Mathematical modeling of hysteresis loops in ferroelectric materials

TL;DR

This paper introduces a new analytical Gibbs free energy model that accurately describes hysteresis loops in ferroelectric materials, allowing for characterization of various patterns through parameter adjustments.

Contribution

A novel mathematical model of Gibbs free energy for ferroelectric hysteresis loops is developed, improving upon previous polarization term approaches.

Findings

Model successfully depicts four hysteresis loop patterns.

Adjusting parameters captures different hysteresis behaviors.

Model aligns well with experimental observations.

Abstract

In published papers, the Gibbs free energy of ferroelectric materials has usually been quantified by the retention of 6th or 8th order polarization terms. In this paper, a newly analytical model of Gibbs free energy, thereout, a new model of polarization-electric field hysteresis loops in ferroelectric materials has been derived mathematically. As a model validation, four patterns of polarization-electric field hysteresis loops of ferroelectric materials have been depicted by using the model. The calculated results indicated that the self-similar model can characterize the various patterns of hysteresis loops in ferroelectric materials through adjusting the external excitation or the synthetically parameter (e.g., electric, temperature, and stress, etc.) employed in the model.