**1.1. Ferroelectric behaviour and pyroelectricity in ferroelectric materials**

It is known that ferroelectric materials present a spontaneous polarization in the absence of an electrical field (*E*), for temperatures below the temperature of the phase transition from the ferroelectric to the paraelectric phase [1]. These materials have regions with uniform polari‐ zation, which are called ferroelectric domains. If an electrical field is applied to the material, the structure of domains changes due to the reorientation of the dipoles with E. In ferroelectrics with normal ferroelectric-paraelectric phase transitions, if the electrical field is strong enough the system can reach a saturated state, showing a high percentage of oriented domains in the E direction, which depends on the structure of the system. When the electrical field is removed, the system exhibits a remanent polarization (*Pr*), which corresponds to the configuration of the minimal energy. On the other hand, for relaxor ferroelectrics, typical slim loops suggest that most of the aligned dipole moments switch back to a randomly oriented state upon removal of the field.

Ferroelectric materials, good isolators by their nature, exhibit temperature-dependent polari‐ zation, i.e., when the sample is heated the polarization changes and an electrical current is produced (pyroelectric current) which disappears at a certain temperature [1]. For normal ferroelectrics, the pyroelectric current (*iP*) achieves a maximum value when the temperature (*T*) increases, and then decreases until zero at the ferroelectric-paraelectric phase transition temperature. For relaxor ferroelectrics, the pyroelectric current is different from zero even at higher temperatures than *Tm*, as well as the temperature of the corresponding maximum for the real part of the dielectric permittivity [27].

However, the study of the pyroelectric behaviour and its corresponding physical parameters may be quite difficult in many ferroelectric systems because, apart from the localized dipolar species, free charges can also exist in the material. The decay of the electrical polarization could be due to dipolar reorientation, the motion of the real charges stored in the material and its ohmic conductivity. The first of these is induced by thermal excitation, which leads to decay of the resultant dipole polarization, and the second is related to the drift of the charges stored in the internal field of the system and their thermal diffusion. During the temperature rise, the dipoles tend to be disordered gradually owing to the increasing thermal motion, and the space charges trapped at different depths are gradually set free. Therefore the pyroelectric behaviour is usually overlapped by other thermally stimulated processes, and a detailed analysis of this phenomenon is very important in order to separate the different components of the electrical current during the heating of the material (*i-T* dependences), to then make a real pyroelectric characterization of any system.

increase of the *Tm* value. The higher barium concentration into *A* sites was obtained for the

On the other hand, a change from normal ferroelectric-paraelectric phase transition to relaxor behaviour has been observed when the barium concentration is increased [22]. For the compositions showing relaxor behaviour, an increase of the frequency dispersion degree was also observed with the increase of barium concentration. The relaxor behaviour is typical of materials with a disorder distribution of different ions in equivalent sites of the structure, which is called compositional disorder. For the studied materials, the relaxor behaviour has been explained with reference to the positional disordering of cations at *A* sites of the structure,

It is known that ferroelectric materials present a spontaneous polarization in the absence of an electrical field (*E*), for temperatures below the temperature of the phase transition from the ferroelectric to the paraelectric phase [1]. These materials have regions with uniform polari‐ zation, which are called ferroelectric domains. If an electrical field is applied to the material, the structure of domains changes due to the reorientation of the dipoles with E. In ferroelectrics with normal ferroelectric-paraelectric phase transitions, if the electrical field is strong enough the system can reach a saturated state, showing a high percentage of oriented domains in the E direction, which depends on the structure of the system. When the electrical field is removed, the system exhibits a remanent polarization (*Pr*), which corresponds to the configuration of the minimal energy. On the other hand, for relaxor ferroelectrics, typical slim loops suggest that most of the aligned dipole moments switch back to a randomly oriented state upon removal

Ferroelectric materials, good isolators by their nature, exhibit temperature-dependent polari‐ zation, i.e., when the sample is heated the polarization changes and an electrical current is produced (pyroelectric current) which disappears at a certain temperature [1]. For normal ferroelectrics, the pyroelectric current (*iP*) achieves a maximum value when the temperature (*T*) increases, and then decreases until zero at the ferroelectric-paraelectric phase transition temperature. For relaxor ferroelectrics, the pyroelectric current is different from zero even at higher temperatures than *Tm*, as well as the temperature of the corresponding maximum for

However, the study of the pyroelectric behaviour and its corresponding physical parameters may be quite difficult in many ferroelectric systems because, apart from the localized dipolar species, free charges can also exist in the material. The decay of the electrical polarization could be due to dipolar reorientation, the motion of the real charges stored in the material and its ohmic conductivity. The first of these is induced by thermal excitation, which leads to decay of the resultant dipole polarization, and the second is related to the drift of the charges stored in the internal field of the system and their thermal diffusion. During the temperature rise, the dipoles tend to be disordered gradually owing to the increasing thermal motion, and the space charges trapped at different depths are gradually set free. Therefore the pyroelectric behaviour is usually overlapped by other thermally stimulated processes, and a detailed analysis of this

compositions with x ≥ 50 at% [22], supporting the decreasing of *Tm* [22].

88 Ferroelectric Materials – Synthesis and Characterization

which delays the evolution of long-range polar ordering [23, 26].

of the field.

the real part of the dielectric permittivity [27].

**1.1. Ferroelectric behaviour and pyroelectricity in ferroelectric materials**

The thermally stimulated discharge current method is a typical technique for this analysis, which has been applied with very good results to ferroelectric materials [28-30]. By using this method, the pyroelectric current can be separated from other stimulated processes (including the electrical conductivity mechanisms), providing better knowledge of the material response in a wide temperature range.

Several analytical methods have been developed to analyse the thermally stimulated processes [30-33]. Among these can be mentioned the initial rise method, the peak shape method and the numerical method using Gaussians [30-33].

For the initial rise method, it is considered that measurements do not depend on the heating rate in the initial rise region [33]. Then, a slow heating rate can be used, reducing the problems related to the difference of temperature between the samples and the thermocouple or gradients of temperature in the sample. The peak shape methods [34] depend on the constant heating rate, but consider more experimental points concerning the initial rise method. However, these methods do not consider the overlapping of several peaks in the material response, as the Gaussian method does. This method considers the overlapping of several peaks in *i-T* dependences, which is very useful for a better understanding of the material response.

The Gaussian method was proposed by Faubert and Sánchez [32]. It consists of fitting the rightmost part (highest temperatures) of the curve with a single time relaxation theoretical curve (Gaussians), and then a new spectrum is obtained by subtracting the theoretical curve from the experimental one (Figure 2). The operation is repeated until the resulting spectrum is smaller than a fixed limit. The final test is carried out summing all the theoretical curves, which may offer the experimental spectrum.

From the so-called area method given by equation (1), where *TF* is the final temperature and *β* is the constant heating rate, which is constant, the relaxation times (*τ*) can be calculated for each theoretical curve (single curves). On the other hand, it is known that the relaxation times usually show a temperature dependence which can be expressed by the Arrhenius law (equation 2, where *kB* and *τ0* are constants). Then, the activation energy value (U) for each process can be obtained from the ln *τ* vs 1/*T* dependence.

$$\pi(T) = \frac{\int\_{\frac{T}{\ell}}^{r\_f} \dot{\imath}(T)dT}{\beta.\dot{\imath}(T)}\tag{1}$$

$$\pi(T) = \pi\_0 e^{\frac{U}{k\_B T}} \tag{2}$$

**Figure 2.** Theoretical decomposition of the *i-T* dependence using the Gaussian method.

The remanent polarization (*Pr*) can be obtained from the pyroelectric current *ip*(*T*) using equation 3, where *A* is the area of the samples. The integration is made from the operation temperature *T* (usually room temperature) until *Tm* (or a higher temperature in the case of relaxor ferroelectrics).

$$P\_r = -\frac{1}{A\mathfrak{B}} \prod\_{T}^{T\_n} i\_p dT\tag{3}$$

Other parameters can be evaluated from the *ip*(*T*) dependence, such as the pyroelectric coefficient (*p*) and several merit figures. The pyroelectric coefficient is related to the variation of *Pr* (equation 4). The current response parameter (*Rv*) is one of the important merit figures which are associated with pyroelectric behaviour, and can be obtained using equation 5.

$$p = \frac{dP\_r}{dT} \tag{4}$$

$$\mathcal{R}\_v = \frac{p}{\mathcal{E}}\tag{5}$$

There are not many reports concerning the pyroelectric behaviour of ferroelectric systems from the Aurivillius family. Most of the studies have been carried out on pure and modified bismuth titanate [35-36]. For niobium- and thallium-modified bismuth titanate, it has been reported that there is a pyroelectric coefficient of 12 μC/m2 K at room temperature [36], which is better than that for pure bismuth titanate ceramics [35]. The *P*-*E* hysteresis loops have showed a remanent polarization of 3.49 μC/cm2 at room temperature [36].

The chapter presents studies on ferroelectric properties and thermally stimulated processes which have been carried out on the Sr1-xBaxBi2Nb2O9 ferroelectric ceramic system with x = 0, 15, 30, 50, 70, 85 and 100 at%. The dependence of the polarization on the applied electric field is discussed at room temperature, for normal and relaxor ferroelectrics compositions. For the thermally stimulated current, the Gaussian method is used to separate the pyroelectric contribution from the other contributions to the total *i(T)* response in the studied samples. The remanent polarization is evaluated, at room temperature, considering the hysteresis ferro‐ electric loops and the pyroelectric current dependence *iP(T)*. The pyroelectric coefficient and the current response merit figure are also evaluated.
