$\pi$–FeMg3Al8Si6 ($E9_{b}$) Structure: A8BC3D6_hP18_189_bfh_a_g_i

Picture of Structure; Click for Big Picture
Prototype : FeMg3Al8Si6
AFLOW prototype label : A8BC3D6_hP18_189_bfh_a_g_i
Strukturbericht designation : $E9_{b}$
Pearson symbol : hP18
Space group number : 189
Space group symbol : $P\bar{6}2m$
AFLOW prototype command : aflow --proto=A8BC3D6_hP18_189_bfh_a_g_i
--params=
$a$,$c/a$,$x_{3}$,$x_{4}$,$z_{5}$,$x_{6}$,$z_{6}$


  • We have been unable to obtain a copy of (Perlitz, 1942), and use the data provided by (Brandes, 1992) and (Foss, 2003). Foss et al. argue that the actual composition of this phase should be FeMg3Al9Si5. This requires a reordering of the atomic positions, as described in A9BC3D5_hP18_189_fi_a_g_bh.

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{Al 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 II} \\ \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 II} \\ \mathbf{B}_{5} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} & = & -x_{3}a \, \mathbf{\hat{x}} & \left(3f\right) & \mbox{Al II} \\ \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{Al III} \\ \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{Al III} \\ \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{Al III} \\ \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{Al III} \\ \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{Si} \\ \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{Si} \\ \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{Si} \\ \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{Si} \\ \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{Si} \\ \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{Si} \\ \end{array} \]

References

  • H. Perlitz and A. Westgren, The Crystal Structure of Al8Si6Mg3Fe, Ark. Kem. Mineral. Geol. 15B, 1–8 (1942).
  • E. A. Brandes and G. B. Brook, eds., Smithells Metals Reference Book (Butterworth Heinemann, Oxford, Auckland, Boston, Johannesburg, Melbourne, New Delhi, 1992), chap. 6, pp. 6–60, seventh edn.

Found in

  • S. Foss, A. Olsen, C. J. Simensen, and J. Taft{o}, 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.

Geometry files


Prototype Generator

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