The crystal structure of Rb₂Ti₂O₅

Recent results have demonstrated an exceptionally high permittivity in the range 200–330 K in crystalline titanium oxide Rb₂Ti₂O₅. In this article, the possibility of a structural transition giving rise to ferroelectricity is carefully inspected. In particular, X-ray diffraction, high-resolution transmission electron microscopy and Raman spectroscopy are performed. The crystal structure is shown to remain invariant and centrosymmetric at all temperatures between 90 K and 450 K. The stability of the C2/m structure is confirmed by density functional theory calculations. These important findings allow the existence of a conventional ferroelectric phase transition to be ruled out as a possible mechanism for the colossal permittivity and polarization observed in this material.

Computing details

Data collection: CrysAlis PRO 1.171.38.41 (Rigaku OD, 2015) for (I), (II); CrysAlis PRO, Agilent Technologies, Version 1.171.37.31 (release 14-01-2014 CrysAlis171 .NET) (compiled Jan 14 2014,18:38:05) for (III). Cell refinement: CrysAlis PRO 1.171.38.41 (Rigaku OD, 2015) for (I), (II); CrysAlis PRO, Agilent Technologies, Version 1.171.37.31 (release 14-01-2014 CrysAlis171 .NET) (compiled Jan 14 2014,18:38:05) for (III). Data reduction: CrysAlis PRO 1.171.38.41 (Rigaku OD, 2015) for (I), (II); CrysAlis PRO, Agilent Technologies, Version 1.171.37.31 (release 14-01-2014 CrysAlis171 .NET) (compiled Jan 14 2014,18:38:05) for (III). For all structures, program(s) used to solve structure: ShelXT (Sheldrick, 2015); program(s) used to refine structure: SHELXL (Sheldrick, 2015); molecular graphics: Olex2 (Dolomanov et al., 2009); software used to prepare material for publication: Olex2 (Dolomanov et al., 2009).

(I)

Crystal data

0.5(O10Rb4Ti4)	F(000) = 316
Mr = 346.74	Dx = 3.876 Mg m^−3
Monoclinic, C2/m	Mo Kα radiation, λ = 0.71073 Å
a = 11.3457 (12) Å	Cell parameters from 1003 reflections
b = 3.8195 (5) Å	θ = 2.9–32.4°
c = 6.9699 (8) Å	µ = 18.90 mm^−1
β = 100.359 (11)°	T = 150 K
V = 297.12 (6) Å^3	Needle, clear light colourless
Z = 2	0.2 × 0.1 × 0.05 mm

Data collection

Saxi-CrysAlisPro-abstract goniometer imported SAXI images diffractometer	348 independent reflections
Radiation source: fine-focus sealed X-ray tube, Enhance (Mo) X-ray Source	320 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.041
ω and φ scans	θmax = 26.4°, θmin = 3.0°
Absorption correction: multi-scan CrysAlisPro 1.171.38.41 (Rigaku Oxford Diffraction, 2015) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.	h = −14→12
Tmin = 0.400, Tmax = 1.000	k = −4→4
1205 measured reflections	l = −8→8

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.050	w = 1/[σ^2(Fo^2) + (0.104P)^2 + 1.3004P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.134	(Δ/σ)max < 0.001
S = 1.11	Δρmax = 1.52 e Å^−3
348 reflections	Δρmin = −1.93 e Å^−3
29 parameters

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

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

	x	y	z	Uiso*/Ueq
Rb1	0.09812 (8)	0.5000	0.84725 (12)	0.0149 (5)
Ti1	0.35229 (14)	0.5000	0.5897 (2)	0.0097 (5)
O1	0.5000	0.5000	0.5000	0.015 (2)
O3	0.1772 (6)	0.5000	0.4776 (9)	0.0149 (14)
O2	0.3767 (6)	0.5000	0.8391 (9)	0.0156 (15)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Rb1	0.0123 (6)	0.0179 (7)	0.0131 (6)	0.000	−0.0016 (4)	0.000
Ti1	0.0055 (9)	0.0109 (10)	0.0105 (9)	0.000	−0.0043 (6)	0.000
O1	0.004 (4)	0.019 (5)	0.022 (5)	0.000	0.000 (4)	0.000
O3	0.006 (3)	0.016 (4)	0.019 (3)	0.000	−0.006 (3)	0.000
O2	0.013 (3)	0.015 (3)	0.016 (3)	0.000	−0.004 (3)	0.000

Geometric parameters (Å, º)

Rb1—Rb1^i	3.3460 (16)	Ti1—O1	1.8910 (15)
Rb1—Ti1^ii	3.5845 (17)	Ti1—O3^viii	1.9805 (17)
Rb1—Ti1^iii	3.5845 (17)	Ti1—O3	2.000 (6)
Rb1—O1^ii	3.1265 (7)	Ti1—O3^ix	1.9805 (17)
Rb1—O1^iii	3.1265 (7)	Ti1—O2	1.710 (7)
Rb1—O3^iv	3.513 (6)	O1—Rb1^vii	3.1266 (7)
Rb1—O3	2.877 (7)	O1—Rb1^ix	3.1266 (7)
Rb1—O2	3.171 (6)	O1—Rb1^viii	3.1266 (7)
Rb1—O2^ii	3.148 (5)	O1—Rb1^x	3.1266 (7)
Rb1—O2^v	2.878 (5)	O1—Ti1^xi	1.8910 (15)
Rb1—O2^vi	2.878 (5)	O3—Rb1^iv	3.513 (6)
Rb1—O2^iii	3.148 (5)	O3—Ti1^ix	1.9805 (17)
Ti1—Rb1^vii	3.5845 (17)	O3—Ti1^viii	1.9805 (17)
Ti1—Rb1^viii	3.7221 (16)	O2—Rb1^v	2.878 (5)
Ti1—Rb1^ix	3.7221 (16)	O2—Rb1^vii	3.148 (5)
Ti1—Rb1^x	3.5845 (17)	O2—Rb1^x	3.148 (5)
Ti1—Ti1^ix	3.091 (2)	O2—Rb1^vi	2.878 (5)
Ti1—Ti1^viii	3.091 (2)
Rb1^i—Rb1—Ti1^iii	76.81 (4)	Ti1^viii—Ti1—Ti1^ix	76.32 (7)
Rb1^i—Rb1—Ti1^ii	76.81 (4)	O1—Ti1—Rb1	170.13 (8)
Rb1^i—Rb1—O3^iv	78.10 (11)	O1—Ti1—Rb1^ix	57.06 (4)
Ti1^ii—Rb1—Ti1^iii	64.39 (4)	O1—Ti1—Rb1^viii	57.06 (4)
O1^ii—Rb1—Rb1^i	107.91 (3)	O1—Ti1—Rb1^x	60.63 (4)
O1^iii—Rb1—Rb1^i	107.91 (3)	O1—Ti1—Rb1^vii	60.63 (4)
O1^iii—Rb1—Ti1^ii	78.53 (3)	O1—Ti1—Ti1^viii	120.80 (7)
O1^ii—Rb1—Ti1^ii	31.81 (2)	O1—Ti1—Ti1^ix	120.80 (7)
O1^ii—Rb1—Ti1^iii	78.53 (3)	O1—Ti1—O3^viii	92.5 (2)
O1^iii—Rb1—Ti1^iii	31.81 (2)	O1—Ti1—O3^ix	92.5 (2)
O1^ii—Rb1—O1^iii	75.30 (2)	O1—Ti1—O3	138.4 (2)
O1^iii—Rb1—O3^iv	49.42 (7)	O3—Ti1—Rb1^x	145.55 (6)
O1^ii—Rb1—O3^iv	49.42 (7)	O3^viii—Ti1—Rb1	90.1 (2)
O1^ii—Rb1—O2^iii	100.64 (10)	O3—Ti1—Rb1^vii	145.55 (6)
O1^iii—Rb1—O2^iii	56.19 (11)	O3^viii—Ti1—Rb1^ix	110.2 (2)
O1^iii—Rb1—O2	101.73 (9)	O3^viii—Ti1—Rb1^x	71.81 (18)
O1^ii—Rb1—O2	101.73 (9)	O3^ix—Ti1—Rb1	90.1 (2)
O1^iii—Rb1—O2^ii	100.64 (10)	O3^ix—Ti1—Rb1^viii	110.2 (2)
O1^ii—Rb1—O2^ii	56.19 (11)	O3—Ti1—Rb1	51.45 (18)
O3—Rb1—Rb1^i	156.98 (13)	O3—Ti1—Rb1^ix	88.05 (16)
O3—Rb1—Ti1^iii	83.76 (10)	O3^viii—Ti1—Rb1^vii	135.68 (18)
O3^iv—Rb1—Ti1^ii	32.39 (2)	O3—Ti1—Rb1^viii	88.05 (16)
O3^iv—Rb1—Ti1^iii	32.39 (2)	O3^ix—Ti1—Rb1^x	135.68 (18)
O3—Rb1—Ti1^ii	83.76 (11)	O3^ix—Ti1—Rb1^vii	71.81 (18)
O3—Rb1—O1^ii	55.36 (8)	O3^ix—Ti1—Rb1^ix	49.88 (19)
O3—Rb1—O1^iii	55.36 (8)	O3^viii—Ti1—Rb1^viii	49.88 (19)
O3—Rb1—O3^iv	78.88 (18)	O3^ix—Ti1—Ti1^ix	39.27 (18)
O3—Rb1—O2^vi	132.53 (11)	O3—Ti1—Ti1^viii	38.83 (5)
O3—Rb1—O2^ii	111.11 (14)	O3—Ti1—Ti1^ix	38.83 (5)
O3—Rb1—O2^v	132.53 (11)	O3^viii—Ti1—Ti1^viii	39.27 (18)
O3—Rb1—O2^iii	111.11 (14)	O3^ix—Ti1—Ti1^viii	114.68 (19)
O3—Rb1—O2	60.76 (17)	O3^viii—Ti1—Ti1^ix	114.68 (19)
O2^iii—Rb1—Rb1^i	52.51 (10)	O3^viii—Ti1—O3^ix	149.3 (4)
O2^ii—Rb1—Rb1^i	52.51 (10)	O3^ix—Ti1—O3	78.10 (19)
O2^vi—Rb1—Rb1^i	60.21 (12)	O3^viii—Ti1—O3	78.10 (19)
O2^v—Rb1—Rb1^i	60.21 (12)	O2—Ti1—Rb1^x	61.44 (17)
O2—Rb1—Rb1^i	142.26 (12)	O2—Ti1—Rb1^vii	61.44 (17)
O2^iii—Rb1—Ti1^iii	28.50 (12)	O2—Ti1—Rb1	59.9 (2)
O2^vi—Rb1—Ti1^ii	134.11 (13)	O2—Ti1—Rb1^ix	144.19 (11)
O2^v—Rb1—Ti1^iii	134.11 (13)	O2—Ti1—Rb1^viii	144.19 (11)
O2^ii—Rb1—Ti1^ii	28.50 (12)	O2—Ti1—Ti1^ix	112.55 (17)
O2^ii—Rb1—Ti1^iii	76.56 (9)	O2—Ti1—Ti1^viii	112.55 (17)
O2^vi—Rb1—Ti1^iii	89.37 (11)	O2—Ti1—O1	110.2 (2)
O2—Rb1—Ti1^iii	132.78 (8)	O2—Ti1—O3	111.4 (3)
O2^iii—Rb1—Ti1^ii	76.56 (9)	O2—Ti1—O3^viii	103.30 (19)
O2—Rb1—Ti1^ii	132.78 (8)	O2—Ti1—O3^ix	103.30 (19)
O2^v—Rb1—Ti1^ii	89.37 (11)	Rb1^viii—O1—Rb1^ix	75.30 (2)
O2^vi—Rb1—O1^iii	98.95 (9)	Rb1^vii—O1—Rb1^ix	104.70 (2)
O2^v—Rb1—O1^ii	98.95 (9)	Rb1^viii—O1—Rb1^vii	180.0
O2^v—Rb1—O1^iii	165.07 (13)	Rb1^viii—O1—Rb1^x	104.70 (2)
O2^vi—Rb1—O1^ii	165.07 (13)	Rb1^vii—O1—Rb1^x	75.30 (2)
O2^ii—Rb1—O3^iv	51.25 (12)	Rb1^x—O1—Rb1^ix	180.0
O2^v—Rb1—O3^iv	116.42 (14)	Ti1—O1—Rb1^x	87.56 (4)
O2^iii—Rb1—O3^iv	51.25 (12)	Ti1^xi—O1—Rb1^ix	87.56 (4)
O2^vi—Rb1—O3^iv	116.42 (14)	Ti1—O1—Rb1^vii	87.56 (4)
O2—Rb1—O3^iv	139.64 (17)	Ti1^xi—O1—Rb1^x	92.44 (4)
O2^vi—Rb1—O2^iii	65.2 (2)	Ti1—O1—Rb1^ix	92.44 (4)
O2^ii—Rb1—O2	142.60 (7)	Ti1—O1—Rb1^viii	92.44 (4)
O2^v—Rb1—O2^iii	112.72 (9)	Ti1^xi—O1—Rb1^viii	87.56 (4)
O2^vi—Rb1—O2^ii	112.72 (9)	Ti1^xi—O1—Rb1^vii	92.44 (4)
O2^v—Rb1—O2^ii	65.2 (2)	Ti1—O1—Ti1^xi	180.0
O2^iii—Rb1—O2	142.60 (7)	Rb1—O3—Rb1^iv	101.12 (18)
O2^v—Rb1—O2	92.89 (15)	Ti1^ix—O3—Rb1	98.4 (2)
O2^vi—Rb1—O2^v	83.14 (17)	Ti1—O3—Rb1	95.6 (2)
O2^ii—Rb1—O2^iii	74.69 (14)	Ti1^ix—O3—Rb1^iv	75.80 (18)
O2^vi—Rb1—O2	92.89 (15)	Ti1^viii—O3—Rb1^iv	75.80 (18)
Rb1^x—Ti1—Rb1^ix	117.69 (4)	Ti1—O3—Rb1^iv	163.3 (3)
Rb1^x—Ti1—Rb1	111.41 (4)	Ti1^viii—O3—Rb1	98.4 (2)
Rb1^vii—Ti1—Rb1	111.41 (4)	Ti1^viii—O3—Ti1	101.90 (19)
Rb1—Ti1—Rb1^viii	130.51 (4)	Ti1^ix—O3—Ti1	101.90 (19)
Rb1—Ti1—Rb1^ix	130.51 (4)	Ti1^viii—O3—Ti1^ix	149.3 (4)
Rb1^vii—Ti1—Rb1^viii	117.69 (4)	Rb1^vi—O2—Rb1^v	83.14 (17)
Rb1^x—Ti1—Rb1^viii	85.29 (3)	Rb1^v—O2—Rb1	87.11 (15)
Rb1^viii—Ti1—Rb1^ix	61.74 (3)	Rb1^v—O2—Rb1^x	67.28 (9)
Rb1^vii—Ti1—Rb1^ix	85.29 (3)	Rb1^vi—O2—Rb1^vii	67.28 (9)
Rb1^vii—Ti1—Rb1^x	64.39 (4)	Rb1^vii—O2—Rb1^x	74.69 (14)
Ti1^ix—Ti1—Rb1^vii	109.48 (2)	Rb1^vii—O2—Rb1	142.60 (7)
Ti1^viii—Ti1—Rb1^ix	101.49 (7)	Rb1^vi—O2—Rb1	87.11 (15)
Ti1^ix—Ti1—Rb1	66.29 (5)	Rb1^vi—O2—Rb1^x	114.8 (2)
Ti1^ix—Ti1—Rb1^x	172.67 (7)	Rb1^x—O2—Rb1	142.60 (7)
Ti1^viii—Ti1—Rb1^vii	172.67 (7)	Rb1^v—O2—Rb1^vii	114.8 (2)
Ti1^ix—Ti1—Rb1^ix	64.22 (5)	Ti1—O2—Rb1	92.2 (2)
Ti1^viii—Ti1—Rb1^x	109.48 (2)	Ti1—O2—Rb1^x	90.1 (2)
Ti1^viii—Ti1—Rb1	66.29 (5)	Ti1—O2—Rb1^vii	90.1 (2)
Ti1^viii—Ti1—Rb1^viii	64.22 (5)	Ti1—O2—Rb1^v	138.40 (9)
Ti1^ix—Ti1—Rb1^viii	101.49 (7)	Ti1—O2—Rb1^vi	138.40 (9)

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

(II)

Crystal data

0.5(O10Rb4Ti4)	F(000) = 316
Mr = 346.74	Dx = 3.860 Mg m^−3
Monoclinic, C2/m	Mo Kα radiation, λ = 0.71073 Å
a = 11.3370 (13) Å	Cell parameters from 1212 reflections
b = 3.8244 (5) Å	θ = 3.0–33.1°
c = 6.9946 (8) Å	µ = 18.82 mm^−1
β = 100.308 (12)°	T = 293 K
V = 298.37 (6) Å^3	Needle, clear light colourless
Z = 2	0.3 × 0.1 × 0.05 mm

Data collection

Saxi-CrysAlisPro-abstract goniometer imported SAXI images diffractometer	351 independent reflections
Radiation source: fine-focus sealed X-ray tube, Enhance (Mo) X-ray Source	333 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.021
ω and φ scans	θmax = 26.4°, θmin = 3.0°
Absorption correction: multi-scan CrysAlisPro 1.171.38.41 (Rigaku Oxford Diffraction, 2015) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.	h = −13→14
Tmin = 0.323, Tmax = 1.000	k = −4→3
1389 measured reflections	l = −8→8

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.028	w = 1/[σ^2(Fo^2) + (0.0437P)^2 + 1.2419P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.073	(Δ/σ)max < 0.001
S = 1.17	Δρmax = 0.68 e Å^−3
351 reflections	Δρmin = −1.45 e Å^−3
29 parameters

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

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

	x	y	z	Uiso*/Ueq
Rb1	0.09851 (5)	0.5000	0.84812 (8)	0.0210 (3)
Ti1	0.35249 (8)	0.5000	0.58849 (14)	0.0108 (3)
O3	0.1780 (3)	0.5000	0.4797 (5)	0.0143 (8)
O1	0.5000	0.5000	0.5000	0.0197 (13)
O2	0.3762 (4)	0.5000	0.8367 (6)	0.0207 (9)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Rb1	0.0189 (4)	0.0210 (4)	0.0241 (4)	0.000	0.0062 (2)	0.000
Ti1	0.0044 (5)	0.0102 (6)	0.0173 (5)	0.000	0.0007 (4)	0.000
O3	0.0057 (16)	0.012 (2)	0.0240 (19)	0.000	−0.0017 (14)	0.000
O1	0.009 (3)	0.013 (3)	0.040 (3)	0.000	0.009 (2)	0.000
O2	0.019 (2)	0.022 (3)	0.0186 (19)	0.000	−0.0011 (16)	0.000

Geometric parameters (Å, º)

Rb1—Rb1^i	3.3468 (11)	Ti1—O3^ix	1.9861 (10)
Rb1—Ti1^ii	3.5945 (10)	Ti1—O3	1.988 (4)
Rb1—Ti1^iii	3.5945 (10)	Ti1—O3^x	1.9861 (10)
Rb1—O3	2.878 (4)	Ti1—O1	1.8842 (9)
Rb1—O3^iv	3.537 (4)	Ti1—O2	1.709 (4)
Rb1—O1^ii	3.1400 (5)	O3—Rb1^iv	3.537 (4)
Rb1—O1^iii	3.1400 (5)	O3—Ti1^x	1.9861 (10)
Rb1—O2^ii	3.153 (3)	O3—Ti1^ix	1.9861 (10)
Rb1—O2^v	2.894 (3)	O1—Rb1^ix	3.1400 (5)
Rb1—O2^iii	3.153 (3)	O1—Rb1^viii	3.1400 (5)
Rb1—O2	3.164 (4)	O1—Rb1^x	3.1400 (5)
Rb1—O2^vi	2.894 (3)	O1—Rb1^vii	3.1400 (5)
Ti1—Rb1^vii	3.5945 (10)	O1—Ti1^xi	1.8841 (9)
Ti1—Rb1^viii	3.5945 (10)	O2—Rb1^vi	2.894 (3)
Ti1—Rb1^ix	3.7281 (10)	O2—Rb1^vii	3.153 (3)
Ti1—Rb1^x	3.7281 (10)	O2—Rb1^viii	3.153 (3)
Ti1—Ti1^x	3.0920 (14)	O2—Rb1^v	2.894 (3)
Ti1—Ti1^ix	3.0920 (14)
Rb1^i—Rb1—Ti1^iii	77.00 (2)	Ti1^ix—Ti1—Ti1^x	76.40 (4)
Rb1^i—Rb1—Ti1^ii	77.00 (2)	O3^x—Ti1—Rb1	90.04 (11)
Rb1^i—Rb1—O3^iv	78.28 (7)	O3—Ti1—Rb1^vii	145.31 (4)
Ti1^ii—Rb1—Ti1^iii	64.28 (2)	O3—Ti1—Rb1^x	88.30 (10)
O3—Rb1—Rb1^i	156.90 (7)	O3—Ti1—Rb1	51.26 (11)
O3^iv—Rb1—Ti1^ii	32.327 (13)	O3^x—Ti1—Rb1^viii	136.01 (10)
O3—Rb1—Ti1^iii	83.49 (6)	O3^ix—Ti1—Rb1^viii	72.25 (10)
O3—Rb1—Ti1^ii	83.49 (6)	O3^ix—Ti1—Rb1	90.04 (11)
O3^iv—Rb1—Ti1^iii	32.327 (13)	O3—Ti1—Rb1^ix	88.30 (10)
O3—Rb1—O3^iv	78.62 (10)	O3^ix—Ti1—Rb1^ix	49.79 (11)
O3—Rb1—O1^iii	55.29 (5)	O3^x—Ti1—Rb1^ix	110.00 (12)
O3—Rb1—O1^ii	55.29 (5)	O3^ix—Ti1—Rb1^vii	136.01 (10)
O3—Rb1—O2	60.33 (10)	O3^ix—Ti1—Rb1^x	110.00 (12)
O3—Rb1—O2^ii	110.74 (9)	O3^x—Ti1—Rb1^vii	72.25 (10)
O3—Rb1—O2^v	132.69 (7)	O3^x—Ti1—Rb1^x	49.79 (11)
O3—Rb1—O2^iii	110.74 (9)	O3—Ti1—Rb1^viii	145.31 (4)
O3—Rb1—O2^vi	132.69 (7)	O3^x—Ti1—Ti1^ix	114.41 (11)
O1^ii—Rb1—Rb1^i	107.89 (2)	O3^ix—Ti1—Ti1^ix	38.96 (10)
O1^iii—Rb1—Rb1^i	107.89 (2)	O3—Ti1—Ti1^x	38.90 (3)
O1^ii—Rb1—Ti1^ii	31.583 (15)	O3—Ti1—Ti1^ix	38.90 (3)
O1^iii—Rb1—Ti1^iii	31.583 (15)	O3^ix—Ti1—Ti1^x	114.41 (11)
O1^iii—Rb1—Ti1^ii	78.231 (19)	O3^x—Ti1—Ti1^x	38.96 (10)
O1^ii—Rb1—Ti1^iii	78.231 (19)	O3^ix—Ti1—O3	77.86 (10)
O1^iii—Rb1—O3^iv	49.18 (4)	O3^x—Ti1—O3	77.86 (10)
O1^ii—Rb1—O3^iv	49.18 (4)	O3^ix—Ti1—O3^x	148.6 (2)
O1^ii—Rb1—O1^iii	75.031 (16)	O1—Ti1—Rb1^vii	60.79 (2)
O1^ii—Rb1—O2	101.41 (6)	O1—Ti1—Rb1^ix	57.30 (2)
O1^ii—Rb1—O2^ii	55.89 (7)	O1—Ti1—Rb1^viii	60.79 (2)
O1^ii—Rb1—O2^iii	100.25 (6)	O1—Ti1—Rb1	169.71 (4)
O1^iii—Rb1—O2	101.41 (6)	O1—Ti1—Rb1^x	57.30 (2)
O1^iii—Rb1—O2^ii	100.25 (6)	O1—Ti1—Ti1^x	121.07 (4)
O1^iii—Rb1—O2^iii	55.89 (7)	O1—Ti1—Ti1^ix	121.07 (4)
O2^v—Rb1—Rb1^i	60.17 (8)	O1—Ti1—O3	139.03 (12)
O2^ii—Rb1—Rb1^i	52.77 (7)	O1—Ti1—O3^x	92.73 (11)
O2^vi—Rb1—Rb1^i	60.17 (8)	O1—Ti1—O3^ix	92.73 (11)
O2^iii—Rb1—Rb1^i	52.77 (7)	O2—Ti1—Rb1^vii	61.30 (11)
O2—Rb1—Rb1^i	142.77 (8)	O2—Ti1—Rb1^viii	61.30 (11)
O2^iii—Rb1—Ti1^ii	76.44 (5)	O2—Ti1—Rb1	59.47 (14)
O2^vi—Rb1—Ti1^iii	89.74 (7)	O2—Ti1—Rb1^x	144.38 (7)
O2—Rb1—Ti1^ii	132.30 (5)	O2—Ti1—Rb1^ix	144.38 (7)
O2^ii—Rb1—Ti1^ii	28.38 (7)	O2—Ti1—Ti1^ix	112.17 (11)
O2—Rb1—Ti1^iii	132.30 (5)	O2—Ti1—Ti1^x	112.17 (11)
O2^v—Rb1—Ti1^ii	89.74 (7)	O2—Ti1—O3	110.73 (18)
O2^v—Rb1—Ti1^iii	134.31 (8)	O2—Ti1—O3^x	103.48 (11)
O2^iii—Rb1—Ti1^iii	28.38 (7)	O2—Ti1—O3^ix	103.48 (11)
O2^vi—Rb1—Ti1^ii	134.31 (8)	O2—Ti1—O1	110.25 (15)
O2^ii—Rb1—Ti1^iii	76.44 (5)	Rb1—O3—Rb1^iv	101.38 (10)
O2^ii—Rb1—O3^iv	51.10 (7)	Ti1^x—O3—Rb1^iv	75.42 (10)
O2^vi—Rb1—O3^iv	116.70 (9)	Ti1—O3—Rb1^iv	162.49 (17)
O2^v—Rb1—O3^iv	116.70 (9)	Ti1^x—O3—Rb1	98.40 (12)
O2^iii—Rb1—O3^iv	51.10 (7)	Ti1^ix—O3—Rb1	98.40 (12)
O2—Rb1—O3^iv	138.95 (10)	Ti1^ix—O3—Rb1^iv	75.42 (10)
O2^vi—Rb1—O1^iii	99.29 (5)	Ti1—O3—Rb1	96.13 (14)
O2^v—Rb1—O1^ii	99.29 (5)	Ti1^x—O3—Ti1	102.14 (10)
O2^vi—Rb1—O1^ii	165.07 (8)	Ti1^ix—O3—Ti1^x	148.6 (2)
O2^v—Rb1—O1^iii	165.07 (8)	Ti1^ix—O3—Ti1	102.14 (10)
O2^iii—Rb1—O2	142.55 (5)	Rb1^vii—O1—Rb1^viii	75.031 (16)
O2^vi—Rb1—O2^v	82.73 (10)	Rb1^viii—O1—Rb1^x	180.0
O2^ii—Rb1—O2	142.55 (5)	Rb1^ix—O1—Rb1^viii	104.969 (16)
O2^vi—Rb1—O2^ii	112.94 (6)	Rb1^ix—O1—Rb1^x	75.031 (16)
O2^vi—Rb1—O2^iii	65.68 (12)	Rb1^vii—O1—Rb1^x	104.969 (16)
O2^v—Rb1—O2	93.21 (10)	Rb1^ix—O1—Rb1^vii	180.0
O2^v—Rb1—O2^iii	112.94 (6)	Ti1—O1—Rb1^ix	92.37 (3)
O2^v—Rb1—O2^ii	65.68 (12)	Ti1—O1—Rb1^vii	87.63 (3)
O2^ii—Rb1—O2^iii	74.67 (9)	Ti1—O1—Rb1^viii	87.63 (3)
O2^vi—Rb1—O2	93.21 (10)	Ti1^xi—O1—Rb1^viii	92.37 (3)
Rb1^ix—Ti1—Rb1^x	61.715 (19)	Ti1^xi—O1—Rb1^x	87.63 (3)
Rb1^vii—Ti1—Rb1^ix	118.09 (2)	Ti1^xi—O1—Rb1^ix	87.63 (3)
Rb1—Ti1—Rb1^ix	130.59 (2)	Ti1^xi—O1—Rb1^vii	92.37 (3)
Rb1^viii—Ti1—Rb1^x	118.09 (3)	Ti1—O1—Rb1^x	92.37 (3)
Rb1^vii—Ti1—Rb1^viii	64.28 (2)	Ti1^xi—O1—Ti1	180.0
Rb1—Ti1—Rb1^x	130.59 (2)	Rb1^v—O2—Rb1^viii	67.06 (6)
Rb1^vii—Ti1—Rb1	110.90 (3)	Rb1^v—O2—Rb1^vii	114.32 (12)
Rb1^vii—Ti1—Rb1^x	85.71 (2)	Rb1^vi—O2—Rb1^vii	67.06 (6)
Rb1^viii—Ti1—Rb1^ix	85.71 (2)	Rb1^v—O2—Rb1	86.79 (10)
Rb1^viii—Ti1—Rb1	110.90 (3)	Rb1^viii—O2—Rb1	142.54 (5)
Ti1^ix—Ti1—Rb1^viii	109.448 (17)	Rb1^vi—O2—Rb1^v	82.73 (10)
Ti1^ix—Ti1—Rb1^x	101.58 (4)	Rb1^vi—O2—Rb1^viii	114.32 (12)
Ti1^ix—Ti1—Rb1^vii	172.28 (4)	Rb1^vi—O2—Rb1	86.79 (10)
Ti1^x—Ti1—Rb1^ix	101.58 (4)	Rb1^vii—O2—Rb1^viii	74.67 (9)
Ti1^ix—Ti1—Rb1	66.29 (3)	Rb1^vii—O2—Rb1	142.54 (5)
Ti1^ix—Ti1—Rb1^ix	64.30 (3)	Ti1—O2—Rb1	92.81 (16)
Ti1^x—Ti1—Rb1	66.29 (3)	Ti1—O2—Rb1^vi	138.61 (5)
Ti1^x—Ti1—Rb1^vii	109.448 (17)	Ti1—O2—Rb1^vii	90.33 (13)
Ti1^x—Ti1—Rb1^x	64.30 (3)	Ti1—O2—Rb1^v	138.61 (5)
Ti1^x—Ti1—Rb1^viii	172.28 (4)	Ti1—O2—Rb1^viii	90.33 (13)

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

(III)

Crystal data

0.5(O10Rb4Ti4)	F(000) = 316
Mr = 346.74	Dx = 3.854 Mg m^−3
Monoclinic, C2/m	Mo Kα radiation, λ = 0.71073 Å
a = 11.3419 (12) Å	Cell parameters from 1105 reflections
b = 3.8198 (5) Å	θ = 2.9–32.9°
c = 7.0103 (8) Å	µ = 18.80 mm^−1
β = 100.298 (11)°	T = 400 K
V = 298.82 (6) Å^3	Needle, clear light colourless
Z = 2	0.3 × 0.1 × 0.05 mm

Data collection

Saxi-CrysAlisPro-abstract goniometer imported SAXI images diffractometer	567 independent reflections
Radiation source: Enhance (Mo) X-ray Source	511 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.023
ω and π scans	θmax = 32.5°, θmin = 3.0°
Absorption correction: multi-scan CrysAlisPro, Agilent Technologies, Version 1.171.37.31 (release 14-01-2014 CrysAlis171 .NET) (compiled Jan 14 2014,18:38:05) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.	h = −14→16
Tmin = 0.277, Tmax = 1.000	k = −5→4
1859 measured reflections	l = −10→10

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0563P)^2 + 1.1457P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.035	(Δ/σ)max < 0.001
wR(F^2) = 0.092	Δρmax = 0.82 e Å^−3
S = 1.08	Δρmin = −1.63 e Å^−3
567 reflections	Extinction correction: SHELXL-2014/7 (Sheldrick 2014, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
30 parameters	Extinction coefficient: 0.0045 (17)
0 restraints

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

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

	x	y	z	Uiso*/Ueq
Rb1	0.09888 (5)	0.5000	0.84866 (7)	0.0267 (2)
Ti1	0.35256 (6)	0.5000	0.58837 (11)	0.0126 (2)
O3	0.1780 (3)	0.5000	0.4786 (5)	0.0174 (7)
O1	0.5000	0.5000	0.5000	0.0245 (11)
O2	0.3763 (4)	0.5000	0.8355 (5)	0.0257 (8)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Rb1	0.0252 (3)	0.0277 (3)	0.0287 (3)	0.000	0.00887 (19)	0.000
Ti1	0.0058 (3)	0.0126 (4)	0.0192 (4)	0.000	0.0016 (2)	0.000
O3	0.0055 (12)	0.0136 (15)	0.0318 (17)	0.000	0.0002 (11)	0.000
O1	0.010 (2)	0.019 (3)	0.048 (3)	0.000	0.015 (2)	0.000
O2	0.0295 (19)	0.024 (2)	0.0219 (16)	0.000	−0.0005 (14)	0.000

Geometric parameters (Å, º)

Rb1—Rb1^i	3.3518 (10)	Ti1—O3^viii	1.9824 (9)
Rb1—Ti1^ii	3.6000 (9)	Ti1—O3	1.992 (3)
Rb1—Ti1^iii	3.6000 (9)	Ti1—O3^ix	1.9824 (9)
Rb1—O3	2.893 (4)	Ti1—O1	1.8844 (8)
Rb1—O3^iv	3.542 (3)	Ti1—O2	1.705 (4)
Rb1—O1^iii	3.1464 (5)	O3—Rb1^iv	3.542 (3)
Rb1—O1^ii	3.1464 (5)	O3—Ti1^ix	1.9824 (9)
Rb1—O2^ii	3.154 (3)	O3—Ti1^viii	1.9824 (9)
Rb1—O2^v	2.899 (3)	O1—Rb1^vii	3.1464 (5)
Rb1—O2	3.164 (4)	O1—Rb1^ix	3.1464 (5)
Rb1—O2^vi	2.899 (3)	O1—Rb1^x	3.1464 (5)
Rb1—O2^iii	3.154 (3)	O1—Rb1^viii	3.1464 (5)
Ti1—Rb1^vii	3.6000 (9)	O1—Ti1^xi	1.8844 (7)
Ti1—Rb1^viii	3.7338 (9)	O2—Rb1^x	3.154 (3)
Ti1—Rb1^ix	3.7338 (9)	O2—Rb1^vi	2.899 (3)
Ti1—Rb1^x	3.6000 (9)	O2—Rb1^vii	3.154 (3)
Ti1—Ti1^ix	3.0926 (12)	O2—Rb1^v	2.899 (3)
Ti1—Ti1^viii	3.0926 (12)
Rb1^i—Rb1—Ti1^iii	76.96 (2)	Ti1^viii—Ti1—Ti1^ix	76.28 (4)
Rb1^i—Rb1—Ti1^ii	76.96 (2)	O3—Ti1—Rb1^ix	88.00 (9)
Rb1^i—Rb1—O3^iv	78.10 (6)	O3^ix—Ti1—Rb1^x	135.90 (9)
Ti1^ii—Rb1—Ti1^iii	64.082 (19)	O3^viii—Ti1—Rb1	89.90 (10)
O3—Rb1—Rb1^i	156.59 (7)	O3^viii—Ti1—Rb1^viii	50.07 (10)
O3^iv—Rb1—Ti1^iii	32.216 (11)	O3^viii—Ti1—Rb1^vii	135.90 (9)
O3—Rb1—Ti1^ii	83.25 (5)	O3^ix—Ti1—Rb1^vii	72.29 (9)
O3^iv—Rb1—Ti1^ii	32.216 (11)	O3^ix—Ti1—Rb1^ix	50.07 (10)
O3—Rb1—Ti1^iii	83.25 (5)	O3^ix—Ti1—Rb1	89.90 (10)
O3—Rb1—O3^iv	78.49 (9)	O3—Ti1—Rb1^viii	88.00 (9)
O3—Rb1—O1^ii	55.10 (4)	O3—Ti1—Rb1^x	145.45 (4)
O3—Rb1—O1^iii	55.10 (4)	O3—Ti1—Rb1	51.62 (10)
O3—Rb1—O2	60.29 (9)	O3^ix—Ti1—Rb1^viii	110.10 (11)
O3—Rb1—O2^iii	110.41 (8)	O3—Ti1—Rb1^vii	145.45 (4)
O3—Rb1—O2^ii	110.41 (8)	O3^viii—Ti1—Rb1^ix	110.10 (11)
O3—Rb1—O2^vi	132.96 (7)	O3^viii—Ti1—Rb1^x	72.29 (9)
O3—Rb1—O2^v	132.96 (7)	O3^ix—Ti1—Ti1^viii	114.39 (9)
O1^ii—Rb1—Rb1^i	107.81 (2)	O3—Ti1—Ti1^viii	38.80 (3)
O1^iii—Rb1—Rb1^i	107.81 (2)	O3^viii—Ti1—Ti1^ix	114.39 (9)
O1^iii—Rb1—Ti1^ii	77.979 (18)	O3—Ti1—Ti1^ix	38.80 (3)
O1^iii—Rb1—Ti1^iii	31.533 (13)	O3^viii—Ti1—Ti1^viii	39.02 (8)
O1^ii—Rb1—Ti1^ii	31.533 (13)	O3^ix—Ti1—Ti1^ix	39.02 (9)
O1^ii—Rb1—Ti1^iii	77.979 (18)	O3^viii—Ti1—O3	77.81 (9)
O1^iii—Rb1—O3^iv	49.10 (4)	O3^ix—Ti1—O3	77.81 (9)
O1^ii—Rb1—O3^iv	49.10 (4)	O3^viii—Ti1—O3^ix	148.91 (19)
O1^ii—Rb1—O1^iii	74.748 (15)	O1—Ti1—Rb1	169.61 (4)
O1^iii—Rb1—O2^ii	99.93 (6)	O1—Ti1—Rb1^x	60.84 (2)
O1^ii—Rb1—O2^iii	99.93 (6)	O1—Ti1—Rb1^ix	57.35 (2)
O1^ii—Rb1—O2^ii	55.76 (6)	O1—Ti1—Rb1^viii	57.35 (2)
O1^iii—Rb1—O2^iii	55.76 (6)	O1—Ti1—Rb1^vii	60.84 (2)
O1^ii—Rb1—O2	101.28 (5)	O1—Ti1—Ti1^ix	121.10 (4)
O1^iii—Rb1—O2	101.28 (5)	O1—Ti1—Ti1^viii	121.10 (4)
O2^vi—Rb1—Rb1^i	60.09 (7)	O1—Ti1—O3^viii	92.87 (10)
O2^iii—Rb1—Rb1^i	52.82 (6)	O1—Ti1—O3	138.78 (11)
O2—Rb1—Rb1^i	143.12 (7)	O1—Ti1—O3^ix	92.87 (10)
O2^ii—Rb1—Rb1^i	52.82 (6)	O2—Ti1—Rb1^vii	61.18 (11)
O2^v—Rb1—Rb1^i	60.09 (7)	O2—Ti1—Rb1^ix	144.50 (7)
O2^iii—Rb1—Ti1^ii	76.22 (5)	O2—Ti1—Rb1^x	61.18 (11)
O2^ii—Rb1—Ti1^ii	28.27 (7)	O2—Ti1—Rb1	59.36 (14)
O2^vi—Rb1—Ti1^ii	89.91 (6)	O2—Ti1—Rb1^viii	144.50 (7)
O2^iii—Rb1—Ti1^iii	28.27 (7)	O2—Ti1—Ti1^viii	112.19 (11)
O2^v—Rb1—Ti1^ii	134.21 (8)	O2—Ti1—Ti1^ix	112.19 (11)
O2^ii—Rb1—Ti1^iii	76.22 (5)	O2—Ti1—O3^viii	103.28 (11)
O2—Rb1—Ti1^iii	132.13 (5)	O2—Ti1—O3	110.97 (17)
O2—Rb1—Ti1^ii	132.13 (5)	O2—Ti1—O3^ix	103.28 (11)
O2^vi—Rb1—Ti1^iii	134.21 (8)	O2—Ti1—O1	110.25 (14)
O2^v—Rb1—Ti1^iii	89.91 (6)	Rb1—O3—Rb1^iv	101.51 (9)
O2^ii—Rb1—O3^iv	50.85 (7)	Ti1^viii—O3—Rb1	98.23 (11)
O2^iii—Rb1—O3^iv	50.85 (7)	Ti1^viii—O3—Rb1^iv	75.49 (9)
O2^v—Rb1—O3^iv	116.65 (8)	Ti1^ix—O3—Rb1^iv	75.49 (9)
O2—Rb1—O3^iv	138.77 (9)	Ti1^ix—O3—Rb1	98.23 (11)
O2^vi—Rb1—O3^iv	116.65 (8)	Ti1—O3—Rb1^iv	162.77 (16)
O2^v—Rb1—O1^iii	99.55 (5)	Ti1—O3—Rb1	95.72 (13)
O2^v—Rb1—O1^ii	164.93 (8)	Ti1^ix—O3—Ti1	102.19 (9)
O2^vi—Rb1—O1^ii	99.55 (5)	Ti1^viii—O3—Ti1^ix	148.91 (19)
O2^vi—Rb1—O1^iii	164.93 (8)	Ti1^viii—O3—Ti1	102.19 (9)
O2^iii—Rb1—O2	142.58 (5)	Rb1^viii—O1—Rb1^vii	180.000 (13)
O2^v—Rb1—O2^ii	112.91 (5)	Rb1^vii—O1—Rb1^ix	105.253 (15)
O2^vi—Rb1—O2	93.49 (9)	Rb1^viii—O1—Rb1^x	105.253 (15)
O2^vi—Rb1—O2^ii	65.89 (12)	Rb1^x—O1—Rb1^ix	180.0
O2^ii—Rb1—O2^iii	74.53 (9)	Rb1^vii—O1—Rb1^x	74.747 (15)
O2^v—Rb1—O2^iii	65.89 (12)	Rb1^viii—O1—Rb1^ix	74.747 (15)
O2^ii—Rb1—O2	142.58 (5)	Ti1—O1—Rb1^viii	92.37 (2)
O2^vi—Rb1—O2^iii	112.91 (5)	Ti1^xi—O1—Rb1^x	92.37 (2)
O2^v—Rb1—O2^vi	82.40 (10)	Ti1^xi—O1—Rb1^viii	87.63 (2)
O2^v—Rb1—O2	93.49 (9)	Ti1—O1—Rb1^ix	92.37 (2)
Rb1^viii—Ti1—Rb1^ix	61.529 (17)	Ti1^xi—O1—Rb1^vii	92.37 (2)
Rb1^x—Ti1—Rb1^ix	118.19 (2)	Ti1—O1—Rb1^vii	87.63 (2)
Rb1—Ti1—Rb1^ix	130.644 (18)	Ti1^xi—O1—Rb1^ix	87.63 (2)
Rb1^vii—Ti1—Rb1^ix	85.962 (18)	Ti1—O1—Rb1^x	87.63 (2)
Rb1^x—Ti1—Rb1^viii	85.962 (18)	Ti1^xi—O1—Ti1	180.0
Rb1^vii—Ti1—Rb1^x	64.082 (19)	Rb1^v—O2—Rb1^vii	67.09 (5)
Rb1—Ti1—Rb1^viii	130.644 (18)	Rb1^x—O2—Rb1	142.57 (5)
Rb1^vii—Ti1—Rb1	110.74 (2)	Rb1^v—O2—Rb1^x	114.11 (12)
Rb1^vii—Ti1—Rb1^viii	118.19 (2)	Rb1^vii—O2—Rb1^x	74.53 (9)
Rb1^x—Ti1—Rb1	110.74 (2)	Rb1^vi—O2—Rb1	86.51 (9)
Ti1^viii—Ti1—Rb1^x	109.602 (15)	Rb1^vi—O2—Rb1^vii	114.11 (12)
Ti1^ix—Ti1—Rb1^viii	101.41 (3)	Rb1^vii—O2—Rb1	142.57 (5)
Ti1^viii—Ti1—Rb1^viii	64.29 (2)	Rb1^v—O2—Rb1^vi	82.40 (9)
Ti1^ix—Ti1—Rb1^vii	109.602 (15)	Rb1^vi—O2—Rb1^x	67.09 (5)
Ti1^ix—Ti1—Rb1^ix	64.29 (2)	Rb1^v—O2—Rb1	86.51 (9)
Ti1^viii—Ti1—Rb1	66.36 (3)	Ti1—O2—Rb1	93.02 (15)
Ti1^viii—Ti1—Rb1^vii	172.20 (3)	Ti1—O2—Rb1^vi	138.77 (5)
Ti1^ix—Ti1—Rb1	66.36 (3)	Ti1—O2—Rb1^x	90.56 (13)
Ti1^viii—Ti1—Rb1^ix	101.41 (3)	Ti1—O2—Rb1^vii	90.56 (13)
Ti1^ix—Ti1—Rb1^x	172.20 (3)	Ti1—O2—Rb1^v	138.77 (5)
Rb1^vii—Ti1—O1—Rb1^viii	180.0	Ti1^viii—Ti1—O2—Rb1^vii	175.43 (3)
Rb1^viii—Ti1—O1—Rb1^x	−105.178 (16)	Ti1^ix—Ti1—O2—Rb1^vii	−100.90 (9)
Rb1—Ti1—O1—Rb1^ix	−142.589 (8)	Ti1^ix—Ti1—O2—Rb1^vi	130.0 (2)
Rb1^x—Ti1—O1—Rb1^vii	−74.822 (16)	Ti1^ix—Ti1—O2—Rb1	41.83 (5)
Rb1—Ti1—O1—Rb1^viii	142.589 (8)	Ti1^ix—Ti1—O2—Rb1^x	−175.43 (3)
Rb1^viii—Ti1—O1—Rb1^vii	180.0	Ti1^viii—Ti1—O2—Rb1^x	100.90 (9)
Rb1^x—Ti1—O1—Rb1^viii	105.178 (16)	Ti1^viii—Ti1—O2—Rb1	−41.83 (5)
Rb1—Ti1—O1—Rb1^x	37.411 (8)	Ti1^viii—Ti1—O2—Rb1^vi	46.3 (3)
Rb1^ix—Ti1—O1—Rb1^x	180.0	Ti1^viii—Ti1—O2—Rb1^v	−130.0 (2)
Rb1—Ti1—O1—Rb1^vii	−37.411 (8)	Ti1^ix—Ti1—O2—Rb1^v	−46.3 (3)
Rb1^vii—Ti1—O1—Rb1^ix	−105.178 (16)	O3—Ti1—O1—Rb1^ix	37.411 (8)
Rb1^x—Ti1—O1—Rb1^ix	180.0	O3^viii—Ti1—O1—Rb1^vii	−142.69 (10)
Rb1^ix—Ti1—O1—Rb1^vii	105.178 (16)	O3—Ti1—O1—Rb1^x	−142.589 (8)
Rb1^ix—Ti1—O1—Rb1^viii	−74.822 (16)	O3^viii—Ti1—O1—Rb1^viii	37.31 (10)
Rb1^vii—Ti1—O1—Rb1^x	74.822 (16)	O3—Ti1—O1—Rb1^vii	142.589 (8)
Rb1^viii—Ti1—O1—Rb1^ix	74.822 (16)	O3—Ti1—O1—Rb1^viii	−37.411 (8)
Rb1^ix—Ti1—O2—Rb1	118.24 (17)	O3^ix—Ti1—O1—Rb1^ix	−37.31 (10)
Rb1^ix—Ti1—O2—Rb1^v	30.1 (4)	O3^ix—Ti1—O1—Rb1^x	142.69 (10)
Rb1^ix—Ti1—O2—Rb1^x	−99.03 (13)	O3^viii—Ti1—O1—Rb1^ix	112.13 (10)
Rb1^viii—Ti1—O2—Rb1^v	153.60 (11)	O3^ix—Ti1—O1—Rb1^vii	67.87 (10)
Rb1^x—Ti1—O2—Rb1^v	129.1 (3)	O3^viii—Ti1—O1—Rb1^x	−67.87 (10)
Rb1^x—Ti1—O2—Rb1^vi	−54.6 (2)	O3^ix—Ti1—O1—Rb1^viii	−112.13 (10)
Rb1^x—Ti1—O2—Rb1^vii	74.54 (9)	O3—Ti1—O2—Rb1^x	142.73 (5)
Rb1—Ti1—O2—Rb1^vi	88.2 (3)	O3^ix—Ti1—O2—Rb1^x	−135.42 (10)
Rb1^vii—Ti1—O2—Rb1^x	−74.54 (9)	O3—Ti1—O2—Rb1	0.000 (1)
Rb1^x—Ti1—O2—Rb1	−142.73 (5)	O3—Ti1—O2—Rb1^vii	−142.73 (5)
Rb1^viii—Ti1—O2—Rb1^x	24.5 (2)	O3^ix—Ti1—O2—Rb1	81.85 (10)
Rb1^ix—Ti1—O2—Rb1^vii	−24.5 (2)	O3^viii—Ti1—O2—Rb1^v	−170.0 (3)
Rb1^vii—Ti1—O2—Rb1	142.73 (5)	O3—Ti1—O2—Rb1^v	−88.2 (3)
Rb1^vii—Ti1—O2—Rb1^v	54.6 (2)	O3^ix—Ti1—O2—Rb1^v	−6.3 (3)
Rb1^viii—Ti1—O2—Rb1	−118.24 (17)	O3^viii—Ti1—O2—Rb1^x	60.88 (13)
Rb1^viii—Ti1—O2—Rb1^vii	99.03 (13)	O3^ix—Ti1—O2—Rb1^vi	170.0 (3)
Rb1—Ti1—O2—Rb1^vii	−142.73 (5)	O3—Ti1—O2—Rb1^vi	88.2 (3)
Rb1—Ti1—O2—Rb1^x	142.73 (5)	O3^viii—Ti1—O2—Rb1^vi	6.3 (3)
Rb1^vii—Ti1—O2—Rb1^vi	−129.1 (3)	O3^viii—Ti1—O2—Rb1	−81.85 (10)
Rb1^ix—Ti1—O2—Rb1^vi	−153.60 (11)	O3^ix—Ti1—O2—Rb1^vii	−60.88 (13)
Rb1—Ti1—O2—Rb1^v	−88.2 (3)	O3^viii—Ti1—O2—Rb1^vii	135.42 (10)
Rb1^viii—Ti1—O2—Rb1^vi	−30.1 (4)	O1—Ti1—O2—Rb1^x	−37.27 (5)
Ti1^viii—Ti1—O1—Rb1^ix	83.57 (4)	O1—Ti1—O2—Rb1	180.000 (1)
Ti1^ix—Ti1—O1—Rb1^viii	−83.57 (4)	O1—Ti1—O2—Rb1^vii	37.27 (5)
Ti1^ix—Ti1—O1—Rb1^vii	96.43 (4)	O1—Ti1—O2—Rb1^v	91.8 (3)
Ti1^viii—Ti1—O1—Rb1^x	−96.43 (4)	O1—Ti1—O2—Rb1^vi	−91.8 (3)
Ti1^ix—Ti1—O1—Rb1^x	171.26 (4)	O2—Ti1—O1—Rb1^ix	−142.589 (8)
Ti1^ix—Ti1—O1—Rb1^ix	−8.74 (4)	O2—Ti1—O1—Rb1^x	37.411 (8)
Ti1^viii—Ti1—O1—Rb1^vii	−171.26 (4)	O2—Ti1—O1—Rb1^vii	−37.411 (8)
Ti1^viii—Ti1—O1—Rb1^viii	8.74 (4)	O2—Ti1—O1—Rb1^viii	142.589 (8)

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