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

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.

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

x

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