Nanocrystalline the electrons accumulate on the grain boundaries

Nanocrystalline spinel ferrites are good dielectric materials with high permittivity and low dielectric losses. The dielectric properties of the prepared samples have been studied in the frequency range from 100Hz to 10MHz at room temperature. Fig.7 shows the variation of relative permittivity, ?’ with frequency at room temperature. It is observed from the figure that initially ?’ decreases rapidly with increase in frequency and later the decrease is sluggish at higher frequencies and becomes almost constant with further increase in frequency. This is the absolutely normal dielectric behaviour which can be explained by the Koop’s theory which considers the dielectric as inhomogeneous medium of two layers of the Maxwell Wagner type 41,42. This model suggests that the dielectric ferrites consist of highly conducting grains separated by poorly conducting grain boundaries wherein the grain boundaries are more effective at low frequencies and the grains dominate at high frequencies. In ferrites, conduction mechanism and dielectric polarization are related. The hopping of electrons between metal ions of different oxidation states present at octahedral sites is responsible for dielectric polarization. During hopping of electrons between Fe3+ and Fe2+, the high resistance grain boundaries make the electrons accumulate on the grain boundaries resulting in space charge polarization which is the reason for comparatively high value of permittivity at low frequencies. At higher frequencies the conducting grains dominate leading to decrease in ?’ due to decrease in space charge polarization. At still higher frequencies the hopping cannot follow the applied field variations, thereby ?’ becomes frequency independent. The dielectric loss ?” shows a similar change with frequency (Fig.8). In the samples studied here, both ?’ and ?” increase with Gd3+ content upto x=0.04 and then decrease for x=0.06. The conduction mechanism is largely affected by the amount of Fe2+ ions. A low concentration of Fe2+ causes a low resistivity and hence a high value of dielectric parameters 43. For the system with x=0.06, an increased amount of Gd ions at octahedral site pushes more of Fe3+ ions to tetrahedral site which decreases rate of hopping leading to the decrease in ?’. Increase in hopping length between cations is responsible for the decline in hopping rate. It is noteworthy that though similar reports have been reported earlier, the synthesized samples in the present study have extremely high permittivity and comparatively low dielectric losses, both of which are desirable in energy storage applications.


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