Rb3AsSe16 Structure: AB3C16_cF160_203_a_bc_eg

Picture of Structure; Click for Big Picture
Prototype : Rb3AsSe16
AFLOW prototype label : AB3C16_cF160_203_a_bc_eg
Strukturbericht designation : None
Pearson symbol : cF160
Space group number : 203
Space group symbol : $Fd\bar{3}$
AFLOW prototype command : aflow --proto=AB3C16_cF160_203_a_bc_eg
--params=
$a$,$x_{4}$,$x_{5}$,$y_{5}$,$z_{5}$


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}{8} \, \mathbf{a}_{1} + \frac{1}{8} \, \mathbf{a}_{2} + \frac{1}{8} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(8a\right) & \mbox{As} \\ \mathbf{B}_{2} & = & \frac{7}{8} \, \mathbf{a}_{1} + \frac{7}{8} \, \mathbf{a}_{2} + \frac{7}{8} \, \mathbf{a}_{3} & = & \frac{7}{8}a \, \mathbf{\hat{x}} + \frac{7}{8}a \, \mathbf{\hat{y}} + \frac{7}{8}a \, \mathbf{\hat{z}} & \left(8a\right) & \mbox{As} \\ \mathbf{B}_{3} & = & \frac{5}{8} \, \mathbf{a}_{1} + \frac{5}{8} \, \mathbf{a}_{2} + \frac{5}{8} \, \mathbf{a}_{3} & = & \frac{5}{8}a \, \mathbf{\hat{x}} + \frac{5}{8}a \, \mathbf{\hat{y}} + \frac{5}{8}a \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{Rb I} \\ \mathbf{B}_{4} & = & \frac{3}{8} \, \mathbf{a}_{1} + \frac{3}{8} \, \mathbf{a}_{2} + \frac{3}{8} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{Rb I} \\ \mathbf{B}_{5} & = & 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(16c\right) & \mbox{Rb II} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} & \left(16c\right) & \mbox{Rb II} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(16c\right) & \mbox{Rb II} \\ \mathbf{B}_{8} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(16c\right) & \mbox{Rb II} \\ \mathbf{B}_{9} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{Se I} \\ \mathbf{B}_{10} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 3x_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{4}\right)a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{Se I} \\ \mathbf{B}_{11} & = & x_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 3x_{4}\right) \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - x_{4}\right)a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - x_{4}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{Se I} \\ \mathbf{B}_{12} & = & \left(\frac{1}{2} - 3x_{4}\right) \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - x_{4}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{Se I} \\ \mathbf{B}_{13} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{Se I} \\ \mathbf{B}_{14} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +3x_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{Se I} \\ \mathbf{B}_{15} & = & -x_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +3x_{4}\right) \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{Se I} \\ \mathbf{B}_{16} & = & \left(\frac{1}{2} +3x_{4}\right) \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{Se I} \\ \mathbf{B}_{17} & = & \left(-x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + y_{5}a \, \mathbf{\hat{y}} + z_{5}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{18} & = & \left(x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - y_{5}\right)a \, \mathbf{\hat{y}} + z_{5}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{19} & = & \left(x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - x_{5}\right)a \, \mathbf{\hat{x}} + y_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - z_{5}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} - x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - y_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - z_{5}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{21} & = & \left(x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & z_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + y_{5}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{22} & = & \left(\frac{1}{2} - x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & z_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - y_{5}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{23} & = & \left(-x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - z_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{5}\right)a \, \mathbf{\hat{y}} + y_{5}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{24} & = & \left(x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - z_{5}\right)a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - y_{5}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{25} & = & \left(x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & y_{5}a \, \mathbf{\hat{x}} + z_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{26} & = & \left(-x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - y_{5}\right)a \, \mathbf{\hat{x}} + z_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - x_{5}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{27} & = & \left(\frac{1}{2} - x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & y_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - x_{5}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{28} & = & \left(x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - y_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - z_{5}\right)a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{29} & = & \left(x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-y_{5}a \, \mathbf{\hat{y}}-z_{5}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{30} & = & \left(-x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{5}\right)a \, \mathbf{\hat{y}}-z_{5}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{31} & = & \left(-x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{5}\right)a \, \mathbf{\hat{x}}-y_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{5}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{32} & = & \left(\frac{1}{2} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{5}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{33} & = & \left(-x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & -z_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}}-y_{5}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{34} & = & \left(\frac{1}{2} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & -z_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{5}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{35} & = & \left(x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{5}\right)a \, \mathbf{\hat{y}}-y_{5}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{36} & = & \left(-x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{5}\right)a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{5}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{37} & = & \left(-x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & -y_{5}a \, \mathbf{\hat{x}}-z_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{38} & = & \left(x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{5}\right)a \, \mathbf{\hat{x}}-z_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{39} & = & \left(\frac{1}{2} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}-y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & -y_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \mathbf{B}_{40} & = & \left(-x_{5}-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{5}\right)a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{Se II} \\ \end{array} \]

References

  • M. Wachhold and W. S. Sheldrick, Methanolothermale Synthese von Rb3AsSe4 textperiodcentered 2Se6 und Cs3AsSe4textperiodcentered 2Cs2As2Se4textperiodcentered 6Te4Se2, zwei Selenidoarsenate mit sechsgliedrigen Chalkogenringen/Methanolothermal Synthesis of Rb3AsSe4textperiodcentered 2Se6 and Cs3AsSe4textperiodcentered 2Cs2As2Se4textperiodcentered 6Te4Se2. Two Selenidoarsenates with Six–Membered Chalcogen Rings, Z. Naturforsch. B 52, 169–175 (1997), doi:10.1515/znb-1997-0204.

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=AB3C16_cF160_203_a_bc_eg --params=

Species:

Running:

Output: