K2Sn(OH)6 ($H6_{2}$) Structure : A6B2C6D_hR15_148_f_c_f_a

Picture of Structure; Click for Big Picture
Prototype : H6K2O6Sn
AFLOW prototype label : A6B2C6D_hR15_148_f_c_f_a
Strukturbericht designation : $H6_{2}$
Pearson symbol : hR15
Space group number : 148
Space group symbol : $R\bar{3}$
AFLOW prototype command : aflow --proto=A6B2C6D_hR15_148_f_c_f_a
--params=
$a$,$c/a$,$x_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$


Other compounds with this structure

  • K2Pt(OH)6 and Na2Sn(OH)6

  • (Wyckoff, 1928) found the positions of the potassium and tin atoms in this structure. He could not locate the oxygen atoms, and so was unable to give an unequivocal determination of the space group, beyond noting that it was rhombohedral. We use the modern structure of (Jacobs, 2000), which agrees with Wyckoff in the positioning of the potassium and tin atoms, and finds both the hydrogen and oxygen locations.
  • (Ewald, 1931) gave this the Strukturbericht designation $H6_{2}$. (Hermann, 1937) began relabeling the $H6$ structures as $I1$, and (Gottfried, 1937) relabeled them as $J1$, but neither they nor successor volumes revisited this structure, so it was never formally relabeled $J12. We will therefore leave it as $H6_{2}$.

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{Sn} \\ \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{K} \\ \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{K} \\ \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{H} \\ \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{H} \\ \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{H} \\ \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{H} \\ \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{H} \\ \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{H} \\ \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

  • R. W. G. Wyckoff, The Crystal Structure of Potassium Hydroxystannate, K2Sn(OH)6, Am. J. Sci. s5–15, 297–302 (1928), doi:10.2475/ajs.s5-15.88.297.
  • P. P. Ewald and C. Hermann, eds., Strukturbericht 1913–1928 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1931).
  • C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928–1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
  • C. Gottfried and F. Schossberger, eds., Strukturbericht Band III 1933–1935 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).

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