Al$_{10}$V Structure: A10B_cF176_227_cfg

Basis vectors

		Lattice coordinates		Cartesian coordinates	Wyckoff position	Atom type
$B_{1}$	=	$0$	=	$0$	(16c)	Al I
$B_{2}$	=	$\frac{1}{2} a_{3}$	=	$\frac{1}{4} a \hat{x} + \frac{1}{4} a \hat{y}$	(16c)	Al I
$B_{3}$	=	$\frac{1}{2} a_{2}$	=	$\frac{1}{4} a \hat{x} + \frac{1}{4} a \hat{z}$	(16c)	Al I
$B_{4}$	=	$\frac{1}{2} a_{1}$	=	$\frac{1}{4} a \hat{y} + \frac{1}{4} a \hat{z}$	(16c)	Al I
$B_{5}$	=	$\frac{1}{2} a_{1} + \frac{1}{2} a_{2} + \frac{1}{2} a_{3}$	=	$\frac{1}{2} a \hat{x} + \frac{1}{2} a \hat{y} + \frac{1}{2} a \hat{z}$	(16d)	V I
$B_{6}$	=	$\frac{1}{2} a_{1} + \frac{1}{2} a_{2}$	=	$\frac{1}{4} a \hat{x} + \frac{1}{4} a \hat{y} + \frac{1}{2} a \hat{z}$	(16d)	V I
$B_{7}$	=	$\frac{1}{2} a_{1} + \frac{1}{2} a_{3}$	=	$\frac{1}{4} a \hat{x} + \frac{1}{2} a \hat{y} + \frac{1}{4} a \hat{z}$	(16d)	V I
$B_{8}$	=	$\frac{1}{2} a_{2} + \frac{1}{2} a_{3}$	=	$\frac{1}{2} a \hat{x} + \frac{1}{4} a \hat{y} + \frac{1}{4} a \hat{z}$	(16d)	V I
$B_{9}$	=	$- (x_{3} - \frac{1}{4}) a_{1} + x_{3} a_{2} + x_{3} a_{3}$	=	$a x_{3} \hat{x} + \frac{1}{8} a \hat{y} + \frac{1}{8} a \hat{z}$	(48f)	Al II
$B_{10}$	=	$x_{3} a_{1} - (x_{3} - \frac{1}{4}) a_{2} - (x_{3} - \frac{1}{4}) a_{3}$	=	$- a (x_{3} - \frac{1}{4}) \hat{x} + \frac{1}{8} a \hat{y} + \frac{1}{8} a \hat{z}$	(48f)	Al II
$B_{11}$	=	$x_{3} a_{1} - (x_{3} - \frac{1}{4}) a_{2} + x_{3} a_{3}$	=	$\frac{1}{8} a \hat{x} + a x_{3} \hat{y} + \frac{1}{8} a \hat{z}$	(48f)	Al II
$B_{12}$	=	$- (x_{3} - \frac{1}{4}) a_{1} + x_{3} a_{2} - (x_{3} - \frac{1}{4}) a_{3}$	=	$\frac{1}{8} a \hat{x} - a (x_{3} - \frac{1}{4}) \hat{y} + \frac{1}{8} a \hat{z}$	(48f)	Al II
$B_{13}$	=	$x_{3} a_{1} + x_{3} a_{2} - (x_{3} - \frac{1}{4}) a_{3}$	=	$\frac{1}{8} a \hat{x} + \frac{1}{8} a \hat{y} + a x_{3} \hat{z}$	(48f)	Al II
$B_{14}$	=	$- (x_{3} - \frac{1}{4}) a_{1} - (x_{3} - \frac{1}{4}) a_{2} + x_{3} a_{3}$	=	$\frac{1}{8} a \hat{x} + \frac{1}{8} a \hat{y} - a (x_{3} - \frac{1}{4}) \hat{z}$	(48f)	Al II
$B_{15}$	=	$(x_{3} + \frac{3}{4}) a_{1} - x_{3} a_{2} + (x_{3} + \frac{3}{4}) a_{3}$	=	$\frac{3}{8} a \hat{x} + a (x_{3} + \frac{3}{4}) \hat{y} + \frac{3}{8} a \hat{z}$	(48f)	Al II
$B_{16}$	=	$- x_{3} a_{1} + (x_{3} + \frac{3}{4}) a_{2} - x_{3} a_{3}$	=	$\frac{3}{8} a \hat{x} - a x_{3} \hat{y} + \frac{3}{8} a \hat{z}$	(48f)	Al II
$B_{17}$	=	$- x_{3} a_{1} + (x_{3} + \frac{3}{4}) a_{2} + (x_{3} + \frac{3}{4}) a_{3}$	=	$a (x_{3} + \frac{3}{4}) \hat{x} + \frac{3}{8} a \hat{y} + \frac{3}{8} a \hat{z}$	(48f)	Al II
$B_{18}$	=	$(x_{3} + \frac{3}{4}) a_{1} - x_{3} a_{2} - x_{3} a_{3}$	=	$- a x_{3} \hat{x} + \frac{3}{8} a \hat{y} + \frac{3}{8} a \hat{z}$	(48f)	Al II
$B_{19}$	=	$- x_{3} a_{1} - x_{3} a_{2} + (x_{3} + \frac{3}{4}) a_{3}$	=	$\frac{3}{8} a \hat{x} + \frac{3}{8} a \hat{y} - a x_{3} \hat{z}$	(48f)	Al II
$B_{20}$	=	$(x_{3} + \frac{3}{4}) a_{1} + (x_{3} + \frac{3}{4}) a_{2} - x_{3} a_{3}$	=	$\frac{3}{8} a \hat{x} + \frac{3}{8} a \hat{y} + a (x_{3} + \frac{3}{4}) \hat{z}$	(48f)	Al II
$B_{21}$	=	$z_{4} a_{1} + z_{4} a_{2} + (2 x_{4} - z_{4}) a_{3}$	=	$a x_{4} \hat{x} + a x_{4} \hat{y} + a z_{4} \hat{z}$	(96g)	Al III
$B_{22}$	=	$z_{4} a_{1} + z_{4} a_{2} - (2 x_{4} + z_{4} - \frac{1}{2}) a_{3}$	=	$- a (x_{4} - \frac{1}{4}) \hat{x} - a (x_{4} - \frac{1}{4}) \hat{y} + a z_{4} \hat{z}$	(96g)	Al III
$B_{23}$	=	$(2 x_{4} - z_{4}) a_{1} - (2 x_{4} + z_{4} - \frac{1}{2}) a_{2} + z_{4} a_{3}$	=	$- a (x_{4} - \frac{1}{4}) \hat{x} + a x_{4} \hat{y} - a (z_{4} - \frac{1}{4}) \hat{z}$	(96g)	Al III
$B_{24}$	=	$- (2 x_{4} + z_{4} - \frac{1}{2}) a_{1} + (2 x_{4} - z_{4}) a_{2} + z_{4} a_{3}$	=	$a x_{4} \hat{x} - a (x_{4} - \frac{1}{4}) \hat{y} - a (z_{4} - \frac{1}{4}) \hat{z}$	(96g)	Al III
$B_{25}$	=	$(2 x_{4} - z_{4}) a_{1} + z_{4} a_{2} + z_{4} a_{3}$	=	$a z_{4} \hat{x} + a x_{4} \hat{y} + a x_{4} \hat{z}$	(96g)	Al III
$B_{26}$	=	$- (2 x_{4} + z_{4} - \frac{1}{2}) a_{1} + z_{4} a_{2} + z_{4} a_{3}$	=	$a z_{4} \hat{x} - a (x_{4} - \frac{1}{4}) \hat{y} - a (x_{4} - \frac{1}{4}) \hat{z}$	(96g)	Al III
$B_{27}$	=	$z_{4} a_{1} + (2 x_{4} - z_{4}) a_{2} - (2 x_{4} + z_{4} - \frac{1}{2}) a_{3}$	=	$- a (z_{4} - \frac{1}{4}) \hat{x} - a (x_{4} - \frac{1}{4}) \hat{y} + a x_{4} \hat{z}$	(96g)	Al III
$B_{28}$	=	$z_{4} a_{1} - (2 x_{4} + z_{4} - \frac{1}{2}) a_{2} + (2 x_{4} - z_{4}) a_{3}$	=	$- a (z_{4} - \frac{1}{4}) \hat{x} + a x_{4} \hat{y} - a (x_{4} - \frac{1}{4}) \hat{z}$	(96g)	Al III
$B_{29}$	=	$z_{4} a_{1} + (2 x_{4} - z_{4}) a_{2} + z_{4} a_{3}$	=	$a x_{4} \hat{x} + a z_{4} \hat{y} + a x_{4} \hat{z}$	(96g)	Al III
$B_{30}$	=	$z_{4} a_{1} - (2 x_{4} + z_{4} - \frac{1}{2}) a_{2} + z_{4} a_{3}$	=	$- a (x_{4} - \frac{1}{4}) \hat{x} + a z_{4} \hat{y} - a (x_{4} - \frac{1}{4}) \hat{z}$	(96g)	Al III
$B_{31}$	=	$- (2 x_{4} + z_{4} - \frac{1}{2}) a_{1} + z_{4} a_{2} + (2 x_{4} - z_{4}) a_{3}$	=	$a x_{4} \hat{x} - a (z_{4} - \frac{1}{4}) \hat{y} - a (x_{4} - \frac{1}{4}) \hat{z}$	(96g)	Al III
$B_{32}$	=	$(2 x_{4} - z_{4}) a_{1} + z_{4} a_{2} - (2 x_{4} + z_{4} - \frac{1}{2}) a_{3}$	=	$- a (x_{4} - \frac{1}{4}) \hat{x} - a (z_{4} - \frac{1}{4}) \hat{y} + a x_{4} \hat{z}$	(96g)	Al III
$B_{33}$	=	$- z_{4} a_{1} - z_{4} a_{2} + (2 x_{4} + z_{4} + \frac{1}{2}) a_{3}$	=	$a (x_{4} + \frac{1}{4}) \hat{x} + a (x_{4} + \frac{1}{4}) \hat{y} - a z_{4} \hat{z}$	(96g)	Al III
$B_{34}$	=	$- z_{4} a_{1} - z_{4} a_{2} - (2 x_{4} - z_{4}) a_{3}$	=	$- a x_{4} \hat{x} - a x_{4} \hat{y} - a z_{4} \hat{z}$	(96g)	Al III
$B_{35}$	=	$- (2 x_{4} - z_{4}) a_{1} + (2 x_{4} + z_{4} + \frac{1}{2}) a_{2} - z_{4} a_{3}$	=	$a (x_{4} + \frac{1}{4}) \hat{x} - a x_{4} \hat{y} + a (z_{4} + \frac{1}{4}) \hat{z}$	(96g)	Al III
$B_{36}$	=	$(2 x_{4} + z_{4} + \frac{1}{2}) a_{1} - (2 x_{4} - z_{4}) a_{2} - z_{4} a_{3}$	=	$- a x_{4} \hat{x} + a (x_{4} + \frac{1}{4}) \hat{y} + a (z_{4} + \frac{1}{4}) \hat{z}$	(96g)	Al III
$B_{37}$	=	$- (2 x_{4} - z_{4}) a_{1} - z_{4} a_{2} + (2 x_{4} + z_{4} + \frac{1}{2}) a_{3}$	=	$a (x_{4} + \frac{1}{4}) \hat{x} + a (z_{4} + \frac{1}{4}) \hat{y} - a x_{4} \hat{z}$	(96g)	Al III
$B_{38}$	=	$(2 x_{4} + z_{4} + \frac{1}{2}) a_{1} - z_{4} a_{2} - (2 x_{4} - z_{4}) a_{3}$	=	$- a x_{4} \hat{x} + a (z_{4} + \frac{1}{4}) \hat{y} + a (x_{4} + \frac{1}{4}) \hat{z}$	(96g)	Al III
$B_{39}$	=	$- z_{4} a_{1} - (2 x_{4} - z_{4}) a_{2} - z_{4} a_{3}$	=	$- a x_{4} \hat{x} - a z_{4} \hat{y} - a x_{4} \hat{z}$	(96g)	Al III
$B_{40}$	=	$- z_{4} a_{1} + (2 x_{4} + z_{4} + \frac{1}{2}) a_{2} - z_{4} a_{3}$	=	$a (x_{4} + \frac{1}{4}) \hat{x} - a z_{4} \hat{y} + a (x_{4} + \frac{1}{4}) \hat{z}$	(96g)	Al III
$B_{41}$	=	$- z_{4} a_{1} - (2 x_{4} - z_{4}) a_{2} + (2 x_{4} + z_{4} + \frac{1}{2}) a_{3}$	=	$a (z_{4} + \frac{1}{4}) \hat{x} + a (x_{4} + \frac{1}{4}) \hat{y} - a x_{4} \hat{z}$	(96g)	Al III
$B_{42}$	=	$- z_{4} a_{1} + (2 x_{4} + z_{4} + \frac{1}{2}) a_{2} - (2 x_{4} - z_{4}) a_{3}$	=	$a (z_{4} + \frac{1}{4}) \hat{x} - a x_{4} \hat{y} + a (x_{4} + \frac{1}{4}) \hat{z}$	(96g)	Al III
$B_{43}$	=	$(2 x_{4} + z_{4} + \frac{1}{2}) a_{1} - z_{4} a_{2} - z_{4} a_{3}$	=	$- a z_{4} \hat{x} + a (x_{4} + \frac{1}{4}) \hat{y} + a (x_{4} + \frac{1}{4}) \hat{z}$	(96g)	Al III
$B_{44}$	=	$- (2 x_{4} - z_{4}) a_{1} - z_{4} a_{2} - z_{4} a_{3}$	=	$- a z_{4} \hat{x} - a x_{4} \hat{y} - a x_{4} \hat{z}$	(96g)	Al III

Prototype	Al $_{10}$ V
AFLOW prototype label	A10B_cF176_227_cfg_d-001
ICSD	58202
Pearson symbol	cF176
Space group number	227
Space group symbol	$F d \overline{3} m$
AFLOW prototype command	aflow --proto=A10B_cF176_227_cfg_d-001 --params= $a, x_{3}, x_{4}, z_{4}$

Encyclopedia of Crystallographic Prototypes

Al $_{10}$ V Structure: A10B_cF176_227_cfg_d-001

Face-centered Cubic primitive vectors

References

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Running:

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Encyclopedia of Crystallographic Prototypes

Al10​V Structure: A10B_cF176_227_cfg_d-001

Face-centered Cubic primitive vectors

References

Found in

Running:

Output:

Al $_{10}$ V Structure: A10B_cF176_227_cfg_d-001