**3. Results and discussion**

### **3.1. Ferroelectric properties**

The hysteresis loops at room temperature are shown in Figure 4 and Figure 5 for the studied samples. The compositions with x ≤ 30 at% show polarization-electrical field (*P*–*E*) loops typical of normal ferroelectric materials. The compositions of SBN and SBBN-15 show wide loops at room temperature. This behaviour could be associated with high dielectric losses in these samples. The composition with 30 at% of barium shows the better response with a clear tendency to saturation with the applied electric field. The samples with x ≥ 50 at% show thin hysteresis loops, which are typical of relaxor ferroelectric systems. These compositions have shown relaxor behaviour in the corresponding dielectric analysis [22]; relaxor ferroelectrics do not show a tendency to saturation in the *P*–*E* dependence even in a very high electric field.

**Figure 4.** Polarization (*P*) dependence on the applied electric field (*E*), at room temperature, for samples with x ≤ 30 at %.

measured (during the third step) using a Keithley 6485 Electrometer, while keeping a temper‐

The hysteresis loops at room temperature are shown in Figure 4 and Figure 5 for the studied samples. The compositions with x ≤ 30 at% show polarization-electrical field (*P*–*E*) loops typical of normal ferroelectric materials. The compositions of SBN and SBBN-15 show wide loops at room temperature. This behaviour could be associated with high dielectric losses in these samples. The composition with 30 at% of barium shows the better response with a clear tendency to saturation with the applied electric field. The samples with x ≥ 50 at% show thin hysteresis loops, which are typical of relaxor ferroelectric systems. These compositions have

ature rate of about 5 K/min.

**Figure 3.** Solid-state reaction method for the sample preparation.

92 Ferroelectric Materials – Synthesis and Characterization

**3. Results and discussion**

**3.1. Ferroelectric properties**

**Figure 5.** Polarization (*P*) dependence with the applied electric field (*E*), at room temperature, for samples with x ≥ 50 at%.


**Table 1.** Values of the remanent polarization (*Pr*), *Pr/Pmax* relationship and the coercive field (*Ec*) for the studied samples at room temperature.

Table 1 shows the values of the remanent polarization (*Pr*), the *Pr*/*Pmax* relationship and the coercive electric field (*Ec*), at room temperature, for the studied compositions. *Pmax* is the polarization at the highest applied electric field. The SBN and SBBN-15 samples show the highest *Pr* values. This is associated with higher dielectric losses for theses samples. The compositions with x ≥ 50 at% show the lower *Pr* values. These ceramics have also presented lower piezoelectric activity [37]. The sample with 30 at% of barium shows the better ferroelec‐ tric response with a high *Pr* value and a *Pr*/*P*max relation, showing a good saturation. For this composition, a better piezoelectric response has been reported [37]. The *Ec* values tend to decrease with the increase of barium concentration. For compositions with x ≤ 50 at%, the *Ec* values are higher than those for other ferroelectrics materials from the Aurivillius family [35].

### **3.2. Thermally stimulated processes and pyroelectricity**

Figure 6 and Figure 7 show the dependence of the thermally stimulated current (*i*) on the temperature in the studied samples. The black points represent the experimental curve and the lines represent the fitting, which was carried out using the Gaussian method.

For the compositions with x ≤ 30 at% (Figure 6), three different contributions were observed below the transition temperature (*Tm*). The contribution at higher temperatures (blue line) is observed from the increase of *i* at temperatures near to and higher than the transition temper‐ ature. The pyroelectric contribution is characterized by an increase to a maximum value, when the temperature (*T*) increases, and then a decrease to zero at the ferroelectric-paraelectric phase transition temperature. From this point of view, the third contribution is not the pyroelectric contribution.

The dielectric analysis of the studied samples has shown a strong influence of the electric conductivity on the dielectric parameters at the higher temperature range [22]. The third contribution could be associated with the electric conductivity processes in this temperature range. The influence of this contribution on the second (black line) is remarkable; this second contribution must be associated with the pyroelectric response. The first contribution (red line) Polarization and Thermally Stimulated Processes in Lead-Free Ferroelectric Ceramics http://dx.doi.org/10.5772/60433 95

**Composition** *Pr (μC/cm2*

94 Ferroelectric Materials – Synthesis and Characterization

**3.2. Thermally stimulated processes and pyroelectricity**

at room temperature.

contribution.

*) Pr/Pmax Ec (kV/cm)*

SBN 18.96 0.55 45 SBBN-15 34.48 0.80 63 SBBN-30 13.45 0.75 42 SBBN-50 8.10 0.24 22 SBBN-70 5.44 0.16 14 SBBN-85 3.68 0.11 12 BBN 3.55 0.14 13

**Table 1.** Values of the remanent polarization (*Pr*), *Pr/Pmax* relationship and the coercive field (*Ec*) for the studied samples

Table 1 shows the values of the remanent polarization (*Pr*), the *Pr*/*Pmax* relationship and the coercive electric field (*Ec*), at room temperature, for the studied compositions. *Pmax* is the polarization at the highest applied electric field. The SBN and SBBN-15 samples show the highest *Pr* values. This is associated with higher dielectric losses for theses samples. The compositions with x ≥ 50 at% show the lower *Pr* values. These ceramics have also presented lower piezoelectric activity [37]. The sample with 30 at% of barium shows the better ferroelec‐ tric response with a high *Pr* value and a *Pr*/*P*max relation, showing a good saturation. For this composition, a better piezoelectric response has been reported [37]. The *Ec* values tend to decrease with the increase of barium concentration. For compositions with x ≤ 50 at%, the *Ec* values are higher than those for other ferroelectrics materials from the Aurivillius family [35].

Figure 6 and Figure 7 show the dependence of the thermally stimulated current (*i*) on the temperature in the studied samples. The black points represent the experimental curve and

For the compositions with x ≤ 30 at% (Figure 6), three different contributions were observed below the transition temperature (*Tm*). The contribution at higher temperatures (blue line) is observed from the increase of *i* at temperatures near to and higher than the transition temper‐ ature. The pyroelectric contribution is characterized by an increase to a maximum value, when the temperature (*T*) increases, and then a decrease to zero at the ferroelectric-paraelectric phase transition temperature. From this point of view, the third contribution is not the pyroelectric

The dielectric analysis of the studied samples has shown a strong influence of the electric conductivity on the dielectric parameters at the higher temperature range [22]. The third contribution could be associated with the electric conductivity processes in this temperature range. The influence of this contribution on the second (black line) is remarkable; this second contribution must be associated with the pyroelectric response. The first contribution (red line)

the lines represent the fitting, which was carried out using the Gaussian method.

**Figure 6.** Thermally stimulated current curves (*i*) in a wide temperature range for the SBN, SBBN-15 and SBBN-30 samples. The black points show the experimental data and the red line (first contribution), black line (second contribu‐ tion) and blue line (third contribution) represent the fitting using the Gaussian method.

is observed at the lower temperature range; it could not be associated with the pyroelectric response or electrical conductivity processes.

The compositions with x > 30 at% show the three contributions for temperatures lower than *Tm* as well (Figure 7).

From the theoretical curves *i*(*T*), which were obtained by using the Gaussian method, the values of the relaxation time (*τ*) were calculated (equation 1). The temperature dependence for *τ* (Figures 8 and 9) was obtained for the first and second contributions, showing a typical Arrhenius dependence (equation 2). The values of ln *τ* are represented by points and the lines represent the fitting using equation 2. From the fitting, the corresponding activation energy values (U) for each contribution were obtained, and are shown in Table 2.

The activation energy values for the first contribution are between 0.40 and 0.60 eV. This contribution is observed in the lower temperature range, showing lower current values than those obtained for the second contribution. The first contribution could be related to space charge, which is injected during the polarization process. For the second contribution, which is associated with the pyroelectric current, the activation energy values tend to increase with the increase of the barium concentration until 30 at%; above that concentration, this parameter decreases.

**Figure 7.** Thermally stimulated current curves (*i*) in a wide temperature range for the compositions with x > 30 at%. The black points show the experimental data and the red line (first contribution), black line (second contribution) and blue line (third contribution) represent the fitting using the Gaussian method.

**Figure 8.** Arrhenius dependence of the first contribution on the *i-T* dependence. The solid points correspond to the relaxation time values, which were obtained using equation 1; the solid lines correspond to the fitting using equation 2.

For materials from the Aurivillius family, the major contribution to the spontaneous polari‐ zation comes from the motion of the *A* cation in the perovskite blocks [20, 23, 26]. The analysis of the dielectric behaviour for the studied samples has shown a lower ferroelectric-paraelectric

Polarization and Thermally Stimulated Processes in Lead-Free Ferroelectric Ceramics http://dx.doi.org/10.5772/60433 97

**Figure 9.** Arrhenius dependence of the second contribution on the *i*-*T* dependence. The solid points correspond to the relaxation time values, which were obtained using equation 1; the solid lines correspond to the fitting using equation 2.

transition temperature for the SBN sample [22] than that of the previous report [20]. This result suggests a decrease of the thermal energy, which is necessary to transition from a ferroelectric phase to a paraelectric phase. The structural study for this composition has also shown a higher occupancy of Bi3+ in *A* sites of the structure [22] than previous reports [14], which can explain the lower *Tm* value considering the lower radii ionic of the Bi3+ than that of the Sr2+. Therefore, a lower activation energy value is necessary for the thermal depoling (pyroelectric contribu‐ tion) of the studied SBN sample compared to previous reports. The SBBN-15 and SBBN-30 samples show an increase of the activation energy value with respect to the SBN composition, which is in agreement with the *Tm* behaviour from 0 to 30 at% [22].


**Table 2.** Activation energy values, which were obtained from the fitting shown in Figures 8 and 9.

For materials from the Aurivillius family, the major contribution to the spontaneous polari‐ zation comes from the motion of the *A* cation in the perovskite blocks [20, 23, 26]. The analysis of the dielectric behaviour for the studied samples has shown a lower ferroelectric-paraelectric

**Figure 8.** Arrhenius dependence of the first contribution on the *i-T* dependence. The solid points correspond to the relaxation time values, which were obtained using equation 1; the solid lines correspond to the fitting using equation 2.

**Figure 7.** Thermally stimulated current curves (*i*) in a wide temperature range for the compositions with x > 30 at%. The black points show the experimental data and the red line (first contribution), black line (second contribution) and

blue line (third contribution) represent the fitting using the Gaussian method.

96 Ferroelectric Materials – Synthesis and Characterization

For compositions with x > 30 at%, the activation energy values for the pyroelectric contribution have shown a decrease with the increase of the barium concentration in the structure. These results are in agreement with the dielectric behaviour of these compositions, which is shown in a decrease of the *Tm* values when the barium concentration increases [22]. The SBBN-50 and SBBN-70 samples have shown a greater increase in the occupancy of Ba2+ and Bi3+ in *A* sites than was observed in the SBBN-30, since the concentration of Ba2+ is higher than that of Bi3+, which explains the decrease of *Tm* from 30 to 70 at% of barium and then by extension the lower activation energy values for the pyroelectric contribution.

For SBBN-85 and BBN, a greater decrease of the Ba2+ occupancy in *A* sites is observed than in SBBN-70 [22], but the *Tm* values are lower. For both compositions, it has also been reported that there is a higher Ba2+ occupancy in Bi3+ sites than in the other compositions [22]. A higher Ba2+ occupancy in Bi3+ sites and the corresponding generated oxygen vacancies would distort the ionic dipoles due to the *A* sites' ions. Then, the decay of the spontaneous polarization could be affected, providing a decrease of the *Tm* values and the activation energy values for the thermal depoling process (pyroelectric response).

For the third contribution, there were not enough experimental points in some compositions. Thus, the activation energy was only estimated for the studied samples, showing values between 0.7 and 1.50 eV. These values are related to electrical conductivity processes, which are governed by double ionized oxygen vacancies [21, 24]. The oxygen vacancies in the structure of the studied samples are generated to compensate the electrical charge unbalance, which is caused by the substitution of trivalent Bi3+ ion for divalent Ba2+ and Sr2+ ions.
