LiClO4·3H2O ($H4_{18}$) Structure : AB6CD7_hP30_186_b_d_a_b2c

Picture of Structure; Click for Big Picture
Prototype : ClH6LiO7
AFLOW prototype label : AB6CD7_hP30_186_b_d_a_b2c
Strukturbericht designation : $H4_{18}$
Pearson symbol : hP30
Space group number : 186
Space group symbol : $P6_{3}mc$
AFLOW prototype command : aflow --proto=AB6CD7_hP30_186_b_d_a_b2c
--params=
$a$,$c/a$,$z_{1}$,$z_{2}$,$z_{3}$,$x_{4}$,$z_{4}$,$x_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$


Other compounds with this structure

  • LiTcO4·3H2O

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{Cl} \\ \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{Cl} \\ \mathbf{B}_{5} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{O I} \\ \mathbf{B}_{6} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{3}\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_{3}\right)c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{O I} \\ \mathbf{B}_{7} & = & x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{O II} \\ \mathbf{B}_{8} & = & x_{4} \, \mathbf{a}_{1} + 2x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{O II} \\ \mathbf{B}_{9} & = & -2x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{O II} \\ \mathbf{B}_{10} & = & -x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{3} & = & \sqrt{3}x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{O II} \\ \mathbf{B}_{11} & = & -x_{4} \, \mathbf{a}_{1}-2x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{4}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{O II} \\ \mathbf{B}_{12} & = & 2x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{3} & = & \frac{3}{2}x_{4}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{O II} \\ \mathbf{B}_{13} & = & x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{O III} \\ \mathbf{B}_{14} & = & x_{5} \, \mathbf{a}_{1} + 2x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{5}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{O III} \\ \mathbf{B}_{15} & = & -2x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{5}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{O III} \\ \mathbf{B}_{16} & = & -x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{3} & = & \sqrt{3}x_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{O III} \\ \mathbf{B}_{17} & = & -x_{5} \, \mathbf{a}_{1}-2x_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{5}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{O III} \\ \mathbf{B}_{18} & = & 2x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{3} & = & \frac{3}{2}x_{5}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{O III} \\ \mathbf{B}_{19} & = & x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{6}+y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{6}+y_{6}\right)a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{H} \\ \mathbf{B}_{20} & = & -y_{6} \, \mathbf{a}_{1} + \left(x_{6}-y_{6}\right) \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{6}-y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{H} \\ \mathbf{B}_{21} & = & \left(-x_{6}+y_{6}\right) \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(-x_{6}+\frac{1}{2}y_{6}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{H} \\ \mathbf{B}_{22} & = & -x_{6} \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{6}+y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{6}-y_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)c \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{H} \\ \mathbf{B}_{23} & = & y_{6} \, \mathbf{a}_{1} + \left(-x_{6}+y_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{6}+y_{6}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)c \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{H} \\ \mathbf{B}_{24} & = & \left(x_{6}-y_{6}\right) \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & \left(x_{6}-\frac{1}{2}y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)c \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{H} \\ \mathbf{B}_{25} & = & -y_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{6}+y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{6}+y_{6}\right)a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{H} \\ \mathbf{B}_{26} & = & \left(-x_{6}+y_{6}\right) \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{6}+y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{H} \\ \mathbf{B}_{27} & = & x_{6} \, \mathbf{a}_{1} + \left(x_{6}-y_{6}\right) \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(x_{6}-\frac{1}{2}y_{6}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{H} \\ \mathbf{B}_{28} & = & y_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{6}+y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{6}-y_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)c \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{H} \\ \mathbf{B}_{29} & = & \left(x_{6}-y_{6}\right) \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{6}-y_{6}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)c \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{H} \\ \mathbf{B}_{30} & = & -x_{6} \, \mathbf{a}_{1} + \left(-x_{6}+y_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & \left(-x_{6}+\frac{1}{2}y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)c \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{H} \\ \end{array} \]

References

  • J.–O. Lundgren, R. Liminga, and R. Tellgren, Neutron diffraction refinement of pyroelectric lithium perchlorate trihydrate, Acta Crystallogr. Sect. B Struct. Sci. 38, 15–20 (1982), doi:10.1107/S0567740882001940.

Found in

  • L. Ojamäe and K. Hermansson, The OH stretching frequency in LiClO4·3H2O(s) from ab initio and model potential calculations, Chem. Phys. 161, 87–98 (1992), doi:10.1016/0301-0104(92)80179-Y.

Geometry files


Prototype Generator

aflow --proto=AB6CD7_hP30_186_b_d_a_b2c --params=

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