LNMFO Case Study

Results and discussion Crystal structure, lattice parameters, density and porosity
The XRD patterns of BDFO, LNMFO and various (1-x) BDFO–x LNMFO composites are shown in Fig. 1. The peaks in the XRD patterns have been identified. As shown of Fig. 1(a) BDFO forms orthorhombic perovskite structure which is consistent with other reports on bulk BDFO [29, 30] and on the other hand, Fig.1(b) shows that LNMFO have spinel structure. It is observed from the XRD patterns that the composites exhibit both the ferrite and ferroelectric phases. The intensity of most of the ferrite peaks increases while that of perovskite peaks decreases with the increase of ferrite content in the composite. The intensity of XRD peaks and number of peaks depend on the
5(a) shows the variation of ε′ with frequency at room temperature. The high value of ε′ at low frequency and the low value of the dielectric constant at high frequency indicate large dielectric dispersion due to Maxwell–Wagner [34, 35] type interfacial polarization, which is in agreement with Koops phenomenological theory [36]. The large values of dielectric constant at lower frequencies may be explained on the basis of space charge polarization due to inhomogeneities present in dielectric structure, viz. porosity and grain boundary for the present ferrite and ferroelectric system. This may be attributed to the dipoles resulting from changes in valence states of cations and space charge polarization. The space charge polarization is governed by number of space charge carriers and resistivity of the grain boundary. The charge carriers, which take part in exchange, can be produced during sintering process [34,35]. As the frequency increases, the ionic and orientational source of polarizability decreases and finally disappears due to molecular and ionic inertia. At higher frequencies, the ε′ remains almost constant due to the inability of electric dipoles to follow up the fast variation of the alternating applied electric field [37] and accordingly the friction between the dipoles will decreased. Due to the friction, the dipoles dissipate energy in the form of heat, affecting the internal viscosity of the system; hence, there is a decrease in the ε′ and these frequency independent values are known as static values of the ε′. In composites, the higher value of the ε′ at lower frequencies is associated with heterogeneous conduction [38] but sometimes the polaron hopping mechanism results in electronic polarization contributing to low frequency dispersion. These frequency independent values are known as static values of ε′. ε′ of the composites decreases with the ferrite content (Table 2). ε′ of composites does not follow the sum rule. This is because the very low