Achieving high energy storage performance and efficiency in lead-free SrTiO3 ceramics via neodymium and lithium co-doping technique

ABSTRACT There is an immediate demand for eco-friendly, high-performance, and highly stable energy storage materials for pulse power systems. Ceramics based on SrTiO3 have a high breakdown strength (BDS) and dielectric constant. In this work, we fabricated a polycrystalline of Sr(1-x)(Nd, Li)xTiO3 ceramics via microwave-assisted heating of the starting materials. X-ray diffraction analysis reveals a pure perovskite phase without any secondary phase. Scanning electron microscopy images exhibit dense grain morphology with a decrease in grain size as the dopant concentration increases. The frequency dependences of the dielectric properties were studied in the frequency range of 100 Hz-1 MHz at room temperature. The polarization-electric field hysteresis loops were examined to ascertain the effect of co-doping on the energy-storage capability of SrTiO3 ceramics. After increasing the co-dopants from 0 to 8%, the energy density increased nine times (from 0.11 J/cm3 to 0.952 J/cm3), and the energy storage efficiency increased from 80.71% to 95.98%, respectively. In addition, the samples demonstrate excellent thermal stability, and their energy storage properties are stable up to 80°C. We may infer from this discovery that the bulk Nd3+ and Li+ co-doped SrTiO3 materials are good candidates for high-energy-density capacitor applications. GRAPHICAL ABSTRACT The energy storage materials of SNLTx ceramics were effectively synthesized using the solid-state reaction method with microwave heating of the starting materials, resulting in small grain size and defect dipoles. A dense microstructure with a grain size enhanced the breakdown strength, resulting in a high energy storage density and energy storage efficiency exceeding 95%, superior to previously reported lead-free ceramics and a promising candidate for environment-friendly ceramics.


Introduction
The fast expansion of the global economy has resulted in a worldwide uptick in the demand for electrical power.The capability to store and release energy is growing in complexity and significance.To attain efficient, versatile, and environmentally friendly energy, there is a pressing need for more robust and highperformance energy storage systems [1,2].Dielectric capacitors are unique among energy storage devices in that they may release their stored energy quickly and produce a high-intensity pulsed current or voltage.As a result, its potential use in pulsed power electronics appears encouraging [3,4].However, their limited usefulness is mainly due to their low energy density.As a result, capacitors need to increase their energy density while their size decreases.
Bulk ceramics may be used in energy storage development, including linear dielectrics, relaxor ferroelectrics, and antiferroelectric [8][9][10][11].According to the preceding calculations (equtions 1-3), the best materials for high energy storage density have a high breakdown strength (E b ), a high P max , and a low P r .In these calculations, P r represents the residual polarization, P max represents the maximum polarization, and E denotes the applied electric field.The linear dielectric SrTiO 3 (ST) ceramic exhibits the potential for energystorage applications among the dielectric materials by having a high E b and small P r .Unfortunately, the low P max indicates that, due to the absence of spontaneous polarization, the material typically displays a low W rec .
Therefore, implementing a higher E b value proves to be a more productive approach.Several multiscale variables influence the parameter E b , including atomic scale doping, nanoscale interface phenomena, microscale grain size variations, macroscale thickness, and porosity characteristics [12][13][14][15].Adding a suitable quantity of Bi 3+ to SrTiO 3 has increased E b by reducing both the sintering -temperature and the grain size [16].The incorporation of Zr 4+ into Sr 0.5 Ca 0.5 TiO 3 ceramics was proposed by Pu et al. to mitigate grain formation [17].Furthermore, the annealing process in an oxygenrich environment boosted the barrier effect at grain boundaries.The researchers achieved a high electric field strength of 440 kV/cm [17].The researcher fabricated Zn and Nb co-doped SrTiO 3 ceramics.They observed that co-doping and compositing techniques achieved a high electric breakdown strength (Eb) of 422 kV/cm and an energy storage density of 2.35 J/cm 3 [18].Dy-doped SrTiO 3 demonstrates a notable achievement in terms of its recoverable energy density, measuring at 4.00 J/cm3, and exhibits an exceptionally high breakdown strength of 510 kV/cm.These outcomes are achieved by subjecting the material to oxygen treatment, which effectively enhances the resistance of both crystal grains and grain boundaries [19].A high breakdown strength of up to 354 kV/cm and a relatively high recoverable energy density of 2.13 J/cm 3 have been achieved by B. Zhong et al. [20].There have lately been significant efforts made to enhance the W rec of ST Chemical alterations (such as doping with metal ions on the A/B sites, creating compounds with complicated endmembers, and adding sintering aids) and using various sintering processes are among them [21][22][23][24][25][26][27][28][29][30].To improve its energy-storage performance, ST may be chemically modified to grain size and boost its breakdown strength.For instance, Liu L. et al. [31] revealed that SrTiO 3 -based ceramics could achieve both high energy storage capability and ultrafast discharge speed thanks to a synergistic impact of chemical alteration and defect chemistry.An energy storage density of 1.1 J/cm 3 and an energy efficiency of 87% has been achieved by doped 5% of Sn in the Ti site of SrTiO 3 has been reported by J. Xie et al. [32].Xu Guo et al. [33] reported a high energy storage density of 4.00 J/cm 3 and high energy storage efficiency of 89.49% at a maximum applied field of 400 kV/cm are simultaneously realized in Dy doped SrTiO 3 ceramics through defect and interface engineering.Figure 1 compares our study's energy storage properties, and those of a different lead-free energy storage ceramic revealed recently measured at 160 kV/cm [33][34][35][36][37][38][39].
Previous studies have also indicated that the A-sites of ABO3 ceramics tend to form Li + -Al 3+ ionic pairs within the same cell along the [001] direction when codoped with Li + and Al 3+ having small ionic radii.This dramatically enhanced energy storage performance due to the local lattice distortion, as observed in [40].The effect of the ionic pair is greater than that of single doping ions, thus greatly influencing the physical properties properties of the ABO 3 ferroelectric ceramics.Moreover, co-doping can enhance the chemical and thermal stability of ABO 3 materials, ensuring that they maintain their energy storage properties over extended periods and under various environmental conditions.Based on the preceding discussion, we present a straightforward and efficient approach to enhance the energy storage capabilities of SrTiO 3 ceramics by introducing ionic pairs with small ionic radii.The primary objective in addressing this issue is to increase the breakdown strength, resulting in better energy storage performance.Recently, Nd 3+ and Li + ions were incorporated into ST to create SNLT ceramics, resulting in a significant increase in the breakdown strength of ST from approximately 70 kV/cm to 160 kV/cm, which may be attributed to the reduction in grain size.A comprehensive analysis that included structural characterization and electrical properties was conducted to investigate the mechanism behind the enhanced energy storage properties.
Stoichiometries ratios of the precursors were taken and ball-milled using high energy ball milling meshing for 4 h by adding acetone as balling media and subsequently irradiated with microwaves in MWSS for 30 minutes duration.The target temperature was 1000°C, and the dwell time was 30 minutes, while heating and cooling rates were 50°C/min.Structural characterization of various calcined samples has been detected using an X-ray diffractometer (PAN analytical X'pert Pro).The calcined powders were re-milled once again for 4 h duration, dried in an oven for 2 hours, mixed with 1 wt% Poly Vinyl Alcohol (PVA) as a binder, and compacted into disc-shaped pellets with a diameter of 10 mm.The green pellets were heated to 500°C at a heating rate of 2°C/min for binder evaporation, then sintered in conventional furnaces at 1300°C for 4 hours with heating and cooling rates of 5°C/min.Phase identification is performed by the usual method of comparative peak matching with the standard (JCPDS Card No. 35-0734) [41,42].The samples' crystallite size (D.P. ) could be estimated as [43].
Where K is Scherrer's constant (0.89), and λ is the wavelength of the X-ray radiation (1.5406 nm).Highresolution transmission electron microscopy (JEM-2100F) was used to measure the crystallite size of the SNLT8% samples.X-ray photoelectron spectroscopy (XPS) (JPS-9200) was used to identify the chemical state of each element used to fabricate the SNLT8% sample.The morphology of the sintered ceramics was observed by FE-SEM (JSM-7600F).The frequencydependent dielectric constant measurements were carried out using an impedance analyzer, Agilent E4294A (100 Hz to 1 MHz).The frequency-dependent dielectric constant measurement was carried out for the sample SNLT8% in the temperature range of 30-600°C and frequency range of 1 kHz to 2 MHz using Agilent E4294A.The samples were polished, and the thickness was decreased to 0.40 mm to investigate the P -E hysteresis loops.The ferroelectric study was carried out at room temperature and a frequency of 10 Hz using Precision Premier II Radians.The energy storage properties are theoretically estimated by integrating the P-E hysteresis loop.

Structural analysis
Figure 2 shows the X-ray diffraction patterns of the prepared SNLTx ceramics.It is observed that the prepared samples contain only a cubic structure with the space group Pm3m (JCPDS Card No. 35-0734) [41,42].No distinct second phase is detected.Figure 2 shows that the intensity of the (111) peaks is decreased with the increase of the co-substitution concentration.The introduction of Nd 3+ and Li + into Sr 2+ can cause a slight shift in the peaks toward higher 2θ, as shown in the right graph in Figure 2.This shift indicates a decrease in the lattice parameter and unit cell volume, as shown in Figure 3(c).This variation can be explained considering that Sr 2+ ions are co-doped by Nd 3+ and Li + ions with a smaller radius.By taking the coordination number into account, the ionic radii of Nd 3+ (IR = 1.27Å) and Li + (IR = 0.73 Å) are smaller compared to that of Sr 2+ (1.44 Å) [44], so that a clear shifting in peaks toward higher 2θ angle is taken place, which lead to a decreasing in lattice parameter as shown in Figure 2b.The decrease in the lattice parameter (a) due to co-doping a small ionic radius in place of a large ionic radius has been reported in the literature [45].The refinement analysis is conducted as shown in Figure 3a to prove all the observations mentioned above.The unit cell volume decreased with increased Nd 3+ and Li + content.This decrease indicates the A-O (A=Sr/Nd, Li) bonds fall with an increase in the Nd 3+ and Li + content.This may affect the rotational mode of the TiO 6 octahedron [46], decreasing the unit cell volume of ST crystal.Additionally, the peak broadening is increased with increased co-doping content, indicating a decrease in crystallite size.
Moreover, the electron density distribution of the TiO 6 octahedron is shown in Figure 3b. Figure 2(c, d) displays the correlation between the lattice parameter, crystallite size, and co-dopant concentrations.The crystallite size and crystalline structure of the x = 0.08 sample were studied using high-resolution transmission electron microscopy (HR-TEM), as shown in Figures 2 (c) and (d). Figure 1(d) of the SAED patterns shows the superimposition of the bright spots with a Debye ring pattern, indicating that the produced samples are nanocrystalline [47], and the crystallite size acquired from TEM is in good agreement with that obtained from XRD.
The variation of Nd 3+ and Li + co-substituted ST lattice parameters can also be explained in terms of tolerance factor t. The formula gives the tolerance factor of strontium titanate [48].R. A. is the radius of the A-site ion, R. B. is the radius of the B-site ion, and R. O. is the ionic radius of oxygen [48].For Nd 3+ and Li + co-doped SrTiO 3 ceramics, the Eq (5) becomes.
Where R O = 1.4Å,R A = R Sr = 1.44Å,R Bi = 1.1 Å, R Li = 0.73Å and R Ti = 0.605Å [44].The values of this tolerance factor were calculated and reported in Table 1.The successive decrease in tolerance factor Figure 3d is noticed with increasing Nd 3+ and Li + concentrations.It is close to 1, indicating that the lattice is highly packed and may consider a solid solution of Nd 3+ and Li + co-doped ST stabilizes the average cubic symmetry in the ceramics.So, in the case of Nd 3+ and Li + co-doping for Sr ions occupying the A sites.The increased concentration rat of Nd 3+ and Li + confirmed that the smaller ions of Nd 3+ and Li + co-doped for larger Sr host ions.

Morphological analysis
The SEM micrographs of SNLTx; 0%≤x ≤ 8%) ceramics are shown in Figure 4a.The images showed that all samples possessed well-densified grains of different sizes and shapes.In general, the grain size of the pure sample is larger than that of the co-doped samples.The average grain size is found to be 10.218 μm, 8.040 μm, 6.844 μm, and 3.46 μm for pure x = 0, 0.02, 0.04, and 0.08 respectively.This size reduction is due to the ionic radius difference between ionic radii of Nd 3+ (1.25 Å) and Li + (0.73Å) and compared to that of Sr 2 + (1.44 Å) [44].It is also observed that the grain distribution becomes uniform with the increase of the Nd 3+ and Li + additives due to the accumulation of Nd 3+ and Li + at grain boundaries, which disturbs the grain growth process.Incorporating Nd 3+ and Li + dopants into the Sr 3+ site of SrTiO 3 is a frequently used technique for altering the material's characteristics.However, it should be noted that this approach may not result in a direct reduction in grain size.Grain size is primarily influenced by factors such as the size of dopants during the sintering process, the duration of sintering, and the presence of an A-site deficit for charge compensation.Nevertheless, introducing dopants might indirectly influence the size of grains by altering the microstructure and thermodynamic characteristics of the material.Here are a few key considerations to consider while reducing grain size in SrTiO 3 by incorporating Nd 3+ and Li + dopants: The ionic radii of Nd3+ and Li+ vary from those of strontium in dopant size.The introduction of Nd 3+ and Li + ions as substitutes for Sr 2+ ions have the potential to induce lattice strain, potentially influencing the grain growth process.The presence of smaller dopants has the potential to impede the process of grain expansion, resulting in the formation of smaller grains.On the other hand, the Sr-site deficiency, the presence of Nd 3+ in the SrTiO 3 lattice, a dopant in Sr 2+ , leads to the formation of Nd � Sr defects, which are compensated by vacancies of Sr ions V 00 Sr .Consequently, a rise in the degree of A-site deficiency results in a reduces the grain size [49].The ionic compensation process, as described by the Thus, the energy needed to form compensating defects determines the solubility at SrTiO 3 two lattice sites.In contrast, dopants at grain boundaries don't require energy to concentrate.Consequently, Nd 3+ and Li + is may abundant near or at grain boundaries, preventing abnormal grain growth  during sintering and promoting fine grain formation in SrTiO 3 [51].As seen in the coming sections, the small grains significantly improved energy storage performance.To determine its constituent makeup, an EDS mapping investigation was performed on 8% Nd and Li co-doped SrTiO 3 ceramic material.Figure 5 displays the results of the measurements.The chosen area showed no signs of segregation in the distribution of five major elements (Sr, Ti, Nd, Li, and O).This result demonstrates that the 8% codoping concentration of Nd 3+ and Li + ions was sufficient to completely dissolve and integrate the doped ions into the SrTiO 3 lattice.

XPS analysis
The chemical states and elements contained in the SNLT8% sample were also identified by XPS studies.Figure 6(a)-(f) displays the survey spectrum and highresolution spectra of Sr 3d, Nd 3d, Li 1s, Ti 2p, and O 1s.At the same time, the adventitious carbon tap used on the XPS sample holder during the XPS measurement was blamed for the peak for C 1s.The survey spectrum (Figure 6a) confirmed the presence of Sr, Nd, Li, Ti, and O in the investigated sample.The ranges of the Sr 3d occupied state (Figure 6b) show the formation of a doublet signal with binding energies of 131.88 eV and 133.7 eV, which correspond to the Sr 3d 5/2 and Sr 3d 3/2 orbitals, respectively.This indicates that strontium was present in the matrix as Sr 2+ [52].Two asymmetric peaks in the XPS spectra of Nd 3d (Figure 6c) have binding energies of 981.14 eV and 1003.05eV, respectively, and may be attributed to the Nd 3d 5/2 and Nd 3d 3/2 states.These peaks are followed by shoulders, separated from the corresponding core peak by around 4.1 eV, and may be considered two satellite peaks.This observable spinorbit splitting indicates that Nd 3+ is present in the sample [53].In the Li 1s spectra, a peak associated with Li 2 CO 3 [54] can be detected at around 60.01 eV (Figure 6d).The XPS spectra of Ti 2p in Figure 6(e) show two sets of peaks, Ti2p 3/2 and Ti2p 1/2 , at binding energies of 456.71 eV and 462.34 eV, respectively, demonstrating that the core valence state of Ti in the SNLT8% lattice is + 4 [55].The shoulder peak, which occurs at 455.41 eV, is caused by the Ti 3+ .The development of oxygen vacancies and titanium 3+ sites in the SrTiO 3 lattice might indicate that oxygen is not sufficiently active to oxidize titanium [56] entirely.Figure 6(f) shows the O1s peak divided into two distinct peaks; the first peak is 528.67 eV, while the second is 530.21 eV.The peak with lower binding energy is caused by the Ti-O bond [57].The peak at lower binding energy denotes an oxygen lattice.The peak at higher binding energy shows a non-oxygen lattice, primarily related to oxygen vacancies [58].increase in frequency and become almost constant at higher frequencies, as seen in Figure 7.As the dipoles can track the alternating electric field, the dielectric constant is most prominent at low frequencies.The dielectric constant and dielectric loss decrease with an increase in frequency, as is typical with polar dielectric materials in general [59].Dipolar, electronic, ionic, and interfacial polarizations, all of which have varying relaxation durations, contribute to the overall polarization of the dielectric material [60].All polarization types react quickly to changes in electric field strength at lower frequencies.This will result in a higher measured dielectric constant [61].

Permittivity analysis
Since there is less time for the interfacial dipoles to align themselves in the direction of the alternating field at higher frequencies, the various polarization contributions begin to relax.Therefore, when the frequency rises, the dielectric constant decreases because the net polarization of the material decreases [62].In addition, it can be shown that higher concentrations of Nd 3+ and Li + result in a higher dielectric constant.It is interesting to note that the loss tangent of the codopant samples is less than that of the pure sample.This difference diminishes approximately as the amount of co-doping increases.This feature helps develop the potential use of this material as an energy storage application.Because oxygen vacancies Vo are the most common flaws in these samples, the collection of peaks that arise is likewise connected to oxygen vacancies.Furthermore, the substitution of monovalent Li + for divalent Ba 2+ results in the creation of extra hole carriers in neutral BT.
It is possible.The behavior of samples is shown in Figure 3 to be dielectric constant dependent on temperature and frequency.It can be observed that the dielectric constant (e) values are more significant at lower frequencies and lower at higher frequencies, which is comparable to the feature reported in the literature [66,67].Dielectric polarization in materials is caused by the contribution of many forms of polarization, including (1) electronic polarization, (2) ionic polarization, (3) dipolar polarization, and (4) space charge or interfacial polarization.Electronic and ionic polarizations at higher frequencies contribute to the dielectric constant, while space charge and dipolar polarizations contribute at lower frequencies [68].Figure 5a,b indicate that the dielectric constant values rise with increasing temperature at all frequencies.This result concludes that the rising dielectric constant with temperature is caused by the growing contribution of space charge polarization [68].Figure 6b shows a collection of relaxation peaks in the loss tangent.These peaks are associated with the displacement of defective dipoles due to an applied external electric field [69].The relaxation behavior may be ascribed to minor position adjustments of the V 00 Sr À 2Nd � Sr À � Under the influence of an external electric field, i.e. the relaxation peaks in Figure 6b can be attributed to small displacements of V 00 Sr Or/and Nd � Sr from their locations.The observed change in dielectric constant with frequency is comparable to the reported variation in dielectric loss with frequency.

Energy storage analysis
The polarization-electric field (P-E) hysteresis loops were carried out to examine the energy storage capability of SNLTx ceramics.Figure 8 depicts the energy storage capabilities of SNLTx ceramics.Figure 8(d) shows the examined ceramics with high P max , low P r , and high breakdown voltage.The maximum polarization (9.56 µC/cm 2 ) observed for the sample SNLT8% at a maximum applied electric field of 160.41 kV/cm is around three times more than that of the pure ST sample (3.54 µC/cm 2 ).This could be because the average grain size of co-doping samples is smaller than that of pure ones, as shown in SEM images.Hence, the energy storage density and efficiency rise with increased Nd 3+ and Li + concentrations.
Additionally, the co-doping-induced dens microstructure may be responsible for increasing the polarization as co-dopants increase.The area between the polarization axis and the discharge curve was integrated using the P-E loop, as illustrated in Figure 8, and based on Eqs (1)-( 3) to get the energy storage density and efficiency.The obtained parameters W rec and ɳ are plotted as a function of Nd 3+ and Li + concentration, as shown in Figure 9b.The energy storage densities of SNLTx may be affected by several parameters, including polarization and breakdown strength.The breakdown strength of the codopant sample is linked to the grain size effect [70,71].Therefore, the variance in breakdown strength is primarily responsible for the discrepancy in energy storage density across the Nd 3+ and Li + co-doped ST lattice.Interestingly, the research obtained a high energy efficiency of 96% and a high energy storage density of 0.952 J/cm 3 .
Finally, we explain the stability of our ideal SNLT8% samples at various temperature conditions.Temperature stability is a well-known essential condition for energy storage technologies.The P-E loops were measured at different temperatures ranging from 25°C to 80°C, at f = 10 Hz and E b = 160 kV/cm, as shown in Figure 9(a).The P max stays constant throughout the investigated temperature range, as observed.The necessary Wrec and data are shown in Figure 9(b).The results show that W rec and (0.952 J/cm 3 and 96%) are unchanged.The composition's high breakdown strength, low dielectric loss, and possible energy storage density with x = 8% show that the Nd 3+ and Li + co-doped SrTiO 3 ceramics have essential properties for energy storage applications.

Conclusion
The polycrystalline Nd 3+ and Li + co-substituted SrTiO 3 samples were successfully prepared by heating the beginning materials with microwave assistance.The sample particles were sintered at 1300°C for four hours to produce ceramics with relative densities that exceeded 96% of their theoretical values.The lattice parameter and grain size decreased as the co-doping concentration increased.Dielectric properties were investigated at ambient temperature and in the frequency range 100 Hz-1 MHz.Both polarization-electric field hysteresis loops were analyzed to determine the effect of co-doping on the energy-storage capacity of SrTiO 3 ceramics.After increasing the co-dopants from 0% to 8%, the energy density increased ninefold (from 0.11 J/cm 3 to 0.952 J/cm 3 ), and the energy storage efficiency increased from 80.71% to 95.98%.Moreover, the samples exhibit exceptional thermal stability, and their energy storage properties are stable up to 80°C.This discovery suggests that bulk Nd 3+ and Li + co-doped SrTiO 3 materials are excellent candidates for applications requiring capacitors with a high energy density.
the Researchers Supporting Project number (RSP2023R393) at King Saud University in Riyadh, Saudi Arabia, for his financial support.

Figure 1 .
Figure 1.A comparison between the energy storage features of SNLTx ceramics and other lead-free ceramics with prospective energy storage applications measured at 160 kV/cm.

Figure 2 .
Figure 2. (a) X-ray diffraction patterns, (b) an enlargement view of the (001) and (111) plans to show the peak shifting, (c) highresolution scanning transmission electron microscopy (HR-TEM) image shows the particle size of the calcined powder, and (d) selected area electron diffraction (SAED) for the SNLT8% sample.

Figure 3 .
Figure 3. (a) shows SNLT4% ceramic XRD pattern Rietveld refinement.They are refined with Fullprof.Experimental data appear as black circles, whereas software-calculated intensities are portrayed as solid red lines.Allowed Bragg diffraction peaks are the green vertical lines.The blue curves at the graph's bottom end show the difference between the experimental arrangement's intensities and the refining program's corresponding intensities.(b) the charge density maps of SNLT4%.The center contour and the region enclosed inside it correspond to the Ti 4+ ion.Additionally, the four atoms surrounding the core ion, positioned at the midpoint of each side of the cube or pseudo-cube, represent the O 2-anions, (c) variation of the unit cell constant and unit cell volume with codopant concentrations.(d) variation of crystallite size in nm and tolerance factor with co-dopant concentrations.

Figure 4 .
Figure 4. Scanning electron microscopy (SEM) image of SNLTx ceramics sintered at (1300°C).The scale bar represents 10 micrometers, and the image was acquired at 10000x magnification.The images exhibit a uniform and dense distribution with different grain sizes.

Figure 5 .
Figure 5. EDS elemental mapping images of 4% of Nd and Li co-doped SrTiO 3 ceramic sample.

Figure 7 Figure 6 .
Figure 7 depicts the frequency dependence of the dielectric constant and the dielectric loss tangent of SNLTx ceramics at room temperature and the frequency range of (100 Hz-1 MHz).The magnitude of the dielectric constant is shown to decline with an

Figure 7 (
b),(c) depicts the dielectric characteristics of 8% Nd and Li co-doped ST ceramics as a function of temperature measured at five distinct frequencies.The graph shows a series of permittivity peaks with temperature-dependent frequency dispersion.Relaxation occurs due to a shift in dipole orientation, which is temperature and frequency dependent.The loss of oxygen from the crystal lattice during the sintering process might cause oxygen vacancies, according to a defect study in doped SrTiO 3 ceramics [63-65].Different defects, such as Nd � Sr , V � O V �� O , Ti 0 Ti and V 00 Sr ., may occur in Nd and Li co-doped SrTiO 3 .Under the influence of Coulomb forces, positively charged defects may combine with negatively charged defects, generating defects dipoles such as:

Figure 7 .
Figure 7. (a) frequency dependence of permittivity and loss tangent at room temperature for the SNLTx ceramics., (b, and c) temperature dependence of dielectric constant and loss tangent for the sample with x=0.08 measured at different frequencies namely 1 kHz, 10 kHz, 100 kHz, 1 MHz, and 2 MHz.

Figure 8 .
Figure 8. Room temperature P-E hysteresis loop with their schematic diagram for calculating the energy storage properties in SNLTx ceramics.The region colored in cyan corresponds to the recovered energy density (W rec ) or the energy density discharged during the discharge process.The area highlighted in yellow corresponds to the energy dissipation (W loss ) that transpires throughout the charge-discharge cycle.The sum of the energy gained (wrec) and the energy lost (W loss ) corresponds to the total energy density (W total ) accumulated during the charging procedure.

Table 1 .
The lattice parameter, unit cell volume, crystallite size, and tolerance factor of SNLTx ceramics as a function of Nd 3+ and Li + concentration.