Frequency dependence of the complex dielectric permittivity of ferroelectric relaxors.

Abstract

Ferroelectric relaxors belong to a class of materials which possess a local polarization until very high temperature and exhibit a wide frequency range dielectric dispersion around and below ${\mathit{T}}_{\mathrm{max}}$, the temperature of the dielectric maximum. By supposing an exponential-type distribution for the volume of the polar microdomains, we have modeled the dielectric behavior of ferroelectric relaxors. From this model, the low-frequency permittivity appears to follow a power law of ${\mathrm{\ensuremath{\omega}}}^{\mathit{n}}$ type with the exponent n inversely proportional to the width of the size distribution. By analyzing experimental data in two typical ferroelectric relaxors with perovskite-type and tungsten bronze-type structures, the temperature dependence of the exponent has been determined. It comes out that the size of nanodomains begins to strongly increase upon cooling through ${\mathit{T}}_{\mathrm{max}}$, giving rise to a peak of the permittivity which does not result from a true phase transition. The peak observed for the imaginary part of the permittivity corresponds to the temperature at which the dispersion of the real part attains maximum. The interval between the largest and smallest cluster sizes has been estimated. It is found that only a small variation in polar cluster size can lead to a wide dielectric dispersion covering several frequency decades.