Dear Steven Mudenda,

Nyquist plots can possess two semicircles in the case of a system with two time constants. If you have a polycrystalline material the high frequency semicircle results from the contribution of crystalline grains (interface states at grain boundaries can not follow the high frequency ac signal), the low frequency semicircle corresponds to the contribution of grain boundaries (mainly shallow interface states at grain boundaries). However, you should know that your electric contacts are Ohmic. If you have a depletion layer at one of the electrodes as well as interface states at the contact interface, you may observe additional semicircles. Their location (high or low frequency) will depend on electrical properties of the material under investigation and parameters of interface states. Therefore, the Muhammad's comment on the quality of surface and proper electrodes is very important.

Moreover, you should try to analyze your Nyquist plots in the logarithmic scale in order to be sure in the number of semicircles. As usually it is not ease to analyze the impedance spectroscopy of complex solid state systems. Very often additional independent measurements are needed.

You can find some approaches for the quantitative analysis of imedance spectroscopy and capacitance-voltage characteristics in the following papers.

Steven Mudeda don't try to confuse yourself from the position and labeling of the semicircles. Generally, in impedance spectroscopy the appearance of the semicirlcles depend upon the relaxation phenomena with sufficiently different relaxation time. From different relaxation time I mean the circles will be resolved as shown in your posted figure. From equation of relaxation time (τ = RC), you can understand that semicircle with smaller resistance (u can guess from the diameter of the circle) will appear at higher frequencies mean at the left side of your posted figure. Generally, grain(Gs) resistance is lower then grain boundary (GBs) resistance, so one can say that the circle at right side of the figure is from grain. Similarly, the higher resistance electro-active region say GBs appear at low frequencies i.e. at right hand side of the figure. I am explaining this by assuming that in the figure the region corresponding to electrode/interface is absent and may appear as a third semicircle if you extend the lower frequency region. This is one way of looking at impedance figure but keep in mind generally, resistance of electrode > resistance of Grain boundaries > resistance of grains. The other option which is considered to be more authentic and reliable is the capacitance of the electro active region which you can calculate by plotting the Z// against frequencies. From peak calculate the capacitance values using relationship 2πfmaxRC = 1. On the basis of the magnitude of the capacitance values you can identify and name different electro active regions as electrode, grain boundary and grain associated with low, intermediate and high frequency arcs in the impedance plane plots respectively. We can extend this discussion if you think its workable for you, take care.

Thanks Muhammed for the response. What about a case where you just have one semi circle, can one say one of the resistance (bulk or electrode interface) is missing or what. In short can one say theres just bulk resistance and no electrode-electrolyte interface resisistance?

I assume that you are just discussing things for the sake of understanding. Its not always necessary to have well transformed semicircles. Some times the relaxation frequencies of different electro active region are so close that one may come up with only one distorted/depressed semicircle. If the relaxation time differs by at least two orders of magnitude then one can expect well resolved semicircles of different electro active regions. These things are a bit tricky and for real good data analysis the actual knowledge of the system (material and measurement methodology) is very important.

Definatley I want to understand because i have some day which have only one semi circle others have distorted semi circles of course.

If the quality of sample is good, surfaces of both side of the pellet are properly cleaned and proper electrodes are used then such changing trend can be addressed by incorporating defect chemistry of the sample.

Dear Steven Mudenda,

Nyquist plots can possess two semicircles in the case of a system with two time constants. If you have a polycrystalline material the high frequency semicircle results from the contribution of crystalline grains (interface states at grain boundaries can not follow the high frequency ac signal), the low frequency semicircle corresponds to the contribution of grain boundaries (mainly shallow interface states at grain boundaries). However, you should know that your electric contacts are Ohmic. If you have a depletion layer at one of the electrodes as well as interface states at the contact interface, you may observe additional semicircles. Their location (high or low frequency) will depend on electrical properties of the material under investigation and parameters of interface states. Therefore, the Muhammad's comment on the quality of surface and proper electrodes is very important.

Moreover, you should try to analyze your Nyquist plots in the logarithmic scale in order to be sure in the number of semicircles. As usually it is not ease to analyze the impedance spectroscopy of complex solid state systems. Very often additional independent measurements are needed.

You can find some approaches for the quantitative analysis of imedance spectroscopy and capacitance-voltage characteristics in the following papers.

Paper

Paper

Paper

Wow, Thanks V.Brus! Much appreciated. let me go through them.

I think left semi circle is in high frequency region and right semicircle is low frequency region. Right?

I also got the similar nested semicircles but opposite