KHF2 ($F5_{2}$) Structure : A2BC_tI16_140_h_d_a

Picture of Structure; Click for Big Picture
Prototype : F2HK
AFLOW prototype label : A2BC_tI16_140_h_d_a
Strukturbericht designation : $F5_{2}$
Pearson symbol : tI16
Space group number : 140
Space group symbol : $I4/mcm$
AFLOW prototype command : aflow --proto=A2BC_tI16_140_h_d_a
--params=
$a$,$c/a$,$x_{3}$


Other compounds with this structure

  • KN3 and CsN3

  • (Bozorth, 1923) originally determined the lattice constants of KHF2 along with the positions of the potassium and fluorine atoms. He also assumed that the hydrogen atoms were on the ($4d$) Wyckoff sites. Both (Peterson, 1952) and (Ibers, 1964) confirmed his data. All three papers point out that it is possible that the hydrogen atoms are on half–filled ($8h$) sites, which would reduce to the ($4d$) site as the $x$ coordinate approached zero. In KN3 and CsN3 the nitrogen atoms occupy the ($4d$) and ($8h$) Wyckoff sites, while the cation occupies the ($4a$) site.

Body-centered Tetragonal primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} & = & \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{K} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} & = & \frac{3}{4}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{K} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} & \left(4d\right) & \mbox{H} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} & \left(4d\right) & \mbox{H} \\ \mathbf{B}_{5} & = & \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{3}\right) \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{y}} & \left(8h\right) & \mbox{F} \\ \mathbf{B}_{6} & = & \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{y}} & \left(8h\right) & \mbox{F} \\ \mathbf{B}_{7} & = & x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} & \left(8h\right) & \mbox{F} \\ \mathbf{B}_{8} & = & -x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} & \left(8h\right) & \mbox{F} \\ \end{array} \]

References

  • J. A. Ibers, Refinement of Peterson and Levy's Neutron Diffraction Data on KHF2, J. Chem. Phys. 40, 402–404 (1964), doi:10.1063/1.1725126.
  • S. W. Peterson and H. A. Levy, A Single Crystal Neutron Diffraction Determination of the Hydrogen Position in Potassium Bifluoride, J. Chem. Phys. 20, 704–707 (1952), doi:10.1063/1.1700520.
  • R. M. Bozorth, The crystal structure of potassium hydrogen fluoride, J. Am. Chem. Soc. 45, 2128–2132 (1923), doi:10.1021/ja01662a013.

Geometry files


Prototype Generator

aflow --proto=A2BC_tI16_140_h_d_a --params=

Species:

Running:

Output: