Nonlinear response of pure and doped Pb(Zr1−xTix)O3 ceramics, with different compositions, has been analyzed in order to evaluate the domain wall motion in these materials. The study of dielectric and converse piezoelectric response shows a clear dependence of the domain wall mobility on the ferroelectric phase. Large lattice distortion in tetragonal samples produces a low mobility of the ferroelectric-ferroelastic domain walls. The influence of the type of defects on the nonlinear response has been explored. The results show that the relative increase of the domain walls mobility in donor-doped materials is greater than the decrease in acceptor-doped materials due to the pinning produced by complex defects. Rayleigh law has been used to evaluate the irreversible contribution of the domain walls movement to the nonlinear dielectric response. The analysis reveals that in presence of oxygen vacancies, the dielectric response cannot be attributed exclusively to the contribution of the irreversible domain wall motion. Furthermore, dielectric constant perpendicular to poling direction has been measured in rhombohedral donor-doped and acceptor-doped samples. The nonlinear response in the perpendicular direction is higher than in the poling direction, and this effect can be enlarged by the presence of complex defects. Dielectric nonlinear response has also been measured at different frequencies in rhombohedral donor-doped sample. A logarithmic dependence on frequency has been observed, which can be explained by the pinning effect on the ferroelectric domain walls by randomly distributed defects.

The dependence of the dielectric constant and its losses on the applied field is studied, as well as the correlation between the dielectric constant and dielectric losses. The results show that hard lead zirconate titanate cannot be described by the Rayleigh model, so the hysteretic response of those materials cannot be attributed exclusively to the contribution of the irreversible processes. The experiments reveal the existence of reversible processes that could be related to the bending of the domain walls, which contribute to the dielectric constant of those materials without producing dielectric losses. The dependence of the dielectric constant on the poling state and on ageing are also studied. It can be reasserted that there are two distinct mechanisms that contribute to the dielectric response. The results show that the reversible contribution is independent of the ageing processes suffered by the sample.

Nonlinear behaviour of power piezoceramic materials has to be studied under strong electric fields. A bridge designed for measuring it at low frequency is described. It consists basically of a capacitance comparison bridge that can be used in two different modes: balanced and unbalanced. The nonlinear electric displacement is split into dissipative and nondissipative terms. Dielectric constant is computed from the last term and related to the instantaneous field. The behaviour of soft and hard PZT ceramic materials has been tested according to this model. In both materials, the dielectric constant not only depends on the instantaneous value of the field but also on its amplitude. While the dependence of the real and imaginary parts of the dielectric constant in soft ceramics is large and practically linear to the field amplitude, in hard PZT it is low and nearly quadratic. The rate between both parts depends on the type of ceramic. Dielectric constant can be divided into two terms. One term is allied to the irreversible motion of domain walls, while the other is related to reversible motion. Balanced and unbalanced modes have been tested for both materials, and results are coherent. Accuracy and limitations of the method are discussed.

A characterization of the nonlinear behavior with high signal excitation in piezoceramic resonators was carried out. The behavior of power devices working at resonance, in which high strains are involved, is explained. A theoretical model previously described is used to explain the motional impedance variation proportional to the square of the motional current. This impedance increase DeltaZ is independent of the frequency and explains: the nonlinear elasticity that produces the A-F effect, the nonlinear mechanical losses that increase greatly close to the resonance, and the hysteresis phenomenon produced with frequency sweeps. Different methods for measuring the mechanical nonlinear coefficients of piezoceramics with high signal excitation are presented. An experimental method is proposed to measure the mechanical loss tangent and the compliance variations as a function of the mean square strain in the piezoceramic. This consists in measuring the maximum admittance and the series resonance frequency for downward frequencies. At this jumping point, the phase angle remains zero whatever the amplitude of the excitation. Two main coefficients characterizing the material mechanical nonlinearity are deduced. Experimental measurements were carried out to compare the nonlinearity of different ceramic materials in longitudinal and transverse mode.

Finding lead-free ceramics with good piezoelectric properties is nowadays one of the most important challenges in materials science. The (K, Na, Li)(Nb, Ta, Sb)O3 system is one of the most promising candidates as a lead-free ceramic for transducer applications and is currently the object of important research work. In this paper, (K0.44Na0.52Li0.04)(Nb0.86Ta0.10Sb0.04)O3 was prepared by a conventional ceramic processing route. For this composition, orthorhombic-to-tetragonal phase transition was observed at temperatures very close to room temperature. As a consequence, good room temperature electromechanical properties were observed, displaying good thermal stability. We show that the most important contribution to dielectric, piezoelectric and elastic response comes from extrinsic effects, as was observed in other perovskite based materials. Nonlinearities in electromechanical properties induced by high electric field or mechanical stress were studied. Non-linear dielectric response was found to be less important than for soft PZT ceramics and was analysed within the Rayleigh framework. The results reveal that the non-linear response at room temperature in this material is mainly due to the irreversible wall domain movement.

A theoretical model that explains the impedance variation due to nonlinear elasticity of piezoelectric materials is described. A modified equivalent circuit is used in order to explain the behavior of a piezoelectric resonator near its series resonance, driven by a high-amplitude signal. A simple relation between the motional impedance Z1 and the motional branch current I1 has been obtained, defining nonlinear impedance coefficients. This model is able to explain and predict: (1) the amplitude-frequency effect, (2) the decreasing of the mechanical quality factor, and (3) the appearance of hysteretic phenomena. An experimental method is proposed to measure the above coefficients, and is used to verify the theoretical model on disk ceramic resonators. Experimental measurements have been carried out to compare the nonlinearity of different ceramic materials.

Temperature dependent dielectric response has been measured in Pb(Zr1−xTix)O3 ceramics. Samples of different compositions (x=0.40, 0.47, and 0.60), pure and doped with Nb-or Fe, were studied at temperatures between 15 and 700K and in the frequency range from 100Hzto1MHz. Unexpected dielectric behavior has been found around room temperature. Anomalous temperature dependent permittivity is observed in pure and Fe-doped samples but not in Nb-doped samples. The anomaly appears related to the presence of oxygen vacancies but not on the sample crystallographic phase. The authors suggest that the anomaly may be a manifestation of the domain wall pinning effect.

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