Role of charge-compensation process on the structural, microstructure and electrical properties of pure and Nb-doped Sr2SnO4

This article explores the charge compensation method by synthesising Sr2SnO4, Sr2Sn0.99Nb0.01O4, and Sr1.995Sn0.99Nb0.01O4. The synthesis of a monophasic, tetragonal sample was achieved using a typical ceramic approach and high-temperature heat treatment. The XRD followed by Rietveld refinement, confirmed the crystallization of material under the space group I4/mmm. The crystallite sizes for all samples determined to be less than 50 nm, while the micro-strain falls within the range of (1.78–2.93) × 10–3. The microstructure exhibits a cuboidal shape for all samples, and the grain size is observed to decrease with the addition of Nb. The dielectric characteristics of the samples indicate the existence of Maxwell-Wagner and Orientational polarization in the sample. The sample Sr2Sn0.99Nb0.01O4 demonstrates a greater conductivity value compared to Sr1.995Sn0.99Nb0.01O4. This is attributed to the presence of excess electrons that compensate for the overall charge, as opposed to Sr1.995Sn0.99Nb0.01O4 where the extra charge is compensated by a cationic vacancy VSr″. The time-temperature-superposition principle (TTSP) is applicable to all compositions and indicates that similar sources are responsible for both conduction and relaxation processes. The dielectric permittivity and dissipation factor are found to be in the range of 150 to 175 and 0.2 to 0.5, respectively. This suggests that they have potential for future use in millimeter-wave communication with dielectric resonator antennas (DRAs). Due to the presence of oxygen ions and the ability to conduct both ions and electrons, at temperatures above 400 °C, it is a suitable choice for electrode materials in the application of intermediate temperature solid oxide fuel cell (IT-SOFCs). Exploring the manipulation of defects using electrical and ionic charge compensation methods shows potential for enhancing materials in semiconductor technology.


Introduction
Defects in the crystal structure are defined as the presence of foreign atom in the ideal crystal that lead to a deviation from their ideal behaviour, either physical or chemical [1][2][3].Extrinsic ionic-type defects are found in the presence of impurity ions dissolved at the lattice sites.The major effect of impurity ions in the defect engineering of a compound results due to the difference in oxidation state relative to the host ion they substitute and need some extra other defect which has opposite charge to preserve the electroneutrality condition [4][5][6][7].The presence of these charge compensation defects has a profound effect on the physical, chemical, and physicochemical properties, and thus the desired properties can be developed through the modification of a host crystal with an appropriate amount of suitable impurity [3,[8][9][10].
Alkaline earth-layered perovskite, with the general formula A 2 BO 4 , has been well known as a phosphor, mixed ionic and electronic conductor, and photocatalyst for water splitting, which is more cost-effective than conventional materials [11][12][13][14].The alkaline earth-based stannates (M 2 SnO 4 : M = Ca, Sr, and Ba) show potential application in a wide range of technological applications due to their intriguing dielectric and electrical properties [15,16].Since these materials were used in the form of polycrystalline because their single crystal form leads to an expensive cost of materials [17], electrical properties in these materials result from the contribution of bulk (grains), grain boundaries, and electrode specimen interfaces.The conduction behaviour in such materials has been explored by finding the value of resistance, either overall or individual, in the grain, grain boundary, and electrode specimen.These contributions were only separated by the use of impedance spectroscopy [18,19].
The physical properties of alkaline earth stannates are modified by independent heterovalent substitution (e.g., La 3+ on Sr 2+ sites or Fe 3+ at Sn 4+ sites of Sr 2 SnO 4 ) or simultaneous heterovalent substitution in equal amounts (e.g., the system Sr 2−x La x Sn 1−x Fe x O 4 ) [11,20].Based on the heterovalent substitution, the overall charge neutrality can be compensated in two ways [21,22]: = ¢ The presence of e¢ in the above equation may reduce the valence state of Sn 4+ to Sn 2+ .This kind of substitution was known as an electronic charge compensation mechanism [23].
(ii) Another approach to maintain the charge neutrality in same heterovalent kind doping can be denoted by following equation: the equation shows that the excess charge can either take place by creating, V Sr ¢¢ or by initially taking the lower amount of Sr in the lattice, which was known as valence-compensated mechanism [23].
The pristine phase of Sr 2 SnO 4 has been well explored as a host material for phosphor application, and with the substitution of rare earth ions, their phosphor application has been modified for different optical imaging and display device applications [24][25][26][27].Depending on the desired properties, the semiconductor material Sr 2 SnO 4 has been tuned for its electrical, optical, and electronic properties, making this a potential application in electrical, electronic, and optoelectronic devices [11,13,14,28,29].Yuexuan Mu et al have studied the integration of photo-stimulated luminescence (PSL), thermal-stimulated luminescence (TSL), and photochromism (PC) in one single material, Sr 2 SnO 4 , by co-doping Er 3+ and Sm 3+ .They found that PSL and TSL were greatly depressed for the concentration of dopant greater than 0.005.Due to variation in the defects and charge compensation process, they proposed a new approach for optical information storage using the PSL as the optical signal by using a reference signal from Er 3+ luminescence [14].Moreover, J. Du et al studied the effect of Si-substitution in Sm 3+ -modified Sr 2 SnO 4 for rewritable optical information storage.They found a tunable luminescence emission in reddish-orange that was controlled by phonon release upon thermal stimulation.Though the substitution of Si to Sn results in a deeper trap level, which works as a photon trapping and de-trapping process in information storage technology [13].D. J. Lee et al have investigated the effect of codoping of Ce 3+ and Eu 3+ ions in Sr 2 SnO 4 for luminescence application.They studied the effect of substitution on size and luminescence by defect formation.The emission intensity of Eu 3+ was drastically enhanced by the substation of Ce 3+ due to energy transfer from Ce 3+ to Eu 3+ .The charge transfer processes were well established for the tuning of colours emitted by phosphor from blue to orange [27].
Furthermore, it has been observed in literature that the effect of substitution in Sr 2 SnO 4 is only studied for its optical and luminescence properties.However, the literature also suggests that doping plays a crucial role in electrical properties for electronic and electrical device applications.It has been carefully observed in the literature that most of the studies have been performed in the literature based on electronic and ionic charge compensation processes, i.e., type 1, while no study so far has been performed in the literature based on valencecompensated processes, i.e., type 2. Thus, it is necessary to study the comparison between these two-charge neutrality processes, which may work as a bridge between materials science and defect engineering to develop new materials as well as basic defect mechanisms.
Therefore, to fulfil the aim of the work, in this manuscript, three samples, Sr 2 SnO 4 , Sr 2 Sn 0.99 Nb 0.01 O 4 , and Sr 1.995 Sn 0.99 Nb 0.01 O 4 , were prepared by using a conventional ceramic route followed by high temperature heat treatment.The preliminary phase identification of samples was performed by powder x-ray diffraction, and to ensure the relevant structural parameters are accurate, the XRD data has been further analyzed by the Rietveld refinement process.The dimensions and defects were analyzed by the Williamson-Hall plot and the size-strain plot methods.At last, the role of defects and the charge compensation process has been analyzed using a frequency-and temperature dependent electrical property measurement system.

Synthesis of materials
The compositions Sr 2 SnO 4 , Sr 2 Sn 0.99 Nb 0.01 O 4 , and Sr 1.995 Sn 0.99 Nb 0.01 O 4 were synthesized using the conventional ceramic route.The initial precursors, SrCO 3 , SnO 2 , and Nb 2 O 5 , having a purity greater than 99.9% were weighed in a stoichiometric ratio and mixed in a planetary ball-mill.The stoichiometric amounts of raw materials were transferred to agate jars and mixed using acetone as the mixing medium for 8 h.The mixed powders were dried in an oven overnight and then placed in an alumina crucible for calcination at 1000 °C for 8 h.Then the calcined powders were grounded, dried, and mixed with 2 % polyvinyl alcohol solution (PVA) as a binder.These powders were made in the form of pellets using a uniaxial hydraulic press into cylindrical pellets (with a diameter of 12 mm and a thickness of 2-3 mm) by applying a load of 70 kN, as shown in figure 1.These pellets were heated initially at a slow rate of 2 °C/min to 500 °C and held at this temperature for 1 h to completely burn off the binder PVA.Subsequently, the temperature has been raised to 1300 °C at a rate of 5 °C/min for the sintering process.The sintering mechanism has been carried out at the same temperature for 6 h and then the samples were cooled to room temperature.The obtained sintered samples were then used for material characterization.

Characterization of materials
To ascertain the formation of a single phase, the powder x-ray diffraction of crushed sintered pellets was performed by employing a Rigaku x-ray diffractometer using Cu K a radiation.The data were collected within the angular range of 2 10 90 q = - and the step size of 2 0.01.∆ q =  Further, the obtained XRD pattern has been analyzed through Rietveld refinement.The Rietveld refinement has been performed by FullProf software.The nano-size distribution of the crystallites and micro-strain in samples were determined using a well-known size-strain plot (SSP), where the full-width at half maxima (FWHM), interplanar spacing (d), and angular position (θ) have been taken into account.For electrical property measurements, the pellets were polished using emery paper of various grades.The polished pellets were washed using isopropanol, then dried and coated on both sides with conducting silver paste (Eltek India), which was cured by heating at 500 °C for 10 min.The four parameters, capacitance (C), dissipation factor (D), impedance (Z), and phase angle (δ) were measured using the Wayne Kerr -ZM 2376 LCR metre at various steady temperatures in the range of 40 °C-580 °C.Capacitance, inductance, and impedance basic accuracy is excellent ±0.05%.The dissipation factor accuracy is ±0.0005 and the quality factor accuracy is ±0.05%.The dielectric constant, ac conductivity, real and imaginary plots of impedance, and modulus were calculated with the help of recorded values.

Results and discussions
It has been found in the literature that the reaction between the raw materials takes place around 950 °C by equations (3)-( 5) [30].Thus, to obtain the single phase of samples, it is necessary to calcine the system above 950 °C.Therefore, the obtained mixture has been calcined at 1000 °C and recorded the XRD pattern as shown in figure 2(b).It can be seen that all the peaks present in doped samples belong to the pristine Sr 2 SnO 4 .The XRD pattern is well matched to the tetragonal structure reported in crystallographic open database file no.COD 1539931 [31].The absence of peaks related to raw materials SrCO 3 , SnO 2 , and Nb 2 O 5 confirms that the samples have a single phase [23,30] and the reaction takes place completely according to equations (3)- (5).The incorporation of Nb at the Sn-site can be further confirmed by enlarging the most intense peak observed at 31.03°and shown in figure 2(c).The XRD peaks' position was found to be shifted towards the lower angle, which might be due to the incorporation of Nb in the lattice.

Crystallite size and micro-strain determination
The effect of dopant as well as the charge compensation process on the physical shape of materials was studied by determining the crystallite size and micro-strain of samples.The peak width in the XRD peaks results from several contributions, such as smaller crystallite size, micro-strain, instrumental broadening, absorption coefficient, etc [32].The other factors except instrumental broadening, smaller crystallite size, and micro-strain have been corrected via the instrumentation of XRD.The instrumental broadening can be corrected from the XRD peaks, which were carried out by recording the XRD pattern for a Si-single crystal.The correction in peak width was carried out by the following equation: The Si b was determined from the XRD pattern of Si.The corrected value of b has been calculated using equation (6) and used to find the value of crystallite size according to the Debye-Scherrer equation.This equation correlate corrected b and crystallite size (D) in following manner [33]: Here, k is Scherrer constant, q is the angular position of XRD peak, and l is the wavelength of Cu-K a radiation.The value of q and corrected b for samples were determined by Gaussian fitting to the XRD peak and given in table 1.The value of crystallite size was obtained by using equation (7) and given in table 1.
It has been observed from table 1 that the value of crystallite size has decreased with Nb substitution.The decrease in crystallite size can be correlated with the smaller ionic radii of Nb as well as their grain growthinhibiting properties [34].
The dopant has a valency higher than the host, which may induce lattice strain in the structure.The induce lattice strain, defined as the ratio of incremental change to their initial value, leads to a shift in the interplanar spacing (d-spacing).The shift in d-value arises based on the nature of the strain, i.e., the compressive strain leads to a decrease in d as well as a lower Bragg angle, while the tensile strain leads to an increase in d as well as an increase in the Bragg angle.Since, here the value of crystallite size might not be correct due to the still presence of micro-strain.Thus, to determine the value of crystallite size and micro-strain accurately, a size-strain plot has been used.According to SSP method, the interplanar spacing (d) was related to D and e by the following equation [33]: All the symbols have their usual meaning as described in the above equation (8).The major advantage of this method is that it gives maximum weight to the XRD peaks obtained at higher angles, where precision is at its highest.The SSP plot for all samples was generated using equation ( 8) and shown in figure  ( ) The calculated value of D and e were given in table 2. It has been observed from table 2 that the value of crystallite size follows a similar trend to Debye with higher values, which confirms the existence of micro-strain in the sample.Moreover, the value of microstrain was found to be higher for doped samples than their pristine form.The microstrain value was higher for sample Sr 1.995 Sn 0.99 Nb 0.01 O 4 than for sample Sr 2 Sn 0.99 Nb 0.01 O 4 .This could be because the structure doesn't have enough Sr lattice.

Rietveld refinement analysis
The structural refinement has been carried out for samples Sr 2 SnO 4 , Sr 2 Sn 0.99 Nb 0.01 O 4 , and Sr 1.995 Sn 0.99 Nb 0.01 O 4 using the 'Full Prof' programme through the Rietveld refinement method [35], and the obtained refinement pattern is shown in figure 4. It has been confirmed from Rietveld refinement that all the composition belongs to tetragonal symmetry under the space group I mmm 4 .

/
The Wyckoff position (as shown in table 2) was used as an initial parameter for refinement.The background for the refinement has been taken as a sixth-order polynomial.During the process of refinement, all the parameters, such as structural parameters (lattice parameter, angle), peak profile parameter (u v w I x , , , , , , and their Wyckoff position, including thermal parameter B and occupancy [21].The quality of the fitting pattern and reliability parameters were judged by calculating the S-parameter using the formula R R . wp p / The parameters obtained from the refinement are given in table 2. The values of the S parameter and χ 2 were found to be in good agreement with the literature, which suggests that the derived parameters are relevant [36].It has been observed from table 2 that the lattice constant and volume decreased with the substitution of Nb at the Sn-site for both samples.This small change in lattice constant can be correlated with the ionic radii of Nb 5+ (0.64 Å) and Sn 4+ (0.69 Å) [37].The change in structural parameters with the dopant can also be seen from table 2 in terms of the lower values of bond lengths Sr-O1, Sn-O1, and Sr-O2, while it increases the bond angle such that Sr-Sn-O1 and O1-Sr-O2.Here O1 and O2 represent the oxygen atoms present in equatorial site and apical site of crystal structure as shown in the right side of figure 4. The substitution of Nb has also been seen in the x-ray density, which shows a higher value for Sr 2 Sn 0.99 Nb 0.01 O 4 and a lower value for Sr

Microstructural and compositional studies
The morphological studies of sintered pellets have been studied by a field-emission scanning electron microscope (FESEM).The high-resolution images of the fractured surface of sintered samples were taken at a scale of 1 μm and shown in figures 5(a)-(c).The morphology of samples shows significant variation in two parameters: first, the grain size, and second, agglomeration between the grains.The shape of the grains was  (0,0,0.3530)( 0,0,0.3530) ( 0,0,0.3530)Sn (0,0,0) ( 0,0,0) ( 0,0,0) Nb -(0,0,0) ( 0,0,0) O1 (0.5,0,0) ( 0.5,0,0) ( 0.5,0,0) O2 (0,0,0.1530)( 0,0,0.1530) ( 0,0,0.found to be cuboidal for all samples similar to discussed in literature [22] because the XRD confirmed the single phase of the samples and their crystallization in a tetragonal crystal structure.Further, the agglomeration between the grains was found to be higher in doped samples than in pristine Sr 2 SnO 4 .However, larger  ).The value of average grain size was found to be decreased with the doping of Nb.However, the role of the charge compensation process directly can be seen from the average grain size value, which suggests that the grain size of Sr 1.995 Sn 0.99 Nb 0.01 O 4 is lower than the sample Sr 2 Sn 0.99 Nb 0.01 O 4 .This variation can be understood in terms of the charge compensation process, which was given by equations (1) and (2).As we can see, the charge compensation process in Sr 2 Sn 0.99 Nb 0.01 O 4 , has been taken place by the creation of electrons (see equation (1)), which majorly act as grain growth inhibitors, while in the case of the sample Sr 1.995 Sn 0.99 Nb 0.01 O 4 , the charge compensation has been taken place by the cationic ordering, such as a lower amount of Sr, which also results in a drastic reduction in grain size [21].
The compositional analysis has been carried out for all samples using energy dispersive x-ray spectroscopy and shown in figures 7(a)-(c).The position of energy for individual elements has been found to be well matched to the reported literature.The weight % and atomic % of individual elements found to be in accordance to their stoichiometric ratio such as for Sr 2 SnO 4 , the ratio of atomic % between Sr and Sn is almost 2:1 while for Sr 2 Sn 0.99 Nb 0.01 O 4, the ratio between Sr, (Sn + Nb) is almost 2:1, and also followed by sample Sr 1.995 Sn 0.99 Nb 0.01 O 4 too [22].
3.5.Dielectric spectroscopy studies 3.5.1.Frequency dependent dielectric and dissipation factor study The dielectric permittivity or relative dielectric constant (ε) of all samples was studied as a function of frequency (1 Hz-2 MHz) and temperature range (40-580) °C and the output is shown in figures 8(a)-(c).The dielectric spectrum looks similar to all samples; it shows a typical characteristic of a dielectric or ferroelectric material, i.e., ε shows a larger value at a lower frequency and decreases with increasing frequency.The higher value of the dielectric constant at lower frequencies is due to the existence of all four types of polarizations such as dipolar, orientational, ionic, and electronic, in the materials.At lower frequencies, there might be charge accumulating at the interface, which would form a parallel plate capacitor since the separation between the walls is very small, resulting in a large value of the dielectric constant.However, at higher frequencies, the charge accumulation doesn't take place, resulting in a small value of the dielectric constant.These polarization processes are explained by the Clausius-Mosotti relation.The dipoles enable them to arrange themselves in the direction of the applied field, and with increasing frequency beyond a certain limit, all the contribution of polarization is found to have ceased.In addition to this explanation, Koop's model was also used to describe the quick and slow decrease of  the dielectric constant in the frequency spectrum by Maxwell-Wagner polarization.According to Maxwell-Wagner polarization, the ceramics structure has been considered to be composed of two layers: one is highly conducting grain and the other is poor conducting grain boundaries, which purely depend on the frequency.The grains are found to be more effective in the higher frequency region than the grain boundary.Since electronic polarization plays a crucial role and has a significant contribution to the dielectric constant in the higher frequency region, the value of the dielectric constant decreases subsequently.Further, the temperature dependence of the dielectric constant at 10 KHz has been shown in figure 8(d).This shows that the dielectric constant was found to be almost constant up to 400 °C, and thereafter, it increases gradually with temperature.In order to understand this variation, the dipole formation in the sample has been taken into account.Since the samples involved in the investigation have been synthesized at high temperature such as 1350 °C, the loss of oxygen can't be controlled, which is given by the following equation: The presence of electrons shown in the above equation may be captured by Sn 4+ and reduced to Sn 2+ .The presence of Sn 2+ at Sn 4+ acts as a negative defect and is denoted by Sn Sn acts as a positive defect, which is situated at a finite distance, form electric dipole.The application of an electric field to materials results in the polarization of this dipole and gives dielectric permittivity.From table 2, it can be seen that the bond length Sn-O1 was found to be higher for Sr 1.995 Sn 0.99 Nb 0.01 O 4 than the rest of the samples, which may be the probable reason for observing lower primitivity.Further, a linear increase in primitivity after 400 °C might be useful for sensing applications.
The frequency-dependent dissipation factor (D) for the investigating samples is shown in figure 9 over a wide range of temperatures (40-580) °C showing a similar behaviour as observed in permittivity, i.e., it decreases with increasing frequency and merges to an almost fixed value at higher frequencies.This nature of decreasing dissipation factor with frequency can be explained by the phenomenon of dipole relaxation.Since the space charges are not able to follow the alternate change of the applied electric field and proceed with relaxation.It is further noticed that the rate of increase of the dissipation factor of samples at lower temperatures is slow, while it becomes relatively higher at higher temperatures.

Electrical conductivity study
The electrical conductivity for the synthesized samples was calculated from the dielectric data using the following empirical formula [38]: Here the angular frequency of alternating current (AC) conductivity is denoted by , w o e denote the dielectric permittivity of free space, r e denote the dielectric constant, and tan d denote the tangent dielectric loss of investigated samples.The frequency dependent electrical conductivity of all samples within the temperature range (40-580) °C is shown in figure 10.The frequency dependent electrical conductivity shows two distinct regions; (i) frequency independent region which is parallel to frequency axis known as direct current (DC) conductivity, , dc s (ii) frequency dependent region, gradually increases with frequency.The crossover frequency from dc conductivity to ac conductivity is known as hopping frequency ( f h ).The total conductivity of electroceramics, glass-ceramics, and polycrystalline ceramic materials has been well described by the Jonscher universal power law and expressed by [39]: Here n denotes the power exponent, which depends on both frequency and temperature and decides the strength between the mobile ions and the host lattice.This exponent represents an imperative information about the conduction mechanism involved in the samples [40].
The ac conductivity spectra of samples shown in figures 10(a)-(c) for samples Sr 2 SnO 4 , Sr 2 Sn 0.99 Nb 0.01 O 4 , and Sr 1.995 Sn 0.99 Nb 0.01 O 4 , respectively, exhibit a similar trend with more or less variation in their numerical value.It has been further observed that the frequency spectrum of samples shifts to higher value of dc s and hopping frequency ( f h ) with increasing temperature.The role of the charge compensation process has been studied by plotting the conductivity spectrum at 600 °C for all samples, as shown in figure 10(d).To understand the conduction mechanism, the Jonscher power law given by equation (11) has been fitted to the experimental data shown by a solid line in figure 10(d) and extracted the parameters, , dc s f , h and n and discussed in the subsequent paragraphs.The value of conductivity was found to be higher for sample Sr 2 Sn 0.99 Nb 0.01 O 4 , while it was lower than Sr 1.995 Sn 0.99 Nb 0.01 O 4 , which might be due to the higher strain arising from the excess cationic vacancies or the lower mobility of the charge carrier (mobility is proportional to the available path, such as Sn-O1, Sn-O2).
The conduction mechanism involved in the samples has been studied by generating an Arrhenius plot through the extracted parameters dc s and shown in figure 11(a).According to the Arrhenius plot, the dc s is correlated with 1000/T by following equation [41]: and their logarithmic relation is given as; Here o s is pre-exponential factor, k B is Boltzmann constant, and E c is the activation energy involved in the conduction processes.It has been observed that three regions of conduction are operative in all the samples, which are represented by R-1, R-2, and R-3.The value of o s and E c have been obtained by employing the fitting of equation ( 13) and given in table 3. The activation energy for all sample exhibit in range (0.74-1.15 eV) in R-1, (0.17-0.38) eV in R-2, and (0.05-0.38 eV) in R-3.The conduction mechanism can be explained in all samples as follows: (i) The values of activation energy 1 eV for samples Sr 2 SnO 4 and Sr 2 Sn 0.99 Nb 0.01 O 4 and < 1 eV for sample Sr 1.995 Sn 0.99 Nb 0.01 O 4 have been observed in R-1.It is known for various perovskite or layered perovskite oxide ceramics that the doubly ionized oxygen vacancies (V O •• ) which need almost 1 eV for the migration within the available sites for it (see equation ( 9)) [18].The total conductivity of polycrystalline ceramics' materials was given by the following equation [33]: Here m denotes mobility and their suffix specifies the charge carrier, such as e for electron and p for hole.Thus, the higher amount of activation energy suggests either their concentration is larger or their mobility.
(ii) The value of activation energy in R-2 exhibits an activation energy of <0.5 eV.Several authors have reported that the migration of electrons or holes within the perovskite and layered perovskite needs <0.5 eV.Several authors have reported that the migration of electron or hole within the perovskite and layered perovskite need less than 0.5 eV [42].Here, it has been noticed that the presence of oxygen vacancy is associated with electrons (see equation ( 9)) in Sr 2 SnO 4 .However, the charge compensation process in Sr 2 Sn it can be seen from equations (15) and ( 16), there is a difference in charge carrier concentration in both samples, which might be a possible reason for the differences observed in activation energy.
(iii) In this again, it has been observed that the value of activation energy found is less than 0.5 eV in R-3, which supports the explanation made in (ii).The lower amount of activation energy in the case of Sr 2 SnO 4 suggests only the presence of electrons through high-temperature heat treatment.
The Arrhenius plot has also been generated using hopping frequency ( f h ) and shown in figure 11(b).The Arrhenius equation can be expressed in a similar way as dc s and written in the following way [41]: Here f o is pre-exponential factor and E r is activation energy involved in the relaxation process.The activation energy has been obtained by least squares linear fitting of equation (17) to the data points, as given in table 3. The activation energy for all samples is in the range (0.44-1.41 eV) in R-1, (0.35-0.47) eV in R-2, and (0.10-0.52 eV) in R-3.This variation can be understood by following way: The energy in R-1 was >1 eV for Sr 2 Sn 0.99 Nb 0.01 O 4, greater than 0.5 eV and less than 1 eV for Sr 1.995 Sn 0.99 Nb 0.01 O 4 , and less than 0.5 eV for Sr 2 SnO 4 .As it is evident from equation (9), the oxygen vacancies present in all samples have been associated with electrons, which take part in the relaxation process.However, for the rest of the sample, the charge carrier remains similar to that discussed in the conduction process.
(ii) The activation energy in R-2 and R-3 found a similar trend as described in the conduction process.The relaxation process has occurred via the transfer of electrons between the oxygen-vacancy site in R-2 and the degenerate site of Sn in R-3.
The correlation between the conduction process and relaxation process has been investigated by plotting σ dc and f h for all compositions, as shown in figure 12(a).A linear fitting between the data points has been carried out to understand the correlation.The value of the slope for all samples is given in table 3, suggesting almost a unit value, which validates the power law f .dc h n s µ The power exponent (n) is an important parameter used to investigate the conduction process.The exponent denotes the dimensionality of conduction process and the strength among the mobile charge carrier with the host lattice [42].The plotting of n as a function of temperature highlights a few more insights about the conduction mechanism.The temperature independent plot of n suggests the possibility of conduction through quantum mechanical tunnelling (QMT) [22], while the minimum value of n followed by an increase indicates the presence of overlapping of the large polaron tunnelling (OLPT) process [41], and at last, the decrease of n with temperature suggests the presence of conduction through the correlated barrier hopping (CBH) model [43].The power exponent (n) as a function of temperature is shown in figure 12(b).The variation looks similar for all samples, i.e., temperature independent.Thus, the QMT model can be applied to all samples to understand the conduction mechanism.In this process, the hopping sites act as a potential barrier, and the mobile species over-cross the barrier with increasing temperatures from one site to another.It has been observed that the value of the power exponent decreased for the doped sample, which suggests the presence of defects that reduce the local strength or dimensionality of the conduction path between the host and mobile species (see equations (15) and ( 16)).Thus, here we propose that the conduction in the sample takes place via the hopping of oxygen ions (overlapping of energy barriers between the potential barriers formed between the hopping sites) through corner sharing within the high temperature region (the mobile species over-crosses the barrier and results in conduction), while the transfer of electrons between Sn-sites occurs through the orientation of the dipole (as discussed in the dielectric study), and in the low temperature region, the conduction takes place through the transfer of electrons between Sn-sites.
In most cases, the ac conductivity spectrum of chalcogenides, polycrystalline ceramics, glass ceramics, and amorphous semiconductors follows the time-temperature superposition principle (TTSP), which suggests the temperature-independent behaviour of spectral line shape [23].The dc conductivity and hopping frequency have been selected as scaling parameters and scaled on the respective axes.The ac conductivity spectrum of all samples has been scaled by dc s while the frequency axis by f h and shown in figure 13(a)-(c).The conductivity spectrum of all samples obtained at different temperatures falls on a single master curve, indicating the universal behaviour of the ac conductivity spectrum and validating the TTSPs.This provides information that the dynamics of the processes that occur in the material have been independent of temperature, although they show a strong dependence on frequency.It further suggests that the hopping of ions and other mobile charge carriers of similar types is frequency independent mobility.Further, the effect of composition on the scaling of conductivity spectra has been studied by plotting the scaled conductivity as a function of scaled frequency at a constant temperature of 500 °C, as shown in figure 13(d).It has been observed from the figure that all the conductivity spectra obtained from different compositions are nicely superimposed on a single master curve, which suggests that even though there is a slight change in the charge compensation process, the mobile charge carrier remains the same within the investigated frequency and temperature scale.

Spectroscopic plot study
The impedance of a material specifies the resistive nature of having the same capacitance, and it can be used as an important parameter to study the relaxation phenomenon involved in the material as well as separate the contribution of grain and grain boundary in the overall material.In order to get more information about the relaxation phenomenon, the imaginary part of impedance (Z′) has been represented in terms of spectroscopic plots [19].The spectroscopic plot for all the samples is shown in figures 14(a)-(c).Initially, Z″ increases with frequency and reaches its maximum value before starting to decrease rapidly.The peak position of Z″ shifts towards higher frequency while their numerical value gradually reduces with increasing temperature, which suggests the presence of a temperature dependent relaxation process in the samples (as shown in the inset of figures 14(a)-(c)) similar to the conduction process.As it was described in the previous section, the conduction process is involved due to presence of various defects, which might also be applicable for the relaxation process.Further, the effect of composition on the impedance has been investigated by plotting the Nyquist plot for all compositions at 500 °C, as shown in figure 14(d).Ideally, the Nyquist plot shows three semicircles corresponding to grain, grain boundary, and electrode interface from higher frequency to lower frequency [42].
The intercept on the real impedance axis gives the value of resistance associated with grain, grain boundary, and electrode interface.Since the frequency range used in the present investigation is not much lower, the contribution associated with the electrode-specimen interface can't be observed.The value of the intercept for sample Sr 1.995 Sn 0.99 Nb 0.01 O 4 was found to be higher (total resistance), while that for sample Sr 2 Sn 0.99 Nb 0.01 O 4 was the lowest, which confirms the associated mobility of charge carriers and charge carrier concentrations because resistance has a converse nature of conductivity.Further, the peak value of Z″ has been related to the resistance of the materials by following eq.[44]: At the maximum value of Z , ¢¢ the value of 1, wt = and the height of the peak is R/2.The value of resistance for all samples at different temperature was obtained by employing this approach.The value of R obtained for all samples was shown as a function of 1000/T in figures 15(a)-(c).The angular frequency and relaxation time for the electroceramics and polycrystalline materials can be expressed as where R is the total resistance, C is their associated capacitance and f is relaxation frequency.Thus, the value of relaxation frequency (f max ) has been obtained by using relation 1 wt = and plotted as a function of 1000/T for the same composition to understand the relaxation process involved in it.The linear relationship of R and f max with 1000/T suggests Arrhenius behaviour in sample represented by in similar way as given following equation [41,44]: Here f o and R o are the pre-exponential factor and E relax and E R T are the activation energy involved in the simultaneous process.The activation energy corresponding to relaxation and conduction processes was determined by least squares fitting and given in table 3. It has been observed from table 3 that the activation energy in region -2 for all the samples was the same indicating a similar kind of charge carriers are involved in the relaxation process within the investigated temperature range (as discussed in TTSP).However, the activation energy in R-1 for the Sr 2 SnO 4 sample shows a similar value, which suggests that the mobile charge carrier also remains the same at higher temperatures.However, the activation energy for the doped sample shows a huge difference, which suggests that even though the charge carrier carriers remain the same in both samples, there might be differences in the mobilities of defects present in the respective samples.Therefore, we can say that the doping of Nb by a charge-compensated process shows improvement in the dielectric parameters (dielectric permittivity and dissipation factor) than a valence-compensated process system, which makes it a suitable candidate for mm-wave communication applications in dielectric resonator antennas (DRA).However, these samples show a significant change in their activation energy, which mostly lies in the range of oxygen ions as well as mixed ionic and electronic conductors used as electrode materials for intermediate temperature solid oxide fuel cell (IT-SOFC) applications.

Conclusion
The preparation of samples with two distinct doping techniques, namely valence and charge compensated procedure, in Sr 2 SnO 4 was carried out using the traditional ceramic route.The x-ray diffraction (XRD) patterns of the mixtures that were made, as well as the powders that underwent calcination and sintering, were obtained in order to gain insight into the reaction mechanism of the samples.The crystallite size and grain size found to be less than 50 nm and 600 nm, respectively.The observation of high dielectric permittivity and low dissipation factor is mostly attributed to Maxwell-Wagner and orientational polarization phenomena.The samples' conductivity spectrum exhibits a universal power law behaviour, indicating the presence of a common charge carrier engaged in both direct current (dc) conduction and hopping processes.The validation of scaling also provides support for the conduction and relaxation process of the sample, where changes in numerical value indicating alterations in either the mobility of charge carriers or their concentration.The potential applicability of the material in mm-Wave communication systems, specifically in Dielectric Resonator Antennas (DRAs), can be inferred from its enhanced dielectric permittivity and dissipation factor.The activation energy values found show that oxygen ions and mixed ionic and electronic conductors might be able to move in the higher temperature range that was studied.This finding suggests that these materials could be suitable for use as electrode materials in intermediate-temperature solid oxide fuel cells (IT-SOFCs).
3. A linear fit to the experimental data validates equation (8) and determines the value of the intercept and slope.The value of crystallite size was obtained from the slope value of the fitted line (as shown by the solid line) , k D l whereas the value of micro-strain was obtained from the intercept value .

Figure 4 .
Figure 4. Rietveld refinement patter of all samples, symbols (o) show experimental pattern, solid line (-) shows calculated patter, residual x-ray diffraction pattern and vertical line shows Braggs position; crystal structure of sample Sr 2 Sn 0.99 Nb 0.01 O 4 as reference shows Sr-O 9 and Sn-O 6 structure.

Figure 10 .
Figure 10.Frequency dependent conductivity of samples (a) Sr 2 SnO 4 , (b) Sr 2 Sn 0.99 Nb 0.01 O 4 , (c) Sr 1.995 Sn 0.99 Nb 0.01 O 4 , and (d) the conductivity spectrum of all samples at 600 °C (symbols are experimental data and solid line is fitted data with equation (11).

Figure 11 .
Figure 11.Arrhenius plot generated for (a) σ dc , and (b) f h for all samples.

Figure 12 .
Figure 12.(a) Variation of log dc s versus f log , h (b) Variation of power exponent (n) with temperature for all samples.
The substitution of Nb at Sn-site of Sr 2 SnO 4 can be denoted by following equation; Nb[ ] • 2

Table 1 .
1.995 Sn 0.99 Nb 0.01 O 4 .The volume of both samples is lower than the host because the molecular weight of Sr 2 Sn 0.99 Nb 0.01 O 4 is higher than that of Sr 1.995 Sn 0.99 Nb 0.01 O 4 , which might be a possible reason for the higher density of sample Sr 2 Sn 0.99 Nb 0.01 O 4 .Angular position, full-width half maxima, cosine and sine of angle and crystallite size.

Table 2 .
Structural, refinement, crystallite size and micro-strain parameters for all samples.Parameters Sr 2 SnO 4 Sr 2 Sn 0.99 Nb 0.01 O 4 Sr 1.995 Sn 0.99 Nb 0.01 O 4 1−x Nb x O 4 has taken place, as shown by the following equation:

Table 3 .
Activation energy obtained from σ dc , f h , and impedance plot.