Crystal structures of two hydrous sodium potassium molybdates: Na₃K(MoO₄)₂(H₂O)₉ and NaK(MoO₄)(H₂O)

Single-crystals of the hydrated sodium potassium orthomolybdate phases Na₃K(MoO₄)₂(H₂O)₉, tris­odium potassium bis­(orthomolybdate) nona­hydrate, and NaK(MoO₄)(H₂O), sodium potassium orthomolybdate monohydrate, were obtained as by-products in a flux growth experiment aiming on the synthesis of silicates from the quaternary system Na₂O–K₂O–CaO–SiO₂. The asymmetric unit of Na₃K(MoO₄)₂(H₂O)₉ (space group P6₃/m, Z = 2) comprises one Na⁺ atom and one water mol­ecule on a mirror plane, one K⁺ atom on a 6 axis, one Mo⁶⁺ cation and one O atom on a threefold rotation axis, and one O atom and one water mol­ecule in general sites. The crystal structure is built from isolated MoO₄ tetra­hedra, which are linked by common corners to trimers containing three face-sharing Na(H₂O)₄O₂ octa­hedra. Linkage between the heteropolyhedral groups is provided by potassium cations, which are coordinated by six water mol­ecules in form of trigonal prisms. The resulting layers are located at z = 1/4 and z = 3/4, respectively. Intra- and inter-layer hydrogen bonds between the water mol­ecules and the oxygen atoms of the MoO₄ tetra­hedra consolidate the structure. The backbone of the crystal structure of NaK(MoO₄)(H₂O) (space group P2₁2₁2₁, Z = 4) is made from chains of edge-sharing Na(H₂O)₂O₄ octa­hedra running parallel [100], which are decorated by MoO₄ tetra­hedra via corner sharing. Neighbouring heteropolyhedral chains are linked by additional potassium cations, which are coordinated by seven oxygen ligands and one water mol­ecule. Moreover, intra- and inter-chain hydrogen bonds exist.

1. Chemical context

Oxidomolybdates offer the crystallographer a rich playground for structural investigations. This phenomenon can be attributed to the fact that the Mo atoms have the capacity to form covalent bonds with four, five or six oxygen atoms. The sharing of common oxygen atoms between the respective polyhedra facilitates the formation of larger negatively charged polyanions, including isolated groups, chains, and ultimately, three-dimensional frameworks (Krivovichev, 2009). Consequently, it is not unexpected that a multitude of molybdate structures have been documented in the present literature. If water mol­ecules are allowed to become incorporated, a further increase in the number of crystalline phases will be observed. In the event that the charge-compensating cations are restricted to group 1 elements, the current web version (5.5.0) of the Inorganic Crystal Structure Database (ICSD; Zagorac et al., 2019) contains a total of 153 entries of anhydrous plus another 41 entries of hydrous phases. Hydrous alkali molybdates have also some industrial applications. For example, sodium molybdate dihydrate is used in corrosion science to protect metal surfaces, as it is a non-oxidizing anodic inhibitor (Vukasovich & Farr, 1986; Milošev, 2024). It is also used as a micronutrient to remedy problems in crops due to low molybdenum concentration in soils (O'Neil, 2013).

To the best of the author's knowledge, only a few systematic investigations on the system Na₂MoO₄ – K₂MoO₄ – H₂O have been performed so far. Mirzoev et al. (2007, 2010) studied the phase relations at 298 and 323 K and observed the following compounds: Na₂(MoO₄)(H₂O)₂, Na₃K(MoO₄)₂, K₂(MoO₄) and Na₃K(MoO₄)₂(H₂O)₉. It was not possible to obtain the nona­hydrate during the crystallization experiments conducted at 323 K. The latter compound was already mentioned in an earlier publication by Klevtsova et al. (1990), even though no detailed information on the synthesis conditions were given. Notably, no further hydrous mixed sodium potassium molybdate was found. As (i) the crystal structure of Na₃K(MoO₄)₂(H₂O)₉ has not been reported or deposited in databases such as the ICSD, and (ii) the existence of a previously unknown phase with composition NaK(MoO₄)(H₂O) was observed in our experiments, a decision was taken to investigate both compounds using single-crystal X-ray diffraction in more detail.

2. Structural commentary

2.1. Na₃K(MoO₄)₂(H₂O)₉

Na₃K(MoO₄)₂(H₂O)₉ is isostructural with Na₃Rb(MoO₄)₂(H₂O)₉ (ICSD-entry no. 39293, based on the data published by Klevtsova et al., 1990) and Na₃K(WO₄)₂(H₂O)₉ (ICSD-entry no. 39294; Klevtsova et al., 1990). The compound crystallizes in the hexa­gonal space group P6₃/m. The unit cell contains two formula units. The structure comprises insular MoO₄ tetra­hedra (Fig. 1) occupying the Wyckoff-position 4f (site symmetry 3..). The Mo—O bond lengths range from 1.753 (3) to 1.768 (2) Å (Table 1). The distances between the Mo atoms and the three basal O2 atoms are slightly larger than the corresponding bond lengths to the apical O1 atom. The average value <Mo—O> = 1.764 Å is in perfect agreement with the value reported by Gagné & Hawthorne (2020) for hexa­valent Mo^[4] obtained from a bond-length dispersion analysis of more than 1700 individual bonds. The six O—Mo—O angles have values that are very close to the ideal tetra­hedral angle of 109.5°. The degree of tetra­hedral distortion can be qu­anti­fied using the following two parameters: quadratic elongation (QE) and angle variance (AV) (Robinson et al., 1971). The numerical values for these parameters reflect the very low degree of distortion: QE = 1.000 and AV = 0.14. The sodium cations are located on mirror planes perpendicular to [001] (Wyckoff-position 6h) and are octa­hedrally coordinated by four water mol­ecules and two oxygen atoms belonging to two symmetry-equivalent MoO₄ units (Fig. 2). Three adjacent octa­hedra form a Na₃O₂(H₂O)₉ group, in which two faces of each octa­hedron are shared by the other two octa­hedra belonging to the same trimer (Fig. 3). The faces are defined by two O1 atoms and one O3W mol­ecule. Notably, the O1–O1 edge is a common element of all three faces. The barycentres of the group (site symmetry ), located at the midpoint of the central O1–O1 edge, have the fractional coordinates of 1/3 2/3 1/4 and 2/3 1/3 3/4, respectively. As may be anti­cipated, the bonds between Na and the two terminal (unshared) O4W oxygen atoms of the Na(H₂O)₄O₂ octa­hedra are significantly shorter [2.343 (2) Å] than the corresponding bond lengths to the bridging O atoms of the group (average value = 2.416 Å). The corresponding distortion parameters have values of QE = 1.018 and AV = 64.18. The trimers are decorated by MoO₄ tetra­hedra on both sides sharing a common oxygen atom O1, which implies that the tetra­hedra point in opposite directions (Fig. 4). The resulting heteropolyhedral unit has the composition Na₃(H₂O)₉(MoO₄)₂. The potassium cations (Wyckoff-position 2a) are coordinated by six water mol­ecules (Fig. 5). The coordination polyhedron corresponds to a trigonal prism with site symmetry . A single K(H₂O)₆ prism shares three O4W–O4W edges with Na₃(H₂O)₉(MoO₄)₂ groups that are directly adjacent. Consequently, mixed-polyhedral layers are formed at z = 1/4 and z = 3/4 that are parallel to (001) (Fig. 6). Further linkage between the polyhedra is facilitated by hydrogen bonding. A projection of the whole structure parallel to [010] is shown in Fig. 7. Indeed, each of the three basal oxygen atoms (O2) of the tetra­hedra are acceptors of one inter-layer (O2⋯H42) and two intra-layer (O2⋯H41, O2⋯H3) hydrogen bonds (Table 2, Figs. 1 and 7). The two symmetry-equivalent hydrogen atoms associated with O3 connect the corresponding Na(H₂O)₄O₂ octa­hedra with two directly adjacent heteropolyhedral layers (Fig. 7). The range of distances between the relevant donors and acceptors is from 2.746 (2) to 2.913 (3) Å. Therefore, all hydrogen bonds can be classified as of medium strength (Steiner, 2002).

Table 1
Selected geometric parameters (Å, °) for Na₃K(MoO₄)₂(H₂O)₉

Mo—O1^i	1.753 (3)	Na—O1	2.418 (2)
Mo—O2^ii	1.7683 (16)	Na—O3W^v	2.437 (3)
Mo—O2	1.7683 (16)	K—O4W^vi	2.8381 (19)
Mo—O2^iii	1.7683 (16)	K—O4W^iv	2.8381 (19)
Na—O4W	2.343 (2)	K—O4W^vii	2.8381 (19)
Na—O4W^iv	2.343 (2)	K—O4W^viii	2.8381 (19)
Na—O3W	2.392 (3)	K—O4W	2.8381 (19)
Na—O1^v	2.418 (2)	K—O4W^ix	2.8381 (19)
O1^i—Mo—O2^ii	109.13 (6)	O3W—Na—O3W^v	157.63 (10)
O1^i—Mo—O2	109.13 (6)	O1^v—Na—O3W^v	81.06 (6)
O2^ii—Mo—O2	109.81 (6)	O1—Na—O3W^v	81.06 (6)
O1^i—Mo—O2^iii	109.13 (6)	O4W^vi—K—O4W^iv	131.88 (2)
O2^ii—Mo—O2^iii	109.81 (6)	O4W^vi—K—O4W^vii	70.73 (8)
O2—Mo—O2^iii	109.81 (6)	O4W^iv—K—O4W^vii	89.86 (6)
O4W—Na—O4W^iv	89.02 (10)	O4W^vi—K—O4W^viii	131.88 (2)
O4W—Na—O3W	94.79 (8)	O4W^iv—K—O4W^viii	89.86 (6)
O4W^iv—Na—O3W	94.79 (8)	O4W^vii—K—O4W^viii	89.86 (6)
O4W—Na—O1^v	175.15 (8)	O4W^vi—K—O4W	89.86 (5)
O4W^iv—Na—O1^v	94.84 (7)	O4W^iv—K—O4W	70.73 (8)
O3W—Na—O1^v	81.99 (6)	O4W^vii—K—O4W	131.88 (2)
O4W—Na—O1	94.84 (7)	O4W^viii—K—O4W	131.88 (2)
O4W^iv—Na—O1	175.15 (8)	O4W^vi—K—O4W^ix	89.85 (5)
O3W—Na—O1	81.99 (6)	O4W^iv—K—O4W^ix	131.88 (2)
O1^v—Na—O1	81.15 (11)	O4W^vii—K—O4W^ix	131.88 (2)
O4W—Na—O3W^v	101.09 (8)	O4W^viii—K—O4W^ix	70.73 (8)
O4W^iv—Na—O3W^v	101.09 (8)	O4W—K—O4W^ix	89.86 (6)
Symmetry codes: (i) ; (ii) ; (iii) ; (iv) ; (v) ; (vi) ; (vii) ; (viii) ; (ix) .

Table 2
Hydrogen-bond geometry (Å, °) for Na₃K(MoO₄)₂(H₂O)₉

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
O3W—H3⋯O2^x	0.85 (1)	1.94 (1)	2.793 (2)	174 (3)
O4W—H41⋯O2^xi	0.86 (1)	1.90 (1)	2.746 (2)	169 (3)
O4W—H42⋯O2^xii	0.86 (1)	2.07 (1)	2.913 (3)	168 (3)
Symmetry codes: (x) ; (xi) ; (xii) .

Figure 1 Single MoO4 tetra­hedron in Na3K(MoO4)2(H2O)9 and the hydrogen bonds (dashed black lines) involving the corresponding oxygen atoms. Molybdenum, oxygen and hydrogen atoms are shown in gray, red and white, respectively. Displacement ellipsoids are given at the 70% probability level except for H atoms, which are shown with an arbitrary radius. [Symmetry codes: (i) 1 − y, x − y + 1, z; (ii) −x + y, 1 − x, z; (iii) x − y, x, 1 − z; (iv) x, y, 1 + z; (v) y, −x + y, 1 − z; (vi) 1 − x, 1 − y, 1 − z; (vii) 1 − y, x − y + 1, 1 + z; (viii) x − y + 1, 1 + x, 1 − z; (ix) y, 1 − x + y, 1 − z; (x) −x + y, 1 − x, 1 + z; (xi) −x, 1 − y, 1 − z.]

Figure 2 Single Na(H2O)4O2 octa­hedron in Na3K(MoO4)2(H2O)9. Sodium, oxygen and hydrogen atoms are shown in yellow, red and white, respectively. Displacement ellipsoids are given at the 70% probability level except for H atoms, which are shown with an arbitrary radius. [Symmetry codes: (i) x, y, −z + ; (ii) −x + y, 1 − x, z.]

Figure 3 Side view of a single Na3O2(H2O)9 group in Na3K(MoO4)2(H2O)9 formed by the condensation of three face-sharing octa­hedra.

Figure 4 Side view of a single decorated Na3(H2O)9(MoO4)2 group in Na3K(MoO4)2(H2O)9 formed by the linkage to two MoO4 tetra­hedra on both sides. [Symmetry codes: (i) y, −x + y, 1 − z; (ii) 1 − x, 1 − y, z + ; (iii) 1 − x, 1 − y, 1 − z.]

Figure 5 Single K(H2O)6 prism in Na3K(MoO4)2(H2O)9. Potassium, oxygen and hydrogen atoms are shown in purple, red and white, respectively. Displacement ellipsoids are given at the 70% probability level except for H atoms, which are shown with an arbitrary radius. [Symmetry codes: (i) −x + y, −x, z; (ii) −y, x − y, z; (iii) −x + y, −x, −z + ; (iv) x, y, −z + ; (v) −y, x − y, −z + .]

Figure 6 Projection of a single heretopolyhedral layer at z = 3/4 in Na3K(MoO4)2(H2O)9 parallel to [001].

Figure 7 Projection of the whole crystal structure of Na3K(MoO4)2(H2O)9 parallel to [010]. Intra- and inter-layer hydrogen bonds are shown with black dashed lines. [Symmetry code: (i) 1 − x, −y, 1 − z.]

2.2. NaK(MoO₄)(H₂O)

NaK(MoO₄)(H₂O) crystallizes in the non-centrosymmetric ortho­rhom­bic space group P2₁2₁2₁ and comprises four formula units in the unit cell. The MoO₄ tetra­hedron (Fig. 8) shows Mo—O bond lengths between 1.754 (3) and 1.785 (3) Å (Table 3) with distortion parameters of QE = 1.0024 and AV = 9.0515. The spread and average value of the Mo—O bonds are consistent with the literature data (Gagné & Hawthorne, 2020). The sodium cations are coordinated by six ligands involving two water mol­ecules and four oxygen atoms (Fig. 9). The water mol­ecules are located in a trans position. Bond lengths within the Na(H₂O)₂O₄ unit range from 2.342 (3) to 2.453 (3) Å with distortion parameters of QE = 1.0129 and AV = 42.43. Adjacent octa­hedra share two trans edges to form chains running parallel [100] (Fig. 10). The corners of neighbouring octa­hedra (O1, O3) are linked via MoO₄ groups that assume a staggered configuration along the chain direction. The comparatively short O1–O3 edge of the attached rigid tetra­hedra acts as a clamp that induces a cooperative rotation/distortion of the octa­hedra. Additional MoO₄ tetra­hedra are connected to one of the vertices of the edge that is common to adjacent octa­hedra inside the chain. Again, the units adopt a staggered configuration when viewed along [100]. The resulting chemical composition of the heteropolyhedral chains corresponds to Na(MoO₄)₂(H₂O). Charge compensation is provided by potassium cations, which are incorporated in the voids between the chains. In more detail, each K⁺ ion is coordinated by eight next oxygen ligands including one water mol­ecule (Fig. 11). Up to 3.2 Å, the K—O bond lengths vary between 2.724 (3) and 3.198 (3) Å (average value: 2.897 Å). The <K—O> distance is in excellent agreement with the value of 2.894 Å reported by Gagné & Hawthorne (2016) for K^[8]. The hydrogen atoms of the water mol­ecule O5W form single hydrogen bonds with the oxygen atoms O2 and O3, respectively (Fig. 8, Table 4). The O3⋯H52 inter­action represents an intra-chain bond, whilst the corresponding O2⋯H51 hydrogen bond connects neighbouring heteropolyhedral chains. The donor–acceptor distances are indicative of hydrogen bonds of medium strength (Steiner, 2002). A projection of the whole crystal structure of NaK(MoO₄)(H₂O) is presented in Fig. 12.

Table 3
Selected geometric parameters (Å, °) for NaK(MoO₄)(H₂O)

Mo—O1	1.754 (3)	Na—O3^iii	2.453 (3)
Mo—O2	1.755 (3)	K—O1^vii	2.724 (3)
Mo—O4^i	1.767 (2)	K—O2	2.791 (3)
Mo—O3^ii	1.785 (3)	K—O3	2.798 (3)
Na—O5W^iii	2.342 (3)	K—O3^viii	2.840 (3)
Na—O4	2.352 (3)	K—O5W	2.919 (3)
Na—O1^iv	2.406 (3)	K—O4^i	2.930 (3)
Na—O5W^v	2.411 (3)	K—O2^ii	2.978 (3)
Na—O4^vi	2.442 (3)	K—O1^ii	3.198 (3)
O1—Mo—O2	107.95 (14)	O2—K—O3^viii	131.11 (8)
O1—Mo—O4^i	112.21 (13)	O3—K—O3^viii	139.67 (4)
O2—Mo—O4^i	105.53 (12)	O1^vii—K—O5W	75.74 (8)
O1—Mo—O3^ii	113.38 (12)	O2—K—O5W	168.15 (8)
O2—Mo—O3^ii	110.03 (14)	O3—K—O5W	79.82 (8)
O4^i—Mo—O3^ii	107.46 (14)	O3^viii—K—O5W	59.86 (7)
O5W^iii—Na—O4	91.84 (12)	O1^vii—K—O4^i	71.77 (8)
O5W^iii—Na—O1^iv	81.07 (10)	O2—K—O4^i	58.63 (8)
O4—Na—O1^iv	88.45 (11)	O3—K—O4^i	133.12 (9)
O5W^iii—Na—O5W^v	170.65 (10)	O3^viii—K—O4^i	81.38 (8)
O4—Na—O5W^v	93.93 (11)	O5W—K—O4^i	132.68 (7)
O1^iv—Na—O5W^v	91.72 (10)	O1^vii—K—O2^ii	146.17 (9)
O5W^iii—Na—O4^vi	93.35 (11)	O2—K—O2^ii	81.77 (7)
O4—Na—O4^vi	170.77 (10)	O3—K—O2^ii	122.05 (8)
O1^iv—Na—O4^vi	84.82 (10)	O3^viii—K—O2^ii	69.32 (8)
O5W^v—Na—O4^vi	80.00 (11)	O5W—K—O2^ii	100.67 (8)
O5W^iii—Na—O3^iii	99.81 (10)	O4^i—K—O2^ii	88.47 (8)
O4—Na—O3^iii	86.15 (10)	O1^vii—K—O1^ii	142.92 (4)
O1^iv—Na—O3^iii	174.55 (13)	O2—K—O1^ii	104.43 (8)
O5W^v—Na—O3^iii	87.93 (10)	O3—K—O1^ii	73.36 (8)
O4^vi—Na—O3^iii	100.47 (11)	O3^viii—K—O1^ii	90.15 (9)
O1^vii—K—O2	108.71 (9)	O5W—K—O1^ii	68.64 (8)
O1^vii—K—O3	90.85 (10)	O4^i—K—O1^ii	142.43 (8)
O2—K—O3	89.04 (8)	O2^ii—K—O1^ii	54.56 (7)
O1^vii—K—O3^viii	80.51 (9)
Symmetry codes: (i) ; (ii) ; (iii) ; (iv) ; (v) ; (vi) ; (vii) ; (viii) .

Table 4
Hydrogen-bond geometry (Å, °) for NaK(MoO₄)(H₂O)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
O5W—H51⋯O2^viii	0.85 (1)	1.93 (2)	2.700 (4)	151 (4)
O5W—H52⋯O3^viii	0.85 (1)	2.05 (2)	2.874 (4)	163 (4)
Symmetry code: (viii) .

Figure 8 Single MoO4 tetra­hedron in NaK(MoO4)(H2O) and the hydrogen bonds (dashed black lines) involving the corresponding oxygen atoms. Molybdenum, oxygen and hydrogen atoms are shown in gray, red and white, respectively. Displacement ellipsoids are given at the 70% probability level except for H atoms, which are shown with an arbitrary radius. [Symmetry codes: (i) x, 1 − y, z; (ii) x − , −y + , 1 − z; (iii) 1 − x, y  + , −z + ; (iv) −x + , −y, z − .]

Figure 9 Single Na(H2O)2O4 octa­hedron in NaK(MoO4)(H2O). Sodium, oxygen and hydrogen atoms are shown in yellow, red and white, respectively. Displacement ellipsoids are given at the 70% probability level except for H atoms, which are shown with an arbitrary radius. [Symmetry codes: (i) −x + , 1 − y, z − ; (ii) −x + , 1 − y, z + ; (iii) 1 − x, y + , −z − ; (iv) x + , −y + , 1 − z.]

Figure 10 Side view of a heteropolyhedral Na(MoO4)2(H2O) chain in NaK(MoO4)(H2O).

Figure 11 Single coordination polyhedron for potassium in NaK(MoO4)(H2O). Potassium, oxygen and hydrogen atoms are shown in purple, red and white, respectively. [Symmetry codes: (i) −x + , −y, z + ; (ii) 1 − x, y − , −z + ; (iii) x, y − 1, z; (iv) x − , −y + , 1 − z.]

Figure 12 Projection of the whole crystal structure of NaK(MoO4)(H2O) parallel to [100]. Intra- and inter-chain hydrogen bonds are shown with black dashed lines. [Symmetry code: (i) -x + , −y, z + .]

2.3. Bond-valence sums

For both alkali molybdate hydrates, calculations of bond-valence sums (BVS) in valence units (v.u.) were performed using the parameter sets for Mo—O, Na—O and K—O listed by Brown & Altermatt (1985) to verify the correctness of the structure models. The BVS values for all atomic sites are summarized in Tables 5 and 6. The calculations were performed both with and without the contributions of the hydrogen atoms of the water mol­ecules. Following the suggestion of Hawthorne (1997), the effect of the hydrogen atoms has been taken into consideration by attributing 0.8 v.u. to the donor oxygen atom and 0.2 v.u. to the acceptor oxygen of the hydrogen bond. The results generally compare well with the expected values of 1.00 v.u. for K, 6.00 for Mo and 2.00 v.u. for O. However, it is noteworthy, that the sodium cations show slightly larger deviations from 1.00 v.u. (BVS values of 1.22 v.u.), indicating an overbonding; that is, the octa­hedral voids occupied by this type of alkali cation are slightly too small.

Table 5
Bond-valence sums for Na₃K(MoO₄)₂(H₂O)₉ in valence units (v.u.)

The values in parentheses for the oxygen atoms refer to the calculations when O—H and O⋯H contributions are taken into consideration (see text).

	Mo	Na	K	Sum
O1	1.516	0.190^×2↓×3→		2.087
O2	1.456^×3↓×1→			1.456 (2.056)
O3		0.203; 0.180		0.383 (1.983)
O4		0.232^×2↓×1→	0.148^×6↓×1→	0.380 (1.981)
Sum	5.884	1.227	0.890

Table 6
Bond valence sums for NaK(MoO₄)(H₂O) in valence units (v.u.)

The values in parentheses for the oxygen atoms refer to the calculations when O—H and O⋯H contributions are taken into consideration (see text).

	Mo	Na	K	Sum
O1	1.512	0.196	0.202; 0.056	1.966
O2	1.508		0.168; 0.102	1.778 (1.978)
O3	1.391	0.173	0.165; 0.148	1.877 (2.077)
O4	1.450	0.227; 0.178	0.116	1.980
O5		0.233; 0.193	0.119	0.545 (2.146)
Sum	5.871	1.200	1.076

2.4. Thermal expansion

Unfortunately, the crystals of Na₃K(MoO₄)₂(H₂O)₉ were not stable at ambient conditions for more than a couple of hours. Therefore, it was decided to determine the thermal expansion tensor only for NaK(MoO₄)(H₂O). For the data collection at 193 K, the crystal was mounted on a LithoLoop (Mol­ecular Dimensions) using a drop of Paratone-N oil (Hampton Research) and immersed in a cold air stream generated by an Oxford Cryosystems Desktop Cooler. The very same sample was then affixed to the tip of a glass fibre with fingernail hardener, in order to obtain data at 296 K. As the refined structural parameters of the room-temperature investigation are essentially identical to those of the low-temperature study, they will not be reported in detail. Instead, the focus will be on determining the thermal expansion tensor from the two sets of lattice parameters. Please refer to Table 7 for the respective values for 193 K. The corresponding values at ambient temperature are as follows: a = 6.4859 (7) Å, b = 8.1025 (8) Å, and c = 10.1835 (12) Å. The average thermal expansion tensor α_ij for a given temperature inter­val, ΔT, can be calculated from the thermal strain tensor ɛ_ij and the relationship α_{ij =} ɛ_ij/ΔT. Due to the ortho­rhom­bic symmetry restrictions, the off-diagonal terms of the symmetric second-rank tensor α_ij with i ≠ j must be strictly zero. The remaining three components can be obtained from the following expressions: ɛ₁₁ = (a/a₀) −1, ɛ₂₂ = (b/b₀) −1 and ɛ₃₃ = (c/c₀) −1. Notably, the lattice parameters with the suffix ‘zero' pertain to the low-tem­per­ature data. In consequence, the off-diagonal components have the following values: α₁₁ = 11 (1) × 10⁻⁶, α₂₂ = 39 (1) × 10⁻⁶, and α_{33 =} 42 (1) × 10⁻⁶. From the comparison of the numerical values it is obvious that the thermal expansion shows a pronounced anisotropy. The expansion along [100], that is, along the rigid chain-like building blocks of the crystal structure, is about a factor four smaller than along [010] and [001], respectively. Notably, α₂₂ and α₃₃ are equal within two standard deviations. By plotting the values of the thermal expansion tensor as a function of all directions one obtains a convenient geometric representation of the anisotropic behaviour of the tensor in the form of a surface in three-dimensional space (Fig. 13).

Table 7
Experimental details

	Na3K(MoO4)2(H2O)9	NaK(MoO4)(H2O)
Crystal data
Mr	590.09	240.04
Crystal system, space group	Hexagonal, P63/m	Orthorhombic, P212121
Temperature (K)	193	193
a, b, c (Å)	9.4974 (11), 9.4974 (11), 12.2139 (14)	6.4781 (8), 8.0697 (10), 10.1399 (13)
α, β, γ (°)	90, 90, 120	90, 90, 90
V (Å^3)	954.10 (19)	530.08 (11)
Z	2	4
Radiation type	Mo Kα	Mo Kα
μ (mm^−1)	1.67	3.27
Crystal size (mm)	0.43 × 0.09 × 0.06	0.18 × 0.14 × 0.06
Data collection
Diffractometer	Xcalibur, Ruby, Gemini ultra	Xcalibur, Ruby, Gemini ultra
Absorption correction	Analytical [CrysAlis PRO (Rigaku OD, 2020). Analytical numeric absorption correction using a multifaceted crystal model based on expressions derived by (Clark & Reid, 1995)]	Analytical [CrysAlis PRO (Rigaku OD, 2020). Analytical numeric absorption correction using a multifaceted crystal model based on expressions derived by (Clark & Reid, 1995)]
Tmin, Tmax	0.981, 0.995	0.738, 0.869
No. of measured, independent and observed [I > 2σ(I)] reflections	7218, 800, 697	3887, 1249, 1208
Rint	0.046	0.039
(sin θ/λ)max (Å^−1)	0.658	0.658
Refinement
R[F^2 > 2σ(F^2)], wR(F^2), S	0.022, 0.06, 1.09	0.024, 0.058, 1.07
No. of reflections	800	1249
No. of parameters	49	79
No. of restraints	5	3
H-atom treatment	H atoms treated by a mixture of independent and constrained refinement	H atoms treated by a mixture of independent and constrained refinement
Δρmax, Δρmin (e Å^−3)	1.16, −0.64	0.43, −0.87
Absolute structure	–	Flack (1983)
Absolute structure parameter	–	−0.01 (7)
Computer programs: CrysAlis PRO (Rigaku OD, 2020), SIR2004 (Burla et al., 2005), SHELXL97 (Sheldrick, 2008), VESTA-3 (Momma & Izumi, 2011) and WinGX (Farrugia, 2012).

Figure 13 Three-dimensional representation surface of the average thermal expansion tensor of NaK(MoO4)(H2O) in the inter­val between 193 and 296 K.

3. Database survey

As mentioned above, Na₃K(MoO₄)₂(H₂O)₉ is isotypic with the corresponding rubidium compound (Klevtsova et al., 1990). For the calculation of several qu­anti­tative descriptors for the characterization of the degree of similarity, the program COMPSTRU (de la Flor et al., 2016) was employed. After a transformation according to a′ = –b, b′ = –a, and c′ = –c the structure of Na₃Rb(MoO₄)₂(H₂O)₉ was transformed to the most similar configuration of Na₃K(MoO₄)₂(H₂O)₉. The calculations revealed the following displacements (in Å) between the corresponding atom pairs in both phases: Mo: 0.011; Na: 0.034; K: 0.000; O1: 0.011; O2: 0.040; O3: 0.063; O4: 0.124. The measure of similarity (Δ) as defined by Bergerhoff et al. (1999) has a value of 0.030. Notably, the most pronounced shifts occur between the oxygen atoms of the water mol­ecules surrounding the potassium cations. The degree of lattice distortion S is related to the spontaneous strain that can be obtained from a comparison of the unit-cell parameters of both phases. In more detail, it is the square root of the sum of the squared eigenvalues of the strain tensor divided by 3. For the given two structure descriptions, S has a value of 0.0075. To the best of the author's knowledge, the presence of the Na₃O₂(H₂O)₉ or more generally, M₃φ₁₁ units built on three octa­hedra sharing two faces, is rather an exception. According to Pauling's third rule (Pauling, 1929), shared faces between coordination polyhedra dramatically decreases the stability of a crystal structure. It is noteworthy, that one of the cesium suboxides contains equivalent anion-centred units with composition O₃Cs₁₁ (Simon et al., 1978).

NaK(MoO₄)(H₂O) represents a new structure type. Nevertheless, its characteristic ^[6]M(TO₄)₂φ chains (φ: H₂O, OH, F) have been already observed in a number of phosphate-, arsenate- and vanadate-based minerals including wherryite [Pb₇Cu₂(SO₄)₄(SiO₄)₂(OH)₂; Cooper & Haw­thorne, 1994] and brackebuschite [Pb₂(Mn³⁺,Fe³⁺)(VO₄)₂(OH); Foley et al., 1997], for example. Further representatives can be found in the review publications of Hawthorne (1998) and Lussier & Hawthorne (2021) on decorated and undecorated chains of edge-sharing octa­hedra. The present phase is the first pure molybdate member of this group of compounds. Further examples of low-hydrated mixed alkali hydrates containing sodium include NaLi(MoO₄)(H₂O)₂ (Makitova et al., 1990) and NaCs(MoO₄)(H₂O)₂ (Klevtsov et al., 1997). However, these two materials are structurally not related to the present compound. The first phase is composed of units of two Na(H₂O)₂O₄ octa­hedra and two Li(H₂O)₂O₃ tetra­gonal pyramids sharing common edges, which are linked by MoO₄ tetra­hedra. The structural backbones of the latter compound comprise chains of face-sharing Na(H₂O)₄O₂ octa­hedra, which are decorated with MoO₄ tetra­hedra. Only very recently, chemically related Na₂(MoO₄)(H₂O)₂, a synthetic compound with some relevance in industrial inorganic chemistry, has also been found in nature in a fumarole deposit of the Tolbachik volcano, Kamchatka, Russia. The new mineral was named natromolybdite (Pekov et al., 2025). It is possible, that a natural equivalent of synthetic NaK(MoO₄)(H₂O) can be found in similar petrographic environments. According to the present investigation, NaK(MoO₄)(H₂O) exhibits high solubility in water and crystallizes readily. This may provide an opportunity for the targeted growth of larger crystals of this acentric phase, which could be further studied for potential applications in nonlinear optics, for example.

4. Synthesis and crystallization

The two compounds were obtained as by-products in crystal growth experiments aimed at synthesizing silicates from the quaternary Na₂O–K₂O–CaO–SiO₂ system. A total of 0.5 g of the nutrient, composed of Na₂O:K₂O:CaO:SiO₂ in a molar ratio of 1:1:6:12, was thoroughly homogenized in an agate mortar with 2.5 g of a Na₂MoO₄–K₂MoO₄ fluxing agent (molar ratio 1:1). The sample was then heated in a covered platinum crucible from room temperature to 1373 K at a heating rate of 2 K min⁻¹. Following a three-day holding period at the maximum temperature, the sample was cooled to 1023 K at a rate of 0.1 K min⁻¹. The crucible was then removed and quenched in air to ambient conditions. Following mechanical removal of the melt cake, the silicate phases were separated by dissolving the flux in distilled water on a watch glass at 295 K and 43% relative humidity (RH). New crystals were formed spontaneously in the remaining solution, which had been saturated with alkali molybdates, through slow evaporation of the solvent over the course of several hours. The presence of two distinct birefringent phases was indicated by differences in morphology (laths, plates). This was subsequently confirmed by single-crystal diffraction experiments. Following exposure to air (295 K, 43% RH) for a period of several hours, the initially transparent lath-shaped crystals of phase 1 [Na₃K(MoO₄)₂(H₂O)₉] exhibited a transition in colour to an opaque hue, suggesting a gradual deterioration due to an ongoing dehydration process.

5. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 7. To prevent possible water release, data acquisitions were performed at 193 K. Unconstrained site-population refinements of the K/Na populations on the relevant sites under the assumption of full occupancy did not show any indications for cation substitutions between the alkali atoms and, therefore, the non-tetra­hedral cation positions were occupied with either Na or K, respectively. Difference-Fourier calculations were employed to reveal the positions of the hydrogen atoms. This procedure allowed the location of the hydrogen atoms of all water sites in the asymmetric units of both phases. The positional parameters of the H-atoms were further optimized by a riding model with water-mol­ecule geometries restrained by DFIX 0.86 0.01 commands for the O—H and DFIX 1.35 0.02 commands for the H⋯H distances (giving H—O—H angles close to 105°). The isotropic displacement parameters for the H atoms of the water mol­ecules were coupled to those of the corresponding oxygen atoms according to U_iso(H) = 1.2×U_eq(O). The Flack parameter of acentric NaK(MoO₄)(H₂O) indicates that the absolute structure has been determined correctly (Table 7).

Supporting information

Computing details

Trisodium potassium bis(orthomolybdate) nonahydrate (Na3KMoO42H2O9)

Crystal data

Na3K(MoO4)2(H2O)9	Dx = 2.054 Mg m^−3
Mr = 590.09	Mo Kα radiation, λ = 0.71073 Å
Hexagonal, P63/m	Cell parameters from 2517 reflections
Hall symbol: -P 6c	θ = 4.9–29.7°
a = 9.4974 (11) Å	µ = 1.67 mm^−1
c = 12.2139 (14) Å	T = 193 K
V = 954.10 (19) Å^3	Lath-shaped fragment, colourless
Z = 2	0.43 × 0.09 × 0.06 mm
F(000) = 580

Data collection

Xcalibur, Ruby, Gemini ultra diffractometer	800 independent reflections
Radiation source: fine-focus sealed X-ray tube, Enhance (Mo) X-ray Source	697 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.046
Detector resolution: 10.3575 pixels mm^-1	θmax = 27.9°, θmin = 3.3°
ω scans	h = −12→12
Absorption correction: analytical [CrysAlisPro (Rigaku OD, 2020). Analytical numeric absorption correction using a multifaceted crystal model based on expressions derived by (Clark & Reid, 1995)]	k = −11→12
Tmin = 0.981, Tmax = 0.995	l = −16→15
7218 measured reflections

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: mixed
R[F^2 > 2σ(F^2)] = 0.022	H atoms treated by a mixture of independent and constrained refinement
wR(F^2) = 0.06	w = 1/[σ^2(Fo^2) + (0.0297P)^2 + 0.6304P] where P = (Fo^2 + 2Fc^2)/3
S = 1.09	(Δ/σ)max = 0.001
800 reflections	Δρmax = 1.16 e Å^−3
49 parameters	Δρmin = −0.64 e Å^−3
5 restraints	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
Primary atom site location: structure-invariant direct methods	Extinction coefficient: 0.0051 (10)

Special details

Geometry. All s.u.'s (except the s.u. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell s.u.'s are taken into account individually in the estimation of s.u.'s in distances, angles and torsion angles; correlations between s.u.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell s.u.'s is used for estimating s.u.'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 > 2σ(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
Mo	0.33333	0.66667	0.97769 (2)	0.01574 (14)
Na	0.16850 (16)	0.45384 (16)	0.25	0.0222 (3)
K	0	0	0.25	0.0362 (3)
O1	0.33333	0.66667	0.1213 (2)	0.0190 (6)
O2	0.1881 (2)	0.4711 (2)	0.93025 (14)	0.0260 (4)
O3W	0.4008 (3)	0.4183 (3)	0.25	0.0275 (5)
H3	0.428 (3)	0.383 (3)	0.1942 (4)	0.033*
O4W	0.0281 (2)	0.2565 (2)	0.11551 (15)	0.0320 (4)
H41	−0.0704 (15)	0.236 (4)	0.110 (2)	0.038*
H42	0.074 (3)	0.307 (4)	0.0563 (16)	0.038*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Mo	0.01825 (16)	0.01825 (16)	0.0107 (2)	0.00912 (8)	0	0
Na	0.0222 (7)	0.0200 (6)	0.0219 (6)	0.0086 (5)	0	0
K	0.0325 (5)	0.0325 (5)	0.0438 (8)	0.0162 (2)	0	0
O1	0.0210 (9)	0.0210 (9)	0.0152 (13)	0.0105 (4)	0	0
O2	0.0277 (9)	0.0240 (9)	0.0233 (9)	0.0106 (7)	−0.0061 (7)	−0.0050 (7)
O3W	0.0396 (15)	0.0378 (14)	0.0172 (11)	0.0283 (13)	0	0
O4W	0.0249 (9)	0.0384 (11)	0.0281 (9)	0.0125 (9)	−0.0010 (8)	−0.0002 (8)

Geometric parameters (Å, º)

Mo—O1^i	1.753 (3)	Na—O1	2.418 (2)
Mo—O2^ii	1.7683 (16)	Na—O3W^v	2.437 (3)
Mo—O2	1.7683 (16)	K—O4W^vi	2.8381 (19)
Mo—O2^iii	1.7683 (16)	K—O4W^iv	2.8381 (19)
Na—O4W	2.343 (2)	K—O4W^vii	2.8381 (19)
Na—O4W^iv	2.343 (2)	K—O4W^viii	2.8381 (19)
Na—O3W	2.392 (3)	K—O4W	2.8381 (19)
Na—O1^v	2.418 (2)	K—O4W^ix	2.8381 (19)
O1^i—Mo—O2^ii	109.13 (6)	O3W—Na—O3W^v	157.63 (10)
O1^i—Mo—O2	109.13 (6)	O1^v—Na—O3W^v	81.06 (6)
O2^ii—Mo—O2	109.81 (6)	O1—Na—O3W^v	81.06 (6)
O1^i—Mo—O2^iii	109.13 (6)	O4W^vi—K—O4W^iv	131.88 (2)
O2^ii—Mo—O2^iii	109.81 (6)	O4W^vi—K—O4W^vii	70.73 (8)
O2—Mo—O2^iii	109.81 (6)	O4W^iv—K—O4W^vii	89.86 (6)
O4W—Na—O4W^iv	89.02 (10)	O4W^vi—K—O4W^viii	131.88 (2)
O4W—Na—O3W	94.79 (8)	O4W^iv—K—O4W^viii	89.86 (6)
O4W^iv—Na—O3W	94.79 (8)	O4W^vii—K—O4W^viii	89.86 (6)
O4W—Na—O1^v	175.15 (8)	O4W^vi—K—O4W	89.86 (5)
O4W^iv—Na—O1^v	94.84 (7)	O4W^iv—K—O4W	70.73 (8)
O3W—Na—O1^v	81.99 (6)	O4W^vii—K—O4W	131.88 (2)
O4W—Na—O1	94.84 (7)	O4W^viii—K—O4W	131.88 (2)
O4W^iv—Na—O1	175.15 (8)	O4W^vi—K—O4W^ix	89.85 (5)
O3W—Na—O1	81.99 (6)	O4W^iv—K—O4W^ix	131.88 (2)
O1^v—Na—O1	81.15 (11)	O4W^vii—K—O4W^ix	131.88 (2)
O4W—Na—O3W^v	101.09 (8)	O4W^viii—K—O4W^ix	70.73 (8)
O4W^iv—Na—O3W^v	101.09 (8)	O4W—K—O4W^ix	89.86 (6)

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

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O3W—H3···O2^x	0.85 (1)	1.94 (1)	2.793 (2)	174 (3)
O4W—H41···O2^xi	0.86 (1)	1.90 (1)	2.746 (2)	169 (3)
O4W—H42···O2^xii	0.86 (1)	2.07 (1)	2.913 (3)	168 (3)

Symmetry codes: (x) y, −x+y, −z+1; (xi) x−y, x, −z+1; (xii) x, y, z−1.

Sodium potassium orthomolybdate monohydrate (NaKMoO4H2O)

Crystal data

NaK(MoO4)(H2O)	F(000) = 456
Mr = 240.04	Dx = 3.008 Mg m^−3
Orthorhombic, P212121	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ac 2ab	Cell parameters from 1970 reflections
a = 6.4781 (8) Å	θ = 5.6–29.5°
b = 8.0697 (10) Å	µ = 3.27 mm^−1
c = 10.1399 (13) Å	T = 193 K
V = 530.08 (11) Å^3	Irregular fragment, colourless
Z = 4	0.18 × 0.14 × 0.06 mm

Data collection

Xcalibur, Ruby, Gemini ultra diffractometer	1249 independent reflections
Radiation source: fine-focus sealed X-ray tube, Enhance (Mo) X-ray Source	1208 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.039
Detector resolution: 10.3575 pixels mm^-1	θmax = 27.9°, θmin = 3.7°
ω scans	h = −8→8
Absorption correction: analytical [CrysAlisPro (Rigaku OD, 2020). Analytical numeric absorption correction using a multifaceted crystal model based on expressions derived by (Clark & Reid, 1995)]	k = −10→10
Tmin = 0.738, Tmax = 0.869	l = −13→13
3887 measured reflections

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: mixed
R[F^2 > 2σ(F^2)] = 0.024	H atoms treated by a mixture of independent and constrained refinement
wR(F^2) = 0.058	w = 1/[σ^2(Fo^2) + (0.0269P)^2] where P = (Fo^2 + 2Fc^2)/3
S = 1.07	(Δ/σ)max = 0.001
1249 reflections	Δρmax = 0.43 e Å^−3
79 parameters	Δρmin = −0.87 e Å^−3
3 restraints	Absolute structure: Flack (1983)
Primary atom site location: structure-invariant direct methods	Absolute structure parameter: −0.01 (7)

Special details

Geometry. All s.u.'s (except the s.u. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell s.u.'s are taken into account individually in the estimation of s.u.'s in distances, angles and torsion angles; correlations between s.u.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell s.u.'s is used for estimating s.u.'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 > 2σ(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
Mo	0.51460 (5)	0.11176 (3)	0.30697 (3)	0.00784 (10)
Na	0.7761 (2)	0.7544 (2)	0.48190 (14)	0.0127 (3)
K	0.49819 (15)	0.13919 (9)	0.65476 (8)	0.01524 (18)
O1	0.7135 (4)	0.1024 (4)	0.1899 (2)	0.0156 (6)
O2	0.5594 (5)	0.2846 (3)	0.4081 (2)	0.0181 (7)
O3	0.7634 (5)	0.3755 (4)	0.7646 (2)	0.0136 (6)
O4	0.5160 (5)	0.9389 (3)	0.4140 (2)	0.0140 (5)
O5W	0.4645 (5)	0.0528 (3)	0.9335 (2)	0.0131 (6)
H51	0.500 (6)	−0.022 (3)	0.987 (3)	0.016*
H52	0.376 (5)	0.009 (4)	0.883 (3)	0.016*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Mo	0.00733 (15)	0.00843 (15)	0.00776 (16)	−0.00002 (14)	0.00045 (13)	0.00036 (10)
Na	0.0095 (8)	0.0153 (7)	0.0133 (7)	−0.0015 (6)	−0.0009 (6)	−0.0002 (7)
K	0.0175 (4)	0.0158 (3)	0.0124 (4)	−0.0007 (4)	−0.0005 (4)	0.0013 (3)
O1	0.0144 (13)	0.0201 (15)	0.0122 (12)	0.0029 (13)	0.0035 (11)	0.0066 (15)
O2	0.0266 (19)	0.0115 (12)	0.0163 (13)	−0.0028 (12)	−0.0006 (13)	−0.0030 (11)
O3	0.0114 (14)	0.0158 (15)	0.0137 (13)	−0.0025 (12)	0.0026 (10)	0.0014 (13)
O4	0.0150 (15)	0.0122 (11)	0.0149 (11)	−0.0003 (13)	0.0007 (13)	0.0056 (10)
O5W	0.0136 (15)	0.0134 (12)	0.0121 (12)	−0.0022 (12)	−0.0044 (11)	0.0016 (10)

Geometric parameters (Å, º)

Mo—O1	1.754 (3)	Na—O3^iii	2.453 (3)
Mo—O2	1.755 (3)	K—O1^vii	2.724 (3)
Mo—O4^i	1.767 (2)	K—O2	2.791 (3)
Mo—O3^ii	1.785 (3)	K—O3	2.798 (3)
Na—O5W^iii	2.342 (3)	K—O3^viii	2.840 (3)
Na—O4	2.352 (3)	K—O5W	2.919 (3)
Na—O1^iv	2.406 (3)	K—O4^i	2.930 (3)
Na—O5W^v	2.411 (3)	K—O2^ii	2.978 (3)
Na—O4^vi	2.442 (3)	K—O1^ii	3.198 (3)
O1—Mo—O2	107.95 (14)	O2—K—O3^viii	131.11 (8)
O1—Mo—O4^i	112.21 (13)	O3—K—O3^viii	139.67 (4)
O2—Mo—O4^i	105.53 (12)	O1^vii—K—O5W	75.74 (8)
O1—Mo—O3^ii	113.38 (12)	O2—K—O5W	168.15 (8)
O2—Mo—O3^ii	110.03 (14)	O3—K—O5W	79.82 (8)
O4^i—Mo—O3^ii	107.46 (14)	O3^viii—K—O5W	59.86 (7)
O5W^iii—Na—O4	91.84 (12)	O1^vii—K—O4^i	71.77 (8)
O5W^iii—Na—O1^iv	81.07 (10)	O2—K—O4^i	58.63 (8)
O4—Na—O1^iv	88.45 (11)	O3—K—O4^i	133.12 (9)
O5W^iii—Na—O5W^v	170.65 (10)	O3^viii—K—O4^i	81.38 (8)
O4—Na—O5W^v	93.93 (11)	O5W—K—O4^i	132.68 (7)
O1^iv—Na—O5W^v	91.72 (10)	O1^vii—K—O2^ii	146.17 (9)
O5W^iii—Na—O4^vi	93.35 (11)	O2—K—O2^ii	81.77 (7)
O4—Na—O4^vi	170.77 (10)	O3—K—O2^ii	122.05 (8)
O1^iv—Na—O4^vi	84.82 (10)	O3^viii—K—O2^ii	69.32 (8)
O5W^v—Na—O4^vi	80.00 (11)	O5W—K—O2^ii	100.67 (8)
O5W^iii—Na—O3^iii	99.81 (10)	O4^i—K—O2^ii	88.47 (8)
O4—Na—O3^iii	86.15 (10)	O1^vii—K—O1^ii	142.92 (4)
O1^iv—Na—O3^iii	174.55 (13)	O2—K—O1^ii	104.43 (8)
O5W^v—Na—O3^iii	87.93 (10)	O3—K—O1^ii	73.36 (8)
O4^vi—Na—O3^iii	100.47 (11)	O3^viii—K—O1^ii	90.15 (9)
O1^vii—K—O2	108.71 (9)	O5W—K—O1^ii	68.64 (8)
O1^vii—K—O3	90.85 (10)	O4^i—K—O1^ii	142.43 (8)
O2—K—O3	89.04 (8)	O2^ii—K—O1^ii	54.56 (7)
O1^vii—K—O3^viii	80.51 (9)

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

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O5W—H51···O2^viii	0.85 (1)	1.93 (2)	2.700 (4)	151 (4)
O5W—H52···O3^viii	0.85 (1)	2.05 (2)	2.874 (4)	163 (4)

Symmetry code: (viii) −x+1, y−1/2, −z+3/2.