$\pi$–FeMg3Al9Si5 Structure: A9BC3D5_hP18_189_fi_a_g_bh

Picture of Structure; Click for Big Picture
Prototype : FeMg3Al9Si5
AFLOW prototype label : A9BC3D5_hP18_189_fi_a_g_bh
Strukturbericht designation : None
Pearson symbol : hP18
Space group number : 189
Space group symbol : $P\bar{6}2m$
AFLOW prototype command : aflow --proto=A9BC3D5_hP18_189_fi_a_g_bh
--params=
$a$,$c/a$,$x_{3}$,$x_{4}$,$z_{5}$,$x_{6}$,$z_{6}$



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{Fe} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(1b\right) & \mbox{Si I} \\ \mathbf{B}_{3} & = & x_{3} \, \mathbf{a}_{1} & = & \frac{1}{2}x_{3}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} & \left(3f\right) & \mbox{Al I} \\ \mathbf{B}_{4} & = & x_{3} \, \mathbf{a}_{2} & = & \frac{1}{2}x_{3}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} & \left(3f\right) & \mbox{Al I} \\ \mathbf{B}_{5} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} & = & -x_{3}a \, \mathbf{\hat{x}} & \left(3f\right) & \mbox{Al I} \\ \mathbf{B}_{6} & = & x_{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{4}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3g\right) & \mbox{Mg} \\ \mathbf{B}_{7} & = & x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3g\right) & \mbox{Mg} \\ \mathbf{B}_{8} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3g\right) & \mbox{Mg} \\ \mathbf{B}_{9} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(4h\right) & \mbox{Si II} \\ \mathbf{B}_{10} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(4h\right) & \mbox{Si II} \\ \mathbf{B}_{11} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(4h\right) & \mbox{Si II} \\ \mathbf{B}_{12} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(4h\right) & \mbox{Si II} \\ \mathbf{B}_{13} & = & x_{6} \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{6}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{Al II} \\ \mathbf{B}_{14} & = & x_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{6}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{Al II} \\ \mathbf{B}_{15} & = & -x_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + z_{6}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{Al II} \\ \mathbf{B}_{16} & = & x_{6} \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{6}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{Al II} \\ \mathbf{B}_{17} & = & x_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{6}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{Al II} \\ \mathbf{B}_{18} & = & -x_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-z_{6}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{Al II} \\ \end{array} \]

References

  • S. Foss, A. Olsen, C. J. Simensen, and J. Tafto, Determination of the crystal structure of the π–AlFeMgSi phase using symmetry– and site–sensitive electron microscope techniques, Acta Crystallogr. Sect. B Struct. Sci. 59, 36–42 (2003), doi:10.1107/S0108768102022887.

Found in

  • ICSD, Inorganic Crystal Structure Database. ID 96905.

Geometry files


Prototype Generator

aflow --proto=A9BC3D5_hP18_189_fi_a_g_bh --params=

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