Synthesis, crystal structure and charge-distribution validation of β-Na4Cu(MoO4)3 adopting the alluadite structure-type

A new variety of tetrasodium copper(II) tris[molybdate(VI)] is characterized by the presence of infinite layers of composition (Cu1/Na1)2Mo3O14 parallel to the (100) plane, which are linked by MoO4 tetrahedra, forming a three-dimensional framework containing two types of hexagonal tunnels in which Na+ cations reside.


Chemical context
In recent years, a number of molybdates have received considerable attention due to their amazing properties and high application potential in various fields, such as photoluminescence (Shi et al., 2014) and Li-ion batteries (Reddy et al., 2013). For example, the copper molybdate Cu 3 Mo 2 O 9 doped with lithium displays high Coulombic efficiency in lithium-ion batteries and excellent charge-discharge stability (Xia et al., 2015). Many new molybdate phases have been synthesized and structurally characterized by X-ray diffraction, among which a large number belong to the alluaudite type, such as Na 25 Cs 8 Fe 5 (MoO 4 ) 24 , which presents a high electrical conductivity (Savina et al., 2014). The alluauditetype structure was first determined on natural minerals by Fisher, who showed that alluaudite compounds crystallize in the monoclinic C2/c space group (Fisher, 1955). Moore proposed the general formula X(2)X(1)M(1)M(2) 2 (PO 4 ) 3 , in which the X and M mono-, bi-or trivalent cations are written according to their size (X are large cations and M are distorted octahedrally coordinated atoms). It represents the parental structure-type of the group referred to as alluaudite-type (Moore, 1971). The size of the channel and the stability of the alluaudite network led to many phases belonging to this structural type. We can totally or partially replace not only the monovalent cations, but also the central atoms of the MO 6 octahedra and TO 4 tetrahedra. It is also possible to make substitutions with cations in different oxidation states adopting the same type of coordination number (Mo 6+ , V 5+ , P 5+ and As 5+ ). Alluaudite molybdates usually have the general formula of X(2)X(1)M(1)M(2) 2 (MoO 4 ) 3 and adopt the C2/c space group, with a ' 12, b ' 13 and c ' 7 Å , examples being the K 0.13 Na 3.87 MgMo 3 O 12 (Ennajeh et al., 2015), Na 3 Fe 2 (MoO 4 ) 3 (Muessig et al., 2003) and Na 4 Co(MoO 4 ) 3 (Nasri et al., 2014) compounds. A review of the literature also reveals the presence of other formulae, such as Na 5 Sc(MoO 4 ) 4 , Na 2 Ni(MoO 4 ) 2 (Klevtsova et al., 1991) and Na 2.2 Zn 0.9 (MoO 4 ) 2 (Efremov et al., 1975), which crystallize in the space group C2/c with cell parameters of about a ' 12, b ' 13 and c ' 7 Å . All alluaudite-type compounds can be described by the general formula given by Moore (1971), but their structures can differ by the number of formula units per unit cell. They are characterized by a three-dimensional heteropolyhedral framework formed by TO 4 tetrahedra and MO 6 octahedra, delimiting two types of channels running along the c axis. A new variety of -Na 4 Cu(MoO 4 ) 3 formulation was obtained by a reaction in the solid state at 873 K.

Structural commentary
The structural unit in -Na 4 Cu(MoO 4 ) 3 is formed by MO 6 (M = Cu1/Na1) octahedra linked by sharing vertices with Mo1O 4 tetrahedra and two slightly different Mo2O 4 tetrahedra, with a partially occupied (0.5 occupancy) Mo2 site. Atom O4 is split into two separate positions, with occupancies of 0.5 for the O4 and O41 atoms. The charge compensation is provided by Na + cations (Fig. 1). The essential building units of the structure are M 2 O 10 units obtained from two edgesharing MO 6 octahedra. These units are connected by Mo1O 4 tetrahedra through vertex-sharing via Mo-O-M mixed bridges. This results in M 2 Mo 2 O 16 units. Each unit is connected to six other identical units by the sharing of vertices, leading to an infinite layer of the M 2 Mo 3 O 14 type parallel to the (100) plane (Fig. 2). The linkage of these layers is ensured by the two slightly different Mo2O 4 tetrahedra, linking via corners. This results in a three-dimensional framework delimited by two kinds of channels running along the c axis at ( 1 2 , 0, z) and (0, 0, z). These channels are occupied by Na + cations (Fig. 3)  Representation of the coordination polyhedra in the structural unit of -Na 4 Cu(MoO 4 ) 3 , showing (a) full atomic, (b) polyhedral. All atoms are represented as displacement ellipsoids at the 50% probability level.

Figure 2
A projection of the polyhedral layers in the bc plane. Table 1 Selected bond lengths (Å ).
atoms with three M 2 O 10 units belonging to the same layer, the other O atom being free and pointing towards the channels where the Na3 cations are located (Fig. 4). There is some compositional flexibility in the alluaudite structure and the studied material is isostructural with Na 5 Sc(MoO 4 ) 4 (Klevtsova et al., 1975) and Na 3 In 2 As 3 O 12 (Khorari et al., 1997). The two crystallographically independent Mo atoms have tetrahedral coordination, with an average Mo-O distance of 1.761 Å for Mo1 and 1.777 Å for Mo2, which is in a good agreement with those typically observed in Rb 2 Cu 2 (MoO 4 ) 3 (Solodovnikov & Solodovnikova, 1997 A projection of the -Na 4 Cu(MoO 4 ) 3 structure, viewed normal to (001), showing the channels where monovalent cations are located.   formula of Brown (Brown & Altermatt, 1985) and (ii) the charge-distribution method Chardi (Nespolo, 2015(Nespolo, , 2016. The charge distribution method is the most recent development of Pauling's concept of bond strength (Pauling, 1929). Instead of empirical parameters used in the bond-valence approach, it exploits the experimental bond lengths deduced from the structural study to compute a non-integer coordination number, ECoN (effective coordination number), around a PCatom (atom placed at the center of a polyhedron, q > 0), which is coordinated by V atoms (atoms located at the vertices, q < 0); q is the formal oxidation number. ECoN takes into account not only the number of V atoms around a given PC atom, but also their weight in terms of relative distances. Calculated charges Q(i) and valences V(i) are in good agreement with the formal oxidation number (q) multiplied by occupancy rates. The dispersion factor MAPD, which measures the mean absolute percentage deviation, is 2.2% for the calculated cationic charges. The variation of the ECoN value to the traditional coordination indicates the degree of distortion. The two validation models results are summarized in Table 2. Comparing our structure with that of a similar formulation, i.e. K 4 Cu(MoO 4 ) 3 (Menard et al., 2011), we found a clear difference, on the one hand, in the crystal symmetry and, on the other hand, in the arrangement of polyhedra. K 4 Cu(MoO 4 ) 3 crystallizes in the Pnma space group. Its structure can be described as being composed of a distorted square-planar CuO 4 polyhedron bound by shared vertices to two Mo1O 4 tetrahedra to form CuMo 2 O 10 -type units. These units are interconnected, on the one hand, by insertion of two Mo2O 4 tetrahedra which share a face with a partial occupation (0.5 occupancy) of Mo2 atoms, and secondly by forming a mixed bridge of the Mo-O-Cu type. This forms ribbons arranged parallel to the [100] direction. This results in a one-dimensional structure in which K + atoms reside in the inter-ribbon spaces (Fig. 5). The structure of our new variety -Na 4 Cu(MoO 4 ) 3 is compared with the variety. Indeed, -Na 4 Cu(MoO 4 ) 3 (Klevtsova et al., 1991) crystallizes in the triclinic system, space group P1, and its structure is formed by the same Cu 2 O 10 dimers present in our structure (here present as mixed-occupied M 2 O 10 units). direction. All the ribbons form a one-dimensional framework with inter-ribbon spaces containing monovalent Na + cations (Fig. 6). This structure has the same arrangement of structural units found in the one-dimensional structure of K 3 Mn(MoO 4 ) 3 (Solodovnikov et al., 1998) (Fig. 7). A projection of the -Na 4 Cu(MoO 4 ) 3 structure, viewed in the (010) plane.

Figure 7
A projection of the K 4 Mn(MoO 4 ) 3 structure, viewed normal to (010). milled in an agate mortar, placed in a porcelain crucible and then preheated slowly in air at 623 K for 24 h, in order to eliminate volatile products. Thereafter, it was heated to a temperature close to that of the fusion at 873 K. It was left at this temperature for 20 d to induce nucleation and crystal growth. The final residue was first cooled slowly (5 K per half day) to 823 K and then rapidly (50 K h À1 ) to room temperature. Green crystals of sufficient size for the measurement of intensities were obtained.

Tetrasodium copper(II) tris[molybdate(VI)]
Crystal data Special details Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å 2 )