Improvements in piezoelectric and energy harvesting properties with a slight change in depolarization temperature in modified BNKT ceramics by a simple technique

Abstract

For many BNT-based ceramics, an attempt to increase the piezoelectric properties usually results in a decrease in depolarization temperature (T_d). This trend limits the applications of the materials. Many previous experiments have used different methods to enhance the piezoelectric properties and improve the T_d characteristic. In this study, we demonstrated a simple technique (thermal annealing) to enhance the piezoelectric properties with a very slight decrease in T_d by ∼2 °C for a modified BNKT ceramic (BNKT doped with ZnO). Other phase transition characteristic temperatures of the studied ceramics were also slightly changed. The optimum dielectric (ε_r = 651, tan δ = 0.0503, T_F–R = 167.38 °C, T_m = 305.41 °C, ε_max = 5551, T_B = 367.15 °C, T_d = 155.98 °C, and γ = 1.43), ferroelectric (P_max = 41.28 μC cm⁻², P_r = 35.85 μC cm⁻², E_c = 42.60 kV cm⁻¹ and R_sq = 1.42), piezoelectric (d₃₃ = 198 pC N⁻¹, k_p = 0.598, and g₃₃ = 34.35 × 10⁻³ Vm N⁻¹), and energy harvesting (FoM = 6.80 pm² N⁻¹) were obtained for the 8 h annealed ceramic. Furthermore, higher energy harvesting properties (which were 32% higher than that of the unannealed ceramic) were obtained after employing this technique.

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1 Introduction

Piezoelectric materials have been extensively designed and applied in many industrial fields, for example in such items as sensors, micro-displacement devices, brakes, sensitive materials, and other components, due to their ability to cause a mutual conversion between mechanical and electrical energy.¹ The development of piezoelectric materials with high energy conversion efficiency is of decisive importance for the requirements of advanced energy harvesting (EH) devices toward miniaturization and integration.² Lead titanate zirconate (PZT) ceramics are the most widely used energy harvesting materials due to their excellent piezoelectric properties,³ i.e., high mechanical quality factor (Q_m), high piezoelectric constant (d₃₃), and large planar electromechanical coupling factor (k_p).⁴ However, lead-based compounds pose a serious environmental threat, and, therefore, efforts have been made to look for cleaner alternatives.^1,3

Recent reports have identified many possible lead-free candidates based on barium titanate (BaTiO₃, BT), potassium sodium niobates (K_0.5Na_0.5NbO₃, KNN), bismuth sodium titanates (Bi_0.5Na_0.5TiO₃, BNT), bismuth potassium titanates (Bi_0.5K_0.5TiO₃, BKT), and bismuth layered ferroelectrics.^2,5 Among them, BNT has been found to be a possible energy storage material due to its high spontaneous polarization (P_m) exceeding 40 μC cm⁻², which results from the hybridization of the Bi 6p and O 2p orbitals.⁶ Nevertheless, a pure BNT ceramic is known to be to be sintered with difficulty, and it also has other issues, such as beginning polarized with just as much complication, not to mention its having a high coercive field (E_c), high conductivity, and poor temperature stability.⁷ Therefore, there is an urgent need for researchers to approach to improve the performance of the BNT ceramic. Numerous approaches, such as the establishment of the morphotropic phase boundaries (MPB), acceptor/donor dopants, compositional tuning, and improvement of the fabrication process conditions, have been proposed for the property optimization of the BNT piezoelectric materials.⁸ Besides BNT, bismuth sodium potassium titanate or Bi_0.5(Na_1−xK_x)_0.5TiO₃ (BNKT) lead-free piezoelectric ceramic is also a good candidate for the replacement of toxic lead compounds for energy harvesting applications. For the Bi_0.5(Na_1−xK_x)_0.5TiO₃ solid solution, Na⁺ is partially substituted by K⁺ on the A-site of BNT,² and it is known that better piezoelectric and/or strain properties at the MPB region between BNT rhombohedral and BKT tetragonal phases near x = 0.16–0.20 can be achieved.^9–11 The dielectric constant of the BNKT ceramic was reported to be 1030.¹⁰ The good piezoelectric coefficients (d₃₃ = 151 pC N⁻¹, d₃₁ = 46.9 pC N⁻¹) were obtained at the optimal composition of x = 0.20.^10,12

It is known that the energy harvesting performances of piezoelectric materials are closely related to their piezoelectric coefficient (d₃₃ α εP_r).¹³ Thus, a higher remanent polarization (P_r) is desirable for achieving better performances of piezoelectric energy harvesting devices.¹⁴ In order to improve the ferroelectric and piezoelectric properties of the BNKT ceramic to achieve excellent energy harvesting devices, it has been modified with other materials, such as ZnO. The ZnO particle has been widely used as a sintering aid in many dielectric and piezoelectric ceramics.¹⁵ As demonstrated in many studies, the addition of ZnO could improve densification for a wide range of dielectric and ferroelectric materials.^15–18 For example, Promsawat et al.¹⁵ reported that the ZnO additive helped to facilitate the densification process and thereby improved the electrical properties of the PMNT ceramics. Lee et al.¹⁶ found that the addition of ZnO improved the piezoelectric properties of the Bi_0.5Na_0.5TiO₃ (BNT) ceramics. The effect of ZnO addition on the electrical properties of the (K_0.44Na_0.52Li_0.04)(Nb_0.86Ta_0.10Sb_0.04)O₃ or KNL–NTS ceramics was investigated by Marcos et al.¹⁷ They also reported that ZnO doping produced an increase in the ferroelectric performance of the KNL–NTS ceramics. Zhang et al.¹⁸ also found that the addition of ZnO could enhance both the ferroelectric and piezoelectric properties of the 0.94Bi_0.5Na_0.5TiO₃–0.06BaTiO₃ or BNT–6BT ceramics. The maximum P_r and low-field d₃₃ values were observed for the BNT–6BT:0.04ZnO ceramics.

For piezoelectric applications, the depolarization temperature (T_d) of BNT-based ceramics is an important factor.^18,19 Many authors have suggested that piezoceramics with a high T_d can be used in a wider range of temperatures because they are more stable. Therefore, several authors have focused on variables that relate to or influence T_d.^20,21 Numerous methods, including doping, the formation of solid solutions, the formation of composites, and the modulation of crystallographic orientation in texturing ceramics, have been found to affect the T_d value.^22–28 However, it should be noted that an effort to raise T_d often leads to a drop in the value of the piezoelectric d₃₃. This tendency restricts the use of the materials in many applications. Therefore, the work to improve the T_d and piezoelectric characteristics of materials based on BNT is still challenging and worthy of continuing research.

It has been proposed that annealing gives several advantages for ferroelectric and piezoelectric characteristics, including those of lead-based piezoelectric ceramics and, more recently, lead-free piezoelectric ceramics.^29,30 Xu et al.³¹ reported that annealing treatment improved the piezoelectric properties of the 0.95(Bi_0.5Na_0.5)_0.97(Li_0.5Nd_0.5)_0.03TiO₃–0.05BaTiO₃ or BNTLN0.03–BT5 ceramics. It also induced subtle structural changes. The microstructures of annealed samples become homogeneous, which leads to the disappearance of the Maxwell–Wagner relaxor. The optimal piezoelectric properties of d₃₃ = 148 pC N⁻¹ and k_p = 0.33 have been obtained by annealing at 900 °C. Wang et al.³² also reported that good ferroelectric and piezoelectric properties were obtained in the Na_0.5K_0.5NbO₃ ceramics after annealing at 900 °C for 4 h dwell time in an air atmosphere. Since annealing has several benefits for the ferroelectric characteristics, it is anticipated that this technique should have a positive effect on the T_d and other properties such as piezoelectric and energy harvesting properties. In the present investigation, the annealing process was then utilized for the modified BNKT ceramics (BNKT added with ZnO). The effect of thermal annealing on phase evolution, microstructural, dielectric, T_d, ferroelectric, piezoelectric, and energy harvesting properties was investigated and discussed in detail.

2 Experimental

The lead-free ceramic with the composition Bi_0.5(Na_0.84K_0.16)_0.5TiO₃ or BNKT was synthesized by a solid-state reaction method. The starting materials used in this study were the reagent-grade powders of Bi₂O₃, Na₂CO₃, K₂CO₃, TiO₂, and ZnO nanoparticles. All carbonate powders were first dried at 120 °C for 24 h to remove any moisture. The carbonate and high-purity oxide starting materials were weighed based on a stoichiometric formula of Bi_0.5(Na_0.84K_0.16)_0.5TiO₃ and then mixed and ball milled in a 99.9% ethanol solution for 24 h. The slurries were dried in an oven for 24 h at a temperature of 120 °C. Dried BNKT powder was calcined in a closed alumina crucible at 900 °C for 2 h with a heating/cooling rate of 5 °C min⁻¹. After calcination, the ZnO nanoparticles (less than 100 nm) were added into the calcined BNKT powder and then milled again in ethanol for 24 h with the formula of Bi_0.5(Na_0.84K_0.16)_0.5TiO₃/0.01ZnO referred to as the BNKT/0.01ZnO. After drying and sieving, the mixed powders were granulated by adding a few drops of 4 wt% PVA as a binder and then pressed into disks with a diameter of 10 mm and a thickness of about 1.3 mm. The pellets were then preheated in the air at 500 °C for 1 h to remove the organic binder and then sintered at 1125 °C for 2 h dwell time with a heating/cooling rate of 5 °C min⁻¹ in closed alumina crucibles. To minimize the loss of the volatile elements, the green pellets were embedded in a powder of the same composition. In order to further improve the quality of the ceramics, the sintered ceramics were annealed at 950 °C with a heating/cooling rate of 5 °C min⁻¹ and various annealing times of 0, 4, 8, and 12 h in an air atmosphere, respectively.

The bulk density of all ceramics was determined using Archimedes' method. An X-ray diffractometer (XRD, PANalytical, X′ Pert ProMPD) was used to identify the phase of all sintered ceramics. The Raman spectra were carried out on the polished sintered pellets and recorded by Raman spectroscopy (T6400 JY, Horiba Jobin Yvon). The surface morphologies of the sintered ceramics were observed using a field-emission scanning electron microscope (FE-SEM, JEOL JSM-6335F). The average grain size of each sample was determined by a mean linear interception method from the SEM micrographs. For electrical measurements, all samples were polished to 1 mm thickness, and high-temperature silver paste was fired on both sides at 700 °C for 30 min in order to form the electrodes. Temperature dependence of dielectric properties was also carried out using a 4192A LCR-meter connected to a high-temperature furnace from room temperature (RT) to 500 °C with various frequency ranges of 1–1000 kHz. A radiant precision ferroelectric tester was used to investigate the ferroelectric properties at both room temperature (RT) and high temperatures (HT) of 25–150 °C. Various AC electric fields of 30–65 kV cm⁻¹ at a frequency of 0.1 Hz were utilized in the hysteresis measurement. For piezoelectric characterization, the samples were poled in silicone oil under a DC electric field of 5 kV mm⁻¹ for 15 min at RT. The piezoelectric coefficient (d₃₃) was measured after aging the ceramics for at least 24 h using a d₃₃ meter (KCF technologies, S5865) at a frequency of 50 Hz. The planar electromechanical coupling factor (k_p) was measured by the resonance and anti-resonance technique using an impedance analyzer (HP 4284A). The piezoelectric voltage constant (g₃₃) and the off-resonance figure of merit (FoM) for energy harvesting were also calculated in this study.

3 Results and discussion

3.1 Densification and phase evolution

In this experiment, the density as a function of annealing times (0–12 h) of the BNKT/0.01ZnO ceramics was determined, and the values are listed in Table 1. The density increased from 5.81 g cm⁻³ for the unannealed ceramic to the maximum value of 5.86 g cm⁻³ for the 8 h annealed ceramic, and then slightly decreased to 5.84 g cm⁻³ for the 12 h annealed ceramic. The annealing process and ZnO additives can help to improve the densification of all ceramics. However, the slightly lower density value after 12 h of annealing may be caused by the high volatilization of some components for overtime annealing,³² such as Bi and K. The high-density sample was responsible for the improved electrical characteristics,^29,33 as shown by the results in the next section.

Table 1 Physical, microstructure and mechanical properties of the BNKT/0.01ZnO ceramics annealed at 950 °C with different annealing times

Annealing time (h)	Density (g cm^−3)	Phase	c/a	c/a − 1	FWHM of (110) (°)	Crystallite size (nm)	Average grain size (μm)
0	5.81	R + T	1.0037	0.0037	0.66	12.54	1.44 ± 0.21
4	5.82	R + T	1.0049	0.0049	0.60	13.80	1.59 ± 0.25
8	5.86	R + T	1.0066	0.0066	0.57	14.52	1.98 ± 0.23
12	5.84	R + T	1.0090	0.0090	0.55	15.05	2.28 ± 0.19

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In order to check the phase-purity and structural parameters, all ceramics were investigated by the X-ray diffraction technique at RT,³³ and the XRD pattern of the BNKT/0.01ZnO ceramics annealed at 950 °C with different annealing times, where 2θ = 20–70° is shown in Fig. 1(a). It is noted that all annealed ceramics exhibited a single perovskite structure without any detectable impurity peaks, indicating that ZnO had diffused into the BNKT lattice to form a complete solid solution. The results of a more detailed XRD analysis performed in a narrow range of 2θ = 39–41° and 2θ = 44–48° are shown in Fig. 1(b) and (c), respectively. Based on peak profile fitting, the unannealed ceramic exhibited the morphotropic phase boundary (MPB) structure, consisting of rhombohedral and tetragonal phases.

Fig. 1 X-ray diffraction patterns of the BNKT/0.01ZnO ceramics annealed at 950 °C with different annealing times, where (a) 2θ = 20–70° (b) 2θ = 39–41°, and (c) 2θ = 44–48°.

This was evidenced by a slight splitting of (111)_R/(11̄1)_R rhombohedral peaks at 2θ ∼ 40° and (002)_T/(200)_T tetragonal peaks at 2θ ∼ 46.5°. This result is also consistent with the work done by Sasaki et al.¹⁰ on the (1 − y)BNT–yBKT ceramics, who found a relatively broad MPB region in the range of y = 0.16–0.20 between BNT rhombohedral and BKT tetragonal ceramics. This result also agrees with the previous experiments.^12,34,35 However, the weak splitting of the (200) peak indicates the rhombohedral rich phase. It should be noted that with a further increase in the annealing time up to 8–12 h, XRD displayed more splitting of (111)_R/(11̄1)_R rhombohedral peaks and (002)_T/(200)_T tetragonal peaks. The phase transition from the mixed rhombohedral–tetragonal to a more tetragonal phase portion was observed when the annealing time was increased. To check this, the c/a − 1 value (where c/a is tetragonally) was calculated (Table 1). The c/a − 1 value increased as the annealing time increased, confirming the increase in the tetragonal phase.

The full width at half maximum (FWHM) values using a certain XRD peak for all ceramics were determined in this investigation.^36,37 In the present work, the FWHM value was calculated from the (110) reflection main peak in the X-ray diffraction pattern, and the values are also included in Table 1. The FWHM of the (110) peaks of the annealed ceramics (4–12 h) was much smaller than that of the unannealed ceramics (0 h), suggesting that annealing improved the degree of crystallinity of the samples. The crystallite size (D) was also used to check the degree of crystallinity of the ceramics. In the current work, the X-ray peak broadening (110) reflection was selected for this proposed, and the calculation was performed based on the Debye–Scherrer formula:³⁷

where λ is taken to be 0.15418 nm as the X-ray source is Cu-Kα, B is the full width at half maximum (FWHM), k is a fixed number 0.9, and θ is the Bragg's angle.^38–43 It can be seen that crystallite size increased from 12.54 nm for the unannealed ceramic to the maximum value of 15.05 nm for the 12 h annealed ceramic. With increasing annealing time, the FWHM of the (110) peak became narrower and the crystallite size increased, indicating an improvement in the degree of crystallinity of the annealed ceramics.⁴⁰ Furthermore, the lower FWHM value (with increasing annealing time) also indicated a better homogeneous chemical distribution in the ceramics.^44,45 In addition, it was proposed that the increase in crystallite size could be accompanied by an improvement in the ceramic's electrical properties.^41,43

To further analyze the evolution of the crystal structure with varying annealing times, Raman spectra were measured in the range of 100–1200 cm⁻¹, which are now presented in Fig. 2. Obviously, four main regions could be detected in the spectrum at room temperature (RT), which is nearly identical to those previously reported data of BNT-based ceramics:^46–50 (1) the mode located below 200 cm⁻¹ associated with the vibration of perovskite A-site, (2) the around 300 cm⁻¹ modes should be related to Ti–O vibrations, (3) the modes approximately 450–650 cm⁻¹ related to TiO₆-octahedra vibration, and (4) the modes over 700 cm⁻¹ related to the A₁ (longitudinal optical) and E (longitudinal optical) overlapping bands.⁴⁷ The Raman peaks at the mode located below 200 cm⁻¹ slightly shifted towards the lower wavenumber for the 8–12 h ceramics. This may be linked with the volatilization of A-site ions for a longer annealing time. The broader and splitting peak of the mode around 300 cm⁻¹ and 450–650 cm⁻¹ was observed with increasing annealing time which corresponds to a higher degree of tetragonally. This result agrees well with previous studies.^46,48 Overall, spectra recorded for the studied ceramics are in good agreement with that of the previously reported for other BNT-based ceramics which had a coexisted phase structure between rhombohedral (R3c) and tetragonal (P4bm) phases.⁵¹ This Raman result also agrees well with the XRD analysis.

Fig. 2 Raman spectra at room temperature of the BNKT/0.01ZnO ceramics annealed at 950 °C with different annealing times.

3.2 Microstructure analysis

Microstructural development during the annealing process was investigated by scanning electron microscopy (SEM). The FE-SEM micrographs of sintered surfaces of the BNKT/0.01ZnO ceramics annealed at 950 °C with different annealing times are shown in Fig. 3. The average grain size of each sample is given in Table 1. It is evident that all ceramics were very dense, smooth, and crack free. The grain was well-crystallized with clear grain boundaries and contained a cubic-like shape. The SEM micrographs clearly showed that the annealing time had an influence on the microstructure of the BNKT/0.01ZnO ceramics. The average grain size increased with increasing annealing time. The average grain size of the unannealed ceramic was found to be 1.44 ± 0.21 μm. The average grain size initially increased with the annealing time and reached a maximum value of 2.28 ± 0.19 μm for the 12 h annealed ceramic. Similar behavior was also reported in a recent investigation.⁵² As the annealing time increased, the grains grew and the average grain size increased, whereas the number and size of the pores decreased. In the current study, a line intercept method was used to find out the average grain size. It should be noted that the percentage increase in grain size for this study is 44% after 12 h of annealing. Fig. 4(a) displays plots of FWHM versus crystallite size and grain size. It was found that the crystallite size had a linearly decreasing trend with FWHM, while grain size had an exponential decay with FWHM. A relation between crystallite size and grain size is also presented in the inset of Fig. 4(a). As crystallite size increased, grain size increased exponentially. Therefore, the obtained data indicated that annealing enhanced both crystallite size and grain size. In the present experiment, the grain size increased exponentially with increasing annealing time, as seen in Fig. 4(b). Normal grain growth can be explained by the phenomenological kinetic grain growth equation, which is written as:⁴where G is the average grain size at the time t, n is the kinetic grain growth exponent, K₀ is the constant, Q is the apparent activation energy, R is the gas constant, and T is the absolute temperature. It was noted from the equation that the average grain size was an exponential function of the annealing time (t) (Fig. 4(b)). To compare the experimental result with the kinetic equation better, log G is plotted versus log t, and there generally exists a reasonably good linear relationship between log G and log t (Fig. 4(c)), which is consistent with eqn (2).⁴ Based on Fig. 4(b), a reasonably good linear relationship between log G and log t was observed, where the slope is 1/n. Generally, a small n value indicates a large grain growth rate, which can be shown by differentiating eqn (2). The n value for this study was found to be 3.05. Therefore, the small n value calculation indicated that the annealing produced a moderate grain growth rate^53,54 with increasing annealing time. The relationships between the grain size and the electrical properties (i.e., dielectric, ferroelectric, and piezoelectric) will be discussed in the next sections. As is known, grain size has a significant influence on the dielectric characteristics and polarization of piezoelectric materials.^9,55

Fig. 3 The FE-SEM micrographs with as sintered surfaces of the BNKT/0.01ZnO ceramics annealed at 950 °C with different annealing times, where (a) 0 h, (b) 4 h, (c) 8 h, and (d) 12 h.

Fig. 4 Plots of (a) FWHM versus grain size and crystallite size (inset shows a relation between grain size and crystallite size), (b) grain size as a function of annealing time, and (c) log G as a function of log t.

3.3 Dielectric properties

The room temperature dielectric constant (ε_r) and dielectric loss (tan δ) at a frequency of 1 kHz are listed in Table 2. The ε_r of the un-annealed ceramic was found to be 501 with tan δ of 0.0425. The ε_r initially increased with the annealing time and reached a maximum value of 651 for the 8 h annealed ceramic, and then slightly decreased to 529 for the 12 h annealed ceramic. The density is believed to be an important factor in the higher electrical properties of the samples,³³ i.e., higher density resulted in higher dielectric properties.

Table 2 Dielectric properties obtained at HT (25–500 °C) and a frequency of 1 kHz of the BNKT/0.01ZnO ceramics annealed at 950 °C with different annealing times

Annealing time (h)	εr	tan δ^a	TF–R (°C)	Tm (°C)	εmax	tan δ^b	TB (°C)	ΔT = TB − Tm (°C)	γ	Td (°C)
a Dielectric loss (tan δ) measured at T = RT and a frequency of 1 kHz.b Dielectric loss (tan δ) measured at T = Tm and a frequency of 1 kHz.
0	501	0.0425	168.25	307.18	4836	0.0334	369.44	62.26	1.48	157.22
4	536	0.0471	167.60	306.20	5437	0.0363	368.33	62.13	1.46	156.17
8	651	0.0503	167.38	305.41	5551	0.0387	367.15	61.74	1.43	155.98
12	529	0.0443	166.41	305.24	5501	0.0384	366.65	61.41	1.39	155.89

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Temperature dependence on the dielectric constant (ε_r) and dielectric loss (tan δ) of the poled BNKT/0.01ZnO ceramics annealed at 950 °C with different annealing times, and measurements at various frequencies from 1–1000 kHz are shown in Fig. 5. The related dielectric properties are also summarized in Table 2. There were two dielectric anomalous peaks in the ε_r–T plot. The first dielectric anomaly peak (shoulder peak), characterized by a large dielectric peak and noticeable frequency dispersion, was noted at a temperature below 200 °C. This temperature corresponds to T_s, indicating the relaxor ferroelectrics which are usually caused by the thermal evolutions of discrete polar nanoregions.⁶ The secondary anomaly broadened peak, at T_m, indicates the maximum dielectric constant (ε_m) in ε_r vs. T plots. The two dielectric anomalous peaks on the dielectric permittivity curves have been commonly reported in BNT-based systems.^56–58 Based on Fig. 6(a), the unannealed ceramic had the ε_max of 4836. The ε_max increased with the annealing time and reached a maximum value of 5551 for the 8 h annealed ceramic. At temperature ≥150 °C, there was a dispersion in tan δ value with frequency. However, the degree of dispersion was lower than that reported in other lead-free materials such as the (Bi_0.5Na_0.5)TiO₃–BaTiO₃ system.³³ From Fig. 5, the tan δ value at T_m for all ceramics was in the range 0.03–0.04, which is acceptable for a characteristic of capacitors at a high temperature.

Fig. 5 Temperature dependence on dielectric constant (ε_r) and dielectric loss (tan δ) of the poled BNKT/0.01ZnO ceramics annealed at 950 °C with different annealing times, measurement at various frequencies from 1–1000 kHz, where (a) 0 h, (b) 4 h, (c) 8 h, and (d) 12 h.

Fig. 6 Plot of (a) ε_max as a function of annealing time (inset: the γ value as various annealing times), and (b) T_m, T_B, and T_F–R values as a function of annealing time.

The reasons for the observed increase in the dielectric characteristics (by annealing) are complex due to the possibility of it being affected by many factors. Xia and Yao⁵⁹ suggested that the observed increases in dielectric characteristics for Pb(Zn_1/3Nb_2/3)O₃ (by annealing) are mostly attributable to many factors: (1) grain size change, (2) density change, (3) internal stress release, (4) a change in the content of the secondary phase, (5) the grain boundary layer, (6) the defect, (7) domain wall motion, and (8) a change in the order degree of B-site ions.⁵⁹ However, it should be noted that the effect of grain size can be linked to a variety of factors, such as domain wall motion, internal stress release, and grain boundary layer characteristics. For the grain size effect, Mudinepalli et al.⁶⁰ investigated the properties of BT based ceramics (Ba_0.8Sr_0.2TiO₃) and proposed that the dielectric constant is affected by domain population and domain wall mobility. They also proposed that a uniform grain size (big grains) can reduce internal stress, making it easy and regular for the domain walls to move, which raises the dielectric constant.⁶⁰ Zhao et al.⁶¹ reported that the critical grain size for the disappearance of ferroelectricity in BT ceramics is 10–30 nm. Furthermore, the strong broadening in the permittivity curve of their fine grain ceramics was explained by the size effect and the effect of a low-permittivity non-ferroelectric layer at the grain boundary. These effects depend on the grain size.^15,61

It is known that piezoceramics with their composition near the MPB composition often present high electrical properties such as high dielectric and piezoelectric properties. This is due to the formation of a mixture phase such as that of the rhombohedral and tetragonal phases which have a larger number of reorientable polarization directions. Therefore, the improvement in the dielectric constant of the 8 h annealed ceramic in the present study may be attributed to the formation of the mixture phase between rhombohedral and tetragonal with an optimal fraction that has better optimal properties. Furthermore, the increase in grain size, degree of composition homogeneity, and density also contributed to the improvement. In addition, it should be noted that the studied was added with BT, and BT ceramics need a high sintering temperature (as compared to BNT ceramics) to achieve the best combination of density and properties. Thus, annealing can help optimize the properties of the ceramics. However, the change in the amount of the secondary phase has less effect since the studied ceramics presented no secondary phase. For the ceramics annealed at 12 h, the ε_max slightly decreased to 5501. This result may be linked to the volatilization of some components for a longer annealing time (i.e., Bi and K).^30,32 This can be linked with a slight decrease in density and a slight decrease in the dielectric constant of this ceramic.

3.4 Phase transition behavior

For phase transition temperatures, the T_m value was corrected from the dielectric data as presented in the previous section. The T_m value slightly shifted down by ∼2 °C with increasing annealing time up to 12 h (Fig. 6(b) and Table 2). The Burn's temperature (T_B) value was also evaluated for the current investigation. Normally, at high temperatures, relaxors exist in a nonpolar paraelectric phase analogous to the ferroelectric paraelectric phase. However, as the temperature drops below the Burns temperature (T_B), they undergo a transformation into an ergodic relaxor (ER) state. This temperature indicates the start of the polarization process in relaxors.⁶² To determine the T_B, there are many techniques, such as the refractive index,^62,63 electrostrictive strain,⁶⁴ or deviation from the Curie–Weiss behavior.⁶² In the present investigation, the T_B was collected from the dielectric constant that starts to deviate from the Curie–Weiss law.⁶⁵ The plot of the inverse dielectric permittivity (1/ε_r) as a function of temperature at 1 kHz that was used to determine the T_B values is shown in the supplementary information in Fig. S1.† Based on Fig. 6(b) and Table 2, the T_B also slightly decreased from 369 °C for the unannealed ceramic to 366 °C for the 12 h annealed ceramic (i.e. a decrease by 3 °C). In addition, the deviation from the Curie–Weiss law can be depicted by ΔT (degree of deviation) as follows: ΔT = T_B − T_m.⁶⁶ The calculated values of ΔT as a function of annealing time are also listed in Table 2. The ΔT values were 62 to 61 °C, which indicated that the degree of diffuse phase transition is moderate. For 12 h annealing, the ΔT decreased by 1 °C, implying that the annealing time had less effect on the degree of deviation for the studied ceramics.⁶⁷

To further confirm the diffuseness of phase transition, the modified Curie–Weiss law is used, which is given in the following equation:^{6,62,65,68,69}

where γ is the degree of diffuseness, C′ is Curie-like constant, T_m is the temperature of the maximum dielectric constant, ε_r is the dielectric constant, and ε_m is the maximum dielectric constant at T_m. The value of γ can be calculated from the slope of the fitting curves.⁶ A higher γ value indicates a stronger degree of diffuse phase transition. The slope of the fitting curve of ln(1/ε_r − 1/ε_m) vs. ln(T − T_m) according to eqn (3) is used to determine the γ value. A linear relationship is observed for all compositions.⁷⁰ According to the γ value in Table 2 and the inset of Fig. 6(a), the γ value shows a slight change from 1.48 for the unannealed ceramic to 1.39 for the 12 h annealed ceramic. Thus, the annealing did not affect the diffuse phase transition too much.

3.5 Depolarization temperature (T_d)

To determine the T_d value, many techniques have been proposed.⁷¹ In the current study, the thermally stimulated depolarization current (TSDC) technique was employed. Plots of the current density–temperature (J–T) from the TSDC technique of the BNKT/0.01ZnO ceramics annealed at 950 °C with different annealing times are shown in Fig. 7. The T_d value is also summarized in Table 2. It was found that the annealing time had no significant effect on the change of the T_d value since the T_d was slightly shifted down from 157 °C for the unannealed ceramic to 156 °C for the 12 h annealed ceramic. To confirm the trend of the value, the T_F–R value was determined at a discontinuous change in dielectric loss (a small sharp peak at temperature ≤150 °C) in dielectric temperature spectra of the poled ceramics (Table 2). This temperature implies ferroelectric-relaxor transition upon heating.⁵⁶ The T_F–R value decreased from 168 to 166 °C after annealing for 12 h (i.e. a decrease of 2 °C). To double check the TSDC result, another different technique was performed. For this purpose, a measurement of the electromechanical coupling coefficient (k_p) was carried out at a range of temperatures.^72,73 The resulting shifting T_d value is shown in the ESI (Fig. S2†). It was found that the T_d value slightly decreased by 2 °C after annealing for 12 h. This result is consistent with the TDSC result.

Fig. 7 Plots current density–temperature (J–T) from the TSDC technique of the BNKT/0.01ZnO ceramics annealed at 950 °C with different annealing times, where (a) 0 h, (b) 4 h, (c) 8 h, and (d) 12 h.

To explain the shift in T_d value, numerous hypotheses and models have been proposed, such as the ion doping model, the charge compensation model, and the stress field model. For the ion doping model, several authors have proposed that some dopant ions can diffuse into the host lattice during processing, hence promoting a more stable ferroelectric phase and causing the T_d value to increase.^19,74–77 Mahajan et al.⁷⁵ also proposed that thermal depolarization behavior is considered to be strongly connected to the rhombohedral–tetragonal phase temperature. Li et al.⁷⁶ found that the direct doping of Zn²⁺ into 0.94BNT–0.06BT may delay the thermal depolarization produced by the reformation of a long-range ferroelectric order due to the high polarizability of the Zn ion. This would cause a large dipole moment of the BO₆ octahedra, enhance the coherence of neighboring dipoles, and inhibit the ferroelectric-relaxor transition. However, the diffusion of dopant ions can have a negative effect, i.e., it can cause composition and charge disorder, hence destabilizing the ferroelectric ordering in the samples. Some composites consisting of piezoelectric and semiconductor phases, such as the 0.94Bi_0.5Na_0.5TiO₃–0.06BaTiO₃/xZnO (BNT–6BT/xZnO) composites, for which ZnO is the semiconductor phase, were suggested using such a charge compensation model.¹⁸ In this case, the application of an external electric field causes a redistribution of the charges in the semiconductor ZnO at the interface between ZnO and BNT–BT. This provides a local electric field to compensate for the ferroelectric depolarization field when the external field is removed, hence stabilizing ferroelectric domains in composites.¹⁸

The stress field model was proposed for many studies on BNT-based ceramics, adding ZnO.^75,78 For this model, it is believed that the thermal deviatoric stresses in a composite are caused by the difference in the coefficients of thermal expansion between ZnO and BNT–BT. This helps to stabilize the ferroelectric phase and broaden the temperature range of depolarization. This model has also been used to explain the increasing trend of T_d in many composites such as Bi_0.5(Na_0.8K_0.2)_0.5TiO₃:Al₂O₃ (BNKT:Al₂O₃).²⁷ The creation of oxygen vacancies, as reported in many experiments, can raise the T_d value, due to the domain walls in the grains of the ceramics being clamped. However, this is generally accompanied by a decline in piezoelectric properties.¹⁹ Doping B₂O₃ (as an interstitial dopant) into BNT–BT ceramics can increase the T_d value. This was proposed to be due to the ability of stress generated from doping to stabilize the ferroelectric phase, thus, improving the T_d value.¹⁹ Thomas⁷⁹ proposed that the stability of a ferroelectric domain may be reduced if the coupling reaction between the A-site cation and the BO₆ octahedron is weak. This model was utilized to explain the reduction in T_d in a number of publications, which were connected with the weak coupling reaction that took place between the A-site cation and the BO₆ octahedron.^80,81 Furthermore, Nagata et al.⁸² proposed that the change in rhombohedral distortion affects the rise in T_d in the 0.92BNT–0.08(Bi_0.5Li_0.5)TiO₃ sample that had been quenched, which was caused by Bi ions being off-center. Khatua et al.⁸³ reported an increase in T_d value without a significant loss of piezoelectricity by grain size effect. They suggested the ferroelectric distortion of the field stabilized ferroelectric phase is dependent on the grain size.

In the current study, the reason for the improvements in piezoelectric properties (see next section) with the slight change in T_d is complex. It could be for a variety of reasons. Normally, the annealing process would result in the formation of oxygen vacancies, which often leads to an increase in T_d value, but will also be followed by a reduction in piezoelectric properties. However, for the present investigation, it is believed that the formation of oxygen vacancies is not too great because the annealing temperature is not too high. Therefore, the T_d value slightly changed. Furthermore, ZnO was added to the studied ceramics. For the ZnO additive, it has been proposed that Zn ions can enter the lattices of many ceramic systems and then help stabilize the ferroelectric ordering.⁷⁶ In addition, annealing improved ferroelectric properties by obtaining the optimal portion of the mixture phase and increasing grain size (see the following sections).

3.6 Ferroelectric properties

Normally, there are many factors affecting the characteristics of the ferroelectric hysteresis loop, which are associated with the material itself and the measurement conditions.⁸⁴ In the current experiment, the polarization–electric field (P–E) hysteresis loop of the BNKT/0.01ZnO ceramics was measured at RT with different annealing times of 0–12 h, and under various electric fields of 30–65 kV cm⁻¹, as shown in Fig. 8. The related ferroelectric properties are summarized in Table 3. It was found that the maximum polarization (P_max), remanent polarization (P_r), and coercive field (E_c) values increased with an increase the applied electric field for all ceramics (Fig. 9(a) and (b)). At 30 kV cm⁻¹ (Fig. 8), all ceramics showed an ellipse-like shape loop. This indicates a near-linear relationship of P–E, where it is known that some low electric fields are not enough to switch the domains.⁸⁵ However, the polarization nonlinearity was developed in both the positive and negative field zones at 40 kV cm⁻¹ electric fields. These results make it clearly evident that the electric field strength of 40 kV cm⁻¹ has sufficient energy to constrain the realignment of some domains in the direction of the applied fields. At 65 kV cm⁻¹ electric fields, polarization nonlinearity developed in both regions of the positive and negative fields with a well-saturated hysteresis loop. This indicates that the electric fields strength of 65 kV cm⁻¹ has enough energy to constrain the realignment of all domains in the direction of the electric field.⁸⁵ For an applied field greater than 65 kV cm⁻¹, however, it caused the ceramics to undergo a dielectric breakdown.

Fig. 8 Polarization–electric field (P–E) hysteresis loop of the BNKT/0.01ZnO ceramics annealed at 950 °C with different annealing times, measured at RT under various electric field of 30–65 kV cm⁻¹, where (a) 0 h, (b) 4 h, (c) 8 h, and (d) 12 h.

Table 3 Ferroelectric, piezoelectric, and energy harvesting properties of the BNKT/0.01ZnO ceramics annealed at 950 °C with different annealing times

Annealing time (h)	Pmax (μC cm^−2)	Pr (μC cm^−2)	Ec (kV cm^−1)	Rsq	d33 (pC N^−1)	kp	g33 (10^−3 Vm N^−1)	FoM (pm^2 N^−1)
0	38.06	33.02	42.98	1.39	151	0.583	34.04	5.14
4	38.31	33.27	42.85	1.40	162	0.586	34.14	5.53
8	41.28	35.85	42.60	1.42	198	0.598	34.35	6.80
12	39.20	35.05	42.58	1.40	165	0.588	35.01	5.74

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Fig. 9 Plots of (a) P_r, (b) E_c values as a function of electric fields from 30–65 kV cm⁻¹, (c) P_r and P_max as a function of annealing time @ E = 65 kV cm⁻¹, and (d) E_c as a function of annealing time @ E = 65 kV cm⁻¹ of the BNKT/0.01ZnO ceramics annealed at 950 °C with different annealing times.

At an electric field of 65 kV cm⁻¹, the unannealed ceramic displayed a well-saturated typical P–E hysteresis loop⁸⁶ with the P_max of 38.06 μC cm⁻², P_r of 33.02 μC cm⁻², and the E_c of 42.98 kV cm⁻¹, indicating a strong ferroelectric ordering. However, the annealing had a significant influence on the P_max, P_r and E_c values, i.e., it improved ferroelectric behavior, as seen from an enhancement trend in both the P_r and P_max values. The P_r increased from 33.02 μC cm⁻² for the un-annealed ceramic to 35.85 μC cm⁻² for the 8 h annealed ceramic and then slightly decreased to 35.05 μC cm⁻² when the annealing time increased up to 12 h (Fig. 9(c)). In addition, the E_c dropped with an increase in the annealing time (Fig. 9(d)). Normally, the improvement of ferroelectric properties can be related to many factors, as described in the previous section, such as MPB, grain size effect, heterogeneous chemical composition, and density. For this work, it was found that these factors were important factors, and it should be noted that ceramics with higher density and grain size values often have a higher P_r value.⁸⁷ The 12 h annealed ceramic, on the other hand, has a lower density and thus a slightly lower P_r value.

For the grain size effect, Hao et al.⁸⁸ studied the properties of (Ba_0.85Ca_0.15)(Zr_0.1Ti_0.9)O₃ and proposed that the fraction of grains responsible for the opposite polarization reverse in ferroelectrics can be expressed using a formula:⁸⁸

f = f₀[1 − exp(−G_ad³/kT)] (4)

where G_a is a constant representing the grain anisotropic energy density, and d is the grain size. This equation illustrates that f is relevant in relation to grain size. Therefore, as grain size increases, the number of grains that contribute to polarization reversals also increases. This increases the ferroelectricity of the ceramics.⁸⁸ For BaTiO₃, Zhao et al.⁶¹ reported a relationship between grain size and the tetragonal distortion (η), where η = c/a − 1. They also proposed that P_s can have a relation with η as the following equation shows:⁶¹and k is a coefficient that relates to the electrostrictive coefficients, and P_s is saturated polarization. When grain size increases, the P_s² thus also increases. In the current work, however, the increase in η or c/a − 1 value indicates the increase in tetragonally of mixture phase (between rhombohedral and tetragonal). Therefore, annealing produced a good fraction of these phases and gave better or optimal ferroelectric properties.

To check the degree of improvement of the ferroelectric performance, the loop squareness (R_sq) may be an indicator for this. Haertling et al.⁸⁹ used the squareness to measure not only the deviation in the polarization axis but also that in the electric field axis with the following empirical equation:^90–92

where P_r is remanent polarization, P_s is saturated polarization and E_c is coercive field. The P_1.1Ec is the polarization at an electric field equal to 1.1 times of E_c.⁹¹ This equation can be used to quantify the changes in hysteresis behavior. For an ideal hysteresis loop, R_sq is equal to 2.0. Based on the on the obtained data (Table 3), the R_sq increased with increasing annealing time, thereby confirming the improvement of ferroelectric performance. Therefore, the ferroelectric properties of the BNKT/0.01ZnO ceramics could be enhanced by optimizing annealing times.

Temperature dependence of polarization–electric field (P–E) hysteresis loops of the BNKT/0.01ZnO ceramics annealed at 950 °C with different annealing times, measured under an electric field of 65 kV cm⁻¹ and a frequency of 0.1 kHz are shown in the ESI in Fig. S3.† All ceramics exhibited well-saturated P–E loops at RT (25 °C). With the increasing temperature up to 125 °C, the P_r and E_c values decreased, and the hysteresis loops started to deform and showed constricted loops for all samples at 150 °C. It was confirmed that the high temperature (∼150 °C) can cause lattice distortion and disrupt the ferroelectric long-range order, leading to a decrease in the polarization states.⁹³ The decrease of P_r and E_c values with increasing temperature (Fig. S4(a) and S4(b)†) is consistent with that reported by Li et al.⁹⁴ in the 0.94(Bi_0.5Na_0.5)TiO₃–0.06BaTiO₃ (BNTBT6) lead-free ceramics. They reported that the P_r and E_c decreased significantly after 96 °C, and then a pinched hysteresis was obtained with the increasing temperature. The change of ferroelectric (FE) ordering, and a phase transition from ferroelectric (FE) to ergodic relaxor (RE) were thus observed.

3.7 Piezoelectric properties

Plots of the piezoelectric coefficient (d₃₃) value of the BNKT/0.01ZnO ceramics at different annealing times are shown in Fig. 10. The related values are also listed in Table 3. The d₃₃ value of the unannealed ceramic in this study was 151 pC N⁻¹. The d₃₃ increased with an increase in the annealing time and achieved the maximum value of 198 pC N⁻¹ for the 8 h annealed ceramic. However, as the annealing time increased to 12 h, these values decreased slightly. The planar electromechanical coupling coefficient (k_p) for this experiment was determined from measured values guided by the following formula:^4,95,96where f_r and f_a are the resonance and anti-resonance frequencies, respectively.⁹⁵ In this work, the maximum k_p of 0.598 was also obtained for the 8 h annealed ceramic (see Table 3). Normally, the improvements of d₃₃ and k_p for many piezoelectric ceramics can be related to many factors. The grain size effect is one of them. Kang et al.⁹⁷ argued that the poling efficiency rose with increasing grain size in the case of lead-free ceramics, such as in the Pb_0.9La_0.1TiO₃ system, which was attributable to improving the facility of 90° domain switching. They also proposed that, as the increase in grain size, it would be expected to enhance the domain switching at the same poling condition, the increases in the d₃₃ and k_p values could be explained by the increased domain mobility.

Fig. 10 Plots of the k_p and d₃₃ values of the BNKT/0.01ZnO ceramics annealed at 950 °C with different annealing times.

The improvement in the d₃₃ value in the many studies can be explained by the following thermodynamic theory of the ferroelectric's equation:^34,88,98

d₃₃ = 2ε₃₃^TQ₁₁P_r (8)

where ε₃₃^T represents the dielectric constant of the material, P_r is the remnant polarization, and Q₁₁ represents the electrostrictive coefficient, which is constant for perovskite materials. This equation demonstrates that the d₃₃ is proportional to the P_r value, which matches the data of the current study. Furthermore, for the 8 h annealed ceramic, the P_r increased from 30.02 μC cm⁻² to 35.85 μC cm⁻² and E_c slightly dropped from 42.98 kV cm⁻¹ to 42.58 kV cm⁻¹ (see Table 3), thus resulting in a significant improvement of the d₃₃ value for this ceramic.⁹⁹ The observed trend in the value of the d₃₃ is consistent with the value of the k_p (see Fig. 10).^7,100–103 Maqbool et al.¹⁰⁴ also found that the d₃₃ and k_p increased when the SrZrO₃ (SZ) concentration that was doped in BNT ceramics increased. The significant increase found in d₃₃ and k_p at SZ4 was related to a large P_r and a lower E_c because a lower E_c allowed the ceramics to be more easily poled, while a high P_r and P_m favored piezoelectricity. Furthermore, several previous studies proposed that the dielectric constant, piezoelectric constant, and k_p followed a similar trend.^105,106 The improvement of d₃₃ and k_p values in the current study is also related to the ferroelectric properties (improve the P_r, P_m, and low E_c), the grain size effect, the MPB, heterogeneous in composition (decrease in the chemical heterogeneity), and also accompanied by the improvement of density, where the trends of d₃₃ and k_p values can be matched with the trend of density value (see Tables 1 and 3).

3.8 Energy harvesting behavior

Piezoelectric materials are now attractive for the development of energy harvesting applications. In this current experiment, the energy harvesting properties of the ceramics were investigated. The piezoelectric voltage constant (g₃₃) is one of the important parameters for energy harvesting applications. It has been suggested that the sample with a higher piezoelectric charge constant should generate a higher voltage,^107,108 thus reflecting the quantity of electrical energy produced by the pressure being applied. The g₃₃ value can be determined by the following relation:^107–111where ε_r is the dielectric constant of the piezoelectric material, ε₀ is the dielectric constant in a vacuum (8.854 × 10⁻¹² F m⁻¹),¹¹² and d₃₃ is the piezoelectric charge constant. From this equation, the generated voltage of the piezoelectric energy harvester depends on the piezoelectric coefficient and dielectric constant of the piezoelectric ceramic. Therefore, the more the piezoelectric charge constant increases, the more the generated voltage also increases.¹⁰⁷ A plot of the g₃₃ value of the BNKT/0.01ZnO ceramics at different annealing times is shown in Fig. 11. The g₃₃ increased with increasing annealing time, and the highest g₃₃ of 35.01 × 10⁻³ Vm N⁻¹ was observed for the 12 h annealed ceramic. The improvement of the g₃₃ value for this ceramic is due to the increase of the d₃₃, and the lowering of the ε_r value. This result is consistent with the work done by Choi et al.¹⁰⁸

Fig. 11 Plots of the g₃₃ and FoM values of the BNKT/0.01ZnO ceramics annealed at 950 °C with different annealing times.

In this study the energy harvesting performance figure of merit which relates to the g₃₃ and d₃₃ parameters, was evaluated.¹¹¹ In the present investigation, the figure of merit (FoM) parameter was evaluated based on the following equation:^108,109

FoM (pm² N⁻¹) = d₃₃ × g₃₃ (10)

where d₃₃ is the piezoelectric charge constant, and g₃₃ is the piezoelectric voltage constant of the device, respectively. Normally, a piezoelectric material with a high FoM value will produce a large amount of power when utilized for energy harvesting.¹¹³ For the present study, the highest FoM of 6.80 pm² N⁻¹ was observed for the 8 h annealed ceramic, which was ∼32% higher than that of the un-annealed ceramic (see Fig. 11 and Table 3). This improvement is due to the improvements in the d₃₃ and g₃₃ values for this composition. The results of a comparison of the FoM value for this study with the results of other earlier research studies for different piezoelectric lead-free ceramics are represented in Table 4.^{98,107–109,111,114–120} The g₃₃ and FoM values for the current experiment are considerably high when compared with other lead free piezoelectric ceramics.

Table 4 Comparison of the d₃₃, g₃₃, and FoM values of the BNKT/0.01ZnO ceramics annealed at 950 °C for 8 h with other lead and lead-free ceramics

System	d33 (pC N^−1)	g33 (10^−3 Vm N^−1)	FoM (pm^2 N^−1)	Ref.
BNKT/0.01ZnO (annealed at 950 °C/8 h)	198	34.35	6.80	This work
(BNT–6BT) + 0.1 mol% Al2O3	205	31.00	6.36	98
Ba(Zr0.04Ti0.96)O3	268	19.11	5.12	107
Ba(Zr0.04Ti0.96)O3 + 1 mol% CuO	302	20.64	6.23	107
PZT-70 vol% P(VDF-CTFE)	92	—	6.44	108
0.55BZT–0.45BCT (sintered 1475 °C)	341	16.00	5.46	109
0.99KNLN0.97−xSTx − 0.01CZ (x = 0.03)	225	28.69	6.46	111
Ba(Zr0.07Ti0.93)O3 + 2 wt% B2O3	291	21.00	6.11	114
(BZT–BCT)-(epoxy-CCTO)	16	—	4.25	115
PZT bulk	556	0.011	6.12	116
PZT micro-pillar	91	0.021	1.91	116
80PZT-PVDF composites (0–3 connectivity)	54	33.95	1.83	117
0.2(PbMg1/3Nb2/3O3)–0.8(PbZr0.475Ti0.525O3) (bulk-type 1 layer)	241	10.89	2.62	118
0.97[0.995BNKT-0.005LN]-0.03BNdT ceramics	258	14.71	3.80	119
0.92(Bi0.5Na0.5)TiO3–0.08(Ba0.5Sr0.5)TiO3	118	—	2.85	120

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Based on the obtained results, the suitable annealing conditions provided the ceramics with excellence and acceptability for all electrical properties. In this study, the optimum annealing time for the enhancement of dielectric, piezoelectric, and energy harvesting performances of the BNKT/0.01ZnO ceramics was found to be 8 h dwell time.

4 Conclusions

In summary, the effect of thermal annealing time on phase formation, microstructure, dielectric, phase transition, ferroelectric, piezoelectric, and energy harvesting properties of the BNKT/0.01ZnO ceramic prepared by a solid-state reaction technique was investigated. The ceramics which were annealed at 950 °C with different annealing times, exhibited the MPB structure where the rhombohedral and tetragonal phases coexisted, as confirmed by the XRD and Raman measurements. The annealing time made a slight change in the phase transition temperatures, also including the T_d. However, it had significant positive effects on the dielectric, ferroelectric, piezoelectric, and energy harvesting properties of the BNKT/0.01ZnO ceramics, where the optimal annealing time for the current investigation was 8 h.

Author contributions

Pharatree Jaita: writing-original draft preparation. Kamonporn Saenkam: methodology-sample preparation. Gobwute Rujijanagul: conceptualization improve the manuscript and supervisions.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This project is funded by National Research Council of Thailand (NRCT) (NRCT5-RSA63004, NRCT5-RSA63004-03) and partially supported by Chiang Mai University, Research Center in Physics, Astronomy, Materials Sciences Research Center, Global Partnership Project (B16F640001), and CMU Junior Research Fellowship Program (JRCMU2565_058). Office of Research Administration, Department of Physics and Materials Science, Faculty of Science, and Science and Technology Research Institute, Chiang Mai University are also acknowledged.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d2ra07587c

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