Multiple relaxation mechanisms in SrBi 2 Nb 2 O 9 ceramic tweaked by tin and samarium incorporation in assistance with single-step microwave sintering

Non-stoichiometric lead free polycrystalline Sr 0.8 Sn 0.2 Bi 1.75 Sm 0.25 Nb 2 O 9 (SSBSN) ferroelectric ceramics were synthesized through conventional solid step route method by incorporating ball milling and microwave sintering method. X-ray diffraction along with the Rietveld refinement technique confirms the single-phase orthorhombic structure with A2 1 crystal symmetry. Additionally, the short-range ordering was confirmed by Raman spectroscopy. Doping induced crystallite size and strain were further calculated from the Williamson-Hall plot, which comes around 150 nm and 1.48 × 10 –3 respectively. A plate like morphology with an average grain size of 0.41 μm was confirmed by scanning electron microscopy (SEM). A diffuse type ferroelectric to paraelectric phase transition was recorded at 395 °C, mostly arising due to structural heterogeneity at the inter-ferroelectric phase boundary. The temperature and frequency-dependent dielectric measurement of SSBSN ceramic reveal a Maxwell–Wagner relaxation, with prominent dielectric loss in a low frequency regime perhaps due to the generation of leakage current in the SSBSN system. Frequency dependent ac conductivity indicates the polaron assisted hopping mechanism in SSBSN, which further obeys Jonscher’s formulation. The intra and intergranular contributions to impedance in SSBSN ceramics were probed by the complex impedance spectroscopy (CIS) technique. A non-Debye type relaxation mechanism in SSBSN ceramics was indicated by the Cole–Cole plot, whereas the conduction mechanism and transport properties were briefly studied using modulus spectroscopy.


Introduction
Piezoelectric and ferroelectric materials based multifunctional devices have been an indispensable element of our technological evolution due to their comprehensive applications in the electronics, sensors, underwater acoustics, transduces, photorefractive devices, tunable capacitors, pyroelectric sensors, ultrasonic medical imaging and many more.Most of these devices comprise lead-based ferroelectric materials (ex: PZT, PbTiO 3 ) as they possess exceptional ferroelectric, piezoelectric, and pyroelectric properties.However, long-term utilization or exposure to lead can cause serious health issues for humans and the environment due to its toxicity [1,2].Thus, from time to time the World Health Organization (WHO) has raised serious concerns regarding the lack of proper disposal of lead and advised material scientists across the globe to search for eco-friendly alternatives [3,4].Among all available alternatives the Bismuth layer structured ferroelectrics (BLSF) compositions, have proved to be the most promising ferroelectric system to replace lead based devices in the future due to their exciting properties such as high Curie temperature, high dielectric constant, low polarization switching voltage, good retention behavior, minimum operating voltages, a high mechanical quality factor, and large solid solubility of dopant ions, which make them eligible candidates for numerous technological and industrial applications such as satellite communication devices, medical diagnostics, industrial automation, ultrasonic motors, transducers, etc. BLSFs were first discovered by B. Aurivillius in 1949 having a structural formula of (Bi 2 O 2 ) 2+ (A m−1 B m O 3m+1 ) 2− where A-site is occupied by mono, dia, and trivalent ion (K + , Ca 2+ , Ba 2+ , Bi 3+ , etc.) or their combination allowing dodecahedral coordination, B-site is occupied by transitional elements like (Ti 4+ , Nb 5+ , Ta 4+ , Mo 6+ , etc.) suited to the octahedral coordination and m is an integer which represents the number of BO 6 octahedral layer sandwiched between two perovskite slab [5][6][7][8].Among several BLSFs, the SrBi 2 Nb 2 O 9 (SBN) is the second-layered Aurivillius compound that belongs to the group of disordered uniaxial ferroelectrics with an orthorhombic crystal structure and A2 1 am space group.SBN and its solid solution have gained substantial interest due to their less distorted NbO 6 octahedra and extraordinary control of rattling space on the dielectric, ferroelectric, and piezoelectric properties.Despite having numerous useful properties, SBN also suffers from a few drawbacks, such as intense spontaneous polarization and high dielectric loss [9,10].Interestingly the electrical and ferroelectric properties of Bi-based SBN strongly depend on the complete or partial site substitution/modification of the parent compound [11].Therefore, controlling these parameters became extremely important to achieve desired properties for technological applications.According to the available literature, Pritam et al. [12] have reported an enhanced dielectric constant of 120 in Sn doped SBN (Sr 0.8 Sn 0.2 Bi 2 Nb 2 O 9 ) compared to undoped one and serves as a basis of the present work.Additionally, the literature suggests that the dielectric and ferroelectric properties of BLSFs can be strongly enhanced by rare earth substitution such as Sm 3+ , Ce 3+ , Nd 3+ , Pr 3+ , Gd 3+ , and Y 3+ as rare earth elements are known to diminish the generation of mobile oxygen vacancies (arise due to high-temperature sintering) in the solid solution due to their peculiar inimitable electronic structure and lattice distortion [13].Numerous studies are available on A site, B site, or Bi site modification in SBN, however very few or no reports exist on multiple site modifications in SBN, and its influence on structural, dielectric, and electrical properties in SBN is rarely available [14][15][16].
Therefore, the present work deals with the investigation of structural contribution to the electrical transport mechanism and multiple relaxation mechanism in Sr 0.8 Sn 0.2 Bi 1.75 Sm 0.25 Nb 2 O 9 (SSBSN) ceramics synthesized through green synthesis microwave sintering (MS) method, as MS will drastically reduce the two-step sintering to single step sintering.Several dielectric-derived parameters like Z*, M*, and σ* have been thoroughly investigated to get a complete understanding of the electrical behavior of microwave sintered SSBSN ceramics.

Materials and methods
The polycrystalline Sr 0.8 Sn 0.2 Bi 1.75 Sm 0.25 Nb 2 O 9 (SSBSN) ceramics were synthesized using the solid-state route (SSR) method by incorporating single step microwave sintering.SSR is the simplest and most effective way to prepare inorganic bulk compositions.Usually, the SSR method is carried out by intermixing followed by high temperature sintering of a homogeneous mixture of different oxides, nitrates, and carbonates [11,17].During the synthesis, numerous parameters like temperature, gas flow, pressure, milling time, etc. can be easily varied to achieve the desired phase and morphology of the composition or its solid solution.Initially, the reagent grade carbonates and oxides of Bi 2 O 3 (99.9%),SnO (99.9%),SrCO 3 (99.5),Sm 2 O 3 (99.9%),and Nb 2 O 5 (99.95%), were used as the starting materials.The stoichiometric proportions of starting materials were extensively wet milled for 24 h. in a Retsch PM100 planetary ball mill using hard tungsten carbide balls of diameter 5 mm (the ball to.powder mass ratio was 10:1).The obtained sullery was mixed with the Polyvinyl Acetate (PVA) binder and compressed into a cylindrical pallet having a diameter of 10.8 mm and thickness of 2 mm.Further, the pallets were sintered in a closed crucible at 1000 °C for 5 h. in a microwave furnace having a frequency of 3.5 GHz.

Characterization techniques
The Phase formation of SSBSN was investigated using Bruker D8 discover equipped with Cu-Kα radiation of wavelength 1.5406 Å, operated at 40 kV and 40 mA.The data was recorded in a step size of 0.02 with a time per step of 2 s for the integrated angular range of 20°-80°.Raman spectra were recorded using a micro-Raman spectrometer equipped with a 532 nm argon-ion laser source with a magnification of 50×.The surface morphology was recorded using Carl Zeiss Merlin VP Compact FE-SEM with 5 kV acceleration voltage and 50 K magnification.The ac conductivity, impedance, and modulus spectroscopy of the prepared composition were calculated using the dielectric data, recorded on high-frequency LCR meter ZM2376 (NF corporation, Japan) with an applied oscillation level voltage of 1 V.

Microstructural analysis
The X-ray diffraction pattern of Sn and Sm doped SBN ceramics was shown in Fig. 1a, indicating the formation of a perfect layered perovskite phase within the targeted composition.[11,18].The obtained diffraction peaks were indexed using orthorhombic symmetry conferring to the JCPDS card no 00-049-0607.The absence of the secondary phase signifies that the Sm and Sn ions have successfully entered their respective sites of the prepared SSBSN solid solution, thus proposing a smooth substitution.Lattice parameters of the prepared composition were found to be.5.516 Å, 5.503 Å, and 25.038 Å respectively [16,19].Further, the XRD pattern of SSBSN was fitted with Rietveld refinement using Fullprof software.The refined XRD pattern is in good agreement with the experimental data having the goodness of fitting around 2.7 as shown in Fig. 1b.The crystallographic findings from the Rietveld refinement are summarized in Table 1, whereas the crystal structure of the same is demonstrated in Fig. 1c.

Crystallite size and the lattice strain estimation
X-ray diffraction is a powerful technique for determining numerous parameters like crystallite size, lattice strain effect, and peak broadening [17,[20][21][22].To know the contribution of the factors mentioned above, it is essential to collect the X-ray diffraction data of standard material and estimate the instrumental broadening using Eq. 1 [23].
Here, β d is the corrected broadening, β measured is measured broadening, and β instrumental is instrumental broadening.The physical broadening and instrumental broadening of the sample are estimated by FWHM (Full-width half maxima) [24].By employing the corrected parameters, the average crystallite size can be determined by Debye Scherrer's equation depicted below.
where D is the crystallite size, λ is the wavelength of X-ray (1.5406 Å), and β is the FWHM [25].The calculated crystallite size is around 80 nm.Based on Debye Scherer's model, only crystallite size plays a significant role in broadening of XRD peaks, however other factors like lattice strain, also known as strain-induced broadening were neglected.Numerous models, such as the Warren-Averbach method, Williamson Hall (W-H) method, etc., deal with the effect of strain and crystallite size on peak broadening discretely and can (1) (2) D = 0.9 cos be employed to estimate the induced strain along with the crystallite size [20,24,26].Among these methods, the W-H method is ideal for this purpose due to its simplified integral breath model, which noticeably differentiates between the crystallite size and strain-driven peak deformation, considering peak broadening as a function of two theta [24,27,28].The total broadening of the diffraction peak is shown below.
where β hkl denotes the FWHM of a XRD peak, β size and β strain are the widths due to the size and strain, respectively.According to the Uniform Deformation Model (UDM), the strain is isotropic and arises in the crystalline structure due to imperfections, depicted in Eq. 4, On rearranging the Eq. 2, 3, and 4, we get Equation 6, known as the uniform deformation model (UDM) equation, reveals the isotropic nature of the crystals.Where D and ε are known as crystallite size and microstrain, respectively [23].
Figure 2 shows the W-H plot of SSBSN ceramics.The calculated value of D and ε comes around 150 nm and 1.48 × 10 -3 , respectively.The slope obtained from the W-H plot is found to be in a positive direction, hence generating the intrinsic strain of 1.48 × 10 -3 in the system [21,29].

Morphological analysis
Figure 3a shows the cross-sectional field-emission scanning electron microscopy (FESEM) micrograph of microwave sintered SSBSN pellet.The SEM micrographs illustrate that the different shapes and sizes of grains have been homogeneously distributed across the surface.The morphology indicates a clear grain boundary with a well-defined compact plate-like structure, which is the signature of the Bismuth layered structured ferroelectrics.Careful investigation of the high-resolution SEM image further indicates the presence of porosity in the composition, mostly arising due to evaporation of Bismuth oxide at high temperatures [30,31].The average grain size was calculated using Image J software at a magnification of 50 KX and a scale of 0.5 μm.Normal distribution curve fitting of the histogram was employed to calculate the mean grain size of the composition, which comes around 0.41 μm depicted in Fig. 3b.

Raman analysis
Raman spectroscopy is a chemical analysis technique, which is used to probe the structural phase transition, crystallinity, lattice symmetry, and polar nanoregions (PNR) linked with the structural disorder of ferroelectric and multiferroic materials [3].The room temperature Raman spectra of the SSBSN ceramics in a spectral range of 100-900 cm −1 are shown in Fig. 4. A couple of intense peaks with strong Raman intensity were observed at 202.4 cm −1 , 570.31 cm −1 , and 838.42 cm −1 ; however, a bunch of weak peaks was also detected at 176.06 cm −1 , 270.16 cm −1 , 329.27 cm −1 , 448.19 cm −1 , and 686.04 cm −1 [32,33].A sub-intense peak was observed at 202 cm-1, which indicates the vibration of A site ions (Sr and Sn) of the pseudoperovskite blocks [34].Peak located at 570.31 cm −1 harmonizes with rigid sublattice mode and depicts the opposite and equal displacement of positive and negative ions.Raman mode corresponds to 838.42 cm −1 attributed to the symmetric stretching of NbO 6 octahedra, hence implying the supremacy of the orthorhombic phase in the SSBSN system, also confirmed from the XRD analysis of the same.Mode corresponds to 202.4 cm −1 and 686.04 cm −1 assigned to the vibrations of A site ions and asymmetric distortion of BO 3 triangular group and deformation of BO 4 tetrahedron respectively.The Raman mode at 270.16 cm −1 is led by a force constant due to Bi-O 2 and

Curie temperature analysis
Figure 5 illustrates the temperature-dependent dielectric constant of SSBSN ceramics measured at a variable frequency and indicates a clear ferroelectric to paraelectric phase transition at 390 °C.A smaller value of the dielectric constant was observed in the temperature range of 50-250 °C, which linearly increases with the increasing temperature, possibly due to the coupling between mobile charge carriers contributing to the polarization process [37].A broad peak of dielectric constant was observed for SSBSN ceramics at a frequency of 100 kHz and 1 MHz, arising due to composition fluctuation in solid solution of SSBSN [34,[38][39][40].It was reported that defects such as impurities and oxygen vacancies play a significant role in the electronic polarization of BLSFs explaining the nature of dielectric constant at higher temperatures [41].
To determine the diffuseness of a relaxor ferroelectrics, the inverse of dielectric constant and temperature obeys the Uchino and Nomura function, a modified version of Curie-Weiss law (CW) is employed in the present work, shown in Eq. 7 [42] Here ε m is the maximum value of dielectric constant at temperature T m , C is the Curie constant and γ is a degree of diffuseness of phase transition its values range between Figure 6 shows the plots of log (1/ε − 1/ε m ) as a function of log (T−T m ) of SSBSN ceramics.For both measurements, the value of γ is 1.83 and 1.98 respectively, which indicates the diffuse phase transition in SSBSN ceramics, arises due to the formation of mobile oxygen vacancies in the solid solution [2,45].

Variation of dielectric constant and loss with frequency
Investigating the temperature and frequency dependent dielectric properties is necessary to understand the conduction mechanism, and relaxation process in solids [46].In this regard, the frequency-dependent variation of real part of the dielectric constant of SSBSN ceramics at several temperatures is shown in Fig. 7a.A strong dispersion behavior was observed at low frequency region, possibly due to the accumulation of space charge in SSBSN solid solution.Such resilient dispersion behavior of dielectric constant emerges to be a common feature in ferroelectrics associated with non-negligible ionic conductivity, also known as low-frequency dielectric dispersion (LFDD) [47][48][49].A high dielectric constant was witnessed at low frequency, irrespective of temperature, possibly due to the contribution from all four types of polarization electronic, ionic, orientational, and space charge polarization to the total dielectric constant.A steady decrease in dielectric constant was observed and can be explained by Koop's theory and Maxwell-Wagner model [50].The tanδ or dielectric loss is the energy utilized in rotating the atomic dipole in a dielectric material and it arises due to two major reasons domain wall motion under the influence of external applied field and space charge relaxation.Further, it depends on three parameters frequency, temperature, and nature of additives [51].Figure 7b shows the frequency dependence of dielectric loss at different temperatures, a high loss was observed in low frequency regions, possibly due to the presence of space charge polarization, however, it drastically decreases at high frequency regions, thus endorsing the surge of domain wall motion in this region [12].

Ac conductivity analysis
To investigate the conduction process and polaron responsible for the conduction, the temperature dependent a.c conductivity as a function of frequency was studied for SSBSN ceramics, which was calculated using Eq. 8.
where f is frequency, ε o and is permittivity in a vacuum, is the permittivity of the medium, and tanδ is known as dielectric loss [52].Figure 8a depicts the variation of ac conductivity as a function of frequency, the conductivity curve can be widely differentiated into three regions; the first is low-frequency regions, in this region, the ac conductivity is independent of frequency and decreases with the decrease in frequency.This decrease in conductivity corresponds to the variation of space-charge polarization at the electrode interface and generation of oxygen vacancies in the system.Here local electric field opposes the applied electric field and limits the conductivity.As we increase the frequency, a flat plateau-like region is spotted, where conductivity is independent of frequency, representing the system's dc conductivity (σ dc ).The third and final region, known as the high-frequency region, which usually demonstrates the dispersive behavior of conductivity, appears due to the short and long polaron hopping in the SSBSN system.The increasing trend of ac conductivity might be due to the anarchizing of cations among the neighboring sites [53].One can notice that the nature of the curve is independent of temperature; however, the onset of the dispersion is shifted to a higher frequency as the temperature is further increased.Additionally, the behavior of a.c.conduction was examined by Jonsher's power law shown in Eq. 9.
where A is a temperature-dependent parameter and s is a dimensionless exponent that describes the degree of interaction, whose value lies between 0 to 1, which represents the resistive and capacitive behavior of a material, respectively.The calculated value of s for SSBSN ceramics is shown in Table 2 and reveals a non-Debye type conduction mechanism.

Complex Impedance Spectroscopy
Complex impedance spectroscopy (CIS) is a powerful tool to probe the dielectric material, which tells us about the individual contribution of different electrical active regions.Usually, CIS is utilized to investigate the microscopic and macroscopic properties of the material like charge transfer resistance, diffusion process, relaxation process, transport number, etc. [54].The complex impedance is depicted in Eq. 10.
Z* is further resolved in real (Z′) and imaginary part (Z″) of impedance and shown below.where f is frequency, ε′ and ε″ are real and imaginary parts of the dielectric constant, and C o is known as the capacitance of vacuum [10,55].
Figure 9a shows the variation of the real part (Z′) of impedance as a function of frequency in a temperature range of 350-550 °C.It was observed that the value of Z′ shows higher values at low-frequency regions, which drastically decreases with increasing frequency till 1 kHz.Beyond that, an independent behavior of the Z′ was observed which eventually merges at high frequency and indicates a release of space charge from the system.The value of Z′ significantly decreases with increasing temperature and indicates the negative temperature coefficients of resistance (NTCR) behavior [47,48,56].Figure 9b shows the variation of the imaginary part of impedance (Z″) with frequency at different temperatures.An asymmetric broadening of the peak was observed with increasing temperature (beyond 405 °C) which indicates multiple relaxations process in the SSBSN ceramics.With the increasing frequency and temperature, the magnitude of Z″ peak was found to shift towards the high-frequency region, indicating that the relaxation mechanism spread over a wide range of frequencies.Irrespective of temperatures, the Z″ attains a constant value beyond 10 kHz, which indicates thermally driven relaxation mechanism in SSBSN ceramics [46,47,57].
The Cole-Cole plot of SSBSN ceramics at different temperatures is shown in Fig. 10.A linear response was observed at a lower temperature (> 400 °C) and implies the insulating behavior of the sample.As the temperature rises above 400 °C, the linear response was found to deviate into a semicircular one, indicating the rise of the conductivity in the material.Each semicircle experiences a small divergence from the origin and depicts non-Debye type relaxation process.This type of behavior in Cole-Cole plot arises due to numerous contributing factors such as grain boundary contribution, stress-strain phenomena, atomic and ionic defects distribution, etc.The emergence of two semicircles was also observed at higher temperatures, revealing that the contribution was from both grain and grain boundaries [12,31,53,58].The lack of a third semicircle rules out the interfacial contribution to total impedance of the system.( 11)

Complex modulus spectroscopy (CMS)
Unlike the resistive part, the capacitive element also significantly contributes to the impedance spectra of the material.Thus, it might be possible that the researcher can observe a single semicircle in a CIS but can observe multiple peaks in the modulus plot.Thus, to precisely know the contribution of resistive or capacitive components, we must need to investigate our data for the complex modulus spectroscopy (CMS).CMS is a convenient technique to examine the transport properties of dynamical systems [59].Mathematically CMS is depicted in Eq. 13 [55,60] M* can be further resolved into real (M′) and imaginary component (M″) Figure 11a illustrates the frequency dependent variation of the real component of modulus at some selected temperatures.It was observed that M′ achieves a constant value above 1 kHz, but approaches zero at the lower frequency region, thus confirming the existence of interfacial or atomic polarization in the SSBSN solid solution.A strong dispersion behavior is observed at the high-frequency region irrespective of temperature, which contributes to the conduction phenomena that arise due to the movement of the charge carrier under the action of an applied electric field in the studied temperature region [55,61].A shift in the dispersion region is also observed at high temperatures and supports the long-range mobility of the charge carrier.Figure 11b shows the variation of the imaginary part of the modulus of SSBSN ceramics at several temperatures, a substantial shift in the peak of M″ observed with increasing temperature, indicating a thermally driven relaxation process in solid solution [62].A nonsymmetrical broad peak is perceived for all measurements, which demonstrates multiple relaxation processes in SSBSN ceramics with different time constants.Finally, a decrease in the magnitude of M″ peak is detected with the increasing temperature, which undoubtedly specifies the surge in the dielectric constant of the SSBSN ceramics [19,31,63].

Conclusion
In summary, we have successfully prepared novel Sr 0.8 Sn 0.2 Bi 1.75 Sm 0.25 Nb 2 O 9 (SSBSN) ferroelectric ceramics through single step solid state route method by incorporating microwave sintering technique, which drastically reduced the processing parameters (temperature and time) of SSBSN ceramics.XRD and Raman spectra validate the defect free orthorhombic crystal structure with A2 1 am space group.Additionally, the Rietveld refinement and Williamson Hall method were used to calculate lattice parameters, atomic position, and strain in SSBSN matrix.A plate like morphology with an average grain size of 0.41 μm was confirmed by scanning electron microscopy (SEM).Temperature dependent dielectric measurement (Tc) indicates diffuse type phase transition, which arises due to the presence of an interacting ferroelectric cluster on the SSBSN.Further, the degree of diffusiveness (γ) was checked by Uchino and Nomura function, which comes around 1.8.Impedance analysis depicts the non-Debye type conduction mechanism with the NTCR behavior, whereas grain, and grain boundary contribution was revealed by Cole Plot.Modulus spectroscopy indicates that the relaxation process in SSBSN was governed by hopping of mobile oxygen vacancies.Ffrequency dependent AC conductivity demonstrates the dispersive behavior of conductivity, arising due to the polaron hopping in the SSBSN matrix.The obtained results support that the SSBSN can be used as a potential candidate for high frequency power transformer applications.

Fig. 1 a
Fig. 1 a XRD pattern of microwave sintered SSBSN ceramics, b Rietveld refinement profiles of SSBSN ceramic carried out through Full prof software, c schematic representation of crystal structure of SSBSN ceramic generated from the refinement parameter

Fig. 5
Fig. 5 The dielectric constant of SSBSN ceramics as a function of temperature at variable frequencies 10 kHz, 100 kHz, 1 MHz Fig. 6 Plot of ln(1/ε − 1/ε m ) as a function of ln(T − T m ) at 1 MHz of SSBSN at 1 MHz and 10 kHz (the experimental data are represented by symbols and the solid line represents the fitting of modified Curie Weiss law

( 8 )Fig. 7 Fig. 8 a
Fig. 7 Variation of a dielectric constant and b dielectric loss as a function of frequency at different temperatures

Fig. 9
Fig. 9 Variation of a real and b imaginary part of impedance as a function of frequency at different temperature