When we measure Impedance spectroscopy, we can know resistance of interior grain correspond with high frequency, and resistance of grain boundary corresponding with lower frequency. The conductivity of grain can calculate from resistance by formula = (1/R)*(S/l)
Where S is area, and l is thickness of pellet which used for measurement.
How can we calculate the grain boundary conductivity because we do not know the dimension of boundary?
Refer this link:doc.utwente.nl/70640/1/Dijk81Grain.pdf
Refer this link:ceramics.eng.uci.edu/.../Grain%20boundary%20ionic%20conductivity%...
Refer this link:www.mines.edu/~cciobanu/publications/porousceramics.pdf
Might I suggest the use of conductive atomic force microscopy to attempt the same. It is possible then to determine the average contribution of grain boundaries and approach an average value from there.
I hope it helps.
At the start , we calculate the resistance grain boundary
σNA=1/2((λ /R)eZ∗ρj))
where R is the atomic volume, λis the grain-boundary length, δ
is the grain-boundary thickness, eZ* is the effective charge of the
metal ions,ρ is the resistance, and j is the current density.
and we know that conductivity is inverted resistance
Thanks Aditya Chauhan. we do not have conductive atomic force microscopy. I mean here that we can estimate the conductivity via impedance spectroscopy. By impedance, we can estimate the resistance of grain and grain boundary, and we need here to calculate through resistance to conductivity..
Thank you Ahmed Alijabery. Yes, conductivity is inverted with resistance but we do not know the grain boundary thickness.
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