Fe12Zr2P7 Structure: A12B7C2_hP21_174_2j2k_ajk_cf

Picture of Structure; Click for Big Picture
Prototype : Fe12Zr2P7
AFLOW prototype label : A12B7C2_hP21_174_2j2k_ajk_cf
Strukturbericht designation : None
Pearson symbol : hP21
Space group number : 174
Space group symbol : $P\bar{6}$
AFLOW prototype command : aflow --proto=A12B7C2_hP21_174_2j2k_ajk_cf
--params=
$a$,$c/a$,$x_{4}$,$y_{4}$,$x_{5}$,$y_{5}$,$x_{6}$,$y_{6}$,$x_{7}$,$y_{7}$,$x_{8}$,$y_{8}$,$x_{9}$,$y_{9}$


Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]

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(1a\right) & \mbox{P I} \\ \mathbf{B}_{2} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} & \left(1c\right) & \mbox{Zr I} \\ \mathbf{B}_{3} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(1f\right) & \mbox{Zr II} \\ \mathbf{B}_{4} & = & x_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} & = & \frac{1}{2}\left(x_{4}+y_{4}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{4}+y_{4}\right)a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{Fe I} \\ \mathbf{B}_{5} & = & -y_{4} \, \mathbf{a}_{1} + \left(x_{4}-y_{4}\right) \, \mathbf{a}_{2} & = & \left(\frac{1}{2}x_{4}-y_{4}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{Fe I} \\ \mathbf{B}_{6} & = & \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} & = & \left(-x_{4}+\frac{1}{2}y_{4}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{4}a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{Fe I} \\ \mathbf{B}_{7} & = & x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} & = & \frac{1}{2}\left(x_{5}+y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{5}+y_{5}\right)a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{Fe II} \\ \mathbf{B}_{8} & = & -y_{5} \, \mathbf{a}_{1} + \left(x_{5}-y_{5}\right) \, \mathbf{a}_{2} & = & \left(\frac{1}{2}x_{5}-y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{Fe II} \\ \mathbf{B}_{9} & = & \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} & = & \left(-x_{5}+\frac{1}{2}y_{5}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{5}a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{Fe II} \\ \mathbf{B}_{10} & = & x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} & = & \frac{1}{2}\left(x_{6}+y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{6}+y_{6}\right)a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{P II} \\ \mathbf{B}_{11} & = & -y_{6} \, \mathbf{a}_{1} + \left(x_{6}-y_{6}\right) \, \mathbf{a}_{2} & = & \left(\frac{1}{2}x_{6}-y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{P II} \\ \mathbf{B}_{12} & = & \left(-x_{6}+y_{6}\right) \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} & = & \left(-x_{6}+\frac{1}{2}y_{6}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{6}a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{P II} \\ \mathbf{B}_{13} & = & x_{7} \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{7}+y_{7}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{7}+y_{7}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{Fe III} \\ \mathbf{B}_{14} & = & -y_{7} \, \mathbf{a}_{1} + \left(x_{7}-y_{7}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{7}-y_{7}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{7}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{Fe III} \\ \mathbf{B}_{15} & = & \left(-x_{7}+y_{7}\right) \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(-x_{7}+\frac{1}{2}y_{7}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{7}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{Fe III} \\ \mathbf{B}_{16} & = & x_{8} \, \mathbf{a}_{1} + y_{8} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{8}+y_{8}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{8}+y_{8}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{Fe IV} \\ \mathbf{B}_{17} & = & -y_{8} \, \mathbf{a}_{1} + \left(x_{8}-y_{8}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{8}-y_{8}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{8}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{Fe IV} \\ \mathbf{B}_{18} & = & \left(-x_{8}+y_{8}\right) \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(-x_{8}+\frac{1}{2}y_{8}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{8}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{Fe IV} \\ \mathbf{B}_{19} & = & x_{9} \, \mathbf{a}_{1} + y_{9} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{9}+y_{9}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{9}+y_{9}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{P III} \\ \mathbf{B}_{20} & = & -y_{9} \, \mathbf{a}_{1} + \left(x_{9}-y_{9}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{9}-y_{9}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{9}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{P III} \\ \mathbf{B}_{21} & = & \left(-x_{9}+y_{9}\right) \, \mathbf{a}_{1}-x_{9} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(-x_{9}+\frac{1}{2}y_{9}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{9}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{P III} \\ \end{array} \]

References

  • E. Ganglberger, Die Kristallstruktur von Fe12Zr2P7, Monatsh. Chem. 99, 557–565 (1968), doi:10.1007/BF00901204.

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=A12B7C2_hP21_174_2j2k_ajk_cf --params=

Species:

Running:

Output: