Bi3Ru3O11 Structure : A3B11C3_cP68_201_be_efh_g

Picture of Structure; Click for Big Picture
Prototype : Bi3O11Ru3
AFLOW prototype label : A3B11C3_cP68_201_be_efh_g
Strukturbericht designation : None
Pearson symbol : cP68
Space group number : 201
Space group symbol : $Pn\bar{3}$
AFLOW prototype command : aflow --proto=A3B11C3_cP68_201_be_efh_g
--params=
$a$,$x_{2}$,$x_{3}$,$x_{4}$,$x_{5}$,$x_{6}$,$y_{6}$,$z_{6}$


Simple Cubic primitive vectors:

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

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(4b\right) & \mbox{Bi I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} & \left(4b\right) & \mbox{Bi I} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Bi I} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Bi I} \\ \mathbf{B}_{5} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{Bi II} \\ \mathbf{B}_{6} & = & \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{Bi II} \\ \mathbf{B}_{7} & = & \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{Bi II} \\ \mathbf{B}_{8} & = & x_{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{Bi II} \\ \mathbf{B}_{9} & = & -x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2}-x_{2} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{Bi II} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{2}-x_{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{Bi II} \\ \mathbf{B}_{11} & = & \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{Bi II} \\ \mathbf{B}_{12} & = & -x_{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{Bi II} \\ \mathbf{B}_{13} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{O I} \\ \mathbf{B}_{14} & = & \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{O I} \\ \mathbf{B}_{15} & = & \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{O I} \\ \mathbf{B}_{16} & = & x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{O I} \\ \mathbf{B}_{17} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{O I} \\ \mathbf{B}_{18} & = & \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{O I} \\ \mathbf{B}_{19} & = & \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{O I} \\ \mathbf{B}_{20} & = & -x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{O I} \\ \mathbf{B}_{21} & = & x_{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(12f\right) & \mbox{O II} \\ \mathbf{B}_{22} & = & \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(12f\right) & \mbox{O II} \\ \mathbf{B}_{23} & = & \frac{1}{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(12f\right) & \mbox{O II} \\ \mathbf{B}_{24} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(12f\right) & \mbox{O II} \\ \mathbf{B}_{25} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(12f\right) & \mbox{O II} \\ \mathbf{B}_{26} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{z}} & \left(12f\right) & \mbox{O II} \\ \mathbf{B}_{27} & = & -x_{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(12f\right) & \mbox{O II} \\ \mathbf{B}_{28} & = & \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(12f\right) & \mbox{O II} \\ \mathbf{B}_{29} & = & \frac{3}{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(12f\right) & \mbox{O II} \\ \mathbf{B}_{30} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(12f\right) & \mbox{O II} \\ \mathbf{B}_{31} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(12f\right) & \mbox{O II} \\ \mathbf{B}_{32} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(12f\right) & \mbox{O II} \\ \mathbf{B}_{33} & = & x_{5} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(12g\right) & \mbox{Ru} \\ \mathbf{B}_{34} & = & \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(12g\right) & \mbox{Ru} \\ \mathbf{B}_{35} & = & \frac{1}{4} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(12g\right) & \mbox{Ru} \\ \mathbf{B}_{36} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(12g\right) & \mbox{Ru} \\ \mathbf{B}_{37} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(12g\right) & \mbox{Ru} \\ \mathbf{B}_{38} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{z}} & \left(12g\right) & \mbox{Ru} \\ \mathbf{B}_{39} & = & -x_{5} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(12g\right) & \mbox{Ru} \\ \mathbf{B}_{40} & = & \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(12g\right) & \mbox{Ru} \\ \mathbf{B}_{41} & = & \frac{3}{4} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(12g\right) & \mbox{Ru} \\ \mathbf{B}_{42} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(12g\right) & \mbox{Ru} \\ \mathbf{B}_{43} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(12g\right) & \mbox{Ru} \\ \mathbf{B}_{44} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(12g\right) & \mbox{Ru} \\ \mathbf{B}_{45} & = & x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + y_{6}a \, \mathbf{\hat{y}} + z_{6}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{46} & = & \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{6}\right)a \, \mathbf{\hat{y}} + z_{6}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{47} & = & \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{x}} + y_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{6}\right)a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{48} & = & x_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{6}\right)a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{49} & = & z_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + y_{6} \, \mathbf{a}_{3} & = & z_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + y_{6}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{50} & = & z_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{3} & = & z_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-y_{6}\right)a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{51} & = & \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{2} + y_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-z_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{y}} + y_{6}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{52} & = & \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-z_{6}\right)a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-y_{6}\right)a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{53} & = & y_{6} \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & y_{6}a \, \mathbf{\hat{x}} + z_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{54} & = & \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-y_{6}\right)a \, \mathbf{\hat{x}} + z_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{55} & = & y_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{3} & = & y_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-z_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{56} & = & \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-y_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-z_{6}\right)a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{57} & = & -x_{6} \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-y_{6}a \, \mathbf{\hat{y}}-z_{6}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{58} & = & \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{6}\right) \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{y}}-z_{6}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{59} & = & \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{x}}-y_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{60} & = & -x_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{61} & = & -z_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2}-y_{6} \, \mathbf{a}_{3} & = & -z_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}}-y_{6}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{62} & = & -z_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{6}\right) \, \mathbf{a}_{3} & = & -z_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{63} & = & \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{2}-y_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{y}}-y_{6}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{64} & = & \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{65} & = & -y_{6} \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & -y_{6}a \, \mathbf{\hat{x}}-z_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{66} & = & \left(\frac{1}{2} +y_{6}\right) \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{x}}-z_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{67} & = & -y_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{3} & = & -y_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \mathbf{B}_{68} & = & \left(\frac{1}{2} +y_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O III} \\ \end{array} \]

References

  • F. Abraham, D. Thomas, and G. Nowogrocki, Structure cristalline de Bi3Ru3O11, Bull. Soc. Fr. Mineral. Cristallogr. 98, 25–29 (1975), doi:10.3406/bulmi.1975.6954.

Found in

  • R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

Geometry files


Prototype Generator

aflow --proto=A3B11C3_cP68_201_be_efh_g --params=

Species:

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