Two-Step Sintering and Sr(Fe_0.5Nb_0.5)O₃ Addition Enhancing Electrical Properties of KNN-Based Lead-Free Piezoelectric Ceramics

Abstract

Lead-free (1−x)(K_0.49Na_0.51)(Nb_0.95Sb_0.05)O₃-xSr(Fe_0.5Nb_0.5)O₃ [(1−x)KNNbS-xSrFNb, x = 0.01–0.07] ceramics with 0.5 wt% CuO were prepared by conventional sintering (CS) and two-step sintering (TSS). Increasing the SrFNb content drives the structure from orthorhombic–tetragonal (O-T, x ≤ 0.03) coexistence to rhombohedral–tetragonal (R-T, x ≥ 0.05) coexistence, and shifts the phase boundary toward room temperature, while Fe³⁺/Nb⁵⁺ B-site disorder induces polar nanoregions, diffuse dielectric behavior (dispersion index γ > 1.7) and a drop of T_m (temperature of dielectric constant maximum) from 295 °C to below room temperature. Increasing SrFNb significantly reduces the average grain size from 0.6 μm to 0.3 μm, while TSS decouples densification from grain growth, raising the maximum relative density from 92.13% to 94.51% at x = 0.05 with only a slight reduction in average grain size from 0.35 μm to 0.32 μm. These changes directly tailor the electrical properties: the near-room-temperature O-T boundary at x = 0.03 gives the best soft-type response (piezoelectric constant d₃₃ = 133 pC/N, electromechanical coupling coefficient K_p = 0.285, remnant polarization P_r = 22.72 μC/cm²), whereas acceptor-oxygen-vacancy dipoles at x = 0.01 pin domain walls, yielding the highest mechanical quality factor Q_m = 329 with low tan δ, and TSS further improves fatigue resistance. Combining SrFNb-driven structural evolution with TSS microstructural control thus offers an effective route to tailor KNN-based lead-free piezoelectrics.

1. Introduction

Piezoelectric ceramics play indispensable roles in modern electronic devices, including high-precision actuators, ultrasonic transducers, sensors, and energy harvesting systems, owing to their unique ability to convert mechanical energy into electrical signals and vice versa [1,2,3,4,5]. For decades, lead zirconate titanate (PZT)-based materials have dominated the commercial piezoelectric ceramics market due to their exceptional piezoelectric performance and temperature stability. However, the toxicity of lead oxide and growing environmental regulations have driven an urgent global pursuit of high-performance lead-free piezoelectric alternatives [5,6,7,8].

Common perovskite structure lead-free piezoelectric materials mainly include three categories, that is, potassium sodium niobate (KNN-based), barium titanate (BT-based) and bismuth sodium titanate (BNT-based). Among various lead-free piezoelectric systems, potassium sodium niobate [(K,Na)NbO₃, KNN]-based ceramics have emerged as the most promising candidate to replace PZT, attributed to their high Curie temperature (T_C ≈ 420 °C), excellent piezoelectric properties and environmental compatibility [9,10,11,12,13,14]. Nevertheless, KNN-based ceramics still face critical challenges that hinder their practical application, including severe volatilization of alkali elements (K⁺, Na⁺) during high-temperature sintering, poor sinterability, and relatively large strain hysteresis, which significantly degrade their performance in precision actuator applications [15,16,17].

To address these issues, two primary strategies have been extensively investigated: compositional doping modification and sintering process optimization. Regarding compositional engineering, A-site or B-site ion substitution has proven effective in tailoring phase structure and electrical properties. Particularly, Sb⁵⁺ doping at the B-site has been demonstrated to effectively shift the polymorphic phase boundary (PPB) toward room temperature and enhance the piezoelectric response [18,19,20]. Such phase-boundary (morphotropic phase boundary (MPB)/PPB) engineering was also demonstrated in other lead-free perovskites, including rhombohedral–tetragonal coexistence in BiFeO₃–Bi_0.5K_0.5TiO₃ and MnO₂-modified Bi_0.5(K_0.2Na_0.8)_0.5TiO₃, which markedly enhance polarization and piezoelectricity [21,22]. In addition, Sr(Fe_0.5Nb_0.5)O₃ was selected over isovalent end-members such as BaZrO₃, SrZrO₃ and BaSnO₃, which only shift the phase boundary without charge fluctuation or acceptor hardening, and Bi-based end-members, which suffer from Bi volatilization and a sharper T_C reduction. In SrFNb, the aliovalent Fe³⁺/Nb⁵⁺ B-site pair creates charge and size disorder that breaks long-range ferroelectric order into polar nanoregions (PNRs), moving the phase boundary toward room temperature while retaining relatively high T_C and low hysteresis; a small amount of non-stoichiometric excess Fe³⁺, together with B-site Cu²⁺ from CuO, can form acceptor-oxygen-vacancy dipoles for high Q_m and low loss [23,24].

In parallel, sintering process optimization is equally crucial for achieving dense KNN-based ceramics with uniform microstructure. Conventional solid-state sintering typically requires temperatures above 1100 °C, which exacerbates alkali volatilization and leads to abnormal grain growth [10,11]. To mitigate this problem, two approaches have been widely adopted: (i) adding sintering aids such as CuO, which promotes liquid-phase sintering, reduces sintering temperature by 50–100 °C, and enhances densification through the formation of low-melting-point liquid phases [25]; (ii) unlike conventional sintering, which holds at a single high temperature where densification and grain growth occur together, so high density is reached only at the cost of grain coarsening and alkali volatilization, two-step sintering first activates densification at a higher temperature and then holds at a lower temperature, where grain-boundary migration is frozen while boundary diffusion continues [26,27]. Qiu et al. showed that CuO acts as both a sintering aid and a defect modifier in the KNN-based ceramics. The CuO-induced defect dipoles effectively pin domain walls, producing a pronounced hardening effect, in the 0.95(K_0.48Na_0.52)NbO₃–0.05(Bi_0.5Na_0.5)HfO₃–0.2 mol% Fe₂O₃–x mol% CuO ceramics, d₃₃ reaches 340 pC/N and Q_m is 256, a fourfold enhancement of Q_m with only a slight reduction in d₃₃ [28]. Tu et al. fabricated (K_0.41Na_0.59)(Nb_0.84Sb_0.06Ta_0.10)O₃ ceramics with CuO sintering aid via two-step sintering. CuO addition significantly enhances relative density to 98.1% and improves piezoelectric properties, achieving d₃₃ = 265 pC/N, Q_m = 420, and dielectric loss tan δ = 0.015 at optimized conditions [29]. Likewise, MnO₂ was reported as an acceptor-type additive to improve the ferroelectric and piezoelectric response of BNT–BT and BKNT ceramics through defect engineering and enhanced densification [21,30]. Various sintering aids have been reported used in the KNN-based ceramics, including ZnO, LiF and borates, most of which merely promote liquid-phase densification [31]. CuO was selected because it uniquely combines densification with electrical-property control: it forms a low-melting K–Cu–Nb–O liquid phase that lowers the sintering temperature and suppresses alkali volatilization, while B-site Cu²⁺ acceptor-oxygen-vacancy dipoles pin domain walls, raising Q_m and reducing tan δ. This dual function is synergistic with two-step sintering.

Therefore, (1−x)(K_0.49Na_0.51)(Nb_0.95Sb_0.05)O₃-xSr(Fe_0.5Nb_0.5)O₃ [(1−x)KNNbS-xSrFNb] ceramics with 0.5 wt% CuO additive were systematically fabricated using both CS and TSS methods in this work. The effects of SrFNb content and sintering strategy on phase structure, microstructure, dielectric relaxation behavior, and piezoelectric properties were comprehensively investigated. Firstly, the optimum sintering temperature was determined using the 0.95(K_0.49Na_0.51)(Nb_0.95Sb_0.05)O₃–0.05Sr(Fe_0.5Nb_0.5)O₃ composition. Then, the effects of Sr(Fe_0.5Nb_0.5)O₃ doping amount prepared at a sintering temperature of 1200–1125 °C 4 h were further investigated. Compared with the samples prepared by CS, the samples fabricated via TSS exhibit improved properties including density, dielectric constant, ferroelectricity and piezoelectricity. This study provides valuable insights into the design of high-performance KNN-based lead-free piezoelectric ceramics with low hysteresis for actuator applications.

2. Experimental Procedure

(1−x)(K_0.49Na_0.51)(Nb_0.95Sb_0.05)O₃-xSr(Fe_0.5Nb_0.5)O₃ [(1−x)KNNbS-xSrFNb, x = 0.01–0.07] ceramics were prepared by conventional sintering (CS) and two-step sintering (TSS) methods, in which 0.5 wt% CuO (99.0%) was used as sintering additive and also induced defect dipoles [32]. Perovskite (1−x)KNNbS-xSrFNb powders were prepared using analytical purity K₂CO₃ (99.0%), Na₂CO₃ (99.8%), SrCO₃ (99.0%), Nb₂O₅ (99.5%), Sb₂O₃ (99.0%) and Fe₂O₃ (99.0%), supplied by China National Pharmaceutical Group Co., Ltd. (Sinopharm), Beijing, China. All raw materials for preparing (1−x)KNNbS-xSrFNb were fully dried in an oven (DHG-9053A, Shanghai Jinghong Laboratory Instrument Co., Ltd., Shanghai, China) at 120 °C for 2 h and the stoichiometrically weighed raw materials were first wet-milled for 24 h in a planetary ball mill (QM-3SP2, Nanjing Nanda Instrument Co., Ltd., Nanjing, China) using zirconia (ZrO₂) balls in nylon jars with anhydrous ethanol as the medium, at a ball-to-powder mass ratio of 5:1 and a rotation speed of 300 rpm; the slurry was then dried at 80 °C and passed through a 100-mesh screen. After calcination (RKJ-4-13, Hefei Kejing Instrument Co., Ltd., Hefei, China) at 850 °C for 2 h, the powders were mixed with 0.5 wt% CuO, wet-milled again in ethanol for 12 h under the same conditions, dried at 80 °C and sieved through an 80-mesh screen before granulation with 8 wt% polyvinyl alcohol (PVA) aqueous solution (Guangzhou Baichuan Chemical Co., Ltd., Guangzhou, China). Subsequently, the granulated powders were uniaxially cold-pressed at 300 MPa for 30 s into discs with 12 mm in diameter and about 1 mm in thickness (769YP-40C, Tianjin Keqi High & New Technology Corporation, Tianjin, China). The pellets were thermally treated for 2 h at 550 °C to eliminate all traces of PVA. To compensate the evaporation of alkali metals, the pellets were put into Al₂O₃ crucible covered with calcined KNN powder. For the 0.95KNNbS-0.05SrFNb ceramics, CS at 1160–1170 °C and TSS with varying T₁ (1190–1200 °C) and holding time (4–6 h) at T₂ = 1125 °C (RKJ-4-13, Hefei Kejing Instrument Co., Ltd., Hefei, China) were systematically investigated. The optimized TSS schedule (1200–1125 °C 4 h) was then applied to the x = 0.01, 0.03, and 0.07 compositions [29,33,34]. For each composition and sintering condition, at least four discs were prepared: one was used for the SEM surface observation, and the remaining three were used for electrical measurements; d₃₃, K_p and Q_m are reported as mean ± standard deviation, with d₃₃ averaged over five points per disc. For the fixed-composition 0.95KNNbS-0.05SrFNb sintering-screening series, four discs were prepared only for the two optimized conditions (CS at 1165 °C and TSS at 1200–1125 °C 4 h).

The crystal structure and microstructure morphology of the sintered (1−x)KNNbS-xSrFNb ceramics were explored by Rigaku D/max-2500/PC X-ray Diffractometer (XRD, Rigaku Corp., Tokyo, Japan) using a Cu Kα target over 2θ = 10–90° with a step size of 0.02° and a scanning speed of 4°/min and JEOL JSM-IT100 InTouchScope scanning electron microscope (SEM, JEOL, Tokyo, Japan) operated at an accelerating voltage of 15 kV after sputter-coating with gold, separately. To explore the electrical performance, the samples were coated with silver paste and sintered at 650 °C for 30 min to form a silver electrode [35]. The ferroelectric hysteresis loop (P-E) and strain curve (S-E) were measured at room temperature using Radiant Precision Premier LC II (Radiant Technologies Inc., Albuquerque, NM, USA) under 25 kV/cm at 1 Hz. The impedance and dielectric properties were measured by HDMS-1000 measurement system (Partulab Technology Co., Ltd., Wuhan, China) from room temperature to 350 °C at a heating rate of 2 °C/min over the frequency range of 100 Hz-2 MHz. The piezoelectric performances were measured by ZJ-6A quasi-static d₃₃/d₃₁ measurement meter (Institute of Acoustics, Chinese Academy of Sciences, Beijing, China) and TH2826 Wide Frequency LCR Meter (Changzhou Tonghui Electronic Co., Ltd., Changzhou, China) after poled at different electric field for 4 min.

3. Results and Discussion

In this work, the 0.95KNNbS-0.05SrFNb ceramics were prepared first, and the influence of sintering temperature and strategy was investigated. Based on the optimized sintering process searched, the influence of SrFNb doping amount on structure and performance of the (1−x)KNNbS-xSrFNb ceramics was further studied.

Figure 1a,b shows the XRD patterns of 0.95KNNbS-0.05SrFNb ceramics prepared by two methods at different sintering conditions and (1−x)KNNbS-xSrFNb ceramics by TSS. Overall, the XRD patterns of all samples exhibit a phase-pure perovskite structure, no detectable peaks attributable to CuO and unreacted SrFNb are observed, indicating that the added CuO and the SrFNb end-member are fully incorporated into the lattice, and the addition of SrFNb forms a homogenous solid solution over the studied range [1,36]. Every reflection can be indexed to the perovskite KNN framework, namely the (100)_pc, (110)_pc, (200)_pc, (210)_pc, (211)_pc and (220)_pc peaks, according to the ICDD PDF-4+ database for the orthorhombic (Amm2, PDF#04-017-0216), tetragonal (P4mm, PDF#97-018-6325) and rhombohedral (R3m, PDF#04-018-7022) polymorphs. All reflections shift systematically to lower 2θ degree with increasing SrFNb; according to the Bragg’s law, the lattice expansion moves the (110)_pc and (200)_pc peaks to lower 2θ angles by about 0.16° and 0.24°, confirming solid-solution formation [16,37].

Figure 1. XRD patterns of (a) the 0.95KNNbS-0.05SrFNb ceramics sintered by CS and TSS at different temperatures, and (b) the (1−x)KNNbS-xSrFNb ceramics with different SrFNb doping contents prepared by TSS and (c) their zoom-in XRD patterns around the (200) peak.

The XRD patterns in the 2θ range of 44.5–46.5°, which highlight the characteristic peaks used to identify the KNN phase structure, are magnified in Figure 1c. It is well established that the {200}_pc diffraction profile serves as a fingerprint for distinguishing the symmetry of perovskite ferroelectrics [38]. Specifically, a single peak is expected for the rhombohedral (R) phase, whereas the orthorhombic (O) phase and tetragonal (T) phase both exhibit doublet splitting but with inverted intensity ratios: the (002)_pc peak is approximately twice as intense as the (020)_pc peak in the O phase, while the opposite intensity ratio is observed in the T phase [38]. In the present (1−x)KNNbS-xSrFNb ceramics, as the SrFNb content increases, the phase structure evolves from an orthorhombic–tetragonal (O-T) coexistence with the O phase dominant at x = 0.01–0.03 to a rhombohedral–tetragonal (R-T) coexistence dominated by the R phase at x = 0.05–0.07. Therefore, the pronounced deviation of the relative peak intensities with 2θ around 45° from these standard ratios strongly indicates the coexistence of multiple phases rather than a single-phase structure, and the increase of SrFNb amount drives the gradual O to R transition [39,40].

Figure 2 shows the SEM images and grain-size distributions of the 0.95KNNbS-0.05SrFNb ceramics sintered by CS (1165 °C) and TSS (1200–1125 °C, 4 h), together with the TSS ceramics of x = 0.01, 0.03, and 0.07. All specimens consist of equiaxed, submicrometer grains with well-defined boundaries, and no secondary phase or macroscopic segregation is resolvable by SEM. The x = 0.05 sample exhibits near-normal grain-size distribution and only isolated residual pores, indicating a dense but not fully pore-free microstructure. The composition series reveal a pronounced grain size reduction: the characteristic grain size is approximately 0.6 μm at x = 0.01–0.03 but decreases to about 0.3 μm at x = 0.05 and remains fine at x = 0.07. This grain-size reduction is not accompanied by monotonic densification: the relative densities of the x = 0.01, 0.03, 0.05, and 0.07 ceramics are 92.77%, 90.81%, 94.51%, and 85.96%, respectively (Table S2), showing that excessive SrFNb addition suppresses grain growth but also promotes pore retention. The x = 0.05 composition therefore achieves the best balance between fine grains and high density. For this composition, TSS increases the relative density from 92.13% to 94.51% (residual porosity from 7.87% to 5.49%) while reducing the average grain size only from 0.35 μm to 0.32 μm (Tables S1 and S2). Because the density gain is considerably larger than the change in grain size, the primary microstructural benefit of TSS enhances pore elimination, with boundary pinning preventing concomitant coarsening [16,29]. In contrast, the CuO-free (K_0.48Na_0.52)Nb_0.965Sb_0.035O₃-based ceramics exhibit a coarser microstructure, with grain sizes mainly distributed in the range of 0.7–1.3 μm [41].

Figure 2. SEM images and grain-size distribution of 0.95KNNbS-0.05SrFNb ceramics sintered at different processes (a1,a2: 1165 °C; b1,b2: 1200–1125 °C 4 h) and (1−x)KNNbS-xSrFNb ceramics with x = 0.01 (c1,c2), x = 0.03 (d1,d2), x = 0.07 (e1,e2).

The bulk density was measured by the geometric method, the theoretical unit-cell volume was derived from the Rietveld-refined lattice parameters (V = abc for the orthorhombic cell, V = a²c for the tetragonal cell, and V = $\sqrt{3}$a²c/2 for the rhombohedral cell in the hexagonal setting), and the theoretical density was calculated from the refined lattice parameters using ρ_theo = ZM/(N_AV) (where ρ_theo is the theoretical density, Z is the number of formula units per unit cell, M is the molar mass of the composition, N_A is Avogadro’s constant, and V is the unit-cell volume). In TSS, the high-T step (1200 °C) activates densification while the low-T step (1125 °C) freezes boundary migration but allows boundary diffusion, decoupling densification from grain growth [42]. Reduced porosity removes low-permittivity, field-concentrating voids and charge-injection sites, mainly raising ε_m, P_r, breakdown and fatigue resistance, and lowering loss; the fine-grained microstructure generation with CuO boundary segregation increases the boundary fraction, homogenizes the field and decreases domains, favoring switching and d₃₃. The enhancement is therefore combined effects, i.e., the densification governs dielectric behavior and the fine-grained microstructure governs switching and piezoelectricity.

Since different phase structures will affect the electrical properties of ceramics, in order to further explain the change of phase structure, GSAS-II Rietveld is used to refine the XRD patterns, and the results are shown in Figure 3. The results of 0.95KNNbS-0.05SrFNb ceramics prepared by CS and TSS methods sintered at different conditions are shown in Figure S1. The high-quality fitting parameters (R_wp < 12.78%, χ² < 1.21) ensures refinement reliability. With increasing the SrFNb content, the structure evolves from O-T coexistence (x ≤ 0.03, O phase > 50%) to R-T coexistence (x ≥ 0.05, R phase dominant). The O phase decreases from 70% to 0%, while the R phase increases to 77.3%, and the T phase decreases slightly to 22.7% at x = 0.07. For the x = 0.05 sample, the few weak unidentified reflections close to the detection limit were incorporated by manually adding peaks to the background function rather than modeled as a separate phase, as their crystal structure could not be determined.

Figure 3. XRD Rietveld refinement results of (1−x)KNNbS-xSrFNb ceramics with different SrFNb doping contents prepared by TSS. (a) x = 0.01; (b) x = 0.03; (c) x = 0.05; (d) x = 0.07.

Based on valence and ionic radii Sr²⁺ (1.44 Å, coordination number (CN)-12), being too large for the octahedral site, enters the perovskite A-site and substitutes K⁺/Na⁺, whereas Fe³⁺ (0.645 Å, CN-6, high spin) and Nb⁵⁺ (0.64 Å, CN-6) occupy the B-site, replacing Nb⁵⁺/Sb⁵⁺. Then, local effective charge is induced in the (1−x)KNNbS-xSrFNb solid solution, i.e., Sr²⁺ substituting K⁺/Na⁺ produces +1 effective charge, and Fe³⁺ replacing Nb⁵⁺/Sb⁵⁺ engenders -2 effective charge; whereas these cations cancel exactly, so the (1−x)KNNbS-xSrFNb unit is self-compensating and needs no oxygen vacancies from a macro perspective, analogous to the A-site donor compensation in MnO-doped potassium sodium niobate ceramics [43]. Residual acceptor charge from CuO and excess Fe³⁺ is balanced by a small oxygen-vacancy concentration, forming acceptor-oxygen-vacancy dipoles; and low tan δ (<0.06) confirms few mobile vacancies. The incorporation of Sr²⁺ and Fe³⁺ ions induces A-site/B-site ionic radius mismatches, decreasing the tolerance factor and causing anisotropic lattice distortions (Table 1), which promote BO₆ octahedral tilting and stabilize the R phase. The continuous composition-dependent evolution and good fitting quality rule out peak overlap, confirming a genuine structural transition. The random aliovalent ions create local fields and polar nanoregions, and shift the phase boundaries toward room temperature, while the acceptor-oxygen-vacancy dipoles pin domain walls, raising Q_m and lowering dielectric loss, with a slightly higher E_c [43].

Table 1. Structural parameters of the (1−x)KNNbS-xSrFNb ceramics with different SrFNb doping contents prepared by TSS obtained by Rietveld refinement.

Composition (mol%)	Phase Content (%)	Unit-Cell Volume (Å3)	a (Å)	b (Å)	c (Å)	α (°)	β (°)	γ (°)
x = 0.01	O (70.6) T (29.4)	125.367 63.117	3.9482 3.9712	5.6264 3.9712	5.6433 4.0020	90 90	90 90	90 90
x = 0.03	O (64.8) T (35.2)	125.339 63.233	3.9539 3.9752	5.6194 3.9752	5.641 4.0013	90 90	90 90	90 90
x = 0.05	R (69.4) T (30.6)	188.312 63.813	5.6113 3.9853	5.6113 3.9853	6.9058 4.0177	90 90	90 90	120 90
x = 0.07	R (77.3) T (22.7)	187.817 62.681	5.6194 3.9890	5.6194 3.9890	6.8819 4.0062	90 90	90 90	120 90

The influence of CS and TSS on dielectric performance at 100 kHz of the 0.95KNNbS-0.05SrFNb ceramics is shown in Figure 4a. As the CS single-step sintering temperature increases from 1160 °C to 1170 °C, the peak dielectric constant rises progressively and the peak profile turns sharper, suggesting that higher sintering temperature facilitates ceramic densification and grain development, and mitigates the damping effect of pore defects on polarization [35,37]. In comparison with the CS method, the TSS strategy yields further improvement in dielectric properties. Particularly, the TSS sample sintered at 1190–1125 °C 4 h achieves the maximum dielectric constant (ε_m) of 2768. Such phenomenon is because two-step sintering elevates the bulk density while restraining abnormal grain growth, thereby strengthening the dielectric response contributed by ferroelectric domain switching [33,42].

Figure 4. Temperature dependence of dielectric performance for the (a) 0.95KNNbS-0.05SrFNb ceramics sintered by CS and TSS at different temperatures at 100 kHz and (b) (1−x)KNNbS-xSrFNb ceramics with different SrFNb doping contents prepared by TSS at 100 kHz.

Figure 4b shows the temperature-dependent dielectric performance of the (1−x)KNNbS-xSrFNb ceramics, tested at 100 kHz to investigate the effect of the SrFNb doping content on the dielectric properties. The x = 0.01 sample exhibits a sharp Curie peak at 295 °C as a normal ferroelectric, with the ε_m value of 4401. Such value is comparable to, or slightly higher than, the Curie-peak permittivity commonly reported for the KNN-based ceramics [41,44]. At x = 0.03, T_m decreases to 266 °C and T_O-T approaches room temperature. At x = 0.05, T_m further decreases to 200 °C with pronounced relaxor behavior, driven by random A-site Sr²⁺ and B-site Fe³⁺/Nb⁵⁺ creating charge mismatch and local electric fields; Sr²⁺ also lowers the tolerance factor, promotes BO₆ tilting and shifts the boundaries to room temperature, lowering T_m [24]. However, the ε_r versus T plot for x = 0.07 does not show a clear transition corresponding to T_C, which suggests that the material is in the paraelectric phase at room temperature [45,46,47]. For dielectric loss, all samples maintain low dielectric loss tan δ (<0.06) at low-to-moderate temperatures, except the phase-boundary x = 0.03 (tan δ = 0.0952 at room temperature), where strongly enhanced domain-wall mobility raises the loss.

Figures S2 and S3 show temperature-dependent dielectric properties at several frequencies of the 0.95KNNbS-0.05SrFNb ceramics sintered at different processes and the (1−x)KNNbS-xSrFNb ceramics by TSS, from which the ferroelectrics type can be judged preliminarily. Compared with the permittivity characteristic, the loss tangent tan δ exhibits more obvious frequency dispersion phenomenon, and the tan δ value decreases significantly near the peak temperature of dielectric constant (T_C or T_m depending on ferroelectrics type). The higher the frequency is, the more the dielectric loss drops around the T_m temperature, because the domain-wall and polar-nanoregion relaxation loss is frozen out at high frequency during the ferroelectric-to-paraelectric transition [48].

In order to analyze the dielectric response characteristic of ferroelectric ceramics, the Curie–Weiss law is used to fit the dielectric data of the (1−x)KNNbS-xSrFNb ceramics above the T_C temperature:

$$1/\epsilon ={\displaystyle \frac{T-T_0}{C}}$$

where C is the Curie–Weiss constant and T₀ is the Curie–Weiss temperature.

The diffuse-phase transition characteristic in the (1−x)KNNbS-xSrFNb ceramics is further studied by the exponential law:

$${\displaystyle \frac{1}{\epsilon }}-{\displaystyle \frac{1}{{\epsilon }_m}}={\displaystyle \frac{{(T-T_m)}^{\mathsf{\gamma }}}{C^{\prime }}}$$

where γ is the dispersion index and C′ is a constant. In general, when γ is 1, it indicates that the material is a normal ferroelectric, and when γ is 2, the material is a typical relaxor ferroelectric [49].

As shown in Figures S4 and S5, the dielectric response characteristics of 0.95KNNbS-0.05SrFNb ceramics sintered at different processes and (1−x)KNNbS-xSrFNb ceramics by TSS can be fitted by both Curie–Weiss law and exponential law, but all have some deviation, with the results summarized in Table 2 and Table 3. The C value of all samples has the order of 10⁶–10⁷ magnitude, it is significantly higher than the typical value for normal ferroelectrics (10⁵ magnitude), indicating a marked deviation from the Curie–Weiss law in the system. All γ values lie between 1.7 and 2, indicating a diffuse-phase transition with strong relaxor character [50].

Table 2. Summary of dielectric and relaxor-related parameters for 0.95KNNbS-0.05SrFNb ceramics sintered by CS and TSS at different temperatures.

Sintering Conditions	εr @RT	tan δ @RT	Tm (°C) @100 kHz	εm (@ Tm)	γ	C (°C)
1160	1136	0.0427	194	1704	1.872	1.64 × 107
1165	1305	0.0516	180	1758	1.923	1.94 × 107
1170	1146	0.0372	204	1940	1.777	1.02 × 107
1200–1125 6 h	1358	0.0285	195	2357	1.744	9.80 × 106
1200–1125 4 h	1264	0.0317	206	2729	1.887	2.20 × 107
1190–1125 4 h	1479	0.0411	200	2768	1.852	1.98 × 107

Table 3. Summary of dielectric and relaxor-related parameters for (1−x)KNNbS-xSrFNb ceramics with different SrFNb doping contents prepared by TSS.

Composition (x)	εr @RT	tan δ @RT	Tm (°C) @100 kHz	εm (@ Tm)	γ	C (°C)
0.01	613	0.0204	295	4401	1.700	3.29 × 106
0.03	845	0.0952	266	3756	1.908	7.83 × 106
0.05	1264	0.0317	206	2729	1.887	2.20 × 107
0.07

For the fixed-composition 0.95KNNbS-0.05SrFNb, the diffuseness exponent broadly follows density as the sintering condition varies. The CS sample at 1165 °C reaches the highest CS density with γ = 1.923, and the TSS 1200–1125 °C 4 h sample reaches the highest TSS density with γ = 1.887, together with a higher ε_m of 2729. Both phenomena indicate that enhanced densification and optimized microstructure effectively boost the dielectric response while maintaining strong relaxor nature. With the increase of SrFNb amount, the γ value presents a first-increasing-then-decreasing change characteristic, and a maximum γ value of 1.908 is obtained when x = 0.03, showing the strongest relaxation degree. This density–γ correlation applies only to the fixed-composition sintering conditions; in the composition series γ is governed mainly by B-site disorder and the phase boundary besides density. This evolution demonstrates that SrFNb doping progressively intensifies the phase transition diffusion and enhances relaxor behavior. γ and the loss dispersion follow the same composition trend as the phase evolution. The large γ, the frequency dispersion of ε_m and tan δ, and the broadened peak with PNR formation are characteristic of relaxor ferroelectrics. The single perovskite phase, high density and uniform grains rule out macroscopic chemical inhomogeneity, confirming the dispersion is intrinsic to PNRs rather than an ordinary diffuse transition [49].

Figure 5 presents the bipolar polarization-electric field (P-E) hysteresis loops with corresponding bipolar strain–electric field (S-E) curves, as well as unipolar S-E curves of (1−x)KNNbS-xSrFNb ceramics fabricated under different sintering conditions and with different compositions. The key ferroelectric parameters, namely remanent polarization (P_r) and coercive field (E_c), derived from the P-E loops are listed in Tables S3 and S4. For the fixed composition of 0.95KNNbS-0.05SrFNb, all samples sintered via various processes exhibit well-saturated P-E loops and typical butterfly-shaped bipolar S-E curves at room temperature, verifying the stable intrinsic ferroelectricity of the SrFNb-modified KNN-based system. As shown in Figure 5a and Table S3, the P_r value of samples prepared by TSS is higher than that of samples via CS, while the E_c value is generally lower than that of conventional sintering [51]. At the sintering temperature of 1200–1125 °C 4 h, P_r, E_c and d₃₃ all reach their respective extreme values, benefiting from the dense microstructure and uniform grain-size distribution induced by the TSS strategy. As the holding time increases, at 1200–1125 °C, the ceramic also exhibits excellent strain performance, the maximum strain is 0.064% and calculated inverse piezoelectric coefficient d₃₃* is 207 pm/V (Figure 5b). The TSS process reduces the average grain size from 0.35 to 0.32 μm together with higher density and improved ferroelectric properties; finer, uniform grains increase the grain-boundary fraction and homogenize the field, which favors domain switching [35].

Figure 5. 0.95KNNbS-0.05SrFNb ceramics sintered by CS and TSS at different temperatures: (a) bipolar P-E loops and S-E curves; (b) unipolar S-E curves; (1−x)KNNbS-xSrFNb ceramics with different SrFNb doping contents prepared by TSS: (c) bipolar P-E loops and S-E curves; (d) unipolar S-E curves.

Under the same TSS sintering process, the effect of SrFNb doping amount on the electrical properties of (1−x)KNNbS-xSrFNb ceramics can be obtained from Figure 5c,d and Table S4. P_r and E_c reach maximum values of 22.72 μC/cm² and 9.47 kV/cm at x = 0.03. Both P_r and E_c values first rise and then fall, mainly because the random A-site Sr²⁺ and B-site Fe³⁺/Nb⁵⁺ occupation increases chemical disorder. The heterovalent and differently sized ions create local charge and size fluctuations that break long-range ferroelectric order and stabilize polar nanoregions, enhancing the relaxor behavior [49,52,53]. The strain performance decreases with the increase of SrFNb doping content, the maximum strain is 0.063% and d₃₃* is 206 pm/V obtained at x = 0.01, followed by a decrease to 0.013% at x = 0.07. Correspondingly, d₃₃* decreases from 206 to 44 pm/V. The total strain consists of intrinsic converse-piezoelectric deformation, reversible domain-wall motion, irreversible non-180° switching and electrostriction, separable by comparing d₃₃ with d₃₃* = S_max/E_max, and by the negative strain and hysteresis. At x = 0.01–0.03, the butterfly loops with large negative strain and maximum d₃₃* are piezoelectric/switching dominated, while the phase-boundary x = 0.03 gives the largest d₃₃, K_p and P_r. At x = 0.05–0.07, PNRs replace macrodomains, the negative strain/hysteresis shrink and electrostriction grows; x = 0.07 is paraelectric at RT and shows the smallest strain, confirming a non-piezoelectric component at high x. Phase-boundary proximity therefore drives the piezoelectric-to-electrostrictive crossover [54].

Through fatigue resistance evaluation under 20 kV/cm alternating current poling (ACP) cycling (Figure 6), (1−x)KNNbS-xSrFNb’s fatigue resistant under cyclic loading can be confirmed. For the x = 0.01 and x = 0.03 ceramics, the P_r and E_c values exhibit a slight enhancement within the span of 10 electric field cycles. (The first cycle curve of x = 0.01 sample was measured after several days of storage at room temperature, so it appears somewhat abnormal due to the existence of CuO-induced acceptor-oxygen-vacancy defect dipoles. After several cycles, the curve returns to its normal symmetric shape since the defect dipoles were disrupted [55]. At x = 0.05, the hysteresis loops remain nearly unchanged after 10 cycling with negligible attenuation of saturation and P_r. While the x = 0.07 composition suffers the most significant polarization attenuation and remarkable shrinkage of the loop area, revealing the poorest fatigue resistance. This is mainly attributed to the high porosity and the increased leakage at high SrFNb content, which facilitate charge injection and destabilize the domains under cycling [14]. With respect to the influences of sintering processes on the fatigue endurance of 0.95KNNbS-0.05SrFNb ceramics (Figure S6), all specimens exhibit excellent fatigue resistance with well-preserved hysteresis loop characteristics, except for the sample fabricated via CS sintering at 1170 °C, which retains merely 66% of its initial remanent polarization after cyclic electrical loading [6]. The performance change is a combined microstructural and electrical effects. Higher density and finer, uniform grains reduce field-concentrating pores, charge injection and microcrack initiation, while Cu/Fe acceptor-oxygen-vacancy dipoles pin domain walls and stabilize the domain configuration. The severely degraded x = 0.07 and CS 1170 °C samples support this-polarization loss is largest where porosity and mobile defects are greatest. The enhanced fatigue resistance therefore originates from the synergy of reduced porosity, grain-size reduction and defect-mediated domain pinning.

Figure 6. Fatigue test of (1−x)KNNbS-xSrFNb ceramics with different SrFNb doping contents prepared by TSS after 10 cycles under 20 kV/cm at 10 Hz and room temperature: (a) x = 0.01; (b) x = 0.03; (c) x = 0.05; (d) x = 0.07.

Figure 7a,b display impedance and phase angle curves of the x = 0.01 and x = 0.03 samples. Both ceramics show perfect resonance–antiresonance behavior with the phase angle approaching 90° at the resonant frequency, confirming favorable piezoelectric activity after alternating current poling. The results of 0.95KNNbS-0.05SrFNb composition under different sintering conditions are shown in Figure S7.

Figure 7. Influence of ACP poling method on performance of (1−x)KNNbS-xSrFNb ceramics with different SrFNb doping contents prepared by TSS. Impedance and phase angle of (a) x = 0.01 and (b) x = 0.03 samples; (c) effects of SrFNb doping amounts on d₃₃, K_p, and Q_m of (1−x)KNNbS-xSrFNb ceramics; (d) comparison of comprehensive properties of x = 0.01 and x = 0.03 ceramics.

Figure 7c shows composition dependence of the d₃₃, Q_m and K_p values of (1−x)KNNbS-xSrFNb ceramics, and Table S3 shows effects of sintering conditions on electrical properties of the 0.95KNNbS-0.05SrFNb ceramics. The optimal comprehensive performance (d₃₃ = 42 pC/N, K_p = 0.128) is achieved in the 0.95KNNbS-0.05SrFNb sample sintered at 1200–1125 °C 4 h. The d₃₃ value demonstrates a progressive enhancement with increasing the SrFNb content, attaining a peak value of 133 pC/N at the composition of x = 0.03 before undergoing a precipitous decline. Simultaneously, the K_p value achieves its maximum value of 0.285 at this critical doping level [33]. Such results can be attributed to that the alternating electric field applied in the ACP process can effectively drive the gradual reorientation of ferroelectric domains and mitigate the pinning effect of defect dipoles [49]. In contrast, the Q_m value reaches a maximum of 329 at x = 0.01 and decreases monotonously with elevating SrFNb doping level. This trend is in good agreement with the dielectric results. The sharp, low-loss ferroelectric peak at x = 0.01 corresponds to minimal energy dissipation, which in turn gives rise to the highest Q_m. The high Q_m at low SrFNb content is governed by acceptor hardening rather than by the perovskite composition itself, and B-site Cu²⁺ (and a small amount of excess Fe³⁺) creates oxygen-vacancy-compensated defect dipoles that establish a symmetry-conforming short-range order and an internal bias field, pinning domain walls and suppressing their vibration under resonance, which minimizes mechanical loss. Increasing SrFNb does not add acceptor charge but introduces B-site charge disorder and polar nanoregions, and moves the phase boundary to room temperature, lowering the domain-wall energy barrier and diluting the Cu²⁺ pinning, so the material softens and Q_m decreases [43].

As shown in Figure 7d, a radar chart compares the key electrical parameters of the x = 0.01 and x = 0.03 samples. Despite a modest 30% decrease in d₃₃, the x = 0.01 sample achieves a threefold enhancement in Q_m. These two compositions can thus be categorized as relatively hard (x = 0.01) and relatively soft (x = 0.03) KNN-based piezoceramics, respectively, offering flexibility for diverse application scenarios. With further SrFNb addition, x = 0.05 and x = 0.07 fall outside the hard/soft piezoelectric classification. At x = 0.05, d₃₃, P_r and K_p drop sharply while Q_m remains moderate, not a distinctly hard or soft piezoceramic. At x = 0.07, T_m falls below room temperature, and the ceramic presents paraelectric and is essentially non-piezoelectric at room temperature [28].

4. Conclusions

Through composition design and using two types of fabrication processes, the enhanced densified (1−x)KNNbS-xSrFNb ceramics with pure phase perovskite structure were prepared under different sintering conditions, and the effects of SrFNb doping amount and sintering conditions were studied systematically. The XRD results demonstrate the presence of multiphase coexistence in the ceramics, with x = 0.01–0.07 samples located at the PPBs. Increasing SrFNb significantly reduces the average grain size from 0.6 μm to 0.3 μm. Furthermore, TSS decouples densification from grain growth, enabling the x = 0.05 ceramic to achieve the maximum relative density of 94.51% with only a slight grain refinement from 0.35 μm to 0.32 μm. Samples made with two-step sintering have better piezoelectric and ferroelectric properties than those made with conventional sintering, with the 1200–1125 °C 4 h sample reaching the highest d₃₃ of about 42 pC/N. The (1−x)KNNbS-xSrFNb ceramics approach relaxor ferroelectrics with apparent diffusion phase transition characteristic; T_m gradually decreases and relaxation factor γ increases first and then decreases with the elevation of SrFNb doping amount. By adjusting the composition, the x = 0.01 sample has the maximum Q_m = 329 and 1/tan δ = 50, and the x = 0.03 sample has the maximum d₃₃ = 133 pC/N and K_p = 0.285, corresponding to hard ceramics and soft ceramics respectively. The TSS process can increase densification, and improve dielectric and piezoelectric properties, and the (1−x)KNNbS-xSrFNb ceramics provide flexibility for diverse application scenarios.