Nb2Zr6O17 Structure : A2B17C6_oI100_46_ab_b8c_3c

Picture of Structure; Click for Big Picture
Prototype : Nb2O17Zr6
AFLOW prototype label : A2B17C6_oI100_46_ab_b8c_3c
Strukturbericht designation : None
Pearson symbol : oI100
Space group number : 46
Space group symbol : $Ima2$
AFLOW prototype command : aflow --proto=A2B17C6_oI100_46_ab_b8c_3c
--params=
$a$,$b/a$,$c/a$,$z_{1}$,$y_{2}$,$z_{2}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$,$x_{8}$,$y_{8}$,$z_{8}$,$x_{9}$,$y_{9}$,$z_{9}$,$x_{10}$,$y_{10}$,$z_{10}$,$x_{11}$,$y_{11}$,$z_{11}$,$x_{12}$,$y_{12}$,$z_{12}$,$x_{13}$,$y_{13}$,$z_{13}$,$x_{14}$,$y_{14}$,$z_{14}$


Other compounds with this structure

  • Nb2Hf6O17, Nb2Zr6O17, Ta2Hf6O17, and Ta2Zr6O17

  • Both (Galy, 1973) and (McCormack, 2019) state that the metallic atom sites are disordered, that is, for the prototype each metallic site has the average composition, Nb0.25Zr0.75. We place the niobium atoms on the ($4a$) and ($4b$) sites, and the zirconium on the ($8c$) sites so that the different symmetries are displayed.
  • (McCormack, 2019) notes that the metallic composition of these compounds can deviate from the stoichiometry shown here.

Body-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & z_{1} \, \mathbf{a}_{1} + z_{1} \, \mathbf{a}_{2} & = & z_{1}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Nb I} \\ \mathbf{B}_{2} & = & z_{1} \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{1}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + z_{1}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Nb I} \\ \mathbf{B}_{3} & = & \left(y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +y_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{2}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Nb II} \\ \mathbf{B}_{4} & = & \left(-y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} +z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - y_{2}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{2}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Nb II} \\ \mathbf{B}_{5} & = & \left(y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +y_{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{O I} \\ \mathbf{B}_{6} & = & \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} +z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - y_{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{O I} \\ \mathbf{B}_{7} & = & \left(y_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(x_{4}+z_{4}\right) \, \mathbf{a}_{2} + \left(x_{4}+y_{4}\right) \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O II} \\ \mathbf{B}_{8} & = & \left(-y_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(-x_{4}+z_{4}\right) \, \mathbf{a}_{2} + \left(-x_{4}-y_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O II} \\ \mathbf{B}_{9} & = & \left(-y_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{4} + z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{4} - y_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{x}}-y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O II} \\ \mathbf{B}_{10} & = & \left(y_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{4} + z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{4} + y_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{x}} + y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O II} \\ \mathbf{B}_{11} & = & \left(y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}+y_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + y_{5}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O III} \\ \mathbf{B}_{12} & = & \left(-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}-y_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-y_{5}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O III} \\ \mathbf{B}_{13} & = & \left(-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5} - y_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{x}}-y_{5}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O III} \\ \mathbf{B}_{14} & = & \left(y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5} + y_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{x}} + y_{5}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O III} \\ \mathbf{B}_{15} & = & \left(y_{6}+z_{6}\right) \, \mathbf{a}_{1} + \left(x_{6}+z_{6}\right) \, \mathbf{a}_{2} + \left(x_{6}+y_{6}\right) \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O IV} \\ \mathbf{B}_{16} & = & \left(-y_{6}+z_{6}\right) \, \mathbf{a}_{1} + \left(-x_{6}+z_{6}\right) \, \mathbf{a}_{2} + \left(-x_{6}-y_{6}\right) \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O IV} \\ \mathbf{B}_{17} & = & \left(-y_{6}+z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6} + z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{6} - y_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{x}}-y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O IV} \\ \mathbf{B}_{18} & = & \left(y_{6}+z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6} + z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6} + y_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{x}} + y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O IV} \\ \mathbf{B}_{19} & = & \left(y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(x_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(x_{7}+y_{7}\right) \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O V} \\ \mathbf{B}_{20} & = & \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(-x_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(-x_{7}-y_{7}\right) \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O V} \\ \mathbf{B}_{21} & = & \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{7} + z_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{7} - y_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O V} \\ \mathbf{B}_{22} & = & \left(y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{7} + z_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{7} + y_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O V} \\ \mathbf{B}_{23} & = & \left(y_{8}+z_{8}\right) \, \mathbf{a}_{1} + \left(x_{8}+z_{8}\right) \, \mathbf{a}_{2} + \left(x_{8}+y_{8}\right) \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O VI} \\ \mathbf{B}_{24} & = & \left(-y_{8}+z_{8}\right) \, \mathbf{a}_{1} + \left(-x_{8}+z_{8}\right) \, \mathbf{a}_{2} + \left(-x_{8}-y_{8}\right) \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O VI} \\ \mathbf{B}_{25} & = & \left(-y_{8}+z_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{8} + z_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{8} - y_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O VI} \\ \mathbf{B}_{26} & = & \left(y_{8}+z_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{8} + z_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{8} + y_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O VI} \\ \mathbf{B}_{27} & = & \left(y_{9}+z_{9}\right) \, \mathbf{a}_{1} + \left(x_{9}+z_{9}\right) \, \mathbf{a}_{2} + \left(x_{9}+y_{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{O VII} \\ \mathbf{B}_{28} & = & \left(-y_{9}+z_{9}\right) \, \mathbf{a}_{1} + \left(-x_{9}+z_{9}\right) \, \mathbf{a}_{2} + \left(-x_{9}-y_{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{O VII} \\ \mathbf{B}_{29} & = & \left(-y_{9}+z_{9}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{9} + z_{9}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{9} - y_{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{O VII} \\ \mathbf{B}_{30} & = & \left(y_{9}+z_{9}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{9} + z_{9}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{9} + y_{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{O VII} \\ \mathbf{B}_{31} & = & \left(y_{10}+z_{10}\right) \, \mathbf{a}_{1} + \left(x_{10}+z_{10}\right) \, \mathbf{a}_{2} + \left(x_{10}+y_{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 VIII} \\ \mathbf{B}_{32} & = & \left(-y_{10}+z_{10}\right) \, \mathbf{a}_{1} + \left(-x_{10}+z_{10}\right) \, \mathbf{a}_{2} + \left(-x_{10}-y_{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 VIII} \\ \mathbf{B}_{33} & = & \left(-y_{10}+z_{10}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{10} + z_{10}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{10} - y_{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 VIII} \\ \mathbf{B}_{34} & = & \left(y_{10}+z_{10}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{10} + z_{10}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{10} + y_{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 VIII} \\ \mathbf{B}_{35} & = & \left(y_{11}+z_{11}\right) \, \mathbf{a}_{1} + \left(x_{11}+z_{11}\right) \, \mathbf{a}_{2} + \left(x_{11}+y_{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 IX} \\ \mathbf{B}_{36} & = & \left(-y_{11}+z_{11}\right) \, \mathbf{a}_{1} + \left(-x_{11}+z_{11}\right) \, \mathbf{a}_{2} + \left(-x_{11}-y_{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 IX} \\ \mathbf{B}_{37} & = & \left(-y_{11}+z_{11}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{11} + z_{11}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{11} - y_{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 IX} \\ \mathbf{B}_{38} & = & \left(y_{11}+z_{11}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{11} + z_{11}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{11} + y_{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 IX} \\ \mathbf{B}_{39} & = & \left(y_{12}+z_{12}\right) \, \mathbf{a}_{1} + \left(x_{12}+z_{12}\right) \, \mathbf{a}_{2} + \left(x_{12}+y_{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{Zr I} \\ \mathbf{B}_{40} & = & \left(-y_{12}+z_{12}\right) \, \mathbf{a}_{1} + \left(-x_{12}+z_{12}\right) \, \mathbf{a}_{2} + \left(-x_{12}-y_{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{Zr I} \\ \mathbf{B}_{41} & = & \left(-y_{12}+z_{12}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{12} + z_{12}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{12} - y_{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{Zr I} \\ \mathbf{B}_{42} & = & \left(y_{12}+z_{12}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{12} + z_{12}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{12} + y_{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{Zr I} \\ \mathbf{B}_{43} & = & \left(y_{13}+z_{13}\right) \, \mathbf{a}_{1} + \left(x_{13}+z_{13}\right) \, \mathbf{a}_{2} + \left(x_{13}+y_{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{Zr II} \\ \mathbf{B}_{44} & = & \left(-y_{13}+z_{13}\right) \, \mathbf{a}_{1} + \left(-x_{13}+z_{13}\right) \, \mathbf{a}_{2} + \left(-x_{13}-y_{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{Zr II} \\ \mathbf{B}_{45} & = & \left(-y_{13}+z_{13}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{13} + z_{13}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{13} - y_{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{Zr II} \\ \mathbf{B}_{46} & = & \left(y_{13}+z_{13}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{13} + z_{13}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{13} + y_{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{Zr II} \\ \mathbf{B}_{47} & = & \left(y_{14}+z_{14}\right) \, \mathbf{a}_{1} + \left(x_{14}+z_{14}\right) \, \mathbf{a}_{2} + \left(x_{14}+y_{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{Zr III} \\ \mathbf{B}_{48} & = & \left(-y_{14}+z_{14}\right) \, \mathbf{a}_{1} + \left(-x_{14}+z_{14}\right) \, \mathbf{a}_{2} + \left(-x_{14}-y_{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{Zr III} \\ \mathbf{B}_{49} & = & \left(-y_{14}+z_{14}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{14} + z_{14}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{14} - y_{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{Zr III} \\ \mathbf{B}_{50} & = & \left(y_{14}+z_{14}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{14} + z_{14}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{14} + y_{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{Zr III} \\ \end{array} \]

References

Found in

  • S. J. McCormack and W. M. Kriven, Crystal structure solution for the $A6$B2O17 ($A$ = Zr, Hf; $B$ = Nb, Ta) superstructure, Acta Crystallogr. Sect. B Struct. Sci. 75, 227–234 (2019), doi:10.1107/S2052520619001963.

Geometry files


Prototype Generator

aflow --proto=A2B17C6_oI100_46_ab_b8c_3c --params=

Species:

Running:

Output: