Stress and frequency dependence of the direct piezoelectric effect in ferroelectric ceramics

It is shown that at weak alternating stress the relationship between the piezoelectrically induced charge and applied stress in ferroelectric ceramics has the same form as the Rayleigh law for magnetization versus magnetic field in ferromagnetic materials. Applicability of the Rayleigh law to the piezoelectric effect is demonstrated in detail for lead zirconate titanate (PZT) ceramics. Experimental results indicate that the dominant mechanism responsible for piezoelectric hysteresis and the dependence of the piezoelectric coefficient on the applied ac stress is the pinning of non-180$°$ domain walls. The dependence of the piezoelectric coefficient on the frequency of the driving stress is examined and is shown to be due to the frequency dispersion of both reversible and irreversible components of domain-wall displacement. Analysis of the stress dependence of the piezoelectric phase angle reveals piezoelectric hysteresis contributions that are not necessarily due to Rayleigh-type displacement of domain walls. Piezoelectric properties of a modified lead titanate composition that exhibits non-Rayleigh type behavior are examined and compared with the properties of PZT ceramics.