A single-crystal neutron diffraction study of RbTiOAsO₄

A rubidium titanyl arsenate single-crystal has been studied by neutron diffraction ([lambda] = 1.207 Å). The polished sample used was 5 × 3 × 2 mm and was cut from a crystal made by top-seeded solution growth. The crystal showed severe extinction. It was, however, possible to obtain a structural model with well defined oxy­gen sites and reasonable anisotropic displacement parameters.

S1. Comment

Rubidium titanyl arsenate (RTA) belongs to the KTiOPO₄ (KTP) family of compounds well known for their non-linear optical and ferroelectric properties (Stucky et al., 1989). The structure is based on a three-dimensional network of arsenic tetrahedra and titanium octahedra with open channels along the c axis where the Rb atoms are situated at two independent sites (Thomas et al., 1992). Additional alkaline positions were detected as `ghost' sites in Cs-rich mixtures of RTA and CsTiOAsO₄ (CTA) (Womersley et al., 1998). The original and additional sites are related by pseudosymmetry retained at room temperature from the high-temperature paraelectric phase (Thomas et al., 1990, 1998). The evolution towards centrosymmetry for the KTP and RbTiOPO₄ structures has been studied extensively by Delarue et al. (1998, 1999). For these isomorphs, split alkaline positions could be refined for structures above 473 K.

A study of the RTA structure at 9.6 K showed additional electron density near the Rb atoms but a structural model with split Rb positions was not applicable (Almgren et al., 1999). However, using synchrotron-radiation data, it is currently shown that there is a partial occupancy of additional sites in RTA at room temperature, which is reported separately (Streltsov et al., 2000). A parallel study of the CTA structure confirms splitting of the alkaline sites in CTA (Nordborg, 2000). In the present study, single-crystal neutron diffraction has been used to improve the structural model for RTA as concerns the O sites. The aim was to get well defined nuclear positions for the O atoms together with reasonable displacement parameters.

The displacement ellipsoids for O atoms have an average value for U_min/U_max of about 0.7. These are more uniform than those obtained previously from X-ray tube data, for which the U_min/U_max average was approximately 0.5 (Almgren et al., 1999). The values presently obtained from a common independent atomic model refinement are comparable to those obtained by multipole refinements in the parallel synchrotron study (Streltsov et al., 2000). The atomic displacement parameters along the principal axes have been calculated using the program ORFFE modified for PC (Busing et al., 1964; Gustafsson, 1993). The Rb1 atom predominantly vibrates in the [-101] direction with an angle to the c axis of 33 (4)°, while the Rb2 atom vibrates in the [001] direction deviating by 18 (7)°. The anisotropy of the ellipsoids is markedly pronounced for the Rb atoms. The displacements along principal axes r₁, r₂ and r₃ are 0.09 (1), 0.138 (9) and 0.201 (6) Å for Rb1, and 0.109 (8), 0.130 (7) and 0.171 (6) Å for Rb2. This is consistent with the r.m.s. parameters obtained from X-ray data.

More uniform r.m.s. displacements of the O atoms have been obtained compared to those from X-ray data previously reported by Almgren et al. (1999). This is represented, for example, by the displacements for O2 along principal axes r₁ and r₃, which are 0.09 (1) and 0.13 (1) Å when derived from neutron data, and 0.06 (2) and 0.134 (9) Å when derived from X-ray data. The corresponding values for O7 are 0.07 (1) and 0.13 (1) Å, and 0.05 (2) and 0.13 (1) Å, respectively. The Rb—O and bond distances are given in Table 1. In CTA, the Cs3 site, which is the additional site at Cs1, is coordinated by 6 O atoms and not binding to O1, O11 and O7 (Nordborg, 2000). This is propably the case also for the Rb1–Rb3 pair as splitting is seen in the c direction which is the direction of the Rb1—O1, Rb1—O11 and Rb1—O7 bonds.

S2. Experimental

The RTA crystals were grown by the top-seeded solution growth technique (Nordborg et al., 2000) using the Rb₅As₃O₁₀ self-flux (Cheng et al., 1994). The starting material for both flux and crystals were prepared simultaneously from powder mixtures of analytical grade Rb₂CO₃, TiO₂ and As₂O₅. A batch of approximately 0.5 g RTA per 1 g Rb₅As₃O₁₀ flux was mixed in a platinum crucible and inserted in a vertical tube furnace. The mixture was homogenized at 1270 K, then the seed was set just below the flux surface and growth was accomplished with the subsequent cooling of 2 K d^-1 from the crystallization temperature at 1190 K. The as-grown RTA crystal had the size of 10 × 12 × 20 mm.

S3. Refinement

Data were collected at beam channel No. H8 at NFL, the Studsvik Neutron Research Laboratory, Sweden. The three standard reflections, (-534), (-733) and (-543), were remeasured every 36 reflections to monitor the experimental stability, no significant variations were noted during the data collection. Intensity profiles were measured for 1/8 of a sphere, with a step size of 0.1° and a scan time of 10 s per step. Each reflection was sampled with 40 steps. Independent structural parameters, including scale factor, positional and displacement parameters for all atoms were refined by conventional full-matrix least squares. Extinction was severe and the best correction was made by refinement of the isotropic parameter for a type-I crystal with Lorentzian mosaic spread implemented by Becker & Coppens (1974). Still, six reflections with extinction correction parameters less than 0.45 had to be excluded from the refinement (the observed structure factor is F_obs = yF_kin, where F_kin is the kinematical value of the structure factor). The minimum extinction correction parameter y_min was then 0.52 for the (220) reflection.

Computing details

Data collection: Huber diffractometer software; cell refinement: Huber diffractometer software; data reduction: Xtal3.6 DIFDAT ADDREF SORTRF (Hall et al., 1999); program(s) used to refine structure: Xtal3.6 CRYLSQ; software used to prepare material for publication: Xtal3.6 CIFIO.

(I)

Crystal data

RbTiOAsO4	F(000) = 31.08
Mr = 288.27	Dx = 4.016 Mg m^−3
Orthorhombic, Pna21	Neutron radiation, λ = 1.207 Å
Hall symbol: P 2c -2n	Cell parameters from 11 reflections
a = 13.26 (2) Å	θ = 24.8–32.1°
b = 6.677 (7) Å	µ = 0.01 mm^−1
c = 10.766 (7) Å	T = 295 K
V = 953.5 (18) Å^3	Rectangular, colourless
Z = 8	5 × 3 × 2 mm

Data collection

Huber four-circle diffractometer	Rint = 0
Radiation source: neutron constant wavelength	θmax = 52.0°, θmin = 5.2°
Double Cu(220) monochromator	h = −17→0
ω/2θ scans	k = 0→8
1174 measured reflections	l = 0→14
1153 independent reflections	3 standard reflections every 36 reflections
1153 reflections with F > 0	intensity decay: none

Refinement

Refinement on F	0 constraints
Least-squares matrix: full	w = 1/σ^2
R[F^2 > 2σ(F^2)] = 0.034	(Δ/σ)max = 0.003
wR(F^2) = 0.033	Δρmax = 0.06 e Å^−3
S = 1.36	Δρmin = −0.06 e Å^−3
1153 reflections	Extinction correction: Becker-Coppens
145 parameters	Extinction coefficient: 7219 (45)
0 restraints

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

	x	y	z	Uiso*/Ueq
Rb1	0.3829 (3)	0.7824 (5)	0.6499 (4)	0.0228 (16)
Rb2	0.1092 (2)	0.6936 (5)	0.9025 (4)	0.0191 (16)
Ti1	0.3740 (3)	0.5053 (9)	0.9782 (7)	0.005 (2)
Ti2	0.2487 (4)	0.2699 (8)	0.7288 (5)	0.004 (2)
As1	0.4997 (2)	0.3284 (4)	0.7213 (4)	0.0055 (10)
As2	0.17972 (18)	0.5050 (5)	0.4667 (4)	0.0065 (10)
O1	0.4878 (3)	0.4890 (6)	0.8374 (4)	0.0118 (17)
O2	0.5106 (3)	0.4610 (6)	0.5885 (4)	0.0113 (18)
O3	0.3948 (3)	0.1877 (5)	0.6990 (4)	0.0098 (15)
O4	0.6000 (3)	0.1765 (5)	0.7407 (4)	0.0103 (16)
O11	0.2813 (3)	0.4524 (6)	0.8382 (4)	0.0098 (16)
O12	0.2176 (3)	0.0566 (6)	0.5878 (4)	0.0108 (17)
O5	0.1102 (3)	0.3031 (6)	0.4311 (4)	0.0112 (16)
O6	0.1070 (3)	0.7036 (5)	0.4984 (4)	0.0119 (16)
O7	0.2588 (3)	0.5448 (5)	0.3449 (4)	0.0106 (17)
O8	0.2571 (3)	0.4590 (6)	0.5869 (16)	0.0122 (18)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Rb1	0.0245 (16)	0.0104 (13)	0.034 (2)	0.0035 (11)	−0.0085 (14)	−0.0046 (14)
Rb2	0.0147 (14)	0.0148 (14)	0.028 (2)	0.0031 (11)	−0.0016 (13)	−0.0026 (13)
Ti1	0.007 (2)	0.005 (2)	0.005 (3)	−0.001 (2)	0.000 (2)	0.001 (2)
Ti2	0.0038 (19)	0.005 (2)	0.005 (2)	0.0002 (17)	−0.0007 (17)	−0.000 (2)
As1	0.0059 (10)	0.0039 (10)	0.0066 (10)	−0.0007 (11)	0.0009 (8)	−0.0007 (12)
As2	0.0093 (10)	0.0037 (10)	0.0065 (10)	0.0008 (12)	0.0001 (15)	0.0004 (8)
O1	0.0115 (17)	0.0115 (16)	0.0123 (19)	−0.0036 (13)	0.0031 (14)	−0.0058 (14)
O2	0.0126 (18)	0.0108 (17)	0.0107 (18)	0.0023 (14)	0.0035 (14)	0.0037 (14)
O3	0.0090 (15)	0.0075 (14)	0.0130 (17)	−0.0004 (12)	0.0002 (13)	−0.0018 (14)
O4	0.0077 (15)	0.0081 (15)	0.0150 (19)	0.0008 (12)	−0.0014 (14)	0.0012 (14)
O11	0.0098 (16)	0.0095 (16)	0.0099 (17)	0.0008 (12)	−0.0021 (14)	−0.0031 (14)
O12	0.0122 (17)	0.0099 (16)	0.0104 (17)	0.0003 (13)	−0.0038 (15)	−0.0021 (14)
O5	0.0172 (17)	0.0049 (14)	0.0114 (17)	−0.0004 (13)	−0.0040 (14)	−0.0008 (15)
O6	0.0146 (16)	0.0045 (15)	0.0165 (18)	0.0015 (13)	0.0044 (14)	0.0006 (14)
O7	0.0127 (17)	0.0094 (17)	0.0097 (17)	0.0028 (14)	0.0049 (15)	0.0037 (14)
O8	0.018 (2)	0.0100 (17)	0.0088 (18)	−0.0038 (15)	−0.0027 (15)	0.0036 (15)

Geometric parameters (Å, º)

Rb1—Rb2	4.574 (7)	Rb2—Ti1	3.800 (7)
Rb1—Ti2	3.806 (7)	Rb2—O1	2.753 (6)
Rb1—As1	3.490 (5)	Rb2—O5	2.926 (6)
Rb1—O1	3.138 (6)	Ti1—O1	2.142 (8)
Rb1—O2	2.812 (6)	Ti1—O11	1.977 (8)
Rb1—O3	2.762 (6)	Ti1—O5^i	2.063 (8)
Rb1—O11	3.283 (6)	Ti1—O2	1.951 (7)
Rb1—O12	2.933 (6)	Ti1—O6	2.042 (8)
Rb1—O5^i	3.031 (6)	Ti1—O12^i	1.728 (7)
Rb1—O6	3.392 (6)	Ti2—O3	2.040 (7)
Rb1—O7^i	3.318 (6)	Ti2—O12	2.122 (7)
Rb1—O8	2.812 (7)	Ti2—O7^i	1.958 (7)
Rb1—Rb2	4.750 (6)	Ti2—O4	2.009 (7)
Rb1—Rb2	3.827 (6)	Ti2—O11	1.749 (7)
Rb1—Rb2	4.053 (6)	Ti2—O8	1.985 (15)
Rb2—Ti1	3.819 (7)	As1—O1	1.654 (6)
Rb2—As2^i	3.556 (5)	As1—O2	1.688 (5)
Rb2—O4	3.025 (5)	As1—O3	1.696 (5)
Rb2—O11	2.879 (6)	As1—O4	1.686 (5)
Rb2—O7^i	2.992 (5)	As2^i—O5^i	1.677 (5)
Rb2—O3^i	3.193 (6)	As2^i—O7^i	1.699 (6)
Rb2—O12^i	3.177 (6)	As2^i—O6^i	1.675 (5)
Rb2—O2^i	3.118 (6)	As2^i—O8^i	1.681 (14)
Rb2—O8^i	3.198 (12)
Rb2—Rb1—Ti2	66.87 (12)	O7^i—Rb2—O2^i	88.98 (15)
Rb2—Rb1—As1	96.24 (12)	O7^i—Rb2—O8^i	50.9 (3)
Rb2—Rb1—O1	83.60 (14)	O7^i—Rb2—Rb1	105.28 (14)
Rb2—Rb1—O2	121.24 (14)	O7^i—Rb2—Ti1	96.33 (17)
Rb2—Rb1—O3	93.36 (13)	O7^i—Rb2—O1	71.71 (17)
Rb2—Rb1—O11	38.77 (9)	O7^i—Rb2—O5	126.72 (16)
Rb2—Rb1—O12	67.88 (13)	Rb1—Rb2—O3^i	45.23 (10)
Rb2—Rb1—O5^i	55.70 (11)	Rb1—Rb2—O12^i	48.43 (11)
Rb2—Rb1—O6	170.03 (13)	Rb1—Rb2—Rb1^i	101.71 (13)
Rb2—Rb1—O7^i	40.78 (10)	Rb1—Rb2—O2^i	88.73 (14)
Rb2—Rb1—O8	64.7 (3)	Rb1—Rb2—O8^i	87.1 (2)
Rb2—Rb1—Rb2	104.10 (9)	Rb1—Rb2—Rb1	121.05 (11)
Rb2—Rb1—Rb2	121.92 (11)	Rb1—Rb2—Ti1	104.65 (15)
Rb2—Rb1—Rb2	101.19 (14)	Rb1—Rb2—O1	138.23 (16)
Ti2—Rb1—As1	154.33 (17)	Rb1—Rb2—O5	87.69 (12)
Ti2—Rb1—O1	126.71 (17)	O3^i—Rb2—O12^i	51.73 (12)
Ti2—Rb1—O2	170.62 (17)	O3^i—Rb2—Rb1^i	56.63 (10)
Ti2—Rb1—O3	31.36 (12)	O3^i—Rb2—O2^i	49.94 (12)
Ti2—Rb1—O11	104.15 (16)	O3^i—Rb2—O8^i	52.8 (3)
Ti2—Rb1—O12	33.64 (12)	O3^i—Rb2—Rb1	131.22 (13)
Ti2—Rb1—O5^i	75.66 (14)	O3^i—Rb2—Ti1	77.19 (14)
Ti2—Rb1—O6	119.57 (14)	O3^i—Rb2—O1	104.74 (15)
Ti2—Rb1—O7^i	30.95 (11)	O3^i—Rb2—O5	83.02 (13)
Ti2—Rb1—O8	115.68 (19)	O12^i—Rb2—Rb1^i	82.53 (12)
Ti2—Rb1—Rb2	147.50 (14)	O12^i—Rb2—O2^i	97.46 (16)
Ti2—Rb1—Rb2	63.55 (12)	O12^i—Rb2—O8^i	50.85 (16)
Ti2—Rb1—Rb2	99.37 (14)	O12^i—Rb2—Rb1	165.49 (13)
As1—Rb1—O1	28.27 (11)	O12^i—Rb2—Ti1	127.67 (18)
As1—Rb1—O2	28.56 (11)	O12^i—Rb2—O1	143.57 (17)
As1—Rb1—O3	141.57 (17)	O12^i—Rb2—O5	130.94 (17)
As1—Rb1—O11	57.54 (12)	Rb1^i—Rb2—O2^i	34.62 (10)
As1—Rb1—O12	157.54 (15)	Rb1^i—Rb2—O8^i	35.01 (10)
As1—Rb1—O5^i	78.83 (13)	Rb1^i—Rb2—Rb1	111.09 (10)
As1—Rb1—O6	74.98 (12)	Rb1^i—Rb2—Ti1	57.31 (12)
As1—Rb1—O7^i	124.79 (16)	Rb1^i—Rb2—O1	61.22 (13)
As1—Rb1—O8	69.48 (18)	Rb1^i—Rb2—O5	87.53 (11)
As1—Rb1—Rb2	52.76 (10)	O2^i—Rb2—O8^i	64.3 (2)
As1—Rb1—Rb2	139.84 (14)	O2^i—Rb2—Rb1	91.78 (14)
As1—Rb1—Rb2	63.76 (10)	O2^i—Rb2—Ti1	30.80 (13)
O1—Rb1—O2	53.68 (14)	O2^i—Rb2—O1	54.88 (14)
O1—Rb1—O3	117.59 (18)	O2^i—Rb2—O5	54.67 (12)
O1—Rb1—O11	50.64 (14)	O8^i—Rb2—Rb1	143.63 (16)
O1—Rb1—O12	150.19 (18)	O8^i—Rb2—Ti1	91.65 (18)
O1—Rb1—O5^i	51.16 (13)	O8^i—Rb2—O1	93.20 (18)
O1—Rb1—O6	86.44 (15)	O8^i—Rb2—O5	118.8 (2)
O1—Rb1—O7^i	100.00 (16)	Rb1—Rb2—Ti1	60.99 (14)
O1—Rb1—O8	86.5 (3)	Rb1—Rb2—O1	50.61 (12)
O1—Rb1—Rb2	80.45 (13)	Rb1—Rb2—O5	48.23 (12)
O1—Rb1—Rb2	152.05 (15)	Ti1—Rb2—O1	33.59 (14)
O1—Rb1—Rb2	42.69 (11)	Ti1—Rb2—O5	32.55 (13)
O2—Rb1—O3	139.29 (18)	O1—Rb2—O5	55.89 (14)
O2—Rb1—O11	83.11 (15)	Rb2—Ti1—O1	120.9 (3)
O2—Rb1—O12	150.8 (2)	Rb2—Ti1—O11	47.48 (17)
O2—Rb1—O5^i	104.55 (16)	Rb2—Ti1—O5^i	74.0 (2)
O2—Rb1—O6	51.71 (13)	Rb2—Ti1—O2	144.5 (3)
O2—Rb1—O7^i	153.20 (18)	Rb2—Ti1—O6	117.5 (2)
O2—Rb1—O8	73.42 (18)	Rb2—Ti1—O12^i	55.5 (2)
O2—Rb1—Rb2	39.05 (11)	Rb2—Ti1—Rb2	122.4 (2)
O2—Rb1—Rb2	111.55 (16)	O1—Ti1—O11	83.6 (3)
O2—Rb1—Rb2	75.04 (14)	O1—Ti1—O5^i	78.6 (3)
O3—Rb1—O11	124.26 (18)	O1—Ti1—O2	83.3 (3)
O3—Rb1—O12	58.32 (13)	O1—Ti1—O6	86.5 (3)
O3—Rb1—O5^i	76.25 (14)	O1—Ti1—O12^i	171.4 (4)
O3—Rb1—O6	90.84 (14)	O1—Ti1—Rb2	45.30 (17)
O3—Rb1—O7^i	52.69 (12)	O11—Ti1—O5^i	92.7 (3)
O3—Rb1—O8	146.38 (18)	O11—Ti1—O2	166.6 (4)
O3—Rb1—Rb2	156.50 (16)	O11—Ti1—O6	88.9 (3)
O3—Rb1—Rb2	55.16 (13)	O11—Ti1—O12^i	96.8 (3)
O3—Rb1—Rb2	77.89 (12)	O11—Ti1—Rb2	116.2 (3)
O11—Rb1—O12	104.66 (17)	O5^i—Ti1—O2	87.6 (3)
O11—Rb1—O5^i	55.02 (12)	O5^i—Ti1—O6	164.7 (3)
O11—Rb1—O6	132.45 (14)	O5^i—Ti1—O12^i	92.8 (3)
O11—Rb1—O7^i	74.42 (14)	O5^i—Ti1—Rb2	49.73 (16)
O11—Rb1—O8	52.4 (4)	O2—Ti1—O6	87.3 (3)
O11—Rb1—Rb2	78.45 (12)	O2—Ti1—O12^i	96.5 (4)
O11—Rb1—Rb2	157.30 (14)	O2—Ti1—Rb2	54.9 (2)
O11—Rb1—Rb2	85.20 (13)	O6—Ti1—O12^i	102.1 (3)
O12—Rb1—O5^i	102.81 (15)	O6—Ti1—Rb2	116.3 (2)
O12—Rb1—O6	121.87 (17)	O12^i—Ti1—Rb2	128.2 (3)
O12—Rb1—O7^i	52.52 (12)	Rb1—Ti2—O3	44.80 (16)
O12—Rb1—O8	88.9 (2)	Rb1—Ti2—O12	49.99 (17)
O12—Rb1—Rb2	113.92 (14)	Rb1—Ti2—O7^i	60.6 (2)
O12—Rb1—Rb2	54.13 (12)	Rb1—Ti2—O4	128.7 (2)
O12—Rb1—Rb2	132.96 (15)	Rb1—Ti2—O11	129.1 (3)
O5^i—Rb1—O6	116.89 (15)	Rb1—Ti2—O8	110.2 (4)
O5^i—Rb1—O7^i	50.29 (12)	O3—Ti2—O12	83.8 (3)
O5^i—Rb1—O8	107.1 (4)	O3—Ti2—O7^i	86.7 (3)
O5^i—Rb1—Rb2	126.66 (13)	O3—Ti2—O4	172.3 (3)
O5^i—Rb1—Rb2	131.40 (14)	O3—Ti2—O11	93.3 (3)
O5^i—Rb1—Rb2	46.04 (11)	O3—Ti2—O8	89.8 (3)
O6—Rb1—O7^i	141.81 (14)	O12—Ti2—O7^i	86.1 (3)
O6—Rb1—O8	115.2 (3)	O12—Ti2—O4	88.6 (3)
O6—Rb1—Rb2	74.56 (10)	O12—Ti2—O11	175.8 (4)
O6—Rb1—Rb2	67.75 (11)	O12—Ti2—O8	83.5 (4)
O6—Rb1—Rb2	70.88 (13)	O7^i—Ti2—O4	92.6 (3)
O7^i—Rb1—O8	102.8 (3)	O7^i—Ti2—O11	96.7 (3)
O7^i—Rb1—Rb2	143.56 (13)	O7^i—Ti2—O8	169.3 (5)
O7^i—Rb1—Rb2	94.43 (13)	O4—Ti2—O11	94.3 (3)
O7^i—Rb1—Rb2	88.50 (14)	O4—Ti2—O8	89.5 (3)
O8—Rb1—Rb2	40.7 (2)	O11—Ti2—O8	93.5 (4)
O8—Rb1—Rb2	113.5 (3)	Rb1—As1—O1	63.95 (19)
O8—Rb1—Rb2	129.2 (3)	Rb1—As1—O2	52.82 (17)
Rb2—Rb1—Rb2	101.71 (13)	Rb1—As1—O3	94.9 (2)
Rb2—Rb1—Rb2	113.11 (10)	Rb1—As1—O4	154.2 (2)
Rb2—Rb1—Rb2	114.72 (11)	O1—As1—O2	107.9 (2)
Rb1—Rb2—Ti1	55.92 (14)	O1—As1—O3	112.8 (3)
Rb1—Rb2—As2^i	54.17 (11)	O1—As1—O4	111.8 (3)
Rb1—Rb2—O4	78.21 (11)	O2—As1—O3	103.9 (3)
Rb1—Rb2—O11	45.57 (11)	O2—As1—O4	110.7 (3)
Rb1—Rb2—O7^i	46.43 (10)	O3—As1—O4	109.4 (2)
Rb1—Rb2—Rb1	119.01 (11)	Rb2—As2^i—O5^i	85.3 (2)
Rb1—Rb2—O3^i	127.52 (12)	Rb2—As2^i—O7^i	57.01 (17)
Rb1—Rb2—O12^i	80.61 (14)	Rb2—As2^i—O6^i	163.0 (2)
Rb1—Rb2—Rb1^i	102.03 (9)	Rb2—As2^i—O8^i	64.0 (4)
Rb1—Rb2—O2^i	135.38 (13)	O5^i—As2^i—O7^i	106.8 (3)
Rb1—Rb2—O8^i	81.8 (2)	O5^i—As2^i—O6^i	111.5 (2)
Rb1—Rb2—Rb1	100.59 (14)	O5^i—As2^i—O8^i	111.4 (3)
Rb1—Rb2—Ti1	135.28 (15)	O7^i—As2^i—O6^i	112.9 (3)
Rb1—Rb2—O1	102.30 (15)	O7^i—As2^i—O8^i	104.2 (4)
Rb1—Rb2—O5	148.29 (15)	O6^i—As2^i—O8^i	109.8 (4)
Ti1—Rb2—As2^i	55.02 (14)	Rb1—O1—Ti1	96.4 (2)
Ti1—Rb2—O4	83.76 (14)	Rb1—O1—As1	87.8 (2)
Ti1—Rb2—O11	30.42 (14)	Rb1—O1—Rb2	86.70 (17)
Ti1—Rb2—O7^i	76.34 (16)	Ti1—O1—As1	129.4 (3)
Ti1—Rb2—Rb1	65.79 (13)	Ti1—O1—Rb2	101.1 (2)
Ti1—Rb2—O3^i	78.33 (14)	As1—O1—Rb2	129.5 (3)
Ti1—Rb2—O12^i	26.63 (13)	Rb1—O2—As1	98.6 (2)
Ti1—Rb2—Rb1^i	97.60 (13)	Rb1—O2—Ti1	121.9 (3)
Ti1—Rb2—O2^i	121.32 (17)	Rb1—O2—Rb2	106.33 (18)
Ti1—Rb2—O8^i	62.60 (15)	As1—O2—Ti1	130.0 (3)
Ti1—Rb2—Rb1	146.87 (16)	As1—O2—Rb2	101.5 (2)
Ti1—Rb2—Ti1	152.06 (18)	Ti1—O2—Rb2	94.3 (3)
Ti1—Rb2—O1	147.77 (17)	Rb1—O3—Ti2	103.8 (2)
Ti1—Rb2—O5	153.47 (17)	Rb1—O3—As1	128.1 (2)
As2^i—Rb2—O4	128.41 (14)	Rb1—O3—Rb2	79.61 (14)
As2^i—Rb2—O11	75.48 (15)	Ti2—O3—As1	127.5 (3)
As2^i—Rb2—O7^i	28.45 (11)	Ti2—O3—Rb2	97.9 (2)
As2^i—Rb2—Rb1	105.23 (13)	As1—O3—Rb2	98.5 (2)
As2^i—Rb2—O3^i	79.98 (12)	Rb2—O4—Ti2	98.2 (2)
As2^i—Rb2—O12^i	58.46 (13)	Rb2—O4—As1	126.5 (2)
As2^i—Rb2—Rb1^i	52.37 (9)	Ti2—O4—As1	131.3 (3)
As2^i—Rb2—O2^i	86.64 (15)	Rb1—O11—Rb2	95.66 (15)
As2^i—Rb2—O8^i	28.2 (2)	Rb1—O11—Ti1	95.5 (2)
As2^i—Rb2—Rb1	133.65 (13)	Rb1—O11—Ti2	98.8 (3)
As2^i—Rb2—Ti1	107.18 (16)	Rb2—O11—Ti1	102.1 (2)
As2^i—Rb2—O1	93.43 (16)	Rb2—O11—Ti2	110.8 (3)
As2^i—Rb2—O5	139.32 (15)	Ti1—O11—Ti2	142.4 (3)
O4—Rb2—O11	55.71 (13)	Rb1—O12—Ti2	96.4 (2)
O4—Rb2—O7^i	123.00 (16)	Rb1—O12—Rb2	77.44 (16)
O4—Rb2—Rb1	79.39 (13)	Rb1—O12—Ti1	123.9 (3)
O4—Rb2—O3^i	124.39 (15)	Ti2—O12—Rb2	96.6 (2)
O4—Rb2—O12^i	98.95 (14)	Ti2—O12—Ti1	139.3 (3)
O4—Rb2—Rb1^i	178.52 (13)	Rb2—O12—Ti1	97.9 (3)
O4—Rb2—O2^i	144.78 (15)	Rb1—O5^i—Ti1	101.5 (3)
O4—Rb2—O8^i	146.34 (15)	Rb1—O5^i—As2^i	104.4 (2)
O4—Rb2—Rb1	67.44 (11)	Rb1—O5^i—Rb2	85.73 (14)
O4—Rb2—Ti1	121.50 (15)	Ti1—O5^i—As2^i	131.5 (3)
O4—Rb2—O1	117.30 (17)	Ti1—O5^i—Rb2	97.7 (2)
O4—Rb2—O5	91.52 (13)	As2^i—O5^i—Rb2	124.4 (2)
O11—Rb2—O7^i	85.66 (16)	Rb1—O6—Ti1	97.6 (2)
O11—Rb2—Rb1	75.18 (12)	Rb1—O6—As2	128.7 (2)
O11—Rb2—O3^i	104.29 (14)	Ti1—O6—As2	133.5 (3)
O11—Rb2—O12^i	54.31 (13)	Rb1—O7^i—Rb2	92.79 (15)
O11—Rb2—Rb1^i	125.48 (14)	Rb1—O7^i—Ti2	88.4 (2)
O11—Rb2—O2^i	151.51 (17)	Rb1—O7^i—As2^i	93.2 (2)
O11—Rb2—O8^i	91.12 (17)	Rb2—O7^i—Ti2	139.8 (3)
O11—Rb2—Rb1	116.62 (15)	Rb2—O7^i—As2^i	94.5 (2)
O11—Rb2—Ti1	177.21 (17)	Ti2—O7^i—As2^i	125.5 (3)
O11—Rb2—O1	146.46 (19)	Rb1—O8—Ti2	109.7 (6)
O11—Rb2—O5	144.91 (16)	Rb1—O8—Rb2	104.3 (2)
O7^i—Rb2—Rb1	133.66 (15)	Rb1—O8—As2	114.1 (4)
O7^i—Rb2—O3^i	103.08 (14)	Ti2—O8—Rb2	99.0 (2)
O7^i—Rb2—O12^i	86.13 (15)	Ti2—O8—As2	132.4 (3)
O7^i—Rb2—Rb1^i	56.93 (11)	Rb2—O8—As2	87.8 (6)

Symmetry code: (i) −x+1/2, y+1/2, z+1/2.