Crystal structure of lutetium aluminate (LUAM), Lu4Al2O9

Simura, R.; Yamane, H.

doi:10.1107/S2056989020005757

research communications

CRYSTALLOGRAPHIC
COMMUNICATIONS

ISSN: 2056-9890

Volume 76| Part 5| May 2020| Pages 752-755

https://doi.org/10.1107/S2056989020005757

Open

access

Crystal structure of lutetium aluminate (LUAM), Lu₄Al₂O₉

Rayko Simura ^a ^* and Hisanori Yamane ^a

^aInstitute of Multidisciplinary Research for Advanced Materials, Tohoku, University, 2-1-1 Katahira, Aoba-ku, Sendai, 980- 8577, Japan
^*Correspondence e-mail: ray@tohoku.ac.jp

Edited by A. M. Chippindale, University of Reading, England (Received 13 April 2020; accepted 26 April 2020; online 30 April 2020)

The crystal structure of the title compound containing lutetium, the last element in the lanthanide series, was determined using a single crystal prepared by heating a pressed pellet of a 2:1 molar ratio mixture of Lu₂O₃ and Al₂O₃ powders in an Ar atmosphere at 2173 K for 4 h. Lu₄Al₂O₉ is isostructural with Eu₄Al₂O₉ and composed of Al₂O₇ ditetrahedra and Lu-centered six- and sevenfold oxygen polyhedra. The unit-cell volume, 787.3 (3) Å³, is the smallest among the volumes of the rare-earth (RE) aluminates, RE₄Al₂O₉. The crystal studied was refined as a two-component pseudo-merohedric twin.

Keywords: crystal structure; Lu₄Al₂O₉; lutetium aluminate monoclinic (LUAM); rare-earth aluminate; Lu₂O₃-Al₂O₃ system; single-crystal X-ray diffraction.

CCDC reference: 1999289

1. Chemical context

In the Al₂O₃-Lu₂O₃ system, where Lu has the largest atomic number among the rare-earth elements (RE), the following three phases have been reported: Lu₃Al₅O₁₂, LuAlO₃, and Lu₄Al₂O₉. These phases have been actively investigated as host materials, not only for phosphors (Ding et al., 2011 ; Xiang et al., 2016 ; Wang et al., 2018 ), but also for scintillators, owing to their large radiation absorption cross sections arising from the presence of Lu. Various scintillation properties of Ce- and Pr-doped Lu₃Al₅O₁₂ and LuAlO₃ crystals have been characterized (Wojtowicz, 1999 ; Nikl, 2000 ; Wojtowicz et al., 2006 ; Nikl et al., 2013 ), and the luminescence properties of Ce- and Pr-doped Lu₄Al₂O₉ evaluated (Lempicki et al., 1996 ; Zhang et al., 1997 , Zhang et al., 1998 ; Drozdowski et al., 2005 ). The crystal structures of the lutetium aluminates Lu₃Al₅O₁₂ (Euler & Bruce, 1965 ) and LuAlO₃ (Dernier & Maines, 1971 ; Shishido et al., 1995 ) have been determined as garnet-type (LUAG) and perovskite-type (LUAP), respectively. However, to date, there have been no reports of the lattice constants of Lu₄Al₂O₉, although Shirvinskaya & Popova (1977 ) treated it as isotypic with Y₄Al₂O₉ and have reported the d-spacings and relative peak intensities in the powder X-ray diffraction pattern (PDF#00-033-0844).

Many REAl₂O₉ compounds have been investigated in detail. After Warshaw & Roy (1959 ) first reported the existence of Y₄Al₂O₉, Reed & Chase (1962 ) determined the space group of this material as P2₁/c using X-ray Weissenberg and precession photography. Christensen & Hazell (1991 ) later determined the crystal structure of Y₄Al₂O₉ using powder synchrotron X-ray and neutron diffraction. Brandle & Steinfink (1969 ) also prepared crystals of REAl₂O₉ (RE = Sm, Gd, Eu, Dy, Ho) and determined the crystal structure of Eu₄Al₂O₉ using X-ray diffraction.

The lattice parameters of RE₄Al₂O₉ have previously been reported for RE = Y (Lehmann et al., 1987 ; Reed & Chase, 1962; Christensen & Hazell, 1991; Yamane et al., 1995b ; Talik et al., 2016 ), La (Dohrup et al., 1996 ), Pr (Dohrup et al., 1996), Nd (Dohrup et al., 1996), Sm (Brandle & Steinfink, 1969; Mizuno et al., 1977a ; Yamane et al., 1995a ), Eu (Brandle & Steinfink, 1969; Mizuno et al., 1977b ; Yamane et al., 1995a), Gd (Brandle & Steinfink, 1969; Mizuno et al., 1977b; Yamane et al., 1995a; Dohrup et al., 1996; Martín-Sedeño et al., 2006 ), Tb (Jero & Kriven, 1988 ; Yamane et al., 1995a; Dohrup et al., 1996; Li et al., 2009 ), Dy (Brandle & Steinfink, 1969; Mizuno et al., 1978 ; Yamane et al., 1995a), Ho (Brandle & Steinfink, 1969; Mizuno, 1979 ; Yamane et al., 1995a), Er (Mizuno, 1979; Yamane et al., 1995a), Tm (Yamane et al., 1995a), and Yb (Mizuno & Noguchi, 1980 ; Yamane et al., 1995a).

Wu & Pelton (1992 ) investigated the phase diagram of the Lu₂O₃–Al₂O₃ system and showed that Lu₄Al₂O₉ melted congruently at 2313 K under an inert atmosphere. Petrosyan et al. (2006 ) studied the same system under a reducing atmosphere and reported that Lu₄Al₂O₉ could be formed by reaction of Lu₂O₃ and Lu₃Al₅O₁₂ at 1923 K, but decomposed into Lu₂O₃ and a melt at 2273 K. Subsequently, Petrosyan et al. (2013 ) observed incongruent melting of Lu₄Al₂O₉ at 2123 K under an Ar / 2% H₂ atmosphere using differential thermal analysis (DTA). Klimm (2010 ) employed DTA to investigate LuAlO₃ melting behavior in a 5 N pure Ar flow and concluded that the congruent and incongruent melting of LuAlO₃ depended on the atmospheric conditions. The author also concluded that the phase diagram at around Lu:Al = 1:1 under an inert atmosphere, previously reported by Wu & Pelton (1992), is correct. Yamane et al. (1995a) reported that only a very small amount of Lu₄Al₂O₉ can be obtained by reactions in air at 1673–2073 K, even though RE₄Al₂O₉ (RE = Y, Sm–Yb) can be synthesized under the same conditions.

Following these reports, the present authors also attempted to synthesize Lu₄Al₂O₉ by heating a 2:1 molar ratio powder mixture of Lu₂O₃ and Al₂O₃ at 2073 K for 2 h in air, but the sample obtained was a mixture of LuAlO₃ and Lu₂O₃ (see Fig. S1a in the supporting information). The method used to prepare the single crystals of Lu₄Al₂O₉ used for the present diffraction study is described below.

2. Structural commentary

X-ray diffraction spots from the Lu₄Al₂O₉ single crystal were indexed on the basis of a monoclinic unit cell with lattice parameters: a = 7.236 (2) Å, b = 10.333 (2) Å, c = 11.096 (3) Å, and β = 108.38 (2)°. As shown in Fig. 1, the unit-cell volume of Lu₄Al₂O₉ calculated from these parameters lies on the extrapolated line of RE₄Al₂O₉ volumes plotted against the effective ionic radii for sixfold coordination of the trivalent rare-earth anions (RE³⁺) (Shannon, 1976 ). In other words, Lu₄Al₂O₉ containing Lu, which has the smallest effective ionic radius of the RE atoms, has the smallest unit-cell volume in the RE₄Al₂O₉ series, in line with predictions arising from the lanthanide contraction.

Figure 1
Unit-cell volume of RE₄Al₂O₉ versus effective ionic radius for the trivalent rare-earth anion (RE³⁺) with sixfold coordination.

The crystal structure of Lu₄Al₂O₉ (space group P2₁/c), determined using Eu₄Al₂O₉ (Brandle & Steinfink, 1969) as the starting model, contains two crystallographically distinct Al sites, four Lu sites, and nine O sites. The two Al sites are tetrahedrally coordinated by oxygen atoms. The two Al tetrahedra are connected through a shared O5 atom, forming an Al₂O₇ ditetrahedral oxy-aluminate group (Fig. 2). The Al₂O₇ dimers lie parallel to the a axis, and are related by the c glide symmetry operation (Fig. 3). The average Al1—O and Al2—O distances in Lu₄Al₂O₉ are 1.744 and 1.756 Å, respectively, which are comparable to values found in Eu₄Al₂O₉ (1.741 and 1.755 Å, Brandle & Steinfink, 1969) and Y₄Al₂O₉ (1.739 and 1.769 Å, Lehmann et al., 1987). The bond-valence sums (BVS; Brown & Altermatt, 1985 ) calculated using the Al—O distances and bond-valence parameters recently reported by Gagne & Hawthorne (2015 ) (r₀ =1.634 Å, b = 0.39) are 3.02 and 2.93 for Al1 and Al2, respectively. These BVS values are close to those expected for trivalent Al. The Al1—O5—Al2 angle of the Al₂O₇ dimer is 134.9 (3)°, which is smaller than the corresponding angles in Eu₄Al₂O₉ (141.9°; Brandle & Steinfink, 1969) and Y₄Al₂O₉ (137.6°; Lehmann et al., 1987).

Figure 2
The atomic arrangement of Lu₄Al₂O₉ depicted with displacement ellipsoids at the 99% probability level. [Symmetry codes: (i) 1 − x, −y, 1 − z; (ii) −x, −y, 1 − z; (iii) x − 1, y, z; (iv) 1 + x, −y + $[{1\over 2}]$ , z − $[{1\over 2}]$ ; (v) x + 1, y, z; (vi) x, −y + $[{1\over 2}]$ , z − $[{1\over 2}]$ ; (vii) x, −y + $[{1\over 2}]$ , z + $[{1\over 2}]$ ; (viii) x, y, z − 1.]

Figure 3
The crystal structure of Lu₄Al₂O₉ highlighting the Al₂O₇ ditetrahedra viewed down the b axis (upper), and the Al₂O₇ ditetrahedra and Lu-centered polyhedra viewed down the a axis (lower).

Of the four crystallographically distinct Lu atoms, Lu1 and Lu3 are coordinated by seven oxygen atoms with five Lu—O distances in the range 2.219 (5)–2.344 (5) Å and two in the range 2.461 (6)–2.573 (6) Å. The remaining Lu atoms, Lu2 and Lu4, are coordinated by six oxygen atoms in distorted octahedra with Lu—O distances in the range 2.172 (6)–2.337 (6) Å.

The averages Lu—O distances for the six-fold coordinated Lu atoms in Lu₄Al₂O₉ are 2.250 and 2.260 Å for Lu2 and Lu4, respectively. These values are 0.02–0.10 Å shorter than those for the LuO₆ octahedra found in Lu₃Al₅O₁₂ (2.352 Å; Euler & Bruce, 1965) and LuAlO₃ (2.330 Å; Shishido et al., 1995).

The average values for the Eu—O and Y—O distances in Eu₄Al₂O₉ and Y₄Al₂O₉ lie in the ranges 2.328–2.439 Å (Brandle & Steinfink, 1969) and 2.286–2.387 Å (Lehmann et al., 1987), respectively. The differences between the RE—O lengths in RE₄Al₂O₉ when RE = Eu and Lu (0.07–0.09 Å), and when RE = Y and Lu (0.02–0.05 Å) correspond to the differences between ^VIr_Eu − ^VIr_Lu (0.086 Å) and ^VIr_Y − ^VIr_Lu (0.039 Å), where ^VIr_Eu, ^VIr_Lu, and ^VIr_Lu are the effective ionic radii in sixfold coordination of Lu³⁺ (0.861 Å), Eu³⁺ (0.947 Å), and Y³⁺ (0.900 Å), respectively (Shannon, 1976). The BVS for Lu1, Lu2, Lu3, and Lu4, calculated using the bond-valence parameters (r₀ = 1.939 Å, b = 0.403) of Gagné & Hawthorne (2015), are 2.766, 2.796, 2.642, and 2.714, respectively, which are smaller than the expected valence value of +3 for the Lu atoms. The polyhedral volumes of Lu1O₇ (18.18 Å³), Lu2O₆ (14.29 Å³), Lu3O₇ (18.56 Å³), and Lu4O₆ (14.24 Å³) are 1.1–1.7 Å³ and 0.5–0.8 Å³ smaller than those for Eu₄Al₂O₉ (Eu1O₇:19.85 Å³, Eu2O₆:15.38 Å³, Eu3O₇:20.14 Å³, and Eu4O₆:15.71 Å³) and for Y₄Al₂O₉ (Y1O₇:18.66 Å³, Y2O₆:14.77 Å³, Y3O₇:19.33 Å³, and Y4O₆:14.98 Å³), respectively. These differences in polyhedral volumes correlate with the differences in ionic radii of the lanthanides.

3. Synthesis and crystallization

The starting powders Al₂O₃ (Sumitomo Chemicals, AKP20, 99.99%) and Lu₂O₃ (Nippon Yttrium, 99.999%) were mixed in a molar ratio of Lu:Al = 2:1, ground with ethanol in an agate mortar, and pressed into a pellet. The pellet was placed in a BN crucible with an inner diameter of 18 mm and a height of 20 mm. The BN crucible was covered with a BN lid, and heated in a chamber with a carbon heater (Shimadzu Mectem, Inc., VESTA). The pellet was heated slowly under vacuum (∼10 ⁻² Pa) from room temperature to 1273 K. During the 5 min. hold at 1273 K, the chamber was filled with Ar (99.9995%) up to 0.15 MPa. The temperature was then raised to 2173 K at a heating rate of 300 Kh⁻¹. After being held at 2173 K for 4 h, the sample was cooled to 1473 K at a rate of 20 Kh⁻¹, and then to room temperature by shutting off the heater. A part of the obtained sample was pulverized in the agate mortar, and powder X-ray diffraction measurements (Bruker D2 Phaser, Cu Kα radiation) confirmed that the major crystalline phase present in the sample was Lu₄Al₂O₉, together with small amounts of LuAlO₃ and unreacted Lu₂O₃ (Fig. S1a). Colorless crystals of Lu₄Al₂O₉ were selected for single-crystal X-ray diffraction studies.

4. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1. The Eu atoms in the rare-earth metal sites in the structural model of Eu₄Al₂O₉ (Brandle & Steinfink, 1969) were replaced by Lu atoms to generate the initial model. Several iterations of refinement yielded an R value of 10.07% and a residual electron density of ∼10 e Å⁻³. A subsequent refinement, performed by implementing the (100) twin plane observed in a study of Y₄Al₂O₉ (Yamane et al., 1995b), yielded an R(F² > 2σ(F²)) value of 1.92% with an approximate volume ratio of 6:4 for the twin domains.

Table 1
Experimental details

Crystal data
Chemical formula	Lu₄Al₂O₉
M_r	897.84
Crystal system, space group	Monoclinic, P2₁/c
Temperature (K)	301
a, b, c (Å)	7.2360 (11), 10.3330 (19), 11.096 (3)
β (°)	108.381 (11)
V (Å³)	787.3 (3)
Z	4
Radiation type	Mo Kα
μ (mm⁻¹)	49.97
Crystal size (mm)	0.12 × 0.05 × 0.04

Data collection
Diffractometer	Bruker D8 QUEST
Absorption correction	Multi-scan (SADABS; Bruker, 2016 )
T_min, T_max	0.451, 0.746
No. of measured, independent and observed [I > 2σ(I)] reflections	32672, 2795, 2719
R_int	0.035
(sin θ/λ)_max (Å⁻¹)	0.748

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.019, 0.043, 1.17
No. of reflections	2795
No. of parameters	138
Δρ_max, Δρ_min (e Å⁻³)	1.49, −1.81
Computer programs: APEX3 (Bruker, 2018 ), SAINT (Bruker, 2017 ), SHELXL2014/7 (Sheldrick, 2015 ), VESTA (Momma & Izumi, 2011 ) and publCIF (Westrip, 2010 ).

Supporting information

CCDC reference: 1999289

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2056989020005757/cq2036sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2056989020005757/cq2036Isup2.hkl

Figure S1. Powder XRD patterns of samples prepared (a) under air and (b) under Ar. DOI: https://doi.org/10.1107/S2056989020005757/cq2036sup3.tif

checkCIF report

Computing details top

Data collection: APEX3 (Bruker, 2018); cell refinement: APEX3 (Bruker, 2018); data reduction: SAINT (Bruker, 2017); program(s) used to refine structure: SHELXL2014/7 (Sheldrick, 2015b); molecular graphics: VESTA (Momma & Izumi, 2011); software used to prepare material for publication: publCIF (Westrip, 2010).

Lutetium aluminate top

Crystal data top

Lu₄Al₂O₉	F(000) = 1528
M_r = 897.84	D_x = 7.575 Mg m⁻³
Monoclinic, P2₁/c	Mo Kα radiation, λ = 0.71073 Å
a = 7.2360 (11) Å	Cell parameters from 1294 reflections
b = 10.3330 (19) Å	θ = 2.8–38.5°
c = 11.096 (3) Å	µ = 49.97 mm⁻¹
β = 108.381 (11)°	T = 301 K
V = 787.3 (3) Å³	Chip, colourless
Z = 4	0.12 × 0.05 × 0.04 mm

Data collection top

Bruker D8 QUEST diffractometer	2719 reflections with I > 2σ(I)
Detector resolution: 7.3910 pixels mm^-1	R_int = 0.035
ω and σcans	θ_max = 32.1°, θ_min = 2.8°
Absorption correction: multi-scan (SADABS; Bruker, 2016)	h = −10→10
T_min = 0.451, T_max = 0.746	k = −15→15
32672 measured reflections	l = −16→16
2795 independent reflections

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	w = 1/[σ²(F_o²) + 17.273P] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.019	(Δ/σ)_max = 0.001
wR(F²) = 0.043	Δρ_max = 1.49 e Å⁻³
S = 1.17	Δρ_min = −1.81 e Å⁻³
2795 reflections	Extinction correction: SHELXL2014/7 (Sheldrick 2015b), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
138 parameters	Extinction coefficient: 0.00026 (2)

Special details top

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

Refinement. Refined as a two-component inversion twin

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Al1	0.2142 (4)	0.1742 (2)	0.1270 (2)	0.0058 (4)
Al2	0.6551 (4)	0.1717 (2)	0.1108 (2)	0.0059 (4)
Lu1	0.52225 (7)	0.11375 (3)	0.78409 (2)	0.00572 (6)
Lu2	0.02236 (6)	0.10027 (3)	0.80405 (2)	0.00574 (6)
Lu3	0.34172 (7)	0.12783 (3)	0.44005 (2)	0.00605 (6)
Lu4	0.83940 (6)	0.12082 (3)	0.41774 (3)	0.00610 (6)
O1	0.7934 (8)	0.2450 (6)	0.7469 (5)	0.0102 (11)
O2	0.2314 (8)	0.2439 (5)	0.7699 (5)	0.0072 (11)
O3	0.2106 (13)	0.0095 (5)	0.1516 (5)	0.0102 (10)
O4	0.0720 (8)	0.2340 (6)	0.9813 (6)	0.0092 (11)
O5	0.4326 (10)	0.2381 (4)	0.1156 (5)	0.0085 (8)
O6	0.6371 (8)	0.2328 (5)	0.9599 (5)	0.0072 (11)
O7	0.6926 (13)	0.0084 (5)	0.1529 (5)	0.0111 (10)
O8	0.0764 (12)	−0.0082 (5)	0.3927 (5)	0.0072 (9)
O9	0.5643 (13)	0.0063 (5)	0.3906 (5)	0.0069 (9)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Al1	0.0071 (12)	0.0044 (8)	0.0067 (9)	0.0012 (8)	0.0032 (8)	0.0005 (7)
Al2	0.0074 (12)	0.0050 (8)	0.0055 (8)	0.0010 (8)	0.0021 (8)	0.0012 (7)
Lu1	0.00622 (14)	0.00463 (12)	0.00594 (10)	0.00019 (12)	0.00140 (14)	−0.00101 (8)
Lu2	0.00566 (13)	0.00433 (12)	0.00733 (10)	−0.00031 (13)	0.00218 (14)	−0.00058 (8)
Lu3	0.00647 (13)	0.00518 (11)	0.00625 (10)	0.00024 (13)	0.00165 (13)	0.00101 (9)
Lu4	0.00538 (14)	0.00435 (10)	0.00863 (10)	0.00048 (13)	0.00231 (15)	0.00137 (9)
O1	0.008 (3)	0.013 (3)	0.008 (2)	0.0039 (19)	0.0002 (18)	0.002 (2)
O2	0.009 (3)	0.006 (2)	0.007 (2)	0.0012 (18)	0.0030 (19)	0.0010 (17)
O3	0.011 (3)	0.006 (2)	0.015 (2)	0.000 (3)	0.007 (3)	0.0006 (17)
O4	0.009 (3)	0.007 (2)	0.009 (2)	0.0039 (18)	−0.0009 (18)	−0.0003 (19)
O5	0.008 (2)	0.0064 (18)	0.012 (2)	−0.003 (2)	0.004 (2)	−0.0003 (15)
O6	0.008 (3)	0.007 (2)	0.007 (2)	0.0017 (18)	0.0018 (18)	0.0009 (17)
O7	0.013 (3)	0.008 (2)	0.016 (2)	0.003 (3)	0.009 (3)	0.0059 (18)
O8	0.005 (3)	0.006 (2)	0.009 (2)	−0.003 (2)	0.000 (3)	−0.0002 (16)
O9	0.010 (3)	0.0042 (19)	0.007 (2)	0.001 (3)	0.003 (3)	0.0001 (16)

Geometric parameters (Å, º) top

Al1—O3	1.724 (6)	Lu3—O5^iv	2.310 (5)
Al1—O4ⁱ	1.733 (6)	Lu3—O6ⁱⁱ	2.529 (5)
Al1—O5	1.754 (7)	Lu3—O4ⁱⁱ	2.573 (6)
Al1—O2ⁱⁱ	1.767 (6)	Lu3—Al2^iv	3.211 (2)
Al1—Lu1ⁱⁱ	3.219 (2)	Lu3—Al1^iv	3.247 (2)
Al1—Lu3ⁱⁱ	3.247 (2)	Lu3—Lu3ⁱⁱⁱ	3.4748 (8)
Al1—Lu3	3.336 (2)	Lu3—Lu4ⁱⁱⁱ	3.4803 (7)
Al2—O7	1.749 (6)	Lu4—O4^ix	2.198 (6)
Al2—O1ⁱⁱ	1.753 (6)	Lu4—O9	2.253 (8)
Al2—O6ⁱ	1.755 (6)	Lu4—O6ⁱⁱ	2.255 (6)
Al2—O5	1.767 (7)	Lu4—O8^v	2.257 (8)
Al2—Lu3ⁱⁱ	3.211 (2)	Lu4—O1ⁱⁱ	2.287 (6)
Al2—Lu1ⁱⁱ	3.272 (2)	Lu4—O8ⁱⁱⁱ	2.311 (5)
Al2—Lu4	3.285 (2)	Lu4—Lu3ⁱⁱⁱ	3.4804 (7)
Lu1—O9ⁱⁱⁱ	2.219 (5)	Lu4—Lu4^x	3.5061 (8)
Lu1—O6	2.233 (5)	Lu4—Lu2^ix	3.5641 (7)
Lu1—O3ⁱⁱⁱ	2.236 (8)	Lu4—Lu3^v	3.5652 (7)
Lu1—O7ⁱⁱⁱ	2.277 (8)	Lu4—Lu1ⁱⁱ	3.5836 (7)
Lu1—O5^iv	2.344 (5)	O1—Al2^iv	1.753 (6)
Lu1—O2	2.461 (6)	O1—Lu2^v	2.172 (6)
Lu1—O1	2.524 (6)	O1—Lu4^iv	2.287 (6)
Lu1—Al1^iv	3.219 (2)	O2—Al1^iv	1.767 (6)
Lu1—Al2^iv	3.272 (2)	O2—Lu3^iv	2.238 (5)
Lu1—Lu2^v	3.5579 (7)	O3—Lu2^vii	2.213 (8)
Lu1—Lu4^iv	3.5836 (7)	O3—Lu1ⁱⁱⁱ	2.236 (8)
Lu1—Lu3	3.6270 (9)	O4—Al1^xi	1.733 (6)
Lu2—O1^vi	2.172 (6)	O4—Lu4^viii	2.198 (6)
Lu2—O3^vii	2.213 (8)	O4—Lu3^iv	2.573 (6)
Lu2—O2	2.235 (6)	O5—Lu3ⁱⁱ	2.310 (5)
Lu2—O7ⁱⁱⁱ	2.263 (8)	O5—Lu1ⁱⁱ	2.344 (5)
Lu2—O8^vii	2.280 (5)	O6—Al2^xi	1.754 (6)
Lu2—O4	2.337 (6)	O6—Lu4^iv	2.255 (6)
Lu2—Lu1^vi	3.5579 (7)	O6—Lu3^iv	2.529 (5)
Lu2—Lu4^viii	3.5641 (7)	O7—Lu2ⁱⁱⁱ	2.263 (8)
Lu2—Lu3^iv	3.6485 (7)	O7—Lu1ⁱⁱⁱ	2.277 (8)
Lu2—Lu4ⁱⁱⁱ	3.7187 (7)	O8—Lu4^vi	2.257 (8)
Lu2—Lu3^vii	3.9156 (7)	O8—Lu2^vii	2.280 (5)
Lu3—O2ⁱⁱ	2.238 (5)	O8—Lu4ⁱⁱⁱ	2.311 (5)
Lu3—O9	2.242 (8)	O9—Lu1ⁱⁱⁱ	2.219 (5)
Lu3—O9ⁱⁱⁱ	2.260 (5)	O9—Lu3ⁱⁱⁱ	2.260 (5)
Lu3—O8	2.302 (7)

O3—Al1—O4ⁱ	117.7 (3)	O2ⁱⁱ—Lu3—O8	96.84 (19)
O3—Al1—O5	116.2 (4)	O9—Lu3—O8	102.35 (18)
O4ⁱ—Al1—O5	94.7 (3)	O9ⁱⁱⁱ—Lu3—O8	80.0 (2)
O3—Al1—O2ⁱⁱ	109.3 (3)	O2ⁱⁱ—Lu3—O5^iv	106.69 (18)
O4ⁱ—Al1—O2ⁱⁱ	121.3 (3)	O9—Lu3—O5^iv	120.4 (2)
O5—Al1—O2ⁱⁱ	94.3 (3)	O9ⁱⁱⁱ—Lu3—O5^iv	74.68 (16)
O3—Al1—Lu1ⁱⁱ	128.9 (3)	O8—Lu3—O5^iv	123.6 (2)
O4ⁱ—Al1—Lu1ⁱⁱ	111.6 (2)	O2ⁱⁱ—Lu3—O6ⁱⁱ	78.65 (19)
O5—Al1—Lu1ⁱⁱ	45.30 (17)	O9—Lu3—O6ⁱⁱ	71.8 (2)
O2ⁱⁱ—Al1—Lu1ⁱⁱ	49.24 (19)	O9ⁱⁱⁱ—Lu3—O6ⁱⁱ	104.6 (2)
O3—Al1—Lu3ⁱⁱ	138.1 (3)	O8—Lu3—O6ⁱⁱ	171.4 (2)
O4ⁱ—Al1—Lu3ⁱⁱ	52.0 (2)	O5^iv—Lu3—O6ⁱⁱ	65.0 (2)
O5—Al1—Lu3ⁱⁱ	43.34 (18)	O2ⁱⁱ—Lu3—O4ⁱⁱ	74.48 (19)
O2ⁱⁱ—Al1—Lu3ⁱⁱ	108.5 (2)	O9—Lu3—O4ⁱⁱ	176.2 (2)
Lu1ⁱⁱ—Al1—Lu3ⁱⁱ	68.24 (5)	O9ⁱⁱⁱ—Lu3—O4ⁱⁱ	103.8 (2)
O3—Al1—Lu3	72.9 (2)	O8—Lu3—O4ⁱⁱ	75.8 (2)
O4ⁱ—Al1—Lu3	155.5 (2)	O5^iv—Lu3—O4ⁱⁱ	63.1 (2)
O5—Al1—Lu3	99.75 (19)	O6ⁱⁱ—Lu3—O4ⁱⁱ	109.64 (15)
O2ⁱⁱ—Al1—Lu3	38.37 (18)	O2ⁱⁱ—Lu3—Al2^iv	96.50 (15)
Lu1ⁱⁱ—Al1—Lu3	67.47 (5)	O9—Lu3—Al2^iv	94.44 (18)
Lu3ⁱⁱ—Al1—Lu3	135.61 (8)	O9ⁱⁱⁱ—Lu3—Al2^iv	86.21 (17)
O7—Al2—O1ⁱⁱ	104.2 (3)	O8—Lu3—Al2^iv	155.68 (16)
O7—Al2—O6ⁱ	124.1 (3)	O5^iv—Lu3—Al2^iv	32.39 (17)
O1ⁱⁱ—Al2—O6ⁱ	119.7 (3)	O6ⁱⁱ—Lu3—Al2^iv	32.95 (13)
O7—Al2—O5	115.6 (4)	O4ⁱⁱ—Lu3—Al2^iv	88.36 (14)
O1ⁱⁱ—Al2—O5	93.5 (3)	O2ⁱⁱ—Lu3—Al1^iv	93.90 (15)
O6ⁱ—Al2—O5	95.4 (3)	O9—Lu3—Al1^iv	151.60 (17)
O7—Al2—Lu3ⁱⁱ	143.2 (3)	O9ⁱⁱⁱ—Lu3—Al1^iv	85.82 (16)
O1ⁱⁱ—Al2—Lu3ⁱⁱ	107.2 (2)	O8—Lu3—Al1^iv	98.38 (18)
O6ⁱ—Al2—Lu3ⁱⁱ	51.62 (19)	O5^iv—Lu3—Al1^iv	31.41 (17)
O5—Al2—Lu3ⁱⁱ	44.47 (16)	O6ⁱⁱ—Lu3—Al1^iv	89.32 (13)
O7—Al2—Lu1ⁱⁱ	123.1 (2)	O4ⁱⁱ—Lu3—Al1^iv	32.07 (14)
O1ⁱⁱ—Al2—Lu1ⁱⁱ	49.8 (2)	Al2^iv—Lu3—Al1^iv	60.46 (5)
O6ⁱ—Al2—Lu1ⁱⁱ	111.7 (2)	O2ⁱⁱ—Lu3—Al1	29.36 (15)
O5—Al2—Lu1ⁱⁱ	43.89 (17)	O9—Lu3—Al1	79.05 (14)
Lu3ⁱⁱ—Al2—Lu1ⁱⁱ	68.03 (5)	O9ⁱⁱⁱ—Lu3—Al1	149.97 (14)
O7—Al2—Lu4	65.8 (2)	O8—Lu3—Al1	85.02 (13)
O1ⁱⁱ—Al2—Lu4	41.4 (2)	O5^iv—Lu3—Al1	134.72 (12)
O6ⁱ—Al2—Lu4	158.5 (2)	O6ⁱⁱ—Lu3—Al1	87.58 (13)
O5—Al2—Lu4	96.12 (18)	O4ⁱⁱ—Lu3—Al1	97.42 (14)
Lu3ⁱⁱ—Al2—Lu4	134.03 (8)	Al2^iv—Lu3—Al1	115.70 (7)
Lu1ⁱⁱ—Al2—Lu4	66.26 (5)	Al1^iv—Lu3—Al1	122.25 (5)
O9ⁱⁱⁱ—Lu1—O6	174.8 (3)	O2ⁱⁱ—Lu3—Lu3ⁱⁱⁱ	142.19 (14)
O9ⁱⁱⁱ—Lu1—O3ⁱⁱⁱ	86.4 (2)	O9—Lu3—Lu3ⁱⁱⁱ	39.67 (13)
O6—Lu1—O3ⁱⁱⁱ	89.4 (2)	O9ⁱⁱⁱ—Lu3—Lu3ⁱⁱⁱ	39.30 (19)
O9ⁱⁱⁱ—Lu1—O7ⁱⁱⁱ	85.8 (2)	O8—Lu3—Lu3ⁱⁱⁱ	91.43 (16)
O6—Lu1—O7ⁱⁱⁱ	98.0 (2)	O5^iv—Lu3—Lu3ⁱⁱⁱ	98.91 (14)
O3ⁱⁱⁱ—Lu1—O7ⁱⁱⁱ	101.03 (18)	O6ⁱⁱ—Lu3—Lu3ⁱⁱⁱ	87.86 (13)
O9ⁱⁱⁱ—Lu1—O5^iv	74.76 (17)	O4ⁱⁱ—Lu3—Lu3ⁱⁱⁱ	143.06 (13)
O6—Lu1—O5^iv	105.69 (19)	Al2^iv—Lu3—Lu3ⁱⁱⁱ	90.40 (5)
O3ⁱⁱⁱ—Lu1—O5^iv	128.4 (2)	Al1^iv—Lu3—Lu3ⁱⁱⁱ	121.35 (4)
O7ⁱⁱⁱ—Lu1—O5^iv	124.3 (2)	Al1—Lu3—Lu3ⁱⁱⁱ	116.13 (4)
O9ⁱⁱⁱ—Lu1—O2	104.5 (2)	O2ⁱⁱ—Lu3—Lu4ⁱⁱⁱ	137.27 (15)
O6—Lu1—O2	80.21 (19)	O9—Lu3—Lu4ⁱⁱⁱ	95.71 (15)
O3ⁱⁱⁱ—Lu1—O2	165.4 (2)	O9ⁱⁱⁱ—Lu3—Lu4ⁱⁱⁱ	39.5 (2)
O7ⁱⁱⁱ—Lu1—O2	70.7 (2)	O8—Lu3—Lu4ⁱⁱⁱ	41.12 (12)
O5^iv—Lu1—O2	64.9 (2)	O5^iv—Lu3—Lu4ⁱⁱⁱ	96.21 (14)
O9ⁱⁱⁱ—Lu1—O1	100.2 (2)	O6ⁱⁱ—Lu3—Lu4ⁱⁱⁱ	144.07 (12)
O6—Lu1—O1	75.68 (19)	O4ⁱⁱ—Lu3—Lu4ⁱⁱⁱ	85.06 (13)
O3ⁱⁱⁱ—Lu1—O1	73.7 (2)	Al2^iv—Lu3—Lu4ⁱⁱⁱ	120.37 (4)
O7ⁱⁱⁱ—Lu1—O1	171.6 (2)	Al1^iv—Lu3—Lu4ⁱⁱⁱ	87.25 (5)
O5^iv—Lu1—O1	63.4 (2)	Al1—Lu3—Lu4ⁱⁱⁱ	123.92 (4)
O2—Lu1—O1	112.92 (16)	Lu3ⁱⁱⁱ—Lu3—Lu4ⁱⁱⁱ	64.036 (14)
O9ⁱⁱⁱ—Lu1—Al1^iv	87.18 (17)	O4^ix—Lu4—O9	163.0 (2)
O6—Lu1—Al1^iv	95.83 (15)	O4^ix—Lu4—O6ⁱⁱ	87.53 (18)
O3ⁱⁱⁱ—Lu1—Al1^iv	160.44 (18)	O9—Lu4—O6ⁱⁱ	77.1 (2)
O7ⁱⁱⁱ—Lu1—Al1^iv	96.91 (18)	O4^ix—Lu4—O8^v	84.7 (2)
O5^iv—Lu1—Al1^iv	32.14 (17)	O9—Lu4—O8^v	110.30 (17)
O2—Lu1—Al1^iv	32.95 (13)	O6ⁱⁱ—Lu4—O8^v	171.9 (2)
O1—Lu1—Al1^iv	89.26 (14)	O4^ix—Lu4—O1ⁱⁱ	75.4 (2)
O9ⁱⁱⁱ—Lu1—Al2^iv	85.38 (16)	O9—Lu4—O1ⁱⁱ	108.45 (19)
O6—Lu1—Al2^iv	92.47 (15)	O6ⁱⁱ—Lu4—O1ⁱⁱ	80.3 (2)
O3ⁱⁱⁱ—Lu1—Al2^iv	100.91 (19)	O8^v—Lu4—O1ⁱⁱ	100.0 (2)
O7ⁱⁱⁱ—Lu1—Al2^iv	155.76 (18)	O4^ix—Lu4—O8ⁱⁱⁱ	95.5 (2)
O5^iv—Lu1—Al2^iv	31.50 (17)	O9—Lu4—O8ⁱⁱⁱ	79.9 (2)
O2—Lu1—Al2^iv	89.77 (14)	O6ⁱⁱ—Lu4—O8ⁱⁱⁱ	98.7 (2)
O1—Lu1—Al2^iv	32.02 (14)	O8^v—Lu4—O8ⁱⁱⁱ	79.7 (3)
Al1^iv—Lu1—Al2^iv	60.13 (5)	O1ⁱⁱ—Lu4—O8ⁱⁱⁱ	170.9 (2)
O9ⁱⁱⁱ—Lu1—Lu2^v	91.9 (2)	O4^ix—Lu4—Al2	104.05 (15)
O6—Lu1—Lu2^v	82.89 (14)	O9—Lu4—Al2	83.86 (13)
O3ⁱⁱⁱ—Lu1—Lu2^v	36.67 (18)	O6ⁱⁱ—Lu4—Al2	91.72 (14)
O7ⁱⁱⁱ—Lu1—Lu2^v	137.63 (18)	O8^v—Lu4—Al2	92.45 (14)
O5^iv—Lu1—Lu2^v	95.47 (17)	O1ⁱⁱ—Lu4—Al2	30.48 (15)
O2—Lu1—Lu2^v	149.10 (13)	O8ⁱⁱⁱ—Lu4—Al2	158.20 (14)
O1—Lu1—Lu2^v	37.17 (13)	O4^ix—Lu4—Lu3ⁱⁱⁱ	135.90 (15)
Al1^iv—Lu1—Lu2^v	125.28 (5)	O9—Lu4—Lu3ⁱⁱⁱ	39.61 (13)
Al2^iv—Lu1—Lu2^v	65.26 (5)	O6ⁱⁱ—Lu4—Lu3ⁱⁱⁱ	92.25 (14)
O9ⁱⁱⁱ—Lu1—Lu4^iv	139.2 (2)	O8^v—Lu4—Lu3ⁱⁱⁱ	91.67 (16)
O6—Lu1—Lu4^iv	37.22 (14)	O1ⁱⁱ—Lu4—Lu3ⁱⁱⁱ	147.82 (15)
O3ⁱⁱⁱ—Lu1—Lu4^iv	85.85 (17)	O8ⁱⁱⁱ—Lu4—Lu3ⁱⁱⁱ	40.93 (18)
O7ⁱⁱⁱ—Lu1—Lu4^iv	135.01 (15)	Al2—Lu4—Lu3ⁱⁱⁱ	120.03 (4)
O5^iv—Lu1—Lu4^iv	79.07 (14)	O4^ix—Lu4—Lu4^x	90.25 (15)
O2—Lu1—Lu4^iv	91.80 (13)	O9—Lu4—Lu4^x	96.21 (15)
O1—Lu1—Lu4^iv	39.37 (13)	O6ⁱⁱ—Lu4—Lu4^x	137.47 (14)
Al1^iv—Lu1—Lu4^iv	86.95 (5)	O8^v—Lu4—Lu4^x	40.44 (13)
Al2^iv—Lu1—Lu4^iv	57.05 (4)	O1ⁱⁱ—Lu4—Lu4^x	139.71 (15)
Lu2^v—Lu1—Lu4^iv	59.875 (14)	O8ⁱⁱⁱ—Lu4—Lu4^x	39.3 (2)
O9ⁱⁱⁱ—Lu1—Lu3	36.30 (13)	Al2—Lu4—Lu4^x	129.75 (4)
O6—Lu1—Lu3	143.97 (15)	Lu3ⁱⁱⁱ—Lu4—Lu4^x	61.365 (15)
O3ⁱⁱⁱ—Lu1—Lu3	110.32 (15)	O4^ix—Lu4—Lu2^ix	39.59 (15)
O7ⁱⁱⁱ—Lu1—Lu3	106.94 (16)	O9—Lu4—Lu2^ix	142.06 (14)
O5^iv—Lu1—Lu3	38.47 (12)	O6ⁱⁱ—Lu4—Lu2^ix	82.47 (14)
O2—Lu1—Lu3	83.91 (13)	O8^v—Lu4—Lu2^ix	93.01 (16)
O1—Lu1—Lu3	81.20 (13)	O1ⁱⁱ—Lu4—Lu2^ix	35.84 (15)
Al1^iv—Lu1—Lu3	56.26 (4)	O8ⁱⁱⁱ—Lu4—Lu2^ix	135.12 (17)
Al2^iv—Lu1—Lu3	55.19 (4)	Al2—Lu4—Lu2^ix	65.06 (4)
Lu2^v—Lu1—Lu3	95.095 (18)	Lu3ⁱⁱⁱ—Lu4—Lu2^ix	172.933 (13)
Lu4^iv—Lu1—Lu3	112.083 (15)	Lu4^x—Lu4—Lu2^ix	120.06 (2)
O1^vi—Lu2—O3^vii	81.6 (2)	O4^ix—Lu4—Lu3^v	45.83 (16)
O1^vi—Lu2—O2	89.32 (19)	O9—Lu4—Lu3^v	149.15 (16)
O3^vii—Lu2—O2	169.1 (2)	O6ⁱⁱ—Lu4—Lu3^v	133.35 (14)
O1^vi—Lu2—O7ⁱⁱⁱ	164.5 (2)	O8^v—Lu4—Lu3^v	39.02 (17)
O3^vii—Lu2—O7ⁱⁱⁱ	113.97 (17)	O1ⁱⁱ—Lu4—Lu3^v	85.63 (15)
O2—Lu2—O7ⁱⁱⁱ	75.2 (2)	O8ⁱⁱⁱ—Lu4—Lu3^v	88.7 (2)
O1^vi—Lu2—O8^vii	91.6 (2)	Al2—Lu4—Lu3^v	98.07 (5)
O3^vii—Lu2—O8^vii	88.2 (2)	Lu3ⁱⁱⁱ—Lu4—Lu3^v	120.326 (15)
O2—Lu2—O8^vii	98.0 (2)	Lu4^x—Lu4—Lu3^v	58.961 (16)
O7ⁱⁱⁱ—Lu2—O8^vii	89.1 (3)	Lu2^ix—Lu4—Lu3^v	61.562 (13)
O1^vi—Lu2—O4	74.9 (2)	O4^ix—Lu4—Lu1ⁱⁱ	86.32 (15)
O3^vii—Lu2—O4	92.4 (2)	O9—Lu4—Lu1ⁱⁱ	85.60 (15)
O2—Lu2—O4	79.5 (2)	O6ⁱⁱ—Lu4—Lu1ⁱⁱ	36.81 (14)
O7ⁱⁱⁱ—Lu2—O4	103.2 (2)	O8^v—Lu4—Lu1ⁱⁱ	144.42 (14)
O8^vii—Lu2—O4	166.2 (2)	O1ⁱⁱ—Lu4—Lu1ⁱⁱ	44.44 (15)
O1^vi—Lu2—Lu1^vi	44.59 (16)	O8ⁱⁱⁱ—Lu4—Lu1ⁱⁱ	135.46 (19)
O3^vii—Lu2—Lu1^vi	37.11 (17)	Al2—Lu4—Lu1ⁱⁱ	56.69 (4)
O2—Lu2—Lu1^vi	133.86 (14)	Lu3ⁱⁱⁱ—Lu4—Lu1ⁱⁱ	117.97 (2)
O7ⁱⁱⁱ—Lu2—Lu1^vi	150.92 (17)	Lu4^x—Lu4—Lu1ⁱⁱ	173.404 (16)
O8^vii—Lu2—Lu1^vi	87.2 (2)	Lu2^ix—Lu4—Lu1ⁱⁱ	59.705 (14)
O4—Lu2—Lu1^vi	84.98 (14)	Lu3^v—Lu4—Lu1ⁱⁱ	121.266 (15)
O1^vi—Lu2—Lu4^viii	38.06 (15)	Al2^iv—O1—Lu2^v	139.9 (3)
O3^vii—Lu2—Lu4^viii	86.66 (16)	Al2^iv—O1—Lu4^iv	108.1 (3)
O2—Lu2—Lu4^viii	82.52 (14)	Lu2^v—O1—Lu4^iv	106.1 (2)
O7ⁱⁱⁱ—Lu2—Lu4^viii	137.89 (15)	Al2^iv—O1—Lu1	98.2 (3)
O8^vii—Lu2—Lu4^viii	129.58 (17)	Lu2^v—O1—Lu1	98.2 (2)
O4—Lu2—Lu4^viii	36.84 (14)	Lu4^iv—O1—Lu1	96.2 (2)
Lu1^vi—Lu2—Lu4^viii	60.420 (13)	Al1^iv—O2—Lu2	127.6 (3)
O1^vi—Lu2—Lu3^iv	85.18 (17)	Al1^iv—O2—Lu3^iv	112.3 (3)
O3^vii—Lu2—Lu3^iv	136.93 (14)	Lu2—O2—Lu3^iv	109.3 (2)
O2—Lu2—Lu3^iv	35.36 (14)	Al1^iv—O2—Lu1	97.8 (2)
O7ⁱⁱⁱ—Lu2—Lu3^iv	83.02 (17)	Lu2—O2—Lu1	103.7 (2)
O8^vii—Lu2—Lu3^iv	133.14 (18)	Lu3^iv—O2—Lu1	101.5 (2)
O4—Lu2—Lu3^iv	44.56 (15)	Al1—O3—Lu2^vii	126.3 (5)
Lu1^vi—Lu2—Lu3^iv	119.653 (15)	Al1—O3—Lu1ⁱⁱⁱ	123.9 (5)
Lu4^viii—Lu2—Lu3^iv	59.233 (14)	Lu2^vii—O3—Lu1ⁱⁱⁱ	106.2 (2)
O1^vi—Lu2—Lu1	128.85 (16)	Al1^xi—O4—Lu4^viii	135.4 (3)
O3^vii—Lu2—Lu1	149.48 (17)	Al1^xi—O4—Lu2	117.6 (3)
O2—Lu2—Lu1	40.30 (14)	Lu4^viii—O4—Lu2	103.6 (2)
O7ⁱⁱⁱ—Lu2—Lu1	35.63 (17)	Al1^xi—O4—Lu3^iv	95.9 (3)
O8^vii—Lu2—Lu1	88.6 (2)	Lu4^viii—O4—Lu3^iv	96.4 (2)
O4—Lu2—Lu1	97.74 (14)	Lu2—O4—Lu3^iv	95.9 (2)
Lu1^vi—Lu2—Lu1	172.025 (12)	Al1—O5—Al2	134.9 (3)
Lu4^viii—Lu2—Lu1	118.072 (14)	Al1—O5—Lu3ⁱⁱ	105.3 (3)
Lu3^iv—Lu2—Lu1	59.438 (13)	Al2—O5—Lu3ⁱⁱ	103.1 (3)
O1^vi—Lu2—Lu4ⁱⁱⁱ	124.70 (15)	Al1—O5—Lu1ⁱⁱ	102.6 (3)
O3^vii—Lu2—Lu4ⁱⁱⁱ	102.42 (15)	Al2—O5—Lu1ⁱⁱ	104.6 (3)
O2—Lu2—Lu4ⁱⁱⁱ	87.60 (14)	Lu3ⁱⁱ—O5—Lu1ⁱⁱ	102.39 (18)
O7ⁱⁱⁱ—Lu2—Lu4ⁱⁱⁱ	54.38 (15)	Al2^xi—O6—Lu1	122.0 (3)
O8^vii—Lu2—Lu4ⁱⁱⁱ	34.8 (2)	Al2^xi—O6—Lu4^iv	125.6 (3)
O4—Lu2—Lu4ⁱⁱⁱ	156.67 (14)	Lu1—O6—Lu4^iv	106.0 (2)
Lu1^vi—Lu2—Lu4ⁱⁱⁱ	117.607 (14)	Al2^xi—O6—Lu3^iv	95.4 (2)
Lu4^viii—Lu2—Lu4ⁱⁱⁱ	159.792 (10)	Lu1—O6—Lu3^iv	99.6 (2)
Lu3^iv—Lu2—Lu4ⁱⁱⁱ	118.642 (17)	Lu4^iv—O6—Lu3^iv	100.7 (2)
Lu1—Lu2—Lu4ⁱⁱⁱ	60.716 (12)	Al2—O7—Lu2ⁱⁱⁱ	126.1 (5)
O1^vi—Lu2—Lu3^vii	85.85 (16)	Al2—O7—Lu1ⁱⁱⁱ	123.6 (5)
O3^vii—Lu2—Lu3^vii	56.75 (14)	Lu2ⁱⁱⁱ—O7—Lu1ⁱⁱⁱ	109.0 (2)
O2—Lu2—Lu3^vii	128.77 (14)	Lu4^vi—O8—Lu2^vii	110.1 (3)
O7ⁱⁱⁱ—Lu2—Lu3^vii	102.54 (16)	Lu4^vi—O8—Lu3	102.9 (2)
O8^vii—Lu2—Lu3^vii	31.5 (2)	Lu2^vii—O8—Lu3	117.4 (3)
O4—Lu2—Lu3^vii	146.03 (14)	Lu4^vi—O8—Lu4ⁱⁱⁱ	100.3 (3)
Lu1^vi—Lu2—Lu3^vii	62.045 (13)	Lu2^vii—O8—Lu4ⁱⁱⁱ	125.0 (2)
Lu4^viii—Lu2—Lu3^vii	119.182 (17)	Lu3—O8—Lu4ⁱⁱⁱ	97.9 (2)
Lu3^iv—Lu2—Lu3^vii	161.782 (11)	Lu1ⁱⁱⁱ—O9—Lu3	120.0 (4)
Lu1—Lu2—Lu3^vii	116.038 (15)	Lu1ⁱⁱⁱ—O9—Lu4	113.8 (3)
Lu4ⁱⁱⁱ—Lu2—Lu3^vii	55.607 (13)	Lu3—O9—Lu4	110.2 (2)
O2ⁱⁱ—Lu3—O9	102.6 (2)	Lu1ⁱⁱⁱ—O9—Lu3ⁱⁱⁱ	108.2 (2)
O2ⁱⁱ—Lu3—O9ⁱⁱⁱ	176.7 (3)	Lu3—O9—Lu3ⁱⁱⁱ	101.0 (3)
O9—Lu3—O9ⁱⁱⁱ	79.0 (3)	Lu4—O9—Lu3ⁱⁱⁱ	100.9 (3)

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

Acknowledgements

We are grateful to Ms Yuko Suzuki and Ms Mitsuyo Takaishi for their assistance with the high-temperature synthesis.

Funding information

Funding for this research was provided by the Mitsubishi Chemical Group, Science and Technology Research Center, Inc. (a joint research with Tohoku University and the Mitsubishi Chemical Group, Science and Technology Research Center, Inc. J180002907).

References

Brandle, C. D. & Steinfink, H. (1969). Inorg. Chem. 8, 1320–1324. CrossRef ICSD CAS Web of Science Google Scholar
Brown, I. D. & Altermatt, D. (1985). Acta Cryst. B41, 244–247. CrossRef CAS Web of Science IUCr Journals Google Scholar
Bruker (2016). SADABS. Bruker AXS Inc., Madison, Wisconsin, USA. Google Scholar
Bruker (2017). SAINT. Bruker AXS Inc., Madison, Wisconsin, USA. Google Scholar
Bruker (2018). APEX3 . Bruker AXS Inc., Madison, Wisconsin, USA. Google Scholar
Christensen, A. N. & Hazell, R. G. (1991). Acta Chem. Scand. 45, 226–230. CrossRef CAS Google Scholar
Dernier, P. D. & Maines, R. G. (1971). Mater. Res. Bull. 6, 433–439. CrossRef CAS Google Scholar
Ding, L., Zhang, Q., Luo, J., Liu, W., Zhou, W. & Yin, S. (2011). J. Alloys Compd. 509, 10167–10171. CrossRef CAS Google Scholar
Dohrup, J., Hoyvald, A., Mogensen, G., Jacobsen, C. J. H. & Villadsen, J. (1996). J. Am. Ceram. Soc. 79, 2959–2960. CrossRef CAS Google Scholar
Drozdowski, W., Lukasiewicz, T., Wojtowicz, A. J., Wisniewski, D. & Kisielewski, J. (2005). J. Cryst. Growth, 275, e709–e714. CAS Google Scholar
Euler, F. & Bruce, J. A. (1965). Acta Cryst. 19, 971–978. CrossRef ICSD IUCr Journals Web of Science Google Scholar
Gagné, O. C. & Hawthorne, F. C. (2015). Acta Cryst. B71, 562–578. Web of Science CrossRef IUCr Journals Google Scholar
Jero, P. D. & Kriven, W. M. (1988). J. Am. Ceram. Soc. 71, C454–C455. CAS Google Scholar
Klimm, D. (2010). J. Cryst. Growth, 312, 730–733. CAS Google Scholar
Lehmann, M. S., Christensen, A. N., Fjellvåg, H., Feidenhans'l, R. & Nielsen, M. (1987). J. Appl. Cryst. 20, 123–129. CrossRef ICSD CAS Web of Science IUCr Journals Google Scholar
Lempicki, A., Brecher, C., Wisniewski, D., Zych, E. & Wojtowicz, A. J. (1996). IEEE Trans. Nucl. Sci. 43, 1316–1320. CAS Google Scholar
Li, Y. Q., Hirosaki, N., Xie, R. J., Takeda, T., Lofland, S. E. & Ramanujachary, K. V. (2009). J. Alloys Compd. 484, 943–948. CAS Google Scholar
Martín-Sedeño, M. C., Marrero-López, D., Losilla, E. R., Bruque, S., Núñez, P. & Aranda, M. A. G. (2006). J. Solid State Chem. 179, 3445–3455. Google Scholar
Mizuno, M. (1979). J. Ceram. Soc. Jpn, 87, 405–412. CAS Google Scholar
Mizuno, M. & Noguchi, T. (1980). J. Ceram. Soc. Jpn, 88, 322–327. CAS Google Scholar
Mizuno, M., Yamada, T. & Noguchi, T. (1977a). J. Ceram. Soc. Jpn, 85, 374–379. CAS Google Scholar
Mizuno, M., Yamada, T. & Noguchi, T. (1977b). J. Ceram. Soc. Jpn, 85, 543–548. CAS Google Scholar
Mizuno, M., Yamada, T. & Noguchi, T. (1978). J. Ceram. Soc. Jpn, 86, 359–364. CAS Google Scholar
Momma, K. & Izumi, F. (2011). J. Appl. Cryst. 44, 1272–1276. Web of Science CrossRef CAS IUCr Journals Google Scholar
Nikl, M. (2000). Phys. Status Solidi A, 178, 595-620. CAS Google Scholar
Nikl, M., Yoshikawa, A., Kamada, K., Nejezchleb, K., Stanek, C. R., Mares, J. A. & Blazek, K. (2013). Prog. Cryst. Growth Charact. Mater. 59, 47–72. CAS Google Scholar
Petrosyan, A. G., Popova, V. F., Gusarov, V. V., Shirinyan, G. O., Pedrini, C. & Lecoq, P. (2006). J. Cryst. Growth, 293, 74–77. CAS Google Scholar
Petrosyan, A. G., Popova, V. F., Ugolkov, V. L., Romanov, D. P. & Ovanesyan, K. L. (2013). J. Cryst. Growth, 377, 178–183. CAS Google Scholar
Reed, J. W. & Chase, A. B. (1962). Acta Cryst. 15, 812. CrossRef IUCr Journals Google Scholar
Shannon, R. D. (1976). Acta Cryst. A32, 751–767. CrossRef CAS IUCr Journals Web of Science Google Scholar
Sheldrick, G. M. (2015). Acta Cryst. C71, 3–8. Web of Science CrossRef IUCr Journals Google Scholar
Shirvinskaya, A. K. & Popova, V. F. (1977). Dokl. Akad. Nauk SSSR, 233, 1110–1113. CAS Google Scholar
Shishido, T., Nojima, S., Tanaka, M., Horiuchi, H. & Fukuda, T. (1995). J. Alloys Compd. 227, 175–179. CAS Google Scholar
Talik, E., Guzik, A., Zajdel, P., Lipifska, L., Baran, M. & Szubka, M. (2016). Mater. Res. Bull. 83, 56–64. CAS Google Scholar
Wang, Z., Zou, J., Zhang, C., Yang, B., Shi, M., Li, Y., Zhou, H., Liu, Y., Li, M. & Liu, Z. (2018). J. Non-Cryst. Solids, 489, 57–63. CAS Google Scholar
Warshaw, I. & Roy, R. (1959). J. Am. Ceram. Soc. 42, 434–438. CAS Google Scholar
Westrip, S. P. (2010). J. Appl. Cryst. 43, 920–925. Web of Science CrossRef CAS IUCr Journals Google Scholar
Wojtowicz, A. J. (1999). Acta Phys. Pol. A, 95, 165–178. CAS Google Scholar
Wojtowicz, A. J., Drozdowski, W., Wisniewski, D., Lefaucheur, J.-L., Galazka, Z., Gou, Z., Lukasiewicz, T. & Kisielewski, J. (2006). Opt. Mater. 28, 85–93. CrossRef CAS Google Scholar
Wu, P. & Pelton, A. D. (1992). J. Alloys Compd. 179, 259–287. CrossRef CAS Web of Science Google Scholar
Xiang, R., Liang, X., Li, P., Di, X. & Xiang, W. (2016). Chem. Eng. J. 306, 858–865. CrossRef CAS Google Scholar
Yamane, H., Ogawara, K., Omori, M. & Hirai, T. (1995a). J. Am. Ceram. Soc. 78, 2385–2390. CrossRef CAS Google Scholar
Yamane, H., Omori, M. & Hirai, T. (1995b). J. Mater. Sci. Lett. 14, 561–563. CrossRef CAS Google Scholar
Zhang, L., Madej, C., Pedrini, C., Dujardin, C., Kamenskikh, I., Belsky, A., Shaw, D. A., Mesnard, P. & Fouassier, C. (1998). J. Electrochem. Soc.: Proceedings of the Sixth International Conference on Luminescent materials 97, 342-351. Google Scholar
Zhang, L., Madej, C., Pédrini, C., Moine, B., Dujardin, C., Petrosyan, A. & Belsky, A. N. (1997). Chem. Phys. Lett. 268, 408–412. CrossRef CAS Google Scholar