1 Introduction

Research has been carried out over the many decades to modify barium titanate and sodium bismuth titanate ceramics with suitable ions doping at lattice sites [1,2,3,4,5,6,7,8,9,10,11,12]. Solid solution of the above these compounds has also studied to enhance the various properties including the electrical, electromechanical and piezoelectric properties. Some researchers have been successful in enhancing the properties as stated above [13,14,15,16,17,18,19,20,21,22]. Swain et al. [23] studied the solid solution of (1 − x)Na0.5Bi0.5TiO3–(x)BaTiO3 with x = 0.05, 0.06, 0.07 and 0.08 in bulk ceramic form, and these showed interesting ferroelectric and piezoelectric properties. They reported the piezoelectric charge constant to be approximately 105 pC/N and electromechanical coupling factor (Kp) to be 21.17% for x = 0.07 ceramic composition. Cernea et al. [24] reported piezoelectric charge constant to be 77 pC/N for 5 mol% of BaTiO3 in Na0.5Bi0.5TiO3 ceramic synthesized by sol–gel route. Similarly, Kang et al. [25] studied the (1 − x)Bi0.5(Na0.78K0.22)0.5TiO3–(x)BaTiO3 lead-free piezoelectric ceramics prepared through sol–gel route. They observed piezoelectric charge constant of 167 pC/N and electromechanical coupling conversion efficiency of 45% for x = 0.06. The results on the piezoelectric and electromechanical coupling conversion properties for the ceramics made from the solid solution of barium titanate and sodium bismuth titanate are interestingly high and can be further improved by rare earth doping A and B sites. This prompted the author to investigate the solid solution based on barium titanate and sodium bismuth titanate which exhibits good piezoelectric and electromechanical properties. In our earlier studies on barium titanate-based ceramics, i.e., Ba(NdxTi1−2xNbx)O3], good dielectric relaxor behavior was observed for higher concentration of x exhibiting higher value of electromechanical coupling conversion in the range 0.49 to 0.67 depending up on x value [26, 27]. In order to further enhance the dielectric and piezoelectric properties, a binary system [Ba(Nd0.1Ti0.8Nb0.1)O3](1−x)[Na0.5Bi0.5TiO3]x with x = 0.00, 0.25 and 0.65 was chosen for present investigation. Dielectric, DC conductivity and electromechanical coupling studies were carried out on the above ceramic samples and were successful in enhancing the dielectric and piezoelectric properties with NBT content especially the piezoelectric charge constant. The results on the above studies are presented in the present paper and have discussed with suitable explanation.

2 Experiment

High-grade carbonates (BaCO3, 99.9%, Merck), (Na2CO3, 99.9%, Merck) and oxides (Nd2O3, 99.9%, Rare Earth India Ltd), (Nb2O5, 99 + %, Nuclear Fuel Complex, India), (TiO2, 99.99%, Sigma-Aldrich), (Bi2O3, 99.9%, Sigma-Aldrich) were used to prepare the present ceramic compositions. Weighed and thoroughly mixed stoichiometric mixture of oxides and carbonates was taken to prepare the ceramic compositions of [Ba(Nd0.1Ti0.8Nb0.1)O3](1−x)[Na0.5Bi0.5TiO3]x (abbreviated as BNNT(1−x)NBTx) with x = 0.00, 0.25 and 0.65. The powder was calcined at 900 °C for 3 h in the conventional high-temperature furnace. Compacted ceramic disks were final sintered at 1175 °C for 2 h in conventional furnace. In the present study, the dielectric, capacitance resonance and anti-resonance data were obtained using HP4192A impedance analyzer. DC conductivity data were obtained using programmable Keithley 617 electrometer. The modulus resonance and anti-resonance data were obtained from the impedance measurements carried out using AUTOLAB PGSTAT30 low-frequency impedance analyzer.

3 Results and discussion

Figure 1a shows the dielectric constant as a function of temperature from 80 to 800 K at constant 10 kHz frequency. It can be seen from these plots that the ceramic materials showed broad diffused phase transition. This is due to the A and B sites cationic disorder in the [Ba(Nd0.1Ti0.8Nb0.1)O3](1−x)[Na0.5Bi0.5TiO3]x with x = 0.00, 0.25 and 0.65 ceramics. The dielectric constant at RT is 730, 590 and 1701 for x = 0, 0.25 and 0.65 compositions, respectively. The higher value of room-temperature dielectric constant and at around Tmax was observed for the ceramic composition x = 0.65. This is due to the more polarization in the crystal structure for x = 0.65 which has rhombohedral symmetry when compared to other compositions which in turn has cubic symmetry at RT (Table 1). The higher value of dielectric constant for x = 0.65 composition and also the dielectric transition temperature when compared to other compositions may also be due to steric effect arising due to substitution of more smaller ionic radii cations like Na+ and Bi+3 at Ba+2 position [28]. Figure 1b shows the inverse of dielectric constant as a function of log(T − Tmax) at 10 kHz frequency following Curie–Weiss square law. Linear fitting is done to obtain the degree of diffusiveness of transition (δ) and degree of relaxor behavior (γ) from the intercept and slope of the linear fitting, respectively. It can be seen from Fig. 1c, d that the degree of relaxor behavior does not change much with x value, i.e., with the increase in NBT content. But the degree of diffusiveness of phase transition is almost the double for x = 0.65 composition when compared to ceramic composition with x = 0.00. This is due to more cationic disorder at A site which leads to broader distribution of transition temperatures.

Fig. 1
figure 1

a Dielectric constant versus temperature plots, b log((1/\(\varepsilon^{\prime}\)) − (1/\(\varepsilon_{\max}^{\prime}\))) versus log(T − Tmax), c degree of relaxor behavior (γ) versus composition and d degree of diffusiveness of phase transition (δ) versus composition at 10 KHz

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Table 1 Parameters obtained from dielectric and DC conductivity data
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Figure 2a shows the DC conductivity as a function of 1000/T (K). The room-temperature resistivity is in the order of Giga Ω-cm with slight variation with composition. From room temperature to 1000/T = 2.5, the ceramic materials showed slight PTCR effect, and at higher temperatures, these materials showed NTCR behavior. Linear fitting to conductivity data was done in the temperature range 445–505 K to obtain the activation energy for conductivity which is summarized in Table 1 and Fig. 2b. The activation energy for conductivity is 0.97 eV, 0.80 eV and 1.34 eV for ceramic compositions x = 0.00, 0.25 and 0.65, respectively. The higher value of activation energy greater than 1 eV for x = 0.65 indicates that the conductivity is due to oxygen vacancy-related phenomenon [29].

Fig. 2
figure 2

a Log(σdc) versus 1000/T and b activation energy (Eact) versus composition in the temperature region (445–505 K)

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Figure 3a shows the capacitance resonance and anti-resonance data at room temperature. It can be seen from figure that resonance and anti-resonance frequency increased with the increase in composition. From the equations on standard on piezoelectricity [22, 30], the thickness mode of electromechanical coupling factor and piezoelectric charge constant (d33) (Eq. 1) was estimated and is depicted in Fig. 3b, d and Table 2. Here in Eq. (1), ρ is the density of the ceramic sample in kg/m3, CT is the capacitance in farads at 1 kHz, d is the diameter of the ceramic disk in meters, h is the thickness of the ceramic sample in meters, fr is the resonance frequency in Hz and fa is the anti-resonance frequency in Hz. It is observed that the electromechanical coupling conversion for these materials is in the range 54–69%. The piezoelectric charge constant for x = 0.00, 0.25 and 0.65 is 29.88 pm V−1, 31.35 pm V−1 and 33.35 pm V−1, respectively. The higher value of piezoelectric charge constant for x = 0.65 is due to the field-induced strains happening due to the presence of polarized oxygen vacancies present in ceramic material at crystal lattice, at interstitial positions and across the grain boundaries. The presence of oxygen vacancies in ceramic composition x = 0.65 can be known from the observation of activation energy for conductivity of 1.34 eV. In the present ceramic material, oxygen vacancies are formed due to multivalent cations occupying at lattice sites and also due to oxygen loss occurring due to sintering at higher temperatures. This result indicates that the oxygen vacancies are desirable to obtain the higher value of piezoelectric charge constant and these materials are best suitable for use in making high-performance transducers and actuators.

$$d_{33} = \sqrt {\left( {C^{T} * \frac{h}{{\frac{{\pi *d^{2} }}{4}}}*\frac{\pi }{2}*\frac{{f_{{\text{r}}} }}{{f_{{\text{a}}} }}*\tan \left( {\frac{\pi }{2}*\left( {\frac{{f_{{\text{a}}} - f_{{\text{r}}} }}{{f_{{\text{a}}} }}} \right)} \right)*\frac{{\left( {\frac{1}{{4*\rho *f_{{\text{a}}}^{2} *h^{2} }}} \right)}}{{1 - \left( {\frac{\pi }{2}*\frac{{f_{{\text{r}}} }}{{f_{{\text{a}}} }}*\tan \left( {\frac{\pi }{2}*\left( {\frac{{f_{{\text{a}}} - f_{{\text{r}}} }}{{f_{{\text{a}}} }}} \right)} \right)} \right)}}} \right)}$$
(1)
Fig. 3
figure 3

a Capacitance versus frequency, b electromechanical coupling factor versus composition and c piezoelectric charge constant versus composition

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Table 2 Parameters obtained from capacitance resonance and anti-resonance data
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Figure 4a shows the modulus resonance and anti-resonance data at different temperatures. The different temperatures reported for the various compositions are due to observance of these data at these temperatures. The resonance frequency decreased with the increase in composition x. Figure 4b and Table 3 show the electromechanical coupling factor for different compositions. The present ceramic material exhibited over 90% electromechanical coupling conversion. This again may be related to studying these properties with the simultaneous application of high temperature and stress. The stress in the present case is due to studying the electromechanical coupling property in a jig with constant but unknown spring constant. The piezoelectric charge constant for the ceramic with x = 0.00 is 10.70 nm V−1 and increases with the increase in NBT content and attained a value of 17.40 nm V−1 for x = 0.65 ceramic (Fig. 4c). In the present samples, all the samples undergo same constant stress due to jig and hence the increase in piezoelectric charge constant may be attributed to high applied temperature. At these high temperatures, the materials usually become dielectrically and elastically soft in nature and these softer materials produce higher strains with applied electric field. From the above discussion, it can be inferred that the present ceramic materials operating at higher temperature are more dielectrically and elastically softer in nature and hence possess higher value of piezoelectric charge constant. The higher value of piezoelectric charge constant for x = 0.65 is due to the compositionally induced softening of lattice with NBT content. The higher value of piezoelectric charge constant is also due to the field-induced strains happening due to the presence of polarized oxygen vacancies at crystal lattice, at interstitial positions and across the grain boundaries. High value of piezoelectric charge constant and electromechanical coupling conversion (d33 = 2800 pC/N and Kt = 0.95) in lead-based single crystals like PMN-0.33PT was reported by Cao [31]. It is to be noted that the unit of d33 presented in this paper is m V−1 and cited from the literature is C/N. They are different in notation, but it is to be noted here that 1 (m/V) = 1 (C/N). In the present ceramics, the higher value of piezoelectric charge constant was observed when compared to that of lead-based single crystal. It is also observed that the values of piezoelectric charge constant at higher-temperature region (798–873 K) are interestingly higher, when compared to at 300 K. This is due to the degree of disorder at A and B sites (due to formation of AO, BO6 polar clusters) in the ceramic samples. This is also due to softening of crystal lattice at higher temperatures. The higher the temperature is, the more the degree of disorder of polar clusters is, and this leads to larger lattice strains with applied electric field due to more soft lattice. This in turn leads to higher value of piezoelectric charge constant. Similar higher value of piezoelectric charge constant in other ceramic material which is a ternary system based on barium titanate, sodium bismuth titanate and calcium titanate due to temperature and composition-induced strains was reported by us [32, 33]. This indicates that the above explanation of strains induced by polarized oxygen vacancies formed due to compositional heterogeneity [34] and also due to stress induced by higher temperatures is responsible for the observed enhanced electromechanical conversion and piezoelectric charge constant is proper to say in this way. These results on the present ceramic materials indicate that these materials can be used to design high-temperature and high-performance transducers.

Fig. 4
figure 4

a Modulus versus frequency plots, b electromechanical coupling factor versus composition and c piezoelectric charge constant versus composition

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Table 3 Parameters obtained from modulus resonance and anti-resonance data
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4 Conclusions

The present paper describes the dielectric and piezoelectric properties in multi-ferroic ceramics [Ba(Nd0.1Ti0.8Nb0.1)O3](1−x)[Na0.5Bi0.5TiO3]x with NBT content for high-temperature transducer application. Ceramic compositions with x = 0.00, 0.25 and 0.65 exhibited diffused phase transition, and with the increase in NBT content, it increases. The values of electromechanical coupling conversion obtained from the capacitance resonance and anti-resonance data at RT are 54%, 69% and 64% for x = 0.00, 0.25 and 0.65 ceramic samples, respectively. The piezoelectric charge constant at RT for x = 0.00, 0.25 and 0.65 is 29.88 pm V−1, 31.35 pm V−1 and 33.35 pm V−1, respectively. These ceramic samples operating at higher temperature showed above 90% electromechanical coupling conversion. The piezoelectric charge constant obtained from modulus resonance and anti-resonance data is 10.70 nm V−1 for x = 0.00 and increases, and with the increase in NBT content, it attained a value of 17.40 nm V−1 for x = 0.65 ceramic. These materials showed three orders of magnitude greater than piezoelectric charge constant studied at higher temperature region (673–898 K) when compared to at RT. This is due to softening of crystal lattice and also due to response of strained polarized oxygen vacancies at these temperatures. These results indicate that the present materials can be used to fabricate high-performance transducers.