Non-Monotonic Transition of Conduction Mechanisms in 0.95[(Bi_0.5Na_0.5)_0.985Sm_0.01](Zr_0.2Ti_0.8)O₃-0.05BiFeO₃-Based Lead-Free Ceramics

Abstract

(Bi_0.5Na_0.5)TiO₃ (BNT)-based ceramics have attracted much attention for energy storage applications, but some fundamental issues remain unclear—in particular, how the conduction mechanism changes with composition and what role oxygen vacancies play. The (0.95−x)[(Bi_0.5Na_0.5)_(1−1.5y)Sm_y](Zr_0.2Ti_0.8)O₃-0.05BiFeO₃-xBa(Sn_0.2Ti_0.8)O₃ (abbreviated as (0.95−x)BNSmZT-0.05BF-xBaSnT, x = 0.05, 0.1, 0.15, 0.2, 0.3, 0.4, y = 0.01) system was investigated, where Ba(Sn_0.2Ti_0.8)O₃ (BaSnT) content varies from 0.05 to 0.4. A non-monotonic conduction transition is revealed by the conductivity and relaxation behavior characterized by impedance spectroscopy and dielectric temperature spectra combined with electric modulus analysis. At low BaSnT (x ≤ 0.1), residual Bi₂Ti₂O₇ at grain boundaries blocks oxygen vacancy migration, giving high activation energy (~2.12 eV) and presenting oxygen vacancy-mediated conduction. At x = 0.15, the impurity disappears and free oxygen vacancies surge, dropping the activation energy to 1.21 eV, corresponding to oxygen-vacancy-dominated ionic conduction with increased carrier density. For x = 0.2–0.4, strong Ba-O-Bi bonds stabilize the migration barrier around 1.57 eV, resulting in mixed oxygen vacancy-mediated conduction. The optimal composition 0.75BNSmZT-0.05BF-0.2BaSnT shows the best dielectric stability and highest resistance. From modulus master curves and broadened M″ peaks, the conduction is identified as correlated hopping of oxygen vacancies, consistent with non-Debye relaxation. This work provides a clear picture of how oxygen vacancy dynamics depend on phase purity, grain boundaries, and A-site chemistry in the BNT-based lead-free ceramics.

1. Introduction

Impedance and modulus studies of (Bi_0.5Na_0.5)TiO₃ (BNT)-based ceramics have established that polarization and conduction are dominated by semiconducting grain interiors, with oxygen vacancy relaxation and grain boundary effects as key contributors, enabling Cole-Cole fitting of non-Debye relaxation [1,2].

Lead-based Pb(Zr_xTi_1−x)O₃ (PZT) ceramics exhibit superior energy storage properties, such as a high recoverable energy density of 39.76 J/cm³ and a breakdown strength of 2157 kV/cm achieved in 0.75Pb(Zr_0.52Ti_0.48)O₃-0.25BiFeO₃ thin films [3]. These outstanding properties highlight the benchmark performance of Pb-based systems. However, the environmental toxicity of lead and increasingly stringent global regulations have driven extensive research toward lead-free alternatives. Growing demand for RoHS-compliant lead-free devices and high-permittivity, low-loss, power-stable ceramics have made lead-free ceramics a leading PZT replacement [2,4]. Building upon optimized compositions, current efforts tailor conduction and relaxation through doping and structural process optimization toward high energy storage, ultrasonic transducer, high-power degradation, and scalable deployment [2,5,6].

The European Union Directives 2002/95/EC and 2002/96/EC strictly restrict the use of lead-containing electronic devices, rendering the research and development of lead-free ferroelectric materials an inevitable trend [7]. BNT is regarded as the most promising alternative to lead-based materials, owing to its high dielectric constant comparable to PZT, applicable piezoelectric coefficient and large remanent polarization (P_r ≈ 38 μC/cm²) [8,9], and tunable bandgap through A/B-site co-substitution for photovoltaic applications [10,11]. At room temperature, the end-component BiFeO₃ crystallizes in a rhombohedral perovskite structure with space group R3c (a = 5.580 Å, c = 13.877 Å, V = 374.26 ų) [12], whereas BNT adopts a tetragonal structure with space group P4mm (a = 3.898 Å, c = 3.948 Å, V = 59.99 ų) [13]. Notably, for the BNT-rich compositions near the morphotropic phase boundary (MPB), such as BNT-0.2BaTiO₃, the symmetry transitions to the tetragonal P4bm phase [13], providing a structural benchmark for the present solid solution. Constructing multi-component solid solutions is the core strategy for optimizing electrical properties of the BNT-based materials. Researchers have introduced end members such as BaTiO₃ (BT), SrTiO₃ (ST) and Bi_0.5K_0.5TiO₃ (BKT) to form binary or ternary systems, thereby tailoring the phase boundary structure [7,11,14,15], including BaTiO₃-Bi_0.5Na_0.5TiO₃-CaBi₄Ti₄O₁₅ compounds with distinct dielectric responses across different compositional regimes [16].

Near the MPB regions, 0.98(0.72Bi_0.5Na_0.5TiO₃-0.28SrTiO₃)-0.02BaBi₂Nb₂O₉ and 0.8Bi_0.5Na_0.5TiO₃-0.2Bi_0.5K_0.5TiO₃ materials exhibit the coexistence of ferroelectric and relaxor ferroelectric phases, where an enhanced piezoelectric response and dielectric properties can be obtained [11,15]. Oxygen vacancy ($V_O^{\cdot \cdot }$) dynamics are recognized as the key factors determining electrical properties and reliability of the BNT-based materials [17,18,19]. In the BNT-based system, volatilization of Bi during sintering process inevitably leads to the formation of oxygen vacancies, resulting in ionic conduction (Type I) or mixed conduction (Type II) mechanisms [17,20,21].

However, the synergistic regulation of phase purity, grain boundary barriers, and oxygen vacancy migration in gradually varied compositions remains elusive. Dy³⁺ doping has been reported to improve insulation by blocking oxygen vacancy migration [22], while Mn modification modulates transport via defect compensation [23]. Comparatively, lead-based PZT ceramics exhibit low activation energies for conduction (0.58–0.73 eV) [24], whereas BNT-based ceramics show significantly higher values (>1.2 eV) [7], indicating superior high-temperature insulation. However, neither of these studies investigated the non-monotonic conduction transition across a compositional series, nor did they elucidate the synergistic competitive relationship among the three influencing factors. In view of this, a ternary solid solution was proposed with gradient modulation of the third-component content in this work, and the competition between grain-boundary blocking and bulk vacancy migration was systematically investigated, in order to uncover the intrinsic physical origin of the non-monotonic conduction transition.

Specifically, the (0.95−x)[(Bi_0.5Na_0.5)_(1−1.5y)Sm_y](Zr_0.2Ti_0.8)O₃-0.05BiFeO₃-xBa(Sn_0.2Ti_0.8)O₃ ceramics were prepared via the solid-state reaction method. The conduction and relaxation behaviors are clarified via dielectric-temperature relationship and impedance spectra, addressing performance degradation under high temperature and high electric field, and providing theoretical support for energy storage application in subsequently fabricated ceramic thick films [25,26]. A non-monotonic transition from grain-boundary-blocked ionic conduction to mixed electronic–ionic conduction is revealed, with the optimal composition (x = 0.2) exhibiting the highest resistance and best dielectric stability.

2. Experimental Procedure

The (0.95−x)[(Bi_0.5Na_0.5)_(1−1.5y)Sm_y](Zr_0.2Ti_0.8)O₃-0.05BiFeO₃-xBa(Sn_0.2Ti_0.8)O₃ ((0.95−x)BNSmZT-0.05BF-xBaSnT, x = 0.05, 0.1, 0.15, 0.2, 0.3, 0.4, y = 0.01) ceramics were prepared via the conventional solid-state reaction technique. The raw material powders, BaCO₃ (99%), ZrO₂ (99%), TiO₂ (98%), Bi₂O₃ (99%), Sm₂O₃ (99.9%), Fe₂O₃ (99%), SnO₂ (99.5%), and Na₂CO₃ (99.5%) (Sinopharm Chemical Reagent Co., Ltd., Shanghai, China) were weighed according to the chemical formula after fully drying. The mixtures were milled with alcohol and ground until homogenous state, then sieved with a 100-mesh sieve. The uniform mixtures were calcined at 850 °C for 3 h, and re-sieved to obtain the final calcined powders. To fabricate ceramics, the calcined powders were granulated with 8 wt% polyvinyl alcohol (PVA) aqueous solution, pressed into green pellets of 12 mm diameter and 1 mm thickness, debindered at 550 °C for 2 h to completely remove PVA, and sintered at 1170 °C for 2 h. After polishing, the ceramic pellets were double-side coated with silver paste and fired at 650 °C for 0.5 h to form Ag conductive electrode.

The crystal structure of the samples was characterized by X-ray (Rigaku D/max-2500/PC X-ray, Rigaku Corp., Tokyo, Japan) diffraction (XRD). Rietveld refinement was carried out using GSAS-II software to determine the phase composition and structural parameters. The surface morphology and grain size of the samples were observed with scanning electron microscopy (SEM, JSMIT100, JEOL Ltd., Tokyo, Japan), and the average grain size was statistically calculated. The dielectric temperature curves and impedance spectra were tested using the Partulab HDMS-1000 (Wuhan Partulab Technology Co. Ltd., Wuhan, China) tester at room temperature to 350 °C and 350 °C to 490 °C, respectively, and the impedance spectra were fitted with an equivalent circuit using the Zview2 software. Ferroelectric properties were characterized using a ferroelectric test system (Precision LC II, Radiant Technologies, Inc., Albuquerque, NM, USA).

3. Results and Discussion

Figure 1 shows XRD patterns of the (0.95−x)BNSmZT-0.05BF-xBaSnT (x = 0.05, 0.1, 0.15, 0.2, 0.3, 0.4) ceramics sintered at 1170 °C for 2 h. For the compositions x > 0.15, pure perovskite structure is obtained in this system, and distinct sharp peaks indicate the formation of a good solid solution. For the compositions with x ≤ 0.15, a secondary phase is found around 2θ of 28.3°, possibly assigned to BiO_2-x (PDF 00-047-1057, cubic structure, space group Fm-3m, a = 5.4754 Å, V = 164.15 ų) or Bi₂Ti₂O₇ (PDF 320118, cubic pyrochlore structure, space group Fd-3m, a = 20.68 Å, V = 8844.06 ų), partially relating to the high volatility and high content of Bi in these compositions [27]. As the BaSnT doping content increases, the relative content of Bi³⁺ in the lattice decreases gradually, and all characteristic diffraction peaks in the XRD patterns shift evidently toward lower angles. This variation is attributed to the difference in ionic radius, where larger Ba²⁺ with an ionic radius of 1.61 Å (12-coordiantion number, 12-CN) substitutes smaller Bi³⁺ with an ionic radius of 1.36 Å (12-CN). Thus, the unit cell expands and the interplanar spacing increases, which eventually causes the diffraction peaks to move to the lower 2θ angle region.

Rietveld refinement of the XRD pattern for the x = 0.2 ceramic (Figure 1b) yields a two-phase model with R factors and goodness of fit (R_wp = 10.53%, R_p = 8.06%, χ² = 7.88), presenting acceptable structure convergence reliability. The refined phase fractions reveal a predominant tetragonal phase (P4bm, 95.44%) with a minor rhombohedral component (R3c, 4.56%).

Figure 2 illustrates SEM images and the grain size of the (0.95−x)BNSmZT-0.05BF-xBaSnT samples, insets showing the corresponding grain size distribution histograms. All ceramics exhibit distinct grains and grain boundaries. The white spots on the grain surfaces arise from incompletely cleaned burial calcined powder, which was covered green pellets to compensate for the volatilization of volatile elements Bi and Na during the sintering process. All samples possess a relatively dense microstructure, and very few pores appear in some compositions, being consistent with their high density as all ceramics have relative density higher than 92% (Figure 2f). For calculating relative density, the cell parameters are refined using XRD patterns and shown in the Supporting Information Table S1. In this system, the densification of (0.95−x)BNSmZT-0.05BF-xBaSnT ceramics is influenced by composition, in which the x = 0.3 composition has the lowest relative density. Owing partially to the liquid-phase sintering mechanism, the grains of x ≥ 0.2 samples present not typical polyhedral morphology [26].

With the addition of BaSnT, the average grain size presents a “climbing ascent” trend. The average grain size increases sharply from 2.31 μm to 3.16 μm as x rises from 0.05 to 0.10. It descends slightly at x = 0.15, and climbs again to a peak value of 3.56 μm when x hits 0.20, then gradually decreases to 3.28 μm for x = 0.4 (Figure 2f).

By increasing the BaSnT content, Bi³⁺ content decreases, and the lattice expands due to the difference in ionic radii as discussed in the XRD measurement, in which the ability to incorporate ions and the formation of a solid solution are enhanced. Consequently, the content of impurity phase decreases, and the inhibitory effect of the secondary phase on grain growth is reduced [28]. At x = 0.15, however, the accumulation of Ba²⁺ in the lattice exceeds the solubility limit. According to the charge compensation rule, excessive Bi³⁺ is more difficult to swap with Ba²⁺, so Bi³⁺ is squeezed out instead. The secondary phase reaches its maximum value here, showing the hardest inhibition on grain growth, and resulting in a slight decrease in grain size. Once x reaches 0.20 and beyond, Bi³⁺ continues to decrease until it can incorporate neatly into the solid solution. The grain size bounces back up and then decreases slowly again due to lattice distortion.

The temperature dependence of dielectric performance of (0.95−x)BNSmZT-0.05BF-xBaSnT ceramics is shown in Figure 3, a clear dielectric frequency dispersion is observed for all samples, i.e., the dielectric constant is higher at low frequencies, then drops and levels off at high frequencies, showing great dependency on frequency. The low-frequency dispersion is attributed to space-charge polarization, grain-boundary polarization, and ferroelectric domain switching, which can follow the external electric field well at low frequencies. At high frequencies, only electronic and ionic polarizations remain active [29]. The relaxor behavior likely results from polar nanoregions (due to chemical compositional disorder), oxygen vacancies (from Bi evaporation during sintering), and lattice/local region inhomogeneity [29,30]. Meanwhile, the dielectric loss is characterized by significant elevation at low frequencies and high temperatures. Such significant elevation of low-frequency dielectric loss, especially at high temperatures, can be attributed to the enhanced migration of free charge carriers at grain boundaries and intensified space-charge polarization at elevated temperatures [29,30].

For the ceramics with compositions x ≤ 0.1, the dielectric constant first decreases around room temperature and then increases at low frequencies. Then, it rises slowly followed by a gentle decline at high frequencies with increasing temperature, presenting wide temperature stability. The pronounced low-temperature dielectric peak and strong frequency dispersion are normally attributed to the non-ergodic to ergodic relaxor (NER→ER) transition [31]. By increasing the BaSnT content, the enhanced A/B-site chemical disorder weakens the long-range correlation among polar nano-regions (PNRs) and reduces their thermal activation energy, thereby progressively shifting the depolarization temperature (T_d) toward lower temperatures [15]. At x > 0.1, the T_d temperature moves to below ambient temperature, leaving the ceramics in a stable ergodic relaxor state throughout the measured temperature range. The increased dielectric loss at high temperatures and low frequencies for x = 0.05 and x ≥ 0.3 samples is mainly dominated by the conductive loss resulting from oxygen vacancy migration and space-charge conduction [32].

Figure 3g shows the dielectric performance–temperature relationship of the (0.95−x)BNSmZT-0.05BF-xBaSnT ceramics measured at 10 kHz. The dielectric constant of this system first increases and then decreases with the rise in BaSnT content, reaching the maximum values at x = 0.15–0.2 compositions. No sharp Curie phase transition peak is observed in the whole temperature range due to composition design strategy, showing typical ergodic relaxor ferroelectric characteristic and being suitable for energy storage application [29,30]. The variation in dielectric performance with BaSnT content can be interpreted as follows. For x = 0.05–0.2 compositions, the system moves closer to the MPB region, resulting in enhanced lattice distortion and ferroelectric polarization. When x > 0.2, excess BaSnT may exceed the solid solubility limitation, leading to lattice mismatch or local phase inhomogeneity. Furthermore, the dielectric stability is weakened by the Bi₂Ti₂O₇ secondary phase in x ≤ 0.1 samples (see Figure 1) [29].

The temperature coefficient of capacitance (TCC), defined as the ratio of dielectric constant at a given temperature to its room-temperature reference value, quantifies the relative variation in permittivity with temperature [26]. In this work, the reference temperature is set to 150 °C for high-temperature applications, and the dielectric temperature stability of (0.95−x)BNSmZT-0.05BF-xBaSnT ceramics in the range of 31–350 °C is shown in Figure 3h using 10 kHz data. The dielectric temperature stability calculation reveals that the x = 0.2 ceramic possesses the optimal stability. Relative to the dielectric constant at 150 °C (Δε_r/ε_{150 °C}), the dielectric constant variation in all compositions remains within 11% over the temperature range of 71~341 °C. Ceramics with x ≥ 0.2 compositions exhibit excellent stability (within 11%) over a wide temperature range of 50~341 °C as shown in Figure 3i, making them promising candidates for high-temperature capacitors [30,32].

The complex impedance spectra (Z′–Z′′) of the (0.95−x)BNSmZT-0.05BF-xBaSnT ceramics are shown in Figure S1. All ceramics exhibit non-ideal semicircular arcs, with a non-monotonic evolution in the curvature radius observed: the semicircle diameter shows an initial increase followed by a decrease by increasing the BaSnT content within x = 0.05–0.3, reaching a maximum value at x = 0.2; at x = 0.4, the impedance increases again but does not exceed the value at x = 0.2, as shown in Figure 4a, using 470 °C data for comparison. The low-frequency intercept with the real axis corresponds to the total resistance R_total, consistent with the arc radius change trend, indicating optimal insulating characteristic for the x = 0.2 composition [7,30].

Figure 4b shows typical complex impedance spectra for the x = 0.2 sample measured at different temperatures, where the non-ideal semicircular arcs are fitted with an equivalent circuit of a parallel R_g-C_g in series with parallel R_gb-CPE₁-C_gb elements using the Zview2 software. R_g is assigned to the grain bulk resistance and R_gb to the grain boundary resistance, with CPE₁ accounting for the non-ideal capacitive behavior at the grain boundaries. The total resistance R_total = R_g + R_gb, obtained from the low-frequency intercept, exhibits a non-monotonic evolution by increasing the BaSnT content, peaking at x = 0.2, as shown in Figure 4a and Figure S1.

The impedance variation with BaSnT content is rationalized by three factors. First, moderate BaSnT content (x ≤ 0.2) is found to suppress Bi³⁺ loss during sintering, thereby lowering the concentration of oxygen vacancies ($V_O^{\cdot \cdot }$)—the main ionic carriers in BNT-based ceramics—and thus increasing resistivity [14,18,33]. However, for excessive BaSnT content (x > 0.2), lattice strain accumulates, promoting the formation of defect clusters and lowering the migration activation energy for oxygen vacancies, resulting in increased conductivity and diminished impedance [18,19]. The modulation of grain boundary barrier and space charge layers play a key role in governing this behavior. The broadened impedance arcs indicate significant grain boundary contribution to the overall resistance [6,30].

Second, the appropriate BaSnT content modifies the grain boundary chemistry, in which acceptor-type defects are reduced, space-charge layer potential is raised, and carrier transport across grain boundaries is blocked [32,34]. Conversely, excessive Ba enrichment at grain boundaries in over-doped compositions disrupts the continuity of insulating intergranular phases and reduces the barrier height [7,30], as corroborated by the systematic leftward shift in impedance arcs shown in Figure S1.

Third, defect compensation equilibrium and carrier type transition also contribute to the conduction. When Ba²⁺ replaces Bi³⁺, charge compensation occurs either by the removal of oxygen vacancies or by the adjustment of electron concentration—a standard Kröger–Vink picture [14,30,33].

Therefore, the highest resistance at x = 0.2 is attributed to both fewer oxygen vacancies and better grain boundary barriers [7,30,32,35]. These findings provide a defect-chemistry-guided composition design strategy for high-insulation lead-free piezoelectric ceramics, consistent with the oxygen vacancy dynamics framework established for the BNT-based ferroelectrics [18,35].

The Arrhenius fitting plots of direct current (DC) conductivity (σ) and relaxation time (τ) as a function of reciprocal temperature for the (0.95−x)BNSmZT-0.05BF-xBaSnT ceramics are presented in Figure S2 and Figure 5 and Table S2, based on which the activation energy (E_a) and the fitted resistance values of grain boundary resistance R_gb and grain resistance R_g are derived from linear regression and equivalent circuit fitting, respectively. A non-monotonic evolution of E_a, extracted from the relaxation time, with the exhibited BaSnT content: increasing from 1.86 eV at x = 0.05 to a maximum value of 2.12 eV at x = 0.1, following by a sharp decline to a minimum value of 1.21 eV at x = 0.15, and subsequently recovering to a relatively stable range of 1.56–1.64 eV for the x = 0.2–0.4 ceramics. The conductivity change trend is inversely correlated with E_a, with the highest E_a value at x = 0.1 corresponding to the lowest conductivity, indicating optimal insulating characteristic. Conversely, the precipitous drop in E_a at x = 0.15 marks a significant transition in the conduction mechanism with enhanced electrical transport [35].

This behavior originates from the synergistic regulation of oxygen vacancy-mediated conduction by phase purity and lattice strain. For x ≤ 0.1 ceramic, Bi volatilization is indicated by the XRD-detected Bi₂Ti₂O₇ impurity phase (Figure 1), generating $V_O^{\cdot \cdot }$, according to the Kröger–Vink equation: ${2Bi}_{Bi}^{\times }+3O_O^{\times }\to 2V_{Bi}^{‴}+2Bi\uparrow +3V_O^{\cdot \cdot }+3/2O_2\uparrow$ [19]. High-resistivity barrier layers are formed at grain boundaries by the low-melting-point Bi₂Ti₂O₇ s phase, obstructing continuous oxygen vacancy migration channels, elevating the activation energy E_a to 2.12 eV and suppressing conductivity [7,18,32].

At x = 0.15, with excess Bi³⁺, the rising Ba²⁺ content drives charge compensation via defect formation, and the expelled excess cations subsequently precipitate as a secondary phase, and the formation of secondary phase is accompanied by the generation of oxygen vacancies, resulting in a significant surge in oxygen vacancy concentration. Concurrently, the oxygen vacancy migration barrier reaches its minimum value of 1.21 eV, which promotes ionic conduction and markedly enhances the overall conductivity [14,18].

At x = 0.2–0.4, when the bonding between oxygen anions and A-site cations is relatively weak, oxygen anions are more prone to migrate to planes with stronger A-site cation-oxygen bonding. Specifically, the Ba-O-Bi bond is more stable than the Bi-O-Na bond, thereby elevating the ionic migration activation energy required for oxygen vacancy migration. Consequently, the E_a value recovers and stabilizes within the range of 1.56–1.64 eV, and the conduction mechanism transitions from ionic conduction to oxygen vacancy-mediated conduction governed by the robust Ba-O-Bi bonding interaction [18,19,28,30].

In summary, the non-monotonic evolution of electrical conduction behavior is governed by the competition between the grain boundary blocking effect of the Bi₂Ti₂O₇ impurity phase and A-site defect chemical equilibrium. Such research provides a phase-engineering strategy for regulating insulating properties of the BNT-based ceramics, being consistent with the oxygen deficiency to excess transition reported in the A-site engineered BNT ceramics [19,36].

In order to systematically explain the physical parameters covering electrical, mechanical, thermal, and chemical coupling behaviors in ionic disordered systems, a jump relaxation model (JRM) is constructed to quantitatively characterize the frequency and temperature-dependent conductance response. The frequency-dependent conductivity behavior in ionic conductors can be elucidated in a double power law, expressed as ${\sigma }_{ac}={\sigma }_{dc}+A{f}^n+B{f}^m$ [29], where A is a constant with temperature; f represents frequency; n represents the exponent in the power law equation, which has a value within the range of 0–1 and represents the frequency-dependent index; and B represents a constant that is less dependent on temperature [7]. To understand the relationship between conductivity behavior and frequency of a material, the alternating current (AC) conductivity is calculated using the formula $\sigma$_ac = $\omega {\epsilon }_0{\epsilon }_r$tan$\delta$, where $\omega$ represents the angular frequency, ${\epsilon }_0$ represents the dielectric constant in the vacuum, ${\epsilon }_r$ represents the relative dielectric constant, and tan$\delta$ represents the dielectric loss [30].

Figure 6a shows the change in AC conductivity with increasing frequency measured at different temperatures for the x = 0.2 ceramic. Many carrier hopping mechanisms are involved in this conduction, including small polarization jumps, correlation barrier jumps, overlapping large pole jumps, quantum tunneling, etc. [30]. In the low frequency region, frequency-dependent changes are observed in the AC conductivity at all temperatures, with the n value decreasing monotonically from 0.94 to 0.85 with increasing temperature, indicating that the carrier dynamics deviate from the ideal Debye relaxation and enter the correlation jump, being consistent with the Dyre’s random free-energy barrier model [37]. An increase in the conductivity is apparent with increasing frequency. The AC conductivity increases monotonically with frequency throughout the entire measured frequency range, without showing an obvious DC conductivity plateau, also confirming the dielectric relaxation behavior of the material. The change in conductivity with temperature indicates that the material exhibits a negative temperature coefficient resistance (NTCR) characteristic [2]. The charge transport mechanism dominated by thermally activated nearest neighbor association jumping is demonstrated.

To further elucidate the conduction mechanism while suppressing contributions from grain boundaries and electrode polarization, the frequency (f) dependence of normalized real and imaginary parts of electric modulus, M′/M′_max and M″/M″_max, are presented in Figure 6b and Figure 6c, respectively. In Figure 6b, as frequency increases, the M′/M′_max-f spectra at all measured temperatures overlap into a single master curve at different high frequencies depending on temperature, indicating that the relaxation dynamics remain unchanged across the entire temperature window [29]. As temperature rises, the dispersion region shifts toward higher frequencies and the steepness of M′ curves increases, reflecting a thermally activated process with progressively shortened relaxation times [38].

In Figure 6c, the peak frequency f_max moves monotonically to higher frequencies with increasing temperature, and only a single peak is reflected at each temperature, confirming that the charge carriers migrate faster at elevated temperatures without any change in the underlying relaxation mechanism [15]. The full width at half maximum (FWHM) of the M″/M″_max peaks in the 480–530 °C range is calculated to be 1.30–1.37 decades, substantially exceeding the ideal Debye value of 1.14 decade [37]. This broadened lineshape provides further evidence for non-ideal relaxation governed by correlated hopping in a randomly disordered energy landscape, being consistent with the Dyre random free-energy barrier model [30,37].

4. Conclusions

The conduction behavior of (0.95−x)BNSmZT-0.05BF-xBaSnT lead-free ceramics was examined as a function of the BaSnT content. A non-monotonic transition is determined: at x ≤ 0.1, Bi₂Ti₂O₇ impurity at grain boundaries blocks oxygen vacancies, resulting in high E_a (~2.12 eV) and oxygen vacancy-mediated conduction. At x = 0.15, charge compensation is achieved through the precipitation of secondary phase and free oxygen vacancies surge, dropping E_a to 1.21 eV, indicative of mixed conduction with enhanced oxygen vacancy mobility. For x = 0.2–0.4, Ba-O-Bi bonds stabilize E_a at ~1.6 eV (mixed conduction with stabilized oxygen vacancy transport). Using modulus analysis, the optimal composition (x = 0.2) shows single-master-curve relaxation and broad M″ peaks (FWHM > 1.14 decades), confirming non-Debye correlated hopping. Furthermore, the conduction mechanism of all (0.95−x)BNSmZT-0.05BF-xBaSnT ceramics is consistently oxygen-vacancy-dominated ionic conduction via correlated hopping. For the first time, a non-monotonic activation energy with two extrema was observed as a function of composition, which is attributed to the competition between the blocking effect of the insulating secondary phase and the promoting effect of Ba²⁺ substitution on oxygen-vacancy transport. The (0.95−x)BNSmZT-0.05BF-xBaSnT ceramics show excellent dielectric temperature stability, especially for x = 0.2 composition, presenting good application prospects in the field of dielectric energy storage.