$F5_{11}$ (KNO2) (obsolete) Structure : ABC2_mC8_8_a_a_b

Picture of Structure; Click for Big Picture
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.
  • (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.

Base-centered Monoclinic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & \left(x_{1}a+z_{1}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{1}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{K} \\ \mathbf{B}_{2} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \left(x_{2}a+z_{2}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{2}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{N} \\ \mathbf{B}_{3} & = & \left(x_{3}-y_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}+y_{3}\right) \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \left(x_{3}a+z_{3}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{3}b \, \mathbf{\hat{y}} + z_{3}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{O} \\ \mathbf{B}_{4} & = & \left(x_{3}+y_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}-y_{3}\right) \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \left(x_{3}a+z_{3}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{3}b \, \mathbf{\hat{y}} + z_{3}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{O} \\ \end{array} \]

References

  • G. E. Ziegler, The Crystal Structure of Potassium Nitrite, KNO2, Zeitschrift für Kristallographie – Crystalline Materials 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.

Geometry files


Prototype Generator

aflow --proto=ABC2_mC8_8_a_a_b --params=

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