Flux syntheses and single-crystal structures of CsNa10M4(AsO4)9 (M = Zr, Hf)

Harrison, W.T.A.

doi:10.1107/S2056989022006338

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Volume 78| Part 7| July 2022| Pages 737-741

https://doi.org/10.1107/S2056989022006338

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Flux syntheses and single-crystal structures of CsNa₁₀M₄(AsO₄)₉ (M = Zr, Hf)

William T. A. Harrison ^a ^*

^aDepartment of Chemistry, University of Aberdeen, Meston Walk, Aberdeen AB24 3UE, Scotland
^*Correspondence e-mail: w.harrison@abdn.ac.uk

Edited by S. Parkin, University of Kentucky, USA (Received 30 May 2022; accepted 15 June 2022; online 21 June 2022)

The isostructural compounds caesium decasodium tetrazirconium nonaarsenate, CsNa₁₀Zr₄(AsO₄)₉, and caesium decasodium tetrahafnium nonaarsenate, CsNa₁₀Hf₄(AsO₄)₉, arose as unexpected single-crystal products from the reactions of Na₂CO₃, MO₂ (M = Zr, Hf) and As₂O₅ in a eutectic flux of NaCl and CsCl. They consist of MO₆ octahedra and AsO₄ tetrahedra sharing vertices to generate three-dimensional polyhedral networks encapsulating the caesium and sodium ions. The MO₆ groups share all their vertices with adjacent As atoms but the As atoms have one or two `terminal' O atoms not bonded to Zr or Hf. The Cs⁺ ion adopts a squashed octahedral geometry and the coordination polyhedra of the partially occupied sodium ions are variously trigonal bipyramidal, tetrahedral, square pyramidal and trigonal pyramidal. Site symmetries: Cs $[\overline{3}]$ ; M 3; As 1 and 2; O 1; Na 1, 2 and 3. The M = Zr crystal was refined as an obverse/reverse rhombohedral twin.

Keywords: crystal structure; zirconium; hafnium; arsenate; ionic conduction.

CCDC references: 2179420; 2179419

1. Chemical context

Potassium titanyl phosphate (KTiOPO₄; KTP) has long been recognized as an important non-linear optical (NLO) material (Zumsteg et al., 1976 ) due to its unique combination of desirable physical properties including `a large hyperpolarizability, excellent temperature window, wide wavelength for phase matching and outstanding crystal stability' (Stucky et al., 1989 ). Work continues to improve the performance of KTP waveguides in optoelectronics (Kores et al., 2021 ) and it is finding new uses as a frequency doubler (to 532 nm green light) for 1064 nm Nd–YAG laser radiation in many areas of medicine (Shim & Kim, 2021 ; McGarey et al., 2021 ). So far as crystal chemistry is concerned, the KTiOPO₄ structure type (space group Pna2₁, a ≃ 12.8, b ≃ 6.4, c ≃ 10.6 Å, Z = 8, Z′ = 2) is remarkably accommodating with respect to partial or complete isovalent or aleovalent substitution at the potassium (Na⁺, Rb⁺, Cs⁺, Tl⁺, NH₄⁺…), titanium (Zr^IV, Hf^IV, V^IV, Sn^IV, Sb^V, Ga³⁺, Fe³⁺, Al³⁺, Cr³⁺…), phosphorus (As^V, Si^IV, Ge^IV) and even oxygen (OH⁻, F⁻) sites and comprehensive reviews on its substitution chemistry have appeared (Sorokina & Voronkova, 2007 ).

In an attempt to grow single crystals of the possible new KTP analogues NaZrOAsO₄ and NaHfOAsO₄ by reacting Na₂CO₃, MO₂ (M = Zr, Hf) and As₂O₅ in a low-melting flux of NaCl and CsCl, the isostructural title compounds CsNa₁₀Zr₄(AsO₄)₉ (I) and CsNa₁₀Hf₄(AsO₄)₉ (II) were the unexpected result and their crystal structures are now described.

2. Structural commentary

Compounds (I) and (II) are isostructural and crystallize in the rhombohedral space group R $[\overline{3}]$ c (No. 167) with an unusually long c unit-cell parameter of nearly 77 Å. This is of course partly a consequence of our choosing the hexagonal (R-centred) setting of the unit cell [the equivalent primitive rhombohedral lattice for (I) has a = b = c ≃ 26.21 Å and α = β = γ ≃ 20.3°] but even so, it is notable that the l index runs well into three figures for (I) in the R-centred setting. This description will focus on the structure of (I) and note significant differences for (II) where applicable.

The asymmetric unit of (I), expanded to show the full coordination polyhedra of the zirconium and arsenic atoms, is shown in Fig. 1. It consists of two zirconium atoms (both with site symmetry 3 on Wyckoff site 12c), two arsenic atoms [As1 on a general position (36f) and As2 with site symmetry 2 (18e)] and six oxygen atoms, one of which is disordered over two adjacent sites (all lying on general positions, 36f), which leads to the unusual 4:9 stoichiometry for the Zr^IV and AsO₄^3– moieties with a net charge of −11. The structure of (I) is completed by a Cs⁺ ion (site symmetry $[\overline{3}]$ , 6b) and four partly occupied sodium cations [one on a general position (36f), one with site symmetry 2 (18e) and two with site symmetry 3 (12c)]. To maintain charge balance, the four sodium ions must have a total occupancy of 10 based on Z = 6 (full occupancy of the four sites would give 13 sodium ions per caesium ion).

Figure 1
The asymmetric unit of (I) expanded to include the full Zr and As coordination polyhedra showing 50% displacement ellipsoids. Only one disorder component about As2 is shown. Symmetry codes: (i) 1 − x, 1 − y, −z; (ii) y, 1 − x − y, −z; (iii) 1 − y, 1 + x − y, z; (iv) $[{4\over 3}]$ − x, $[{2\over 3}]$ − x + y, $[{1\over 6}]$ − z; (v) x − y, x, −z; (vi) y − x, 1 − x, z.

Both zirconium atoms adopt almost regular ZrO₆ octahedral geometries (Müller-Buschbaum, 2010 ) when crystal symmetry is taken into account: the mean Zr1—O separation (to 3 × O3 and 3 × O5) is 2.070 Å and the quadratic elongation and angular variance are 1.001 and 4.43°², respectively (Robinson et al., 1971 ). Equivalent data for Zr2 (bonded to to 3 × O2 and 3 × O4) are 2.072 Å, 1.003 and 9.86°², respectively. The `extrapolated' (Brese & O'Keeffe, 1991 ) bond-valence sums (BVS) in valence units are 4.10 and 4.07 for Zr1 and Zr2, respectively, in acceptable agreement with the expected value of 4.00. The mean Hf—O distances in (II) are 2.062 Å for Hf1 (BVS = 4.13, quadratic elongation = 1.002, angular variance = 5.38°²) and 2.065 Å for Hf2 (4.10, 1.004, 13.20°²). It may be seen that the Hf—O bonds are slightly shorter than the Zr—O bonds, which is in accordance with ionic radii data (Shannon, 1976 ): r₆(Zr^IV) = 0.72 (6 = six-coordinate) and r₆(Hf^IV) = 0.71 Å and is presumed to arise from the lanthanide contraction effect.

The As1 atom in (I) is surrounded by four oxygen atoms (O1–O4) in the geometry of a slightly distorted tetrahedron [mean As—O = 1.677 Å, spread of O—As—O angles = 103.0 (2)–114.9 (2)°, τ₄ (Yang et al., 2007 ) = 0.95]. Atom As2 is also tetrahedral (to 2 × O5 and 2 × O6), with the latter O atom disordered over two adjacent sites in almost equal occupancies of 0.45 (3):0.55 (3) [O6A⋯O6B = 0.909 (13) Å]. Of the six oxygen atoms in the structure of (I), four of them (O2–O5) bridge zirconium and arsenic atoms with a mean Zr—O—As bond angle of 141.5° [equivalent mean Hf—O—As bond angle in (II) = 140.4°] and two (O1 and O6) are `terminal' and only bonded to arsenic: all of the O atoms also form one or more bonds to nearby caesium and/or sodium ions.

The caesium ion in (I) adopts a grossly squashed octahedral coordination to six O1 atoms with Cs1—O1 = 3.235 (4) Å: the cis O—Cs—O bond angles are compressed to 62.30 (10) or expanded to 117.70 (10)°: the Cs1 BVS of 0.61 compared to an expected value of 1.00 suggests significant underbonding. The interpretation of the sodium-ion coordination polyhedra are complicated by the positional disorder of atom O6 but can be described as distorted trigonal bipyramidal (Na1), very distorted tetrahedral (Na2), square-based pyramidal (Na3) and squashed trigonal pyramidal (Na4). It is notable that Na4 is only three coordinate but similar NaO₃ geometries have been observed in dehydrated sodium aluminosilicate zeolites (Adams et al., 1982 ).

The extended structure of (I) (Fig. 2) can be conceptually broken down into two different types of layers lying parallel to (001). The first layer (type `A') occurs at z ≃ 0, 1/6, 1/3, 1/2, 2/3 and 5/6 with adjacent A-layers laterally displaced by 1/3 in x and 2/3 in y and consists of the Zr2 and As1 centred polyhedra as well as the caesium ions. Fig. 3 shows that each Zr2O₆ octahedron is connected by two As1O₄ tetrahedra (via O2 and O4) to result in a `honeycomb' array of polyhedral 12-rings (six octahedra and 12 tetrahedra) encapsulating the Cs⁺ ions. Atom O3 of the arsenate group provides the link to the type `B' layers on either side of the A layer. This inter-octahedral connectivity via O3 leads to a distinctive `lantern' motif (Fig. 4) in which three tetrahedra link two octahedra [Zr1⋯Zr2 = 4.886 (2); Hf1⋯Hf2 in (II) = 4.863 (2) Å]: similar `lanterns' are a feature of the polyhedral connectivity in the scandium tungstate [M₂(XO₄)₃] (Abrahams & Bernstein, 1966 ), Nasicon [AM₂(XO₄)₃] (Anantharamulu et al., 2011 ) and langbeinite [A₂M₂(XO₄)₃] (Norberg, 2002 ) structure types but they differ from (I) because all the vertices of the constituent tetrahedra in these structures link to adjacent octahedra, hence their 2:3 M:X ratios compared to the 4:9 ratio for (I).

Figure 2
The unit-cell of (I) in polyhedral representation viewed approximately down [110]. A single O atom at the average location of O6A and O6B in the asymmetric unit has been used to construct the As2 tetrahedron. Colour code: Zr1O₆ octahedra blue, Zr2O₆ octahedra green, As1O₄ tetrahedra peach, As2O₄ tetrahedra rose, Cs sky blue, Na yellow, O (polyhedral corners) red.

Figure 3
View down [001] of an `A'-type layer in the structure of (I) in polyhedral representation. Atom and polyhedron colours as in Fig. 2

except O3 is blue.

Figure 4
Detail of the extended structure of (I) showing a Zr₂As₃O₁₈ `lantern' motif of Zr1 and Zr2 octahedra linked by three As1 tetrahedra via atoms O2 and O3. In (I), this motif has crystallographically imposed threefold symmetry about a rotation axis passing through the zirconium atoms. Symmetry codes: (i) 1 − y, 1 + x − y, z; (ii) y − x, 1 − x, z.

The B layers in (I) (Fig. 5) lie at z ≃ 1/12, 1/4, 5/12, 7/12, 3/4 and 11/12 and are associated with the Zr1 and As2 species. These also feature polyhedral 12-rings (six octahedra and six tetrahedra) but only one As2 tetrahedron (with two terminal As2—O6 bonds) links adjacent Zr1 octahedra via atom O5. There are numerous sodium sites associated with the B layers. The disorder of the sodium ions in the vicinities of the B layers and possible small [110] channels (see Fig. 2) suggests the possibility of ionic conductivity (Norberg, 2002). An analysis of the stucture with PLATON (Spek, 2020 ) with the sodium ions removed indicated that there was 119.4 Å³ of free space per unit cell (∼2.1%).

Figure 5
View down [001] of a `B'-type layer in the structure of (I) in polyhedral representation. Atom and polyhedron colours as in Fig. 2

except O3 is blue.

3. Database survey

A survey of the Inorganic Crystal Structure Database (ICSD) (Belsky et al., 2002 ) revealed 11 matches for crystal structures containing Zr + As + O, the majority of these being Nasicon (Anantharamulu et al., 2011) derivatives such as NaZr₂(AsO₄)₃ (Chakir et al., 2003 ) or KZr₂(AsO₄)₃ (Elbrahimi & Durand, 1990 ) as well as one KTP analogue, viz. RbZrOAsO₄ (Simpson & Harrison, 2004 ). There were no hits for the combination of Hf + As + O.

4. Synthesis and crystallization

Compound (I) was prepared by mixing 1.00 g of Na₂CO₃, 0.581 g of ZrO₂ and 1.399 g of As₂O₅ (Na:Zr:As molar ratio ≃ 4:1:3) in an agate mortar: 1.00 g of this mixture was added to 3.0 g of a eutectic-melt mixture (T_melt ≃ 500°C) of NaCl/CsCl (∼0.35:0.65 mol) and placed in a flat-bottom alumina crucible. The crucible was rapidly heated to 500°C in a muffle furnace and then ramped at 12°C min⁻¹ to 700°C and cooled at the same rate to 400°C and then removed from the furnace and left to cool. The gummy white product was washed with copious amounts of hot water followed by acetone to result in a mass of tiny colourless rods of (I). Compound (II) was made in the same way starting from a pre-mixture of 1.00 g Na₂CO₃, 1.12 g HfO₂ and 1.57 g As₂O₅ and tiny colourless rods of (II) were the result.

Caution! Arsenic compounds are highly toxic and carcinogenic. Take all appropriate safety precautions, especially with respect to dust contamination.

5. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1. The crystal chosen for data collection for (I) was found to be twinned over its rhombohedral obverse and reverse settings (Herbst-Irmer & Sheldrick, 2002 ) in a 0.797 (3):0.203 (3) ratio, which was processed as a SHELXL HKLF 5 refinement. To ensure charge balance, the occupancies of the four partially occupied sodium sites must sum to 10.0 Na per caesium ion and this was achieved by using a SUMP card (linear free variable restraint) in SHELXL, as unrestrained refinements tended to drift to a collective occupancy of above 10 (full occupancy of the four sodium sites would give 13 Na to 1 Cs). This needed cautious damped refinement cycles to begin with, but as the refinement converged, the damping could be removed to give refined fractional site occupancies of Na1 = 0.852 (5), Na2 = 0.860 (9), Na3 = 0.731 (12) and Na4 = 0.423 (11) for (I) and Na1 = 0.887 (7), Na2 = 0.846 (11), Na3 = 0.735 (16) and Na4 = 0.337 (14) for (II). The final difference map for (II) features electron density peaks of ∼2 e Å⁻³ near some of the sodium ions, perhaps suggesting that they are localizing over split multiple sites at low temperatures, but efforts to model this did not lead to satisfactory refinements. The value of U_eq for Na4 is small, which might indicate partial occupancy of caesium on this site (i.e., a formula of Cs_1+xNa_10-xHf₄(AsO₄)₉, but attempts to model this were inconclusive.

Table 1
Experimental details

	(I)	(II)
Crystal data
Chemical formula	CsNa₁₀Zr₄(AsO₄)₉	CsNa₁₀Hf₄(AsO₄)₉
M_r	1977.97	2327.05
Crystal system, space group	Trigonal, R $[\overline{3}]$ c:H	Trigonal, R $[\overline{3}]$ c:H
Temperature (K)	293	120
a, c (Å)	9.2218 (5), 76.982 (5)	9.1795 (2), 76.527 (8)
V (Å³)	5669.6 (7)	5584.5 (6)
Z	6	6
Radiation type	Mo Kα	Mo Kα
μ (mm⁻¹)	10.07	20.25
Crystal size (mm)	0.10 × 0.10 × 0.10	0.08 × 0.08 × 0.08

Data collection
Diffractometer	Bruker SMART CCD	Nonius KappaCCD
Absorption correction	Multi-scan (SADABS; Bruker, 1999 )	Multi-scan (SORTAV; Blessing, 1995 )
T_min, T_max	0.350, 0.495	0.40, 0.50
No. of measured, independent and observed [I > 2σ(I)] reflections	2288, 2288, 1694	11660, 1434, 1164
R_int	–	0.070
(sin θ/λ)_max (Å⁻¹)	0.756	0.650

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.040, 0.093, 1.00	0.032, 0.078, 1.06
No. of reflections	2288	1434
No. of parameters	112	107
No. of restraints	1	7
Δρ_max, Δρ_min (e Å⁻³)	1.85, −1.63	2.57, −2.00
Computer programs: SMART and SAINT (Bruker, 1999), DENZO/SCALEPACK (Otwinowski & Minor, 1997 ), SHELXS and SHELXS97 (Sheldrick, 2008 ), SHELXL2018/3 (Sheldrick, 2015 ), ORTEP-3 for Windows (Farrugia, 2012 ), ATOMS (Dowty, 2005 ) and publCIF (Westrip, 2010 ).

Supporting information

CCDC references: 2179420; 2179419

Crystal structure: contains datablocks I, II, global. DOI: https://doi.org/10.1107/S2056989022006338/pk2665sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2056989022006338/pk2665Isup2.hkl

Structure factors: contains datablock II. DOI: https://doi.org/10.1107/S2056989022006338/pk2665IIsup3.hkl

checkCIF report

Computing details top

Data collection: SMART (Bruker, 1999) for (I); DENZO/SCALEPACK (Otwinowski & Minor, 1997) for (II). Cell refinement: SAINT (Bruker, 1999) for (I); DENZO/SCALEPACK (Otwinowski & Minor, 1997) for (II). Data reduction: SAINT (Bruker, 1999) for (I); DENZO/SCALEPACK (Otwinowski & Minor, 1997) for (II). Program(s) used to solve structure: SHELXS (Sheldrick, 2008) for (I); SHELXS97 (Sheldrick, 2008) for (II). For both structures, program(s) used to refine structure: SHELXL2018/3 (Sheldrick, 2015); molecular graphics: ORTEP-3 for Windows (Farrugia, 2012) and ATOMS (Dowty, 2005); software used to prepare material for publication: SHELXL2018/3 (Sheldrick, 2015) and publCIF (Westrip, 2010).

Caesium decasodium tetrazirconium nonaarsenate (I) top

Crystal data top

CsNa₁₀Zr₄(AsO₄)₉	D_x = 3.476 Mg m⁻³
M_r = 1977.97	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3c:H	Cell parameters from 2999 reflections
a = 9.2218 (5) Å	θ = 2.6–30.8°
c = 76.982 (5) Å	µ = 10.07 mm⁻¹
V = 5669.6 (7) Å³	T = 293 K
Z = 6	Prism, colourless
F(000) = 5460	0.10 × 0.10 × 0.10 mm

Data collection top

Bruker SMART CCD diffractometer	1694 reflections with I > 2σ(I)
ω scans	θ_max = 32.5°, θ_min = 2.6°
Absorption correction: multi-scan (SADABS; Bruker, 1999)	h = −12→12
T_min = 0.350, T_max = 0.495	k = −13→13
2288 measured reflections	l = 0→114
2288 independent reflections

Refinement top

Refinement on F²	1 restraint
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F² > 2σ(F²)] = 0.040	w = 1/[σ²(F_o²) + (0.0452P)²] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.093	(Δ/σ)_max < 0.001
S = 1.00	Δρ_max = 1.85 e Å⁻³
2288 reflections	Δρ_min = −1.63 e Å⁻³
112 parameters

Special details top

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.

Refinement. Refined as a 2-component obverse/reverse twin.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Cs1	0.000000	0.000000	0.000000	0.0381 (2)
Na1	0.3350 (5)	0.0681 (4)	0.04049 (4)	0.0410 (9)	0.852 (5)
Na2	0.4054 (5)	0.333333	0.083333	0.0411 (13)	0.860 (9)
Na3	0.000000	0.000000	0.05355 (8)	0.0321 (17)	0.731 (12)
Na4	0.666667	0.333333	0.06014 (12)	0.021 (2)	0.423 (11)
Zr1	0.333333	0.666667	0.05681 (2)	0.01237 (15)
Zr2	0.333333	0.666667	−0.00666 (2)	0.01204 (15)
As1	0.34556 (6)	0.39774 (6)	0.02640 (2)	0.01350 (11)
As2	0.666667	0.73010 (9)	0.083333	0.0309 (2)
O1	0.1757 (5)	0.2319 (4)	0.03370 (5)	0.0251 (8)
O2	0.3084 (5)	0.4671 (5)	0.00779 (5)	0.0251 (8)
O3	0.4373 (5)	0.5591 (4)	0.04062 (5)	0.0192 (7)
O4	0.4946 (5)	0.3445 (5)	0.02328 (5)	0.0217 (8)
O5	0.5457 (5)	0.7825 (5)	0.07152 (5)	0.0234 (8)
O6A	0.603 (2)	0.5691 (13)	0.09411 (18)	0.036 (5)	0.45 (3)
O6B	0.5238 (19)	0.5873 (11)	0.09900 (16)	0.034 (4)	0.55 (3)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Cs1	0.0436 (4)	0.0436 (4)	0.0271 (4)	0.02182 (18)	0.000	0.000
Na1	0.072 (2)	0.0286 (15)	0.0375 (16)	0.0369 (17)	−0.0102 (17)	−0.0033 (13)
Na2	0.0307 (18)	0.0138 (18)	0.073 (3)	0.0069 (9)	−0.0044 (10)	−0.009 (2)
Na3	0.0216 (19)	0.0216 (19)	0.053 (4)	0.0108 (9)	0.000	0.000
Na4	0.015 (3)	0.015 (3)	0.034 (5)	0.0074 (14)	0.000	0.000
Zr1	0.0109 (2)	0.0109 (2)	0.0153 (3)	0.00546 (10)	0.000	0.000
Zr2	0.0109 (2)	0.0109 (2)	0.0144 (3)	0.00543 (10)	0.000	0.000
As1	0.0135 (2)	0.0114 (2)	0.0162 (2)	0.00670 (18)	0.00020 (18)	0.00004 (18)
As2	0.0460 (5)	0.0276 (3)	0.0254 (4)	0.0230 (3)	−0.0191 (4)	−0.0095 (2)
O1	0.0227 (19)	0.0166 (17)	0.029 (2)	0.0041 (15)	0.0059 (16)	0.0051 (16)
O2	0.029 (2)	0.0199 (18)	0.0268 (19)	0.0131 (17)	−0.0026 (17)	0.0055 (16)
O3	0.0199 (17)	0.0165 (16)	0.0220 (17)	0.0097 (14)	0.0002 (15)	−0.0050 (15)
O4	0.0246 (19)	0.0293 (19)	0.0227 (18)	0.0219 (17)	0.0003 (15)	−0.0034 (17)
O5	0.0178 (17)	0.028 (2)	0.0252 (18)	0.0123 (16)	−0.0095 (15)	−0.0076 (17)
O6A	0.034 (8)	0.024 (5)	0.034 (6)	0.001 (4)	−0.010 (6)	0.003 (4)
O6B	0.032 (7)	0.021 (4)	0.032 (5)	0.000 (4)	−0.014 (5)	0.004 (4)

Geometric parameters (Å, º) top

Cs1—O1ⁱ	3.235 (4)	Na4—O6A^vi	2.694 (17)
Cs1—O1ⁱⁱ	3.235 (4)	Na4—O6A^xii	2.694 (17)
Cs1—O1ⁱⁱⁱ	3.235 (4)	Zr1—O5	2.041 (3)
Cs1—O1	3.235 (4)	Zr1—O5^xiii	2.041 (3)
Cs1—O1^iv	3.235 (4)	Zr1—O5^ix	2.041 (3)
Cs1—O1^v	3.235 (4)	Zr1—O3^ix	2.099 (3)
Na1—O6B^vi	2.193 (9)	Zr1—O3^xiii	2.099 (3)
Na1—O3^vii	2.394 (5)	Zr1—O3	2.099 (3)
Na1—O1^v	2.482 (5)	Zr2—O2^xiii	2.062 (4)
Na1—O6A^vi	2.485 (16)	Zr2—O2^ix	2.062 (4)
Na1—O4	2.582 (5)	Zr2—O2	2.062 (4)
Na1—O1	2.632 (5)	Zr2—O4^xiv	2.081 (3)
Na2—O6A	2.185 (10)	Zr2—O4^iv	2.081 (3)
Na2—O6A^vi	2.185 (10)	Zr2—O4^xv	2.081 (3)
Na2—O6B	2.361 (12)	As1—O1	1.647 (4)
Na2—O6B^vi	2.361 (12)	As1—O2	1.673 (4)
Na2—O5^viii	2.495 (5)	As1—O4	1.691 (3)
Na2—O5^ix	2.495 (5)	As1—O3	1.694 (4)
Na3—O1ⁱⁱ	2.463 (5)	As2—O6A	1.538 (10)
Na3—O1	2.463 (5)	As2—O6A^xii	1.538 (10)
Na3—O1^v	2.463 (5)	As2—O5^xii	1.686 (4)
Na3—O6B^viii	2.47 (2)	As2—O5	1.686 (4)
Na3—O6B^x	2.47 (2)	As2—O6B	1.786 (13)
Na3—O6B^vi	2.47 (2)	As2—O6B^xii	1.786 (13)
Na4—O6A^xi	2.694 (17)	O6A—O6B	0.909 (13)

O1ⁱ—Cs1—O1ⁱⁱ	180.0 (3)	O5^xiii—Zr1—O3^ix	87.67 (16)
O1ⁱ—Cs1—O1ⁱⁱⁱ	62.30 (10)	O5^ix—Zr1—O3^ix	91.79 (15)
O1ⁱⁱ—Cs1—O1ⁱⁱⁱ	117.70 (10)	O5—Zr1—O3^xiii	87.66 (16)
O1ⁱ—Cs1—O1	117.70 (10)	O5^xiii—Zr1—O3^xiii	91.79 (15)
O1ⁱⁱ—Cs1—O1	62.30 (10)	O5^ix—Zr1—O3^xiii	176.01 (15)
O1ⁱⁱⁱ—Cs1—O1	180.00 (9)	O3^ix—Zr1—O3^xiii	88.35 (14)
O1ⁱ—Cs1—O1^iv	62.30 (10)	O5—Zr1—O3	91.79 (15)
O1ⁱⁱ—Cs1—O1^iv	117.70 (10)	O5^xiii—Zr1—O3	176.01 (15)
O1ⁱⁱⁱ—Cs1—O1^iv	62.30 (10)	O5^ix—Zr1—O3	87.67 (16)
O1—Cs1—O1^iv	117.70 (10)	O3^ix—Zr1—O3	88.35 (14)
O1ⁱ—Cs1—O1^v	117.70 (10)	O3^xiii—Zr1—O3	88.35 (14)
O1ⁱⁱ—Cs1—O1^v	62.30 (10)	O2^xiii—Zr2—O2^ix	93.66 (15)
O1ⁱⁱⁱ—Cs1—O1^v	117.70 (10)	O2^xiii—Zr2—O2	93.66 (15)
O1—Cs1—O1^v	62.30 (10)	O2^ix—Zr2—O2	93.66 (15)
O1^iv—Cs1—O1^v	180.00 (16)	O2^xiii—Zr2—O4^xiv	92.00 (16)
O6B^vi—Na1—O3^vii	104.6 (4)	O2^ix—Zr2—O4^xiv	88.01 (15)
O6B^vi—Na1—O1^v	93.4 (5)	O2—Zr2—O4^xiv	173.98 (15)
O3^vii—Na1—O1^v	87.41 (15)	O2^xiii—Zr2—O4^iv	173.98 (15)
O6B^vi—Na1—O6A^vi	21.3 (3)	O2^ix—Zr2—O4^iv	92.00 (16)
O3^vii—Na1—O6A^vi	90.3 (4)	O2—Zr2—O4^iv	88.01 (15)
O1^v—Na1—O6A^vi	108.7 (4)	O4^xiv—Zr2—O4^iv	86.15 (14)
O6B^vi—Na1—O4	118.5 (3)	O2^xiii—Zr2—O4^xv	88.01 (15)
O3^vii—Na1—O4	119.01 (18)	O2^ix—Zr2—O4^xv	173.98 (15)
O1^v—Na1—O4	127.39 (17)	O2—Zr2—O4^xv	92.01 (16)
O6A^vi—Na1—O4	115.1 (3)	O4^xiv—Zr2—O4^xv	86.15 (14)
O6B^vi—Na1—O1	85.3 (5)	O4^iv—Zr2—O4^xv	86.15 (14)
O3^vii—Na1—O1	165.74 (19)	O1—As1—O2	111.5 (2)
O1^v—Na1—O1	81.68 (19)	O1—As1—O4	108.17 (19)
O6A^vi—Na1—O1	101.8 (5)	O2—As1—O4	109.94 (19)
O4—Na1—O1	62.47 (13)	O1—As1—O3	114.88 (19)
O6B^vi—Na1—O4^vii	132.4 (6)	O2—As1—O3	108.98 (18)
O3^vii—Na1—O4^vii	58.02 (13)	O4—As1—O3	103.03 (18)
O1^v—Na1—O4^vii	125.80 (15)	O6A—As2—O6A^xii	78.4 (18)
O6A^vi—Na1—O4^vii	111.4 (6)	O6A—As2—O5^xii	112.1 (4)
O4—Na1—O4^vii	61.11 (16)	O6A^xii—As2—O5^xii	125.4 (7)
O1—Na1—O4^vii	122.35 (15)	O6A—As2—O5	125.4 (7)
O6A—Na2—O6A^vi	140.7 (13)	O6A^xii—As2—O5	112.1 (4)
O6A—Na2—O6B	22.7 (4)	O5^xii—As2—O5	103.8 (3)
O6A^vi—Na2—O6B	161.0 (11)	O6A—As2—O6B	30.6 (6)
O6A—Na2—O6B^vi	161.0 (11)	O6A^xii—As2—O6B	106.8 (15)
O6A^vi—Na2—O6B^vi	22.7 (4)	O5^xii—As2—O6B	103.3 (4)
O6B—Na2—O6B^vi	176.2 (9)	O5—As2—O6B	103.1 (5)
O6A—Na2—O5^viii	118.7 (7)	O6A—As2—O6B^xii	106.8 (15)
O6A^vi—Na2—O5^viii	95.2 (5)	O6A^xii—As2—O6B^xii	30.6 (6)
O6B—Na2—O5^viii	96.8 (5)	O5^xii—As2—O6B^xii	103.0 (5)
O6B^vi—Na2—O5^viii	79.9 (4)	O5—As2—O6B^xii	103.2 (4)
O6A—Na2—O5^ix	95.2 (5)	O6B—As2—O6B^xii	136.7 (12)
O6A^vi—Na2—O5^ix	118.7 (7)	As1—O1—Na3	157.7 (2)
O6B—Na2—O5^ix	79.9 (4)	As1—O1—Na1ⁱⁱ	117.0 (2)
O6B^vi—Na2—O5^ix	96.8 (5)	Na3—O1—Na1ⁱⁱ	74.73 (13)
O5^viii—Na2—O5^ix	64.2 (2)	As1—O1—Na1	93.24 (18)
O6A—Na2—O6A^vii	113.6 (6)	Na3—O1—Na1	72.10 (12)
O6A^vi—Na2—O6A^vii	40.3 (6)	Na1ⁱⁱ—O1—Na1	146.6 (2)
O6B—Na2—O6A^vii	124.1 (3)	As1—O1—Cs1	105.65 (17)
O6B^vi—Na2—O6A^vii	58.3 (4)	Na3—O1—Cs1	91.66 (16)
O5^viii—Na2—O6A^vii	92.7 (2)	Na1ⁱⁱ—O1—Cs1	93.89 (14)
O5^ix—Na2—O6A^vii	149.8 (3)	Na1—O1—Cs1	91.09 (13)
O6A—Na2—O6A^xii	40.3 (6)	As1—O2—Zr2	148.2 (2)
O6A^vi—Na2—O6A^xii	113.6 (6)	As1—O3—Zr1	130.8 (2)
O6B—Na2—O6A^xii	58.3 (5)	As1—O3—Na1^xvi	108.79 (18)
O6B^vi—Na2—O6A^xii	124.1 (3)	Zr1—O3—Na1^xvi	120.42 (18)
O5^viii—Na2—O6A^xii	149.8 (2)	As1—O4—Zr2^xv	148.4 (2)
O5^ix—Na2—O6A^xii	92.7 (2)	As1—O4—Na1	93.97 (17)
O6A^vii—Na2—O6A^xii	114.9 (5)	Zr2^xv—O4—Na1	109.81 (17)
O1ⁱⁱ—Na3—O1	85.6 (2)	As1—O4—Na1^xvi	87.30 (16)
O1ⁱⁱ—Na3—O1^v	85.6 (2)	Zr2^xv—O4—Na1^xvi	96.88 (15)
O1—Na3—O1^v	85.6 (2)	Na1—O4—Na1^xvi	121.76 (18)
O1ⁱⁱ—Na3—O6B^viii	83.5 (2)	As2—O5—Zr1	138.4 (2)
O1—Na3—O6B^viii	87.5 (2)	As2—O5—Na2^xiii	95.98 (16)
O1^v—Na3—O6B^viii	167.5 (3)	Zr1—O5—Na2^xiii	124.11 (18)
O1ⁱⁱ—Na3—O6B^x	87.5 (2)	As2—O6A—Na2	118.8 (6)
O1—Na3—O6B^x	167.5 (3)	As2—O6A—Na1^vi	116.7 (8)
O1^v—Na3—O6B^x	83.5 (2)	Na2—O6A—Na1^vi	115.9 (6)
O6B^viii—Na3—O6B^x	102.1 (3)	As2—O6A—Na4^xi	147.0 (14)
O1ⁱⁱ—Na3—O6B^vi	167.5 (3)	Na2—O6A—Na4^xi	75.0 (4)
O1—Na3—O6B^vi	83.5 (2)	Na1^vi—O6A—Na4^xi	75.8 (3)
O1^v—Na3—O6B^vi	87.5 (2)	As2—O6A—Na2^xvi	83.8 (9)
O6B^viii—Na3—O6B^vi	102.1 (3)	Na2—O6A—Na2^xvi	106.0 (9)
O6B^x—Na3—O6B^vi	102.1 (3)	Na1^vi—O6A—Na2^xvi	109.3 (5)
O6A^xi—Na4—O6A^vi	108.1 (5)	Na4^xi—O6A—Na2^xvi	63.2 (5)
O6A^xi—Na4—O6A^xii	108.1 (5)	As2—O6B—Na1^vi	120.5 (5)
O6A^vi—Na4—O6A^xii	108.1 (5)	As2—O6B—Na2	101.0 (7)
O5—Zr1—O5^xiii	92.21 (16)	Na1^vi—O6B—Na2	120.8 (4)
O5—Zr1—O5^ix	92.21 (16)	As2—O6B—Na3^xvii	116.8 (7)
O5^xiii—Zr1—O5^ix	92.20 (16)	Na1^vi—O6B—Na3^xvii	79.9 (6)
O5—Zr1—O3^ix	176.01 (15)	Na2—O6B—Na3^xvii	118.3 (6)

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

Caesium decasodium tetrahafnium nonaarsenate (II) top

Crystal data top

CsNa₁₀Hf₄(AsO₄)₉	D_x = 4.152 Mg m⁻³
M_r = 2327.05	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3c:H	Cell parameters from 22894 reflections
a = 9.1795 (2) Å	θ = 2.9–27.5°
c = 76.527 (8) Å	µ = 20.25 mm⁻¹
V = 5584.5 (6) Å³	T = 120 K
Z = 6	Prism, colourless
F(000) = 6228	0.08 × 0.08 × 0.08 mm

Data collection top

Nonius KappaCCD diffractometer	1164 reflections with I > 2σ(I)
ω scans	R_int = 0.070
Absorption correction: multi-scan (SORTAV; Blessing, 1995)	θ_max = 27.5°, θ_min = 3.2°
T_min = 0.40, T_max = 0.50	h = −11→11
11660 measured reflections	k = −11→11
1434 independent reflections	l = −99→99

Refinement top

Refinement on F²	7 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F² > 2σ(F²)] = 0.032	w = 1/[σ²(F_o²) + (0.0359P)² + 136.7342P] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.078	(Δ/σ)_max = 0.008
S = 1.06	Δρ_max = 2.57 e Å⁻³
1434 reflections	Δρ_min = −2.00 e Å⁻³
107 parameters

Special details top

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Cs1	0.000000	0.000000	0.000000	0.0162 (3)
Na1	0.3354 (5)	0.0688 (5)	0.04043 (5)	0.0256 (11)	0.887 (7)
Na2	0.4061 (6)	0.333333	0.083333	0.0208 (15)*	0.846 (11)
Na3	0.000000	0.000000	0.05288 (11)	0.018 (2)	0.735 (16)
Na4	0.666667	0.333333	0.06123 (16)	0.002 (4)*	0.337 (14)
Hf1	0.333333	0.666667	0.05673 (2)	0.00710 (15)
Hf2	0.333333	0.666667	−0.00682 (2)	0.00611 (15)
As1	0.34520 (9)	0.39770 (9)	0.02639 (2)	0.00578 (18)
As2	0.666667	0.73244 (13)	0.083333	0.0205 (3)
O1	0.1730 (6)	0.2332 (6)	0.03369 (6)	0.0113 (11)
O2	0.3086 (6)	0.4663 (6)	0.00745 (6)	0.0109 (11)
O3	0.4389 (6)	0.5622 (6)	0.04043 (6)	0.0068 (10)
O4	0.4922 (6)	0.3405 (6)	0.02356 (6)	0.0097 (11)
O5	0.5461 (6)	0.7864 (6)	0.07152 (6)	0.0127 (11)
O6A	0.602 (2)	0.569 (2)	0.0942 (2)	0.008 (2)	0.35 (2)
O6B	0.5276 (16)	0.5861 (12)	0.09848 (14)	0.029 (4)	0.65 (2)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Cs1	0.0181 (4)	0.0181 (4)	0.0125 (5)	0.0091 (2)	0.000	0.000
Na1	0.049 (3)	0.014 (2)	0.023 (2)	0.023 (2)	−0.0094 (18)	−0.0012 (16)
Na3	0.002 (3)	0.002 (3)	0.049 (5)	0.0012 (13)	0.000	0.000
Hf1	0.00580 (19)	0.00580 (19)	0.0097 (3)	0.00290 (9)	0.000	0.000
Hf2	0.00499 (19)	0.00499 (19)	0.0084 (3)	0.00250 (9)	0.000	0.000
As1	0.0056 (4)	0.0037 (4)	0.0086 (3)	0.0027 (3)	0.0002 (3)	0.0002 (3)
As2	0.0312 (7)	0.0178 (4)	0.0170 (6)	0.0156 (4)	−0.0165 (5)	−0.0083 (3)
O1	0.007 (3)	0.007 (3)	0.015 (3)	0.000 (2)	0.001 (2)	0.001 (2)
O2	0.015 (3)	0.009 (3)	0.011 (2)	0.007 (2)	−0.003 (2)	0.000 (2)
O3	0.005 (2)	0.005 (2)	0.011 (2)	0.003 (2)	−0.0006 (19)	−0.0054 (19)
O4	0.010 (3)	0.013 (3)	0.010 (2)	0.010 (2)	0.002 (2)	0.000 (2)
O5	0.007 (3)	0.017 (3)	0.012 (2)	0.004 (2)	−0.006 (2)	−0.006 (2)
O6A	0.008 (2)	0.008 (2)	0.008 (2)	0.0042 (11)	0.00000 (10)	0.00000 (10)
O6B	0.030 (7)	0.021 (5)	0.022 (5)	0.003 (5)	−0.014 (5)	0.002 (4)

Geometric parameters (Å, º) top

Cs1—O1	3.218 (5)	Na4—O6A^vi	2.654 (18)
Cs1—O1ⁱ	3.218 (5)	Na4—O6A^xii	2.654 (18)
Cs1—O1ⁱⁱ	3.218 (5)	Hf1—O5^xiii	2.039 (5)
Cs1—O1ⁱⁱⁱ	3.218 (5)	Hf1—O5^ix	2.039 (5)
Cs1—O1^iv	3.218 (5)	Hf1—O5	2.039 (5)
Cs1—O1^v	3.218 (5)	Hf1—O3^ix	2.084 (4)
Na1—O6B^vi	2.212 (10)	Hf1—O3^xiii	2.084 (4)
Na1—O3^vii	2.377 (6)	Hf1—O3	2.084 (4)
Na1—O1ⁱⁱⁱ	2.443 (6)	Hf2—O2	2.051 (5)
Na1—O6A^vi	2.467 (17)	Hf2—O2^ix	2.052 (5)
Na1—O4	2.524 (6)	Hf2—O2^xiii	2.052 (5)
Na1—O1	2.649 (6)	Hf2—O4^xiv	2.077 (5)
Na1—O4^vii	2.972 (6)	Hf2—O4ⁱⁱ	2.077 (5)
Na2—O6A	2.170 (16)	Hf2—O4^xv	2.077 (5)
Na2—O6A^vi	2.170 (16)	As1—O1	1.644 (5)
Na2—O6B	2.320 (10)	As1—O2	1.680 (5)
Na2—O6B^vi	2.320 (10)	As1—O4	1.689 (5)
Na2—O5^viii	2.458 (7)	As1—O3	1.696 (4)
Na2—O5^ix	2.458 (7)	As2—O6A	1.552 (15)
Na3—O1^v	2.421 (7)	As2—O6A^xi	1.552 (15)
Na3—O1ⁱⁱⁱ	2.421 (7)	As2—O5	1.684 (5)
Na3—O1	2.421 (7)	As2—O5^xi	1.684 (5)
Na3—O6B^viii	2.534 (17)	As2—O6B	1.750 (11)
Na3—O6B^x	2.534 (17)	As2—O6B^xi	1.750 (11)
Na3—O6B^vi	2.534 (17)	O6A—O6B	0.842 (15)
Na4—O6A^xi	2.654 (18)

O1—Cs1—O1ⁱ	180.00 (19)	O5^ix—Hf1—O3	87.7 (2)
O1—Cs1—O1ⁱⁱ	117.59 (14)	O5—Hf1—O3	92.3 (2)
O1ⁱ—Cs1—O1ⁱⁱ	62.41 (14)	O3^ix—Hf1—O3	87.88 (18)
O1—Cs1—O1ⁱⁱⁱ	62.41 (14)	O3^xiii—Hf1—O3	87.88 (18)
O1ⁱ—Cs1—O1ⁱⁱⁱ	117.59 (14)	O2—Hf2—O2^ix	94.29 (18)
O1ⁱⁱ—Cs1—O1ⁱⁱⁱ	180.00 (19)	O2—Hf2—O2^xiii	94.29 (18)
O1—Cs1—O1^iv	117.59 (14)	O2^ix—Hf2—O2^xiii	94.28 (18)
O1ⁱ—Cs1—O1^iv	62.41 (14)	O2—Hf2—O4^xiv	92.38 (19)
O1ⁱⁱ—Cs1—O1^iv	62.41 (14)	O2^ix—Hf2—O4^xiv	173.05 (19)
O1ⁱⁱⁱ—Cs1—O1^iv	117.59 (14)	O2^xiii—Hf2—O4^xiv	87.19 (19)
O1—Cs1—O1^v	62.41 (14)	O2—Hf2—O4ⁱⁱ	87.18 (19)
O1ⁱ—Cs1—O1^v	117.59 (14)	O2^ix—Hf2—O4ⁱⁱ	92.38 (19)
O1ⁱⁱ—Cs1—O1^v	117.59 (14)	O2^xiii—Hf2—O4ⁱⁱ	173.05 (19)
O1ⁱⁱⁱ—Cs1—O1^v	62.41 (14)	O4^xiv—Hf2—O4ⁱⁱ	85.96 (19)
O1^iv—Cs1—O1^v	180.0 (3)	O2—Hf2—O4^xv	173.04 (19)
O6B^vi—Na1—O3^vii	103.8 (4)	O2^ix—Hf2—O4^xv	87.18 (19)
O6B^vi—Na1—O1ⁱⁱⁱ	94.4 (4)	O2^xiii—Hf2—O4^xv	92.38 (19)
O3^vii—Na1—O1ⁱⁱⁱ	86.5 (2)	O4^xiv—Hf2—O4^xv	85.96 (19)
O6B^vi—Na1—O6A^vi	19.8 (4)	O4ⁱⁱ—Hf2—O4^xv	85.96 (19)
O3^vii—Na1—O6A^vi	90.7 (5)	O1—As1—O2	110.9 (3)
O1ⁱⁱⁱ—Na1—O6A^vi	108.7 (5)	O1—As1—O4	108.0 (2)
O6B^vi—Na1—O4	118.4 (3)	O2—As1—O4	110.3 (2)
O3^vii—Na1—O4	119.4 (2)	O1—As1—O3	115.4 (2)
O1ⁱⁱⁱ—Na1—O4	127.6 (2)	O2—As1—O3	108.7 (2)
O6A^vi—Na1—O4	115.0 (4)	O4—As1—O3	103.3 (2)
O6B^vi—Na1—O1	86.1 (4)	O6A—As2—O6A^xi	78.0 (15)
O3^vii—Na1—O1	165.2 (2)	O6A—As2—O5	125.7 (7)
O1ⁱⁱⁱ—Na1—O1	81.7 (2)	O6A^xi—As2—O5	112.6 (6)
O6A^vi—Na1—O1	101.5 (5)	O6A—As2—O5^xi	112.6 (6)
O4—Na1—O1	62.78 (17)	O6A^xi—As2—O5^xi	125.7 (7)
O6B^vi—Na1—O4^vii	130.4 (5)	O5—As2—O5^xi	103.0 (3)
O3^vii—Na1—O4^vii	58.22 (16)	O6A—As2—O6B	28.8 (6)
O1ⁱⁱⁱ—Na1—O4^vii	126.1 (2)	O6A^xi—As2—O6B	104.5 (12)
O6A^vi—Na1—O4^vii	110.9 (5)	O5—As2—O6B	104.3 (5)
O4—Na1—O4^vii	61.4 (2)	O5^xi—As2—O6B	104.8 (4)
O1—Na1—O4^vii	123.09 (19)	O6A—As2—O6B^xi	104.5 (12)
O6A—Na2—O6A^vi	141.3 (12)	O6A^xi—As2—O6B^xi	28.8 (6)
O6A—Na2—O6B	21.3 (4)	O5—As2—O6B^xi	104.8 (4)
O6A^vi—Na2—O6B	160.8 (9)	O5^xi—As2—O6B^xi	104.3 (5)
O6A—Na2—O6B^vi	160.8 (9)	O6B—As2—O6B^xi	132.5 (10)
O6A^vi—Na2—O6B^vi	21.3 (4)	As1—O1—Na3	157.3 (3)
O6B—Na2—O6B^vi	177.8 (8)	As1—O1—Na1^v	118.2 (3)
O6A—Na2—O5^viii	118.4 (6)	Na3—O1—Na1^v	75.36 (17)
O6A^vi—Na2—O5^viii	94.8 (5)	As1—O1—Na1	91.9 (2)
O6B—Na2—O5^viii	97.9 (4)	Na3—O1—Na1	71.66 (16)
O6B^vi—Na2—O5^viii	80.2 (3)	Na1^v—O1—Na1	146.7 (3)
O6A—Na2—O5^ix	94.8 (5)	As1—O1—Cs1	105.5 (2)
O6A^vi—Na2—O5^ix	118.4 (6)	Na3—O1—Cs1	90.6 (2)
O6B—Na2—O5^ix	80.2 (3)	Na1^v—O1—Cs1	94.33 (17)
O6B^vi—Na2—O5^ix	97.9 (4)	Na1—O1—Cs1	90.47 (16)
O5^viii—Na2—O5^ix	64.8 (3)	As1—O2—Hf2	147.4 (3)
O1^v—Na3—O1ⁱⁱⁱ	87.0 (3)	As1—O3—Hf1	130.0 (3)
O1^v—Na3—O1	87.0 (3)	As1—O3—Na1^xvi	108.8 (2)
O1ⁱⁱⁱ—Na3—O1	87.0 (3)	Hf1—O3—Na1^xvi	121.1 (2)
O1^v—Na3—O6B^viii	84.6 (2)	As1—O4—Hf2^xiv	146.9 (3)
O1ⁱⁱⁱ—Na3—O6B^viii	170.0 (4)	As1—O4—Na1	95.3 (2)
O1—Na3—O6B^viii	87.2 (2)	Hf2^xiv—O4—Na1	110.6 (2)
O1^v—Na3—O6B^x	87.2 (2)	As1—O4—Na1^xvi	86.8 (2)
O1ⁱⁱⁱ—Na3—O6B^x	84.5 (2)	Hf2^xiv—O4—Na1^xvi	95.70 (19)
O1—Na3—O6B^x	170.0 (4)	Na1—O4—Na1^xvi	122.6 (2)
O6B^viii—Na3—O6B^x	100.3 (3)	As2—O5—Hf1	137.1 (3)
O1^v—Na3—O6B^vi	170.0 (4)	As2—O5—Na2^xiii	96.1 (2)
O1ⁱⁱⁱ—Na3—O6B^vi	87.2 (2)	Hf1—O5—Na2^xiii	125.3 (2)
O1—Na3—O6B^vi	84.6 (2)	As2—O6A—Na2	119.0 (8)
O6B^viii—Na3—O6B^vi	100.3 (3)	As2—O6A—Na1^vi	116.5 (9)
O6B^x—Na3—O6B^vi	100.3 (3)	Na2—O6A—Na1^vi	116.2 (7)
O6A^xi—Na4—O6A^vi	110.0 (4)	As2—O6A—Na4^xii	146.0 (12)
O6A^xi—Na4—O6A^xii	110.0 (4)	Na2—O6A—Na4^xii	74.0 (5)
O6A^vi—Na4—O6A^xii	110.0 (4)	Na1^vi—O6A—Na4^xii	77.5 (5)
O5^xiii—Hf1—O5^ix	92.17 (19)	As2—O6A—Na2^xvi	83.9 (8)
O5^xiii—Hf1—O5	92.17 (19)	Na2—O6A—Na2^xvi	105.6 (8)
O5^ix—Hf1—O5	92.17 (19)	Na1^vi—O6A—Na2^xvi	109.2 (6)
O5^xiii—Hf1—O3^ix	87.7 (2)	Na4^xii—O6A—Na2^xvi	62.2 (5)
O5^ix—Hf1—O3^ix	92.3 (2)	As2—O6B—Na1^vi	120.8 (5)
O5—Hf1—O3^ix	175.57 (19)	As2—O6B—Na2	103.8 (6)
O5^xiii—Hf1—O3^xiii	92.3 (2)	Na1^vi—O6B—Na2	120.7 (4)
O5^ix—Hf1—O3^xiii	175.56 (19)	As2—O6B—Na3^xvii	115.6 (6)
O5—Hf1—O3^xiii	87.7 (2)	Na1^vi—O6B—Na3^xvii	77.3 (5)
O3^ix—Hf1—O3^xiii	87.89 (18)	Na2—O6B—Na3^xvii	117.8 (5)
O5^xiii—Hf1—O3	175.56 (19)

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

Acknowledgements

We thank the EPSRC National Crystallography Service (University of Southampton) for the X-ray data collection for (II).

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