A study of frequency and temperature dependence of ionic conductance

Abstract

An approach to study the frequency and temperature dependence of the bulk ionic conductivity, based on the log-log representation of the frequency response, is described. Experimental results obtained on β-PbF2 thin-film samples are used to illustrate this approach. The analysis of these results permits to separate the different physical mechanisms involved and to model the cells. Using CPE (Constant Phase Element) Y=Y0(jω)n for the interfaces, but also for the bulk ionic conductance, permits to fit the experimental results. A progressive increase of the slope n of the admittance which corresponds to the bulk ionic conductivity is observed when the temperature decreases. A graphical method is described which can be used to determine the activation energy in this case of a CPE behavior of the conductance. It is based on the obtention of a unique curye which describes the frequency and temperature dependence of the reduced conductance G=YrTτ plotted versus the reduced radial frequency u=ωτ. This curve shows the whole conductance variation which starts from pure transport with n=0 at low frequencies and high temperature, and tends for high frequencies or low temperatures toward the dielectric response (n→1), corresponding to ion displacements limited to only one jump. The observed CPE behavior of the conductance at constant temperature thus appears to be the result of the very slow variation rate of the slope n of the reduced conductance versus the radial frequency.