Dielectric Anomalies and High-Temperature Dielectric Relaxation Dependence on B-Site Ordering of Li-Substituted Pb(Yb_1/2Nb_1/2)O₃

Abstract

B-site ordering of Li-modified Pb_0.95Li_0.05(Yb_1/2Nb_1/2)O₃ (PLYN) ceramics can be changed by duration during sintering. In this paper, the conventional solid-state reaction method was employed to prepare antiferroelectric perovskite Li-substituted PLYN ceramics. Crystal structure evolution dependence of sintering time was investigated using X-ray diffraction (XRD), Raman spectroscopy, and dielectric response. Two dielectric anomalies responses, attributed to the transition from B-site order to disorder and antiferroelectric-paraelectric phase transition depend on B-site ordering. The high-temperature dielectric relaxation associated with charged carries (oxygen-vacancy hopping) was characterized by isothermal electric modulus and universal dielectric response. Impedance spectroscopy was used to uncover the relationship between defect type and the oxygen partial pressure (pO₂) dependence on sintering time in PLYN systems. These findings provide new insights into the interplay among B-site ordered phase structure, dielectric response, and defect types.

1. Introduction

Perovskites with complex B-site compositions are essential materials for inducing colossal effects such as ferroelectric, piezoelectric, and ferromagnetic properties [1,2,3]. The discovery of Pb(Zr_xTi_1−x)O₃ (PZT) and its abnormally high piezoelectric and electromechanical properties in the nearly Morphotropic phase (MPB) rapidly dominated the global market for piezoelectric materials and devices [4,5]. Additionally, various types of PZT (PZT-4, PZT-5A, PZT-5H, PZT-8, etc.) exhibiting “hard” and “soft” characteristics through acceptor or donor doping have been established. Similarly, the Pb(Mg_1/3Nb_2/3)O₃ (PMN) system demonstrates a large dielectric constant, the excellent electro-strictive coefficient, and low strain hysteresis, being PMN materials actively studied for medical and underwater transducer applications [6,7,8,9]. These crystal structure and physical properties are mainly dependent on B-site ordering in the Pb(B′_xB″_1−x)O₃ system [10]. Short-range 1:1 B-site ordering is generally observed in the Pb(B′_1/3B″_2/3)O₃ system. The Pb(B′_1/2B″_1/2)O₃ system exhibits three B-site ordering state: complete ordering, ordering variably influenced by different thermal processes, and no ordering. It suggests that differences in both charge and size between B′ and B″ complexes minimize electrostatic and elastic energies in the B-site ordered crystal structure. Furthermore, distinct superlattice reflections corresponding to B-site ordering are observed in the Pb(B′_1/3B″_2/3)O₃ system through X-ray diffraction (XRD) patterns [11,12,13].

Pb(Yb_1/2Nb_1/2)O₃ (PYN) is classified among the Pb(B′_1/2B″_1/2)O₃ complex perovskites, characterized by highly ordered B-site cations [14,15]. PYN undergoes an antiferroelectric-paraelectric phase transition at its Curie temperature (T_c = 583 K). Above T_c, the PYN system exhibits a cubic phase (space group: Fm-3m) corresponding to 1:1 ordering of B-site ions. Below T_c, the B-site ordering and the antiparallel displacement of Pb²⁺ ions induce the formation of an orthorhombic phase structure (space group: Pnam). During the sintering process, the volatilization of Pb²⁺/Nb⁵⁺ cations makes it difficult to obtain the pure perovskite phase of PYN. Bokov et al. found that due to the comparatively low temperatures (800 °C), the compositionally ordered perovskite structure of PYN is formed, and the ratio of ordered structure to disordered structure decreases during sintering at higher temperatures [16]. The presence of pure and doped Li in PYN results in apparent anomalies in the temperature dependence of the permittivity, attributed to the B-site ordering. Vedantam et al. [13] observed a phase transition from antiferroelectric to relaxor ferroelectric in Ba_xPb_1−x(Yb_0.5Nb_0.5)O₃ with increasing x, indicating a decrease in the antiparallel displacement of Pb²⁺ due to Ba²⁺ substitution. In the Raman spectra of pure PYN, there are 60 Raman active modes associated with the antiferroelectric orthorhombic phase. Increasing the amount of Ba²⁺ cations, and the number of Raman active modes at A- and B-sites, while increasing the deviation and rotation of BO₆ octahedral due to local lattice distortion caused Ba²⁺ doping. Kim et al. [17] investigated the crystal structure, the dielectric response, and ferroelectric properties in (1−x)Pb(Yb_1/2Nb_1/2)O₃-xBa(Yb_1/2Nb_1/2)O₃ (0 ≤ x ≤ 0.3) antiferroelectric ceramics. With increasing Ba(Yb_1/2Nb_1/2)O₃ content, the superstructure with antiparallel modulation displacement of Pb²⁺ ions and B-site order gradually weakens and disappears. The two diffraction peaks 2θ about 45° amalgamate one peak of (400), suggesting the phase transition from orthorhombic phase to pseudo-cubic phase. The temperature dependence of the dielectric constant of (1−x)Pb(Yb_1/2Nb_1/2)O₃-xBa(Yb_1/2Nb_1/2)O₃ shows a diffuse phase transition from antiferroelectric phase structure (such as: PbZrO₃) to relaxor ferroelectric phase structure (such as: Pb(Mg_1/3Nb_2/3)O₃) with increasing amount x [18]. It is noteworthy that the temperature dependence of dielectric response and P-E loops of the Pb_0.86Ba_0.14(Yb_1/2Nb_1/2)O₃ system exhibits similarities to that of Bi_0.5Na_0.5TiO₃.

In this study, we investigated the relationship between phase structure, dielectric response, and defects by varying the sintering times of Pb_0.95Li_0.05(Yb_1/2Nb_1/2)O₃ samples (1, 4, 6, 8, and 12 h). All ceramic samples exhibited two dielectric responses across the entire temperature range examined. Understanding the behavior of the crystal structure and impedance response in this solid solution system is essential. These analyses contribute to a deeper understanding of the structure and electric mechanisms within the Pb(B′_1/2B″_1/2)O₃ system, highlighting its unique original antiferroelectric behavior and its potential for use in antiferroelectric capacitors for energy storage.

2. Results and Discussion

Figure 1 displays the XRD patterns of Pb_0.95Li_0.05(Yb_1/2Nb_1/2)O₃ ceramics prepared after varying sintering times for 1, 4, 6, 8, and 12 h, identified as: PLYN-1h, PLYN-4h, PLYN-6h, PLYN-8h, and PLYN-12h. These patterns predominantly exhibit a perovskite structure, alongside traces of a pyrochlore structure with superlattice diffractions. The intensity of this secondary phase increases with the increasing sintering temperature time. The triangle makers in the XRD patterns signify superlattice reflections stemming from the antiparallel displacement of Pb²⁺ cations and B-site ordering within the PLYN system. The reflection peak (200) was not split into (002) and (200) peaks. This suggests that real perovskite structures can deviate from the ideal cubic phase, displaying three main structural distortions: (i) vibration displacements of A-site cations around the center of four BO₆ octahedra; (ii) distortion of the anion octahedra; (iii) tilting of the BO₆ octahedra, influenced by the “lone-pair electron effect” at the A-site. These variations lead to variations in the B′-O and B″-O bond lengths, as well as deviations in O-B′-O and O-B″-O bond angles within the A(B′_xB″_1−x)O₃ system [19]. Furthermore, the occurrence of F-centering reactions due to B-site ordering suggests that the crystal structure of A(B′_xB″_1−x)O₃ effectively doubles the perovskite unit cell along all the crystallographic axis directions. The emergence of an antiferroelectric orthorhombic phase in Pb_0.95Li_0.05(Yb_1/2Nb_1/2)O₃ results from interactions between the volume disparity of NbO₆ and YbO₆ octahedra, structural imperfections in YbO₆ octahedra due to rigid rotation, and the “lone-pair effect” of Pb²⁺ cations. The perovskite structural tolerance factor is calculated after Equation (1):

$$\tau ={\displaystyle \frac{R_A+R_O}{\sqrt{2}(R_B+R_O)}}$$

(1)

where R_A, R_B and R_O are the cation radii of A-site, the cation radii of B-site and the oxygen radii, respectively [20]. The tolerance factor (τ) of antiferroelectric (AFE) perovskites falls within the limited distribution 0.78 ≤ τ ≤ 1.00, whereas ferroelectric (FE) perovskites encompass the range 0.78 ≤ τ ≤ 1.05. Therefore, PYN-based ceramics exhibit a series of antiferroelectric perovskite properties, originating from the superlattice refection [17]. The radius of Li⁺ [0.76 Å (CN12)] at the A-site is smaller than the one of Pb²⁺ [1.49 Å (CN12)] [19]. Compared to the pure Pb(Yb_1/2Nb_1/2)O₃ solid solution [τ = 0.92(38)], the presence of a small amount of Li⁺ at the A-site [PLYN, τ = 0.91(21)] significantly reduces and eventually eliminates the pyrochlore phase only observed in the PLYN-12 system. This emphasizes the importance of reducing the tolerance factor and optimizing sintering temperature and time for achieving high-purity perovskite structures in PLYN ceramics [11].

To gain further insight into the static and dynamic behavior of the local structure within the B-ordered perovskite lattice, the room temperature Raman spectra of PLYN are presented in Figure 2a. Theoretical Raman active modes for orthorhombic symmetries include: Γ_{(O, Raman)} = 18 A_g + 18 B_1g + 12 B_2g + 12 B_3g, while for cubic symmetries, they are Γ_{(C, Raman)} = A_1g+E_g + 2 F_2g [13,21,22,23]. The Raman data were fitted using the Lorentzian function, and the fitting results are shown in Figure 2b. Eight peaks were obtained and labeled as Peak 1, 2, 3, 4, 5, 6, 7 and Peak 8. Figure 2c shows the variation in Raman shifts in the eight peaks as a function of sintering times. The mode at 55 cm⁻¹ corresponds to Pb–O stretching. The mode is influenced by the mass of A-site cations and the A–O binding force. Hence the corresponding mode occurs in the low-frequency region. For many lead-based complex perovskites, this mode is observed in the 50–60 cm⁻¹ range [13]. Peak 4 is consistent with this mode. Unfortunately, the scattering of phonons of Yb-O/Nb-O bonds and YbO₃/NbO₃ octahedron Raman modes is weak, resulting in only a slight increase in the width of neighboring modes. Raman spectral deconvolution of the A-site was performed using eight Gaussian–Lorentzian peak functions via a best-fitting algorithm, as shown in Figure 2b. Notably, there are no significant shifts in the wavenumbers of the Raman peaks with increasing sintering time, as shown in Figure 2c. This suggests that the crystal structure of PLYN exhibits orthorhombic symmetry, consistent with the XRD results. The sintering time dependence of full width at half maximum (FWHM) of the related modes in PLYN is illustrated in Figure 2d. An anomaly in the FWHM of all parks is observed in the sintering time 6 h, indicating the appearance of the same pyrochlore due to a higher degree of disorder in the PLYN lattice [23]. In essence, this suggests that the suitable sintering time for PLYN enables the adjustment of the phase structure ratio and B-site order.

SEM micrographs of the PLYN-1h, PLYN-4h, PLYN-6h, PLYN-8h, and PLYN-12h ceramics are shown in Figure 3a–e. Among these, the PLYN-8 ceramic exhibits the most dense and homogeneous grains compared to all other samples. The appearance of a liquid phase during the sintering process could enhance the diffusion rate of ions across grain boundaries and/or weld the smaller grains together [24]. This phenomenon is particularly evident when the sintering time increases from 1 h to 8 h, allowing ample time for the formation of low melting temperature liquid phases. However, with further increases in sintering time, Pb²⁺ and Li⁺ cations volatilize, leading to the formation of the micro-holes in localized regions. This observation is in good agreement with the trend of relative density, as depicted in Figure 3f.

Figure 4a–e depict the temperature dependence of the real part of the dielectric permittivity (ε′) and dielectric loss (tanδ) over the frequency range from 100 Hz to 1 MHz for PLYN-1h, PLYN-4h, PLYN-6h, PLYN-8h, and PLYN-12h. Two anomalies are observed in ε′. Firstly, a high-temperature diffusion phase transition occurs at T_C (approximately at 546 K), indicating a paraelectric-antiferroelectric phase transition. Secondly, between 470 and 546 K, a significant dielectric response anomaly is observed, suggesting the formation of B-site disorder. To further investigate the paraelectric-antiferroelectric phase transition, the modified Curie–Weiss law was employed to fit the ε′ at temperatures considerably higher than T_C:

$${\displaystyle \frac{1}{\epsilon }}-{\displaystyle \frac{1}{{\epsilon }_m}}={\displaystyle \frac{{(T-T_{CW})}^{\gamma }}{C}}$$

(2)

where T_CW is the Curie–Weiss temperature, C the Curie coefficient, ε_m the dielectric parameter at T_C, and γ the diffuseness constant. When the exponent γ approaches 1, it signifies the presence of a normal ferroelectric material characterized by long-range ferroelectric ordering. Conversely, when γ tends toward 2, it indicates a conventional relaxor ferroelectric material [25,26]. Figure 4f demonstrates that the values of γ for PLYN-1h, PLYN-4h, PLYN-6h, PLYN-8h, and PLYN-12h are 1.112, 1.108, 1.063, 0.982, and 0.889, respectively. These values diverge from the γ value of normal ferroelectric (such as BaTiO₃) and relaxor ferroelectric materials (such as Pb(Mg_1/3Nb_2/3)O₃). Furthermore, when coupled with the slender P-E loops, it suggests that PLYN exhibits weakly antiferroelectric properties [27].

In order to characterize the two dielectric anomalies in the PLYN system, impedance spectroscopy stands out as one of the most relevant techniques for investigating phase transitions and defect behaviors across a broad frequency range. The temperature dependence of the imaginary part of the modulus (M″) is depicted in Figure 5a–e [28]. The M″ peak rapidly shifts to higher frequencies as temperature increases across the entire testing temperature range. This suggests the involvement of a single thermal activation process [29]. To describe M″ in Equation (3), a combination of the Fourier transforms of a relaxation function (ω(t)) and the Kohlrausch–Williams–Watts function (KWW) is employed:

$$M^{″}=M_{\max }^{″}/\{(1-\beta )+{\displaystyle \frac{\beta }{1+\beta }}[\beta ({\omega }_{\max }/\omega )+{(\omega /{\omega }_{\max })}^{\beta }]\}$$

(3)

where M″_max is the peak value of M″ and ω_max the corresponding frequency. The quantity (1 − β) serves as a measure of the degree of correlation between the carriers involved in the conduction process. As (1 − β) approaches zero, it indicates that charge carriers undergo long-distance jump motion, confined within potential wells and free to move solely within those wells. Figure 5f shows the variation in β with temperature. As β increases, the PLYN system approaches closer to the ideal Debye relaxation, which is associated with the paraelectric-antiferroelectric phase transition and with a sharp reduction in the number of dipoles. The β curve reaches a maximum value, suggesting the complete transformation from the antiferroelectric orthorhombic phase to the paraelectric cubic phase. Subsequently, as temperature rises further, the decreasing β values correspond to the thermal activation of carriers, leading to charge-mismatch and the activation of oxygen vacancies induced by volatile elements.

Figure 6a–e depict the real part of the ac conductivity (σ_ac) for the different sintering times of PLYN at the testing temperature. The conductivity behavior was described via the universal dielectric response (UDR) law [30,31]:

$${\sigma }_{\mathrm{ac}}={\sigma }_{\mathrm{dc}}+{\sigma }_0{f}^s$$

(4)

where σ_ac is the dc bulk conductivity, f the frequency, σ₀ a constant, and 0 < s ≤ 1. The relationship, involving local interactions between charges and dipoles, is described by Equation (4). As temperature increases, the activation hopping of electrons over barriers becomes easier, leading to the formation of DC conductivity at low frequencies. The UDR law properly fits the curves of σ_ac for all PLYN samples. For temperatures over the melting temperature of PbO and Li₂O, it is easy for Pb²⁺ and Li⁺ to volatilize and produce oxygen vacancies. The defect compensation should follow Equations (5) and (6):

$${Pb}^{2+}\to {Pb}_{gas}+V_{Pb}^{••}+V_O^{••}$$

(5)

$${Li}^{+}\to {Li}_{gas}+V_{Li}^{•}+1/2V_O^{••}$$

(6)

During the oxygen annealing process, defect reactions occur in the PLYN system:

$$2V_{A-site}^{\prime }+V_O^{••}+1/2O_2\leftrightarrow 2V_{A-site}^{\prime }+O_O^X+2h^{•}$$

(7)

$$V_O^{••}+1/2O_2+2e^{\prime }\leftrightarrow O_O^X$$

(8)

where $V_{Pb}^{••}$ represents the lead vacancies, $V_{Li}^{•}$ represents the lithium vacancies, O₂ is the oxygen and $V_O^{••}$ represents oxygen vacancies.

Figure 6f illustrates the mechanism behind the hopping of carriers within potential wells and its effect on conductivity behavior. In a low-temperature state, high-energy hopping carriers struggle to overcome the depth of the potential well, resulting in a single particle hopping back and forth within a double well with infinite barriers on either side, forming the entire contribution by σ_ac [32]. At high temperature, the frequency dependence of conductivity can be divided into two parts due to potential barriers caused by short-distance motion of cations and the hopping of small polarons. At high frequency, the short-distance migration of carriers is unaffected by potential barriers, leading to exponential growth in a part of σ_ac. Conversely, at sufficiently low frequencies, activation carriers are blocked by potential barriers related to the hopping of small polarons contributing to σ_ac. The index ‘s’ increases with temperature due to the dominating mechanism of classical hopping of electrons over barriers. However, factors such as the antiferroelectric-paraelectric phase transition, intrinsic oxygen vacancies, and mismatched crystal cells with different charged cations induce complex conductivity behavior across a range of temperatures, as depicted in Figure 7. To further understand this complex conductivity behavior, the correlated barrier hopping (CBH) model is employed [33]. The binding energy is calculated using the following equation:

$$S=1-\beta$$

(9)

and

$$\beta ={\displaystyle \frac{6K_{B}T}{W_m}}$$

(10)

where W_m is the binding energy, which is defined as the energy required to remove an electron completely from one site to another site. Figure 7a–e display the temperature dependence of W_m ranging from 0.5 to 0.9 eV. Figure 7f depicts the defect equilibria along with a reduced electroneutrality condition, illustrating various oxygen partial chemistries (pO₂) to elucidate different types of activation defects in the ABO₃ system [34,35,36,37,38]. Theoretical analysis of the defect chemistry diagram can be segmented into three sections: (i) In a low pO₂ region, n-type-doped ABO₃ is prevalent; (ii) In a medium PO₂ region, a balanced electroneutrality coexistence occurs between local n-type-doped and local p-type-doped ABO₃; (iii) In a high PO₂ region, p-type-doped ABO₃ predominates [39,40,41]. In a n-type solid solution system, where the conduction of electrons is independent of pO₂, it is controlled by cation donors, maintaining a constant ratio between electrons concentration and pO₂. Conversely, when the bilection concentration is governed by oxygen vacancies, a log-plot of conductivity versus pO₂ yields a slope of 1/6. If cation donors or anion vacancies are compensated by cation vacancies, the relationship between the log-plot of conductivity and pO₂ shows a slope of 1/4. The W_m value of PLYN falls within the range 0.5 to 0.9 eV, differing from the formation of partial Schottky acceptor defects (E_a ≥ 1.5 eV) in the n-type BaTiO₃-BiMeO₃ system and the negative slope observed in K_0.5Na_0.5NbO₃ and K_0.5Na_0.5NbO₃-Na, indicating electron conducting and fewer A-site vacancies. This aligns well with the highest pO₂ region, demonstrating a series of p-type solid solution properties, reflecting a lower energy barrier between two potential wells for PLYN. To further understand the bulk conductivity characteristic in the PLYN system, the values of the binding energy minimum hopping distance R_min are calculated [42,43]:

$$R_{min}={\displaystyle \frac{2e^2}{\pi {\epsilon }_0\epsilon W_m}}$$

(11)

where ε₀ is the dielectric permittivity of free space and ε is the dielectric constant at probing frequency. Figure 8a–e display the temperature dependence of R_min at 1 kHz. The minimum value of R_min is typically observed at around the antiferroelectric-paraelectric phase transition temperature. As per the hopping model, the behavior of σ_ac indicates that conductivity drives charge transport at low frequencies, while hopping among finite clusters dominates at higher frequencies. Throughout the entire temperature range, R_min was consistently measured to be approximately 40.00~140.00 × 10⁻¹² m. The data on ac conductivity have been used to determine the density of states at the Fermi level (N(E_f)). In the equation, ε₀ is the dielectric permittivity of free space and ε is the dielectric constant at probing frequency. Figure 8a–e display the temperature dependence of R_min at 1 kHz. The minimum value of R_min is typically observed at around the antiferroelectric-paraelectric phase transition temperature. As per the hopping models, the behavior of σ_ac indicates that conductivity drives charge transport at low frequencies, while hopping among finite clusters dominates at higher frequencies. Throughout the entire range, the probing temperature R_min was consistently measured to be approximately 40.00~140.00 × 10⁻¹² m. The data on ac conductivity have been used to determine the density of states at the N(E_f) employing the following relation [33,42]:

$${\delta }_{AC}\left(\omega \right)={\displaystyle \frac{\pi }{3}}{e}^2\omega K_{B}T{\left\{N\left(E_f\right)\right\}}^2{\alpha }^{-5}{\left\{ln\left({\displaystyle \frac{f_0}{\omega }}\right)\right\}}^4$$

(12)

where e is the electronic charge, f₀ the photon frequency and α the localized wave function, assuming f_o = 10¹³ Hz, α = 10¹⁰ m⁻¹ at various operating frequencies and temperatures. At 1 kHz, the temperature dependence of N(E_f) differs among PLYN-1h, PLYN-4h, PLYN-6h, PLYN-8h, and PLYN-12h. In samples with shorter sintering times (PLYN-1h, PLYN-4h and PLYN-6h), factors such as the number of holes in bulk, the phase transitions, and type of defects significantly influence N(E_f). Consequently, N(E_f) for PLYN-1h, PLYN-4h and PLYN-6h exhibits a complex nature across the entire range of probing temperatures. Conversely, in samples with sufficiently long sintering times, the temperature dependence of N(E_f) for PLYN-8h and PLYN-12h reveals that hopping between the pairs of sites dominates the charge transport mechanism. A theoretical nonlinear relationship between defect concentration and pO₂ is depicted in Figure 8f. The mix conductance in the hopping transport mechanism is divided into electronic and ionic charge carriers. Based on the predicted pO₂ dependence of conductivity in an ideal ABO₃ structure, real defect models, such as A_1−δBO_3−x and A_1−2δBO_3−y (where δ represents the A-site vacancy concentrations, and x and y are oxygen vacancies concentrations), exhibit different conductivity behaviors. A_1−2δBO_3−x possesses a higher number of A-site vacancies compared to A_1−δBO_3−y, indicative of a transition from high pO₂ to low pO₂ conditions. This difference in stoichiometry leads to theoretically distinct types of doping. Moreover, the temperature dependence of N(E_f) for PLYN-12 is observed at temperatures 10 K higher than those for PLYN-8h. With increasing sintering time, PLYN ceramics release significant amounts of Pb²⁺ and Li⁺ ions from the A-site, forming a similar A_1−2δBO_3−x-type defect structure.

3. Experimental Part

The PLYN ceramics were synthesized using a two-step conventional mixed oxide method. Raw materials used included PbO (99.9%), Yb₂O₃ (99.99%), Nb₂O₅ (99.99%), and Li₂CO₃ (99%). Initially, Yb₂O₃ and Nb₂O₅ were thoroughly mixed and sintered at 1000 °C for 2 h to form YbNbO₄. The YbNbO₄, Li₂CO₃, and PbO were mixed stoichiometrically according to the PLYN formula. An excess of 2% PbO and Li₂CO₃ (to compensate for evaporation at high temperature) was further added. The resulting mixtures were ground thoroughly and calcined at 850 °C. The calcined powder was further ground, granulated with a polyvinyl alcohol binder, then pressed into compacts with a diameter of 10 mm and a thickness ranging from 1 to 2 mm at a pressure of 350 MPa. Subsequently, the compacts were heated to 550 °C to remove the binder. Finally, the green compacts were placed into sealed crucibles fully surrounded by the same composition powder, and sintered at 1200 °C for various durations: 1, 4, 6, 8, and 12 h.

For room temperature crystal structure analysis, X-ray diffraction (XRD) was conducted on the samples using Cu Kα radiation (λ = 1.54059 Å, PANalytical X-Pert-PRO, Almelo, The Netherlands). Raman spectra were recorded via a DXR Raman microscope spectrometer (λ = 532 nm, DXR3, Thermo Fisher Scientific Co, Waltham, MA, USA). The surface microstructure of the ceramics was examined using a field emission scanning electron microscope (FE-SEM, Model S4800, Hitachi High-Technologies, Tokyo, Japan). To measure the electrical properties, silver electrode paste was applied onto cylindrical samples and fired at 650 °C for 30 min. The dielectric properties were measured using an impedance analyzer (Agilent 4294 A, Agilent Technologise, Santa Clara, CA, USA) over a frequency range from 100 Hz to 1 MHz and within a temperature range of 300 to 800 K. Additionally, impedance spectroscopy data were collected using an impedance analyzer of Agilent 4294A over a frequency range from 40 Hz to 1 MHz and within a temperature range of 573 to 853 K.

4. Conclusions

The crystal structure and dielectric response of PLYN ceramics with varying sintering times were investigated. The temperature dependence of the dielectric permittivity suggests two processes: B-site ordering to disordering and antiferroelectric-paraelectric phase transition. The phase transition was characterized using a modified Curie–Weiss law. Dielectric anomalies and different types of defect behavior were identified through impedance spectroscopy, corroborating the results derived from the characteristic value of β. The complex conductivity PLYN with varying sintering times obeys to a universal dielectric response function. The range of the W_m value for PLYN, ranging from 0.5 eV to 0.9 eV, aligns well with the highest pO₂ region, indicating a series of p-type solid solution properties. The density of states at the Fermi level N(E_f) for all PLYN samples was quantitatively characterized based on the predicted pO₂ dependence of conductivity in an ideal ABO₃ structure. These findings establish a relationship among crystal structure, dielectric response and defect behavior in the PLYN system. The reduction in tolerance factor and the application of reasonable sintering temperature and time are essential for achieving high-purity perovskite in PLYN ceramics.