A Temperature-dependent Constitutive Model for Relaxor Ferroelectrics

Abstract

This paper addresses the development of a temperature-dependent constitutive model for relaxor ferroelectric materials. These compounds exhibit a diffuse transition region between the paraelectric and ferroelectric phases due to the chemical heterogeneity of the materials. At low temperatures, the materials exhibit significant dielectric hysteresis in the relation between the applied field E and the macroscopic polarization P, with the degree of hysteresis decreasing as the temperature increases to freezing temperature Tf. Above the freezing temperature, the relation is single-valued, but nonlinear. These phenomena are modeled by assuming that the material is comprised of an aggregate of micropolar regions having a range of Curie temperatures. Thermodynamic principles are employed to obtain a micropolar model, which predicts the saturation polarization and distribution of regions as a function of temperature. A corresponding macroscopic model is then constructed to predict the dielectric behavior of the material above the freezing temperature. Hysteresis below the freezing point is incorporated through the quantification of energy required to bend and translate domain walls pinned at sites, including inclusions, point defects, and local fields, inherent to the material. The resulting ordinary differential equation (ODE) model quantifies the constitutive nonlinearities and hysteresis exhibited by the materials through a wide range of temperatures and input drive levels. The predictive capabilities of the model are illustrated through a comparison with PMN (lead magnesium niobate) and PMN-PT-BT (PT: lead titanate; BT: barium titanate) data collected at temperatures ranging from 133 to 313 K.