$F5_{11}$ (KNO$_{2}$) Structure (Obsolete): ABC2_mC8_8_a_a_b-001
| Prototype | KNO$_{2}$ |
| AFLOW prototype label | ABC2_mC8_8_a_a_b-001 |
| Strukturbericht designation | $F5_{11}$ |
| ICSD | 26764 |
| Pearson symbol | mC8 |
| Space group number | 8 |
| Space group symbol | $Cm$ |
| AFLOW prototype command |
aflow --proto=ABC2_mC8_8_a_a_b-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak x_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
The room-temperature structure of KNO$_{2}$ was first considered to have monoclinic symmetry, …, but recent studies have established the structure to be rhombohedral …
(Rao, 1975). The $F5_{11}$ structure is thus neither the ground state structure of KNO$_{2}$ nor the room-temperature structure, which is somewhat disordered with space group $R\overline{3}m$ #166. We present this structure as part of the historical record.- (Ziegler, 1936) gave this structure in the $Am$ setting of space group #8. We used FINDSYM to transform it to the standard $Cm$ setting, which involved a considerable change in the orientation and length of the primitive lattice vectors.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\left(a x_{1} + c z_{1} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{1} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | K I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | N I |
| $\mathbf{B_{3}}$ | = | $\left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | O I |
| $\mathbf{B_{4}}$ | = | $\left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | O I |
References
- G. E. Ziegler, The Crystal Structure of Potassium Nitrite, KNO$_{2}$, Z. Kristallogr. A 94, 491–499 (1936), doi:10.1524/zkri.1936.94.1.491.
- C. N. R. Rao, B. Prakash, and M. Natarajan, Crystal Structure Transformations in Inorganic Nitrities, Nitrates, and Carbonates (National Bureau of Standards, 1975). National Standard Reference Data Series, NSRDS-NBS 53.
Prototype Generator
aflow --proto=ABC2_mC8_8_a_a_b --params=$a,b/a,c/a,\beta,x_{1},z_{1},x_{2},z_{2},x_{3},y_{3},z_{3}$