### Fig. pattern that the composite confirms the presence of

Fig.

1 shows the XRD pattern of 0.2BFO + 0.8LNMFO composite. It is observed from the

XRD pattern that the composite confirms the presence of the ferrite and

ferroelectric phases. The lattice parameter of ferroelectric phase is measured

by solving different sets of three equations corresponding to three consecutive

peaks. Then by taking the average the accurate value of the lattice parameter

is obtained. The values of lattice parameter of all the peaks for the ferrite

phase obtained for each reflected plane are plotted against the Nelson–Riley

function 17:

, where ? is Bragg’s

angle. A straight line has been obtained and the accurate value of the lattice

parameter has been determined from the extrapolation of these lines to

.

Fig.

1: XRD pattern of 0.2BFO + 0.8LNMFO composite sintered at 900 °c.

Fig.

2: Variation of Density and Porosity for 0.2BFO + 0.8LNMFO composite.

Fig.

2 shows the variation of ?B

and P as a function of sintering temperature. The bulk density of the composite

increases with Ts up to 900°C

then decreases for further increasing Ts.

On the other hand, porosity shows the

opposite trend of density as shown in fig. 2. The increase in ?B with Ts is

expected because during the sintering process, the thermal energy generates a

force that drives the grain boundaries to grow over pores, thereby decreasing

the pore volume and denser the material. A further increase of Ts at

9250C, the ?B decreases because the intragranular porosity

increase resulting from the increase of thickness of grain boundary where pores

or vacant sites are trapped.

3.2 Microstructure

Fig. 3: The FESEM microstructure of 0.2BFO +

0.8LNMFO composite sintered at (a) 850,

(b) 875, (c) 900 and (d) 925 °C.

The FESEM images of 0.2BFO + 0.8LNMFO composite

sintered at various Ts are shown in Fig. 3. It is noticed that the optimum

temperature of the composite is 900°C.

The average grain size has been calculated by linear intercept technique. The D

is significantly decreases with Ts. The uniformity in the grain size

can control the properties of materials such as the magnetic permeability. The grain

growth behavior reflects the competition between the driving forces for grain

boundary movement and the retarding force exerted by pores 18. When the

driving force of the grain boundary in each grain is homogeneous, the sintered sample

attains a uniform grain size distribution; in contrast, if this driving force

is inhomogeneous discontinuous grain growth occurs.

3.5 Dielectric

Properties

Fig. 7(a) shows the

variation of ?? with frequency at room temperature for 0.2BFO + 0.8LNMFO

composite. It is observed that the value of ?? decreases rapidly with

the increase in frequency and remain constant at higher frequency. At low

frequency region this dielectric dispersion is due to Maxwell–Wagner 27,28

type interfacial polarization in agreement with Koop’s phenomenological theory

29. The interfacial polarization originates due to the inhomogeneities of the

sample resulting from impurities, porosity, interfacial defects and grain

structure. These inhomogeneities are generated in the sample during high

temperature calcination and sintering processes. At higher frequencies, ??

remains almost frequency independent due to the inability of electric dipoles

to follow up the fast variation of the alternating applied electric field 30.

FIG.

7: VARIATION OF (a) DIELECTRIC CONSTANT AND (b) DIELECTRIC LOSS WITH FREQUENCY

OF 0.5BDFO–0.5LNMFO COMPOSITE.

Fig.

7(b) shows the variation of dielectric loss as a function of frequency. It is

observed that the composites exhibit a loss peak according to Debye relaxation

theory. This loss peak occurs when the jumping frequency of electron is equal

to the frequency of applied field and the condition ?? =1 (? = 2?f) is satisfied

31.

3.6

ELECTRIC MODULUS ANALYSIS

We have studied the complex electric modulus because it is possible to

separate the electrode polarization effect the grain boundary conduction

process through complex electric modulus study. The analysis of electrical

relaxation in this system is carried out using the dielectric modulus M* as

formulated by Macedo et al. 32

Simplifying

and substituting

by

, we get

FIG.

9: ELECTRIC MODULUS SPECTRA OF 0.5BDFO–0.5LNMFO COMPOSITE (a) REAL PART (M?)

AND (b) IMAGINARY PART (M?).

The

variation of real part M?(?) of the electric modulus as a

function of frequency as shown in Fig. 9(a). The zero values of M?(?)

in the low frequency region confirm the presence of an appreciable electrode

and/or ionic polarization in the composites under the studied frequency ranges

and a continuous dispersion on increasing the frequency may be contributed to

the conduction phenomena due to short range mobility of carriers. This implies

the lack of restoring force for flow of charge under the influence of a steady

electric field 32. Fig. 9(b) shows the variation imaginary M??(?)

part of dielectric modulus with frequency. The modulus curves indicate not only

the considerable shift in the M?max towards lower frequency

side but also broadening of peaks with change the Ts. It is observed

that M??(?) increases in the lower frequency region and exhibits

a single relaxation peak centered at the dispersion region of M?(?).In

the higher frequency region M??(?) decreases and becomes constant

which may be attributed due to limited carriers in potential wells. The low

frequency region below the peak in M??(?) spectra determines the

range in which charge carriers are mobile over long distances, i.e., in between

grains and at frequency above the peak the carriers are spatially confined to

their potential wells, being mobile over short distances, i.e., inside the

grains of the composite and associated with relaxation polarization process,

i.e., the carriers can execute only localized motion