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Studies on the activation energy from the ac conductivity measurements of rubber ferrite composites containing manganese zinc ferrite
Physica B 407 (2012) 4097–4103
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Studies on the activation energy from the ac conductivity measurements of rubber ferrite composites containing manganese zinc ferrite Mohd. Hashim a,n, Alimuddin a, Shalendra Kumar b, Sagar E. Shirsath c, E.M. Mohammed d, Hanshik Chung e, Ravi Kumar f a
Department of Applied Physics, Aligarh Muslim University, Aligarh 202002, UP, India Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea c Spin Device Technology Center, Faculty of Engineering, Shinshu University, Nagano, Japan d Department of Physics, Maharajas College, Ernakulam 682011, Kerala, India e Department of Mechanical and Precision Engineering and The Institute of Marine Industry, Gyeongsang National University, Tongyeong 650-160, Republic of Korea f Centre for Material Science Engineering, National Institute of Technology, Hamirpur, HP, India b
a r t i c l e i n f o
abstract
Article history: Received 19 January 2012 Received in revised form 1 June 2012 Accepted 2 June 2012 Available online 21 June 2012
Manganese zinc ferrites (MZF) have resistivities between 0.01 and 10 O m. Making composite materials of ferrites with either natural rubber or plastics will modify the electrical properties of ferrites. The moldability and flexibility of these composites find wide use in industrial and other scientific applications. Mixed ferrites belonging to the series Mn(1 x)ZnxFe2O4 were synthesized for different ‘x’ values in steps of 0.2, and incorporated in natural rubber matrix (RFC). From the dielectric measurements of the ceramic manganese zinc ferrite and rubber ferrite composites, ac conductivity and activation energy were evaluated. A program was developed with the aid of the LabVIEW package to automate the measurements. The ac conductivity of RFC was then correlated with that of the magnetic filler and matrix by a mixture equation which helps to tailor properties of these composites. & 2012 Elsevier B.V. All rights reserved.
Keywords: Magnetic materials Rubber ferrite composites Activation energy AC conductivity Polymer Electrical properties
1. Introduction Ferrites are one of the most useful magnetic material ever discovered, which finds a wide range of technological applications. Ferrites in the ceramic form find applications in various devices like transformer cores, magnetic memories, isolators, noise filters, TV yokes etc. [1–4]. Rubber ferrite composites (RFC) are increasingly used as microwave absorbers and in other devices where flexibility and moldability are the important criteria. Manganese–zinc ferrite (MZF) are used in many electronic devices because of their high permeability, low eddy current loss and moderate resistivity [5,6]. From both the application point of view and the fundamental point of view the electrical properties are important for ferrites and composites containing mixed ferrites. Electrical properties namely ac conductivity and activation energy for conduction reveal a wealth of information regarding the usefulness of these materials for various applications. Moreover the study of ac electrical conductivity sheds light on the mobility and activation of charge carriers in these
n
Corresponding author. Tel.: þ91 9359380185. E-mail address: [email protected] (Mohd. Hashim).
0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2012.06.006
materials under an ac field [7]. Though literature on the ac conductivity [8] of ceramic ferrite fillers exists, data on rubber ferrite composites are rather scarce. Hence studies on ac
Fig. 1. SEM image of RFC sample with Mn0.6Zn0.4Fe2O4.
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Fig. 2. Variation of log F (F in Hz) with ln sac (sac in S/m) of MZF.
Fig. 3. (A) Variation of log F (F in Hz) with ln sac (sac in S/m) of RFC. (B) Variation of log F (F in Hz) with ln sac (sac in S/m) of blank NR.
Mohd. Hashim et al. / Physica B 407 (2012) 4097–4103
conductivity and activation energy of RFC and the correlation with that of the corresponding fillers have significance. The incorporation of mixed ferrites namely MZF in various matrices enable one to prepare RFC [9]. RFC can easily be molded into any complex shapes. A specific recipe is used for the incorporation of ferrites in natural rubber matrix. Microwave absorption property make them useful in the construction of microwave absorbers [10,11]. Keeping all above important facts in mind, it is very necessary to study MZF materials for their extensive use in various applications. Therefore, in this study we have made an attempt to carry out systematic study of MZF/RFC by evaluating ac conductivity and dielectric properties.
2. Experimental 2.1. Sample preparation and structural characterization Mixed ferrites containing manganese and zinc belonging to the series Mn(1 x)ZnxFe2O4 for various x (0rx r1 in steps of 0.2) were prepared by employing ceramic techniques. These precharacterized powder samples were then dispersed in a natural rubber matrix. The loading of the magnetic filler was changed in steps of 30 parts per hundred grams of rubber (phr) up to 120 phr according to a specific recipe. SEM images were taken to carry out the study related to surface morphology of the prepared samples. 2.2. ac conductivity evaluation from dielectric measurements
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of 0.5–2000 mS/m. For RFC samples conductivity reduces by one order of magnitude and for natural rubber samples this reduces by an order of two. In manganese zinc ferrites the conduction mechanism is either due to the hopping of charge carriers between Fe2 þ and Fe3 þ ions or Mn3 þ and Mn2 þ ions. As the frequency of the applied field increases, hopping of carriers also increases, thereby increasing the conductivity. But at higher frequencies the hopping of the charge carriers could not follow the applied field frequency. The observed increase in the ac conductivity (upto 4 MHz) can be explained with the help of Eq. (2). The decrease in conductivity at high frequencies may be due to the lagging in hopping of the charge carriers with the applied field frequency. These changes are clearly depicted in Fig. 2. From Fig. 2 it can be seen that for x¼0.2 the lagging of ac conductivity above 4 MHz is noticeable as compared to other compositions [14]. The frequency dependence of the conductivity can also be explained with the help of the Maxwell–Wagner two layer model and the heterogeneous model of the polycrystalline structure of ferrites [15]. At low frequencies the ac conductivity is related to the resistive grain boundaries and at high frequencies the ac conductivity is due to the conductive grains. The ac conductivity of such a system is related to the dielectric permittivity by the equation e00 ¼(g g0 )/e0 o, where e0 and e00 are the real and imaginary parts of the dielectric permittivity, g and g0 are the ac and dc conductivities respectively, and o is the angular frequency. The frequency dependence of ac conductivity is almost the same for rubber ferrite composites containing different loadings of the filler (Fig. 3). Pure natural rubber (NR) also shows the same
The dielectric studies of both the ceramic MZF and RFC were carried out by using a homemade dielectric cell [12] and an impedance analyzer. Ceramic samples are made into pellets of 10 mm diameter and 2 mm thickness using a hydraulic press by applying pressure of 4–10 ton/in2. RFC samples having same dimensions were cut from molded sheets. Thickness of the pellets was measured using precession screw gage. The capacitance (C) and dielectric loss (tan d) are measured in the frequency range from 100 kHz to 8 MHz. Dielectric constant (er) was calculated using the following formula:
er ¼
Cd
e0 A
ð1Þ
where d is the thickness of the sample, C is the measured capacitance, A is the area of cross section of the sample pellet and e0 is the dielectric permittivity of the free space. Ac conductivity [13] was calculated from the values of er and tan d for both the ceramic and RFC samples using the relation
sac ¼ 2pf e0 er tand
ð2Þ
where f is the frequency of the applied voltage. The loss factor tan d and permittivity were measured using the impedance analyzer HP-4285A. From these values ac conductivity was calculated with the help of a virtual instrument package called LabVIEW.
3. Results and discussions SEM image of RFC sample with Mn0.6Zn0.4Fe2O4 was taken. It was observed that the approximate particle size of the ferrite particles is in the range of 250–500 nm (Fig. 1). 3.1. Frequency dependence In the case of manganese zinc ferrites, for all the compositions it was found that the ac conductivity increases with increase of frequency. The ac conductivity of the ceramic MZF lies in the range
Fig. 4. Variation of composition (x) vs. sac (sac in S/m) of MZF at 100 kHz and 2 MHz.
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trend for conductivity. It may be noted that the behavior of RFC resembles that of pure NR as far as the variation of ac conductivity with frequency is concerned. However, the absolute value of the ac conductivity of RFC gets modified in accordance with a weighted behavior corresponding to the amount of the filler in the matrix.
3.2. Compositional dependence
Fig. 5. Variation of porosity with composition (MZF).
It was found that the ac electrical conductivity initially decreases with increase of zinc content and reaches a minimum value at around x ¼0.4, and thereafter it increases with increase of zinc content. The change in conductivity with composition is plotted and is shown in Fig. 4. The variation of conductivity with composition for ceramic samples can be explained by considering the porosity of the material. El Hiti has reported on dc
Fig. 6. Variation of composition (x) vs. sac (sac in S/m) for different temperatures of RFC for 100 kHz and 2 MHz.
Fig. 7. Plots of loading vs. ln sac (sac in S/m) of RFC for x¼ 0.0, 0.4, 0.6 and 1.0.
Mohd. Hashim et al. / Physica B 407 (2012) 4097–4103
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conductivity variation with temperature, composition and porosity of mixed ferrite samples [7,8]. The porosity of ceramic manganese zinc samples for all compositions was calculated and it was found that initially, the porosity increases with increase of zinc content and shows a maximum value for x¼0.4 (Fig. 5). Thereafter the porosity decreases with increase of zinc content. This explains the compositional dependence of ac electrical conductivity in ceramic manganese zinc ferrite system. For rubber ferrite composites also the same variation is observed for all loadings. The variation pattern is plotted and representative graphs are shown in Fig. 6. 3.3. Loading dependence The addition of magnetic filler into a rubber matrix will impart the bulk conductivity to the polymer depending on the filler conductivity. An increase in conductivity for RFC is observed with increase of the volume fraction of the filler. The maximum conductivity is observed for the higher volume fraction of 120 phr. The ac conductivity has been evaluated for frequencies from 75 kHz upto 8 MHz and only representative graphs are included here (Fig. 7). For lower loadings of the filler, the conductivity of the matrix was affected by three parameters namely the intrinsic conductivity of the filler, the shape of the filler and also the surface tension of the matrix and the filler [16]. Percolation limits will be low for fibrous fillers whereas it is high for irregular shaped fillers, since the fibrous fillers will afford many more inter particle contacts. MZF particles crystallize in spherical shape. This is the reason for not observing drastic changes but only marginal changes in the conductivity for higher volume fraction of the filler [17]. The effect of adding filler modifies the ac conductivity of RFC only up to 30–40 phr as evident from Fig. 7. Porosity is the predominant factor in determining the percolation threshold as far as ac conductivity is concerned. Once the porous fillers are occupied by available rubber, no more ‘structure’ is available for further interaction. This has parallels as far as the reinforcing properties of carbon black in natural rubber are concerned where the tensile strength is limited because of its ‘structure’. A clear picture will emerge only on subjecting the sample surface to morphological studies. This has not been carried out in the present study. 3.4. Temperature dependence The temperature dependence is studied in the range of 303–393 K for different frequencies for all the samples. It was observed that the conductivity increases with increase of temperature. The variation pattern of conductivity with temperature for different compositions is shown in Fig. 8. The variation observed is also same for the rubber ferrite composites. The dependence is depicted in Fig. 9. The ac electrical conductivities of pure natural rubber were also studied for different temperatures and plotted as shown in Fig. 10. For natural rubber the conductivity decreases with temperature. 3.5. Activation energy From the slope of the graphs, the activation energy of conduction was estimated using the relation Es ð3Þ sac ¼ s0 exp kT where s0 is a constant, Es is the activation energy, k is Boltzmann’s constant and T is the absolute temperature. The activation energy for conduction was calculated for both ceramic and composite
Fig. 8. Variation of 1000/T with ln sac (sac in S/m) of MZF at 100 kHz and 2 MHz.
samples. Representative graphs are shown in Figs. 11 and 12 for different loadings of the filler and for different compositions of MZF. For the ceramic samples the variation in activation energy with composition is almost opposing when compared with the ac conductivity variation. The activation energy of the ceramic MZF increases initially with the zinc content and reaches a maximum at x¼0.4 as shown in Fig. 10, whereas the conductivity shows a minimum for this composition as shown in Fig. 3. Ravinder and Latha have reported the activation energy of ceramic samples of MZF series in the paramagnetic and ferromagnetic regions and evaluated the change in activation energy (DE). The reported DE values for MnFe2O4 and Mn0.2Zn0.8Fe2O4 are 0.42 eV and 0.27 eV respectively [18,19]. In the case of RFC samples with different loadings of the filler, the change in activation energy with composition is not noticeable. But the activation energy for conduction required by the composite samples is less than the activation energy required for the filler. The low conductivity in polymers, even with their low activation energies can be attributed to the low mobility of carriers in the polymer. Further, activation energy in these materials are very sensitive to the impurities, their crystal qualities etc. In MZF it is known fact that Zn ions occupy tetrahedral A-site, so they push some of the Fe3 þ ions to
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Fig. 9. (A) Plots of 1000/T vs. ln sac (sac in S/m) of RFC for x ¼ 0.0, 0.2 and 0.4. (B) Plots of 1000/T vs. ln sac (sac in S/m) of RFC for x¼ 0.6, 0.8 and 1.0.
Fig. 11. Variation of activation energy with loading of RFC at 1 MHz. Fig. 10. Variation of ln sac in S/m with 1000/T of blank NR.
octahedral B-site. As the Fe3 þ ions increases at B-site, there is more possibility of hopping between Fe3 þ and Fe2 þ ions. As the hopping possibility increases conductivity increases, results in decrease in resistivity and activation energy. There are reports that the activation energy for conduction of inorganic semiconductor is higher than the corresponding activation energy of conduction of polymeric semiconductors. For example, for germanium, with conductivity 0.1–0.01 S/cm, the activation energy for conduction is about 0.6 eV and for an
organic semiconductor with the same conductivity, the activation energy of conduction is between 0.1 and 0.03 eV. These factors may account for the low activation energy and low conductivity displayed by composite samples [20].
4. Conclusions Increase in conductivity with increase in frequency for both ceramic and rubber ferrite composites are observed. Porosity of
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Acknowledgements Financial assistance from U.G.C. is acknowledged by Mohd. Hashim through grant No. MANF-MUS-UTT-1092. This work is also supported by BK21 project corp.
References
Fig. 12. Variation of activation energy with composition at 1 MHz.
the ceramic samples affects the ac electrical conductivity and causes variation in ac electrical conductivity with zinc substitution. All the samples show that the conductivity with volume fraction of the magnetic filler shows a continuous increase up to a loading of 30–40 phr and thereafter flattens off. Hopping probabilities between Fe3 þ and Fe2 þ affect the activation and changes with zinc content. Temperature variations carried out on MZF samples were limited to 425 K since it was intended for RFCs. This is because RFCs thermally degrade at around 425 K. The leveling of ac conductivity at 30–40 phr (sac vs. log F) can be attributed to the available pore sites.
[1] A. Goldman, Modern Ferrite Technology, 2nd ed., Springer, New York, 2006. [2] B.D. Cullity, Introduction to Magnetic Materials, Addison-Wesley, London, 1972. [3] Sagar E. Shirsath, R.H. Kadam, S.M. Patange, M.L. Mane, Ali Ghasemi, Akimitsu Morisako, Appl. Phys. Lett. 100 (2012) 042407. [4] A. Narayanaswamy, N. Sivakumar, Bull. Mater. Sci. 31 (2008) 373. [5] P.J.B. Clarricoats, Microwave Ferrites, Chapman & Hall, London, 1961. [6] H. Waqas, A.H. Qureshi, K. Subhan, M. Shahzad, Ceramics 38 (2012) 1235. [7] M.A. El Hiti, J. Magn. Magn. Mater. 192 (1996) 305. [8] M.A. El Hiti, J. Magn. Magn. Mater. 164 (1996) 187. [9] E.M. Mohammed, K.A. Malini, Philip Kurian, M.R. Anantharaman, Mater. Res. Bull. 37 (2002) 753. [10] Adriana M. Gama, Mirabel C. Rezende, Christine C. Dantas, J. Magn. Magn. Mater. 323 (2011) 2782. [11] S. Bakhtiari, S.I. Ganchev, R Zoughi, IEEE Trans. 42 (1994) 1261. [12] E.M. Mohammed, M.R. Anantharaman, J. Instrum. Soc. India 32 (2002) 165. [13] S. Sindhu, M.R. Anantharaman, Bindu P. Thampi, K.A. Malini, Philip Kurian, Bull. Mater. Sci. 25 (2002) 599. [14] M.A. El Hiti, J. Phys. D: Appl. Phys. 29 (1996) 501. [15] C.G. Koops, Phys. Rev. 83 (1951) 121. [16] Terje A. Skotheim, Handbook of Conducting Polymers, vols. I–II, Marcel Dekker Inc., New York, USA, 1986. [17] M.R. Anantharaman, S. Sindhu, S. Jagatheesan, K.A. Malini, P. Kurian, J. Phys. D: Appl. Phys. 32 (1999) 1801. [18] Gerad Kraus, Reinforcement of Elastomers, John Wiley & Sons, New York, 1970. [19] K. Latha, D. Ravinder, Phys. Stat. Sol. a 139 (1993) K109. [20] David Jiles, Magnetism and Magnetic Materials, , 1990.
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Studies on the activation energy from the ac conductivity measurements of rubber ferrite composites containing manganese zinc ferrite Mohd. Hashim a,n, Alimuddin a, Shalendra Kumar b, Sagar E. Shirsath c, E.M. Mohammed d, Hanshik Chung e, Ravi Kumar f a
Department of Applied Physics, Aligarh Muslim University, Aligarh 202002, UP, India Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea c Spin Device Technology Center, Faculty of Engineering, Shinshu University, Nagano, Japan d Department of Physics, Maharajas College, Ernakulam 682011, Kerala, India e Department of Mechanical and Precision Engineering and The Institute of Marine Industry, Gyeongsang National University, Tongyeong 650-160, Republic of Korea f Centre for Material Science Engineering, National Institute of Technology, Hamirpur, HP, India b
a r t i c l e i n f o
abstract
Article history: Received 19 January 2012 Received in revised form 1 June 2012 Accepted 2 June 2012 Available online 21 June 2012
Manganese zinc ferrites (MZF) have resistivities between 0.01 and 10 O m. Making composite materials of ferrites with either natural rubber or plastics will modify the electrical properties of ferrites. The moldability and flexibility of these composites find wide use in industrial and other scientific applications. Mixed ferrites belonging to the series Mn(1 x)ZnxFe2O4 were synthesized for different ‘x’ values in steps of 0.2, and incorporated in natural rubber matrix (RFC). From the dielectric measurements of the ceramic manganese zinc ferrite and rubber ferrite composites, ac conductivity and activation energy were evaluated. A program was developed with the aid of the LabVIEW package to automate the measurements. The ac conductivity of RFC was then correlated with that of the magnetic filler and matrix by a mixture equation which helps to tailor properties of these composites. & 2012 Elsevier B.V. All rights reserved.
Keywords: Magnetic materials Rubber ferrite composites Activation energy AC conductivity Polymer Electrical properties
1. Introduction Ferrites are one of the most useful magnetic material ever discovered, which finds a wide range of technological applications. Ferrites in the ceramic form find applications in various devices like transformer cores, magnetic memories, isolators, noise filters, TV yokes etc. [1–4]. Rubber ferrite composites (RFC) are increasingly used as microwave absorbers and in other devices where flexibility and moldability are the important criteria. Manganese–zinc ferrite (MZF) are used in many electronic devices because of their high permeability, low eddy current loss and moderate resistivity [5,6]. From both the application point of view and the fundamental point of view the electrical properties are important for ferrites and composites containing mixed ferrites. Electrical properties namely ac conductivity and activation energy for conduction reveal a wealth of information regarding the usefulness of these materials for various applications. Moreover the study of ac electrical conductivity sheds light on the mobility and activation of charge carriers in these
n
Corresponding author. Tel.: þ91 9359380185. E-mail address: [email protected] (Mohd. Hashim).
0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2012.06.006
materials under an ac field [7]. Though literature on the ac conductivity [8] of ceramic ferrite fillers exists, data on rubber ferrite composites are rather scarce. Hence studies on ac
Fig. 1. SEM image of RFC sample with Mn0.6Zn0.4Fe2O4.
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Mohd. Hashim et al. / Physica B 407 (2012) 4097–4103
Fig. 2. Variation of log F (F in Hz) with ln sac (sac in S/m) of MZF.
Fig. 3. (A) Variation of log F (F in Hz) with ln sac (sac in S/m) of RFC. (B) Variation of log F (F in Hz) with ln sac (sac in S/m) of blank NR.
Mohd. Hashim et al. / Physica B 407 (2012) 4097–4103
conductivity and activation energy of RFC and the correlation with that of the corresponding fillers have significance. The incorporation of mixed ferrites namely MZF in various matrices enable one to prepare RFC [9]. RFC can easily be molded into any complex shapes. A specific recipe is used for the incorporation of ferrites in natural rubber matrix. Microwave absorption property make them useful in the construction of microwave absorbers [10,11]. Keeping all above important facts in mind, it is very necessary to study MZF materials for their extensive use in various applications. Therefore, in this study we have made an attempt to carry out systematic study of MZF/RFC by evaluating ac conductivity and dielectric properties.
2. Experimental 2.1. Sample preparation and structural characterization Mixed ferrites containing manganese and zinc belonging to the series Mn(1 x)ZnxFe2O4 for various x (0rx r1 in steps of 0.2) were prepared by employing ceramic techniques. These precharacterized powder samples were then dispersed in a natural rubber matrix. The loading of the magnetic filler was changed in steps of 30 parts per hundred grams of rubber (phr) up to 120 phr according to a specific recipe. SEM images were taken to carry out the study related to surface morphology of the prepared samples. 2.2. ac conductivity evaluation from dielectric measurements
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of 0.5–2000 mS/m. For RFC samples conductivity reduces by one order of magnitude and for natural rubber samples this reduces by an order of two. In manganese zinc ferrites the conduction mechanism is either due to the hopping of charge carriers between Fe2 þ and Fe3 þ ions or Mn3 þ and Mn2 þ ions. As the frequency of the applied field increases, hopping of carriers also increases, thereby increasing the conductivity. But at higher frequencies the hopping of the charge carriers could not follow the applied field frequency. The observed increase in the ac conductivity (upto 4 MHz) can be explained with the help of Eq. (2). The decrease in conductivity at high frequencies may be due to the lagging in hopping of the charge carriers with the applied field frequency. These changes are clearly depicted in Fig. 2. From Fig. 2 it can be seen that for x¼0.2 the lagging of ac conductivity above 4 MHz is noticeable as compared to other compositions [14]. The frequency dependence of the conductivity can also be explained with the help of the Maxwell–Wagner two layer model and the heterogeneous model of the polycrystalline structure of ferrites [15]. At low frequencies the ac conductivity is related to the resistive grain boundaries and at high frequencies the ac conductivity is due to the conductive grains. The ac conductivity of such a system is related to the dielectric permittivity by the equation e00 ¼(g g0 )/e0 o, where e0 and e00 are the real and imaginary parts of the dielectric permittivity, g and g0 are the ac and dc conductivities respectively, and o is the angular frequency. The frequency dependence of ac conductivity is almost the same for rubber ferrite composites containing different loadings of the filler (Fig. 3). Pure natural rubber (NR) also shows the same
The dielectric studies of both the ceramic MZF and RFC were carried out by using a homemade dielectric cell [12] and an impedance analyzer. Ceramic samples are made into pellets of 10 mm diameter and 2 mm thickness using a hydraulic press by applying pressure of 4–10 ton/in2. RFC samples having same dimensions were cut from molded sheets. Thickness of the pellets was measured using precession screw gage. The capacitance (C) and dielectric loss (tan d) are measured in the frequency range from 100 kHz to 8 MHz. Dielectric constant (er) was calculated using the following formula:
er ¼
Cd
e0 A
ð1Þ
where d is the thickness of the sample, C is the measured capacitance, A is the area of cross section of the sample pellet and e0 is the dielectric permittivity of the free space. Ac conductivity [13] was calculated from the values of er and tan d for both the ceramic and RFC samples using the relation
sac ¼ 2pf e0 er tand
ð2Þ
where f is the frequency of the applied voltage. The loss factor tan d and permittivity were measured using the impedance analyzer HP-4285A. From these values ac conductivity was calculated with the help of a virtual instrument package called LabVIEW.
3. Results and discussions SEM image of RFC sample with Mn0.6Zn0.4Fe2O4 was taken. It was observed that the approximate particle size of the ferrite particles is in the range of 250–500 nm (Fig. 1). 3.1. Frequency dependence In the case of manganese zinc ferrites, for all the compositions it was found that the ac conductivity increases with increase of frequency. The ac conductivity of the ceramic MZF lies in the range
Fig. 4. Variation of composition (x) vs. sac (sac in S/m) of MZF at 100 kHz and 2 MHz.
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trend for conductivity. It may be noted that the behavior of RFC resembles that of pure NR as far as the variation of ac conductivity with frequency is concerned. However, the absolute value of the ac conductivity of RFC gets modified in accordance with a weighted behavior corresponding to the amount of the filler in the matrix.
3.2. Compositional dependence
Fig. 5. Variation of porosity with composition (MZF).
It was found that the ac electrical conductivity initially decreases with increase of zinc content and reaches a minimum value at around x ¼0.4, and thereafter it increases with increase of zinc content. The change in conductivity with composition is plotted and is shown in Fig. 4. The variation of conductivity with composition for ceramic samples can be explained by considering the porosity of the material. El Hiti has reported on dc
Fig. 6. Variation of composition (x) vs. sac (sac in S/m) for different temperatures of RFC for 100 kHz and 2 MHz.
Fig. 7. Plots of loading vs. ln sac (sac in S/m) of RFC for x¼ 0.0, 0.4, 0.6 and 1.0.
Mohd. Hashim et al. / Physica B 407 (2012) 4097–4103
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conductivity variation with temperature, composition and porosity of mixed ferrite samples [7,8]. The porosity of ceramic manganese zinc samples for all compositions was calculated and it was found that initially, the porosity increases with increase of zinc content and shows a maximum value for x¼0.4 (Fig. 5). Thereafter the porosity decreases with increase of zinc content. This explains the compositional dependence of ac electrical conductivity in ceramic manganese zinc ferrite system. For rubber ferrite composites also the same variation is observed for all loadings. The variation pattern is plotted and representative graphs are shown in Fig. 6. 3.3. Loading dependence The addition of magnetic filler into a rubber matrix will impart the bulk conductivity to the polymer depending on the filler conductivity. An increase in conductivity for RFC is observed with increase of the volume fraction of the filler. The maximum conductivity is observed for the higher volume fraction of 120 phr. The ac conductivity has been evaluated for frequencies from 75 kHz upto 8 MHz and only representative graphs are included here (Fig. 7). For lower loadings of the filler, the conductivity of the matrix was affected by three parameters namely the intrinsic conductivity of the filler, the shape of the filler and also the surface tension of the matrix and the filler [16]. Percolation limits will be low for fibrous fillers whereas it is high for irregular shaped fillers, since the fibrous fillers will afford many more inter particle contacts. MZF particles crystallize in spherical shape. This is the reason for not observing drastic changes but only marginal changes in the conductivity for higher volume fraction of the filler [17]. The effect of adding filler modifies the ac conductivity of RFC only up to 30–40 phr as evident from Fig. 7. Porosity is the predominant factor in determining the percolation threshold as far as ac conductivity is concerned. Once the porous fillers are occupied by available rubber, no more ‘structure’ is available for further interaction. This has parallels as far as the reinforcing properties of carbon black in natural rubber are concerned where the tensile strength is limited because of its ‘structure’. A clear picture will emerge only on subjecting the sample surface to morphological studies. This has not been carried out in the present study. 3.4. Temperature dependence The temperature dependence is studied in the range of 303–393 K for different frequencies for all the samples. It was observed that the conductivity increases with increase of temperature. The variation pattern of conductivity with temperature for different compositions is shown in Fig. 8. The variation observed is also same for the rubber ferrite composites. The dependence is depicted in Fig. 9. The ac electrical conductivities of pure natural rubber were also studied for different temperatures and plotted as shown in Fig. 10. For natural rubber the conductivity decreases with temperature. 3.5. Activation energy From the slope of the graphs, the activation energy of conduction was estimated using the relation Es ð3Þ sac ¼ s0 exp kT where s0 is a constant, Es is the activation energy, k is Boltzmann’s constant and T is the absolute temperature. The activation energy for conduction was calculated for both ceramic and composite
Fig. 8. Variation of 1000/T with ln sac (sac in S/m) of MZF at 100 kHz and 2 MHz.
samples. Representative graphs are shown in Figs. 11 and 12 for different loadings of the filler and for different compositions of MZF. For the ceramic samples the variation in activation energy with composition is almost opposing when compared with the ac conductivity variation. The activation energy of the ceramic MZF increases initially with the zinc content and reaches a maximum at x¼0.4 as shown in Fig. 10, whereas the conductivity shows a minimum for this composition as shown in Fig. 3. Ravinder and Latha have reported the activation energy of ceramic samples of MZF series in the paramagnetic and ferromagnetic regions and evaluated the change in activation energy (DE). The reported DE values for MnFe2O4 and Mn0.2Zn0.8Fe2O4 are 0.42 eV and 0.27 eV respectively [18,19]. In the case of RFC samples with different loadings of the filler, the change in activation energy with composition is not noticeable. But the activation energy for conduction required by the composite samples is less than the activation energy required for the filler. The low conductivity in polymers, even with their low activation energies can be attributed to the low mobility of carriers in the polymer. Further, activation energy in these materials are very sensitive to the impurities, their crystal qualities etc. In MZF it is known fact that Zn ions occupy tetrahedral A-site, so they push some of the Fe3 þ ions to
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Fig. 9. (A) Plots of 1000/T vs. ln sac (sac in S/m) of RFC for x ¼ 0.0, 0.2 and 0.4. (B) Plots of 1000/T vs. ln sac (sac in S/m) of RFC for x¼ 0.6, 0.8 and 1.0.
Fig. 11. Variation of activation energy with loading of RFC at 1 MHz. Fig. 10. Variation of ln sac in S/m with 1000/T of blank NR.
octahedral B-site. As the Fe3 þ ions increases at B-site, there is more possibility of hopping between Fe3 þ and Fe2 þ ions. As the hopping possibility increases conductivity increases, results in decrease in resistivity and activation energy. There are reports that the activation energy for conduction of inorganic semiconductor is higher than the corresponding activation energy of conduction of polymeric semiconductors. For example, for germanium, with conductivity 0.1–0.01 S/cm, the activation energy for conduction is about 0.6 eV and for an
organic semiconductor with the same conductivity, the activation energy of conduction is between 0.1 and 0.03 eV. These factors may account for the low activation energy and low conductivity displayed by composite samples [20].
4. Conclusions Increase in conductivity with increase in frequency for both ceramic and rubber ferrite composites are observed. Porosity of
Mohd. Hashim et al. / Physica B 407 (2012) 4097–4103
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Acknowledgements Financial assistance from U.G.C. is acknowledged by Mohd. Hashim through grant No. MANF-MUS-UTT-1092. This work is also supported by BK21 project corp.
References
Fig. 12. Variation of activation energy with composition at 1 MHz.
the ceramic samples affects the ac electrical conductivity and causes variation in ac electrical conductivity with zinc substitution. All the samples show that the conductivity with volume fraction of the magnetic filler shows a continuous increase up to a loading of 30–40 phr and thereafter flattens off. Hopping probabilities between Fe3 þ and Fe2 þ affect the activation and changes with zinc content. Temperature variations carried out on MZF samples were limited to 425 K since it was intended for RFCs. This is because RFCs thermally degrade at around 425 K. The leveling of ac conductivity at 30–40 phr (sac vs. log F) can be attributed to the available pore sites.
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