$\alpha$–LiIO3 Structure : ABC3_hP10_173_b_a_c

Picture of Structure; Click for Big Picture
Prototype : ILiO3
AFLOW prototype label : ABC3_hP10_173_b_a_c
Strukturbericht designation : None
Pearson symbol : hP10
Space group number : 173
Space group symbol : $P6_{3}$
AFLOW prototype command : aflow --proto=ABC3_hP10_173_b_a_c
--params=
$a$,$c/a$,$z_{1}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$


  • LiIO3 is known to exist in three forms:
    • $\alpha$–LiIO3, stable below 470 K: (Zachariasen, 1931) originally determined that the structure of $\alpha$–LiIO3 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.
    • $\beta$–LiIO3, stable from 573 up to the melting point at 708 K.
    • $\gamma$–LiIO3, stable between the $\alpha$– and $\beta$–phases, with an orthorhombic structure in space group $Pna2_1$ #33.

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} & = & z_{1} \, \mathbf{a}_{3} & = & z_{1}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Li} \\ \mathbf{B}_{2} & = & \left(\frac{1}{2} +z_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{1}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Li} \\ \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{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{I} \\ \mathbf{B}_{4} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{I} \\ \mathbf{B}_{5} & = & x_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{3}+y_{3}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{3}+y_{3}\right)a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{O} \\ \mathbf{B}_{6} & = & -y_{3} \, \mathbf{a}_{1} + \left(x_{3}-y_{3}\right) \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{3}-y_{3}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{O} \\ \mathbf{B}_{7} & = & \left(-x_{3}+y_{3}\right) \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \left(-x_{3}+\frac{1}{2}y_{3}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{O} \\ \mathbf{B}_{8} & = & -x_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{3}+y_{3}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{3}-y_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{O} \\ \mathbf{B}_{9} & = & y_{3} \, \mathbf{a}_{1} + \left(-x_{3}+y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{3}+y_{3}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{O} \\ \mathbf{B}_{10} & = & \left(x_{3}-y_{3}\right) \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{3} & = & \left(x_{3}-\frac{1}{2}y_{3}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{O} \\ \end{array} \]

References

  • A. Rosenzweig and B. Morosin, A reinvestigation of the crystal structure of LiIO3, 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).

Geometry files


Prototype Generator

aflow --proto=ABC3_hP10_173_b_a_c --params=

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