Abstract:We present a method for numerical calculation of two dimensional distributions of the attempt relaxation times and activation energies from the temperature dependence of the experimental dielectric permittivity dispersion. We introduce empirical attempts to account for broad and/or asymmetric dispersions with the idea of using a weighted collection of Debye relaxation times. Then we present a modification of the aforementioned idea including attempt relaxation time and activation energy using the Arrhenius law, which significantly complicates the computation of the aforementioned distribution. Incorporating the activation energy and the attempt relaxation time into the equation transforms the discretized matrix equations into tensor equations. We rework the tensor equations into simpler matrix equations, thus permitting us to solve the presented discretized integral equation by using existing Least Distance Problem solving methods. Also, we present a regularization method and a way to choose the regularization parameter based on a best fit criterion. In the end we discuss the method showing some simulated results and experimental results. We then point out some problems involved in the calculations and propose methods to reduce their significance.
The complex dielectric permittivity of 0.05PMN-0.95PSN ceramic was measured in the frequency range from 20 Hz to 3 GHz. Two anomalies of complex dielectric permittivity were observed 398 and 286 K which can be attributed to the ferroelectric and antiferroelectric phase transitions respectively. From frequency dependences of the real and imaginary parts of dielectric permittivity the distribution of relaxation times f(τ) was calculated. The distribution of relaxation times data together with the dielectric dispersion data shows the competing interactions between these two phase transitions and appearance of the dipolar glass state below the antiferroelectric phase transition.
In this paper the method of calculation of two dimensional distribution function from dielectric spectra is presented. Simulation showed, that it is possible to obtain distribution function from experimental dielectric spectra.
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