Compositely modulated structures of phosphor materials Sr_xLi_2+xAl_2–xO₄:Eu²⁺

Composite crystals Sr_xLi_2+xAl_2−xO₄:Eu²⁺ were synthesized and their structures were determined using single-crystal X-ray diffraction. The commensurate structure with a modulation wavevector q = 5c*/6 was analyzed in a conventional manner in 3D space, while a structure model in (3+1)-dimensional superspace was used for the other two crystals with modulation wavevectors slightly differing from 5c*/6. The superstructure of the commensurate phase was described using the space group P4/n and a common superspace group I4/m(00γ)00 was used for the (3+1)D structures of all three crystals. The whole structure of each crystal consists of two substructures. Basis vectors a and b are common, but c is different for the two substructures. The first substructure is a host framework constructed by (Li/Al)O₄ tetrahedra sharing edges. A linear connection of cavities is seen to be channel-like, in which Sr ions locate as guest cations forming the second substructure. The crystal of q = 5c*/6 contains five Sr ions per six cavities in a channel. Sr ions are distributed at seven sites, some of which are partially occupied. Statistical disorder of local structure models for the location of Sr ions in the channel was assumed to explain the results. Such a partially disordered character was also seen in the incommensurate phases and properly embodied by a (3+1)D model containing an atomic domain of the Sr ion with occupational modulation. Plots of the occupation factor, interatomic distances and the bond valence sum at each metal site as functions of t (= x₄ − q·r) are roughly identical in the three crystals, which are considered as members of the same series of composite crystals.

Computing details

(I_3d)

Crystal data

Sr0.8333Al1.1667Li2.8333O4	Dx = 3.173 Mg m^−3
Mr = 188.2	Mo Kα radiation, λ = 0.71073 Å
Tetragonal, P4/n	Cell parameters from 28522 reflections
Hall symbol: -P 4a	θ = 1.1–35.7°
a = 7.8733 (4) Å	µ = 11.58 mm^−1
c = 19.0635 (19) Å	T = 293 K
V = 1181.72 (15) Å^3	Irregular
Z = 12	0.01 × 0.01 × 0.01 mm
F(000) = 1048

Data collection

Bruker CCD diffractometer	898 reflections with I > 2σ(I)
Radiation source: X-ray tube	Rint = 0.056
Absorption correction: multi-scan SADABS	θmax = 35.7°, θmin = 1.1°
Tmin = 0.814, Tmax = 0.863	h = −12→12
28522 measured reflections	k = −12→12
2758 independent reflections	l = −31→31

Refinement

Refinement on F^2	0 restraints
R[F^2 > 2σ(F^2)] = 0.038	62 constraints
wR(F^2) = 0.048	Weighting scheme based on measured s.u.'s w = 1/(σ^2(I) + 0.000004I^2)
S = 1.84	(Δ/σ)max = 0.008
2758 reflections	Δρmax = 2.97 e Å^−3
138 parameters	Δρmin = −3.08 e Å^−3

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Sr1	0	0.5	−0.02698 (12)	0.0259 (5)
Sr2b	0	0.5	0.15286 (19)	0.0275 (8)	0.653 (7)
Sr2a	0	0.5	0.2567 (2)	0.0193 (10)	0.299 (9)
Sr3b	0	0.5	0.3059 (13)	0.076 (9)	0.176 (12)
Sr3a	0	0.5	0.43643 (14)	0.0261 (6)	0.872 (4)
Sr4	0	0.5	0.61806 (11)	0.0176 (4)
Sr5	0	0.5	0.79350 (12)	0.0136 (2)
Al1	0.1916 (3)	1.1506 (4)	0.2921 (3)	0.0142 (8)	0.523 (6)
Al2	0.3068 (5)	1.3504 (5)	−0.1236 (2)	0.0036 (11)	0.387 (8)
Al3	0.6918 (6)	0.6450 (6)	0.5394 (3)	0.0084 (13)	0.328 (7)
Al4	0.3222 (8)	1.3622 (8)	0.0443 (3)	0.0287 (19)	0.276 (7)
Al5	−0.1398 (10)	1.1828 (8)	0.3738 (4)	0.0150 (18)	0.144 (8)
Al6	−0.1340 (9)	1.1615 (10)	0.2076 (8)	0.042 (2)	0.092 (16)
Li1	0.1916 (3)	1.1506 (4)	0.2921 (3)	0.0142 (8)	0.477 (6)
Li2	0.3068 (5)	1.3504 (5)	−0.1236 (2)	0.0036 (11)	0.613 (8)
Li3	0.6918 (6)	0.6450 (6)	0.5394 (3)	0.0084 (13)	0.672 (7)
Li4	0.3222 (8)	1.3622 (8)	0.0443 (3)	0.0287 (19)	0.724 (7)
Li5	−0.1398 (10)	1.1828 (8)	0.3738 (4)	0.0150 (18)	0.856 (8)
Li6	−0.1340 (9)	1.1615 (10)	0.2076 (8)	0.042 (2)	0.908 (16)
O1	0.0992 (5)	1.2237 (5)	0.2086 (5)	0.0167 (11)
O2	0.0975 (7)	1.2306 (8)	0.3744 (4)	0.0218 (19)
O3	0.4062 (7)	1.2606 (8)	−0.0443 (4)	0.026 (2)
O4	0.4144 (7)	1.2526 (8)	0.1221 (4)	0.0193 (18)
O5	0.4172 (5)	1.2504 (5)	0.2928 (5)	0.0198 (12)
O6	0.5897 (7)	0.7426 (8)	0.4617 (4)	0.0223 (18)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Sr1	0.0183 (5)	0.0183 (5)	0.0412 (12)	0	0	0
Sr2b	0.0193 (11)	0.0193 (11)	0.044 (2)	0	0	0
Sr2a	0.0207 (15)	0.0207 (15)	0.017 (2)	0	0	0
Sr3b	0.031 (2)	0.031 (2)	0.17 (3)	0	0	0
Sr3a	0.0178 (7)	0.0178 (7)	0.0427 (14)	0	0	0
Sr4	0.0151 (5)	0.0151 (5)	0.0228 (9)	0	0	0
Sr5	0.0145 (3)	0.0145 (3)	0.0117 (4)	0	0	0
Al1	0.0166 (14)	0.0168 (14)	0.0093 (12)	0.0056 (10)	0.001 (2)	0.000 (2)
Al2	0.0032 (19)	0.0048 (19)	0.003 (2)	−0.0026 (15)	0.0001 (17)	−0.0020 (17)
Al3	0.007 (2)	0.009 (2)	0.009 (2)	−0.0002 (17)	−0.0036 (19)	−0.001 (2)
Al4	0.053 (4)	0.021 (3)	0.012 (3)	0.018 (3)	0.002 (2)	0.000 (2)
Al5	0.014 (3)	0.010 (2)	0.021 (4)	0.0011 (19)	0.001 (3)	−0.008 (2)
Al6	0.021 (3)	0.088 (5)	0.018 (3)	−0.022 (3)	−0.008 (6)	0.006 (7)
Li1	0.0166 (14)	0.0168 (14)	0.0093 (12)	0.0056 (10)	0.001 (2)	0.000 (2)
Li2	0.0032 (19)	0.0048 (19)	0.003 (2)	−0.0026 (15)	0.0001 (17)	−0.0020 (17)
Li3	0.007 (2)	0.009 (2)	0.009 (2)	−0.0002 (17)	−0.0036 (19)	−0.001 (2)
Li4	0.053 (4)	0.021 (3)	0.012 (3)	0.018 (3)	0.002 (2)	0.000 (2)
Li5	0.014 (3)	0.010 (2)	0.021 (4)	0.0011 (19)	0.001 (3)	−0.008 (2)
Li6	0.021 (3)	0.088 (5)	0.018 (3)	−0.022 (3)	−0.008 (6)	0.006 (7)
O1	0.0101 (18)	0.0192 (19)	0.0209 (19)	0.0020 (14)	−0.002 (3)	0.001 (3)
O2	0.012 (3)	0.032 (4)	0.022 (3)	0.001 (3)	0.002 (3)	−0.008 (3)
O3	0.015 (3)	0.039 (4)	0.024 (3)	0.002 (3)	−0.004 (3)	0.012 (4)
O4	0.018 (3)	0.032 (4)	0.008 (3)	0.011 (3)	0.000 (3)	−0.002 (3)
O5	0.021 (2)	0.026 (2)	0.0122 (18)	0.0075 (17)	0.000 (4)	0.002 (4)
O6	0.016 (3)	0.036 (4)	0.015 (3)	0.007 (3)	−0.003 (3)	0.008 (3)

Geometric parameters (Å, º)

Al1—O1	1.844 (10)	Al1—O5	1.942 (5)
Al1—O2	1.845 (9)	Al1—O5^i	1.893 (5)
O1—Al1—O2	118.0 (3)	O2—Al1—O5	102.9 (4)
O1—Al1—O5	103.9 (3)	O2—Al1—O5^i	115.0 (4)
O1—Al1—O5^i	113.8 (4)	O5—Al1—O5^i	99.9 (2)

Symmetry code: (i) −y+3/2, x+1/2, z.

(I_4d)

Crystal data

Sr0.833Al1.167Li2.833O4	F(000) = 175
Mr = 188.1	Dx = 3.149 Mg m^−3
Tetragonal, I4/m(00γ)00†	Mo Kα radiation, λ = 0.71073 Å
q = 0.833333c*‡	µ = 11.49 mm^−1
a = 7.8957 (3) Å	T = 293 K
c = 3.1830 (3) Å	Irregular
V = 198.43 (2) Å^3	0.01 × 0.01 × 0.01 mm
Z = 2

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₁, −x₂, x₃, x₄; (3) −x₂, x₁, x₃, x₄; (4) x₂, −x₁, x₃, x₄; (5) −x₁, −x₂, −x₃, −x₄; (6) x₁, x₂, −x₃, −x₄; (7) x₂, −x₁, −x₃, −x₄; (8) −x₂, x₁, −x₃, −x₄; (9) x₁+1/2, x₂+1/2, x₃+1/2, x₄; (10) −x₁+1/2, −x₂+1/2, x₃+1/2, x₄; (11) −x₂+1/2, x₁+1/2, x₃+1/2, x₄; (12) x₂+1/2, −x₁+1/2, x₃+1/2, x₄; (13) −x₁+1/2, −x₂+1/2, −x₃+1/2, −x₄; (14) x₁+1/2, x₂+1/2, −x₃+1/2, −x₄; (15) x₂+1/2, −x₁+1/2, −x₃+1/2, −x₄; (16) −x₂+1/2, x₁+1/2, −x₃+1/2, −x₄.

‡ ;

Data collection

Bruker CCD diffractometer	866 reflections with I > 2σ(I)
Radiation source: X-ray tube	Rint = 0.043
Absorption correction: multi-scan SADABS	θmax = 35.6°, θmin = 2.1°
Tmin = 0.793, Tmax = 0.863	h = −12→12
12403 measured reflections	k = −12→12
1641 independent reflections	l = −6→6

Refinement

Refinement on F^2	0 restraints
R[F^2 > 2σ(F^2)] = 0.031	28 constraints
wR(F^2) = 0.041	Weighting scheme based on measured s.u.'s w = 1/(σ^2(I) + 0.000004I^2)
S = 1.98	(Δ/σ)max = 0.005
1641 reflections	Δρmax = 1.47 e Å^−3
69 parameters	Δρmin = −1.22 e Å^−3

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Al1	0.14298 (9)	0.31593 (12)	0.5	0.0185 (2)	0.2917
Li1	0.14298 (9)	0.31593 (12)	0.5	0.0185 (2)	0.7083
O1	0.26113 (8)	0.09144 (7)	0.5	0.02143 (18)
Sr1	0	0	0	0.0629 (18)	0.6
Sr2	0	0	0.433 (6)	0.085 (3)	0.2

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Al1	0.0151 (4)	0.0285 (5)	0.0120 (4)	−0.0061 (3)	0	0
Li1	0.0151 (4)	0.0285 (5)	0.0120 (4)	−0.0061 (3)	0	0
O1	0.0310 (3)	0.0154 (3)	0.0178 (3)	−0.0050 (2)	0	0
Sr1	0.044 (3)	0.044 (3)	0.101 (2)	0	0	0
Sr2	0.036 (4)	0.036 (4)	0.182 (8)	0	0	0

Geometric parameters (Å, º)

	Average	Minimum	Maximum
Al1—O1		1.934 (4)	2.138 (4)
Al1—O1^i		1.899 (4)	1.903 (4)
Al1—O1^ii		1.847 (2)	2.005 (2)
Al1—O1^iii		1.842 (2)	1.998 (2)
Al1—O11^iv		1.847 (2)	2.005 (2)
Al1—O11^v		1.842 (2)	1.998 (2)
Al1—O11^vi		1.934 (4)	2.138 (4)
Al1—O11^vii		1.899 (4)	1.903 (4)
O1—Al1—O1^i	104.50 (11)	100.34 (16)	108.01 (16)
O1—Al1—O1^ii	98.91 (10)	93.68 (11)	104.07 (11)
O1—Al1—O1^iii	98.91 (10)	92.82 (10)	103.59 (10)
O1—Al1—O11^iv	98.91 (10)	93.68 (11)	104.07 (11)
O1—Al1—O11^v	98.91 (10)	92.82 (10)	103.59 (10)
O1—Al1—O11^vi	0.0 (5)	0.0 (5)	0.0 (5)
O1—Al1—O11^vii	104.50 (11)	100.34 (16)	108.01 (16)
O1^i—Al1—O1^ii	118.21 (11)	113.61 (10)	122.17 (10)
O1^i—Al1—O1^iii	118.21 (11)	114.29 (12)	122.76 (13)
O1^i—Al1—O11^iv	118.21 (11)	113.61 (10)	122.17 (10)
O1^i—Al1—O11^v	118.21 (11)	114.29 (12)	122.76 (13)
O1^i—Al1—O11^vi	104.50 (11)	100.34 (16)	108.01 (16)
O1^i—Al1—O11^vii	0.0 (5)	0.0 (5)	0.0 (5)
O1^ii—Al1—O1^iii	112.83 (12)	110.13 (10)	118.00 (18)
O1^ii—Al1—O11^iv	0.0 (5)	0.0 (5)	0.0 (5)
O1^ii—Al1—O11^v	112.83 (12)	110.13 (10)	118.00 (18)
O1^ii—Al1—O11^vi	98.91 (11)	93.68 (13)	104.07 (14)
O1^ii—Al1—O11^vii	118.21 (13)	113.61 (14)	122.17 (12)
O1^iii—Al1—O11^iv	112.83 (12)	110.13 (11)	118.00 (17)
O1^iii—Al1—O11^v	0.0 (5)	0.0 (5)	0.0 (5)
O1^iii—Al1—O11^vi	98.91 (11)	92.82 (11)	103.59 (13)
O1^iii—Al1—O11^vii	118.21 (12)	114.29 (14)	122.76 (14)
O11^iv—Al1—O11^v	112.83 (12)	110.13 (10)	118.00 (18)
O11^iv—Al1—O11^vi	98.91 (11)	93.68 (13)	104.07 (14)
O11^iv—Al1—O11^vii	118.21 (13)	113.61 (14)	122.17 (12)
O11^v—Al1—O11^vi	98.91 (11)	92.82 (11)	103.59 (13)
O11^v—Al1—O11^vii	118.21 (12)	114.29 (14)	122.76 (14)
O11^vi—Al1—O11^vii	104.50 (11)	100.34 (16)	108.01 (16)

Symmetry codes: (i) −x₂, x₁, x₃, x₄; (ii) −x₁, −x₂, −x₃, −x₄; (iii) −x₁, −x₂, −x₃+1, −x₄; (iv) −x₁+1, −x₂+1, x₃−1, x₄; (v) −x₁+1, −x₂+1, x₃, x₄; (vi) x₁−1, x₂−1, −x₃+1, −x₄; (vii) −x₂, x₁−1, −x₃+1, −x₄.

(II)

Crystal data

Sr0.824Al1.176Li2.824O4	F(000) = 174
Mr = 187.5	Dx = 3.162 Mg m^−3
Tetragonal, I4/m(00γ)00†	Mo Kα radiation, λ = 0.71073 Å
q = 0.824370c*‡	µ = 11.46 mm^−1
a = 7.8785 (2) Å	T = 293 K
c = 3.1736 (2) Å	Prismatic
V = 196.99 (1) Å^3	0.02 × 0.01 × 0.01 mm
Z = 2

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₁, −x₂, x₃, x₄; (3) −x₂, x₁, x₃, x₄; (4) x₂, −x₁, x₃, x₄; (5) −x₁, −x₂, −x₃, −x₄; (6) x₁, x₂, −x₃, −x₄; (7) x₂, −x₁, −x₃, −x₄; (8) −x₂, x₁, −x₃, −x₄; (9) x₁+1/2, x₂+1/2, x₃+1/2, x₄; (10) −x₁+1/2, −x₂+1/2, x₃+1/2, x₄; (11) −x₂+1/2, x₁+1/2, x₃+1/2, x₄; (12) x₂+1/2, −x₁+1/2, x₃+1/2, x₄; (13) −x₁+1/2, −x₂+1/2, −x₃+1/2, −x₄; (14) x₁+1/2, x₂+1/2, −x₃+1/2, −x₄; (15) x₂+1/2, −x₁+1/2, −x₃+1/2, −x₄; (16) −x₂+1/2, x₁+1/2, −x₃+1/2, −x₄.

‡ ;

Data collection

Bruker CCD diffractometer	852 reflections with I > 2σ(I)
Radiation source: X-ray tube	Rint = 0.065
Absorption correction: multi-scan SADABS	θmax = 36.4°, θmin = 2.3°
Tmin = 0.799, Tmax = 0.863	h = −13→12
12939 measured reflections	k = −13→13
1489 independent reflections	l = −7→7

Refinement

Refinement on F^2	0 restraints
R[F^2 > 2σ(F^2)] = 0.041	2 constraints
wR(F^2) = 0.050	Weighting scheme based on measured s.u.'s w = 1/(σ^2(I) + 0.000004I^2)
S = 2.37	(Δ/σ)max = 0.049
1489 reflections	Δρmax = 3.01 e Å^−3
63 parameters	Δρmin = −2.69 e Å^−3

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Al1	0.14277 (14)	0.31657 (18)	0.5	0.0201 (4)	0.2939
Li1	0.14277 (14)	0.31657 (18)	0.5	0.0201 (4)	0.7061
O1	0.26153 (11)	0.09127 (9)	0.5	0.0199 (2)
Sr1	0	0	0	0.0221 (10)	0.668 (7)
Sr2	0	0	0.4838 (11)	0.0206 (4)	0.166 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Al1	0.0160 (6)	0.0313 (9)	0.0130 (6)	−0.0070 (6)	0	0
Li1	0.0160 (6)	0.0313 (9)	0.0130 (6)	−0.0070 (6)	0	0
O1	0.0295 (5)	0.0140 (4)	0.0162 (4)	−0.0044 (3)	0	0
Sr1	0.0167 (5)	0.0167 (5)	0.033 (3)	0	0	0
Sr2	0.0202 (5)	0.0202 (5)	0.0216 (11)	0	0	0

Geometric parameters (Å, º)

	Average	Minimum	Maximum
Al1—O1		1.929 (7)	2.164 (7)
Al1—O1^i		1.837 (4)	2.001 (4)
Al1—O1^ii		1.837 (4)	2.001 (4)
Al1—O1^iii		1.889 (7)	1.900 (7)
O1—Al1—O1^i	98.89 (16)	92.35 (18)	104.34 (16)
O1—Al1—O1^ii	98.88 (16)	92.35 (17)	104.34 (16)
O1—Al1—O1^iii	104.42 (17)	100.3 (3)	107.6 (3)
O1^i—Al1—O1^ii	112.95 (19)	110.19 (15)	118.3 (3)
O1^i—Al1—O1^iii	118.2 (2)	113.5 (2)	123.1 (2)
O1^ii—Al1—O1^iii	118.2 (2)	113.5 (2)	123.1 (2)

Symmetry codes: (i) −x₁+1/2, −x₂+1/2, x₃−1/2, x₄; (ii) −x₁+1/2, −x₂+1/2, x₃+1/2, x₄; (iii) −x₂, x₁, x₃, x₄.

(III)

Crystal data

Sr0.827Al1.173Li2.827O4	F(000) = 174
Mr = 187.7	Dx = 3.152 Mg m^−3
Tetragonal, I4/m(00γ)00†	Mo Kα radiation, λ = 0.71073 Å
q = 0.827300c*‡	µ = 11.45 mm^−1
a = 7.8908 (6) Å	T = 293 K
c = 3.1767 (3) Å	Plate
V = 197.80 (3) Å^3	0.02 × 0.02 × 0.004 mm
Z = 2

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₁, −x₂, x₃, x₄; (3) −x₂, x₁, x₃, x₄; (4) x₂, −x₁, x₃, x₄; (5) −x₁, −x₂, −x₃, −x₄; (6) x₁, x₂, −x₃, −x₄; (7) x₂, −x₁, −x₃, −x₄; (8) −x₂, x₁, −x₃, −x₄; (9) x₁+1/2, x₂+1/2, x₃+1/2, x₄; (10) −x₁+1/2, −x₂+1/2, x₃+1/2, x₄; (11) −x₂+1/2, x₁+1/2, x₃+1/2, x₄; (12) x₂+1/2, −x₁+1/2, x₃+1/2, x₄; (13) −x₁+1/2, −x₂+1/2, −x₃+1/2, −x₄; (14) x₁+1/2, x₂+1/2, −x₃+1/2, −x₄; (15) x₂+1/2, −x₁+1/2, −x₃+1/2, −x₄; (16) −x₂+1/2, x₁+1/2, −x₃+1/2, −x₄.

‡ ;

Data collection

Bruker CCD diffractometer	836 reflections with I > 2σ(I)
Radiation source: X-ray tube	Rint = 0.068
Absorption correction: multi-scan SADABS	θmax = 35.6°, θmin = 2.2°
Tmin = 0.770, Tmax = 0.863	h = −12→12
12328 measured reflections	k = −12→12
1410 independent reflections	l = −7→7

Refinement

Refinement on F^2	0 restraints
R[F^2 > 2σ(F^2)] = 0.038	2 constraints
wR(F^2) = 0.042	Weighting scheme based on measured s.u.'s w = 1/(σ^2(I) + 0.000004I^2)
S = 2.18	(Δ/σ)max = 0.050
1410 reflections	Δρmax = 2.51 e Å^−3
63 parameters	Δρmin = −2.24 e Å^−3

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Al1	0.14221 (13)	0.31750 (16)	0.5	0.0239 (4)	0.2932
Li1	0.14221 (13)	0.31750 (16)	0.5	0.0239 (4)	0.7068
O1	0.26203 (10)	0.09135 (8)	0.5	0.0232 (2)
Sr1	0	0	0	0.0237 (11)	0.617 (9)
Sr2	0	0	0.4476 (6)	0.0235 (3)	0.192 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Al1	0.0197 (5)	0.0374 (8)	0.0144 (6)	−0.0080 (5)	0	0
Li1	0.0197 (5)	0.0374 (8)	0.0144 (6)	−0.0080 (5)	0	0
O1	0.0339 (4)	0.0176 (3)	0.0180 (4)	−0.0056 (3)	0	0
Sr1	0.0182 (5)	0.0182 (5)	0.035 (3)	0	0	0
Sr2	0.0234 (4)	0.0234 (4)	0.0235 (7)	0	0	0

Geometric parameters (Å, º)

	Average	Minimum	Maximum
Al1—O1		1.932 (6)	2.200 (6)
Al1—O1^i		1.838 (3)	2.007 (3)
Al1—O1^ii		1.838 (3)	2.007 (3)
Al1—O1^iii		1.891 (6)	1.899 (6)
O1—Al1—O1^i	98.64 (13)	91.25 (15)	104.53 (13)
O1—Al1—O1^ii	98.62 (13)	91.25 (14)	104.53 (13)
O1—Al1—O1^iii	104.38 (14)	100.1 (2)	107.8 (2)
O1^i—Al1—O1^ii	113.13 (16)	110.02 (13)	119.2 (3)
O1^i—Al1—O1^iii	118.18 (16)	113.00 (18)	123.53 (19)
O1^ii—Al1—O1^iii	118.20 (16)	112.99 (18)	123.53 (19)

Symmetry codes: (i) −x₁+1/2, −x₂+1/2, x₃−1/2, x₄; (ii) −x₁+1/2, −x₂+1/2, x₃+1/2, x₄; (iii) −x₂, x₁, x₃, x₄.