Modeling of hybrid relaxor-ferroelectric Ba(Zr_0.2Ti_0.8)O₃ ceramics

Abstract

In this work, a model based on the existence of polarized nanoregions (PNRs) in a dielectric matrix is presented for a quantitative analysis of the hysteresis behavior in relaxor ferroelectrics. The PNRs are simulated by spheroids covered with a thin dielectric envelope. The electric field dependence of the polarization is described by the Landau-Ginzburg-Devonshire equation. The phase transition temperature of the individual spheroids appears to be strongly dependent on its orientation relatively to the external electric field. In addition, it depends on the aspect ratio of the spheroid and its size. The polarization in a relaxor ferroelectric was calculated by summation of the polarizations of individual spheroids. The final result is obtained by replacing the sum by a convolution integral of averaged angular dependence of polarization and the PNR size distribution. The obtained theoretical calculations are compared with experimental results.

Keywords:

• Relaxor ferroelectrics
• polar nanoregions
• P–E hysteresis

Additional information

Funding

This work was supported by the Russian Science Foundation under grant No. 18-19-00512 and by the German Research Foundation (DFG) Priority Program SPP1599 »Caloric Effects in Ferroic Materials: New Concepts for Cooling«, Project B6.