Synchrotron X-ray study of ortho­rhombic Rb₃Ta₅O₁₄ with a modified pyrochlore structure

The structure of a new orthorhombic trirubidium pentatantalum oxide (Rb₃Ta₅O₁₄) phase with Pnma symmetry was identified from a half sphere of synchrotron X-ray data measured at a wavelength of 0.85 Å. This notionally linked TaO₆ octahedral structure broadly consists of three different modifications of the pyrochlore ring motif with layer stacking normal to (205) planes. Successive pyrochlore layers do not simply stack normal to these planes but are offset along the [100] axis. An unusual aspect of this structure is the occurrence of TaO₅ trigonal bipyramids in structurally complex regions where the modified pyrochlore rings connect.

S1. Comment

The structure of this RbTaO phase, as shown in Fig. 1, contains four independent Rb atoms, seven independent Ta atoms, seventeen independent O atoms and is comprised of three distinct Rb filled cavities (see Fig. 2(a)) delimited by predominantly corner sharing TaO₆ octahedra. One of those cavities having explicit 1 symmetry is large enough to hold four Rb (2× Rb3 and 2× Rb4) atoms, while the other two exhibit explicit m symmetry, with pseudo 1 symmetry, and contain only two Rb atoms (2× Rb1 or 2× Rb2). A diverse range of polyhedral linkages are exhibited by this structure: the Ta1O₆ and Ta2O₆ octahedra share one common edge: Ta4O₆ octahedra share a single edge with a Ta6O₆ octahedra: the Ta6O₆ octahedra edge shares with two Ta4O₆ octahedra and a Ta5O₅ trigonal bipyramid.

The structure reported here closely resembles that of the analogue material Cs₃Ta₅O₁₄ as reported by Serafin & Hoppe (1982). Those authors report an orthorhombic unit cell, a=26.235, b=7.429, c=7.388 Å with Pbam symmetry. Their structure has two distinct cavities, consisting of a large 4× Cs filled cavity linked to four equivalent 2× Cs filled cavities. In their analogue both cavities have mirror symmetry, though for the larger cavity it is explicitly 2/m. There is a very good structural match between Cs₃Ta₅O₁₄ and Rb₃Ta₅O₁₄ if a pseudo mirror plane present at y=1/2 in the latter structure becomes exact. This would halve the b axis giving close lattice parameter agreement. It would also require the Rb3 and Rb4 atoms to sit exactly on a mirror plane and force the Rb1 and Rb2 filled cavities to adopt some common, intermediate, and presumably more regular geometry. In so doing the Ta6 centered octahedra, which edge shares with two other octahedra and the Ta5 trigonal-bipyramid, would have to deform further into a trigonal-bipyramid identical to, but still edge sharing with, that of Ta5. Ta1, Ta2, Ta3 and Ta4 already have decidedly asymmetric octahedral geometries with five short and one long Ta—O bond, so a structural transition of the type just described for Ta6 is not unreasonable.

The Cs₃Ta₅O₁₄ structure reported by Serafin & Hoppe (1982) could be considered an archetype from which Rb₃Ta₅O₁₄ deviates. But in fact those authors reported a rather large agreement index R(F)=0.10 and refined their structure with isotropic Ta and O atoms constraints. It is not inconceivable that those authors may have overlooked a very subtle deviation from their own archetype, towards that of Rb₃Ta₅O₁₄. It would have been apparent as very weak l=n+1/2 reflections corresponding to a doubling of their c axis.

To aid in classifying this material more completely, it is useful to relate its structure to polyhedral stacking sequences of related archetype structures. The hexagonal tungsten bronze (HTB) archetype (Kihlborg & Hussain 1979), K_0.32WO₃ has P6₃/mcm symmetry consisting of entirely corner shared WO₆ octahedra arranged in linked coplanar six membered rings such that each octahedron is involved in two rings. This leads to hexagonal shaped cavities containing K atoms and small triangular shaped cavities where three six-membered rings pack. HTB has a one layer repeat structure, with successive octahedral ring system layers stacked, corner-sharing, in perfect alignment. In the Cd₂Nb₂O₇ pyrochlore (Lukaszewicz et al., 1994) variation on HTB, additional tilting of the octahedra in the plane of the six membered rings leads the triangular cavities to split into two separate classes, one small and one large alternating in sequence around each ring. The smaller cavities are actually capped by isolated NbO₆ octahedra on a second layer, with the pyrochlore ring structure repeated again in the third layer, i.e. it is a two layer repeat structure.

Figure 3 shows a (2 0 5) plane cross section through the Rb₃Ta₅O₁₄ structure. It clearly shows three distinct variations of the pyrochlore ring system which extend in chains infinitely along the b axis. The next (2 0 5) plane layer (Fig. 4) illustrates a network of cavities and channels with isolated polyhedra delimiting the channel and cavity walls. These are analogues of the cavity capping octahedra above the small triangular cavities around the true pyrochlore rings in the Cd₂Nb₂O₇ structure. Subsequent layers are simply repeats of these first two layers, but with an offset equal to one unit cell translation along the a axis. This description suggests that Rb₃Ta₅O₁₄ has a two layer repeat structure similar to pyrochlore, but in fact the small planar sub-sections illustrated in Figures 3 and 4 coexist in the same plane, alternating as chains of rings and channels running parallel to b. Strictly speaking then, Rb₃Ta₅O₁₄ is a single layer structure, with large oscillatory offsets oriented such that the structure normal to those planes is never repeated with perfect alignment.

It can be seen in Fig. 3 that the large and very distorted eight membered pyrochlore-like ring system has two pairs of nearly parallel edges comprised of pairs of edge sharing (Ta1O₆ and Ta2O₆) octahedra. Those edge sharing octahedra are corner linked to a trigonal bipyramid (Ta5O₅) and octahedra (Ta6O₆) that edge share in successive isolated layers. Unbroken chains of Ta1 and Ta2 centered octahedra, followed by Ta5O₅ and Ta6O₆ polyhedra repeat infinitely along the a axis and clearly delimit the walls of a long channel containing the Rb3 and Rb4 atoms, as shown in Fig 2(a).

The two distinct six membered, pyrochlore-like ring systems are also shown in Fig. 3. One of those, containing the Rb1 atoms, is comprised entirely of corner sharing octahedra and more closely resembles the pyrochlore archetype. The other pyrochlore like ring containing the Rb2 atoms is comprised of two pairs of octahedra, each pair edge sharing to a common third octahedra, though only one of which is fully contained in the Fig.3 planar subsection. This edge sharing deforms the pyrochlore ring structure to a greater extent than is seen for the Rb1 pyrochlore ring. A sequence of purely corner sharing Ta7O₆ octahedra form continuous chains parallel to the a axis which appear in Fig. 2(a) as walls separating the Rb1 and Rb2 filled channels.

The pyrochlore-like layers, isolated layers and channels are all different aspects of a structure that could be described more collectively as a network of three complex, irregularly shaped, Rb filled cavities with edges delimited by Ta—O polyhedra. Each has six large openings where the cavity faces intersect, typically hexagonal in shape but for the large 4× Rb filled cavities connected along the [1 0 0] axis, those channels resemble larger puckered octagonal faces.

All of the three independent cavities in Rb₃Ta₅O₁₄ interfaces with two cavities of the same type stacked along the short a axis (see Fig. 2(a)) and also to four cavities of an alternate size along the four approximate [0 ±1 ±1] vectors (actually [5 2 - 2] in Fig. 2(c)). Figure 2(b) and (c) are images of the lattice oriented to highlight the continuous channels through the cavity [0 ±1 ±1] interfaces. The projection axes of these figures correspond broadly to uninterupted horizontal and diagonal paths in the plane of the Fig. 4 isolated polyhedral layer. For Fig. 2(b) the planar cavity interfaces are oriented at around 30° to the image projection vector so the linear channels appear quite narrow. In this image the channels intersect different cavities in the sequence 2× Rb1–4× Rb(3,4)–2× Rb2–4× Rb(3,4). In Fig. 2(c) the ≈ [0 ±1 ±1] cavity interfaces are normal to the viewing vector, but the off centered alignment of consecutive interfaces reduces the aparent aperture of the channels. Here the channels intersect the cavities in two distinct sequences i.e. 2× Rb1–4× Rb(3,4)–2× Rb1–4× Rb(3,4) and 2× Rb2–4× Rb(3,4)–2× Rb2–4× Rb(3,4)

In the current Rb₃Ta₅O₁₄ study, the atomic displacement parameters of all 28 atoms were refined using an anisotropic model. For all Rb atoms, very large mean squared displacements were observed. This matches similar findings for the Cs atoms in Cs₃Ta₅O₁₄. Large displacement parameters have been reported for Rb atoms in a number of other inorganic materials (Desgardin et al., 1977; Okada et al., 1977; Goodenough et al., 1976; Gasperin & le Bihan, 1980; Michel, 1980). In general such displacements should be understandable in terms of the the atomic packing, interpreted in terms of coordination number, bond lengths and bond angles.

The O coordination numbers are 18, 15, 11 and 15 for Rb1, Rb2, Rb3 and Rb4 respectively, with all coordinating Rb—O contacts shorter than 4.25 Å. For Rb1 the shortest two of those contacts are collinear along a ≈ [0 0 1] vector and are matched by a correspondingly small U₃₃ component. In contrast Rb2 has more nearly isotropic vibrational motion reflecting the more even, angular distribution of its contacts. Two Rb3 atoms are located close to the centre of the large cavity. They have one short Rb3—O16 bond and also four short Rb3—Rb contacts in the (0 1 0) plane [Rb3—Rb3: 3.5097 (18) and 4.1508 (19) Å; Rb3—Rb4: 3.6412 (15)and 3.8795 (18) Å]. These bonds are significantly shorter than the 4.95 Å Rb—Rb bonds in metallic (bcc) Rb (Barrett, 1956). Vibrations orthogonal to that plane are consequently much larger for Rb3. The Rb4 atoms are located near wedge shaped corners of the large cavity and have very large U₂₂ vibrations (.1057 (11) Ų). This is quite understandable because the planes of that `wedge' are actually planar intercavity interfaces, i.e. channels along which the Rb4 atoms have a greater degree of freedom. These channels were shown in Fig. 2(b). Rb4 has one very short Rb4—O15 bond to an O atom in the middle of the `wedge edge' and may undergo some degree of librational motion with respect to that "edge" axis.

The existance of such short Rb3—Rb3 bonds in this structure, oriented along [1 0 0] channels suggest that some degree of metallic conductivity may occur. If Li could be substituted for Rb this material may be an ionic conductor.

S2. Experimental

Rb₃Ta₅O₁₄ crystals were grown as a by product of attempts to form four layered Rb₂Ca₂Ta₄O₁₃ perovskites using a flux technique. Reagent grade chemicals, 5.0 g in total were comprised of Rb₂CO₃ (0.2 mmol) CaCO₃ (0.4 mmol) Ta₂O₅(0.4 mmol) with an RbCl(39 mmol) flux. The dry mixture was placed in a Pt crucible and heated rapidly to 1373 K in a resistance furnace. This maximum temperature was sustained for 10 h, followed thereafter by very slow cooling at 2.8 K h^-1 down to 723 K. Subsequently the sample was cooled rapidly to room temperature. Transparent rectangular prisms of the Rb₃Ta₅O₁₄ phase described herein grew in conjunction with another, as yet unsolved, hexagonal phase of expected composition Ca₂Ta₂O₇, as determined approximately using X-ray fluorescence. For the particular single-crystal used for this experiment an EDAX analysis showed no measurable Ca content.

S3. Refinement

A small 66× 56× 19 µm crystal exhibiting (100), (010) and (001) faces was used for structural analysis. A half sphere of diffraction data to 2θ=100° was measured at 0.8499 (1) Å wavelength, carefully chosen to avoid the 0.81554 Å Rb K absorption edge (Sasaki, 1990). The data were measured using the Diff14A software (Vaalsta & Hester, 1997) to drive a horizontal-type four-circle Rigaku diffractometer mounted on BL14A (Satow &Iitaka 1989) of the Photon factory synchrotron Tsukuba. The wavelength was calibrated using a spherically ground standard Si crystal. An 8 channel avalanche photodiode detector was used for photon counting (Kishimoto et al., 1998). Six standard reflections were measured every 194 reflections and variation of those standards remained within 0.8% for four of the more intense standards and within 2.5% for the weaker two.

The direct methods phasing algorithms of the SHELXS97 (Sheldrick 1997) package provided an initial solution assuming P2₁11 symmetry. This was subsequently refined and transformed to the correct origin using Xtal3.7 (Hall et al. 2001), with PLATON (Spek 2001) suggesting the final Pnma symmetry adopted here. The measured reflection intensities largely conform with the systematic absences expected of this space group, though of the 2436 measured absences, 273 had I ≥ 3σ(I), especially those violating the conditions 0kl:k+l=2n and hk0;h=2n. Inspection of the the most intense of those reflections suggested poor equivalence amongst Friedel pairs, which typically differed by more than a factor of 2. It is possible that these absence violations are Renninger reflections arising from multiple scattering from other reciprocal lattice points on the Ewald sphere. The high scattering cross section of Ta in conjunction with the high density of reciprocal lattice points owing to the large c axis parameter in real space, serve to enhance the likelihood of such scattering processes. On the other hand the atomic displacement parameters as well as the charge density, as detailed below, suggest that some small structural cause may exist, lowering the symmetry.

The merging R-Factor reduced from 5.89% to 5.3% after applying an analytical absorption correction (Meulenaer & Tompa 1965). Dispersion and absorption coefficients were determined from the tables of Sasaki (1989,1990) and the final weighted least squares R-factor reduced to wR(F)=0.046.

The final Δρ difference maps indicate a maximum peak of 7.4 e Å^-3 very close to the Rb1 atom core, with all other peaks ≤4.7 e Å^-3. The largest magnitude electron depletion of -9.2 e Å^-3 is also located diametrically across the Rb1 nucleus, giving the appearance of a strong dipole across this atom. Omitting the Rb1 atom from a structure factor calculation, reveals a rounded triangular region of electron density with two vertices symmetric across the mirror plane. This suggests that either the mirror plane is only a pseudo mirror or Rb1 may be statically disordered, dynamically disordered or a mixture of both. Similar Δρ topography is observed around Rb2, also on the mirror plane, but the maximum and minimum values are around 1/4 the values for Rb1. Minor evidence of other potential mirror plane irregularities comes from Ta1, Ta2, Ta5, Ta6, O1, O2, O5 and O6 which all have m-symmetry in conjunction with slightly larger U₂₂ vibrational components. On the other hand O9 and O10 also have m-symmetry but do not exhibit such tendencies.

To test if the mirror symmetry was really broken by the Rb1 atom site, the structure was refined in three lower symmetry subgroups of Pnma. The Δρ topography localized around Rb1 atom persisted in all of Pn2₁a, P2₁/n11 and P112₁/a albeit with slightly different maximum and minimum magnitudes. R-factors for the three lower symmetry solutions were wR(F)=0.042, 0.045 and 0.049 respectively. This common topography suggests that the Pnma symmetry adopted here is appropriate and either the Rb1 atom is vibrating anharmonically, or it is disordered across three positions (two related by m-symmetry). A refinement of two disordered Rb1 atom sites was attempted in the Pnma space group and this reduced wR(F) from 0.0462 to 0.0458. Purely for conciseness though, only the simplest structural form was adopted herein.

Additional strong Δρ depletions ≥-7.8 e/ų are located around several of the Ta atoms. Given the large atomic number of Ta and the typically deformed octahedral environment of these atoms, such large residual charge densities are not unexpected.

Computing details

Data collection: Diff14A (Vaalsta & Hester, 1997; cell refinement: Xtal LATCON (Hall, du Boulay & Olthof-Hazekamp, 2000); data reduction: Xtal DIFDAT SORTRF ABSORB ADDREF; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: Xtal CRYLSQ (Hall, du Boulay & Olthof-Hazekamp, 2000); molecular graphics: ATOMS (Dowty, 1995) and Xtal ORTEP (Hall, du Boulay & Olthof-Hazekamp, 2000); software used to prepare material for publication: Xtal BONDLA CIFIO (Hall, du Boulay & Olthof-Hazekamp, 2000).

Figures

	Fig. 1. Selectively labeled bonds with mean squared atomic displacements (ORTEP; Johnson, 1970) shown at the 90% probability level and projected down the a axis of Rb3Ta5O14. Ta5 and Ta6 are occluded behind the Ta1 and Ta2 atoms respectively.
	Fig. 2. Polyhedral (Dowty, 1995) sphere, 13 Å radius, centered on 1/2 1/2 1/2 showing the [100] channels (a), the [0 1 0] channels (b) and [52–2] channels (c).
	Fig. 3. An ATOMS (Dowty, 1995) polyhedral view of a (205) plane slice through the Rb3Ta5O14 unit cell showing the pyrochlore-like layering.
	Fig. 4. A second (205) plane slice revealing the isolated polyhedral layers by which successive pyrochlore-like layers connect.

(I)

Crystal data

O14Rb3Ta5	F(000) = 4704
Mr = 1385.13	Dx = 6.653 Mg m^−3
Orthorhombic, Pnma	Synchrotron radiation, λ = 0.8499 Å
Hall symbol: -p 2ac 2n	Cell parameters from 10 reflections
a = 7.3677 (3) Å	θ = 21.6–43.8°
b = 14.7904 (19) Å	µ = 62.9 mm^−1
c = 25.379 (3) Å	T = 298 K
V = 2765.6 (5) Å^3	Prism, colourless
Z = 8	0.07 × 0.04 × 0.04 mm

Data collection

Tsukuba-BL14A diffractometer	Rint = 0.053
ω/2θ scans	θmax = 50.0°, θmin = 1.9°
Absorption correction: analytical Xtal ABSORB	h = −13→13
Tmin = 0.093, Tmax = 0.220	k = −26→26
35705 measured reflections	l = 0→45
8727 independent reflections	6 standard reflections every 194 reflections
8498 reflections with F > 0.00σ(F)	intensity decay: none

Refinement

Refinement on F	0 constraints
Least-squares matrix: block diagonal per atom	Weighting scheme based on measured s.u.'s
R[F^2 > 2σ(F^2)] = 0.043	(Δ/σ)max = 0.002
wR(F^2) = 0.047	Δρmax = 7.30 e Å^−3
S = 3.24	Δρmin = −8.47 e Å^−3
8498 reflections	Extinction correction: Zachariasen, Eq22 p292 "Cryst. Comp." Munksgaard 1970
219 parameters	Extinction coefficient: 3229 (79)
0 restraints

Special details

Refinement. The structure reported herein exhibits substantial excess charge density around the Rb1 atom site. Currently we cannot say with any certainty whether this is static or dynamic disorder.

A static disorder model was identified that does soak up this residual charge density in the Pnma structure reported here:

Rb1a. 3238 (5). 25000. 20886 (13). 0265 (6) Uani ? ? 0.33333 ? ? Rb1b. 3679 (4). 2664 (2). 20624 (11). 0452 (7) Uani ? ? 0.33333 ? ?

Populations on Rb1a and Rb1b were initially constrained so Rb1a+2*Rb1b =1.0 but the populations refined to 0.345 (9) and 0.327 (5) respectively so that 1/3 occupancies can be assumed.

Rather than report a potentially incorrect static disorder model we would prefer to reserve a judgement on this until after further study. Consequently we have opted to report here only the simplest structural model.

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

	x	y	z	Uiso*/Ueq
Ta1	0.59012 (5)	0.25000	0.055516 (12)	0.00847 (11)
Ta2	0.56477 (4)	0.75000	0.056538 (12)	0.00790 (11)
Ta3	0.87054 (3)	0.122947 (14)	0.153044 (9)	0.00797 (8)
Ta4	0.86990 (3)	0.619041 (14)	0.143707 (9)	0.00798 (8)
Ta5	0.10701 (4)	0.25000	0.055358 (12)	0.00766 (11)
Ta6	0.08242 (4)	0.75000	0.061507 (12)	0.00728 (10)
Ta7	0.14177 (3)	0.510800 (15)	0.244574 (9)	0.00820 (8)
Rb1	0.3492 (3)	0.25000	0.20738 (6)	0.0614 (11)
Rb2	0.3772 (2)	0.75000	0.20607 (6)	0.0434 (7)
Rb3	0.77262 (18)	0.48708 (8)	0.01916 (4)	0.0448 (5)
Rb4	0.3709 (2)	0.49714 (10)	0.11782 (4)	0.0570 (7)
O1	0.8554 (8)	0.25000	0.0140 (2)	0.009 (2)
O2	0.8292 (9)	0.75000	0.0189 (2)	0.010 (2)
O3	0.6766 (7)	0.1562 (3)	0.10024 (17)	0.0128 (16)
O4	0.6557 (7)	0.6541 (3)	0.10003 (19)	0.0142 (17)
O5	0.3505 (9)	0.25000	0.0841 (3)	0.014 (2)
O6	0.3275 (9)	0.75000	0.0881 (3)	0.014 (2)
O7	0.0439 (7)	0.1418 (3)	0.08610 (17)	0.0143 (17)
O8	0.0340 (7)	0.6249 (3)	0.07541 (17)	0.0127 (16)
O9	0.9087 (10)	0.25000	0.1707 (3)	0.014 (2)
O10	0.9497 (10)	0.75000	0.1378 (2)	0.011 (2)
O11	0.7068 (7)	0.0946 (3)	0.20634 (17)	0.0135 (17)
O12	0.7142 (7)	0.6091 (3)	0.20344 (17)	0.0130 (16)
O13	1.0823 (6)	0.0851 (3)	0.19225 (17)	0.0113 (15)
O14	1.0809 (6)	0.5991 (3)	0.19004 (17)	0.0118 (16)
O15	0.4014 (6)	0.5111 (3)	0.22497 (18)	0.0124 (17)
O16	0.8478 (7)	0.0015 (2)	0.12222 (18)	0.0104 (16)
O17	0.5121 (6)	0.1633 (3)	−0.00075 (16)	0.0119 (16)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ta1	0.00412 (11)	0.01309 (11)	0.00819 (11)	0.00000	−0.00125 (10)	0.00000
Ta2	0.00292 (11)	0.01326 (11)	0.00751 (10)	0.00000	−0.00061 (9)	0.00000
Ta3	0.00584 (9)	0.00896 (8)	0.00912 (8)	−0.00045 (6)	−0.00032 (7)	0.00080 (6)
Ta4	0.00563 (9)	0.00884 (8)	0.00945 (8)	−0.00037 (6)	−0.00032 (7)	0.00086 (6)
Ta5	0.00433 (11)	0.01144 (11)	0.00722 (10)	0.00000	0.00070 (9)	0.00000
Ta6	0.00347 (11)	0.01085 (10)	0.00752 (10)	0.00000	0.00033 (9)	0.00000
Ta7	0.00286 (8)	0.01291 (8)	0.00883 (8)	0.00011 (7)	−0.00047 (7)	0.00035 (7)
Rb1	0.0707 (13)	0.0767 (12)	0.0368 (7)	0.00000	−0.0074 (9)	0.00000
Rb2	0.0410 (8)	0.0501 (7)	0.0392 (7)	0.00000	0.0011 (7)	0.00000
Rb3	0.0415 (6)	0.0664 (6)	0.0265 (3)	−0.0166 (5)	−0.0049 (5)	0.0027 (4)
Rb4	0.0418 (7)	0.1057 (11)	0.0234 (4)	−0.0116 (6)	0.0050 (5)	−0.0050 (5)
O1	0.005 (2)	0.011 (2)	0.010 (2)	0.00000	0.000 (2)	0.00000
O2	0.009 (2)	0.012 (2)	0.010 (2)	0.00000	0.000 (2)	0.00000
O3	0.0111 (18)	0.0141 (15)	0.0131 (16)	−0.0007 (15)	−0.0046 (16)	0.0019 (14)
O4	0.0109 (18)	0.0167 (17)	0.0151 (17)	0.0015 (16)	−0.0037 (17)	0.0044 (15)
O5	0.010 (2)	0.017 (2)	0.016 (2)	0.00000	0.001 (2)	0.00000
O6	0.006 (2)	0.020 (2)	0.016 (2)	0.00000	−0.003 (2)	0.00000
O7	0.014 (2)	0.0180 (17)	0.0111 (15)	−0.0004 (17)	0.0028 (17)	−0.0022 (15)
O8	0.014 (2)	0.0123 (15)	0.0120 (15)	0.0015 (15)	0.0029 (17)	−0.0001 (13)
O9	0.015 (3)	0.010 (2)	0.016 (2)	0.00000	−0.005 (3)	0.00000
O10	0.013 (3)	0.0061 (18)	0.014 (2)	0.00000	−0.001 (2)	0.00000
O11	0.016 (2)	0.0109 (14)	0.0138 (16)	0.0002 (15)	0.0055 (17)	0.0020 (13)
O12	0.0113 (18)	0.0151 (16)	0.0125 (16)	−0.0015 (15)	0.0027 (17)	0.0010 (14)
O13	0.0081 (16)	0.0130 (15)	0.0127 (15)	0.0004 (14)	−0.0023 (15)	0.0030 (13)
O14	0.0070 (16)	0.0144 (15)	0.0139 (16)	−0.0010 (14)	−0.0040 (15)	0.0034 (14)
O15	0.0035 (16)	0.0237 (19)	0.0100 (15)	−0.0001 (15)	−0.0026 (15)	−0.0032 (15)
O16	0.012 (2)	0.0092 (14)	0.0095 (15)	0.0028 (13)	−0.0005 (16)	−0.0001 (11)
O17	0.0063 (16)	0.0166 (17)	0.0128 (15)	−0.0022 (14)	−0.0026 (16)	0.0001 (13)

Geometric parameters (Å, º)

Ta1—O3^i	1.902 (4)	Rb1—O7^i	4.134 (5)
Ta1—O3	1.902 (4)	Rb1—O7	4.134 (5)
Ta1—O5	1.909 (7)	Rb1—O9	4.226 (8)
Ta1—O17^i	2.003 (4)	Rb1—Rb1^xi	4.272 (3)
Ta1—O17	2.003 (4)	Rb1—Rb1^x	4.272 (3)
Ta1—O1	2.220 (6)	Rb1—Rb4^i	4.3072 (17)
Ta2—O4^ii	1.918 (5)	Rb1—Rb4	4.3072 (17)
Ta2—O4	1.918 (5)	Rb2—O6	3.016 (7)
Ta2—O6	1.923 (7)	Rb2—O14^xii	3.148 (5)
Ta2—O17^iii	1.992 (4)	Rb2—O14^vii	3.148 (5)
Ta2—O17^iv	1.992 (4)	Rb2—O12^ii	3.242 (5)
Ta2—O2	2.170 (6)	Rb2—O12	3.242 (5)
Ta3—O11	1.860 (5)	Rb2—O12^viii	3.325 (5)
Ta3—O13	1.934 (4)	Rb2—O12^xiii	3.325 (5)
Ta3—O9	1.9519 (18)	Rb2—O15^ii	3.571 (5)
Ta3—O16	1.967 (4)	Rb2—O15	3.571 (5)
Ta3—O3	2.020 (5)	Rb2—O10^vii	3.595 (7)
Ta3—O7^v	2.144 (5)	Rb2—O4^ii	3.669 (5)
Ta4—O16^i	1.871 (4)	Rb2—O4	3.669 (5)
Ta4—O12	1.907 (5)	Rb2—O14^viii	3.766 (5)
Ta4—O14	1.972 (4)	Rb2—O14^xiii	3.766 (5)
Ta4—O4	1.997 (5)	Rb2—O10^xiii	3.999 (6)
Ta4—O10	2.030 (2)	Rb2—Rb2^xiii	4.306 (2)
Ta4—O8^v	2.115 (5)	Rb2—Rb2^xiv	4.306 (2)
Ta5—O7	1.840 (5)	Rb2—Rb4^ii	4.3595 (17)
Ta5—O7^i	1.840 (5)	Rb2—Rb4	4.3595 (17)
Ta5—O5	1.937 (7)	Rb3—O16^i	2.679 (5)
Ta5—O2^vi	1.941 (6)	Rb3—O17^i	2.981 (5)
Ta5—O1^vii	2.130 (6)	Rb3—O3^i	3.038 (5)
Ta6—O8^ii	1.917 (4)	Rb3—O8^v	3.147 (5)
Ta6—O8	1.917 (4)	Rb3—O7^xv	3.243 (5)
Ta6—O6	1.928 (7)	Rb3—O8^iii	3.245 (5)
Ta6—O1^iv	1.971 (6)	Rb3—O4	3.325 (5)
Ta6—O2^vii	2.157 (6)	Rb3—O17^iv	3.378 (5)
Ta6—O10^vii	2.168 (6)	Rb3—Rb3^xvi	3.5097 (19)
Ta7—O15^viii	1.932 (5)	Rb3—O1	3.5615 (16)
Ta7—O14^vii	1.955 (4)	Rb3—Rb4^iii	3.6412 (16)
Ta7—O15	1.977 (5)	Rb3—O7^iv	3.768 (5)
Ta7—O13^ix	1.992 (4)	Rb3—Rb4	3.8796 (18)
Ta7—O12^viii	2.035 (4)	Rb3—O2	3.9110 (15)
Ta7—O11^x	2.052 (4)	Rb3—Rb3^iii	4.1508 (19)
Ta7—Rb4	3.6385 (13)	Rb3—Rb4^v	5.072 (2)
Rb1—O9^x	3.126 (7)	Rb4—O15	2.736 (5)
Rb1—O5	3.128 (7)	Rb4—O13^ix	3.093 (5)
Rb1—O13^ix	3.156 (5)	Rb4—O4	3.162 (5)
Rb1—O13^vii	3.156 (5)	Rb4—O14^vii	3.193 (5)
Rb1—O11^viii	3.343 (4)	Rb4—O3^i	3.228 (5)
Rb1—O11^x	3.343 (4)	Rb4—O7^i	3.267 (5)
Rb1—O9^vii	3.377 (8)	Rb4—O8	3.300 (5)
Rb1—O11^i	3.496 (5)	Rb4—O16^i	3.515 (5)
Rb1—O11	3.496 (5)	Rb4—O11^i	3.607 (5)
Rb1—O3^i	3.891 (5)	Rb4—O12	3.723 (5)
Rb1—O3	3.891 (5)	Rb4—O5	3.757 (2)
Rb1—O15^i	3.906 (5)	Rb4—O6	3.829 (2)
Rb1—O15	3.906 (5)	Rb4—O16^ix	3.856 (5)
Rb1—O13^viii	3.923 (5)	Rb4—O17^iv	3.951 (4)
Rb1—O13^x	3.923 (5)	Rb4—O17^i	3.971 (4)
O3^i—Ta1—O3	93.62 (19)	O12—Ta4—O8	176.97 (18)
O3^i—Ta1—O5	94.8 (2)	O14—Ta4—O4	173.25 (18)
O3^i—Ta1—O17^i	93.15 (18)	O14—Ta4—O10	87.6 (2)
O3^i—Ta1—O17	171.16 (18)	O14—Ta4—O8	92.52 (18)
O3^i—Ta1—O1	89.31 (18)	O4—Ta4—O10	86.5 (2)
O3—Ta1—O5	94.8 (2)	O4—Ta4—O8	89.22 (19)
O3—Ta1—O17^i	171.16 (18)	O10—Ta4—O8	74.6 (2)
O3—Ta1—O17	93.15 (18)	O7—Ta5—O7^i	120.9 (2)
O3—Ta1—O1	89.31 (18)	O7—Ta5—O5	94.25 (18)
O5—Ta1—O17^i	90.3 (2)	O7—Ta5—O2	118.20 (14)
O5—Ta1—O17	90.3 (2)	O7—Ta5—O1	89.37 (17)
O5—Ta1—O1	174.1 (3)	O7^i—Ta5—O5	94.25 (18)
O17^i—Ta1—O17	79.57 (18)	O7^i—Ta5—O2	118.20 (14)
O17^i—Ta1—O1	85.10 (17)	O7^i—Ta5—O1	89.37 (17)
O17—Ta1—O1	85.10 (17)	O5—Ta5—O2	98.1 (3)
O4—Ta2—O4	95.4 (2)	O5—Ta5—O1	172.6 (3)
O4—Ta2—O6	94.4 (2)	O2—Ta5—O1	74.5 (2)
O4—Ta2—O17	91.85 (19)	O8—Ta6—O8	149.7 (2)
O4—Ta2—O17	169.78 (19)	O8—Ta6—O6	96.29 (16)
O4—Ta2—O2	86.57 (18)	O8—Ta6—O1	102.84 (13)
O4—Ta2—O6	94.4 (2)	O8—Ta6—O2	86.07 (15)
O4—Ta2—O17	169.78 (19)	O8—Ta6—O10	75.63 (13)
O4—Ta2—O17	91.85 (19)	O8—Ta6—O6	96.29 (16)
O4—Ta2—O2	86.57 (18)	O8—Ta6—O1	102.84 (13)
O6—Ta2—O17	92.2 (2)	O8—Ta6—O2	86.07 (15)
O6—Ta2—O17	92.2 (2)	O8—Ta6—O10	75.63 (13)
O6—Ta2—O2	178.5 (3)	O6—Ta6—O1	97.1 (3)
O17—Ta2—O17	80.11 (18)	O6—Ta6—O2	170.4 (3)
O17—Ta2—O2	86.68 (17)	O6—Ta6—O10	96.3 (3)
O17—Ta2—O2	86.68 (17)	O1—Ta6—O2	73.3 (2)
O11—Ta3—O13	94.8 (2)	O1—Ta6—O10	166.6 (2)
O11—Ta3—O9	98.3 (2)	O2—Ta6—O10	93.3 (2)
O11—Ta3—O16	91.62 (19)	O15—Ta7—O14	94.1 (2)
O11—Ta3—O3	94.5 (2)	O15—Ta7—O15	171.00 (19)
O11—Ta3—O7	172.72 (18)	O15—Ta7—O13	93.83 (19)
O13—Ta3—O9	92.6 (2)	O15—Ta7—O12	88.8 (2)
O13—Ta3—O16	90.51 (19)	O15—Ta7—O11	88.4 (2)
O13—Ta3—O3	169.39 (18)	O15—Ta7—Rb4	141.17 (14)
O13—Ta3—O7	87.97 (18)	O14—Ta7—O15	92.42 (19)
O9—Ta3—O16	169.4 (2)	O14—Ta7—O13	87.33 (18)
O9—Ta3—O3	91.1 (2)	O14—Ta7—O12	92.39 (18)
O9—Ta3—O7	88.3 (2)	O14—Ta7—O11	172.18 (18)
O16—Ta3—O3	84.18 (18)	O14—Ta7—Rb4	61.16 (13)
O16—Ta3—O7	81.62 (18)	O15—Ta7—O13	92.66 (19)
O3—Ta3—O7	82.18 (18)	O15—Ta7—O12	84.7 (2)
O16^i—Ta4—O12	96.1 (2)	O15—Ta7—O11	85.9 (2)
O16^i—Ta4—O14	95.7 (2)	O15—Ta7—Rb4	47.82 (13)
O16^i—Ta4—O4	91.0 (2)	O13—Ta7—O12	177.35 (19)
O16^i—Ta4—O10	155.9 (2)	O13—Ta7—O11	85.12 (17)
O16^i—Ta4—O8	81.36 (18)	O13—Ta7—Rb4	58.20 (13)
O12—Ta4—O14	89.4 (2)	O12—Ta7—O11	95.06 (17)
O12—Ta4—O4	89.2 (2)	O12—Ta7—Rb4	119.43 (13)
O12—Ta4—O10	107.9 (2)	O11—Ta7—Rb4	112.71 (13)

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