This paper summarizes a mathematical model for characterizing hysteresis in ferroelectric materials. The model is based on the quantification of energy required to bend and translate domain walls and is developed in two steps. In the first, the underlying anhysteretic polarization is quantified 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 quantification 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.

Date Published: 4 June 1999
PDF: 12 pages
Proc. SPIE 3667, Smart Structures and Materials 1999: Mathematics and Control in Smart Structures, (4 June 1999); doi: 10.1117/12.350070

Published in SPIE Proceedings Vol. 3667:
Smart Structures and Materials 1999: Mathematics and Control in Smart Structures
Vasundara V. Varadan, Editor(s)