Dear Dr. Punia:

Despite of difficulty of data interpretation, analysis of electrical behaviour of materials via small signal in alternate current called of Impedance or impedance spectroscopy has gradually expanded yourself.

The impedance of a sample is typically represented by Z* being a function of the frequency of measurement, in a conventional formalism Z*(angular frequency).

The impedance Z* or Z*(angular frequency) is a complex number, in this sense, as follow Z* = Z' + jZ". Z" represents the core of the impedance spectroscopy. If Z" is null, the Ohm's law is retrieved. But, Z" represents the fraction absorbed of the original signal to separate "charges" at a specific frequency that coincide with natural frequency of oscillation of a specific mechanism present in the material. In another words, when the frequency of measurement is equal to a frequency natural of oscillation of a charge configuration, a kind of resonance phenomenon occurs that increase the absorption of original signal, Z" reach to a maximum, that is observed as a maximum in the function Z" x log(f). In this sense, it is possible to say that charges were separated in highest extension, for this condition since that energy is not storage a relaxation phenomenon occurs, then at the frequency of peak, an relaxation occurs.

In abroad sense, for each relaxation frequency there is a semicircle centered on abscissas axis, Z' axis in "Cole-Cole representation". Therefore, at an electroceramic a specific relaxation phenomenon is expected at grain and another at grain boundary.

In a general way, is not possible, by the visual inspection, identify both semicircles since each relaxation frequency should differ of at around three orders of magnitude. See there are more complex cases, which a single grain phenomenon is identified while three grain boundaries phenomena are presents.

All above can be written with different words; however frequencies of relaxation ascribed to the grains boundary appears alway at low frequency domain.

A priori, therefore, relaxation frequencies of grain boundary should be lower than relaxation frequency of grain. Sometimes, some kind of doubt emerges about the contribution at low frequencies to overall response, since, as an example, grain boundary exists but electrode polarization can also exist.

See, the impedance can be transformed in several another functions. The most common is the transformation of Z* in Complex permittivity function and Electric modulus function M*, but there is wide set of them (functions)...I attached a paper authored by me, where there is a set of formulas showing this. Depending on the choice of the researcher, an imaginary component in a type of representation can be converted in real component in another; also if a transformation selected is reciprocal of another function witha component of small value can be transformed in one of great numeric value and vice-versa. In the paper "Catalysis Today 78 (2003) pp 529-538, I comment:..."M* = M' + jM". This formalism is particularly suitable to detect phenomena as electrode polarization..."

Please if and when necessary, any item of the paper in attach can be discussed in more details, e-mail me. I try to attach another papers but was not possible.

Kind regards

Marcos Nobre

The Z0 vs.Z00 curve is composed of two semicircles, a small semi-

circle at high frequencies indicates the effect of grain and

large semicircle at low frequencies indicates the grain

boundary effect. The intercept of the semicircle on the

real axis gives the resistance of grain (Rb) and grain boundary (Rgb) of the corresponding component con-tributing towards the impedance of the sample. The ca-

pacitance (C) of each component can be calculated using

the formula omeg*time(tou) = 2 pi*fmax*RC= 1,

fmax is the frequency of the maximum of the semicircle, omega=2pi*f max and tou is

the relaxation time.

Whether you present your data as "M" or "Z" depends on the nature of your investigation.

The following is a quote form the attached paper by A.R. West et al, Adv. Mater. 2 (1990) No. 3:

"The value of presenting data as both M“ and Z” spectroscopic

plots is that they give different weightings to the data

and therefore, highlight different features of the sample.

Thus, impedance plots pick out the most resistive elements in

the sample, since the impedance peak height, Z” is equal

to R/2 for that particular element. Modulus plots pick out

those elements with the smallest capacitance since the M”

peak maximum is equal to c0/2C for that particular element.

In materials that are inhomogeneous and are represented by

more than one RC element, the resulting M” and Z” spectra

may look very different (as in Fig. 5 b)."

Dear Dr. Punia:

Despite of difficulty of data interpretation, analysis of electrical behaviour of materials via small signal in alternate current called of Impedance or impedance spectroscopy has gradually expanded yourself.

The impedance of a sample is typically represented by Z* being a function of the frequency of measurement, in a conventional formalism Z*(angular frequency).

The impedance Z* or Z*(angular frequency) is a complex number, in this sense, as follow Z* = Z' + jZ". Z" represents the core of the impedance spectroscopy. If Z" is null, the Ohm's law is retrieved. But, Z" represents the fraction absorbed of the original signal to separate "charges" at a specific frequency that coincide with natural frequency of oscillation of a specific mechanism present in the material. In another words, when the frequency of measurement is equal to a frequency natural of oscillation of a charge configuration, a kind of resonance phenomenon occurs that increase the absorption of original signal, Z" reach to a maximum, that is observed as a maximum in the function Z" x log(f). In this sense, it is possible to say that charges were separated in highest extension, for this condition since that energy is not storage a relaxation phenomenon occurs, then at the frequency of peak, an relaxation occurs.

In abroad sense, for each relaxation frequency there is a semicircle centered on abscissas axis, Z' axis in "Cole-Cole representation". Therefore, at an electroceramic a specific relaxation phenomenon is expected at grain and another at grain boundary.

In a general way, is not possible, by the visual inspection, identify both semicircles since each relaxation frequency should differ of at around three orders of magnitude. See there are more complex cases, which a single grain phenomenon is identified while three grain boundaries phenomena are presents.

All above can be written with different words; however frequencies of relaxation ascribed to the grains boundary appears alway at low frequency domain.

A priori, therefore, relaxation frequencies of grain boundary should be lower than relaxation frequency of grain. Sometimes, some kind of doubt emerges about the contribution at low frequencies to overall response, since, as an example, grain boundary exists but electrode polarization can also exist.

See, the impedance can be transformed in several another functions. The most common is the transformation of Z* in Complex permittivity function and Electric modulus function M*, but there is wide set of them (functions)...I attached a paper authored by me, where there is a set of formulas showing this. Depending on the choice of the researcher, an imaginary component in a type of representation can be converted in real component in another; also if a transformation selected is reciprocal of another function witha component of small value can be transformed in one of great numeric value and vice-versa. In the paper "Catalysis Today 78 (2003) pp 529-538, I comment:..."M* = M' + jM". This formalism is particularly suitable to detect phenomena as electrode polarization..."

Please if and when necessary, any item of the paper in attach can be discussed in more details, e-mail me. I try to attach another papers but was not possible.

Kind regards

Marcos Nobre