Compositional Dependent Dielectric Constant

The behavior of the dielectric constant (ε 0 and ε 00) with Zn concentration is dependent on many factors like hopping mechanism at octahedral site, lattice parameter and crystallite size. It is well known that the polarization and volume of the unit cell are inversely proportional to each other [42]. It is clearly seen from Figure 10 that value of dielectric constant decreases continuously (pure Fe2O<sup>3</sup> > Zn 2% > Zn 4%) with increase in Zn2<sup>+</sup> ions up to 4% concentration due to its increased lattice parameter, which yields increase in unit cell volume. Also, this can be justified based on the hopping mechanism. The hopping of ions between Fe2<sup>+</sup> and Fe3<sup>+</sup> in octahedral site is responsible for polarization. The decrease in dielectric constant with addition of Zn ions up to 4% arises from a decrease in Fe2<sup>+</sup> ions at the octahedral site which reduces the electrons (n-type charge carriers) at the cost of increased holes (p-type charge carriers). The mobility of holes is less comparable to electrons and these holes contribute towards polarization resulting in a reduction of dielectric constant. The increase in dielectric constant for Zn 6% is due to decrease in its lattice parameter which reduces the cell volume resulting in large polarization and consequently increase in dielectric constant. Secondly, dielectric constant depends on crystallite size also. It is clearly seen from XRD that crystallite size is increased up to Zn 4% and then decreases for Zn 6%, which is in accordance with variation of dielectric constant with composition.
