A theory of domain switch for the nonlinear behaviour of ferroelectrics

摘要

While there has been some significant progress in the study of piezoelectric behaviour of composite materials, the success has been primarily confined to the linear range. The linear behaviour of such a composite system involves issues of homogenization and many well-developed methods in the uncoupled fields can be readily extended to the coupled field. Nonlinear properties of piezoelectric materials-such as ferroelectricity-involve not only issues of homogenization but, equally importantly, the irreversible thermodynamics and physics of domain switch. This paper seeks to integrate the aspects of thermodynamics, physics and mechanics (homogenization) involved to develop a nonlinear theory for the coupled electromechanical properties of ferroelectrics. The theory starts out with the formulation of Gibbs free energy of the system at its generic state and, by considering the thermodynamic driving force and resistance force during domain switching, a kinetic equation is established to determine the volume concentration of the new domain at a given applied stress and/or electrical field. The overall strain and the overall polarization of the system are then determined. The developed theory is a coupled theory with an evolving microstructure, and is applied to calculate the nonlinear stress-strain relation and depolarization of a poled lead zirconate titanate (PZT) under a compressive stress. The calculated results display the essential features of ferroelectric behaviour, and are found to be in good quantitative accord with experimental data.