Studies on the structure, optical, ac conduction mechanism by OLPT model and impedance spectroscopy of La-doped Ba2SnO4 Ruddlesden Popper Oxide

The conventional ceramic route has been used to prepare the La-doped Ba 2 SnO 4 samples by heat-treatment at 1000 o C and sintered at 1250 o C. The phase identification was carried out using XRD and found to be single phase up to 4 atoms %. The solubility of La at Ba-site were further reconfirmed using FTIR and Raman analysis. The AC conductivity spectra of all samples follow universal Johnscher’s power law ; however, the thermal dependence of 𝜎 𝑑𝑐 and 𝑓 ℎ suggest Arrhenius type conduction within the sample. Further, the scaled conductivity 𝜎 𝑎𝑐 /𝜎 𝑑𝑐 and frequency 𝑓/𝑓 ℎ at all temperatures superimposes on a single master curve, indicates the invariance of conduction mechanism. The impedance spectroscopy studies suggest the major contribution of grain in the conduction and relaxation. The present material could be potentially used in semiconductor device, UV-detector, and mixed ionic and electronic conductor (MIECs) by utilizing absorption states and thermo-curves as metastable state.


Introduction:
The ternary oxides belonging to the Ruddlesden Popper (RP) phase were identified by the general chemical formula An+1BnO3n+1, consisting of n-layered perovskite (ABO3) slabs sandwiched along the c-axis by two rock salt layers of A-O [1][2][3]. Because of their exceptional electronic and ionic transmission behaviour, this form structure gained considerable interest from researchers in discovering its potential used in superconductors, supercapacitors, as thermoelectric materials, as multiferroic materials and as cathode materials for solid oxide fuel cells [4][5][6][7][8][9]. Due to their lower thermal expansion coefficients (TECs) than the conventional perovskite-based manganite, the rare earth-based nickelate, cobaltite, and ferrite were more extensively studied among the investigated K2NiF4 type phase [10][11][12]. Another advantage of these structures over perovskites is that perovskites have a compact structure, so they only have an oxygen deficiency phase, while RP phases have both an oxygen deficiency and in efficient phase. Because of this exceptional property, these typical structures can be used in mixed ionic and electronic conductor (MIEC) applications [1,13,14].
Rare-earth based nickelate/cobaltite Ln2NiO4/Ln2CoO4 (Ln: La, Pr, Nd) have been recognized as auspicious cathode materials due to their ability to replace conventional electrode materials used at high temperatures [7,10,11]. There are two types of oxygen sites in the structure: an equatorial oxygen site inside the perovskite, and an axial oxygen site that serves as a connection between the perovskite and the rock-salt layer [15]. The interstitial incorporation of oxygen between the perovskite and rock salt layers causes an extraordinarily large change in oxygen non-stoichiometry (δ) for solid oxide fuel cells at intermediate temperatures (IT-SOFCs). The transition metal was used as a source of conduction in these materials, which was accomplished through an oxidation (Ni 2+ /Co 2+ to Ni 3+ Co 3+ ) and reduction (Ni 3+ /Co 3+ to Ni 2+ /Co 2+ ) process.
A.P. Khandelwal et al. studied the electrical properties of Nd2NiO4 and reported that the replacement of alkali earth metals at the Nd-site improved mixed electronic and ionic conductivity [16]. By tuning the valence states of Fe, Chao Jin et al. mentioned that Sr substitution at the Ba-site of Ba2FeO4 could be used as a new cathode material for IT-SOFCs [17]. Since the chemical used in nickelates is so expansive, it's unlikely that these conventional materials will ever be commercialized in bulk. It is therefore essential to find an alternative to this material, not just for the development of new materials but also for the understanding of the fundamental solid-state physics. It has been noted on the basis of literature that alkaline earth-based stannates (M2SnO4, M: Ca, Sr, Ba) completely fulfil the requisite requirements possessed by La2NiO4, La2CoO4, Ba2FeO4, etc. such as, (i) it has multivalent ion Sn, that exist in Sn 4+ /Sn 2+ , (ii) larger the volume for tuning the oxygen non-stoichiometry (δ).
Alkaline earth based stannates (M2SnO4) also belongs to the RP phase, which belongs to the space group 4/ and crystallized into tetragonal structure ( = ≠ , = = = 90 ) [18]. Alkaline earth orthostannates have recently received more attention as a new phosphor material, owing to their stable crystalline nature and high physical and chemical stability [19]. Rare earth metals and transition metals were used to control the photoluminescence properties of the host phosphor material that are used in flat panel displays, field emission displays, and electroluminescence devices [20,21]. Detailed electrical properties of Ba2SnO4 have already been described in the literature; two types of conduction mechanisms have been found to be operative within the investigated temperature range, assigned to electronic conduction at low temperatures and ionic conduction at higher temperatures [15].
The modification in Ba2SnO4 lattice manipulates the sources of charge carriers and semiconducting properties that played the crucial role in the electrical properties. The doping of various atoms in the solids can be done on the basis of Hume-Rothery criteria [22]; the difference of ionic radii between the host and dopants should be lye below ±15%. Since the difference between the ionic radii of La and Ba was found to be less than 15  BaSnO3 system and studied their electrical properties using impedance spectroscopy and found their application as oxygen ion and hydroxyl ion conductor [29]. Masahiro et al. synthesized the ceramics of La-doped BaSnO3 using polymerized complex method and reported it as ntype degenerate semiconductor [23]. The multifunctional application of La-doped BaSnO3 enforce us to choose La as dopant for present system and will be expect to be as interesting as reported in literature. It is very interesting that no research has been available in the literature so far on the partial substitution of La at the Ba site in Ba2SnO4. Therefore, an attempt has been made in this manuscript to replace Ba with La in Ba2SnO4.
In present investigation the synthesis of La doped at the site of Ba2SnO4 have been carried out using traditional ceramic route by calcining at 1000 o C. The phase identification of the synthesized samples is confirmed using X-ray diffraction (XRD) followed by Rietveld refinement. The solubility limit of La in Ba2SnO4 lattice has been investigated by Raman spectroscopy and Fourier transform infrared spectroscopy (FTIR). The morphological and electrical properties of sintered ceramics were further studied using a field emission scanning electron microscope and a high precision LCR meter respectively.

Experimental:
The

Characterization techniques:
The thermal analysis of prepared mixture was performed using thermogravimetric and

Determination of calcination temperature
The thermogravimetric (TG) and differential scanning calorimetry (DSC) analyses of B2LS0 and B2LS2 were carried out to determine the calcination temperature for the prepared mixture of samples, as shown in Fig. 1 The primary difference between the TGA curve of B2LS0 and B2LS2 is additional weight loss of 6.37 % in B2LS2, which may be attributed to the hygroscopic aspect of La2O3 [31]. The DSC curve of each sample shows an endothermic peak present at 828 o C and 830 o C in sample B2LS0 and B2LS2 respectively. The appearance of an endothermic peak in each sample indicates the initiation of a reaction between the raw materials. The reaction between the reactants is expected to proceed in the same manner as B2LS0; The weight loss has been calculated from equation (1) and (2) are almost 16.03 %. The weight loss occurred up to 100 o C in B2LS2 is assigned to the evaporation of water molecules adsorbed at the surface of particles that adsorbed during the mixing of solids [32]. Since CO2 loss is the primary cause of weight loss in both samples, and the total weight loss obtained experimentally is nearly half of what is predicted. The huge difference between experimental and theoretical weight loss suggesting that the decomposition of BaCO3 does not takes place completely because the reaction not only depends on temperature but also on time. Furthermore, the presence of a weak endothermic reaction peak about 830 o C in the DSC curves of both samples suggests that the reaction begins before complete decomposition of BaCO3. The presence of reaction peak was in well agreement with the earlier study [33]. Since the amount of doping was quite low, so no significant changes have been observed in present investigation except the hygroscopic properties of La. Therefore, to obtain the phase pure powder the mixture of raw materials should be calcined at 1000 o C for 6 h.

Determination of phase and crystal structure:
The phase and crystal structure of the prepared samples were determined using powder X-ray diffraction (XRD) analysis. The XRD pattern of calcined powders has been recorded within the angular range 25-80 o and shown in Fig. 2. All the diffraction peaks observed in XRD pattern are fine and sharp, suggesting that the sample is crystalline. In order to determine the phase of the sample, the experimental XRD pattern is compared to the JCPDS database and found to be very similar to the JCPDS file (no-43-0071) of parent phase Ba2SnO4 [34]. It has also been observed that as La is incorporated into the lattice, the size and width of the peaks gradually that the number of Ba sites is greater than that of BaSnO3. The solubility limit of La is found to be close to the La-doping in alkaline perovskite oxides [30,31,35]. This indicates that while there are more sites in Ba2SnO4 than in BaSnO3, the La is only occupying the sites that are available in BaSnO3. In order to understand such behaviour theoretical study must be needed.

Fourier transform infrared (FTIR) Spectroscopy analysis:
Fourier transform infrared (FTIR) spectrum analysis is used to identify the presence of various functional groups in samples, as shown in Fig. 3 (a). The FTIR spctra of all samples are similar to the FTIR spectra of pure Ba2SnO4 reported in literature [22]. The FTIR spectra shows bands at 518 cm -1 , 623 cm -1 , 850 cm -1 , 1020 cm -1 , 1122 cm -1 , 1419 cm -1 , 1952 cm -1 and a wide band 2424-3645 cm -1 in B2LS0. However, the addition of La to the sample suppressed a few of the bands (1020, 1122, 1952 cm -1 ) and moved the other bands to higher wavenumbers. The vibrations of BaO and SnO6 octahedra are assigned to the two bands present at 515 cm -1 and 616 cm -1 , respectively [32,36]. The expand view of the characteristic band has been shown in Where is a constant considered to be as effective bond length and is the reduced mass of band arrangement. Since La has a higher mass than Ba, the reduced mass decreases as La is incorporated, resulting in a higher wavenumber needed to vibrate the specific band. Besides these characteristics bands, few more bands are observed at 856, 1024, 1120, 1450, 1936 cm -1 assigned to the physically adsorbed -CO2 and the bands at 1936 and 3294 cm -1 is assigned to the adsorbed -OH at the surface of the sample [36]. It is noticed that with increasing the concentration of La at the Ba site above x=0.04, a weak XRD peak belongs to phase La2Sn2O7 is appeared in XRD pattern. However, the vibrational band associated with La2Sn2O7 is observed within the wavenumber range 550 to 680 cm -1 [37]. So, the identification of the pyrochlore phase present in the sample can't be done using this analysis. Therefore, the identification of pyrochlore phase is further analyzed using Raman spectroscopy and discussed in susequent section.

Raman Spectroscopy analysis:
Raman spectroscopy is a novel non-destructive and more sensitive technique in comparison with XRD, that usually revealed the local structural information of material [36]. It has piqued interest because of its ability to detect structural changes that alter crystal symmetry at the submicron scale, as well as provide an estimation of the factors that cause these structural changes. Fig. 4 illustrates the Raman spectrum of all samples recorded at room temperature within the wavenumber range 100-1000 cm -1 . Raman spectrum of the synthesized samples is compared with the Raman spectrum of K2NiF4 type layered perovskite materials [15].
Theoretical calculation revealed that the A2BO4 type structures have total 14 optical modes, and among them only 4 modes were found to be Raman active. In A2BO4 type structure, B atom was shared by 6 oxygen (4 equatorial oxygen O1 under D2h symmetry and two apical oxygen O2 under C4ν symmetry) while 9 oxygens were shared by atom A. The rock salt A-O is connected with the perovskite through apical oxygen along c-direction. The AO9 dodecahedral involves four equatorial oxygen O2 at same position Z and one apical oxygen along c direction and also four O1 at z=0 as shown in Fig. 4. The 14 optical modes have been obtained by the contribution of phonon associated with various atoms are given below; (1) → 2ℎ → 2 + 2 + 2 (2) → 4ν → 1 + + 2 + = 2 1 + 2 + 4 2 + 5 + 2 Among 14 optical modes only four modes are Raman active (two A1g and two Eg), while experimentally more than four modes are found to be active in present samples [15,38]. The various Raman bands observed in the synthesized sample are assigned to different modes and listed in Table 1 (3)). It is further noticed that a new Raman band is appeared at 597 cm -1 for samples B2LS6 and B2LS10 because of the presence of pyrochlore phase (La2Sn2O7) present in sample. The Raman study is completely agreed with XRD analysis, that further reconfirm that the solubility La is limited into the lattice between 0.04 < x ≤ 0.06 weight %.  With the addition of La, the absorption peak shifts to a higher wavelength, which may be due to an inter-shell transition from the energy level of La [36]. The magnitude of absorption varies with La within the UV-region, which could be utilized as metastable state for UV-detector application. The optical band gap of the samples is determined from UV absorption data using Tauc relation given by [39]: Where is the absorption coefficient, ℎ is the energy of photon, B is an energy independent constant, is the energy band gap of the material and is known as index parameter, which decides the nature of transition. Based on available literature, four values of is possible such as 2, 3/2, 1, and 1/2 for indirect allowed (indirect band gap) and indirect forbidden, direct forbidden and direct allowed (direct band gap) electronic transition respectively [40]. The direct band gap results due to transition of photon from the bottom of conduction band to top of valence band whereas indirect band gap results due to transition of photon from the intermediate energy states such as defects [41]. The Tauc plot is generated using equation (4) for the presence of pyrochlore phase in sample B2LS6 and B2LS10, the UV-Vis spectra also reflect two bandgap one is may be of B2LS composition and other for pyrochlore phase. In present case, the discussion for sample B2LS6 and B2LS10 excluded due to presence of pyrochlore phase and solubility limit of La into the lattice. One major change has been observed that the direct bandgap and indirect bandgap of the La-doped samples are found to be lower than undoped. In order to understand this variation, the charge compensation mechanism has been taken into account. Since La acts as donor for Ba-site and the charge compensation mechanism takes place by following equation; Since the samples are synthesized at high temperature, so the loss of oxygen can't be ruled out and given by; The position of defect state 2̇ formed below the conduction band that might be one of the possible reasons for decreasing the bandgap. However, as La is increased, the concentration of defect state 2̇ increases, since this defect has a positive charge and as its concentration increases, a small amount of columbic repulsive force between defect states acts, which may be an explanation for the bandgap rising. Moreover, the presence of indirect bandgap in samples suggests the presence of defect such as oxygen vacancy (see equation (6)) [33,44].
Since the difference between the direct and indirect bandgap has been found to be 0.49 eV, 0.31 eV, 0.24 eV and 0.25 eV for samples B2LS0, B2LS1, B2LS2 and B2LS4 respectively.
Since the value of difference has been decreased with La, that might be due to increase of oxygen vacancy. The value of direct bandgap reflects inorganic semiconducting nature of samples, and utilized it for semiconductor device application.

Morphological studies of sintered pellets of system (Ba1-xLax)2SnO4
To at Ba 2+ site of Ba2SnO4 act as a donor and charge neutrality may be maintained by equation (5). As the concentration of La in the Ba2SnO4 increases the concentration of either electron or ′′ increases. It is well reported in literature that the donors act as grain growth inhibitor whereas oxygen vacancies promotes the grain growth process [45]. This might be possible reason for the variation of grain size observed in present samples.

Reitveld profile analysis:
Structural parameters of the single-phase samples have been determined using Reitveld refinement analysis performed on powder X-ray diffraction data. The refinement has been performed using FullProf software suite by adopting crystal structure as tetragonal with space group (#139, I4/mmm). The peak function has been modelled as Pseudo-Voight (A combination of Lorentzian and Gaussian function) given by; . . = * + (1 − ) * Where, , , are the positive constant, contribution of Lorentzian and Gaussian function present in XRD peak respectively. The background for the XRD diffraction pattern has been described in terms of 12 th order polynomial function [46]. The refinement has been processed until the achievement of best fit. The Reitveld refined pattern of single-phase solid solutions are shown in Fig. 8(a). The quality of fitting has been judged by calculating a parameter S using weighted profile pattern (Rwp) and pattern profile (Rp) through formula, = / . The value of S for all samples found to be unity suggests that the parameters derived from refinements are relevant. The refined parameters along with other relevant structural parameters such as most affected bond length and bond angles are given in Table 2.   From Table 2, it has been noticed that the value of lattice parameters (a, b) found to be decrease while parameter c shows random variation. However, the volume of unit cell and x-ray density found to be decrease with incorporation of La into the lattice. Further, the different bond lengths Ba-Sn, Ba-O1, Ba-O2 and Sn-O1 were also found to be decrease with La that supports the experimental results. The variation in these structural parameters were found due to difference in ionic radii of dopant La 3+ (1.21 Å) to host Ba 2+ (1.44 Å) [47]. The crystal structure of a reference sample has been generated using crystallographic information file (CIF) through the Vesta Software and shown in Fig. 8(b). In the crystal structure, the perovskite (BaSnO3) is sandwiched between two adjacent rock salt layers (BaO). The position coordinate of the atoms was already given in Table 2, that indicates that with incorporation of La, the z-coordinate of Ba and O2 shifted from their mean position. In this figure the number of unit cell along a,baxis is higher compared to c-axis, that might be a possible reason that the solubility of La at Ba-site takes place similar to the perovskite BaSnO3. As La occupied the sites available in lattice, the charge compensation mechanism takes place by equation (5)

Electrical Properties Measurement
The electrical properties of silver coated pellets have been measured as a function of frequency (20 Hz-2 MHz) and temperature range 300-600 o C. The frequency dependence conductivity for many polycrystalline, ceramics, glass-ceramics etc. have been well explained by Johnscher's power law given by A. K. Jonscher's in 1978 expressed mathematically in following form; Where, is a temperature dependent constant, is power exponent parameter which usually lies in between 0 to 1, is angular frequency = 2 , and is angular frequency. The Jonscher's power law has been further modified as [46]; In above equation f ℎ = ( ) 1/ , and the parameter is an important parameter called as power exponent that usually lies between = 0 to 1 such that = 0 indicates frequency independent region (linear plateau parallel to frequency axis) called as dc conductivity (σdc), and = 1 indicates frequency dependence of conductivity. Frequency dependence of ac conductivity for all samples were depicted in Fig. 9 (a) for a reference sample B2LS2. Since the frequency dependence of ac conductivity for rest samples are similar to B2LS2 with only change in their magnitude so their plots have been given in supplementary file. The value of σ , f ℎ and were obtained at each temperature by employ fitting of equation (9) to experimental data, shown by solid line in each figure. The thermal dependence of dc conductivity has been shown in Fig. 9 (b), to study about the conduction mechanism operative in samples. Arrhenius model gives a relation between the dc conductivity and temperature by following relation [7]; Where, is preexponential factor, is Boltzmann constant and . is activation energy for the migration of charge species within the samples. The activation energy of each samples has obtained by fitting of equation (10) to experimental data as shown by solid line. The thermal dependence dc conductivity curve shows two regions with different value of activation energy as mentioned in each fig. The conduction mechanism of undoped sample was already reported in literature, therefore, here only it has been considered as reference [15]. The activation energy for undoped samples found to be 1.38 eV (high-temperature region) and 0.54 eV (low temperature region), and with incorporation of La, the activation energy in both regions were decreased, while dc conductivity was increased. This variation can be understood in terms of charge compensation mechanism given by equation (5). Since the doping of La at Ba-site leads to an excess positive charge (2 . ) that can be compensated either by creation of electron ( ′) or ′′ . The dc conductivity of doped sample increases with doping concentration of La suggest that the excess of positive charge on lattice compensated by generation of electron to maintain the overall charge neutrality. Further, the detailed conduction mechanism has been explored in further section.
In order to understand about the relaxation mechanism in depth, the logarithmic of hopping frequency ( ℎ ) has been plotted with respect to inverse of temperature and shown in Fig. 10.
The activation energy for relaxation process ( . ) has been calculated using similar equation to Arrhenius equation that is given by [48]; Where, is preexponential factor, and is Boltzmann constant. The linear fitting of equation (11) to the experimental data shown by solid line gives the value of . The value of activation energy found highest for undoped and it decreased with incorporation of La similar to dc conductivity.
Since the optical band gap is lowest for sample B2LS1, i.e., 3.23 eV, while the activation energy for all samples were found to be less than the separation between valence band and conduction band, that exclude any type of intrinsic conduction. As the samples were synthesized at high temperature, the presence of oxygen vacancy can't be ruled out and given by equation (6). The electrons present in equation (6)  The dc conductivity results in high temperature region reflect the ionic migration that transformed to polaronic with incorporation of La, while the low temperature region reflects the electronic conduction that remain same for all samples. Since, the conductivity in undoped samples results due to migration of oxygen vacancy and electron, however, the activation energy gradually decreased with incorporation of La that observed either of decrease in oxygen vacancy or increase of hopping length. The dc conductivity was found to be increased that may be due to either larger charge carrier concentration or higher mobility. Increasing in mobility may also leads to an increase in activation energy that does not support the present result.
Therefore, the reason for increasing the dc conductivity is increase of charge carrier concentration. Also, La acts as donor for Ba-site of Ba2SnO4 and the overall charge has been compensated by creation of electron as given by equation (5). Due to electronic charge compensation mechanism, the number of electrons within the samples also increase and it results to rise in dc conductivity. In order to see the role of temperature and composition on conduction and relaxation process occurred in sample; the time temperature superposition principle (TTSP) has been taken into account and given by [50]: The TTSP curve has been generated by scaling the frequency axis ( ) with hopping frequency ( ℎ ) and ac conductivity ( ) with dc conductivity ( ) at each temperature and shown for sample B2LS1 and B2LS4 in Fig. 11 (a) and (b) respectively. All the thermal curve perfectly superimposes on each other at all temperatures, indicating reflects that the sources of charge carriers are remain same at all temperature. Therefore, the conduction in sample within low temperature region take place via hopping of electron between the degenerate sites of Sn while in high temperature region the conduction take place via orientation of electron from Sn 4+ to Sn 2+ through polaron. In order to explore the conduction mechanism, the variation of power exponent as a function of temperature has been illustrated in Fig. 12. The power exponent represents the dimensionality of conduction as well as the strength among the host lattice with the mobile species. Based on the variation of power exponent, different models are well discussed in the literature to explore the ac conduction mechanism involved in the samples [15]. Few of them are given below;

Minimum values of followed by an increase suggests that the conduction in samples
occurred by overlapping of large polaron tunneling (OLPT) model.

Temperature independent variation of suggests the occurrence of conduction through
Quantum mechanical tunneling (QMT).

3.
Decrease of with temperature suggests the presence of correlated barrier hopping (CBH) in the samples.
Based on the variation observed for power exponent, the OLPT model is most suitable to analyse the detailed ac conduction mechanism in present samples. In OLPT model, the power exponent depend both on frequency and temperature. Initially had dropped to a minimum value with increasing temperature and then escalated with further increase in temperature [51]. The ac conductivity in OLPT model is usually given by following equation [52]; ( ) = [ Here, kB is the Boltzmann's constant, is the number of defect state near the Fermi level, is the inverse of localization length, is the hopping length, is the energy required for overlapping of the polaron and is the length of polaron. The hopping length is further determined by solving the quadratic equation [53]; Where = 1/ , ′ = 2 , and ′ = 2 . Also, the frequency exponent can be expressed in this model is given by; , and as the initial parameters [52]. All the parameters were derived from the least square fitting and given in Table 3.  shows experimental data and solid line shows fitted data using equation (13).
From Table 3, it has been noticed that with incorporation of La 3+ the value of charge carrier concentration increases that might be possible reason for rise in dc conductivity. It is also clear that the value of hopping length ( ) decreases with La 3+ , that follow similar trend of the inter atomic distance given in Table 2  BaSnO3. As a result of this explanation, we can infer that there is a difference in conductivity between these two compounds. Thus, in the present sample, conductivity is ensured by the overlapping of large polarons within the large tunnels, while in BaSnO3, it is ensured by the overlapping of small polarons within the small tunnels [56].
Moreover, the contribution of grain, grain boundary, and electrode to the overall electrical properties can be studied using Nyquist plot. The Nyquist plot has been shown in Fig. 14 for all samples obtained at selected temperatures such as 300 o C, 400 o C, 500 o C, and 600 o C. A depressed semi-circular arc has been observed for all samples. Further, the Nyquist plot has been fitted with a Cole-Cole equation to determine the contribution of grain and grain boundary is given by [57]; The resistance of grain and grain boundary were determined by employing the equation (16) to experimental data shown by solid line in Fig. 14. Ideally, three semi-circular arcs have been observed that assigned to the grain, grain boundary, and electrode contribution respectively [51]. Although they are found to be present separately not only at higher frequency but also due to large difference in their relaxation time. The measurement cannot be performed at higher frequency due to limitation of instrument used in present investigation. In present sample, only a singular arc has been observed that indicates the resistance can be given by Rtotal= Rg+Rgb+Relec. Since the arcs observed in present investigation are depressed that reflects the distribution of relaxation time among the grains/grain boundaries. Further, the SEM analysis shows agglomeration among the grains that might be one of the reasons that the contribution of grain boundaries was not separable. The value of resistance obtained by fitting of cole-cole equation has been given in Table 4. At the top of the semicircle, following condition should be satisfied [57]; The value of effective capacitance was calculated using the frequency and resistance at each temperature for all samples and given in Table 4. The value of effective capacitance calculated from equation (17) was found to be in agreement with the effective capacitance arised due to major effect of interface present within the samples [22,58]. Therefore, in order to further study about the role of grain to the electrical conduction and relaxation mechanism, the thermal dependence of effective resistance was taking into account. The conduction mechanism of charge carrier within grain has been discussed by determining the grain resistance for all samples. capacitance reflects the contribution of interface, that might be due to presence of multivalent ion at the interface such as Sn 4+ . The multivalent ion captures the electron present at the interface and reduced the multivalent states of Sn 4+ to Sn 2+ . Since the grain boundary shows higher insulating than grain so that it needs slightly higher activation energy for the migration of charge carrier [15,59]. With increasing the doping concentration, the value of activation energy found to be gradual increase that might be due to large size of polaron (See Table 3). Based on the value of activation energy, the present materials can be utilized as mixed ionic and electronic conductor and semiconductor device applications.

Conclusions:
A few compositions of the system Ba2-xLaxSnO4 (where x=0, 0.01,0.02,0.04,0.06,0.10) have been successfully synthesized using the solid-state ceramic route. The XRD studies along with FTIR, Raman and UV-Vis. study suggests the solubility of La at the site of Ba in Ba2SnO4 was limited between 4 to 6 atoms %. The compositions having a doping concentration above than 4 atom % contains impurity of La2Sn2O7 pyrochlore phase. Rietveld refinement studies performed on XRD data indicated lower unit cell volume, density, and bond length Ba/La-O1 and Ba/La-O2. The incorpration of La results decrease of crystallite size, and average grain size whereas increase of micro-strain due to lower ionic radii of La 3+ than Ba 2+ . The optical band gap of all samples obtained using Tauc plot was found to be in the range of (3. 23

Conflict of Interest
There is no any conflict of interest in this manuscript.

Data availability statement
The raw/processed data required to reproduce these findings cannot be shared at this time as the data also a part of an ongoing study.