In my results, the peak of loss tangent shifts toward lower temperature when frequency increased while the peak of dielectric constant shifts toward higher temperature with an increase in frequency. Should we recommend these materials as relaxors?
In dielectric relaxation, a peak in loss tangent or dielectric loss is observed when plotted as a function of frequency which shits with the increase in temperature. In this case dielectric constant decreases with frequency but it does not show any peak with frequency. Similarly, if the dielectric relaxation of dipolar type is considered, a peak in loss tangent is observed as a function of temperature which shifts with the increase with frequency. No peak is observed in dielectric constant with temperature . Since you are observing a peak in dielectric constant with temperature, it may not be dielectric relaxation. In case of phase transition, a peak in dielectric constant may be observed. You may go through the literature to know whether any phase transition is observed at the peak temperature in your material.
Is it possible to share more details? Data, composition, mechanical and thermal relaxation results? In the absence of further information it is hard to give any meaningful explanation.
According to the Debye Theory of dielectric conductance one has the following functional forms for the real part of the dielectric conductance, the phase shift :
tan Phi = A [Zeta/(1+ Zeta2)] and (J1 - Ju ) = B [1 /(1+ Zeta2)).
where Zeta= omega x tho, tho is the relaxation time, which depends on the temperature exponentially: tho = tho0 exp(Q/RT) Q is the activation enthalpy for the electric dipole relaxation.
Tan Phi has maximum when zeta=1. Which for the peak position tells us that when the frequency increases relaxation time should decrease and consequently temperature shifts to higher values. This is just the opposite way suggested by Dr. Puri.
On the other hand the real part of the dielectric conductance draws S-type curve having an inflection point at Zeta=1/3, which also corresponds to the maximum if one plots the derivative of (J1-Ju) with respect to the normalized frequency denoted by Zeta. -This mostly done electronically in practice- Again the peak in derivative of (J1-Ju) shifts to higher temperatures when one increases the frequency. This is also proper result. I have observed that behaviour in Internal Friction studies and NMR work many times in my life. The tanPhi function known as the Lorenzian function which is very popular in mathematical physics dealing with simple relaxation phenomenon.
Dear Maalti,
I understand that you have performed two different kind of measurements, loss tangent (or internal friction measurements) by a clasical DMA (dynamic mechanical analyser) and dielectrical measurements by the usual techniques as well.
The microscopic mechanisms contributing to mechanical relaxation and to dielectric relaxation are usually completely different. I donot know what is your material, but you may have two different mechanisms: one which responds to the electric field, given place to a dielectric relaxation, and eventually another completely different which respond to the elastic field during DMA measurements.
Although I have not idea about your material, I may comment that in an anelastic relaxation mechanism (by DMA) the relaxation peak must shift towards higher temperature when increasing the frequency. If you observe the opposite behaviour, it means that you are not in presence of an anelastic relaxation. Probably your microstructure is evolving during the runs in temperature. You may verify it by two methods:
First: an anelastic relaxation has always an associated change of the dynamic modulus according the Debye equations, so plot also the J' or E' function in comparison with the loss tangent J'' or E''. If there is a relaxation both functions should behave accordingly. I send you here attached one of my papers with an overview about the anelastic relaxation theory.
Second: if the microstructure evolves, you shold be able of evidence this evolution on time. When measuring as a function of temperature in a clasical heating run, please stop the temperature ramp at the maximum of the loss angle peak, and measure the loss angle as a function of time. If you have a true relaxation it will be constant, whereas in case your microstructure change you will observe probably a decrease of the loss angle as a function of time. In this case you should analyse what could be happening in your material, if there is just a microstructural evolution or it is in proximity of a phase transition.
I hope this could be useful for you.
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