*2.2.4.1. De-aging by electric field cycles*

The reduction of the internal bias field during de-aging by electrical cycling depends on: i) time exposure to the field (so frequency and number of cycles), ii) temperature, and iii) electric field amplitude. Early experiments on the kinetics of de-aging in acceptor-doped lead zirconate titanate (PZT) suggested that the de-aging is a thermally activated process.[10] The kinetics of internal field relaxation follows an exponential function of the type:

$$E\_{\rm int}(t) = E\_{\rm int}^0 \exp\left(-\frac{t}{\tau}\right) \tag{2}$$

where *Eint* <sup>0</sup> represents the internal bias field before the electrical cycling and *τ* is the time needed for the relaxation of the internal bias. These two parameters can be obtained from the slope and the intercept of the *ln*(*Eint*)−*t* plot. Carl and Hardtl [10] found that the activation energies in undoped PZT lie between 0.25 and 0.5 eV, those in specimens doped with Mn or Fe range between 0.6 and0.7 eV, while thatfoundin theAl-dopedspecimens is about 0.8 eV.The authors also noticed that these activation energy values are similar to the activation energy of the electricalconductivityandcametotheconclusionthatthemechanismsofaging/de-agingshould be somehowconnectedto thepropertyof electrical charges transport.This ideahasbeenfurther explored by Morozov and Damjanovic [13], who performed a systematic study of charge migration processes in hard, undoped and soft PZT ceramics. They found that in hard compo‐ sitions, the activation energy of alternating current (AC) conductivity is similar to the activa‐ tion energy of the de-pinching process found by Carl and Hardtl in the same compositions. [10] It was concluded that the aging/de-aging process in acceptor doped ferroelectrics should be based on charge transport by the local movements of defect dipoles through short range migration of oxygen vacancies. The activation energy of long-range charge migration under constant electric field (DC conductivity) was found to be significantly larger.[13]

### *2.2.4.2. De-aging by heating-quenching*

The aging effects can be relaxed by heating the system at T > Tc and by subsequently quenching it to a temperature much lower than Tc. The heating process produces a thermal disordering of defects at high temperature and the quench allows keeping the defects in a disordered configuration also at lower temperatures. The relaxation of the internal bias in aged samples upon heating-quenching has been observed in several experimental studies; see for instance Ref. 14 among others.

### **2.3. Fatigue**

applied in the reverse direction. Indirect experimental proof of the domain effect model is based on the measurement of the dielectric permittivity and loss. Acceptor-doped aged systems usually show a reduction of permittivity and loss compared to the non-aged specimens. In early studies this was attributed to the clamping of domain walls due to the presence of an internal bias, which results in a reduction of the extrinsic contribution to dielectric loss.[10] Theoretical models based on the drift/diffusion of charge carriers, driven by the compensation of the depolarizing field and by the spatial gradient of their concen‐ tration, indicate that mobile charged species can migrate to domain walls and hinder domain

**Figure 3.** Scheme of symmetry conforming property of defects in different crystal structures: tetragonal (a, b); ortho‐ rhombic (c, d); rhombohedral (e, f). The scheme refers to the presence of an acceptor D3+ in the B4+ site of the ABO3

The interface regions between dissimilar phases, such as undesired secondary phases, pores and electrodes, are often the location of space charge accumulation, which could represent another source of internal bias field responsible for deformations and asymmetries in hyste‐ resis loops. Systematic investigations of the effect of impurities on the efficiency of the poling process have been presented in early reports [12], where it was proposed that in presence of certain impurity species the poling efficiency decreases due to the effect of space charges.

The aged state is an out-of-equilibrium state and therefore it can be destabilized by several processes. These include: i) electrical bipolar cycles at sufficient amplitude; ii) heating/ quenching from T > Tc to T « Tc; iii) light illumination in some cases. The recovery process from the aged state results in the re-establishment of unbiased hysteresis loops, and is usually called *rejuvenation* or *de-aging*. The study of the kinetics of de-aging, either electric field-induced or thermally-induced, can contribute to further understand the microscopic mechanisms of

wall movement.[11]

**c. Grain boundary effect**

perovskite-type compounds. After [7].

210 Ferroelectric Materials – Synthesis and Characterization

*2.2.4. Rejuvenation or de-aging*

aging.

The term *fatigue* in ferroelectric/ferroelastic materials indicates the degradation of the switch‐ able polarization after a certain number of electrical cycles. Additionally, fatigue can determine the appearance of asymmetric loops due to the effect of biasing mechanisms, which induce preferential polarization and strain states. Besides, asymmetric hysteresis loops often observed in DC poled systems have been also classified in the literature as fatigue-like effects.[15] The biasing processes under repeated AC electric field cycles or DC poling fields depend in turn on several other factors, such as the composition and stoichiometry of the material, tempera‐ ture, geometry of sample and electrodes, electrical loading characteristics, including the electric field amplitude and frequency. Hence a succinct classification of the entire phenom‐ enology becomes challenging.

### *2.3.1. Hysteresis loops after different types of fatigue-like loading*

Fig. 4 shows the typical hysteresis loops observed after different types of fatigue-like electrical loading. Fig. 4a is relative to the effects of fatigue under unipolar AC electrical loading after 109 cycles on the bipolar P-E and S-E curves of Pb0.99[Zr0.45Ti0.47(Ni0.33Sb0.67)0.08]O3 (PIC 151) ceramics.[15] Fig. 4b shows the P-E and S-E bipolar loops of 0.94Bi1/2Na1/2TiO3–0.06BaTiO3 (0.94BNT-0.06BT) after 1, 104 and 107 electric field bipolar cycles.[16] Fig. 4c displays the bipolar P-E and S-E curves of PZT 4D ceramics previously poled under a DC poling field of ± 2.5kV/mm applied at T = 125 °C for 5 minutes.[17] It can be seen that the sign of the DC poling field significantly affects the shape of the P-E and S-E loops. In particular, samples pre-poled under positive DC field show P-E loops shifted towards left and S-E loops with a suppression of the left wing; opposite effects can be noticed in samples poled under negative DC field. However, it is worth recalling that to correctly establish the sign and value of polarization and strain in samples subjected to previously electrical loading, polarization and strain must be monitored for the entire electrical history. During DC poling of PZT 4D, polarization and strain were not monitored, therefore, the sign and values in Fig. 4c have relative validity; only the polarization and strain amplitudes are meaningful. Fig. 4d shows the P-E and S-E curves of BaTiO3 ceramics sintered at different temperatures after one loading-unloading cycle up to approximately 3 kV/mm field amplitude and 10 Hz frequency. It can be concluded that the deformation of the hysteresis loops is caused by the presence of an internal bias field which forces the systems into preferred polarization and strain states.

**Figure 4.** Fatigue-like effects on P-E and S-E hysteresis loops: (a) after unipolar electrical fatigue cycles in PIC 151 ce‐ ramics, courtesy of N. Balke, after [15]; (b) after unipolar electrical fatigue cycles in 0.94BNT-0.06BT ceramics, courtesy of Z. Luo, after [16]; (c) PZT 4D after DC poling of 2.5kV/mm applied for 5 minutes at 125°C [17]; (d) after one AC poling cycle in BaTiO3 ceramics sintered at different temperatures [17].
