New triple molybdates Cs₃LiCo₂(MoO₄)₄ and Rb₃LiZn₂(MoO₄)₄, filled derivatives of the Cs₆Zn₅(MoO₄)₈ type

Two new isotypic triple molybdates, namely tri­cesium lithium dicobalt tetra­kis­(tetra­oxo­molybdate), Cs₃LiCo₂(MoO₄)₄, and tri­rubidium lithium dizinc tetra­kis­(tetra­oxo­molybdate), Rb₃LiZn₂(MoO₄)₄, crystallize in the non-centrosymmetric cubic space group I3d and adopt the Cs₆Zn₅(MoO₄)₈ structure type. In the parent structure, the Zn positions have 5/6 occupancy, while they are fully occupied by statistically distributed M²⁺ and Li⁺ cations in the title compounds. In both structures, all corners of the (M_2/3Li_1/3)O₄ tetra­hedra (M = Co and Zn), having point symmetry , are shared with the MoO₄ tetra­hedra, which lie on threefold axes and share corners with three (M,Li)O₄ tetra­hedra to form open mixed frameworks. Large alkaline cations occupy distorted cubocta­hedral cavities with symmetry. The mixed tetra­hedral frameworks in the structures are close to those of mayenite (12CaO·7Al₂O₃) and the related compounds 11CaO·7Al₂O₃·CaF₂, wadalite (Ca₆Al₅Si₂O₁₆Cl₃) and Na₆Zn₃(AsO₄)₄·3H₂O, but the terminal vertices of the MoO₄ tetra­hedra are directed in opposite directions along the threefold axes compared with the configurations of Al(Si)O₄ or AsO₄ tetra­hedra. The cation arrangements in Cs₃LiCo₂(MoO₄)₄, Rb₃LiZn₂(MoO₄)₄ and Cs₆Zn₅(MoO₄)₈ repeat the structure of Y₃Au₃Sb₄, being stuffed derivatives of the Th₃P₄ type.

S1. Comment

Double molybdates of alkaline and bivalent ions formed in the systems A₂MoO₄–MMoO₄ (A = Li, Na, K, Rb and Cs; M = Mg, Mn, Fe, Co, Ni, Cu, Zn, Cd, Pb and Ba) have been well known for at least three decades, and some of them, such as K₄Zn(MoO₄)₃ and A₂Pb(MoO₄)₂ (A = K, Rb and Cs), may be used as ferroelastic and other inorganic materials (Solodovnikov et al., 1994). Most of the studied [or 'The most frequently studied'?] structures of these molybdates, for example, Li₂Ni₂(MoO₄)₃ (Ozima & Sato, 1977), K₂Zn₂(MoO₄)₃ (Gicquel-Mayer & Perez, 1975), K₂Ni(MoO₄)₂ (Klevtsova & Klevtsov, 1978) and Rb₂Cu₂(MoO₄)₃ (Solodovnikov & Solodovnikova, 1997), contain MO₆ octahedra and MoO₄ tetrahedra linked by the corners. Other O-atom coordinations of bivalent cations were found in the structures of Rb₄Mn(MoO₄)₃ and Cs₄Cu(MoO₄)₃ (Solodovnikov et al., 1988), with trigonal bipyramids around M²⁺ (M = Mn and Cu), and in K₄Zn(MoO₄)₃ (Gicquel-Mayer et al., 1980) and Cs₆Zn₅(MoO₄)₈ (Solodovnikov et al., 1987; Mueller et al., 1987), with ZnO₄ tetrahedra. The latter structure is unique among double salts with tetrahedral oxoanions and has an incomplete Zn position (site occupation factor = 5/6), leading to the formula Cs₃(Zn_5/6□_1/6)₃(MoO₄)₄, where □ denotes a cationic vacancy. The only triple molybdate known to date, which contains two monovalent cations along with a bivalent cation, viz. AgKCu₃(MoO₄)₄ (Szillat & Mūller-Buschbaum, 1995), has a crystal structure very close to that of K₂Cu₃(MoO₄)₄ (Glinskaya et al., 1980), with highly distorted CuO₆ octahedra. This paper presents the crystal structure determination of two new triple molybdates, Cs₃LiCo₂(MoO₄)₄, (I), and Rb₃LiZn₂(MoO₄)₄, (II), isolated upon studying the phase formation in the systems Cs₂MoO₄–Li₂MoO₄–CoMoO₄ and Rb₂MoO₄–Li₂MoO₄–ZnMoO₄.

In the title structures, the Li⁺ and M²⁺ (M = Co and Zn) cations are statistically distributed in the 12a Wyckoff position (site symmetry 4), whereas the Cs and Mo atoms occupy the 12b (site symmetry 4) and 16c (site symmetry 3) positions, respectively. Atoms, O1 and O2 are in the special 16c and general 48e positions, respectively, forming tetrahedral environments around the M,Li position and Mo atoms. Among molybdates, tetrahedral coordination of Co²⁺ is found for the first time. Metal–oxygen distances in the (M_2/3Li_1/3)O₄ tetrahedra (M = Co and Zn) are in a good agreement with the Co—O (1.967–1.980 Å) and Li—O (1.774–2.092 Å) bond lengths in β_II-Li₂CoSiO₄ (Yamaguchi et al., 1979) and the Zn—O (1.858–2.038 Å) bond lengths in K₄Zn(MoO₄)₃ (Gicquel-Mayer et al., 1980). In the Cs₆Zn₅(MoO₄)₈ structure (Solodovnikov et al., 1987; Mueller et al., 1987), the slightly increased Zn—O distances (1.98–2.00 Å) could be caused by the presence of vacancies in the Zn positions.

In the structures of (I) and (II), the (M_2/3Li_1/3)O₄ tetrahedra (M = Co and Zn) share all corners with the MoO₄ tetrahedra, which their three corners with the adjacent (M, Li)O₄ tetrahedra to form open mixed frameworks (Fig. 1). Characteristic details of the frameworks are the eight-membered rings of alternating (M_2/3Li_1/3)O₄ and MoO₄ tetrahedra (1–8 in Fig. 2). Each (M_2/3Li_1/3)O₄ tetrahedron takes part in four rings, whereas the MoO₄ tetrahedron connects three rings. The eight-membered ring together with four terminal MoO₄ tetrahedra (9–12 in Fig. 2) attached to the (M_2/3Li_1/3)O₄ tetrahedra form a cage around the large cations Cs⁺ or Rb⁺, having a distorted 12-fold cuboctahedral coordination.

Both compounds adopt the Cs₆Zn₅(MoO₄)₈ structure type (Solodovnikov et al., 1987; Mueller et al., 1987). Thus, (I) and (II) may be considered as completely filled derivatives of the Cs₆Zn₅(MoO₄)₈ structure following the scheme 5Zn²⁺ + □ → 4M²⁺ + 2Li⁺. It is interesting that the cation arrangements in these three compounds repeat the atomic arrangement of the Y₃Au₃Sb₄ structure (Dwight, 1977), being in turn a stuffed derivative of the Th₃P₄ type.

The mixed tetrahedral frameworks in (I), (II) and Cs₆Zn₅(MoO₄)₈ are close to those of mayenite (12CaO·7 A l₂O₃; Bartl & Scheller, 1970) and the related compounds 11CaO·7 A l₂O₃·CaF₂ (Williams, 1973), wadalite (Ca₆Al₅Si₂O₁₆Cl₃; Tsukimura et al., 1993) and Na₆Zn₃(AsO₄)₄·3H₂O (Grey et al., 1989). However, there is an important difference; the terminal vertices of the MoO₄ tetrahedra are oppositely directed along the threefold axes compared with the Al(Si)O₄ or AsO₄ tetrahedra. The latter arrangement substantially changes the configuration of the tetrahedral cage around the out-of-framework ions, instead providing three new inner sites occupied by two Ca²⁺ or Na⁺ cations, and O^2-, F^- or Cl^- anions or wer molecules.

S2. Experimental

Compounds (I) and (II) were revealed upon studying the systems Cs₂MoO₄–Li₂MoO₄–CoMoO₄ and Rb₂MoO₄–Li₂MoO₄–ZnMoO₄. Polycrystalline samples of the compounds were prepared by solid-state reactions from simple molybdates at 773 K for 150 h. Single crystals were grown by spontaneous crystallization of melted mixtures of Li₂MoO₄, Cs₂MoO₄, 2CoMoO₄ and 2Cs₂Mo₂O₇, and sintered Rb₃LiZn₂(MoO₄)₄ and 3Rb₂Mo₂O₇, upon slow cooling at rates of 3 K h^-1 in the ranges 873–673 K and 793–673 K, respectively. X-ray powder diffraction patterns of ground crystals of both compounds were consistent with their calculated powder diffractograms, experimental X-ray diffraction data for corresponding sintered samples and the powder pattern reported for Cs₆Zn₅(MoO₄)₈ (Solodovnikov et al., 1987). The crystals have the shapes of partly faceted fragments of a cubic habit with the maximum dimensions of 2 mm.

S3. Refinement

In both structures, the contents of the M,Li positions (M = Co and Zn) were accepted as 2/3M + 1/3Li taking into account their complete occupations and electroneutrality requirements in accordance with X-ray diffraction data for corresponding sintered samples.

Computing details

For both compounds, data collection: SMART or APEX2? (Bruker, 2004); cell refinement: SMART or APEX2?; data reduction: SAINT (Bruker, 2004); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: BS (Ozawa & Kang, 2004); software used to prepare material for publication: SHELXL97.

Figures

	Fig. 1. A view of the Cs3LiCo2(MoO4)4 structure.
	Fig. 2. The tetrahedral cage around the Cs atom in the Cs3LiCo2(MoO4)4 structure. An eight-membered ring is indicated by the tetrahedra labelled 1–8; attached tetrahedra are numbered 9–12.

(I) tricesium lithium dicobalt tetrakis(tetraoxomolybdate)

Crystal data

Cs3LiCo2(MoO4)4	Dx = 4.231 Mg m^−3
Mr = 1163.34	Mo Kα radiation, λ = 0.71073 Å
Cubic, I43d	Cell parameters from 2582 reflections
Hall symbol: I -4bd 2c 3	θ = 4.1–29.0°
a = 12.2239 (2) Å	µ = 10.40 mm^−1
V = 1826.54 (5) Å^3	T = 293 K
Z = 4	Fragment, blue
F(000) = 2072	0.11 × 0.10 × 0.01 mm

Data collection

Bruker-Nonius X8 APEX CCD diffractometer	705 independent reflections
Radiation source: fine-focus sealed X-ray tube	615 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.038
φ scans, frame data integration	θmax = 35.9°, θmin = 4.1°
Absorption correction: multi-scan (SADABS; Bruker, 2004)	h = −19→11
Tmin = 0.394, Tmax = 0.903	k = −19→19
8959 measured reflections	l = −19→12

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.018	w = 1/[σ^2(Fo^2) + (0.0203P)^2] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.038	(Δ/σ)max < 0.001
S = 0.99	Δρmax = 0.54 e Å^−3
705 reflections	Δρmin = −0.61 e Å^−3
20 parameters	Absolute structure: Flack (1983), 303 Friedel pairs
0 restraints	Absolute structure parameter: −0.002 (17)

Special details

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

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Cs	0.8750	0.0000	0.2500	0.03197 (10)
Mo	0.399978 (17)	0.399978 (17)	0.399978 (17)	0.01762 (7)
Co	0.6250	0.5000	0.2500	0.0216 (2)	0.666667
Li	0.6250	0.5000	0.2500	0.0216 (2)	0.333333
O1	0.31880 (16)	0.31880 (16)	0.31880 (16)	0.0305 (8)
O2	0.53058 (16)	0.40826 (17)	0.33772 (18)	0.0293 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cs	0.02465 (17)	0.03562 (13)	0.03562 (13)	0.000	0.000	0.000
Mo	0.01762 (7)	0.01762 (7)	0.01762 (7)	0.00285 (7)	0.00285 (7)	0.00285 (7)
Co	0.0166 (4)	0.0241 (3)	0.0241 (3)	0.000	0.000	0.000
Li	0.0166 (4)	0.0241 (3)	0.0241 (3)	0.000	0.000	0.000
O1	0.0305 (7)	0.0305 (7)	0.0305 (7)	−0.0018 (8)	−0.0018 (8)	−0.0018 (8)
O2	0.0221 (9)	0.0328 (10)	0.0329 (10)	−0.0009 (8)	0.0099 (8)	0.0025 (8)

Geometric parameters (Å, º)

Cs—O2^i	3.262 (2)	Mo—Cs^xvii	4.4604 (2)
Cs—O2^ii	3.262 (2)	Mo—Cs^xviii	4.4604 (2)
Cs—O2^iii	3.262 (2)	Mo—Cs^xix	4.4604 (2)
Cs—O2^iv	3.262 (2)	Co—O2^xx	1.9338 (19)
Cs—O1^v	3.350 (2)	Co—O2^xxi	1.9338 (19)
Cs—O1^vi	3.350 (2)	Co—O2	1.9338 (19)
Cs—O1^vii	3.350 (2)	Co—O2^xxii	1.9338 (19)
Cs—O1^viii	3.350 (2)	Co—Cs^xv	3.7428
Cs—O2^ix	3.361 (2)	Co—Cs^xvii	3.7428
Cs—O2^x	3.361 (2)	Co—Cs^xviii	3.7428
Cs—O2^xi	3.361 (2)	Co—Cs^xxiii	3.7428
Cs—O2^xii	3.361 (2)	O1—Cs^xv	3.350 (2)
Mo—O1	1.719 (4)	O1—Cs^viii	3.350 (2)
Mo—O2^xiii	1.7715 (18)	O1—Cs^xvi	3.350 (2)
Mo—O2^xiv	1.7715 (18)	O2—Li^viii	1.9338 (19)
Mo—O2	1.7715 (18)	O2—Co^viii	1.9338 (19)
Mo—Cs^viii	4.0192 (2)	O2—Cs^xv	3.262 (2)
Mo—Cs^xv	4.0192 (2)	O2—Cs^xvii	3.361 (2)
Mo—Cs^xvi	4.0192 (2)
O2^i—Cs—O2^ii	129.44 (4)	O1—Mo—Cs^xv	55.211 (4)
O2^i—Cs—O2^iii	74.31 (7)	O2^xiii—Mo—Cs^xv	122.71 (7)
O2^ii—Cs—O2^iii	129.44 (4)	O2^xiv—Mo—Cs^xv	126.13 (7)
O2^i—Cs—O2^iv	129.44 (4)	O2—Mo—Cs^xv	52.60 (8)
O2^ii—Cs—O2^iv	74.31 (7)	Cs^viii—Mo—Cs^xv	90.670 (6)
O2^iii—Cs—O2^iv	129.44 (4)	O1—Mo—Cs^xvi	55.211 (4)
O2^i—Cs—O1^v	169.84 (3)	O2^xiii—Mo—Cs^xvi	52.60 (8)
O2^ii—Cs—O1^v	50.46 (7)	O2^xiv—Mo—Cs^xvi	122.71 (7)
O2^iii—Cs—O1^v	98.21 (5)	O2—Mo—Cs^xvi	126.13 (7)
O2^iv—Cs—O1^v	60.63 (4)	Cs^viii—Mo—Cs^xvi	90.670 (6)
O2^i—Cs—O1^vi	60.63 (4)	Cs^xv—Mo—Cs^xvi	90.670 (6)
O2^ii—Cs—O1^vi	169.84 (3)	O1—Mo—Cs^xvii	132.266 (3)
O2^iii—Cs—O1^vi	50.46 (7)	O2^xiii—Mo—Cs^xvii	70.65 (7)
O2^iv—Cs—O1^vi	98.21 (5)	O2^xiv—Mo—Cs^xvii	117.26 (8)
O1^v—Cs—O1^vi	120.00 (4)	O2—Mo—Cs^xvii	42.03 (8)
O2^i—Cs—O1^vii	50.46 (7)	Cs^viii—Mo—Cs^xvii	161.457 (3)
O2^ii—Cs—O1^vii	98.21 (5)	Cs^xv—Mo—Cs^xvii	84.618 (1)
O2^iii—Cs—O1^vii	60.63 (4)	Cs^xvi—Mo—Cs^xvii	107.272 (1)
O2^iv—Cs—O1^vii	169.84 (3)	O1—Mo—Cs^xviii	132.266 (3)
O1^v—Cs—O1^vii	120.00 (4)	O2^xiii—Mo—Cs^xviii	117.26 (8)
O1^vi—Cs—O1^vii	90.01 (8)	O2^xiv—Mo—Cs^xviii	42.03 (8)
O2^i—Cs—O1^viii	98.21 (5)	O2—Mo—Cs^xviii	70.65 (7)
O2^ii—Cs—O1^viii	60.63 (4)	Cs^viii—Mo—Cs^xviii	84.618 (1)
O2^iii—Cs—O1^viii	169.84 (3)	Cs^xv—Mo—Cs^xviii	107.272 (1)
O2^iv—Cs—O1^viii	50.46 (7)	Cs^xvi—Mo—Cs^xviii	161.457 (3)
O1^v—Cs—O1^viii	90.01 (8)	Cs^xvii—Mo—Cs^xviii	79.716 (5)
O1^vi—Cs—O1^viii	120.00 (4)	O1—Mo—Cs^xix	132.266 (3)
O1^vii—Cs—O1^viii	120.00 (4)	O2^xiii—Mo—Cs^xix	42.03 (8)
O2^i—Cs—O2^ix	57.46 (6)	O2^xiv—Mo—Cs^xix	70.65 (7)
O2^ii—Cs—O2^ix	120.13 (6)	O2—Mo—Cs^xix	117.26 (8)
O2^iii—Cs—O2^ix	110.18 (4)	Cs^viii—Mo—Cs^xix	107.272 (1)
O2^iv—Cs—O2^ix	71.99 (4)	Cs^xv—Mo—Cs^xix	161.457 (3)
O1^v—Cs—O2^ix	132.54 (3)	Cs^xvi—Mo—Cs^xix	84.618 (1)
O1^vi—Cs—O2^ix	62.29 (6)	Cs^xvii—Mo—Cs^xix	79.716 (5)
O1^vii—Cs—O2^ix	107.09 (7)	Cs^xviii—Mo—Cs^xix	79.716 (5)
O1^viii—Cs—O2^ix	59.67 (4)	O2^xx—Co—O2^xxi	106.71 (13)
O2^i—Cs—O2^x	110.18 (4)	O2^xx—Co—O2	110.87 (6)
O2^ii—Cs—O2^x	71.99 (4)	O2^xxi—Co—O2	110.87 (6)
O2^iii—Cs—O2^x	57.46 (6)	O2^xx—Co—O2^xxii	110.87 (6)
O2^iv—Cs—O2^x	120.13 (6)	O2^xxi—Co—O2^xxii	110.87 (6)
O1^v—Cs—O2^x	59.67 (4)	O2—Co—O2^xxii	106.71 (13)
O1^vi—Cs—O2^x	107.09 (7)	O2^xx—Co—Cs^xv	158.93 (7)
O1^vii—Cs—O2^x	62.29 (6)	O2^xxi—Co—Cs^xv	63.52 (7)
O1^viii—Cs—O2^x	132.54 (3)	O2—Co—Cs^xv	60.61 (7)
O2^ix—Cs—O2^x	166.10 (7)	O2^xxii—Co—Cs^xv	90.20 (6)
O2^i—Cs—O2^xi	120.13 (6)	O2^xx—Co—Cs^xvii	60.61 (7)
O2^ii—Cs—O2^xi	110.18 (4)	O2^xxi—Co—Cs^xvii	90.20 (6)
O2^iii—Cs—O2^xi	71.99 (4)	O2—Co—Cs^xvii	63.52 (7)
O2^iv—Cs—O2^xi	57.46 (6)	O2^xxii—Co—Cs^xvii	158.93 (7)
O1^v—Cs—O2^xi	62.29 (6)	Cs^xv—Co—Cs^xvii	99.6
O1^vi—Cs—O2^xi	59.67 (4)	O2^xx—Co—Cs^xviii	63.52 (7)
O1^vii—Cs—O2^xi	132.54 (3)	O2^xxi—Co—Cs^xviii	158.93 (7)
O1^viii—Cs—O2^xi	107.09 (7)	O2—Co—Cs^xviii	90.20 (6)
O2^ix—Cs—O2^xi	90.839 (9)	O2^xxii—Co—Cs^xviii	60.61 (7)
O2^x—Cs—O2^xi	90.839 (9)	Cs^xv—Co—Cs^xviii	131.8
O2^i—Cs—O2^xii	71.99 (4)	Cs^xvii—Co—Cs^xviii	99.6
O2^ii—Cs—O2^xii	57.46 (6)	O2^xx—Co—Cs^xxiii	90.20 (6)
O2^iii—Cs—O2^xii	120.13 (6)	O2^xxi—Co—Cs^xxiii	60.61 (7)
O2^iv—Cs—O2^xii	110.18 (4)	O2—Co—Cs^xxiii	158.93 (7)
O1^v—Cs—O2^xii	107.09 (7)	O2^xxii—Co—Cs^xxiii	63.52 (7)
O1^vi—Cs—O2^xii	132.54 (3)	Cs^xv—Co—Cs^xxiii	99.6
O1^vii—Cs—O2^xii	59.67 (4)	Cs^xvii—Co—Cs^xxiii	131.8
O1^viii—Cs—O2^xii	62.29 (6)	Cs^xviii—Co—Cs^xxiii	99.6
O2^ix—Cs—O2^xii	90.839 (9)	Mo—O1—Cs^xv	99.87 (6)
O2^x—Cs—O2^xii	90.839 (9)	Mo—O1—Cs^viii	99.87 (6)
O2^xi—Cs—O2^xii	166.10 (7)	Cs^xv—O1—Cs^viii	117.12 (3)
O1—Mo—O2^xiii	107.78 (8)	Mo—O1—Cs^xvi	99.87 (6)
O1—Mo—O2^xiv	107.78 (8)	Cs^xv—O1—Cs^xvi	117.12 (3)
O2^xiii—Mo—O2^xiv	111.11 (7)	Cs^viii—O1—Cs^xvi	117.12 (3)
O1—Mo—O2	107.78 (8)	Mo—O2—Co	144.02 (12)
O2^xiii—Mo—O2	111.11 (7)	Mo—O2—Cs^xv	101.84 (9)
O2^xiv—Mo—O2	111.11 (7)	Co—O2—Cs^xv	88.30 (7)
O1—Mo—Cs^viii	55.211 (4)	Mo—O2—Cs^xvii	117.31 (10)
O2^xiii—Mo—Cs^viii	126.13 (7)	Co—O2—Cs^xvii	85.48 (7)
O2^xiv—Mo—Cs^viii	52.60 (8)	Cs^xv—O2—Cs^xvii	119.35 (6)
O2—Mo—Cs^viii	122.71 (7)

Symmetry codes: (i) z+3/4, y−1/4, x−1/4; (ii) −z+1, x−1/2, −y+1/2; (iii) z+3/4, −y+1/4, −x+3/4; (iv) −z+1, −x+1/2, y; (v) −x+1, y−1/2, −z+1/2; (vi) y+3/4, −x+1/4, −z+3/4; (vii) y+3/4, x−1/4, z−1/4; (viii) −x+1, −y+1/2, z; (ix) y+1/2, −z+1/2, −x+1; (x) y+1/2, z−1/2, x−1/2; (xi) −y+5/4, x−3/4, −z+3/4; (xii) −y+5/4, −x+3/4, z−1/4; (xiii) y, z, x; (xiv) z, x, y; (xv) −y+1/2, z, −x+1; (xvi) z, −x+1, −y+1/2; (xvii) z+1/2, x−1/2, y+1/2; (xviii) y+1/2, z+1/2, x−1/2; (xix) x−1/2, y+1/2, z+1/2; (xx) −x+5/4, z+1/4, −y+3/4; (xxi) −x+5/4, −z+3/4, y−1/4; (xxii) x, −y+1, −z+1/2; (xxiii) z+1/2, −x+3/2, −y.

(II) 'trirubidium lithium dizinc tetrakis(tetraoxomolybdate)'

Crystal data

Rb3LiZn2(MoO4)4	Dx = 4.074 Mg m^−3
Mr = 1033.95	Mo Kα radiation, λ = 0.71073 Å
Cubic, I43d	Cell parameters from 5301 reflections
Hall symbol: I -4bd 2c 3	θ = 2.4–34.5°
a = 11.9018 (14) Å	µ = 14.37 mm^−1
V = 1685.9 (3) Å^3	T = 293 K
Z = 4	Fragment, colourless
F(000) = 1880	0.10 × 0.10 × 0.08 mm

Data collection

Bruker-Nonius X8 APEX CCD diffractometer	643 independent reflections
Radiation source: fine-focus sealed X-ray tube	617 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.023
φ scans, frame data integration	θmax = 35.7°, θmin = 4.2°
Absorption correction: multi-scan (SADABS; Bruker, 2004)	h = −14→18
Tmin = 0.264, Tmax = 0.317	k = −10→19
7827 measured reflections	l = −19→17

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.009P)^2] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.011	(Δ/σ)max = 0.001
wR(F^2) = 0.026	Δρmax = 0.31 e Å^−3
S = 1.07	Δρmin = −0.25 e Å^−3
643 reflections	Extinction correction: SHELXL97, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
21 parameters	Extinction coefficient: 0.00099 (7)
0 restraints	Absolute structure: Flack (1983), 365 Friedel pairs
Primary atom site location: structure-invariant direct methods	Absolute structure parameter: 0.004 (6)

Special details

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

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Rb	0.8750	0.0000	0.2500	0.03614 (8)
Mo	0.392600 (10)	0.392600 (10)	0.392600 (10)	0.01671 (5)
Zn	0.6250	0.5000	0.2500	0.01845 (9)	0.666667
Li	0.6250	0.5000	0.2500	0.01845 (9)	0.333333
O1	0.30910 (10)	0.30910 (10)	0.30910 (10)	0.0284 (4)
O2	0.52855 (9)	0.39715 (11)	0.33085 (10)	0.0258 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Rb	0.02241 (16)	0.04301 (13)	0.04301 (13)	0.000	0.000	0.000
Mo	0.01671 (5)	0.01671 (5)	0.01671 (5)	0.00341 (4)	0.00341 (4)	0.00341 (4)
Zn	0.0133 (2)	0.02103 (13)	0.02103 (13)	0.000	0.000	0.000
Li	0.0133 (2)	0.02103 (13)	0.02103 (13)	0.000	0.000	0.000
O1	0.0284 (4)	0.0284 (4)	0.0284 (4)	−0.0014 (4)	−0.0014 (4)	−0.0014 (4)
O2	0.0214 (5)	0.0257 (5)	0.0302 (6)	0.0001 (4)	0.0088 (4)	0.0024 (5)

Geometric parameters (Å, º)

Rb—O2^i	3.0307 (12)	Mo—Rb^xvi	3.8286 (5)
Rb—O2^ii	3.0307 (12)	Mo—Rb^viii	3.8286 (5)
Rb—O2^iii	3.0307 (12)	Zn—O2^xvii	1.9345 (12)
Rb—O2^iv	3.0307 (12)	Zn—O2^xviii	1.9345 (12)
Rb—O1^v	3.2339 (19)	Zn—O2	1.9345 (12)
Rb—O1^vi	3.2339 (19)	Zn—O2^xix	1.9345 (12)
Rb—O1^vii	3.2339 (19)	Zn—Rb^xvi	3.6442 (4)
Rb—O1^viii	3.2339 (19)	Zn—Rb^xx	3.6442 (4)
Rb—O2^ix	3.3270 (13)	Zn—Rb^xxi	3.6442 (4)
Rb—O2^x	3.3270 (13)	Zn—Rb^xxii	3.6442 (4)
Rb—O2^xi	3.3270 (13)	O1—Rb^xvi	3.2339 (19)
Rb—O2^xii	3.3270 (13)	O1—Rb^viii	3.2339 (19)
Mo—O1	1.721 (2)	O1—Rb^xv	3.2339 (19)
Mo—O2^xiii	1.7780 (10)	O2—Li^viii	1.9345 (12)
Mo—O2^xiv	1.7780 (10)	O2—Zn^viii	1.9345 (12)
Mo—O2	1.7780 (10)	O2—Rb^xvi	3.0307 (12)
Mo—Rb^xv	3.8286 (5)	O2—Rb^xx	3.3270 (13)
O2^i—Rb—O2^ii	130.81 (3)	O2^x—Rb—O2^xii	90.360 (3)
O2^i—Rb—O2^iii	72.12 (5)	O2^xi—Rb—O2^xii	170.91 (4)
O2^ii—Rb—O2^iii	130.81 (3)	O1—Mo—O2^xiii	107.72 (4)
O2^i—Rb—O2^iv	130.81 (3)	O1—Mo—O2^xiv	107.72 (4)
O2^ii—Rb—O2^iv	72.12 (5)	O2^xiii—Mo—O2^xiv	111.17 (4)
O2^iii—Rb—O2^iv	130.81 (3)	O1—Mo—O2	107.72 (4)
O2^i—Rb—O1^v	167.99 (3)	O2^xiii—Mo—O2	111.17 (4)
O2^ii—Rb—O1^v	53.51 (4)	O2^xiv—Mo—O2	111.17 (4)
O2^iii—Rb—O1^v	96.74 (3)	O1—Mo—Rb^xv	57.080 (3)
O2^iv—Rb—O1^v	59.95 (2)	O2^xiii—Mo—Rb^xv	50.64 (4)
O2^i—Rb—O1^vi	59.95 (2)	O2^xiv—Mo—Rb^xv	124.31 (4)
O2^ii—Rb—O1^vi	167.99 (3)	O2—Mo—Rb^xv	124.52 (4)
O2^iii—Rb—O1^vi	53.51 (4)	O1—Mo—Rb^xvi	57.080 (3)
O2^iv—Rb—O1^vi	96.74 (3)	O2^xiii—Mo—Rb^xvi	124.31 (4)
O1^v—Rb—O1^vi	117.33 (3)	O2^xiv—Mo—Rb^xvi	124.52 (4)
O2^i—Rb—O1^vii	53.51 (4)	O2—Mo—Rb^xvi	50.64 (4)
O2^ii—Rb—O1^vii	96.74 (3)	Rb^xv—Mo—Rb^xvi	93.266 (4)
O2^iii—Rb—O1^vii	59.95 (2)	O1—Mo—Rb^viii	57.080 (3)
O2^iv—Rb—O1^vii	167.99 (3)	O2^xiii—Mo—Rb^viii	124.52 (4)
O1^v—Rb—O1^vii	117.33 (3)	O2^xiv—Mo—Rb^viii	50.64 (4)
O1^vi—Rb—O1^vii	94.69 (5)	O2—Mo—Rb^viii	124.31 (4)
O2^i—Rb—O1^viii	96.74 (3)	Rb^xv—Mo—Rb^viii	93.266 (4)
O2^ii—Rb—O1^viii	59.95 (2)	Rb^xvi—Mo—Rb^viii	93.266 (4)
O2^iii—Rb—O1^viii	167.99 (3)	O2^xvii—Zn—O2^xviii	107.20 (8)
O2^iv—Rb—O1^viii	53.51 (4)	O2^xvii—Zn—O2	110.62 (4)
O1^v—Rb—O1^viii	94.69 (5)	O2^xviii—Zn—O2	110.62 (4)
O1^vi—Rb—O1^viii	117.33 (3)	O2^xvii—Zn—O2^xix	110.62 (4)
O1^vii—Rb—O1^viii	117.33 (3)	O2^xviii—Zn—O2^xix	110.62 (4)
O2^i—Rb—O2^ix	111.99 (2)	O2—Zn—O2^xix	107.20 (8)
O2^ii—Rb—O2^ix	70.98 (2)	O2^xvii—Zn—Rb^xvi	155.06 (4)
O2^iii—Rb—O2^ix	59.83 (4)	O2^xviii—Zn—Rb^xvi	65.02 (4)
O2^iv—Rb—O2^ix	117.00 (4)	O2—Zn—Rb^xvi	56.23 (3)
O1^v—Rb—O2^ix	57.06 (2)	O2^xix—Zn—Rb^xvi	94.09 (3)
O1^vi—Rb—O2^ix	111.79 (4)	O2^xvii—Zn—Rb^xx	56.23 (3)
O1^vii—Rb—O2^ix	61.41 (4)	O2^xviii—Zn—Rb^xx	94.09 (3)
O1^viii—Rb—O2^ix	130.63 (2)	O2—Zn—Rb^xx	65.02 (4)
O2^i—Rb—O2^x	59.83 (4)	O2^xix—Zn—Rb^xx	155.06 (4)
O2^ii—Rb—O2^x	117.00 (4)	Rb^xvi—Zn—Rb^xx	99.6
O2^iii—Rb—O2^x	111.99 (2)	O2^xvii—Zn—Rb^xxi	65.02 (4)
O2^iv—Rb—O2^x	70.98 (2)	O2^xviii—Zn—Rb^xxi	155.06 (4)
O1^v—Rb—O2^x	130.63 (2)	O2—Zn—Rb^xxi	94.09 (3)
O1^vi—Rb—O2^x	61.41 (4)	O2^xix—Zn—Rb^xxi	56.23 (3)
O1^vii—Rb—O2^x	111.79 (4)	Rb^xvi—Zn—Rb^xxi	131.8
O1^viii—Rb—O2^x	57.06 (2)	Rb^xx—Zn—Rb^xxi	99.6
O2^ix—Rb—O2^x	170.91 (4)	O2^xvii—Zn—Rb^xxii	94.09 (3)
O2^i—Rb—O2^xi	117.00 (4)	O2^xviii—Zn—Rb^xxii	56.23 (3)
O2^ii—Rb—O2^xi	111.99 (3)	O2—Zn—Rb^xxii	155.06 (4)
O2^iii—Rb—O2^xi	70.98 (2)	O2^xix—Zn—Rb^xxii	65.02 (4)
O2^iv—Rb—O2^xi	59.83 (4)	Rb^xvi—Zn—Rb^xxii	99.6
O1^v—Rb—O2^xi	61.41 (4)	Rb^xx—Zn—Rb^xxii	131.8
O1^vi—Rb—O2^xi	57.06 (2)	Rb^xxi—Zn—Rb^xxii	99.6
O1^vii—Rb—O2^xi	130.63 (2)	Mo—O1—Rb^xvi	96.38 (4)
O1^viii—Rb—O2^xi	111.79 (4)	Mo—O1—Rb^viii	96.38 (4)
O2^ix—Rb—O2^xi	90.360 (3)	Rb^xvi—O1—Rb^viii	118.781 (14)
O2^x—Rb—O2^xi	90.360 (3)	Mo—O1—Rb^xv	96.38 (4)
O2^i—Rb—O2^xii	70.98 (2)	Rb^xvi—O1—Rb^xv	118.781 (14)
O2^ii—Rb—O2^xii	59.83 (4)	Rb^viii—O1—Rb^xv	118.781 (14)
O2^iii—Rb—O2^xii	117.00 (4)	Mo—O2—Zn	139.90 (8)
O2^iv—Rb—O2^xii	111.99 (2)	Mo—O2—Rb^xvi	102.39 (5)
O1^v—Rb—O2^xii	111.79 (4)	Zn—O2—Rb^xvi	91.72 (4)
O1^vi—Rb—O2^xii	130.63 (2)	Mo—O2—Rb^xx	117.93 (5)
O1^vii—Rb—O2^xii	57.06 (2)	Zn—O2—Rb^xx	83.17 (4)
O1^viii—Rb—O2^xii	61.41 (4)	Rb^xvi—O2—Rb^xx	122.16 (4)
O2^ix—Rb—O2^xii	90.360 (3)

Symmetry codes: (i) z+3/4, y−1/4, x−1/4; (ii) −z+1, x−1/2, −y+1/2; (iii) z+3/4, −y+1/4, −x+3/4; (iv) −z+1, −x+1/2, y; (v) −x+1, y−1/2, −z+1/2; (vi) y+3/4, −x+1/4, −z+3/4; (vii) y+3/4, x−1/4, z−1/4; (viii) −x+1, −y+1/2, z; (ix) y+1/2, z−1/2, x−1/2; (x) y+1/2, −z+1/2, −x+1; (xi) −y+5/4, x−3/4, −z+3/4; (xii) −y+5/4, −x+3/4, z−1/4; (xiii) y, z, x; (xiv) z, x, y; (xv) z, −x+1, −y+1/2; (xvi) −y+1/2, z, −x+1; (xvii) −x+5/4, z+1/4, −y+3/4; (xviii) −x+5/4, −z+3/4, y−1/4; (xix) x, −y+1, −z+1/2; (xx) z+1/2, x−1/2, y+1/2; (xxi) y+1/2, z+1/2, x−1/2; (xxii) z+1/2, −x+3/2, −y.