Structural and thermal properties of the monoclinic Lu₂SiO₅ single crystal: evaluation as a new laser matrix

The crystal structure of monoclinic Lu₂SiO₅ (LSO) crystals, grown by the Czochralski method, was determined at room temperature by X-ray diffraction. The unit-cell parameters are a = 10.2550 (2), b = 6.6465 (2), c = 12.3626 (4) Å, β = 102.422 (1)° in space group I2/a. The linear thermal expansion tensor was determined along the a, b, c and c* directions over the temperature range from 303.15 to 768.15 K, and the principal coefficients of the thermal expansion tensor are found to be α_I = −1.0235 × 10⁻⁶ K, α_II = 4.9119 × 10⁻⁶ K and α_III = 10.1105 × 10⁻⁶ K. The temperature dependence of the cell volume and monoclinic angle were also evaluated. In addition, the specific heat and the thermal diffusivity were measured over the temperature ranges from 293.15 to 673.15 K and from 303.15 to 572.45 K, respectively. As a result, the anisotropic thermal conductivity could be calculated and is reported for the first time, to the best of the authors' knowledge. The specific heat capacity of LSO is 139.54 J mol⁻¹ K⁻¹, and the principal components of the thermal conductivity are k_I = 2.26 W m⁻¹ K⁻¹, k_II = 3.14 W m⁻¹ K⁻¹ and k_II = 3.67 W m⁻¹ K⁻¹ at 303.15 K. A new structure model was proposed to better understand the relationships between the crystal structure and anisotropic thermal properties. In comparison with other laser matrix crystals, it is found that LSO possesses relatively large anisotropic thermal properties, and owing to its small heat capacity it has a moderate thermal conductivity, which is similar to those of the tungstates but lower than those of the vanadates.

Computing details

Data collection: APEX2 Software Suite (Bruker,2005); cell refinement: APEX2 Software Suite (Bruker,2005); data reduction: APEX2 Software Suite (Bruker,2005); program(s) used to solve structure: SIR97 (Altomare,1999); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: SHELXTL (Bruker, 1997); software used to prepare material for publication: WinGX (Farrugia,1999).

Figures

(LSO)

Crystal data

Lu2O5Si	F(000) = 1568
Mr = 458.03	Dx = 7.394 Mg m^−3
Monoclinic, I2/a	Mo Kα radiation, λ = 0.71073 Å
a = 10.2550 (2) Å	Cell parameters from 3016 reflections
b = 6.6465 (2) Å	θ = 2.4–34.8°
c = 12.3626 (4) Å	µ = 47.90 mm^−1
β = 102.422 (1)°	T = 293 K
V = 822.91 (4) Å^3	Prism, colourless
Z = 8	0.14 × 0.12 × 0.05 mm

Data collection

Bruker APEX2 CCD area-detector diffractometer	1731 independent reflections
Radiation source: fine-focus sealed tube	1650 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.029
φ and ω scans	θmax = 35.0°, θmin = 3.4°
Absorption correction: numerical APEX2 Software Suite (Bruker,2005)	h = −12→16
Tmin = 0.060, Tmax = 0.212	k = −8→10
4061 measured reflections	l = −19→18

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.030	w = 1/[σ^2(Fo^2) + (0.033P)^2 + 14.9602P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.072	(Δ/σ)max = 0.001
S = 1.17	Δρmax = 3.92 e Å^−3
1731 reflections	Δρmin = −2.12 e Å^−3
74 parameters	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.00515 (16)

Special details

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 (Ų)

	x	y	z	Uiso*/Ueq
Lu1	0.69550 (2)	0.37736 (4)	0.35906 (2)	0.00707 (9)
Lu2	0.92962 (2)	0.74393 (4)	0.46264 (2)	0.00744 (9)
O1	0.4738 (5)	0.3513 (8)	0.2985 (4)	0.0105 (8)
O6	0.7038 (5)	0.7109 (8)	0.3794 (4)	0.0101 (8)
O3	0.7356 (5)	0.0713 (8)	0.2980 (4)	0.0103 (8)
O5	0.8795 (5)	0.4032 (7)	0.4822 (4)	0.0074 (7)
O7	1.0494 (5)	1.0051 (8)	0.4115 (4)	0.0108 (8)
Si1	0.37528 (17)	0.4083 (3)	0.18224 (14)	0.0060 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Lu1	0.00594 (12)	0.00740 (14)	0.00787 (12)	−0.00015 (8)	0.00148 (8)	−0.00105 (7)
Lu2	0.00595 (13)	0.00740 (14)	0.00900 (13)	−0.00026 (8)	0.00166 (8)	−0.00068 (8)
O1	0.0101 (19)	0.012 (2)	0.0096 (18)	0.0010 (16)	0.0015 (15)	0.0006 (15)
O6	0.0069 (18)	0.012 (2)	0.0101 (18)	0.0000 (16)	−0.0008 (14)	0.0019 (16)
O3	0.0092 (19)	0.011 (2)	0.0111 (18)	−0.0023 (16)	0.0035 (15)	−0.0002 (16)
O5	0.0070 (17)	0.0064 (19)	0.0088 (16)	0.0007 (14)	0.0014 (14)	0.0013 (14)
O7	0.015 (2)	0.011 (2)	0.0088 (17)	−0.0053 (17)	0.0066 (15)	−0.0034 (16)
Si1	0.0062 (6)	0.0052 (7)	0.0067 (6)	−0.0007 (5)	0.0015 (5)	−0.0009 (5)

Geometric parameters (Å, º)

Lu1—O5	2.161 (5)	Lu2—Si1^viii	3.0863 (16)
Lu1—O6	2.231 (5)	Lu2—Lu1^vii	3.3505 (3)
Lu1—O3^i	2.231 (4)	Lu2—Lu2^v	3.5885 (5)
Lu1—O3	2.238 (5)	Lu2—Lu1^ii	3.6957 (4)
Lu1—O1	2.242 (5)	O1—Si1	1.614 (5)
Lu1—O5^ii	2.263 (4)	O1—Lu2^iv	2.262 (5)
Lu1—Si1^iii	3.2166 (18)	O6—Si1^ix	1.641 (5)
Lu1—Lu2^iv	3.3505 (3)	O6—Lu2^ii	2.623 (5)
Lu1—Lu1^ii	3.4231 (5)	O3—Si1^iii	1.626 (5)
Lu1—Lu2	3.4667 (4)	O3—Lu1^i	2.231 (4)
Lu1—Lu1^i	3.5614 (5)	O5—Lu2^v	2.163 (5)
Lu1—Lu2^ii	3.6957 (4)	O5—Lu1^ii	2.263 (4)
Lu2—O5^v	2.163 (5)	O7—Si1^x	1.630 (5)
Lu2—O7^vi	2.260 (5)	O7—Lu2^vi	2.260 (5)
Lu2—O1^vii	2.262 (5)	Si1—O3^ix	1.626 (5)
Lu2—O7	2.293 (5)	Si1—O7^x	1.630 (5)
Lu2—O6	2.334 (5)	Si1—O6^iii	1.641 (5)
Lu2—O5	2.346 (5)	Si1—Lu2^xi	3.0863 (16)
Lu2—O6^ii	2.623 (5)	Si1—Lu1^ix	3.2166 (18)
O5—Lu1—O6	80.51 (17)	O7—Lu2—O6^ii	131.66 (16)
O5—Lu1—O3^i	102.05 (18)	O6—Lu2—O6^ii	72.13 (18)
O6—Lu1—O3^i	86.26 (18)	O5—Lu2—O6^ii	71.44 (16)
O5—Lu1—O3	96.54 (17)	O5^v—Lu2—Si1^viii	101.83 (12)
O6—Lu1—O3	159.38 (17)	O7^vi—Lu2—Si1^viii	30.84 (12)
O3^i—Lu1—O3	74.3 (2)	O1^vii—Lu2—Si1^viii	175.43 (13)
O5—Lu1—O1	155.54 (17)	O7—Lu2—Si1^viii	100.57 (11)
O6—Lu1—O1	97.23 (18)	O6—Lu2—Si1^viii	94.08 (13)
O3^i—Lu1—O1	102.09 (17)	O5—Lu2—Si1^viii	99.56 (11)
O3—Lu1—O1	93.66 (18)	O6^ii—Lu2—Si1^viii	32.13 (12)
O5—Lu1—O5^ii	77.95 (18)	O5^v—Lu2—Lu1^vii	41.94 (12)
O6—Lu1—O5^ii	80.70 (17)	O7^vi—Lu2—Lu1^vii	118.43 (12)
O3^i—Lu1—O5^ii	166.79 (19)	O1^vii—Lu2—Lu1^vii	41.72 (13)
O3—Lu1—O5^ii	118.86 (16)	O7—Lu2—Lu1^vii	63.16 (12)
O1—Lu1—O5^ii	77.65 (17)	O6—Lu2—Lu1^vii	128.39 (12)
O5—Lu1—Si1^iii	108.78 (13)	O5—Lu2—Lu1^vii	91.23 (11)
O6—Lu1—Si1^iii	169.39 (13)	O6^ii—Lu2—Lu1^vii	149.53 (11)
O3^i—Lu1—Si1^iii	96.49 (13)	Si1^viii—Lu2—Lu1^vii	137.49 (3)
O3—Lu1—Si1^iii	28.02 (12)	O5^v—Lu2—Lu1	107.85 (13)
O1—Lu1—Si1^iii	72.19 (14)	O7^vi—Lu2—Lu1	136.80 (12)
O5^ii—Lu1—Si1^iii	95.98 (12)	O1^vii—Lu2—Lu1	74.24 (13)
O5—Lu1—Lu2^iv	114.14 (12)	O7—Lu2—Lu1	143.12 (11)
O6—Lu1—Lu2^iv	102.14 (12)	O6—Lu2—Lu1	39.49 (13)
O3^i—Lu1—Lu2^iv	143.67 (13)	O5—Lu2—Lu1	37.81 (11)
O3—Lu1—Lu2^iv	97.69 (12)	O6^ii—Lu2—Lu1	77.61 (11)
O1—Lu1—Lu2^iv	42.17 (12)	Si1^viii—Lu2—Lu1	109.39 (3)
O5^ii—Lu1—Lu2^iv	39.70 (12)	Lu1^vii—Lu2—Lu1	104.218 (8)
Si1^iii—Lu1—Lu2^iv	69.70 (3)	O5^v—Lu2—Lu2^v	39.07 (12)
O5—Lu1—Lu1^ii	40.41 (12)	O7^vi—Lu2—Lu2^v	121.08 (13)
O6—Lu1—Lu1^ii	83.62 (12)	O1^vii—Lu2—Lu2^v	80.28 (13)
O3^i—Lu1—Lu1^ii	142.27 (13)	O7—Lu2—Lu2^v	123.06 (13)
O3—Lu1—Lu1^ii	107.44 (12)	O6—Lu2—Lu2^v	109.55 (13)
O1—Lu1—Lu1^ii	115.18 (12)	O5—Lu2—Lu2^v	35.53 (11)
O5^ii—Lu1—Lu1^ii	38.25 (12)	O6^ii—Lu2—Lu2^v	88.75 (12)
Si1^iii—Lu1—Lu1^ii	100.06 (3)	Si1^viii—Lu2—Lu2^v	103.43 (3)
Lu2^iv—Lu1—Lu1^ii	74.057 (9)	Lu1^vii—Lu2—Lu2^v	64.255 (8)
O5—Lu1—Lu2	41.71 (12)	Lu1—Lu2—Lu2^v	70.628 (9)
O6—Lu1—Lu2	41.70 (12)	O5^v—Lu2—Lu1^ii	85.44 (12)
O3^i—Lu1—Lu2	83.69 (13)	O7^vi—Lu2—Lu1^ii	94.00 (11)
O3—Lu1—Lu2	126.90 (12)	O1^vii—Lu2—Lu1^ii	120.85 (13)
O1—Lu1—Lu2	138.56 (13)	O7—Lu2—Lu1^ii	159.89 (11)
O5^ii—Lu1—Lu2	87.92 (12)	O6—Lu2—Lu1^ii	76.23 (12)
Si1^iii—Lu1—Lu2	148.70 (3)	O5—Lu2—Lu1^ii	35.94 (11)
Lu2^iv—Lu1—Lu2	125.719 (10)	O6^ii—Lu2—Lu1^ii	36.62 (12)
Lu1^ii—Lu1—Lu2	64.874 (7)	Si1^viii—Lu2—Lu1^ii	63.72 (3)
O5—Lu1—Lu1^i	101.67 (12)	Lu1^vii—Lu2—Lu1^ii	119.001 (8)
O6—Lu1—Lu1^i	123.18 (12)	Lu1—Lu2—Lu1^ii	56.992 (9)
O3^i—Lu1—Lu1^i	37.24 (13)	Lu2^v—Lu2—Lu1^ii	54.746 (8)
O3—Lu1—Lu1^i	37.10 (12)	Si1—O1—Lu1	132.4 (3)
O1—Lu1—Lu1^i	99.87 (12)	Si1—O1—Lu2^iv	131.1 (3)
O5^ii—Lu1—Lu1^i	155.96 (12)	Lu1—O1—Lu2^iv	96.11 (19)
Si1^iii—Lu1—Lu1^i	61.05 (3)	Si1^ix—O6—Lu1	137.6 (3)
Lu2^iv—Lu1—Lu1^i	126.070 (12)	Si1^ix—O6—Lu2	118.3 (3)
Lu1^ii—Lu1—Lu1^i	133.144 (12)	Lu1—O6—Lu2	98.82 (19)
Lu2—Lu1—Lu1^i	107.970 (10)	Si1^ix—O6—Lu2^ii	89.7 (2)
O5—Lu1—Lu2^ii	83.69 (12)	Lu1—O6—Lu2^ii	98.85 (18)
O6—Lu1—Lu2^ii	44.54 (12)	Lu2—O6—Lu2^ii	106.92 (18)
O3^i—Lu1—Lu2^ii	129.34 (13)	Si1^iii—O3—Lu1^i	126.5 (3)
O3—Lu1—Lu2^ii	155.89 (12)	Si1^iii—O3—Lu1	111.7 (2)
O1—Lu1—Lu2^ii	78.05 (13)	Lu1^i—O3—Lu1	105.7 (2)
O5^ii—Lu1—Lu2^ii	37.47 (12)	Lu1—O5—Lu2^v	141.2 (2)
Si1^iii—Lu1—Lu2^ii	129.66 (3)	Lu1—O5—Lu1^ii	101.34 (18)
Lu2^iv—Lu1—Lu2^ii	60.999 (8)	Lu2^v—O5—Lu1^ii	98.36 (18)
Lu1^ii—Lu1—Lu2^ii	58.133 (7)	Lu1—O5—Lu2	100.48 (18)
Lu2—Lu1—Lu2^ii	67.548 (9)	Lu2^v—O5—Lu2	105.40 (19)
Lu1^i—Lu1—Lu2^ii	166.114 (13)	Lu1^ii—O5—Lu2	106.59 (18)
O5^v—Lu2—O7^vi	99.84 (18)	Si1^x—O7—Lu2^vi	103.9 (2)
O5^v—Lu2—O1^vii	79.30 (18)	Si1^x—O7—Lu2	145.8 (3)
O7^vi—Lu2—O1^vii	144.72 (17)	Lu2^vi—O7—Lu2	110.26 (17)
O5^v—Lu2—O7	85.83 (18)	O1—Si1—O3^ix	110.3 (3)
O7^vi—Lu2—O7	69.74 (17)	O1—Si1—O7^x	114.5 (3)
O1^vii—Lu2—O7	75.04 (17)	O3^ix—Si1—O7^x	109.0 (3)
O5^v—Lu2—O6	147.30 (19)	O1—Si1—O6^iii	112.2 (3)
O7^vi—Lu2—O6	108.15 (18)	O3^ix—Si1—O6^iii	108.1 (3)
O1^vii—Lu2—O6	87.10 (17)	O7^x—Si1—O6^iii	102.4 (3)
O7—Lu2—O6	119.30 (18)	O1—Si1—Lu2^xi	120.22 (19)
O5^v—Lu2—O5	74.60 (19)	O3^ix—Si1—Lu2^xi	129.20 (19)
O7^vi—Lu2—O5	129.21 (16)	O7^x—Si1—Lu2^xi	45.30 (17)
O1^vii—Lu2—O5	85.01 (17)	O6^iii—Si1—Lu2^xi	58.20 (17)
O7—Lu2—O5	154.36 (16)	O1—Si1—Lu1^ix	116.5 (2)
O6—Lu2—O5	74.69 (18)	O3^ix—Si1—Lu1^ix	40.28 (18)
O5^v—Lu2—O6^ii	107.99 (16)	O7^x—Si1—Lu1^ix	70.75 (19)
O7^vi—Lu2—O6^ii	62.41 (16)	O6^iii—Si1—Lu1^ix	129.0 (2)
O1^vii—Lu2—O6^ii	151.79 (16)	Lu2^xi—Si1—Lu1^ix	106.31 (5)
O5—Lu1—Lu2—O5^v	29.5 (3)	Lu1^i—Lu1—O6—Lu2	−79.63 (17)
O6—Lu1—Lu2—O5^v	−178.0 (2)	Lu2^ii—Lu1—O6—Lu2	108.8 (2)
O3^i—Lu1—Lu2—O5^v	−86.54 (18)	O5—Lu1—O6—Lu2^ii	−90.63 (17)
O3—Lu1—Lu2—O5^v	−21.53 (19)	O3^i—Lu1—O6—Lu2^ii	166.48 (18)
O1—Lu1—Lu2—O5^v	172.3 (2)	O3—Lu1—O6—Lu2^ii	−173.9 (4)
O5^ii—Lu1—Lu2—O5^v	103.69 (18)	O1—Lu1—O6—Lu2^ii	64.75 (18)
Si1^iii—Lu1—Lu2—O5^v	5.59 (14)	O5^ii—Lu1—O6—Lu2^ii	−11.41 (16)
Lu2^iv—Lu1—Lu2—O5^v	116.70 (12)	Si1^iii—Lu1—O6—Lu2^ii	61.1 (7)
Lu1^ii—Lu1—Lu2—O5^v	72.01 (12)	Lu2^iv—Lu1—O6—Lu2^ii	22.22 (15)
Lu1^i—Lu1—Lu2—O5^v	−57.92 (12)	Lu1^ii—Lu1—O6—Lu2^ii	−49.92 (12)
Lu2^ii—Lu1—Lu2—O5^v	136.09 (12)	Lu2—Lu1—O6—Lu2^ii	−108.8 (2)
O5—Lu1—Lu2—O7^vi	−97.7 (3)	Lu1^i—Lu1—O6—Lu2^ii	171.57 (5)
O6—Lu1—Lu2—O7^vi	54.8 (3)	O5^v—Lu2—O6—Si1^ix	−155.3 (3)
O3^i—Lu1—Lu2—O7^vi	146.2 (2)	O7^vi—Lu2—O6—Si1^ix	57.2 (3)
O3—Lu1—Lu2—O7^vi	−148.8 (2)	O1^vii—Lu2—O6—Si1^ix	−90.3 (3)
O1—Lu1—Lu2—O7^vi	45.1 (3)	O7—Lu2—O6—Si1^ix	−19.3 (4)
O5^ii—Lu1—Lu2—O7^vi	−23.6 (2)	O5—Lu2—O6—Si1^ix	−175.9 (3)
Si1^iii—Lu1—Lu2—O7^vi	−121.7 (2)	O6^ii—Lu2—O6—Si1^ix	109.0 (3)
Lu2^iv—Lu1—Lu2—O7^vi	−10.54 (19)	Si1^viii—Lu2—O6—Si1^ix	85.2 (3)
Lu1^ii—Lu1—Lu2—O7^vi	−55.23 (19)	Lu1^vii—Lu2—O6—Si1^ix	−96.8 (3)
Lu1^i—Lu1—Lu2—O7^vi	174.83 (19)	Lu1—Lu2—O6—Si1^ix	−158.9 (4)
Lu2^ii—Lu1—Lu2—O7^vi	8.85 (19)	Lu2^v—Lu2—O6—Si1^ix	−168.9 (2)
O5—Lu1—Lu2—O1^vii	102.5 (2)	Lu1^ii—Lu2—O6—Si1^ix	146.9 (3)
O6—Lu1—Lu2—O1^vii	−105.1 (2)	O5^v—Lu2—O6—Lu1	3.6 (4)
O3^i—Lu1—Lu2—O1^vii	−13.61 (19)	O7^vi—Lu2—O6—Lu1	−143.95 (17)
O3—Lu1—Lu2—O1^vii	51.4 (2)	O1^vii—Lu2—O6—Lu1	68.53 (19)
O1—Lu1—Lu2—O1^vii	−114.8 (2)	O7—Lu2—O6—Lu1	139.58 (16)
O5^ii—Lu1—Lu2—O1^vii	176.62 (18)	O5—Lu2—O6—Lu1	−17.09 (16)
Si1^iii—Lu1—Lu2—O1^vii	78.52 (15)	O6^ii—Lu2—O6—Lu1	−92.11 (15)
Lu2^iv—Lu1—Lu2—O1^vii	−170.37 (14)	Si1^viii—Lu2—O6—Lu1	−115.90 (14)
Lu1^ii—Lu1—Lu2—O1^vii	144.94 (14)	Lu1^vii—Lu2—O6—Lu1	62.0 (2)
Lu1^i—Lu1—Lu2—O1^vii	15.01 (14)	Lu2^v—Lu2—O6—Lu1	−10.09 (18)
Lu2^ii—Lu1—Lu2—O1^vii	−150.98 (14)	Lu1^ii—Lu2—O6—Lu1	−54.23 (13)
O5—Lu1—Lu2—O7	137.1 (3)	O5^v—Lu2—O6—Lu2^ii	105.7 (3)
O6—Lu1—Lu2—O7	−70.4 (3)	O7^vi—Lu2—O6—Lu2^ii	−41.8 (2)
O3^i—Lu1—Lu2—O7	21.0 (2)	O1^vii—Lu2—O6—Lu2^ii	170.6 (2)
O3—Lu1—Lu2—O7	86.0 (3)	O7—Lu2—O6—Lu2^ii	−118.31 (19)
O1—Lu1—Lu2—O7	−80.1 (3)	O5—Lu2—O6—Lu2^ii	85.03 (19)
O5^ii—Lu1—Lu2—O7	−148.7 (2)	O6^ii—Lu2—O6—Lu2^ii	10.0 (2)
Si1^iii—Lu1—Lu2—O7	113.2 (2)	Si1^viii—Lu2—O6—Lu2^ii	−13.78 (17)
Lu2^iv—Lu1—Lu2—O7	−135.7 (2)	Lu1^vii—Lu2—O6—Lu2^ii	164.16 (7)
Lu1^ii—Lu1—Lu2—O7	179.6 (2)	Lu1—Lu2—O6—Lu2^ii	102.1 (2)
Lu1^i—Lu1—Lu2—O7	49.6 (2)	Lu2^v—Lu2—O6—Lu2^ii	92.03 (17)
Lu2^ii—Lu1—Lu2—O7	−116.3 (2)	Lu1^ii—Lu2—O6—Lu2^ii	47.89 (14)
O5—Lu1—Lu2—O6	−152.5 (3)	O5—Lu1—O3—Si1^iii	118.3 (3)
O3^i—Lu1—Lu2—O6	91.4 (2)	O6—Lu1—O3—Si1^iii	−161.3 (4)
O3—Lu1—Lu2—O6	156.5 (2)	O3^i—Lu1—O3—Si1^iii	−140.9 (4)
O1—Lu1—Lu2—O6	−9.7 (3)	O1—Lu1—O3—Si1^iii	−39.4 (3)
O5^ii—Lu1—Lu2—O6	−78.3 (2)	O5^ii—Lu1—O3—Si1^iii	38.5 (3)
Si1^iii—Lu1—Lu2—O6	−176.43 (19)	Lu2^iv—Lu1—O3—Si1^iii	2.8 (3)
Lu2^iv—Lu1—Lu2—O6	−65.31 (18)	Lu1^ii—Lu1—O3—Si1^iii	78.4 (3)
Lu1^ii—Lu1—Lu2—O6	−110.00 (18)	Lu2—Lu1—O3—Si1^iii	149.73 (18)
Lu1^i—Lu1—Lu2—O6	120.06 (18)	Lu1^i—Lu1—O3—Si1^iii	−140.9 (4)
Lu2^ii—Lu1—Lu2—O6	−45.92 (18)	Lu2^ii—Lu1—O3—Si1^iii	29.2 (5)
O6—Lu1—Lu2—O5	152.5 (3)	O5—Lu1—O3—Lu1^i	−100.7 (2)
O3^i—Lu1—Lu2—O5	−116.1 (2)	O6—Lu1—O3—Lu1^i	−20.3 (6)
O3—Lu1—Lu2—O5	−51.1 (2)	O3^i—Lu1—O3—Lu1^i	0.0
O1—Lu1—Lu2—O5	142.8 (3)	O1—Lu1—O3—Lu1^i	101.5 (2)
O5^ii—Lu1—Lu2—O5	74.1 (2)	O5^ii—Lu1—O3—Lu1^i	179.45 (16)
Si1^iii—Lu1—Lu2—O5	−23.96 (18)	Si1^iii—Lu1—O3—Lu1^i	140.9 (4)
Lu2^iv—Lu1—Lu2—O5	87.16 (18)	Lu2^iv—Lu1—O3—Lu1^i	143.75 (15)
Lu1^ii—Lu1—Lu2—O5	42.47 (18)	Lu1^ii—Lu1—O3—Lu1^i	−140.62 (14)
Lu1^i—Lu1—Lu2—O5	−87.47 (18)	Lu2—Lu1—O3—Lu1^i	−69.3 (2)
Lu2^ii—Lu1—Lu2—O5	106.54 (18)	Lu2^ii—Lu1—O3—Lu1^i	170.13 (13)
O5—Lu1—Lu2—O6^ii	−75.6 (2)	O6—Lu1—O5—Lu2^v	−149.6 (4)
O6—Lu1—Lu2—O6^ii	76.9 (2)	O3^i—Lu1—O5—Lu2^v	−65.5 (4)
O3^i—Lu1—Lu2—O6^ii	168.31 (17)	O3—Lu1—O5—Lu2^v	9.8 (4)
O3—Lu1—Lu2—O6^ii	−126.69 (19)	O1—Lu1—O5—Lu2^v	123.8 (4)
O1—Lu1—Lu2—O6^ii	67.2 (2)	O5^ii—Lu1—O5—Lu2^v	128.0 (3)
O5^ii—Lu1—Lu2—O6^ii	−1.46 (17)	Si1^iii—Lu1—O5—Lu2^v	35.7 (4)
Si1^iii—Lu1—Lu2—O6^ii	−99.57 (13)	Lu2^iv—Lu1—O5—Lu2^v	111.3 (3)
Lu2^iv—Lu1—Lu2—O6^ii	11.55 (12)	Lu1^ii—Lu1—O5—Lu2^v	119.1 (4)
Lu1^ii—Lu1—Lu2—O6^ii	−33.14 (12)	Lu2—Lu1—O5—Lu2^v	−131.4 (4)
Lu1^i—Lu1—Lu2—O6^ii	−163.08 (12)	Lu1^i—Lu1—O5—Lu2^v	−27.4 (4)
Lu2^ii—Lu1—Lu2—O6^ii	30.93 (12)	Lu2^ii—Lu1—O5—Lu2^v	165.5 (3)
O5—Lu1—Lu2—Si1^viii	−80.43 (18)	O6—Lu1—O5—Lu1^ii	91.30 (19)
O6—Lu1—Lu2—Si1^viii	72.04 (19)	O3^i—Lu1—O5—Lu1^ii	175.36 (17)
O3^i—Lu1—Lu2—Si1^viii	163.49 (14)	O3—Lu1—O5—Lu1^ii	−109.31 (19)
O3—Lu1—Lu2—Si1^viii	−131.51 (15)	O1—Lu1—O5—Lu1^ii	4.7 (5)
O1—Lu1—Lu2—Si1^viii	62.34 (19)	O5^ii—Lu1—O5—Lu1^ii	8.9 (2)
O5^ii—Lu1—Lu2—Si1^viii	−6.28 (12)	Si1^iii—Lu1—O5—Lu1^ii	−83.41 (16)
Si1^iii—Lu1—Lu2—Si1^viii	−104.39 (6)	Lu2^iv—Lu1—O5—Lu1^ii	−7.8 (2)
Lu2^iv—Lu1—Lu2—Si1^viii	6.72 (4)	Lu2—Lu1—O5—Lu1^ii	109.5 (2)
Lu1^ii—Lu1—Lu2—Si1^viii	−37.97 (4)	Lu1^i—Lu1—O5—Lu1^ii	−146.55 (13)
Lu1^i—Lu1—Lu2—Si1^viii	−167.90 (4)	Lu2^ii—Lu1—O5—Lu1^ii	46.42 (14)
Lu2^ii—Lu1—Lu2—Si1^viii	26.11 (4)	O6—Lu1—O5—Lu2	−18.16 (17)
O5—Lu1—Lu2—Lu1^vii	73.12 (18)	O3^i—Lu1—O5—Lu2	65.9 (2)
O6—Lu1—Lu2—Lu1^vii	−134.42 (18)	O3—Lu1—O5—Lu2	141.23 (17)
O3^i—Lu1—Lu2—Lu1^vii	−42.97 (13)	O1—Lu1—O5—Lu2	−104.8 (4)
O3—Lu1—Lu2—Lu1^vii	22.04 (15)	O5^ii—Lu1—O5—Lu2	−100.59 (13)
O1—Lu1—Lu2—Lu1^vii	−144.11 (18)	Si1^iii—Lu1—O5—Lu2	167.12 (10)
O5^ii—Lu1—Lu2—Lu1^vii	147.26 (12)	Lu2^iv—Lu1—O5—Lu2	−117.30 (12)
Si1^iii—Lu1—Lu2—Lu1^vii	49.16 (6)	Lu1^ii—Lu1—O5—Lu2	−109.5 (2)
Lu2^iv—Lu1—Lu2—Lu1^vii	160.273 (10)	Lu1^i—Lu1—O5—Lu2	103.98 (13)
Lu1^ii—Lu1—Lu2—Lu1^vii	115.583 (9)	Lu2^ii—Lu1—O5—Lu2	−63.04 (13)
Lu1^i—Lu1—Lu2—Lu1^vii	−14.353 (14)	O5^v—Lu2—O5—Lu1	−150.9 (3)
Lu2^ii—Lu1—Lu2—Lu1^vii	179.661 (10)	O7^vi—Lu2—O5—Lu1	118.9 (2)
O5—Lu1—Lu2—Lu2^v	17.45 (18)	O1^vii—Lu2—O5—Lu1	−70.61 (19)
O6—Lu1—Lu2—Lu2^v	169.92 (18)	O7—Lu2—O5—Lu1	−109.3 (4)
O3^i—Lu1—Lu2—Lu2^v	−98.63 (13)	O6—Lu2—O5—Lu1	17.74 (17)
O3—Lu1—Lu2—Lu2^v	−33.62 (15)	O6^ii—Lu2—O5—Lu1	93.65 (18)
O1—Lu1—Lu2—Lu2^v	160.22 (18)	Si1^viii—Lu2—O5—Lu1	109.39 (14)
O5^ii—Lu1—Lu2—Lu2^v	91.60 (12)	Lu1^vii—Lu2—O5—Lu1	−111.91 (14)
Si1^iii—Lu1—Lu2—Lu2^v	−6.51 (6)	Lu2^v—Lu2—O5—Lu1	−150.9 (3)
Lu2^iv—Lu1—Lu2—Lu2^v	104.611 (12)	Lu1^ii—Lu2—O5—Lu1	105.3 (2)
Lu1^ii—Lu1—Lu2—Lu2^v	59.921 (8)	O5^v—Lu2—O5—Lu2^v	0.0
Lu1^i—Lu1—Lu2—Lu2^v	−70.015 (12)	O7^vi—Lu2—O5—Lu2^v	−90.2 (2)
Lu2^ii—Lu1—Lu2—Lu2^v	123.999 (11)	O1^vii—Lu2—O5—Lu2^v	80.3 (2)
O5—Lu1—Lu2—Lu1^ii	−42.47 (18)	O7—Lu2—O5—Lu2^v	41.6 (5)
O6—Lu1—Lu2—Lu1^ii	110.00 (18)	O6—Lu2—O5—Lu2^v	168.6 (2)
O3^i—Lu1—Lu2—Lu1^ii	−158.55 (13)	O6^ii—Lu2—O5—Lu2^v	−115.5 (2)
O3—Lu1—Lu2—Lu1^ii	−93.55 (15)	Si1^viii—Lu2—O5—Lu2^v	−99.75 (15)
O1—Lu1—Lu2—Lu1^ii	100.30 (18)	Lu1^vii—Lu2—O5—Lu2^v	38.96 (15)
O5^ii—Lu1—Lu2—Lu1^ii	31.68 (12)	Lu1—Lu2—O5—Lu2^v	150.9 (3)
Si1^iii—Lu1—Lu2—Lu1^ii	−66.43 (6)	Lu1^ii—Lu2—O5—Lu2^v	−103.8 (2)
Lu2^iv—Lu1—Lu2—Lu1^ii	44.690 (11)	O5^v—Lu2—O5—Lu1^ii	103.8 (2)
Lu1^i—Lu1—Lu2—Lu1^ii	−129.936 (12)	O7^vi—Lu2—O5—Lu1^ii	13.6 (3)
Lu2^ii—Lu1—Lu2—Lu1^ii	64.078 (8)	O1^vii—Lu2—O5—Lu1^ii	−175.9 (2)
O5—Lu1—O1—Si1	155.8 (3)	O7—Lu2—O5—Lu1^ii	145.4 (3)
O6—Lu1—O1—Si1	72.8 (4)	O6—Lu2—O5—Lu1^ii	−87.5 (2)
O3^i—Lu1—O1—Si1	−14.9 (4)	O6^ii—Lu2—O5—Lu1^ii	−11.64 (17)
O3—Lu1—O1—Si1	−89.6 (4)	Si1^viii—Lu2—O5—Lu1^ii	4.10 (18)
O5^ii—Lu1—O1—Si1	151.6 (4)	Lu1^vii—Lu2—O5—Lu1^ii	142.80 (15)
Si1^iii—Lu1—O1—Si1	−107.9 (4)	Lu1—Lu2—O5—Lu1^ii	−105.3 (2)
Lu2^iv—Lu1—O1—Si1	172.9 (5)	Lu2^v—Lu2—O5—Lu1^ii	103.8 (2)
Lu1^ii—Lu1—O1—Si1	159.1 (3)	O5^v—Lu2—O7—Si1^x	80.6 (5)
Lu2—Lu1—O1—Si1	79.3 (4)	O7^vi—Lu2—O7—Si1^x	−177.3 (7)
Lu1^i—Lu1—O1—Si1	−52.8 (4)	O1^vii—Lu2—O7—Si1^x	0.6 (5)
Lu2^ii—Lu1—O1—Si1	113.2 (4)	O6—Lu2—O7—Si1^x	−77.3 (6)
O5—Lu1—O1—Lu2^iv	−17.2 (5)	O5—Lu2—O7—Si1^x	40.7 (8)
O6—Lu1—O1—Lu2^iv	−100.13 (19)	O6^ii—Lu2—O7—Si1^x	−168.9 (4)
O3^i—Lu1—O1—Lu2^iv	172.17 (18)	Si1^viii—Lu2—O7—Si1^x	−178.1 (5)
O3—Lu1—O1—Lu2^iv	97.42 (19)	Lu1^vii—Lu2—O7—Si1^x	43.7 (5)
O5^ii—Lu1—O1—Lu2^iv	−21.34 (17)	Lu1—Lu2—O7—Si1^x	−33.9 (7)
Si1^iii—Lu1—O1—Lu2^iv	79.16 (15)	Lu2^v—Lu2—O7—Si1^x	68.1 (6)
Lu1^ii—Lu1—O1—Lu2^iv	−13.8 (2)	Lu1^ii—Lu2—O7—Si1^x	145.1 (3)
Lu2—Lu1—O1—Lu2^iv	−93.6 (2)	O5^v—Lu2—O7—Lu2^vi	−102.1 (2)
Lu1^i—Lu1—O1—Lu2^iv	134.28 (13)	O7^vi—Lu2—O7—Lu2^vi	0.0
Lu2^ii—Lu1—O1—Lu2^iv	−59.70 (13)	O1^vii—Lu2—O7—Lu2^vi	177.9 (3)
O5—Lu1—O6—Si1^ix	170.0 (4)	O6—Lu2—O7—Lu2^vi	100.0 (2)
O3^i—Lu1—O6—Si1^ix	67.2 (4)	O5—Lu2—O7—Lu2^vi	−142.0 (3)
O3—Lu1—O6—Si1^ix	86.7 (6)	O6^ii—Lu2—O7—Lu2^vi	8.4 (3)
O1—Lu1—O6—Si1^ix	−34.6 (4)	Si1^viii—Lu2—O7—Lu2^vi	−0.8 (2)
O5^ii—Lu1—O6—Si1^ix	−110.7 (4)	Lu1^vii—Lu2—O7—Lu2^vi	−139.1 (2)
Si1^iii—Lu1—O6—Si1^ix	−38.3 (10)	Lu1—Lu2—O7—Lu2^vi	143.39 (10)
Lu2^iv—Lu1—O6—Si1^ix	−77.1 (4)	Lu2^v—Lu2—O7—Lu2^vi	−114.60 (17)
Lu1^ii—Lu1—O6—Si1^ix	−149.2 (4)	Lu1^ii—Lu2—O7—Lu2^vi	−37.6 (5)
Lu2—Lu1—O6—Si1^ix	151.9 (5)	Lu1—O1—Si1—O3^ix	−120.9 (4)
Lu1^i—Lu1—O6—Si1^ix	72.2 (4)	Lu2^iv—O1—Si1—O3^ix	49.7 (4)
Lu2^ii—Lu1—O6—Si1^ix	−99.3 (4)	Lu1—O1—Si1—O7^x	2.4 (5)
O5—Lu1—O6—Lu2	18.17 (17)	Lu2^iv—O1—Si1—O7^x	173.0 (3)
O3^i—Lu1—O6—Lu2	−84.72 (19)	Lu1—O1—Si1—O6^iii	118.5 (4)
O3—Lu1—O6—Lu2	−65.1 (5)	Lu2^iv—O1—Si1—O6^iii	−70.8 (4)
O1—Lu1—O6—Lu2	173.55 (17)	Lu1—O1—Si1—Lu2^xi	53.4 (4)
O5^ii—Lu1—O6—Lu2	97.39 (18)	Lu2^iv—O1—Si1—Lu2^xi	−135.9 (3)
Si1^iii—Lu1—O6—Lu2	169.9 (5)	Lu1—O1—Si1—Lu1^ix	−77.4 (4)
Lu2^iv—Lu1—O6—Lu2	131.01 (12)	Lu2^iv—O1—Si1—Lu1^ix	93.3 (4)
Lu1^ii—Lu1—O6—Lu2	58.88 (13)

Symmetry codes: (i) −x+3/2, −y+1/2, −z+1/2; (ii) −x+3/2, y, −z+1; (iii) −x+1, y−1/2, −z+1/2; (iv) x−1/2, −y+1, z; (v) −x+2, −y+1, −z+1; (vi) −x+2, −y+2, −z+1; (vii) x+1/2, −y+1, z; (viii) x+1/2, y+1/2, z+1/2; (ix) −x+1, y+1/2, −z+1/2; (x) −x+3/2, −y+3/2, −z+1/2; (xi) x−1/2, y−1/2, z−1/2.