KB6H6 Structure: A6B6C_cF104_202_h_h_c

Picture of Structure; Click for Big Picture
Prototype : KB6H6
AFLOW prototype label : A6B6C_cF104_202_h_h_c
Strukturbericht designation : None
Pearson symbol : cF104
Space group number : 202
Space group symbol : $Fm\bar{3}$
AFLOW prototype command : aflow --proto=A6B6C_cF104_202_h_h_c
--params=
$a$,$y_{2}$,$z_{2}$,$y_{3}$,$z_{3}$


Face-centered Cubic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{K} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{K} \\ \mathbf{B}_{3} & = & \left(y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(-y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{y}} + z_{2}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{B} \\ \mathbf{B}_{4} & = & \left(-y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(-y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{y}} + z_{2}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{B} \\ \mathbf{B}_{5} & = & \left(y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(-y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{y}}-z_{2}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{B} \\ \mathbf{B}_{6} & = & \left(-y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(-y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{y}}-z_{2}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{B} \\ \mathbf{B}_{7} & = & \left(y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(-y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & z_{2}a \, \mathbf{\hat{x}} + y_{2}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{B} \\ \mathbf{B}_{8} & = & \left(-y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(-y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & z_{2}a \, \mathbf{\hat{x}}-y_{2}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{B} \\ \mathbf{B}_{9} & = & \left(y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(-y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & -z_{2}a \, \mathbf{\hat{x}} + y_{2}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{B} \\ \mathbf{B}_{10} & = & \left(-y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(-y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & -z_{2}a \, \mathbf{\hat{x}}-y_{2}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{B} \\ \mathbf{B}_{11} & = & \left(-y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{x}} + z_{2}a \, \mathbf{\hat{y}} & \left(48h\right) & \mbox{B} \\ \mathbf{B}_{12} & = & \left(y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(-y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(-y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{x}} + z_{2}a \, \mathbf{\hat{y}} & \left(48h\right) & \mbox{B} \\ \mathbf{B}_{13} & = & \left(-y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{x}}-z_{2}a \, \mathbf{\hat{y}} & \left(48h\right) & \mbox{B} \\ \mathbf{B}_{14} & = & \left(y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(-y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(-y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{x}}-z_{2}a \, \mathbf{\hat{y}} & \left(48h\right) & \mbox{B} \\ \mathbf{B}_{15} & = & \left(y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{y}} + z_{3}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{H} \\ \mathbf{B}_{16} & = & \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{y}} + z_{3}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{H} \\ \mathbf{B}_{17} & = & \left(y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{y}}-z_{3}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{H} \\ \mathbf{B}_{18} & = & \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{y}}-z_{3}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{H} \\ \mathbf{B}_{19} & = & \left(y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & z_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{H} \\ \mathbf{B}_{20} & = & \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & z_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{H} \\ \mathbf{B}_{21} & = & \left(y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -z_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{H} \\ \mathbf{B}_{22} & = & \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -z_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{H} \\ \mathbf{B}_{23} & = & \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}} + z_{3}a \, \mathbf{\hat{y}} & \left(48h\right) & \mbox{H} \\ \mathbf{B}_{24} & = & \left(y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}} + z_{3}a \, \mathbf{\hat{y}} & \left(48h\right) & \mbox{H} \\ \mathbf{B}_{25} & = & \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}}-z_{3}a \, \mathbf{\hat{y}} & \left(48h\right) & \mbox{H} \\ \mathbf{B}_{26} & = & \left(y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}}-z_{3}a \, \mathbf{\hat{y}} & \left(48h\right) & \mbox{H} \\ \end{array} \]

References

  • J. A. Wunderlich and W. N. Lipscomb, Structure of B12H12–2 Ion, J. Am. Chem. Soc. 82, 4427–4428 (1960), doi:10.1021/ja01501a076.

Found in

  • P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds, ASM International (2013).

Geometry files


Prototype Generator

aflow --proto=A6B6C_cF104_202_h_h_c --params=

Species:

Running:

Output: