Orthorhombic Sr4Ru3O10 Structure : A10B3C4_oP68_55_2e2fgh2i_adef_2e2f

Picture of Structure; Click for Big Picture
Prototype : O10Ru3Sr4
AFLOW prototype label : A10B3C4_oP68_55_2e2fgh2i_adef_2e2f
Strukturbericht designation : None
Pearson symbol : oP68
Space group number : 55
Space group symbol : $Pbam$
AFLOW prototype command : aflow --proto=A10B3C4_oP68_55_2e2fgh2i_adef_2e2f
--params=
$a$,$b/a$,$c/a$,$z_{3}$,$z_{4}$,$z_{5}$,$z_{6}$,$z_{7}$,$z_{8}$,$z_{9}$,$z_{10}$,$z_{11}$,$z_{12}$,$x_{13}$,$y_{13}$,$x_{14}$,$y_{14}$,$x_{15}$,$y_{15}$,$z_{15}$,$x_{16}$,$y_{16}$,$z_{16}$


  • This structure consists of triple–layer ruthenate structures separated by 2.37 Å from each other. In the $Pbam$ #55 space group shown here there are two inequivalent stacks in the orthorhombic cell.
  • This cell is very problematic. (Crawford, 2002) note that the x–ray scattering intensities are pseudo body–centered, but found that refining this structure in a body–centered cell with space group $Bbcm$ ($Cmca$ #64 in our standard orientation) led to non–positive definite thermal parameters. However, if we allow a lattice and atom position uncertainty of only 0.01 Å in the atomic coordinates, AFLOW-SYM and FINDSYM place the structure in base–centered space group $Cmca$ #64, oC68. In that case there is only one triple–layer stack in the primitive cell, and the two stacks in the conventional orthorhombic cell are equivalent.

Simple Orthorhombic primitive vectors:

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

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

References

  • M. K. Crawford, R. L. Harlow, W. Marshall, Z. Li, G. Cao, R. L. Lindstrom, Q. Huang, and J. W. Lynn, Structure and magnetism of single crystal Sr4Ru3O10: A ferromagnetic triple–layer ruthenate, Phys. Rev. B 65, 214412 (2002), doi:10.1103/PhysRevB.65.214412.

Geometry files


Prototype Generator

aflow --proto=A10B3C4_oP68_55_2e2fgh2i_adef_2e2f --params=

Species:

Running:

Output: