Al₆Ti₂O₁₃, a new phase in the Al₂O₃-TiO₂ system

The compound Al₆Ti₂O₁₃ (hexa­aluminium dititanium trideca­oxide) has been synthesized using an arc-imaging furnace, which allows fast cooling of melted oxides. The structure consists of infinite double chains of polyhedra running along the c axis. These chains are built up by four kinds of strongly distorted oxygen octa­hedra randomly occupied by either Ti or Al (point symmetry m or m2m), and by trigonal bipyramids exclusively occupied by Al (point symmetry m2m).

S1. Comment

The structural examination of the titanium suboxides with the general formula Ti_nO_2n-p (where n and p are positive integers) led to the evolution of the principle of crystallographic shear as an underlying structural principle (Hyde & Andersson, 1989). This concept is devoted to the question of how structures with similar stoichiometry are related (Gibb & Anderson, 1972b). After the validation of this concept for titanium oxides by means of transmission electron microscopy (TEM) and single-crystal X-ray diffraction, the investigations were extended to pseudo-binary systems, M₂O₃–TiO₂, where M₂O₃ denotes an oxide of a trivalent cation with an ionic radius similar to Ti⁴⁺, e.g. Cr³⁺ (Bursill et al., 1971; Gibb & Anderson, 1972a) and Fe³⁺ (Gibb & Anderson, 1972b).

Nevertheless, relatively little attention has been paid to the phase system Al₂O₃–TiO₂, in which only one compound is known, namely β-Al₂TiO₅, which adopts the pseudobrookite (Pauling, 1930) structure type (Austin & Schwartz, 1953). This compound has been studied extensively because of its physical properties. As a result of the low thermal expansion (Bayer, 1971, and references cited therein), it has, for instance, found a number of commercial applications with major European motor manufacturers as exhaust port liners in both petrol and diesel engines as a means of improving thermal efficiency. It is also under serious consideration for use in exhaust manifold inserts, piston crowns and turbocharger liners. Additionally, it finds application in non-ferrous metallurgical industries (Thomas & Stevens, 1989). Later TEM investigations of Al₂O₃–TiO₂ samples with 50 to 70 mol% Al₂O₃ (Mazerolles et al.,1994) revealed new phases with c axes of 12.4 and 16.8 Å, respectively, that were deemed by electron diffraction patterns to be structurally related to β-Al₂TiO₅.

Our research interest regarding high refractory oxides (Kamiya et al., 1980; Yashima et al., 1993) led us to the reinvestigation of the Al₂O₃–TiO₂ system using an arc-imaging furnace. This method of preparation ensures the complete melting of the oxides, avoiding the diffusion problems often observed in solid-state reactions, as well as reactions with the crucible material. In the course of these experiments, we were able to synthesize homogenous samples of the title novel compound suitable for single-crystal X-ray diffraction. The stoichiometry of the investigated sample was confirmed to be Al₆Ti₂O₁₃, as indicated from an energy-dispersive X-ray diffraction study of multiple crystalline fragments.

The structure of the title compound was solved and refined in space group Cm2m. There are five crystallographically independent metal (M) atomic sites and eight such O atomic sites in the unit cell. Three of the M sites have point symmetry m, while the other two have point symmetry m2m. One of the M sites with point symmetry m2m is situated in a trigonal bipyramid of O atoms. The population refinement indicated that this site is wholly occupied by Al. This site is named Al1. The remaining M sites, named M2, M3, M4 and M5, are all located in distorted oxygen octahedra and are populated with both Ti and Al, in the ratio of 2/7 Ti and 5/7 A l.

It should be noted that the refinement of the occupancies of the M2–M5 sites individually gave results that were either within experimental error of the 2/7 Ti: 5/7 A l ratio, or were so highly correlated with the displacement parameters as to be unreliable. Consequently, it was decided to fix the occupancies of these sites to be the same. Small variations from this Ti:Al ratio among the different sites cannot be ruled out.

The rather high residual electron density prompted us to carry out a thorough examination of all electron-density features (especially near the highest peaks). The residual electron density displayed in Fig. 1(a) illustrates typical electron features found on the mirror planes, while the rest of the structural model is relatively free from any residual electron density, e.g. Fig. 1(b). The 2.8 (2) e Å⁻³ peak located 0.709 (8) Å from atom O4 is the most pronounced peak, while another electron-density peak of 2.5 (2) e Å⁻³ is positioned 0.4993 (2) Å from the Al1 site. The electron-density holes follow the same patterns as the peaks, with the largest hole of −2.3 (2) e Å⁻³ located 0.455 (5) Å from the M2 site.

It is not totally unexpected to find some rather high peaks of residual electron density, as Al₆Ti₂O₁₃ samples in general should be likely to contain intergrowths of related compounds. High-resolution TEM studies of Al-enriched β-Al₂TiO₅ crystals (Mazerolles et al.,1994) showed intergrowth between β-Al₂TiO₅, the present Al₆Ti₂O₁₃ and still another phase of unknown composition. This was indicated as an observation of two unknown materials with c axes of 12.4 Å and 16.8 Å, respectively. The former probably corresponds to the structure analysed in the present study. The latter may correspond to an as yet unknown structure with an Al-richer composition. It is therefore possible that a small amount of intergrowth with β-Al₂TiO₅ and/or the still unknown Al-richer compound is present in the crystal studied here.

The arrangement of atoms in the new structure, Al₆Ti₂O₁₃, is shown in Fig. 2. Viewing the atomic lattice along the c axis reveals layers of atoms which are separated by b/2, and each layer is further divided into infinite double strings consisting of metal and O atoms, as seen in Fig. 3. These double strings can be regarded as the equatorial plane of a double chain of polyhedra of the same height, as shown in Fig. 4. Four different types of distorted octahedra and one type of trigonal bipyramid are connected by common edges and apices. The centres of all four octahedra are occupied by both Al³⁺ and Ti⁴⁺ ions, whereas the trigonal bipyramid is exclusively centred by Al³⁺ ions (the Al1 site). The M—O distances within the octahedra range between 1.790 (8) (M4—O7) and 2.093 (8) Å (M3—O6), while they range more tightly between 1.789 (8) (Al1—O1) and 1.936 (6) Å (Al1—O3) for the trigonal bipyramid.

For each octahedron, the shortest M—O distance is found for the O atoms which lie inside the double chain (Fig. 2; atoms O1, O4 and O7). These belong to only three adjacent polyhedra, whereas all other O atoms connect to four. With the exception of the octahedron formed by M2, the next shortest distances are found for the apical atoms (Fig. 2; atoms O3, O5, O6 and O8). Furthermore, all the octahedra in the double strings share edges with the nearest neighbouring octahedra, forming an edge-sharing chain [–M2O₆—M4O₆—M3O₆—M5O₆—M3O₆—M4O₆—M2O₆–] of octahedra. The shortest M—M distance is 2.839 (6) Å and this is located between M3 and M4, sharing an octahedral edge formed by O4 and O7. The shortest O—O distance of 2.449 (9) Å is found between O4 and O7.

The whole Al₆Ti₂O₁₃ structure can be built up by the above-described double chains, as shown in Fig. 4, with the layers sharing polyhedra edges as well. Channels along [100] and [010] result, whereas layers of condensed polyhedra are formed parallel to <010>. However, it should be noted that all polyhedra are strongly distorted. The bonding angle found in the equatorial plane of the trigonal bipyramid is either 127.8 (2) or 104.4 (3)°, which are far from the ideal 120°. The distorted nature of the octahedra is easily described by the divergence from the ideal 90 and 180° bonding angles found in a perfect octahedron. The ideally 90° bond angles in the M2O₆ octahedron vary between 78.0 (2) and 103.2 (2)°, while the vertical O3^iv—M2—O3^v angle is 142.3 (4)°, which is far from 180° [symmetry codes: (iv) 1/2 + x, 1/2 + y, z; (v) −1/2 + x, 1/2 + y, z]. Analogous distortion is seen in all other polyhedra, as well as in the similar compound β-Al₂TiO₅ (Morosin & Lynch, 1972).

Among the octahedra, we find an AlO₅ trigonal bipyramid, which is a less common coordination for Al in crystalline oxides (Santamaria-Perez & Vegas, 2003). A quick review of all Al-containing structures reported to the Inorganic Crystal Structure Database (ICSD, 2001) shows that about 4% have one or more crystallographically independent atomic sites, partly or fully occupied by Al, coordinated to five O atoms. One of the most commonly investigated structure types with AlO₅ polyhedra is the magnetoplumbite structure (Adelsköld, 1938), e.g. SrO(Al₂O₃)₆ (Lindop et al., 1975) and CaO(Al₂O₃)₃(Fe₂O₃)₃ (Harder & Müller-Buschbaum, 1977), with the latter having mixed Al/Fe occupancies on all metal sites. Other examples of five-coordinated Al can be found in the families of aluminosilicates, for instance kyanite (Norton, 1925; Burnham, 1963) and andalusite (Taylor, 1929; Burnham & Buerger, 1961), which both are polymorphs of Al₂SiO₅. Recent studies have revealed that AlO₅ units are also present in amorphous alumina (Gutierrez & Johansson, 2002), as well as in liquid alumina (Landron et al., 2001).

Al and Ti have a tendency to share atomic sites, as the atomic radii of Al³⁺ and Ti⁴⁺ (53 and 61 pm, respectively; Shannon, 1976) are alike enough to facilitate site sharing in oxide structures. Thus, it is not unexpected that no apparent ordering exists for the crystallographically independent octahedra centres. Similar disorder has, for instance, been seen in studies of β-Al₂TiO₅ (Morosin & Lynch, 1972; Epicier et al., 1991) which, like Al₆Ti₂O₁₃, is composed of strongly distorted octahedra. However, the trigonal bipyramid is, in contrast with the octahedra, exclusively occupied by Al according to the present X-ray single-crystal structure analysis. A similar situation was found in the compound SrFe₇Al₅O₁₉, where cation ordering happens in such a way that the bipyramids are exclusively centred by Al³⁺ (Pausch & Müller-Buschbaum, 1976).

S2. Experimental

An appropriate sample for the structure determination of Al₆Ti₂O₁₃ was prepared by melting the corresponding oxides in an arc-imaging furnace followed by a 15 min soaking period immediately below the solidification point, which was indicated by a deformation of the sample surface as well as by a change in reflectivity. It should be noted that the solidification point temperature was not determined directly, but it is known from the literature (Lang et al., 1952, and references cited therein) that equimolar melts of alumina and titania solidify between 2073 and 2133 K. The sample obtained had a flattened spherical shape with a diameter of 2–3 mm. The crushed sample was examined by a conventional light microscope. Some parts of the sample were transparent white, while others are transparent deep-blue to light-blue. The Al to Ti ratio was analysed in a multitude of crystalline fragments from the Al₆Ti₂O₁₃ sample using an energy dispersive X-ray spectrometer (Jeol JED-2001 and JSM-6100). All selected fragments had different sizes and shapes, and every measurement on them gave an Al/Ti ratio of 3:1, as expected for an homogeneously synthesized globule containing a 3:2 ratio of Al₂O₃ and TiO₂. No traces of Cu contamination from the water-cooled sample stage that was used during sample preparation with the arc-imaging furnace were found.

S3. Refinement

The systematic absences (hkl: h + k = 2n, 0kl: k = 2n, h0l: h = 2n, hk0: h + k = 2n, h00: h = 2n and 0k0: k = 2n) suggested Cmmm, Cm2m and C222 as possible space groups. SIR97 (Altomare et al., 1999) was used with a cell setting of P1 to produce a set of atomic positions that were refined using the Xtal3.72 software package (Hall et al., 2000). Adding a symmetry operation of (x + 1/2, y + 1/2, z) revealed the complete structure and determined the space group to be Cm2m. The non-standard setting of space group Amm2 was selected as it is a non-isomorphic subgroup of Cmcm, which is the established space group for the related compound β-Al₂TiO₅ (Austin & Schwartz, 1953). Both the refined isotropic extinction parameter (Zachariasen, 1967) and the Flack (1983) parameter have unusually large standard uncertainties, even though the determined value of each was extremely stable during the refinement, as indicated by the low (Δ/σ)_max. About 3% of the reflections were affected by extinction, with a maximum correction of y = 0.88 for the 200 reflection (the observed structure factor is F_obs = yF_kin, where F_kin is the kinematic value). Most of the affected reflections have a y value of 0.99 or 0.98. Nevertheless, the refined extinction was deemed necessary for successfully describing this structure. The refined Flack parameter of 0.5 (2) is ambiguous, but a test using fixed Flack parameter values between 0.3 and 0.7 revealed that values within this interval have an almost non-existent influence on the final structure parameters. All that can be said from the final Flack parameter is that the crystal fragment used for diffraction is likely to contain domains of its inversion twin.

Computing details

Data collection: RAPID AUTO (Rigaku, 2003); cell refinement: RAPID AUTO; data reduction: RAPID AUTO, and DIFDAT, SORTRF and ADDREF in Xtal3.7 (Hall et al., 2000); program(s) used to solve structure: SIR97 (Altomare et al., 1999); program(s) used to refine structure: CRYLSQ in Xtal3.7 (Hall et al., 2000); molecular graphics: DIAMOND (Brandenburg, 2001), and FOURR, SLANT and CONTRS in Xtal3.7 (Hall et al., 2000); software used to prepare material for publication: BONDLA, ATABLE, and CIFIO in Xtal3.7 (Hall et al., 2000).

Figures

	Fig. 1. Δρ maps for Al6Ti2O13. with positive and negative contours as solid and dotted lines, respectively, at increments of 0.4 e Å^−3 [σ(Δρ) = 0.20 e Å^−3]. The zero contours are dashed and the numbers indicate atomic position distance from the viewed plane. (a) The slightly chaotic residual electron density in the mirror plane as centred on M2, compared with (b), which is also centred on M2.
	Fig. 2. A displacement ellipsoid plot of the Al6Ti2O13 structure. The displacement ellipsoids are drawn at the 90% probability level. [Symmetry codes: (i) −1/2 + x, −1/2 + y, z; (ii) 1/2 + x, −1/2 + y, z; (iii) x, y, 1 − z; (iv) 1/2 + x, 1/2 + y, z;(v) −1/2 + x, 1/2 + y, z; (vi) x, y, −z.]
	Fig. 3. The atomic arrangement, viewed along [001], with the unit cell outlined.
	Fig. 4. Polyhedra representation of the complete Al6Ti2O13 structure, viewed along [100]. The unit cell is outlined.

hexaaluminium dititanium tridecaoxide

Crystal data

Al6Ti2O13	F(000) = 452
Mr = 465.68	Dx = 3.601 Mg m^−3
Orthorhombic, Cm2m	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: c -2 -2	Cell parameters from 23733 reflections
a = 3.6509 (19) Å	θ = 3.2–70.9°
b = 9.368 (5) Å	µ = 2.57 mm^−1
c = 12.554 (6) Å	T = 293 K
V = 429.4 (4) Å^3	Crystal fragment, blue
Z = 2	0.13 × 0.08 × 0.06 mm

Data collection

Rigaku R-AXIS RAPID Query diffractometer	1955 independent reflections
Radiation source: normal-focus sealed tube	1770 reflections with F > 2σ(F)
Graphite monochromator	Rint = 0.053
ω scans	θmax = 45.3°, θmin = 3.3°
Absorption correction: gaussian (RAPID AUTO; Rigaku, 2003)	h = −7→7
Tmin = 0.789, Tmax = 0.889	k = −18→18
4576 measured reflections	l = −24→25

Refinement

Refinement on F	w = 1/[σ^2(F) + 0.01(F)^2]
Least-squares matrix: full	(Δ/σ)max = 0.001
R[F^2 > 2σ(F^2)] = 0.074	Δρmax = 2.83 e Å^−3
wR(F^2) = 0.123	Δρmin = −2.26 e Å^−3
S = 1.39	Extinction correction: isotropic Gaussian [Zachariasen (1967); Larson (1970, Eq. 22, p. 292)], Zachariasen, 1967; Larson (1970), Eq. 22, p. 292
1995 reflections	Extinction coefficient: 4 (3) × 10^2
70 parameters	Absolute structure: Flack (1983), with how many Friedel pairs
1 restraint	Absolute structure parameter: 0.5 (2)
36 constraints

Special details

Refinement. The followin constraints were used during refinement:

H-atom parameters constrained x(Al2)=0.0 + 1.0*x(Ti2) H-atom parameters constrained y(Al2)=0.0 + 1.0*y(Ti2) H-atom parameters constrained z(Al2)=0.0 + 1.0*z(Ti2) H-atom parameters constrained U11(Al2)=0.0 + 1.0*U11(Ti2) H-atom parameters constrained U22(Al2)=0.0 + 1.0*U22(Ti2) H-atom parameters constrained U33(Al2)=0.0 + 1.0*U33(Ti2) H-atom parameters constrained U12(Al2)=0.0 + 1.0*U12(Ti2) H-atom parameters constrained U13(Al2)=0.0 + 1.0*U13(Ti2) H-atom parameters constrained U23(Al2)=0.0 + 1.0*U23(Ti2)

H-atom parameters constrained x(Al3)=0.0 + 1.0*x(Ti3) H-atom parameters constrained y(Al3)=0.0 + 1.0*y(Ti3) H-atom parameters constrained z(Al3)=0.0 + 1.0*z(Ti3) H-atom parameters constrained U11(Al3)=0.0 + 1.0*U11(Ti3) H-atom parameters constrained U22(Al3)=0.0 + 1.0*U22(Ti3) H-atom parameters constrained U33(Al3)=0.0 + 1.0*U33(Ti3) H-atom parameters constrained U12(Al3)=0.0 + 1.0*U12(Ti3) H-atom parameters constrained U13(Al3)=0.0 + 1.0*U13(Ti3) H-atom parameters constrained U23(Al3)=0.0 + 1.0*U23(Ti3)

H-atom parameters constrained x(Al4)=0.0 + 1.0*x(Ti4) H-atom parameters constrained y(Al4)=0.0 + 1.0*y(Ti4) H-atom parameters constrained z(Al4)=0.0 + 1.0*z(Ti4) H-atom parameters constrained U11(Al4)=0.0 + 1.0*U11(Ti4) H-atom parameters constrained U22(Al4)=0.0 + 1.0*U22(Ti4) H-atom parameters constrained U33(Al4)=0.0 + 1.0*U33(Ti4) H-atom parameters constrained U12(Al4)=0.0 + 1.0*U12(Ti4) H-atom parameters constrained U13(Al4)=0.0 + 1.0*U13(Ti4) H-atom parameters constrained U23(Al4)=0.0 + 1.0*U23(Ti4)

H-atom parameters constrained x(Al5)=0.0 + 1.0*x(Ti5) H-atom parameters constrained y(Al5)=0.0 + 1.0*y(Ti5) H-atom parameters constrained z(Al5)=0.0 + 1.0*z(Ti5) H-atom parameters constrained U11(Al5)=0.0 + 1.0*U11(Ti5) H-atom parameters constrained U22(Al5)=0.0 + 1.0*U22(Ti5) H-atom parameters constrained U33(Al5)=0.0 + 1.0*U33(Ti5) H-atom parameters constrained U12(Al5)=0.0 + 1.0*U12(Ti5) H-atom parameters constrained U13(Al5)=0.0 + 1.0*U13(Ti5) H-atom parameters constrained U23(Al5)=0.0 + 1.0*U23(Ti5)

i.e., basically placing Ti and Al together at same site as Al3+ and Ti4+ have similar ionic radii, so no hope of distinguish them from each other during refinement. And the residual electron density does not contradict this approach···

The z parameter of Al1 was after a couple of refinement cycles restrained to its current position, and no other restraints were used.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Al1	0.50000	0.22544	0.50000	0.0211 (18)
Ti2	0.50000	0.5324 (5)	0.38150 (16)	0.0131 (8)	0.28600
Al2	0.50000	0.5324 (5)	0.38150 (16)	0.0131 (8)	0.71400
Ti3	0.50000	0.2048 (5)	0.23660 (15)	0.0128 (7)	0.28600
Al3	0.50000	0.2048 (5)	0.23660 (15)	0.0128 (7)	0.71400
Ti4	0.50000	0.4805 (5)	0.1427 (2)	0.0124 (7)	0.28600
Al4	0.50000	0.4805 (5)	0.1427 (2)	0.0124 (7)	0.71400
Ti5	0.50000	0.1580 (6)	0.00000	0.0091 (9)	0.28600
Al5	0.50000	0.1580 (6)	0.00000	0.0091 (9)	0.71400
O1	0.50000	0.4165 (9)	0.50000	0.011 (2)
O2	0.50000	0.6861 (11)	0.50000	0.017 (3)
O3	0.50000	0.0988 (8)	0.3782 (4)	0.014 (2)
O4	0.50000	0.3874 (10)	0.2863 (6)	0.022 (3)
O5	0.50000	0.6527 (11)	0.2457 (5)	0.017 (2)
O6	0.50000	0.0284 (9)	0.1344 (4)	0.0103 (19)
O7	0.50000	0.2969 (7)	0.1033 (4)	0.0116 (17)
O8	0.50000	0.5902 (9)	0.00000	0.010 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Al1	0.0051 (14)	0.0181 (15)	0.040 (3)	0.00000	0.00000	0.00000
Ti2	0.0085 (9)	0.0197 (8)	0.0113 (7)	0.00000	0.00000	0.0013 (6)
Al2	0.0085 (9)	0.0197 (8)	0.0113 (7)	0.00000	0.00000	0.0013 (6)
Ti3	0.0078 (8)	0.0233 (9)	0.0075 (6)	0.00000	0.00000	−0.0010 (5)
Al3	0.0078 (8)	0.0233 (9)	0.0075 (6)	0.00000	0.00000	−0.0010 (5)
Ti4	0.0059 (7)	0.0141 (7)	0.0173 (8)	0.00000	0.00000	−0.0031 (6)
Al4	0.0059 (7)	0.0141 (7)	0.0173 (8)	0.00000	0.00000	−0.0031 (6)
Ti5	0.0076 (11)	0.0114 (8)	0.0083 (8)	0.00000	0.00000	0.00000
Al5	0.0076 (11)	0.0114 (8)	0.0083 (8)	0.00000	0.00000	0.00000
O1	0.013 (3)	0.014 (2)	0.006 (2)	0.00000	0.00000	0.00000
O2	0.005 (3)	0.023 (4)	0.025 (4)	0.00000	0.00000	0.00000
O3	0.007 (2)	0.026 (3)	0.0073 (17)	0.00000	0.00000	0.0027 (15)
O4	0.014 (2)	0.034 (3)	0.019 (2)	0.00000	0.00000	−0.007 (2)
O5	0.007 (2)	0.033 (3)	0.0111 (18)	0.00000	0.00000	0.001 (2)
O6	0.006 (2)	0.0146 (18)	0.0099 (15)	0.00000	0.00000	0.0052 (15)
O7	0.011 (2)	0.0152 (17)	0.0085 (14)	0.00000	0.00000	0.0030 (13)
O8	0.008 (3)	0.010 (2)	0.010 (2)	0.00000	0.00000	0.00000

Geometric parameters (Å, º)

Al1—O1	1.789 (8)	Al3—O6	2.093 (8)
Al1—O2	1.862 (2)	Al3—O7	1.883 (6)
Al1—O2	1.862 (2)	Ti4—O4	2.003 (8)
Al1—O3	1.936 (6)	Ti4—O5	2.067 (10)
Al1—O3	1.936 (6)	Ti4—O6^i	1.882 (2)
Ti2—O1	1.842 (6)	Ti4—O6	1.882 (2)
Ti2—O2	2.070 (8)	Ti4—O7	1.790 (8)
Ti2—O3^i	1.929 (3)	Ti4—O8	2.065 (5)
Ti2—O3	1.929 (3)	Al4—O4	2.003 (8)
Ti2—O4	1.809 (10)	Al4—O5	2.067 (10)
Ti2—O5	2.044 (8)	Al4—O6^i	1.882 (2)
Al2—O1	1.842 (6)	Al4—O6	1.882 (2)
Al2—O2	2.070 (8)	Al4—O7	1.790 (8)
Al2—O3^i	1.929 (3)	Al4—O8	2.065 (5)
Al2—O3	1.929 (3)	Ti5—O6	2.079 (7)
Al2—O4	1.809 (10)	Ti5—O6^ii	2.079 (7)
Al2—O5	2.044 (8)	Ti5—O7	1.837 (7)
Ti3—O3	2.036 (7)	Ti5—O7^ii	1.837 (7)
Ti3—O4	1.821 (11)	Ti5—O8	1.933 (3)
Ti3—O5	1.893 (3)	Ti5—O8	1.933 (3)
Ti3—O5	1.893 (3)	Al5—O6	2.079 (7)
Ti3—O6	2.093 (8)	Al5—O6^ii	2.079 (7)
Ti3—O7	1.883 (6)	Al5—O7	1.837 (7)
Al3—O3	2.036 (7)	Al5—O7^ii	1.837 (7)
Al3—O4	1.821 (11)	Al5—O8	1.933 (3)
Al3—O5	1.893 (3)	Al5—O8	1.933 (3)
Al3—O5	1.893 (3)
O1—Al1—O3	127.8 (2)	O6—Al3—O5	80.4 (3)
O1—Al1—O3	127.8 (2)	O6—Al3—O5	80.4 (3)
O1—Al1—O2	101.4 (3)	O7—Al3—O5	99.9 (2)
O1—Al1—O2	101.4 (3)	O7—Al3—O5	99.9 (2)
O3—Al1—O3	104.4 (3)	O5—Al3—O5	149.3 (5)
O3—Al1—O2	83.0 (2)	O4—Ti4—O5	77.1 (4)
O3—Al1—O2	83.0 (2)	O4—Ti4—O7	80.2 (4)
O3—Al1—O2	83.0 (2)	O4—Ti4—O8	176.0 (4)
O3—Al1—O2	83.0 (2)	O4—Ti4—O6	98.8 (2)
O2—Al1—O2	157.2 (5)	O4—Ti4—O6^i	98.8 (2)
O1—Ti2—O2	80.2 (3)	O5—Ti4—O7	157.3 (3)
O1—Ti2—O4	95.2 (4)	O5—Ti4—O8	98.9 (4)
O1—Ti2—O5	177.3 (4)	O5—Ti4—O6	81.3 (3)
O1—Ti2—O3	102.0 (2)	O5—Ti4—O6^i	81.3 (3)
O1—Ti2—O3^i	102.0 (2)	O7—Ti4—O8	103.8 (3)
O2—Ti2—O4	175.4 (4)	O7—Ti4—O6	102.3 (3)
O2—Ti2—O5	102.5 (4)	O7—Ti4—O6^i	102.3 (3)
O2—Ti2—O3	78.0 (2)	O8—Ti4—O6	80.4 (2)
O2—Ti2—O3^i	78.0 (2)	O8—Ti4—O6^i	80.4 (2)
O4—Ti2—O5	82.1 (4)	O6—Ti4—O6^i	151.7 (4)
O4—Ti2—O3	103.2 (2)	O4—Al4—O5	77.1 (4)
O4—Ti2—O3^i	103.2 (2)	O4—Al4—O7	80.2 (4)
O5—Ti2—O3	78.7 (2)	O4—Al4—O8	176.0 (4)
O5—Ti2—O3^i	78.7 (2)	O4—Al4—O6	98.8 (2)
O3—Ti2—O3^i	142.3 (4)	O4—Al4—O6^i	98.8 (2)
O1—Al2—O2	80.2 (3)	O5—Al4—O7	157.3 (3)
O1—Al2—O4	95.2 (4)	O5—Al4—O8	98.9 (4)
O1—Al2—O5	177.3 (4)	O5—Al4—O6	81.3 (3)
O1—Al2—O3	102.0 (2)	O5—Al4—O6^i	81.3 (3)
O1—Al2—O3^i	102.0 (2)	O7—Al4—O8	103.8 (3)
O2—Al2—O4	175.4 (4)	O7—Al4—O6	102.3 (3)
O2—Al2—O5	102.5 (4)	O7—Al4—O6^i	102.3 (3)
O2—Al2—O3	78.0 (2)	O8—Al4—O6	80.4 (2)
O2—Al2—O3^i	78.0 (2)	O8—Al4—O6^i	80.4 (2)
O4—Al2—O5	82.1 (4)	O6—Al4—O6^i	151.7 (4)
O4—Al2—O3	103.2 (2)	O6—Ti5—O7	80.8 (3)
O4—Al2—O3^i	103.2 (2)	O6—Ti5—O6^ii	108.5 (4)
O5—Al2—O3	78.7 (2)	O6—Ti5—O7^ii	170.7 (4)
O5—Al2—O3^i	78.7 (2)	O6—Ti5—O8	78.93 (18)
O3—Al2—O3^i	142.3 (4)	O6—Ti5—O8	78.93 (18)
O3—Ti3—O4	99.1 (3)	O7—Ti5—O6^ii	170.7 (4)
O3—Ti3—O6	98.6 (3)	O7—Ti5—O7^ii	89.8 (4)
O3—Ti3—O7	178.1 (4)	O7—Ti5—O8	103.46 (18)
O3—Ti3—O5	79.7 (2)	O7—Ti5—O8	103.46 (18)
O3—Ti3—O5	79.7 (2)	O6^ii—Ti5—O7^ii	80.8 (3)
O4—Ti3—O6	162.2 (3)	O6^ii—Ti5—O8	78.93 (18)
O4—Ti3—O7	82.8 (4)	O6^ii—Ti5—O8	78.93 (18)
O4—Ti3—O5	102.8 (3)	O7^ii—Ti5—O8	103.46 (18)
O4—Ti3—O5	102.8 (3)	O7^ii—Ti5—O8	103.46 (18)
O6—Ti3—O7	79.4 (3)	O8—Ti5—O8	141.6 (4)
O6—Ti3—O5	80.4 (3)	O6—Al5—O7	80.8 (3)
O6—Ti3—O5	80.4 (3)	O6—Al5—O6^ii	108.5 (4)
O7—Ti3—O5	99.9 (2)	O6—Al5—O7^ii	170.7 (4)
O7—Ti3—O5	99.9 (2)	O6—Al5—O8	78.93 (18)
O5—Ti3—O5	149.3 (5)	O6—Al5—O8	78.93 (18)
O3—Al3—O4	99.1 (3)	O7—Al5—O6^ii	170.7 (4)
O3—Al3—O6	98.6 (3)	O7—Al5—O7^ii	89.8 (4)
O3—Al3—O7	178.1 (4)	O7—Al5—O8	103.46 (18)
O3—Al3—O5	79.7 (2)	O7—Al5—O8	103.46 (18)
O3—Al3—O5	79.7 (2)	O6^ii—Al5—O7^ii	80.8 (3)
O4—Al3—O6	162.2 (3)	O6^ii—Al5—O8	78.93 (18)
O4—Al3—O7	82.8 (4)	O6^ii—Al5—O8	78.93 (18)
O4—Al3—O5	102.8 (3)	O7^ii—Al5—O8	103.46 (18)
O4—Al3—O5	102.8 (3)	O7^ii—Al5—O8	103.46 (18)
O6—Al3—O7	79.4 (3)	O8—Al5—O8	141.6 (4)

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