A Domain Wall Model for Ferroelectric Hysteresis

This paper summarizes a mathematical model for characterizing hysteresis in ferroelectric materials. The model is based on the quanti cation of energy required to bend and translate domain walls and is developed in two steps. In the rst, the underlying anhysteretic polarization is quanti ed through constitutive equations derived using Boltzmann statistics. Three anhysteretic models are considered including the Langevin and Ising spin relations as well as a third formulation which combines attributes of the other two. Hysteresis is then incorporated through the consideration of domain wall motion 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.