Rayleigh Law Response in Ferroelectric Ceramics: Quantifying Domain Wall Dynamics and Structural Relationships

The polarization and strain responses in ferroelectric materials are non-linear and hysteretic. A number of mathematical and phenomenological approaches have been used to describe and quantify this behavior. In order to fully describe this response dielectric and piezoelectric coefficients must include real and imaginary components and suitable non-linear terms. The Rayleigh Law has been shown to provide a suitable description of the non-linear dielectric and piezoelectric response in bulk, single crystal, and thin film piezoelectrics. It has also been shown to be mathematically consistent with physical models for domain wall motion. The Rayleigh Law fitting of the polarization-field and strain-field hysteresis loops at subswitching fields (E<1/2E_C) provides a straightforward and compact approach to quantify of this complex response. The coefficients obtained from this analysis can be applied to quantify variations in extrinsic domain-wall response. Rayleigh coefficients will be used to discuss the role of crystal structure, and symmetry on the dielectric and piezoelectric properties ferroelectric ceramic materials.