*2.2.3. Microscopic mechanisms of aging*

Three main microscopic mechanisms have been proposed for the origin of aging, namely a) *volume effect*, b) *domain effect*, and c) *grain boundary effect*. Up to the present, a definitive agreement on which mechanism is the main cause of the aging process has not been achieved, also due to the fact that often these mechanisms can possibly overlap.

### **a. Volume effect**

According to the volume effect model, unintentional and intentional defects, which can be present in the system, are stabilized in preferred lattice sites, creating an internal bias that constrains the switching of the polarization along specific directions. One of the first micro‐ structural schemes of the volume effect model was proposed by Arlt and Neumann [6], and later extended by Ren with the *symmetry-conforming property of point defects*, which was used to describe aging phenomenon in different crystal structures [7]. According to the symmetryconforming property principle, point defects (e.g., oxygen vacancies in acceptor-doped perovskites) distribute in the lattice with the same symmetry of the crystal structure, leading to a *defect dipole PD* parallel to the spontaneous polarization (Fig. 3). During cooling from T > Tc (Tc is a Curie temperature), the crystal structure abruptly changes into a lower symmetry structure stable at T < Tc, while the existing cubic structured defects are still arranged in their original symmetry. The reason is that the kinetics of defects migration is slower compared to the movement of ions driven by the phase transition. In the ABO3 perovskite structure, the presence of an acceptor element in the B-site generates oxygen vacancies, which enable to accomplish charge neutrality. The lattice sites, where the defects can be located soon after cooling from T > Tc, are represented by the octahedron's corners, which all have the same probability of occupancy (*P*<sup>1</sup> *<sup>V</sup>* =...=*P*<sup>6</sup> *<sup>V</sup>* ), as shown by the equal white proportions at the octahedron corners in Fig. 3a. However, over time, the defects tend to rearrange assuming the same symmetry of the crystal structure. The relaxation time of this process reduces with increasing temperature (in the range T < Tc), because thermal energy promotes short range migration of the defects towards a more stable configuration. After aging, the probability of occupancy for all the octahedron's corners is not the same anymore; the location with highest probability of oxygen-vacancy formation is the octahedron's corner that allows the formation of a defect dipole (acceptor ion-oxygen vacancy) parallel to the spontaneous polarization. In Figs. 3b, 3d and 3f, this location is identified by the octahedron corner with the largest white portion. Strong experimental evidence supporting the volume effect model against other aging mechanisms was obtained from targeted tests carried out on a single crystal-single domain of Mn-doped BaTiO3.[8]

### **b. Domain effect**

F p c a t

Fig. 2. Hysteres prepared ceram corresponds to a aged ceramics. T the blue curve w S-E loops of th subsequently ag

208 Ferroelectric Materials – Synthesis and Characterization

sis loops compa mics and aged c a poled non-age The red curve w was obtained wit he as-prepared a ed ceramics (po

**Figure 1.** Definition of the internal bias field, Eint, in (a) pinched and (b, c) asymmetric P-E loops. After [4].

 arison of CuO-m ceramics (aging ed sample, red an was generated by th a positive ele and aged cerami sitive field paral

**Figure 2.** Hysteresis loops comparison of CuO-modified BaTiO3 ceramics: (a) P-E loops of the as-prepared ceramics and aged ceramics (aging at room temperature for 24h); (b) the black line corresponds to a poled non-aged sample, red and blue curves are relative to poled and subsequently aged ceramics. The red curve was generated by applying a pos‐ itive field parallel to the poling, while the blue curve was obtained with a positive electric field antiparallel to the pre‐ vious poling field; (c) S-E loops of the as-prepared and aged ceramics; (d) S-E loops of poled non-aged, and poled and

modified BaTiO g at room temp nd blue curves a y applying a pos ectric field antipa ics; (d) S-E loo llel to poling). A

O3 ceramics: (a) perature for 24h are relative to p itive field parall arallel to the pre ps of poled non

) P-E loops of t h); (b) the blac poled and subseq lel to the poling evious poling fie n-aged, and pol

the asck line quently g, while eld; (c) led and

*volume*  ment on e to the

esent in ins the s of the with the enon in , point e same taneous ructure uctured defects e ABO3 cancies,

ing, namely a) *v* efinitive agreem ved yet, also due

which can be pre as that constrai ructural schemes ended by Ren w aging phenome operty principle e lattice with th el to the spont e), the crystal str xisting cubic stru he kinetics of d ransition. In the ates oxygen vac

the origin of agi the present, a de not been achiev

tional defects, w g an internal bi he first microstr , and later exte sed to describe conforming pro distribute in the *pole PD* paralle urie temperature Tc, while the ex eason is that th n by the phase tr he B-site genera

After [5].

n proposed for t *y effect*. Up to t ng process has n

tional and intent e sites, creating ections. One of th nd Neumann [6] *s*, which was us the symmetryped perovskites) to a *defect dip* Tc (Tc is the Cu ure stable at T < ymmetry. The r nt of ions driven tor element in th

verlap.

**s of aging**  anisms have been *grain boundary* cause of the agin s can possibly ov

model, unintent preferred lattice ong specific dire osed by Arlt an *of point defects* . According to in acceptor-dop cture, leading t ooling from T > ymmetry structu heir original sy to the movemen nce of an accept

4

**pic mechanisms** croscopic mecha *in effect*, and c) sm is the main c hese mechanisms

subsequently aged ceramics (positive field parallel to poling). After [5].

e volume effect e stabilized in p e polarization alo model was propo *rming property*  l structures [7]. xygen vacancies he crystal struc g. 3). During co es into a lower sy l arranged in th wer compared t cture, the presen

**2.2.3 Microscop** Three main mic *effect*, b) *domai* which mechanis fact that often th

**(a) Volume effe** According to th the system, are switching of the volume effect m *symmetry-confo* different crystal defects (e.g., ox symmetry of th polarization (Fig abruptly change defects are still migration is slo perovskite struc

**ect** 

s

**2** T *e* w f

**(** A t s v *s* d d s p a d m p

The domain effect model is based on the concept that mobile defects can diffuse towards domain walls to minimize the local depolarizing fields and may act as pinning agents on domain walls. By performing in situ high-energy X-ray Bragg scattering experiments during the application of an electric field, Tutuncu *et al.* [9] showed that in a pre-poled sample of 0.36BiScO3-0.64PbTiO3, the volume fractions of domains oriented along the electric field is different when the electric field is increased along the previous poling direction and when

**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 perovskite-type compounds. After [7].

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 wall movement.[11]

### **c. Grain boundary effect**

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.

### *2.2.4. Rejuvenation or de-aging*

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 aging.
