Modern $C26$ (NO$_{2}$) Structure: AB2_cI36_204_d_g-001
| Prototype | NO$_{2}$ |
| AFLOW prototype label | AB2_cI36_204_d_g-001 |
| Strukturbericht designation | $C26$ |
| ICSD | 201140 |
| Pearson symbol | cI36 |
| Space group number | 204 |
| Space group symbol | $Im\overline{3}$ |
| AFLOW prototype command |
aflow --proto=AB2_cI36_204_d_g-001
--params=$a, \allowbreak x_{1}, \allowbreak y_{2}, \allowbreak z_{2}$ |
- (Hermann, 1937) listed two possible structures for the low temperature solid cubic phase of NO$_{2}$, 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 (1.88Å) between oxygen atoms on different NO$_{2}$ molecules, and that this structure does not form the (NO$_{2}$)$_{2}$ aggregate molecule found in the $C26_{b}$ structure, making
making this proposed structure very unlikely.
- Recognizing this, (Hendricks, 1931) suggested that NO$_{2}$ 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 No$_{2}$, AB2_cI36_204_d_g, is set in space group $Im\overline{3}$, confirming Hendricks. We follow (Villars, 2005) and give this the $C26$ designation, depreciating the $C26_{b}$ label.
- We used the experimental data for this phase collected at 20K.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}$ | (12d) | N I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}$ | (12d) | N I |
| $\mathbf{B_{3}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{y}}$ | (12d) | N I |
| $\mathbf{B_{4}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{y}}$ | (12d) | N I |
| $\mathbf{B_{5}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}$ | = | $a x_{1} \,\mathbf{\hat{z}}$ | (12d) | N I |
| $\mathbf{B_{6}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}$ | = | $- a x_{1} \,\mathbf{\hat{z}}$ | (12d) | N I |
| $\mathbf{B_{7}}$ | = | $\left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}+y_{2} \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (24g) | O I |
| $\mathbf{B_{8}}$ | = | $- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (24g) | O I |
| $\mathbf{B_{9}}$ | = | $\left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+y_{2} \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{y}}- a z_{2} \,\mathbf{\hat{z}}$ | (24g) | O I |
| $\mathbf{B_{10}}$ | = | $- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{y}}- a z_{2} \,\mathbf{\hat{z}}$ | (24g) | O I |
| $\mathbf{B_{11}}$ | = | $y_{2} \, \mathbf{a}_{1}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{z}}$ | (24g) | O I |
| $\mathbf{B_{12}}$ | = | $- y_{2} \, \mathbf{a}_{1}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{z}}$ | (24g) | O I |
| $\mathbf{B_{13}}$ | = | $y_{2} \, \mathbf{a}_{1}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $- a z_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{z}}$ | (24g) | O I |
| $\mathbf{B_{14}}$ | = | $- y_{2} \, \mathbf{a}_{1}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $- a z_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{z}}$ | (24g) | O I |
| $\mathbf{B_{15}}$ | = | $z_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}$ | (24g) | O I |
| $\mathbf{B_{16}}$ | = | $z_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}$ | (24g) | O I |
| $\mathbf{B_{17}}$ | = | $- z_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}- a z_{2} \,\mathbf{\hat{y}}$ | (24g) | O I |
| $\mathbf{B_{18}}$ | = | $- z_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}- a z_{2} \,\mathbf{\hat{y}}$ | (24g) | O I |
References
- A. Kvick, R. K. McMullan, and M. D. Newton, The structure of dinitrogen tetroxide N$_{2}$O$_{4}$: Neutron diffraction study at 100, 60 and 20 K and {\em 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).
- S. B. Hendricks, Die Kristallstruktur von N$_{2}$O$_{4}$, Z. Physik 70, 699–700 (1931), doi:10.1007/BF01340758.
Found in
- P. Villars and K. Cenzual, eds., Crystal Structure Data of Inorganic Compounds (Springer-Verlag, Berlin, Heidelberg, 2005). Landolt-Bornstein Volume III 43A2.
Prototype Generator
aflow --proto=AB2_cI36_204_d_g --params=$a,x_{1},y_{2},z_{2}$