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Chapter IV- Electrical and magnetic properties of ME composites
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Chapter IV- Electrical and Magnetic properties of ME
composites
A. Electric properties
4. A.1. DC resistivity
A large number of applications of ceramic materials depend on their
electrical properties. Composite materials are formed from combination of two
or more single phase compounds. Physical properties of composites are
determined by the properties of their constituent phases and the interaction
between them. Composite have some properties which give rise to sum of their
constituents. The electrical properties of composite are quantitatively
considered as sum properties of their individual electrical and ionic behavior. A
sum property of a composite is the weighed sum of the contributions from their
individual component phases and is proportional to the volume fraction of
these phases in composites [1]. The sum of their properties denotes the average
or enhancement effects which are already present in the constituent phases of
these composites [2]. In the present chapter the properties like DC resistivity,
AC conductivity and dielectric properties of the individual phases and their
composites are discussed in the first section.
Electrical resistivity is a physical property of dielectric crystals, required
not only for the practical applications but also for the interpretation of various
physical phenomena. The first step in understanding of electrical transport
mechanism in any solid is to know whether conductivity is ionic, electronic or
mixed partially ionic and electric. There are several ways of determining the
nature of conductivity. The simplest way is to measure dc conductivity as a
function of temperature using electrodes, which blocks ionic conduction. In
case of pure ionic conduction, dc conductivity decreases with temperature and
tends to become zero after sufficiently long time, whereas for a pure electronic
conductor it is essentially independent of temperature. For mixed conduction it
decreases with temperature but tends to stabilize at some finite constant value
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Chapter IV- Electrical and magnetic properties of ME composites
[3]. The conductivity of a solid dielectric depends on the mobility of charge
carriers and their concentration. The variation of conductivity with temperature
can be expressed by exponential relation as follows
σ = σ 0 exp(− ∆E kT )
(4.1)
where ∆E = activation energy , k = Boltzmann constant, T = Absolute
temperature and σ0 = Constant
In terms of resistivity it can be written as,
ρ = ρ 0 exp(∆E kT )
(4.2)
Most of the polar dielectric materials show temperature dependent
resistivity behavior. It shows decrease in resistivity with increase in
temperature and sudden change is observed near the Curie temperature.
Verway et al. [4] observed discontinuities in temperature dependent plots. The
conduction in ferrite, ferroelectric and their composites results from the
hopping process of charge carriers. The energy required for hopping of an
electron from one ion to another is known as activation energy. In composite
materials resistivity can be explained on the basis of location of cation in
structure and hopping mechanism. The electrical conductivity in ferrite is
caused by the simultaneous presence of ferrous and ferric ions on octahedral
site. The resistivity can be increased by addition of small amount of foreign
oxides. The hopping of 3d electrons among Fe2+ and Fe3+ arranged on B sites
could play a substantial role in the conduction process. The electrical
conductivity depends on chemical composition, thermal condition of
preparation, porosity and grain size of constituent phases.
4. A.1.1. Conduction mechanism in ferrites and ferroelectrics
Ferrites (magnetic-ceramics) and ferroelectrics (electro-ceramics) show
semiconducting properties [5, 6]. Though ferrites are semiconductors, the
conduction mechanism is quite different than that of semiconductors. In
ferrites, the carrier concentration is almost constant but mobility of carriers is
affected by temperature. Conventional band theory and free electron theory
fails to explain conduction in ferrites as there are no Bloch type of wave
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functions as well as no free electrons [5]. Band theory is in accordance with
increase in carrier concentration with temperature whereas hopping model
considers that conductivity is due to change in mobility of charge carriers with
temperature. Similarly, ferroelectric semiconductors display a number of
properties not inherent in common semiconductors owing to the spontaneous
polarization and to the phase transition at Curie temperature [6]. One of this
property is the posistor effect (PTC effect) that shows up a growth in resistivity
of a ferroelectric material with temperature when it passes from the
ferroelectric phase into paraelectric phase. The PTC effect underlines the
operating principle of posistors, i.e. thermally sensitive resistors. This is unlike
to semiconductor based thermistors in which resistance diminishes with
increase in temperature. The PTC region lies within the temperature interval of
crystal lattice rearrangement during phase transition and hence for the
ferroelectrics with a diffused phase transition shows a smooth increase in
resistivity over the entire temperature interval where the diffused phase
transition takes place [6]. The conduction in ferrite and ferroelectric can be
explained in terms of polaron hopping process [4, 7]. There are experimental
evidences for the existence of polarons and its hopping process [8, 9].
Moreover, when the cation to anion ratio in these oxides departs from the ideal
value, the oxygen vacancies in sintered ceramics, on thermal excitation, can
provide the trapped electrons to give rise to n - type conductivity in a oxygen
deficient ferrite/ ferroelectric. Similarly, p - type conductivity has also been
observed [10].
4. A.1.2.Electron - hopping and polarons
An electron in crystal lattice interacts through its electrical charge with
the ions or atoms of the lattice and creates a local deformation of the lattice.
The deformation further follows the electron as it moves through the lattice.
The electron coupled with this strain field is called a polaron. If the polaron or
its strain field spreads beyond lattice constant, it is called large polaron and if
the strain field extends over a distance less than a lattice constant is called as a
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small polaron. An electron associated with large polaron moves in a band and
electron associated with small polaron is trapped on a single ion. Thus the
interaction between the conduction electron or a hole with nearby ions may
result in the displacement of the ions and hence in the polarization of the
surrounding region, so that a carrier becomes situated at the centre of the
polarization potential well. If the potential well is deep enough, the carrier may
be trapped at the lattice site and its transition to the neighbouring site can be
determined by the thermal activation. This process is called hopping of
electron.
If size of the potential well is comparable to the ionic volume,
interaction between nearest neighbour is important, and then small polaron
model is used. Small polaron formation is favoured in solids, which at low
temperature behaves like particle moving in a narrow conduction band. At
elevated temperature, small polaron may absorb one or more phonons resulting
in hopping mechanism. When the tunneling time is less than the time for
successive hopping transition, conduction by small polaron becomes
prominent. Bosman and Van Daal [11] have given the detailed analysis of
conduction due to polaron hopping. Many researchers [8, 9] have reported that
the conduction in ferrites is mainly due to small polaron hopping. The most
common effect of polaron is seen in temperature dependence of the electrical
resistivity.
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Results and discussion
Figure 4.1 Variation of DC resistivity with temperature for (x) NiFe1.9Mn0.1O4 +
(1-x) BaZr0.08Ti0.92O3 ME composites
The temperature dependence of dc resistivity for (x) NiFe1.9Mn0.1O4 + (1-x)
BaZr0.08Ti0.92O3 ME composites is shown in Fig.4.1. Decrease in resistivity with
temperature reflects the semiconductor behavior of the samples. The decrease in
resistivity with increase in temperature is due to the increase in the thermally
activated drift mobility of charge carriers according to the hopping conduction
mechanism [12]. Also the resistivity of (x) NiFe1.9Mn0.1O4 + (1-x) BaZr0.08Ti0.92O3
ME composites is found to decrease with increase in ferrite content, this is because
when the ferrite particles make chains, the electrical resistivity of the composites is
reduced significantly due to the low resistivity of the ferrite phase [13] as well as the
parallel connectivity between ferrite and ferroelectric grains in all composites [1].
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Figure 4.2 Variation of DC resistivity with temperature for (25%) Co1.2xMnxFe1.8O4
+ (75%) BaZr0.08Ti0.92O3 ME composites
The temperature dependence of dc resistivity for (x) Co1.2-yMnyFe1.8O4 + (1-x)
BaZr0.08Ti0.92O3 ME composites is shown in figure 4.2.
It also shows the
semiconducting behavior. The resistivity of (25%) Co1.2-yMnyFe1.8O4 (CMFO, y = 0.0
to 0.4 in step of 0.1) + (75%) BaZr0.08Ti0.92O3 ME composites is found to be decreases
with the increase in Mn content for Co-ferrite due to low resistivity of Mn ferrite.
The resistivity and activation energy for ME composites are given in Table
4.1. It is well known that the electron and hole hopping between Fe2+/Fe3+, Ni2+/Ni3+,
Mn2+/Mn3+, Ba2+/Ba3+, Ti3+/Ti4+ and Zr3+/Zr4+ ions, with activation energy <0.2 eV is
responsible for electrical conduction in the composites. The calculated activation
energies are 0.38, 0.33 eV, 0.26 eV, 0.20 eV and 0.22 eV for (x) NiFe1.9Mn0.1O4 + (1Composite Materials Laboratory,
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Chapter IV- Electrical and magnetic properties of ME composites
x) BaZr0.08Ti0.92O3 ME composites with x = 0.0, 0.1, 0.2, 0.3 and 1 respectively and
for (25wt %) Co1.2-yMnyFe1.8O4 + (75wt %) BaZr0.08Ti0.92O3 ME composites are 0.31,
0.29, 0.30, 0.28 and 0.23 eV for the composite with y = 0, 0.1, 0.2, 0.3 and 1,
respectively, suggesting the temperature dependence of charge mobility.
Table 4.1 DC resistivity and activation energy for studied ME composites
System
Resistivity at
Activation
RT
energy (eV)
(Ωcm)
(0.25) Co1.2Fe1.8O4 + (0.75) BaZr0.08Ti0.92O3
~1010
0.31
(0.25) Co1.1Mn0.1Fe1.8O4+ (0.75)
~108
0.29
(0.25) CoMn0.2Fe1.8O4+ (0.75) BaZr0.08Ti0.92O3
~109
0.30
(0.25) Co0.9Mn0.3Fe1.8O4+ (0.75)
~109
0.28
~108
0.23
(0.1) NiFe1.9Mn0.1O4 + (0.9) BaZr0.08Ti0.92O3
~1011
0.33
(0.2) NiFe1.9Mn0.1O4 + (0.8) BaZr0.08Ti0.92O3
~1010
0.26
(0.3) NiFe1.9Mn0.1O4 + (0.7) BaZr0.08Ti0.92O3
~109
0.22
BaZr0.08Ti0.92O3
BaZr0.08Ti0.92O3
(0.25) Co0.8Mn0.4Fe1.8O4+ (0.75)
BaZr0.08Ti0.92O3
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B. Dielectric Properties
4. B.1. Dielectric Constant
4. B.1.1. Introduction
Ceramics are electrical insulators with dielectric strength, dielectric
constant and loss tangent values tailored for specific device or circuit
applications. In capacitor applications, ceramics with a high dielectric constant
are used to increase the charge that can be stored. In microelectronic circuits,
low dielectric constant materials are sought to reduce inductive cross talk and
noise generation in the circuit. In high voltage insulator applications, high
electrical resistivity (Ωcm) and high dielectric strength are required. Parameters
that are important to consider when specifying dielectric ceramics and
substrates include dielectric strength, dielectric constant (relative permittivity),
loss tangent (tan δ), electrical resistivity, and operating frequency. Dielectric
strength is the maximum voltage field that the ceramic or material can
withstand before electrical breakdown. The dielectric constant is the relative
permittivity of a material compared to a vacuum or free space. In dielectric
materials, the loss tangent or loss coefficient is the ratio of the imaginary or
loss permittivity to the real permittivity of a material. Resistivity is the
longitudinal electrical resistance (Ω cm) of a uniform rod of unit length and
unit cross-sectional area. Operating frequency is the frequency range that the
material is capable for operating within, while providing acceptable
performance and/or without excessive power losses.
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Chapter IV- Electrical and magnetic properties of ME composites
4. B.1.2. Dielectric Constant and Polarization
The dielectric displacement (D) found in a dielectric material when
subjected to an alternating field (E) is given by,
D = ε *E
(4.3)
where ε* is the dielectric constant of the material and it is a complex quantity
Thus
ε * = ε '− jε ''
(4.4)
For an alternating field, the displacement (D) and electric field (E) are not in
phase. Hence the dielectric constant is a complex quantity involving real (ε')
and imaginary (ε'') parts, which are related by a loss factor (tan δ) as,
tan δ =
ε ''
ε'
(4.5)
Therefore, the power loss per unit volume of the material is given by
P = ω E 2ε 0ε ' tan δ
(4.6)
where, symbols have their usual meaning.
The frequency and time dependence of complex dielectric constant (assuming
Koop’s two layer model) can be given as,
 ε0 + ε0 − ε0   ε0 − ε∞ 
ωτ
+i
2 2
2 2 
 1+ ω τ   1+ ω τ 
ε* = 
(4.7)
where ε0 - Low frequency dielectric constant
ε - High frequency dielectric constant
τ - Relaxation time
ω - Angular frequency
From equations 4.4 and 4.5, we have
tan δ = loss current / charging current
=
tan δ =
ε ''
ε'
(ε 0 − ε ∞ )ωτ
ε 0 + ε ∞ω 2τ 2
These are known as Debye equations
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Chapter IV- Electrical and magnetic properties of ME composites
4. B.1.3. Frequency dependence of the dielectric constant
The dielectric constant (ε') - frequency relationship describes the dispersion
characteristic of a dielectric. A monotonic decrease in permittivity with increase in
frequency
is
known
as
relaxation
dispersion
typical
for
dipole
and
migrational/interfacial polarization. Ionic and electronic types of polarization
experiences resonance dispersion, where the permittivity first grows, then decreases,
traverses the minimum and reaches a constant value at very high frequencies [6]. It
was observed earlier that resistivity and dielectric constant for polycrystalline sintered
composites exhibit relaxation dispersion with respect to frequency. This dispersion is
explained with the help of Koop’s two layer model [14]. Koop has given a general
model for inhomogeneous dielectric, which comprises of well conducting grains that
are well separated by a low conducting layer (grain boundaries). These layers
constitute a condenser in which ferrite / ferroelectric grains and their boundaries have
different properties leading to two parallel resistance and capacitance circuit, one for
grain and the other for grain boundaries, which in turn are connected in series.
Besides this, the polycrystalline sintered ceramic material consists of cracks, pores
and other defects and due to non - homogeneity there is regions of different
permittivity. Thus the conducting grains, less conducting boundaries are separated by
voids or pores. This gives rise to conducting, less conducting and non - conducting
matrix and appears apparent dielectric relaxation as a result of interfacial polarization,
which was explained by Maxwell and Wagner [14–16]. The grain boundaries are
effective at low frequencies while the grains are effective at higher frequencies.
4. B.1.4. Temperature dependence of the dielectric constant
In non polar dielectrics temperature has no direct impact on the polarization
process. The electronic polarizability of the material is temperature independent.
However, as the dielectric material expands under heat, the number of polarized
molecules per unit volume decreases. Thus the permittivity and dielectric constant
decreases with increase in temperature for non polar dielectrics.
In polar dielectrics, especially solid ionic dielectrics and for Curie temperature
Tc > 0, the dielectric constant increases with increase in temperature due to growing
effect of ionic polarization and dipole polarization, which comes into play as a
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relaxation time decreases with increase in temperature starting from very low
temperatures [6]. A further increase in temperature, however, adds to the random
vibrational motion of the molecules, which becomes less susceptible to the orientation
in the field direction and hence the dielectric constant decreases. This process results
in a typical “dipole” maximum on the ε' -T characteristics. The decrease in dielectric
constant above ferroelectric Curie temperature in ferroelectrics generally obeys CurieWeiss law. There are also ferroelectrics with a diffused phase transition (DPT) noted
for the absence of a definite transition point. Here, the phase transition takes place
within a more or less broad temperature range, where spontaneous polarization
gradually decreases and dielectric constant vs. temperature plots show a diffused
(broad) maximum. In this temperature region, known as Curie region the ferroelectric
and paraelectric phases co-exist. It is difficult to determine with accuracy, the
temperature for which the spontaneous polarization is zero. This type of transition is
commonly found in relaxor ferroelectrics. The phase transition of ferroelectrics is
smeared as a consequence of the chemical composition and microstructure developed
during sintering.
Thus, the Curie - Weiss formula can in general be written as
1
(T − Tc)γ
=
ε ' ε 'max
C'
1
−
(4.9)
where C΄ is Curie constant and γ is the critical exponent called as diffusivity
parameter which is a measure of broadness in DPT. The value of γ = 1 for the sharp
phase transition is observed in BaTiO3 obeying Curie- Weiss law. But γ ≥1 and γ ≤ 2
for relaxor ferroelectrics with DPT type transition [17].
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4. B.2. Results and discussion
4. B.2.1. Variation of dielectric constant (ઽઽ') and dielectric loss (tan δ) with
frequency
Figure 4.3 Variation of ε' with frequency for (x) NiFe1.9Mn0.1O4 + (1-x)
BaZr0.08Ti0.92O3 ME composites
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Figure 4.4 Variation of ε' with frequency for Co1.2-xMnxFe1.8O4 (CMFO) ferrite
system
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Figure 4.5 Variation of ε' with frequency for (25%) Co1.2-xMnxFe1.8O4 + (75%)
BaZr0.08Ti0.92O3 ME composites
Figures 4.3, 4.4 and 4.5 show the frequency dependence of the dielectric
constant for studied systems of ferrite, ferroelectric and their ME composites. It is
observed that the dielectric constant decreases steeply at lower frequencies and
remains constant at higher frequencies, indicating the usual dielectric dispersion. This
may be attributed to the polarizations due to the changes in valence states of cations
and space charge polarization (i.e. Maxwell- Wagner) [14-16] , as the dielectric
constant is a combined effect of dipolar, electronic, ionic and interfacial polarizations.
At lower frequency, the dipolar and interfacial polarizations contribute significantly to
the dielectric constant and at higher frequency only electronic polarization becomes
significant. At higher frequencies, the dielectric constant remains independent of
frequency due to the inability of electric dipoles to follow the fast variation of the
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alternating applied electric field and accordingly the friction between them will
increases. Also, as the frequency increases, ionic and orientation sources of
polarizability decreases and finally disappear due to the inertia of the molecules and
ions.
In composites, the higher value of dielectric constant at lower frequencies is
associated with heterogeneous conduction [18], but sometimes the polaron hopping
mechanism results in electronic polarization contributing to low frequency dispersion.
The dielectric behavior in composites can also be explained on the basis of
polarization mechanism in ferrites because the conduction beyond the phase
percolation limits due to the presence of ferrite phase [19]. According to Rabinkin et
al [20], the polarization in ferrites is through a mechanism similar to the conduction
process. The presence of Fe3+ and Fe2+ ions render ferrite materials to be dipolar.
Rotational displacement of dipoles results in to orientational polarization. In ferrites,
rotation of Fe2+ ↔ Fe3+ dipoles may be visualized as the exchange of electrons
between the ions so that the dipoles align themselves in response to the alternating
field. The existence of inertia to the charge movement would cause relaxation of the
polarization. The polarization at lower frequencies results from electron hopping
between Fe3+ ↔ Fe2+ ions in the ferrite lattice. The polarization decreases with
increase in frequency and reaches a constant value due to the fact that beyond a
certain frequency of external field the electron exchange Fe3+ ↔ Fe2+cannot follow
the alternating field [21] . In present work, the presence of Ni2+/Ni3+ , Co2+/Co3+ and
Mn2+/Mn3+ ions and in BaZr0.08Ti0.92O3 ferroelectric phase, the presence of Ba2+/Ba3+
ions give rise to p-type carriers. The local displacement of p-type carriers in the
external electric field direction contributes to the net polarization in additional to that
of n-type carriers. However, the p-type carrier contribution is smaller than that from
the electronic exchange between Fe3+/Fe2+ and Zr4+/Zr3+ or Ti4+/Ti3+ ions and it is
opposite in sign [22]. Since the mobility of p-type carriers is smaller than n-type
carriers , their contribution to polarization decreases more rapidly and then decreases
with increase in frequency as it is observed in the present compositions.
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Figure 4.6 Variation of tan δ with frequency for Co1.2-xMnxFe1.8O4 (CMFO)
ferrite system
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Figure 4.7 Variation of tan δ with frequency for (x) NiFe1.9Mn0.1O4 + (1-x)
BaZr0.08Ti0.92O3 ME composites
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Figure 4.8 Variation of tan δ with frequency for (x) Co1.2-xMnxFe1.8O4 + (1-x)
BaZr0.08Ti0.92O3 ME composites
Figures 4.6, 4.7 and 4.8 show the variation of loss tangent (tan δ) with
frequency for studies systems of ferrite, ferroelectric and ME composite. The physical
significance of tan δ is the energy dissipation in the dielectric system which is
proportional to the imaginary part (ε'') of the dielectric constant. The dielectric loss
possesses similar behavior to that of dielectric constant (ε') with respect to frequency.
This loss factor curve is considered to be caused by domain wall resonance. At higher
frequencies, losses are found to be low if domain wall motion is inhibited and
magnetization is forced to change by rotation [22]. At lower frequencies tan δ is large
and it decreases with increasing frequency. The maximum dielectric loss is attributed
to the fact that the period of relaxation process is same as the period of applied field.
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When the relaxation time is large as compared to the period and frequency of the
applied field respectively, losses are small [25].
4. B.2.2. Variation of dielectric constant (ઽ
ઽ') and dielectric loss (tan δ)
with temperature
Figure 4.9 Variation of ε' with temperature for (x) NiFe1.9Mn0.1O4 + (1-x)
BaZr0.08Ti0.92O3 ME composites
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Figure 4.10 Variation of ε' with temperature for (25%) Co1.2-xMnxFe1.8O4 +
(75%) BaZr0.08Ti0.92O3 ME composites
Figures 4.9 and 4.10 show the temperature dependence of the
dielectric constant of studied ME composites at 1 kHz. The variation of dielectric
constant with temperature for all the compositions is normally an expected behavior
that has been observed in most of the ferrites, ferroelectrics and ME composites [24,
25]. Basically the charge hopping is a thermally activated process that results increase
in dielectric polarization proportional to the temperature. The incorporation of the
non-ferroelectric (i.e. ferrite) phase in the pure ferroelectric phase dilutes the
ferroelectric properties of the composites, resulting in the reduction of dielectric
constant and broadness of the peak.
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As reported earlier, the ferroelectric to paraelectric phase transition Tc for
BaZrxTi1-xO3 system is shifted towards lower temperatures with increasing Zr
concentration which may be attributed to the well-known pinching effect in Zr doped
BaTiO3 ceramics [36]. In the present case, temperature dependent dielectric constant
measurements for studied ME composite shows two dielectric maxima, one below
100 oC and the second above 500 oC. The dielectric maxima below 100 oC
corresponds to the transition temperature of ferroelectric phase and that above 500 oC
corresponds to the transition temperature of ferrite phase of the ME composites. For
BaZr0.8Ti0.92O3 (BZT), the observed Tc is nearly equal to 65-70 oC as comparable to
the reported value [27, 28]. For NiFe1.9Mn0.1O4, the observed value of Tc is nearly
equal to 535-540 oC, which is less than that of pure NiFe2O4 parent phase. This is due
to the doping of 10% Mn into pure nickel ferrite result in decrease in Tc due to low
phase transition temperatures of corresponding Mn (300 oC) and Ni (585 oC) ferrites .
Also for Co1.2-xMnxFe1.8O4 (CMFO) system, it is observed that as Mn content
increases in the cobalt ferrite, the phase transition temperature of the ferrite phase
decreases. The observed values of Curie temperature (Tc )are 560 oC, 515 oC, 480 oC,
465 oC and 440 oC for CMFO0+BZT, CMFO1+BZT, CMFO2+BZT, CMFO3+BZT
and CMFO4+BZT respectively. This is due to the phase transition temperatures of
corresponding Mn (300 oC) and Co (550 oC) ferrites [29].
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Figure 4.11 Variation of tan δ with temperature for (x) NiFe1.9Mn0.1O4 + (1-x)
BaZr0.08Ti0.92O3 ME composites
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Figure 4.12 Variation of tan δ with temperature for (25%) Co1.2xMnxFe1.8O4 +
(75%) BaZr0.08Ti0.92O3 ME composites
Figures 4.11 and 4.12 show the variation of dielectric loss (tan δ) as a function
of temperature for studied ME composites. The loss curves are also show increasing
behavior with increase in temperature and can be explained on the lines similar to
those used for explaining dielectric constant. As seen from graphs, dielectric loss is
minimum at lower temperatures and increases with increase in temperature. The
increase in dielectric loss is a result of decreasing resistivity of the samples with
temperature. These curves can be understood on the basis of the Debye equation
(Eq.4.8) for loss [30].
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Chapter IV- Electrical and magnetic properties of ME composites
4. B.3. AC conductivity
A capacitor when charged under an ac voltage will have some loss current due
to ohmic resistance or impedance by heat absorption. If Q be the charge in coulombs
due to a potential difference of V volts between two plates of a condenser of area, A
and interpolate distance, d, then ac conductivity (σac) due to ac voltage v(v0 ejωt) is
given by the relation
σ ac =
J
E
(4.10)
where, J is the current density and E is the electric field strength vector. But the
electric field vector, E= D/ε. D is the displacement vector if the dipole charges, ε is
the complex permittivity of the material. For a parallel plate capacitor the electric
field intensity (E) is the ratio of potential difference between the plates of the
capacitor to the inter plate distance. i.e.
E=
V
D
(4.11)
Since the current density J = dq / dt but q is given by
Q Vε
=
,
A d
∴J =
∴J =
dq d  V ε  ε dV
= 
=
dt dt  d  d dt
ε
d
Vjω
(4.12)
(4.13)
(4.14)
Substituting for E and J in (4.10)
σ AC =
J
= ε jω
E
(4.15)
Since ε being a complex quantity
= (ε '− jε '') jω = ε ' jω + ωε ''
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Chapter IV- Electrical and magnetic properties of ME composites
In order that ac conductivity may be a real quantity, the term containing j has to be
neglected hence
σ AC = ωε ''
(4.17)
In any dielectric material there will be some power loss because of the work
done to overcome the frictional damping forces encountered by the dipoles during
their rotation. If an AC field is considered then in an ideal case the charging current Ic
will be 90o out of phase with the voltage. But in most of the capacitors due to the
absorption of electrical energy some loss current, IL will also be produced, which will
be in phase with the voltage. Charging current, Ic and loss current, IL, will make
angles δ and θ, respectively with the total current, I, passing through the capacitor.
The loss current is represented by sin δ of the total current, I. Generally, sin δ is called
the loss factor but when δ is small then sin δ = δ= tan δ. But the two components ε’
and ε’’ of the complex dielectric constant, ε, will be frequency dependent and is given
by
ε '(ω ) = D0 cos δ / E0
(4.18)
ε ''(ω ) = D0 sin δ / E0
(4.19)
Since the displacement vector in a time varying field will not be in phase with E and
hence there will be a phase difference d between them.
From equations 4.18 and 4.19 we have
tan δ =
ε ''(ω )
ε '(ω )
(4.20)
Substituting the value of ε'' (ω) from 4.20 in 4.17 then we have
σ AC = ω tan δε '(ω )
(4.21)
Where ω = 2π f and ε ' = ε 0ε r , here εr is the relative permittivity of the material and
εo the permittivity of free space.
Therefore,
σ AC = 2π f tan δε 0ε r
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Chapter IV- Electrical and magnetic properties of ME composites
134
This equation is used to calculate the ac conductivity using dielectric constant and tan
δ at a given frequency.
4. B.3.1. Variation of AC conductivity with frequency
Figure 4.13 Variation of σAC with frequency for Co1.2-xMnxFe1.8O4 (CMFO)
ferrite system
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Chapter IV- Electrical and magnetic properties of ME composites
135
Figure 4.14 Variation of σAC with frequency for (x) NiFe1.9Mn0.1O4 + (1-x)
BaZr0.08Ti0.92O3 ME composites
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Chapter IV- Electrical and magnetic properties of ME composites
136
Figure 4.15 Variation of σAC with frequency for (25%) Co1.2-xMnxFe1.8O4 + (75%)
BaZr0.08Ti0.92O3 ME composites
To understand the conduction mechanism in composites the AC conductivity
measurement was carried out at room temperature in the frequency range from 20Hz
to 1MHz. Figures 4.13 to 4.15 show the variation of AC conductivity (σAC) with
frequency for studied system of ferrite, ferroelectric and ME composites. The plots
are almost linear indicating that the conductivity increases with increases in
frequency. Similar results were reported by earlier workers [31-32]. Frequency
dependent of AC conductivity indicates that conduction occurs due to hopping of
small polarons among the localized states. Hopping conduction is favored in ionic
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Chapter IV- Electrical and magnetic properties of ME composites
137
lattice in which the same kind of cations exists in two oxidation states [32]. Also, for
ionic solids, the concept of small polaron conduction is valid. While Alder and
Fienleib [31], have shown that the conduction in ferrite is due to hopping of charges
which gives rise to the linearity between AC conductivity and angular frequency as
already stated the concept of small polaron is valid in ferrites. The electrical
conductivity is due to migration of ions and this ionic transport depends on the
angular frequency. Thus it has been shown that the ac conductivity is proportional to
angular frequency. The treatment of conduction by polaron is discussed by Austin and
Mott [33]. In large polaron model, AC conductivity is due to band mechanism at all
temperatures. AC conductivity decreases with increases in frequency. In case of small
polaron model, the AC conductivity increases with increase in frequency [34]. All the
plots are linear confirming that the conduction in all composites is due to small
polaron hopping. In few cases the conductivity slightly decreases, attributing to the
conduction by mixed polarons [34].
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Chapter IV- Electrical and magnetic properties of ME composites
138
C. Magnetic properties
4. C.1. Magnetic hysteresis
A great deal of information about the magnetic properties of a material can be
obtained by studying its hysteresis loop. Hysteresis is a well known phenomenon in
ferromagnetic materials. The choice of a ferrite for a particular application is
dependent on its magnetic properties. Magnetic properties are strongly dependent on
chemical composition, sintering temperature, grain size, crystal structure and porosity
of the material [35]. Ferrite being magnetic materials, so it is becomes necessary to
study the magnetic properties of these ferrites individually and in composite materials.
It has been observed that the presence of ferroelectric phase in the composite affects
the magnetic properties of the ferrite phase. Magnetic properties of ferrite and their
composites with ferroelectric phase have been discussed on the basis of magnetic
parameters such as saturation magnetization, magnetic moment, coercivity, magnetic
loss and retentivity.
Figure 4.16 Magnetic (B-H) hysteresis loop for NiFe1.9Mn0.1O4 system
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Chapter IV- Electrical and magnetic properties of ME composites
139
Figure 4.17 Magnetic (B-H) hysteresis loop for (x) NiFe1.9Mn0.1O4 + (1-x)
BaZr0.08Ti0.92O3 ME composite.
Figures 4.16 and 4.17 shows the B-H hysteresis loop of spinel ferrite
(NiFe1.9Mn0.1O4) phase and that of ME composites with varying ferrite content (x =
0.1, 0.2 and 0.3) respectively. At room temperature, all the samples exhibited B-H
hysteresis loop typical of magnetic behavior, and this indicates that the presence of an
ordered magnetic structure can exist in the mixed spinel–perovskite system. The B-H
hysteresis loops of the composites shift towards the field axis with low ferrite content.
Magnetization in case of all composites saturates at magnetic field strength of above ~
1kOe. The saturation magnetization (Ms) of 46 emu/gm was observed for the ferrite
phase. From Table 4.2, it is observed that in composites the magnetic parameters like
saturation magnetization Ms, magnetic moment nB ,Bohr magneton and retentivity Mr
increases with ferrite content increases. This is due to the individual grains of ferrites
contributing to magnetization. The presence of pores among the grains breaks the
magnetic circuits and results in a reduction of magnetic properties with increasing
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Chapter IV- Electrical and magnetic properties of ME composites
pore concentration [36]. Therefore, in composites, ferroelectric material in the
presence of magnetic field acts as a pore causing the reduction of magnetic
parameters. After saturation of a ferrite phase in a strong magnetic field, the
magnetization vector rotates towards the nearest preferred field direction and results
in high anisotropy when the field is reduced to zero. The stress and shape anisotropy
are the most important parameters for getting the maximum magnetoelectric output in
such composites. The increased values of retentivity suggests that most of the
magnetization vectors are turned out of the magnetically preferred direction by
making a small angle with the direction of the applied field and suffer stresses [29],
which result in high magnetization.
Table 4.2: Magnetic Parameters of (x) NiFe1.9Mn0.1O4 and (1-x) BaZr0.08Ti0.92O3 ME
composites.
Ms
µB
Mr
(x)
(emu/g)
(Bohr magneton)
(emu/g)
0.1
3.38
0.14
1.0
0.2
6.66
0.28
2.80
0.3
13.38
0.56
4.50
1.0
46.00
1.92
9.65
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Chapter IV- Electrical and magnetic properties of ME composites
141
Figure 4.18 Magnetic (B-H) hysteresis loop for Co1.2-xMnxFe1.8O4 (CMFO) ferrite
system
Magnetic hysteresis loops were recorded at room temperature for all the
compositions of Co1.2-xMnxFe1.8O4 (0≤x≤0.4) CMFO system and are shown in Figure
4.18. The observed values of magnetic parameters are shown in Table 4.3. It is
observed that Ms increases with increasing Mn content up to x = 0.2 and then
decreases to a small value. The changes in the magnetization at room temperature, on
the substitution of Mn for Co, may be due to the following factors such as
1) The difference in the contributions from the magnetic moment of the
substituted ion on A-site and B-site of the spinel ferrite,
2) decreasing contribution from the magnetocrystalline anisotropy of Co after
substitution of Mn.
A maximum magnetization of 138.50 emu/g is obtained for the composition
with 20% Mn. The increase in magnetization with Mn content may be attributed to
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Chapter IV- Electrical and magnetic properties of ME composites
the substitution of Co2+ by Mn2+ and this enhances the saturation magnetization as the
magnetic moments for Co2+ and Mn2+ are 3 µB and 5 µB respectively. The magnetic
moment per formula unit in Bohr magneton (µB) was calculated by using the
following relation [37] and is tabulated in Table 4.3,
µB =
M ×MS
5585
(4.23)
where, M is the molecular weight of particular composition and Ms is saturation
magnetization (emu/g).
The initial increase in the saturation magnetization of Co1.2-xMnxFe1.8O4 at
lower concentrations of Mn (i.e. x = 0.1 and x = 0.2), indicates that initially the Mn2+
ions are substituted in the (octahedral) B site and at higher concentrations of Mn (i.e.
x =0.3 and x = 0.4), the Mn2+ ions may be distributed in the (tetrahedral) A site of the
spinel lattice [38]. Also, it is found the coercivity (coercive force) of all the samples
almost decrease linearly with increasing Mn content. The observed variation in the
coercivity of the Co1.2-xMnxFe1.8O4 system is similar to that of reported in the previous
studies on Mn substituted CoFe2O4 [39-40]. However, for the composition with x =
0.3, unexpectedly slight increase in coercivity is observed. This is probably due to
some peculiar changes in the cation distribution in the octahedral and tetrahedral sites
near this composition [36].
Table 4.3 Magnetic parameters for Co1.2-xMnxFe1.8O4 (0≤x≤0.4) CMFO ferrite system
Saturation
mag. Ms
(emu/g)
Co1.2Fe1.8O4
106.50
1520.82
93.02
4.48
Co1.1Mn0.1Fe1.8O4
123.74
1300.03
109.63
5.20
CoMn0.2Fe1.8O4
138.5
1187.87
123.48
5.81
Co0.9Mn0.3Fe1.8O4
124.71
1221.53
112.60
5.22
Co0.8Mn0.4Fe1.8O4
97.78
1165.36
108.17
4.09
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Coercivity Remanence
Hc
Mr
(Oe)
(emu/g)
µB
(Bohr
magneton)
Ferrite
compositions
Chapter IV- Electrical and magnetic properties of ME composites
143
Figure 4.19 Magnetic (B-H) hysteresis loop for (25%) Co1.2-xMnxFe1.8O4 (CMFO)
+ (75%) BaZr0.08Ti0.92O3 (BZT) ME composites
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Chapter IV- Electrical and magnetic properties of ME composites
144
Figure 4.19 shows the B-H hysteresis loop of ME composites recorded at
room temperature. All samples exhibits the B-H hysteresis loop of magnetic behavior
indicating the presence of ordered magnetic dipoles existed in the mixed spinel–
perovskite system. The saturation magnetization (Ms) increases from CMFO0+BZT to
CMFO2+BZT and then decreases (Table 4.4). A maximum MS of 16.89 emu/gm is
achieved for CFMO2+BZT composite. The magnetization increase with Mn content
for ferrite phase may be attributed to the substitution of Co2+ by Mn2+ which enhances
the Ms. The initial increase in the saturation magnetization for x = 0.1 and x = 0.2 of
Co1.2-xMnxFe1.8O4, indicates at lower concentrations (i.e. x = 0.1 and 0.2), the Mn2+
ions are substituted in the octahedral (B- site) and at higher concentrations (i.e. x = 0.3
and 0.4), the rest of the Mn2+ ions are distributed in the tetrahedral (A- site) of the
spinel lattice [41]
The magnetic parameters like Ms, magnetic moment (nB) in Bohr magneton
(µB), coercivity (HC) and remanance (Mr) for (25 wt. %) Co1.2-xMnxFe1.8O4 + (75 wt.
%) BaZr0.08Ti0.92O3 ME composites are shown in Table 4.4. The presence of pores
among the grains breaks the magnetic circuits and results in a reduction of magnetic
properties with increasing pore concentration [36]. Therefore, in composites,
ferroelectric (non-magnetic) material in the presence of magnetic field acts as a pore
causing the reduction of magnetic parameters which is observed at 100% ferrite
phase. The magnetization in all composites is saturated for higher magnetic field
strength (~ 1.5 kOe). After saturation of a ferrite phase in a strong magnetic field, the
magnetization vector rotates towards the nearest preferred field direction and results
in high anisotropy when the field is reduced to zero. The stress and shape of
anisotropy are most important parameters for getting the maximum magnetoelectric
output in such composites. The increase in values of remanance for y = 0.1 and y =
0.2 suggests that most of the magnetization vectors are driven out of the magnetically
preferred direction by making a small angle with the direction of the applied field and
suffer stresses [37], which result in high magnetization.
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Chapter IV- Electrical and magnetic properties of ME composites
145
Table 4.4 Magnetic properties of (25 wt. %) Co1.2-yMnyFe1.8O4 + (75 wt. %)
BaZr0.08Ti0.92O3 ME composite
Composition
Ms
(emu/gm)
nB
(µB)
Mr
(emu/gm)
Hc
(Oe)
CMFO0+BZT
13.16
0.55
5.79
336.56
CMFO1+BZT
16.48
0.69
8.36
425.64
CMFO2+BZT
16.89
0.71
7.39
375.10
CMFO3+BZT
15.69
0.66
7.11
386.77
CMFO4+BZT
13.94
0.58
5.04
288.28
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Chapter IV- Electrical and magnetic properties of ME composites
References
[1]
J. Ryu, S. Priya, K. Uchino and H.-E. Kim, J. Electroceram. 8 (2002) 107.
[2]
M. Fiebig, J. Phys. D: Appl. Phys. 38 (2005) R123.
[3]
V. M. Jamadar Ph. D. Thesis, Shivaji University, Kolhapur (1990)
[4]
E. J. W. Verway, P.W. Haailman, F. C. Romeijn and G. W. Oosterhaut,
Phillips Res. Repts. 5 (1970) 173
[5]
V. R. K. Murthy and B. Vishwanathan “Ferrites, Materials Science and
Technology” Narosa Publishing House, Mumbai (1990)
[6]
B.M. Tareev, N.V. Korotkova, V.M. Petrov and A.A.
Preobrazhensky
“Electrical and Radio Engineering Materials” MIR Publishers, Moscow
(1980)
[7]
Om Prakash, K.D. Mandal, C.C. Christopher, M.S. Sastry and Devendra
Kumar, Bull. Mater. Sci., 17 (1994) 253
[8]
N.F. Mott and R.W. Gurney “Electronic Processes in Ionic Crystals” Oxford
University Press, London (1978)
[9]
M.I. Kinger, J. Phys. C (GB), 1 (1975) 3395
[10]
J.H. Jonker, J. Phys. Chem. Solid, 9 (1959) 165
[11]
A.J. Bosmon and H.J. Van Daal, Adv. Phys., 19 (1970) 1
[12]
[13]
D.R. Patil and B.K. Chougule, J. Alloys Comp.470 (2009) 531
C.M. Kanamadi, G. Seeta Rama Raju, H.K. Yang, B.C. Choi and J.H. Jeong,
J. Alloys Comp.479 (2009) 807.
[14]
C.G. Koops Phy. Rev., 83 (1951) 121
[15]
J.C. Maxwell “Electricity and Magnetism” Oxford Univ. Press, London
(1993) 828
[16]
K.W. Wagner Ann. Physik., 40 (1993) 818
[17]
R.N.P Choudhary, S.R. Shanigrahi and A.K. Singh, Bull. Mater. Sci., 22
(1999) 75
[18]
Y. Zhi, A. Chen, J. Appl. Phys. 91 (2002) 794.
[19]
T.G. Lupeiko, I.B. Lopatina, I.V. Kozyrev, L.A. Derbaremdiker,
Inorg.
Mater. 28 (1992) 481.
[20]
L T Rabinkin and Z I Novikova “Ferrites” I2 (1960)146(Minsk: Acad. Nauk.
USSR)
Composite Materials Laboratory,
Department of Physics,
Shivaji University, Kolhapur
Chapter IV- Electrical and magnetic properties of ME composites
[21]
147
N Popandian, P Balay and A Narayanasamy,. J Phys. Condens. Matter
14
(2002) 3221.
[22]
K.K. Patankar, S. L. Kadam, V. L. Mathe, C. M. Kanamadi, V.P.Kothavale
and B. K. Chougule, Brit. Ceram. Trans., 102 (2003) 19.
[23]
S.L. Kadam, K.K. Patankar, V.L. Mathe, M.B. Kothale, R.B. Kale and B.K.
Chougule, J. Electroceram., 9 (2003) 193.
[24]
H. Watanabe, J. Phys. Chem. Solids 25 (1964) 147
[25]
M.A. Ahmed, S.T. Bishay, G. Abdelatif, J. Phys. Chem.Solid.; 62(2001)1039.
[26]
Z. Yu, R.Y.Guo, A.S. Bhalla, J. Appl. Phys. 88(2000)410.
[27]
B.Jaffe, W.Cook, H.Jaffe, “Piezoelectric Ceramics” Academic, London, 1971.
[28]
D.Hennings, A.Schnell, J. Am. Ceram. Soc.; 65(1982)539.
[29]
J. Smit, H.P.J. Wijn “Ferrites” London: Cleaver-Human Press 1959.
[30]
L.L. Hench and J.K.West “ Principles of Electronic Ceramics” John Wiley
and Sons, New York (1990) 202
[31]
D. Alder and Feienleib Phys. Rev. B 2 (1970) 3112
[32]
O. Prakash, K.D. Mandal and C. C. Chistopher “ Electronic Pocesses in Ionic
Crystals’ Oxford University Press, London (1948)
[33]
I. G. Austin and N. F. Mott Adv. Phys. 18 (1969) 41
[34]
S. L. Kadam,C. M. Kanamadi, K. K. Patankar and B. K .Chougule Mater.
Lett. 59 (2005) 215.
[35]
A. E. Clark and E. P. Wolfhart “Ferromagnetic Materials” I Ed. Amsterdam:
North-Holland 1982., pp. 531
[36]
Mallapur M M M.Phil Thesis Shivaji University, Kolhapur ( 2003).
[37]
Yangy H., Wangy Z. and Songy L. J. Phys. D: Appl. Phys. 29 (1996) 2574.
[38]
Bhame S.D. Ph.D Thesis “Structural, magnetic and magnetostrictive
properties of substituted lanthanum manganites and spinel ferrites”
University of Pune, Mahatashtra, India (2007).
[39]
B. Zhou, Y. W. Zhang, C. S. Liao, and C. H. Yan, J. Magn. Magn. Mater. 247
(2002)70
[40]
C H Kim, Y Myung, Y J Cho, H S Kim, S H Park, and J Park J. Phys. Chem.
C 113 (2009)7085
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