Rb2Mo2O7 Structure : A2B7C2_oC88_40_abc_2b6c_a3b

Picture of Structure; Click for Big Picture
Prototype : Mo2O7Rb2
AFLOW prototype label : A2B7C2_oC88_40_abc_2b6c_a3b
Strukturbericht designation : None
Pearson symbol : oC88
Space group number : 40
Space group symbol : $Ama2$
AFLOW prototype command : aflow --proto=A2B7C2_oC88_40_abc_2b6c_a3b
--params=
$a$,$b/a$,$c/a$,$z_{1}$,$z_{2}$,$y_{3}$,$z_{3}$,$y_{4}$,$z_{4}$,$y_{5}$,$z_{5}$,$y_{6}$,$z_{6}$,$y_{7}$,$z_{7}$,$y_{8}$,$z_{8}$,$x_{9}$,$y_{9}$,$z_{9}$,$x_{10}$,$y_{10}$,$z_{10}$,$x_{11}$,$y_{11}$,$z_{11}$,$x_{12}$,$y_{12}$,$z_{12}$,$x_{13}$,$y_{13}$,$z_{13}$,$x_{14}$,$y_{14}$,$z_{14}$,$x_{15}$,$y_{15}$,$z_{15}$


Base-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & -z_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & z_{1}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Mo I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1}-z_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + z_{1}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Mo I} \\ \mathbf{B}_{3} & = & -z_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & z_{2}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Rb I} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1}-z_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + z_{2}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Rb I} \\ \mathbf{B}_{5} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{3}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Mo II} \\ \mathbf{B}_{6} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{3}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Mo II} \\ \mathbf{B}_{7} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(y_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(y_{4}+z_{4}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{O I} \\ \mathbf{B}_{8} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(-y_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(-y_{4}+z_{4}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{O I} \\ \mathbf{B}_{9} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{5}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{O II} \\ \mathbf{B}_{10} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(-y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(-y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{5}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{O II} \\ \mathbf{B}_{11} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(y_{6}-z_{6}\right) \, \mathbf{a}_{2} + \left(y_{6}+z_{6}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Rb II} \\ \mathbf{B}_{12} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(-y_{6}-z_{6}\right) \, \mathbf{a}_{2} + \left(-y_{6}+z_{6}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Rb II} \\ \mathbf{B}_{13} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Rb III} \\ \mathbf{B}_{14} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Rb III} \\ \mathbf{B}_{15} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(y_{8}-z_{8}\right) \, \mathbf{a}_{2} + \left(y_{8}+z_{8}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Rb IV} \\ \mathbf{B}_{16} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(-y_{8}-z_{8}\right) \, \mathbf{a}_{2} + \left(-y_{8}+z_{8}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Rb IV} \\ \mathbf{B}_{17} & = & x_{9} \, \mathbf{a}_{1} + \left(y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Mo III} \\ \mathbf{B}_{18} & = & -x_{9} \, \mathbf{a}_{1} + \left(-y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(-y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Mo III} \\ \mathbf{B}_{19} & = & \left(\frac{1}{2} +x_{9}\right) \, \mathbf{a}_{1} + \left(-y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(-y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{9}\right)a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Mo III} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} - x_{9}\right) \, \mathbf{a}_{1} + \left(y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{9}\right)a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Mo III} \\ \mathbf{B}_{21} & = & x_{10} \, \mathbf{a}_{1} + \left(y_{10}-z_{10}\right) \, \mathbf{a}_{2} + \left(y_{10}+z_{10}\right) \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}} + y_{10}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O III} \\ \mathbf{B}_{22} & = & -x_{10} \, \mathbf{a}_{1} + \left(-y_{10}-z_{10}\right) \, \mathbf{a}_{2} + \left(-y_{10}+z_{10}\right) \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}}-y_{10}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O III} \\ \mathbf{B}_{23} & = & \left(\frac{1}{2} +x_{10}\right) \, \mathbf{a}_{1} + \left(-y_{10}-z_{10}\right) \, \mathbf{a}_{2} + \left(-y_{10}+z_{10}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{10}\right)a \, \mathbf{\hat{x}}-y_{10}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O III} \\ \mathbf{B}_{24} & = & \left(\frac{1}{2} - x_{10}\right) \, \mathbf{a}_{1} + \left(y_{10}-z_{10}\right) \, \mathbf{a}_{2} + \left(y_{10}+z_{10}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{10}\right)a \, \mathbf{\hat{x}} + y_{10}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O III} \\ \mathbf{B}_{25} & = & x_{11} \, \mathbf{a}_{1} + \left(y_{11}-z_{11}\right) \, \mathbf{a}_{2} + \left(y_{11}+z_{11}\right) \, \mathbf{a}_{3} & = & x_{11}a \, \mathbf{\hat{x}} + y_{11}b \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O IV} \\ \mathbf{B}_{26} & = & -x_{11} \, \mathbf{a}_{1} + \left(-y_{11}-z_{11}\right) \, \mathbf{a}_{2} + \left(-y_{11}+z_{11}\right) \, \mathbf{a}_{3} & = & -x_{11}a \, \mathbf{\hat{x}}-y_{11}b \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O IV} \\ \mathbf{B}_{27} & = & \left(\frac{1}{2} +x_{11}\right) \, \mathbf{a}_{1} + \left(-y_{11}-z_{11}\right) \, \mathbf{a}_{2} + \left(-y_{11}+z_{11}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{11}\right)a \, \mathbf{\hat{x}}-y_{11}b \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O IV} \\ \mathbf{B}_{28} & = & \left(\frac{1}{2} - x_{11}\right) \, \mathbf{a}_{1} + \left(y_{11}-z_{11}\right) \, \mathbf{a}_{2} + \left(y_{11}+z_{11}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{11}\right)a \, \mathbf{\hat{x}} + y_{11}b \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O IV} \\ \mathbf{B}_{29} & = & x_{12} \, \mathbf{a}_{1} + \left(y_{12}-z_{12}\right) \, \mathbf{a}_{2} + \left(y_{12}+z_{12}\right) \, \mathbf{a}_{3} & = & x_{12}a \, \mathbf{\hat{x}} + y_{12}b \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O V} \\ \mathbf{B}_{30} & = & -x_{12} \, \mathbf{a}_{1} + \left(-y_{12}-z_{12}\right) \, \mathbf{a}_{2} + \left(-y_{12}+z_{12}\right) \, \mathbf{a}_{3} & = & -x_{12}a \, \mathbf{\hat{x}}-y_{12}b \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O V} \\ \mathbf{B}_{31} & = & \left(\frac{1}{2} +x_{12}\right) \, \mathbf{a}_{1} + \left(-y_{12}-z_{12}\right) \, \mathbf{a}_{2} + \left(-y_{12}+z_{12}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{12}\right)a \, \mathbf{\hat{x}}-y_{12}b \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O V} \\ \mathbf{B}_{32} & = & \left(\frac{1}{2} - x_{12}\right) \, \mathbf{a}_{1} + \left(y_{12}-z_{12}\right) \, \mathbf{a}_{2} + \left(y_{12}+z_{12}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{12}\right)a \, \mathbf{\hat{x}} + y_{12}b \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O V} \\ \mathbf{B}_{33} & = & x_{13} \, \mathbf{a}_{1} + \left(y_{13}-z_{13}\right) \, \mathbf{a}_{2} + \left(y_{13}+z_{13}\right) \, \mathbf{a}_{3} & = & x_{13}a \, \mathbf{\hat{x}} + y_{13}b \, \mathbf{\hat{y}} + z_{13}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O VI} \\ \mathbf{B}_{34} & = & -x_{13} \, \mathbf{a}_{1} + \left(-y_{13}-z_{13}\right) \, \mathbf{a}_{2} + \left(-y_{13}+z_{13}\right) \, \mathbf{a}_{3} & = & -x_{13}a \, \mathbf{\hat{x}}-y_{13}b \, \mathbf{\hat{y}} + z_{13}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O VI} \\ \mathbf{B}_{35} & = & \left(\frac{1}{2} +x_{13}\right) \, \mathbf{a}_{1} + \left(-y_{13}-z_{13}\right) \, \mathbf{a}_{2} + \left(-y_{13}+z_{13}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{13}\right)a \, \mathbf{\hat{x}}-y_{13}b \, \mathbf{\hat{y}} + z_{13}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O VI} \\ \mathbf{B}_{36} & = & \left(\frac{1}{2} - x_{13}\right) \, \mathbf{a}_{1} + \left(y_{13}-z_{13}\right) \, \mathbf{a}_{2} + \left(y_{13}+z_{13}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{13}\right)a \, \mathbf{\hat{x}} + y_{13}b \, \mathbf{\hat{y}} + z_{13}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O VI} \\ \mathbf{B}_{37} & = & x_{14} \, \mathbf{a}_{1} + \left(y_{14}-z_{14}\right) \, \mathbf{a}_{2} + \left(y_{14}+z_{14}\right) \, \mathbf{a}_{3} & = & x_{14}a \, \mathbf{\hat{x}} + y_{14}b \, \mathbf{\hat{y}} + z_{14}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O VII} \\ \mathbf{B}_{38} & = & -x_{14} \, \mathbf{a}_{1} + \left(-y_{14}-z_{14}\right) \, \mathbf{a}_{2} + \left(-y_{14}+z_{14}\right) \, \mathbf{a}_{3} & = & -x_{14}a \, \mathbf{\hat{x}}-y_{14}b \, \mathbf{\hat{y}} + z_{14}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O VII} \\ \mathbf{B}_{39} & = & \left(\frac{1}{2} +x_{14}\right) \, \mathbf{a}_{1} + \left(-y_{14}-z_{14}\right) \, \mathbf{a}_{2} + \left(-y_{14}+z_{14}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{14}\right)a \, \mathbf{\hat{x}}-y_{14}b \, \mathbf{\hat{y}} + z_{14}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O VII} \\ \mathbf{B}_{40} & = & \left(\frac{1}{2} - x_{14}\right) \, \mathbf{a}_{1} + \left(y_{14}-z_{14}\right) \, \mathbf{a}_{2} + \left(y_{14}+z_{14}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{14}\right)a \, \mathbf{\hat{x}} + y_{14}b \, \mathbf{\hat{y}} + z_{14}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O VII} \\ \mathbf{B}_{41} & = & x_{15} \, \mathbf{a}_{1} + \left(y_{15}-z_{15}\right) \, \mathbf{a}_{2} + \left(y_{15}+z_{15}\right) \, \mathbf{a}_{3} & = & x_{15}a \, \mathbf{\hat{x}} + y_{15}b \, \mathbf{\hat{y}} + z_{15}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O VIII} \\ \mathbf{B}_{42} & = & -x_{15} \, \mathbf{a}_{1} + \left(-y_{15}-z_{15}\right) \, \mathbf{a}_{2} + \left(-y_{15}+z_{15}\right) \, \mathbf{a}_{3} & = & -x_{15}a \, \mathbf{\hat{x}}-y_{15}b \, \mathbf{\hat{y}} + z_{15}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O VIII} \\ \mathbf{B}_{43} & = & \left(\frac{1}{2} +x_{15}\right) \, \mathbf{a}_{1} + \left(-y_{15}-z_{15}\right) \, \mathbf{a}_{2} + \left(-y_{15}+z_{15}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{15}\right)a \, \mathbf{\hat{x}}-y_{15}b \, \mathbf{\hat{y}} + z_{15}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O VIII} \\ \mathbf{B}_{44} & = & \left(\frac{1}{2} - x_{15}\right) \, \mathbf{a}_{1} + \left(y_{15}-z_{15}\right) \, \mathbf{a}_{2} + \left(y_{15}+z_{15}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{15}\right)a \, \mathbf{\hat{x}} + y_{15}b \, \mathbf{\hat{y}} + z_{15}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O VIII} \\ \end{array} \]

References

  • Z. A. Solodovnikova and S. F. Solodovnikov, Rubidium dimolybdate, Rb2Mo2O7, and caesium dimolybdate, Cs2Mo2O7, Acta Crystallogr. C 62, i53–i56 (2006), doi:10.1107/S0108270106014880.

Geometry files


Prototype Generator

aflow --proto=A2B7C2_oC88_40_abc_2b6c_a3b --params=

Species:

Running:

Output: