KNO2 III Structure : ABC2_mP16_14_e_e_2e

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Prototype : KNO2
AFLOW prototype label : ABC2_mP16_14_e_e_2e
Strukturbericht designation : None
Pearson symbol : mP16
Space group number : 14
Space group symbol : $P2_{1}/c$
AFLOW prototype command : aflow --proto=ABC2_mP16_14_e_e_2e
--params=
$a$,$b/a$,$c/a$,$\beta$,$x_{1}$,$y_{1}$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$



Simple Monoclinic primitive vectors:

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

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} + y_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & \left(x_{1}a+z_{1}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{1}b \, \mathbf{\hat{y}} + z_{1}c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{K} \\ \mathbf{B}_{2} & = & -x_{1} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{1}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta - x_{1}a - z_{1}c\cos\beta\right) \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{1}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{1}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{K} \\ \mathbf{B}_{3} & = & -x_{1} \, \mathbf{a}_{1}-y_{1} \, \mathbf{a}_{2}-z_{1} \, \mathbf{a}_{3} & = & \left(-x_{1}a-z_{1}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{1}b \, \mathbf{\hat{y}}-z_{1}c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{K} \\ \mathbf{B}_{4} & = & x_{1} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{1}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{1}a + z_{1}c\cos\beta\right) \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{1}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{1}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{K} \\ \mathbf{B}_{5} & = & x_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \left(x_{2}a+z_{2}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{2}b \, \mathbf{\hat{y}} + z_{2}c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{N} \\ \mathbf{B}_{6} & = & -x_{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta - x_{2}a - z_{2}c\cos\beta\right) \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{2}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{2}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{N} \\ \mathbf{B}_{7} & = & -x_{2} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & \left(-x_{2}a-z_{2}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{2}b \, \mathbf{\hat{y}}-z_{2}c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{N} \\ \mathbf{B}_{8} & = & x_{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{2}a + z_{2}c\cos\beta\right) \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{2}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{2}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{N} \\ \mathbf{B}_{9} & = & x_{3} \, \mathbf{a}_{1} + y_{3} \, \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(4e\right) & \mbox{O I} \\ \mathbf{B}_{10} & = & -x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta - x_{3}a - z_{3}c\cos\beta\right) \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{3}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{3}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O I} \\ \mathbf{B}_{11} & = & -x_{3} \, \mathbf{a}_{1}-y_{3} \, \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(4e\right) & \mbox{O I} \\ \mathbf{B}_{12} & = & x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{3}a + z_{3}c\cos\beta\right) \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{3}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O I} \\ \mathbf{B}_{13} & = & x_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \left(x_{4}a+z_{4}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{4}b \, \mathbf{\hat{y}} + z_{4}c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O II} \\ \mathbf{B}_{14} & = & -x_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta - x_{4}a - z_{4}c\cos\beta\right) \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{4}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{4}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O II} \\ \mathbf{B}_{15} & = & -x_{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \left(-x_{4}a-z_{4}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{4}b \, \mathbf{\hat{y}}-z_{4}c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O II} \\ \mathbf{B}_{16} & = & x_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{4}a + z_{4}c\cos\beta\right) \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{4}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O II} \\ \end{array} \]

References

  • N. Onoda–Yamamuro, H. Honda, R. Ikeda, O. Yamamuro, T. Matsuo, K. Oikawa, T. Kamiyama, and F. Izumi, Neutron powder diffraction study of the low–temperature phases of KNO2, J. Phys.: Condens. Matter 10, 3341–3351 (1998), doi:10.1088/0953-8984/10/15/011.
  • G. E. Ziegler, The Crystal Structure of Potassium Nitrite, KNO2, Zeitschrift für Kristallographie – Crystalline Materials 34, 491–499 (1936), doi:10.1524/zkri.1936.94.1.491.

Found in

  • C. Duan, W. N. Mei, R. W. Smith, J. Liu, M. M. Ossowski, and J. R. Hardy, Order–disorder phase transitions in KNO2, CsNO2, and TlNO2 crystals: A molecular dynamics study, Phys. Rev. B 63, 144105 (2001), doi:10.1103/PhysRevB.63.144105.

Geometry files


Prototype Generator

aflow --proto=ABC2_mP16_14_e_e_2e --params=

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Running:

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