  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.
