Microstructural and high-temperature dielectric, piezoelectric and complex impedance spectroscopic properties of K_0.5Bi_0.5TiO₃ modified NBT-BT lead-free ferroelectric ceramics

Abstract

Solid solutions (1-x-y)(Na_0.5Bi_0.5)TiO₃-xBaTiO₃-y(K_0.5 Bi_0.5)TiO₃ with (x (mol.%) = 0, 7 and 100); y(mol.%) = 0, 20 and 100) compositions have been prepared by a conventional solid-state reaction method, and their structure, dielectric properties and depolarization temperature have been examined. At room temperature, X-ray diffraction (XRD) patterns reveal that the crystalline structure of the ceramics was perovskite. The morphotropic phase boundary (MPB) of the ternary system lying between rhombohedral (R3c) and tetragonal (P4mm) phases is in the range of (x (mol.%) = 7 and y (mol.%) = 20). The Raman-active modes for 0.73NBT-0.07BT-0.20KBT were separated and identified under the framework of group theory. SEM micrographs illustrate the quasi-uniform distribution of the grains, which are compact. The dielectric properties of the ceramics were studied in the frequency range of 1 kHz–100 kHz from ambient temperature to 600 °C. Dielectric measurements indicate that all ceramics show a diffuse phase transition near the temperature (T_m) for diffusivity of the order of 1.4–1.7 and a shift of (T_m) towards high temperatures. The resistance and capacitance of the various contributors (grain and grain boundary) in our samples are also discussed using a brick-layer model. Excellent piezoelectric properties for d₃₃ = 146 pCN⁻¹ and electromechanical coupling factors k_p = 29.4% were observed at morphotropic phase boundary (MPB), which was assumed to be associated with the coexistence of rhombohedral and tetragonal phases and accurate grain size. This work establishes a new approach for improving lead-free piezoelectric ceramics based on 0.73NBT-0.07BT-0.20KBT.

1. Introduction

Piezoelectric devices are essential elements of ultrasonic transducers, actuators and sensors [1,2]. However, lead-based materials dominate the field of piezoelectric engineering. Nonetheless, a primary environmental consideration with lead-based materials is the environmental risk, since lead itself is a toxic material [3,4]. Although lead-free ferroelectric ceramic materials, such as sodium-potassium niobate K_0.5Na_0.5NbO₃ (KNN) and barium titanate BaTiO₃ (BT), will have been around for some time, they exhibit considerably inferior piezoelectric and ferroelectric properties [[5], [6], [7]]. Although efforts have been made to obtain lead-free ferroelectric ceramics with strong piezoelectric capabilities by a variety of doping methods, an effective substitute for the material lead zirconate titanate (PZT) has not yet been found [8]. However, several different lead-free material systems have demonstrated significant promise. Numerous studies on lead-free piezoceramics have been conducted; for instance, perovskite lead-free solid solutions based on (Na_0.5Bi_0.5)TiO₃, BaTiO₃ and (K_0.5 Bi_0.5)TiO₃ systems with the composition close to the morphotropic phase boundary (MPB) have the best electromechanical, electrical, and piezoelectric properties [[9], [10], [11]]. X. Huang et al. [12] performed 0.80NBT-0.06BT-0.14KBT specimens utilizing a conventional solid-state approach. Nevertheless, a small proportion of the second phase was identified in the high-Ba content samples (x (mol.%) = 6 and y (mol.%) = 14). Sodium bismuth titanate, with a rhombohedral structure, is thought to be a possible strong candidate for the main component in lead-free piezoelectric materials, as NBT is a highly ferroelectric component that has a significant coercive field (Ec = 73 kV/cm) at room temperature, an elevated Curie temperature (Tc = 320 °C), and a large remanent polarization (Pr = 38 μC/cm²) [[13], [14], [15]]. Accordingly, the ternary system of (1-x-y)NBT-xBT-yKBT would be exceedingly suitable for the enhancement of ferroelectric and piezoelectric properties in the composition near the morphotropic phase boundary (MPB). Due to the greater degree of compositional freedom and the ease with which the electromechanical characteristics can be improved. However, according to earlier studies, the ternary system’s MPB range is regrettably still inexact. Furthermore, the ratio of NBT to BT in compounds from which the MPB region appears remains the main topic of discussion, as several investigators have obtained divergent results. The phases of both end-components, NBT and BT, have been taken as reference structures. The low depolarization temperature (T_d) near the morphotropic phase boundary (MPB), which is a legacy of pure NBT, still continues to be a significant barrier impeding its deployment [16]. Recently, investigations have indicated that the (T_d) of the composition (1-x-y)NBT-xBT-yKBT outside MPB is significantly larger compared to that near MPB [17,18]. Furthermore, attention was paid to the effect of additive doping on (T_d). Nagata et al. [19] observed that the (T_d) of x(Bi_1/2Na_1/2)TiO₃–y(Bi_1/2Li_1/2)TiO₃–z(Bi_1/2K_1/2)TiO₃ and doped in wt % MnCO₃ decreased upon increasing the Mn concentration. In-depth information about the BNKBT system, including its piezoelectric, dielectric, and ferroelectric properties as well as the variation in depolarization temperature, was reported by Wang et al. [20] Nevertheless, it remains unclear which factor is the main contributor to the depolarization behavior so far. In the current study, we discovered that the (1-x-y)NBT-xBT-yKBT system can exhibit an antiferroelectric-like phase near the MPB phase area at (T_d) = 206 °C. We anticipate that the enhanced depolarization temperature can be achieved almost entirely without compromising the piezoelectric constant. The current work’s objectives and originality include: (i) to research the structural changes brought on by the Ba/K substitution, (ii) to examine ceramic samples' dielectric characteristics (dielectric constant, dielectric losses, conductivity, relaxation phenomena) as just a function of the Ba/K ratio in to better understand the correlations among structure, micro-structure, and properties. Moreover, the (1-x-y)NBT-xBT-yKBT materials' piezoelectric and electromechanical coupling characteristics have been determined.

2. Experimental procedure

2.1. Material synthesis and characterization

(1-x-y)NBT-xBT-yKBT polycrystalline materials were produced with a solid-state technique based on the following chemical reaction:

$$\left(1-\mathrm{x}-\mathrm{y}\right)\left({\mathrm{N}\mathrm{a}}_{0.5}{\mathrm{B}\mathrm{i}}_{0.5}\right)\mathrm{T}\mathrm{i}{\mathrm{O}}_3-\mathrm{x}\mathrm{B}\mathrm{a}\mathrm{T}\mathrm{i}{\mathrm{O}}_3-\mathrm{y}\left({\mathrm{K}}_{0.5}{\mathrm{B}\mathrm{i}}_{0.5}\right)\mathrm{T}\mathrm{i}{\mathrm{O}}_3+\left[\left(1+3\mathrm{x}+3\mathrm{y}\right)/4\right]\mathrm{C}{\mathrm{O}}_2\uparrow$$ (1)

The elaboration of the ternary system of (1-x-y)NBT-xBT-yKBT was realized by a solid-state approach, through the use of titanium oxide TiO₂ (Sigma-Aldrich 98.99%), bismuth oxide Bi₂O₃ (Sigma-Aldrich 98.99%), carbonates Na₂CO₃, BaCO₃ and K₂CO₃ (Sigma-Aldrich 98.99%) as initial components, and taken in stoichiometric quantities according to reaction (1) and subsequently being heated for 4 h at 1000 °C in air and then ground again for 1 h. Temperatures and duration of the calcination were based on a previous study [21]. Afterward, the dried powders were ground, mixed with a 3 wt% polyvinyl alcohol (PVA) binder, die-pressed into small pellets of 12 cm diameter and approximately 2 mm thick under a pressure of 6 tons/cm², and finally sintered in the air at temperatures of 1100 °C for 4 h. Above this sintering temperature, the pellets start to melt or deform at (1150 °C). The density of the pellet was measured by means of the Archimedes procedure, and it was proved to be about ∼97.6% of the theoretical density of the material. Fig. 1 shows the successive steps of (1-x-y)NBT-xBT-yKBT phase preparation by solid-state process.

Fig. 1.

Schematic representation of the sample preparation (1-x-y)NBT xBT-yKBT.

The measurements and characterization were performed on five samples of our system (1-x-y)NBT-xBT-yKBT (NBT, KBT, NBT-0.07BT, NBT-0.20KBT, and 0.73NBT-0.07BT-0.20KBT).

XRD analysis: Using an XPERT-PRO X-ray diffractometer (XRD) with Cu–K radiation (λ = 1.54 Å) and a step size of 0.02° and the number of counts collected for each peak was at least several thousand (13000/s), the phase formation analysis was carried out in the range of 2θ∼10–90°. The tetragonal perovskite KBT (space group: P4mm) was used as the model structure, and the crystal phases were refined based on the Rietveld refinement method using the FULLPROF suite software [22]. Based on Rietveld refinements of the experimental diffraction data, the crystallite sizes and lattice constants have been estimated.

Raman spectroscopy measurement: The Raman spectrometer (VERTEX 70v Bruker spectrometer), which has a monochromatic radiation source with a wavelength of 410 nm, was utilized to research the relationship between the Raman band and various kinds of atomic bonds. After the specimen was treated, the Raman spectra were recorded at room temperature.

Scanning electron microscope measurement: Scanning electron microscopy was used to examine the microstructures of the sintered specimens (SEM, FEI Quanta 200 EDAX model). In the meantime, Image J software was used to determine the typical grain size of the ceramic specimens. The densities of ceramic samples were calculated experimentally using Archimedes' principle based on the formula: ρ = $\frac{w_a}{w_a-w_l}\times {\rho }_{liquid}$. Where $w_a$ is the weight of the sample in the air, $w_l$ is the weight of the sample in the liquid, ρ the sample’s density and ρliquid is the density of the liquid in which the sample is submerged. Each sample’s theoretical density is calculated using the Rietveld refinement. The proportional density (calculated from the Experimental and theoretical density).

Dielectric properties measurement: To undertake electrical tests, a layer of silver paste was added to both faces, and the specimen was then heated for 30 min at 80 °C. Using an LCR-Meter (Agilent 4284A) operating in the frequency range 1 kHz⁻¹ MHz, the relative permittivity (ε_r) and dielectric loss (tanδ) values were calculated as a function of temperature at various temperatures ranging from ambient to 600 °C. Samples for piezoelectric measurements were poled under applied fields of 3 kV/mm, at 120 °C, 30 min in a silicone oil bath. Piezoelectric properties were measured by a resonance–antiresonance method on the basis of IEEE 176-1987 standards, using an impedance analyzer (Agilent 4284A) [23]. The free permittivity (${\epsilon }_{\mathrm{i}\mathrm{i}}^{\mathrm{T}}$), was determined from the capacitance at 1 kHz of the poled specimen. The elastic constants (${\mathrm{S}}_{\mathrm{j}\mathrm{j}}^{\mathrm{E}}$), was calculated from the frequency constant ($N_{\mathrm{i}\mathrm{j}}$), and the measured density (${\rho }_0$) by the relation of ${\mathrm{S}}_{11}^{\mathrm{E}}$ = 10⁹/($\pi$² $N_P^2{\rho }_0$). Finally, the piezoelectric constants (dij), was calculated from the k_ij, ${\epsilon }_{\mathrm{i}\mathrm{i}}^{\mathrm{T}}$ and ${\mathrm{S}}_{\mathrm{j}\mathrm{j}}^{\mathrm{E}}$ by the relation of dij = kij(${\epsilon }_{\text{ii}}^{\text{T}}{S}_{\text{jj}}^{\text{E}}$)^1/2 or directly using a d₃₃ Meter Sinocera S5865. The electromechanical coupling (Kp) can be estimated from the ratio of resonance frequency (fr) and anti-resonance frequency (fa) and the relative change of (fr) and (fa) with respect to the (fa) based on the Onoe’s formulas [24,25].

$${\mathrm{K}}_{\mathrm{p}}={\left[2.51\times \left(\frac{{\mathbf{f}}_{\mathbf{a}}-{\mathbf{f}}_{\mathbf{r}}}{{\mathbf{f}}_{\mathbf{r}}}\right)\right]}^{1/2}$$ (2)

3. Results and discussion

3.1. X-ray diffraction (XRD) analysis

For a proper study of the effect of xBT and yKBT on the structural characteristics of (1-x-y) NBT-xBT-yKBT ceramics with (x(mol.%) = 0, 7 and NBT); y(mol.%) = 0, 20 and KBT), based on chemical reaction (1), calcined at 1000 °C for 4 h, the room temperature XRD diagrams of these ceramics and the parent material, i.e. NBT, elaborated under the same experimental conditions, are displayed in Fig. 2. As it can be observed, the specimens acquired have a single phase of the perovskite-type structure, and show an excellent agreement with the standard JCPDS card (n °: 36–0340) [26], (n°: 36-0339) [27] for NBT and KBT respectively. The resulting peaks are indexed based on the pseudo-cubic Bragg reflections. In addition, to better understand the effect of xBT and yKBT content, we have also plotted the expanded XRD diffraction diagrams in the 2θ range of 38–42°, as displayed in Fig. 3. As the Ba²⁺ and K⁺ concentration increases, the XRD peaks shift to lower 2θ values (higher d-spacing) in a progressive manner as a result of the difference in radii of Ba²⁺, K⁺ and Na⁺ (rBa²⁺ = 1.61 Å, rK⁺ = 1.33 Å, and rNa⁺ = 1.02 Å, with 12 fold co-ordination) [28,29]. This type of occurrence was also reported in K-doped N_0.25K_0.25Bi_0.5TiO₃ materials [30] and Sr-doped NBT ceramics [31].

Fig. 2.

X-ray patterns of (1-x-y)NBT-xBT-yKBT ceramics calcined at 1000 °C for 4 h.

Fig. 3.

Detailed scan of X-ray reflections for (1-x-y)NBT-xBT-yKBT in the 38°–42° 2θ-region.

3.2. Rietveld refinement approach

In order to know the crystal structure and the structural parameters, the Bragg peaks were related to a theoretical reference model by the Rietveld refinement method by means of the open source software Fullprof. In the first step, the cosine Fourier series function is employed to fit the background refinement, and the diffraction peak profiles were adjusted with the pseudo-Voigt function. The different parameters obtained during this refinement have been put in the background, thermal parameters, profile half-width parameters (u,v,w), zero shifting, preferred orientation, scale factor, Wyckoff positions, displacement, atomic positional (x, y, z) and unit cell parameter (a, b, c). Accordingly, to achieve convergence and the best quality of the process, concordance indices or profile fit (Rp, Rwp and χ²) (with values <2%) are provided. Nevertheless, throughout the refinement work, the occupancy of all atomic sites remained fixed. On the other hand, we attempted to quantify the phase’s fraction and identified the morphotropic phase boundary (MPB) by means of this structural refinement model. The output of the Rietveld refinement is shown in Table 1. Fig. 4 displays the Rietveld refinement of the various compositions of the (1-x-y)NBT-xBT-yKBT ceramics. At room temperature, NBT crystallizes in a rhombohedral structure of space group R3c and the cellular parameters will increase along with the xBT and yKBT content. For pure KBT the XRD diagrams exhibit characteristic peaks of the tetragonal symmetry. Moreover, in a certain concentration range of NBT and BT materials, there does exist a region where tetragonal and rhombohedral structures coexist. Because of this, the phase transitions in the (1-x)NBT-xBT solid solutions depend on the concentration of alkali elements as well as temperature. Furthermore, 0.93NBT-0.07BT exhibits a morphotropic phase boundary (MPB) at room temperature, whereby rhombohedral and tetragonal symmetries coexist. In addition, the co-occurrence of tetragonal and rhombohedral phases along with the space group P4mm and R3c in the morphotropic phase boundary (MPB) zone at room temperature was similarly confirmed for the NBT-0.20KBT system. Moreover, we note that compounding of the phases (Rh and T) occurs in the following system: 0.73NBT-0.07BT-0.20KBT.

Table 1.

The lattice parameters, strain, Phase fraction (%), average crystallite size, and cell volume of the (1-x-y)NBT-xBT-yKBT ceramics.

Sample	Structure	Phase fraction (%)	Lattice parameter (Å)	Average crystallite size (nm)	Strain (ϵ) x 10−2	Cell Volume (Å3)	Reliability Parameters χ2 (%)
Pure NBT	Rhombohedral	R3c 100%	a = b = 5.4634 c = 13.4271	131.87	0.0056	350.31	1.41
Pure KBT	Tetragonal	P4mm 100%	a = b = 3.653 c = 3.7915	131.81	0.0058	56.73	1.50
NBT-0.07BT	Rh + T	R3c 75.12% P4mm 24.88%	a = b = 5.4886 c = 13.5643 a = b = 3.771 c = 3.8156	134.11	0.0062	354.52 58.12	1.54
NBT-0.20KBT	Rh + T	R3c 73.32% P4mm 26.68%	a = b = 5.4885 c = 13.4763 a = b = 3.7952 c = 3.8453	136.21	0.0063	356.17 58.28	1.63
0.73NBT-0.07BT-0.20KBT	Rh + T	R3c 71.89% P4mm 28.11%	a = b = 5.4967 c = 13.4842 a = b = 3.8191 c = 3.8527	137.14	0.0070	357.29 59.38	1.81

Fig. 4.

Rietveld refined powder XRD profile of the (1-x-y)NBT-xBT-yKBT ceramics.

The width of the X-ray diffraction peaks was used to calculate the average value ofcrystallite size using the Williamson-Hall (W–H) method [32]. Furthermore, this approach shows that the total width of the XRD peak results from the broadening of the crystal size and the microstrain and could be expressed as below from equations (3), (4), (5), (6). The crystallite size obtained is slightly greater than that calculated using the Debye-Scherrer equation because the microstrain-induced broadening effect is completely eliminated in the latter. The combined effects of crystallite size, ${\beta }_{size}$, and microstrain, ${\beta }_{strain}$, contribute to the total broadening, ${\beta }_{total}$, of the peaks.

$${\beta }_{total}={\beta }_{size}+{\beta }_{strain}$$ (3)

The Scherrer equation is used to compute the crystallite size:

$${\beta }_{size}=\frac{K\times \lambda }{D\times \mathit{COS}\theta }$$ (4)

while the microstrain is determined using the Stokes & Wilson formula [32].

$${\beta }_{strain}=4\epsilon \times \mathit{tan}\theta$$ (5)

$\lambda =0.154nm\text{,}$ is the X-ray wavelength used, K = 0.89 a Scherrer constant, a diffraction angle is used to determine the peak position in radians, and D stands for the crystallite size. We get the following total broadening by combining these latter equations (Sherrer and Stokes & Wilson) with equation (2) and multiplying both sides by $\cos \mathrm{\theta }$:

$${\beta }_{total}\mathit{cos}Ɵ=\frac{K\lambda }{D}+4Ɛ\mathit{sin}Ɵ$$ (6)

The intercept of the fitting line associated with the following values ${\beta }_t\mathit{cos}\theta$ versus 4$\mathit{sin}\theta$ yields the average crystallite size (see Fig. 5).

Fig. 5.

Williamson-Hall plot for (1-x-y)NBT-xBT-yKBT ceramics: (a) Pure NBT, (b) Pure KBT, (c) NBT-0.07BT, (d) NBT-0.20KBT, and (e) 0.73NBT-0.07BT-0.20KBT.

Table 1 shows the crystallite size and strain obtained using this method for (1-x-y)NBT-xBT-yKBT. The calculated values of strain for pure NBT, pure KBT, NBT-0.07BT, NBT-0.20KBT and 0.73NBT-0.07BT-0.20KBT are 0.0056, 0.0058, 0.0062, 0.0063 and 0.0070, respectively. Moreover, the average crystallite size increases to 131.87 nm for NBT and then increases to 137.14 nm for 0.73NBT-0.07BT-0.20KBT. This might be caused by a change in the structural phase (from T to Rh + T) as well as a change in residual stresses brought on by a rise in xBT and yKBT concentration.

3.3. Bonding charge density

The software used for both the computations of the electronic state and the depiction of the three-dimensional picture of the crystal structure is VESTA [33]. Utilizing the fundamental structural characteristics, we created the three-dimensional crystal structures of pure NBT, pure KBT, and one of the composites, namely 0.73NBT-0.07BT-0.20KBT, in VESTA. The three-dimensional crystal structure of the aforementioned samples is shown in Fig. 6, and all other samples have a similar structure. This three-dimensional structure depicts how the atoms of the two phases are arranged in the composite structure, and it is clear from the structure that the two phases diffuse to generate a single matrix.

Fig. 6.

3-Dimensional Vesta structure: (a) rhombohedral (R3c) for NBT, (b) tetragonal (P4mm) for KBT, and (c) rhombohedral (R3c) as well as tetragonal (P4mm) for composite 0.73NBT-0.07BT-0.20KBT.

The mapping of the electron density using the GFourier program, which enables the characterization and visualization of the electron density in the unit cell, is another significant outcome of the Rietveld refinement process. In order to identify the atomic positions of the constituent elements in the unit cell for crystals and to learn more about the nature of the chemical bonds between the ions forming (1-x-y)NBT xBT-yKBT powders, one must measure the electronic charge density. In other words, the heavier electron density contours show where a larger element is located among the other primary elements in the unit cell.

The equation: is typically used to determine the diffusion density ρ(x,y,z):

$$\rho \left(x,y,z\right)=\frac{1}{V}{\sum }_{hkl}{\left|F_{hkl}\right|e^{-2\pi i}\left({h_x+k}_y{+l}_z-{\alpha }_{hkl}\right)}_{.}$$ (7)

The electron density at a position (x, y, z) inside a volume V unit cell is represented by ρ(x,y,z), based on equation (7), the phase angle of each Bragg reflection is represented by ${\alpha }_{hkl}$, and the amplitude of the structure factor is represented by F(hkl). A 3D Fourier card of each individual atom in the unit cell for pure NBT, pure KBT, and the composite, or 0.73NBT-0.07BT-0.20KBT, is shown in Fig. 7. The Na/Bi cation’s ascending levels of electron density are indicated by the regions colored from red to violet-brown, although the zero level density contour is shown in black. The Ti and Na/Bi/K cations are situated at (0, 0, 0.5) and (0.031, 0.28, 0.998) in the under investigation 0.73NBT-0.07BT-0.20KBT system, respectively. Fig. 7 shows the maximum electron density for K (Z = 19) and Bi (Z = 83), which is ∼570 e/ų in the xy direction about K/Bi atoms. This is caused by the K/Bi atoms' high atomic number in comparison to the other elements in the compound.

Fig. 7.

Three-dimensional electron density distribution in the unit cell of (1-x-y)NBT-xBT-yKBT systems: (a) Pure NBT, (b) Pure KBT, (c) NBT-0.07BT, (d) NBT-0.20KBT, and (e) 0.73NBT-0.07BT-0.20KBT.

However, electron density contour maps reveal information on the connection between structure and conductivity [34]. In general, the anion conduction mechanism in ABO₃-type ferroelectric perovskites is thought to involve a hopping process in which developing anions pass through the bottleneck or the start of the critical radius of a triangle via socket points that are present between the A-site and B-site ions [35]. P. Singh et al. [34] claim that the oxide ion moves through interstitials, saddle points, and –O₁–O₁– pathways as it moves around the edges of TiO₆ octahedra. A significant number of defects between dopant and oxygen vacancies are more likely to arise as a result of the oxide ion migration mechanism, which has an impact on the material’s conductivity. This mechanism is consistent with how our samples' conductivity behaves, which will be looked at in more depth later.

3.4. Raman analysis

Raman spectroscopy is a very accurate and sensitive analysis to understand local structural deformations, crystal symmetry, phase transitions and its relationship to doping [36,37]. The irreducible representation associated with the optical vibrations of the rhombohedral symmetry and the R3c space group of the perovskite phase is the following:

Γ_vib = 4A₁⊕9Ε (8)

The Raman modes associated with lattice displacements parallel to and perpendicular to the unit cell’s c-axis are A1 and E symmetry, respectively [38]. It should be mentioned that NBT crystallizes in the rhombohedral R3c phase at low temperatures up to ∼220 °C. Therefore, the irreducible representation reveals 13 active Raman modes, according to equation (8). The normalized Raman spectra for the (1-x-y) NBT-xBT-yKBT systems, in the range 100–1000 cm⁻¹ are presented in Fig. 8.

Fig. 8.

Evolution of the Raman spectra of the (1-x-y) NBT-xBT-yKBT system.

The Raman bands are comparatively broad, which could be due to the disorder in the A-sublattice, the overlapping Raman modes, and as well as the ceramic shape of the materials. The NBT phase presents wide bands showing the polycrystalline nature of the sample, which can be grouped into four frequency ranges: a low wavenumber range of 100–200 cm⁻¹, a middle wavenumber range of 200–400 cm⁻¹, a high wavenumber range of 450–650 cm⁻¹, and the very high wavenumber range of 650–1000 cm⁻¹. The main four bands are associated, respectively, with Na/Bi–O bonds vibration at the A-site of the perovskite solid solution, Ti–O vibrations, TiO₆ octahedra, and oxygen octahedra vibrations and rotations [39,40]. From the analysis of Fig. 8, it can be concluded that the evolution of the Raman spectra upon increasing the Ba²⁺ and K⁺ content reveals interesting changes. When compared to pure NBT, an evident difference can be identified in the room temperature Raman spectrum of the 0.73NBT-0.07BT-0.20KBT material: the intensity of the first band was significantly reduced, the third band splits into tree peaks, located at about 502, 538, and 620 cm⁻¹, respectively. In addition, the Raman intensities of the modes at about 270 and 510 cm⁻¹ present a noticeable decrease for the NBT-0.07BT, NBT-0.20KBT, and 0.73NBT-0.07BT-0.20KBT compositions. This outcome is consistent with the observation that structural phase transitions are linked to Raman spectroscopic changes. The polycrystalline character of the specimens and the random occupancy of A- and B-site ions contributed to this disorder. As the xBT and yKBT composition rises, as the ratio of xBT to yKBT increases, the bands shift to shorter wavelengths. Probably, this phenomenon is associated with the influence of the higher cationic mass of the elements caused by the substitution of sodium and bismuth with barium and potassium in the NBT A-site.

3.5. Microstructural characterization

Fig. 9 displays the surface morphologies (SEM) of (1-x-y)NBT-xBT-yKBT ceramics. All specimens exhibit a fully dense, rectangular or squared-shaped microstructure. These samples display clearly visible grains and grain boundaries, suggesting the polycrystalline nature of the materials. Using ImageJ software, 100 particles in SEM images were used to calculate the particle size distributions of the (1-x-y)NBT xBT-yKBT systems [41]. The relative density (ρ_r) of the sintered (1-x-y)NBT-xBT-yKBT ceramics is measured by Archimedes' principle whose value is between 95% and 97%. Maximum grain size and ρ_r are obtained in the case of NBT-0.20KBT composition. The compositions of pure NBT, pure KBT, NBT-0.07BT, NBT-0.20KBT and 0.73NBT-0.07BT-0.20KBT have grain sizes of 2.4 μm, 2.2 μm, 2.9 μm, 2.4 μm, and 2.7 μm, respectively. The average grain size increases slightly evidently with increasing amount of xBT (see Fig. 10). It is generally found that, for polycrystalline ferroelectric compounds, the electrical properties depend strongly on the grain size and density [42]. When the size of the grains increases, the gain limit phase decreases, which enhances their electrical response [42,43]. Additionally, larger grains encourage the rotation of the polarization vector, which improves the material’s dielectric, and piezoelectric characteristics [44,45].

Fig. 9.

SEM micrographs of the sintered (1-x-y)NBT-xBT-yKBT ceramics: (a) Pure NBT, (b) Pure KBT, (c) NBT-0.07BT, (d) NBT-0.20KBT, and (e) 0.73NBT-0.07BT-0.20KBT.

Fig. 10.

Average grain size of (1-x-y)NBT-xBT-yKBT samples sintered at 1100 °C for 4 h.

3.6. Dielectric measurements

Fig. 11 displays the temperature dependence of the dielectric constant (ε_r) and dielectric loss (tanδ) of (1-x-y)NBT-xBT-yKBT ceramics with different contents of xBT and yKBT measured at 1 kHz, 5 kHz, 10 kHz, 50 kHz, and 100 kHz. In a curve, there are two abnormal dielectric peaks that may be seen: a broad, frequency-independent maximum at around (T_m = 340 °C), exhibiting the relaxor behavior indicated by (the maximum dielectric constant), represents the transition between the antiferroelectric and the paraelectric state [[46], [47], [48], [49]].

Fig. 11.

The dielectric permittivity (ε_r) and dielectric loss (tan δ) against temperature of ceramics measured under varied frequencies (1 kHz, 5 kHz, 10 kHz, 50 kHz, and 100 kHz): (a) Pure NBT, (b) Pure KBT, (c) NBT-0.07BT, (d) NBT-0.20KBT, and (e) 0.73NBT-0.07BT-0.20KBT.

The second anomaly occurred at about (T_d∼230 °C) and is related to the depolarization temperature linked to the ferroelectric to antiferroelectric transition [50,51]. Thus, a polar vector reorientation brought on by the emergence of a new orthorhombic phase can explain NBT’s antiferroelectric behavior in this temperature range (230 °C) [52,53]. The T_d has an important place in the practical applications of various materials. In the current investigation, the T_d of all ceramic specimens is identified based on the peak dielectric loss and they are comparable to the values reported in the literature [46,54,55] and the pooled dielectric data are shown in Table 2. All specimens show a typical relaxing ferroelectric behavior featuring a diffuse dielectric constant and frequency dispersion. The maximum permittivity (ε_rmax) at this temperature shifts to higher temperatures as the barium and potassium content rises. Between room temperature and 300 °C, dielectric losses are minimal. There is a sharp increase in dielectric loss at high temperatures, which might be related to an increase in electrical conductivity. The relaxor ferroelectric materials obey the modified Curie-Weiss law [56,57] which is given in equation:

$$\frac{\mathbf{1}}{{\mathit{\epsilon }}_{\mathit{r}}}=\frac{\mathbf{1}}{{\mathit{\epsilon }}_{\mathit{r}\mathit{max}}}\left[\mathbf{1}+\frac{{\left(\mathit{T}-{\mathit{T}}_{\mathit{m}}\right)}^{\mathit{\gamma }}}{\mathbf{2}{\mathit{\delta }}^{\mathit{\gamma }}}\right]$$ (9)

Table 2.

Physical properties (1-x-y)NBT-xBT-yKBT systems obtained at 100 kHZ

Sample	Ɛr at room temperature	tanδ at room temperature	Ɛrmax at Tm	Td (°C)	Tm (°C)
NBT	724	0.15	3829	231	343
KBT	348	0.19	1761	224	365
NBT-0.07BT	1325	0.28	5452	217	373
NBT-0.20KBT	987	0.17	5126	213	385
0.73NBT-0.07BT-0.20KBT	2274	0.048	8475	206	387

For ferroelectric materials the value of γ is less than 1 and for relaxor it is varying from 1 to 2. Where δ (Gaussian coefficient of diffuseness) is a coefficient related to the peak broadening of the phase transition. Equation (9) was adapted in the T_m region in agreement with the results from the experimental data for the dielectric constant. The finding shows that all the tested sites are aligned on a straight line, suggesting that these materials do indeed fit this modified law. Moreover, the γ values for pure NBT, pure KBT, NBT-0.07BT, NBT-0.20KBT, and 0.73NBT-0.07BT-0.20KBT samples are 1.6, 1.4, 1.5, 1.6, and 1.7, respectively. This indicates that the addition of KBT in NBT-xBT lattice enhances the relaxor property behavior of the NBT-xBT system.

3.7. Impedance spectroscopy study

The CIS is typically employed to study the electrical response over a wide range of temperatures and frequencies [58,59]. It is a widely applied technique for the examination of the electrical properties and microstructure of materials. The data for the resistive and reactive components, which correspond to the real and imaginary parts, respectively, will be provided by the impedance measurements on a particular material. It can be represented in a conventional manner in a plot in the complex plane (Nyquist diagram) under different representations: Complex impedance (Z*) and Complex permittivity (ε*).

Z* = Z′−jZ″ = (Y*)⁻¹ = Rs−1/jωCs (10)

ε∗ = ε′−jε″ (11)

where j =$\sqrt{-1}$ , ω = 2πf is the angular frequency and C_o is the geometrical capacitance (C_o = ε_o·a²/d, ε_o = 8.85 × 10⁻¹² F/m, a² and d: are electrode surface area and spacing, respectively).

The variation of the complex impedance (Z″) with the real part of the impedance (Z′) (cole - cole plots), according to equations (10), (11), of typical pure NBT ceramics at different temperatures (400 °C, 420 °C, 440 °C, 460 °C, 480 °C, and 500 °C) is shown in Fig. 12(a). The -Z″ vs. Z′ curves typically characterized semicircle arcs whose diameters narrowed at the observed temperature due to the overlap of two semicircles corresponding to the contributions of intra-grain resistance (Rg) and grain boundary resistance (Rgb) in the high-frequency region with a low-frequency peak due to the contribution of the electrode polarization (Re), and all centers of these semicircle arcs were above the Z'. In addition, by using a model (inset in Fig. 12(b)), we were able to fit the experimental Nyquist plots performed. The circuit contains, grain resistance and capacitance (Rg, Cg), grain boundary resistance and capacitance (Rgb, Cgb), in parallel and series combinations. Table 3 collects the adjusted grain strength and capacity (Rg, Cg) and grain boundaries (Rgb, Cgb) for all materials. This feature of the -Z″ vs Z′ curves was indicative of the non-ideal Debye relaxation process [[60], [61], [62]]. The same type of complex impedance plot character was identified for all other specimens. The resistance decreases as the temperature increases, indicating the negative temperature coefficient of resistance (NTCR), and the characteristic of a semi-conductors i.e., the enhancement of the conductivity of the material [62]. According to M. Benyoussef et al. [53], the reason for this phenomenon is the increased mobility of space charges with increasing temperature.

Fig. 12.

The complex impedance spectroscopy of NBT ceramics at different temperatures (a), Fitted Nyquist plot of impedance at 500 °C along with equivalent circuit (b), Complex impedance (Z″) with real impedance (Z′) of (1-x-y)NBT-xBT-yKBT at 400 °C (C).

Table 3.

A comparison of the electrical characteristics Rgb (kΩ), Cg (pF), Rgb (kΩ), and Cgb (pF) obtained by fitting the experimental data using the equivalent circuit for (1-x-y)NBT-xBT-yKBT at 500 °C.

Sample	Rg (kΩ)	Rgb (kΩ)	Cg (pF)	Cgb (pF)
NBT	10.39	1.13	0.81	0.22
KBT	8.35.	2.43	0.97	0.46
NBT-0.07BT	7.27	3.45	1.42	0.78
NBT-0.20KBT	9.54	1.59	0.89	0.19
0.73NBT-0.07BT-0.20KBT	7.13	5.78	1.59	0.86

Therefore, the charge transport mechanism in the intra-grain zone and at the grain boundaries is thermally activated. The radius of the semicircular arc continues to shrink as more barium and potassium is added to the NBT phase, indicating a rise in conductivity for (NBT-0.20KBT, NBT-0.07BT, and 0.73NBT-0.07BT-0.20KBT) (see Fig. 12(c)). In addition, the asymmetric shrinkage of the semicircles with increasing temperature would suggest an inhomogeneous distribution of the relaxation time (τ = 1/ω) [24,63,64].

3.8. Piezoelectric properties

Fig. 13 exhibits the variation of the electromechanical coupling coefficient (k_p), according to equation (2), and piezoelectric coefficient (d₃₃) with the variation of xBT and yKBT contents in the (1-x-y)NBT-xBT-yKBT system. The same trend can be seen, d₃₃ and k_p increase with increasing x,y(mol.%), reach the maximum value of d₃₃ = 146 pCN⁻¹ and k_p = 0.294 at 0.73NBT-0.07BT-0.20KBT then decrease at pure KBT. The high piezoelectric response for 0.73NBT-0.07BT-0.20KBT MPB composition, sintered at 1100 °C, can be related to the high relative density (∼97%), larger grain size (2.7 μm) and presence of mixed structures. Higher the dielectric constant (ε_r) values of piezoelectric ceramics, larger are the d₃₃ values [65,66]. In the context of lead-free piezoelectric ceramics, NBT-0.06BT ceramic exhibits a piezoelectric constant of 125 pC/N as a result of the existence of morphotropic phase boundary (MPB) [67].

Fig. 13.

Piezoelectric constant d33 and electromechanical coupling factor kp as a function of xBT and yKBT content for (1-x-y)NBT-xBT-yKBT ceramics.

Moreover, two-phase presence throughout 0.73NBT-0.07BT-0.20KBT compounds results in fewer grain boundaries that serve as energy barriers [68] and creates an ideal environment for simpler domain motion, both of which enhance the significant piezoelectric characteristics [65,66]. In 0.73NBT-0.07BT-0.20KBT ceramics, it is clear that the presence of MPB between the Rh + T phases is important to improve the piezoelectric characteristics. On the basis of these findings, we are able to confirm that the electrical performance is quite sensitive to the subtle variation in composition. This has rendered this composition suitable for piezoelectric applications.

4. Conclusion

Polycrystalline powders of (1-x-y)NBT-xBT-yKBT have been developed by solid-state route. The effects of concurrent Ba²⁺/K⁺ substitution at the A site in NBT on structural and dielectric properties were examined. The refined structural parameters provided a confirmation of the good quality of the specimens and the absence of any impurity phase in the prepared materials. The structural study of the solid solution (1-x-y)NBT-xBT-yKBT was carried out in order to identify the influence of the Ba²⁺/K⁺ substitution on the cationic distribution within the structure, on the change in bond distances, on the bond angles, the axial ratio and on the microstructure. As the barium and potassium content increases, the structure evolves from a rhombohedral R3c, rhombohedral (space group R3c) + tetragonal (space group P4mm) structure, and finally to a tetragonal (space group P4mm) structure for pure KBT. The three-dimensional crystal structure was generated using VESTA. SEM images revealed a homogeneous microstructure consisting of grains of almost equal size, high densification and low porosity. The average grain size ranges from 2.2 μm, to 2.9 μm. The evolutions in the Raman spectra with increasing xBT and yKBT contents were examined and thoroughly discussed in relation to the structural transitions. The dielectric constant increases with the ferroelectric phase and improves over the two constituent phases in the 0.73NBT-0.07BT-0.20KBT system, indicating its MPB nature. The very high values of the dielectric constant render it appropriate for high-temperature ceramic capacitors. The diffusive phase transition exhibited a dispersive behavior indicated by the degree of diffuseness and modelled via the modified Curie-Weiss law relation. This behavior appears to be associated with the cationic distribution within the structure. The relaxation frequency (f_max = 1/τ) varies accordingly with the temperature as well as the composition of the xKBT. To further understand the electrical characteristics of the ceramics and how they relate to the grains and grain boundaries, complex impedance spectroscopy was conducted across a wide frequency range (1 kHz–100kHz) at various temperatures. Additionally, by using theoretical modeling, the experimental results from the Nyquist plot have been appropriately explained, and grains and grain boundaries have both been identified as factors in the conduction process. Enhanced piezoelectric constant d₃₃ (146 pCN⁻¹) as well as electromechanical coupling factor kp (0.294) for the 0.73NBT-0.07BT-0.20KBT compound. According to our research, Ba²⁺/K⁺ doping can be a potent tool for modifying the local structure of the NBT system as well as its dielectric, ferroelectric, piezoelectric, and electromechanical proprieties.

Author contribution statement

Mohammed Mesrar: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Wrote the paper.

Abdelhalim Elbasset, Nor Said Echatoui, Farid Abdi, Taj Dine Lamcharfi: Contributed reagents, materials, analysis tools or data; Wrote the paper.

Funding statement

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Data availability statement

Data will be made available on request.

Declaration of interest’s statement

The authors declare no conflict of interest.