A TiP₂O₇ superstructure

A room-temperature structural model of titanium pyrophos­phate, TiP₂O₇, has been determined from synchrotron X-ray data. The structure consists of TiO₆ octahedra and PO₄ tetrahedra sharing corners in a three-dimensional network. The PO₄ tetrahedra form P₂O₇ groups connecting the TiO₆ octahedra. The 3 × 3 × 3 superstructure differs substantially from the parent AB₂O₇ structure. The P-O-P bonding angles of the pyrophosphate group are between 141.21 (12) and 144.51 (13)° for those groups not located on the threefold axis. The individual TiO₆ octahedra and PO₄ tetrahedra are somewhat distorted.

S1. Comment

The parent structure of AB₂O₇ was originally described by Levi & Peyronel (1935) with A^IV = Si, Ti, Zr, Sn or Hf and B^V = P. From powder studies a small cubic unit cell in the space group Pa3 and a = 7.80 (1) Å was found for TiP₂O₇. Further powder studies have expanded the family to include among others, ZrV₂O₇ (Peyronel, 1942), UP₂O₇, ThP₂O₇ (Burdese & Borlera, 1963), AP₂O₇ (A = Si, Ge, Sn, Pb, Ti, Zr, Hf, Ce, U) (Völlenke et al., 1963), AP₂O₇ (A = Ge, Zr, U) (Hagmann & Kierkegaard, 1969), HfV₂O₇ (Baran, 1976), ReP₂O₇ (Banks & Sacks, 1982), MoP₂O₇ (Kinomura et al., 1985) and NbP₂O₇ (Fukuoka et al., 1995). These materials have recently attained a renewed interest because of their small thermal expansion, Korthuis et al. (1995) found that ZrV₂O₇ and the mixed phase of ZrV_{2 - x}P_xO₇, with x up to 0.3, have negative expansion coefficient above 375 K. The materials could also be of use in HPLC as a biocompatible packing material as suggested by Inoue & Ohtaki (1993). \sch

Evidence of a possible 3 × 3 × 3 superstructure at room temperature was first proposed by Völlenke et al. (1963) after careful examination of powder diffraction data for GeP₂O₇. The small AB₂O₇ parent structure had in most cases an unrealistic short B—O—B bridging bond distance in the B₂O₇-group, built by two connected BO₄-tetrahedra. In the smaller parent structure, all B₂O₇-groups are forced to a 180° B—O—B bonding angle since they are located on a threefold axis. The expansions to a 3 × 3 × 3 superstructure removes 96 of the 108 B₂O₇-groups in the unit cell from the threefold axis, allowing them to adopt B—O—B angles less then 180°. The ability to bend the B—O—B angle increases the bond distances for the B—O bonds connecting the BO₄-tetrahedra. For most AB₂O₇ materials, a phase transition occurs at elevated temperatures from the superstructure to the small cubic structure. ZrV₂O₇ has, for example, two phase transitions, first to an incommensurate phase at 350 K (Withers et al., 1998), and then to the AB₂O₇ parent structure at 375 K (Korthuis et al., 1995).

Most of the structural studies of the superstructure have been based on powder diffraction data. So far, only two single-crystal investigations of the superstructures have been published. The SiP₂O₇ superstructure suggested by Tillmanns et al. (1973) was limited by low resolution and therefore restricted to an isotropic model. Evans et al. (1998) studied the ZrV₂O₇ structure using synchrotron X-rays resulting in a model closely related to the parent AB₂O₇ structure. High resolution neutron powder studies of ZrP₂O₇ by Khosrovani et al. (1996) gave P—O—P angles in the range of 134–162° that are far from the 180° of the parent structure. This structural model also contains a wide range of P—O bond distances, in the range 1.44 (1)–1.66 (1) Å. Recent X-ray powder studies combined with NMR data of TiP₂O₇ by Sanz et al. (1997) and further NMR studies by Helluy et al. (2000) shows a distorted structure that is less correlated to the smaller substructure. The model obtained in the powder study by Sanz et al. (1997) was geometrically constrained and only six isotropic displacement parameters were refined for the 50 atoms.

Small, high quality crystals of TiP₂O₇ were prepared in our search for new modifications and isomorphic materials in the KTP family of compounds (KTP = potassium titanyl phosphate, KTiOPO₄; Tordjman et al., 1974) to improve the crystal growth and decrease the ionic conductivity. Our preparation method differs from the usual way of obtaining powder/crystals of TiP₂O₇, which is by reaction of TiO₂ and H₃PO₄ in an autoclave at temperatures around 500 K forming the hydrated phosphate α-Ti(HPO₄)₂·H₂O. Further calcination at temperatures around 900 K results in the formation of TiP₂O₇ (Soria et al., 1993). The good quality of our crystals, prepared by the method described below, prompted us to collect TiP₂O₇ single-crystal data at the MAX II synchrotron radiation facility at Lund University, Sweden.

The TiP₂O₇ structure is built up by TiO₆-octahedra and PO₄-tetrahedra. The TiO₆-octahedra are connected by pyrophosphate groups in a three-dimensional network. Fig. 1 shows the refined TiP₂O₇ room-temperature superstructure together with the smaller parent structure of AB₂O₇ in the (001) plane. The selected distances and angles are listed in Table 1.

The highest intensity of a superlattice reflection for ZrV₂O₇ (Evans et al., 1998) were about 1% of the strongest sublattice reflection, while our data collected for TiP₂O₇ shows much stronger superlattice reflections. Table 2 gives hkl statistics for the TiP₂O₇ data generated by SAINT+ (Bruker, 1999). The mean I/σ(I) is 114.96 for the sublattice and 41.95 for the superlattice, so a rather high proportion of the superlattice reflections has intensities comparable to the sublattice reflections. The highest intensity of a superlattice reflection is approximately 30% of the strongest sublattice reflection.

The TiP₂O₇ superstructure differs considerably from the parent AB₂O₇ structure as indicated by the high intensity of the superlattice reflection (h,k,l ≠ 3n), while the ZrV₂O₇ superstructure (Evans et al., 1998) is closely related to the parent AB₂O₇ substructure. The TiO₆-octahedra and PO₄-tetrahedra in TiP₂O₇ are slightly more distorted then the ZrO₆-octahedra and VO₄-tetrahedra in ZrV₂O₇. The largest difference between the TiP₂O₇ and ZrV₂O₇ superstructure are the B—O—B bridging angles of the B₂O₇-groups located outside a threefold axis. All Ti—O bonds are in the range 1.8884 (16)–1.9453 (16) Å with a mean bonding distance of 1.915 (14) Å. The O—Ti—O angles are between 86.75 (7) and 92.81 (8)°, while the P—O bonds in the Ti—O—P chain are in the range 1.4893 (18)–1.5069 (17) Å with a mean bonding distance of 1.500 (5) Å. The PO₄ tetrahedra bond angles are between 104.16 (10) and 113.61 (10)°.

There are six independent P₂O₇-groups in the unit cell, two of them are constrained to a 180° P—O—P bridging angle, while the other four have P—O—P angles of 141.21 (12)–144.51 (13)° between the PO₄-tetrahedra. This is in good agreement with the combined X-ray powder diffraction/NMR study on TiP₂O₇ by (Sanz et al., 1997), who reported bridging P—O—P angles in the range 139–145°. The mean P—O bond in the bridging P—O—P is for the four unconstrained pyrophosphate groups 1.575 (5) Å compered to 1.536 (4) Å for the constrained ones. The oxygen atoms O5 and O6 bridging PO₄-tetrahedra in the two pyrophosphate group located at a threefold axis show enlarged displacement parameters compared to all other oxygen atoms, as can be seen in Fig. 2, indicating the structural disorder previously suggested by Sanz et al. (1997). The P9—O5—P10 pyrophosphate group seems to have a unlimited numbers of possible bond configurations as shown by the shape of the displacement parameter, while P11—O6—P11 has two possible bond configurations as can be seen in the displacement plot in Fig. 2. The ZrV₂O₇ (Evans et al., 1998) superstructure does not show any enlarged displacement parameters for the oxygen atoms at a threefold axis and has V—O—V angles in the range 159.3 (2)–167.6 (2)°.

Related literature

For related literature, see: Banks & Sacks (1982); Baran (1976); Bruker (1999); Burdese & Borlera (1963); Cerenius et al. (2000); Evans et al. (1998); Fukuoka et al. (1995); Hagmann & Kierkegaard (1969); Hall et al. (2000); Helluy et al. (2000); Inoue & Ohtaki (1993); Khosrovani et al. (1996); Kinomura et al. (1985); Korthuis et al. (1995); Levi & Peyronel (1935); Peyronel (1942); Sanz et al. (1997); Sasaki (1989, 1990); Sheldrick (1997); Soria et al. (1993); Tillmanns et al. (1973); Tordjman et al. (1974); Völlenke et al. (1963); Withers et al. (1998); Zachariasen (1967).

S2. Experimental

The crystals were obtained by spontaneous crystallization from a flux, in a platinum crucible, containing Zn₃(PO₄)₂, P₂O₅, ZnO and TiO₂ carefully mixed together in the molar ratios 1.00:1.55:0.55:1.10. The flux were first dehydrated at 523 K for 15 h and then heated to 1373 K, after which the temperature was decreased to 1073 K by 2.3 K/h. The flux was dissolved in 6 M HCl and the result was a crystalline powder with a weak orange colour. EDX analysis (Electro-scan S4–8DV equipped with a Link eX1 EDX system) indicates no zinc on any of the small, well developed crystals faces.

S3. Refinement

The X-ray beam at the MAX II beamline 711 (Cerenius et al., 2000) was focused, vertically by a bendable quartz mirror coated with Pt, and horizontally by an asymmetrically cut Si(111) monochromator (an asymmetric angle of 7° is used). A 100 µm collimator with an inherent ionization chamber/counting device and the program SAINT+ (Bruker, 1999) was used to adjust for the intensity changes during the data collection. The different series of frames are later normalized with SADABS (part of the SAINT+ package). The X-ray wavelength was calibrated against Si-powder. A total of eight series of frames were collected over 11 h, with a nominal measuring time of 2 sec per frame. The systematic absences (0kl, k = 2n + 1 and 00 l, l = 2n+1) suggested the space group Pa3 (# 205). The structure was solved by direct methods in SHELXS97 (Sheldrick, 1997) and further least-squares refinement was carried out with the Xtal3.7 software package (Hall et al., 2000). 200 weak reflections with F<4σ(F), that had no effect on the final structural model except for improving the s.u. of some atoms, were added during the final least-squares refinement. Anomalous scattering factors for neutral atoms for the appropriate wavelength were taken from Sasaki (1989). The linear absorption coefficient µ was calculated using mass attenuation coefficients for neutral atoms at the wavelength 0.8522 Å (Sasaki, 1990). About 0.5% of the reflections were affected by extinction (Zachariasen, 1967) with a maximum correction of y = 0.76 for the 006 reflection (the observed structure factor is F_obs = yF_kin, were F_kin is the kinematic value of the structure factor).

Computing details

Data collection: SMART-NT (Bruker, 1998); cell refinement: SAINT+ (Bruker, 1999); data reduction: SAINT+ (Bruker, 1999), Xtal3.7 (Hall et al., 2000) DIFDAT ADDREF ABSORB SORTRF; program(s) used to refine structure: SHELXS97 (Sheldrick, 1997), Xtal3.7 (Hall et al., 2000) CRYLSQ; molecular graphics: ORTEPIII (Burnett & Johnson, 1996); software used to prepare material for publication: Xtal3.7 (Hall et al., 2000) BONDLA ATABLE CIFIO.

Figures

Fig. 1. Two polyhedra layers of (a) the TiP2O7 superstructure and (b) the substructure (Levi & Peyronel, 1935) in the (001) plane.

Fig. 2. ORTEPIII (Burnett & Johnson, 1996) views of different pyrophosphate groups. (a) shows a normal bent P2O7 group while (b) and (c) show two kinds of statistical disorder on the threefold symmetry axis. Displacement ellipsoids are drawn at the 80% probability level. [Symmetry codes: (i) 1 - x, - y, - z; (ii) 1 - z, 1 - x, - y; (iii) z + 1/2, - x + 1/2, - y; (iv) 1 - z, - x, - y; (v) 1 - z, x - 1/2, - y + 1/2; (vi) y + 1/2, - z + 1/2, 1 - x; (vii) z + 1/2, x, -y + 1/2; (viii) x + 1/2, y, - z + 1/2; (ix) y + 1/2, z, - x + 1/2; (x) - z + 1/2, x - 1/2, y; (xi) - y + 1/2, - z, x - 1/2.]

(I)

Crystal data

TiP2O7	Melting point: not measured K
Mr = 221.82	Synchrotron x-ray vertical wiggler radiation, λ = 0.8522 (5) Å
Cubic, Pa3	Cell parameters from 7382 reflections
Hall symbol: -P 2ac 2ab 3	θ = 3.6–43.5°
a = 23.5340 (5) Å	µ = 3.74 mm^−1
V = 13034.3 (5) Å^3	T = 293 K
Z = 108	Rectangular, colourless
F(000) = 11664	0.06 × 0.02 × 0.02 mm
Dx = 3.052 Mg m^−3

Data collection

Bruker SMART area 1000 CCD diffractometer	8970 independent reflections
Radiation source: MAX II beamline 711	8363 reflections with F > 4σ(F)
Si(111) assymetric crystal monochromator	Rint = 0.099
area detector scans	θmax = 43.5°, θmin = 1.8°
Absorption correction: multi-scan SADABS (Bruker, 1998)	h = −30→26
Tmin = 0.619, Tmax = 0.928	k = −36→35
82262 measured reflections	l = −34→20

Refinement

Refinement on F	0 constraints
Least-squares matrix: full	w = 1/σ^2(F)
R[F^2 > 2σ(F^2)] = 0.046	(Δ/σ)max = 0.002
wR(F^2) = 0.059	Δρmax = 1.14 e Å^−3
S = 2.78	Δρmin = −1.29 e Å^−3
8563 reflections	Extinction correction: Gaussian (Zachariasen, 1967), Eq22 p292 "Cryst. Comp." Munksgaard 1970
408 parameters	Extinction coefficient: 2303 (43)
0 restraints

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

	x	y	z	Uiso*/Ueq
Ti1	0.656509 (16)	0.160871 (16)	0.169981 (16)	0.00674 (16)
Ti2	0.840233 (16)	−0.003435 (15)	0.178285 (16)	0.00642 (16)
Ti3	0.151885 (16)	−0.007970 (16)	0.164157 (16)	0.00642 (16)
Ti4	0.498987 (15)	−0.004946 (16)	0.163064 (16)	0.00632 (17)
Ti5	0.834060 (15)	0.334060 (15)	0.165940 (15)	0.00629 (11)
Ti6	1	0	0	0.00581 (15)
P1	0.78869 (2)	0.12394 (2)	0.13763 (2)	0.0062 (2)
P2	0.86374 (2)	0.20085 (2)	0.20655 (2)	0.0063 (2)
P3	0.62838 (2)	0.02533 (2)	0.20162 (2)	0.0066 (2)
P4	0.71337 (2)	−0.03675 (2)	0.13010 (2)	0.0061 (2)
P5	0.79039 (2)	0.03176 (2)	−0.03638 (2)	0.0064 (2)
P6	0.87058 (2)	−0.02133 (2)	0.04500 (2)	0.0061 (2)
P7	0.28624 (2)	0.02618 (2)	0.19636 (2)	0.0066 (2)
P8	0.36998 (2)	−0.03562 (2)	0.12360 (2)	0.0064 (2)
P9	0.12310 (2)	0.12310 (2)	0.12310 (2)	0.00695 (15)
P10	0.69856 (2)	0.19856 (2)	0.30144 (2)	0.00702 (15)
P11	0.53761 (2)	−0.03761 (2)	0.03761 (2)	0.00635 (16)
O1	0.81178 (8)	0.17684 (7)	0.17166 (8)	0.0169 (9)
O2	0.68668 (7)	0.00194 (8)	0.17786 (8)	0.0154 (8)
O3	0.81727 (7)	0.01098 (8)	0.02117 (7)	0.0124 (8)
O4	0.31292 (7)	−0.00797 (8)	0.14586 (7)	0.0162 (8)
O5	0.66089 (10)	0.16089 (10)	0.33911 (10)	0.0573 (16)
O6	0.5	0	0	0.037 (2)
O7	0.72509 (7)	0.12814 (7)	0.14237 (8)	0.0140 (8)
O8	0.87117 (7)	−0.07744 (7)	0.19154 (7)	0.0139 (8)
O9	0.80986 (8)	0.07093 (7)	0.16541 (7)	0.0141 (8)
O10	0.85824 (8)	0.26433 (7)	0.20113 (7)	0.0138 (8)
O11	0.68105 (8)	0.23322 (7)	0.14212 (8)	0.0168 (9)
O12	0.18132 (8)	−0.08233 (7)	0.17883 (8)	0.0165 (8)
O13	0.63414 (7)	0.08882 (7)	0.20247 (8)	0.0140 (8)
O14	0.58070 (7)	0.00588 (7)	0.16380 (7)	0.0122 (8)
O15	0.12347 (7)	−0.00010 (7)	0.23995 (7)	0.0113 (7)
O16	0.77582 (7)	−0.03918 (7)	0.14399 (7)	0.0113 (7)
O17	0.86788 (7)	0.31319 (7)	0.09470 (7)	0.0135 (8)
O18	0.50743 (7)	−0.07451 (7)	0.20365 (8)	0.0135 (8)
O19	0.49292 (7)	0.03666 (7)	0.23141 (7)	0.0101 (7)
O20	0.90446 (7)	0.03269 (7)	0.21170 (7)	0.0131 (8)
O21	0.17576 (7)	−0.01031 (7)	0.08536 (7)	0.0127 (8)
O22	0.87816 (7)	−0.00015 (7)	0.10491 (6)	0.0096 (7)
O23	0.91957 (7)	−0.00688 (7)	0.00682 (7)	0.0111 (7)
O24	0.08364 (7)	−0.04439 (8)	0.14278 (8)	0.0150 (8)
O25	0.22335 (7)	0.02472 (7)	0.18604 (7)	0.0137 (8)
O26	0.58611 (7)	0.19490 (8)	0.19196 (8)	0.0156 (8)
O27	0.80249 (7)	−0.00473 (7)	0.24998 (7)	0.0125 (8)
O28	0.41758 (7)	−0.01881 (7)	0.16290 (7)	0.0103 (7)
O29	0.48794 (7)	0.06470 (7)	0.12126 (7)	0.0100 (7)
O30	0.62209 (7)	0.14061 (8)	0.09873 (7)	0.0145 (8)
O31	0.12114 (8)	0.06545 (8)	0.14993 (8)	0.0184 (9)
O32	0.69123 (9)	0.17878 (9)	0.24157 (8)	0.0216 (10)
O33	0.50739 (7)	−0.04426 (7)	0.09319 (7)	0.0117 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ti1	0.00690 (16)	0.00628 (16)	0.00703 (16)	0.00027 (11)	0.00021 (10)	−0.00070 (10)
Ti2	0.00659 (16)	0.00629 (16)	0.00638 (16)	0.00045 (10)	−0.00027 (11)	0.00023 (10)
Ti3	0.00605 (16)	0.00696 (16)	0.00625 (16)	0.00054 (11)	0.00036 (10)	0.00019 (10)
Ti4	0.00680 (17)	0.00659 (16)	0.00557 (16)	0.00062 (10)	−0.00006 (10)	−0.00011 (10)
Ti5	0.00629 (11)	0.00629 (11)	0.00629 (11)	0.00012 (10)	−0.00012 (10)	−0.00012 (10)
Ti6	0.00581 (15)	0.00581 (15)	0.00581 (15)	0.00071 (14)	0.00071 (14)	0.00071 (14)
P1	0.0056 (2)	0.0065 (2)	0.0066 (2)	0.00068 (15)	−0.00019 (15)	0.00043 (15)
P2	0.0065 (2)	0.0057 (2)	0.0068 (2)	0.00061 (15)	0.00077 (15)	0.00029 (15)
P3	0.0061 (2)	0.0073 (2)	0.0065 (2)	0.00030 (15)	0.00012 (15)	0.00052 (16)
P4	0.0056 (2)	0.0070 (2)	0.0057 (2)	−0.00077 (15)	−0.00060 (15)	0.00073 (15)
P5	0.0062 (2)	0.0078 (2)	0.0053 (2)	−0.00040 (15)	0.00021 (15)	0.00003 (15)
P6	0.0057 (2)	0.0068 (2)	0.0058 (2)	−0.00011 (15)	0.00013 (15)	−0.00036 (15)
P7	0.0060 (2)	0.0079 (2)	0.0060 (2)	−0.00090 (15)	−0.00048 (15)	0.00061 (15)
P8	0.0063 (2)	0.0074 (2)	0.0056 (2)	−0.00016 (15)	−0.00005 (15)	0.00051 (15)
P9	0.00695 (15)	0.00695 (15)	0.00695 (15)	0.00039 (16)	0.00039 (16)	0.00039 (16)
P10	0.00702 (15)	0.00702 (15)	0.00702 (15)	0.00015 (15)	−0.00015 (15)	−0.00015 (15)
P11	0.00635 (16)	0.00635 (16)	0.00635 (16)	−0.0006 (5)	0.0006 (5)	0.0006 (5)
O1	0.0126 (8)	0.0127 (8)	0.0252 (9)	0.0005 (6)	−0.0083 (6)	−0.0082 (6)
O2	0.0073 (7)	0.0219 (9)	0.0168 (8)	0.0019 (6)	0.0022 (6)	−0.0094 (6)
O3	0.0087 (7)	0.0205 (8)	0.0080 (7)	0.0052 (6)	−0.0009 (5)	0.0030 (5)
O4	0.0085 (8)	0.0306 (10)	0.0096 (8)	0.0070 (6)	−0.0001 (5)	−0.0068 (6)
O5	0.0573 (16)	0.0573 (16)	0.0573 (16)	−0.0250 (11)	0.0250 (11)	0.0250 (11)
O6	0.037 (2)	0.037 (2)	0.037 (2)	0.030 (4)	−0.030 (4)	−0.030 (4)
O7	0.0059 (7)	0.0146 (8)	0.0216 (9)	0.0001 (5)	0.0017 (5)	−0.0038 (6)
O8	0.0166 (8)	0.0090 (7)	0.0160 (8)	0.0046 (5)	−0.0006 (6)	0.0024 (5)
O9	0.0198 (9)	0.0088 (7)	0.0138 (8)	0.0054 (6)	0.0008 (6)	0.0041 (5)
O10	0.0176 (8)	0.0071 (7)	0.0168 (8)	0.0011 (5)	−0.0041 (6)	0.0016 (5)
O11	0.0179 (9)	0.0072 (8)	0.0252 (9)	−0.0044 (6)	0.0021 (6)	0.0025 (6)
O12	0.0224 (9)	0.0094 (8)	0.0176 (8)	0.0059 (6)	−0.0023 (6)	0.0025 (6)
O13	0.0176 (8)	0.0071 (7)	0.0172 (8)	−0.0008 (5)	0.0021 (6)	0.0027 (5)
O14	0.0069 (7)	0.0196 (8)	0.0101 (7)	−0.0008 (5)	−0.0020 (5)	−0.0006 (5)
O15	0.0176 (8)	0.0108 (7)	0.0054 (7)	−0.0025 (5)	0.0011 (5)	−0.0020 (5)
O16	0.0063 (7)	0.0143 (8)	0.0133 (7)	0.0007 (5)	−0.0019 (5)	−0.0027 (5)
O17	0.0147 (8)	0.0161 (8)	0.0097 (7)	−0.0011 (6)	0.0026 (5)	−0.0059 (5)
O18	0.0153 (8)	0.0098 (7)	0.0155 (8)	0.0050 (5)	0.0042 (6)	0.0057 (5)
O19	0.0134 (7)	0.0107 (7)	0.0062 (7)	−0.0009 (5)	0.0026 (5)	−0.0004 (5)
O20	0.0064 (7)	0.0175 (8)	0.0153 (8)	−0.0021 (5)	−0.0014 (5)	−0.0033 (6)
O21	0.0127 (8)	0.0187 (8)	0.0066 (7)	0.0010 (6)	0.0040 (5)	−0.0009 (5)
O22	0.0106 (7)	0.0130 (7)	0.0051 (7)	−0.0014 (5)	0.0010 (5)	−0.0008 (5)
O23	0.0066 (7)	0.0169 (8)	0.0099 (7)	−0.0003 (5)	0.0021 (5)	0.0008 (5)
O24	0.0087 (8)	0.0195 (9)	0.0166 (8)	−0.0023 (6)	−0.0020 (5)	−0.0003 (6)
O25	0.0061 (7)	0.0188 (8)	0.0161 (8)	−0.0015 (5)	−0.0009 (5)	−0.0032 (6)
O26	0.0112 (8)	0.0185 (9)	0.0172 (8)	0.0042 (6)	0.0063 (6)	0.0017 (6)
O27	0.0168 (8)	0.0126 (8)	0.0081 (7)	−0.0016 (5)	0.0037 (5)	−0.0019 (5)
O28	0.0082 (7)	0.0136 (7)	0.0090 (7)	−0.0015 (5)	−0.0021 (5)	−0.0016 (5)
O29	0.0138 (7)	0.0065 (7)	0.0097 (7)	0.0034 (5)	0.0010 (5)	0.0006 (5)
O30	0.0160 (8)	0.0196 (8)	0.0080 (7)	0.0023 (6)	−0.0025 (6)	−0.0040 (6)
O31	0.0214 (9)	0.0133 (8)	0.0207 (9)	0.0090 (6)	0.0099 (7)	0.0083 (6)
O32	0.0265 (10)	0.0254 (10)	0.0128 (9)	0.0065 (7)	−0.0082 (7)	−0.0101 (7)
O33	0.0144 (8)	0.0127 (8)	0.0080 (7)	−0.0058 (5)	0.0055 (5)	−0.0040 (5)

Geometric parameters (Å, º)

Ti1—O7	1.9028 (17)	P2—O1	1.578 (2)
Ti1—O11	1.9138 (18)	P2—O10	1.5051 (17)
Ti1—O13	1.9333 (17)	P2—O12	1.4938 (18)
Ti1—O26	1.9114 (18)	P2—O11	1.4982 (18)
Ti1—O30	1.9224 (17)	P3—O2	1.5805 (18)
Ti1—O32	1.919 (2)	P3—O13	1.5003 (17)
Ti2—O8	1.9135 (17)	P3—O14	1.5037 (17)
Ti2—O20	1.9042 (17)	P3—O15^i	1.5040 (17)
Ti2—O22	1.9453 (16)	P4—O2	1.5770 (19)
Ti2—O27	1.9070 (17)	P4—O16	1.5068 (17)
Ti2—O9	1.9145 (17)	P4—O17	1.5008 (18)
Ti2—O16	1.9122 (17)	P4—O18^ii	1.4968 (18)
Ti3—O12	1.9137 (18)	P5—O3	1.5726 (17)
Ti3—O21	1.9385 (17)	P5—O19^ii	1.5047 (16)
Ti3—O24	1.8887 (18)	P5—O20	1.5042 (17)
Ti3—O25	1.9197 (17)	P5—O21	1.4893 (17)
Ti3—O31	1.9031 (19)	P6—O3	1.5707 (18)
Ti3—O15	1.9141 (16)	P6—O23	1.5008 (17)
Ti4—O14	1.9398 (17)	P6—O22	1.5059 (16)
Ti4—O18	1.9057 (18)	P6—O24	1.5000 (18)
Ti4—O19	1.8884 (16)	P7—O4	1.5662 (19)
Ti4—O28	1.9434 (16)	P7—O25	1.5004 (17)
Ti4—O29	1.9293 (16)	P7—O27	1.5067 (17)
Ti4—O33	1.8972 (17)	P7—O26	1.5013 (18)
Ti5—O10	1.9243 (17)	P8—O4	1.5815 (18)
Ti5—O10	1.9243 (17)	P8—O28	1.5056 (17)
Ti5—O10	1.9243 (17)	P8—O30	1.5064 (17)
Ti5—O17	1.9199 (17)	P8—O29	1.5069 (17)
Ti5—O17	1.9199 (17)	P9—O5	1.541 (2)
Ti5—O17	1.9199 (17)	P9—O31	1.4970 (19)
Ti6—O23	1.9065 (16)	P9—O31^iii	1.4970 (19)
Ti6—O23	1.9065 (16)	P9—O31^iv	1.4970 (19)
Ti6—O23	1.9065 (16)	P10—O5	1.536 (2)
Ti6—O23	1.9065 (16)	P10—O32	1.494 (2)
Ti6—O23	1.9065 (16)	P10^v—O32	1.494 (2)
Ti6—O23	1.9065 (16)	P10^v—O32	1.494 (2)
P1—O1	1.5770 (19)	P11—O6	1.5332 (5)
P1—O7	1.5041 (17)	P11—O33	1.4972 (17)
P1—O8	1.4952 (18)	P11—O33	1.4972 (17)
P1—O9	1.4940 (18)	P11—O33^ii	1.4972 (17)
O7—Ti1—O11	89.27 (8)	O8—P1—O9	112.02 (10)
O7—Ti1—O13	90.62 (8)	O1—P2—O10	104.16 (10)
O7—Ti1—O26	175.73 (8)	O1—P2—O12	109.11 (10)
O7—Ti1—O30	87.66 (8)	O1—P2—O11	108.04 (10)
O7—Ti1—O32	91.58 (8)	O10—P2—O12	112.56 (10)
O11—Ti1—O13	176.46 (8)	O10—P2—O11	112.40 (10)
O11—Ti1—O26	88.94 (8)	O12—P2—O11	110.26 (11)
O11—Ti1—O30	92.81 (8)	O2—P3—O13	105.85 (10)
O11—Ti1—O32	88.68 (8)	O2—P3—O14	109.41 (10)
O13—Ti1—O26	91.40 (8)	O2—P3—O15^i	104.57 (10)
O13—Ti1—O30	90.73 (8)	O13—P3—O14	112.25 (10)
O13—Ti1—O32	87.78 (8)	O13—P3—O15^i	113.01 (10)
O26—Ti1—O30	88.55 (8)	O14—P3—O15^i	111.26 (10)
O26—Ti1—O32	92.26 (8)	O2—P4—O16	104.83 (10)
O30—Ti1—O32	178.32 (8)	O2—P4—O17	109.64 (10)
O8—Ti2—O20	92.12 (7)	O2—P4—O18^ii	107.21 (10)
O8—Ti2—O22	90.36 (7)	O16—P4—O17	111.40 (10)
O8—Ti2—O27	91.05 (7)	O16—P4—O18^ii	110.87 (10)
O8—Ti2—O9	179.46 (9)	O17—P4—O18^ii	112.51 (10)
O8—Ti2—O16	88.28 (7)	O3—P5—O19^ii	104.76 (9)
O20—Ti2—O22	89.12 (7)	O3—P5—O20	105.89 (10)
O20—Ti2—O27	90.66 (7)	O3—P5—O21	110.24 (9)
O20—Ti2—O9	87.34 (8)	O19^ii—P5—O20	110.81 (10)
O20—Ti2—O16	179.36 (7)	O19^ii—P5—O21	111.04 (10)
O22—Ti2—O27	178.58 (7)	O20—P5—O21	113.61 (10)
O22—Ti2—O9	89.68 (7)	O3—P6—O23	106.87 (9)
O22—Ti2—O16	90.37 (7)	O3—P6—O22	105.60 (9)
O27—Ti2—O9	88.91 (7)	O3—P6—O24	107.59 (10)
O27—Ti2—O16	89.84 (7)	O23—P6—O22	113.25 (9)
O9—Ti2—O16	92.26 (8)	O23—P6—O24	112.14 (10)
O12—Ti3—O21	92.40 (8)	O22—P6—O24	110.93 (10)
O12—Ti3—O24	86.61 (8)	O4—P7—O25	105.12 (10)
O12—Ti3—O25	90.05 (8)	O4—P7—O27	106.65 (10)
O12—Ti3—O31	178.86 (8)	O4—P7—O26	109.13 (10)
O12—Ti3—O15	92.68 (7)	O25—P7—O27	112.03 (10)
O21—Ti3—O24	88.79 (8)	O25—P7—O26	110.78 (10)
O21—Ti3—O25	90.81 (7)	O27—P7—O26	112.72 (10)
O21—Ti3—O31	88.15 (8)	O4—P8—O28	108.67 (9)
O21—Ti3—O15	174.61 (7)	O4—P8—O30	105.84 (10)
O24—Ti3—O25	176.62 (8)	O4—P8—O29	105.63 (9)
O24—Ti3—O31	92.40 (8)	O28—P8—O30	113.37 (10)
O24—Ti3—O15	89.71 (8)	O28—P8—O29	111.50 (9)
O25—Ti3—O31	90.94 (8)	O30—P8—O29	111.33 (10)
O25—Ti3—O15	90.99 (7)	O5—P9—O31	107.30 (12)
O31—Ti3—O15	86.75 (7)	O5—P9—O31^iii	107.30 (12)
O14—Ti4—O18	90.28 (7)	O5—P9—O31^iv	107.30 (11)
O14—Ti4—O19	89.96 (7)	O31^iii—P9—O31	111.55 (11)
O14—Ti4—O28	177.84 (8)	O31^iii—P9—O31^iv	111.55 (11)
O14—Ti4—O29	91.53 (7)	O31^iv—P9—O31	111.55 (11)
O14—Ti4—O33	88.20 (7)	O5—P10—O32^iii	107.33 (12)
O18—Ti4—O19	91.52 (7)	O5—P10—O32^iv	107.33 (12)
O18—Ti4—O28	87.69 (7)	O5—P10—O32	107.33 (12)
O18—Ti4—O29	178.10 (8)	O32^iii—P10—O32^iv	111.53 (11)
O18—Ti4—O33	90.25 (7)	O32^iii—P10—O32	111.53 (11)
O19—Ti4—O28	90.82 (7)	O32^iv—P10—O32	111.53 (11)
O19—Ti4—O29	89.06 (7)	O6—P11—O33	106.89 (7)
O19—Ti4—O33	177.45 (8)	O6—P11—O33	106.89 (7)
O28—Ti4—O29	90.50 (7)	O6—P11—O33^ii	106.89 (7)
O28—Ti4—O33	91.09 (7)	O33—P11—O33	111.93 (10)
O29—Ti4—O33	89.23 (7)	O33—P11—O33^ii	111.93 (10)
O10—Ti5—O10	90.71 (8)	O33—P11—O33^ii	111.93 (10)
O10—Ti5—O10	90.71 (8)	P1—O1—P2	144.51 (13)
O10—Ti5—O17	177.28 (8)	P3—O2—P4	143.04 (12)
O10—Ti5—O17	89.15 (7)	P5—O3—P6	141.21 (12)
O10—Ti5—O17	92.01 (7)	P7—O4—P8	143.41 (12)
O10—Ti5—O10	90.71 (8)	P9^i—O5—P10	180.0 (2)
O10—Ti5—O17	92.01 (8)	P11—O6—P11	180
O10—Ti5—O17	177.28 (8)	Ti1—O7—P1	153.63 (12)
O10—Ti5—O17	89.15 (7)	Ti2—O8—P1	160.44 (12)
O10—Ti5—O17	89.15 (8)	P1—O9—Ti2	163.15 (12)
O10—Ti5—O17	92.01 (8)	Ti5—O10—P2	155.30 (12)
O10—Ti5—O17	177.28 (9)	Ti1—O11—P2	165.23 (13)
O17—Ti5—O17	88.14 (7)	Ti3—O12—P2	169.56 (13)
O17—Ti5—O17	88.14 (7)	Ti1—O13—P3	153.23 (12)
O17—Ti5—O17	88.14 (7)	Ti4—O14—P3	141.73 (11)
O23—Ti6—O23	90.37 (7)	P3—O15—Ti3	149.73 (11)
O23—Ti6—O23	90.37 (7)	P4—O16—Ti2	148.01 (11)
O23—Ti6—O23	180	P4—O17—Ti5	155.94 (12)
O23—Ti6—O23	89.63 (7)	Ti4—O18—P4	151.12 (12)
O23—Ti6—O23	89.63 (7)	Ti4—O19—P5	144.35 (10)
O23—Ti6—O23	90.37 (7)	Ti2—O20—P5	143.55 (11)
O23—Ti6—O23	89.63 (7)	Ti3—O21—P5	154.83 (11)
O23—Ti6—O23	180	Ti2—O22—P6	139.78 (10)
O23—Ti6—O23	89.63 (7)	Ti6—O23—P6	146.34 (11)
O23—Ti6—O23	89.63 (7)	Ti3—O24—P6	153.08 (12)
O23—Ti6—O23	89.63 (7)	Ti3—O25—P7	156.46 (12)
O23—Ti6—O23	180	Ti1—O26—P7^vi	156.41 (12)
O23—Ti6—O23	90.37 (7)	Ti2—O27—P7^i	148.43 (11)
O23—Ti6—O23	90.37 (7)	Ti4—O28—P8	141.15 (10)
O23—Ti6—O23	90.37 (7)	Ti4—O29—P8^vi	139.57 (10)
O1—P1—O7	104.68 (10)	Ti1—O30—P8^ii	153.01 (12)
O1—P1—O8	108.25 (10)	Ti3—O31—P9	152.29 (13)
O1—P1—O9	108.78 (10)	Ti1—O32—P10	161.00 (14)
O7—P1—O8	112.02 (10)	Ti4—O33—P11	139.09 (11)
O7—P1—O9	110.75 (10)

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