$D0_{7}$ (CrO$_{3}$) Structure (<em>Obsolete</em>): AB3_oC16_20_a

Prototype	CrO $_{3}$
AFLOW prototype label	AB3_oC16_20_a_bc-001
Strukturbericht designation	$D 0_{7}$
ICSD	none
Pearson symbol	oC16
Space group number	20
Space group symbol	$C 22 2_{1}$
AFLOW prototype command	aflow --proto=AB3_oC16_20_a_bc-001 --params= $a, b / a, c / a, x_{1}, y_{2}, x_{3}, y_{3}, z_{3}$

This is the determination of the orthorhombic structure of CrO $_{3}$ given the $D 0_{7}$ structure by (Hermann, 1937). This structure is superceded by the one found by (Byström, 1950), which we call the orthorhombic CrO $_{3}$ phase. The current structure has the Cr atom at the center of a distorted oxygen octahedron, while the newer structure as the Cr atom at center of a distorted tetrahedron.

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
$B_{1}$	=	$x_{1} a_{1} + x_{1} a_{2}$	=	$a x_{1} \hat{x}$	(4a)	Cr I
$B_{2}$	=	$- x_{1} a_{1} - x_{1} a_{2} + \frac{1}{2} a_{3}$	=	$- a x_{1} \hat{x} + \frac{1}{2} c \hat{z}$	(4a)	Cr I
$B_{3}$	=	$- y_{2} a_{1} + y_{2} a_{2} + \frac{1}{4} a_{3}$	=	$b y_{2} \hat{y} + \frac{1}{4} c \hat{z}$	(4b)	O I
$B_{4}$	=	$y_{2} a_{1} - y_{2} a_{2} + \frac{3}{4} a_{3}$	=	$- b y_{2} \hat{y} + \frac{3}{4} c \hat{z}$	(4b)	O I
$B_{5}$	=	$(x_{3} - y_{3}) a_{1} + (x_{3} + y_{3}) a_{2} + z_{3} a_{3}$	=	$a x_{3} \hat{x} + b y_{3} \hat{y} + c z_{3} \hat{z}$	(8c)	O II
$B_{6}$	=	$- (x_{3} - y_{3}) a_{1} - (x_{3} + y_{3}) a_{2} + (z_{3} + \frac{1}{2}) a_{3}$	=	$- a x_{3} \hat{x} - b y_{3} \hat{y} + c (z_{3} + \frac{1}{2}) \hat{z}$	(8c)	O II
$B_{7}$	=	$- (x_{3} + y_{3}) a_{1} - (x_{3} - y_{3}) a_{2} - (z_{3} - \frac{1}{2}) a_{3}$	=	$- a x_{3} \hat{x} + b y_{3} \hat{y} - c (z_{3} - \frac{1}{2}) \hat{z}$	(8c)	O II
$B_{8}$	=	$(x_{3} + y_{3}) a_{1} + (x_{3} - y_{3}) a_{2} - z_{3} a_{3}$	=	$a x_{3} \hat{x} - b y_{3} \hat{y} - c z_{3} \hat{z}$	(8c)	O II

H. Bräkken, Die Kristallstrukturen der Trioxyde von Chrom, Molybdän und Wolfram, Z. Kristallgr. 78, 484–488 (1931), doi:10.1524/zkri.1931.78.1.484.
C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturebericht Band II, 1928-1932 (Akademsiche Verlagsgesellschaft M. B. H, Leipzig, 1937).

A. Byström and K.-A. Wilhelmi, The Crystal Structure of Chromium Trioxide, Acta Chem. Scand. 4, 1131–1141 (1950), doi:10.3891/acta.chem.scand.04-1131.

Encyclopedia of Crystallographic Prototypes