$C26_{a}$ (NO$_{2}$) (Obsolete) Structure: AB2_cI36_199_b_c-001
| Prototype | NO$_{2}$ |
| AFLOW prototype label | AB2_cI36_199_b_c-001 |
| Strukturbericht designation | $C26_{a}$ |
| ICSD | 31175 |
| Pearson symbol | cI36 |
| Space group number | 199 |
| Space group symbol | $I2_13$ |
| AFLOW prototype command |
aflow --proto=AB2_cI36_199_b_c-001
--params=$a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}$ |
- (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.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(x_{1} + \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (12b) | N I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(x_{1} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (12b) | N I |
| $\mathbf{B_{3}}$ | = | $x_{1} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\left(x_{1} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}$ | (12b) | N I |
| $\mathbf{B_{4}}$ | = | $- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- \left(x_{1} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12b) | N I |
| $\mathbf{B_{5}}$ | = | $\left(x_{1} + \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+a x_{1} \,\mathbf{\hat{z}}$ | (12b) | N I |
| $\mathbf{B_{6}}$ | = | $- \left(x_{1} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a x_{1} \,\mathbf{\hat{z}}$ | (12b) | N I |
| $\mathbf{B_{7}}$ | = | $\left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (24c) | O I |
| $\mathbf{B_{8}}$ | = | $\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (24c) | O I |
| $\mathbf{B_{9}}$ | = | $\left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}- a z_{2} \,\mathbf{\hat{z}}$ | (24c) | O I |
| $\mathbf{B_{10}}$ | = | $- \left(y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}- a \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24c) | O I |
| $\mathbf{B_{11}}$ | = | $\left(x_{2} + y_{2}\right) \, \mathbf{a}_{1}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (24c) | O I |
| $\mathbf{B_{12}}$ | = | $- \left(x_{2} + y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24c) | O I |
| $\mathbf{B_{13}}$ | = | $\left(- x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{2} \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (24c) | O I |
| $\mathbf{B_{14}}$ | = | $\left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}- \left(y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a y_{2} \,\mathbf{\hat{z}}$ | (24c) | O I |
| $\mathbf{B_{15}}$ | = | $\left(x_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{2}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (24c) | O I |
| $\mathbf{B_{16}}$ | = | $- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (24c) | O I |
| $\mathbf{B_{17}}$ | = | $- \left(x_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}- a z_{2} \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24c) | O I |
| $\mathbf{B_{18}}$ | = | $\left(x_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}- \left(y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}- a \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (24c) | O I |
References
- L. Vegard, Die Struktur von festem N$_{2}$O$_{4}$ bei der Temperatur von flüssiger Luft, Z. Physik 68, 184–203 (1931), doi:10.1007/BF01390966.
- P. Villars and K. Cenzual, eds., Crystal Structure Data of Inorganic Compounds, vol. III (Springer-Verlag, Berlin, Heidelberg, 2005).
- S. B. Hendricks, Die Kristallstruktur von N$_{2}$O$_{4}$, Z. Physik 70, 699–700 (1931), doi:10.1007/BF01340758.
Found in
- C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928-1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
Prototype Generator
aflow --proto=AB2_cI36_199_b_c --params=$a,x_{1},x_{2},y_{2},z_{2}$