The incommensurately and commensurately modulated crystal structures of chromium(II) diphosphate

Chromium(II) diphosphate, Cr₂P₂O₇, has an incommensurately modulated structure at ambient conditions with a = 7.05, b = 8.41, c = 4.63 Å, β = 108.71° and q = (−0.361, 0, 0.471). It undergoes a phase transition towards a commensurate structure with a commensurate q vector, q = (−, 0, ½), at T_c = 285 K. The incommensurate structure has been solved by the charge-flipping method, which yielded both the basic positions of the atoms and the shapes of their modulation functions. The structure model for the commensurate structure was derived directly from the incommensurate structure. The structure analysis shows that the modulation leads to a change of the coordination of the Cr²⁺ ions from distorted octahedra in the average structure towards a sixfold coordination in the form of a more regular octahedron and a fivefold coordination in the form of a square pyramid. The fivefold and sixfold coordination polyhedra alternate along the lattice direction a with the pattern 5-6-5 5-6-5 in the commensurate structure. In the incommensurate structure this pattern is occasionally disturbed by a 5-6-5-5 motif. Both structures can be described in superspace using the same superspace group and a similar modulated structure model. The same superspace model can also be used for the low-temperature phases of other metal diphosphates with the thortveitite stucture type at high temperature. Their low-temperature structures can be obtained from the superspace model by varying the q vector and the origin in the internal dimension t₀.

Computing details

For all compounds, data collection: CrysAlis CCD (Oxford diffraction, 2004); cell refinement: CrysAlis CCD (Oxford diffraction, 2004); data reduction: CrysAlis CCD (Oxford diffraction, 2004); program(s) used to solve structure: (BayMEM; van Smaalen et al., 2003); program(s) used to refine structure: (Jana2000; Petricek et al., 2000); molecular graphics: (Diamond; Brandenburg et al., 2005); software used to prepare material for publication: (Jana2000; Petricek et al., 2000).

Figures

(_alpha2-Cr2P2O7)

Crystal data

Cr2(P2O7)	F(000) = 268
Mr = 277.9	Dx = 3.567 Mg m^−3
Monoclinic, C2/m(α0γ)0s†	Mo Kα radiation, λ = 0.71073 Å
q = -0.36100a* + 0.47100c*	Cell parameters from 3302 reflections
a = 7.0192 Å	θ = 4.6–36.0°
b = 8.4063 Å	µ = 4.80 mm^−1
c = 4.6264 Å	T = 298 K
β = 108.6111°	Column, blue
V = 258.71 Å^3	0.14 × 0.09 × 0.04 mm
Z = 2

† 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	2409 independent reflections
Radiation source: X-ray tube	1433 reflections with I > 3σ(I)
Graphite monochromator	Rint = 0.018
Detector resolution: 8.3438 pixels mm^-1	θmax = 26.4°, θmin = 2.9°
Rotation method data acquisition using ω scans	h = −10→10
Absorption correction: gaussian CrysAlis RED, Oxford Diffraction Ltd., Version 1.171.27p5 beta Analytical numeric absorption correction using a multifaceted crystal model.	k = −10→10
Tmin = 0.435, Tmax = 0.677	l = −7→7
20404 measured reflections

Refinement

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0004F^2)
R[F^2 > 2σ(F^2)] = 0.023	(Δ/σ)max = 0.007
wR(F^2) = 0.058	Δρmax = 0.52 e Å^−3
S = 1.61	Δρmin = −0.49 e Å^−3
2409 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
179 parameters	Extinction coefficient: 0.059 (10)

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
P	0.8028 (13)	−0.0194 (14)	0.5834 (10)	0.0059 (2)
P(a)	0.790 (3)	−0.015 (2)	0.574 (4)	0.007 (3)	0.5
P(b)	0.820 (2)	0.0057 (19)	0.589 (4)	0.003 (2)
O1	0.6374 (2)	0	0.2773 (3)	0.0087 (4)
O2	1	−0.0643 (3)	0.5	0.0176 (6)
O2(a)	1.0004 (13)	−0.0540 (9)	0.531 (2)	0.026 (3)	0.5
O3	0.80616 (16)	−0.14655 (13)	0.7588 (3)	0.0129 (4)
O3(a)	0.8427 (15)	−0.1478 (14)	0.732 (3)	0.029 (4)	0.5
O3(b)	0.7616 (11)	−0.1500 (12)	0.772 (2)	0.001 (2)	0.5
Cr	0.5	−0.18787 (7)	0	0.00773 (16)
Cr(a)	0.4743 (10)	−0.1898 (3)	0.019 (2)	0.0113 (14)	0.5

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
P	0.0056 (4)	0.0059 (4)	0.0047 (4)	−0.0003 (3)	−0.0004 (3)	0.0001 (3)
P(a)	0.000 (5)	0.007 (4)	0.015 (3)	−0.006 (3)	0.003 (3)	−0.014 (2)
P(b)	−0.008 (3)	0.002 (4)	0.008 (2)	−0.004 (3)	−0.0098 (19)	−0.003 (3)
O1	0.0098 (7)	0.0060 (6)	0.0082 (7)	0	−0.0002 (6)	0
O2	0.0086 (9)	0.0231 (11)	0.0231 (10)	0	0.0079 (7)	0
O2(a)	0.010 (3)	0.054 (7)	0.022 (4)	0.000 (5)	0.015 (3)	−0.011 (5)
O3	0.0149 (6)	0.0099 (5)	0.0112 (5)	0.0026 (4)	0.0004 (4)	0.0026 (4)
O3(a)	0.036 (7)	0.012 (5)	0.020 (5)	0.012 (6)	−0.019 (5)	−0.005 (4)
O3(b)	−0.003 (4)	0.004 (3)	0.000 (3)	0.005 (3)	−0.004 (3)	−0.002 (2)
Cr	0.0083 (2)	0.0047 (2)	0.0072 (2)	0	−0.00176 (16)	0
Cr(a)	0.014 (3)	0.0036 (7)	0.012 (2)	−0.0017 (8)	−0.0015 (17)	0.0007 (9)

Geometric parameters (Å, º)

	Average	Minimum	Maximum
P—O1	1.53 (4)	1.52 (3)	1.54 (5)
P—O2	1.60 (6)	1.59 (7)	1.61 (5)
P—O3	1.51 (7)	1.43 (5)	1.55 (8)
P—O3^i	1.49 (8)	1.46 (10)	1.57 (8)
Cr—O1	2.079 (2)	2.046 (2)	2.104 (3)
Cr—O1^ii	2.080 (2)	2.046 (2)	2.104 (3)
Cr—O3^iii	2.708 (4)	2.378 (5)	3.431 (5)
Cr—O3^iv	2.023 (4)	1.981 (4)	2.048 (4)
Cr—O3^v	2.716 (4)	2.378 (5)	3.431 (5)
Cr—O3^vi	2.023 (4)	1.981 (4)	2.048 (4)
O1—P—O2	105 (2)	101.0 (16)	109 (3)
O1—P—O3	112 (4)	110 (5)	117 (3)
O1—P—O3^iv	66 (3)	64 (3)	69 (3)
O1—P—O3^vii	165 (4)	163 (5)	168 (3)
O1—P—O3^viii	62 (3)	59 (3)	64 (3)
O1—P—O3^i	111 (5)	108 (5)	113 (6)
O2—P—O3	103 (4)	101 (5)	109 (3)
O2—P—O3^iv	77 (3)	69 (3)	82 (2)
O2—P—O3^vii	72.7 (17)	66.9 (16)	78.1 (14)
O2—P—O3^viii	101 (3)	90 (2)	105 (3)
O2—P—O3^i	111 (4)	106 (4)	113 (4)
O3—P—O3^iv	63 (3)	60 (3)	67 (3)
O3—P—O3^vii	55.9 (13)	53.8 (11)	57.2 (14)
O3—P—O3^viii	155 (4)	153 (3)	160 (3)
O3—P—O3^i	114 (3)	112.6 (18)	115 (3)
O3^i—P—O3	114 (2)	112.6 (18)	115 (3)
O3^i—P—O3^iv	172 (3)	170 (3)	177 (4)
O3^i—P—O3^vii	83.2 (14)	82.5 (11)	84.4 (14)
O3^i—P—O3^viii	54 (2)	53.1 (16)	56 (2)
O1—Cr—O1^ii	79.93 (9)	78.94 (8)	81.67 (9)
O1—Cr—O2^ix	141.28 (11)	138.77 (12)	147.94 (10)
O1—Cr—O2^iv	96.19 (15)	94.15 (16)	100.21 (15)
O1—Cr—O3^iii	83.86 (11)	76.40 (9)	89.29 (11)
O1—Cr—O3	44.72 (7)	44.08 (7)	45.31 (8)
O1—Cr—O3^iv	95.19 (11)	92.75 (11)	97.00 (11)
O1—Cr—O3^x	123.75 (10)	122.09 (10)	125.25 (10)
O1—Cr—O3^v	85.76 (11)	79.29 (9)	91.00 (11)
O1—Cr—O3^vi	165.17 (15)	160.22 (15)	169.20 (15)
O1^ii—Cr—O1	79.93 (9)	78.94 (8)	81.67 (9)
O1^ii—Cr—O2^ix	96.10 (15)	94.15 (16)	100.18 (15)
O1^ii—Cr—O2^iv	141.23 (11)	138.77 (12)	147.89 (10)
O1^ii—Cr—O3^iii	85.90 (10)	79.29 (9)	91.00 (11)
O1^ii—Cr—O3	123.71 (10)	122.10 (10)	125.25 (10)
O1^ii—Cr—O3^iv	165.23 (15)	160.22 (15)	169.21 (15)
O1^ii—Cr—O3^x	44.72 (7)	44.09 (7)	45.31 (8)
O1^ii—Cr—O3^v	83.72 (11)	76.39 (9)	89.29 (11)
O1^ii—Cr—O3^vi	95.19 (11)	92.74 (11)	97.00 (11)
O3^iii—Cr—O3	94.31 (10)	89.55 (10)	104.58 (10)
O3^iii—Cr—O3^iv	80.28 (15)	78.50 (15)	84.22 (14)
O3^iii—Cr—O3^x	84.07 (10)	74.64 (9)	87.63 (9)
O3^iii—Cr—O3^v	165.32 (14)	163.83 (13)	166.7 (2)
O3^iii—Cr—O3^vi	110.00 (15)	106.52 (16)	112.07 (14)
O3^iv—Cr—O3^iii	80.28 (15)	78.50 (15)	84.22 (14)
O3^iv—Cr—O3	54.98 (12)	53.82 (12)	57.02 (12)
O3^iv—Cr—O3^x	135.75 (14)	131.45 (14)	137.29 (14)
O3^iv—Cr—O3^v	110.06 (15)	106.52 (16)	112.07 (14)
O3^iv—Cr—O3^vi	92.60 (16)	91.43 (16)	94.89 (16)
O3^v—Cr—O3^iii	165.32 (14)	163.83 (13)	166.7 (2)
O3^v—Cr—O3	83.96 (10)	74.64 (9)	87.59 (9)
O3^v—Cr—O3^iv	110.06 (15)	106.52 (16)	112.07 (14)
O3^v—Cr—O3^x	94.18 (10)	89.55 (10)	104.58 (10)
O3^v—Cr—O3^vi	80.34 (15)	78.50 (15)	84.22 (14)
O3^vi—Cr—O3^iii	110.00 (15)	106.52 (16)	112.07 (14)
O3^vi—Cr—O3	135.68 (14)	131.45 (14)	137.29 (14)
O3^vi—Cr—O3^iv	92.60 (16)	91.43 (16)	94.89 (16)
O3^vi—Cr—O3^x	54.95 (12)	53.82 (12)	57.02 (12)
O3^vi—Cr—O3^v	80.34 (15)	78.50 (15)	84.22 (14)
P—O2—P^xi	146 (4)	143 (4)	155 (3)

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

(_alpha1-Cr2P2O7_superspace)

Crystal data

Cr2(P2O7)	F(000) = 268
Mr = 277.9	Dx = 3.545 Mg m^−3
Monoclinic, C2/m(α0γ)0s†	Mo Kα radiation, λ = 0.71073 Å
q = -0.33330a* + 0.50000c*	Cell parameters from 4589 reflections
a = 7.0464 Å	θ = 2.8–26.5°
b = 8.4073 Å	µ = 4.77 mm^−1
c = 4.6394 Å	T = 140 K
β = 108.708°	Irregular column, blue
V = 260.32 Å^3	0.14 × 0.09 × 0.04 mm
Z = 2

† 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	1598 independent reflections
Radiation source: X-ray tube	1466 reflections with I > 3σ(I)
Graphite monochromator	Rint = 0.014
Detector resolution: 8.3438 pixels mm^-1	θmax = 26.6°, θmin = 3.4°
Rotation method data acquisition using ω scans	h = −9→9
Absorption correction: gaussian CrysAlis RED, Oxford Diffraction Ltd., Version 1.171.27p5 beta Analytical numeric absorption correction using a multifaceted crystal model.	k = −10→10
Tmin = 0.435, Tmax = 0.677	l = −6→6
13281 measured reflections

Refinement

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0004F^2)
R[F^2 > 2σ(F^2)] = 0.021	(Δ/σ)max = 0.001
wR(F^2) = 0.044	Δρmax = 0.35 e Å^−3
S = 1.71	Δρmin = −0.34 e Å^−3
1598 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
105 parameters	Extinction coefficient: 0.039 (9)

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

	x	y	z	Uiso*/Ueq
P	0.80598 (6)	−0.01568 (5)	0.58475 (10)	0.00406 (17)
O1	0.63867 (18)	0	0.2766 (3)	0.0057 (4)
O2	1	−0.07145 (17)	0.5	0.0086 (5)
O3	0.80778 (14)	−0.14622 (11)	0.7572 (2)	0.0075 (3)
Cr	0.5	−0.18740 (3)	0	0.00463 (14)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
P	0.0032 (3)	0.0044 (2)	0.0041 (3)	−0.00011 (13)	0.0005 (2)	0.00005 (13)
O1	0.0058 (6)	0.0044 (6)	0.0058 (7)	0	0.0004 (5)	0
O2	0.0046 (7)	0.0120 (7)	0.0102 (7)	0	0.0036 (5)	0
O3	0.0071 (5)	0.0070 (4)	0.0071 (5)	0.0006 (3)	0.0004 (4)	0.0010 (4)
Cr	0.0048 (2)	0.0031 (2)	0.0044 (2)	0	−0.00074 (15)	0

Geometric parameters (Å, º)

	Average	Minimum	Maximum
P—O1	1.5379 (17)	1.5335 (17)	1.5409 (17)
P—O2	1.601 (2)	1.597 (2)	1.608 (2)
P—O3	1.518 (4)	1.513 (3)	1.521 (4)
P—O3^i	1.498 (4)	1.490 (4)	1.509 (3)
Cr—O1	2.0809 (18)	2.0586 (18)	2.1088 (17)
Cr—O1^ii	2.0809 (18)	2.0586 (18)	2.1088 (17)
Cr—O3^iii	2.769 (5)	2.366 (3)	3.487 (6)
Cr—O3^iv	2.023 (4)	1.977 (4)	2.049 (3)
Cr—O3^v	2.769 (5)	2.366 (3)	3.486 (6)
Cr—O3^vi	2.023 (4)	1.977 (4)	2.049 (3)
O1—P—O2	105.42 (10)	103.35 (10)	107.08 (10)
O1—P—O3	111.36 (15)	110.95 (14)	111.92 (18)
O1—P—O3^iv	65.99 (10)	64.47 (10)	67.19 (11)
O1—P—O3^vii	165.09 (11)	164.79 (10)	165.67 (11)
O1—P—O3^viii	62.27 (9)	60.17 (9)	63.94 (9)
O1—P—O3^i	111.05 (15)	110.38 (13)	111.78 (18)
O2—P—O3	103.5 (2)	102.2 (2)	105.37 (16)
O2—P—O3^iv	76.35 (15)	70.48 (14)	79.66 (19)
O2—P—O3^vii	73.57 (9)	68.27 (11)	78.09 (8)
O2—P—O3^viii	102.42 (15)	97.08 (13)	105.35 (13)
O2—P—O3^i	111.0 (2)	110.5 (2)	111.47 (16)
O3—P—O3^iv	62.95 (17)	60.24 (11)	67.4 (2)
O3—P—O3^vii	55.87 (15)	54.52 (10)	57.91 (19)
O3—P—O3^viii	154.01 (18)	152.09 (18)	157.50 (14)
O3—P—O3^i	113.9 (2)	113.4 (2)	114.4 (2)
O3^i—P—O3	113.9 (2)	113.4 (2)	114.4 (2)
O3^i—P—O3^iv	172.36 (19)	169.3 (2)	177.41 (14)
O3^i—P—O3^vii	82.45 (15)	81.21 (16)	83.73 (13)
O3^i—P—O3^viii	54.15 (15)	52.71 (15)	55.00 (12)
O1—Cr—O1^ii	80.26 (6)	79.13 (6)	81.90 (7)
O1—Cr—O2^ix	139.44 (8)	136.57 (9)	144.11 (7)
O1—Cr—O2^iv	95.41 (9)	92.58 (9)	97.78 (10)
O1—Cr—O3^iii	83.15 (9)	75.35 (8)	90.43 (8)
O1—Cr—O3	44.78 (7)	44.18 (6)	45.46 (6)
O1—Cr—O3^iv	94.95 (10)	92.88 (13)	96.55 (10)
O1—Cr—O3^x	123.69 (7)	121.59 (9)	125.63 (7)
O1—Cr—O3^v	85.76 (9)	78.71 (9)	92.54 (9)
O1—Cr—O3^vi	166.28 (14)	161.13 (14)	170.14 (16)
O1^ii—Cr—O1	80.26 (6)	79.13 (6)	81.90 (7)
O1^ii—Cr—O2^ix	95.41 (9)	92.57 (9)	97.79 (10)
O1^ii—Cr—O2^iv	139.45 (8)	136.56 (9)	144.12 (7)
O1^ii—Cr—O3^iii	85.76 (9)	78.70 (9)	92.54 (9)
O1^ii—Cr—O3	123.69 (7)	121.58 (9)	125.63 (7)
O1^ii—Cr—O3^iv	166.28 (14)	161.13 (14)	170.15 (16)
O1^ii—Cr—O3^x	44.78 (7)	44.17 (6)	45.46 (6)
O1^ii—Cr—O3^v	83.15 (9)	75.35 (8)	90.43 (8)
O1^ii—Cr—O3^vi	94.95 (10)	92.88 (13)	96.55 (10)
O3^iii—Cr—O3	94.79 (10)	90.18 (11)	105.42 (11)
O3^iii—Cr—O3^iv	81.00 (15)	78.87 (17)	84.60 (18)
O3^iii—Cr—O3^x	83.77 (10)	73.55 (11)	87.76 (11)
O3^iii—Cr—O3^v	165.37 (10)	164.11 (8)	166.56 (14)
O3^iii—Cr—O3^vi	109.39 (15)	106.60 (18)	112.14 (17)
O3^iv—Cr—O3^iii	81.00 (15)	78.87 (18)	84.60 (17)
O3^iv—Cr—O3	54.90 (12)	53.29 (13)	57.36 (17)
O3^iv—Cr—O3^x	135.65 (13)	131.02 (16)	137.13 (13)
O3^iv—Cr—O3^v	109.39 (15)	106.60 (17)	112.14 (19)
O3^iv—Cr—O3^vi	92.28 (13)	90.91 (9)	94.19 (17)
O3^v—Cr—O3^iii	165.37 (10)	164.11 (8)	166.56 (14)
O3^v—Cr—O3	83.77 (10)	73.54 (11)	87.77 (11)
O3^v—Cr—O3^iv	109.39 (15)	106.60 (18)	112.14 (17)
O3^v—Cr—O3^x	94.79 (10)	90.18 (11)	105.42 (11)
O3^v—Cr—O3^vi	80.99 (15)	78.86 (17)	84.60 (18)
O3^vi—Cr—O3^iii	109.39 (15)	106.60 (17)	112.14 (19)
O3^vi—Cr—O3	135.65 (13)	131.02 (16)	137.12 (13)
O3^vi—Cr—O3^iv	92.28 (13)	90.91 (10)	94.19 (18)
O3^vi—Cr—O3^x	54.90 (12)	53.30 (13)	57.35 (17)
O3^vi—Cr—O3^v	80.99 (15)	78.86 (18)	84.60 (17)
P—O2—P^xi	143.3 (3)	140.1 (4)	144.9 (2)

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

(alpha1-Cr2P2O7_supercell)

Crystal data

Cr2(P2O7)	F(000) = 1608
Mr = 277.9	Dx = 3.545 Mg m^−3
Monoclinic, I2/c	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -I2yc	Cell parameters from 4589 reflections
a = 21.1392 Å	θ = 2.8–26.5°
b = 8.4073 Å	µ = 4.77 mm^−1
c = 9.2788 Å	T = 140 K
β = 108.708°	Irregular column, blue
V = 1561.93 Å^3	0.14 × 0.09 × 0.04 mm
Z = 12

Data collection

Oxford Diffraction CCD diffractometer	1598 independent reflections
Radiation source: X-ray tube	1466 reflections with I > 3σ(I)
Graphite monochromator	Rint = 0.014
Detector resolution: 8.3438 pixels mm^-1	θmax = 26.6°, θmin = 3.4°
Rotation method data acquisition using ω scans	h = −26→26
Absorption correction: gaussian CrysAlis RED, Oxford Diffraction Ltd., Version 1.171.27p5 beta Analytical numeric absorption correction using a multifaceted crystal model.	k = −10→10
Tmin = 0.435, Tmax = 0.677	l = −11→11
13281 measured reflections

Refinement

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0004F^2)
R[F^2 > 2σ(F^2)] = 2.05
wR(F^2) = 4.35	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
S = 1.74	Extinction coefficient: 0.03852

Special details

Refinement. This sturcutre was obtained by transformation of the superspace struture model into the supercell description. It has not been refined, only zero refinement cycles have been run to obtain the R-factors. For this reason also the standard deviations of the atomic positions and distances are missing. For the refinement details interested reader should refer to the CIF of the modulated structure model, that has been deposited together with this CIF.

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

	x	y	z	Uiso*/Ueq
P-1	0.26637	−0.016404	0.298253	0.0041
P-2	0.605125	−0.012662	0.283663	0.0041
P-3	0.9363	−0.017968	0.790748	0.0041
O1-1	0.215454	−0.004228	0.138077	0.0057
O1-2	0.544184	−0.001568	0.138518	0.0057
O1-3	0.879031	0.008382	0.138295	0.0057
O2-1	0.335982	−0.066992	0.278751	0.0086
O2-2	1	−0.083281	0.75	0.0086
O3-1	0.251667	−0.155888	0.386693	0.0065
O3-2	0.597313	−0.147007	0.385089	0.0068
O3-3	0.950247	−0.141609	0.365348	0.0093
O3-4	0.271849	−0.140358	0.880569	0.0068
O3-5	0.621092	−0.143655	0.862703	0.0098
O3-6	0.923398	−0.148771	0.891108	0.0059
Cr-1	0.17817	−0.188629	−0.010977	0.005
Cr-2	0.490328	−0.188103	0.011986	0.0046
Cr-3	0.835755	−0.185473	−0.003236	0.0042

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
P-1	0.003168	0.004376	0.004109	−0.000111	0.000455	0.000052
P-2	0.003168	0.004376	0.004109	−0.000111	0.000455	0.000052
P-3	0.003168	0.004376	0.004109	−0.000111	0.000455	0.000052
O1-1	0.005788	0.00439	0.005764	0	0.000374	0
O1-2	0.005788	0.00439	0.005764	0	0.000374	0
O1-3	0.005788	0.00439	0.005764	0	0.000374	0
O2-1	0.00459	0.011956	0.010189	0	0.003619	0
O2-2	0.00459	0.011956	0.010189	0	0.003619	0
O3-1	0.006032	0.006037	0.007129	0.000102	0.001703	0.000363
O3-2	0.00522	0.008336	0.006186	0.001441	0.001088	0.001437
O3-3	0.010033	0.006571	0.007982	0.000222	−0.001703	0.001243
O3-4	0.006133	0.006997	0.006413	0.0011	0.000722	0.001613
O3-5	0.010744	0.006496	0.008714	0.000077	−0.001872	0.000303
O3-6	0.004427	0.007455	0.006171	0.00058	0.002246	0.00113
Cr-1	0.005768	0.003058	0.004253	0.000145	−0.001105	−0.000056
Cr-2	0.004813	0.003072	0.004359	−0.00029	−0.00074	0.000112
Cr-3	0.003879	0.00309	0.004469	0.000145	−0.000383	−0.000056

Geometric parameters (Å, º)

P-1—O1-1	1.5335	Cr-1—O3-1^v	2.035
P-1—O2-1	1.5968	Cr-1—O3-4^vi	2.5253
P-1—O3-1	1.5195	Cr-1—O3-5^vii	1.9775
P-1—O3-4^i	1.509	Cr-2—O1-2	2.068
P-2—O1-2	1.5392	Cr-2—O1-2^iv	2.0909
P-2—O2-1^ii	1.5989	Cr-2—O3-2^ii	2.3662
P-2—O3-2	1.5127	Cr-2—O3-3^viii	2.0015
P-2—O3-5^i	1.49	Cr-2—O3-6^vii	2.0304
P-3—O1-3^iii	1.541	Cr-3—O1-1^iv	2.1005
P-3—O2-2	1.6076	Cr-3—O1-3	2.1088
P-3—O3-3^iii	1.495	Cr-3—O3-1^ii	2.4348
P-3—O3-6	1.5211	Cr-3—O3-2^viii	2.0475
Cr-1—O1-1	2.0587	Cr-3—O3-4^ix	2.0487
Cr-1—O1-3^iv	2.0586	Cr-3—O3-6^vi	2.3778
O1-1—P-1—O2-1	107.085	O1-2—Cr-2—O1-2^iv	79.131
O1-1—P-1—O3-1	111.924	O1-2—Cr-2—O3-2^ii	91.138
O1-1—P-1—O3-4^i	110.385	O1-2—Cr-2—O3-3^viii	95.093
O2-1—P-1—O3-1	102.193	O1-2—Cr-2—O3-6^vii	170.072
O2-1—P-1—O3-4^i	111.474	O1-2^iv—Cr-2—O1-2	79.131
O3-1—P-1—O3-4^i	113.359	O1-2^iv—Cr-2—O3-2^ii	90.434
O1-2—P-2—O2-1^ii	103.343	O1-2^iv—Cr-2—O3-3^viii	161.128
O1-2—P-2—O3-2	111.214	O1-2^iv—Cr-2—O3-6^vii	96.555
O1-2—P-2—O3-5^i	111.785	O3-2^ii—Cr-2—O3-3^viii	107.745
O2-1^ii—P-2—O3-2	105.372	O3-2^ii—Cr-2—O3-6^vii	79.893
O2-1^ii—P-2—O3-5^i	110.517	O3-3^viii—Cr-2—O3-6^vii	91.721
O3-2—P-2—O3-5^i	113.893	O1-1^iv—Cr-3—O1-3	79.739
O1-3^iii—P-3—O2-2	105.823	O1-1^iv—Cr-3—O3-1^ii	82.381
O1-3^iii—P-3—O3-3^iii	110.995	O1-1^iv—Cr-3—O3-2^viii	167.637
O1-3^iii—P-3—O3-6	110.944	O1-1^iv—Cr-3—O3-4^ix	95.875
O2-2—P-3—O3-3^iii	111.085	O1-1^iv—Cr-3—O3-6^vi	88.666
O2-2—P-3—O3-6	103.017	O1-3—Cr-3—O3-1^ii	83.335
O3-3^iii—P-3—O3-6	114.38	O1-3—Cr-3—O3-2^viii	96.369
O1-1—Cr-1—O1-3^iv	81.895	O1-3—Cr-3—O3-4^ix	163.993
O1-1—Cr-1—O3-1^v	92.902	O1-3—Cr-3—O3-6^vi	85.223
O1-1—Cr-1—O3-4^vi	88.081	O3-1^ii—Cr-3—O3-2^viii	108.969
O1-1—Cr-1—O3-5^vii	164.681	O3-1^ii—Cr-3—O3-4^ix	80.819
O1-3^iv—Cr-1—O3-1^v	170.146	O3-1^ii—Cr-3—O3-6^vi	166.557
O1-3^iv—Cr-1—O3-4^vi	92.543	O3-2^viii—Cr-3—O3-4^ix	90.912
O1-3^iv—Cr-1—O3-5^vii	92.885	O3-2^viii—Cr-3—O3-6^vi	79.281
O3-1^v—Cr-1—O3-4^vi	78.866	O3-4^ix—Cr-3—O3-6^vi	110.196
O3-1^v—Cr-1—O3-5^vii	94.192	P-1—O2-1—P-2^ii	144.871
O3-4^vi—Cr-1—O3-5^vii	106.604	P-3—O2-2—P-3^x	140.055

Symmetry codes: (i) x, −y, z−1/2; (ii) −x+1, y, −z+1/2; (iii) x, −y, z+1/2; (iv) −x+1, −y, −z; (v) −x+1/2, −y−1/2, −z+1/2; (vi) x, y, z−1; (vii) x−1/2, −y−1/2, z−1; (viii) −x+3/2, −y−1/2, −z+1/2; (ix) x+1/2, −y−1/2, z−1; (x) −x+2, y, −z+3/2.