Rb₂Lu[Si₄O₁₀]F, a tubular chain silicate

Single crystals of Rb₂Lu[Si₄O₁₀]F (dirubidium lutetium tetra­silicate fluoride) were obtained in flux-synthesis experiments in the system SiO₂–Lu₂O₃–RbF. The compound belongs to the group of tubular chain silicates, i.e. it is based on multiple chains of condensed [SiO₄] tetra­hedra forming closed columns. The periodicity of the unbranched multiple chains is four and corresponds to the length of the b axis. Adjacent columns are connected by Lu³⁺ cations, which are coordinated by four oxide and two fluoride anions in the form of slightly distorted octa­hedra. By sharing common fluoride corners, the single octa­hedra are linked into chains running parallel to the silicate tubes. Electroneutrality is achieved by the incorporation of additional Rb⁺ cations. All four symmetrically independent rubidium ions, four out of twelve oxide as well as the two fluoride anions are located on mirror planes. The remaining atoms reside on general positions.

Related literature

Oxosilicates that contain monovalent alkali cations, trivalent rare earth elements and additional fluorine anions have potential application in the field of luminescense (Jacobsen & Meyer, 1994; Tang et al., 2008; Schäfer & Schleid, 2007, 2011; Kahlenberg & Manninger, 2014). For structures isotypic to that of the title compound, see: Chigarov et al. (1983); Hung et al. (2003). For general aspects of the crystal chemistry of silicates, see: Liebau (1985). For the definition of distortion parameters, see: Robinson et al. (1971). For bond-valence analysis, see: Brown (2002). For the definition and calculation of similarity descriptors, see: Tasci et al. (2012); Bergerhoff et al. (1999). For the Inorganic Structure Database, see: ICSD (2014).

Experimental

Crystal data

• Rb₂Lu[Si₄O₁₀]F

• M_r = 637.27

• Monoclinic, P 2₁ /m

• a = 11.6695 (3) Å

• b = 8.52379 (18) Å

• c = 11.8165 (3) Å

• β = 111.753 (3)°

• V = 1091.67 (5) ų

• Z = 4

• Mo Kα radiation

• μ = 18.4 mm⁻¹

• T = 298 K

• 0.32 × 0.08 × 0.08 mm

Data collection

• Oxford Diffraction Xcalibur (Ruby, Gemini ultra) diffractometer

• Absorption correction: analytical [CrysAlis PRO (Oxford Diffraction, 2006), based on expressions derived by Clark & Reid (1995)] T_min = 0.106, T_max = 0.562

• 15185 measured reflections

• 2388 independent reflections

• 2276 reflections with I > 2σ(I)

• R_int = 0.028

Refinement

• R[F² > 2σ(F²)] = 0.017

• wR(F²) = 0.037

• S = 1.2

• 2388 reflections

• 178 parameters

• Δρ_max = 0.67 e Å⁻³

• Δρ_min = −0.69 e Å⁻³

Data collection: CrysAlis PRO (Oxford Diffraction, 2006); cell refinement: CrysAlis PRO; data reduction: CrysAlis PRO; program(s) used to solve structure: SIR2002 (Burla et al., 2003); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ATOMS for Windows (Dowty, 2011); software used to prepare material for publication: publCIF (Westrip, 2010) and WinGX (Farrugia, 2012).

Supporting information

S1. Comment

Up to now several alkali-REE-fluoride silicates (REE is a rare earth metal) including compounds such as KEu₂[Si₄O₁₀]F (Jacobsen & Meyer, 1994), K₉(REE)₃[Si₁₂O₃₂]F₂ (Tang et al., 2008; Kahlenberg & Manninger, 2014), Cs₂Y[Si₄O₁₀]F₂ (Schäfer & Schleid, 2007) or Rb₃Sc₂[Si₄O₁₀]F₅ (Schäfer & Schleid, 2011) have been reported. In the course of an ongoing project on the synthesis of new representatives of this class, single-crystals of the previously unknown compound Rb₂Lu[Si₄O₁₀]F have been structurally characterized. Following Liebau's classification of oxosilicates (Liebau, 1985), the crystal structure of this phase belongs to the group of tubular chain silicates and is based on unbranched multiple silicate chains running along [010] (Fig. 1). The periodicity of the chains is four. Alternatively, the tubular chains can also be thought of as being built from the condensation of an infinite number of fundamental rings with mean planes perpendicular to the chain direction (Liebau, 1985). In Rb₂Lu[Si₄O₁₀]F these rings are eight-membered (Fig. 2) and exhibit a twisted chair conformation. Within the tubes, cages can be identified that are formed by additional four-, six- and eight-membered rings, the mean planes of which are running parallel to the chains. These six- and eight-membered rings are in boat configurations.

According to the Si:O ratio of 1:2.5 the structure is exclusively based on tertiary (Q³) [SiO₄] tetrahedra. This structural feature is also reflected in the spread of the Si—O bond lengths. Each of the four crystallographically independent tetrahedra has one short (1.569 (3)–1.581 (3) Å) Si—O bond involving the non-bridging O atoms. The distances between Si and the bridging O atoms are considerably longer. The O–Si–O angles show a significant scatter throughout all present [SiO₄] tetrahedra. Nevertheless, the values are in the expected limits for silicates (Liebau, 1985). Numerically, the degree of distortion can be expressed by the quadratic elongation λ and the angle variance σ² (Robinson et al., 1971). For the four tetrahedra these two parameters vary between 1.001 and 1.005 (for λ) and 5.29 and 23.24 (for σ²) indicating that the deviation from regularity is not very pronounced. The Lu³⁺ cations are octahedrally coordinated by four oxygen and two additional fluoride anions (Fig. 3). The latter two are in trans-configuration. By sharing common fluorine corners, the octahedra in turn form chains running parallel to the directions of the silicate tubes (Fig. 4). However, these chains are not straight. The polyhedra are tilted with tilt angles (Lu—F1—Lu) and (Lu—F2—Lu) of 160.5 (3) and 156.3 (3)°, respectively. Charge compensation is achieved by the incorporation of additional Rb⁺ ions. The coordination numbers of these cations are as follows: Rb1, Rb3: 10-coordinate, including one F atom each; Rb2: 10-coordinate; Rb4: 9-coordinate, including one F atom (Fig. 5–8). The Rb2 cations, which are exclusively coordinated by O atoms, are located within the abovementioned cages of the tubes. The remaining rubidium cations reside in tunnel-like cavities formed by [SiO₄]-tetrahedra and [LuO₄F₂]-octahedra. A side view of the crystal structure is given in Fig. 9.

Bond valence sum calculations using the parameter sets for the Rb–O, Rb–F, Lu–O, Lu–F and Si–O bonds given by Brown (2002) resulted in the following values (in v.u.) for the cation-anion interactions up to 3.4 Å: Rb(1): 1.152, Rb(2): 1.324, Rb(3): 1.008, Rb(4): 0.936, Lu: 3.140, Si(1): 4.062, Si(2): 4.044, Si(3): 4.082 and Si(4): 4.028.

The present compound is isostructural with K₂Lu[Si₄O₁₀](OH) (Chigarov et al., 1983) and K₂In[Si₄O₁₀](OH) (Hung et al., 2003). For the calculation of several quantitative descriptors for the characterization of the degree of similarity between the crystal structures of Rb₂Lu[Si₄O₁₀]F and K₂Lu[Si₄O₁₀](OH) containing the same REE, the program COMPSTRU (Tasci et al., 2012) was employed. For the two structures, the degree of lattice distortion (S), i.e. the spontaneous strain obtained from the eigenvalues of the finite Lagrangian strain tensor calculated in a Cartesian reference system, has a value of (S) = 0.0053. For further investigations on an atomic level, the proton positions of the hydroxyl groups in K₂Lu[Si₄O₁₀](OH) have been neglected. After a transformation to the standard setting according to a' = b, b' = c and c' = a and the application of an origin shift of p = (0, 1/2, 1/2) the structure of K₂Lu[Si₄O₁₀](OH) was mapped on the most similar configuration of Rb₂Lu[Si₄O₁₀]F. The calculations revealed the following atomic displacements (in Å) between the corresponding atoms in Rb₂Lu[Si₄O₁₀]F (first entry) and K₂Lu[Si₄O₁₀](OH) (second entry): Rb1—K1: 0.091; Rb2—K3: 0.063; Rb3—K2: 0.275; Rb4—K4: 0.064; Lu—Lu: 0.098; Si1—Si1: 0.055; Si2—Si2: 0.114; Si3—Si4: 0.089; Si4—Si3: 0.095; O1—O4: 0.083; O2—O13: 0.134; O3—O9: 0.067; O4—O5: 0.207; O5—O3: 0.168; O6—O11: 0.149; O7—O10: 0.101; O8—O2: 0.116; O9—O7: 0.082; O10—O14: 0.173; O11—O6: 0.247; O12—O8: 0.134; F1—O1: 0.246; F2—O12: 0.125, i.e. the maximum displacement is 0.275 Å. The measure of similarity (Δ) as defined by Bergerhoff et al. (1999) has a value of 0.022.

Related literature

Oxosilicates that contain monovalent alkali cations, trivalent rare earth elements and additional fluorine anions have potential application in the field of luminescense (Jacobsen & Meyer, 1994; Tang et al., 2008; Schäfer & Schleid, 2007, 2011; Kahlenberg & Manninger, 2014). For structures isotypic to that of the title compound, see: Chigarov et al. (1983); Hung et al. (2003). For general aspects of the crystal chemistry of silicates, see: Liebau (1985). For the definition of distortion parameters, see: Robinson et al. (1971). For bond-valence analysis, see: Brown (2002). For the definition and calculation of similarity descriptors, see: Tasci et al. (2012); Bergerhoff et al. (1999). For the Inorganic Structure Database, see: ICSD (2014).

S2. Experimental

Single-crystals of Rb₂Lu[Si₄O₁₀]F were obtained in the course of a series of flux syntheses experiments aiming on the preparation of new Rb-REE-fluoride silicates. 0.1 g of the nutrient consisting of a mixture of Lu₂O₃:SiO₂ in the molar ratio 1:4 was homogenized in an agate mortar with 0.1 g RbF, transferred into a platinum tube and welded shut. The container was heated in a laboratory chamber furnace from 373 K to 1373 K with a ramp of 50 K/h and isothermed for 2 h at the target temperature. Subsequently, the sample was cooled down to 1073 K with a rate of 5 K and, finally, the temperature was reduced to 373 K with a rate of 100 K/h. After the removal of the platinum tube the solidified melt cake was immediately crashed in an agate mortar and transferred to a glass slide under a polarizing binocular. A first optical inspection revealed the presence of two phases: a polycrystalline matrix of RbF in which transparent birefringent single-crystals up to 400µm in size were embedded. One of the optically biaxial crystals showing sharp extinction when observed between crossed polarizers was selected for further structural studies and was mounted on the tip of a glass fiber using fingernail hardener as glue.

S3. Refinement

Similar sets of lattice parameters could be found in the recent WEB-based version of the Inorganic Crystal Structure Database (ICSD, 2014) for the chemically closely related compounds K₂Lu[Si₄O₁₀]F (Chigarov et al., 1983) and K₂In[Si₄O₁₀](OH) (Hung et al., 2003) pointing to isostructural relationships, which were confirmed by subsequent structure analysis. A data set corresponding to a hemisphere of reciprocal space was collected.

Computing details

Data collection: CrysAlis PRO (Oxford Diffraction, 2006); cell refinement: CrysAlis PRO (Oxford Diffraction, 2006); data reduction: CrysAlis PRO (Oxford Diffraction, 2006); program(s) used to solve structure: SIR2002 (Burla et al., 2003); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ATOMS for Windows (Dowty, 2011); software used to prepare material for publication: publCIF (Westrip, 2010) and WinGX (Farrugia, 2012).

Figures

	Fig. 1. A single tubular chain consisting of [SiO4]-tetrahedra in a projection parallel to [101]. Large blue spheres represent Rb2 cations.
	Fig. 2. Connectivity of the silicon atoms within a single tubular chain (view perpedicular to (011)). Red spheres represent the Q^3- connected Si atoms. Large blue spheres represent Rb2 cations. The sizes of the different ring types are indicated.
	Fig. 3. Representation of the coordination polyhedron around Lu. Ellipsoids are drawn at the 60% level. [Symmetry codes: (i) x, y - 1, z; (ii) -x + 1, -y, -z + 1.]
	Fig. 4. Projection of a single chain of corner-sharing [LuO4F2]-octahedra parallel to [001]. Small grey and green spheres represent oxygen and fluoride anions, respectively.
	Fig. 5. Representation of the coordination polyhedron around Rb1. Ellipsoids are drawn at the 60% probability level. [Symmetry codes: (i) x, 3/2 - y, z; (ii) x, 1/2 - y, z; (iii) x, 1 + y, z; (iv) 1 - x, -1/2 + y, 1 - z; (v) 1 - x, 2 - y, 1 - z; (vi) 1 - x, 1/2 + y, 1 - z.]
	Fig. 6. Representation of the coordination polyhedron around Rb2. Ellipsoids are drawn at the 60% probability level. [Symmetry codes: (i) x, 1/2 - y, -1 + z; (ii) x, y, -1 + z; (iii) x, 3/2 - y, z; (iv) x, -1 + y, z; (v) -x, -1/2 + y, 1 - z; (vi) -x, 1/2 + y, 1 - z; (vii) -x, -y, 1 - z; (viii) 1 - x, -1/2 + y, 1 - z.]
	Fig. 7. Representation of the coordination polyhedron around Rb3. Ellipsoids are drawn at the 60% probability level. [Symmetry codes: (i) -x, 1/2 + y, 1 - z; (ii) -x, 1 - y, 1 - z; (iii) x, 3/2 - y, z; (iv) x, 1/2 - y, z; (v) x, 1 + y, z.]
	Fig. 8. Representation of the coordination polyhedron around Rb4. Ellipsoids are drawn at the 60% probability level. [Symmetry codes: (i) x, 3/2 - y, z; (ii) x, -1 + y, z; (iii) x, 3/2 - y, -1 + z; (iv) x, -1 + y, -1 + z; (v) x, y, -1 + z; (vi) x, 1/2 - y, z; (vii) 1 - x, -1/2 + y, 1 - z.]
	Fig. 9. Side view of the crystal structure of Rb2Lu[Si4O10]F. [SiO4]- and [LuO4F2]-polyhedra are shown in light-grey and blue. Small grey spheres represent oxygen atoms. Fluoride and rubidium ions are given as green and pink spheres, respectively.

Dirubidium lutetium tetrasilicate fluoride

Crystal data

Rb2Lu[Si4O10]F	F(000) = 1160
Mr = 637.27	Dx = 3.877 Mg m^−3
Monoclinic, P21/m	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2yb	Cell parameters from 8764 reflections
a = 11.6695 (3) Å	θ = 3.0–29.4°
b = 8.52379 (18) Å	µ = 18.4 mm^−1
c = 11.8165 (3) Å	T = 298 K
β = 111.753 (3)°	Prism, colourless
V = 1091.67 (5) Å^3	0.32 × 0.08 × 0.08 mm
Z = 4

Data collection

Oxford Diffraction Xcalibur (Ruby, Gemini ultra) diffractometer	2388 independent reflections
Graphite monochromator	2276 reflections with I > 2σ(I)
Detector resolution: 10.3575 pixels mm^-1	Rint = 0.028
ω scans	θmax = 26.4°, θmin = 3.0°
Absorption correction: analytical [CrysAlis PRO (Oxford Diffraction, 2006), based on expressions derived by Clark & Reid (1995)]	h = −14→14
Tmin = 0.106, Tmax = 0.562	k = −10→10
15185 measured reflections	l = −14→14

Refinement

Refinement on F^2	0 constraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.017	Secondary atom site location: difference Fourier map
wR(F^2) = 0.037	w = 1/[σ^2(Fo^2) + (0.008P)^2 + 3.5409P] where P = (Fo^2 + 2Fc^2)/3
S = 1.2	(Δ/σ)max = 0.001
2388 reflections	Δρmax = 0.67 e Å^−3
178 parameters	Δρmin = −0.69 e Å^−3
0 restraints

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
Lu	0.293348 (13)	0.003290 (17)	0.709429 (13)	0.00494 (5)
Rb1	0.44695 (5)	0.75	0.54955 (5)	0.01305 (11)
Rb2	0.08212 (5)	0.25	0.07908 (5)	0.01314 (11)
Rb3	−0.00057 (5)	0.75	0.52863 (5)	0.01827 (13)
Rb4	0.46419 (5)	0.25	0.03113 (5)	0.01750 (12)
Si1	0.38671 (9)	−0.06260 (11)	0.22969 (8)	0.00464 (19)
Si2	0.01773 (9)	0.06858 (11)	0.75550 (9)	0.00508 (19)
Si3	0.24334 (9)	0.43354 (11)	0.38343 (8)	0.00493 (19)
Si4	0.22493 (9)	0.93232 (11)	0.96450 (8)	0.00543 (19)
O1	0.4021 (3)	0.75	0.2204 (3)	0.0099 (8)
O2	0.7259 (3)	0.75	0.6326 (4)	0.0129 (8)
O3	0.2743 (2)	0.9946 (3)	0.1053 (2)	0.0084 (5)
O4	0.3423 (2)	0.9684 (3)	0.3435 (2)	0.0100 (5)
O5	−0.0274 (3)	0.25	0.7485 (3)	0.0112 (8)
O6	−0.1052 (2)	0.9599 (3)	0.7182 (2)	0.0090 (5)
O7	0.0945 (2)	0.0289 (3)	0.9002 (2)	0.0084 (5)
O8	0.1833 (3)	0.75	0.9630 (3)	0.0100 (8)
O9	0.5102 (2)	0.0289 (3)	0.2481 (2)	0.0110 (5)
O10	0.0957 (2)	0.0320 (3)	0.6743 (2)	0.0096 (5)
O11	0.3210 (2)	0.9616 (3)	0.9020 (2)	0.0095 (5)
O12	0.2534 (3)	0.0222 (3)	0.5157 (2)	0.0156 (6)
F1	0.2695 (3)	0.75	0.6782 (3)	0.0142 (7)
F2	0.3190 (3)	0.25	0.7478 (3)	0.0172 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Lu	0.00544 (8)	0.00452 (8)	0.00516 (8)	0.00016 (5)	0.00231 (6)	0.00015 (5)
Rb1	0.0146 (3)	0.0120 (2)	0.0119 (2)	0	0.0043 (2)	0
Rb2	0.0170 (3)	0.0114 (2)	0.0131 (2)	0	0.0080 (2)	0
Rb3	0.0248 (3)	0.0133 (3)	0.0122 (3)	0	0.0016 (2)	0
Rb4	0.0143 (3)	0.0133 (3)	0.0212 (3)	0	0.0024 (2)	0
Si1	0.0050 (5)	0.0044 (4)	0.0044 (4)	0.0007 (4)	0.0015 (4)	0.0002 (4)
Si2	0.0043 (5)	0.0047 (5)	0.0053 (4)	0.0002 (4)	0.0007 (4)	0.0003 (4)
Si3	0.0049 (5)	0.0052 (5)	0.0044 (4)	−0.0007 (4)	0.0013 (4)	−0.0001 (4)
Si4	0.0055 (5)	0.0057 (5)	0.0042 (4)	0.0006 (4)	0.0009 (4)	0.0007 (4)
O1	0.0112 (19)	0.0054 (17)	0.0149 (19)	0	0.0071 (16)	0
O2	0.0094 (19)	0.0051 (17)	0.021 (2)	0	0.0015 (16)	0
O3	0.0070 (12)	0.0113 (13)	0.0050 (12)	0.0022 (10)	0.0001 (10)	−0.0006 (10)
O4	0.0100 (13)	0.0113 (13)	0.0101 (12)	0.0043 (10)	0.0053 (11)	−0.0006 (10)
O5	0.0093 (19)	0.0069 (18)	0.0156 (19)	0	0.0027 (16)	0
O6	0.0048 (12)	0.0099 (12)	0.0097 (12)	−0.0021 (10)	−0.0002 (10)	−0.0001 (10)
O7	0.0074 (13)	0.0118 (13)	0.0063 (12)	0.0036 (10)	0.0029 (10)	−0.0007 (10)
O8	0.0134 (19)	0.0035 (17)	0.0127 (18)	0	0.0045 (16)	0
O9	0.0082 (13)	0.0091 (13)	0.0145 (13)	−0.0019 (10)	0.0028 (11)	−0.0004 (11)
O10	0.0084 (13)	0.0127 (13)	0.0076 (12)	0.0016 (10)	0.0030 (10)	0.0011 (10)
O11	0.0089 (13)	0.0137 (13)	0.0069 (12)	0.0010 (10)	0.0042 (10)	0.0023 (10)
O12	0.0179 (15)	0.0221 (15)	0.0075 (12)	0.0039 (11)	0.0054 (11)	0.0023 (11)
F1	0.0164 (17)	0.0044 (14)	0.0194 (17)	0	0.0039 (14)	0
F2	0.0220 (18)	0.0056 (15)	0.0250 (18)	0	0.0100 (15)	0

Geometric parameters (Å, º)

Si1—O9	1.581 (3)	Rb1—O4^xi	3.332 (3)
Si1—O1^i	1.6157 (11)	Rb2—O7^xii	2.875 (2)
Si1—O4^i	1.631 (3)	Rb2—O7^xiii	2.875 (2)
Si1—O3^i	1.640 (2)	Rb2—O6^iii	2.921 (3)
Si2—O10	1.579 (3)	Rb2—O6^xiv	2.921 (3)
Si2—O6^i	1.625 (3)	Rb2—O8^xiv	2.949 (4)
Si2—O5	1.6259 (14)	Rb2—O3^iv	3.058 (2)
Si2—O7	1.645 (3)	Rb2—O3^i	3.058 (2)
Si3—O12^ii	1.569 (3)	Rb2—O7^xv	3.214 (3)
Si3—O6^iii	1.630 (3)	Rb2—O7^xvi	3.214 (3)
Si3—O4^iv	1.631 (3)	Rb2—O2^v	3.312 (4)
Si3—O2^v	1.6318 (15)	Rb3—O10^xvi	2.909 (3)
Si4—O11	1.574 (3)	Rb3—O10^xiv	2.909 (2)
Si4—O8	1.6264 (14)	Rb3—O10^vii	2.927 (3)
Si4—O3^vi	1.634 (3)	Rb3—O10^ii	2.927 (3)
Si4—O7^vii	1.648 (3)	Rb3—F1	2.988 (3)
Lu—F2	2.1487 (7)	Rb3—O12^xvi	3.407 (3)
Lu—O12	2.167 (3)	Rb3—O12^xiv	3.407 (3)
Lu—O9^viii	2.175 (3)	Rb3—O5^xiv	3.409 (4)
Lu—F1^i	2.1906 (6)	Rb3—O6	3.426 (3)
Lu—O10	2.200 (2)	Rb3—O6^iv	3.426 (3)
Lu—O11^i	2.205 (2)	Rb4—O11^xi	2.949 (3)
Rb1—O9^v	2.938 (3)	Rb4—O11^v	2.949 (3)
Rb1—O9^ix	2.938 (3)	Rb4—O11^xvii	3.045 (3)
Rb1—O4^iv	2.947 (3)	Rb4—O11^xviii	3.045 (3)
Rb1—O4	2.947 (3)	Rb4—O9^ii	3.065 (3)
Rb1—F1	2.989 (3)	Rb4—O9	3.065 (3)
Rb1—O2	3.031 (4)	Rb4—F2^xii	3.142 (3)
Rb1—O12^ii	3.158 (3)	Rb4—O3^iv	3.444 (3)
Rb1—O12^vii	3.158 (3)	Rb4—O3^i	3.444 (3)
Rb1—O4^x	3.332 (3)
F2—Lu—O12	96.25 (12)	O6^i—Si2—O7	104.51 (14)
F2—Lu—O9^viii	91.29 (11)	O5—Si2—O7	106.84 (17)
O12—Lu—O9^viii	92.79 (10)	O12^ii—Si3—O6^iii	112.89 (15)
F2—Lu—F1^i	177.69 (12)	O12^ii—Si3—O4^iv	111.44 (15)
O12—Lu—F1^i	86.05 (11)	O6^iii—Si3—O4^iv	109.22 (14)
O9^viii—Lu—F1^i	88.38 (11)	O12^ii—Si3—O2^v	114.08 (18)
F2—Lu—O10	89.16 (11)	O6^iii—Si3—O2^v	104.29 (16)
O12—Lu—O10	89.57 (10)	O4^iv—Si3—O2^v	104.34 (17)
O9^viii—Lu—O10	177.53 (9)	O11—Si4—O8	114.10 (17)
F1^i—Lu—O10	91.08 (11)	O11—Si4—O3^vi	112.49 (14)
F2—Lu—O11^i	89.10 (11)	O8—Si4—O3^vi	108.21 (17)
O12—Lu—O11^i	173.81 (10)	O11—Si4—O7^vii	113.66 (14)
O9^viii—Lu—O11^i	90.18 (9)	O8—Si4—O7^vii	104.55 (16)
F1^i—Lu—O11^i	88.61 (11)	O3^vi—Si4—O7^vii	102.93 (13)
O10—Lu—O11^i	87.40 (9)	Si1^vii—O1—Si1^ii	162.7 (3)
O9—Si1—O1^i	112.24 (17)	Si3^ix—O2—Si3^v	146.9 (3)
O9—Si1—O4^i	110.99 (14)	Si4^xii—O3—Si1^vii	132.77 (16)
O1^i—Si1—O4^i	107.06 (17)	Si3^iv—O4—Si1^vii	142.83 (17)
O9—Si1—O3^i	111.24 (14)	Si2^ii—O5—Si2	144.0 (2)
O1^i—Si1—O3^i	107.75 (16)	Si2^vii—O6—Si3^xvi	144.19 (17)
O4^i—Si1—O3^i	107.32 (13)	Si2—O7—Si4^i	129.48 (16)
O10—Si2—O6^i	111.85 (14)	Si4—O8—Si4^iv	145.7 (3)
O10—Si2—O5	113.95 (17)	Lu^vii—F1—Lu^ii	160.51 (16)
O6^i—Si2—O5	106.95 (16)	Lu—F2—Lu^ii	156.30 (18)
O10—Si2—O7	112.13 (14)

Symmetry codes: (i) x, y−1, z; (ii) x, −y+1/2, z; (iii) −x, y−1/2, −z+1; (iv) x, −y+3/2, z; (v) −x+1, −y+1, −z+1; (vi) x, y, z+1; (vii) x, y+1, z; (viii) −x+1, −y, −z+1; (ix) −x+1, y+1/2, −z+1; (x) −x+1, −y+2, −z+1; (xi) −x+1, y−1/2, −z+1; (xii) x, y, z−1; (xiii) x, −y+1/2, z−1; (xiv) −x, −y+1, −z+1; (xv) −x, −y, −z+1; (xvi) −x, y+1/2, −z+1; (xvii) x, y−1, z−1; (xviii) x, −y+3/2, z−1.