182_c_b_g --params=

Species:

Running:

Output: