Reinvestigation of the crystal structure of Ca₂Ce₈(SiO₄)₆O₂ apatite by Rietveld refinement

Ca₂Ln₈(SiO₄)₆O₂ apatites with Ln = La, Ce, Pr, Nd, Sm, Eu, Gd and Tb crystallize in space group P6₃/m. The crystal structure of apatite-type Ca₂Ce₈(SiO₄)₆O₂ [dicalcium octa­cerium hexa­kis­(silicate) dioxide], which has been synthesized by calcination, was refined from powder X-ray diffraction data using the Rietveld method. A database survey shows that contrary to the previously published Ca₂Ce₈(SiO₄)₆O₂ structure [Skakle et al. (2000). Powder Diffr. 15, 234–238], the cell volume of the structure reported here is consistent with those of other Ln apatites.

1. Chemical context

Contaminated metallic wastes produced by the nuclear industry need to be managed. This is often achieved by melting them with an oxide slag to make the waste packages more dense and to concentrate the residual plutonium or uranium oxide contamination of the metal. Laboratory work on actinides is facilitated by the use of surrogates that mimic their properties of inter­est. Cerium can thus be used to simulate the presence of plutonium (Ramsey et al., 1995). The reactivity of cerium(IV) oxide added to melted stainless steel and an SiO₂–CaO–Al₂O₃ glass slag under neutral conditions and at high temperature was studied. Powdered stainless steel from Alfa Aesar and an SiO₂–CaO–Al₂O₃ lab-made glass frit were fused at 1723 K under argon for 6 h in a graphite crucible. Cerium(IV) oxide was introduced to simulate PuO₂. The Ellingham diagram predicts that Ce^IV is reduced to Ce^III under these conditions, which is the predominant cerium form at 1723 K. The same behavior is expected for Pu (Ellingham, 1944). After melting, SEM observations of the sample showed that cerium was concentrated in the glass, as expected, but in two different forms. Cerium is present in the homogeneous part of the glass, at a typical content of 5 wt.% but is also found inside large crystals of hundreds of micrometers across. The X-ray diffractogram of bulk material shows an amorphous bump, attributed to the glass, and a typical pattern for an apatite structure in space group type P6₃/m. The approximate composition of this phase was determined as Ca_2.4±0.3Ce_7.6±0.3(SiO₄)₆O₂ and a cell volume of roughly 560 ų. However, the diffraction data is inconsistent with the PDF card for Ca₂Ce₈(SiO₄)₆O₂ (#00-055-0835; ICDD, 2015) with a cell volume of 530.96 ų (Skakle et al., 2000). The difference between the two volumes, 5.2%, cannot be explained by the difference in composition between the two phases. For instance, the cell volumes of the apatites Ca₂Nd₈(SiO₄)₆O₂ (#00-028-0228) and Ca_2.8Nd_7.8(SiO₄)₆O₂ (#04-007-5969) are 552.20 and 551.76 ų, respectively, a difference of just 0.08%. Moreover, the difference between the cell volumes of Ca₂La₈(SiO₄)₆O₂ (#00-029-0337) and Ca₄La₆(SiO₄)₆O₂ (#04-007-9090) is 0.3%. In other words, the 5.2% difference between the cell volume of Ca₂Ce₈(SiO₄)₆O₂ (Skakle et al., 2000) and Ca_2.4±0.3Ce_7.6±0.3(SiO₄)₆O₂ (this work) cannot be explained by their differing calcium contents. These are the reasons why the structure of Ca₂Ce₈(SiO₄)₆O₂ was reinvestigated in the present work.

2. Structural commentary

Apatites are mineral phases whose general formula is A₁₀(XO₄)₆Z₂, where A = Ca, Sr, Ba, or many rare earth elements, X = B, Si, P, V, As and Z = OH, Cl, F, O, etc. (Byrappa &Yoshimura, 2001). Generally, apatites crystallize in the hexa­gonal crystal system in space group P6₃/m. There are two types of A cations in these structures: Type I (Wyckoff position 4f) A cations are aligned along the threefold rotation axes. Theses cations are separated on each of these axes by one-half the value of the c parameter. Type I cations are sometimes called columnar cations. They are ninefold coordinated by oxygen atoms and these columns of AO₉ polyhedra are linked together by XO₄ tetra­hedra, with three of the oxygen atoms belonging to one column and the fourth to an adjacent column (Elliott, 1994). This results in a skeleton of XO₄ tetra­hedra (point group symmetry m..) alongside the columnar A cations. This skeleton defines channels that are collinear to the c axis and which correspond to the sixfold screw axes. The Z anions and the remaining A cations, also called type II cations and located on mirror planes (6h), are located inside these channels with the Z anions positioned in ellipsoidal cavities along the c axis. Type II cations are sevenfold coordinated, and these sites are smaller than those centered on type I cations. For the present structure, type I cations are statistically occupied by Ca and Ce whereas type II cations are solely occupied by Ce.

The refined title structure is displayed in Fig. 1. In the case of the synthesized Ca₂Ce₈(SiO₄)₆O₂ apatite, the possible substitution of trivalent Ce by tetra­valent Ce would require one positive charge, which should be balanced by replacing calcium by a monovalent cation. No such element was detected by energy-dispersive X-ray fluorescence (EDS). Such a substitution of Ce³⁺ by Ce⁴⁺ in a britholite was investigated by Terra (2005). However, the characterization of the substitution gave unclear results, revealing that the substitution was not successful. This indicates that the presence of tetra­valent Ce in the synthesized apatite is also unlikely. It should be noted that there is no obvious explanation for the differences between our structure model (in particular in terms of lattice parameters) and the structure model with the same composition reported by Skakle et al. (2000; #00-055-0835). These authors stated that the difference might result from a different synthesis route, i.e. hydro­thermal for their Ce-apatite versus solid-state routes for other Ln-apatites. However, in our opinion, differences in the synthesis route can result only in slight differences between the resulting structures for a given composition. On the other hand, differences occur mainly because of slight variations in the composition, especially for wet synthesis routes for which the presence of carbonate or hydrogenphosphate in the structure can be difficult to avoid. Another known source of variations in the lattice volume is the presence of radiation defects, but this does not seem relevant here. Table 1 reports some bond lengths compared with the already published Ce-apatite #00-055-0835 (Skakle et al., 2000) and La-apatite #00-029-0337 (Smith & McCarthy, 1977). As already noticed by Skakle et al. (2000), the Si1—O1 bond length of their structure model was rather short (1.42 Å), with the corresponding SiO₄ tetra­hedron highly distorted, as shown by the distorsion index calculated by VESTA (Momma & Izumi, 2011). The Si—O bond lengths of the redetermined structure are in good agreement with expected values and those of other La-apatites (Table 1). Likewise, the distorsion index of the SiO₄ tetra­hedron is smaller with an order of magnitude for the redetermined structure and other La-apatites.

Table 1
Selected bond lengths (Å) and angles (°) in the redetermined structure and the already published Ce apatite structure (Skakle et al., 2000) and Ca₂La₈(SiO₄)₆O₂

Bond length and angles	Skakle et al. (2000)	This work	La-apatite (Smith & McCarthy, 1977)
Ca/Ln—O1	2.51 (3)	2.468 (10)	2.485
Si1—O1	1.42 (5)	1.590 (16)	1.616
Si1—O2	1.59 (6)	1.614 (13)	1.625
Si1—O3	1.62 (3)	1.608 (7)	1.621
O1—Si1—O2	123 (2)	114.7 (7)	94.93
O1—Si1—O3	109.2 (21)	108.5 (5)	108.22
O2—Si1—O3	106.5 (20)	108.2 (5)	110.94
O3—Si1—O3	99.4 (17)	108.6 (4)	105.35
Distortion index of the SiO4 tetra­hedron*	0.04458	0.00396	0.00139
* as calculated by VESTA (Momma & Izumi, 2011).

Figure 1 Polyhedral representation of the Ca2Ce8(SiO4)6O2 structure. SiO4 tetra­hedra are in blue, the mixed Ca/Ce sites are shown as pink/yellow and the Ce sites as yellow spheres, respectively.

3. Database survey

The focus here is on silicate oxide apatites containing calcium and lanthanides. For most lanthanides, the structures published with the highest notation index are those of Ca₂Ln₈(SiO₄)₆O₂ apatites, indicating that they were refined in terms of lattice parameters and atomic positions. The cell parameters in apatite structure are highly dependent on the nature of the lanthanide. Structure data for La (#00-029-0337), Pr (#00-029-0362), Sm (#00-029-0365), Eu (#00-029-0320), Gd (#00-028-0212) apatites (Smith & McCarthy, 1977), as well as the Ce (#00-055-0835) (Skakle et al., 2000) and the Nd (#00-028-0228) apatite (Fahey et al., 1985) have been reported. Fig. 2 shows the ionic radius of Ln³⁺ in a VIII-coordinated environment (Shannon, 1976) as a function of the volume of the Ln-apatite.

Figure 2 Plot of the volume of Ca2Ln^III8(SiO4)6O2 Ln-apatites versus ionic radii of Ln^3+ ions in a VIII-coordinated environment.

The linear correlation indicates that the ionic radius of the lanthanide controls the cell volume. For the Ce-apatite (#00-055-0835), the cell volume in the published structure is 530.96 ų, which does not follow the general trend (Skakle et al., 2000). However, the structure reported in the current article fits with the linear correlation between ionic radius and cell volume. Table 2 compiles the corresponding lattice parameters and cell volumes.

Table 2
Cell parameters (Å) and volumes (ų) for the title phase compared with isotypic Ca₂Ln^III₈(SiO₄)₆O₂ phases

Ln	Gd	Eu	Sm	Nd	Ce	Ce	La	Pr
Ref. PDF	28–0212	29–0320	29–0365	28–0228	This work	55–0835	29–0337	29–0362
a	9.421 (2)	9.440 (2)	9.466	9.529 (5)	9.59912 (6)	9.4343 (3)	9.651	9.565
c	6.888 (2)	6.918 (2)	6.949	7.022 (1)	7.09284 (6)	6.8885 (4)	7.151	7.060
V	529.4	533.9	539.2	552.2	566.00 (1)	530.98 (4)	576.8	559.4

The database survey was extended to cerium-based P6₃/m phases and identified a number of silicate apatites (also known as britholites) as possible matches. The Ce_9.33(SiO₄)₆O₂ phase, characterized by Rocchini et al. (2000), has a chemical composition similar to the structure reported here as it contains Ce^III without calcium (#00-054-0618, a = 9.598 Å, c = 7.106 Å, V = 566.91 ų). Natural britolithe with composition Ca₄(Ce,La,Nd,Ca,Th)₆(SiO₄)₆O₂ (#00-046-1294; a = 9.59 Å, c = 7.04 Å, V = 561.53 ų) is a silicate apatite that contains a combination of rare earth elements with cerium (Orlandi et al., 1989). The lattice parameters are very close to the values reported in this paper but this phase is too rich in calcium, i.e. 10.11 wt.% compared with 4.5 wt.% for the Ca₂Ce₈(SiO₄)₆O₂ apatite. Oxyfluorinated silicate phases should also be considered. Within this compositional frame, the closest synthetic britolithe reported is cerium calcium strontium silicate fluoride oxide (#01-077-0619; a = 9.64 Å, c = 7.08 Å, V = 569.64 ų) the formula of which is (Ce_0.4Ca_0.35Sr_0.25)₄(Ce_0.86Ca_0.14)₆(SiO₄)₆(O_0.5F_0.38)₂ (Genkina et al., 1991). This apatite seems to be an isotype of the current redetermined structure because its calcium content is similar (5.26 wt.% versus 4.5 wt.%). However, this material differs from the one reported here because it contains Sr (5.13 wt.%) and fluorine (0.85 wt.%).

4. Synthesis and crystallization

The usual synthesis protocol for Ca₂Ln₈(SiO₄)₆O₂ apatites is a calcination of CaO, Ln₂O₃ and SiO₂ in appropriate amounts under air above 1673 K (Nicoleau et al., 2016). A trivalent Ln precursor is used, with the same oxidation state as found in the final apatite. However, cerium oxide is usually only available as CeO₂, in which cerium is tetra­valent. The synthesis of Ce₂O₃ is known to be quite difficult and this phase is not fully stable under air (Bärnighausen & Schiller, 1985; Strydom & van Vuuren, 1987; Perrichon et al., 1994; Hamm et al., 2014). Hence, a particular synthesis protocol was adopted to successfully prepare the Ca₂Ce₈(SiO₄)₆O₂ phase. Metallic silicon was added to a mixture of CeO₂, SiO₂ and CaO to ensure a double reaction during the thermal treatment: (i) in situ reduction of CeO₂ to Ce₂O₃ with oxidation of Si to SiO₂ and (ii) synthesis of the apatite by calcination of Ce₂O₃, SiO₂ and CaO. Silicon was chosen because it reduces CeO₂ to Ce₂O₃ and is inert to CaO, SiO₂ and the alumina crucible used for the reaction (Ellingham, 1944). Moreover, the product of the reaction relates to the final composition of the apatite without by-products. The following amounts of precursors were used: 688.5 mg of CeO₂, 28.1 mg of Si, 120.2 mg of SiO₂ and 56.1 mg of CaO. The mixture was manually milled three times in an agate mortar and gently pressed in an alumina crucible. The sample was then heat treated under argon at 1873 K for 1 h with a heating ramp of 10 K min⁻¹, then cooled at a controlled rate of 30 K min⁻¹. A radially and axially shrunk pellet was obtained with a homogeneous brownish color, which was crushed in an agate mortar before X-ray diffraction measurements. The powdered sample was analyzed in a Panalytical XPert MPD Pro diffractometer in Bragg Brentano geometry for 5 h with 2θ varying between 15 and 130°, using copper radiation. The powder was polished for SEM observation and EDS measurements. The average composition measured from six points was Ca_2.1Ce_7.9(SiO₄)₆O₂, which is close to the fixed composition of Ca₂Ce₈(SiO₄)₆O₂ chosen for the refinement.

5. Refinement

Details of the data collection and structure refinement are summarized in Table 3 and Fig. 3. The occupancies of the Si and O atoms were fixed to unity in agreement with the general observation that there are no vacancies on these sites for apatites. The total occupancies of the 6h and 4f sites were constrained to unity and the Ca₂Ce₈(SiO₄)₆O₂ composition was kept fixed. The 6h site was considered as fully occupied by cerium since the refined calcium content was very low (0.9%). It is the same case as in the Pr-apatite structure (#00-029-0362) but not for the La (#00-029-0337) and Nd (#00-028-0228) apatites where calcium contents on the 6h site were determined to be 1.4% and 4%, respectively. The 4f site was modelled as half-occupied by Ca and Ce ions. Isotropic displacement parameters (U_iso) were constrained to 0.008 Ų for the 4f site atoms, 0.006 Ų for the 6h site atoms, 0.005 Ų for Si and 0.003 Ų for oxygen sites. The residual electron density is 5.75 e Å⁻³ at a distance of 0.97Å from site Ce_b.

Table 3
Experimental details

Crystal data
Chemical formula	Ca2Ce8(SiO4)6O2
Mr	1785.6
Crystal system, space group	Hexagonal, P63/m
Temperature (K)	293
a, c (Å)	9.59912 (6), 7.09284 (6)
V (Å^3)	566.00 (1)
Z	1
Radiation type	Cu Kα1, λ = 1.540562, 1.544390 Å
Specimen shape, size (mm)	Flat sheet, 25 × 25
Data collection
Diffractometer	Panalytical XPert MPD Pro
Specimen mounting	Packed powder pellet
Data collection mode	Reflection
Scan method	Step
2θ values (°)	2θmin = 10.023 2θmax = 130.010 2θstep = 0.017
Refinement
R factors and goodness of fit	Rp = 0.045, Rwp = 0.059, Rexp = 0.034, R(F) = 0.046, χ^2 = 3.098
No. of parameters	28
Computer programs: Data Collector (Panalytical, 2011), JANA2006 (Petříček et al., 2014), VESTA (Momma & Izumi, 2011) and publCIF (Westrip, 2010).

Figure 3 Experimental and calculated X-ray powder data profiles of Ca2Ce8(SiO4)6O2, with difference plot.

Supporting information

Computing details

Data collection: Data Collector (Panalytical, 2011); cell refinement: JANA2006 (Petříček et al., 2014); data reduction: JANA2006 (Petříček et al., 2014); program(s) used to solve structure: JANA2006 (Petříček et al., 2014); program(s) used to refine structure: JANA2006 (Petříček et al., 2014); molecular graphics: VESTA (Momma & Izumi, 2011); software used to prepare material for publication: publCIF (Westrip, 2010).

Dicalcium octacerium hexakis(silicate) dioxide

Crystal data

Ca2Ce8(SiO4)6O2	y
Mr = 1785.6	Dx = 5.239 Mg m^−3
Hexagonal, P63/m	Cu Kα1 radiation, λ = 1.540562, 1.544390 Å
a = 9.59912 (6) Å	T = 293 K
c = 7.09284 (6) Å	Particle morphology: plate-like
V = 566.00 (1) Å^3	brown
Z = 1	flat_sheet, 25 × 25 mm
F(000) = 796	Specimen preparation: Prepared at 1873 K and 100 kPa, cooled at 30 K min^−1

Data collection

Panalytical XPert MPD Pro diffractometer	Data collection mode: reflection
Radiation source: sealed X-ray tube	Scan method: step
Specimen mounting: packed powder pellet	2θmin = 10.023°, 2θmax = 130.010°, 2θstep = 0.017°

Refinement

Rp = 0.045	28 parameters
Rwp = 0.059	0 restraints
Rexp = 0.034	9 constraints
R(F) = 0.046	Weighting scheme based on measured s.u.'s
6881 data points	(Δ/σ)max = 0.005
Profile function: pseudo-Voigt	Background function: Legendre polynoms

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ca_a	0.333333	0.666667	−0.0009 (7)	0.008*	0.5
Ce_a	0.333333	0.666667	−0.0009 (7)	0.008*	0.5
Ce_b	0.23194 (13)	−0.01214 (18)	0.25	0.006*
Si_c	0.4040 (6)	0.3713 (6)	0.25	0.005*
O1_c	0.3293 (13)	0.4865 (12)	0.25	0.003*
O2_c	0.5980 (14)	0.4634 (13)	0.25	0.003*
O3_c	0.3410 (7)	0.2594 (8)	0.0668 (9)	0.003*
O4_d	0	0	0.25	0.003*

Geometric parameters (Å, º)

Ca_a—Ca_a^i	3.534 (7)	Ce_a—O1_c	2.468 (10)
Ca_a—Ca_a^ii	3.559 (7)	Ce_a—O1_c^vi	2.468 (8)
Ca_a—Ce_a	0	Ce_a—O1_c^vii	2.468 (13)
Ca_a—Ce_a^i	3.534 (7)	Ce_a—O2_c^iii	2.437 (11)
Ca_a—Ce_a^ii	3.559 (7)	Ce_a—O2_c^iv	2.437 (10)
Ca_a—Si_c^iii	3.246 (6)	Ce_a—O2_c^v	2.437 (13)
Ca_a—Si_c^iv	3.246 (8)	Ce_b—O3_c^viii	2.396 (7)
Ca_a—Si_c^v	3.246 (5)	Ce_b—O3_c^ix	2.396 (7)
Ca_a—O2_c^iii	2.437 (11)	Ce_b—O4_d	2.2870 (15)
Ca_a—O2_c^iv	2.437 (10)	Si_c—O1_c	1.590 (16)
Ca_a—O2_c^v	2.437 (13)	Si_c—O2_c	1.614 (13)
Ce_a—Ce_a^i	3.534 (7)	Si_c—O3_c	1.600 (7)
Ce_a—Ce_a^ii	3.559 (7)	Si_c—O3_c^ii	1.600 (7)
Ca_a^i—Ca_a—Ca_a^ii	180.0 (5)	Ca_a^i—Ce_a—O2_c^v	43.5 (3)
Ca_a^i—Ca_a—Ce_a	0	Ca_a^ii—Ce_a—Ce_a^i	180.0 (5)
Ca_a^i—Ca_a—Ce_a^i	0.0 (5)	Ca_a^ii—Ce_a—Ce_a^ii	0.0 (5)
Ca_a^i—Ca_a—Ce_a^ii	180.0 (5)	Ca_a^ii—Ce_a—O1_c	43.9 (2)
Ca_a^i—Ca_a—Si_c^iii	57.01 (10)	Ca_a^ii—Ce_a—O1_c^vi	43.87 (19)
Ca_a^i—Ca_a—Si_c^iv	57.01 (11)	Ca_a^ii—Ce_a—O1_c^vii	43.9 (3)
Ca_a^i—Ca_a—Si_c^v	57.01 (9)	Ca_a^ii—Ce_a—O2_c^iii	136.5 (3)
Ca_a^i—Ca_a—O2_c^iii	43.5 (3)	Ca_a^ii—Ce_a—O2_c^iv	136.5 (3)
Ca_a^i—Ca_a—O2_c^iv	43.5 (3)	Ca_a^ii—Ce_a—O2_c^v	136.5 (3)
Ca_a^i—Ca_a—O2_c^v	43.5 (3)	Ce_a^i—Ce_a—Ce_a^ii	180.0 (5)
Ca_a^ii—Ca_a—Ce_a	0	Ce_a^i—Ce_a—O1_c	136.1 (2)
Ca_a^ii—Ca_a—Ce_a^i	180.0 (5)	Ce_a^i—Ce_a—O1_c^vi	136.13 (19)
Ca_a^ii—Ca_a—Ce_a^ii	0.0 (5)	Ce_a^i—Ce_a—O1_c^vii	136.1 (3)
Ca_a^ii—Ca_a—Si_c^iii	122.99 (10)	Ce_a^i—Ce_a—O2_c^iii	43.5 (3)
Ca_a^ii—Ca_a—Si_c^iv	122.99 (11)	Ce_a^i—Ce_a—O2_c^iv	43.5 (3)
Ca_a^ii—Ca_a—Si_c^v	122.99 (9)	Ce_a^i—Ce_a—O2_c^v	43.5 (3)
Ca_a^ii—Ca_a—O2_c^iii	136.5 (3)	Ce_a^ii—Ce_a—O1_c	43.9 (2)
Ca_a^ii—Ca_a—O2_c^iv	136.5 (3)	Ce_a^ii—Ce_a—O1_c^vi	43.87 (19)
Ca_a^ii—Ca_a—O2_c^v	136.5 (3)	Ce_a^ii—Ce_a—O1_c^vii	43.9 (3)
Ce_a—Ca_a—Ce_a^i	0	Ce_a^ii—Ce_a—O2_c^iii	136.5 (3)
Ce_a—Ca_a—Ce_a^ii	0	Ce_a^ii—Ce_a—O2_c^iv	136.5 (3)
Ce_a—Ca_a—Si_c^iii	0	Ce_a^ii—Ce_a—O2_c^v	136.5 (3)
Ce_a—Ca_a—Si_c^iv	0	O1_c—Ce_a—O1_c^vi	73.8 (4)
Ce_a—Ca_a—Si_c^v	0	O1_c—Ce_a—O1_c^vii	73.8 (4)
Ce_a—Ca_a—O2_c^iii	0	O1_c—Ce_a—O2_c^iii	94.4 (3)
Ce_a—Ca_a—O2_c^iv	0	O1_c—Ce_a—O2_c^iv	153.3 (4)
Ce_a—Ca_a—O2_c^v	0	O1_c—Ce_a—O2_c^v	126.7 (3)
Ce_a^i—Ca_a—Ce_a^ii	180.0 (5)	O1_c^vi—Ce_a—O1_c^vii	73.8 (4)
Ce_a^i—Ca_a—Si_c^iii	57.01 (10)	O1_c^vi—Ce_a—O2_c^iii	126.7 (4)
Ce_a^i—Ca_a—Si_c^iv	57.01 (11)	O1_c^vi—Ce_a—O2_c^iv	94.4 (3)
Ce_a^i—Ca_a—Si_c^v	57.01 (9)	O1_c^vi—Ce_a—O2_c^v	153.3 (6)
Ce_a^i—Ca_a—O2_c^iii	43.5 (3)	O1_c^vii—Ce_a—O2_c^iii	153.3 (3)
Ce_a^i—Ca_a—O2_c^iv	43.5 (3)	O1_c^vii—Ce_a—O2_c^iv	126.7 (5)
Ce_a^i—Ca_a—O2_c^v	43.5 (3)	O1_c^vii—Ce_a—O2_c^v	94.4 (4)
Ce_a^ii—Ca_a—Si_c^iii	122.99 (10)	O2_c^iii—Ce_a—O2_c^iv	73.2 (5)
Ce_a^ii—Ca_a—Si_c^iv	122.99 (11)	O2_c^iii—Ce_a—O2_c^v	73.2 (5)
Ce_a^ii—Ca_a—Si_c^v	122.99 (9)	O2_c^iv—Ce_a—O2_c^v	73.2 (3)
Ce_a^ii—Ca_a—O2_c^iii	136.5 (3)	O3_c^viii—Ce_b—O3_c^ix	139.4 (4)
Ce_a^ii—Ca_a—O2_c^iv	136.5 (3)	O3_c^viii—Ce_b—O4_d	105.0 (2)
Ce_a^ii—Ca_a—O2_c^v	136.5 (3)	O3_c^ix—Ce_b—O4_d	105.0 (2)
Si_c^iii—Ca_a—Si_c^iv	93.17 (18)	Ca_a^x—Si_c—Ca_a^xi	65.98 (17)
Si_c^iii—Ca_a—Si_c^v	93.17 (18)	Ca_a^x—Si_c—O1_c	136.4 (2)
Si_c^iii—Ca_a—O2_c^iii	28.7 (3)	Ca_a^x—Si_c—O2_c	46.6 (4)
Si_c^iii—Ca_a—O2_c^iv	64.6 (4)	Ca_a^x—Si_c—O3_c	114.9 (5)
Si_c^iii—Ca_a—O2_c^v	97.0 (4)	Ca_a^x—Si_c—O3_c^ii	62.4 (3)
Si_c^iv—Ca_a—Si_c^v	93.17 (16)	Ca_a^xi—Si_c—O1_c	136.4 (2)
Si_c^iv—Ca_a—O2_c^iii	97.0 (3)	Ca_a^xi—Si_c—O2_c	46.6 (4)
Si_c^iv—Ca_a—O2_c^iv	28.7 (4)	Ca_a^xi—Si_c—O3_c	62.4 (3)
Si_c^iv—Ca_a—O2_c^v	64.6 (3)	Ca_a^xi—Si_c—O3_c^ii	114.9 (5)
Si_c^v—Ca_a—O2_c^iii	64.6 (3)	O1_c—Si_c—O2_c	114.7 (7)
Si_c^v—Ca_a—O2_c^iv	97.0 (2)	O1_c—Si_c—O3_c	108.5 (5)
Si_c^v—Ca_a—O2_c^v	28.7 (3)	O1_c—Si_c—O3_c^ii	108.5 (5)
O2_c^iii—Ca_a—O2_c^iv	73.2 (5)	O2_c—Si_c—O3_c	108.2 (5)
O2_c^iii—Ca_a—O2_c^v	73.2 (5)	O2_c—Si_c—O3_c^ii	108.2 (5)
O2_c^iv—Ca_a—O2_c^v	73.2 (3)	O3_c—Si_c—O3_c^ii	108.6 (4)
Ca_a—Ce_a—Ca_a^i	0	Ce_a—O1_c—Ce_a^ii	92.3 (5)
Ca_a—Ce_a—Ca_a^ii	0	Ce_a—O1_c—Si_c	129.2 (3)
Ca_a—Ce_a—Ce_a^i	0	Ce_a^ii—O1_c—Si_c	129.2 (3)
Ca_a—Ce_a—Ce_a^ii	0	Ca_a^x—O2_c—Ca_a^xi	93.0 (5)
Ca_a—Ce_a—O1_c	0	Ca_a^x—O2_c—Ce_a^x	0.0 (5)
Ca_a—Ce_a—O1_c^vi	0	Ca_a^x—O2_c—Ce_a^xi	93.0 (5)
Ca_a—Ce_a—O1_c^vii	0	Ca_a^x—O2_c—Si_c	104.7 (4)
Ca_a—Ce_a—O2_c^iii	0	Ca_a^xi—O2_c—Ce_a^x	93.0 (5)
Ca_a—Ce_a—O2_c^iv	0	Ca_a^xi—O2_c—Ce_a^xi	0.0 (5)
Ca_a—Ce_a—O2_c^v	0	Ca_a^xi—O2_c—Si_c	104.7 (4)
Ca_a^i—Ce_a—Ca_a^ii	180.0 (5)	Ce_a^x—O2_c—Ce_a^xi	93.0 (5)
Ca_a^i—Ce_a—Ce_a^i	0.0 (5)	Ce_a^x—O2_c—Si_c	104.7 (4)
Ca_a^i—Ce_a—Ce_a^ii	180.0 (5)	Ce_a^xi—O2_c—Si_c	104.7 (4)
Ca_a^i—Ce_a—O1_c	136.1 (2)	Ce_b^v—O3_c—Si_c	146.2 (5)
Ca_a^i—Ce_a—O1_c^vi	136.13 (19)	Ce_b—O4_d—Ce_b^xii	120.00 (5)
Ca_a^i—Ce_a—O1_c^vii	136.1 (3)	Ce_b—O4_d—Ce_b^xiii	120.00 (6)
Ca_a^i—Ce_a—O2_c^iii	43.5 (3)	Ce_b^xii—O4_d—Ce_b^xiii	120.00 (6)
Ca_a^i—Ce_a—O2_c^iv	43.5 (3)

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