Dielectric studies and ac conductivity of terbium fumarate heptahydrate single crystals. Dr. M.D.Shah Deptt. of Physics GDC Tral

The dielectric study is an important part of material characterization. It indicates the response of the material to an electric field. One of the important electrical properties of dielectric materials is permittivity (or relative permittivity, which is generally referred to as the dielectric constant). It depends on the chemical structure and the imperfections (defects) of the material, as well as on other physical parameters including temperature and pressure, etc

The change in dielectric constant w. r The change in dielectric constant w.r.to the temperature can be used to study the phase transition of a material. The capacitors typically use a solid dielectric material with high permittivity as the intervening medium . The advantage of using such a dielectric material is that it prevents the conducting plates on which the charges are stored from coming into direct electrical contact.

The dielectric constant (ε'), dielectric loss tan(δ) as well as a The dielectric constant (ε'), dielectric loss tan(δ) as well as a.c conductivity (σa.c)of TFH single crystals have been measured in the frequency range (20Hz-3MHz) and the temperature range (15 oC-130 oC). The dielectric constant (ε') was determined by using the relation of parallel plate capacitor : ε'= C.t /εoA The conductivity (σa.c) of the material was computed by using the relation: σ a.c= 2πfεoε' tanδ. Both dielectric constant and ac conductivity were observed to change with the change in temperature and frequency.

A dielectric material is made up of atoms or molecules that possess one or more of five basic types of electric polarization: 1. Electronic polarization 2. Atomic or ionic polarization 3. Dipolar or Orientation polarization 4. Spontaneous polarization 5. Interface or space charge polarization

Dependence of dielectric constant on temperature: The variation of real dielectric constant (ε') corresponding to different temperatures at different frequencies in the frequency range of 1 KHz to 3 MHz of applied a.c field is shown in Fig.1

Fig.1 Variation of dielectric constant with temperature at different frequency

Dependence of dielectric loss on temperature Fig.2 shows the variation of dielectric loss verses temperature at different frequencies showing a peak around 85 0C

Dependence of dielectric constant and dielectric loss on frequency The variation of dielectric constant (ε') and dielectric loss (tanδ) as a function of frequency at different temperatures as shown in figure.3 show a normal behaviour of dielectric materials. Both dielectric constant and dielectric loss decrease with increase in frequency. The low value of dielectric loss indicates that the grown crystals are reasonably of good quality.

At low frequency, the charge on the defects can be rapidly redistributed so that defects closer to the positive side of the applied field become negatively charged, while as the defects closer to the negative side of the applied field become positively charged. This leads to a screening of the field and overall reduction in the electric field. Since the capacitance is inversely proportional to the electric field, therefore the reduction in the field for a given voltage results in the increase in capacitance as the frequency is lowered and consequently the dielectric constant increases.

Fig.3 Variation of dielectric constant and dielectric loss with frequency

the dielectric response of a solid can be found by the variation of log susceptibility ( χ ) verses log ω (say at a temperature of 50 oC fig 4). It satisfies the power law equation that χ ∞ log ω – (1-n) , where 0 ˂ n ˂1. For the material under study, the value of n has been found to be equal to 0.7 and as reported in the literature the value of n has been estimated to lie between 0.5 -1.0

Fig.4 log χ verses log ω

AC hopping conduction The conductivity (σa.c) shows a strong dependence on both temperature and frequency of the applied a.c field as shown in figure below. The increase in conductivity in the temperature range 60 < T < 85 oC may be due to an increase in the concentration of mobile charge carriers due to the dissociation of water molecules present in the material into H+ and OH- ions. In the hydrogen bonded systems, the +vely charged rare earth cations and –vely charged carboxylate anions(fumarate ions)may serve as the channels for proton transport.

The activation energy (Ea) was calculated before and after the transition temperature by using the Arrhenius equation σ = σo exp (Ea/kT). Activation energy is the energy required to surmount a barrier of a height equal to B.E of a polaran in order to move to a neighbouring site.

Frequency dependent conductivity The conductivity representation is a most prominent representation to relate the macroscopic measurement to the microscopic movement of the ions. In general, the ac conductivity decreases with increasing frequency in the case of band conduction, while as it increases with increasing frequency in the case of hopping conduction. In the material under study, the magnitude of conductivity is high at higher frequencies, thereby supporting the small polaron hopping model.

From the experimental data in a limited frequency region it was noted σac(ω) =A×ωs Where ω =2πf is the angular frequency and 0 ˂ s ˂1. At extremely low frequencies, the ordered solids show no frequency dependence of their conductivity at frequencies below phonon frequencies. One encounters a region, where the high frequency cut-off starts and ‘s’ decreases to zero with increasing frequency. It is evident from inset figure 5 that the magnitude of ac conductivity decreases by increasing the frequency beyond the high frequency cut-off.

Proton conduction mechanism The application of an electric field causes directional flow of charge carriers by hopping mechanism. When a proton tries to move, it has a strain field (a cloud of virtual thermal phonons) forming a quasi particle like polaron. At higher frequencies of applied ac field, this quasi-particle disperses. When the cloud of phonons disperses, protons move and contribute to the conductivity.

Inherent protonic charge carriers (protonic defects) are solvated by very few types of species. These are essentially water (e.g., in hydrated acidic polymers) etc. A common and important characteristic of the specie is their involvement in hydrogen bonding. Strong hydrogen bonding is frequently considered to be a precursor of proton-transfer reactions. The proton transfers along the hydrogen-bond network. long-range proton transport also requires rapid bond breaking and forming processes. This can occur in weakly hydrogen bonded systems.

Applications of proton conductivity The electrolyte is the heart of any fuel cell. It mediates the electrochemical reaction occurring at the electrodes through conducting a specific ion at very high rates during the operation of the fuel cell. Proton-conducting materials are used as the electrolyte for low- and intermediate temperature fuel cells, which are currently attracting significant interest.

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