F6KP Structure: A24BC_cF104_209_j_a_b

Picture of Structure; Click for Big Picture
Prototype : F6KP
AFLOW prototype label : A24BC_cF104_209_j_a_b
Strukturbericht designation : None
Pearson symbol : cF104
Space group number : 209
Space group symbol : $F432$
AFLOW prototype command : aflow --proto=A24BC_cF104_209_j_a_b
--params=
$a$,$x_{3}$,$y_{3}$,$z_{3}$


  • The (96j) Wyckoff positions are decorated by F atoms with a site occupation of 0.25. Hence, the prototype material is F6KP as opposed to F24KP.

Face-centered Cubic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{K} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{P} \\ \mathbf{B}_{3} & = & \left(-x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}+y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}} + z_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{4} & = & \left(x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}-y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}} + z_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{5} & = & \left(x_{3}+y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}-y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}}-z_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{6} & = & \left(-x_{3}-y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}+y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}}-z_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{7} & = & \left(x_{3}+y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & z_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + y_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{8} & = & \left(-x_{3}-y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & z_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}}-y_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{9} & = & \left(-x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}+y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}-y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -z_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + y_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{10} & = & \left(x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}-y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}+y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -z_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}}-y_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{11} & = & \left(x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}+y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}} + z_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{12} & = & \left(-x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}-y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}} + z_{3}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{13} & = & \left(-x_{3}-y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}+y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}}-z_{3}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{14} & = & \left(x_{3}+y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}-y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}}-z_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{15} & = & \left(x_{3}-y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}+y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}}-z_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{16} & = & \left(-x_{3}+y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}-y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}}-z_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{17} & = & \left(-x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}+y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + z_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{18} & = & \left(x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}-y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + z_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{19} & = & \left(-x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}-y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + z_{3}a \, \mathbf{\hat{y}}-y_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{20} & = & \left(x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}+y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + z_{3}a \, \mathbf{\hat{y}} + y_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{21} & = & \left(x_{3}-y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}+y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-z_{3}a \, \mathbf{\hat{y}}-y_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{22} & = & \left(-x_{3}+y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}-y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}}-z_{3}a \, \mathbf{\hat{y}} + y_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{23} & = & \left(-x_{3}+y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & z_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{24} & = & \left(x_{3}-y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & z_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{25} & = & \left(x_{3}+y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}-y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}+y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -z_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \mathbf{B}_{26} & = & \left(-x_{3}-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}+y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}-y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -z_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(96j\right) & \mbox{F} \\ \end{array} \]

References

  • Y. P. Mascarenhas and S. H. Pulcinelli, A redetermination of the structure of α–potassium fluorophosphate, Acta Crystallogr. Sect. A 37, C175 (1981), doi:10.1107/S0108767381094294.

Found in

  • P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds, ASM International (2013).

Geometry files


Prototype Generator

aflow --proto=A24BC_cF104_209_j_a_b --params=

Species:

Running:

Output: