K2GeF6 ($J1_{13}$) Structure : A6BC2_hP9_164_i_a_d

Picture of Structure; Click for Big Picture
Prototype : F6GeK2
AFLOW prototype label : A6BC2_hP9_164_i_a_d
Strukturbericht designation : $J1_{13}$
Pearson symbol : hP9
Space group number : 164
Space group symbol : $P\bar{3}m1$
AFLOW prototype command : aflow --proto=A6BC2_hP9_164_i_a_d
--params=
$a$,$c/a$,$z_{2}$,$x_{3}$,$z_{3}$


Other compounds with this structure

  • (NH4)$_2$GeF6, Cs2CeCl6, K2PtF6, and K2SiF6

Trigonal 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} & = & 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{Ge} \\ \mathbf{B}_{2} & = & \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(2d\right) & \mbox{K} \\ \mathbf{B}_{3} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{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(2d\right) & \mbox{K} \\ \mathbf{B}_{4} & = & x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{F} \\ \mathbf{B}_{5} & = & x_{3} \, \mathbf{a}_{1} + 2x_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{3}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{F} \\ \mathbf{B}_{6} & = & -2x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{3}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{F} \\ \mathbf{B}_{7} & = & -x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & \sqrt{3}x_{3}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{F} \\ \mathbf{B}_{8} & = & 2x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{3}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{F} \\ \mathbf{B}_{9} & = & -x_{3} \, \mathbf{a}_{1}-2x_{3} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{3}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{F} \\ \end{array} \]

References

  • J. L. Hoard and W. B. Vincent, Structures of Complex Fluorides. Potassium Hexafluogermanate and Ammonium Hexafluogermanate, J. Am. Chem. Soc. 61, 2849–2852 (1939), doi:10.1021/ja01265a082.

Found in

Geometry files


Prototype Generator

aflow --proto=A6BC2_hP9_164_i_a_d --params=

Species:

Running:

Output: