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.

KEYWORDS:

• Strontium titanate
• co-doping
• dielectric properties
• energy storage density
• energy storage efficiency

1. 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 high-performance 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.

The polarization-electric field (P-E) hysteresis loop, as illustrated in Eqs. (1)-(3) may be used to analyze the energy storage qualities of dielectric capacitors [5–7].

(1) $W_{tot}={\int }_0^{P_{max}}PdE$(1)

(2) $W_{\mathrm{r}\mathrm{e}\mathrm{c}}={\int }_{P_r}^{P_{max}}PdE$(2)

(3) $\eta =\frac{{\int }_{P_r}^{P_{max}}PdE}{{\int }_0^{P_{max}}PdE}\times 100$(3)

Bulk ceramics may be used in energy storage development, including linear dielectrics, relaxor ferroelectrics, and antiferroelectric [8–11]. According to the preceding calculations (equtions 1(1) $W_{tot}={\int }_0^{P_{max}}PdE$(1) -3(3) $\eta =\frac{{\int }_{P_r}^{P_{max}}PdE}{{\int }_0^{P_{max}}PdE}\times 100$(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 SrTiO₃ (ST) ceramic exhibits the potential for energy-storage 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 [12–15]. Adding a suitable quantity of Bi³⁺ to SrTiO₃ has increased E_b by reducing both the sintering -temperature and the grain size [16]. The incorporation of Zr⁴⁺ into Sr_0.5Ca_0.5TiO₃ ceramics was proposed by Pu et al. to mitigate grain formation [17]. Furthermore, the annealing process in an oxygen-rich 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 SrTiO₃ 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/cm³ [18]. Dy-doped SrTiO₃ 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/cm³ 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 [21–30]. 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 SrTiO₃-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/cm³ and an energy efficiency of 87% has been achieved by doped 5% of Sn in the Ti site of SrTiO₃ has been reported by J. Xie et al. [32]. Xu Guo et al. [33] reported a high energy storage density of 4.00 J/cm³ and high energy storage efficiency of 89.49% at a maximum applied field of 400 kV/cm are simultaneously realized in Dy doped SrTiO₃ 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 [33–39].

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.

Previous studies have also indicated that the A-sites of ABO3 ceramics tend to form Li⁺-Al³⁺ ionic pairs within the same cell along the [001] direction when co-doped with Li⁺ and Al³⁺ 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 ABO₃ ferroelectric ceramics. Moreover, co-doping can enhance the chemical and thermal stability of ABO₃ 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 SrTiO₃ 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, Nd³⁺ 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.

2. Experimental

A polycrystalline of Sr_(1-x)(Nd, Li)_xTiO₃; (0%≤x ≤ 8%) abbreviated as (SNLTx) has been fabricated using the solid-state reaction method. The SrCO₃, Li₂CO₃, Nd₂O_3, and TiO₂ (Sigma-Aldrich, 99.99% purity) were used to obtain Nd³⁺ and Li⁺ co-doped ST powders.

(4) $\left(1-x\right)SrC{O}_3+Ti{O}_2+\left(\frac{x}{4}\right)N{d}_2{O}_3\frac{air-30min}{1000}\to S{r}_{\left(1-x\right)}N{d}_{x/2}L{i}_{x/2}Ti{O}_3+\left(4-\frac{3x}{4}\right)C{O}_2\uparrow$(4)

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].

(5) $D_p=\frac{K\lambda }{\beta Cos\theta }$(5)

Where K is Scherrer’s constant (0.89), and λ is the wavelength of the X-ray radiation (1.5406 nm). High-resolution 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 frequency-dependent 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.

3. Result and discussion

3.1. 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 Nd³⁺ and Li⁺ into Sr²⁺ 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 Sr²⁺ ions are co-doped by Nd³⁺ and Li⁺ ions with a smaller radius. By taking the coordination number into account, the ionic radii of Nd³⁺ (IR = 1.27 Å) and Li⁺ (IR = 0.73 Å) are smaller compared to that of

Figure 2. (a) X-ray diffraction patterns, (b) an enlargement view of the (001) and (111) plans to show the peak shifting, (c) high-resolution 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. (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 Ti⁴⁺ 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 co-dopant concentrations. (d) variation of crystallite size in nm and tolerance factor with co-dopant concentrations.

Sr²⁺(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 Nd³⁺ and Li⁺ content. This decrease indicates the A-O (A=Sr/Nd, Li) bonds fall with an increase in the Nd³⁺ and Li⁺ content. This may affect the rotational mode of the TiO₆ 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 TiO₆ 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 Nd³⁺ 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].

(6) $t=\frac{R_A-R_O}{\sqrt{2(R_B+R_O}}$(6)

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 Nd³⁺ and Li⁺ co-doped SrTiO₃ ceramics, the Eq (5) becomes.

(7) $t=\frac{\left(1-x\right)R_{S{r}^{2+}}+\left(\frac{x}{2}\right)(R_{N{d}^{3+}}+R_{L{i}^{+}})+R_O}{\sqrt{2(R_{T{i}^{4+}}+R_O}}$(7)

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 Nd³⁺ and Li⁺ concentrations. It is close to 1, indicating that the lattice is highly packed and may consider a solid solution of Nd³⁺ and Li⁺ co-doped ST stabilizes the average cubic symmetry in the ceramics. So, in the case of Nd³⁺ and Li⁺ co-doping for Sr ions occupying the A sites. The increased concentration rat of Nd³⁺ and Li⁺ confirmed that the smaller ions of Nd³⁺ and Li⁺ co-doped for larger Sr host ions.

Table 1. The lattice parameter, unit cell volume, crystallite size, and tolerance factor of SNLTx ceramics as a function of Nd³⁺ and Li⁺ concentration.

Co-doping content	a (Å)	Unit cell volume (Å)^3	The crystallite size (nm)	Tolerance factor (t)
0%	3.90412	59.6071	64.06	1.001588
2%	3.88512	58.6424	63.61	0.997885
4%	3.87973	58.3990	58.54	0.994182
8%	3.86758	57.8510	57.05	0.986775

3.2. 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 Nd³⁺ (1.25 Å) and Li⁺ (0.73Å) and compared to that of Sr²⁺(1.44 Å) [44]. It is also observed that the grain distribution becomes uniform with the increase of the Nd³⁺ and Li⁺ additives due to the accumulation of Nd³⁺ and Li⁺ at grain boundaries, which disturbs the grain growth process. Incorporating Nd³⁺ and Li⁺ dopants into the Sr³⁺ site of SrTiO₃ 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 SrTiO₃ by incorporating Nd³⁺ and Li⁺ dopants: The ionic radii of Nd3+ and Li+ vary from those of strontium in dopant size. The introduction of Nd³⁺ and Li⁺ ions as substitutes for Sr²⁺ 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 Nd³⁺ in the SrTiO₃ lattice, a dopant in Sr²⁺, leads to the formation of $N{d}_{Sr}^{\cdot }$ defects, which are compensated by vacancies of Sr ions $V_{Sr}^{{ }^{\prime \prime }}$. 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 Kroger-Vink notation, may be represented as follows [50]:

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.

(8) $N{d}_2{O}_3\rightleftharpoons 2N{d}_{Sr}^{\cdot }+V_{Sr}^{{ }^{\prime \prime }}+3O_O^x$(8)

Also, the replacement of monovalent Li⁺ in place of divalent Sr²⁺ resulting in the formation of excess hole carriers in the neutral ST:

(9) $L{i}_{2}C{O}_3+V_{Sr}^{{ }^{\prime \prime }}\to 2N{a}_{Sr}^{\prime }+SrO+C{O}_2\uparrow$(9)

Thus, the energy needed to form compensating defects determines the solubility at SrTiO₃ two lattice sites. In contrast, dopants at grain boundaries don’t require energy to concentrate. Consequently, Nd³⁺ and Li⁺ is may abundant near or at grain boundaries, preventing abnormal grain growth during sintering and promoting fine grain formation in SrTiO₃ [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 SrTiO₃ 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% co-doping concentration of Nd³⁺ and Li⁺ ions was sufficient to completely dissolve and integrate the doped ions into the SrTiO₃ lattice.

Figure 5. EDS elemental mapping images of 4% of Nd and Li co-doped SrTiO₃ ceramic sample.

3.3. 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 high-resolution 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 Sr²⁺ [52]. Two asymmetric peaks in the XPS spectra of Nd 3d (Figure 6c) have binding energies of 981.14 eV and 1003.05 eV, 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 spin-orbit splitting indicates that Nd³⁺ is present in the sample [53]. In the Li 1s spectra, a peak associated with Li₂CO₃ [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 Ti³⁺. The development of oxygen vacancies and titanium 3+ sites in the SrTiO₃ 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].

Figure 6. (a) an XPS survey is shown for the SNLT8% sample with all the significant peaks indicated, (b) high-resolution XPS spectra of Sr 3d, (c) high-resolution XPS spectra of Nd 3d, (d) high-resolution XPS spectra of Li 1s, (e) high-resolution XPS spectra of Ti 2p, and (f) high-resolution XPS spectra of O 1s.

3.4. Permittivity analysis

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 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].

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.

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 Nd³⁺ and Li⁺ result in a higher dielectric constant. It is interesting to note that the loss tangent of the co-dopant 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.

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 SrTiO₃ ceramics [63–65]. Different defects, such as $N{d}_{Sr}^{\cdot }$, $V_O^{\cdot }$ $V_O^{\cdot \cdot }$, $T{i}_{Ti}^{\prime }$ and $V_{Sr}^{{ }^{\prime \prime }}$., may occur in Nd and Li co-doped SrTiO₃. Under the influence of Coulomb forces, positively charged defects may combine with negatively charged defects, generating defects dipoles such as:

(10) $(T{i}_{Ti}^{\prime }-N{d}_{Sr}^{\cdot })\left(T{i}_{Ti}^{\prime }-V_O^{\cdot }\right)\left(V_{Sr}^{{ }^{\prime \prime }}-V_O^{\cdot \cdot }\right)\left(V_{Sr}^{{ }^{\prime \prime }}-2N{d}_{Sr}^{\cdot }\right)$(10)

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 Ba²⁺ results in the creation of extra hole carriers in neutral BT.

(11) $L{i}_{2}C{O}_3+V_{Sr}^{{ }^{\prime \prime \prime }}\to 2L{i}_{Ba}^{\prime }+BaO+C{O}_2\uparrow$(11)

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 $\left(V_{Sr}^{{ }^{\prime \prime }}-2N{d}_{Sr}^{\cdot }\right)$ Under the influence of an external electric field, i.e. the relaxation peaks in Figure 6b can be attributed to small displacements of $V_{Sr}^{{ }^{\prime \prime }}$Or/and $N{d}_{Sr}^{\cdot }$ from their locations. The observed change in dielectric constant with frequency is comparable to the reported variation in dielectric loss with frequency.

3.5. 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/cm²) 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/cm²). 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 Nd³⁺ and Li⁺ concentrations.

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.

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)(1) $W_{tot}={\int }_0^{P_{max}}PdE$(1) -(3(3) $\eta =\frac{{\int }_{P_r}^{P_{max}}PdE}{{\int }_0^{P_{max}}PdE}\times 100$(3) ) to get the energy storage density and efficiency. The obtained parameters W_rec and ɳ are plotted as a function of Nd³⁺ 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 co-dopant 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 Nd³⁺ 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/cm³.

Figure 9. (a) P-E loops of the SNLT8% ceramic measured at different temperatures at 160 kV/cm and 10 Hz frequency. (b) the variation of W_rec and η values with co-dopants concentrations. (c) the energy storage density W_rec and energy storage efficiency η values were calculated from Figure 9a with different temperatures.

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/cm³ and 96%) are unchanged. The composition’s high breakdown strength, low dielectric loss, and possible energy storage density with x = 8% show that the Nd³⁺ and Li⁺ co-doped SrTiO₃ ceramics have essential properties for energy storage applications.

4. Conclusion

The polycrystalline Nd³⁺ and Li⁺ co-substituted SrTiO₃ 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 SrTiO₃ ceramics. After increasing the co-dopants from 0% to 8%, the energy density increased ninefold (from 0.11 J/cm³ to 0.952 J/cm³), 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 Nd³⁺ and Li⁺ co-doped SrTiO₃ materials are excellent candidates for applications requiring capacitors with a high energy density.

Authorship contribution statement

Mahmoud Alkathy: Writing, Correction, formal analysis, and original draft preparation.

Srinivas Pattipaka: Analysis and writing the original draft.

Mansour K. Gatasheh: Investigator.

H. Kassim: Synthetization, Methodology, and Formal Analysis.

Mohamed Saad Daoud: Investigator

Prof Eiras: Writing, Correction, supervision, and approval of the final version.

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

All data generated or analyzed during this study are included in this article.

Additional information

Funding

The authors thank the Sao Paulo Research Foundation (FAPESP: Grant No. # 2017/13769-1 and Grant No # 2023/05716-6) for their financial support. Dr. Mansour is grateful to the Researchers Supporting Project number (RSP2023R393) at King Saud University in Riyadh, Saudi Arabia, for his financial support.