Indian Journal of Pure & Applied Physics
Vol. 43, September 2005, pp. 688-690
Frequency dependent dielectric behaviour of cadmium and chromium
co-substituted nickel ferrite
U N Trivedi, M C Chhantbar, K B Modi & H H Joshi
Department of Physics, Saurashtra University, Rajkot 360 005
Received 1 April 2004; accepted 4 April 2005
The frequency dependent dielectric properties of Ni1−xCdxCrxFe2−xO4 (x = 0.0, 0.3, 0.5, 0.7 and 1.0) spinel ferrite
system are studied by measuring dielectric constant (ε′), dielectric loss (D) and conductivity (σa.c) at 300 K in the frequency
range 100 Hz-2 MHz. The highest value of σa.c and ε′ is observed for x = 0.3 composition. The values ε′ and σa.c decrease
with increase in frequency for all the compositions, exhibiting normal ferrimagnetic behaviour and are attributed to
Maxwell-Wagner type interfacial polarization. The observed broadening of relaxation peak with content in dielectric loss
versus frequency curve is due to the strengthening of dipole-dipole interactions.
Keywords: Ferrites, Dielectric properties, Polarization, Dipole-dipole interactions
IPC Code: G01R27/26
1 Introduction
The ferrites behave as inhomogeneous dielectric
materials in which individual highly conducting
grains are separated by low conductivity layers. The
dielectric properties of ferrites are dependent upon
several factors namely, chemical composition, method
of preparation, grain size etc. The dielectric constants
as high as 105 at low frequencies are observed in case
of ferrites with sufficiently low loss1.
In recent times, the polarization studies were
further extended to understand and interpret the
earlier theories in microscopic manner relevant to
different materials. These theories were also extended
to interpret the low frequency dielectric properties of
ceramic materials that include ferrites.
The electrical and dielectric properties of Ni-based
system substituted with magnetic, non-magnetic
cations have been studied in the present paper. The
thermal variations of dc resistivity and thermoelectric
power have been studied for Zn0.3Ni0.7+xMnxFe2−2xO4
system by Bhige et al1. Metal-insulator type transition
in aluminium and chromium co-substituted nickel
ferrite was observed by Chhaya and Kulkarni2. They
explained such behaviour on the basis of Cr-spins and
3d transition metal electron correlation. The effect of
composition, frequency and temperature dependent
dielectric and ac conductivity behaviour was studied
for a series ZnxMg0.8−xNi0.2Fe2O4 ferrite system by El
Hiti et al while ac electrical conductivity studies have
been performed for Ni-Mg, Co-SbNi, Ni-Zn ferrites
by others3 and references therein. The dielectric
constant and the dielectric loss have been measured
for samples of the type NiAlxFe2−xO4 system by
Ahmed et al4. The comprehensive study on
composition and temperature dependent electrical
resistivity, thermoelectric power and permeability
measurements on Ni1+xMnxFe2-2xO4 system has been
carried out by Shora et al5. The aim of the present
work is to study the mechanism of dielectric
polarization and conduction, which is in continuation
of our earlier study on structural and magnetic
properties of the Ni1−xCdxCrxFe2−xO4 system6.
2 Experimental Details
The powdered samples of Ni1−xCdxCrxFe2−xO4 have
been prepared by usual double sintering ceramic
technique, with composition x = 0.0, 0.3, 0.5, 0.7 and
1.0. The details regarding sample preparation and Xray diffractometry have been given in our earlier
paper6.
The samples for electrical measurements were in
the form of disc 10 mm in diameter and 3 mm thick
and both the faces of each disc samples were polished
by rubbing zero grade emery paper, washed in dilute
HCl and acetone. Finally, graphite was rubbed on
both flat faces of samples on which aluminium foil
was also kept for good electrical contacts. The ac
electrical measurements were carried out by using
Hewlett-Packard (Model 4284 A) made precision
LCR meter in the frequency range 100Hz-2MHz at
300 K.
TRIVEDI et al.: DIELECTRIC PROPERTIES OF NICKEL FERRITE
3 Results and Discussion
The variation of dielectric constant (ε′) with
frequency in the range 100Hz-2MHz at 300K for all
the compositions is shown in Fig. 1(a). The variation
of ε′ with frequency reveals the dispersion due to
Maxwell-Wagner7,8 type interfacial polarization
which is in agreement with Koops phenomenological
theory9. The large values of ε′ at lower frequency are
due to the predominance of the species like Fe2+, Cu1+
ions, interfacial dislocation pile ups, Oxygen
Fig. 1(a)—Variation of dielectric constant (ε′) with frequency;
(b) – Plot of dielectric loss (D) versus frequency; (c) – Frequency
dependent conductivity of Ni-Cd-Fe-Cr-O system.
689
vacancies, grain boundary defects etc7,8. The value of
ε′ decreases with increasing frequency reaching a
constant value for all the compositions. This is
obvious because of the fact that only species
contributing to polarisability are bound to be lagging
behind the applied field at higher frequency.
According to Novikova et al.10 the polarization in
ferrites is through a mechanism similar to the
conduction process. The exchange of electrons
between ferrous ion (Fe2+) and ferric ion (Fe3+) on
octahedral site may lead to local displacement of
electrons in the direction of the applied field and these
electrons determine the polarization. The polarization
decreases with increase in frequency and then reaches
a constant value due to the fact that beyond a certain
frequency of external filed the electron hopping
cannot follow the alternating field. The maximum
value for ε’ is found for typical composition x = 0.3,
with addition of Cd2+ and Cr3+ beyond x = 0.3, the
value ε′ decreases.
It is known that different size of dipoles as well as
different levels of heterogeneity present in these
materials interrupt the flow of the charge carriers at
the interfaces and lead to the formation of barrier
layer. It is assumed that the dipoles in dielectrics
usually interact with neighbouring dipoles and
orientation of the dipoles with applied electric field
would be very much dependent on the dipole-dipole
interaction. If this interaction is weak, it will be easier
to orient dipoles and vice-versa.
Plots of dissipation factor (D) versus log f
(frequency in Hz) for all the compositions with x =
0.0, 0.3, 0.5, 0.7 and 1.0 are shown in Fig. 1(b). It is
observed that the position of the dielectric loss
maxima shifts towards the lower frequency with
increasing Cd-Cr content (x). According to the Debye
relaxation theory, the loss peak occurs when applied
field is in phase with the dielectrics and the condition
ωϒ = 1 is satisfied where ω = 2πf, f being the
frequency of an applied electric field. It can also be
inferred that the relaxation time increases with
increasing content (x) indicating that various dipoles
of different size might have got lower mobility and
they respond slower to frequency. It is important to
note that the relaxation peak becomes broader on
increasing
Cd-Cr
concentration
suggesting
strengthening of the dipole-dipole interactions, which
causes dipole orientations difficult. This explains
delayed relaxation of the dipoles giving rise to a broad
hump around their dielectric anomaly. Furthermore,
shifting of the relaxation peak towards lower
690
INDIAN J PURE & APPL PHYS, VOL 43, SEPTEMBER 2005
frequency side with an increase in content (x)
suggests that on the substitution of Cd-Cr in NiFe2O4,
the dipole-dipole interactions become stronger
causing hindrance to the rotation of dipoles.
Therefore, on increasing Cd-Cr content (x) the
resonance between rotation of the dipoles and applied
field takes place at lower frequency.
Figure 1(c) shows the variation of ac conductivity
(logσac) with frequency at 300K. All the samples
show increase in σac with the increase in frequency
from 100Hz-2MHz, which is the normal behaviour of
ferrites. The conduction mechanism in the ferrites can
be explained on the basis of hopping of charge
carriers between Fe2+-Fe3+ ions on octahedral sites.
The increase in the frequency of the applied filed
enhances the hopping of charge carriers resulting in
an increase in the conduction process thereby
increasing the conductivity. At high frequency σac
remains constant because the hopping frequency no
longer follows the external applied field variations
and lags behind it.
The numbers of ferrous (Fe2+) ions play a dominant
role in the mechanism of conduction and dielectric
polarization. The presence of small amount of Fe2+
ions increases electrical conductivity of a ferrite. The
magnitude of electron exchange between Fe2+ and
Fe3+ ions depends upon the concentration of Fe2+/Fe3+
present on the crystallographically equivalent state in
the lattice i.e. on B-site. The Fe2+ ions concentration is
a characteristic property of a given ferrite material
and its value depends upon various material synthesis
parameters e.g. sintering temperature atmosphere,
cooling rate, type of annealing etc. The presence of
Fe2+ ion which takes part in the electron exchange is
responsible for the conduction and polarization. Thus,
the highest value of ε′ and σac for x = 0.3 sample may
be attributed to the enhanced formation of Fe2+ ions.
For the composition with x > 0.3, the reduction in σac
is ascribed to decreasing octahedral ferric-ion
concentration. The dielectric constant may be thought
to be directly proportional to electrical conductivity,
evidenced through comparison of Fig. 1(a and c).
4 Conclusions
The frequency dependence of dielectric constant
and conductivity can be understood through MaxwellWagner type of interfacial polarization. The
maximum value of ε′ and σac observed for x = 0.3
composition is ascribed to excess formation of ferrous
ions in the system. The broadening of the relaxation
peak and its shifting towards lower frequency side
with increase in Cd-Cr substitution is due to the
strengthening of dipole-dipole interactions.
Acknowledgement
One of the authors (KBM) is thankful to AICTE,
New Delhi, for the financial assistantance in the form
of career award for young teachers and MCC is
thankful to Nuclear Science Centre, New Delhi, for
providing financial assistance in the form of research
fellowship.
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