Journal of Alloys and Compounds 579 (2013) 576–582

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Journal of Alloys and Compounds

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Effect of Tb–Mn substitution on DC and AC conductivity of Y-typehexagonal ferrite

0925-8388/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.jallcom.2013.06.182

⇑ Corresponding authors. Tel.: +92 300 9879344 (M.N. Ashiq).E-mail addresses: irshadalibzu@gmail.com (I. Ali), naeemashiqqau@yahoo.com

(M.N. Ashiq).

Irshad Ali a,⇑, M.U. Islam a, Muhammad Naeem Ashiq b,⇑, M. Asif Iqbal a, Hasan M. Khan a, Nazia Karamat b

a Department of Physics, Bahauddin Zakariya University, Multan 60800, Pakistanb Institute of Chemical Science, Bahauddin Zakariya University, Multan 60800, Pakistan

a r t i c l e i n f o a b s t r a c t

Article history:Received 4 April 2013Received in revised form 18 June 2013Accepted 29 June 2013Available online 19 July 2013

Keywords:ConductivityHexaferritesMicroemulsion methodCole–cole plotGrain boundaries

Single phase nanostructured Tb–Mn substituted Y-type hexaferrites with nominal compositionSr2Co2�xMnx TbyFe12�yO22 (x = 0.0–1, Y = 0.0–0.1) were synthesized by the normal microemulsionmethod. The values of activation energy calculated from DC electrical conductivity increases with thesubstitution of Tb–Mn suggests that the conduction mechanism in the present ferrite system is polaronhopping. The appearance of broad Debye peaks in imaginary electric modulus plots (m00) show the exis-tence of relaxation process in all these samples. The complex impedance plane plots show a single semi-circle, which indicates the capacitive and resistive properties of the materials are due to contribution ofgrains and grain boundaries in ferrites. It is observed that Tb–Mn Substitution makes comparativelysmall difference on the grain resistance, but leads to a remarkable rise of grain boundary resistance. Highvalues of quality factor are obtained required for power applications and high frequency multilayer chipinductors.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

Ferrites are very key materials for technological applications [1].They have been widely used for their excellent magnetic properties[2], e.g. magnetic fluids, hyperthermal cancer treatment, in mag-netic resonance imaging (MRI) enhancement, high density mag-netic recording and drug delivery, etc. Especially hexa ferriteshave attracted much attention over the decade due to their versa-tile applications [3,4]. Due to development in the field of telecom-munication, the operational frequency of electronic devices israpidly moving to gigahertz frequencies. Polycrystalline hexafer-rites, having low AC electrical conductivity and consequently, loweddy currents and dielectric losses, are particularly well suited foruse in high-frequency applications. The experimental measure-ments for electric conduction, thermoelectric power, charge carri-ers concentration, charge carriers mobility and activation energygive much information on the behavior of the free and localizedcharge carriers. Their properties are heavily dependent on theirstructure, composition and ion distribution [5,6]. Gorter made thefirst attempt to determine the position of the magnetic ions and ori-entations of the spins in the crystal lattice by considering exchangeinteractions [7]. It was observed that the spins are collinear in thebasal plane particularly in Y-type hexagonal structure. The struc-

ture of Y-type hexaferrite has space group (R3m). The Y-type hex-agonal ferrites have a crystalline structure built up as asuperposition of S and T blocks. The unit cell is composed of the se-quence STSTST including three formula units. Each formula unitconsists of two layered spinel S block and four-layered antiferro-magnetic T block. The metallic cations are distributed among sixsub lattices [7]. Therefore, by tailoring the composition and thestructure of the Y-type hexaferrite, it is possible to improve theproperties required for specific applications. Because of this possi-bility to tailor the properties of ferrites, they have been synthesizedby various methods, including solid state reaction [8], hydrother-mal [9], sol–gel [10], sol–gel autocombustion [11], co-precipitation[12], citrate precursor technique [13], thermal plasma [14], pulsedwire discharge [15], etc. In the present work, we have used the nor-mal microemulsion method which is better to obtain the nano-sizematerials as compared to others. The surfactant used form the mi-celle which acts as a nanoreactor so the size and shape of particlescan be controlled. It is well known that the microemulsion methodhas been proved to be one of the most effective routes to realize thelow temperature sintering of ferrites. The study of DC electricalconductivity, AC conductivity, and drift mobility give much morevaluable information on the behavior of free and localized electriccharge carriers. This leads to good explanation and understandingof the mechanism of electric conduction in the studied samples.Therefore, the authors aimed to study the effect of temperatureand composition on the DC electrical conductivity and driftmobility. Moreover special intention have been on the frequency

1.5 2.0 2.5 3.0 3.50.045

0.050

0.055

0.060

0.065

0.070

0.075

0.080

0.085

0.090

0.095

0.100 x= 0.0 y=0.0 x=0.2 y= 0.02 x=0.4 y=0.04 x=0.6 y=0.06 x=0.8 y=0.08 x=1.0 y=0.1

Dc

Log

σ(Ω

-cm

)-1

1000/(T)K

Fig. 1. Change in DC electrical conductivity with temperature for (Tb–Mn)substituted Co2Sr2Fe12O22 hexa ferrites.

I. Ali et al. / Journal of Alloys and Compounds 579 (2013) 576–582 577

dependent AC conductivity and complex plane plot (Nyqiust plot)for a series of Mn–Tb substituted Co2Sr2Fe12O22 Y-type hexaferrites.

2. Experimental procedure

2.1. Chemicals

The chemicals of analytical grade were used to synthesize Y-type strontiumhexa-ferrites Sr2Co2�xMnx TbyFe12�yO22. The starting materials were Fe(NO3)3�9H2O(Riedel-de Haen, 97%), Co(NO3)2�6H2O (Merck, >99%), MnCl2. 2H2O(Merck, >99%),Sr(No3)2 (Merck, 99%), Tb2O3 (Merck, 99%), (cetyltrimethyl ammonium bromide)CTAB (Merck, 97%) as a surfactant, NH3 (Fisher Scientific, 35%) as a precipitatingagent and methanol (Merck, 99%) as washing agent.

2.2. Synthetic procedure

The Y-type hexaferrite samples with nominal composition Sr2Co2�xMnx Tby-

Fe12�yO22 (x = 0.0–1, Y = 0.0–0.1) were prepared by the normal microemsulsionmethod. The metallic salt solution of the required molarities were prepared indeionized water and mixed in a baker. The CTAB was also added in metals solutionswith ratio 1: 1.5 (metals: CTAB). The solution was stirred on the magnetic hot plateat 60 �C until it formed a clear solution. The ammonia solution was added dropwiseto form the precipitates. After that the precipitates were washed with deionizedwater and finally with methanol. Then the precipitates were dried in an oven at150 �C and finally annealed at 1050 �C for 8 h using box furnace (Heyaius, D-6450Hanau, Germany).The formation of substituted Y-type hexaferrites from the start-ing materials can be shown in Scheme 1.

2.3. Characterization

The DC electrical conductivity was obtained by a simple two-probe methodwithin temperature range of 300–573 K. A Keithly source meter model-197 wasused for the said purpose. The DC conductivity was calculated by using the formula

rDC ¼ d=RA ð1Þ

where R is the resistance, d is the thickness of the sample and A is area of electrode.Drift mobility, ld of all the samples were calculated using the relation.

ld ¼ rDC=ne ð2Þ

where e is the charge of electron, rDC is conductivity and n is the concentration ofcharge carrier and can be calculated from the well-known equation:

n ¼ NAdbPFe=M ð3Þ

where NA is the Avogadro’s number, db is the measured bulk density of sample, PFe isthe number of iron atoms in the chemical formula of the ferrites and M is the molec-ular weight of the samples.

Dielectric data and Impedance was measured on a Agilent impedance analyzermodel E4991ARF. The AC conductivity was calculated from dielectric constant anddielectric loss tangent (tand) as

rAC ¼ 2pfeo�e tan d ð4Þ

where rAC is the AC conductivity and f is the frequency, p and eo are constants.Impedance measurements were performed in the frequency range from 1 MHz

to 3 GHz at room temperature by taking the absolute value of impedance |Z| withvarying complex angle hZ. The real and imaginary parts of impedance can be writtenas

Z0 ¼ R ¼ jZj cos hZ ð5Þ

Z00 ¼ X ¼ jZj sin hZ ð6Þ

Scheme 1. Formation of Tb–Mn substituted Y-ty

The real and imaginary parts of the electrical modulus, M0 and M00 respectivelythey can be calculated as fallows [16]:

M0 ¼ e0=fðe0Þ2 þ ðe00Þ2g ð7Þ

M00 ¼ e00=fðe0Þ2 þ ðe00Þ2g ð8Þ

where e0 and e00 are real and complex parts of permittivity respectively.

3. Results and discussion

3.1. DC conductivity

The relation between electrical conductivity and temperature[11] may be expressed as

r ¼ r0 exp DE=dBT ð9Þ

where r is DC conductivity, DE is the activation energy in (eV) forconduction, kB is the Boltzmann constant and T is the temperaturein Kelvin (K). Fig. 1 describes DC electrical conductivity versus tem-perature (103/T) from room temperature up to about 678 K. Theconductivity behavior for all samples is analogous with each other.The conductivity increases with increasing temperature, indicatingthe semiconductor behavior of the samples [17–19]. Deep observa-tion of DC conductivity curves shows two distinct regions. Thisbehavior of different regions was examined before for Y-hexaferrite[20] and spinal ferrite [21]. First region appears in ferrite at lowtemperatures. Low activation energies of first region suggest thatthe conduction in this region may be due to the free charge carriers

pe hexaferrites from their starting materials.

Table 1Compresses the DC activation energy, exponential n and AC activation energy of Tb–Mn substituted hexaferrites, Sr2Co(2�x)MnxTbyFe(12�y)O22, (x = 0.00–1.00; y = 0.00–0.10).

Compositional formula rDc (X cm)�1 EDC1 (ev) EDC2 (ev) (EDC1 + EDC2)/2 n (±0.01) EAC

Sr2Co2Fe12O22 8.1 � 10�7 0.352 0.51 0.431 0.81 0.078Sr2Co1.8Mn0.2Tb.02Fe11.98O22 2.3 � 10�7 0.356 0.52 0.438 0.76 0.102Sr2Co1.6Mn0.4Tb.04Fe11.96O22 3.4 � 10�8 0.358 0.57 0.464 0.58 0.193Sr2Co1.4Mn0.6Tb.06Fe11.94O22 1.2 � 10�8 0.362 0.58 0.471 0.96 0.019Sr2Co1.2Mn0.8Tb.08Fe11.92O22 4.7 � 10�9 0.364 0.59 0.477 0.90 0.046Sr2Co1Mn1Tb0.1Fe11.90O22 6.6 � 10�10 0.366 0.60 0.483 0.97 0.011

250 300 350 400 450 500 550 600 650 700

0.0

2.0x10-11

4.0x10-11

6.0x10-11

8.0x10-11

1.0x10-10

1.2x10-10

1.4x10-10

1.6x10-10

1.8x10-10

x= 0.00 y=0.0 x=0.02 y= 0.2 x=0.04 y=0.4 x=0.06 y=0.6 x=0.08 y=0.8 x=0.10 y=1.0

Mob

ility

(cm

2 v-1s-1

)

T(K)

Fig. 2. Change in drift mobility with temperature for (Tb–Mn) substitutedCo2Sr2Fe12O22 hexa ferrites.

578 I. Ali et al. / Journal of Alloys and Compounds 579 (2013) 576–582

(not localized) of impurities. The second region appears at hightemperature, where the conductivity is due to the polaran hoppingand activation energy is high in this region.

The values of activation energy of the present investigated sam-ples for the Tb–Mn doped can be viewed from Table 1, which ishigh than the already reported values of activation energy [7]. Itwas expected because the sample with lower conductivity hashigher values of activation energy and vice versa. The activationenergy E increases with increasing the Mn-Tb contents. This showsthat the energy barrier, which oxide ions must overcome to hop toneighbor vacant sites, becomes high with the increase of the Mn-Tb contents. A little variation is expected from order to disorderstate due to compositional changes (the cation sites are occupiedby metal ions in a statistical manner) [22]. The substitution of(Mn–Tb) in Sr2Co2Fe12O22, increases vacancies at the oxide-ionsites in order to maintain charge balance which consequently in-creases the activation energy Eg [23]. Measured values of DC con-ductivity of present investigated samples vary 8.1 � 10�7 to6.6 � 10�10 (X cm)�1 which are lower than the already reportedvalues 8.6 � 10�7 to 2.8 � 10�7 (X cm)�1[5]. Lowering of conduc-

Table 2Real and imaginary parts of electric modulus and impedance, AC conductivity at 1 MHz a(x = 0.00–1.00; y = 0.00–0.10).

Compositional formula M0 M00 Z0 (X

Sr2Co2Fe12O22 0.061 0.008 327Sr2Co1.8Mn0.2Tb.02Fe11.98O22 0.075 0.012 342Sr2Co1.6Mn0.4Tb.04Fe11.96O22 0.089 0.016 406Sr2Co1.4Mn0.6Tb.06Fe11.94O22 0.102 0.019 529Sr2Co1.2Mn0.8Tb.08Fe11.92O22 0.117 0.020 608Sr2Co1Mn1Tb0.1Fe11.90O22 0.151 0.017 736

tivity may be due to highly resistive nature of the substituent rareearth ion Tb3+. The decrease in conductivity is beneficial for micro-wave devices applications.

The increase in activation energy would hinder the oxide-ionmigration, eventually to low values of conductivity. The DC electri-cal conductivity tends to decrease. This behavior may be clarifiedon the basis of cations distribution at numerous sites in the hexag-onal structure. The Mn2+ ions occupy octahedral sites while Co2+

and Fe3+ occupy both the octahedral (B) as well as tetrahedral(A) sites [24]. It has also been reported that the Tb3+ ion occupiesthe octahedral site. The hopping of electrons between Fe2+ andFe3+ at the octahedral site is main factor for conduction mechanismin ferrites, because Tb3+ occupies the octahedral B-site which de-creases the number of iron ions at that site and also hopping ofelectrons between the ferrous and ferric ions thus decreasing theconductivity. Comparison of the compositional dependence forDC conductivity and activation energy shows a good correspon-dence, that is samples having high conductivity have low activa-tion energy and vice versa [7,25].

3.2. Drift mobility

The variation in drift mobility with the temperature for Tb–Mnsubstituted Co2Sr2Fe12O22 ferrite samples is shown in Fig. 2. Thesesamples show a bend at a specific temperature i.e. the drift mobil-ity increases with the increase in temperature and above the spe-cific temperature, the drift mobility increases abruptly withincrease in the temperature. The drift mobility of all the synthe-sized samples decreases with increasing Tb–Mn concentrationand listed in Table 2. The decrease drift mobility is may be dueto decrease in conductivity by doping Tb–Mn ions. The calculatedvalues of drift mobility for the Tb–Mn doped samples are in therange 10�12–10�15 cm2 v�1 s�1 K�1, which are slightly lower thanthe reported values of 10�11–10�14 cm2 v�1 s�1 K�1 [26]. Thisbehavior is to be expected as the drift mobility has a direct relationwith conductivity as mentioned in the Eq. (2). These results can beclarified on the basis of the electrical conductivity data of thesesamples. The initial increase in the drift mobility with increase inthe temperature is due to the increase in the electrical conductivityin the temperature range which causes to increase the mobility ofthe charge carriers. The increase in drift mobility above transitiontemperature is due to the fact that the electrical conductivity fur-ther increases above this temperature and as a result the mobilityof charge carrier increases rapidly.

nd drift mobility and of Tb–Mn substituted hexaferrites, Sr2Co(2�x)MnxTbyFe(12�y)O22

) Z00 (X) ld (cm2 v�1 s�1) rAC (X cm)�1

62 577 3.3 � 10�12 1.3 � 10�4

41 677 4.1 � 10�13 1.2 � 10�4

71 770 1.44 � 10�13 1.1 � 10�4

63 778 5.4 � 10�14 9.7 � 10�5

63 879 2.1 � 10�14 8.1 � 10�5

32 941 2.5 � 10�15 4.1 � 10�5

14 16 18 20 22

0.0

5.0x10-2

1.0x10-1

1.5x10-1

2.0x10-1

2.5x10-1

3.0x10-1

13 14 15 16 17 18 19

0.0

5.0x10-4

1.0x10-3

1.5x10-3

2.0x10-3

2.5x10-3

3.0x10-3

x= 0.00 y=0.0 x=0.02 y= 0.2 x=0.04 y=0.4 x=0.06 y=0.6 x=0.08 y=0.8 x=0.10 y=1.0

σ ac(Ω

-cm

)-1

lnf (Hz)

σ ac(Ω

-cm

)-1

lnf (Hz)

Fig. 3. Variation in AC conductivity with frequency of (Tb–Mn) substitutedCo2Sr2Fe12O22 hexa ferrites at room temperature.

6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

x= 0.00 y=0.0 x=0.02 y= 0.2 x=0.04 y=0.4 x=0.06 y=0.6 x=0.08 y=0.8 x=0.10 y=1.0

Log

σ ac

Log (w)

Fig. 4. Variation in logr with logx of (Tb–Mn) substituted Co2Sr2Fe12O22 hexaferrites.

0.00E+0005.00E+0081.00E+0091.50E+0092.00E+0092.50E+0093.00E+009

-5.0x1030.0

5.0x1031.0x1041.5x1042.0x1042.5x1043.0x1043.5x1044.0x1044.5x1045.0x1045.5x1046.0x1046.5x1047.0x1047.5x1048.0x1048.5x104

0.0 5.0x108 1.0x109 1.5x109 2.0x109 2.5x109 3.0x1090

50100150200250300350400450500550600650

Ferequency (Hz)

x= 0.0 y=0.0 x=0.2 y= 0.02 x=0.4 y=0.04 x=0.6 y=0.06 x=0.8 y=0.08 x=1.0 y=0.1

Fig. 5. Variation of impedance with frequency of (Tb–Mn) substituted Co2Sr2Fe12-

O22 hexa ferrites at room temperature.

14 16 18 20 22

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28 x= 0.0 y=0.0 x=0.2 y=0.02 x=0.4 y=0.04 x=0.6 y=0.06 x=0.8 y=0.08 x=1.0 y=0.1

M′

lnf (Hz)

Fig. 6a. Variation in real part of electric modulus with frequency of (Tb–Mn)substituted Co2Sr2Fe12O22 hexa ferrites at room temperature.

14 16 18 20 220.000

0.005

0.010

0.015

0.020

0.025

0.030

x= 0.0 y=0.0 x=0.2 y=0.02 x=0.4 y=0.04 x=0.6 y=0.06 x=0.8 y=0.08 x=1.0 y=0.1

M′′

ln (Hz)

Fig. 6b. Variation in real part of electric modulus with frequency of (Tb–Mn)substituted Co2Sr2Fe12O22 hexa ferrites at room temperature.

I. Ali et al. / Journal of Alloys and Compounds 579 (2013) 576–582 579

3.3. AC conductivity

In our present experimental case Composition dependent ACconductivity varies from 10�4 to 10�5 (X cm)�1. Which is slightlyhigher than the already reported values 10�6–10�7 (X cm)�1 [27].Compositional dependent AC conductivity is listed in Table 2.The decrease in AC conductivity with increasing substitution levelmay be attributed to increase in impedance. It is observed that ACconductivity increases with increasing frequency of the appliedfield as shown in Fig. 3. Since the increase in frequency enhancesthe hopping of the charge carriers between Fe2+ and Fe3+, the con-ductivity increases. This behavior of ac conductivity can be ex-plained on the basis of Maxwell–Wagner model and Koop’sphenomenological theory. According to which the ferrites areimagined to act as a multilayer capacitor in which the ferrite sam-ples are characterized by a microstructure consisting of conductinggrains separated by highly resistive thin layers (grain boundaries).According to this model our results of ac conductivity at low fre-quencies describe the grain boundary behavior, while the disper-sion at high frequency may be attributed to the conductivity ofgrains [28]. At low frequencies, the low conductivity is clearlyobservable which is attributed to the blocking effects at grainboundaries [29] and moreover appearance of the plateau

0.080 0.088

0.010

0.012

0.014 x=0.0, y= 0.0

M′′

0.095 0.100

0.005

0.006

0.007

x=0.2, y= 0.02

0.115 0.120 0.125

0.005

0.006

0.007

0.008 x=0.4, y= 0.04

M′′

51.041.031.0

0.017

0.018

0.019

0.020

0.021

0.022 x=0.6, y= 0.06

0.15 0.16 0 .17

0.0175

0.0200

0.0225

0.0250

0.0275

x=0.8, y= 0.08

M′′

M ′ M ′

M ′ M ′

M ′ M ′

0.24 0.27

0.016

0.020

0.024

0.028 x=1.0, y= 0.10

M′′

M′′

M′′

Fig. 7. Cole–cole plots of (Tb–Mn) substituted Co2Sr2Fe12O22 hexa ferrites at room temperature.

580 I. Ali et al. / Journal of Alloys and Compounds 579 (2013) 576–582

appearing at low frequencies is also due to the grain boundary con-tribution to the total conductivity, comparatively high values of theAC conductivity observed at higher frequencies is due to the bulkcontribution [29].

The dependence of the AC conductivity on frequency can be ex-pressed by the following equation [30]:

rtotðxÞ ¼ rDC þ Axn ð10Þ

where A is a pre-exponential factor has the units of electrical con-ductivity and n is the frequency exponent is dimensionless, which

generally is less than or equal to one. When n = 0, the electrical con-duction is frequency independent or dc conduction and for n 6 1,the conduction is frequency dependent or AC conduction [31]. Thisvalue of n is used to explain the conduction mechanism operative inthe studied samples. The hopping of electron between Fe2+/Fe3+

ions is responsible for conduction mechanism in ferrites. The valueof exponent ‘n’ was extracted from the slope of log(r) versus log(x).Fig. 4 shows plot of log(r) versus log(x) and values are listed Table 1showing variation of exponent ‘n’ with composition. In the presentstudy, the value of exponent varies between 0.81 and 0.97, suggest-

I. Ali et al. / Journal of Alloys and Compounds 579 (2013) 576–582 581

ing that the conduction phenomena in the studied samples followhopping conduction.

For ions vibrating in their cages and hopping to immediate sitesthrough barriers of energy EAC will fallow the following equation.

s0ðTÞ ¼ s1 expðEAC=kTÞ ð11Þ

where s1 the reciprocal of the attempt frequency of ions and s0 therelaxation time for autonomous ion-hopping. Commonly the energybarrier (Ac activation energy) will be lesser than the activation en-ergy for the dc conductivity and given by the relation.

Edc ¼ EAC=ð1� nÞ ð12Þ

The higher values of ‘‘n’’ actually indicate the higher degree ofcooperativity in the ion-hopping process which is mainly due tothe increase of interactions among the mobile oxygen ions[32,33]. In fact, by using the experimental values obtained for EDC

and n, the activation energy EAC for the barrier that oxygen ionsmust overcome to hop (independently) between neighboring va-cant sites in the Mn–Tb substituted Sr2Co2Fe12O22 ferrites, can thusbe estimated according to Eq. (12). A value EAC is found, dependentof Mn–Tb –contents and listed in Table 1. Higher degree of struc-tural disorder is produced due to high rare earth-contents [29]which is accredited to the difference in size of dopant and host ionsat various hexagonal conduction sites. An enhanced ion–ion inter-action are expected and subsequently higher values of the expo-nent n. Higher the value of n increase the energy penalty thatthese correlations impose on long-range or dc ionic conductivity.This clarifies the increasing difference found between Edc and EAC.

4000

3.4. Impedance analysis

3.4.1. ImpedanceFig. 5 and inset show the variation of the impedance (Z) with

frequency and follow the equation:

jZj ¼ Z0 þ jZ00 ð13Þ

Z0 and Z00 are real and imaginary parts of the impedance respec-tively. The values of Z0 and Z00 at 1 MHz are listed in Table 2. It hasbeen observed that values of impedance and its components in-crease with (Tb–Mn) substitution which is inconsistent with com-positional dependence of AC conductivity, i.e. increase inimpedance results in decrease AC conductivity. It is found that,the magnitude of Z decreases with the increase of frequency indi-cating increase in AC conductivity. It also indicates the semicon-ducting type behavior in these systems.

0.0 5.0x108 1.0x109 1.5x109 2.0x109 2.5x109 3.0x1090

500

1000

1500

2000

2500

3000

3500

x= 0.0 y=0.0 x=0.2 y= 0.02 x=0.4 y=0.04 x=0.6 y=0.06 x=0.8 y=0.08 x=1.0 y=0.1

Q fa

ctor

Frequency HZ

Fig. 8. Variation of Q values with frequency of (Tb–Mn) substituted Co2Sr2Fe12O22

hexa ferrites.

3.4.2. Nyqiust plot (cole–cole plot)The impedance spectroscopy is extensively used to describe the

electrical properties of materials and interfaces present in thesematerials. The impedance measurements data gives both resistive(real) and reactive (imaginary) components of a material. It can bedemonstrated in terms of any of the four complex variables, per-mittivity (e�), admittance (Y�), impedance (Z�), electric modulus(M�) and dielectric loss (tand) in a complex plane plot (Nyqiustplot).Their relation to one another is as follows [34,35]:

tan d ¼ e00=e0 ¼ Y 00=Y 0 ¼ Z00=Z0 ¼ M00=M0 ð14Þ

In the present case Nyqiust plot of Complex electric modulusare plotted which is a power ful technique to study relaxation phe-nomenon (i.e. contribution of bulk, grain boundary and materialelectrode interface effect) in the material. Moreover, It helps indetermining inter particle interactions like grains, grain bound-aries. In order to study the frequency dependences of the interfa-

cial polarization effect, electrical modulus (M) can be used whichgenerates electric charge accumulation around the ceramic parti-cles by displacing relaxation peaks.

M ¼ 1=e� ¼ 1=ðe0 � je00Þ ¼ M0 � jM00 ð15Þ

Figs. 6a and 6b show the variation of both real and imaginaryparts of electric modulus against frequency. The Maxwell–Wagnermodel provides information for the behavior of complex conduc-tivity in heterogeneous systems with two or more phases [36]. Ina heterogeneous system, in the first case if the region of continuityof the grain boundary occupies a small volume, the spectrum ofimpedance (Z00 versus Z0) provides better visualization of the semicircles in the plane. There is a probable relationship between thebehavior of grain boundary, and the appearance of the peaks ofZ00 as functions of frequency, in second case if the region of grainboundary occupies a large volume, the graph of the modulus(M� = 1/e�) M00 versus M0, provides better information about thesemicircles, suggesting that there is a probable relationship be-tween the behavior of grain boundary and the appearance of thepeaks of M00 as a function of frequency [37] second case is in greatagreement. The values of M0 and M00 are calculated for the Tb–Mndoped samples and listed in Table 2. These values of both realand imaginary part of the electric modulus varies from6.1 � 10�2 to 1.5 � 10�1 and 8 � 10�3 to 1.7 � 10�2, respectively.These values are comparable with already reported values for Y-type hexaferrites [38].

Fig. 7 shows the complex impedance (Cole–Cole) plots of the(Mn–Tb) substituted Sr2Co2Fe12O22 ferrites. The left end (lower fre-quency) of the semicircle stands for the grain resistance [39] whilethat at intermediate frequencies represents grain boundary contri-bution [40] and the right one (higher frequency) stands for thewhole resistance of the grains and grain boundaries [39]. Substitu-tion makes comparatively small difference on the grain resistance,but leads to a remarkable rise of grain boundary resistance. Higherthe Tb contents the higher the grain boundary resistance. The dom-inant conduction mechanism in ferrites is the hopping mechanism,which is an easy electron transfer between Fe2+ and Fe3+. Increas-ing substitution level of Tb at the expanse of Fe will restrain theelectron transfer between Fe2+ and Fe3+ Thus, the resistivity of fer-rite changes with the grain boundary content and composition.Obviously the Tb substitution effects the grain boundary resis-tance. High resistance regions are formed at grain boundaries toimpede conductivity. The high resistance of the grain boundarywill determine the resistivity and dielectric properties.

582 I. Ali et al. / Journal of Alloys and Compounds 579 (2013) 576–582

3.4.3. Quality factorFig. 8 shows the variation of Q values with frequency for Tb–Mn

substituted Co2Sr2Fe12O22 ferrites. The maximum values of qualityfactor occurred above the 2 GHz frequency and the Q values werefound quite high. This high Q values and a resonance frequencyabove 2 GHz, clearly suggest that these materials can be used inhigh frequency multilayer chip inductors [41].

4. Conclusions

Single phase nanostructured Tb–Mn substituted Y-type hexa-ferrites with nominal composition Sr2Co2�xMnxTbyFe12�yO22

(x = 0.0–1, Y = 0.0–0.1) were synthesized by the microemulsion. Ithas been observed that samples having high conductivity havelow activation energy. The variation in exponent n found to becomposition dependent and varies from 0.81 to 0.97 which con-firms that the conduction is due to hopping of charges. The fre-quency dependent AC conductivity was explained on the basis ofMaxwell–Wagner model and Koop’s phenomenological theory.The presence of Debye peaks in imaginary electric modulus versusfrequency curves confirms the existence of relaxation phenomenain the given frequency range The substitution of Tb–Mn plays animportant role to modify the electrical and dielectric propertiesof Sr2Co2�xMnxTbyFe12�yO22 ferrites especially high values of qual-ity factor are obtained required for power applications and highfrequency multilayer chip inductors.

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