Domain Wall Theory for Ferroelectric Hysteresis

Abstract

This paper addresses the modeling of hysteresis in ferroelectric materials through consideration of domain wall bending and translation. The development is considered in two steps. In the rst step, dielectric constitutive relations are obtained through consideration of Langevin, Ising spin and preferred orientation theory with domain interactions incorporated through mean eld relations. This yields a model for the anhysteretic polarization that occurs in the absence of domain wall pinning. In the second step, hysteresis is incorporated through the consideration of domain wall dynamics and the quanti cation of energy losses due to inherent inclusions or pinning sites within the material. This yields a model analogous to that developed by Jiles and Atherton for ferromagnetic materials. The viability of the model is illustrated through comparison with experimental data from a PMN-PT-BT actuator operating at a temperature within the ferroelectric regime.

Optimal Control of Hysteresis in Smart Actuators: A Viscosity Solutions Approach

“…It belongs to the class of Duhem hysteresis models and can be rewritten as a system involving both continuous control and switching control. Note that a low dimensional model for ferroelectric hysteresis has been proposed by Smith and Hom [7]. Their model has the same structure as that of the ferromagnetic hysteresis model we use in this paper.…”

Modeling, Inverse Problems and Feedback Control for Distributed Dynamical Systems

“…The initial theory for ferroelectric materials was presented in [65,70,71] and extensions to incorporate the temperaturedependence in relaxor ferroelectric materials is summarized in [72]. The extension of the models to piezoceramic transducers was reported in [73,74,75,76].…”

Parameter Estimation Techniques for a Polarization Hysteresis Model

“…Additionally, the N d × 1 vectors P and P are defined componentwise by (14) and the N d × N matrix A is defined row-wise by…”

“…A number of modeling strategies for these compounds have been proposed but three stand out in the sense that they provide unified frameworks for characterizing hysteresis in ferroelectric, ferromagnetic and ferroelastic materials, which are collectively referred to as ferroic compounds. These three approaches are the following: (i) homogenized free energy models [9,13,18], (ii) Preisach formulations [1,2,12,19], and (iii) domain wall models [6,8,11,14,15]. The first two are formulated as integral equations whereas the domain wall models are typically posed as differential equations.…”