Na5Fe3F14 (High–temperature) Structure: A14B3C5_tP44_94_c3g_ad_bg

Picture of Structure; Click for Big Picture
Prototype : Na5Fe3F14
AFLOW prototype label : A14B3C5_tP44_94_c3g_ad_bg
Strukturbericht designation : None
Pearson symbol : tP44
Space group number : 94
Space group symbol : $P4_{2}2_{1}2$
AFLOW prototype command : aflow --proto=A14B3C5_tP44_94_c3g_ad_bg
--params=
$a$,$c/a$,$z_{3}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$,$x_{8}$,$y_{8}$,$z_{8}$


Simple Tetragonal primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 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(2a\right) & \mbox{Fe I} \\ \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}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Fe I} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{Na I} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} & \left(2b\right) & \mbox{Na I} \\ \mathbf{B}_{5} & = & z_{3} \, \mathbf{a}_{3} & = & z_{3}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{F I} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{F I} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{3}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{F I} \\ \mathbf{B}_{8} & = & -z_{3} \, \mathbf{a}_{3} & = & -z_{3}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{F I} \\ \mathbf{B}_{9} & = & \frac{1}{2} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{Fe II} \\ \mathbf{B}_{10} & = & \frac{1}{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{Fe II} \\ \mathbf{B}_{11} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{4}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - z_{4}\right)c \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{Fe II} \\ \mathbf{B}_{12} & = & \frac{1}{2} \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-z_{4}c \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{Fe II} \\ \mathbf{B}_{13} & = & x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + y_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F II} \\ \mathbf{B}_{14} & = & -x_{5} \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-y_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F II} \\ \mathbf{B}_{15} & = & \left(\frac{1}{2} - y_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F II} \\ \mathbf{B}_{16} & = & \left(\frac{1}{2} +y_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F II} \\ \mathbf{B}_{17} & = & \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{5}\right)c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F II} \\ \mathbf{B}_{18} & = & \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{5}\right)c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F II} \\ \mathbf{B}_{19} & = & y_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & y_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F II} \\ \mathbf{B}_{20} & = & -y_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & -y_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F II} \\ \mathbf{B}_{21} & = & x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + y_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F III} \\ \mathbf{B}_{22} & = & -x_{6} \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-y_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F III} \\ \mathbf{B}_{23} & = & \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F III} \\ \mathbf{B}_{24} & = & \left(\frac{1}{2} +y_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F III} \\ \mathbf{B}_{25} & = & \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{6}\right)c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F III} \\ \mathbf{B}_{26} & = & \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{6}\right)c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F III} \\ \mathbf{B}_{27} & = & y_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & y_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F III} \\ \mathbf{B}_{28} & = & -y_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & -y_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F III} \\ \mathbf{B}_{29} & = & x_{7} \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + y_{7}a \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F IV} \\ \mathbf{B}_{30} & = & -x_{7} \, \mathbf{a}_{1}-y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}}-y_{7}a \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F IV} \\ \mathbf{B}_{31} & = & \left(\frac{1}{2} - y_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{7}\right)c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F IV} \\ \mathbf{B}_{32} & = & \left(\frac{1}{2} +y_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{7}\right)c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F IV} \\ \mathbf{B}_{33} & = & \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{7}\right)c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F IV} \\ \mathbf{B}_{34} & = & \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{7}\right)c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F IV} \\ \mathbf{B}_{35} & = & y_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & y_{7}a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F IV} \\ \mathbf{B}_{36} & = & -y_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & -y_{7}a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{F IV} \\ \mathbf{B}_{37} & = & x_{8} \, \mathbf{a}_{1} + y_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + y_{8}a \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Na II} \\ \mathbf{B}_{38} & = & -x_{8} \, \mathbf{a}_{1}-y_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-y_{8}a \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Na II} \\ \mathbf{B}_{39} & = & \left(\frac{1}{2} - y_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{8}\right)c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Na II} \\ \mathbf{B}_{40} & = & \left(\frac{1}{2} +y_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{8}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{8}\right)c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Na II} \\ \mathbf{B}_{41} & = & \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{8}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{8}\right)c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Na II} \\ \mathbf{B}_{42} & = & \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{8}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{8}\right)c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Na II} \\ \mathbf{B}_{43} & = & y_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & y_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}}-z_{8}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Na II} \\ \mathbf{B}_{44} & = & -y_{8} \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & -y_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}}-z_{8}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Na II} \\ \end{array} \]

References

  • M. Vlasse, F. Menil, C. Moriliere, J. M. Dance, A. Tressaud, and J. Portier, Etude cristallographique et par effet Mössbauer du fluorure ferrimagnétique Na5Fe3F14gamma, J. Solid State Chem. 17, 291–298 (1976), doi:10.1016/0022-4596(76)90134-1.

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=A14B3C5_tP44_94_c3g_ad_bg --params=

Species:

Running:

Output: