Flux syntheses and single-crystal structures of CsNa10 M 4(AsO4)9 (M = Zr, Hf).

The isostructural compounds caesium deca-sodium tetra-zirconium nona-arsenate, CsNa10Zr4(AsO4)9, and caesium deca-sodium tetra-hafnium nona-arsenate, 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 octa-hedra and AsO4 tetra-hedra 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 octa-hedral geometry and the coordination polyhedra of the partially occupied sodium ions are variously trigonal bipyramidal, tetra-hedral, square pyramidal and trigonal pyramidal. Site symmetries: Cs ; 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. © William T. A. Harrison 2022.

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 (ZrIV, HfIV, VIV, SnIV, SbV, Ga3+, Fe3+, Al3+, Cr3+…), phospho­rus (AsV, SiIV, GeIV) 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.

Structural commentary

Compounds (I) and (II) are isostructural and crystallize in the rhombohedral space group R 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 ZrIV and AsO4 3– moieties with a net charge of −11. The structure of (I) is completed by a Cs+ ion (site symmetry , 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)  − x,  − x + y,  − 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 ▸): r 6(ZrIV) = 0.72 (6 = six-coordinate) and r 6(HfIV) = 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 [M 2(XO4)3] (Abrahams & Bernstein, 1966 ▸), Nasicon [AM 2(XO4)3] (Anantharamulu et al., 2011 ▸) and langbeinite [A 2 M 2(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.

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.

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.

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 Cs1+xNa10-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 c:H	Trigonal, R 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[F 2 > 2σ(F 2)], wR(F 2), 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
Δρmax, Δρmin (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 ▸).

Crystal structure: contains datablock(s) I, II, global. DOI: 10.1107/S2056989022006338/pk2665sup1.cif

Structure factors: contains datablock(s) I. DOI: 10.1107/S2056989022006338/pk2665Isup2.hkl

Structure factors: contains datablock(s) II. DOI: 10.1107/S2056989022006338/pk2665IIsup3.hkl

CCDC references: 2179420, 2179419

Additional supporting information: crystallographic information; 3D view; checkCIF report

CsNa10Zr4(AsO4)9	Dx = 3.476 Mg m−3
Mr = 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

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

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(Fo2) + (0.0452P)2] where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.093	(Δ/σ)max < 0.001
S = 1.00	Δρmax = 1.85 e Å−3
2288 reflections	Δρmin = −1.63 e Å−3
112 parameters

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.

	x	y	z	Uiso*/Ueq	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)

	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)

Cs1—O1i	3.235 (4)	Na4—O6Avi	2.694 (17)
Cs1—O1ii	3.235 (4)	Na4—O6Axii	2.694 (17)
Cs1—O1iii	3.235 (4)	Zr1—O5	2.041 (3)
Cs1—O1	3.235 (4)	Zr1—O5xiii	2.041 (3)
Cs1—O1iv	3.235 (4)	Zr1—O5ix	2.041 (3)
Cs1—O1v	3.235 (4)	Zr1—O3ix	2.099 (3)
Na1—O6Bvi	2.193 (9)	Zr1—O3xiii	2.099 (3)
Na1—O3vii	2.394 (5)	Zr1—O3	2.099 (3)
Na1—O1v	2.482 (5)	Zr2—O2xiii	2.062 (4)
Na1—O6Avi	2.485 (16)	Zr2—O2ix	2.062 (4)
Na1—O4	2.582 (5)	Zr2—O2	2.062 (4)
Na1—O1	2.632 (5)	Zr2—O4xiv	2.081 (3)
Na2—O6A	2.185 (10)	Zr2—O4iv	2.081 (3)
Na2—O6Avi	2.185 (10)	Zr2—O4xv	2.081 (3)
Na2—O6B	2.361 (12)	As1—O1	1.647 (4)
Na2—O6Bvi	2.361 (12)	As1—O2	1.673 (4)
Na2—O5viii	2.495 (5)	As1—O4	1.691 (3)
Na2—O5ix	2.495 (5)	As1—O3	1.694 (4)
Na3—O1ii	2.463 (5)	As2—O6A	1.538 (10)
Na3—O1	2.463 (5)	As2—O6Axii	1.538 (10)
Na3—O1v	2.463 (5)	As2—O5xii	1.686 (4)
Na3—O6Bviii	2.47 (2)	As2—O5	1.686 (4)
Na3—O6Bx	2.47 (2)	As2—O6B	1.786 (13)
Na3—O6Bvi	2.47 (2)	As2—O6Bxii	1.786 (13)
Na4—O6Axi	2.694 (17)	O6A—O6B	0.909 (13)
O1i—Cs1—O1ii	180.0 (3)	O5xiii—Zr1—O3ix	87.67 (16)
O1i—Cs1—O1iii	62.30 (10)	O5ix—Zr1—O3ix	91.79 (15)
O1ii—Cs1—O1iii	117.70 (10)	O5—Zr1—O3xiii	87.66 (16)
O1i—Cs1—O1	117.70 (10)	O5xiii—Zr1—O3xiii	91.79 (15)
O1ii—Cs1—O1	62.30 (10)	O5ix—Zr1—O3xiii	176.01 (15)
O1iii—Cs1—O1	180.00 (9)	O3ix—Zr1—O3xiii	88.35 (14)
O1i—Cs1—O1iv	62.30 (10)	O5—Zr1—O3	91.79 (15)
O1ii—Cs1—O1iv	117.70 (10)	O5xiii—Zr1—O3	176.01 (15)
O1iii—Cs1—O1iv	62.30 (10)	O5ix—Zr1—O3	87.67 (16)
O1—Cs1—O1iv	117.70 (10)	O3ix—Zr1—O3	88.35 (14)
O1i—Cs1—O1v	117.70 (10)	O3xiii—Zr1—O3	88.35 (14)
O1ii—Cs1—O1v	62.30 (10)	O2xiii—Zr2—O2ix	93.66 (15)
O1iii—Cs1—O1v	117.70 (10)	O2xiii—Zr2—O2	93.66 (15)
O1—Cs1—O1v	62.30 (10)	O2ix—Zr2—O2	93.66 (15)
O1iv—Cs1—O1v	180.00 (16)	O2xiii—Zr2—O4xiv	92.00 (16)
O6Bvi—Na1—O3vii	104.6 (4)	O2ix—Zr2—O4xiv	88.01 (15)
O6Bvi—Na1—O1v	93.4 (5)	O2—Zr2—O4xiv	173.98 (15)
O3vii—Na1—O1v	87.41 (15)	O2xiii—Zr2—O4iv	173.98 (15)
O6Bvi—Na1—O6Avi	21.3 (3)	O2ix—Zr2—O4iv	92.00 (16)
O3vii—Na1—O6Avi	90.3 (4)	O2—Zr2—O4iv	88.01 (15)
O1v—Na1—O6Avi	108.7 (4)	O4xiv—Zr2—O4iv	86.15 (14)
O6Bvi—Na1—O4	118.5 (3)	O2xiii—Zr2—O4xv	88.01 (15)
O3vii—Na1—O4	119.01 (18)	O2ix—Zr2—O4xv	173.98 (15)
O1v—Na1—O4	127.39 (17)	O2—Zr2—O4xv	92.01 (16)
O6Avi—Na1—O4	115.1 (3)	O4xiv—Zr2—O4xv	86.15 (14)
O6Bvi—Na1—O1	85.3 (5)	O4iv—Zr2—O4xv	86.15 (14)
O3vii—Na1—O1	165.74 (19)	O1—As1—O2	111.5 (2)
O1v—Na1—O1	81.68 (19)	O1—As1—O4	108.17 (19)
O6Avi—Na1—O1	101.8 (5)	O2—As1—O4	109.94 (19)
O4—Na1—O1	62.47 (13)	O1—As1—O3	114.88 (19)
O6Bvi—Na1—O4vii	132.4 (6)	O2—As1—O3	108.98 (18)
O3vii—Na1—O4vii	58.02 (13)	O4—As1—O3	103.03 (18)
O1v—Na1—O4vii	125.80 (15)	O6A—As2—O6Axii	78.4 (18)
O6Avi—Na1—O4vii	111.4 (6)	O6A—As2—O5xii	112.1 (4)
O4—Na1—O4vii	61.11 (16)	O6Axii—As2—O5xii	125.4 (7)
O1—Na1—O4vii	122.35 (15)	O6A—As2—O5	125.4 (7)
O6A—Na2—O6Avi	140.7 (13)	O6Axii—As2—O5	112.1 (4)
O6A—Na2—O6B	22.7 (4)	O5xii—As2—O5	103.8 (3)
O6Avi—Na2—O6B	161.0 (11)	O6A—As2—O6B	30.6 (6)
O6A—Na2—O6Bvi	161.0 (11)	O6Axii—As2—O6B	106.8 (15)
O6Avi—Na2—O6Bvi	22.7 (4)	O5xii—As2—O6B	103.3 (4)
O6B—Na2—O6Bvi	176.2 (9)	O5—As2—O6B	103.1 (5)
O6A—Na2—O5viii	118.7 (7)	O6A—As2—O6Bxii	106.8 (15)
O6Avi—Na2—O5viii	95.2 (5)	O6Axii—As2—O6Bxii	30.6 (6)
O6B—Na2—O5viii	96.8 (5)	O5xii—As2—O6Bxii	103.0 (5)
O6Bvi—Na2—O5viii	79.9 (4)	O5—As2—O6Bxii	103.2 (4)
O6A—Na2—O5ix	95.2 (5)	O6B—As2—O6Bxii	136.7 (12)
O6Avi—Na2—O5ix	118.7 (7)	As1—O1—Na3	157.7 (2)
O6B—Na2—O5ix	79.9 (4)	As1—O1—Na1ii	117.0 (2)
O6Bvi—Na2—O5ix	96.8 (5)	Na3—O1—Na1ii	74.73 (13)
O5viii—Na2—O5ix	64.2 (2)	As1—O1—Na1	93.24 (18)
O6A—Na2—O6Avii	113.6 (6)	Na3—O1—Na1	72.10 (12)
O6Avi—Na2—O6Avii	40.3 (6)	Na1ii—O1—Na1	146.6 (2)
O6B—Na2—O6Avii	124.1 (3)	As1—O1—Cs1	105.65 (17)
O6Bvi—Na2—O6Avii	58.3 (4)	Na3—O1—Cs1	91.66 (16)
O5viii—Na2—O6Avii	92.7 (2)	Na1ii—O1—Cs1	93.89 (14)
O5ix—Na2—O6Avii	149.8 (3)	Na1—O1—Cs1	91.09 (13)
O6A—Na2—O6Axii	40.3 (6)	As1—O2—Zr2	148.2 (2)
O6Avi—Na2—O6Axii	113.6 (6)	As1—O3—Zr1	130.8 (2)
O6B—Na2—O6Axii	58.3 (5)	As1—O3—Na1xvi	108.79 (18)
O6Bvi—Na2—O6Axii	124.1 (3)	Zr1—O3—Na1xvi	120.42 (18)
O5viii—Na2—O6Axii	149.8 (2)	As1—O4—Zr2xv	148.4 (2)
O5ix—Na2—O6Axii	92.7 (2)	As1—O4—Na1	93.97 (17)
O6Avii—Na2—O6Axii	114.9 (5)	Zr2xv—O4—Na1	109.81 (17)
O1ii—Na3—O1	85.6 (2)	As1—O4—Na1xvi	87.30 (16)
O1ii—Na3—O1v	85.6 (2)	Zr2xv—O4—Na1xvi	96.88 (15)
O1—Na3—O1v	85.6 (2)	Na1—O4—Na1xvi	121.76 (18)
O1ii—Na3—O6Bviii	83.5 (2)	As2—O5—Zr1	138.4 (2)
O1—Na3—O6Bviii	87.5 (2)	As2—O5—Na2xiii	95.98 (16)
O1v—Na3—O6Bviii	167.5 (3)	Zr1—O5—Na2xiii	124.11 (18)
O1ii—Na3—O6Bx	87.5 (2)	As2—O6A—Na2	118.8 (6)
O1—Na3—O6Bx	167.5 (3)	As2—O6A—Na1vi	116.7 (8)
O1v—Na3—O6Bx	83.5 (2)	Na2—O6A—Na1vi	115.9 (6)
O6Bviii—Na3—O6Bx	102.1 (3)	As2—O6A—Na4xi	147.0 (14)
O1ii—Na3—O6Bvi	167.5 (3)	Na2—O6A—Na4xi	75.0 (4)
O1—Na3—O6Bvi	83.5 (2)	Na1vi—O6A—Na4xi	75.8 (3)
O1v—Na3—O6Bvi	87.5 (2)	As2—O6A—Na2xvi	83.8 (9)
O6Bviii—Na3—O6Bvi	102.1 (3)	Na2—O6A—Na2xvi	106.0 (9)
O6Bx—Na3—O6Bvi	102.1 (3)	Na1vi—O6A—Na2xvi	109.3 (5)
O6Axi—Na4—O6Avi	108.1 (5)	Na4xi—O6A—Na2xvi	63.2 (5)
O6Axi—Na4—O6Axii	108.1 (5)	As2—O6B—Na1vi	120.5 (5)
O6Avi—Na4—O6Axii	108.1 (5)	As2—O6B—Na2	101.0 (7)
O5—Zr1—O5xiii	92.21 (16)	Na1vi—O6B—Na2	120.8 (4)
O5—Zr1—O5ix	92.21 (16)	As2—O6B—Na3xvii	116.8 (7)
O5xiii—Zr1—O5ix	92.20 (16)	Na1vi—O6B—Na3xvii	79.9 (6)
O5—Zr1—O3ix	176.01 (15)	Na2—O6B—Na3xvii	118.3 (6)

CsNa10Hf4(AsO4)9	Dx = 4.152 Mg m−3
Mr = 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

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

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(Fo2) + (0.0359P)2 + 136.7342P] where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.078	(Δ/σ)max = 0.008
S = 1.06	Δρmax = 2.57 e Å−3
1434 reflections	Δρmin = −2.00 e Å−3
107 parameters

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.

	x	y	z	Uiso*/Ueq	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)

	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)

Cs1—O1	3.218 (5)	Na4—O6Avi	2.654 (18)
Cs1—O1i	3.218 (5)	Na4—O6Axii	2.654 (18)
Cs1—O1ii	3.218 (5)	Hf1—O5xiii	2.039 (5)
Cs1—O1iii	3.218 (5)	Hf1—O5ix	2.039 (5)
Cs1—O1iv	3.218 (5)	Hf1—O5	2.039 (5)
Cs1—O1v	3.218 (5)	Hf1—O3ix	2.084 (4)
Na1—O6Bvi	2.212 (10)	Hf1—O3xiii	2.084 (4)
Na1—O3vii	2.377 (6)	Hf1—O3	2.084 (4)
Na1—O1iii	2.443 (6)	Hf2—O2	2.051 (5)
Na1—O6Avi	2.467 (17)	Hf2—O2ix	2.052 (5)
Na1—O4	2.524 (6)	Hf2—O2xiii	2.052 (5)
Na1—O1	2.649 (6)	Hf2—O4xiv	2.077 (5)
Na1—O4vii	2.972 (6)	Hf2—O4ii	2.077 (5)
Na2—O6A	2.170 (16)	Hf2—O4xv	2.077 (5)
Na2—O6Avi	2.170 (16)	As1—O1	1.644 (5)
Na2—O6B	2.320 (10)	As1—O2	1.680 (5)
Na2—O6Bvi	2.320 (10)	As1—O4	1.689 (5)
Na2—O5viii	2.458 (7)	As1—O3	1.696 (4)
Na2—O5ix	2.458 (7)	As2—O6A	1.552 (15)
Na3—O1v	2.421 (7)	As2—O6Axi	1.552 (15)
Na3—O1iii	2.421 (7)	As2—O5	1.684 (5)
Na3—O1	2.421 (7)	As2—O5xi	1.684 (5)
Na3—O6Bviii	2.534 (17)	As2—O6B	1.750 (11)
Na3—O6Bx	2.534 (17)	As2—O6Bxi	1.750 (11)
Na3—O6Bvi	2.534 (17)	O6A—O6B	0.842 (15)
Na4—O6Axi	2.654 (18)
O1—Cs1—O1i	180.00 (19)	O5ix—Hf1—O3	87.7 (2)
O1—Cs1—O1ii	117.59 (14)	O5—Hf1—O3	92.3 (2)
O1i—Cs1—O1ii	62.41 (14)	O3ix—Hf1—O3	87.88 (18)
O1—Cs1—O1iii	62.41 (14)	O3xiii—Hf1—O3	87.88 (18)
O1i—Cs1—O1iii	117.59 (14)	O2—Hf2—O2ix	94.29 (18)
O1ii—Cs1—O1iii	180.00 (19)	O2—Hf2—O2xiii	94.29 (18)
O1—Cs1—O1iv	117.59 (14)	O2ix—Hf2—O2xiii	94.28 (18)
O1i—Cs1—O1iv	62.41 (14)	O2—Hf2—O4xiv	92.38 (19)
O1ii—Cs1—O1iv	62.41 (14)	O2ix—Hf2—O4xiv	173.05 (19)
O1iii—Cs1—O1iv	117.59 (14)	O2xiii—Hf2—O4xiv	87.19 (19)
O1—Cs1—O1v	62.41 (14)	O2—Hf2—O4ii	87.18 (19)
O1i—Cs1—O1v	117.59 (14)	O2ix—Hf2—O4ii	92.38 (19)
O1ii—Cs1—O1v	117.59 (14)	O2xiii—Hf2—O4ii	173.05 (19)
O1iii—Cs1—O1v	62.41 (14)	O4xiv—Hf2—O4ii	85.96 (19)
O1iv—Cs1—O1v	180.0 (3)	O2—Hf2—O4xv	173.04 (19)
O6Bvi—Na1—O3vii	103.8 (4)	O2ix—Hf2—O4xv	87.18 (19)
O6Bvi—Na1—O1iii	94.4 (4)	O2xiii—Hf2—O4xv	92.38 (19)
O3vii—Na1—O1iii	86.5 (2)	O4xiv—Hf2—O4xv	85.96 (19)
O6Bvi—Na1—O6Avi	19.8 (4)	O4ii—Hf2—O4xv	85.96 (19)
O3vii—Na1—O6Avi	90.7 (5)	O1—As1—O2	110.9 (3)
O1iii—Na1—O6Avi	108.7 (5)	O1—As1—O4	108.0 (2)
O6Bvi—Na1—O4	118.4 (3)	O2—As1—O4	110.3 (2)
O3vii—Na1—O4	119.4 (2)	O1—As1—O3	115.4 (2)
O1iii—Na1—O4	127.6 (2)	O2—As1—O3	108.7 (2)
O6Avi—Na1—O4	115.0 (4)	O4—As1—O3	103.3 (2)
O6Bvi—Na1—O1	86.1 (4)	O6A—As2—O6Axi	78.0 (15)
O3vii—Na1—O1	165.2 (2)	O6A—As2—O5	125.7 (7)
O1iii—Na1—O1	81.7 (2)	O6Axi—As2—O5	112.6 (6)
O6Avi—Na1—O1	101.5 (5)	O6A—As2—O5xi	112.6 (6)
O4—Na1—O1	62.78 (17)	O6Axi—As2—O5xi	125.7 (7)
O6Bvi—Na1—O4vii	130.4 (5)	O5—As2—O5xi	103.0 (3)
O3vii—Na1—O4vii	58.22 (16)	O6A—As2—O6B	28.8 (6)
O1iii—Na1—O4vii	126.1 (2)	O6Axi—As2—O6B	104.5 (12)
O6Avi—Na1—O4vii	110.9 (5)	O5—As2—O6B	104.3 (5)
O4—Na1—O4vii	61.4 (2)	O5xi—As2—O6B	104.8 (4)
O1—Na1—O4vii	123.09 (19)	O6A—As2—O6Bxi	104.5 (12)
O6A—Na2—O6Avi	141.3 (12)	O6Axi—As2—O6Bxi	28.8 (6)
O6A—Na2—O6B	21.3 (4)	O5—As2—O6Bxi	104.8 (4)
O6Avi—Na2—O6B	160.8 (9)	O5xi—As2—O6Bxi	104.3 (5)
O6A—Na2—O6Bvi	160.8 (9)	O6B—As2—O6Bxi	132.5 (10)
O6Avi—Na2—O6Bvi	21.3 (4)	As1—O1—Na3	157.3 (3)
O6B—Na2—O6Bvi	177.8 (8)	As1—O1—Na1v	118.2 (3)
O6A—Na2—O5viii	118.4 (6)	Na3—O1—Na1v	75.36 (17)
O6Avi—Na2—O5viii	94.8 (5)	As1—O1—Na1	91.9 (2)
O6B—Na2—O5viii	97.9 (4)	Na3—O1—Na1	71.66 (16)
O6Bvi—Na2—O5viii	80.2 (3)	Na1v—O1—Na1	146.7 (3)
O6A—Na2—O5ix	94.8 (5)	As1—O1—Cs1	105.5 (2)
O6Avi—Na2—O5ix	118.4 (6)	Na3—O1—Cs1	90.6 (2)
O6B—Na2—O5ix	80.2 (3)	Na1v—O1—Cs1	94.33 (17)
O6Bvi—Na2—O5ix	97.9 (4)	Na1—O1—Cs1	90.47 (16)
O5viii—Na2—O5ix	64.8 (3)	As1—O2—Hf2	147.4 (3)
O1v—Na3—O1iii	87.0 (3)	As1—O3—Hf1	130.0 (3)
O1v—Na3—O1	87.0 (3)	As1—O3—Na1xvi	108.8 (2)
O1iii—Na3—O1	87.0 (3)	Hf1—O3—Na1xvi	121.1 (2)
O1v—Na3—O6Bviii	84.6 (2)	As1—O4—Hf2xiv	146.9 (3)
O1iii—Na3—O6Bviii	170.0 (4)	As1—O4—Na1	95.3 (2)
O1—Na3—O6Bviii	87.2 (2)	Hf2xiv—O4—Na1	110.6 (2)
O1v—Na3—O6Bx	87.2 (2)	As1—O4—Na1xvi	86.8 (2)
O1iii—Na3—O6Bx	84.5 (2)	Hf2xiv—O4—Na1xvi	95.70 (19)
O1—Na3—O6Bx	170.0 (4)	Na1—O4—Na1xvi	122.6 (2)
O6Bviii—Na3—O6Bx	100.3 (3)	As2—O5—Hf1	137.1 (3)
O1v—Na3—O6Bvi	170.0 (4)	As2—O5—Na2xiii	96.1 (2)
O1iii—Na3—O6Bvi	87.2 (2)	Hf1—O5—Na2xiii	125.3 (2)
O1—Na3—O6Bvi	84.6 (2)	As2—O6A—Na2	119.0 (8)
O6Bviii—Na3—O6Bvi	100.3 (3)	As2—O6A—Na1vi	116.5 (9)
O6Bx—Na3—O6Bvi	100.3 (3)	Na2—O6A—Na1vi	116.2 (7)
O6Axi—Na4—O6Avi	110.0 (4)	As2—O6A—Na4xii	146.0 (12)
O6Axi—Na4—O6Axii	110.0 (4)	Na2—O6A—Na4xii	74.0 (5)
O6Avi—Na4—O6Axii	110.0 (4)	Na1vi—O6A—Na4xii	77.5 (5)
O5xiii—Hf1—O5ix	92.17 (19)	As2—O6A—Na2xvi	83.9 (8)
O5xiii—Hf1—O5	92.17 (19)	Na2—O6A—Na2xvi	105.6 (8)
O5ix—Hf1—O5	92.17 (19)	Na1vi—O6A—Na2xvi	109.2 (6)
O5xiii—Hf1—O3ix	87.7 (2)	Na4xii—O6A—Na2xvi	62.2 (5)
O5ix—Hf1—O3ix	92.3 (2)	As2—O6B—Na1vi	120.8 (5)
O5—Hf1—O3ix	175.57 (19)	As2—O6B—Na2	103.8 (6)
O5xiii—Hf1—O3xiii	92.3 (2)	Na1vi—O6B—Na2	120.7 (4)
O5ix—Hf1—O3xiii	175.56 (19)	As2—O6B—Na3xvii	115.6 (6)
O5—Hf1—O3xiii	87.7 (2)	Na1vi—O6B—Na3xvii	77.3 (5)
O3ix—Hf1—O3xiii	87.89 (18)	Na2—O6B—Na3xvii	117.8 (5)
O5xiii—Hf1—O3	175.56 (19)