Incommensurate structure of InAl_1 - xTi_xO_3 + x/2 [x = 0.701 (1)]: comparison between modulated and composite models

The structure of the monoclinic phase of the compound InAl_1 - xTi_xO_3 + x/2 with x = 0.701 (1) has been analyzed within the (3 + 1)-dimensional superspace formalism. Two different models were refined describing the structure as an incommensurate modulated layer and modulated composite, respectively. Both models include the same composition-structure relation. In the composite approach it is derived from the mismatching between the two subsystems. In the incommensurate modulated system, it is derived from a closeness condition between O atomic domains. The distribution and coordination of the cations is discussed and compared with previously proposed models for similar compounds.

Computing details

For both compounds, data collection: CrysAlis CCD software (Oxford Diffraction, 2005); cell refinement: CrysAlis RED software (Oxford Diffraction, 2005); data reduction: CrysAlis RED software (Oxford Diffraction, 2005); program(s) used to refine structure: (Jana2000; Petricek and Dusek, 2000); software used to prepare material for publication: (Jana2000; Petricek and Dusek, 2000).

(I)

Crystal data

Al0.256In1.044O3.35Ti0.700	Z = 2
Mr = 213.89	F(000) = 193
Monoclinic, C2/m(0β0)s0†	Dx = 5.968 Mg m^−3
q = 0.35030b*	Mo Kα radiation, λ = 0.71073 Å
a = 5.857 (4) Å	µ = 12.35 mm^−1
b = 3.361 (3) Å	T = 293 K
c = 6.355 (5) Å	Plate, colourless
β = 107.96 (5)°	0.15 × 0.06 × 0.02 mm
V = 119.00 (17) Å^3

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₁, x₂, −x₃, 1/2+x₄; (3) −x₁, −x₂, −x₃, −x₄; (4) x₁, −x₂, x₃, 1/2−x₄; (5) 1/2+x₁, 1/2+x₂, x₃, x₄; (6) 1/2−x₁, 1/2+x₂, −x₃, 1/2+x₄; (7) 1/2−x₁, 1/2−x₂, −x₃, −x₄; (8) 1/2+x₁, 1/2−x₂, x₃, 1/2−x₄.

Data collection

Oxford Diffraction CCD diffractometer	994 reflections with I > 3σ(I)
Radiation source: fine-focus sealed X-ray tube	Rint = 0.045
Graphite monochromator	θmax = 36.7°, θmin = 3.7°
Absorption correction: numerical gaussian	h = −9→8
Tmin = 0.31, Tmax = 0.83	k = −5→5
8896 measured reflections	l = −10→9
1733 independent reflections

Refinement

Refinement on F	1 constraint
R[F^2 > 2σ(F^2)] = 0.032	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0004F^2)
wR(F^2) = 0.059	(Δ/σ)max = 0.001
S = 1.49	Δρmax = 2.47 e Å^−3
1733 reflections	Δρmin = −2.37 e Å^−3
57 parameters	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
6 restraints	Extinction coefficient: 0.00103 (6)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
In1	0	0	0	0.00571 (11)
Al	0.5	0	0.5	0.0100 (3)	0.256 (8)
Ti	0.5	0	0.5	0.0100 (3)	0.700 (6)
In2	0.5	0	0.5	0.0100 (3)	0.044 (10)
O1	0.3888 (4)	0	0.1709 (4)	0.0053 (6)
O2	0.1597 (4)	0	0.4983 (4)	0.0181 (7)	0.6751

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
In1	0.00514 (15)	0.00373 (16)	0.0086 (2)	0	0.00267 (11)	0
Al	0.0110 (4)	0.0137 (4)	0.0045 (4)	0	0.0012 (3)	0
Ti	0.0110 (4)	0.0137 (4)	0.0045 (4)	0	0.0012 (3)	0
In2	0.0110 (4)	0.0137 (4)	0.0045 (4)	0	0.0012 (3)	0
O1	0.0061 (8)	0.0055 (10)	0.0039 (9)	0	0.0011 (7)	0
O2	0.0232 (13)	0.0181 (10)	0.0092 (11)	0	−0.0007 (9)	0

Bond lengths (Å)

	Average	Minimum	Maximum
In1—O1	2.200 (3)	2.162 (3)	2.239 (3)
In1—O1^i	2.208 (2)	2.145 (2)	2.273 (3)
In1—O1^ii	2.207 (2)	2.145 (2)	2.273 (3)
In1—O1^iii	2.200 (3)	2.162 (3)	2.239 (3)
In1—O1^iv	2.207 (2)	2.145 (2)	2.273 (3)
In1—O1^v	2.208 (2)	2.145 (2)	2.273 (3)
Al—O1	1.993 (3)	1.959 (3)	2.028 (3)
Al—O1^vi	1.993 (3)	1.959 (3)	2.028 (3)
Al—O2	1.894 (12)	1.811 (8)	1.936 (11)
Al—O2^vii	1.975 (7)	1.819 (7)	2.416 (6)
Al—O2^viii	1.975 (7)	1.819 (7)	2.416 (6)
Al—O2^vi	1.894 (12)	1.811 (8)	1.936 (11)
Al—O2^ix	1.975 (7)	1.819 (7)	2.416 (6)
Al—O2^x	1.975 (7)	1.819 (7)	2.416 (6)
Ti—O1	1.993 (3)	1.959 (3)	2.028 (3)
Ti—O1^vi	1.993 (3)	1.959 (3)	2.028 (3)
Ti—O2	1.894 (12)	1.811 (8)	1.936 (11)
Ti—O2^vii	1.975 (7)	1.819 (7)	2.416 (6)
Ti—O2^viii	1.975 (7)	1.819 (7)	2.416 (6)
Ti—O2^vi	1.894 (12)	1.811 (8)	1.936 (11)
Ti—O2^ix	1.975 (7)	1.819 (7)	2.416 (6)
Ti—O2^x	1.975 (7)	1.819 (7)	2.416 (6)
In2—O1	1.993 (3)	1.959 (3)	2.028 (3)
In2—O1^vi	1.993 (3)	1.959 (3)	2.028 (3)
In2—O2	1.894 (12)	1.811 (8)	1.936 (11)
In2—O2^vii	1.975 (7)	1.819 (7)	2.416 (6)
In2—O2^viii	1.975 (7)	1.819 (7)	2.416 (6)
In2—O2^vi	1.894 (12)	1.811 (8)	1.936 (11)
In2—O2^ix	1.975 (7)	1.819 (7)	2.416 (6)
In2—O2^x	1.975 (7)	1.819 (7)	2.416 (6)
O1—O1^xi	2.857 (5)	2.857 (5)	2.857 (4)
O1—O1^iv	2.833 (3)	2.772 (3)	2.897 (3)
O1—O1^v	2.832 (3)	2.772 (3)	2.897 (3)
O1—O2	2.775 (13)	2.690 (11)	2.89 (2)
O1—O2^vii	2.794 (8)	2.649 (6)	3.204 (6)
O1—O2^viii	2.795 (8)	2.649 (6)	3.204 (6)
O1—O2^vi	2.796 (9)	2.644 (7)	2.875 (17)
O1—O2^ix	2.803 (10)	2.654 (9)	3.146 (7)
O1—O2^x	2.803 (10)	2.654 (9)	3.146 (7)
O2—O2^xii	2.933 (6)	2.816 (6)	4.357 (6)
O2—O2^xiii	2.935 (6)	2.816 (6)	4.357 (6)
O2—O2^i	3.257 (16)	2.877 (11)	3.641 (11)
O2—O2^ii	3.250 (16)	2.877 (11)	3.641 (11)
O2—O2^vii	3.251 (16)	2.877 (11)	3.641 (11)
O2—O2^viii	3.258 (16)	2.877 (11)	3.641 (11)
O2—O2^xiv	2.351 (13)	2.342 (11)	2.357 (14)
O2—O2^ix	2.432 (9)	2.373 (10)	2.467 (8)
O2—O2^x	2.433 (9)	2.373 (10)	2.467 (8)

Symmetry codes: (i) x₁−1/2, x₂−1/2, x₃, x₄; (ii) x₁−1/2, x₂+1/2, x₃, x₄; (iii) −x₁, −x₂, −x₃, −x₄; (iv) −x₁+1/2, −x₂−1/2, −x₃, −x₄; (v) −x₁+1/2, −x₂+1/2, −x₃, −x₄; (vi) −x₁+1, −x₂, −x₃+1, −x₄; (vii) x₁+1/2, x₂−1/2, x₃, x₄; (viii) x₁+1/2, x₂+1/2, x₃, x₄; (ix) −x₁+1/2, −x₂−1/2, −x₃+1, −x₄; (x) −x₁+1/2, −x₂+1/2, −x₃+1, −x₄; (xi) −x₁+1, −x₂, −x₃, −x₄; (xii) x₁, x₂−1, x₃, x₄; (xiii) x₁, x₂+1, x₃, x₄; (xiv) −x₁, −x₂, −x₃+1, −x₄.

(II)

Crystal data

Al0.253In1.046O3.35Ti0.701	Z = 2
Mr = 214.08	F(000) = 194
Monoclinic, C2/m(0β0)s0†	Dx = 5.973 Mg m^−3
q = 0.35030b*‡	Mo Kα radiation, λ = 0.71073 Å
a = 5.857 (4) Å	µ = 12.37 mm^−1
b = 3.361 (3) Å	T = 293 K
c = 6.355 (5) Å	Plate, colourless
β = 107.96 (5)°	0.15 × 0.06 × 0.02 mm
V = 119.00 (17) Å^3

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₁, x₂, −x₃, 1/2+x₄; (3) −x₁, −x₂, −x₃, −x₄; (4) x₁, −x₂, x₃, 1/2−x₄; (5) 1/2+x₁, 1/2+x₂, x₃, x₄; (6) 1/2−x₁, 1/2+x₂, −x₃, 1/2+x₄; (7) 1/2−x₁, 1/2−x₂, −x₃, −x₄; (8) 1/2+x₁, 1/2−x₂, x₃, 1/2−x₄.

‡ ;

Data collection

Oxford Diffraction CCD diffractometer	994 reflections with I > 3σ(I)
Radiation source: fine-focus sealed X-ray tube	Rint = 0.045
Graphite monochromator	θmax = 36.7°, θmin = 3.7°
Absorption correction: numerical gaussian	h = −9→8
Tmin = 0.31, Tmax = 0.83	k = −5→5
8896 measured reflections	l = −10→9
1733 independent reflections

Refinement

Refinement on F	1 constraint
R[F^2 > 2σ(F^2)] = 0.032	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0004F^2)
wR(F^2) = 0.060	(Δ/σ)max = 0.0004
S = 1.53	Δρmax = 2.47 e Å^−3
1733 reflections	Δρmin = −2.36 e Å^−3
57 parameters	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
6 restraints	Extinction coefficient: 0.00100 (6)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
In1	0	0	0	0.00571 (11)
Al	0.5	0	0.5	0.0100 (3)	0.255 (8)
Ti	0.5	0	0.5	0.0100 (3)	0.701 (6)
In2	0.5	0	0.5	0.0100 (3)	0.044 (10)
O1	0.3888 (4)	0	0.1709 (4)	0.0052 (6)
O2	0.6597 (4)	0.25	0.4983 (4)	0.0181 (8)	0.5

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
In1	0.00514 (15)	0.00373 (16)	0.0086 (2)	0	0.00267 (11)	0
Al	0.0110 (4)	0.0137 (4)	0.0045 (4)	0	0.0012 (3)	0
Ti	0.0110 (4)	0.0137 (4)	0.0045 (4)	0	0.0012 (3)	0
In2	0.0110 (4)	0.0137 (4)	0.0045 (4)	0	0.0012 (3)	0
O1	0.0061 (8)	0.0055 (10)	0.0039 (9)	0	0.0011 (7)	0
O2	0.0232 (13)	0.0180 (10)	0.0092 (11)	0	−0.0007 (9)	0

Bond lengths (Å)

	Average	Minimum	Maximum
In1—O1	2.200 (3)	2.162 (3)	2.239 (3)
In1—O1^i	2.208 (2)	2.145 (2)	2.273 (3)
In1—O1^ii	2.207 (2)	2.145 (2)	2.273 (3)
In1—O1^iii	2.200 (3)	2.162 (3)	2.239 (3)
In1—O1^iv	2.207 (2)	2.145 (2)	2.273 (3)
In1—O1^v	2.208 (2)	2.145 (2)	2.273 (3)
Al—O1	1.993 (3)	1.959 (3)	2.028 (3)
Al—O1^vi	1.993 (3)	1.959 (3)	2.028 (3)
Al—O2^vii	90.4 (3)	1.940 (7)	4.802 (8)
Al—O2	79.3 (4)	1.829 (9)	1.940 (7)
Al—O2^viii	134.3 (6)	1.829 (9)	2.422 (8)
Al—O2^i	101.4 (3)	1.801 (9)	3.865 (9)
Al—O2^ii	112.3 (8)	1.801 (9)	1.935 (14)
Al—O2^vi	134.3 (6)	1.829 (9)	2.422 (8)
Al—O2^ix	79.3 (4)	1.829 (9)	1.940 (7)
Al—O2^x	90.4 (3)	1.940 (7)	4.802 (8)
Al—O2^xi	112.3 (8)	1.801 (9)	1.935 (14)
Al—O2^xii	101.4 (3)	1.801 (9)	3.865 (9)
Ti—O1	1.993 (3)	1.959 (3)	2.028 (3)
Ti—O1^vi	1.993 (3)	1.959 (3)	2.028 (3)
Ti—O2^vii	90.4 (3)	1.940 (7)	4.802 (8)
Ti—O2	79.3 (4)	1.829 (9)	1.940 (7)
Ti—O2^viii	134.3 (6)	1.829 (9)	2.422 (8)
Ti—O2^i	101.4 (3)	1.801 (9)	3.865 (9)
Ti—O2^ii	112.3 (8)	1.801 (9)	1.935 (14)
Ti—O2^vi	134.3 (6)	1.829 (9)	2.422 (8)
Ti—O2^ix	79.3 (4)	1.829 (9)	1.940 (7)
Ti—O2^x	90.4 (3)	1.940 (7)	4.802 (8)
Ti—O2^xi	112.3 (8)	1.801 (9)	1.935 (14)
Ti—O2^xii	101.4 (3)	1.801 (9)	3.865 (9)
In2—O1	1.993 (3)	1.959 (3)	2.028 (3)
In2—O1^vi	1.993 (3)	1.959 (3)	2.028 (3)
In2—O2^vii	90.4 (3)	1.940 (7)	4.802 (8)
In2—O2	79.3 (4)	1.829 (9)	1.940 (7)
In2—O2^viii	134.3 (6)	1.829 (9)	2.422 (8)
In2—O2^i	101.4 (3)	1.801 (9)	3.865 (9)
In2—O2^ii	112.3 (8)	1.801 (9)	1.935 (14)
In2—O2^vi	134.3 (6)	1.829 (9)	2.422 (8)
In2—O2^ix	79.3 (4)	1.829 (9)	1.940 (7)
In2—O2^x	90.4 (3)	1.940 (7)	4.802 (8)
In2—O2^xi	112.3 (8)	1.801 (9)	1.935 (14)
In2—O2^xii	101.4 (3)	1.801 (9)	3.865 (9)
O1—O1^xiii	2.857 (5)	2.857 (5)	2.857 (4)
O1—O1^iv	2.833 (3)	2.772 (3)	2.897 (3)
O1—O1^v	2.832 (3)	2.772 (3)	2.897 (3)
O1—O2^vii	115.8 (3)	2.776 (10)	5.161 (9)
O1—O2	113.2 (4)	2.649 (10)	2.776 (10)
O1—O2^viii	190.0 (7)	2.649 (10)	3.207 (8)
O1—O2^i	121.2 (4)	2.688 (10)	4.336 (11)
O1—O2^ii	164.5 (9)	2.688 (10)	2.89 (2)
O1—O2^vi	190.6 (8)	2.663 (9)	3.153 (9)
O1—O2^ix	113.1 (5)	2.663 (9)	2.781 (12)
O1—O2^x	116.3 (4)	2.781 (12)	5.165 (9)
O1—O2^xi	165.9 (7)	2.640 (8)	2.876 (16)
O1—O2^xii	121.7 (3)	2.640 (8)	4.357 (9)
O2—O2^vii	2.848 (9)	2.817 (12)	2.893 (7)
O2—O2^viii	2.848 (9)	2.817 (12)	2.893 (7)
O2—O2^i	3.254 (19)	2.871 (15)	3.647 (15)
O2—O2^ii	3.254 (19)	2.871 (15)	3.647 (15)
O2—O2^xiv	3.254 (19)	2.871 (15)	3.647 (15)
O2—O2^xv	3.253 (19)	2.871 (15)	3.647 (15)
O2—O2^vi	2.351 (16)	2.351 (16)	2.352 (15)
O2—O2^ix	2.351 (16)	2.350 (16)	2.352 (15)
O2—O2^xvi	2.432 (11)	2.373 (10)	2.465 (13)
O2—O2^xii	2.432 (11)	2.372 (10)	2.465 (13)

Symmetry codes: (i) x₁−1/2, x₂−1/2, x₃, x₄; (ii) x₁−1/2, x₂+1/2, x₃, x₄; (iii) −x₁, −x₂, −x₃, −x₄; (iv) −x₁+1/2, −x₂−1/2, −x₃, −x₄; (v) −x₁+1/2, −x₂+1/2, −x₃, −x₄; (vi) −x₁+1, −x₂, −x₃+1, −x₄; (vii) x₁, x₂−1, x₃, x₄; (viii) x₁, x₂+1, x₃, x₄; (ix) −x₁+1, −x₂+1, −x₃+1, −x₄; (x) −x₁+1, −x₂+2, −x₃+1, −x₄; (xi) −x₁+3/2, −x₂+1/2, −x₃+1, −x₄; (xii) −x₁+3/2, −x₂+3/2, −x₃+1, −x₄; (xiii) −x₁+1, −x₂, −x₃, −x₄; (xiv) x₁+1/2, x₂−1/2, x₃, x₄; (xv) x₁+1/2, x₂+1/2, x₃, x₄; (xvi) −x₁+3/2, −x₂−1/2, −x₃+1, −x₄.