Hello Govind,

when you find two peaks in f vs Z'' you should expect to find two peaks in f vs M' as well.

Because M'' is dependent from Z' 

and M' is dependent from -Z''

Have a look to the attached papers.

For general questions regarding impedance spectroscopy you will find a very good introduction in "Impedance Spectroscopy: Theory, Experiment, and Applications, 2nd Edition" by Evgenij Barsoukov (Editor) and J. Ross Macdonald (Editor) 

http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471647497.html

Article Electrical properties of nanoscaled host/guest compounds

Article Correlating the Integral Sensing Properties of Zeolites with...

Dear Govind,

just couple more comments :

1. Thomas is right, the "Modulus" is just another way of representing the electrical response data. Myself, I would have to transform the impedance data to the Modulus to see whether the two "relaxation peaks" seen in imaginary part of the impedance are reproduced in the same way in the Modulus. But be aware that some of these representations  are in fact quite misleading. A typical example is a "complex conductivity" or "complex dielectric constant/function" in spatially non-homogeneous systems. There one can get relative dielectric constant of the order of 10^5 (!!!), a complete nonsence just because one misinterprets the interface capacitance in terms of dielectric constant. So I would stick to the complex impedance, admittance, capacitance and inductance .

2. Imaginary part of the complex impedance DOES NOT describes only relaxation processes, it just describes out of phase part of the response.

3. The processes you describe - grains, grain boundaries and the electrode effects are in fact NOT the dielectric relaxation processes propper. The characteristic response time is in fact the "conductivity relaxation time" which is tau=eps/sigma (sigma= dc conductivity) and has nothing to do with some kind of dielectric relaxation. It just signifies the onset of current relaxation when the fast polarisation (eps) takes over the dc conductivity (sigma). At low frequencies the system responds first of all through dc conduction (sigma), while at higher frequencies (beyond the conductivity relaxation time tau) it responds through the fast polarisation (eps). These two fundamentally different physical processes (dc conduction and polarisation) are 90 degrees out of the phase relative to each other and are the reason of the frequency dependent impedance.

I hope that this will also help you on the way

With best regards

Petr

 My thanks to Dr. Thomas and Dr.Peter for your valuable opinion. 

Dear Govind

If you get two clear and prominent peaks in log f vs Z'' (or two clear semi circle in Z' vs Z''), you can expect the same from Log f  vs M''. (high freq region is grain, lower freq region is grain boundary)

Also form the nyquist plot , you can calculate the capacitance value for both grain and grain boundary effect

In case you may get two overlapped semicircle in Z' vs Z'' plot, that time we can't expect two peaks in M'' spectra. 

You can identify the dominant effect (it may be grain and grain boundary) from the frequency region and can calculate the relaxation time also.

please go through our article, you may get some ideas:

http://www.sciencedirect.com/science/article/pii/S0167273814003580

Thanks

Consider the Modulus comments above only as initial hints for your study (grain boundary and electrode effects). More practical figures (and grains' correlated parameters) you will take from your model (Z-fitting).

Dear Thomas,

It is not necessary to get the two distinct peaks in M' vs. freq. plot if you are getting two peaks in the Z'' vs. f plots because M' depends on the product of the frequency and the Z''.

Dear Govind,

Try plotting the M' vs. M''. If you get two dispersed semicircles, you will get the two distinct peaks in M'' vs. freq. plot.

Best Wishes,

Manish