Effect of sodium substitution by yttrium on the structural, dielectric and electrical properties of Ba2Na(1-3x)YxNb5O15 ceramics

The effects of Na+ substitution by Y3+ on the structural, microstructural, dielectric and electrical properties of Ba2Na(1-3x)YxNb5O15 compositions with (x = 0, 0.02 and 0.04) have been studied in detail. The solid solutions of different compositions were prepared by the solid state reaction route method and characterized by X-Ray Diffraction (XRD), Scanning Electron Microscopy (SEM), and Complex Impedance Spectroscopy (CIS) techniques. The XRD study confirmed that all prepared compositions have a single-phase orthorhombic tungsten bronze structure with space group Cmm2 at room temperature. The microstructural studies revealed a grain shape and size change in response to increasing Y3+ concentration. The dielectric properties of the obtained compositions are evaluated over a temperature range of 40–600 °C. The dielectric properties were improved for the Y2O3-substituted Ba2NaNb5O15 compound compared to the undoped Ba2NaNb5O15 compound. The non-Debye type relaxation mechanism is confirmed by the -Z″ versus Z′ traces. The grain contribution was studied using an equivalent electrical circuit with a Resistor R, a Capacitor C, and a Constant-Phase Element CPE in parallel, in the absence of the grain boundary response and the electrode effect in the frequency range 10 Hz-1MHz. The experimental AC conductivity data were evaluated by using Jonscher's power law. The activation energies obtained from the relaxation and conduction processes, present two different regions as a function of temperature related to the two electrical processes for the prepared ceramics.


Introduction
Ferroelectric materials have increasingly been used in modern electronics sectors due to their numerous applications, such as piezoelectric, optoelectric, nonlinear optical, and pyroelectric devices [1][2][3].Pb-free ferroelectric materials have captured the interest of the scientific and commercial sectors, owing to the severity of environmental concerns surrounding the use of lead [2,4,5].Over the past few years, researchers have conducted numerous extensive studies on lead-free ferroelectric ceramics of perovskite structure ABO 3 , with particular attention to BaTiO 3 and Bi 0.5 Na 0.5 TiO 3 -based ceramics as relaxor ferroelectrics [6][7][8][9][10].Although some research has been dedicated to developing lead-free dielectric capacitors with different crystal structures, limited attention has been given to exploring other promising lead-free dielectric capacitors for energy storage applications.Further investigation is needed to identify these materials.As the second most important dielectric material for the perovskite type, lead-free Tungsten Bronze (TB) is known for its complex and intriguing structure.This dielectric material, similar to perovskites, comprises deformed BO 6 octahedra connected by corners, creating three distinct sites: triangular, square and pentagonal.The chemical formula can be written as (A2) 2 (A1)C 2 B 5 O 15 , where the A1 and A2 (pentagonal and square sites respectively) may be occupied by all or part of a larger cation such as Sr 2+ , Ba 2+ , Ca 2+ , Na + , or K + , B-site is filled by a high valence cation such as W 6+ , Nb 5+ or Ti 4+ , and the C site is usually vacant due to the gap being too small [11][12][13][14][15][16][17][18][19][20][21].Among the tungsten bronze systems, the compound Ba 2 NaNb 5 O 15 (BNN) has recently received much attention [12,13,22,23].The structural, dielectric and electrical properties of Ba 2 NaNb 5 O 15 ceramics have been extensively studied [12,24,25].Note that in this structure, the pentagonal sites are occupied by Ba 2+ ions, the square sites by Na + (and induce an intense deformation), while the triangular tunnel remains empty.Niobium ions Nb 5+ are statistically distributed in site B to form Nb(1)O 6 , Nb(2)O 6 , Nb(3)O 6 and Nb(4)O 6 octahedra, as shown in Fig. 1 [12,23,26].
Regarding the structural properties of this compound, BNN is a uniaxial material, it shows a series of phase transitions: orthorhombic (ferroelectroelastic) to tetragonal (ferroelectric) at about 300 • C, tetragonal (ferroelectric) to tetragonal (paraelectric) at T c = 580 • C; on the other hand, its room temperature space group is Cmm2 [12,27].The ferroelastic structure (Cmm2) was symmetry at room temperature as confirmed by Jamieson and Niizeki et al. [28,29].The modification of the structural, dielectric and electric properties of the TB ceramics by the introduction of elements with strong charges like Bi 3+ , Nd 3+ ,Y 3+ , … that replace the elements with weak charges like Na + and K + in the A1 and A2 sites have been widely reported [22,[30][31][32].Finlay D. Morrison et al. reported that the Curie temperature (T c ) associated with the tetragonal (ferroelectric) to tetragonal (paraelectric) transformation in the compound Ba 4 R 0.67 Nb 10 O 30 (where R--La 3+ , Nd 3+ , Sm 3+ , Gd 3+ , Dy 3+ , and Y 3+ ) decreases as the rare-earth ionic radius increase, resulting in a decrease in the tetragonal distortion [33].In addition, tungsten bronze ceramics' dielectric and electrical performance are highly dependent on their crystal structure and morphology [14,34,35].For example, liangliang Liu et al. have found that the grain size distribution dominated the ferroelectric nature of KSr 2 Nb 5 O 15 tungsten bronze (KSN).In other words, the dielectric anomalies are not only controlled by the compositions, but also by the microstructures of the ceramics [14].The ceramic type consists of conductive grains separated by insulating grain boundaries, as described by the Maxwell-Wagner model.At low frequencies, the high value of ε′ can be attributed to factors such as grain boundary effects, oxygen vacancies, interfacial dislocations and charged defects.However, as the frequency increases, the decrease in ε′ is due to the fact that all species contributing to the polarization lag behind the external field [36].Research on the characterization of Ba 2 Na (1-3x) (A 3+ ) x Nb 5 O 15 compounds (with A 3+ high valence ions) has remained so far insufficient, either XRD or by CIA.In this work, doping with high valence ions changes the concentration of oxygen vacancies in our material, whereby Y 3+ ions partially replace Na + ions in the BNN compound.The structure, microstructure, dielectric and electrical properties of BNN and Y 3+ doped BNN samples can be studied to find a relationship between these properties.

Materials and methods
Ceramics with compositions BaNa (1− 3x) Y x Nb 5 O 15 (x = 0.00, 0.02, and 0.04) (denoted as BNN, BNYN0.02, and BNYN0.04,respectively) were synthesized by a high temperature solid-state reaction method.The high purity starting materials are: Na 2 CO 3 , BaCO 3 , Y 2 O 3 and Nb 2 O 5 (Sigma-Aldrich 99 %).All starting materials were preheated to 300 • C for one day (24 h), then weighed in stoichiometric amounts and mixed well by ethanol milling in the presence of zirconia balls for 2h.Then, the mixed powders were dried overnight at 80 • C, homogenized in an agate mortar for 30 min, and then calcined at 1200 • C for 6 h in the air.After grinding and drying, the undoped and Y 3+ doped BNN ceramics were grounded again with the addition of an appropriate amount of polyvinyl alcohol (PVA) as a binder, and then uniaxially pressed (20 KN) in the mold (2 mm thickness and 12 mm diameter).Finally, the formed  pellets were sintered in air at 1300 • C (6h).The temperature was increased to 700 • C with a rate of 10 • C.min − 1 , after a plateau of 1 h at this temperature and with a speed of 5 • C.min − 1 the temperature rises to the sintering temperature, followed by a second 6 h plateau at T = 1300 • C and allowed to cool to room temperature.The surfaces of the pellets were properly polished to obtain conductive electrodes for measuring dielectric and electrical properties.A silver layer was used on the top and bottom surfaces of the pellets to serve as a parallel plate.

Characterization
The Crystal structure identification of BNN, BNYN0.02, and BNYN0.04 powders was performed by XRD.The instrument used was a D2 PHASER diffractometer equipped with a copper anode (CuKα 1 et CuKα 2 ).The diffractograms were recorded at 293 K (0.01 • steps, 5 • -70 • 2θ range).To have both surfaces of the sintered pellets flat and parallel, it is necessary to go through a polishing step with emery paper, and then heat treated at 1300 • C (30 min).The surface morphology of BNN, BNYN0.02 and BNYN0.04 ceramics sintered at 1300 • C was observed by SEM (TESCAN VEGA III LM).Image J software was used to estimate the average grain size from the SEM images.The sintered ceramics were coated with silver on both sides, then annealed at 300 • C (30 min) to make the silver adhere to the sample, before analyzing its dielectric and electrical properties, using a bioLogic impedance analyzer (MTZ-35) equipped with a temperature controller, both room temperature and high temperature impedance measurements were performed.Electrical and dielectric measurements were performed in the temperature range of 40 • C-600 • C and at frequencies from 1Hz to 1 MHz.

Crystal structure
The X-ray diffraction spectra recorded at room temperature of the different compounds Ba 2 Na (1-3x) Y x Nb 5 O 15 as (x = 0, 0.02 and 0.04) are presented in Fig. 2(a).Note that a first indexation was performed for these compositions using the computer program Full prof.The XRD spectra of the ceramics are in agreement with the standard JCPDS card N o .70-1388 [37].The crystallographic planes (hkl) corresponding to the standard JCPDS card N o .70-1388 in the range 2θ 5 • -35 • are shown in Fig. 2(b).
For more details on the different structural parameters of the synthesized products, the XRD spectra of the analyzed powders were refined with the Jana 2006 software [38].The structural model related to the orthorhombic phase of Ba 2 NaNb 5 O 15 is the starting model used to refine the composition of BNN, BNYN0.02 and BNYN0.04,such as space group (N • .35), lattice parameters a = 17.58881Å, b = 17.62308Å and c = 3.992668 Å [23].All samples show a pure phase, which can be well indexed to an orthorhombic tungsten bronze structure with a space group Cmm2.Fig. 3(a-c) shows the profile refinement of BNN, BNYN0.02 and BNYN0.04 compounds respectively.Table 1 shows the cell parameters (a, b, c, and V) and reliability parameters (Rp (%), Rwp (%), and GOF).The tetragonal-orthorhombic phase transition is accompanied by a 45 • rotation about the c-axis of the crystallographic axes, and the crystallographic axes are therefore classified as c < a < b [9].The reliability factors R p and R wp indicate that the experimental and calculated data are in good agreement and confirm the structural model.

Microstructure of ceramic samples
Fig. 4(a-c) shows the micrographs of BNN, BNYN0.02 and BNYN0.04 ceramics, respectively.It is evident in the SEM images that all samples sintered at 1300 • C have a uniform, regulated grain shape without porosities, high densities and well-defined grain boundaries.ImageJ software is used to estimate the average grain size (D).The grain size distribution plots of the samples are shown in the insets in Fig. 3.The average grain size (D) values for BNN, BNYN0.02, and BNYN0.04 are 4.807 μm, 5.267 μm, and 4.8835 μm respectively.The analysis of these values shows that the average grain size increases when Y 3+ ions partially replace Na + for BNYN0.02 and then decreases for BNYN0.04.In tungsten bronze structure ceramics, a typical feature in morphology is the anisometric pillar-type grain due to the abnormal growth along c axis [11,13,39].The images we examined show few pillar-type grains, indicating that adding

Table 1
The structural parameters (a, b, c, V and space group) and the reliability factors of Ba Y 3+ inhibits abnormal grain growth when a significant amount of Y 3+ segregates at grain boundaries.The effect in restraining grain growth of Y 2 O 3 is consistent with the literature [40][41][42].It can be seen that the relative permittivity and dielectric loss first decrease and then increase with increasing Y 2 O 3 content.When the Y 2 O 3 content is 0.02, the relative permittivity reaches its minimum value.This phenomenon could be related to the variation of polarization due to the decrease of the cell volume and the increase of the grain size.At low Y 2 O 3 content, the polarization by ion and electron displacement is weakened, as well as the spontaneous polarization.In addition, the dielectric constant and dielectric loss decrease rapidly with increasing frequency.In general, the highest value of the dielectric constant at low frequency is due to the occurrence of all types of polarizations (ionic, electronic, interfacial, dipolar, etc.) in samples prepared at room temperature [43,44].Comparison of the relative permittivity and dielectric loss results obtained for our samples with the results obtained in the literature shows similar values to those found for other ceramics as shown in Table 2.

Study of dielectric properties
The dielectric constant (ε ′ ) as a function of temperature for Ba 2 Na (1-3x) Y x Nb 5 O 15 with (x = 0, 0.02, and 0.04) at different frequencies (1 KHz-1 MHz) in the temperature range between 40 and 600 • C is shown in Fig. 6(a-c).
We can see in Fig. 7 corresponds to the variation of the relative permittivity as a function of the temperature of the compound BNN, at about T m = 571 • C the presence of a large peak which is a sign of phase transition from tetragonal ferroelectric (P4bm) to tetragonal     paraelectric (P4/mbm).Moreover, at about T d = 350 • C, another anomaly appears.This anomaly, which corresponds to the formation of a structural transition from orthorhombic (Cmm2) to tetragonal (P4bm), has been attributed to the ferroelastic-ferroelectric transition [27].The same anomalies were observed for the BNYN0.02 and BNYN0.04 compounds, but with decreased transition temperatures T m and T d Fig. 6(b) and (c).These results are in good accord with structural studies performed for compounds BNN, BNYN0.02 and BNYN0.04 that show an orthorhombic structure of the Cmm2 space group at room temperature.
Fig. 8(a-c) illustrates the variation of the dielectric loss with temperature, for all the samples studied.In Fig. 8(a-c), In low temperature regions, it is obvious that the dielectric loss increases slowly with temperature and then increases significantly at high temperatures.This behavior may be due to the improved charge transport characteristics in the prepared ceramics that are thermally activated during the temperature increase, i.e. the increase of the charge carriers mobility by the thermal activation [48].
In other words, the observed characteristics have a solid practical relationship with the phase transition observed for the prepared composition; precisely for the compound BNYN0.04 it is very clear that this sample undergoes two anomalies in the temperature range 40 • C-600 • C related to the phase transitions indicated previously in the part of the dielectric constant, we also notice the presence of the phenomenon of dielectric relaxation associated with the migration of charge carriers.At high temperatures and low frequencies, the observed dielectric loss increase can be attributed to the polarization of space charges [49].The highest values of the dielectric parameters (ε' & tanδ) observed above 300 • C, may be related to the formation of oxygen vacancies in the prepared ceramics.The oxygen vacancies play an important role in changing the values of relative permittivity and dielectric loss, which may control the properties of electric charge carriers present in these materials.The substitution of Na + ions by Y 3+ ions in the square sites of the BNN structure leads to the creation of ionized vacancies of sodium (V ″ Na ) similarly to the substitution of bivalent ions such as Ba 2+ ,Ca 2+ , Sr 2+ , … by trivalent ions such as rare earth (La 3+ ,Sm 3+ , …) [50][51][52].
equation ( 1) that shows the formation of the sodium vacancies (V ″ Na ) is the following: (1)

Complex impedance analysis (CIA) 3.4.1. Nyquist plot
Complex impedance analysis, using Nyquist diagrams to understand grain properties, grain boundaries and possible electrode effects on resistive, capacitive, inductive and reactive material properties [53].The complex impedance Z* can be obtained from the expression (2) below: Where, Z′ and Z″ represent respectively the real and the imaginary part of the impedance and j = ̅̅̅̅̅̅ ̅ − 1 √ is the imaginary factor [19].The expressions (3,4) of Z′ and Z″ are respectively the following: Where, R (g, gb, and e) represent the resulting resistance of grains, grain boundaries, and electrode effects, respectively, while C (g, gb, and e) represents the resulting capacitance of the same components [19].Fig. 9(a-c) shows Nyquist plots (plots of the imaginary part against the real part of the impedance) for BNN, BNYN0.02, and BNYN0.04 ceramics at different temperatures.
The Nyquist plots (Cole-Cole) show well resolved semicircles for all temperatures studied [350 • C-450 • C].As the temperature increases, one can observe that the rayon of the semicircles decreases, indicating a decrease in Resistance (R).This behavior confirms that the conduction process is thermally activated in these materials, and also the semiconducting nature of our samples [12,19,53,54].
The experimental Nyquist diagrams obtained are poorly fitted by an electrical model in order to find the values of various electrical parameters of the proposed electrical circuit.The model of the equivalent circuit that we suggests related to the contribution of grains composed of Capacitors (C g ), Resistors (R g ) and Constant Phase Element (CPE g ) is shown in Fig. 10(b).
However, the non-ideal capacitive behavior of our samples is confirmed by the presence of a CPE in the equivalent circuit (non-Debye type relaxation) [53,55].The correlation between CPE and C is expressed by the following equation ( 5): Where α is the degree of energy dissipation (α < 1), the value of α is between 0 and 1 for non-ideal capacitive behavior, α = 1 for a pure capacitor and α = 0 for a pure resistor [56].The relation that allows us to calculate the depression angle β caused by the CPE phase element is the following: β = π 2 (1-α) [57].Fig. 10(a) which shows the impedance spectrum fitted with the MT-Lab software of the BNYN0.02ceramic at different temperatures.The results obtained at different temperatures for the prepared compounds are presented in Table 3.
Furthermore, the representation of a semicircle for the compound BNYN0.04 at 450 • C (see Fig. 11) allows confirmation of the deviation from the Debye behavior, it was established that the sample deviates from the Debye behavior by an angle of 43.412 • .
In general, Nyquist traces (-Z″ vs. Z′) include multiple semicircles in different frequency regions, i.e., three semicircles represent the existence of an electrode effect, a grain boundary effect, and a bulk (grain) effect, two semicircles represent the existence of a grain boundary effect and a grain effect, and one semicircle represents the existence of a grain effect [58,59].To study the charge carrier activity at the grain and grain boundary level, the activation energies of the ceramics can be calculated using the following equation ( 6

R-
Where, R is the resistance of the grains of the material obtained by the complex impedance, R 0 is the pre-exponential constant, k B is the Boltzmann constant and T is the test temperature.The activation energies are determined from the slope of the lines obtained by plotting Ln (R g ) versus 1000/T as shown in Fig. 12(a-c).Two linear slopes are observed in Fig. 12, i.e., two different temperature regions, which can be explained by the contribution of two conduction processes to the electrical properties of BNN ceramics, BNYN0.02 and BNYN0.04.The E 1 and E 2 values obtained by linear fitting for BNN, BNYN0.02 and BNYN0.04 ceramics are 0.468, 0.66, 0.859 eV, and 1.235, 0.651, 0.758 eV respectively.
The activation energies corresponding to region 1 and region 2 are similar to those obtained by electrical conductivity.The origin of  these two activation energies will be detailed in the discussion of electrical conductivity.

The real and the imaginary part of the impedance
The variation of the real part of the impedance (Z′) with frequency at different temperatures is shown in Fig. 13(a-c).It can be observed that the value of the Z′ decreases with increasing temperature and frequency, suggesting an increase in electrical conductivity as well as a decrease in electrical resistance.This type of behavior confirms the presence of the negative temperature coefficient of resistivity (NTCR) in all prepared materials [12,63].
On the other hand, for all temperatures and in the high frequency region, the Z′ values merge and then become frequency independent, this can be due to the release of a space charge due to the reduction of the barrier properties of the material [63].The remarkable decrease in barrier properties in our materials with increasing temperature can be justified by the increased AC conductivity of the materials at high frequencies [64,65].This particular frequency at which the value of Z′ becomes frequency independent and shifts to the low frequency side is caused by the insertion of Y 3+ into the base compound BNN; this indicates that the Y 3+ doped compounds begin to release space charge from the lowest frequencies: 10 4 Hz for BNYN0.02 and less than 10 3 Hz for BNYN0.04.The plots of (-Z″) as a function of frequency (1Hz-1MHz) show two aspects: (I) the relaxation frequency related to the maximum peak of each temperature studied.The presence of a relaxation mechanism in the prepared ceramics is confirmed by the broadening of the corresponding peak at each temperature.The leading cause of the creation of this mechanism is the thermal activation of charge carriers at high temperature, (II) the intensity of the -Z″ peak as a function of frequency decreases with increasing temperature and shifts to higher frequency values, suggesting that the relaxation process is thermally activated with space charge accumulation at the  barrier [66][67][68][69][70].The relaxation frequency ƒ max and the relaxation time τ are related to each other by the following relationship τ = 1 2π.ƒ max .Therefore, the relaxation frequency ƒ max and the relaxation time τ are inversely proportional.Seeing that the highest ƒ max frequency is that of the BNN compound, it is therefore very easy to confirm that the longest relaxation time τ is that of the BNYN0.04sample.In addition, the mobility of oxygen vacancies is reduced as the relaxation time increases [71].which indicates that the mobility of the oxygen vacancies is weakened by the substitution of the sodium ion Na + by the yttrium ion Y 3+ and this can be confirmed by the intensity of the relaxation peak which is proportional to the concentration of the mobile oxygen vacancies [72].

Electrical resistivity
One of the most important parameters to consider in high-temperature applications is electrical resistivity.Electrical resistivity ρ was calculated from material resistance data and the geometric parameters of the samples [73].Equation ( 7) is used to calculate ρ.
Where R material is the material resistance, t the sample thickness and A the electrode surface.C), which is superior to that of pure BNN ceramics at 10 KHz.The increase in electrical resistivity observed for compounds containing Y 3+ ions is explained by the decrease in the concentration of oxygen vacancies (OVs) in these compounds.Oxygen vacancies can be doubly ionized, singly ionized or neutral.They are mobile charge carriers that play an important role in the conduction process [76,77].The improvement in resistivity is accompanied by a decrease in electrical conductivity.a similar behavior was observed for perovskite structure oxides containing titanium ions in which DC conductivity decreases with the reduction of oxygen vacancies [78,79].

Electrical conductivity analysis
The conductivity AC is one of the factors that control the conduction mechanisms in this type of material and to better understand this mechanism, (σ AC ) is therefore determined by the following equation ( 8) [61]: Where, ω is the angular frequency, ε'' is the imaginary part of the material permittivity and ε 0 is the vacuum permittivity.Fig. 16(a-c) includes the ac conductivity analysis of undoped and Y 2 O 3 -doped BNN ceramics in the temperature range of 350 • C-450 • C.
We can observe in Fig. 16(a-c) two different regions, the first region is related to low frequencies that form a plateau, while the second region at high frequencies that is characterized by a gradual increase in conductivity, and on the other hand, we see no dispersion of conductivity.Therefore, we can conclude that the short-range movement of ionic species has replaced the long-range jump in the samples [12].
To fully understand the conduction mechanisms and the species responsible for conduction in our samples, we fitted the AC conductivity by Jonscher's power law using equation ( 9) [9,[80][81][82].
Where σ dc is the conductivity in the continuous current of the material, ''A'' is the pre-exponential factor that determines the polarization strength and the parameter ''n'' which is independent of the frequency and depends on two factors: temperature and intrinsic material property [83].The determination of the value of "n" is very important to understand the different conduction mechanisms in our materials and the transport properties of charge carriers (vacancies, electrons, ions …).If ''n'' is superior to 1 (n > 1), it means that the charge carriers move with a localized jump without the species leaving the vicinity, if n is inferior to 1 (n < 1), it means that the charge carriers move with a translational motion (a sudden jump) [84][85][86].The red lines in Fig. 17(a-c) show the nonlinear curves fitted to Equation (9) of the Jonscher power law for compositions BNN, BNYN0.02, and BNYN0.04,respectively.The values of the fitting parameters A, n, and σ dc for all compositions in the temperature range of 350 • C-450 • C are shown in Table 4.
The traces of n as a function of temperature n(T) can be used to determine the conduction pattern in the prepared samples.In the literature, many researchers have reported several types of models [85,86].Fig. 17(a-c) represents the temperature dependence of the ''n'' parameter (350 • C-450 • C) and Fig. 17(d-e) shows the temperature variation of ''1-n'' for undoped and Y 2 O 3 -doped BNN compounds.
In Fig. 17 (a), it can be seen that the exponent n increases with increasing temperature, indicating that Non-overlapping Small Polaron Tunneling (NSPT) is the suitable model to describe the mechanism of electrical conduction (charge transport) in the base E.H. Yahakoub et al. compound BNN.According to this model, the increase of the frequency leads to the decrease of the tunneling distance until reaching the minimum value which is still non-zero, but equivalent to the dispersion between the atoms.And also, the conductivity AC in this sample is due to the addition of a charge carrier on a site that causes a local distortion of the lattice [85].The W h energy of the polaron jumps from one position to another related to the NSPT model was established from the linear fit of the (1-n NSPT ) experimental data Fig. 17    values found for W 1 h and W 2 h are respectively W 1 h = 0.182 eV and W 2 h = 0.069 eV.Furthermore, in Fig. 17 (b and c), we observe that the exponent ''n'' is inversely proportional to the increase in temperature.This indicates that the conduction model of charge transport in Y 2 O 3 -doped compounds (BNYN0.02and BNYN0.04) is Correlated with Barrier Hopping (CBH) [89].According to this model, charge carriers can move from one site to another through thermal activation, crossing the potential barrier between them.This mechanism plays an essential role in the regulation of the AC conductivity observed in these samples [84].Similarly, we have calculated the barrier height W m for the CBH model Fig. 17 4.This indicates that this type of conductivity exhibits Arrhenius behavior which can be written according to equation (10) [66]: Where σ 0 is a pre-exponential factor, k B and E 1,2 are the Boltzmann constant and the activation energy, respectively.The activation energies obtained by the slope of the linear fit curves (Ln(σ dc ) vs10 3 /T) are shown in Fig. 18 (a,b and c).The plots of Ln(σ dc ) versus 1000/T show two different regimes with two different slopes for the three ceramics, indicating that each compound has two types of activation energies corresponding to the two different types of charge carriers, the activation energy values found E 1 (region 1) and E 2 (region 2) are grouped in Table 5.
We all know that E dc is the sum of charge carrier generation and long-distance charge carrier migration, or jump free energy [77,91].With increasing Y 3+ substitution in the A2 site, the Edc values of BaNa (1-3x) Y x Nb 5 O 15 ceramics (x = 0.00, 0.02, 0.04) increase progressively in region 1 and decrease in region 2. For ferroelectric ceramics, the activation energy for the interaction of small polarons lies between 0.2 and 1.5 eV [92].In addition, the activation energy for the conduction of small polarons is influenced by the movement       of the domain walls, which in turn depends on the potential barriers present in the grain boundaries that are more dominated at high temperatures.These potential barriers reflect the deformation of the crystal lattice and the grain size of the material, which can have an impact on the mobility of small polarons [93].Consequently, the increase in activation energy E 1 for compounds BNYN0.02 and BNYN0.04 is caused by the higher Y 3+ content in the grain boundaries, which provides more channels for carrier transport, particularly for long-distance migration.In addition, the activation energy E 2 related to the grain response decreased due to the low charge carrier concentrations resulting from the Y 3+ deficiency in these regions.
In general, the thermal activation energy is controlled by the oxygen vacancies (V ˙˙o ) in this type of ferroelectric oxide [91].It is well known that during the sintering process of ferroelectric perovskites, oxygen vacancies can occur due to the release of oxygen from the crystal lattice [94].equation ( 11) that shows the formation of the oxygen vacancies (V ˙˙o ) is the following: (11) For stoichiometric ABO 3 perovskites, the activation energy E a is about 2 eV, while the E a value for non-stoichiometric ABO 2.95 and ABO 2.90 perovskites is 1 eV and 0.5 eV respectively [80,95].For the ceramics prepare BNN, BNYN0.02 and BNYN0.04, the activation energy values E 1 are 0.473, 0.749 and 0.982 eV, respectively, and the activation energy values E 2 are 1.262, 0.656 and 0.505 eV, which suggests that conduction in our samples is controlled by oxygen vacancies.Moreover, it is well known that the most mobile ionic species in ferroelectric oxides (tungsten bronze, perovskite, spinel) are single (0.3-0.5eV) and doubly ionized (0.6-1.2 eV) oxygen vacancies [80,[96][97][98][99].We find that the activation energy values decrease for grains and increase for grain boundaries with increasing Y 3+ concentration, suggesting that these ions are incorporated into the crystal lattice and that the type of species responsible for the conduction mechanism in ceramics changes with increasing Y 3+ concentration.
The conducting electrons created by the single and doubly ionized oxygen vacancies are written according to equations 12 and 13 [50]: The conductivity of a material is mainly controlled by two factors: the content of charge carriers and the possibility of transporting them inside the material [100].The formation of oxygen vacancies (OVs) in oxide materials is very easy by losing oxygen from the crystal lattice during heating at elevated temperatures [101].The precise location of these electrons in these materials was still difficult to determine, as mentioned by Ihrig and Hennings [102].However, it was very likely that these electrons clung to defects in oxygen, forming color centers, that could easily be thermally activated and transformed into conducting electrons (carriers) [103].On the other hand, the decrease in AC conductivity for the two Y 3+ doped compounds (BNYN0.02and BNYN0.04), as shown in Fig. 15(d), is a logical consequence of the decrease in oxygen vacancy mobility in these compounds, as previously mentioned.

Conclusion
A general study of the structural, dielectric, and electrical properties of Ba 2 Na (1-3x) Y x Nb 5 O 15 solid solution compositions (0 ≤ x ≤ 0.04) synthesized by the conventional solid-state method was performed.The X-ray diffraction study confirmed that the structure of all samples synthesized at 1200 • C is tungsten bronze with an orthorhombic space group Cmm2.The lattice parameters for the studied ceramics rank such that c<a<b indicating the crystallographic axes rotate 45 • around the c axis at the tetragonal-orthorhombic transition.The SEM images showed high densification, low porosity, and a homogeneous microstructure consisting of regular grain size.The average grain size was between 4.807 and 5.267 μm.The largest value of the average grain size (D = 5.267 μm) was noticed for the compound BNYN0.02which explains the volume reduction of this compound.The evolution of permittivity, and losses as a function of temperature (40 • C-600 • C) and 10 Hz-1 MHz frequency of the studied ceramics, shows that there are two phase transitions for the undoped BNN compound: the first one at about T d = 350 • C associated with the symmetry change of the material (ferroelastic (Cmm2) to ferroelectric (P4bm)) and the second one at about T m = 571 • C corresponding to another symmetry change (ferroelectric (P4mm) to paraelectric (P4/mbm)).The partial substitution of Na + by a high valence ion Y 3+ leads to a decrease of T m and T d .The introduction of Y 2 O 3 in the Ba 2 NaNb 5 O 15 structure has a significant effect on the electrical conductivity and the resistance of the grains.The study of Nyquist diagrams of all ceramics confirms the semiconducting nature of our samples and the conduction process is thermally activated in these ceramics.The resistivity ρ of the prepared ceramics decreases with increasing temperature, validating the NTCR and indicating semiconductor-like behavior for all prepared samples.The Joncher power law fits the experimental AC conductivity data.The obtained ''n'' parameter values suggest that the small polaron non-overlapping tunneling effect (NSPT) is the

Fig. 5 (
Fig.5(a-b) shows the evolution of relative permittivity and dielectric loss versus frequency for BNN, BNYN0.02 and BNYN0.04 ceramics at room temperature.It can be seen that the relative permittivity and dielectric loss first decrease and then increase with increasing Y 2 O 3 content.When the Y 2 O 3 content is 0.02, the relative permittivity reaches its minimum value.This phenomenon could be related to the variation of polarization due to the decrease of the cell volume and the increase of the grain size.At low Y 2 O 3 content, the polarization by ion and electron displacement is weakened, as well as the spontaneous polarization.In addition, the dielectric constant and dielectric loss decrease rapidly with increasing frequency.In general, the highest value of the dielectric constant at low frequency is due to the occurrence of all types of polarizations (ionic, electronic, interfacial, dipolar, etc.) in samples prepared at room temperature[43,44].Comparison of the relative permittivity and dielectric loss results obtained for our samples with the results obtained in the literature shows similar values to those found for other ceramics as shown in Table2.The dielectric constant (ε ′ ) as a function of temperature for Ba 2 Na (1-3x) Y x Nb 5 O 15 with (x = 0, 0.02, and 0.04) at different frequencies (1 KHz-1 MHz) in the temperature range between 40 and 600 • C is shown in Fig.6(a-c).We can see in Fig.7corresponds to the variation of the relative permittivity as a function of the temperature of the compound BNN, at about T m = 571 • C the presence of a large peak which is a sign of phase transition from tetragonal ferroelectric (P4bm) to tetragonal

Fig. 10 .
Fig. 10.(a) Plot of the imaginary part (Z″) versus the real part (Z′) fitted with the MT-Lab software for the composition of BNYN0.02 at different temperatures.(b) Represents the equivalent electrical circuits corresponding to the response of the grains.

Fig. 11 .
Fig. 11.Verification of experimental results of Nyquist traces for BNYN0.04 ceramic at 450 • C as a function of depression angle β.

Fig. 14 (
Fig. 14(a-c) shows the variation of the imaginary part of the impedance (Z″) as a function of frequency at different temperatures (350 • C-450 • C) for BNN, BNYN0.02 and BNYN0.04 ceramics.The plots of (-Z″) as a function of frequency (1Hz-1MHz) show two aspects: (I) the relaxation frequency related to the maximum peak of each temperature studied.The presence of a relaxation mechanism in the prepared ceramics is confirmed by the broadening of the corresponding peak at each temperature.The leading cause of the creation of this mechanism is the thermal activation of charge carriers at high temperature, (II) the intensity of the -Z″ peak as a function of frequency decreases with increasing temperature and shifts to higher frequency values, suggesting that the relaxation process is thermally activated with space charge accumulation at the

Fig. 15 (
a, b and c) shows the variation of electrical resistivity ρ as a function of temperature for BNN, BNYN0.02 and BNYN0.04.As can be seen, the resistivity of the prepared ceramics decreases with increasing temperature where the value of ρ at 1 KHz decreases from 3.38 × 10 3 Ω m (350 • C) to 5.02 × 10 2 Ω m (450 • C) for BNN, from 2.45 × 10 4 Ω m (350 • C) to 5.65 × 10 3 Ω m (450 • C) for BNYN0.02 and from 4.50 × 10 5 Ω m (350 • C) to 8.41 × 10 4 Ω m (450 • C) for BNYN0.04.This shows that resistivity depends on the Negative Temperature Coefficient Response (NTCR) and also indicates semiconductor-like behavior for all prepared samples [74,75].Fig. 15(d) shows the effect of substituting sodium by yttrium on the resistivity of different compositions at different temperatures.Resistivity increases significantly with increasing Y 3+ content.BNYN0.04 ceramics have the highest resistivity (1.5 × 10 5 Ω m 350 • C and 3.6 × 10 4 Ω m 450 (d)  with n NSPT = 1+ 4×KB×T Wh[87,88].It was very clear that Fig.17 (d)  shows two different regions which suggest that two jump energies of the polarons W 1 h and W 2 h exist, this can be explained by the presence of two types of polarons in the BNN material.The

Fig. 16 .
Fig. 16.Conductivity AC as a function of frequency at different temperatures (350 • C-450 • C) for (a)BNN, (b)BNYN0.02,(c)BNYN0.04and (d) comparison of conductivity AC at T = 410 • C for BNN, BNYN0.02 and BNYN0.04.The red lines show the fit by Jonscher's power law.(For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.) (f et e) with n CBH = 1-6×KB×T Wm [90].The values found for W 1 m and W 2 m of the compounds BNYN0.02 and BNYN0.04 are W 1 m = 0.438 eV, W 2 m = 0.203 eV and W 1 m = 0.783 eV, W 2 m = 0.401 eV respectively.The conductivity dc of the prepared samples is increased with temperature as shown in Table

Table 5
The energy of activation by conduction of the elaborated ceramics.model for understanding the charge transport mechanism in the BNN base compound, and for Y-doped BNN compounds, the Correlated Barrier Hopping (CBH) mechanism is the appropriate model.The obtained conduction activation energy values indicate that single and double-ionized oxygen vacancies are responsible for electrical conduction in Ba 2 Na (1-3x) Y x Nb 5 O 15 ceramics. appropriate