*3.6. Dielectric Properties*

Materials under the oscillating electric field impart dielectric behavior which can be expressed as a complex form consisting of real (ε 0 ) and imaginary (ε") components that can be represented as <sup>ε</sup>\*<sup>=</sup> <sup>ε</sup> 0+ iε". The real component (ε 0 ) of dielectric constant depicts the energy storage and imaginary component signifies the dissipated energy in the material. Various external parameters like microstructure, frequency of applied electric field, sintering temperature, type of cation substitution, etc. affect the dielectric properties. Both components of the dielectric constant can be evaluated using the following relation:

$$
\varepsilon'' = \varepsilon' \times \tan \delta \tag{14}
$$

Both real, and imaginary, components of dielectric constant have strong frequency dependence at room temperature in Zn doped hematite, and is demonstrated in Figure 10. The dielectric constant decreases with an increase in frequency, which agrees well with previous studies [40]. The strong degradation.

nanoparticles.

**Rate Constant (k) (min)−<sup>1</sup>**

**Samples** 

following relation [39],

decrease in dielectric constant with rise in frequency can be understood on the basis of Maxwell Wagner model and Koop's phenomenological theory, which explains that ferrites are formed by highly conducting grains, embedded in the insulating matrix, i.e., grain boundaries [3]. High dielectric constant value at lower frequencies is contributed by grain boundaries.As the frequency increases, grains start to predominate over grain boundaries, which reduces the dielectric constant. The dispersion in dielectric constant with frequency can also be understood in terms of space charge polarization, due to the hopping of electrons between ferric and ferrous ions [41]. At low frequencies, hopping of electrons within grains causes the electrons to pile up at grain boundaries resulting in space charge polarization and contributes to higher value of dielectric constant. On the other hand, a reduction in orientation polarizability can be seen with increase in frequency, as the electron exchange between Fe2<sup>+</sup> and Fe3<sup>+</sup> ions loses the ability to follow alternative field and lags behind the field. As a result, probability of electrons reaching the grain boundary reduces. Consequently, the dielectric constant decreases and becomes almost constant at higher frequencies. Zn 2% 0.01728 80 0.98381 40.1 133.3 Zn 4% 0.02277 87 0.99605 30.4 101.1 Zn 6% 0.00963 57 0.97569 72.0 239.1 *3.6. Dielectric Properties*  Materials under the oscillating electric field impart dielectric behavior which can be expressed as a complex form consisting of real (ε′) and imaginary (ε″) components that can be represented as ε٭ = ε′+ iε″. The real component (ε′) of dielectric constant depicts the energy storage and imaginary component signifies the dissipated energy in the material. Various external parameters like microstructure, frequency of applied electric field, sintering temperature, type of cation substitution, etc. affect the dielectric properties. Both components of the dielectric constant can be evaluated using the following relation: (14) ߜܽ݊ݐ ൈ ′ߝ = "ߝ

*Crystals* **2020**, *10*, x FOR PEER REVIEW 12 of 19

mitigate the effects of greenhouse gases. The power consumption can be estimated using the

ܲൈݐଽ ൈ 4.68

where, t90 signifies the time taken by any dye to be degraded 90% of its initial concentration, EC is electricity cost, P is power consumed (in Watt) of UV light source. Power consumers consuming a maximum 500 units of electricity per month pay INR 4.68 per unit in our locality, as shown in Figure 9b. The electricity cost is also found to be minimum for 4% Zn doped sample which has maximum %

**Table 3.** Calculated photodegradation parameters of pure Fe2O3, Zn 2%, Zn 4% and Zn 6%

**% Degradation (in** 

Pure Fe2O3 0.01087 63 0.9962 63.8 211.8

ܧ =

ݐଽ = ln 10 ݇⁄ (12)

**90 min) R2 t1/2 (min) t90 (min)** 

1000 ൈ 60 (13)

**Figure 10.** Variation of (**a**) real component (ε′) and (**b**) Imaginary component (ε″) of dielectric constant with frequency of pure Fe2O3, Zn 2%, Zn 4% and Zn 6% nanoparticles. **Figure 10.** Variation of (**a**) real component (ε 0 ) and (**b**) Imaginary component (ε") of dielectric constant with frequency of pure Fe2O<sup>3</sup> , Zn 2%, Zn 4% and Zn 6% nanoparticles.
