Effects of frequency and temperature evolution of polar nanoregions on susceptibility dispersion and polarization mechanism in relaxors

A generic theory for the frequency and temperature effects on the characteristic evolution of polar nanoregions (PNRs) is essential for improving and optimizing the design of relaxor-based piezoelectric and electrocaloric cooling devices. Pauli's master equation was used to deduce analytical expressions for both the polarization dynamics and frequency-tunable susceptibility dispersions of relaxors. This was done by coupling the intrinsic equilibrium and dynamic factors of bulk relaxors and thin-films. It has been found that for relaxors to comply with Vogel-Fulcher relation, the evolution of PNR mean volume and coercive field of localized electric hysteresis for PNRs has to obey the classic Merz's switching law. The evolution of PNR mean volume in Pb(Mg _1/3Nb _2/3)O ₃ crystal was calculated in the temperature range of 200-300 K and at different frequencies up to 10 ¹² Hz. Our results were in good agreement with the mean-field percolation theory and experimental correlation lengths. Hence, the proposed theory may serve as a new basis for studying the relationship between macroscopic dielectric, electrocaloric as well as other important properties of relaxors and evolutions of their typical microstructures.