Study On The Applicability Of Jonscher Power Law To The Analysis Of Electrical Behavior In Solid Materials

For the studies of motion of the charge carriers in single crystal, polycrystalline and glassy materials, the so-called "universal dynamic response (UDR)" as follows is an effective method:Recently, some authors found that there exists a "window" effect, i.e. the power law exponent, s, obtained from curve-fitting are sensitively affected by the frequency window employed in the analysis. So it is important for the researchers to choose a suitable frequency window which may truly describe the nature of the materials.In this thesis, frequency dependence of ac conductivity in 50Li₂O-50P₂O₅ glasses were investigated in the frequency range from 40 to 110MHZ and over a temperature range from 473 to 553K. Based on the analysis of the experimental data according to the power law and the comparison between the results of dc conductivity deduced from two different methods, we proposed a simple method to choose frequency window. Further discussions verified that our choice was reasonable.Following the above analysis, we discussed the ac conductivity spectra of four different materials (40Fe₂O₃-60P₂O₅ glass, 10Li₂O-36Fe₂O₃-54P₂O₅ glass, 8mol% Y₂O₃ stabilized ZrO₂ and 12mol% CaO stabilized ZrO₂) based on the power law. It was found that, in each case, the power law exponent first decreases with increasing temperature, at certain temperature it exhibits a minimum and then increases again. Such a phenomenon has been noticed in the previous reports but there has no detailed discussion. Comparing with the previous reports we concluded that, at certain conditions, the high temperature should have the same contribution to the exponent variation as the high frequency.Finally, we explored the applicability of the power law to the electrical behavior of the grain-boundary phase in a polycrystalline solid. The frequency dependence of the grain-boundary conductivity of five samples, all having the same nominal chemical composition of (ZrO₂)_0.90-(Y₂O₃)_0.04-(CaO)_0.06, was measured using complex impedance method in the temperature range from 773 to 1073 K and then analyzed using the power law. By examining the best-fit values of the three parameters,σ_dc,ω_p and s, including in the power law, it was concluded that the power law is sufficiently suitable for the describing the frequency dependence of the grain-boundary conductivity. Analyzing the temperature dependence of the resultantω_p and s would yield a reasonable estimation for the activation energy for grain-boundary conduction and the disassociated energy of the charge carrier in the space charge layer, respectively. Therefore, we believe that the power law would be a powerful tool for studying the grain-boundary effect in the electrical properties of the solid electrolytes.