Piezoelectric ceramics relaxor ferroelectrics

Finally, it is worth mentioning that a phenomenon analogous to the difference between the normal and giant flexoelectricity of calamitic and bent-core nematics, respectively, exists in crystals, ceramics and polymers too. The flexoelectric response (defined in Eq. (3.1)) of perovskite-type ferroelectrics, " of relaxor ferroelectric ceramics and polyvinylidene fluoride (PVDF) films are four orders of magnitude larger than the flexoelectricity of dielectric crystals. In those sohd ferroelectric materials the polarization induced by flexing is evidently of piezoelectric origin. 

Figure 7 shows the ac strain amplitude versus dc bias fields, measured up to the fourth harmonic, with a driving 0.37 MV.m-i peak-to-peak ac field at 120 Hz for PLZT (9.5/65/35). In this case, the first harmonic piezoelectric strain is dominant and seems to increase with the dc bias field until a maximum is reached at 1.2 MV.m-i dc. The theoretical curve seen in this figure is the result of fitting the data collected at 120 Hz to the first harmonic term in equation (4), while fixing the ac field value. This general behaviour of relaxor ferroelectrics has been previously observed for PMN electrostrictive ceramics (Masys et al. 2003). 

If all the coefficients of equation (2) are known, one can accurately predict the longitudinal strain under a varying electric field for a given piezoelectric or electrostrictive material, and even for a material exhibiting both piezoelectric and electrostrictive effects, such as irreversible electrostrictive materials. For ideal reversible electrostrictive materials, which possess no remnant polarization at zero electric field, the odd power term of the electric field in equation (2) vanishes. However, we will consider the relaxor PLZT ceramics studied in this chapter as irreversible electrostrictives, to account for any ferroelectric behaviour under dc bias fields, and we will therefore include both terms of the electric field in equation (2). 

The increased strain with increasing dc bias in figure 7 can be explained by previous dielectric measurements of PLZT (9.0/65/35) ceramics as a function of both tempierature and dc bias (Bobnar et al. 1999) They have observed a sharp increase in the dielectric permittivity with increasing dc bias fields at temperatures dose to the ferroelectric-relaxor phase transition, indicating that the dc bias is inducing the creation of electric dipoles at this transition, and hence increasing the overall piezoelectric response. 

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