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D.Ravinder et al Int. Journal of Engineering Research and Application
ISSN : 2248-9622, Vol. 3, Issue 5, Sep-Oct 2013, pp.2021-2024

RESEARCH ARTICLE

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OPEN ACCESS

Dielectric Properties of Copper Substituted Nickel Nano-Ferrites
Rapolu Sridhar1, D.Ravinder2*, K.Vijaya Kumar3
1

Vignan’s Institute of Technology & Aeronautical Engineering College, Deshmukhi, Nalgonda-508284, A.P.,
India.
2*
Department of Physics, Nizam College, Basheerbagh, Osmania University, Hyderabad- 500001, A.P., India.
3
Department of Physics, JNTU Hyderabad College of Engineering, Nachupally (Kondagattu),
Karimnagar-505501, A.P., India.

ABSTRACT
Mixed Ni1-X CuX Fe2 O4 (0 ≤ X ≥ 1) nano-ferrites have been synthesized by Citrate-gel auto combustion
technique. The structural characterization was carried out by X-Ray Diffractometer (XRD) and the crystallite
size was found to be in the range of 36- 58nm. The dielectric properties such as Dielectric constant (ε'),
Dielectric loss tangent (tan δ) and AC conductivity (σ ac) were studied at room temperature as function of
frequency in the range 20Hz – 2MHz. The real part of dielectric constant (ε ') and dielectric loss tangent (tan δ)
showed a decreases with the increase in frequency where as the ac conductivity (σ ac) increases with increase in
frequency. The dielectric constant (ε ') shows an increasing trend with increase of Cu substitution in Ni nanoferrites.
Keywords: Nano - Ferrites; Citrate-Gel Technique; X-Ray Diffraction; Dielectric Properties

I.

Introductions

In the recent years many physicists have
studied the electrical and magnetic properties of nano
crystalline spinel ferrites in view of their many
applications [1, 2]. As a common feature, the nano
crystalline spinel ferrites have very high dielectric
constants at low frequencies, so they are very useful
in designing microwave devices such as circulators
and isolators [3]. These ferrites are very important
group of magnetic materials due to their extensive use
in a wide range of applications from low to high
permeability devices including electronics, ferrofluid,
magnetic drug delivery microwave devices and high
density information storage devices [4-8].
The electrical conductivity and dielectric
behavior in ferrites depends on many factors;
preparation method, sintering temperature, amount
and type of substitution. Several investigators have
studied the frequency and temperature dependence of
the dielectric constant [9-11]. The aim of the present
work was to investigate the AC conductivity and
dielectric constant as a function of frequency at room
temperature for Ni nano-ferrite and the study includes
effect of Cu2+ on the conduction mechanism.

II.

Experimental details

The mixed Ni-Cu ferrite powders having the
chemical formula Ni1-xCuxFe2O4 (where x = 0, 0.2,
0.4, 0.5, 0.6, 0.8 and 1.0) were synthesized by citrate
gel auto combustion technique. Analytical grade of
Nickel Nitrate (Ni(NO3)26H2O) Copper Nitrate
(Cu(NO3)23H2O) Ferric Nitrate (Fe(NO3)29H2O)
Citric Acid-Citrate (C6H8O7H2O) Ammonia (NH3)
raw materials were used to prepare the Ni-Cu nano
ferrites. Metal nitrates and citric acid were dissolved
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in deionized water. Metal nitrate solutions were mixed
with citric acid solution in 1:3 molar ratio of nitrate to
citric acid. The pH of the solution was adjusted to 7
using ammonia. The solution was first heated at 80 oC
to transform into gel and then ignited in a selfpropagating combustion manner to form a fluffy loose
powder. The as-burnt ferrite powders were grained by
agate motor then calcined at 700oC for 5hr. The
calcined ferrite powders were again grained by agate
motor.. The calcinations powder of each sample is
prepared into pellets were sintered at 1100oC for 12
hours.
The structural characterization was carried
out using X-Ray Diffractomerter Bruker (Karlsruhe,
Germany) D8 advanced system with a diffracted
beam monochromatic Cu Kα radiation (λ = 1.5405 Å)
radiation source between the Bragg Angles 20° to 80°
in steps of 0.04°/Sec. The capacitance and tangent
loss were recorded using a PRECISION LCR
METER – E4980A in the frequency range from 20Hz
to 2MHz at room temperature.

III.

RESULTS AND DISCUSSION

The X-ray diffraction pattern (Fig1.) of
crystalline phases were identified by PDF-4 reference
data from the international centre for diffraction data
(ICDD). All Bragg reflections have been indexed,
which confirm the formation of cubic spinel structure
in single phase without any impurity peak. The
strongest reflection comes from the (311) plane,
which denotes the spinel phase. The peaks indexed to
(111), (220), (311), (400), (511) and (440) planes of a
cubic unit cell, all planes are the allowed planes which
indicates the formation of cubic spinel structure in
single phase [12]. The values of the crystal size varied
2021 | P a g e
D.Ravinder et al Int. Journal of Engineering Research and Application
ISSN : 2248-9622, Vol. 3, Issue 5, Sep-Oct 2013, pp.2021-2024
from 36.7 nm to 58.91 nm. Though all the samples
were prepared under identical condition, the
crystallite size was not the same for all Cu
concentrations. This was probably due to the
preparation condition followed here which gave rise
to different rate of ferrite formation for different
concentrations of Cu, favoring the variation of
crystallite size.
Compositional variation of dielectric
constant at 2 MHz frequency is shown Fig 2. It was
observed that dielectric constant increased with the
increase of Cu concentration and the dielectric
constant is maximum at X=1.0 and minimum at X= 0.
It is due to the fact that resistivity decreases with the
increase in Cu concentration which increases the
probability of electrons reaching the grain boundary.
This increases the polarization and hence the
dielectric constant increases [13].
Fig.3 shows the variation of dielectric
constant versus frequency at room temperature. It can
be seen from the figure that the value of dielectric
constant decreases initially with increase in frequency
and reached a constant value at higher frequency. The
decrease of dielectric constant with increase of
frequency as observed in the case of Ni-Cu nano
ferrites is normal dielectric behavior of spinel ferrites.
The normal dielectric behavior can be explained on
the basis of Maxwell-Wagner interfacial type
polarization, which is in agreement with Koop’s
phenomenological theory [14, 15].A similar variation
of the dielectric constant with frequency was observed
in the case of ZnFe2O, MnFe2O4 [16],ZnxCu1-xFe2O4
and
MnxCu1-xFe2O4 [17] ferrite systems. The
dielectric polarization in ferrites is similar to the
conduction hopping mechanism. Hopping between
Fe2+ and Fe3+ results in the local displacement of
electrons in the direction of the applied field and these
electrons determine the polarization. The polarization
decreased with increasing frequency and then reached
a constant value due to the fact that beyond a certain
external field frequency the electron exchange
between Fe2+  Fe3+ cannot follow the alternating
field. The large value of the dielectric constant at
lower frequency is due to the predominance of species
like Fe2+ ions, interfacial dislocations piled up,
oxygen vacancies, and grain boundary defects, while
the decrease in dielectric constant with frequency is
natural because of the fact that any species
contributing to polarizability is found to show lagging
behind the applied field at some higher frequencies.
Fig 4. Shows the variation of dielectric loss
tangent (tanδ) with frequency for Ni1-xCuxFe2O4 nanoferrites. By an increase in frequency, for X=0,0.2,0.6
the value of tanδ decreases linearly which is normal
behavior of ferrites and for X=0.4,0.5,0.8 and 1.0 the
value of tanδ increasing initially and exhibit the loss
factor which is maximum between 3 X105 Hz to
6X105Hz and further decrease by increasing the
frequency. The loss factor depends upon various
factors such as stoichiometry, density, grain size, Fe2+
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content and structural homogeneity, which in turn
depend on the composition and processing
temperature [18]. All the samples exhibit dispersion
due to the Maxwell-Wagner interfacial type
polarization
in
agreement
with
Koop’s
phenomenological theory [14, 15, 19-21].
Iwauchi [16] pointed out that there is a
strong correlation between the dielectric behavior and
the conduction mechanism in ferrites. In the low
frequency region, which corresponds to high
resistivity (due to grain boundaries), more energy is
required for electron exchange between Fe2+ and Fe3+
ions and thus energy loss is high. In the high
frequency range, which corresponds to low resistivity
(due to the grains), a small energy is needed for
electron transfer between Fe2+ and Fe3+ ions in grains
and accompanied by a small eddy current and hence a
decrease in the energy loss all the samples show
dispersion in tan δ in lower frequencies.
Fig. 5 shows that ac conductivity rises with
the rise in the frequency, which is in agreement with
the reports [22, 23]. The conductivity of ferrites, in
general, depends on the density, porosity, grain size.
Grain boundary and chemical composition of samples
[24, 25].

IV.

CONCLUSION

The Citrate – Gel technique method is a
conveniant and varsalite one for obtaining very
homogeneous and reactive nanostructured Ni-Cu
nano-ferrites. X-ray diffraction patterns confirmed
the formation of single phased cubic spinel structure
without any impurity peak. The Crystallite size of the
nano-ferrite was in the range of 36-58 nm. Dielectric
constant increases with the increase of Cu
concentration and the dielectric constant is maximum
at X=1.0 and minimum at X= 0. The dielectric
constant (ε'') and dielectric loss tangent (tan δ)
decreases with increase of frequency. The ac
conductivity (σac) rises with the rise in the frequency.

ACKNOWLEDGEMENTS
One of the authors (D.R) is grateful to Prof.
T.L.N. Swamy, Principal Nizam College for his
encouragement to carry out this research work. One of
the authors (R.S) is grateful to Prof. N.Venkateswarlu,
Principal, Vignan’s Institute of Technology &
Aeronautical Engineering College, Hyderabad. And
the author (K.V.K) is grateful to Dr. M. Thirumala
Chary, Principal, Professor & HOD of Chemistry,
JNTUH College of Engineering, Nachupally,
Karimnagar, (Dist).

REFERENCES
[1]
[2]

K. J. STANDLEY, “Oxide Magnetic
Materials” (Clarendon Press, Oxford, 1972).
D.R.BROUN
and
E.
ALBERSSCHOENBERG, Electronics 26 (1953) 146.

2022 | P a g e
D.Ravinder et al Int. Journal of Engineering Research and Application
ISSN : 2248-9622, Vol. 3, Issue 5, Sep-Oct 2013, pp.2021-2024
[3]

K.LATHA,
K.S.MOHAN
and
D.
RAVINDER, Phys.Status Solidi A 142
(1994) K103
[4]
Y. Qu, H. Yang, N. Yang, Y. Fan, H. Zhu,
and Zou, Ma-ter. Lett. 60, 3548-3552 (2006).
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P.C. Dorsey, P. Lubitz, D.B. Chrisey, and
J.S.Horwitz, J. Appl. Phys. 85, 6338-6345
(1999).
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M.H. Sousa and F.A. Tourinho, J. Phys.
Chem. B 105, 1168-1175 (2001).
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F. Mazaleyrat and L.K. Varga, J. Magn.
Magn. Mater. 215, 253-259 (2000).
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D. E. Speliotis, J. Magn. Magn. Mater. 93,
29-35 (1999).
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A.M. Abo ElAta,M.A.ElHiti, J. Phys. III
(France) 7 (1997) 883.
[10] M.A. El Hiti, M.A. Ahmed, M.M. Mosaad,
S.M. Attia, J. Magn. Magn. Mater. 150
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[11] M.A. Ahmed, M.K. El Nimr, A. Taw"k,
A.M. El Hasab, J. Magn. Magn. Mater. 98
(1991) 33.
[12] S.A. Mazen, S.F. Mansour, H.M. Zaki,
published on line 15 June 2003. “Some
physical and magnetic properties of Mg-Zn
ferrite”. Cryst. Res. Technol. 38, No 6,471478 (2003).

[13]
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[18]

[17]
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[23]
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[25]

www.ijera.com

A. K. Singh, T. C. Goel, R. G. Mendiratta J.
Appl. Phys. 91 (2002) 6626-6629.
Maxwell, J.C.: A Treatise on Elec. And
Magn. Vol.2. Oxford, New York (1954)
Koops, C.G.: Phys. Rav. 83, 121 (1951)
K.Iwauchi, Jpn. J. Appl. Phys. 10,
1520(1971).
A. Verma, T.C. Goal, R.G. Mendiratta, P.
Kishan J. Magn. Magn. Mater. 208 (2000), p.
13
N. Rezlescu and E. Rezlescu, Phys. Status
Solidi A 23, 575 (1974).
Wagner, K. W.: Ann. Phys. 40, 817 (1913)
Kale, G.M., Asokan, T.: Appl. Phys. Lett.
62, 19 (1993)
Austin, I.G., Mott, N.F.: Adv.Phys. 18, 41
(1969)
Batoo, K.M., Kumar, S., Lee, C.G., Current,
A.: Appl. Phys. 9, 826 (2009)
Ajmal M and Maqsood A 2008 Mater. Lett.
62, 2077-2080 (2008).
Gul, I.H., Abbasi, A.Z., Amin, F., Rehman,
M.A., Maqsood, A.: J. Magn. Magn. Matter
311, 494 (2007)
Gul, I.H., Ahmed, W., Maqsood, A.: J.
Magn. Magn. Mater. 320, 270 (2008) 494
(2007)

Fig 1. X-ray diffraction pattern of Ni-Cu nano-ferrites

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2023 | P a g e
D.Ravinder et al Int. Journal of Engineering Research and Application
ISSN : 2248-9622, Vol. 3, Issue 5, Sep-Oct 2013, pp.2021-2024

Fig 2: Dielectric constant as a function of X (Cu)
at 2M Hz in Ni-Cu nano- ferrites.

Fig 4: Frequency dependence of dielectric
loss tangent for Ni-Cu nano - ferrites.

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Fig 3: Frequency dependence of dielectric
constant for Ni-Cu nano-ferrites.

Fig 5: Frequency dependence of
ac conductivity for Ni-Cu nano- ferrites.

2024 | P a g e

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Dielectric Properties of Copper Substituted Nickel Nano-Ferrites

  • 1. D.Ravinder et al Int. Journal of Engineering Research and Application ISSN : 2248-9622, Vol. 3, Issue 5, Sep-Oct 2013, pp.2021-2024 RESEARCH ARTICLE www.ijera.com OPEN ACCESS Dielectric Properties of Copper Substituted Nickel Nano-Ferrites Rapolu Sridhar1, D.Ravinder2*, K.Vijaya Kumar3 1 Vignan’s Institute of Technology & Aeronautical Engineering College, Deshmukhi, Nalgonda-508284, A.P., India. 2* Department of Physics, Nizam College, Basheerbagh, Osmania University, Hyderabad- 500001, A.P., India. 3 Department of Physics, JNTU Hyderabad College of Engineering, Nachupally (Kondagattu), Karimnagar-505501, A.P., India. ABSTRACT Mixed Ni1-X CuX Fe2 O4 (0 ≤ X ≥ 1) nano-ferrites have been synthesized by Citrate-gel auto combustion technique. The structural characterization was carried out by X-Ray Diffractometer (XRD) and the crystallite size was found to be in the range of 36- 58nm. The dielectric properties such as Dielectric constant (ε'), Dielectric loss tangent (tan δ) and AC conductivity (σ ac) were studied at room temperature as function of frequency in the range 20Hz – 2MHz. The real part of dielectric constant (ε ') and dielectric loss tangent (tan δ) showed a decreases with the increase in frequency where as the ac conductivity (σ ac) increases with increase in frequency. The dielectric constant (ε ') shows an increasing trend with increase of Cu substitution in Ni nanoferrites. Keywords: Nano - Ferrites; Citrate-Gel Technique; X-Ray Diffraction; Dielectric Properties I. Introductions In the recent years many physicists have studied the electrical and magnetic properties of nano crystalline spinel ferrites in view of their many applications [1, 2]. As a common feature, the nano crystalline spinel ferrites have very high dielectric constants at low frequencies, so they are very useful in designing microwave devices such as circulators and isolators [3]. These ferrites are very important group of magnetic materials due to their extensive use in a wide range of applications from low to high permeability devices including electronics, ferrofluid, magnetic drug delivery microwave devices and high density information storage devices [4-8]. The electrical conductivity and dielectric behavior in ferrites depends on many factors; preparation method, sintering temperature, amount and type of substitution. Several investigators have studied the frequency and temperature dependence of the dielectric constant [9-11]. The aim of the present work was to investigate the AC conductivity and dielectric constant as a function of frequency at room temperature for Ni nano-ferrite and the study includes effect of Cu2+ on the conduction mechanism. II. Experimental details The mixed Ni-Cu ferrite powders having the chemical formula Ni1-xCuxFe2O4 (where x = 0, 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0) were synthesized by citrate gel auto combustion technique. Analytical grade of Nickel Nitrate (Ni(NO3)26H2O) Copper Nitrate (Cu(NO3)23H2O) Ferric Nitrate (Fe(NO3)29H2O) Citric Acid-Citrate (C6H8O7H2O) Ammonia (NH3) raw materials were used to prepare the Ni-Cu nano ferrites. Metal nitrates and citric acid were dissolved www.ijera.com in deionized water. Metal nitrate solutions were mixed with citric acid solution in 1:3 molar ratio of nitrate to citric acid. The pH of the solution was adjusted to 7 using ammonia. The solution was first heated at 80 oC to transform into gel and then ignited in a selfpropagating combustion manner to form a fluffy loose powder. The as-burnt ferrite powders were grained by agate motor then calcined at 700oC for 5hr. The calcined ferrite powders were again grained by agate motor.. The calcinations powder of each sample is prepared into pellets were sintered at 1100oC for 12 hours. The structural characterization was carried out using X-Ray Diffractomerter Bruker (Karlsruhe, Germany) D8 advanced system with a diffracted beam monochromatic Cu Kα radiation (λ = 1.5405 Å) radiation source between the Bragg Angles 20° to 80° in steps of 0.04°/Sec. The capacitance and tangent loss were recorded using a PRECISION LCR METER – E4980A in the frequency range from 20Hz to 2MHz at room temperature. III. RESULTS AND DISCUSSION The X-ray diffraction pattern (Fig1.) of crystalline phases were identified by PDF-4 reference data from the international centre for diffraction data (ICDD). All Bragg reflections have been indexed, which confirm the formation of cubic spinel structure in single phase without any impurity peak. The strongest reflection comes from the (311) plane, which denotes the spinel phase. The peaks indexed to (111), (220), (311), (400), (511) and (440) planes of a cubic unit cell, all planes are the allowed planes which indicates the formation of cubic spinel structure in single phase [12]. The values of the crystal size varied 2021 | P a g e
  • 2. D.Ravinder et al Int. Journal of Engineering Research and Application ISSN : 2248-9622, Vol. 3, Issue 5, Sep-Oct 2013, pp.2021-2024 from 36.7 nm to 58.91 nm. Though all the samples were prepared under identical condition, the crystallite size was not the same for all Cu concentrations. This was probably due to the preparation condition followed here which gave rise to different rate of ferrite formation for different concentrations of Cu, favoring the variation of crystallite size. Compositional variation of dielectric constant at 2 MHz frequency is shown Fig 2. It was observed that dielectric constant increased with the increase of Cu concentration and the dielectric constant is maximum at X=1.0 and minimum at X= 0. It is due to the fact that resistivity decreases with the increase in Cu concentration which increases the probability of electrons reaching the grain boundary. This increases the polarization and hence the dielectric constant increases [13]. Fig.3 shows the variation of dielectric constant versus frequency at room temperature. It can be seen from the figure that the value of dielectric constant decreases initially with increase in frequency and reached a constant value at higher frequency. The decrease of dielectric constant with increase of frequency as observed in the case of Ni-Cu nano ferrites is normal dielectric behavior of spinel ferrites. The normal dielectric behavior can be explained on the basis of Maxwell-Wagner interfacial type polarization, which is in agreement with Koop’s phenomenological theory [14, 15].A similar variation of the dielectric constant with frequency was observed in the case of ZnFe2O, MnFe2O4 [16],ZnxCu1-xFe2O4 and MnxCu1-xFe2O4 [17] ferrite systems. The dielectric polarization in ferrites is similar to the conduction hopping mechanism. Hopping between Fe2+ and Fe3+ results in the local displacement of electrons in the direction of the applied field and these electrons determine the polarization. The polarization decreased with increasing frequency and then reached a constant value due to the fact that beyond a certain external field frequency the electron exchange between Fe2+  Fe3+ cannot follow the alternating field. The large value of the dielectric constant at lower frequency is due to the predominance of species like Fe2+ ions, interfacial dislocations piled up, oxygen vacancies, and grain boundary defects, while the decrease in dielectric constant with frequency is natural because of the fact that any species contributing to polarizability is found to show lagging behind the applied field at some higher frequencies. Fig 4. Shows the variation of dielectric loss tangent (tanδ) with frequency for Ni1-xCuxFe2O4 nanoferrites. By an increase in frequency, for X=0,0.2,0.6 the value of tanδ decreases linearly which is normal behavior of ferrites and for X=0.4,0.5,0.8 and 1.0 the value of tanδ increasing initially and exhibit the loss factor which is maximum between 3 X105 Hz to 6X105Hz and further decrease by increasing the frequency. The loss factor depends upon various factors such as stoichiometry, density, grain size, Fe2+ www.ijera.com www.ijera.com content and structural homogeneity, which in turn depend on the composition and processing temperature [18]. All the samples exhibit dispersion due to the Maxwell-Wagner interfacial type polarization in agreement with Koop’s phenomenological theory [14, 15, 19-21]. Iwauchi [16] pointed out that there is a strong correlation between the dielectric behavior and the conduction mechanism in ferrites. In the low frequency region, which corresponds to high resistivity (due to grain boundaries), more energy is required for electron exchange between Fe2+ and Fe3+ ions and thus energy loss is high. In the high frequency range, which corresponds to low resistivity (due to the grains), a small energy is needed for electron transfer between Fe2+ and Fe3+ ions in grains and accompanied by a small eddy current and hence a decrease in the energy loss all the samples show dispersion in tan δ in lower frequencies. Fig. 5 shows that ac conductivity rises with the rise in the frequency, which is in agreement with the reports [22, 23]. The conductivity of ferrites, in general, depends on the density, porosity, grain size. Grain boundary and chemical composition of samples [24, 25]. IV. CONCLUSION The Citrate – Gel technique method is a conveniant and varsalite one for obtaining very homogeneous and reactive nanostructured Ni-Cu nano-ferrites. X-ray diffraction patterns confirmed the formation of single phased cubic spinel structure without any impurity peak. The Crystallite size of the nano-ferrite was in the range of 36-58 nm. Dielectric constant increases with the increase of Cu concentration and the dielectric constant is maximum at X=1.0 and minimum at X= 0. The dielectric constant (ε'') and dielectric loss tangent (tan δ) decreases with increase of frequency. The ac conductivity (σac) rises with the rise in the frequency. ACKNOWLEDGEMENTS One of the authors (D.R) is grateful to Prof. T.L.N. Swamy, Principal Nizam College for his encouragement to carry out this research work. One of the authors (R.S) is grateful to Prof. N.Venkateswarlu, Principal, Vignan’s Institute of Technology & Aeronautical Engineering College, Hyderabad. And the author (K.V.K) is grateful to Dr. M. Thirumala Chary, Principal, Professor & HOD of Chemistry, JNTUH College of Engineering, Nachupally, Karimnagar, (Dist). REFERENCES [1] [2] K. J. STANDLEY, “Oxide Magnetic Materials” (Clarendon Press, Oxford, 1972). D.R.BROUN and E. ALBERSSCHOENBERG, Electronics 26 (1953) 146. 2022 | P a g e
  • 3. D.Ravinder et al Int. Journal of Engineering Research and Application ISSN : 2248-9622, Vol. 3, Issue 5, Sep-Oct 2013, pp.2021-2024 [3] K.LATHA, K.S.MOHAN and D. RAVINDER, Phys.Status Solidi A 142 (1994) K103 [4] Y. Qu, H. Yang, N. Yang, Y. Fan, H. Zhu, and Zou, Ma-ter. Lett. 60, 3548-3552 (2006). [5] P.C. Dorsey, P. Lubitz, D.B. Chrisey, and J.S.Horwitz, J. Appl. Phys. 85, 6338-6345 (1999). [6] M.H. Sousa and F.A. Tourinho, J. Phys. Chem. B 105, 1168-1175 (2001). [7] F. Mazaleyrat and L.K. Varga, J. Magn. Magn. Mater. 215, 253-259 (2000). [8] D. E. Speliotis, J. Magn. Magn. Mater. 93, 29-35 (1999). [9] A.M. Abo ElAta,M.A.ElHiti, J. Phys. III (France) 7 (1997) 883. [10] M.A. El Hiti, M.A. Ahmed, M.M. Mosaad, S.M. Attia, J. Magn. Magn. Mater. 150 (1995) 399. [11] M.A. Ahmed, M.K. El Nimr, A. Taw"k, A.M. El Hasab, J. Magn. Magn. Mater. 98 (1991) 33. [12] S.A. Mazen, S.F. Mansour, H.M. Zaki, published on line 15 June 2003. “Some physical and magnetic properties of Mg-Zn ferrite”. Cryst. Res. Technol. 38, No 6,471478 (2003). [13] [14] [15] [16] [18] [17] [19] [20] [21] [22] [23] [24] [25] www.ijera.com A. K. Singh, T. C. Goel, R. G. Mendiratta J. Appl. Phys. 91 (2002) 6626-6629. Maxwell, J.C.: A Treatise on Elec. And Magn. Vol.2. Oxford, New York (1954) Koops, C.G.: Phys. Rav. 83, 121 (1951) K.Iwauchi, Jpn. J. Appl. Phys. 10, 1520(1971). A. Verma, T.C. Goal, R.G. Mendiratta, P. Kishan J. Magn. Magn. Mater. 208 (2000), p. 13 N. Rezlescu and E. Rezlescu, Phys. Status Solidi A 23, 575 (1974). Wagner, K. W.: Ann. Phys. 40, 817 (1913) Kale, G.M., Asokan, T.: Appl. Phys. Lett. 62, 19 (1993) Austin, I.G., Mott, N.F.: Adv.Phys. 18, 41 (1969) Batoo, K.M., Kumar, S., Lee, C.G., Current, A.: Appl. Phys. 9, 826 (2009) Ajmal M and Maqsood A 2008 Mater. Lett. 62, 2077-2080 (2008). Gul, I.H., Abbasi, A.Z., Amin, F., Rehman, M.A., Maqsood, A.: J. Magn. Magn. Matter 311, 494 (2007) Gul, I.H., Ahmed, W., Maqsood, A.: J. Magn. Magn. Mater. 320, 270 (2008) 494 (2007) Fig 1. X-ray diffraction pattern of Ni-Cu nano-ferrites www.ijera.com 2023 | P a g e
  • 4. D.Ravinder et al Int. Journal of Engineering Research and Application ISSN : 2248-9622, Vol. 3, Issue 5, Sep-Oct 2013, pp.2021-2024 Fig 2: Dielectric constant as a function of X (Cu) at 2M Hz in Ni-Cu nano- ferrites. Fig 4: Frequency dependence of dielectric loss tangent for Ni-Cu nano - ferrites. www.ijera.com www.ijera.com Fig 3: Frequency dependence of dielectric constant for Ni-Cu nano-ferrites. Fig 5: Frequency dependence of ac conductivity for Ni-Cu nano- ferrites. 2024 | P a g e