Simulation of Nonlinear Pyroelectric Response of Ferroelectrics near Phase Transition: Fractional Differential Approach

Abstract

The paper is devoted to mathematical modeling pyroelectric current of ferroelectric single crystal under the conditions of intensive light heating in view of fractal behavior of these materials. The proposed approach is based on numerical simulation of thermal distribution in a ferroelectric sample using time fractional operator as well as computation of pyroelectric response. The simulation results for typical TGS ferroelectric crystal were described in one-dimensional case of the model in comparison with experimental data. Pyroelectric signals depending on temperature pyroelectric coefficient and thermal physical characteristics were also analyzed.

Numerical simulation of polarization switching kinetics in ferroelectrics based on fractional Kolmogorov – Avrami model

“…The theory of fractional differentiation is used to describe processes and phenomena in complex structures that exhibit fractal characteristics, heterogeneity, long-range correlations, and time memory effects [19,20,21]. A fractional approach has been adopted for simulation of polarization reversal processes [22,23], polarization current formation [16,24,25], and polarization hysteresis in ferroelectrics [26,27,28]. The time-fractional derivative is used to formalize a special property of ferroelectrics like memory effect.…”