AFLOW Prototype: ABC2_mC8_8_a_a_b
Prototype | : | KNO2 |
AFLOW prototype label | : | ABC2_mC8_8_a_a_b |
Strukturbericht designation | : | $F5_{11}$ |
Pearson symbol | : | mC8 |
Space group number | : | 8 |
Space group symbol | : | $Cm$ |
AFLOW prototype command | : | aflow --proto=ABC2_mC8_8_a_a_b --params=$a$,$b/a$,$c/a$,$\beta$,$x_{1}$,$z_{1}$,$x_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$ |
The room–temperature structure of KNO2 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 KNO2 nor the room–temperature structure, which is somewhat disordered with space group $R\overline{3}m$. We present this structure as part of the historical record.
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & \left(x_{1}a+z_{1}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{1}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \text{K} \\ \mathbf{B}_{2} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \left(x_{2}a+z_{2}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{2}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \text{N} \\ \mathbf{B}_{3} & = & \left(x_{3}-y_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}+y_{3}\right) \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \left(x_{3}a+z_{3}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{3}b \, \mathbf{\hat{y}} + z_{3}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \text{O} \\ \mathbf{B}_{4} & = & \left(x_{3}+y_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}-y_{3}\right) \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \left(x_{3}a+z_{3}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{3}b \, \mathbf{\hat{y}} + z_{3}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \text{O} \\ \end{array} \]