Topological Features of the Alluaudite-Type Framework and Its Derivatives: Synthesis and Crystal Structure of NaMnNi 2 (H 2/3 PO 4 ) 3

: A new sodium manganese-nickel phosphate of alluaudite supergroup with the general formula NaMnNi 2 (H 2/3 PO 4 ) 3 was synthesized by a hydrothermal method. The synthesis was carried out in the temperature range from 540 to 660 K and at the general pressure of 80 atm from the oxides mixture in the molar ratio MnCl 2 : 2NiCl 2 : 2Na 3 PO 4 : H 3 BO 3 : 10H 2 O. The crystal structure was studied by a single-crystal X-ray diffraction analysis: space group C 2/ c (No. 15), a = 16.8913(4), b = 5.6406(1), c = 8.3591(3) Å, β = 93.919(3), V = 794.57(4) Å 3 . The compound belongs to the alluaudite structure type based upon a mixed hetero-polyhedral framework formed by MX 6 -octahedra and TX 4 tetrahedra. The characteristic feature of the title compound is the absence of cations or H 2 O molecules in channel II, while the negative charge of the framework is balanced by the partial protonation of PO 4 tetrahedra. The presence of the transition metals at the A -type sites results in the changes of stoichiometry and the local topological features. Topological analysis of the hetero-polyhedral alluaudite-type frameworks and its derivatives (johillerite-, KCd 4 (VO 4 ) 3 -, and keyite-type) and quantitative characterization of their differences was performed by means of natural tilings.

The present work continues our systematic study of topologic features of compounds with hetero-polyhedral frameworks [36][37][38][39][40] and their comparison with zeolites. Here we report the results of hydrothermal synthesis of novel mixed nickel-manganese phosphate with an alluaudite-type structure and its characterization by the means of single-crystal X-ray diffraction analysis.

Synthesis and Sample Characterization
Single crystals of NaMnNi 2 (H 2/3 PO 4 ) 3 (1) were synthesized by a hydrothermal method. The synthesis was carried out in the temperature range from 540 to 660 K and at the general pressure of 80 atm from the mixture of oxides taken in the molar ratio MnCl 2 : 2NiCl 2 : 2Na 3 PO 4 : H 3 BO 3 : 10H 2 O. A standard Cu-lined stainless steel autoclave of 5 mL capacity was used. The coefficient of the autoclave filling was selected so that the pressure was constant. The experimental duration was 20 days and corresponds to the full completion of the chemical reaction. Final cooling after the synthesis experiment to room temperature was done over 24 h. The precipitate was separated by filtration and washed several times with hot distilled water and finally dried at room temperature for 12 h. The reaction products were small green crystals of the new phase in the estimated yield of 5%, which have been selected manually for the further studies.
The elemental contents of the selected crystals were determined by a Jeol JSM6480LV scanning electron microscope equipped with an INCA Wave 500 wave length spectrometer. The conditions of analysis were: accelerating voltage of 20 kV, a current of 20 nA, and a beam diameter 3 of µm. Chemical composition of 1 is (at.%): Na 5.86, Mn 6.59, Ni 9.58, P 16.56, O 61.41.

Single Crystal X-ray Diffraction Analysis
A yellow, round-shaped grain of 1 (0.04 × 0.05 × 0.11 mm 3 ) was selected carefully under a polarizing microscope and used for single-crystal X-ray diffraction data collection. The single-crystal X-ray diffraction data were collected at room temperature on an Xcalibur S Oxford Diffraction diffractometer with graphite monochromatized MoKα radiation (λ = 0.71073 Å) and a CCD detector using the ω scanning mode. The raw data were integrated and then scaled, merged, and corrected for Lorentz-polarization effects using the CrysAlis package [41]. The C2/c (No. 15) space group was chosen based on the reflection statistics and confirmed by the successful refinement of the crystal structure. The experimental details of the data collection and refinement are listed in Table 1.
The structural determinations and refinements were carried out using the Jana2006 program package [42]. Atomic scattering factors for neutral atoms together with anomalous dispersion corrections were taken from International Tables for Crystallography [43]. Illustrations were produced with the Jana2006 program package in combination with the program DIAMOND 3 [44]. The distribution of cations on the structural A-, M1, and M2-sites was proposed taking into account site-scattering factors [45], interatomic distances and ionic radii of the cations. Table 2 lists the fractional atomic coordinates, occupancies, site symmetries and equivalent atomic displacement parameters (U eq ). Selected interatomic distances are given in Table 3. CDS 2042360 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge via  Bond-valence sums (BVS, Table 4) can be used for the indirect verification of mixed oxygen/hydroxyl site presence in the structure. BVS calculations were calculated using the bond valence parameters for the Na + -O, Mn 2+ -O, Ni 2+ -O, and P 5+ -O bonds [46].

Topological Analysis and Complexity Calculations
Topological analysis of the frameworks was performed by means of natural tilings (the smallest polyhedral cationic clusters forming a framework) analysis of the 3D cation nets [47]. The complexity parameters were calculated as the Shannon information amounts per atom (I G ) and per reduced unit cell (I G,total ) [48,49]. The topological and complexity analysis was done using the ToposPro software [50].
The systematic of the alluaudite-type compounds has previously been reported on the basis of the distribution of extra-framework cations within the channels [19]. The studied compounds belongs to the "KCd 4 (VO 4 ) 3 " subgroup [52] with the general formula A2A1 {M1M2 2 (TO 4 )} [19]. The main characteristic feature of 1 is the absence of any cations or H 2 O molecules in the channel II [A(2) = ] with the negative charge of the framework balanced by the partial protonation of PO 4 tetrahedra ( Table 3). The compound Na 2 FeNi 2 (PO 4 ) 3 reported in Reference [29] belongs to the same family, but differs from 1 by the presence of Na in both types of channels (<Na (A1 ) -O> = 2.625 Å, <Na (A2) -O> = 2.525 Å) and by the absence of hydroxyl groups. The M1O 6 -and M2O 6 -octahedra of the heteropolyhedral framework in the compound Na 2 FeNi 2 (PO 4 ) 3 are occupied by Fe 3+ and Ni atoms, respectively, with the following mean <M-O> distances: <M1-O> = 2.137 Å, <M2-O> = 2.043 Å [29].
The systematic of the alluaudite-type compounds has previously been reported on the basis of the distribution of extra-framework cations within the channels [19]. The studied compounds belongs to the "KCd4(VO4)3" subgroup [52] with the general formula A2A1'{M1M22(TO4)} [19]. The main characteristic feature of 1 is the absence of any cations or H2O molecules in the channel II [A(2) = □] with the negative charge of the framework balanced by the partial protonation of PO4 tetrahedra (Table 3). The compound Na2FeNi2(PO4)3 reported in Reference [29] belongs to the same family, but differs from 1 by the presence of Na in both types of channels (<Na (A1') -O> = 2.625 Å , <Na (A2) -O> = 2.525 Å ) and by the absence of hydroxyl groups. The M1O6-and M2O6-octahedra of the heteropolyhedral framework in the compound Na2FeNi2(PO4)3 are occupied by Fe 3+ and Ni atoms, respectively, with the following mean <M-O> distances: <M1-O> = 2.137 Å , <M2-O> = 2.043 Å [29].

Hydrogen Bonding
In the crystal structure of 1, channel II is filled only by statistically disordered hydrogen atoms of P1Ø 4-and P2Ø 4-tetrahedra (Figure 2a). The strong hydrogen bonds are formed between O2-oxygens and O4-oxygens with the distance O2···O4 = 2.482 (7)

General Formula and Stoichiometry of the Alluaudite-type Heteropolyhedral Framework
The crystal structures of minerals and synthetic compounds with the alluaudite structure type are based upon a mixed hetero-polyhedral MT-framework of MX 6 -octahedra and TX 4 -tetrahedra [60][61][62] containing two types of symmetrically non-equivalent M1X 6octahedra and M2X 6 -octahedra and two types of symmetrically non-equivalent T1X 4tetrahedra and T2X 4 -tetrahedra. The anionic X-ligands of the framework are represented by bridging O atoms shared between two (p II -ligands [60,61]) as well as three M and T cations (p III -ligands). The general crystal chemical formula of the framework (taking into account the degree of sharing of X-ligands) can be written as: which the charge (W) determined by the oxidation states of the M-cations and T-cations.
As it was mentioned above, in the majority of the alluaudite-type structures, the anionic X-ligands are represented by the oxygen atoms. However, in the case of the charge deficiency of bridging p II -ligands, they could be partially protonated and Equation (4) can be rewritten as: If X = O 2and X = (OH) -, Formula (5) can also be modified as: where x = 0-1. The charge of the alluaudite-type framework can be defined using the following equation: where V M and V T are the valences of the M and T cations, respectively. The simplified formula is: Formulas (5) and (6)   In accordance with the rules for the description of ordered microporous and mesoporous materials with inorganic hosts approved by the International Zeolite Association, the crystal chemical formula for such a material has to be written in the following order: |guest composition| [host composition] h{dimensionality of the host D h } p{dimensionality of the pore system D p -shape of the pore i m i n -direction of the channel [uvw]} (symmetry) [44,45]. Consequently, the general crystal chemical formula of the studied compounds and related materials (Table 3)   In accordance with the rules for the description of ordered microporous and mesoporous materials with inorganic hosts approved by the International Zeolite Association, the crystal chemical formula for such a material has to be written in the following order: |guest composition| [host composition] h {dimensionality of the host D h } p {dimensionality of the pore system D p -shape of the pore n m i i -direction of the channel [uvw]} (symmetry) [44,45]. Consequently, the general crystal chemical formula of the studied compounds and related materials (Table 3) can be written as follows (Z = 1):

The Influence of the Hetero-Polyhedral Substitutions at Extraframework A-Sites on the Stoichiometry of the Alluaudite-Type Framework
In the alluaudite-type structures, extra-framework alkaline and alkaline-earth Acations may possess high mobility and migrate along the channels. Moreover, transition metal cations can also fill the channels through incorporation into the A(1) -site (the 4e Wyckoff site with the coordinates (0 y 1 4 ), y~0.25) or A(2)-site (the 4a site with the coordinates (0 0 0)) in the centers of flat squares. The incorporation of these elements changes the ratio between the p II -and p III -type X-ligands as well as the topology of the framework. As a result, Formula (4) can be rewritten as: where x = 0-1. The derivative of the alluaudite-type framework containing occupied A(1) sites is described by the formula (10) and can be denoted as the johillerite-type (by the analogy with the mineral johillerite, NaCuMgMg 2 (AsO 4 ) 3 [63,64]), while the derivative with the occupied A(2) sites and the formula (11) is denoted as the KCd 3 (VO 4 ) 3 -type [52,65]. Taking into account that both derivatives also contain bridging p II -type X-ligands that can be partially protonated, Formulas (10) and (11) can be modified as: or If X = O 2and X = OH -, Formulas (12) and (13) can be simplified by the following.
The keyite-type derivative of the alluaudite-type framework is characterized by the presence of transition metals in both A(1) and A(2) sites. Its general formula can be written as: Because of the absence of the p II -type X-ligands, the protonation is no longer possible (X = O 2-) and the simplified formula of the keyite-type derivative (named after the mineral keyite, ( 0.5 Cu 0.5 )CuCdZn 2 (AsO 4 ) 3 ·H 2 O [66]) is:

Topological Features of Alluaudite-Type Framework and Its Derivatives
The presence of transition metals at the A sites of the alluaudite-type framework results in the changes of stoichiometry and the local topological features. The topological analysis using a ToposPro software [50] makes it possible to find common tilings in generally similar heteropolyhedral frameworks of aluaudite-type and its derivatives (the johillerite, KCd 4 (VO 4 ) 3 , and keyite types) and to investigate their differences.

Conclusions
The occupancy of the A sites by additional transition metal cations significantly changes the topology of its derivatives. Detailed analysis of the alluaudite-type framework as well as its derivatives shows the influence of the different types of the cation arrangement within extra-framework sites on the stoichiometry (the possible amount of OH groups), complexity parameters of the frameworks, and types of natural tiling.