Verification of the de Wolff hypothesis concerning the symmetry of β-MnO₂

The symmetry lowering from tetragonal to orthorhombic is demonstrated using high-resolution diffraction and also justified by using the magnetic superspace groups formalism for the rutile-type compound β-MnO₂. The (lower) orthorhombic symmetry is observed at temperatures both below and above the Néel temperature. The magnetic ordering of β-MnO₂ is of spin density type and not screw-type helical. The results support the de Wolff [Acta Cryst. (1959), 12, 341–345] hypothesis about the orthorhombic symmetry of β-MnO₂.

Computing details

(I)

Crystal data

MnO2	V = 55.63 (1) Å^3
Mr = 86.9	Z = 2
Orthorhombic, Pnnm	F(000) = 82
Hall symbol: -P -2xabc;-2yabc;-2z	Dx = 5.190 Mg m^−3
a = 4.40458 (11) Å	Synchrotron radiation
b = 4.39506 (12) Å	T = 295 K
c = 2.87357 (5) Å

Data collection

2θmin = 10.006°, 2θmax = 62.146°, 2θstep = 0.006°

Refinement

Rp = 0.066	24 parameters
Rwp = 0.099	0 restraints
Rexp = 0.005	0 constraints
R(F) = 0.022	Weighting scheme based on measured s.u.'s
10296 data points	(Δ/σ)max = 0.048
Excluded region(s): from 0 to 10.000	Background function: 10 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: none

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

	x	y	z	Uiso*/Ueq
Mn	0	0	0	0.0015 (3)*
O	0.3069 (13)	0.3052 (14)	0	0.0023 (8)*

(II)

Crystal data

MnO2	V = 55.49 (1) Å^3
Mr = 86.9	Z = 2
Orthorhombic, Pnnm	F(000) = 82
Hall symbol: -P -2xabc;-2yabc;-2z	Dx = 5.203 Mg m^−3
a = 4.4004 (3) Å	Synchrotron radiation
b = 4.3910 (3) Å	T = 90 K
c = 2.87183 (15) Å

Data collection

2θmin = 10.006°, 2θmax = 62.146°, 2θstep = 0.006°

Refinement

Rp = 0.112	24 parameters
Rwp = 0.150	0 restraints
Rexp = 0.006	0 constraints
R(F) = 0.087	Weighting scheme based on measured s.u.'s
10296 data points	(Δ/σ)max = 0.043
Excluded region(s): from 0 to 10.000	Background function: 10 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: none

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

	x	y	z	Uiso*/Ueq
Mn	0	0	0	0.0069 (9)*
O	0.306 (4)	0.304 (4)	0	0.007 (3)*

(III)

Crystal data

F2Mn	V = 78.67 (1) Å^3
Mr = 92.9	Z = 2
Orthorhombic, Pnnm	F(000) = 86
Hall symbol: -P -2xabc;-2yabc;-2z	Dx = 3.923 Mg m^−3
a = 4.8795 (4) Å	Synchrotron radiation
b = 4.8696 (4) Å	T = 295 K
c = 3.31072 (18) Å

Data collection

2θmin = 8.002°, 2θmax = 62.146°, 2θstep = 0.006°

Refinement

Rp = 0.048	19 parameters
Rwp = 0.064	0 restraints
Rexp = 0.006	0 constraints
R(F) = 0.034	Weighting scheme based on measured s.u.'s
10296 data points	(Δ/σ)max = 0.049
Excluded region(s): from 0 to 8.000	Background function: 5 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: none

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

	x	y	z	Uiso*/Ueq
Mn	0	0	0	0.0063 (6)*
F	0.306 (3)	0.303 (3)	0	0.0097 (15)*

(IV)

Crystal data

F2Mn	V = 78.48 (1) Å^3
Mr = 92.9	Z = 2
Orthorhombic, Pnnm	F(000) = 86
Hall symbol: -P -2xabc;-2yabc;-2z	Dx = 3.933 Mg m^−3
a = 4.8781 (5) Å	Synchrotron radiation
b = 4.8677 (5) Å	T = 100 K
c = 3.30492 (19) Å

Data collection

2θmin = 8.002°, 2θmax = 62.146°, 2θstep = 0.006°

Refinement

Rp = 0.054	19 parameters
Rwp = 0.070	0 restraints
Rexp = 0.006	0 constraints
R(F) = 0.025	Weighting scheme based on measured s.u.'s
10296 data points	(Δ/σ)max = 0.048
Excluded region(s): from 0 to 8.000	Background function: 5 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: none

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

	x	y	z	Uiso*/Ueq
Mn	0	0	0	0.0030 (6)*
F	0.305 (3)	0.303 (3)	0	0.0046 (16)*