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The crystal structure of monobarium dititanium pentaoxide, BaTi2O5, synthesized by a floating-zone method, was studied by X-ray diffraction. Previous reports describe the structure as being in the monoclinic centrosymmetric space group C2/m. We have recently found that this material exhibits ferroelectricity, and therefore BaTi2O5 should have lower symmetry. The crystal structure of BaTi2O5 was refined in space group C2, revealing a displacement of the Ti atoms along the b axis. This result is consistent with the fact that the ferroelectricity of BaTi2O5 was only observed along the b axis.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270103021395/sk1654sup1.cif
Contains datablocks global, I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108270103021395/sk1654Isup2.hkl
Contains datablock I

Comment top

Since BaTi2O5 decomposes into BaTiO3 and Ba6Ti17O40 at more than 1400 K (Ritter et al., 1986), this compound has been regarded as a metastable phase or a low temperature phase. Harrison (1956) reported the crystal structure of BaTi2O5, based on Weissenberg camera data. He showed the crystal structure to be monoclinic [space group C2/m, with a = 16.892 (13) Å, b = 3.930 (1) Å, c = 9.410 (4) Å, β = 103°2(3)'; the original description was in the A2/m setting]. The R value of that analysis was about 20%. The reported density measured by a flotation method was 4.4 Mg m−3, which differs significantly from the value calculated from the lattice parameters and Z value (5.1 Mg m−3).

The crystal structure of BaTi2O5 was refined using the data collected with a four-circle X-ray diffractiometer (Tillmanns, 1974). The single-crystal used for that analysis was prepared by rapid solidification of a melt with a composition BaO:TiO2=30:70 in molar ratio. The crystal structure was refined with the model of C2/m by Harrison (1956). The reported R2 and R1 values were 0.031 and 0.026, respectively [with intensity data of I > 2σ(I)].

Recently, we have synthesized BaTi2O5 single crystals of more than 1 cm in size by a floating-zone method (Akashi et al., 2003a) and characterized the dielectric properties. The electric-field–polarization (P–E) curves along the b axis showed ferroelectricity (Akashi et al., 2003b). However, the existence of ferroelectricity is not consistent with the centrosymmetric structure of space group C2/m.

The X-ray diffraction data collected for the present study were indexed with a monoclinic lattice. The refined lattice parameters were in agreement with the reported values within standard uncertainties. The space group can be either C2, Cm or C2/m, according to the experimental systematic extinctions. The measured density by the Archimedian method was 5.09 Mg m−3, which agreed well with the calculated density (5.119 Mg m−3).

Refinement using the structural model in C2/m reported by Harrison (1956) converged to an R1 value of 0.0513 (wR2 = 0.143). The U22 anisotropic displacement parameter for the Ti1 site refined to 0.020 (1) Å2, which is 3–4 times greater than the values of U11 [0.005 (1) Å2] and U33 [0.006 (1) Å2] for the same site, and U22 [0.004 (1)–0.006 (1) Å2] for other Ti sites. The anisotropic displacement parameter B22 of the Ti1 site reported by Tillmanns (1974) was also over ten times greater than other parameters.

Since the displacement parameter of the Ti1 site along the b axis was so large, we refined the structure in space group C2, in which the mirror plane of C2/m perpendicular to the b axis is removed. The R1 and wR2 values using all data were 0.0462 and 0.1121, respectively. The U22 value of the Ti1 site refined to 0.0054 (6) Å2. The crystal structure refined with the C2 model is illustrated in Fig. 1 using 99% probability displacement ellipsoids for Ba and Ti atoms. The elongation of the displacement ellipsoids was insignificant, as shown in Fig. 1.

The arrangement of the Ba and O atoms is close to the cubic closest packing. The most closely packed layers are aligned parallel to the (313), (313), (511) and (511) planes. Ti atoms occupy octahedral sites in the O-atom packing; Fig. 2 shows the crystal structure of BaTi2O5 using Ti-atom-centered O-atom octahedra. All atoms in the structure are arranged approximately along the (104), (401) and (010) planes.

There are three kinds of Ti sites in the crystal structure of BaTi2O5. The vertex O atoms link octahedra of the same kind of Ti site along the b axis. In the ac plane, the Ti1-centered O-atom octahedra (Ti1—O6) connect to the Ti1O6 and Ti3O6 octahedra via shared apexes, and to the Ti2O6 octahedra via shared edges. The Ti2O6 and Ti3O6 octahedra share edges and connect along? the b axis.

The Ba1 atoms are surrounded by 12 O atoms and are positioned? in the large tunnels of TiO6 octahedra along the b axis. The Ba2 atoms are situated in the 12-fold coordination sites of the O atoms belonging to the Ti1O6 and Ti3O6 octahedra. The arrangement of the Ba2 atoms and Ti1O6 and Ti3O6 octahedra along the b axis is similar to that in the perovskite-type structure.

Selected interatomic distances and bond angles are listed in Table 1. The Ba1—O distances [2.673 (9)–3.279 (7) Å] are close to the Ba—O distances (2.653–3.278 Å) reported for Ba5Ti17O40, in which the Ba atoms are coordinated by 12 O atoms (Hofmeister et al., 1984). The Ba2—O distances [2.766 (8)–2.998 (5) Å] have a smaller deviation than the Ba1—O distances. The bond-valence sums calculated from the parameters presented by Brese & O'Keeffe (1991) are 2.49 and 2.45 for atoms Ba1 and Ba2, respectively. These values are smaller than that of Ba calculated for tetragonal BaTiO3 (2.78; Buttner & Maslen, 1992) and are close to that of Ba in Ba6Ti17O40 (2.13–2.64).

The Ti3—O bond lengths are in the range 1.710 (5)–2.474 (5) Å and are greater than the Ti1—O [1.765 (10)–2.171 (10) Å] and Ti2—O [1.796 (5)–2.150 (5) Å] distances. The bond-valence sums for atoms Ti1, Ti2 and Ti3 are 3.99, 3.95 and 4.09, respectively. These values imply that the valence of the Ti atoms is 4. The bond-valence sums for the O atoms (1.93–2.19) are close to 2, except for sites O3 (2.31) and O6 (2.32). Atom O6 is surrounded by one Ti3 and three Ba1 atoms. The O6—Ti3 distance [1.710 (5) Å] is the shortest of the Ti—O bond lengths in BaTi2O5. The O6—Ba distances [2.673 (9), 2.703 (5), 2.727 (9) Å] are also shorter than the average O—Ba distance in BaTi2O5 (2.908 Å). Atoms Ti1 and Ti2 and two Ba1 atoms coordinate with atom O3; the O3—Ba1 distances [2.673 (7) and 2.742 (8) Å] are shorter than the average O—Ba distances. The short O—Ba distances are related to the large bond-valence sums for atoms O3 and O6.

The O1—Ti1—O1 and Ti1—O1—Ti1 bond angles are both 176.5 (3)°, meaning that atoms O1 and Ti1 are aligned almost linearly along the b axis. The Ti1—O1 bond lengths are alternately 1.765 (10) and 2.171 (10) Å; atom Ti1 shifts from the center of the Ti1O6 octahedron along the b axis. On the other hand, atoms Ti2 and Ti3 lie almost in the ac plane and apart from the (104) and (401) planes in the Ti2O6 and Ti3O6 octahedra. The O5—Ti2—O5 and Ti2—O5—Ti2 bond angles are 152.3 (3)°, and the O4—Ti3—O4 and Ti3—O4—Ti3 angles are 159.3 (3)°. The Ti2—O5 bond lengths [2.025 (10) and 2.028 (10) Å] are close to the Ti3—O4 bond legnths [1.983 (11) and 2.018 (11) Å].

The atomic coordination of (x, y, z) is equivalent to that of (-x, y, −z) because of the twofold symmetry along the b axis in space group C2, and therefore ferroelectricity is expected only in the direction of the b axis. This fact is in accordance with the observed dielectric properties of a BaTi2O5 single-crystal (Akashi et al., 2003a,b). By selecting the Ba1 site as a reference (y = 0.000), the y positions are +0.002 for atom Ba2, +0.012 for atom Ti2, +0.009 for atom Ti3, and +0.009–0.021 for atoms O1–O8. On the other hand, the Ti1 site is at −0.031, and the displacement is about 0.18 Å from the average y position of the O-atom sites. The spontaneous polarization (0.10 C/m2) can be calculated by assuming nominal charges of Ba2+, Ti4+ and O2−. This value is about two-thirds of that calculated for tetragonal BaTiO3 (0.16 C/m2). The value of 0.10 C/m2 was measured at 523 K, applying an electric field of 10 6 V m−1 (Akashi et al., 2003b). Generally, the Ti4+ ion has a d0 electron configuration and tends to stay in a distorted O-atom octahedron because of the second-order Jahn–Teller effect (Wheeler et al., 1986). The Ti4+ ions of BaTi2O5 are situated in the distorted O-atom octahedra. The displacement of Ti atoms in the Ti1 sites is mainly responsible for the ferroelectricity.

Experimental top

BaCO3 (99.9%) and TiO2 (99.9%) powders in a Ba/Ti molar ratio of 2:1 were weighed and mixed in an agate motor. The mixed powder was isostatically pressed into a rod at 10 MPa and heated at 1503 K for 43 ks. The sintered rod, about 6 mm in diameter, was melted and solidified directionally by the floating-zone method at a rate of 5.6 τimes 10−6 m s−1 in flowing 79%-Ar–21%-O2 gas. Colorless and transparent single crystals of BaTi2O5 (3 mm in diameter and 2 mm in length) were synthesized. The crystals were cleaved into smaller pieces for use in the X-ray diffraction experiment.

Refinement top

The largest displacements? in the difference map were close to atoms Ba1 and Ba2. The refinement of the Flack parameter was obtained by way of the TWIN/BASF instructions (Flack & Bernardinelli, 2000). The Flack parameter indicates a 70:30 ratio of two possible polarities of the structure. Since one of three principal mean-square atomic displacements for the O5 site ?tended to a small negative value when the refinement included? anisotropic displacement parameters, all O-atom sites were refined with isotropic displacement parameters.

Computing details top

Data collection: SMART and SAINT (Bruker, 1999); cell refinement: SMART and SAINT; data reduction: XPREP (Bruker, 1997); program(s) used to solve structure: ??; program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ATOMS (Dowty, 1999) and CrystalMaker (Palmer, 2002); software used to prepare material for publication: SHELXL97 (Sheldrick, 1997).

Figures top
[Figure 1] Fig. 1. The arrangement of atomic positions in the structure of BaTi2O5, illustrated with 99% probability displacement ellipsoids (Ba and Ti atoms) and spheres (O atoms). For symmetry codes see Table 1.
[Figure 2] Fig. 2. The structure of BaTi2O5, with Ti-centered O-atom octahedra.
monobarium dititanium pentaoxide top
Crystal data top
BaTi2O5F(000) = 840
Mr = 313.14Dx = 5.119 Mg m3
Dm = 5.09 Mg m3
Dm measured by Archimedian method
Monoclinic, C2Mo Kα radiation, λ = 0.71073 Å
Hall symbol: C 2yCell parameters from 818 reflections
a = 16.899 (3) Åθ = 2.2–30.0°
b = 3.9350 (6) ŵ = 13.32 mm1
c = 9.4105 (15) ÅT = 293 K
β = 103.103 (3)°Prismatic, colorless
V = 609.48 (17) Å30.20 × 0.14 × 0.12 mm
Z = 6
Data collection top
Bruker SMART CCD? area-detector
diffractometer
1636 independent reflections
Radiation source: fine-focus sealed tube1557 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.066
ω scansθmax = 30.0°, θmin = 2.2°
Absorption correction: analytical
face indexed (XPREP; Bruker, 1997)
h = 1723
Tmin = 0.189, Tmax = 0.347k = 55
2619 measured reflectionsl = 1313
Refinement top
Refinement on F2 w = 1/[σ2(Fo2) + (0.0689P)2]
where P = (Fo2 + 2Fc2)/3
Least-squares matrix: full(Δ/σ)max < 0.001
R[F2 > 2σ(F2)] = 0.045Δρmax = 2.76 e Å3
wR(F2) = 0.112Δρmin = 3.05 e Å3
S = 1.08Extinction correction: SHELXL97, Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
1636 reflectionsExtinction coefficient: 0.0254 (11)
74 parametersAbsolute structure: Flack (1983)
1 restraintAbsolute structure parameter: 0.30 (8)
Crystal data top
BaTi2O5V = 609.48 (17) Å3
Mr = 313.14Z = 6
Monoclinic, C2Mo Kα radiation
a = 16.899 (3) ŵ = 13.32 mm1
b = 3.9350 (6) ÅT = 293 K
c = 9.4105 (15) Å0.20 × 0.14 × 0.12 mm
β = 103.103 (3)°
Data collection top
Bruker SMART CCD? area-detector
diffractometer
1636 independent reflections
Absorption correction: analytical
face indexed (XPREP; Bruker, 1997)
1557 reflections with I > 2σ(I)
Tmin = 0.189, Tmax = 0.347Rint = 0.066
2619 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0451 restraint
wR(F2) = 0.112Δρmax = 2.76 e Å3
S = 1.08Δρmin = 3.05 e Å3
1636 reflectionsAbsolute structure: Flack (1983)
74 parametersAbsolute structure parameter: 0.30 (8)
Special details top

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

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ba10.36904 (2)0.00011 (10)0.01784 (4)0.00766 (18)
Ba20.00000.5017 (3)0.50000.00730 (19)
Ti10.03911 (9)0.0310 (5)0.21058 (15)0.0046 (3)
Ti20.20711 (7)0.0118 (6)0.37260 (13)0.0052 (3)
Ti30.33375 (7)0.5087 (7)0.30576 (13)0.0052 (3)
O10.0355 (3)0.521 (2)0.2097 (6)0.0084 (10)*
O20.1089 (3)0.009 (3)0.4279 (5)0.0074 (9)*
O30.1527 (3)0.012 (2)0.1850 (5)0.0067 (9)*
O40.1745 (3)0.513 (3)0.6622 (5)0.0085 (10)*
O50.2354 (3)0.512 (2)0.3989 (5)0.0071 (9)*
O60.2892 (3)0.509 (3)0.1234 (5)0.0090 (10)*
O70.4423 (3)0.519 (3)0.2881 (5)0.0089 (10)*
O80.00000.015 (4)0.00000.0100 (14)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Ba10.0090 (3)0.0067 (3)0.0076 (3)0.0001 (3)0.00255 (16)0.0000 (3)
Ba20.0098 (3)0.0063 (3)0.0056 (3)0.0000.0013 (2)0.000
Ti10.0052 (6)0.0037 (8)0.0054 (6)0.0006 (7)0.0022 (4)0.0002 (7)
Ti20.0056 (5)0.0056 (6)0.0040 (5)0.0010 (8)0.0000 (4)0.0004 (9)
Ti30.0054 (5)0.0060 (6)0.0046 (5)0.0003 (8)0.0021 (4)0.0009 (9)
Geometric parameters (Å, º) top
Ba1—O6i2.673 (9)Ti1—O1i1.765 (10)
Ba1—O3ii2.673 (7)Ti1—O7vii1.947 (5)
Ba1—O6ii2.703 (5)Ti1—O81.9502 (19)
Ba1—O62.727 (9)Ti1—O31.996 (5)
Ba1—O3iii2.742 (8)Ti1—O22.123 (5)
Ba1—O8iv2.954 (9)Ti1—O12.171 (10)
Ba1—O1ii2.960 (5)Ti1—Ti22.9069 (19)
Ba1—O1iv2.980 (5)Ti2—O31.796 (5)
Ba1—O8v3.035 (10)Ti2—O21.849 (5)
Ba1—O7i3.186 (7)Ti2—O5i2.025 (10)
Ba1—O4vi3.258 (5)Ti2—O52.028 (10)
Ba1—O73.279 (7)Ti2—O4vi2.099 (5)
Ba2—O7vii2.766 (8)Ti2—O5vi2.150 (5)
Ba2—O7vi2.766 (8)Ti2—Ti33.067 (3)
Ba2—O2viii2.858 (9)Ti2—Ti3i3.083 (3)
Ba2—O22.858 (9)Ti2—Ti2ix3.1853 (19)
Ba2—O7ix2.862 (8)Ti2—Ti2vi3.1853 (19)
Ba2—O7x2.862 (8)Ti2—Ti3vi3.2536 (17)
Ba2—O2xi2.899 (9)Ti3—O61.710 (5)
Ba2—O2xii2.899 (8)Ti3—O71.879 (5)
Ba2—O12.928 (5)Ti3—O4vi1.983 (11)
Ba2—O1viii2.928 (5)Ti3—O4ix2.018 (11)
Ba2—O42.998 (5)Ti3—O52.047 (5)
Ba2—O4viii2.998 (5)Ti3—O2ix2.474 (5)
O1i—Ti1—O7vii94.1 (4)O5i—Ti2—O4vi79.3 (3)
O1i—Ti1—O894.9 (4)O5—Ti2—O4vi79.0 (3)
O7vii—Ti1—O8104.55 (18)O3—Ti2—O5vi176.2 (2)
O1i—Ti1—O396.7 (3)O2—Ti2—O5vi87.1 (2)
O7vii—Ti1—O3161.8 (3)O5i—Ti2—O5vi80.7 (3)
O8—Ti1—O389.03 (15)O5—Ti2—O5vi80.6 (3)
O1i—Ti1—O295.2 (4)O4vi—Ti2—O5vi85.73 (19)
O7vii—Ti1—O287.8 (2)O6—Ti3—O797.3 (2)
O8—Ti1—O2163.4 (4)O6—Ti3—O4vi97.1 (4)
O3—Ti1—O276.7 (2)O7—Ti3—O4vi98.0 (4)
O1i—Ti1—O1176.5 (3)O6—Ti3—O4ix96.8 (4)
O7vii—Ti1—O182.8 (3)O7—Ti3—O4ix95.4 (4)
O8—Ti1—O184.3 (5)O4vi—Ti3—O4ix159.3 (3)
O3—Ti1—O186.7 (3)O6—Ti3—O5102.3 (2)
O2—Ti1—O186.4 (3)O7—Ti3—O5160.2 (2)
O3—Ti2—O289.1 (2)O4vi—Ti3—O581.3 (3)
O3—Ti2—O5i100.0 (3)O4ix—Ti3—O580.7 (3)
O2—Ti2—O5i99.3 (4)O6—Ti3—O2ix177.0 (2)
O3—Ti2—O5100.0 (3)O7—Ti3—O2ix85.61 (19)
O2—Ti2—O599.9 (4)O4vi—Ti3—O2ix82.6 (3)
O5i—Ti2—O5152.3 (3)O4ix—Ti3—O2ix82.7 (3)
O3—Ti2—O4vi98.0 (2)O5—Ti3—O2ix74.69 (18)
O2—Ti2—O4vi172.8 (2)
Symmetry codes: (i) x, y1, z; (ii) x+1/2, y1/2, z; (iii) x+1/2, y+1/2, z; (iv) x+1/2, y1/2, z; (v) x+1/2, y+1/2, z; (vi) x+1/2, y1/2, z+1; (vii) x1/2, y1/2, z; (viii) x, y, z+1; (ix) x+1/2, y+1/2, z+1; (x) x1/2, y+1/2, z; (xi) x, y+1, z; (xii) x, y+1, z+1.

Experimental details

Crystal data
Chemical formulaBaTi2O5
Mr313.14
Crystal system, space groupMonoclinic, C2
Temperature (K)293
a, b, c (Å)16.899 (3), 3.9350 (6), 9.4105 (15)
β (°) 103.103 (3)
V3)609.48 (17)
Z6
Radiation typeMo Kα
µ (mm1)13.32
Crystal size (mm)0.20 × 0.14 × 0.12
Data collection
DiffractometerBruker SMART CCD? area-detector
diffractometer
Absorption correctionAnalytical
face indexed (XPREP; Bruker, 1997)
Tmin, Tmax0.189, 0.347
No. of measured, independent and
observed [I > 2σ(I)] reflections
2619, 1636, 1557
Rint0.066
(sin θ/λ)max1)0.704
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.045, 0.112, 1.08
No. of reflections1636
No. of parameters74
No. of restraints1
Δρmax, Δρmin (e Å3)2.76, 3.05
Absolute structureFlack (1983)
Absolute structure parameter0.30 (8)

Computer programs: SMART and SAINT (Bruker, 1999), SMART and SAINT, XPREP (Bruker, 1997), ??, SHELXL97 (Sheldrick, 1997), ATOMS (Dowty, 1999) and CrystalMaker (Palmer, 2002).

Selected geometric parameters (Å, º) top
Ba1—O6i2.673 (9)Ti1—O1i1.765 (10)
Ba1—O3ii2.673 (7)Ti1—O7vii1.947 (5)
Ba1—O6ii2.703 (5)Ti1—O81.9502 (19)
Ba1—O62.727 (9)Ti1—O31.996 (5)
Ba1—O3iii2.742 (8)Ti1—O22.123 (5)
Ba1—O8iv2.954 (9)Ti1—O12.171 (10)
Ba1—O1ii2.960 (5)Ti1—Ti22.9069 (19)
Ba1—O1iv2.980 (5)Ti2—O31.796 (5)
Ba1—O8v3.035 (10)Ti2—O21.849 (5)
Ba1—O7i3.186 (7)Ti2—O5i2.025 (10)
Ba1—O4vi3.258 (5)Ti2—O52.028 (10)
Ba1—O73.279 (7)Ti2—O4vi2.099 (5)
Ba2—O7vii2.766 (8)Ti2—O5vi2.150 (5)
Ba2—O7vi2.766 (8)Ti2—Ti33.067 (3)
Ba2—O2viii2.858 (9)Ti2—Ti3i3.083 (3)
Ba2—O22.858 (9)Ti2—Ti2ix3.1853 (19)
Ba2—O7ix2.862 (8)Ti2—Ti2vi3.1853 (19)
Ba2—O7x2.862 (8)Ti2—Ti3vi3.2536 (17)
Ba2—O2xi2.899 (9)Ti3—O61.710 (5)
Ba2—O2xii2.899 (8)Ti3—O71.879 (5)
Ba2—O12.928 (5)Ti3—O4vi1.983 (11)
Ba2—O1viii2.928 (5)Ti3—O4ix2.018 (11)
Ba2—O42.998 (5)Ti3—O52.047 (5)
Ba2—O4viii2.998 (5)Ti3—O2ix2.474 (5)
O1i—Ti1—O7vii94.1 (4)O5i—Ti2—O4vi79.3 (3)
O1i—Ti1—O894.9 (4)O5—Ti2—O4vi79.0 (3)
O7vii—Ti1—O8104.55 (18)O3—Ti2—O5vi176.2 (2)
O1i—Ti1—O396.7 (3)O2—Ti2—O5vi87.1 (2)
O7vii—Ti1—O3161.8 (3)O5i—Ti2—O5vi80.7 (3)
O8—Ti1—O389.03 (15)O5—Ti2—O5vi80.6 (3)
O1i—Ti1—O295.2 (4)O4vi—Ti2—O5vi85.73 (19)
O7vii—Ti1—O287.8 (2)O6—Ti3—O797.3 (2)
O8—Ti1—O2163.4 (4)O6—Ti3—O4vi97.1 (4)
O3—Ti1—O276.7 (2)O7—Ti3—O4vi98.0 (4)
O1i—Ti1—O1176.5 (3)O6—Ti3—O4ix96.8 (4)
O7vii—Ti1—O182.8 (3)O7—Ti3—O4ix95.4 (4)
O8—Ti1—O184.3 (5)O4vi—Ti3—O4ix159.3 (3)
O3—Ti1—O186.7 (3)O6—Ti3—O5102.3 (2)
O2—Ti1—O186.4 (3)O7—Ti3—O5160.2 (2)
O3—Ti2—O289.1 (2)O4vi—Ti3—O581.3 (3)
O3—Ti2—O5i100.0 (3)O4ix—Ti3—O580.7 (3)
O2—Ti2—O5i99.3 (4)O6—Ti3—O2ix177.0 (2)
O3—Ti2—O5100.0 (3)O7—Ti3—O2ix85.61 (19)
O2—Ti2—O599.9 (4)O4vi—Ti3—O2ix82.6 (3)
O5i—Ti2—O5152.3 (3)O4ix—Ti3—O2ix82.7 (3)
O3—Ti2—O4vi98.0 (2)O5—Ti3—O2ix74.69 (18)
O2—Ti2—O4vi172.8 (2)
Symmetry codes: (i) x, y1, z; (ii) x+1/2, y1/2, z; (iii) x+1/2, y+1/2, z; (iv) x+1/2, y1/2, z; (v) x+1/2, y+1/2, z; (vi) x+1/2, y1/2, z+1; (vii) x1/2, y1/2, z; (viii) x, y, z+1; (ix) x+1/2, y+1/2, z+1; (x) x1/2, y+1/2, z; (xi) x, y+1, z; (xii) x, y+1, z+1.
 

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