Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A9BC3D5_hP18_189_fi_a_g_bh-001

This structure originally had the label A9BC3D5_hP18_189_fi_a_g_bh. Calls to that address will be redirected here.

If you are using this page, please cite:
D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)

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https://aflow.org/p/0WD7
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π-FeMg $_{3}$ Al $_{9}$ Si $_{5}$ Structure: A9BC3D5_hP18_189_fi_a_g_bh-001

Prototype	Al $_{9}$ FeMg $_{3}$ Si $_{5}$
AFLOW prototype label	A9BC3D5_hP18_189_fi_a_g_bh-001
ICSD	96905
Pearson symbol	hP18
Space group number	189
Space group symbol	$P \overline{6} 2 m$
AFLOW prototype command	aflow --proto=A9BC3D5_hP18_189_fi_a_g_bh-001 --params= $a, c / a, x_{3}, x_{4}, z_{5}, x_{6}, z_{6}$

This is a reanalysis of the $π$ –FeMg $_{3}$ Al $_{8}$ Si $_{6}$ ( $E 9_{b}$ ) structure. The space group and occupied Wyckoff positions are unchanged, but the ordering, stoichiometry, and atomic positions are different.

a_{1} a_{2} a_{3} = = = \frac{1}{2} a \hat{x} - \frac{3}{2} a \hat{y} \frac{1}{2} a \hat{x} + \frac{3}{2} a \hat{y} c \hat{z}

Picture of Structure; Click for Big Picture

Basis vectors

		Lattice coordinates		Cartesian coordinates	Wyckoff position	Atom type
$B_{1}$	=	$0$	=	$0$	(1a)	Fe I
$B_{2}$	=	$\frac{1}{2} a_{3}$	=	$\frac{1}{2} c \hat{z}$	(1b)	Si I
$B_{3}$	=	$x_{3} a_{1}$	=	$\frac{1}{2} a x_{3} \hat{x} - \frac{3}{2} a x_{3} \hat{y}$	(3f)	Al I
$B_{4}$	=	$x_{3} a_{2}$	=	$\frac{1}{2} a x_{3} \hat{x} + \frac{3}{2} a x_{3} \hat{y}$	(3f)	Al I
$B_{5}$	=	$- x_{3} a_{1} - x_{3} a_{2}$	=	$- a x_{3} \hat{x}$	(3f)	Al I
$B_{6}$	=	$x_{4} a_{1} + \frac{1}{2} a_{3}$	=	$\frac{1}{2} a x_{4} \hat{x} - \frac{3}{2} a x_{4} \hat{y} + \frac{1}{2} c \hat{z}$	(3g)	Mg I
$B_{7}$	=	$x_{4} a_{2} + \frac{1}{2} a_{3}$	=	$\frac{1}{2} a x_{4} \hat{x} + \frac{3}{2} a x_{4} \hat{y} + \frac{1}{2} c \hat{z}$	(3g)	Mg I
$B_{8}$	=	$- x_{4} a_{1} - x_{4} a_{2} + \frac{1}{2} a_{3}$	=	$- a x_{4} \hat{x} + \frac{1}{2} c \hat{z}$	(3g)	Mg I
$B_{9}$	=	$\frac{1}{3} a_{1} + \frac{2}{3} a_{2} + z_{5} a_{3}$	=	$\frac{1}{2} a \hat{x} + \frac{3}{6} a \hat{y} + c z_{5} \hat{z}$	(4h)	Si II
$B_{10}$	=	$\frac{1}{3} a_{1} + \frac{2}{3} a_{2} - z_{5} a_{3}$	=	$\frac{1}{2} a \hat{x} + \frac{3}{6} a \hat{y} - c z_{5} \hat{z}$	(4h)	Si II
$B_{11}$	=	$\frac{2}{3} a_{1} + \frac{1}{3} a_{2} - z_{5} a_{3}$	=	$\frac{1}{2} a \hat{x} - \frac{3}{6} a \hat{y} - c z_{5} \hat{z}$	(4h)	Si II
$B_{12}$	=	$\frac{2}{3} a_{1} + \frac{1}{3} a_{2} + z_{5} a_{3}$	=	$\frac{1}{2} a \hat{x} - \frac{3}{6} a \hat{y} + c z_{5} \hat{z}$	(4h)	Si II
$B_{13}$	=	$x_{6} a_{1} + z_{6} a_{3}$	=	$\frac{1}{2} a x_{6} \hat{x} - \frac{3}{2} a x_{6} \hat{y} + c z_{6} \hat{z}$	(6i)	Al II
$B_{14}$	=	$x_{6} a_{2} + z_{6} a_{3}$	=	$\frac{1}{2} a x_{6} \hat{x} + \frac{3}{2} a x_{6} \hat{y} + c z_{6} \hat{z}$	(6i)	Al II
$B_{15}$	=	$- x_{6} a_{1} - x_{6} a_{2} + z_{6} a_{3}$	=	$- a x_{6} \hat{x} + c z_{6} \hat{z}$	(6i)	Al II
$B_{16}$	=	$x_{6} a_{1} - z_{6} a_{3}$	=	$\frac{1}{2} a x_{6} \hat{x} - \frac{3}{2} a x_{6} \hat{y} - c z_{6} \hat{z}$	(6i)	Al II
$B_{17}$	=	$x_{6} a_{2} - z_{6} a_{3}$	=	$\frac{1}{2} a x_{6} \hat{x} + \frac{3}{2} a x_{6} \hat{y} - c z_{6} \hat{z}$	(6i)	Al II
$B_{18}$	=	$- x_{6} a_{1} - x_{6} a_{2} - z_{6} a_{3}$	=	$- a x_{6} \hat{x} - c z_{6} \hat{z}$	(6i)	Al II

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 59, 36–42 (2003), doi:10.1107/S0108768102022887.

Found in

A. Jain, S. Ping, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, and K. A. Persson, Commentary: The Materials Project: A materials genome approach to accelerating materials innovation, APL Materials 1, 011002 (2013), doi:10.1063/1.4812323.
ICSD, Inorganic Crystal Structure Database. ID 96905.

a

c / a

x_{3}

x_{4}

z_{5}

x_{6}

z_{6}

Encyclopedia of Crystallographic Prototypes

π-FeMg $_{3}$ Al $_{9}$ Si $_{5}$ Structure: A9BC3D5_hP18_189_fi_a_g_bh-001

Hexagonal primitive vectors

References

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Encyclopedia of Crystallographic Prototypes

π-FeMg3​Al9​Si5​ Structure: A9BC3D5_hP18_189_fi_a_g_bh-001

Hexagonal primitive vectors

References

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π-FeMg $_{3}$ Al $_{9}$ Si $_{5}$ Structure: A9BC3D5_hP18_189_fi_a_g_bh-001