Ca₁₀(Cr^VO₄)₆(Cr^VIO₄), a disordered mixed-valence chromium compound exhibiting inversion twinning

The structure analysis of so-called 9CaO·4CrO₃·Cr₂O₃ proved it to be the title compound, deca­calcium hexa­kis­[chro­mate(V)] chromate(VI), with the simultaneous presence of unusual chromium oxidation states. The structure determination was carried out on a crystal that had inversion twinning. The Cr^VIO₄ tetra­hedron is situated on a threefold axis and is disordered over two possible orientations that share three O atoms, while the Cr^VO₄ tetra­hedra are in general positions and are ordered. The charge is balanced by Ca²⁺ cations, one of which is located on a threefold axis. The Ca²⁺ ions are coordinated by six, seven or eight O atoms. The compound is a significant phase in the CaO-CrO_x system and its formation reduces the refractoriness of calcium-rich compositions in an oxidizing atmosphere.

S1. Comment

In a reaction between magnesia-chrome brick from the refractory lining of rotary cement kilns and the raw material for portland cement clinkers, calcium chromates of various composition are formed. The reaction is deleterious to the lining, the quality of the product and possibly to the environment. For example, chromate compounds with empirical formulae Ca₁₀Cr₆O₂₅, Ca₃Cr₂O₈ and Ca₅Cr₃O₁₂ form in oxidizing atmospheres at temperatures higher than 1173 K when the CaO:Cr₂O₃ molar ratio is larger than or equal to 3:1. These compounds have been extensively studied by the use of several techniques for the determination of the total chromium content and for the determination of chromium oxidation states, often average ones (Adendorff et al., 1992; Mirtič et al., 1992; Arčon et al., 1998). When heating takes place in the absence of oxygen, no calcium chromates will be formed (Ford et al., 1949).

The title compound has attracted interest as a significant phase in the CaO–CrO_x system. Its formation reduces refractoriness of calcium-rich compositions of the system in an oxidizing atmosphere and represents a novel type of mixed-valence Cr^V/Cr^VI compound. The first preparation of a mixed-valence chromium compound from aqueous solution has been reported by Casari et al. (2006), namely NH₄Cr(CrO₄)₂, which constituted a new structure type among the Cr^III/Cr^VI ternary oxides.

The synthetists and suppliers of the crystals used in this study, Figusch & Pánek (1976), assumed the composition to be 9CaO.4CrO₃.Cr₂O₃. The diffraction pattern and the values of the lattice parameters are very similar to those of Ca₃(VO₄)₂ (Gopal & Calvo, 1973), Ca₃(AsO₄)₂ (Gopal & Calvo, 1971) and β-Ca₃(PO₄)₂ (Schroeder et al., 1977; Yashima et al., 2003), so that similarity/isomorphism of their crystal structures was assumed. The initial model of the structure was based on analogy with Ca₃(VO₄)₂ (Gopal & Calvo, 1973), as the electron paramagnetic resonance (EPR) measurements (Plesch, 1979) confirmed the presence of Cr^V. In Ca₃(VO₄)₂, one formula unit lies on the threefold axis, with one of the calcium-ion sites on this axis being half-occupied. Disregarding the Ca atom in the half-filled site, the displacement parameters of some atoms appeared to be anomalously high. These results suggest a variability in the environment of the Ca site depending on whether the site is empty or occupied. Problems occurring in analogous structures were encountered again, namely one of the calcium-ion sites on the threefold axis being half-occupied and the displacement parameters of an O atom on a threefold axis appearing to be anomalously high. Gopal & Calvo (1973) explained the higher values of the displacement parameters by positional disorder. The refinement of site occupancy factors resulted in a distinct decrease of the occupancies of these two atomic positions. This corresponds to a CaO deficit with regard to the chemical composition Ca₃(VO₄)₂ (Gyepesová et al., 1981). The experimentally measured density was in good agreement with the calculated one either without 2.5 CaO or 3 Ca atoms in the hexagonal cell. Assuming that three Ca atoms are missing in the hexagonal cell, six of the Cr atoms must be hexavalent from the total of 42 Cr atoms. Taking this into account, another model (still not very satisfactory) for the title compound was presented (Gyepesová & Handlovič, 1980). Investigation of the electron structure of the title compound has also been performed using EPR methods and magnetic susceptibility measurements, which showed the presence of antiferromagnetism at low temperatures, and X-ray photoelectron spectroscopy methods, which indicated diferences in the oxidation states of the Cr atoms at the surface of the crystals (Stö\&ser et al., 1986).

The current determination of the title compound revealed that the crystal used was an almost ideal racemic twin. The atomic numbering scheme is shown in Fig. 1 and selected geometric parameters are given in Table 1. The CrO₄ group on the threefold axis is disordered, with refined occupancies for Cr3A and Cr3B of 0.695 (6) and 0.305 (6), respectively, and with the same values applied to atoms O3A and O3B. The disordered CrO₄ tetrahedra share three symmetry-related O9 atoms in a plane perpendicular to the c axis, as shown in Figs. 1 and 2. Significant differences in the Cr—O bond lengths in the CrO₄ tetrahedra (Table 1) prove the presence of Cr in two oxidation states, viz. Cr^VI on the threefold axis (Cr3A and Cr3B) and Cr^V in general positions (Cr1 and Cr2), giving a final formula of Ca₁₀(Cr^VO₄)₆(Cr^VIO₄). The Ca atoms are coordinated by six, seven and eight O atoms, respectively, and the corresponding Ca—O distances for Ca1, Ca2 and Ca3 are in the ranges 2.364 (3)-2.753 (2), 2.339 (3)–2.508 (3) and 2.400 (3)–2.865 (3) Å, respectively. Atom Ca4 on the threefold axis is surrounded by six O atoms in an octahedral arrangement (Table 1 and Fig. 2). The projection of the structure along the a axis is shown in Fig. 3.

A comparison with β-Ca₃(PO₄)₂ (Schroeder et al., 1977; Yashima et al., 2003) reveals that the expected close similarity/isomorphism of their crystal structures is not fully obvious, as the `half-filled Ca sites' for β-Ca<sub>3</sub>(PO<sub>4</sub>)<sub>2</sub> are occupied in the title compound by the O atom on the threefold axis. Moreover, the title compound contains three fewer Ca atoms in the unit cell than β-Ca<sub>3</sub>(PO<sub>4</sub>)<sub>2</sub>. The O atom for the minor disorder component (O3B) is in the same position as in β-Ca<sub>3</sub>(PO<sub>4</sub>)<sub>2</sub>, but the fact that it does not have full site occupancy caused problems with the atomic displacement parameters for β-Ca<sub>3</sub>(PO<sub>4</sub>)<sub>2</sub>. The structure of the title compound can also be compared to Ca<sub>10</sub>K(PO<sub>4</sub>)<sub>7</sub> (Sandström & Boström, 2006), which was obtained from a melt and is structurally related to β-Ca<sub>3</sub>(PO<sub>4</sub>)<sub>2</sub> and presumably represents one end-member of a solid solution series. That structure contains four Ca, one K, three P and ten unique O atoms, of which the K, one Ca, one P and one O atom are located on threefold rotation axes. The K<sup>+</sup> cation occupies a position equivalent to the `half-filled site' (Ca4) in the β-Ca₃(PO₄)₂ structure.

Study of CaO sintering with the addition of Cr₂O₃ in air, where the title compound occurs (in the subsolidus area), shows an intensification of shrinkage, which may indicate increased grain boundary diffusion compared to pure CaO. The acceleration of this process depends on transport of Ca²⁺ ions (Figusch et al., 1979). From a stereochemical viewpoint, there are free spaces in the title compound in the vicinity of the threefold axes and their size is affected by the disorder of the O- and Cr-atom positions. In this way, a rapid transfer of Ca²⁺ ions across the free spaces can be assumed in the chemical potential gradient.

Related literature

For related literature, see: Adendorff et al. (1992); Arčon et al. (1998); Casari et al. (2006); Figusch & Pánek (1976); Figusch et al. (1979); Ford et al. (1949); Gopal & Calvo (1971, 1973); Gyepesová & Handlovič (1980); Gyepesová et al. (1981); Mirtič et al. (1992); Plesch (1979); Sandström & Boström (2006); Schroeder et al. (1977); Yashima et al. (2003).

S2. Experimental

The title compound, originally described under an oxide formula 9CaO.4CrO₃.Cr₂O₃, is congruently melting at 1501 K and its primary crystallization field (PCF) was found in compositions from 44 to 53 wt% Cr₂O₃ in the CaO–Cr₂O₃ system in air (Ford et al., 1949). Three samples (denoted 1, 2 and 3) within the indicated PCF were prepared from CaCO₃, CrO₃, HNO₃ and H₂O containing 46, 49 and 51 wt% Cr₂O₃, respectively (Figusch & Pánek, 1976). Aqueous solutions of the starting materials were evaporated to dryness and the dry residues subsequently decomposed by slow heating up to 1173 K. X-ray powder diffraction patterns showed the presence of Ca₅(CrO₄)₃OH and CaCrO₄ at this stage. Portions of the samples (from 10 to 15 g) were heated in a Pt crucible to 1523 K, held there for 3 h, then cooled at a controlled cooling rate of 50 K h^-1 to a temperature of 1453 (sample 1) or 1323 K (samples 2 and 3), then cooled to room temperature by removal from the furnace. Inspection of crushed samples revealed fragments of crystals of the title compound with an edge size up to 1 mm. The crystals are opaque, black, dark-green translucent in thin layers and show conchoidal fracture. In samples 2 and 3, minor amounts of CaCrO₄ were also observed, in disagreement with the pseudobinary phase diagram by Ford et al. (1949), which may indicate a nonequilibrium with a higher content of oxygen in the melt.

S3. Refinement

The refinement could not proceed successfuly until racemic twin treatment of the data was introduced, which converged to refined volume fractions 0.53 (3):0.47 (3). The site occupancies of Cr3A/Cr3B and O3A/O3B in the disordered CrO₄ group were constrained to the same (and complementary) values.

Computing details

Data collection: SMART (Bruker, 2003); cell refinement: SAINT (Bruker, 2003); data reduction: SAINT (Bruker, 2003) and SADABS (Sheldrick, 2003); program(s) used to solve structure: SHELXTL (Sheldrick, 2008); program(s) used to refine structure: SHELXTL (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 2012); software used to prepare material for publication: SHELXTL (Sheldrick, 2008).

Figures

	Fig. 1. The atom-numbering scheme for the title compound, with displacement ellipsoids drawn at the 50% probability level. The minor component of the disordered chromate group is shown with broken bonds. [Symmetry codes: (i) -x+y, -x, z; (ii) -y, x-y, z.]
	Fig. 2. A schematic drawing showing the connectivity of the Ca atoms. Vertical lines represent the threefold axes parallel to the c axis. The medium-sized spheres (dark-green in the electronic version of the paper) represent Cr atoms.
	Fig. 3. The structure of the title compound shown in polyhedral representation in projection along the a axis. The disordered CrO4 tetrahedra share three O9 atoms in a plane perpendicular to the c axis.

decacalcium hexakis[chromate(V)] chromate(VI)

Crystal data

Ca10(CrO4)6(CrO4)	Dx = 3.166 Mg m^−3
Mr = 1212.80	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3c	Cell parameters from 8192 reflections
Hall symbol: R 3 -2"c	θ = 2.4–28.3°
a = 10.7580 (1) Å	µ = 5.01 mm^−1
c = 38.0730 (3) Å	T = 183 K
V = 3816.02 (6) Å^3	Pyramid, dark-green
Z = 6	0.09 × 0.08 × 0.08 mm
F(000) = 3552

Data collection

Siemens SMART CCD area-detector diffractometer	2034 independent reflections
Radiation source: fine-focus sealed tube	1918 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.036
ω scans	θmax = 28.3°, θmin = 2.4°
Absorption correction: multi-scan (SADABS; Sheldrick, 2003)	h = −14→14
Tmin = 0.661, Tmax = 0.690	k = −14→14
13345 measured reflections	l = −48→49

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)] = 0.024	w = 1/[σ^2(Fo^2) + (0.0367P)^2 + 8.2518P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.060	(Δ/σ)max < 0.001
S = 1.04	Δρmax = 0.47 e Å^−3
2034 reflections	Δρmin = −0.66 e Å^−3
144 parameters	Absolute structure: Flack (1983), 995 Friedel pairs
1 restraint	Absolute structure parameter: 0.53 (3)

Special details

Experimental. Data were collected at low temperature using a Siemens SMART CCD diffractometer equiped with a LT-2 device. A full sphere of reciprocal space was scanned by 0.3° steps in ω with a crystal–to–detector distance of 5.0 cm, 15 s per frame. Preliminary orientation matrix was obtained from the first 100 frames using SMART (Bruker, 2003). The collected frames were integrated using the preliminary orientation matrix which was updated every 100 frames. Final cell parameters were obtained by refinement on the position of 8192 reflections with I>10σ(I) after integration of all the frames data using SAINT (Bruker, 2003).

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	Occ. (<1)
Ca1	0.28499 (9)	0.15823 (8)	−0.06050 (2)	0.01475 (17)
Ca2	0.19733 (9)	−0.19629 (9)	0.00064 (2)	0.00867 (17)
Ca3	0.38785 (9)	0.18174 (8)	0.034490 (19)	0.00836 (17)
Ca4	0.6667	0.3333	0.10044 (5)	0.0110 (2)
Cr1	0.31082 (7)	0.13996 (7)	0.132847 (13)	0.00709 (14)
Cr2	0.17809 (7)	−0.13622 (7)	−0.099116 (13)	0.00704 (14)
Cr3A	0.0000	0.0000	0.00182 (5)	0.0075 (6)	0.695 (6)
Cr3B	0.0000	0.0000	0.02671 (13)	0.0118 (13)	0.305 (6)
O3A	0.0000	0.0000	−0.0419 (2)	0.0152 (17)	0.695 (6)
O3B	0.0000	0.0000	0.0673 (5)	0.019 (4)	0.305 (6)
O1	0.2825 (3)	0.0882 (3)	0.09083 (7)	0.0195 (6)
O2	0.2354 (3)	0.2354 (3)	0.14633 (7)	0.0147 (6)
O3	0.2772 (3)	−0.0159 (3)	0.15446 (6)	0.0101 (5)
O4	0.4905 (3)	0.2456 (3)	0.14215 (8)	0.0106 (6)
O5	0.1515 (4)	−0.1249 (4)	−0.05569 (8)	0.0239 (8)
O6	0.2564 (3)	−0.2373 (3)	−0.10949 (8)	0.0107 (6)
O7	0.3013 (3)	0.0339 (3)	−0.11153 (7)	0.0123 (5)
O8	0.0148 (3)	−0.2215 (3)	−0.11737 (7)	0.0177 (6)
O9	−0.0044 (4)	0.1451 (3)	0.01383 (9)	0.0171 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ca1	0.0210 (4)	0.0150 (4)	0.0120 (3)	0.0118 (3)	−0.0049 (3)	−0.0044 (3)
Ca2	0.0077 (4)	0.0101 (4)	0.0078 (3)	0.0041 (3)	−0.0007 (3)	−0.0019 (3)
Ca3	0.0075 (4)	0.0080 (4)	0.0082 (3)	0.0028 (3)	−0.0023 (3)	−0.0015 (3)
Ca4	0.0141 (3)	0.0141 (3)	0.0049 (4)	0.00703 (16)	0.000	0.000
Cr1	0.0061 (3)	0.0084 (3)	0.0064 (3)	0.0034 (2)	0.0015 (2)	0.0007 (3)
Cr2	0.0072 (3)	0.0082 (3)	0.0062 (3)	0.0042 (2)	−0.0003 (3)	−0.0008 (3)
Cr3A	0.0057 (6)	0.0057 (6)	0.0111 (14)	0.0028 (3)	0.000	0.000
Cr3B	0.0097 (14)	0.0097 (14)	0.016 (3)	0.0048 (7)	0.000	0.000
O3A	0.016 (2)	0.016 (2)	0.014 (4)	0.0079 (12)	0.000	0.000
O3B	0.024 (6)	0.024 (6)	0.009 (9)	0.012 (3)	0.000	0.000
O1	0.0284 (16)	0.0243 (17)	0.0094 (12)	0.0160 (15)	−0.0017 (12)	−0.0007 (12)
O2	0.0171 (14)	0.0209 (15)	0.0134 (13)	0.0150 (12)	0.0048 (11)	0.0042 (11)
O3	0.0084 (12)	0.0067 (12)	0.0113 (12)	0.0007 (11)	0.0006 (9)	0.0003 (9)
O4	0.0065 (13)	0.0079 (12)	0.0160 (15)	0.0025 (11)	0.0003 (12)	−0.0007 (10)
O5	0.0262 (17)	0.0248 (17)	0.0065 (13)	0.0021 (14)	0.0011 (12)	0.0010 (11)
O6	0.0077 (12)	0.0077 (13)	0.0168 (15)	0.0038 (11)	0.0020 (11)	0.0020 (11)
O7	0.0150 (13)	0.0070 (12)	0.0130 (12)	0.0040 (11)	0.0030 (11)	0.0016 (10)
O8	0.0098 (14)	0.0288 (16)	0.0120 (13)	0.0078 (13)	−0.0013 (11)	0.0036 (12)
O9	0.0185 (12)	0.0133 (14)	0.0244 (13)	0.0116 (13)	0.0070 (10)	0.0016 (12)

Geometric parameters (Å, º)

Ca1—O3^i	2.364 (3)	Cr1—O3	1.736 (3)
Ca1—O7	2.414 (3)	Cr1—Ca1^vi	3.1588 (10)
Ca1—O2^ii	2.502 (3)	Cr1—Ca2^iv	3.1744 (9)
Ca1—O8^iii	2.537 (3)	Cr1—Ca2^viii	3.3877 (10)
Ca1—O1^i	2.592 (3)	Cr1—Ca1^viii	3.7043 (10)
Ca1—O5^iii	2.609 (3)	Cr2—O8	1.673 (3)
Ca1—O5	2.646 (3)	Cr2—O5	1.693 (3)
Ca1—O3A	2.753 (2)	Cr2—O7	1.704 (3)
Ca1—Cr2	3.1426 (9)	Cr2—O6	1.722 (3)
Ca1—Cr1^i	3.1586 (10)	Cr2—Ca1^vii	3.1984 (10)
Ca1—Cr2^iii	3.1985 (10)	Cr2—Ca3^ii	3.2173 (10)
Ca1—Cr3A	3.5650 (15)	Cr2—Ca3^v	3.2996 (10)
Ca2—O8^iv	2.339 (3)	Cr2—Ca4^ii	3.5207 (9)
Ca2—O5	2.410 (3)	Cr2—Ca2^i	3.6295 (10)
Ca2—O4^ii	2.424 (3)	Cr3A—Cr3B	0.947 (4)
Ca2—O4^v	2.437 (3)	Cr3A—O3A	1.666 (8)
Ca2—O7^vi	2.442 (3)	Cr3A—O9	1.650 (2)
Ca2—O3^v	2.472 (3)	Cr3A—O9^vii	1.650 (2)
Ca2—O9^vii	2.508 (3)	Cr3A—O9^iii	1.650 (2)
Ca2—O2^ii	3.004 (3)	Cr3A—Ca1^iii	3.5651 (15)
Ca2—Cr1^v	3.1745 (9)	Cr3A—Ca1^vii	3.5651 (15)
Ca2—Cr1^ii	3.3878 (10)	Cr3A—Ca2^iii	3.6674 (9)
Ca2—Ca4^ii	3.5990 (14)	Cr3A—Ca2^vii	3.6675 (9)
Ca2—Cr2^vi	3.6293 (10)	Cr3B—O3B	1.547 (18)
Ca3—O3^i	2.354 (3)	Cr3B—O9	1.659 (3)
Ca3—O1	2.400 (3)	Cr3B—O9^vii	1.659 (3)
Ca3—O2^ii	2.411 (3)	Cr3B—O9^iii	1.659 (3)
Ca3—O6^viii	2.413 (3)	Cr3B—Ca3^iii	3.6280 (10)
Ca3—O9^vii	2.438 (3)	Cr3B—Ca3^vii	3.6280 (10)
Ca3—O6^iv	2.453 (3)	O3A—Ca1^iii	2.753 (2)
Ca3—O7^viii	2.703 (3)	O3A—Ca1^vii	2.753 (2)
Ca3—O8^iv	2.865 (3)	O1—Ca1^vi	2.592 (3)
Ca3—Cr2^viii	3.2172 (10)	O2—Ca3^viii	2.410 (3)
Ca3—Cr2^iv	3.2996 (10)	O2—Ca1^viii	2.502 (3)
Ca3—Ca4	3.6151 (14)	O2—Ca2^viii	3.004 (3)
Ca3—Cr3B	3.6280 (10)	O3—Ca3^vi	2.354 (3)
Ca4—O4^ix	2.284 (3)	O3—Ca1^vi	2.365 (3)
Ca4—O4^x	2.284 (3)	O3—Ca2^iv	2.472 (3)
Ca4—O4	2.284 (3)	O4—Ca2^viii	2.424 (3)
Ca4—O6^xi	2.307 (3)	O4—Ca2^iv	2.437 (3)
Ca4—O6^iv	2.307 (3)	O5—Ca1^vii	2.609 (3)
Ca4—O6^viii	2.307 (3)	O6—Ca4^ii	2.307 (3)
Ca4—Cr2^xi	3.5207 (9)	O6—Ca3^ii	2.413 (3)
Ca4—Cr2^iv	3.5207 (9)	O6—Ca3^v	2.453 (3)
Ca4—Cr2^viii	3.5206 (9)	O7—Ca2^i	2.443 (3)
Ca4—Cr1^ix	3.5414 (9)	O7—Ca3^ii	2.703 (3)
Ca4—Cr1^x	3.5414 (9)	O8—Ca2^v	2.339 (3)
Ca4—Cr1	3.5414 (9)	O8—Ca1^vii	2.537 (3)
Cr1—O1	1.671 (3)	O8—Ca3^v	2.865 (3)
Cr1—O2	1.675 (3)	O9—Ca3^iii	2.438 (3)
Cr1—O4	1.719 (3)	O9—Ca2^iii	2.508 (3)
O3^i—Ca1—O7	155.86 (11)	O4^ix—Ca4—Cr1^x	97.15 (8)
O3^i—Ca1—O2^ii	68.57 (10)	O4^x—Ca4—Cr1^x	23.80 (7)
O7—Ca1—O2^ii	96.83 (9)	O4—Ca4—Cr1^x	93.65 (8)
O3^i—Ca1—O8^iii	120.10 (10)	O6^xi—Ca4—Cr1^x	85.01 (6)
O7—Ca1—O8^iii	66.60 (10)	O6^iv—Ca4—Cr1^x	154.81 (9)
O2^ii—Ca1—O8^iii	156.37 (12)	O6^viii—Ca4—Cr1^x	85.90 (6)
O3^i—Ca1—O1^i	64.66 (9)	Cr2^xi—Ca4—Cr1^x	70.853 (16)
O7—Ca1—O1^i	101.07 (9)	Cr2^iv—Ca4—Cr1^x	178.92 (3)
O2^ii—Ca1—O1^i	100.06 (10)	Cr2^viii—Ca4—Cr1^x	72.539 (17)
O8^iii—Ca1—O1^i	68.70 (9)	Cr1^ix—Ca4—Cr1^x	108.54 (3)
O3^i—Ca1—O5^iii	73.59 (10)	O4^ix—Ca4—Cr1	93.65 (8)
O7—Ca1—O5^iii	125.09 (10)	O4^x—Ca4—Cr1	97.15 (8)
O2^ii—Ca1—O5^iii	137.55 (10)	O4—Ca4—Cr1	23.80 (7)
O8^iii—Ca1—O5^iii	62.98 (9)	O6^xi—Ca4—Cr1	154.81 (9)
O1^i—Ca1—O5^iii	79.95 (9)	O6^iv—Ca4—Cr1	85.90 (6)
O3^i—Ca1—O5	124.77 (9)	O6^viii—Ca4—Cr1	85.01 (6)
O7—Ca1—O5	64.26 (9)	Cr2^xi—Ca4—Cr1	178.92 (3)
O2^ii—Ca1—O5	73.07 (10)	Cr2^iv—Ca4—Cr1	72.541 (17)
O8^iii—Ca1—O5	111.07 (10)	Cr2^viii—Ca4—Cr1	70.853 (17)
O1^i—Ca1—O5	162.11 (12)	Cr1^ix—Ca4—Cr1	108.54 (3)
O5^iii—Ca1—O5	116.47 (16)	Cr1^x—Ca4—Cr1	108.54 (3)
O3^i—Ca1—O3A	99.74 (15)	O1—Cr1—O2	115.72 (15)
O7—Ca1—O3A	103.35 (14)	O1—Cr1—O3	102.52 (14)
O2^ii—Ca1—O3A	109.47 (14)	O1—Cr1—O4	112.02 (15)
O8^iii—Ca1—O3A	91.32 (15)	O2—Cr1—O3	121.04 (14)
O1^i—Ca1—O3A	138.66 (7)	O2—Cr1—O4	105.11 (14)
O5^iii—Ca1—O3A	58.72 (8)	O4—Cr1—O3	99.38 (13)
O5—Ca1—O3A	58.32 (8)	O1—Cr1—Ca1^vi	55.02 (11)
O3^i—Ca1—Cr2	154.94 (7)	O2—Cr1—Ca1^vi	137.31 (11)
O7—Ca1—Cr2	32.47 (6)	O4—Cr1—Ca1^vi	117.00 (10)
O2^ii—Ca1—Cr2	89.15 (7)	O3—Cr1—Ca1^vi	47.56 (9)
O8^iii—Ca1—Cr2	84.91 (7)	O1—Cr1—Ca2^iv	110.00 (11)
O1^i—Ca1—Cr2	133.54 (7)	O2—Cr1—Ca2^iv	133.87 (10)
O5^iii—Ca1—Cr2	121.74 (9)	O4—Cr1—Ca2^iv	49.46 (9)
O5—Ca1—Cr2	32.59 (6)	O3—Cr1—Ca2^iv	50.71 (9)
O3A—Ca1—Cr2	76.33 (9)	Ca1^vi—Cr1—Ca2^iv	75.87 (3)
O3^i—Ca1—Cr1^i	32.81 (6)	O1—Cr1—Ca2^viii	129.41 (12)
O7—Ca1—Cr1^i	129.89 (7)	O2—Cr1—Ca2^viii	62.40 (11)
O2^ii—Ca1—Cr1^i	82.79 (7)	O4—Cr1—Ca2^viii	42.73 (9)
O8^iii—Ca1—Cr1^i	94.97 (7)	O3—Cr1—Ca2^viii	121.80 (9)
O1^i—Ca1—Cr1^i	31.88 (6)	Ca1^vi—Cr1—Ca2^viii	159.25 (3)
O5^iii—Ca1—Cr1^i	75.48 (8)	Ca2^iv—Cr1—Ca2^viii	84.30 (4)
O5—Ca1—Cr1^i	153.94 (8)	O1—Cr1—Ca4	79.96 (11)
O3A—Ca1—Cr1^i	124.13 (9)	O2—Cr1—Ca4	117.33 (10)
Cr2—Ca1—Cr1^i	159.50 (4)	O4—Cr1—Ca4	32.41 (11)
O3^i—Ca1—Cr2^iii	95.93 (7)	O3—Cr1—Ca4	111.99 (10)
O7—Ca1—Cr2^iii	96.60 (7)	Ca1^vi—Cr1—Ca4	102.58 (2)
O2^ii—Ca1—Cr2^iii	164.17 (7)	Ca2^iv—Cr1—Ca4	64.54 (3)
O8^iii—Ca1—Cr2^iii	31.29 (7)	Ca2^viii—Cr1—Ca4	62.54 (2)
O1^i—Ca1—Cr2^iii	69.06 (7)	O1—Cr1—Ca1^viii	84.32 (11)
O5^iii—Ca1—Cr2^iii	31.88 (7)	O2—Cr1—Ca1^viii	34.17 (9)
O5—Ca1—Cr2^iii	120.68 (8)	O4—Cr1—Ca1^viii	107.47 (9)
O3A—Ca1—Cr2^iii	75.39 (9)	O3—Cr1—Ca1^viii	147.48 (10)
Cr2—Ca1—Cr2^iii	106.69 (3)	Ca1^vi—Cr1—Ca1^viii	127.73 (3)
Cr1^i—Ca1—Cr2^iii	82.17 (2)	Ca2^iv—Cr1—Ca1^viii	155.68 (3)
O3^i—Ca1—Cr3A	76.53 (7)	Ca2^viii—Cr1—Ca1^viii	71.55 (2)
O7—Ca1—Cr3A	123.67 (7)	Ca4—Cr1—Ca1^viii	100.47 (2)
O2^ii—Ca1—Cr3A	88.38 (7)	O8—Cr2—O5	106.06 (15)
O8^iii—Ca1—Cr3A	114.63 (8)	O8—Cr2—O7	120.89 (14)
O1^i—Ca1—Cr3A	133.23 (7)	O5—Cr2—O7	105.20 (14)
O5^iii—Ca1—Cr3A	64.30 (7)	O8—Cr2—O6	105.61 (15)
O5—Ca1—Cr3A	64.03 (7)	O5—Cr2—O6	115.04 (17)
O3A—Ca1—Cr3A	26.85 (16)	O7—Cr2—O6	104.56 (13)
Cr2—Ca1—Cr3A	92.07 (3)	O8—Cr2—Ca1	120.14 (11)
Cr1^i—Ca1—Cr3A	106.44 (3)	O5—Cr2—Ca1	57.34 (11)
Cr2^iii—Ca1—Cr3A	91.15 (3)	O7—Cr2—Ca1	49.53 (9)
O8^iv—Ca2—O5	139.87 (12)	O6—Cr2—Ca1	134.11 (10)
O8^iv—Ca2—O4^ii	80.30 (10)	O8—Cr2—Ca1^vii	51.96 (10)
O5—Ca2—O4^ii	86.37 (11)	O5—Cr2—Ca1^vii	54.50 (11)
O8^iv—Ca2—O4^v	120.21 (11)	O7—Cr2—Ca1^vii	135.81 (10)
O5—Ca2—O4^v	90.27 (11)	O6—Cr2—Ca1^vii	119.51 (9)
O4^ii—Ca2—O4^v	71.59 (13)	Ca1—Cr2—Ca1^vii	93.22 (4)
O8^iv—Ca2—O7^vi	69.30 (10)	O8—Cr2—Ca3^ii	129.76 (10)
O5—Ca2—O7^vi	137.44 (11)	O5—Cr2—Ca3^ii	123.34 (12)
O4^ii—Ca2—O7^vi	135.50 (10)	O7—Cr2—Ca3^ii	57.14 (10)
O4^v—Ca2—O7^vi	96.15 (10)	O6—Cr2—Ca3^ii	47.44 (8)
O8^iv—Ca2—O3^v	139.00 (10)	Ca1—Cr2—Ca3^ii	95.70 (3)
O5—Ca2—O3^v	75.38 (10)	Ca1^vii—Cr2—Ca3^ii	166.36 (3)
O4^ii—Ca2—O3^v	132.25 (10)	O8—Cr2—Ca3^v	60.26 (11)
O4^v—Ca2—O3^v	64.92 (9)	O5—Cr2—Ca3^v	117.10 (11)
O7^vi—Ca2—O3^v	69.70 (9)	O7—Cr2—Ca3^v	135.70 (9)
O8^iv—Ca2—O9^vii	80.92 (11)	O6—Cr2—Ca3^v	46.39 (9)
O5—Ca2—O9^vii	75.01 (12)	Ca1—Cr2—Ca3^v	174.43 (3)
O4^ii—Ca2—O9^vii	122.89 (9)	Ca1^vii—Cr2—Ca3^v	82.88 (3)
O4^v—Ca2—O9^vii	157.66 (10)	Ca3^ii—Cr2—Ca3^v	87.45 (3)
O7^vi—Ca2—O9^vii	84.25 (10)	O8—Cr2—Ca4^ii	120.09 (11)
O3^v—Ca2—O9^vii	94.69 (9)	O5—Cr2—Ca4^ii	81.02 (14)
O8^iv—Ca2—O2^ii	72.83 (8)	O7—Cr2—Ca4^ii	113.41 (9)
O5—Ca2—O2^ii	67.96 (9)	O6—Cr2—Ca4^ii	34.10 (11)
O4^ii—Ca2—O2^ii	58.39 (9)	Ca1—Cr2—Ca4^ii	113.33 (3)
O4^v—Ca2—O2^ii	125.62 (9)	Ca1^vii—Cr2—Ca4^ii	102.22 (3)
O7^vi—Ca2—O2^ii	133.97 (9)	Ca3^ii—Cr2—Ca4^ii	64.71 (3)
O3^v—Ca2—O2^ii	141.28 (10)	Ca3^v—Cr2—Ca4^ii	63.92 (2)
O9^vii—Ca2—O2^ii	64.58 (9)	O8—Cr2—Ca2^i	86.90 (10)
O8^iv—Ca2—Cr1^v	141.77 (9)	O5—Cr2—Ca2^i	128.07 (12)
O5—Ca2—Cr1^v	77.79 (8)	O7—Cr2—Ca2^i	35.17 (9)
O4^ii—Ca2—Cr1^v	100.61 (7)	O6—Cr2—Ca2^i	108.79 (10)
O4^v—Ca2—Cr1^v	32.43 (7)	Ca1—Cr2—Ca2^i	72.48 (2)
O7^vi—Ca2—Cr1^v	85.51 (7)	Ca1^vii—Cr2—Ca2^i	122.06 (3)
O3^v—Ca2—Cr1^v	32.92 (6)	Ca3^ii—Cr2—Ca2^i	70.69 (2)
O9^vii—Ca2—Cr1^v	125.96 (7)	Ca3^v—Cr2—Ca2^i	112.96 (3)
O2^ii—Ca2—Cr1^v	140.00 (6)	Ca4^ii—Cr2—Ca2^i	135.35 (3)
O8^iv—Ca2—Cr1^ii	75.14 (8)	Cr3B—Cr3A—O3A	180.0
O5—Ca2—Cr1^ii	75.14 (8)	Cr3B—Cr3A—O9	73.91 (13)
O4^ii—Ca2—Cr1^ii	28.77 (7)	O3A—Cr3A—O9	106.09 (13)
O4^v—Ca2—Cr1^ii	98.21 (7)	Cr3B—Cr3A—O9	73.91 (13)
O7^vi—Ca2—Cr1^ii	144.22 (7)	O3A—Cr3A—O9^vii	106.09 (13)
O3^v—Ca2—Cr1^ii	145.74 (7)	O9—Cr3A—O9^vii	112.63 (11)
O9^vii—Ca2—Cr1^ii	94.18 (7)	Cr3B—Cr3A—O9^iii	73.91 (13)
O2^ii—Ca2—Cr1^ii	29.62 (6)	O3A—Cr3A—O9^iii	106.09 (13)
Cr1^v—Ca2—Cr1^ii	122.33 (3)	O9—Cr3A—O9^iii	112.63 (11)
O8^iv—Ca2—Ca4^ii	114.58 (8)	O9^vii—Cr3A—O9^iii	112.63 (11)
O5—Ca2—Ca4^ii	72.00 (9)	Cr3B—Cr3A—Ca1	131.73 (3)
O4^ii—Ca2—Ca4^ii	38.73 (7)	O3A—Cr3A—Ca1	48.27 (3)
O4^v—Ca2—Ca4^ii	38.78 (7)	O9—Cr3A—Ca1	99.05 (12)
O7^vi—Ca2—Ca4^ii	132.54 (7)	O9^vii—Cr3A—Ca1	65.01 (12)
O3^v—Ca2—Ca4^ii	93.53 (6)	O9^iii—Cr3A—Ca1	144.94 (13)
O9^vii—Ca2—Ca4^ii	142.64 (9)	Cr3B—Cr3A—Ca1^iii	131.73 (3)
O2^ii—Ca2—Ca4^ii	86.87 (6)	O3A—Cr3A—Ca1^iii	48.27 (3)
Cr1^v—Ca2—Ca4^ii	62.676 (18)	O9—Cr3A—Ca1^iii	65.01 (12)
Cr1^ii—Ca2—Ca4^ii	60.822 (16)	O9^vii—Cr3A—Ca1^iii	144.94 (13)
O8^iv—Ca2—Cr2^vi	77.25 (8)	O9^iii—Cr3A—Ca1^iii	99.05 (12)
O5—Ca2—Cr2^vi	140.63 (8)	Ca1—Cr3A—Ca1^iii	80.53 (4)
O4^ii—Ca2—Cr2^vi	119.65 (7)	Cr3B—Cr3A—Ca1^vii	131.73 (3)
O4^v—Ca2—Cr2^vi	73.18 (8)	O3A—Cr3A—Ca1^vii	48.27 (3)
O7^vi—Ca2—Cr2^vi	23.69 (6)	O9—Cr3A—Ca1^vii	144.94 (13)
O3^v—Ca2—Cr2^vi	65.26 (6)	O9^vii—Cr3A—Ca1^vii	99.05 (12)
O9^vii—Ca2—Cr2^vi	107.69 (8)	O9^iii—Cr3A—Ca1^vii	65.01 (12)
O2^ii—Ca2—Cr2^vi	149.90 (6)	Ca1—Cr3A—Ca1^vii	80.53 (4)
Cr1^v—Ca2—Cr2^vi	69.150 (19)	Ca1^iii—Cr3A—Ca1^vii	80.52 (4)
Cr1^ii—Ca2—Cr2^vi	141.28 (3)	Cr3B—Cr3A—Ca2^iii	90.71 (3)
Ca4^ii—Ca2—Cr2^vi	108.85 (3)	O3A—Cr3A—Ca2^iii	89.29 (3)
O3^i—Ca3—O1	140.50 (10)	O9—Cr3A—Ca2^iii	35.25 (12)
O3^i—Ca3—O2^ii	70.30 (10)	O9^vii—Cr3A—Ca2^iii	88.86 (12)
O1—Ca3—O2^ii	139.16 (11)	O9^iii—Cr3A—Ca2^iii	147.88 (13)
O3^i—Ca3—O6^viii	84.89 (10)	Ca1—Cr3A—Ca2^iii	65.12 (2)
O1—Ca3—O6^viii	94.64 (11)	Ca1^iii—Cr3A—Ca2^iii	70.09 (2)
O2^ii—Ca3—O6^viii	118.65 (11)	Ca1^vii—Cr3A—Ca2^iii	137.44 (5)
O3^i—Ca3—O9^vii	82.67 (11)	Cr3B—Cr3A—Ca2	90.70 (3)
O1—Ca3—O9^vii	82.45 (11)	O3A—Cr3A—Ca2	89.30 (3)
O2^ii—Ca3—O9^vii	75.68 (10)	O9—Cr3A—Ca2	147.87 (13)
O6^viii—Ca3—O9^vii	156.26 (10)	O9^vii—Cr3A—Ca2	35.24 (12)
O3^i—Ca3—O6^iv	131.27 (10)	O9^iii—Cr3A—Ca2	88.86 (12)
O1—Ca3—O6^iv	84.30 (10)	Ca1—Cr3A—Ca2	70.10 (2)
O2^ii—Ca3—O6^iv	85.60 (10)	Ca1^iii—Cr3A—Ca2	137.44 (5)
O6^viii—Ca3—O6^iv	70.17 (14)	Ca1^vii—Cr3A—Ca2	65.12 (2)
O9^vii—Ca3—O6^iv	132.42 (10)	Ca2^iii—Cr3A—Ca2	119.985 (1)
O3^i—Ca3—O7^viii	67.06 (9)	Cr3B—Cr3A—Ca2^vii	90.71 (3)
O1—Ca3—O7^viii	77.38 (9)	O3A—Cr3A—Ca2^vii	89.29 (3)
O2^ii—Ca3—O7^viii	136.91 (10)	O9—Cr3A—Ca2^vii	88.86 (12)
O6^viii—Ca3—O7^viii	63.67 (9)	O9^vii—Cr3A—Ca2^vii	147.87 (13)
O9^vii—Ca3—O7^viii	92.81 (9)	O9^iii—Cr3A—Ca2^vii	35.24 (12)
O6^iv—Ca3—O7^viii	128.17 (9)	Ca1—Cr3A—Ca2^vii	137.44 (5)
O3^i—Ca3—O8^iv	140.88 (9)	Ca1^iii—Cr3A—Ca2^vii	65.12 (2)
O1—Ca3—O8^iv	66.01 (10)	Ca1^vii—Cr3A—Ca2^vii	70.09 (2)
O2^ii—Ca3—O8^iv	74.58 (8)	Ca2^iii—Cr3A—Ca2^vii	119.985 (1)
O6^viii—Ca3—O8^iv	127.95 (10)	Ca2—Cr3A—Ca2^vii	119.985 (1)
O9^vii—Ca3—O8^iv	72.33 (10)	Cr3A—Cr3B—O3B	180.0
O6^iv—Ca3—O8^iv	60.54 (10)	Cr3A—Cr3B—O9	72.8 (2)
O7^viii—Ca3—O8^iv	141.72 (9)	O3B—Cr3B—O9	107.2 (2)
O3^i—Ca3—Cr2^viii	74.23 (7)	Cr3A—Cr3B—O9^vii	72.8 (2)
O1—Ca3—Cr2^viii	84.84 (8)	O3B—Cr3B—O9^vii	107.2 (2)
O2^ii—Ca3—Cr2^viii	135.89 (8)	O9—Cr3B—O9^vii	111.66 (18)
O6^viii—Ca3—Cr2^viii	31.71 (7)	Cr3A—Cr3B—O9^iii	72.8 (2)
O9^vii—Ca3—Cr2^viii	124.76 (7)	O3B—Cr3B—O9^iii	107.2 (2)
O6^iv—Ca3—Cr2^viii	99.09 (7)	O9—Cr3B—O9^iii	111.66 (18)
O7^viii—Ca3—Cr2^viii	31.97 (6)	O9^vii—Cr3B—O9^iii	111.66 (18)
O8^iv—Ca3—Cr2^viii	144.89 (6)	Cr3A—Cr3B—Ca3	94.68 (8)
O3^i—Ca3—Cr2^iv	150.08 (7)	O3B—Cr3B—Ca3	85.32 (8)
O1—Ca3—Cr2^iv	69.21 (7)	O9—Cr3B—Ca3	94.77 (12)
O2^ii—Ca3—Cr2^iv	82.44 (7)	O9^vii—Cr3B—Ca3	34.06 (13)
O6^viii—Ca3—Cr2^iv	98.09 (8)	O9^iii—Cr3B—Ca3	144.85 (14)
O9^vii—Ca3—Cr2^iv	102.78 (8)	Cr3A—Cr3B—Ca3^iii	94.68 (8)
O6^iv—Ca3—Cr2^iv	30.55 (7)	O3B—Cr3B—Ca3^iii	85.32 (8)
O7^viii—Ca3—Cr2^iv	140.51 (6)	O9—Cr3B—Ca3^iii	34.06 (13)
O8^iv—Ca3—Cr2^iv	30.46 (6)	O9^vii—Cr3B—Ca3^iii	144.85 (14)
Cr2^viii—Ca3—Cr2^iv	121.98 (3)	O9^iii—Cr3B—Ca3^iii	94.77 (12)
O3^i—Ca3—Ca4	122.79 (7)	Ca3—Cr3B—Ca3^iii	119.34 (2)
O1—Ca3—Ca4	71.32 (8)	Cr3A—Cr3B—Ca3^vii	94.68 (8)
O2^ii—Ca3—Ca4	119.86 (8)	O3B—Cr3B—Ca3^vii	85.32 (8)
O6^viii—Ca3—Ca4	38.94 (8)	O9—Cr3B—Ca3^vii	144.84 (14)
O9^vii—Ca3—Ca4	152.63 (9)	O9^vii—Cr3B—Ca3^vii	94.77 (12)
O6^iv—Ca3—Ca4	39.09 (7)	O9^iii—Cr3B—Ca3^vii	34.06 (13)
O7^viii—Ca3—Ca4	89.09 (6)	Ca3—Cr3B—Ca3^vii	119.34 (2)
O8^iv—Ca3—Ca4	89.50 (6)	Ca3^iii—Cr3B—Ca3^vii	119.34 (2)
Cr2^viii—Ca3—Ca4	61.709 (17)	Cr3A—O3A—Ca1	104.88 (16)
Cr2^iv—Ca3—Ca4	61.014 (17)	Cr3A—O3A—Ca1^iii	104.88 (16)
O3^i—Ca3—Cr3B	81.86 (9)	Ca1—O3A—Ca1^iii	113.65 (13)
O1—Ca3—Cr3B	70.86 (10)	Cr3A—O3A—Ca1^vii	104.88 (16)
O2^ii—Ca3—Cr3B	96.52 (10)	Ca1—O3A—Ca1^vii	113.65 (13)
O6^viii—Ca3—Cr3B	135.24 (8)	Ca1^iii—O3A—Ca1^vii	113.64 (13)
O9^vii—Ca3—Cr3B	22.41 (9)	Cr1—O1—Ca3	138.31 (18)
O6^iv—Ca3—Cr3B	144.29 (8)	Cr1—O1—Ca1^vi	93.10 (12)
O7^viii—Ca3—Cr3B	71.79 (6)	Ca3—O1—Ca1^vi	118.96 (12)
O8^iv—Ca3—Cr3B	85.57 (7)	Cr1—O2—Ca3^viii	136.61 (15)
Cr2^viii—Ca3—Cr3B	103.62 (4)	Cr1—O2—Ca1^viii	123.73 (14)
Cr2^iv—Ca3—Cr3B	114.18 (4)	Ca3^viii—O2—Ca1^viii	99.64 (11)
Ca4—Ca3—Cr3B	140.45 (8)	Cr1—O2—Ca2^viii	87.98 (12)
O4^ix—Ca4—O4^x	76.98 (12)	Ca3^viii—O2—Ca2^viii	86.96 (9)
O4^ix—Ca4—O4	76.98 (12)	Ca1^viii—O2—Ca2^viii	97.55 (9)
O4^x—Ca4—O4	76.98 (12)	Cr1—O3—Ca3^vi	134.78 (15)
O4^ix—Ca4—O6^xi	105.92 (9)	Cr1—O3—Ca1^vi	99.63 (11)
O4^x—Ca4—O6^xi	102.53 (9)	Ca3^vi—O3—Ca1^vi	105.41 (10)
O4—Ca4—O6^xi	176.93 (11)	Cr1—O3—Ca2^iv	96.38 (12)
O4^ix—Ca4—O6^iv	102.53 (9)	Ca3^vi—O3—Ca2^iv	110.90 (10)
O4^x—Ca4—O6^iv	176.93 (11)	Ca1^vi—O3—Ca2^iv	107.19 (11)
O4—Ca4—O6^iv	105.92 (9)	Cr1—O4—Ca4	123.79 (16)
O6^xi—Ca4—O6^iv	74.63 (12)	Cr1—O4—Ca2^viii	108.49 (13)
O4^ix—Ca4—O6^viii	176.93 (11)	Ca4—O4—Ca2^viii	99.67 (10)
O4^x—Ca4—O6^viii	105.92 (9)	Cr1—O4—Ca2^iv	98.11 (12)
O4—Ca4—O6^viii	102.53 (9)	Ca4—O4—Ca2^iv	99.29 (10)
O6^xi—Ca4—O6^viii	74.63 (12)	Ca2^viii—O4—Ca2^iv	130.05 (13)
O6^iv—Ca4—O6^viii	74.63 (12)	Cr2—O5—Ca2	141.0 (2)
O4^ix—Ca4—Cr2^xi	87.33 (7)	Cr2—O5—Ca1^vii	93.62 (13)
O4^x—Ca4—Cr2^xi	82.61 (7)	Ca2—O5—Ca1^vii	101.66 (11)
O4—Ca4—Cr2^xi	156.54 (9)	Cr2—O5—Ca1	90.08 (13)
O6^xi—Ca4—Cr2^xi	24.74 (7)	Ca2—O5—Ca1	110.41 (11)
O6^iv—Ca4—Cr2^xi	94.35 (8)	Ca1^vii—O5—Ca1	122.56 (16)
O6^viii—Ca4—Cr2^xi	94.04 (8)	Cr2—O6—Ca4^ii	121.16 (16)
O4^ix—Ca4—Cr2^iv	82.61 (7)	Cr2—O6—Ca3^ii	100.86 (11)
O4^x—Ca4—Cr2^iv	156.54 (9)	Ca4^ii—O6—Ca3^ii	99.97 (11)
O4—Ca4—Cr2^iv	87.33 (7)	Cr2—O6—Ca3^v	103.06 (12)
O6^xi—Ca4—Cr2^iv	94.04 (8)	Ca4^ii—O6—Ca3^v	98.81 (10)
O6^iv—Ca4—Cr2^iv	24.74 (7)	Ca3^ii—O6—Ca3^v	135.61 (14)
O6^viii—Ca4—Cr2^iv	94.35 (7)	Cr2—O7—Ca1	97.99 (12)
Cr2^xi—Ca4—Cr2^iv	108.07 (3)	Cr2—O7—Ca2^i	121.14 (13)
O4^ix—Ca4—Cr2^viii	156.54 (9)	Ca1—O7—Ca2^i	111.84 (11)
O4^x—Ca4—Cr2^viii	87.33 (7)	Cr2—O7—Ca3^ii	90.88 (11)
O4—Ca4—Cr2^viii	82.61 (7)	Ca1—O7—Ca3^ii	134.21 (11)
O6^xi—Ca4—Cr2^viii	94.35 (7)	Ca2^i—O7—Ca3^ii	101.04 (10)
O6^iv—Ca4—Cr2^viii	94.04 (8)	Cr2—O8—Ca2^v	150.77 (16)
O6^viii—Ca4—Cr2^viii	24.74 (7)	Cr2—O8—Ca1^vii	96.75 (12)
Cr2^xi—Ca4—Cr2^viii	108.07 (3)	Ca2^v—O8—Ca1^vii	111.10 (12)
Cr2^iv—Ca4—Cr2^viii	108.07 (3)	Cr2—O8—Ca3^v	89.29 (13)
O4^ix—Ca4—Cr1^ix	23.80 (7)	Ca2^v—O8—Ca3^v	91.64 (10)
O4^x—Ca4—Cr1^ix	93.65 (8)	Ca1^vii—O8—Ca3^v	105.39 (10)
O4—Ca4—Cr1^ix	97.15 (8)	Cr3A—O9—Cr3B	33.27 (14)
O6^xi—Ca4—Cr1^ix	85.90 (6)	Cr3A—O9—Ca3^iii	137.80 (19)
O6^iv—Ca4—Cr1^ix	85.01 (6)	Cr3B—O9—Ca3^iii	123.5 (2)
O6^viii—Ca4—Cr1^ix	154.81 (9)	Cr3A—O9—Ca2^iii	122.44 (17)
Cr2^xi—Ca4—Cr1^ix	72.538 (17)	Cr3B—O9—Ca2^iii	130.38 (18)
Cr2^iv—Ca4—Cr1^ix	70.851 (16)	Ca3^iii—O9—Ca2^iii	98.63 (8)
Cr2^viii—Ca4—Cr1^ix	178.92 (3)

Symmetry codes: (i) −x+y+2/3, y+1/3, z−1/6; (ii) −y+2/3, −x+1/3, z−1/6; (iii) −y, x−y, z; (iv) x+1/3, x−y−1/3, z+1/6; (v) x−1/3, x−y−2/3, z−1/6; (vi) −x+y+1/3, y−1/3, z+1/6; (vii) −x+y, −x, z; (viii) −y+1/3, −x+2/3, z+1/6; (ix) −y+1, x−y, z; (x) −x+y+1, −x+1, z; (xi) −x+y+4/3, y+2/3, z+1/6.