Features of Structures and Ionic Conductivity of Na 3 Fe 2 (PO 4 ) 3 Polycrystals Obtained by Solid Phase and Melt Methods

: This article investigates the structures and conductive properties of polycrystals of Na 3 Fe 2 (PO 4 ) 3 obtained by solid-state and melt synthesis methods using concentrated optical radiation. It has been established that in the melt synthesis method, the material is synthesized under signiﬁcantly non-equilibrium thermodynamic conditions, leading to the creation of deformations in the sample, which contribute to the enhancement of ionic conductivity. Additionally, the synthesis duration is reduced by half. Through a comparative assessment of the structural parameters and conductive properties of these materials, it is demonstrated that polycrystals obtained by the melt method exhibit better texture and higher ionic conductivity. The occurrence of deformations during the synthesis of α -Na 3 Fe 2 (PO 4 ) 3 under high temperature-gradient conditions indicates the elasticity of the crystalline framework {[Fe 2 (PO 4 )] 3 − } 3 ∞ . It is concluded that the non-equilibrium thermodynamic conditions of α -Na 3 Fe 2 (PO 4 ) 3 synthesis promote the formation of deformations in the crystalline structure of polycrystals, leading to a partial increase in symmetry and ionic conductivity.


Introduction
Currently, there is a growing interest in materials from the NASICON family due to their potential use as structural materials, for example, as electrode materials in sodium-ion batteries (SIB) [1][2][3][4][5][6].Replacing lithium-ion batteries (LIB) with SIBs could lead to the development of a cost-effective current source production technology.This, in turn, may significantly reduce the cost of SIBs [7][8][9][10].The relevance of developing a technology for obtaining efficient cathode materials is evident, as the key components of SIBs are the cathode materials, which primarily determine the final energy density and cost of the battery [8,9].However, sodium-containing cathode materials in SIBs generate lower energy densities compared to LIBs, as Na + ions have a larger ionic radius and redox potential [9][10][11][12][13].Therefore, there is a need for the development of a technology for obtaining more efficient sodium-containing cathode materials for SIBs [9,[14][15][16].
Many polycrystals from the NASICON family are considered potential structural materials for creating electrodes (anodes and cathodes) in SIBs [2,17,18].Within this family, orthophosphate Na 3 Fe 2 (PO 4 ) 3 stands out as an ionic conductor and a promising material for creating the cathodes of SIBs [19,20].
It is known that many oxide ionic conductors show promise as cathode materials for use in power sources [21].However, these ionic conductors possess anionic conductivity (for oxygen) and are therefore used as cathodes in solid oxide fuel cells (SOFC).Considerable attention is also given to the research into oxide ionic conductors, such as the Ruddlesden-Popper phase materials, for use in SOFCs [22].In contrast to oxide ionic conductors, Na 3 Fe 2 (PO 4 ) 3 exhibits cationic sodium conductivity.
It should be noted that the structure of the three-dimensional rhombohedral crystalline framework of α-Na 3 Fe 2 (PO 4 ) 3 at room temperature is ordered but monoclinically distorted (space group C2/m).After the phase transition α→β, the cationic sublattice becomes partially ordered with space group R3c.The subsequent transition β→γ leads to complete disordering of the cationic sublattice and uniform distribution of sodium cations throughout the extensive M(1)-and M(2)-type voids.Importantly, sodium cations can move in three dimensions due to the presence of "windows" between the A-and B-type cavities [28,29].Probability pathways for sodium cation diffusion in Na 3 Fe 2 (PO 4 ) 3 along the channels of the crystal framework have been established [27].The relationship between phase transitions and the redistribution of sodium cations in the structure of Na 3 Fe 2 (PO 4 ) 3 are discussed in [25][26][27][28][29].
The distinctive feature of the low-temperature phase α-Na 3 Fe 2 (PO 4 ) 3 is the presence of superstructural distortions and dipolar ordering of the anti-ferroelectric type (AFE) [23,26].Using Raman spectroscopy in α-Na 3 Fe 2 (PO 4 ) 3 , bands attributed to the vibrations of the phosphate anion and various ions were detected [20,29].At room temperature, the most thermo-sensitive modes are located in the low-frequency range of 100-400 cm −1 , near 500 cm −1 , while modes corresponding to the stretching of the valence bond of the (PO 4 ) unit lie in the frequency range of 970-1200 cm −1 .These data suggest that despite the "rigidity" of the anionic crystalline framework, there is a certain degree of "elasticity" due to the ability of the (PO 4 ) unit to undergo displacement and stretching.
It should be noted that in the low-symmetry monoclinic phase of α-Na 3 Fe 2 (PO 4 ) 3 , the distribution of sodium cations occurs within the capacious B-cavities (M(2)), where the dipolar ordering of the cationic sub-lattice takes place [30].While the ionic conductivity of α-Na 3 Fe 2 (PO 4 ) 3 is not particularly high, this phase is characterized by structural stability and thermal stability.The presence of "conductive channels" in the crystalline framework of α-Na 3 Fe 2 (PO 4 ) 3 allows for ionic conductivity, and the structural stability will contribute to small volume changes during intercalation and deintercalation of Na ions in SIBs.Therefore, α-Na 3 Fe 2 (PO 4 ) 3 is considered a promising cathode material for SIBs.However, cathode materials made from polycrystals of α-Na 3 Fe 2 (PO 4 ) 3 synthesized by solid-state methods in SIBs currently exhibit a relatively low specific capacity of 61 mAh g −1 , which decreases to 57 mAh g −1 after 500 cycles at a voltage of 2.5 V [2].Therefore, it is necessary to enhance the conducting and electrochemical properties of α-Na 3 Fe 2 (PO 4 ) 3 through structural modification.
It has been observed that depending on the synthesis process parameters, polycrystals of α-Na 3 Fe 2 (PO 4 ) 3 can exhibit different modifications.It is known that Na 3 Fe 2 (PO 4 ) 3 can crystallize in both monoclinic C2/m and rhombic R3c : H space groups [2,24,26,32].Presumably, the formation of various low-symmetry crystals of α-Na 3 Fe 2 (PO 4 ) 3 results from the emergence of stresses and deformations in the crystalline framework, induced by non-equilibrium thermodynamic conditions during crystallization.These findings suggest that the structure of Na 3 Fe 2 (PO 4 ) 3 is highly sensitive to deformations, allowing it to adopt its crystalline structure in one or another polymorphic modification.Therefore, the thermodynamic conditions of crystallization play a crucial role in shaping the structural characteristics and properties of polycrystals of this type.
It has already been demonstrated that the synthesis of α-Na 3 Fe 2 (PO 4 ) 3 under the influence of hydrostatic pressure partially enhances the ionic conductivity of this compound by partially relieving the monoclinic distortion of the crystalline framework during crystallization [30].The increase in specific discharge capacity in SIBs when using α-Na 3 Fe 2 (PO 4 ) 3 , synthesized by the hot-pressing method as a cathode material, has been reported in [33].This is likely attributed to the fact that polycrystals with higher conductivity slightly accelerate the intercalation/deintercalation process during electrochemical processes in SIBs.
Another important factor in improving the quality of Na 3 Fe 2 (PO 4 ) 3 cathode material is the use of different synthesis methods.For instance, Na 3 Fe 2 (PO 4 ) 3 synthesized via the solgel method has led to an increase in initial specific discharge capacity up to 92.5 mAh•g −1 in SIBs, attributed to the porous structure of the cathode material [34].
The method of irradiation-induced sintering using concentrated optical energy has not yet been tested for polycrystal formation of orthophosphates.This method differs from solid-state synthesis in that it produces a glass phase from the initial mixture through optical heating via non-contact zone melting [35].Subsequently, polycrystals are obtained from the glass phase using ceramic technology.
This synthesis approach has been tested in the production of a range of optical and HTSC ceramic materials.For instance, results obtained in the synthesis of an optical material under the influence of optical radiation (visible light) demonstrate improvements in the structure and conducting properties of the sample [36].Specific compositions of bismuth-containing HTSC ceramics, prepared from glass phases synthesized under the influence of optical radiation (visible light), show enhancements in the structure and critical parameters of the samples [37].
The thermodynamic conditions of sample synthesis are favorable for obtaining effective optical materials and HTSC ceramics.In this regard, the synthesis of Na 3 Fe 2 (PO 4 ) 3 via the melt method under the influence of optical radiation is of particular interest, as in this case, the thermodynamic conditions of synthesis significantly differ from those of the solid-state method.
Further investigation is required to elucidate the influence of thermodynamic factors during the synthesis of Na 3 Fe 2 (PO 4 ) 3 on the structure and conducting properties of this material.This includes a comprehensive examination of the interplay between synthesis conditions, structure, and conducting properties.
This study aims to investigate the characteristics of the structures and conducting properties of polycrystals of Na 3 Fe 2 (PO 4 ) 3 obtained through solid-state synthesis (Type 1 samples) and the melt method using concentrated optical radiation (Type 2 samples).

Materials and Research Methods
Sample synthesis.Polycrystalline samples of Na 3 Fe 2 (PO 4 ) 3 of two types were used for this study.Type 1 samples were synthesized through a solid-state reaction method.The starting reactants included sodium carbonate (Na 2 CO 3 ), iron oxide (Fe 2 O 3 ), and ammonium dihydrogen phosphate (NH 4 H 2 PO 4 ).It is worth noting that all reagents used were of analytical grade purity.
The synthesis process began with the mechanical milling of a mixture of the initial reactants in a planetary mill (Germany).Subsequently, the mixture was pressed into tablets and subjected to preliminary annealing for 2 h at a temperature of 620 K.After another round of milling, the resulting powders were once again pressed into tablets.
In the case of solid-state synthesis, the production of Type 1 samples was carried out in two stages by annealing the initial reactants using a muffle furnace.The first annealing was conducted at 870 K.After milling the resulting mass, the powders were once again pressed into tablets and subjected to a second annealing at 1070 K.It is worth mentioning that during the first stage of annealing for 8 h, phase formation took place, followed by sintering of the Na 3 Fe 2 (PO 4 ) 3 polycrystal during the second 8 h annealing.These polycrystals are designated as Type 1 samples.
In the melt synthesis method, the glass phase (zone recrystallization) was achieved using the URN-2-ZP radiation heating setup (USSR, Moscow) via the method of non-contact zone melting under the influence of optical radiation [35].A focused source of local heating in the setup was provided by the light energy from a high-pressure xenon arc lamp, which was directed by two elliptical reflectors.
The starting mixture consisted of powders that underwent a heat treatment for 2 h at 620 K.The initial mixture samples were pressed into two cylindrical shapes, each with a diameter of 1 cm and a length of 3 cm.One end of each cylinder was tapered.The cylindrical ends of the samples were affixed to the upper and lower rods, while the tapered ends were directed towards each other.The setup was configured so that the focused light energy was directed onto the tapered ends of the samples.The optical system of the apparatus allowed for the sintering of the samples under the influence of radiant energy of optical radiation with a power of up to 5 kW.During the melting process, the power of the light energy was regulated.When pulses of light energy were absorbed by the material, it led to the excitation of the electronic and phonon subsystems of the sample, potentially resulting in rapid localized temperature increases.Such brief heating of the sample could lead to its melting.At the start of the heating process, a droplet of molten material formed on the tapered portion of the lower cylindrical sample, while the tapered portion of the upper cylindrical sample served as a nucleation site for the solidification process.Solidification occurred by pulling the nucleation site out of the hot molten zone.As the pointed end of the lower sample heated and the upper and lower rods melted, smooth translational movements were made.The setup allowed for the recrystallization of the sample through its progressive downward movement at a specified linear velocity V through the molten zone.Since the material was melted without a crucible, the molten zone was maintained by surface tension forces.Optimal conditions for obtaining the melt and glass phases were established during the experiment.The optimal duration of the technological process was 5 min.It is worth noting that the processes of melting and cooling of the material occur under highly non-equilibrium thermodynamic conditions.Melting occurs due to the electromagnetic energy from the powerful flux of optical radiation (quantum E = hν) onto the surface of the sample (similar to a shock wave).Part of the energy of the shock wave is transferred to heating and melting the surface, while the other part propagates further into the volume of the sample through heat transfer.It should be emphasized that the melting of the sample occurs layer by layer (stepwise) due to the uneven heating.The cooling of the melt also occurs under non-equilibrium thermodynamic conditions (under conditions of a strong temperature gradient between the nucleation site and the melt).Moreover, the temperature of the melt reaches 1270 K, and the cooling process (heat transfer to the surrounding environment) occurs rapidly, as the process is conducted in an open space.
An advantage of this synthesis method is that the process of obtaining the glass phase is carried out without the use of a crucible, allowing for free access of oxygen to the sample.Additionally, the technological process time is significantly reduced (almost twice as fast as in the solid-phase synthesis method), leading to a reduction in energy consumption.After the completion of the zone recrystallization process, the sample was obtained in the form of an elongated dark glass phase.
To obtain polycrystals, the obtained glass phase was subjected to grinding, after which the powders were pressed into tablets under the action of uniaxial pressure of 5 kN.The prepared samples were annealed in a muffle furnace for 8 h at a temperature of 1070 K.These polycrystals will be referred to as Type 2 samples.
The specific synthesis parameters for samples of each type are provided in Table 1.Table 1 presents the synthesis parameters for the first and second stages for samples of Types 1 and 2, respectively.During the first stage of phase formation, the synthesis parameters (temperatures and duration of annealing) for samples of Types 1 and 2 significantly differed.However, during the second stage of synthesis (i.e., the stage of crystallite formation in polycrystals), the samples were annealed under identical technological conditions.The phase purity of the synthesized samples and structural parameters were determined using Bruker D8ADVANCEECO X-ray diffractometers (CuK α radiation), (Karisruhe, Germany).Microstructural and elemental analyses of the samples were performed using JEOL-6490LA scanning electron microscopes (Tokyo, Japan) equipped with an energydispersive X-ray spectrometer system from OXFORD Instruments Analytical Limited (Oxford, UK) and JSM-6390LV (Tokyo, Japan) with an integrated energy-dispersive X-ray spectrometer (EDS).The investigation of the conductive parameters of the samples was carried out using the impedance method with the E7-30 device (Minsk, Belarus), an electric furnace, and a temperature sensor "Temodat" (Perm, Russia).

Structural Parameters of Samples
The synthesized samples exhibited a light burgundy color and took the form of ceramic tablets with a diameter of 10 mm and a thickness of 1.5 mm.
The structural parameters of the obtained polycrystalline samples of Na 3 Fe 2 (PO 4 ) 3 were investigated using powder X-ray diffraction methods with a diffractometer, as well as with a scanning electron microscope Hitachi TM3030 equipped with a Bruker microanalysis system.Figure 1 shows the diffractograms of Na 3 Fe 2 (PO 4 ) 3 samples of both types.  1 presents the synthesis parameters for the first and second stages for samples of Types 1 and 2, respectively.During the first stage of phase formation, the synthesis parameters (temperatures and duration of annealing) for samples of Types 1 and 2 significantly differed.However, during the second stage of synthesis (i.e., the stage of crystallite formation in polycrystals), the samples were annealed under identical technological conditions.
The phase purity of the synthesized samples and structural parameters were determined using Bruker D8ADVANCEECO X-ray diffractometers (CuKα radiation), (Karisruhe, Germany).Microstructural and elemental analyses of the samples were performed using JEOL-6490LA scanning electron microscopes (Tokyo, Japan) equipped with an energy-dispersive X-ray spectrometer system from OXFORD Instruments Analytical Limited (Oxford, UK) and JSM-6390LV (Tokyo, Japan) with an integrated energy-dispersive X-ray spectrometer (EDS).The investigation of the conductive parameters of the samples was carried out using the impedance method with the E7-30 device (Minsk, Belarus), an electric furnace, and a temperature sensor "Temodat" (Perm, Russia).

Structural Parameters of Samples
The synthesized samples exhibited a light burgundy color and took the form of ceramic tablets with a diameter of 10 mm and a thickness of 1.5 mm.
The structural parameters of the obtained polycrystalline samples of Na3Fe2(PO4)3 were investigated using powder X-ray diffraction methods with a diffractometer, as well as with a scanning electron microscope Hitachi TM3030 equipped with a Bruker microanalysis system.Figure 1 shows the diffractograms of Na3Fe2(PO4)3 samples of both types.In the diffractograms of both polycrystals, peaks are visible at corresponding angles of X-ray beam scanning, however, the intensity of the peaks in sample Type 2 is twice as high as in Type 1.These data indicate that the crystallites in Type 2 polycrystals formed better and are more textured compared to Type 1 samples.The structural parameters of the samples were determined by analyzing the main peaks from the angular values using the CellRef v2.2 and Origin 2018 software.The calculated structural parameters of the samples are provided in Table 2.The parameters of the elementary cells for the polycrystals Na 3 Fe 2 (PO 4 ) 3 provided in Table 2 are comparable with the literature data from other authors [2,24,28] and the data for the monocrystal [22], as presented in Table 2.For comparison, the standard values of the Na 3 Fe 2 (PO 4 ) 3 (available in the Crystallography Open Database (JCPDS: 45-0319) elementary cell parameters (space group C2/c, a = 15.346Å, b = 6.744(6)Å, c = 21.644(1)Å) are also included [2].
The structural parameters of the samples were determined by analyzing the main peaks from the angular values using the Origin software.The calculated structural parameters of the samples are provided in Table 2.
According to [28], the monoclinic distortion in polycrystals Na 3 Fe 2 (PO 4 ) 3 is associated with deformations of both the anionic and cationic sublattices of the crystalline framework, leading to the compensated dipole ordering of the AFE type.It should be noted that the lattice parameters a, c, and β for polycrystal Type 1 are slightly increased, whereas the parameters a, c, and angle β are slightly decreased compared to those of sample Type 2. These changes in the structural parameters of the polycrystals Na 3 Fe 2 (PO 4 ) 3 may be related to additional deformations of the dipole moments of elementary cells, induced by different thermodynamic synthesis conditions.According to tabulated data, the monoclinic distortions of elementary cells in Type 1 samples are smaller than in Type 2.
It is evident that how the initial annealing process is conducted plays a pivotal role in the sample preparation process.For Type 1 samples, the phase formation during the initial annealing process occurred through heat transfer in a mode of gradual heating in the muffle furnace.
Conversely, the phase formation in Type 2 samples took place under significant temperature-gradient conditions, as the sample was heated by intense pulses of quantum energy onto the surface.Consequently, substantial temperature gradients were established between the surface of the sample and its subsequent layers in the bulk.In such conditions, the cooling process occurs.Given that the duration of the melting and cooling processes were relatively brief, these factors could lead to the emergence of significant mechanical stress gradients on the surface and within the volume of the sample.
Thus, the process of melting and the transition from liquid melt to solid glassy state occurs under pronounced non-equilibrium thermodynamic conditions.Apparently, despite the secondary annealing of the sample at a moderate temperature regime, residual deformations are retained in the polycrystal after annealing.The presence of residual deformations in the Type 2 sample may be the cause of a partial reduction in monoclinic distortion.
The investigation of the microstructure and elemental analysis of the synthesized samples allowed for the determination of distinctive features in the structure and composition of each sample.Data on the microstructures of the polycrystals of the first and second types are presented in Figure 2a,b.
Based on microstructural and X-ray phase analysis, it can be concluded that the texture of Type 2 polycrystals is significantly higher compared to Type 1 samples.The crystallites in Type 2 polycrystals exhibit a clearly ordered orientation, unlike Type 1 samples, which lack directional order in the arrangement of crystallites.Non-equilibrium temperature gradients create deformations (under conditions of rapid cooling by a directed heat transfer flow in the glassy phase structure) that persist during crystallization (during secondary annealing of the sample) and influence the formation of crystallite orientation in the polycrystal.
Ceramics 2023, 6, FOR PEER REVIEW 7 The investigation of the microstructure and elemental analysis of the synthesized samples allowed for the determination of distinctive features in the structure and composition of each sample.Data on the microstructures of the polycrystals of the first and second types are presented in Figure 2a Based on microstructural and X-ray phase analysis, it can be concluded that the texture of Type 2 polycrystals is significantly higher compared to Type 1 samples.The crystallites in Type 2 polycrystals exhibit a clearly ordered orientation, unlike Type 1 samples, which lack directional order in the arrangement of crystallites.Non-equilibrium temperature gradients create deformations (under conditions of rapid cooling by a directed heat transfer flow in the glassy phase structure) that persist during crystallization (during secondary annealing of the sample) and influence the formation of crystallite orientation in the polycrystal.
One can speak of the influence of the mechanical pressure created by the "chemical press" (analogous to the pressure created by a hydraulic press) on the sample.From this point of view, such an effect cannot be achieved under equilibrium temperature conditions during annealing (as in the annealing of Type 1 samples).Additionally, Type 1 samples are characterized by noticeably pronounced heterogeneity of crystallites in size and irregularity (chaotic distribution) across the surface of the sample.
Based on the microstructural analysis of the polycrystals, it can be concluded that Type 2 samples exhibit a higher degree of crystallinity and texture compared to Type 1 samples.
Regarding the elemental composition of polycrystals, there is a deviation from the stoichiometric atomic ratio.The results of the elemental composition of the polycrystals are presented in Figure 3 and Table 3.One can speak of the influence of the mechanical pressure created by the "chemical press" (analogous to the pressure created by a hydraulic press) on the sample.From this point of view, such an effect cannot be achieved under equilibrium temperature conditions during annealing (as in the annealing of Type 1 samples).Additionally, Type 1 samples are characterized by noticeably pronounced heterogeneity of crystallites in size and irregularity (chaotic distribution) across the surface of the sample.
Based on the microstructural analysis of the polycrystals, it can be concluded that Type 2 samples exhibit a higher degree of crystallinity and texture compared to Type 1 samples.
Regarding the elemental composition of polycrystals, there is a deviation from the stoichiometric atomic ratio.The results of the elemental composition of the polycrystals are presented in Figure 3 and Table 3.   Analysis of the results of the elemental composition study of Type 1 and Type 2 polycrystals shows that there are no significant changes in the content of Na, P, and oxygen cations, but the content of these elements turned out to be lower compared to the stoichiometric composition.As for Fe cations, no changes are observed.Based on the research  Analysis of the results of the elemental composition study of Type 1 and Type 2 polycrystals shows that there are no significant changes in the content of Na, P, and oxygen cations, but the content of these elements turned out to be lower compared to the stoichiometric composition.As for Fe cations, no changes are observed.Based on the research results, it can be concluded that the slight decrease in Na and P cations relative to the stoichiometric composition can be attributed to the fact that under extreme temperaturegradient conditions, these elements may have evaporated slightly due to their low melting points.Consequently, the oxygen content may have changed as well.Since the material melting process was of short duration, this effect did not have a noticeable impact on phase formation.The diffraction patterns of Type 2 samples indicate the formation of Na 3 Fe 2 (PO 4 ) 3 polycrystals (see Figure 1).
Therefore, due to the improvement in texture in Type 2 samples and the barely noticeable influence of this melt method (using optical heating) on the phase formation of Na 3 Fe 2 (PO 4 ) 3 , it can be concluded that this method can be used in obtaining orthophosphate materials.

Ionic Conductivity of Na 3 Fe 2 (PO 4 ) 3 Polycrystals
The determination of the ionic conductivity of the synthesized polycrystals was carried out using the impedance method in the temperature range of 290 to 570 K. Silver paste was used as the electrode materials.The temperature dependence of the ionic conductivity of Na 3 Fe 2 (PO 4 ) 3 polycrystals of both types is presented in Figure 4.
Ceramics 2023, 6, FOR PEER REVIEW 9 paste was used as the electrode materials.The temperature dependence of the ionic conductivity of Na3Fe2(PO4)3 polycrystals of both types is presented in Figure 4.The temperature dependences of the ionic conductivity of Na3Fe2(PO4)3 polycrystals of both types follow the Arrhenius law and are characterized by three linear segments (in coordinates lg σ(1/T)), corresponding to the three phases α, β, and γ, respectively.These phases are separated by inclined "steps" since the phase transitions of polycrystals are usually broadened in the temperature dependencies of conductivity.The reason for this The temperature dependences of the ionic conductivity of Na 3 Fe 2 (PO 4 ) 3 polycrystals of both types follow the Arrhenius law and are characterized by three linear segments (in coordinates lg σ(1/T)), corresponding to the three phases α, β, and γ, respectively.These phases are separated by inclined "steps" since the phase transitions of polycrystals are usually broadened in the temperature dependencies of conductivity.The reason for this is the isotropic orientation of crystallites in the polycrystal.However, the temperature of the phase transition (the usually established transition temperature T C for polycrystals coincides with the temperature of the phase transition established in single crystals).From Figure 4, it can be seen that the conductivities of Type 2 samples are higher than the conductivities of Type 1 samples throughout the entire temperature range.To conduct a comparative analysis of the conductivity properties of the samples, additional processing of the experimental data was required.The conductivity parameters and phase transition temperatures for the two types of samples were determined.The calculated parameters of ionic conductivity and phase transition temperatures are provided in Table 4. From Table 4, it can be observed that the ionic conductivity parameters for both types of Na 3 Fe 2 (PO 4 ) 3 polycrystals are close.However, the ionic conductivity of the samples of the first type is lower than that of the second type.Although the activation energies and phase transition temperatures for both samples are identical, this is likely due to the similarity in the composition and structure of the samples.Presumably, the higher ionic conductivity of the second type of sample is attributed to the presence of a higher level of deformation in the crystalline structure, associated with more significant changes in structural parameters, such as the angular displacement β, compared to the sample of the first type.It is also possible that these structural changes may partially reduce the strong monoclinic distortions of the crystalline framework of α-Na 3 Fe 2 (PO 4 ) 3 , leading to an increase in conductivity.
In the study [30], a slight increase in conductivity was also observed in the sample synthesized under the influence of hydrostatic pressure.Although in this case, the increase in conductivity is associated with the overall compression deformation of the sample, it also leads to a partial reduction in the monoclinic distortion of the anionic crystalline framework, and consequently an increase in the "conductivity window" between the M(1) and M(2) sites in the conduction channel.
It should be noted that in the system of solid solutions Na 3 Fe 2(1−x) Sc 2x (PO 4 ) 3 (0 < x < 0.06), an increase in conductivity was observed [38].The replacement of iron M-cations (r Fe = 0.54) with Sc atoms (r Sc = 0.82) in Na 3 Fe 2 (PO 4 ) 3 also leads to local tensile deformations of the crystalline framework, due to the difference in ionic radii of the substituted elements.These deformations partially reduce the monoclinic distortion of the crystalline framework of the solid solution and partially increase its ionic conductivity.This type of deformation arises from the action of a "chemical press" (local tensile deformation of the crystalline framework).
These results indicate that the crystalline framework of Na 3 Fe 2 (PO 4 ) 3 is highly "elastic", primarily due to the presence of polyhedral units (PO 4 ) in the anionic framework, which is supported by spectroscopic data from the study [31].
The obtained results can be explained by the fact that the polycrystals of Na 3 Fe 2 (PO 4 ) 3 of the first type were formed under more equilibrium thermodynamic conditions.Therefore, the anionic crystalline framework underwent relatively less deformation during synthesis compared to the synthesis of polycrystals under the influence of optical radiation or the influence of hydrostatic pressure.Likely, the thermodynamic factor influencing both the degree of deformation of the polycrystalline structures (i.e., the existing mechanical stresses within the structure) and the degree of "openness" of the "conductivity window" between the M(1) and M(2) sites in the conduction channel contributes to the ambiguity of the obtained crystal structures [12,13].
Certainly, the technology for producing Type 2 polycrystals, obtained through the melt method under the influence of optical radiation, is of practical interest.This technology allows for an increase in the conductivity of the samples, which does not preclude an increase in capacitance properties during electrochemical processes in sodium-ion batteries (SIB).Therefore, it may find applications in the development of cathode materials with different compositions for SIBs.This technology warrants further investigation, as it could prove effective in the creation of cathode materials with various compositions for sodium-ion batteries.

Conclusions
Based on the presented experimental results and analysis of the structural conductive properties of Na 3 Fe 2 (PO 4 ) 3 polycrystals obtained through different technological processes, the following conclusions can be drawn: (1) Polycrystals of Na 3 Fe 2 (PO 4 ) 3 prepared by solid-state methods exhibit monoclinically distorted symmetry (space group C2/m at room temperature T = 295 K).It has been established that relative equilibrium thermodynamic conditions for the synthesis of polycrystals (Type 1 samples) contribute to the formation of monoclinically distorted crystalline structures.However, the synthesis of Na 3 Fe 2 (PO 4 ) 3 polycrystals under sharply gradient temperature conditions (in non-equilibrium thermodynamic conditions) using the melt method under the influence of optical radiation (Type 2 samples) leads to the creation of more noticeable shifts and angular deformations in the crystalline framework structure, contributing to the partial removal of monoclinic distortions.(2) It is concluded that the crystalline framework of Na 3 Fe 2 (PO 4 ) 3 is "elastic", making the polycrystal structure highly sensitive to external non-equilibrium thermodynamic, mechanical, and chemical influences.The texture of polycrystals obtained by solidstate methods (Type 1 samples) is less ordered compared to samples obtained by the melt method under the influence of optical radiation (Type 2 samples).(3) It has been established that samples of both types have similar conductive properties, but the ionic conductivity of Type 2 samples is slightly higher than that of Type 1.It is concluded that the higher ionic conductivity of Type 2 samples is attributed to the presence of more pronounced shifting and angular deformations in the crystalline framework, which may partially alleviate the strong monoclinic distortions in the crystal structure of α-Na 3 Fe 2 (PO 4 ) 3 and lead to a greater openness of the "conductivity window" in the conductivity channel.(4) The technology of producing Na 3 Fe 2 (PO 4 ) 3 polycrystals through the melt method under the influence of optical radiation can be employed in the development of cathode materials with different compositions to enhance intercalation and deintercalation processes in sodium-ion batteries.

Figure 2 .
Figure 2. Microstructures of polycrystals and percentage of elemental composition for Na3Fe2(PO4)3 (at a scale of 30 µm), obtained by the solid-phase method: (a) sample Type 1; and melt method (b) Type 2 sample.

Figure 2 .
Figure 2. Microstructures of polycrystals and percentage of elemental composition for Na 3 Fe 2 (PO 4 ) 3 (at a scale of 30 µm), obtained by the solid-phase method: (a) sample Type 1; and melt method (b) Type 2 sample.

Table 3 .
Average values of the elemental composition of amorphous precursors (Atom %).

Table 3 .
Average values of the elemental composition of amorphous precursors (Atom %).