Lack of a threefold rotation axis in α-Fe₂O₃ and α-Cr₂O₃ crystals

The crystal structure of α-Fe₂O₃ and α-Cr₂O₃ is usually described with the corundum-type trigonal crystal structure based on the space group . There are, however, some observations of the magnetic ordering of both α-Fe₂O₃ and α-Cr₂O₃ that are incompatible with the trigonal symmetry. We show experimental evidence based on X-ray powder diffraction and supported by transmission electron microscopy that the symmetry of the crystal structure of both α-Fe₂O₃ and α-Cr₂O₃ is monoclinic and it is described with the space group C2/c (derived from by removing the threefold rotation axis). The magnetic orderings of α-Fe₂O₃ and α-Cr₂O₃ are compatible with the magnetic space groups C2/c and C2/c′, respectively. These findings are in agreement with the idea from Curie [(1894), J. Phys. 3, 393–415] that the dissymmetry of the magnetic ordering should be associated with a dissymmetry of the crystal structure.

Computing details

Figures

(global)

Crystal data

Cr2O3	β = 162.471660°
Mr = 152	V = 193.06 Å^3
Monoclinic, C2/c	Z = 4
Hall symbol: -C 2yc	? radiation, λ = 0.400860 Å
a = 9.505855 Å	T = 293 K
b = 4.959861 Å	?, ? × ? × ? mm
c = 13.596130 Å

Data collection

Radiation source: synchrotron

2θmin = 5°, 2θmax = 29.999°, 2θstep = 0.001°

Refinement

Rp = 0.088	8 parameters
Rwp = 0.128	0 restraints
Rexp = 0.087	0 constraints
χ^2 = 2.190	Weighting scheme based on measured s.u.'s
36001 data points	(Δ/σ)max = 0.041
Excluded region(s): from 30 to 60.000	Background function: 5 Legendre polynoms
Profile function: Lorentzian	Preferred orientation correction: none

Special details

Refinement. Unit-cell parameters are obtained from powder SR diffraction refinement. Atomic positions were derived from the rhombohedral (R-3c) crystal structure.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Cr1	0	0	0.1518	0.038*
O1	−0.4587	−0.1529	−0.0558	0.038*
O2	0	0.3058	0.25	0.038*

(II)

Crystal data

Fe2O3	β = 162.40490°
Mr = 159.7	V = 201.31 Å^3
Monoclinic, C2/c	Z = 4
Hall symbol: -C 2yc	? radiation, λ = 0.400860 Å
a = 9.618170 Å	T = 293 K
b = 5.035249 Å	?, ? × ? × ? mm
c = 13.750989 Å

Data collection

Radiation source: synchrotron

2θmin = 5°, 2θmax = 29.999°, 2θstep = 0.001°

Refinement

Rp = 0.112	8 parameters
Rwp = 0.138	0 restraints
Rexp = 0.094	0 constraints
χ^2 = 2.132	Weighting scheme based on measured s.u.'s
43001 data points	(Δ/σ)max < 0.001
Excluded region(s): from 30 to 60.000	Background function: 5 Legendre polynoms
Profile function: Lorentzian	Preferred orientation correction: none

Special details

Refinement. Unit-cell parameters are obtained from powder SR diffraction refinement. Atomic positions were derived from the rhombohedral (R-3c) crystal structure.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Fe1	0	0	0.1447	0.038*
O1	−0.459	−0.153	−0.056	0.038*
O2	0	0.3061	0.25	0.038*