$\alpha$–NbO2 Structure: AB2_tI96_88_2f_4f

Picture of Structure; Click for Big Picture
Prototype : NbO2
AFLOW prototype label : AB2_tI96_88_2f_4f
Strukturbericht designation : None
Pearson symbol : tI96
Space group number : 88
Space group symbol : $I4_{1}/a$
AFLOW prototype command : aflow --proto=AB2_tI96_88_2f_4f
--params=
$a$,$c/a$,$x_{1}$,$y_{1}$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$


  • Although Bolzan et al. (Bolzan, 1994) also gives structural information $\alpha$–NbO2, Pynn {\em et al.} (Pynn, 1996) is the only reference we found which unambiguously states that this structure is reported in setting 2 of space group #88.

Body-centered Tetragonal primitive vectors:

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

Basis vectors:

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

References

  • R. Pynn, J. D. Axe, and R. Thomas, Structural distortions in the low–temperature phase of NbO2, Phys. Rev. B 13, 2965–2975 (1976), doi:10.1103/PhysRevB.13.2965.

Found in

  • A. A. Bolzan, C. Fong, B. J. Kennedy, and C. J. Howard, A Powder Neutron Diffraction Study of Semiconducting and Metallic Niobium Dioxide, J. Solid State Chem. 113, 9–14 (1994), doi:10.1006/jssc.1994.1334.

Geometry files


Prototype Generator

aflow --proto=AB2_tI96_88_2f_4f --params=

Species:

Running:

Output: