Investigation of the piezoelectric nonlinearity in pzt thin films using optical interferometry

In this paper we shall try to demonstrate how these two techniques can be used not only for routine piezoelectric measurements, but to give a deeper insight into different processes operating in ferroelectric materials. 

3 Investigation of the piezoelectric nonlinearity in pzt thin films using optical interferometry 

The origin of the nonlinearity and hysteresis in the films is most likely due to displacement of domain walls [4], If domain walls move in a medium with a random distribution of pinning center, the response of the material can be described, in the first approximation by Rayleigh relations. We next demostrate how optical interferometry can be sued to verify whether this particular model applies to the investigated pzt thin film. In the case of the converse piezoelectric effect, when the driving field E is varied between — Eo and Eo, the piezoelectric strain x is hysteretic and can be expressed by the following Rayleigh relations  

13 Piezoelectric Relaxation and Nonlinearity investigated by Optical Interferometry 

Interesting properties of the Rayleigh relationships can be obtained from the expansion of Equation (13.1) in Fourier series. For E = Eq sin(ut), one obtains  

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