MoAlB Structure: ABC_oC12_63_c_c

Prototype	AlBMo
AFLOW prototype label	ABC_oC12_63_c_c_c-005
ICSD	251808
Pearson symbol	oC12
Space group number	63
Space group symbol	$C m c m$
AFLOW prototype command	aflow --proto=ABC_oC12_63_c_c_c-005 --params= $a, b / a, c / a, y_{1}, y_{2}, y_{3}$

(Ade, 2015) give atomic positions for WAlB that do not reproduce their interatomic distances and make the W-B distance far too small. We find that the parameters $(y_{A l}, y_{B}, y_{W}) = (0.19950, 0.03547, 0.41002)$ reproduce the reported distances.
The ICSD entry gives the structure type as UBC, but XtalFinder (Hicks, 2021) finds that the structures are essentially unmatchable.

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

Basis vectors

		Lattice coordinates		Cartesian coordinates	Wyckoff position	Atom type
$B_{1}$	=	$- y_{1} a_{1} + y_{1} a_{2} + \frac{1}{4} a_{3}$	=	$b y_{1} \hat{y} + \frac{1}{4} c \hat{z}$	(4c)	Al I
$B_{2}$	=	$y_{1} a_{1} - y_{1} a_{2} + \frac{3}{4} a_{3}$	=	$- b y_{1} \hat{y} + \frac{3}{4} c \hat{z}$	(4c)	Al I
$B_{3}$	=	$- y_{2} a_{1} + y_{2} a_{2} + \frac{1}{4} a_{3}$	=	$b y_{2} \hat{y} + \frac{1}{4} c \hat{z}$	(4c)	B I
$B_{4}$	=	$y_{2} a_{1} - y_{2} a_{2} + \frac{3}{4} a_{3}$	=	$- b y_{2} \hat{y} + \frac{3}{4} c \hat{z}$	(4c)	B I
$B_{5}$	=	$- y_{3} a_{1} + y_{3} a_{2} + \frac{1}{4} a_{3}$	=	$b y_{3} \hat{y} + \frac{1}{4} c \hat{z}$	(4c)	Mo I
$B_{6}$	=	$y_{3} a_{1} - y_{3} a_{2} + \frac{3}{4} a_{3}$	=	$- b y_{3} \hat{y} + \frac{3}{4} c \hat{z}$	(4c)	Mo I

M. Ade and H. Hillebrecht, Ternary Borides Cr $_{2}$ AlB $_{2}$ , Cr $_{2}$ AlB $_{4}$ , and Cr $_{4}$ AlB $_{6}$ : The First Members of the Series (CrB $_{2}$ ) $_{n}$ CrAl with $n = 1, 2, 3$ and a Unifying Concept for Ternary Borides as MAB-Phases, Inorg. Chem. 54, 6122–6135 (2015), doi:10.1021/acs.inorgchem.5b00049.
D. Hicks, C. Toher, D. C. Ford, F. Rose, C. D. Santo, O. Levy, M. J. Mehl, and S. Curtarolo, AFLOW-XtalFinder: a reliable choice to identify crystalline prototypes 7, 30 (2021), doi:10.1038/s41524-020-00483-4.

H. Zhang, J. Kim, R. Su, P. Richardson, J. Xi, E. Kisi, J. O'Connor, L. Shi, and I. Szlufarska, Defect behavior and radiation tolerance of MAB phases (MoAlB and Fe $_{2}$ AlB $_{2}$ ) with comparison to MAX phases, Acta Mater. 196, 505–515 (2020), doi:10.1016/j.actamat.2020.07.002.

Encyclopedia of Crystallographic Prototypes