$\beta$–NbO2 Structure: AB2_tI48_80_2b_4b

Picture of Structure; Click for Big Picture
Prototype : NbO2
AFLOW prototype label : AB2_tI48_80_2b_4b
Strukturbericht designation : None
Pearson symbol : tI48
Space group number : 80
Space group symbol : $I4_{1}$
AFLOW prototype command : aflow --proto=AB2_tI48_80_2b_4b
--params=
$a$,$c/a$,$x_{1}$,$y_{1}$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$


  • This crystal is not quite stoichiometric. The actual composition was found to be NbO2–x, where $0.002 \le x \le 0.01$.

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(8b\right) & \mbox{Nb I} \\ \mathbf{B}_{2} & = & \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(8b\right) & \mbox{Nb I} \\ \mathbf{B}_{3} & = & \left(\frac{3}{4} +x_{1} + z_{1}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - y_{1} + z_{1}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{1} - y_{1}\right) \, \mathbf{a}_{3} & = & -y_{1}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{1}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{1}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{Nb I} \\ \mathbf{B}_{4} & = & \left(\frac{3}{4} - x_{1} + z_{1}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +y_{1} + z_{1}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{1} + y_{1}\right) \, \mathbf{a}_{3} & = & y_{1}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{1}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{1}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{Nb I} \\ \mathbf{B}_{5} & = & \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(8b\right) & \mbox{Nb II} \\ \mathbf{B}_{6} & = & \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(8b\right) & \mbox{Nb II} \\ \mathbf{B}_{7} & = & \left(\frac{3}{4} +x_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2} - y_{2}\right) \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{Nb II} \\ \mathbf{B}_{8} & = & \left(\frac{3}{4} - x_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2} + y_{2}\right) \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{Nb II} \\ \mathbf{B}_{9} & = & \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(8b\right) & \mbox{O I} \\ \mathbf{B}_{10} & = & \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(8b\right) & \mbox{O I} \\ \mathbf{B}_{11} & = & \left(\frac{3}{4} +x_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3} - y_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O I} \\ \mathbf{B}_{12} & = & \left(\frac{3}{4} - x_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3} + y_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O I} \\ \mathbf{B}_{13} & = & \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(8b\right) & \mbox{O II} \\ \mathbf{B}_{14} & = & \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(8b\right) & \mbox{O II} \\ \mathbf{B}_{15} & = & \left(\frac{3}{4} +x_{4} + z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{4} - y_{4}\right) \, \mathbf{a}_{3} & = & -y_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O II} \\ \mathbf{B}_{16} & = & \left(\frac{3}{4} - x_{4} + z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +y_{4} + z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{4} + y_{4}\right) \, \mathbf{a}_{3} & = & y_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O II} \\ \mathbf{B}_{17} & = & \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(8b\right) & \mbox{O III} \\ \mathbf{B}_{18} & = & \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(8b\right) & \mbox{O III} \\ \mathbf{B}_{19} & = & \left(\frac{3}{4} +x_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - y_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5} - y_{5}\right) \, \mathbf{a}_{3} & = & -y_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O III} \\ \mathbf{B}_{20} & = & \left(\frac{3}{4} - x_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +y_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5} + y_{5}\right) \, \mathbf{a}_{3} & = & y_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O III} \\ \mathbf{B}_{21} & = & \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(8b\right) & \mbox{O IV} \\ \mathbf{B}_{22} & = & \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(8b\right) & \mbox{O IV} \\ \mathbf{B}_{23} & = & \left(\frac{3}{4} +x_{6} + z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - y_{6} + z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{6} - y_{6}\right) \, \mathbf{a}_{3} & = & -y_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{6}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O IV} \\ \mathbf{B}_{24} & = & \left(\frac{3}{4} - x_{6} + z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +y_{6} + z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6} + y_{6}\right) \, \mathbf{a}_{3} & = & y_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{6}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O IV} \\ \end{array} \]

References

  • H.–J. Schweizer and R. Gruehn, Zur Darstellung und Kristallstruktur von β–NbO2 / Synthesis and Crystal Structure of β–NbO2, Z. Naturforsch. B 37, 1361–1368 (1982), doi:10.1515/znb-1982-1101.

Found in

  • P. Villars and L. D. Calvert, eds., Pearson's Handbook of Crystallographic Data (ASM International, Materials Park OH, 1991), vol. IV, chap. , p. 4535.

Geometry files


Prototype Generator

aflow --proto=AB2_tI48_80_2b_4b --params=

Species:

Running:

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