NO2 (Modern, $C26$) Structure : AB2_cI36_204_d_g

Picture of Structure; Click for Big Picture
Prototype : NO2
AFLOW prototype label : AB2_cI36_204_d_g
Strukturbericht designation : $C26$
Pearson symbol : cI36
Space group number : 204
Space group symbol : $Im\bar{3}$
AFLOW prototype command : aflow --proto=AB2_cI36_204_d_g
--params=
$a$,$x_{1}$,$y_{2}$,$z_{2}$


  • (Hermann, 1937) listed two possible structures for the low temperature solid cubic phase of NO2, which were given Strukturbericht designations $C26_{a}$ and $C26_{b}$, the only structures with Roman subscripts in the original series.
  • $C26_{a}$ (AB2_cI36_199_b_c) was set in space group $I2_{1}3$ #199. Hermann noted that this structure has a very short distance (1.88 Å) between oxygen atoms on different NO2 molecules, and that this structure does not form the (NO2)2 aggregate molecule found in the $C26_{b}$ structure, making making this proposed structure very unlikely.
  • Recognizing this, (Hendricks, 1931) suggested that NO2 was actually in space group $I23$ #197. (Hermann, 1997) gave this structure the $C26_{b}$ designation, but noted that based on Hendricks's atomic positions the space group was actually $Im\overline{3}$ #204.
  • The modern accepted structure for NO2 (AB2_cI36_204_d_g) is set in space group $Im\overline{3}$ #204, confirming Hendricks. We follow (Villars, 2005) and give this the $C26$ designation.
  • We used the experimental data for this phase collected at 20 K.

Body-centered Cubic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{2} + x_{1} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} & \left(12d\right) & \mbox{N} \\ \mathbf{B}_{2} & = & -x_{1} \, \mathbf{a}_{2}-x_{1} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} & \left(12d\right) & \mbox{N} \\ \mathbf{B}_{3} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{y}} & \left(12d\right) & \mbox{N} \\ \mathbf{B}_{4} & = & -x_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{y}} & \left(12d\right) & \mbox{N} \\ \mathbf{B}_{5} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} & = & x_{1}a \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{N} \\ \mathbf{B}_{6} & = & -x_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2} & = & -x_{1}a \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{N} \\ \mathbf{B}_{7} & = & \left(y_{2}+z_{2}\right) \, \mathbf{a}_{1} + z_{2} \, \mathbf{a}_{2} + y_{2} \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{y}} + z_{2}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O} \\ \mathbf{B}_{8} & = & \left(-y_{2}+z_{2}\right) \, \mathbf{a}_{1} + z_{2} \, \mathbf{a}_{2}-y_{2} \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{y}} + z_{2}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O} \\ \mathbf{B}_{9} & = & \left(y_{2}-z_{2}\right) \, \mathbf{a}_{1}-z_{2} \, \mathbf{a}_{2} + y_{2} \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{y}}-z_{2}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O} \\ \mathbf{B}_{10} & = & \left(-y_{2}-z_{2}\right) \, \mathbf{a}_{1}-z_{2} \, \mathbf{a}_{2}-y_{2} \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{y}}-z_{2}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O} \\ \mathbf{B}_{11} & = & y_{2} \, \mathbf{a}_{1} + \left(y_{2}+z_{2}\right) \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & z_{2}a \, \mathbf{\hat{x}} + y_{2}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O} \\ \mathbf{B}_{12} & = & -y_{2} \, \mathbf{a}_{1} + \left(-y_{2}+z_{2}\right) \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & z_{2}a \, \mathbf{\hat{x}}-y_{2}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O} \\ \mathbf{B}_{13} & = & y_{2} \, \mathbf{a}_{1} + \left(y_{2}-z_{2}\right) \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & -z_{2}a \, \mathbf{\hat{x}} + y_{2}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O} \\ \mathbf{B}_{14} & = & -y_{2} \, \mathbf{a}_{1} + \left(-y_{2}-z_{2}\right) \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & -z_{2}a \, \mathbf{\hat{x}}-y_{2}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O} \\ \mathbf{B}_{15} & = & z_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + \left(y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{x}} + z_{2}a \, \mathbf{\hat{y}} & \left(24g\right) & \mbox{O} \\ \mathbf{B}_{16} & = & z_{2} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2} + \left(-y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{x}} + z_{2}a \, \mathbf{\hat{y}} & \left(24g\right) & \mbox{O} \\ \mathbf{B}_{17} & = & -z_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + \left(y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{x}}-z_{2}a \, \mathbf{\hat{y}} & \left(24g\right) & \mbox{O} \\ \mathbf{B}_{18} & = & -z_{2} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2} + \left(-y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{x}}-z_{2}a \, \mathbf{\hat{y}} & \left(24g\right) & \mbox{O} \\ \end{array} \]

References

  • Å. Kvick, R. K. McMullan, and M. D. Newton, The structure of dinitrogen tetroxide N2O4: Neutron diffraction study at 100, 60 and 20 K and ab initio theoretical calculations, J. Chem. Phys. 76, 3754–3761 (1982), doi:10.1063/1.443414.
  • C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928–1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).

Found in

  • P. Villars and K. Cenzual, eds., Crystal Structure Data of Inorganic Compounds (Springer–Verlag, Berlin, Heidelberg, 2005). Landolt–Bornstein Volume III 43A2.

Geometry files


Prototype Generator

aflow --proto=AB2_cI36_204_d_g --params=

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