Caesium neodymium sulfate, CsNd(SO₄)₂

The crystal structure of caesium neodymium(III) sulfate, CsNd(SO₄)₂, was determined from intensity data collected on a Rigaku tabletop XtaLAB mini II diffractometer at the Inter­national Union of Crystallography Congress 2017, in Hyderabad, India. CsNd(SO₄)₂ is the fourth crystal structure to be reported in the CsPr(SO₄)₂ family: the Cs and Nd atoms have site symmetries of 2.. and ..2, respectively. In the extended structure, NdO₈ square anti­prisms and SO₄ tetra­hedra are connected into layers, which propagate in the (101) plane and CsO₁₄ polyhedra connect the layers into a three-dimensional network.

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Structure description

Double salts of the form M⁺REE³⁺(SO₄)₂·nH₂O (where M⁺ is an alkali metal cation, usually Rb⁺ or Cs⁺) were first reported by Bukovec and coworkers in a series of articles in the 1970s (e.g. Bukovec & Golič, 1975; Bukovec et al., 1977, 1978). It was not possible to determine the crystal structures for all of these compounds (e.g. Bukovec et al., 1980). Double salts have often been studied for the properties that result from two different cations in combination (e.g. Meyn et al., 1993). CsNd(SO₄)₂·4H₂O was studied for its dehydration kinetics, resulting in the decomposition products of CsNd(SO₄)₂·H₂O and then CsNd(SO₄)₂; however, no crystal structure has been reported for the latter two compounds (Bukovec et al., 1980). CsNd(SO₄)₂ is isostructural with three other compounds with reported crystal structures, namely CsPr(SO₄)₂ (Bukovec et al., 1978), RbDy(SO₄)₂ (Sarukhanyan et al., 1984) and a bis­muth-chromate analogue, RbBi(CrO₄)₂ (Riou et al., 1984).

The crystal structure of CsNd(SO₄)₂ is an infinite, three dimensional framework. The structure may be considered as a layered structure, incorporating layers of edge- and corner-linked SO₄ and NdO₈ polyhedra in the ac plane, with fourteen-coordinate Cs⁺ cations bridging the layers with seven Cs—O bonds to each layer (Table 1; Figs. 1 and 2). Isostructural networks have been reported (three with crystal structures) as discussed above.

Table 1
Selected bond lengths (Å)

Cs1—O3	3.161 (8)	Nd1—O2^ii	2.464 (8)
Cs1—O2^i	3.223 (9)	Nd1—O3	2.522 (8)
Cs1—O3^ii	3.254 (8)	Nd1—O4^iii	2.566 (9)
Cs1—O4^iii	3.305 (8)	S1—O3	1.472 (8)
Cs1—O1^i	3.316 (8)	S1—O1	1.480 (8)
Cs1—O2^iv	3.444 (9)	S1—O4	1.487 (9)
Cs1—O1	3.570 (9)	S1—O2	1.491 (7)
Nd1—O1^v	2.456 (8)
Symmetry codes: (i) ; (ii) ; (iii) ; (iv) ; (v) x, y, z+1.

Figure 1 Displacement elliposid (90% probability level) representation of two unit cells of CsNd(SO4)2: O atoms are red, S atoms yellow, Cs magenta and Nd pale-lavender.

Figure 2 Polyhedral representation of CsNd(SO4)2. Sulfate tetra­hedra are yellow, NdO8 polyhedra are pale-lavender and Cs^+ cations in magenta. Outlines of the unit cell are shown as dotted black lines.

The bond-valence sums for all cationic elements are slightly low, especially the metallic elements Cs and Nd. Bond-valence sums for Cs (0.851 to 0.892) and Nd (2.749 to 2.756) especially are poor, whether using the values of Brown & Altermatt (1985) or the revised values of Gagné & Hawthorne (2015). It would be of inter­est to study the bond-valence behaviour of each element in more detail, in a fashion similar to the studies on Pb (Krivovichev & Brown, 2001), Tl (Locock & Burns, 2004) and Te (Mills & Christy, 2013), among others. Specific studies on Cs and Nd should generate bond-valence sums closer to the expected values of 1 and 3 valence units.

Synthesis and crystallization

CsNd(SO₄)₂ was synthesized from a complex mixture of several inorganic compounds dissolved in diluted sulfuric acid (Sigma Aldrich, initial purity 99.999%, pH = −1 after dilution), including caesium nitrate (Sigma Aldrich, 99%) and neodymium(III) oxide (Sigma Aldrich, 99.9%). Initial hydro­thermal synthesis at 200°C did not yield any crystals. Subsequently, the vessel was left at room temperature over a period of months. During this time, pale-purple plate-like crystals were observed growing on the bottom of the Teflon vessel. Single crystal X-ray diffraction showed these to be crystals of the title compound.

Refinement

Considering the relatively simple nature of the crystal structure of CsNd(SO₄)₂, the structure determination was complicated due to complex twinning observed in some crystals. This twinning was observed on crystals run on the micro-focus MX1 and MX2 macromolecular beamlines of the Australian Synchrotron. The extraneous diffraction spots led to the pseudo-hexa­gonal unit cell a = 10.902 (2), b = 13.934 (3), c = 10.957 (2) Å, α = β = 90°, γ = 119.73 (3) and V = 1445.4 (5) ų. This cell was shown to be a transposition of the Pnna cell due to twinning of CsNd(SO₄)₂ crystals by using the JANA2006 crystallographic program (Petříček et al., 2014). Firstly, the program searched for higher symmetry supercells, which may induce reticular twinning, but no such cells were found. An averaging procedure was then performed, which takes into account twinning by sygonic and also metric merohedry. This procedure showed that R_int values were significantly lower for the ortho­rhom­bic mmm Laue symmetry group (0.07) rather than any hexa­gonal Laue group (0.4). Finally, the space-group test, which took twinning matrices into account, showed that the space group Pnna had the best figure of merit, consistent with the space group determined from a non-twinned crystal fragment (see below). Using JANA2006, the crystal was found to be comprised of three twin components. A CIF of the structure model refined from the twinned crystal using synchrotron diffraction data on the MX1 beamline (Cowieson et al., 2015) may be found in the supporting information. The first component was found to have a twin volume fraction of 0.271 (3) and matrix of [1 0 0 / 0 1 0 / 0 0 1], the second 0.00048 (10) and [ 0 / 0 1 0 / − 0 ] and the third 0.729 (3) and [− 0 / 0 1 0 / − 0 −]. Practically, the second twin component has a negligible effect on the twinning, and the crystal is best considered to be a two-component twin with the two components in a 27:73 ratio.

Whilst it was possible to solve the structure after the treatment of twinning, the final values of R₁ and wR₂ at convergence were higher than those obtained from a non-twinned fragment. The crystal structure reported here was solved on a Rigaku XtaLAB mini II diffractometer at the Inter­national Union of Crystallography Congress 2017, Hyderabad, India, using a single, non-twinned crystal fragment. This crystal was obtained by crushing a large, highly twinned, pale-purple crystalline mass in oil, and mounting a smaller, single fragment (dimensions 0.024 ×0.024 ×0.053 µm) that floated away after crushing.

Structure solution was carried out by direct methods using SHELXT (Sheldrick, 2015a) and structure refinement by full-matrix least-squares was implemented by SHELXL (Sheldrick, 2015b) in the OLEX2 environment (Dolomanov et al., 2009). Full collection and refinement details are shown in Table 2. The residual Fourier peaks are relatively large (3.61 e Å⁻³ maximum, −3.20 e Å⁻³ minimum), but not unreasonably so for small inorganic crystals with heavy scattering elements. A bond-valence summary is shown in Table 2, using the parameters of Gagné & Hawthorne (2015) for S—O, Cs—O and Nd—O bonds.

Table 2
Bond-valence sums (in valence units) for atoms in CsNd(SO₄)₂

	Cs1	Nd1	S1	Σ
O1	0.084 (×2↓), 0.045 (×2↓)	0.386 (×2↓)	1.471	1.986
O2	0.105 (×2↓), 0.061 (×2↓)	0.378 (×2↓)	1.431	1.975
O3	0.122 (×2↓), 0.097 (×2↓)	0.323 (×2↓)	1.501	2.043
O4	0.086 (×2↓)	0.287 (×2↓)	1.445	1.818
Σ	0.851	2.749	5.848

Full crystal data, data collection and structure refinement details are summarized in Table 3.

Table 3
Experimental details

Crystal data
Chemical formula	CsNd(SO4)2
Mr	469.27
Crystal system, space group	Orthorhombic, Pnna
Temperature (K)	293
a, b, c (Å)	9.574 (2), 14.115 (3), 5.4666 (11)
V (Å^3)	738.7 (3)
Z	4
Radiation type	Mo Kα
μ (mm^−1)	12.46
Crystal size (mm)	0.05 × 0.02 × 0.02
Data collection
Diffractometer	Rigaku XtaLAB Mini II
Absorption correction	Gaussian (ABSPACK in CrysAlis PRO; Rigaku OD, 2017)
Tmin, Tmax	0.554, 0.759
No. of measured, independent and observed [I > 2σ(I)] reflections	3915, 1092, 771
Rint	0.102
(sin θ/λ)max (Å^−1)	0.712
Refinement
R[F^2 > 2σ(F^2)], wR(F^2), S	0.064, 0.170, 1.04
No. of reflections	1092
No. of parameters	56
Δρmax, Δρmin (e Å^−3)	3.61, −3.20
Computer programs: CrysAlis PRO (Rigaku OD, 2017), SHELXT2014/5 (Sheldrick, 2015a), SHELXL2016/6 (Sheldrick, 2015b), CrystalMaker (Palmer, 2009) and publCIF (Westrip, 2010).

Structural data

Computing details

Data collection: CrysAlis PRO (Rigaku OD, 2017); cell refinement: CrysAlis PRO (Rigaku OD, 2017); data reduction: CrysAlis PRO (Rigaku OD, 2017); program(s) used to solve structure: SHELXT2014/5 (Sheldrick, 2015a); program(s) used to refine structure: SHELXL2016/6 (Sheldrick, 2015b); molecular graphics: CrystalMaker (Palmer, 2009); software used to prepare material for publication: publCIF (Westrip, 2010).

caesium neodymium(III) sulfate

Crystal data

CsNd(SO4)2	Dx = 4.219 Mg m^−3
Mr = 469.27	Mo Kα radiation, λ = 0.71073 Å
Orthorhombic, Pnna	Cell parameters from 968 reflections
a = 9.574 (2) Å	θ = 2.9–29.9°
b = 14.115 (3) Å	µ = 12.46 mm^−1
c = 5.4666 (11) Å	T = 293 K
V = 738.7 (3) Å^3	Fragment, pale purple
Z = 4	0.05 × 0.02 × 0.02 mm
F(000) = 844

Data collection

Rigaku XtaLAB Mini II diffractometer	771 reflections with I > 2σ(I)
Radiation source: fine-focus sealed X-ray tube	Rint = 0.102
CCD plate scans	θmax = 30.4°, θmin = 2.9°
Absorption correction: gaussian (ABSPACK in Crys Alis PRO; Rigaku OD, 2017)	h = −13→13
Tmin = 0.554, Tmax = 0.759	k = −20→18
3915 measured reflections	l = −5→7
1092 independent reflections

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.064	w = 1/[σ^2(Fo^2) + (0.0907P)^2] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.170	(Δ/σ)max < 0.001
S = 1.04	Δρmax = 3.61 e Å^−3
1092 reflections	Δρmin = −3.20 e Å^−3
56 parameters

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

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

	x	y	z	Uiso*/Ueq
Cs1	0.92197 (10)	0.750000	0.250000	0.0213 (3)
Nd1	0.750000	0.500000	0.68152 (16)	0.0165 (3)
S1	0.5851 (3)	0.58533 (19)	0.2371 (6)	0.0149 (6)
O1	0.6532 (9)	0.6041 (6)	−0.0010 (13)	0.0190 (17)
O2	0.4359 (7)	0.6153 (7)	0.2254 (16)	0.0226 (19)
O3	0.6571 (8)	0.6370 (5)	0.4342 (14)	0.0169 (17)
O4	0.5960 (9)	0.4831 (6)	0.2998 (16)	0.0201 (19)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cs1	0.0134 (5)	0.0257 (5)	0.0248 (6)	0.000	0.000	0.0007 (5)
Nd1	0.0119 (4)	0.0224 (5)	0.0152 (5)	−0.0009 (4)	0.000	0.000
S1	0.0066 (11)	0.0228 (14)	0.0153 (14)	−0.0009 (9)	0.0005 (11)	0.0001 (12)
O1	0.010 (4)	0.035 (4)	0.012 (4)	0.000 (4)	0.002 (3)	−0.002 (4)
O2	0.006 (3)	0.043 (5)	0.018 (5)	0.003 (4)	0.001 (3)	0.005 (4)
O3	0.007 (4)	0.028 (4)	0.015 (4)	−0.003 (3)	−0.002 (3)	−0.006 (3)
O4	0.018 (4)	0.020 (4)	0.022 (5)	−0.003 (3)	0.004 (4)	0.003 (3)

Geometric parameters (Å, º)

Cs1—O3	3.161 (8)	Cs1—O1^i	3.570 (9)
Cs1—O3^i	3.161 (8)	Nd1—O1^viii	2.456 (8)
Cs1—O2^ii	3.223 (9)	Nd1—O1^ix	2.456 (8)
Cs1—O2^iii	3.223 (9)	Nd1—O2^iv	2.464 (8)
Cs1—O3^iv	3.254 (8)	Nd1—O2^x	2.464 (8)
Cs1—O3^v	3.254 (8)	Nd1—O3	2.522 (8)
Cs1—O4^vi	3.305 (8)	Nd1—O3^vi	2.522 (8)
Cs1—O4^vii	3.305 (8)	Nd1—O4^vi	2.566 (9)
Cs1—O1^ii	3.316 (8)	Nd1—O4	2.566 (9)
Cs1—O1^iii	3.316 (8)	S1—O3	1.472 (8)
Cs1—O2^v	3.444 (9)	S1—O1	1.480 (8)
Cs1—O2^iv	3.444 (9)	S1—O4	1.487 (9)
Cs1—O1	3.570 (9)	S1—O2	1.491 (7)
O3—Cs1—O3^i	73.3 (3)	O3—S1—O1	110.4 (5)
O3—Cs1—O2^ii	94.3 (2)	O3—S1—O4	106.2 (5)
O3^i—Cs1—O2^ii	89.56 (19)	O1—S1—O4	110.2 (5)
O3—Cs1—O2^iii	89.56 (19)	O3—S1—O2	109.8 (5)
O3^i—Cs1—O2^iii	94.3 (2)	O1—S1—O2	109.5 (5)
O2^ii—Cs1—O2^iii	175.3 (3)	O4—S1—O2	110.6 (5)
O3—Cs1—O3^iv	97.97 (16)	O3—S1—Nd1	52.3 (3)
O3^i—Cs1—O3^iv	166.2 (3)	O1—S1—Nd1	121.9 (3)
O2^ii—Cs1—O3^iv	80.4 (2)	O4—S1—Nd1	54.1 (4)
O2^iii—Cs1—O3^iv	96.3 (2)	O2—S1—Nd1	128.6 (4)
O3—Cs1—O3^v	166.2 (3)	O3—S1—Nd1^x	120.9 (3)
O3^i—Cs1—O3^v	97.97 (16)	O1—S1—Nd1^x	125.8 (4)
O2^ii—Cs1—O3^v	96.3 (2)	O4—S1—Nd1^x	72.4 (4)
O2^iii—Cs1—O3^v	80.4 (2)	O2—S1—Nd1^x	38.3 (4)
O3^iv—Cs1—O3^v	92.5 (3)	Nd1—S1—Nd1^x	103.51 (8)
O3—Cs1—O4^vi	55.2 (2)	O3—S1—Nd1^xi	125.0 (3)
O3^i—Cs1—O4^vi	119.1 (2)	O1—S1—Nd1^xi	29.7 (3)
O2^ii—Cs1—O4^vi	121.5 (2)	O4—S1—Nd1^xi	80.8 (4)
O2^iii—Cs1—O4^vi	58.8 (2)	O2—S1—Nd1^xi	118.4 (4)
O3^iv—Cs1—O4^vi	60.3 (2)	Nd1—S1—Nd1^xi	107.56 (7)
O3^v—Cs1—O4^vi	124.6 (2)	Nd1^x—S1—Nd1^xi	113.33 (8)
O3—Cs1—O4^vii	119.1 (2)	O3—S1—Cs1^xii	113.3 (3)
O3^i—Cs1—O4^vii	55.2 (2)	O1—S1—Cs1^xii	57.6 (3)
O2^ii—Cs1—O4^vii	58.8 (2)	O4—S1—Cs1^xii	140.4 (4)
O2^iii—Cs1—O4^vii	121.5 (2)	O2—S1—Cs1^xii	54.0 (4)
O3^iv—Cs1—O4^vii	124.6 (2)	Nd1—S1—Cs1^xii	165.42 (9)
O3^v—Cs1—O4^vii	60.3 (2)	Nd1^x—S1—Cs1^xii	85.59 (6)
O4^vi—Cs1—O4^vii	174.0 (3)	Nd1^xi—S1—Cs1^xii	78.39 (6)
O3—Cs1—O1^ii	135.92 (19)	O3—S1—Cs1^xiii	51.4 (3)
O3^i—Cs1—O1^ii	110.7 (2)	O1—S1—Cs1^xiii	133.7 (4)
O2^ii—Cs1—O1^ii	43.53 (19)	O4—S1—Cs1^xiii	115.7 (4)
O2^iii—Cs1—O1^ii	132.05 (19)	O2—S1—Cs1^xiii	59.1 (4)
O3^iv—Cs1—O1^ii	68.0 (2)	Nd1—S1—Cs1^xiii	82.85 (7)
O3^v—Cs1—O1^ii	56.75 (19)	Nd1^x—S1—Cs1^xiii	75.37 (6)
O4^vi—Cs1—O1^ii	128.2 (2)	Nd1^xi—S1—Cs1^xiii	163.41 (8)
O4^vii—Cs1—O1^ii	56.7 (2)	Cs1^xii—S1—Cs1^xiii	88.59 (6)
O3—Cs1—O1^iii	110.7 (2)	O3—S1—Cs1	47.0 (3)
O3^i—Cs1—O1^iii	135.92 (19)	O1—S1—Cs1	63.5 (3)
O2^ii—Cs1—O1^iii	132.05 (19)	O4—S1—Cs1	120.4 (4)
O2^iii—Cs1—O1^iii	43.53 (19)	O2—S1—Cs1	127.8 (4)
O3^iv—Cs1—O1^iii	56.75 (19)	Nd1—S1—Cs1	78.61 (6)
O3^v—Cs1—O1^iii	68.0 (2)	Nd1^x—S1—Cs1	162.66 (9)
O4^vi—Cs1—O1^iii	56.7 (2)	Nd1^xi—S1—Cs1	81.72 (6)
O4^vii—Cs1—O1^iii	128.2 (2)	Cs1^xii—S1—Cs1	89.34 (6)
O1^ii—Cs1—O1^iii	96.2 (3)	Cs1^xiii—S1—Cs1	87.95 (6)
O3—Cs1—O2^v	125.10 (19)	O3—S1—Cs1^vi	119.4 (3)
O3^i—Cs1—O2^v	59.14 (19)	O1—S1—Cs1^vi	101.5 (3)
O2^ii—Cs1—O2^v	110.1 (3)	O4—S1—Cs1^vi	13.4 (4)
O2^iii—Cs1—O2^v	69.7 (3)	O2—S1—Cs1^vi	105.7 (4)
O3^iv—Cs1—O2^v	133.29 (18)	Nd1—S1—Cs1^vi	67.16 (5)
O3^v—Cs1—O2^v	42.33 (18)	Nd1^x—S1—Cs1^vi	68.67 (5)
O4^vi—Cs1—O2^v	128.3 (2)	Nd1^xi—S1—Cs1^vi	71.75 (5)
O4^vii—Cs1—O2^v	52.0 (2)	Cs1^xii—S1—Cs1^vi	127.29 (7)
O1^ii—Cs1—O2^v	88.46 (19)	Cs1^xiii—S1—Cs1^vi	124.77 (7)
O1^iii—Cs1—O2^v	88.6 (2)	Cs1—S1—Cs1^vi	126.57 (6)
O3—Cs1—O2^iv	59.14 (19)	S1—O1—Nd1^xi	132.9 (5)
O3^i—Cs1—O2^iv	125.10 (19)	S1—O1—Cs1^xii	100.3 (4)
O2^ii—Cs1—O2^iv	69.7 (3)	Nd1^xi—O1—Cs1^xii	109.5 (2)
O2^iii—Cs1—O2^iv	110.1 (3)	S1—O1—Cs1	94.8 (4)
O3^iv—Cs1—O2^iv	42.33 (18)	Nd1^xi—O1—Cs1	110.2 (3)
O3^v—Cs1—O2^iv	133.29 (18)	Cs1^xii—O1—Cs1	106.3 (2)
O4^vi—Cs1—O2^iv	52.0 (2)	S1—O1—Nd1	40.3 (3)
O4^vii—Cs1—O2^iv	128.3 (2)	Nd1^xi—O1—Nd1	110.0 (3)
O1^ii—Cs1—O2^iv	88.6 (2)	Cs1^xii—O1—Nd1	138.1 (2)
O1^iii—Cs1—O2^iv	88.46 (19)	Cs1—O1—Nd1	72.26 (14)
O2^v—Cs1—O2^iv	175.6 (2)	S1—O1—Cs1^xiii	34.2 (3)
O3—Cs1—O1	41.67 (18)	Nd1^xi—O1—Cs1^xiii	167.1 (3)
O3^i—Cs1—O1	65.81 (19)	Cs1^xii—O1—Cs1^xiii	77.87 (15)
O2^ii—Cs1—O1	132.85 (18)	Cs1—O1—Cs1^xiii	76.74 (13)
O2^iii—Cs1—O1	51.65 (18)	Nd1—O1—Cs1^xiii	60.79 (9)
O3^iv—Cs1—O1	114.82 (19)	S1—O2—Nd1^x	119.7 (5)
O3^v—Cs1—O1	125.26 (19)	S1—O2—Cs1^xii	104.0 (4)
O4^vi—Cs1—O1	54.6 (2)	Nd1^x—O2—Cs1^xii	121.7 (3)
O4^vii—Cs1—O1	120.3 (2)	S1—O2—Cs1^xiii	99.1 (4)
O1^ii—Cs1—O1	175.8 (2)	Nd1^x—O2—Cs1^xiii	99.5 (3)
O1^iii—Cs1—O1	88.02 (17)	Cs1^xii—O2—Cs1^xiii	110.1 (3)
O2^v—Cs1—O1	91.51 (19)	S1—O2—Cs1	38.7 (3)
O2^iv—Cs1—O1	91.69 (18)	Nd1^x—O2—Cs1	155.8 (3)
O3—Cs1—O1^i	65.81 (19)	Cs1^xii—O2—Cs1	80.60 (16)
O3^i—Cs1—O1^i	41.67 (18)	Cs1^xiii—O2—Cs1	78.74 (15)
O2^ii—Cs1—O1^i	51.65 (18)	S1—O3—Nd1	100.2 (4)
O2^iii—Cs1—O1^i	132.85 (18)	S1—O3—Cs1	113.1 (4)
O3^iv—Cs1—O1^i	125.26 (19)	Nd1—O3—Cs1	105.9 (3)
O3^v—Cs1—O1^i	114.82 (19)	S1—O3—Cs1^xiii	107.9 (4)
O4^vi—Cs1—O1^i	120.3 (2)	Nd1—O3—Cs1^xiii	109.6 (3)
O4^vii—Cs1—O1^i	54.6 (2)	Cs1—O3—Cs1^xiii	118.5 (2)
O1^ii—Cs1—O1^i	88.02 (17)	S1—O3—Cs1^xii	49.8 (3)
O1^iii—Cs1—O1^i	175.8 (2)	Nd1—O3—Cs1^xii	149.9 (3)
O2^v—Cs1—O1^i	91.69 (18)	Cs1—O3—Cs1^xii	87.65 (17)
O2^iv—Cs1—O1^i	91.51 (19)	Cs1^xiii—O3—Cs1^xii	85.63 (17)
O1—Cs1—O1^i	87.8 (3)	S1—O4—Nd1	97.9 (4)
O1^viii—Nd1—O1^ix	90.1 (4)	S1—O4—Cs1^vi	160.6 (5)
O1^viii—Nd1—O2^iv	74.4 (3)	Nd1—O4—Cs1^vi	100.9 (3)
O1^ix—Nd1—O2^iv	88.7 (3)	S1—O4—Nd1^x	82.4 (4)
O1^viii—Nd1—O2^x	88.7 (3)	Nd1—O4—Nd1^x	122.8 (3)
O1^ix—Nd1—O2^x	74.4 (3)	Cs1^vi—O4—Nd1^x	91.3 (2)
O2^iv—Nd1—O2^x	156.2 (4)	S1—O4—Nd1^xi	75.8 (3)
O1^viii—Nd1—O3	77.7 (2)	Nd1—O4—Nd1^xi	120.6 (3)
O1^ix—Nd1—O3	166.2 (3)	Cs1^vi—O4—Nd1^xi	90.6 (2)
O2^iv—Nd1—O3	81.9 (3)	Nd1^x—O4—Nd1^xi	114.9 (2)
O2^x—Nd1—O3	111.2 (3)	S1—O4—Cs1^xiii	48.1 (3)
O1^viii—Nd1—O3^vi	166.2 (3)	Nd1—O4—Cs1^xiii	73.10 (19)
O1^ix—Nd1—O3^vi	77.7 (2)	Cs1^vi—O4—Cs1^xiii	143.7 (2)
O2^iv—Nd1—O3^vi	111.2 (3)	Nd1^x—O4—Cs1^xiii	65.27 (14)
O2^x—Nd1—O3^vi	81.9 (3)	Nd1^xi—O4—Cs1^xiii	123.8 (2)
O3—Nd1—O3^vi	115.2 (3)	S1—O4—Cs1	44.4 (3)
O1^viii—Nd1—O4^vi	137.4 (3)	Nd1—O4—Cs1	66.90 (18)
O1^ix—Nd1—O4^vi	114.4 (3)	Cs1^vi—O4—Cs1	142.6 (2)
O2^iv—Nd1—O4^vi	72.0 (3)	Nd1^x—O4—Cs1	125.5 (2)
O2^x—Nd1—O4^vi	130.1 (3)	Nd1^xi—O4—Cs1	69.23 (13)
O3—Nd1—O4^vi	72.3 (3)	Cs1^xiii—O4—Cs1	69.26 (11)
O3^vi—Nd1—O4^vi	55.4 (3)	S1—O4—Cs1^xii	28.9 (3)
O1^viii—Nd1—O4	114.4 (3)	Nd1—O4—Cs1^xii	126.7 (3)
O1^ix—Nd1—O4	137.4 (3)	Cs1^vi—O4—Cs1^xii	132.0 (2)
O2^iv—Nd1—O4	130.1 (3)	Nd1^x—O4—Cs1^xii	68.85 (14)
O2^x—Nd1—O4	72.0 (3)	Nd1^xi—O4—Cs1^xii	62.84 (12)
O3—Nd1—O4	55.4 (3)	Cs1^xiii—O4—Cs1^xii	66.96 (11)
O3^vi—Nd1—O4	72.3 (3)	Cs1—O4—Cs1^xii	66.87 (10)
O4^vi—Nd1—O4	71.2 (4)

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

 

Footnotes

‡Now at School of Earth, Atmosphere and the Environment, Monash University, Clayton 3800, Victoria, Australia.