Two layers are supposed to form on the surface of the metal (untitled 3), The impedance data (untitled2) can be fitted by using any of the attached equivalent circuits (untitled & untitled1)
I see the most meaning circuit that simulate the formed layer is the circuit attached in (untitled) but many publication perform as my work, they use the another circuit (untitled1)
Could you please help me to understand the physical meaning of each circuit?
Thanks in advance
In my opinion the second circuit is more suiatble.
In any case I wonder if you tried to elaborate your experimental data avoiding the use of constant phase elements. If you use simple capacitive elements instead of Qs are you able to obtain good fittings?
Thank you all for this interesting replies.
Unfortunately, Prof. Lucia, I couldn't obtain good fitting with ideal capacities elements instead of Qs.
Well, each dielectric slab you have onto the surface of your electrode can be represented with an RC mesh.
Usually Q elements are used to evercome the difficulty in reproducing experimental data as the dielectric slabs are not ideal in the sense tha they are not uniform in their entire depth. I am not used to use Q elements as they do not have a direct physical meaning . I prefer to add one more slab, in other words, one more mesh to fit the data taking into account of the intephase complexity. So, can you try to fit your data with three or four RC meshes? Does it work better? Attached to your question I see the Nyquist plot of your experimental data. Can you enlarge the plot reducing the x axis range? Can you plot your data as -wZ" vs wZ' where w is the angular frequency and Z" and Z' are as usual the in quadrature and in phase impedance respectively. This plot is partcularly useful for interpreting EIS data referring to sequences of adjacent dielectric layers. Let me know.
Dear Yasser,
I think your impedance spectrum exhibited two time constant. In the first equivalent circuit the capacitance and resistor are in parallel combination, whereas in second equivalent circuit they are in series combination. Both are identical only, so you can use any one of them. This is up to my experience.
Hope it will be useful for you.
I totally agree with Oskar.
However I recommend to use Bode - plots instead of Nyquist plots. because you can better assess spectra over a much larger dynamic range and not only about a decade as in a linear plot.
Dear Yasser
The equivalent circuit give the idea of the double layer formed under the experimental condition between the electrolyte and electrode. before we have to go for equivalent circuit, first we have know the basic electronic circuits with different elements like capacitor, resistor, inductor and the combination of these elements in parallel and series connection. when we are applying sinus wave (combination of voltage, current and frequency) to these circuit they are behave according to the connection. then only we have to know the exact meaning for equivalent circuit elements in EIS fitted equivalent circuit.. normally your type of material the equivalent circuit with series is best one, because the layers are serially arranged on the base material. also you have see the si square values in when you fitting the equivalent circuit model....
you have also refer the papers which is related to your work..
Firstly, I would like to thank any one interest to answer my question,
The attached plot is the Bode plot.
Dear Yasser,
You have scan up to 10-3 Hz then only you will the clear idea about the working system and equivalent circuits.
You may increase your confidence in the physical meaning of the used equivalent circuits by a very simple SEM observations of the surface and cross-section of your specimens. It is possible that the parameters obtained from the equivalent circuit are related with the thickness and the amount of defects on the coating.
actually, in my opinion the Bode - plot does not justify a fit with the equivalent circuits shown above useing two CPEs. You will get results, but quite meaningless.
I support the idea to make SEM pictures from the surface and cross sections in oder to understand your system. Fitting curcuits to single measurements make not much sense, honestly. I propose to make more experiments and to compare materials, without too much of extensive fitting.
Dear Yasser,
I fully agree with Oscar, and let me add the following:
1. The two equivalent circuits are equivalent to each other. If you would assign parameters to one, you can find parameters for the other that would generate the same spectrum at all frequencies. Thus you cannot prefer one over the other just from your impedance data.
2. It looks like a significant part of the fun happens out of your frequency range. If you can measure several orders of magnitude downward it would be great. To check my hunch, take either one of your equivalent circuits (see above, it doesn't matter which one), fit its parameters and draw the spectrum it predicts over a larger frequency range. My guess is that you would find yourself drawing an elephant after looking at its tail. This is a well-known problem of fitting equivalent circuits, and one of that method's (many) drawbacks. For an alternative, see for instance: S. Hershkovitz, S. Baltianski and Y. Tsur, Harnessing evolutionary programming for impedance spectroscopy analysis: a case study of mixed ionic electronic conductors , Solid State Ionics, 188, 104-109 (2011). doi:10.1016/j.ssi.2010.10.004
3. Yet another problem in equivalent circuits that might be relevant to your case is over-fitting. The circuits you chose have 7 degrees of freedom. I am not quite sure if your data justifies it. You did mention that replacing both Q with C did not work well (that is reducing the number of free parameters from 7 to 5). Still, you may want to do discrepancy-complexity plot in order to check how many free parameter a proper model for your data SHOULD have.
All the best,
Yoed
Thank you so much Dr. Yoed for your illustrations, and maybe extensive work is required to understand the real meaning of the impedance parameters.
Yoed Tsur Hello Sir
My question is not related to the above but about your one vary famous and highly cited article "Crystal and Defect Chemistry of Rare Earth Cations in BaTiO3". Sir if I consider only Yb, Er codoped TiO2 then what will be the mechanism to know about the position of RE ions (Yb, Er) in the TiO2 host? if sintered at high temperate like 1000 C. Both will be substituted at Ti4+ site or Ti3+ or with O?
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