Dear Dr. Punia:

Your question is compact but has a large number of concepts that turn any answer long and sometimes over-simplified.

See, firstly is necessary some careful in the parameter that is being discussed. Depending on the text, some authors use dielectric constant as being dielectric permittivity. In fact, a good approaching (Materials, Chemistry of Materials, Materials Engineering and Solid State Physics) is to work with dielectric permittivity that represent the real part of complex number called of complex dielectric permittivity.

In a over simplified manner, the parameter real part of dielectric permittivity represents the intrinsic property that each material have to maintains charges separated (Polarization Phenomenon), while the parameter imaginary part of complex dielectric permittivity represents an intrinsic property that each material have to allow charge to move.

As a whole, ideal dielectric material are isolator materials. In the practice, functional materials are imperfect dielectrics exhibiting some degree of electrical semiconductivity. Then, according with stats above, ideal dielectric has not an imaginary component of dielectric permittivity. Otherwise, a great part of the Materials of Engineering shows some amount at the parameter imaginary part of dielectric permittivity that imply in electric conduction (charge moving).

The charge can be an electron the typical carrier. Also, can be only a charge density ascribed to particular set of dipole under electric relaxation, but in movement also. In the first case, the long range conductivity is operational, while in the second case, short range conductivity is operational.

Immediately above, there is a phrase from it is possible the follow interpretation: if electron can freely move by the materials, this material is not an ideal dielectric. This idea can be extended to materials that allow the electric dipole formation. Here, seems the proper moment to the parameter temperature exhibits all your power. A priori, the mobile charges are bonded to its proper defect or defect cluster that in a general way are thermal activated. This trend means that at each temperature a dielectric semiconductor or a dielectric with very slight semiconduction degree exhibits a value of real part of the complex dielectric permittivity and a value of imaginary part of dielectric permittivity. There is no universal role, instead there is a great number of variants, but as expected result when part real of dielectric permittivity increases, the correspondent imaginary part decreases and vice-versa.

Further picture can be reached with the material characterization as function of temperature. Here, it is important have in mind that previously, the concept dielectric ideal was extended giving a new set of dielectric classification that was called of se dielectric-semiconductor (a dielectric with very slight degree of semiconduction). From this point, dielectric-semiconductors should be subdivided in two classes. The first class is represented by normal or conventional dielectric-semiconductors. Another class is of ferroelectric. Ferroelectric is a particular dielectric that undergoes phase transition with changing of crystalline symmetry or space group or both, as a function of temperature. Thus, all ferroelectric is a dielectric-semiconductor normal but neither all dielectric-semiconductor normal is a ferroelectric.

Again, via over-simplification, the class called above of dielectric-semiconductor normal can be further mentioned in a simple way as dielectric. Then, all ferroelectric is a dielectric but neither all dielectric is a ferroelectric. When both materials are characterized as a function of temperature, the major probability is that results be as follow: ferroelectric materials exhibits a complex behavior of parameter dielectric permittivity (real component of the complex number complex dielectric permittivity) being typical a maximum. Under temperature effects, dielectrics exhibit smooth curves sometimes with strong dispersion at low temperature (great values of dielectric permittivity). Another time, a strong dispersion is detected at high temperature domain.

The overall behaviour of dielectric permittivity parameter of dielectrics depending on the type and concentration of defects. By thermodynamic consideration, during measurements, defects are not being created, but can undergo ionization, electrons can be emitted or trapped. In this sense, as an example, in original state, oxygen vacancies should be in neutral state, as a function of temperature increasing, some ionization might take place providing further number of carriers. See, this meant that the electrical conductivity increases. See, the impedance is a complex function that can transformed in electrical conductivity, in fact the real part of electrical conductivity is a function of imaginary part of dielectric permittivity.

In a polycrystalline materials are common both grain and grain-boundary phenomena. In a broad sense, being absent a universal role, the grain-boundary is a proper region to accumulate charge, also called space-charge. See, If have not some kind of mis-interpretation by the author during paper development that gives origin to the core of your sub-question; the question would be interpreted as two phenomena that occurs simultaneously, but stemming of different parts of ceramic microstructure. But can be really some kind of absence of completeness. If the paper that you made mention is authored by me, contact me.

Kind regards

Marcos Nobre

In a non- metallic system, d.c. conductivity, in general, increases with temperature. However, in case of dielectric constant, it may increase or decrease with temperature depending upon the type of polarization present. At low frequencies, all types of polarizations may be effective. However, as frequency increases some may not be effective and hence, dielectric constant at higher frequencies may be quite small as compared to static value at low frequencies. Temperature dependence for different kind of polarizations may not be same. If dielectric loss occurs in a certain frequency range due to lag of polarization, additional contribution to the conductivity occurs which is known as a. c. Conductivity. In conclusion, temperature dependence of conductivity and dielectric constant may not follow similar behaviour. Temperature dependence in two cases originate due to quite different reasons.

Dear Punia, 

My experience is very little, as compare to Dr. Nobre and Dr. Kumar, they have given almost all idea about to dielectric study rather spectroscopy including conductivity. So dont think there is any need further to answer your Main Question. But your Question's supply part need to address a little bit more. your supply query is:

"In many publications, authors say that with increasing temp oxygen vacancies increases due to the increase of space polarization. As a result the dielectric constant increases. Many authors say that conductivity increases. How is this possible?"

The increase or decrease of dielectric constant with temperature may related to the degree of crystallinity.  In literature it is reported that, with increasing  of degree of crystallinity the dielectric constant will increase in microwave frequency range 

Dear Suman,

which material is that? One has to know the material to work out its polarization mechanisms. It is so that the orientation polarization of permanent dipoles decreases with the temperature as the thermal energy is dispersing one. The ionic polarization also decreases with the temperature as the density of the ions decrease with temperature increase.

The behavior is the same with the electronic polarization.

If any increase of the polarization is observed with the temperature increase this would be due structural change in the material.

So, all the above answers including mine are not rigorous as the question is not specific.

Best wishes

Is there any relationship between dielectric properties and photocatalytic activity?

Besides the space charge polarization, dielectric constant also depends on the other polarization of the materials. Since the increasing temperature can enhance the contribution of the rotational or ionic polarization in the solid materials, the increasing dielectric constant may also be reason of that.

Further, the ac conductivity depends on the hopping of the charge carriers present in the material. Since the number of free charge carriers increases with increasing temperature, the ac conductivity increases.

You may follow

[1] M.N. Siddique, A. Ahmed, P. Tripathi, Electric transport and enhanced dielectric permittivity in pure and Al doped NiO nanostructures, J. Alloys Compd. 735 (2018) 516–529. doi:10.1016/j.jallcom.2017.11.114.

Space charge polarization occurred due to presence of different boundary region and difference of conductivity so dielectric constant increases for increment of temperature .

Conductivity depends on different transport mechanism depends on s it may be explained by CBH model or any other model

Amit Mahajan

Sir, will you please discuss a little about the intrinsic and extrinsic contribution in dielectric constant.

because it effect on dipole orientation, A dielectric constant refers to molecules polarized by an electric filed, such as turning in the direction of the field. At a higher temperature molecules move, shake, twist, and vibrate, so the polarization is reduced, because the molecules don't point in the direction of the field all the time or as much as at a lower temperature

is any mathematical equation for liquid dielectric constant dependent on temperature ?

Temperature dependence for different kind of polarizations may not be same. If dielectric loss occurs in a certain frequency range due to lag of polarization, additional contribution to the conductivity occurs which is known as a. c. Conductivity. temperature dependence of conductivity and dielectric constant may not follow similar behaviour

Following.

The effect of temperature on the dielectric constant is similar to that of frequency. With increased temperature, the mobility of polar molecules increases, which increases the dielectric constant.

If the dielectric varies randomly with temperature means, what may be the reasons?

Basically, as per my understanding, with temperature the change in dielectric constant comes from the change in orientation polarization, as the dipoles get more energy to get oriented with the increase in temperature. Around curie temperature when the dielectric is going through transition, the the dipoles get their maximum energy to get reoriented and hence the maximum dielectric constant. With further increase in temperature, as we know the structure changes from a ferro phase to para and hence the dipoles start to disappear that consequently leads to decreasing polarisation.

P. S. I have here discussed about the dielectric behaviour of a ferroelectric material.

In most of the graphs as temperature increases the dielectric values increases due to thermal activation. But in my case the dielectric varies randomly with temperature? What are the reason for the random changes?

I too got similar results when recorded the temperature-dependent dielectric parameters and A.C. conductivity of conducting polymers and their composites @Helen Kas

@Helen Kas Random behaivour is due to measurement problem. Your contact is not good with material which allows air gap (Capactiance fluctuates). Generally that leads to random behaviour.

Dear Dr. Punia,

As per your question of change in dielectric constant with temperature, I would like to draw your attention towards the origin of dielectric constant. The origin of the major contribution/dominating part to dielectric constant is different in different frequency regions for example in lower frequency below 10 Hz the origin of dielectric constant is space charge or sometimes it is called electrode polarization or Maxwell-Wagner effect. However, it could depend on the sate of matter also. Beyond this frequency region till GHz, the major contribution to dielectric constant is dipolar and so on. A general trend could be found in text books dedicated to solid state physics.

Now the answer for the question of change in temperature lies in the binding forces associated to the origin. For example a liquid crystal material which is anisotropic in dielectric nature. We can understand the behaviour of dielectric constant in cooling cycle of a liquid crystal material. This material could be isotropic at high temperature and can have higher ordered LC phases like nematic smectic A, smectic C etc in cooling cycle. If we talk about dielectric constant in the frequency range from 100 Hz to few MHz, the behaviour of the material is analyzed in terms of dipolar fluctuations.

In isotropic phase, the dipoles are randomly oriented and this orientation is dominated by thermal fluctuations. there at this temperature range the contribution to dielectric constant is due to induced dipolar process and dielectric constant value would be very low. At further lower temperature in nematic phase, the material becomes slightly ordered in terms of molecular orientation (assuming rod shape molecules) but positionally disordered, there can be expected a small increment in the value due to increase in the ordering of fluctuating dipoles due to ordered phase. If the temperature is further reduced to another phase which could be smectic A phase. This phase is more ordered and molecules are restricted to 2D system in the form of layers. This means that the ordering of dipoles is increased and still have tendency to fluctuate with applied field. Applied field should also be sufficiently small to just fluctuate the dipoles but not to the molecules. On further reduce in temperature to other smectic phase like chiral smectic C phase, the dielectric constant shows a tremendous increment in the value due to phase ordering and tendency to fluctuate.

Now if the material attains crystalline phase after further reduce in temperature, the dielectric constant get reduced. The question arises why the value decreases even an increase in the ordering of material. This result is contradictory to our the ordering concept. Here the reduction in value is due to the fact that the dipoles loses their tendency to fluctuate at these frequencies.

Regards