Influence of Zn substitution on structural, microstructural and dielectric properties of...

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Materials Science and Engineering B 167 (2010) 187–192 Contents lists available at ScienceDirect Materials Science and Engineering B journal homepage: www.elsevier.com/locate/mseb Influence of Zn substitution on structural, microstructural and dielectric properties of nanocrystalline nickel ferrites Seema Sharma a,, Kavita Verma a , Umesh Chaubey a , Vidyanand Singh b , B.R. Mehta b a Ferroelectrics Laboratory, Department of Physics, A N College, Patna 800013, India b Thin Film Laboratory, Department of Physics, Indian Institute of Delhi, Hauz Khas, New Delhi 110016, India article info Article history: Received 8 July 2009 Received in revised form 9 February 2010 Accepted 10 February 2010 Keywords: Nanocrystalline XRD HRTEM Dielectric constant abstract Nanosized nickel–zinc ferrites having the chemical formula Ni (1x) Zn x Fe 2 O 4 for 0 x 1 were synthesized by citrate precursor method. The synthesized nanopowder was densified at a temperature 850 C. XRD diffraction results confirm the spinel structure for the prepared compounds. Lattice parameter decreases from 8.490 to 8.337 Å with increase in the Zn content. The average particle size identified by HRTEM was 45 nm and indicates nanocrystalline nature of the compounds. The Zn content has a significant influence on the dielectric properties of as sintered samples, such as dielectric constant, dielectric loss tangent and dc resistivity. These values decrease with increasing zinc content. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Nickel–zinc ferrite with spinel structure have been studied extensively due to its remarkable magnetic properties (high satura- tion magnetization—close to that of magnetite), large permeability at high frequency, and remarkably high electrical resistivity [1,2]. Ferrites have many applications in microwave devices [3] and therefore it is advantageous to improve their dielectric property. Though intense research effort has been carried out, the study of nickel–zinc ferrite nanoparticle is yet to be exploited systemati- cally. It is commonly known that nanoparticle with controlled size, and composition is of fundamental and technological interest. The nanocrystalline spinel NiZn ferrite are of interest due to their poten- tial application in non-resonant devices, radio frequency circuit, high quality filters, rod antennas, transformer cores, read/write heads for high speed digital tapes and operating devices [3,4]. Major difficulties associated with the study of nanometer sys- tem are their preparation. The advent of low temperature method of synthesis, e.g., chemical method has made the preparation and investigation of ultrafine particle a reality [5,6]. The citrate pre- cursor method has proved to be a very versatile and cheap viable method for the synthesis of nanoscale particles in the case of ferrites. The wet chemical method for obtaining the nanocrys- talline Ni–Zn ferrite evinces a series of advantages compared to the ceramic method [7–9]. The most important of these are: the homo- geneous distribution of ions at the molecular level, short time and Corresponding author. Tel.: +91 612 2540482; fax: +91 612 2540482. E-mail address: seema [email protected] (S. Sharma). low temperature preparation, low cost and high efficiency. At the same time, the method can offer a rigorous control on the crys- tallites size. This important particularity offers the possibility of controlling the subsequent properties of the nanocrystalline sys- tem, since they depend to a great extent on the dimensions of the nanocrystallites, not only on their chemical composition and preparation condition. In this paper, we present citrate precursor method, a simple method to synthesize nickel ferrite, zinc fer- rite and nickel–zinc ferrite powders. The powders prepared have advantages over the ceramic method, such as good stoichiometric control, small size and lower calcining temperature. In the present work, the powders are calcined at different temperatures up to 750 C and investigations on the structural, microstructural and dielectric properties have been reported. 2. Experimental procedure Ceramic samples of Ni (1x) Zn (x) Fe 2 O 4 (x = 0, 0.3, 0.4, 0.5, 0.6, 0.7 and 1) were synthesized from nickel nitrate, zinc nitrate, iron(III) nitrate, and citric acid . The chemicals were weighed according to the required stoichiometric proportion. Iron(III) nitrate solution was prepared in deionised water with continuous stirring. The sep- arate solution of nickel nitrate, zinc nitrate and citric acid were prepared in deionised water and then they were mixed together with continuous stirring. The solution was added to iron nitrate solution under constant stirring. Small amounts of ammonium hydroxide solution were introduced to the precursor solution to increase the pH 8 so as to prepare the coating solution with uni- formly dispersed citrate complexes of metal ions. This mixture was heated at 60 C to obtain a homogeneous uniformly coloured 0921-5107/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2010.02.015

Transcript of Influence of Zn substitution on structural, microstructural and dielectric properties of...

Page 1: Influence of Zn substitution on structural, microstructural and dielectric properties of nanocrystalline nickel ferrites

Materials Science and Engineering B 167 (2010) 187–192

Contents lists available at ScienceDirect

Materials Science and Engineering B

journa l homepage: www.e lsev ier .com/ locate /mseb

Influence of Zn substitution on structural, microstructural and dielectricproperties of nanocrystalline nickel ferrites

Seema Sharmaa,∗, Kavita Vermaa, Umesh Chaubeya, Vidyanand Singhb, B.R. Mehtab

a Ferroelectrics Laboratory, Department of Physics, A N College, Patna 800013, Indiab Thin Film Laboratory, Department of Physics, Indian Institute of Delhi, Hauz Khas, New Delhi 110016, India

a r t i c l e i n f o

Article history:Received 8 July 2009Received in revised form 9 February 2010Accepted 10 February 2010

a b s t r a c t

Nanosized nickel–zinc ferrites having the chemical formula Ni(1−x)ZnxFe2O4 for 0 ≤ x ≤ 1 were synthesizedby citrate precursor method. The synthesized nanopowder was densified at a temperature 850 ◦C. XRDdiffraction results confirm the spinel structure for the prepared compounds. Lattice parameter decreasesfrom 8.490 to 8.337 Å with increase in the Zn content. The average particle size identified by HRTEMwas ∼45 nm and indicates nanocrystalline nature of the compounds. The Zn content has a significant

Keywords:NanocrystallineXRDHD

influence on the dielectric properties of as sintered samples, such as dielectric constant, dielectric losstangent and dc resistivity. These values decrease with increasing zinc content.

1

etaFtTncanthh

toicmftcg

0d

RTEMielectric constant

. Introduction

Nickel–zinc ferrite with spinel structure have been studiedxtensively due to its remarkable magnetic properties (high satura-ion magnetization—close to that of magnetite), large permeabilityt high frequency, and remarkably high electrical resistivity [1,2].errites have many applications in microwave devices [3] andherefore it is advantageous to improve their dielectric property.hough intense research effort has been carried out, the study ofickel–zinc ferrite nanoparticle is yet to be exploited systemati-ally. It is commonly known that nanoparticle with controlled size,nd composition is of fundamental and technological interest. Theanocrystalline spinel NiZn ferrite are of interest due to their poten-ial application in non-resonant devices, radio frequency circuit,igh quality filters, rod antennas, transformer cores, read/writeeads for high speed digital tapes and operating devices [3,4].

Major difficulties associated with the study of nanometer sys-em are their preparation. The advent of low temperature methodf synthesis, e.g., chemical method has made the preparation andnvestigation of ultrafine particle a reality [5,6]. The citrate pre-ursor method has proved to be a very versatile and cheap viableethod for the synthesis of nanoscale particles in the case of

errites. The wet chemical method for obtaining the nanocrys-alline Ni–Zn ferrite evinces a series of advantages compared to theeramic method [7–9]. The most important of these are: the homo-eneous distribution of ions at the molecular level, short time and

∗ Corresponding author. Tel.: +91 612 2540482; fax: +91 612 2540482.E-mail address: seema [email protected] (S. Sharma).

921-5107/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.mseb.2010.02.015

© 2010 Elsevier B.V. All rights reserved.

low temperature preparation, low cost and high efficiency. At thesame time, the method can offer a rigorous control on the crys-tallites size. This important particularity offers the possibility ofcontrolling the subsequent properties of the nanocrystalline sys-tem, since they depend to a great extent on the dimensions ofthe nanocrystallites, not only on their chemical composition andpreparation condition. In this paper, we present citrate precursormethod, a simple method to synthesize nickel ferrite, zinc fer-rite and nickel–zinc ferrite powders. The powders prepared haveadvantages over the ceramic method, such as good stoichiometriccontrol, small size and lower calcining temperature. In the presentwork, the powders are calcined at different temperatures up to750 ◦C and investigations on the structural, microstructural anddielectric properties have been reported.

2. Experimental procedure

Ceramic samples of Ni(1−x)Zn(x)Fe2O4 (x = 0, 0.3, 0.4, 0.5, 0.6, 0.7and 1) were synthesized from nickel nitrate, zinc nitrate, iron(III)nitrate, and citric acid . The chemicals were weighed accordingto the required stoichiometric proportion. Iron(III) nitrate solutionwas prepared in deionised water with continuous stirring. The sep-arate solution of nickel nitrate, zinc nitrate and citric acid wereprepared in deionised water and then they were mixed togetherwith continuous stirring. The solution was added to iron nitrate

solution under constant stirring. Small amounts of ammoniumhydroxide solution were introduced to the precursor solution toincrease the pH ∼ 8 so as to prepare the coating solution with uni-formly dispersed citrate complexes of metal ions. This mixturewas heated at ∼60 ◦C to obtain a homogeneous uniformly coloured
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, 0.4, 0

bcsaupma

psrctT(fAwTta1o6t

3

0et5stotmt

P

wdi

the unit cell, so 8 is included in the formula. X-ray density �x wascalculated using Eq. (2). It decreased from 5.386 to 5.255 g/cm3.The calculated and the experimental density of all the Zn substi-tuted Ni ferrites were found to be greater than 93% of the X-raydensity. As X-ray density depends upon the lattice parameters and

Fig. 1. (a) XRD patterns of the as dried gel of Ni(1−x)Zn(x)Fe2O4, x = 0.3

rown transparent glassy material. The dried citrate mixture wasalcined for 1 h at 550, 650 and 750 ◦C respectively to obtain a spineltructure. Then the obtained ferrite powder was mixed with anppropriate amount of 5 wt% polyvinyl alcohols as a binder for gran-lation. Then the granulated powders were uniaxially pressed at aressure of 1300 kg cm−2 to form green toroidal and pellet speci-ens. After binder burnt out at 600 ◦C, the specimens were sintered

t 850 ◦C for 2 h in air.The X-ray diffraction (XRD) measurements of the powder sam-

les were recorded in a wide range of Bragg angles 2� at acanning rate of 2◦ min−1, carried out on a Philips PW 1830 X-ay diffractometer that was operated at a voltage of 40 kV and aurrent of 30 mA with Cu K� radiation (1.5405 Å). High Resolu-ion Transmission Electron Microscopy (HRTEM) was performed byECHNAI G20-STWIN (200 kV) machine with a line resolution 2.32in angstrom). These images were taken by drop coating nickel–zincerrite powders on a carbon-coated copper grid. Energy Dispersivebsorption Spectroscopy (EDAX) photograph of nickel–zinc ferriteere carried out by the HRTEM equipment as mentioned above.

he frequency dependence of dielectric properties of specimen sin-ered at 850 ◦C were measured by impedance spectroscopy with

HP4194A impedance analyzer at several frequencies between00 kHz and 1 MHz. Measurements were accomplished with firedn silver electrodes painted on the ceramic discs and annealed at50 ◦C. The resistivity (�) of the sample was measured at roomemperature by the two-probe method.

. Results and discussions

XRD profiles of the as dried gel of Ni(1−x)Zn(x)Fe2O4 (x = 0.3, 0.4,.5, 0.6 and 0.7) samples at 200 ◦C has been shown in Fig. 1a. Theyxhibit the amorphous nature of the samples. Fig. 1b shows theypical XRD patterns for the Ni:Zn::50:50 composition calcined at50, 650 and 750 ◦C. All the compositions are characterized by aingle phase with spinel structure. The diffraction lines of charac-eristic (2 2 0), (3 1 1), (2 2 2), (4 0 0), (5 1 1), (4 4 0) and (6 2 0) planesf the Ni0.5Zn0.5Fe2O4 powder is clearly observed. Scherrer’s equa-ion [10] for broadening resulting from a small crystalline size, the

ean, effective or apparent dimension of the crystalline composinghe powder is

k�

hkl =

ˇ1/2 cos �(1)

here � and � have their usual meaning, ˇ the breadth of the pureiffraction profile in radians on 2� scale and k is a constant approx-

mately equal to unity and related both to the crystalline shape and

.5, 0.6 and 0.7 samples. (b) XRD patterns of Ni0.5Zn0.5Fe2O4 samples.

to the way in which ˇ is defined. The best possible value of k hasbeen estimated as 0.9 [11]. The particle sizes of all the samples in ourstudy have been estimated by using the above Scherrer’s equationand was found to be ∼45 nm for the strongest peak.

The lattice parameter of as synthesized ferrite is determined byusing the formula [12]:

a = �

2(h2 + k2 + l2)

sin �(2)

where (h k l) are the Miller indices, and � is the diffraction angle cor-responding to the (h k l) plane. With the increase in Zn ion content,the lattice parameters of the ferrite powders increase from 0.833 to0.840 nm as shown in Fig. 2. This result suggests the formation of acompositionally homogeneous solid solution. This increase can beattributed to the substitution of the larger Zn2+ ions for the smallerNi2+ ions [13,14].

The X-ray density (�x) of the samples was calculated using therelation given by Smit and Wijn [15]:

�x = 8M

Naa3(3)

where M is the molecular weight of the samples, Na the Avogadro’snumber and a is the lattice parameter. As there are 8 molecules in

Fig. 2. Variation of X-ray density and lattice parameters with x (Zn) inNi(1−x)Zn(x)Fe2O4.

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tsifatFmt

S. Sharma et al. / Materials Science

hese parameters decreases with the increase in Zn concentrationo the corresponding X-ray density decreased with the increasen Zn concentration. Similar trend has been reported by Ghazan-ar et al. [16]. However, O’-Neill reported that in high-temperaturennealed ZnFe O samples, quenched to room temperature, a par-

2 4ial site exchange occurs between tetrahedral Zn2+ and octahedrale3+ ions [17]. Moreover, Shinoda and co-workers stated that uponilling nanocrystalline NiFe2O4 bulk material, some Ni2+ ions move

o tetrahedral sites [18].

Fig. 3. Energy dispersive absorption spectroscopy photograph of Ni(1−x)Z

ngineering B 167 (2010) 187–192 189

EDS spectra of the samples Ni(1−x)Zn(x)Fe2O4 (x = 0.3, 0.4, 0.5, 0.6and 0.7) are shown in Fig. 3. The peaks of the elements Fe, Ni, Znand O were observed and have been assigned. Peaks for Cu and Care from the grid used and a small amount of Si is from the detec-tor (Li-drifted Si detector). The calculated percentage of Ni/Zn value

matches well with the amount of Ni/Zn used in the respective pre-cursors. Fig. 4 shows the HRTEM photographs of Ni(1−x)Zn(x)Fe2O4samples. The particle size of the samples was found to lie between40 and 50 nm as observed from the HRTEM study. Fig. 5 shows

n(x)Fe2O4: (a) x = 0.3, (b) x = 0.4, (c) x = 0.5, (d) x = 0.6 and (e) x = 0.7.

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spc

dfaraps

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elected area electron diffraction pattern of Ni0.5Zn0.5Fe2O4 com-ound. This figure demonstrates the crystalline nature of theompound.

The room temperature values of dielectric constant (ε′), theielectric loss tangent (tan ı) and DC resistivity for mixed Ni–Znerrites at 100 kHz are given in Table 1. The values of ε′ and tan ıre found to decrease with increasing of zinc content. Iwauchi [19]

eported a strong correlation between the conduction mechanismnd the dielectric behaviours of the ferrites starting with the sup-osition that the mechanism of polarization process in ferrite isimilar to that the conduction process [20]. It was observed that the

Fig. 4. HRTEM photographs of Ni(1−x)Zn(x)Fe2O4: (a) x =

ngineering B 167 (2010) 187–192

electron exchange between Fe2+/Fe3+ result in local displacementsdetermining the polarization of the ferrites. A similar model is pro-posed for the composition dependence of the dielectric constants ofmixed Ni–Zn ferrites. In this model the electron exchange betweenFe2+ and Fe3+ in an n-type and the hole exchange between Ni3+ andNi2+ in p-type ferrites results in local displacements of electrons orholes in the direction of the electric field that then cause polariza-

tion [20,21]. Table 1 reveals that the variation of dielectric constantruns parallel to the variation of available ferrous ions on octahedralsites. It is also pertinent to mention that the variation of electricalconductivity runs parallel to the variation of ferrous ion concen-

0.3, (b) x = 0.4, (c) x = 0.5, (d) x = 0.6 and (e) x = 0.7.

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S. Sharma et al. / Materials Science and E

Fig. 5. Selected area electron diffraction showing the characteristic crystal planesof Ni0.5Zn0.5Fe2O4.

Table 1Composition dependence of dielectric data for mixed Ni–Zn ferrites at room tem-perature and frequency 100 kHz.

Composition ε′ tan ı DC resistivity � × 106 (� cm)

NiFe2O4 65.98 0.43 1.678Ni0.7Zn0.3Fe2O4 63.41 0.41 1.567Ni0.6Zn0.4Fe2O4 59.54 0.39 0.567Ni0.5Zn0.5Fe2O4 56.76 0.36 0.246

tta

qidcm

Fs

Ni0.4Zn0.6Fe2O4 51.63 0.34 0.198Ni0.3Zn0.7Fe2O4 49.32 0.31 0.065ZnFe2O4 47.94 0.29 0.0046

ration. Thus, it is the number of ferrous ions on octahedral siteshat plays a dominant role in the processes of conduction as wells dielectric polarization.

The variation of the dielectric constant as a function of fre-uency for all the ferrite samples at room temperature is shown

n Fig. 6. It can be seen from the figure that the dielectric constantecreases with increasing frequency. The decrease of dielectriconstant with increase of frequency as observed in the case ofixed Ni–Zn ferrites is a normal dielectric behaviour of spinel fer-

ig. 6. Dielectric constant as a function of frequency for Ni(1−x)Zn(x) Fe2O4 ferriteintered at 850 ◦C.

ngineering B 167 (2010) 187–192 191

rites. The normal dielectric behaviour was also observed by severalinvestigators in the case of LiTi, NiCuZn, MgTiZn and CoZn fer-rites [22–24]. It can be seen from Fig. 6 that the dispersion in ε′ isanalogous to Maxwell–Wagner interfacial polarization [25,26], inagreement with Koops phenomenological theory [27]. The disper-sion of the dielectric constant is maximum for sample with x = 0.3.This maximum dielectric dispersion may be explained on the basisof available ferrous ions on octahedral sites. In the case of x = 0.3the concentration of ferrous ions is higher than in other compo-sitions of mixed Ni–Zn ferrites. As a consequence, it is possible forthese ions to be polarized to the maximum possible extent. Further,as the frequency of the externally applied field increases gradually,though the number of ferrous ions is present in the ferrite material,the dielectric constant decreases from 60.76 at 100 kHz to 37.21 at1 MHz.

The reduction occurs because beyond a certain frequency of theexternally applied electric field, the electronic exchange betweenferrous and ferric ions, i.e., Fe2+/Fe3+ cannot follow the alternat-ing field. The variation of the dispersion of ε′ with compositionfor other mixed nickel–zinc ferrites explained by the fact that theelectron exchange between Fe2+ and Fe3+ in an n-type semicon-ducting ferrite and hole exchange between Ni3+ and Ni2+ in a p-typesemiconducting ferrite cannot follow the frequency of the appliedalternating field beyond a critical value of the frequency.

DC electrical resistivity of the said system was found to decreasefrom 1.678 × 106 to 0.0046 × 106 � cm with the increase in Zn con-centration from 0.0 to 1.0 at room temperature as tabulated inTable 1. This decrease in resistivity is due to the fact that Zn hassmaller value of resistivity (5.92 × 10−6 � cm) as compared to thatof Ni (7.0 × 10−6 � cm) [28]. The decrease in resistivity may alsobe due to the presence of Fe2+ ions as Zn is added, which areproduced during sintering. Another reason for decrease in � onincreasing Zn is due to the reason that Zn ions prefer the occu-pation of tetrahedral (A) sites and Ni ions prefer the occupationof octahedral (B) sites, while Fe ions partially occupy the A andB sites. On increasing Zn ion substitution (at A sites), Ni ion con-centration (at B sites) will decrease. This leads to the migrationof some Fe ions from A sites to B sites to substitute the reduc-tion in Ni ions concentration at B sites. As a result, the number offerrous and ferric ions at the B sites (which are responsible for elec-trical conduction in ferrites) increases. Consequently, resistivitydecreases on increasing Zn ion substitution. Therefore, � decreasesby increasing Zn contents [29,30]. Similar trend but with differ-ent magnitude of resistivity have been reported by Ghazanfar et al.[16].

4. Conclusions

Nanocrystalline single phase nickel–zinc ferrite powders,Ni1−xZnxFe2O4 (x = 0.0–1) were synthesized by citrate precursormethod. X-ray diffraction (XRD), High Resolution TransmissionElectron Microscopy (HRTEM) was used to characterize the com-positions. XRD results show that the dried gel powders areamorphous, and the characteristic peaks of the spinel nickel–zincferrite powders appear after the gel is calcined at 550 ◦C for1 h. When the calcining temperatures are 650 and 750 ◦C, purespinel structure is obtained. The average particle sizes identifiedby HRTEM are found to be ∼45 nm. The unit cell parameter ‘a’decreases linearly with concentration of nickel due to the smallionic radius of nickel. The synthesized powders exhibited high

sintering activity, and can be sintered at temperature 850 ◦C. Zncontent has significant influence on the electric properties, suchas dielectric constant, dielectric loss tangent and dc resistivity fornickel–zinc ferrites. All the parameters decrease with the increasein the Zn concentration.
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eferences

[1] R.A. McCurie, Ferromagnetic Materials, Structure and Properties, AcademicPress, 1994.

[2] A. Verma, T.C. Goel, R.G. Mendiratta, R.G. Gupta, J. Magn. Magn. Mater. 192(1999) 271.

[3] V.K. Sankaranarayanan, Q.A. Pankhurst, D.P.E. Dickson, C.E. Johnson, J. Magn.Magn. Mater. 125 (1993) 199.

[4] V.K. Sankaranarayanan, N.S. Gajbhiye, J. Am. Ceram. Soc. 73 (1990) 1301.[5] P.M. Pechini, US Patent 3 (1967) p. 330697.[6] S. Zahi, A.R. Daud, M. Hashim, Mater. Chem. Phys. 106 (2007) 452.[7] A. Nutan Gupta, C. Verma, S. Kashyap, D.C. Dube, J. Magn. Magn. Mater. 308

(2007) 137.[8] Mona M. Bahout, S. Bertrand, O. Pena, J. Solid State Chem. 178 (2005) 1080.[9] A. Goldman, Am. Ceram. Soc. Bull. 63 (1984) 582.10] P. Scherrer, Gottin Nachricht 2 (1998) 98.

11] H.P. Klug, L.E. Alexander, X-ray Diffraction Procedure, second ed., Wiley, New

York, 1974.12] C.C. Hwang, J.S. Tsai, T.H. Huang, Mater. Chem. Phys. 93 (2005) 330.13] S.M. Haque, Md.A. Choudhury, Md.F. Islam, J. Magn. Magn. Mater. 251 (2002)

292.14] K.B. Modi, P.V. Tanna, S.S. Laghate, H.H. Joshi, J. Mater. Sci. Lett. 19 (2000) 1111.

[[[

[[

ngineering B 167 (2010) 187–192

15] J. Smit, H.P.J. Wijn, Ferrites, John Wiley, New York, 1959.16] U. Ghazanfar, S.A. Siddiqi, G. Abbas, Mater. Sci. Eng. B 118 (2005) 84.17] H.S.C. O’Neill, Eur. J. Miner. 4 (1989) 571.18] C.N. Chinnasamy, A. Narayanasamy, N. Ponpandian, K. Chattopadhyay, K. Shin-

oda, B. Jeyadevan, K. Tohji, K. Nakatsuka, T. Furubayashi, I. Nakatani, Phys. Rev.B 63 (2001) 4108.

19] K. Iwauchi, Jpn. J. Appl. Phys. 10 (1971) 1520.20] L.S.I. Rabinkin, Z.I. Novika, Ferrites Minsk (1960) 146.21] J. Azadmanjiri, H.K. Salehani, M.R. Barati, F. Farzan, J. Mater. Lett. 61 (2007) 84.22] M.B. Reddy, P.V. Reddy, J. Phys. D: Appl. Phys. 24 (1991) 975.23] M.U. Islam, F. Aen, S.B. Niazi, M. Azhar Khan, M. Ishaque, T. Abbas, M.U. Rana,

Mater. Chem. Phys. 109 (2008) 482.24] Zhenxing Yue, Ji Zhou, Zhilun Gui, Longtu Li, J. Magn. Magn. Mater. 264 (2003)

258.25] J.C. Maxwell, Electricity and Magnetism, vol. 1, Oxford Univ. Press, Oxford, 1929,

Section 328, p. 752.

26] K.W. Wagner, Ann. Phys. (Leipzig) 40 (1913) 817.27] C.G. Koops, Phys. Rev. 83 (1951) 121.28] C. Kittel, An Introduction to Solid State Physics, seventh ed., Wiley, New York,

London, 1976, p. 160.29] G. Joshi, A. Khot, S. Sawant, Solid State Commun. 65 (1988) 1593.30] M. El-Shabasy, J. Magn. Magn. Mater. 172 (1997) 188.