Li7TaO6 Structure : A8B6C_hR15_148_cf_f_a

Picture of Structure; Click for Big Picture
Prototype : Li7O6Ta
AFLOW prototype label : A8B6C_hR15_148_cf_f_a
Strukturbericht designation : None
Pearson symbol : hR15
Space group number : 148
Space group symbol : $R\bar{3}$
AFLOW prototype command : aflow --proto=A8B6C_hR15_148_cf_f_a
--params=
$a$,$c/a$,$x_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$


  • The Li–I (2c) site is half–occupied.

Rhombohedral primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac{1}{\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & - \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Ta} \\ \mathbf{B}_{2} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & x_{2}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{Li I} \\ \mathbf{B}_{3} & = & -x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2}-x_{2} \, \mathbf{a}_{3} & = & -x_{2}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{Li I} \\ \mathbf{B}_{4} & = & x_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{3}-z_{3}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{3}+\frac{1}{\sqrt{3}}y_{3}-\frac{1}{2\sqrt{3}}z_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{3}+y_{3}+z_{3}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{Li II} \\ \mathbf{B}_{5} & = & z_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + y_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-y_{3}+z_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{\sqrt{3}}x_{3}-\frac{1}{2\sqrt{3}}y_{3}-\frac{1}{2\sqrt{3}}z_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{3}+y_{3}+z_{3}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{Li II} \\ \mathbf{B}_{6} & = & y_{3} \, \mathbf{a}_{1} + z_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{3}+y_{3}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{3}-\frac{1}{2\sqrt{3}}y_{3}+\frac{1}{\sqrt{3}}z_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{3}+y_{3}+z_{3}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{Li II} \\ \mathbf{B}_{7} & = & -x_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{3}+z_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{3}-\frac{1}{\sqrt{3}}y_{3}+\frac{1}{2\sqrt{3}}z_{3}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{3}+y_{3}+z_{3}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{Li II} \\ \mathbf{B}_{8} & = & -z_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-y_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(y_{3}-z_{3}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{\sqrt{3}}x_{3}+\frac{1}{2\sqrt{3}}y_{3}+\frac{1}{2\sqrt{3}}z_{3}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{3}+y_{3}+z_{3}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{Li II} \\ \mathbf{B}_{9} & = & -y_{3} \, \mathbf{a}_{1}-z_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{3}-y_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{3}+\frac{1}{2\sqrt{3}}y_{3}-\frac{1}{\sqrt{3}}z_{3}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{3}+y_{3}+z_{3}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{Li II} \\ \mathbf{B}_{10} & = & x_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{4}-z_{4}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{4}+\frac{1}{\sqrt{3}}y_{4}-\frac{1}{2\sqrt{3}}z_{4}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{4}+y_{4}+z_{4}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{O} \\ \mathbf{B}_{11} & = & z_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + y_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-y_{4}+z_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{\sqrt{3}}x_{4}-\frac{1}{2\sqrt{3}}y_{4}-\frac{1}{2\sqrt{3}}z_{4}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{4}+y_{4}+z_{4}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{O} \\ \mathbf{B}_{12} & = & y_{4} \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{4}+y_{4}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{4}-\frac{1}{2\sqrt{3}}y_{4}+\frac{1}{\sqrt{3}}z_{4}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{4}+y_{4}+z_{4}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{O} \\ \mathbf{B}_{13} & = & -x_{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{4}+z_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{4}-\frac{1}{\sqrt{3}}y_{4}+\frac{1}{2\sqrt{3}}z_{4}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{4}+y_{4}+z_{4}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{O} \\ \mathbf{B}_{14} & = & -z_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-y_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(y_{4}-z_{4}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{\sqrt{3}}x_{4}+\frac{1}{2\sqrt{3}}y_{4}+\frac{1}{2\sqrt{3}}z_{4}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{4}+y_{4}+z_{4}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{O} \\ \mathbf{B}_{15} & = & -y_{4} \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{4}-y_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2\sqrt{3}}x_{4}+\frac{1}{2\sqrt{3}}y_{4}-\frac{1}{\sqrt{3}}z_{4}\right)a \, \mathbf{\hat{y}}-\frac{1}{3}\left(x_{4}+y_{4}+z_{4}\right)c \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{O} \\ \end{array} \]

References

  • G. Wehrum and R. Hoppe, Zur Kenntnis ‘Kationen–reicher’ Tantalate Über Li7[TaO6], Z. Anorg. Allg. Chem. 620, 659–664 (1994), doi:10.1002/zaac.19946200414.

Found in

  • L. Kahle, X. Cheng, T. Binninger, S. D. Lacey, A. Marcolongo, F. Zipoli, E. Gilardi, C. Villevieille, M. El Kazzi, N. Marzari, and D. Pergolesi, The solid–state Li–ion conductor Li7TaO6: A combined computational and experimental study, http://arxiv.org/abs/1910.11079 (2019). ArXiv:1910.11079 [cond–mat.mtrl–sci].

Geometry files


Prototype Generator

aflow --proto=A8B6C_hR15_148_cf_f_a --params=

Species:

Running:

Output: