Positive and negative monoclinic deformation of corundum-type trigonal crystal structures of M2O3 metal oxides

Fabrykiewicz, P.; Przeniosło, R.; Sosnowska, I.; Fauth, F.

doi:10.1107/S2052520618014968

Positive and negative monoclinic deformation of corundum-type trigonal crystal structures of M₂O₃ metal oxides

P. Fabrykiewicz, R. Przeniosło, I. Sosnowska and F. Fauth

The crystal structures of several transition metal oxides, Ti₂O₃, V₂O₃, Cr₂O₃, Al₂O₃ and α-Fe₂O₃, are studied using synchrotron radiation X-ray powder diffraction. The observed angular dependence of the integral breadths is described by two models: (i) the distorted corundum-type structure model described by the space group C2/c and (ii) the Stephens model of anisotropic Bragg peak broadening. These two models are shown to be equivalent. Ti₂O₃, V₂O₃ and Cr₂O₃ show a `positive' distortion which is related to the possible metal–metal bond suggested by Goodenough in the literature (the deformation leads to shorter metal–metal distances) whereas Al₂O₃ and α-Fe₂O₃ show a `negative' distortion which leads to relatively longer metal–metal distances.

Keywords: synchrotron powder diffraction; peak broadening; metal–metal bond; corundum-type structure; Ti₂O₃; tistarite; V₂O₃; karelianite; Cr₂O₃; eskolaite; Al₂O₃; corundum; α-Fe₂O₃; hematite.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S2052520618014968/dq5032sup1.cif Contains datablocks global, I, II, III, IV, V, VI, VII, VIII, IX, X
	Portable Document Format (PDF) file https://doi.org/10.1107/S2052520618014968/dq5032sup2.pdf Supplementary material
	Text file https://doi.org/10.1107/S2052520618014968/dq5032sup3.txt Stephens model beta vs 2-theta data for V2O3
	Text file https://doi.org/10.1107/S2052520618014968/dq5032sup4.txt Stephens model beta vs 2-theta data for Al2O3

CCDC references: 1874880; 1874881; 1874882; 1874883; 1874884; 1874885; 1874886; 1874887; 1874888; 1874889

Computing details top

(I) top

Crystal data top

O₃Ti₂	V = 313.64 (1) Å³
M_r = 143.8	Z = 6
Trigonal, R3c	F(000) = 408
Hall symbol: -R 3;-2"c	D_x = 4.567 Mg m⁻³
a = 5.15941 (10) Å	Synchrotron radiation
c = 13.6050 (3) Å	T = 290 K

Data collection top

2θ_min = 7.006°, 2θ_max = 82.144°, 2θ_step = 0.006°

Refinement top

R_p = 0.055	33 parameters
R_wp = 0.095	0 restraints
R_exp = 0.007	0 constraints
R(F) = 0.029	Weighting scheme based on measured s.u.'s
13629 data points	(Δ/σ)_max = 0.043
Excluded region(s): from 0 to 7.000	Background function: 20 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: none

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Ti1	0	0	0.34470 (15)	0.0039 (4)*
O1	0.3124 (12)	0	0.25	0.0031 (12)*

(II) top

Crystal data top

O₃Ti₂	β = 161.828 (2)°
M_r = 143.8	V = 209.09 (4) Å³
Monoclinic, C2/c	Z = 4
Hall symbol: -C 2yc	F(000) = 272
a = 9.5465 (8) Å	D_x = 4.567 Mg m⁻³
b = 5.1618 (2) Å	Synchrotron radiation
c = 13.6049 (10) Å	T = 290 K

Data collection top

2θ_min = 7.006°, 2θ_max = 82.144°, 2θ_step = 0.006°

Refinement top

R_p = 0.052	33 parameters
R_wp = 0.093	0 restraints
R_exp = 0.007	0 constraints
R(F) = 0.030	Weighting scheme based on measured s.u.'s
13629 data points	(Δ/σ)_max = 0.045
Excluded region(s): from 0 to 7.000	Background function: 20 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: none

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Ti1	0	0	0.344695	0.0039 (4)*
O1	−0.46859	−0.156197	−0.062393	0.0029 (11)*
O2	0	0.312393	0.25	0.0029 (11)*

(III) top

Crystal data top

O₃V₂	V = 297.45 (1) Å³
M_r = 149.9	Z = 6
Trigonal, R3c	F(000) = 420
Hall symbol: -R 3;-2"c	D_x = 5.020 Mg m⁻³
a = 4.95311 (11) Å	Synchrotron radiation
c = 13.9999 (4) Å	T = 290 K

Data collection top

2θ_min = 7.006°, 2θ_max = 82.144°, 2θ_step = 0.006°

Refinement top

R_p = 0.042	33 parameters
R_wp = 0.064	0 restraints
R_exp = 0.006	0 constraints
R(F) = 0.021	Weighting scheme based on measured s.u.'s
13629 data points	(Δ/σ)_max = 0.046
Excluded region(s): from 0 to 7.000	Background function: 20 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: none

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
V1	0	0	0.34639 (16)	0.0036 (4)*
O1	0.3113 (14)	0	0.25	0.0024 (14)*

(IV) top

Crystal data top

O₃V₂	β = 162.972 (4)°
M_r = 149.9	V = 198.30 (6) Å³
Monoclinic, C2/c	Z = 4
Hall symbol: -C 2yc	F(000) = 280
a = 9.7622 (14) Å	D_x = 5.020 Mg m⁻³
b = 4.9547 (4) Å	Synchrotron radiation
c = 14.0000 (19) Å	T = 290 K

Data collection top

2θ_min = 7.006°, 2θ_max = 82.144°, 2θ_step = 0.006°

Refinement top

R_p = 0.042	33 parameters
R_wp = 0.064	0 restraints
R_exp = 0.006	0 constraints
R(F) = 0.022	Weighting scheme based on measured s.u.'s
13629 data points	(Δ/σ)_max = 0.048
Excluded region(s): from 0 to 7.000	Background function: 20 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: none

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
V1	0	0	0.346394	0.0036 (4)*
O1	−0.467024	−0.155675	−0.061349	0.0024 (13)*
O2	0	0.311349	0.25	0.0024 (13)*

(V) top

Crystal data top

Cr₂O₃	V = 289.52 (1) Å³
M_r = 152	Z = 6
Trigonal, R3c	F(000) = 432
Hall symbol: -R 3;-2"c	D_x = 5.230 Mg m⁻³
a = 4.95895 (2) Å	Synchrotron radiation
c = 13.59477 (8) Å	T = 290 K

Data collection top

2θ_min = 7.006°, 2θ_max = 82.144°, 2θ_step = 0.006°

Refinement top

R_p = 0.024	33 parameters
R_wp = 0.037	0 restraints
R_exp = 0.007	0 constraints
R(F) = 0.017	Weighting scheme based on measured s.u.'s
13629 data points	(Δ/σ)_max = 0.046
Excluded region(s): from 0 to 7.000	Background function: 20 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: none

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Cr1	0	0	0.34744 (5)	0.00258 (11)*
O1	0.3054 (5)	0	0.25	0.0023 (4)*

(VI) top

Crystal data top

Cr₂O₃	β = 162.4720 (11)°
M_r = 152	V = 193.01 (2) Å³
Monoclinic, C2/c	Z = 4
Hall symbol: -C 2yc	F(000) = 288
a = 9.5047 (4) Å	D_x = 5.230 Mg m⁻³
b = 4.95980 (11) Å	Synchrotron radiation
c = 13.5948 (5) Å	T = 290 K

Data collection top

2θ_min = 7.006°, 2θ_max = 82.144°, 2θ_step = 0.006°

Refinement top

R_p = 0.024	33 parameters
R_wp = 0.037	0 restraints
R_exp = 0.007	0 constraints
R(F) = 0.017	Weighting scheme based on measured s.u.'s
13629 data points	(Δ/σ)_max = 0.046
Excluded region(s): from 0 to 7.000	Background function: 20 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: none

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Cr1	0	0	0.347437	0.00258 (11)*
O1	−0.458163	−0.152721	−0.055442	0.0023 (4)*
O2	0	0.305442	0.25	0.0023 (4)*

(VII) top

Crystal data top

Al₂O₃	V = 254.98 (1) Å³
M_r = 102	Z = 6
Trigonal, R3c	F(000) = 300
Hall symbol: -R 3;-2"c	D_x = 3.984 Mg m⁻³
a = 4.76002 (10) Å	Synchrotron radiation
c = 12.9944 (4) Å	T = 290 K

Data collection top

2θ_min = 7.006°, 2θ_max = 82.144°, 2θ_step = 0.006°

Refinement top

R_p = 0.018	33 parameters
R_wp = 0.027	0 restraints
R_exp = 0.007	0 constraints
R(F) = 0.035	Weighting scheme based on measured s.u.'s
13629 data points	(Δ/σ)_max = 0.046
Excluded region(s): from 0 to 7.000	Background function: 20 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: none

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Al1	0	0	0.35223 (17)	0.0038 (5)*
O1	0.3066 (7)	0	0.25	0.0018 (8)*

(VIII) top

Crystal data top

Al₂O₃	β = 162.399 (5)°
M_r = 102	V = 169.99 (6) Å³
Monoclinic, C2/c	Z = 4
Hall symbol: -C 2yc	F(000) = 200
a = 9.0899 (15) Å	D_x = 3.984 Mg m⁻³
b = 4.7593 (4) Å	Synchrotron radiation
c = 12.994 (2) Å	T = 290 K

Data collection top

2θ_min = 7.006°, 2θ_max = 82.144°, 2θ_step = 0.006°

Refinement top

R_p = 0.018	33 parameters
R_wp = 0.027	0 restraints
R_exp = 0.007	0 constraints
R(F) = 0.035	Weighting scheme based on measured s.u.'s
13629 data points	(Δ/σ)_max = 0.044
Excluded region(s): from 0 to 7.000	Background function: 20 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: none

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Al1	0	0	0.352225	0.0038 (5)*
O1	−0.459882	−0.153294	−0.056588	0.0018 (8)*
O2	0	0.306588	0.25	0.0018 (8)*

(IX) top

Crystal data top

Fe₂O₃	V = 302.07 (1) Å³
M_r = 159.7	Z = 6
Trigonal, R3c	F(000) = 456
Hall symbol: -R 3;-2"c	D_x = 5.267 Mg m⁻³
a = 5.03612 (3) Å	Synchrotron radiation
c = 13.75243 (10) Å	T = 290 K

Data collection top

2θ_min = 7.006°, 2θ_max = 82.144°, 2θ_step = 0.006°

Refinement top

R_p = 0.024	33 parameters
R_wp = 0.037	0 restraints
R_exp = 0.007	0 constraints
R(F) = 0.017	Weighting scheme based on measured s.u.'s
13629 data points	(Δ/σ)_max = 0.050
Excluded region(s): from 0 to 7.000	Background function: 20 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: none

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Fe1	0	0	0.35525 (5)	0.00402 (13)*
O1	0.3056 (5)	0	0.25	0.0033 (5)*

(X) top

Crystal data top

Fe₂O₃	β = 162.4049 (14)°
M_r = 159.7	V = 201.38 (2) Å³
Monoclinic, C2/c	Z = 4
Hall symbol: -C 2yc	F(000) = 304
a = 9.6195 (5) Å	D_x = 5.267 Mg m⁻³
b = 5.03568 (14) Å	Synchrotron radiation
c = 13.7525 (7) Å	T = 290 K

Data collection top

2θ_min = 7.006°, 2θ_max = 82.144°, 2θ_step = 0.006°

Refinement top

R_p = 0.023	33 parameters
R_wp = 0.036	0 restraints
R_exp = 0.007	0 constraints
R(F) = 0.017	Weighting scheme based on measured s.u.'s
13629 data points	(Δ/σ)_max = 0.050
Excluded region(s): from 0 to 7.000	Background function: 20 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: none

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Fe1	0	0	0.355246	0.00402 (13)*
O1	−0.458409	−0.152803	−0.055606	0.0033 (5)*
O2	0	0.305606	0.25	0.0033 (5)*

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