Characterization of fractional order for high-frequency bandwidth model of dielectric ferroelectrics

Fractional operators are particularly well adapted for modeling dielectric losses of a ferroelectric material. Common integer derivative operators are generally limited to a relatively weak frequency bandwidth, whereas an approach based on fractional derivatives gives rise to good accuracy between measured hysteresis and simulated loops beyond the frequency bandwidth of classical piezoelectric systems. This article demonstrates the relation between the fractional operator used for the modeling of hysteresis plots (high electric field amplitude, relatively low frequency) and the fractional behavior of a ceramic characterized by the frequency analyzer characterization (low electric field amplitude but high frequency) bandwidth measurements obtained using impedance spectroscopy. In both cases, it was concluded that the dynamic losses had the same physical origin and could consequently be modeled using the same operator and parameters. This notion is particularly interesting as it enables to limit the piezoceramic characterization to the impedance analyzer and to anticipate the high-level excitation behavior in simulation. Finally, it confirms that the fractional operator provides a good view of the dynamic behavior and broadens its domain application to the dynamic variation of the well-known piezoelectric coefficients.