Mixed Valanced V³⁺,V²⁺ Phosphate Na₇V₄(PO₄)₆: A Structural Analogue of Mineral Yurmarinite

Abstract

Two sodium vanadium phosphates, synthetic analogues of the minerals kosnarite, Na₃V₂(PO₄)₃, and yurmarinite, Na₇V₄(PO₄)₆, were obtained by hydrothermal synthesis simulating a natural hydrothermal solution. While the Na₃V₂(PO₄)₃ phase belongs to the NASICON family and is well-known for its high-ionic conductivity, the new Na₇V₄(PO₄)₆ compound is a rare case of V²⁺-containing oxosalts, which are hard to prepare due to their instability in air. Here we report the crystal structure of heterovalent vanadium phosphate studied by single crystal X-ray diffraction, XANES spectroscopy, and topological ion migration modelling. A discussion of divalent vanadium compounds of both natural and synthetic origin is also given, with a review of the methods for their synthesis and a comparative analysis of V–O bond lengths.

1. Introduction

Due to its high chemical activity, variable valence, and ability to form different stable complexes, vanadium is an essential element of more than 200 minerals. V³⁺-containing minerals are mostly igneous silicates, V⁵⁺ in the form of [VO₄]³⁻ anion occurs mainly as hydrothermal vanadates, and V⁴⁺ as the (VO)²⁺ cation forms minerals of mixed origin, such as metamorphic, hydrothermal or weathering [1]. The genesis of V natural phases correlates with the oxidation state of vanadium, which directly depends on the pH value of the crystallization medium and the reduction potential [2]. While V³⁺ is generally stable under highly anoxic conditions, V⁴⁺ is present in moderately reducing environments, particularly under acidic conditions, and V⁵⁺ is stable under oxygen conditions and in sub-oxygen alkaline environments [3]. Accordingly, only the III, IV, and V valence states of vanadium are relevant under conditions typical for the earth’s surface.

Conversely, divalent vanadium is unstable in the air and rarely forms natural phases. The unique V²⁺-bearing mineral dellagiustaite, Al(V²⁺,V³⁺)₂O₄, was recently found in rocks from Sierra de Comechingones, San Luis, Argentina, and in late pyroclastic ejecta of small Cretaceous basalt volcanoes exposed at Mt Carmel, Northern Israel [4]. It crystallizes in the inverse spinel structure type and cannot be labeled as “vanadium coulsonite” because of the predominance of Al over V³⁺ in the tetrahedral position. Dellagiustaite is associated with hibonite, CaAl₁₂O₁₉, and grossite, CaAl₄O₇, which constitute the modal composition of the rock. At the same time, V and Al metal alloys indicate significantly reducing conditions in the assemblages from both localities. The authors propose that mineral formation results from the interaction of deep-seated magmas and CH₄ ± H₂ fluids in volcanic feeder systems [4].

We obtained a new sodium phosphate, Na₇V₄(PO₄)_6, with V atoms in the 2+ and 3+ oxidation states under hydrothermal conditions. It was synthesized together with the NASICON-type Na₃V₂(PO₄)₃. The new compound is isostructural to the fumarole mineral yurmarinite, Na₇(Fe³⁺,Mg,Cu)₄(AsO₄)₆ [5]. Presumably, yurmarinite was formed under strongly oxidizing conditions of the Arsenatnaya fumarole in association with several alluaudite-type arsenates, namely hatertite, Na₂(Ca,Na)(Fe³⁺,Cu)₂(AsO₄)₃, bradaczekite, NaCu₄(AsO₄)₃, and johillerite, NaMg₃Cu(AsO₄)₃. The high volatility of O in fumarolic gases causes high-valency states of As⁵⁺ and Fe³⁺ in all phases [5]. In octahedral positions of yurmarinite crystal structure, Mg²⁺ and Cu²⁺ cations isomorphically substitute Fe³⁺. Moreover, the yurmarinite structure-type unites synthetic phosphates [6], arsenates [7,8,9], and even molybdates [10] with the general formula (X)₆(M1)(M2)(M3)₃(TO₄)₆ [11]. Most of them contain Na in the X and M1 positions but Fe²⁺ and Fe³⁺ inside the M2 and M3 octahedra. The preparation of heterovalent iron compounds is standard. However, the oxosalts containing V²⁺ are exotic because of their complicated synthesis and low stability. As part of our program of studying mineralogically probable V-bearing phases [12,13,14,15], we present here the results of hydrothermal synthesis, crystal structure, and comparative crystal chemistry of a new sodium and vanadium (II, III) orthophosphate Na₇V₄(PO₄)₆.

2. Materials and Methods

2.1. Hydrothermal Synthesis and Scanning Electron Microscopy

High-temperature hydrothermal synthesis was carried out in a phosphate system with sodium and vanadium cations. Chemically pure primary reagents V₂O₃ 2 g (13.3 mmol) and NaCl 2 g (34.2 mmol) were ground and mixed as powders in the presence of a small amount of 0.3 g Na₃C₆H₅O₇ (1.2 mmol) taken as redox agent. All components were dissolved in 7 mL of 1M aqueous solutions of H₃PO₄ and placed in a copper-lined nickel–chromium alloy autoclave of 14 mL capacity. The synthesis was performed at a temperature of 723 K and a pressure of 50 MPa. The synthesis duration was 20 days, sufficient to complete the crystallization reactions. The product was cooled to room temperature for over 24 h and washed with hot distilled water. As a result, well-faceted crystals of two phases were obtained: black flattened crystals with rhombohedral habitus and a vitreous luster (Figure 1) and yellow crystals of cubic shape with a strong luster.

X-ray microprobe spectral analysis was performed at a Jeol JSM-6480LV SEM with an energy-dispersive spectrometer Oxford X-Man^N (Laboratory of Analytical Techniques of High Spatial Resolution, Dept. of Petrology, Moscow State University, Russia). EDS analysis revealed that both crystalline phases include V, Na, P, and O atoms. After a preliminary X-ray experiment, yellow isometric crystals were identified as Na₃V₂(PO₄)₃ with the NASICON structure type [16]. The second black phase of the rhombohedral habitus was diagnosed as a new compound and became the subject of X-ray diffraction analysis and crystal–chemical discussion.

2.2. X-ray Diffraction and X-ray Absorption Spectroscopy

Low-temperature (T = 110 K) X-ray diffraction experimental data were collected on a Bruker D 8 Quest single-crystal X-ray diffractometer, (Bruker Corporation, Billerica, MA, USA) (MoKα radiation). The dataset was corrected for background, Lorentz and polarization effects, and absorption. All calculations were performed within the WinGX program system, Version 2021.3 [17]. The trigonal crystal structure of the new phase was solved by direct methods in the rhombohedral space group R$\overline{3}$c and refined in the anisotropic approximation of thermal vibrations of atoms with the SHELX programs (SHELXS 2014/6 [18], SHELXL 2018/3 [19]) using the F² data to residuals R = 0.023 and S = 1.04. As a result of the refinement, the crystal–chemical formula of the new compound was established to be Na₇V₄[PO₄]₆. The results of semiquantitative EDS analysis support it. Furthermore, the formula’s electroneutrality may be achieved by supposing a mixed population of two octahedral structural sites by V³⁺ and V²⁺ ions. Therefore, the compound presents a rare case of V²⁺/V³⁺ heterovalent phosphate with the crystal–chemical formula Na₇(V³⁺_0.75V²⁺_0.25)(V³⁺_0.75V²⁺_0.25)₃[PO₄]₆. The simplified formula Na₇V³⁺₃V²⁺[PO₄]₆ clearly shows three times more V³⁺ than V²⁺ ions. The range of V–O distances, bond valence calculation, and XANES spectroscopy confirm it. In

Table 1. Experimental details for Na₇V₄(PO₄)₆.

Crystal Data
Chemical formula	Na7V4P6O24
Mr	934.51
Crystal system, space group	Trigonal, R$\overline{3}$c:H
Temperature (K)	110
a, c (Å)	13.3463 (19), 17.809 (4)
V (Å3)	2747.2 (10)
Z	6
Radiation type	Mo Kα
µ (mm−1)	2.81
Crystal size (mm)	0.08 × 0.08 × 0.04
Data Collection 1
Diffractometer	Bruker D8 Quest
Absorption correction	Multi-scan
Tmin, Tmax	0.453, 0.494
No. of measured, independent and observed [I > 2σ(I)] reflections	9263, 894, 781
Rint	0.045
(sin θ/λ)max (Å−1)	0.703
Refinement
R[F2 > 2σ(F2)], wR(F2), S	0.023, 0.059, 1.04
No. of reflections	894
No. of parameters	65
Δρmax, Δρmin (e Å−3)	0.46, −0.49

¹ Computer programs: CrysAlis PRO [20], SADABS 2016/2 [21], Diamond [22].

, we report the crystallographic characteristics of the phase, the experimental conditions of data collection, and the results of crystal structure refinement. Table S1 lists the atomic coordinates and equivalent anisotropic displacement parameters. Figure S1 shows the calculated pattern for Na₇V₄[PO₄]₆. Characteristic distances are given in

Table 2. Selected distances (Å).

V1 Octahedron		Na1 0ctahedron
V1—O3 × 6	2.0173 (13)	Na1—O4 × 6	2.3653 (14)
V2 Octahedron		Na2 [6+3] Polyhedron
V2—O1 × 2	1.9878 (13)	Na2—O4	2.2706 (16)
V2—O2 × 2	1.9942 (14)	Na2—O1	2.5290 (16)
V2—O3 × 2	2.0548 (13)	Na2—O4	2.5718 (17)
		Na2—O2	2.5721 (16)
P Tetrahedron		Na2—O4	2.6202 (17)
P—O4	1.5103 (14)	Na2—O2	2.6401 (17)
P—O2	1.5428 (15)	Na2—O1	2.8084 (17)
P—O1	1.5513 (14)	Na2—O3	2.8765 (16)
P—O3	1.5676 (14)	Na2—O1	3.0213 (14)

. We deposited structural data via the joint CCDC/FIZ Karlsruhe deposition service as CSD 2214946. It can be obtained free of charge from FIZ Karlsruhe via www.ccdc.cam.ac.uk/structures accessed on 24 October 2022.

To confirm the presence of V²⁺ in the compound, we studied X-ray absorption near-edge structure (XANES) at the K-edge of vanadium (obtained at the Structural Materials Science beamline [23] of the Kurchatov Synchrotron Radiation Source, Moscow, Russia). The parameters of the experiment were the following. The electron beam’s energy of X-ray synchrotron radiation was 2.5 GeV at an average current of 60–100 mA. The absorption spectra were collected in the fluorescent radiation detection mode, i.e., the X-ray intensity was measured up to the sample, and the fluorescent radiation was detected. An ionization chamber was used to measure the X-ray beam intensity. The fluorescent radiation was captured with the help of an Amptek SDD detector. X-ray absorption spectra were processed by standard procedures for background extraction and normalized to the magnitude of the absorption jump. This procedure was performed using the Larch software package [24].

3. Results

3.1. Crystal Structure Description in terms of Close-Packing

The crystal structure of Na₇V₄(PO₄)₆ is based on the main structural units shown in Figure 2a. They are two symmetrically independent vanadium octahedra and an orthophosphate tetrahedron. The PO₄ polyhedron has minimal C₁ symmetry and represents a distorted trigonal pyramid. Three oxygen atoms O₁–O₃ are located at distances of 1.543(1)–1.568(1) Å from the P atom (Table 2). They lie in a plane approximately parallel to (001). Additionally, they are involved in the coordination of vanadium cations (Figure 2b). The fourth oxygen vertex O4 at a shortened P–O4 distance of 1.510(1) Å points almost perpendicular to the base of the phosphate tetrahedron along the c-axis (Figure 2 and Figure 3). In addition to phosphorus, the O4 atom coordinates sodium cations. V atoms occupy two positions in the structure with site symmetry 32 and 2. In an octahedron with D₃ symmetry, all V1–O3 bond lengths are equivalent and equal to 2.017(1) Å; in the octahedron with lower C₂ symmetry, the V-O bond lengths vary from 1.988(1) to 2.055(1) Å (Table 2). The average V–O distances in both polyhedra are close and equal to 2.017 and 2.012 Å, respectively.

In the crystal structure of Na₇V₄(PO₄)₆, vanadium polyhedra unite in the cluster, in which every V₁O₆ octahedron on a three-fold axis shares common edges with three surrounding V₂O₆ octahedra (Figure 2b and Figure 3a). These clusters do not link with each other along the [001] direction. Instead, they form the close-packed layers parallel to the (001) plane and alternate along the c-axis in a sequence (ABCABC) (Figure 3b and Figure 4a). Furthermore, all oxygen vertices of VO₆ polyhedra in the cluster are shared with orthophosphate tetrahedra. Thus, tetramers of V-centered octahedra unite via PO₄ groups along the [001] direction into a close-packed framework crystal structure (Figure 3).

The negative charge of the heteropolyhedral anionic framework [V₄(PO₄)₆]^7- is compensated by Na cations, which occupy two symmetrically different sites in the structure. Regular Na₁O₆ octahedra with C_3i symmetry have six identical Na1–O4 distances of 2.362(1) Å (Table 2). The Na₂O₆ octahedron with intrinsic C₁ symmetry is strongly distorted: the Na-O bond lengths range in the interval 2.271(2)–2.640(2) Å with an average value of 2.534 Å. Three additional oxygen atoms are at distances of 2.808(2), 2.877(2), and 3.021(1) Å (Table 2). Sodium polyhedra share faces and edges to form clusters of seven units with a central Na₁O₆ octahedron and Na₂O₆ octahedra multiplied by six due to the $\overline{3}$ inversion axis. Similar to vanadium tetramers, these clusters in a cut layer parallel to the (001) plane are arranged in the densest manner (Figure 4). These layered fragments alternate in the sequence (ABCABC) corresponding to the cubic close-packing (Figure 3). Along the c-axis, sodium heptamers interconnect through common O₄–O₄ edges of Na₂O₆ polyhedra and form a three-periodic cationic framework.

3.2. BVS Calculations and XANES Spectroscopy

The requirement for electroneutrality of the title compound is achieved by including vanadium cations of two valence states, V²⁺ and V³⁺. Close values of V–O distances characterize both polyhedra centered with vanadium (Table 2). Furthermore, the average V–O bond lengths are almost equal: 2.017 and 2.012 Å, which indicates the mixed occupancy of both structural positions by V atoms in the 3+ and 2+ oxidation states. The calculation of bond–valence sums [25,26] confirms the statistical distribution of V³⁺ and V²⁺ ions (

Table 3. Bond–valence data ¹.

	V1	V2	P	Na1	Na22	$\mathsf{\Sigma }$
O1		0.510 ×2↓	1.189		0.134, 0.075, 0.049	1.96
O2		0.501 ×2↓	1.215		0.123, 0.107	1.95
O3	0.471 ×6↓	0.425 ×2↓	1.135		0.066	2.10
O4			1.328	0.189 ×6↓	0.230, 0.123, 0.111	1.98
$\mathsf{\Sigma }$	2.83	2.87	4.87	1.13	1.02

¹ Symbols ^×2↓ and ^×6↓ mark a multiplication of the corresponding contribution along the column due to the symmetry; ² Contributions from all nine neighboring O atoms were taken into account.

). Based on the theoretical ratio V³⁺/V²⁺ = 3:1, the total vanadium contributions 2.83 and 2.87 are quite close to 2.75, which indicates a mixed valence state of V in both structural sites: Na₇V^2.75V^2.75₃[PO₄]_6.

In order to determine the formal oxidation state of the absorbing atom (V), the analysis of the shape and position of the XANES spectrum could be used [27,28,29,30]. We applied the procedure described in [31]. The oxidation state of vanadium atoms in the sample under study was determined by interpolating the edge position shift. We considered that the position of the edge jump is the energy at which the normalized absorption equals 0.5. Therefore, the spectrum shift at the level of half the absorption jump is assumed to be proportional to the formal oxidation state of the metal (V). The experimental XANES spectra are shown in Figure 5. The spectra of compounds VSO₄·6H₂O and V₂(SO₄)₃ [32] were used as standards because of the same octahedral coordination of vanadium atoms as in the Na₇V₄(PO₄)₆ phase. Thus, it was determined that the formal oxidation state of the metal is 2.57, which qualitatively confirms the assumption that there are vanadium atoms with two oxidation states: 3+ and 2+.

3.3. The Comparative Crystal Chemistry of Na₇V₄(PO₄)₆ and the Database Survey of V²⁺-Containing Oxosalts

As mentioned in the Introduction, the titled vanadium phosphate is a member of the family of compounds with the general formula (X)₆(M1)(M2)(M3)₃(TO₄)₆, which includes the fumarole mineral yurmarinite, Na₇(Fe³⁺,Mg,Cu)₄(AsO₄)₆ [5] and synthetic iron (II, III) phosphate Na₇Fe₄(PO₄)₆ [6]. In these two phases, the valence state of the Fe atoms was confirmed by Mössbauer or Raman spectroscopy.

Table 4. Unit-cell parameters (Å), volumes (ų), and interatomic distances (Å) for V/Fe octahedra in Na₇V₄(PO₄)₆,Na₇Fe₄(PO₄)₆, and yurmarinite, Na₇(Fe³⁺,Mg,Cu)₄(AsO₄)₆ crystal structures (space group R$\overline{3}$ c, Z = 6).

	Na7V4(PO4)6	Na7Fe4(PO4)6	Yurmarinite, Na7(Fe3+, Mg, Cu)4(AsO4)6
a (b)	13.3463(19)	13.392(2)	13.7444(2)
c	17.809(4)	17.858(3)	18.3077(3)
V	2747.2(10)	2773.7(8)	2995.14(8)
M2–O3 × 6	2.0173(13)	2.063(2)	1.9429(18)
<M2–O>	2.02	2.06	1.94
M3–O1 × 2	1.9877(13)	1.974(2)	1.991(2)
M3–O2 × 2	1.9942(14)	1.997(2)	2.0142(19)
M3–O3 × 2	2.0548(13)	2.085(1)	2.1170(19)
<M3–O>	2.01	2.02	2.04

shows the cation–anion distances for the transition-metal octahedral sites M2 (Wyckoff site 6a, site symmetry 32) and M3 (Wyckoff site 18e, site symmetry 2) populated by V or Fe. The close average values of the M−O bond lengths in the M2O₆ and M3O₆ octahedra, equal to 2.02 Å and 2.01 Å, indicate the mixed occupancy of the V positions in the Na₇V₄(PO₄)₆ crystal structure. In addition, the M–O bond lengths are close enough in the Fe- and V-bearing phases. This similarity results from the close values of the cationic radii of these transition metals in the same valence states and in the same octahedral coordination (rV²⁺ = 0.79 Å, rFe²⁺ = 0.78 Å; rV³⁺ = 0.64 Å, rFe³⁺ = 0.63 Å [33]). The V ionic radii are slightly smaller than those of iron; accordingly, the unit-cell parameters and volume of Na₇V₄(PO₄)₆ are also smaller than those of Na₇Fe₄(PO₄)₆. The unit-cell parameters of yurmarinite are the largest due to the larger size of arsenate tetrahedra compared to phosphate groups.

Table 5. Synthetic and natural oxygen-containing inorganic compounds with divalent vanadium.

Compound/ Mineral	Space Group, Z, ρ, mg/m3	Unit-Cell Para-Meters, a, b, c, Å and Angles,°	R	Range of V–O Distances in Octahedra, Å	Synthesis Technique/Natural Genesis	Ref.
(NH4)2V(SO4)2·6H2O NH4,V-analogue of picromerite and Tutton’s salt	P21/a 2, 1.80	a = 9.42(3) b = 12.76(3) c = 6.22(2) β =107.2(2)	0.08	2.118–2.164 <2.15>	Modification of Kranz method to obtain VOSO4, its further cooling and electrolytic reduction in H2SO4 solution, then the addition of pyrogallol and recrystallization in N2 atmosphere.	[34]
V(H2O)6SO4 V-analogue of hexahydrite	C2/c 8, 1.91	a = 10.081(3) b = 7.286(2) c = 24.445(7) β = 98.78(2)	0.039	2.123–2.136 <2.13> 2.120–2.150 <2.13>	Modification of the Kranz method. Electrochemical reduction of VOSO4·2H2O in the solution of H2SO4 under N2 or Ag atmosphere followed by adding ethanol on cooling.	[35]
V(H2O)6SO4·H2O	P21/c 4, 1.86	a = 14.130(3) b = 6.501(1) c = 11.017(2) β = 105.64(2)	0.029	2.102–2.137 <2.12> 2.119–2.150 <2.13>	Recrystallization of VSO4·6H2O precursor in the solution of H2SO4 in N2 atmosphere with the addition of ethanol and cooling.	[36]
Li2VPO4F closely related to tavorite str. type	C2/c 4, 3.17	a = 7.2255(1) b = 7.9450(1) c = 7.3075(1) β = 116.771(1)	0.049 *	2.119–2.139 <2.13>	Solid-state synthesis of LiV(PO4)F at 750 °C in an Ar atmosphere, followed by Li-intercalation with LiAlH4 in tetrahydrofuran under Ar.	[37]
Li2V2(SO4)3 derivative of NASICON str. type	C2/c 4, 3.01	a =13.0582(5) b = 8.6526(4) c = 8.72447(4) β = 115.443(2)	0.042 *	2.073–2.230 <2.14>	Electrochemical Li-intercalation in V2(SO4)3 with n–butyllithium C4H9Li in a vacuum.	[38]
V2+,3+2OPO4 (high-T modif.)	I41/amd 4, 3.97	a = 5.362(5) c = 12.378(9)	0.044	2.047–2.074 <2.06>	Reduction of VPO4 by metallic V at 500 °C and 900 °C via chemical vapor transport in I2.	[39]
V2+,3+2OPO4 (low-temperature modification)	C2/c 4, 3.98	a = 7.56825(7) b = 7.60013(7) c = 7.21794(6) β =121.2751(5)	0.074 *	2.054–2.123 <2.09> 1.972–2.079 <2.03>	β-VOPO4 preparation at 600 °C in flowing O2;further solid-state synthesis at 1000 °C with metallic V in a vacuum.	[40]
SrV3+,2+10O15 **	Ccmb 4, 5.20	a = 9.915 b =11.574 c = 9.324	0.08	1.948–2.192 <2.01> 1.950–2.148 <2.05> 1.965–2.195 <2.04>	Solid-state synthesis at 1900 °C in H2 atmosphere	[41]
Al(V2+,3+)2O4 (frustrated spinel)	R$\overline{3}$m 2, 4.65	a = 5.7613(2) c = 28.6876(10)	0.011 *	2.052–2.063 <2.06> 2.007	Solid-state synthesis with metallic Al at 1150 °C for 150 h in vacuum, phase transition at 427 °C	[42,43]
Al(V2+,3+)2O4 (inverse spinel)	Fd$\overline{3}$m 8, 4.66	a = 8.1546(6)	No data	2.040	Solid-state synthesis with metallic V at 900 °C in a vacuum	[44,45]
Dellagiustaite, Al(V2+,V3+)2O4 (inverse spinel)	Fd$\overline{3}$m 8, 4.62	a = 8.1950(1)	0.014	2.045	High redox conditions, probable crystallization from high-temperature melts of volcanic magma	[4]
NaV3+,2+3(PO4)3	Imma 4, 3.42	a = 10.488(2) b =13.213(3) c = 6.455(7)	0.056	1.959–2.062 <1.99> 2.042–2.086 <2.06>	Step-wise solid-state synthesis at 900 °C in a vacuum	[46]
Na7V3+,2+4(PO4)6 V, P-analogue of yurmarinite	R$\overline{3}$c 6, 3.39	a =13.3463(19) c = 17.809(4)	0.023	2.017 1.988–2.055 <2.01>	High-temperature hydrothermal synthesis at 450 °C with Na3C6H5O7 redox agent	This work

* Based on power data, including synchrotron and neutron radiation sources; ** Isostructural with BaV^3+,2+₁₀O₁₅ [47].

lists all V²⁺-bearing oxosalts with known crystal structures collected in the ICSD database. Five listed phases include exceptionally V²⁺ compounds, while seven of the other listed compounds contain both V²⁺ and V³⁺ cations. In all crystal structures, V occupies octahedral positions.

Urusov and Serezhkin [48] showed that the V²⁺ and V³⁺ cations form regular octahedra with average V–O bond lengths equal to 2.13 and 2.01 Å. Similarly, the data from Table 5 show that the average V–O distances range slightly from 2.12 Å to 2.18 Å for V²⁺-centered octahedra and from 2.01 Å to 2.09 Å for polyhedra isomorphically occupied by V²⁺ and V³⁺ cations. It is consistent with the smaller ionic radius of V³⁺ (0.64 Å) compared to V²⁺ (0.79 Å) [33]. For the title Na₇V₄(PO₄)₆ compound, with a mixed valence state of vanadium, the average <V–O> distance of 2.02 Å lies in the lower part of the region for compounds with V^2+,3+-centered polyhedra.

Although the first inorganic oxide of divalent vanadium was synthesized more than a hundred years ago, the number of compounds containing V²⁺ ions in “formula” amounts is still small. The main reason for the small number of V²⁺ oxosalts is their high instability in the air, which significantly complicates the synthesis and preparation of precursors [49]. Three methods for synthesizing vanadium oxosalts are commonly used, and all require an inert atmosphere and redox reagents. First, Kranz suggested a synthesis by a stepwise reduction of V₂O₅ by electrolysis [50]. This method was modified by Shlenck’s techniques and became the basis for the synthesizing of V²⁺ hydrate sulfates (Table 5). One major feature of these compounds is the presence of water molecules in V²⁺ octahedral coordination. Consequently, all the structures possess low density equal to 1.8–1.9 Mg/m³.

The second method, the Li-intercalation, was used to obtain Li₂V²⁺(PO₄)F related to tavorite and Li₂V²⁺₂(SO₄)₃ with the NASICON-derived structure. Later, by the third method, heterovalent (V^2+,3+) compounds were synthesized using a high-temperature solid-state reaction. As a result, α-CrPO₄-type NaV^3+,2+₃(PO₄)₃, two polymorphic oxophosphates V^2+,3+₂OPO₄, two isostructural oxides SrV^3+,2+₁₀O₁₅ and BaV^3+,2+₁₀O₁₅, and two spinel polymorphs Al(V^2+,3+)₂O₄ were obtained by the third method. Interestingly, both spinels and exceptionally Sr or Ba vanadium oxides feature structures based on the hexagonal close-packing and thus have a high density of 4.6–5.2 Mg/m³. Noteworthy, the same inverse spinel, Al(V²⁺,V³⁺)₂O₄, called dellagiustaite, was recently found in nature and presented a unique mineral with V²⁺ cations as an essential element in its composition. However, it is difficult to establish the genesis of dellagiustaite due to the lack of information about the exact location of the outcrop and related rocks [4]. However, exclusively reducing conditions are necessary for mineral formation because it is associated with almost pure vanadium alloys.

We successfully obtained heterovalent V(II, III) phosphate under hydrothermal conditions. In solution under normal conditions, vanadium dissolves and exists as the V²⁺ cation under acidic and redox conditions exclusively, i.e., at pH = −2–2 and Eh = −1–0 V, according to the thermodynamic data of the Gibbs free energy for vanadium (see, for example, [51]). The high solubility of phosphoric acid and the use of Na₃C₆H₅O₇ as a redox agent allowed us to obtain two sodium vanadium phosphates: NASICON Na₃V³⁺₂(PO₄)₃ with the kosnarite structure type and Na₇V^3+,2+₄(PO₄)₆ with the yurmarinite structure type. Therefore, we can assume that the "metastable" Na₇V₄(PO₄)₆ was formed as a primary phase at a higher temperature and a lower pH value. It is likely that the more stable compound Na₃V₂(PO₄)₃ was formed subsequently upon smooth cooling of the autoclave.

3.4. Topological Analysis of Ion Conductivity of Na₇V₄(PO₄)₆

Vanadium provides an excellent opportunity to exchange more than one electron per transition metal, resulting in a high theoretical energy density [52]. In addition, the presence of many Na⁺ ions in the crystal structure can also lead to the possible activation of plenty of redox transitions V²⁺/V³⁺/V⁴⁺/V⁵⁺ during the electrochemical extraction of sodium. Currently, four Na,V³⁺ phosphates are known to possess electrochemical properties. We obtained one of them, Na₃V₂(PO₄)₃, as a byproduct of the synthesis. It is a synthetic variety of mineral kosnarite, KZr₂(PO₄)₃, whose crystal structure is close to that of the sodium superionic conductor NASICON. Na₃V₂(PO₄)₃ exhibits high energy density, thermal and structure stability, ion conductivity, and a high-voltage plateau at 3.4 V [53,54,55,56]. Likewise, other Na,V³⁺ phosphates, namely Na₃V(PO₄)₂ [57,58], Na₃V₃(PO₄)₄ [59], and NaV₃(PO₄)₃ [30,46] represent high-voltage cathode/high-performance anode materials for sodium batteries [60]. We emphasize that the Na₃V(PO₄)₂ crystal structure is also related to mineral aphthitalite; both Na₃V₃(PO₄)₄ and NaV₃(PO₄)₃ crystal structures are closely related to that of α-CrPO₄. To evaluate the electrochemical properties without sufficient substance for experimental measurements, we applied the theoretical calculation of the ionic conductivity of Na₇V₄(PO₄)₆.

To find the migration paths of Na⁺ cations throughout the framework [61], we used the geometrical–topological approach from the ToposPro package [62]. The method is based on the Voronoi–Dirichlet partition model, which helps to find out the centers of vacations and channel lines. The Voronoi–Dirichlet partition model is founded on the following basement. The convex Voronoi polyhedra bend around each of the “framework” atoms. This bending results in the forming of voids located most distant from the structure atoms. Linked together, voids form the net, whose periodicity reflects the ion migration path’s topology. Remarkably, the net of voids should be infinite—like a chain, a layer, or a framework—to promote conductivity.

The primary geometric parameters for the Voronoi–Dirichlet model are the radius of the spherical domain R_sd and the channel radius R_ch. In our calculation, the threshold value of R_sd is set equal to 1.31 Å, which is 10% lower than the experimental value for “real” sodium atoms in the structure (1.50 Å and 1.46 Å). It is much smaller than the theoretical average value of 1.54 Å [63] and close to 1.35 Å estimated from the migration maps of Na-ion conductors in recent studies [64,65]. The threshold value of R_ch was asserted to be 2.0 Å following [64]. Theoretically, the structural channel is assumed accessible for ion flotation if the sum of the radii of the mobile ion (Na) and the framework atom (O) exceeds the channel radius R_ch by 10–15%. In contrast with the theoretical preposition, the topological analysis shows the absence of migration paths for Na⁺ cations, even though the lowest values of the threshold parameters were taken. Small structural voids with a radius of 1.31 Å to 1.57 Å do not connect with each other in the crystal structure of Na₇V₄(PO₄)₆ and therefore do not form infinite channels large enough for Na⁺ passing.

4. Conclusions

Under high-temperature (450 °C) hydrothermal conditions, we successfully synthesized a new phase Na₇V₄(PO₄)₆, a V^3+,2+ analogue of the fumarole mineral yurmarinite. We showed that the crystal structure of Na₇V₄(PO₄)₆ is based on densely packed layers of vanadium or sodium clusters, which alternate in the ABCABC sequence, and link by [PO₄] tetrahedra. Besides the new compound Na₇V₄(PO₄)₆, the research revealed only twelve oxosalts with V²⁺ or isomorphic V²⁺/V³⁺ cations, including the unique divalent vanadium mineral dellagiustaite. Our study presents the first case of hydrothermally synthesized Na₇V^3+,2+₄(PO₄)₆ crystals in addition to electrolysis, Li-intercalation, and the solid-state method used previously to prepare V²⁺ inorganic compounds. We conducted the X-ray diffraction study, BVS calculations, crystal–chemical comparative analysis of V²⁺-bearing compounds, and XANES measurements of Na₇V₄(PO₄)₆ crystals, which confirmed the presence of V²⁺ ions in it. Furthermore, the disability of Na-ion migration through Na₇V₄(PO₄)₆ was shown by performing the topological analysis of its crystal structure.