Let us say you measure the pure dc conductivity of your sample, by applying a pure dc voltage with a battery, and measuring the current, and with the known geometric factor determine the conductivity.
2) Ac measurements
Alternately from the complex impedance plot, determine the fitting parameters, Rg and Rgb, thereby the total resistance will be Rg +Rgb, and with the same geometric factor if you determine the conductivity, you should obtain the same, or a close enough value for the conductivity as we obtain in the step No. 1 described above.
Of course while measuring the impedance values (Z' and Z'') as a function of frequency, you must have a lot of data points, and when you are fitting the semi circless due to grain and grain boundary contributions, The fitting of the experimental data to the equivalent circuit should be good. Moreover you should measure both Z' and Z'' over a large frequency range (preferably from mill Hertz to MHz). the measurements will definitely take quite some time, as you are going to very low frequencies, and you need a good dielectric spectrometer.
We use a Novacontrol dielectric spectrometer, and have seen that the dc conductivity value for the sample, using the same geometric factor, yields the dc conductivity value matches quite closely.
K. Sreenivas Sir, Your answer is very helpful to me. Thankyou for sharing this. Can you please share some reference for the above said statement. It would be great help.
K. Sreenivas Sir, Your answer is very helpful to me. Thankyou for sharing this. Can you please share some reference for the above said statement. It would be great help.