Hi Bhasker

In order to find the conductivity value from (polarization) resistance of the given Nyquist plot, the following steps are necessary:

1-Rp=(Rp+Rs)-Rs

where

Rp is the polarization resistance

Rs is the solution (Ohmic) resistance

from the given Nyquist plot, the values;

Rp+Rs=2.1E5 =210000 Ohms

Rs=2.58 Ohms

so, Rp=210000-2.58=210007.42 Ohms.

Then you can use the following equation to determine the value of the conductivity:

   c=1/r       Equ.1

where

c is the conductivity of the sample material.

r is the resistivity of the sample material

Since  r=RA/L   Equ.2

where A is the cross sectional area of the sample

L is the length of the sample

so, you can substitute the obtained value of R , and by knowing the constant value of A and L, you can determine r from Equ.2, then by substitution the calculated value of r in Equ.1 you can determine c.  

@Khalid sir: thank you for your valuable guidance. I would like to have one more question to be answered if possible.

My sample is CeO2 pellet as electrolyte (i.e. ionic conductor at high temperature) with platinum as electrodes. I want to find grain resistance (Rg) and grain boundary resistance (Rgb). What I understood from literature is as follows:

1. If we have two semi circle arc (one at high frequency and second at intermediate frequency) followed by third open arc at low frequency, in this case the magnitude of first arc is Rg and magnitude of 2nd arc represents Rgb while open arc corresponds to electrode resistance.

2. If we have only one arc followed by open arc at low frequency which is my present case as shown in figure, in this case we take left intercept of 1st arc on x-axis as Rg while magnitude of arc as Rgb. 

And finally we use R = Rb + Rgb as total resistance followed by your explained method of conductivity.

Is above mentioned procedure correct ? What is difference between your explained procedure and the above mentioned procedure ?

Thanking you and regards,

My explanation is applicable for a metallic(solid) electrode in aqueous solution.   So, if your sample was CeO2 pellet as the electrolyte (i.e. ionic conductor at high temperature) with platinum as a counter electrode, in this case the  grain resistance (Rg) is equivalent to Rs and grain boundary resistance (Rgb) is equivalent to Rp.   So you are correct.

But how about using thickness for conductivity ? what thickness have you have used for grain?

Excellent detailed answer by Khaled.

To Bhasker, in a perfect condition your assumptions are right, however in reality there is always an influence of electrode (anode and cathode) Interfacial resistances that effect the electrolyte resistance. So it's not just a direct measurement of the first x intercept at the real axes. Yet for simplicity we assume it so.

If u are really interested the u can apply biases and remove that interfacial resistances, but that's a topic for some other day I suppose

Can Sindirac , the factors A, L account for the thickness parameters. Which in this case will be Area specific resistance

So you mean that taking account the pellet thickness for the calculation grain conductivity (and grain boundary and electrode conductivity also ? ) ) Waqas Tanveer