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Electrical transport behavior of nonstoichiometric magnesium–zinc ferrite
Materials Research Bulletin 45 (2010) 954–960
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Electrical transport behavior of nonstoichiometric magnesium–zinc ferrite S. Ghatak a, M. Sinha b, A.K. Meikap a,*, S.K. Pradhan b a b
Department of Physics, National Institute of Technology, Deemed University, Mahatma Gandhi Avenue, Durgapur 713209, West Bengal, India Department of Physics, University of Burdwan, Golapbag, Burdwan 713104, West Bengal, India
A R T I C L E I N F O
A B S T R A C T
Article history: Received 23 September 2009 Received in revised form 23 March 2010 Accepted 14 April 2010 Available online 20 April 2010
This paper presents the direct current conductivity, alternate current conductivity and dielectric properties of nonstoichiometric magnesium–zinc ferrite below room temperature. The frequency exponent (s) of conductivity shows an anomalous temperature dependency. The magnitude of the temperature exponent (n) of dielectric permittivity strongly depends on frequency and its value decreases with increasing frequency. The grain boundary contribution is dominating over the grain contribution in conduction process and the temperature dependence of resistance due to grain and grain boundary contribution exhibits two activation regions. The ferrite shows positive alternating current magnetoconductivity. The solid state processing technique was used for the preparation of nanocrystalline ferrite powder from oxides of magnesium, zinc and iron. The X-ray diffraction methods were used in determining the structure and composition of obtained ferrite, while multimeter, impedance analyzer, liquid nitrogen cryostat and electromagnet were used in the study of conducting and dielectric properties of ferrite. ß 2010 Elsevier Ltd. All rights reserved.
PACS: 73.63.Bd 73.63.b 72.15.Gd 77.22.d Keywords: A. Nanostructures C. X-ray diffraction D. Electrical properties D. Dielectric properties
1. Introduction The potential application of Nanocrystalline materials has increased their importance to researchers during the last few decades. The unusual properties of these materials are attributed to the presence of large number of atoms at the grain boundaries or interfacial boundaries compared to coarse grained polycrystalline counterparts. Nanocrystalline spinel ferrites are technologically important materials that have application in magnetic, electronic and microwave fields. Magnetic nanocrystalline materials are considered as a promising one in atomic engineering of materials with functional magnetic properties [1–3]. Some of them show superparamagnetism [4] in single domain below a certain critical size. Magnetic nanocrystals have a potential application in magnetic recording medium, information storage, color imaging, bio-processing magnetic refrigeration and magneto-optical devices [5–7]. Mixed zinc ferrites are also technologically important materials with applications ranging from magnetic storage devices to catalytic water splitting [8]. Mg–Zn ferrite is important as core materials over a wide range of frequencies starting from a few hundred Hz to several MHz. The high permeability and high
* Corresponding author. Tel.: +91 343 2546808; fax: +91 343 2547375. E-mail address: [email protected] (A.K. Meikap). 0025-5408/$ – see front matter ß 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.materresbull.2010.04.008
electrical resistivity in this frequency range make them particularly useful for inductor and transformer cores and in switch mode power supplies (SMPS) [9]. It is also shows the gas sensing properties in nano-particles form [10]. It was seen in mechanosynthesised nanocrystalline Zn ferrite that a substantial amount of Fe3+ ions is displaced to tetrahedral site and of Zn2+ cations into octahedral sites [11]. Similar results were found in ball-milled Mg ferrite samples [12]. Physical properties of nanocrystalline ferrites depend on their microstructure. The grain and grain boundary mainly determine the microstructure. Thus, the information regarding the physical parameters of these components leads to the understanding of the overall properties of the materials. To have knowledge of above objectives of solid electrolytes and ceramic oxides, ac complex impedance had been experimentally determined [13–15]. The information about the grain and grain boundary contribution of the nanomaterials can be obtained by analyzing these data by an equivalent circuit. The complex impedance and dielectric properties of polycrystalline bulk Mg–Zn ferrite above room temperature are analyzed extensively by Abdullah and Yusoff [16] and Mazen et al. [17]. But the systematic study on the magnetic field dependent ac conductivity and dielectric properties of nanocrystalline Mg–Zn ferrite below room temperature is not yet been reported. Synthesis of nanocrystalline Mg–Zn ferrite powders by mechanical process and characterization by XRD and SEM is
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reported in this article. The direct (dc) conductivity, magnetoconductivity, frequency dependent conductivity and dielectric response of Mg–Zn ferrite powders are measured in the temperature range 77 T 300 K, in presence and in absence of magnetic field up to 1 T and in the frequency range 20 Hz to 1 MHz. 2. Sample preparation and experimental technique So far magnetic nanocrystals have been prepared by different synthetic methods [18–20]. High energy ball milling is one of the important solid state processing techniques for the preparation of nanocrystalline ferrite samples [21–24]. Accurately weighted powders of MgO (Merck, 99% purity), ZnO (Merck, 99% purity) and a-Fe2O3 (Glaxo, 99% purity), in 0.5:0.5:1 mol.% was ground in an agate mortar in presence of doubly distilled acetone for more than 5 h. The homogeneous powder mixture was milled by a planetary ball mill (Model P5, M/S Fritsch, Gmbh, Germany) at a rotation speed of 300 rpm of the disc and that of vials of about 450 rpm. Milling was done at room temperature in hardened chrome steel vials of volume 80 ml using 30 hardened chrome steel ball of 10 mm diameter, at BPMR 40:1. The milling time was kept between 1 and 25 h, depending upon the process of Mg–Zn ferrite formation. The X-ray powder diffraction patterns of the unmilled and ballmilled samples were obtained using Ni-filtered Cu Ka radiation from a highly stabilized and automated Philips generator (PW 1830) operated at 35 kV and 25 mA. The generator is coupled with a Philips X-ray powder diffractometer consisting of a PW 3710 mpd controller, PW 1050/37 goniometer and a proportional counter. The step scan data (of step size 0.028 2u and counting time 10 s) for the entire angular range (15–808 2u) of the experimental samples were taken. Microstructural parameters of the investigated samples have been determined by Rietveld’s technique based on structure and microstructure refinement method [25–29]. The dc electrical conductivity of the samples was measured by a standard four probe method by using the 81/2 – digit Agilent 3458A multimeter. The dielectric response of the samples was measured in a 4284A Agilent Impedance analyzer within a frequency range 20 Hz–1 MHz at different temperatures. The temperature dependent conductivity was measured in a Liquid nitrogen cryostat along with the ITC 502S Oxford temperature controller. To measure the transport property, samples were prepared as 1 cm diameter pellets by pressing the powder under a hydraulic pressure of 500 MPa with fine copper wires as the connecting wire and silver paint as coating materials. The density of the pressed pellets lies in the range 3.14–3.83 g/cm3. which is similar to the previous studies [30,31]. The capacitance (CP) and the dissipation factor (D) were measured at various frequencies and temperatures. The real part of ac conductivity and real and imaginary part of dielectric permittivity have been calculated using the relations s0 (f) = 2pfe0e00 (f), e0 (f) = CPd/e0A and e00 (f) = e0 (f)D respectively, where e0 = 8.854 1012 F/m, A and d are the area and thickness of the sample respectively. CP is the capacitance measured in farad; f is the frequency in Hz. The magnetoconductivity measurement was done in presence of varying and transverse magnetic field B 1 T by using an electromagnet.
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ferrite phase is found as a major phase and a small amount of aFe2O3 phase remains unreacted after 3 h of milling. The amount of ferrite content increases with milling time in the expense of aFe2O3 phase. The particle size of a-Fe2O3 phase reduces rapidly from 57 to 6 nm within 3 h of milling and then slowly up to 3.5 nm within 12 h milling. The ferrite phase is formed with a size of 3 nm and there is no significant change in size of ferrite particles up to 12 h milling. The details of the microstructure characterization and quantitative estimations of multiphase were discussed already in the previous works [32,33]. Fig. 1 represents the scanning electron micrograph of two representative Mg–Zn ferrite samples. The picture indicates that the materials are not closely packed and the grains are well resolved and have almost circular (spherical) shape and have a narrow size distribution. It is clearly seen in the micrographs that the grains are at nanoscale. The average grain size determined from SEM was noted as 20–35 nm. Generally in ferrite phase, the number of Fe2+ ions in the octahedral sites plays a dominant role in the mechanism of conduction. The conductivity in the ferrite is due to the motion of electrons via iron ions of different valencies, which are being transported through the grain and across the grain boundaries. The dc conductivity of the investigated samples was measured over a temperature range 77 T 300 K. The conductivity of the samples increases with increasing temperature. According to the hopping theory the conductivity is given by the relation [34] C T
s ðTÞ ¼ exp
Ea kT
(1)
3. Results and discussion X-ray powder diffraction patterns have been recorded for different unmilled and ball-milled samples. Rietveld’s analysis method has been employed for estimation of microstructure characterization and quantitative estimation of multiphase. The powder pattern of unmilled sample contains only the individual reflections of starting phases ZnO, MgO and a-Fe2O3. The (Mg, Zn)
Fig. 1. (a) SEM micrograph of 3 h ball-milled homogeneous mixture of ZnO, MgO, aFe2O3 powders (MZF3 h). (b) SEM micrograph of 12 h ball-milled homogeneous mixture of ZnO, MgO, a-Fe2O3 powders (MZF12 h).
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Fig. 3. AC conductivity as a function of frequency of different unmilled and ballmilled homogeneous mixture of ZnO, MgO, a-Fe2O3 powders at T = 300 K. Fig. 2. dc conductivity as a function of temperature of different unmilled and ballmilled homogeneous mixture of ZnO, MgO, a-Fe2O3 powders.
where C is a constant, k is the Boltzmann constant and Ea represents the activation energy of the conduction mechanism. The logarithm conductivity [ln(Ts)] has been studied as a function of reciprocal temperature (103/T) for the investigated samples. According to Fig. 2 the linear variation of ln(Ts) with 103/T indicates the prevalence of a simple hopping type charge transport in all the investigated samples. The values of activation energy Ea have been calculated from the slopes of the different straight line curves in Fig. 2 and its values increasing from 7 to 14 meV with increasing milling time from 0 to 12 h. It is observed that activation energy increases from 7 to 12 meV for 3 h milling, after that no considerable change has observed in further increase in milling time from 3 to 12 h. This large increase of Ea within 3 h milling may be due to the large decrease of particle size in the samples. By further milling the particle size does not change much more due to which a small activation energy change has been observed. The ac conductivity of Mg–Zn ferrite samples are investigated in the frequency range 20 Hz to 1 MHz and in the temperature range 77 T 300 K. The measured data showed that the variation of conductivity with frequency at a particular temperature is prominent at higher frequencies, whereas at low frequencies it is almost independent with frequencies, this could be attributed to the dc contribution. A general feature of amorphous semiconductors or disordered systems is that the frequency dependent conductivity sac(f) obeys a power law with frequency. The total conductivity s0 (f) at a particular temperature over a wide range of frequencies can be expressed as [35–37]
s 0 ð f Þ ¼ s dc þ s ac ð f Þ ¼ s dc þ a f s
in Fig. 4 for different samples. The frequency exponent ‘s’ is found to be weak temperature dependent at lower temperature (T < 200 K), but above 200 K the estimated values of ‘s’ gradually decrease with increasing temperature. In general two physical processes such as correlated barrier hopping (CBH) [37] and quantum mechanical tunneling (electron tunneling [38], small polaron tunneling [37] and large polaron tunneling [36]) govern the conduction process of disordered systems. As the nature of temperature dependency of ‘s’ for different conduction processes are different, the exact nature of charge transport may be obtained experimentally from the temperature variation of the frequency exponent ‘s’. According to the electron tunneling theory, the frequency exponent ‘s’ is temperature independent, whereas for small polaron tunneling ‘s’ increases with increasing temperature and for large polaron tunneling ‘s’ decreases first and then increases with increasing temperature. But according to the
(2)
where sdc is the dc conductivity, a is the temperature dependent constant and the frequency exponent s < 1. The value of sac(f) has been determined upon subtraction of the dc contribution from the total frequency dependent conductivity s0 (f). Fig. 3 shows the linear variation of ln[sac(f)] with ln(f) at T = 300 K for the different samples. Similar behavior was observed for all other temperatures in different samples. The value of ‘s’ at each temperature has been calculated from the slope of ln[sac(f)] vs. ln(f) plot for each temperature. The trend of change in ‘s’ with temperature is shown
Fig. 4. The temperature variation of the frequency exponents (s) for unmilled and different ball-milled homogeneous mixtures of ZnO, MgO, a-Fe2O3 powders. Inset shows variation of s in the temperature range 77 T 175 K.
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correlated barrier hopping model ‘s’ only decreases with the increase in temperature. From the trend of change in ‘s’ with temperature (T > 200 K), it is presumed that the correlated barrier hopping is suitable for explaining the behavior of our investigated data. According to this model, the charge carrier hops between the sites over the potential barrier separating them and the frequency exponent ‘s’ is given by the expression [37]. s¼1
6kB T W H kB Tlnð1=vt 0 Þ
(2a)
where WH is the effective barrier height and to is the characteristic relaxation time. According to Eq. (2a), for large values of WH/kBT, the variation of ‘s’ with frequency is so small that it is effectively independent of frequency [39,40]. Moreover it has been observed in our study that ‘s’ is independent of frequency [linear variation of ln[sac(f)] with ln(f) in Fig. 3]. Therefore, we fitted our experimental data with Eq. (2a) as function of temperature alone with WH and vto as fitting parameters. In Fig. 4 the points represent the experimental data whereas solid lines are the theoretical best fit values obtained from Eq. (2a) for different samples. The best fitted values of the parameters WH and to (at a fixed frequency of f = 1 MHz) are laying between 0.70–1.03 eV and 1.41 1014 to 1.92 1013 S, respectively, for different samples. The values of WH are, as expected, higher than the activation energy measured from grain and grain boundary contribution (discussed later) and the values of the characteristic relaxation time to are comparable with those that would be expected for typical inverse phonon frequency. However at low temperature, T < 200 K, the value of ‘s’ decreases slowly and follows a linear variation as shown in inset of Fig. 4. According to the theory of CBH model, at lower temperature where the value of WH/kBT is large, Eq. (2a) transforms to a linear temperature dependency of ‘s’. So the observed linear temperature dependency of ‘s’ may be due to the high value of WH/kBT at low temperature. Therefore, from the trend of variation of ‘s’ with temperature, it may be concluded that the ac conductivity in the investigated samples can be described by the CBH model. Temperature dependence of real part of ac conductivity (s0 (f)) for different frequencies of MZF12h has been shown in Fig. 5. Two different slopes are observed in the ln[Ts0 (f)] vs. 103/T plot in the two temperature range. In order to calculate the activation energy in the two temperature range, the experimental data have been analyzed by Eq. (1). The values of Ea at different frequencies have
Fig. 5. AC conductivity as a function of temperature of 12 h ball-milled homogeneous mixture of ZnO, MgO, a-Fe2O3 powders at different frequencies.
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been calculated from the slopes of ln[Ts0 (f)] vs. 103/T plot in the two temperature range. It is observed that the activation energy decreases 368–228 meV in the high temperature region and remains almost constant (6.7–9.1 meV) at low temperature region with increasing frequencies from 1 to 500 kHz. Such anomalies may arise due to various reasons such as transformation of magnetic phase or structural phase or a change in the conduction mechanism. Since the Curie points of the investigated ferrites are well above room temperature, the above behavior may not be due to magnetic and structural phase transformation. So the conduction mechanism may take important role for such behavior, which would be more clear by observing temperature dependency of the total resistivity due to grain and grain boundary effect (discussed later). The variation of real part of dielectric permittivity e0 (f) with temperature is shown in Fig. 6a for the sample MZF12h for different yet constant frequencies. In the e0 –T plot there is no sharp peak till the temperature is raised to 300 K, which is the maximum temperature employed in our investigation. At a particular frequency the real part of dielectric permittivity increases with temperature and is found to follow a power law e0 (f) / Tn, which are shown as the solid lines in Fig. 6a. The values of n have been calculated from the power law fitting and found to be strongly
Fig. 6. (a) Thermal variation of dielectric constant of 12 h ball-milled homogeneous mixture of ZnO, MgO, a-Fe2O3 powders (MZF12 h) at different frequencies. (b) Variation of dielectric constant as function of frequency at different temperatures of 8 h ball-milled homogeneous mixture of ZnO, MgO, a-Fe2O3 powders.
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frequency dependent. Its value decreases with increasing frequencies for all the samples, which implies that, a larger variation in the e0 (f) with temperature is observed at lower frequency in compare to higher frequency. Generally the ferrite exhibits interfacial polarization due to structural inhomogeneities and existence of free charges [41]. It is thought that the hopping electrons at low frequencies may be trapped by the inhomogeneities. The increase of e0 (f) with temperature at a particular frequency is due to the drop in the resistance of the ferrite with increasing temperature. The low resistance promotes electron hopping, hence resulting in a larger polarizability or larger e0 (f). The frequency dependence of real part of the dielectric permittivity e0 (f) have also been studied for different samples and shown in Fig. 6b for MZF8 h sample at different yet constant temperatures. A weak variation is noticed in the dielectric permittivity at lower temperature, although a large variation of the same is observable at higher temperature for all the samples. At a fixed temperature, the dielectric permittivity e0 (f) increase sharply with decreasing frequency and this sharp increase shifts to lower frequencies as the temperature is reduced. Such sudden increase of real part of the dielectric constant e0 (f) at low frequency can be attributed to the presence of large degree of dispersion due to charge transfer within the interfacial diffusion layer present between the electrodes. The magnitude of the dielectric dispersion is temperature dependent. At lower temperature, the freezing of the electric dipoles through the relaxation process is easier. So there exists decay in polarization with respect to the applied electric field, which is evidenced by the sharp decrease in e0 (f) at lower frequency region. When the temperature is high, the rate of polarization formed is quick and thus the relaxation occurs in high frequency. Due to this, the position of the sharp increase shifts towards higher frequency by increasing temperature. Therefore, the frequency behavior of e0 (f) is due to inhomogeneous nature (containing different permittivity and conductivity regions) of the samples, where the charge carriers are blocked by poorly conducting region. The effective dielectric permittivity of such inhomogeneous systems is given by Maxwell– Wagner capacitor model [42–44]. The complex impedance of such systems can also be modeled by an ideal equivalent circuit consisting of resistance and capacitance due to grain and interfacial grain boundary contribution and it can be expressed as Z¼
1 ¼ Z = iZ == ivC 0 eðvÞ
Z= ¼
Rg 1 þ ðvRg C g Þ2
Z == ¼
þ
(3) Rgb
1 þ ðvRgb C gb Þ2
vR2gb C gb vR2g C g þ 2 1 þ ðvRg C g Þ 1 þ ðvRgb C gb Þ2
Fig. 7. The real part of the complex impedance vs. frequency at T = 300 K of different ball-milled homogeneous mixtures of ZnO, MgO, a-Fe2O3 powders with and without magnetic field.
well fitted with the theory. The values of the grain capacitance (Cb) are smaller than the grain boundary capacitance (Cgb). This is because both the capacitances are inversely proportional to the thickness of the grain and grain boundaries. As the thickness of the grains are much larger than the grain boundaries, the values of Cb < Cgb. The resistance due to interfacial grain boundary is much larger in compare to the grain resistance. This implies that the grain boundary contribution dominates over the grain contribution. Since the ferrites are semiconductors, the conduction process can be explained by hopping mechanism, where the carrier mobility is dominated by a factor that increases with temperature exponentially. This temperature dependent factor is determined by thermal activation in order to overcome the potential barrier between the sites by hopping. Both grain and grain boundary resistances follow this mechanism and the total resistance (R = Rg + Rgb) variation can be expressed as R / exp(Ea/kBT), where Ea is the activation energy. The plots of ln(R) vs. 103/T in Fig. 8 support the above explanation. As seen from Fig. 8 samples exhibit two different activations, one with Ea of 0.43–1.78 meV for the low temperature region and the other with Ea of 43– 281 meV for high temperature region for different samples. This discrepancy
(4)
(5)
where sub indexes ‘g’ and ‘gb’ refer to the grain and interfacial grain boundary respectively, R is resistance, C is capacitance, v = 2pf and C0 is free space capacitance. The real part of the complex impedance have been calculated from the experimental data for real (e0 ) and imaginary (e00 ) part of the dielectric permittivity by using the relation Z0 (f) = e00 (f)/[vC0(e0 (f)2 + e00 (f)2)] for different samples and analyzed by Eq. (4). Fig. 7 shows the frequency dependence of the real part of the complex impedance at room temperatures for different samples with and without magnetic field. The points are the experimental data and the solid lines are the theoretical values obtained from Eq. (4). The grain and grain boundary resistances and capacitances have been extracted from this analysis at room temperature, whose values lie within the range 0.20–3.59 MV for Rg, 15.45–99.57 MV for Rgb, 0.16– 0.45 nF for Cg and 0.29–0.86 mF for Cgb for different samples. It is observed from Fig. 7 that the experimental data are reasonably
Fig. 8. Variation of R (=Rg + Rgb) with temperature of unmilled and ball-milled homogeneous mixture of ZnO, MgO, a-Fe2O3 powders.
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theoretical and experimental is necessary to formulate the true mechanism for this issue. 4. Conclusion
Fig. 9. Magnetic field dependence of the ac conductivity of 8 h ball-milled homogeneous mixture of ZnO, MgO, a-Fe2O3 powders at different temperatures.
probably arises due to the anomalous conduction mechanism in the investigated samples. Ponpandian et al. [45] also observed similar behavior in nanocrystalline Ni ferrite and they reported that at low temperature only electrons take part in conduction, however at high temperatures both electrons and holes take part in conduction. We presume that observed two activation regions in our investigated samples may be due to the same reason as observed in Ni ferrite. Magnetic field dependent real part of the ac conductivity of the different samples at room temperature and f = 1 MHz is shown in Fig. 9. The ac magnetoconductivity increases with the increase of magnetic field for all the investigated samples. At present we have not found the theoretical model in the literature to explain directly the behavior of ac conductivity in presence of magnetic field. Electron micrographs of our investigated samples indicate the heterogeneous nature with spherical grain, which implies that the materials consist of grain and interfacial grain boundary regions. For such heterogeneous samples, it was already discussed that the impedance and the dielectric response can be interpreted by grain and grain boundary resistances and capacitances. As the real part of ac conductivity is related with the dielectric response by the relation s0 (B,f) = ve0e00 (B,f), As e00 (B,f) depends on the values of grain and grain boundary resistances and capacitances, the ac conductivity can be written as [46]
s 0 ðB; f Þ ¼
1 v2 t g t gb þ v2 t ðt g þ t gb Þ d AðRg þ Rgb Þ 1 þ v2 t 2
(6)
where tg = CgRg, tgb = CgbRgb and t = RgRgb(Cg + Cg)/(Rg + Rgb). If the value of any of these resistances is changed by a magnetic field, that will affect the measured ac conductivity. From the analysis of the real part of complex impedance in presence of constant magnetic field B = 0.8 T, it is observed that the values of grain and grain boundary resistances and capacitances lie within the range 0.15–3.6 MV for Rg, 7.59–90.51 MV for Rgb, 0.12–0.31 nF for Cg and 0.21–0.78 mF for Cgb for different samples i.e. the total contribution due to grain and grain boundary resistances (R = Rg + Rgb) decreases with increasing magnetic field. So we may presume that the influence of the magnetic field on the ac conductivity is due to the change of grain and grain boundary resistances by the applied magnetic field. But due to lack of analytical expression for grain or grain boundary resistances with magnetic field, we are not able to compare the measured data directly with theory. Therefore, a more explicit study both
The above experimental observations suggest the following facts: (i) a nonstoichiometric Mg–Zn–ferrite phase can be obtained in a considerable amount (84%) by ball milling the stoichiometric powder mixture of MgO, ZnO and a-Fe2O3 up to 12 h. (ii) The particle size of ferrite phase in the ball-milled samples remains almost unaltered (3 nm). (iii) The dc conductivity of the investigated samples follows the simple hopping type conduction mechanism. (iv) The real part of the complex ac conductivity was found to follow the power law s0 (f) / fs. A detailed analysis of the temperature dependence of the universal dielectric response parameter ‘s’ revealed that the correlated barrier hopping is the dominating charge transport mechanism. (v) At a particular frequency the real part of the dielectric permittivity was found to follow the relation e0 (f,T) / Tn. The magnitude of the temperature exponent ‘n’ strongly depends on frequency and its value decreases with increasing frequency. (vi) The frequency dependent real part of the dielectric permittivity shows large degree of dispersion at low frequency, but rapid polarization at high frequencies, which can be interpreted by Maxwell–Wagner capacitor model. (vii) The grain resistance and capacitance are smaller than grain boundary resistance and capacitance by two and three orders respectively and the total resistance due to grain and grain boundary decreases by the application of magnetic field. (viii) The ac conductivity shows the positive variation in presence of magnetic field, it may be concluded that such observation may be due to the change of grain and grain boundary resistances caused by the magnetic field. Acknowledgements This work has been carried out under grant nos. F.27-1/ 2002.TS.V dated 19.03.2002 and F.28-1/2003.TS.V dated 3103.2003 sanctioned by the MHRD, Government of India. The authors gratefully acknowledge the principal assistance received from the above organization during this work. References [1] T. Hirai, J. Kobayashi, I. Koasawa, Langmuir 15 (1999) 6291. [2] R.H. Kodama, J. Magn. Magn. Mater. 200 (1999) 359. [3] K.V.P.M. Shafi, Y. Koltypin, A. Gedanken, R. Prozorov, J. Balogh, J. Lendvai, I. Felner, J. Phys. Chem. 101B (1997) 6409. [4] M. Elbschutz, S. Shtrikman, J. Appl. Phys. 39 (1968) 997. [5] I. Anton, I.D. Dabata, L. Vekas, J. Magn. Magn. Mater. 85 (1990) 219. [6] R.D. McMickael, R.D. Shull, L.J. Swartzendruber, L.H. Bennett, R.E. Watson, J. Magn. Magn. Mater. 111 (1992) 29. [7] D.L. Leslie-Pelecky, R.D. Rieke, Chem. Mater. 8 (1996) 1770. [8] Y. Tamaura, Y. Ueda, J. Matsunami, N. Hasegawa, M. Nezuka, T. Sano, M. Tsusi, Sol. Energy 65 (1999) 55. [9] S.F. Mansour, Egypt. J. Solids 21 (2005). [10] D.C. Bharti, K. Mukherjee, S.B. Majumdar, Mater. Chem. Phys 120 (2010) 509. [11] S. Bid, S.K. Pradhan, Mater. Chem. Phys. 82 (2003) 27. [12] S.K. Pradhan, S. Bid, M. Gateshki, V. Petkov, Mater. Chem. Phys. 93 (2005) 224. [13] W.I. Archer, R.D. Armstrong, Electrochemistry 7 (1979) 157. [14] T. Straton, A. MacHale, D. Button, H.L. Turner, N.B. Hannay, U. Colombo (Eds.), Electronic Materials, Plenum, New York, 1979, pp. 71–81. [15] Y.C. Yeh, T.Y. Tseng, J. Mater. Sci. 24 (1989) 2739. [16] M.H. Abdullah, A.N. Yusoff, J. Alloys Compd. 233 (1996) 129. [17] S.A. Mazen, H.M. Zaki, S.F. Mansour, Int. J. Pure Appl. Phys. 3 (2007) 40. [18] D. Niznansky, N. Viart, J.L. Renspinger, IEEE Trans. Magn. 30 (1994) 821. [19] J.M. Yang, W.J. Tsuo, F.S. Yen, J. Solid State Chem. 145 (1999) 50. [20] Y. Shi, J. Ding, X. Liu, J.J. Wang, J. Magn. Magn. Mater. 205 (1999) 249. [21] P. Druska, U. Steinike, V. Sepelak, J. Solid State Chem. 146 (1999) 13. [22] V. Sepelak, K. Tkacova, V.V. Boldyrev, U. Steinike, Mater. Sci. Forum 783 (1996) 228. [23] V. Sepelak, A. Yu, U. Rogachev, D. Steinike, C. Uecker, S. Wibmann, K.D. Becker, Acta Crystallogr. Suppl. Issue A 52 (1996) C-367. [24] V. Sepelak, A. Yu, U. Rogachev, D. Steinike, C. Uecker, F. Krumcich, S. Wibmann, K.D. Becker, Mater. Sci. Forum 139 (1997) 235.
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Materials Research Bulletin journal homepage: www.elsevier.com/locate/matresbu
Electrical transport behavior of nonstoichiometric magnesium–zinc ferrite S. Ghatak a, M. Sinha b, A.K. Meikap a,*, S.K. Pradhan b a b
Department of Physics, National Institute of Technology, Deemed University, Mahatma Gandhi Avenue, Durgapur 713209, West Bengal, India Department of Physics, University of Burdwan, Golapbag, Burdwan 713104, West Bengal, India
A R T I C L E I N F O
A B S T R A C T
Article history: Received 23 September 2009 Received in revised form 23 March 2010 Accepted 14 April 2010 Available online 20 April 2010
This paper presents the direct current conductivity, alternate current conductivity and dielectric properties of nonstoichiometric magnesium–zinc ferrite below room temperature. The frequency exponent (s) of conductivity shows an anomalous temperature dependency. The magnitude of the temperature exponent (n) of dielectric permittivity strongly depends on frequency and its value decreases with increasing frequency. The grain boundary contribution is dominating over the grain contribution in conduction process and the temperature dependence of resistance due to grain and grain boundary contribution exhibits two activation regions. The ferrite shows positive alternating current magnetoconductivity. The solid state processing technique was used for the preparation of nanocrystalline ferrite powder from oxides of magnesium, zinc and iron. The X-ray diffraction methods were used in determining the structure and composition of obtained ferrite, while multimeter, impedance analyzer, liquid nitrogen cryostat and electromagnet were used in the study of conducting and dielectric properties of ferrite. ß 2010 Elsevier Ltd. All rights reserved.
PACS: 73.63.Bd 73.63.b 72.15.Gd 77.22.d Keywords: A. Nanostructures C. X-ray diffraction D. Electrical properties D. Dielectric properties
1. Introduction The potential application of Nanocrystalline materials has increased their importance to researchers during the last few decades. The unusual properties of these materials are attributed to the presence of large number of atoms at the grain boundaries or interfacial boundaries compared to coarse grained polycrystalline counterparts. Nanocrystalline spinel ferrites are technologically important materials that have application in magnetic, electronic and microwave fields. Magnetic nanocrystalline materials are considered as a promising one in atomic engineering of materials with functional magnetic properties [1–3]. Some of them show superparamagnetism [4] in single domain below a certain critical size. Magnetic nanocrystals have a potential application in magnetic recording medium, information storage, color imaging, bio-processing magnetic refrigeration and magneto-optical devices [5–7]. Mixed zinc ferrites are also technologically important materials with applications ranging from magnetic storage devices to catalytic water splitting [8]. Mg–Zn ferrite is important as core materials over a wide range of frequencies starting from a few hundred Hz to several MHz. The high permeability and high
* Corresponding author. Tel.: +91 343 2546808; fax: +91 343 2547375. E-mail address: [email protected] (A.K. Meikap). 0025-5408/$ – see front matter ß 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.materresbull.2010.04.008
electrical resistivity in this frequency range make them particularly useful for inductor and transformer cores and in switch mode power supplies (SMPS) [9]. It is also shows the gas sensing properties in nano-particles form [10]. It was seen in mechanosynthesised nanocrystalline Zn ferrite that a substantial amount of Fe3+ ions is displaced to tetrahedral site and of Zn2+ cations into octahedral sites [11]. Similar results were found in ball-milled Mg ferrite samples [12]. Physical properties of nanocrystalline ferrites depend on their microstructure. The grain and grain boundary mainly determine the microstructure. Thus, the information regarding the physical parameters of these components leads to the understanding of the overall properties of the materials. To have knowledge of above objectives of solid electrolytes and ceramic oxides, ac complex impedance had been experimentally determined [13–15]. The information about the grain and grain boundary contribution of the nanomaterials can be obtained by analyzing these data by an equivalent circuit. The complex impedance and dielectric properties of polycrystalline bulk Mg–Zn ferrite above room temperature are analyzed extensively by Abdullah and Yusoff [16] and Mazen et al. [17]. But the systematic study on the magnetic field dependent ac conductivity and dielectric properties of nanocrystalline Mg–Zn ferrite below room temperature is not yet been reported. Synthesis of nanocrystalline Mg–Zn ferrite powders by mechanical process and characterization by XRD and SEM is
S. Ghatak et al. / Materials Research Bulletin 45 (2010) 954–960
reported in this article. The direct (dc) conductivity, magnetoconductivity, frequency dependent conductivity and dielectric response of Mg–Zn ferrite powders are measured in the temperature range 77 T 300 K, in presence and in absence of magnetic field up to 1 T and in the frequency range 20 Hz to 1 MHz. 2. Sample preparation and experimental technique So far magnetic nanocrystals have been prepared by different synthetic methods [18–20]. High energy ball milling is one of the important solid state processing techniques for the preparation of nanocrystalline ferrite samples [21–24]. Accurately weighted powders of MgO (Merck, 99% purity), ZnO (Merck, 99% purity) and a-Fe2O3 (Glaxo, 99% purity), in 0.5:0.5:1 mol.% was ground in an agate mortar in presence of doubly distilled acetone for more than 5 h. The homogeneous powder mixture was milled by a planetary ball mill (Model P5, M/S Fritsch, Gmbh, Germany) at a rotation speed of 300 rpm of the disc and that of vials of about 450 rpm. Milling was done at room temperature in hardened chrome steel vials of volume 80 ml using 30 hardened chrome steel ball of 10 mm diameter, at BPMR 40:1. The milling time was kept between 1 and 25 h, depending upon the process of Mg–Zn ferrite formation. The X-ray powder diffraction patterns of the unmilled and ballmilled samples were obtained using Ni-filtered Cu Ka radiation from a highly stabilized and automated Philips generator (PW 1830) operated at 35 kV and 25 mA. The generator is coupled with a Philips X-ray powder diffractometer consisting of a PW 3710 mpd controller, PW 1050/37 goniometer and a proportional counter. The step scan data (of step size 0.028 2u and counting time 10 s) for the entire angular range (15–808 2u) of the experimental samples were taken. Microstructural parameters of the investigated samples have been determined by Rietveld’s technique based on structure and microstructure refinement method [25–29]. The dc electrical conductivity of the samples was measured by a standard four probe method by using the 81/2 – digit Agilent 3458A multimeter. The dielectric response of the samples was measured in a 4284A Agilent Impedance analyzer within a frequency range 20 Hz–1 MHz at different temperatures. The temperature dependent conductivity was measured in a Liquid nitrogen cryostat along with the ITC 502S Oxford temperature controller. To measure the transport property, samples were prepared as 1 cm diameter pellets by pressing the powder under a hydraulic pressure of 500 MPa with fine copper wires as the connecting wire and silver paint as coating materials. The density of the pressed pellets lies in the range 3.14–3.83 g/cm3. which is similar to the previous studies [30,31]. The capacitance (CP) and the dissipation factor (D) were measured at various frequencies and temperatures. The real part of ac conductivity and real and imaginary part of dielectric permittivity have been calculated using the relations s0 (f) = 2pfe0e00 (f), e0 (f) = CPd/e0A and e00 (f) = e0 (f)D respectively, where e0 = 8.854 1012 F/m, A and d are the area and thickness of the sample respectively. CP is the capacitance measured in farad; f is the frequency in Hz. The magnetoconductivity measurement was done in presence of varying and transverse magnetic field B 1 T by using an electromagnet.
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ferrite phase is found as a major phase and a small amount of aFe2O3 phase remains unreacted after 3 h of milling. The amount of ferrite content increases with milling time in the expense of aFe2O3 phase. The particle size of a-Fe2O3 phase reduces rapidly from 57 to 6 nm within 3 h of milling and then slowly up to 3.5 nm within 12 h milling. The ferrite phase is formed with a size of 3 nm and there is no significant change in size of ferrite particles up to 12 h milling. The details of the microstructure characterization and quantitative estimations of multiphase were discussed already in the previous works [32,33]. Fig. 1 represents the scanning electron micrograph of two representative Mg–Zn ferrite samples. The picture indicates that the materials are not closely packed and the grains are well resolved and have almost circular (spherical) shape and have a narrow size distribution. It is clearly seen in the micrographs that the grains are at nanoscale. The average grain size determined from SEM was noted as 20–35 nm. Generally in ferrite phase, the number of Fe2+ ions in the octahedral sites plays a dominant role in the mechanism of conduction. The conductivity in the ferrite is due to the motion of electrons via iron ions of different valencies, which are being transported through the grain and across the grain boundaries. The dc conductivity of the investigated samples was measured over a temperature range 77 T 300 K. The conductivity of the samples increases with increasing temperature. According to the hopping theory the conductivity is given by the relation [34] C T
s ðTÞ ¼ exp
Ea kT
(1)
3. Results and discussion X-ray powder diffraction patterns have been recorded for different unmilled and ball-milled samples. Rietveld’s analysis method has been employed for estimation of microstructure characterization and quantitative estimation of multiphase. The powder pattern of unmilled sample contains only the individual reflections of starting phases ZnO, MgO and a-Fe2O3. The (Mg, Zn)
Fig. 1. (a) SEM micrograph of 3 h ball-milled homogeneous mixture of ZnO, MgO, aFe2O3 powders (MZF3 h). (b) SEM micrograph of 12 h ball-milled homogeneous mixture of ZnO, MgO, a-Fe2O3 powders (MZF12 h).
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Fig. 3. AC conductivity as a function of frequency of different unmilled and ballmilled homogeneous mixture of ZnO, MgO, a-Fe2O3 powders at T = 300 K. Fig. 2. dc conductivity as a function of temperature of different unmilled and ballmilled homogeneous mixture of ZnO, MgO, a-Fe2O3 powders.
where C is a constant, k is the Boltzmann constant and Ea represents the activation energy of the conduction mechanism. The logarithm conductivity [ln(Ts)] has been studied as a function of reciprocal temperature (103/T) for the investigated samples. According to Fig. 2 the linear variation of ln(Ts) with 103/T indicates the prevalence of a simple hopping type charge transport in all the investigated samples. The values of activation energy Ea have been calculated from the slopes of the different straight line curves in Fig. 2 and its values increasing from 7 to 14 meV with increasing milling time from 0 to 12 h. It is observed that activation energy increases from 7 to 12 meV for 3 h milling, after that no considerable change has observed in further increase in milling time from 3 to 12 h. This large increase of Ea within 3 h milling may be due to the large decrease of particle size in the samples. By further milling the particle size does not change much more due to which a small activation energy change has been observed. The ac conductivity of Mg–Zn ferrite samples are investigated in the frequency range 20 Hz to 1 MHz and in the temperature range 77 T 300 K. The measured data showed that the variation of conductivity with frequency at a particular temperature is prominent at higher frequencies, whereas at low frequencies it is almost independent with frequencies, this could be attributed to the dc contribution. A general feature of amorphous semiconductors or disordered systems is that the frequency dependent conductivity sac(f) obeys a power law with frequency. The total conductivity s0 (f) at a particular temperature over a wide range of frequencies can be expressed as [35–37]
s 0 ð f Þ ¼ s dc þ s ac ð f Þ ¼ s dc þ a f s
in Fig. 4 for different samples. The frequency exponent ‘s’ is found to be weak temperature dependent at lower temperature (T < 200 K), but above 200 K the estimated values of ‘s’ gradually decrease with increasing temperature. In general two physical processes such as correlated barrier hopping (CBH) [37] and quantum mechanical tunneling (electron tunneling [38], small polaron tunneling [37] and large polaron tunneling [36]) govern the conduction process of disordered systems. As the nature of temperature dependency of ‘s’ for different conduction processes are different, the exact nature of charge transport may be obtained experimentally from the temperature variation of the frequency exponent ‘s’. According to the electron tunneling theory, the frequency exponent ‘s’ is temperature independent, whereas for small polaron tunneling ‘s’ increases with increasing temperature and for large polaron tunneling ‘s’ decreases first and then increases with increasing temperature. But according to the
(2)
where sdc is the dc conductivity, a is the temperature dependent constant and the frequency exponent s < 1. The value of sac(f) has been determined upon subtraction of the dc contribution from the total frequency dependent conductivity s0 (f). Fig. 3 shows the linear variation of ln[sac(f)] with ln(f) at T = 300 K for the different samples. Similar behavior was observed for all other temperatures in different samples. The value of ‘s’ at each temperature has been calculated from the slope of ln[sac(f)] vs. ln(f) plot for each temperature. The trend of change in ‘s’ with temperature is shown
Fig. 4. The temperature variation of the frequency exponents (s) for unmilled and different ball-milled homogeneous mixtures of ZnO, MgO, a-Fe2O3 powders. Inset shows variation of s in the temperature range 77 T 175 K.
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correlated barrier hopping model ‘s’ only decreases with the increase in temperature. From the trend of change in ‘s’ with temperature (T > 200 K), it is presumed that the correlated barrier hopping is suitable for explaining the behavior of our investigated data. According to this model, the charge carrier hops between the sites over the potential barrier separating them and the frequency exponent ‘s’ is given by the expression [37]. s¼1
6kB T W H kB Tlnð1=vt 0 Þ
(2a)
where WH is the effective barrier height and to is the characteristic relaxation time. According to Eq. (2a), for large values of WH/kBT, the variation of ‘s’ with frequency is so small that it is effectively independent of frequency [39,40]. Moreover it has been observed in our study that ‘s’ is independent of frequency [linear variation of ln[sac(f)] with ln(f) in Fig. 3]. Therefore, we fitted our experimental data with Eq. (2a) as function of temperature alone with WH and vto as fitting parameters. In Fig. 4 the points represent the experimental data whereas solid lines are the theoretical best fit values obtained from Eq. (2a) for different samples. The best fitted values of the parameters WH and to (at a fixed frequency of f = 1 MHz) are laying between 0.70–1.03 eV and 1.41 1014 to 1.92 1013 S, respectively, for different samples. The values of WH are, as expected, higher than the activation energy measured from grain and grain boundary contribution (discussed later) and the values of the characteristic relaxation time to are comparable with those that would be expected for typical inverse phonon frequency. However at low temperature, T < 200 K, the value of ‘s’ decreases slowly and follows a linear variation as shown in inset of Fig. 4. According to the theory of CBH model, at lower temperature where the value of WH/kBT is large, Eq. (2a) transforms to a linear temperature dependency of ‘s’. So the observed linear temperature dependency of ‘s’ may be due to the high value of WH/kBT at low temperature. Therefore, from the trend of variation of ‘s’ with temperature, it may be concluded that the ac conductivity in the investigated samples can be described by the CBH model. Temperature dependence of real part of ac conductivity (s0 (f)) for different frequencies of MZF12h has been shown in Fig. 5. Two different slopes are observed in the ln[Ts0 (f)] vs. 103/T plot in the two temperature range. In order to calculate the activation energy in the two temperature range, the experimental data have been analyzed by Eq. (1). The values of Ea at different frequencies have
Fig. 5. AC conductivity as a function of temperature of 12 h ball-milled homogeneous mixture of ZnO, MgO, a-Fe2O3 powders at different frequencies.
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been calculated from the slopes of ln[Ts0 (f)] vs. 103/T plot in the two temperature range. It is observed that the activation energy decreases 368–228 meV in the high temperature region and remains almost constant (6.7–9.1 meV) at low temperature region with increasing frequencies from 1 to 500 kHz. Such anomalies may arise due to various reasons such as transformation of magnetic phase or structural phase or a change in the conduction mechanism. Since the Curie points of the investigated ferrites are well above room temperature, the above behavior may not be due to magnetic and structural phase transformation. So the conduction mechanism may take important role for such behavior, which would be more clear by observing temperature dependency of the total resistivity due to grain and grain boundary effect (discussed later). The variation of real part of dielectric permittivity e0 (f) with temperature is shown in Fig. 6a for the sample MZF12h for different yet constant frequencies. In the e0 –T plot there is no sharp peak till the temperature is raised to 300 K, which is the maximum temperature employed in our investigation. At a particular frequency the real part of dielectric permittivity increases with temperature and is found to follow a power law e0 (f) / Tn, which are shown as the solid lines in Fig. 6a. The values of n have been calculated from the power law fitting and found to be strongly
Fig. 6. (a) Thermal variation of dielectric constant of 12 h ball-milled homogeneous mixture of ZnO, MgO, a-Fe2O3 powders (MZF12 h) at different frequencies. (b) Variation of dielectric constant as function of frequency at different temperatures of 8 h ball-milled homogeneous mixture of ZnO, MgO, a-Fe2O3 powders.
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frequency dependent. Its value decreases with increasing frequencies for all the samples, which implies that, a larger variation in the e0 (f) with temperature is observed at lower frequency in compare to higher frequency. Generally the ferrite exhibits interfacial polarization due to structural inhomogeneities and existence of free charges [41]. It is thought that the hopping electrons at low frequencies may be trapped by the inhomogeneities. The increase of e0 (f) with temperature at a particular frequency is due to the drop in the resistance of the ferrite with increasing temperature. The low resistance promotes electron hopping, hence resulting in a larger polarizability or larger e0 (f). The frequency dependence of real part of the dielectric permittivity e0 (f) have also been studied for different samples and shown in Fig. 6b for MZF8 h sample at different yet constant temperatures. A weak variation is noticed in the dielectric permittivity at lower temperature, although a large variation of the same is observable at higher temperature for all the samples. At a fixed temperature, the dielectric permittivity e0 (f) increase sharply with decreasing frequency and this sharp increase shifts to lower frequencies as the temperature is reduced. Such sudden increase of real part of the dielectric constant e0 (f) at low frequency can be attributed to the presence of large degree of dispersion due to charge transfer within the interfacial diffusion layer present between the electrodes. The magnitude of the dielectric dispersion is temperature dependent. At lower temperature, the freezing of the electric dipoles through the relaxation process is easier. So there exists decay in polarization with respect to the applied electric field, which is evidenced by the sharp decrease in e0 (f) at lower frequency region. When the temperature is high, the rate of polarization formed is quick and thus the relaxation occurs in high frequency. Due to this, the position of the sharp increase shifts towards higher frequency by increasing temperature. Therefore, the frequency behavior of e0 (f) is due to inhomogeneous nature (containing different permittivity and conductivity regions) of the samples, where the charge carriers are blocked by poorly conducting region. The effective dielectric permittivity of such inhomogeneous systems is given by Maxwell– Wagner capacitor model [42–44]. The complex impedance of such systems can also be modeled by an ideal equivalent circuit consisting of resistance and capacitance due to grain and interfacial grain boundary contribution and it can be expressed as Z¼
1 ¼ Z = iZ == ivC 0 eðvÞ
Z= ¼
Rg 1 þ ðvRg C g Þ2
Z == ¼
þ
(3) Rgb
1 þ ðvRgb C gb Þ2
vR2gb C gb vR2g C g þ 2 1 þ ðvRg C g Þ 1 þ ðvRgb C gb Þ2
Fig. 7. The real part of the complex impedance vs. frequency at T = 300 K of different ball-milled homogeneous mixtures of ZnO, MgO, a-Fe2O3 powders with and without magnetic field.
well fitted with the theory. The values of the grain capacitance (Cb) are smaller than the grain boundary capacitance (Cgb). This is because both the capacitances are inversely proportional to the thickness of the grain and grain boundaries. As the thickness of the grains are much larger than the grain boundaries, the values of Cb < Cgb. The resistance due to interfacial grain boundary is much larger in compare to the grain resistance. This implies that the grain boundary contribution dominates over the grain contribution. Since the ferrites are semiconductors, the conduction process can be explained by hopping mechanism, where the carrier mobility is dominated by a factor that increases with temperature exponentially. This temperature dependent factor is determined by thermal activation in order to overcome the potential barrier between the sites by hopping. Both grain and grain boundary resistances follow this mechanism and the total resistance (R = Rg + Rgb) variation can be expressed as R / exp(Ea/kBT), where Ea is the activation energy. The plots of ln(R) vs. 103/T in Fig. 8 support the above explanation. As seen from Fig. 8 samples exhibit two different activations, one with Ea of 0.43–1.78 meV for the low temperature region and the other with Ea of 43– 281 meV for high temperature region for different samples. This discrepancy
(4)
(5)
where sub indexes ‘g’ and ‘gb’ refer to the grain and interfacial grain boundary respectively, R is resistance, C is capacitance, v = 2pf and C0 is free space capacitance. The real part of the complex impedance have been calculated from the experimental data for real (e0 ) and imaginary (e00 ) part of the dielectric permittivity by using the relation Z0 (f) = e00 (f)/[vC0(e0 (f)2 + e00 (f)2)] for different samples and analyzed by Eq. (4). Fig. 7 shows the frequency dependence of the real part of the complex impedance at room temperatures for different samples with and without magnetic field. The points are the experimental data and the solid lines are the theoretical values obtained from Eq. (4). The grain and grain boundary resistances and capacitances have been extracted from this analysis at room temperature, whose values lie within the range 0.20–3.59 MV for Rg, 15.45–99.57 MV for Rgb, 0.16– 0.45 nF for Cg and 0.29–0.86 mF for Cgb for different samples. It is observed from Fig. 7 that the experimental data are reasonably
Fig. 8. Variation of R (=Rg + Rgb) with temperature of unmilled and ball-milled homogeneous mixture of ZnO, MgO, a-Fe2O3 powders.
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theoretical and experimental is necessary to formulate the true mechanism for this issue. 4. Conclusion
Fig. 9. Magnetic field dependence of the ac conductivity of 8 h ball-milled homogeneous mixture of ZnO, MgO, a-Fe2O3 powders at different temperatures.
probably arises due to the anomalous conduction mechanism in the investigated samples. Ponpandian et al. [45] also observed similar behavior in nanocrystalline Ni ferrite and they reported that at low temperature only electrons take part in conduction, however at high temperatures both electrons and holes take part in conduction. We presume that observed two activation regions in our investigated samples may be due to the same reason as observed in Ni ferrite. Magnetic field dependent real part of the ac conductivity of the different samples at room temperature and f = 1 MHz is shown in Fig. 9. The ac magnetoconductivity increases with the increase of magnetic field for all the investigated samples. At present we have not found the theoretical model in the literature to explain directly the behavior of ac conductivity in presence of magnetic field. Electron micrographs of our investigated samples indicate the heterogeneous nature with spherical grain, which implies that the materials consist of grain and interfacial grain boundary regions. For such heterogeneous samples, it was already discussed that the impedance and the dielectric response can be interpreted by grain and grain boundary resistances and capacitances. As the real part of ac conductivity is related with the dielectric response by the relation s0 (B,f) = ve0e00 (B,f), As e00 (B,f) depends on the values of grain and grain boundary resistances and capacitances, the ac conductivity can be written as [46]
s 0 ðB; f Þ ¼
1 v2 t g t gb þ v2 t ðt g þ t gb Þ d AðRg þ Rgb Þ 1 þ v2 t 2
(6)
where tg = CgRg, tgb = CgbRgb and t = RgRgb(Cg + Cg)/(Rg + Rgb). If the value of any of these resistances is changed by a magnetic field, that will affect the measured ac conductivity. From the analysis of the real part of complex impedance in presence of constant magnetic field B = 0.8 T, it is observed that the values of grain and grain boundary resistances and capacitances lie within the range 0.15–3.6 MV for Rg, 7.59–90.51 MV for Rgb, 0.12–0.31 nF for Cg and 0.21–0.78 mF for Cgb for different samples i.e. the total contribution due to grain and grain boundary resistances (R = Rg + Rgb) decreases with increasing magnetic field. So we may presume that the influence of the magnetic field on the ac conductivity is due to the change of grain and grain boundary resistances by the applied magnetic field. But due to lack of analytical expression for grain or grain boundary resistances with magnetic field, we are not able to compare the measured data directly with theory. Therefore, a more explicit study both
The above experimental observations suggest the following facts: (i) a nonstoichiometric Mg–Zn–ferrite phase can be obtained in a considerable amount (84%) by ball milling the stoichiometric powder mixture of MgO, ZnO and a-Fe2O3 up to 12 h. (ii) The particle size of ferrite phase in the ball-milled samples remains almost unaltered (3 nm). (iii) The dc conductivity of the investigated samples follows the simple hopping type conduction mechanism. (iv) The real part of the complex ac conductivity was found to follow the power law s0 (f) / fs. A detailed analysis of the temperature dependence of the universal dielectric response parameter ‘s’ revealed that the correlated barrier hopping is the dominating charge transport mechanism. (v) At a particular frequency the real part of the dielectric permittivity was found to follow the relation e0 (f,T) / Tn. The magnitude of the temperature exponent ‘n’ strongly depends on frequency and its value decreases with increasing frequency. (vi) The frequency dependent real part of the dielectric permittivity shows large degree of dispersion at low frequency, but rapid polarization at high frequencies, which can be interpreted by Maxwell–Wagner capacitor model. (vii) The grain resistance and capacitance are smaller than grain boundary resistance and capacitance by two and three orders respectively and the total resistance due to grain and grain boundary decreases by the application of magnetic field. (viii) The ac conductivity shows the positive variation in presence of magnetic field, it may be concluded that such observation may be due to the change of grain and grain boundary resistances caused by the magnetic field. Acknowledgements This work has been carried out under grant nos. F.27-1/ 2002.TS.V dated 19.03.2002 and F.28-1/2003.TS.V dated 3103.2003 sanctioned by the MHRD, Government of India. The authors gratefully acknowledge the principal assistance received from the above organization during this work. References [1] T. Hirai, J. Kobayashi, I. Koasawa, Langmuir 15 (1999) 6291. [2] R.H. Kodama, J. Magn. Magn. Mater. 200 (1999) 359. [3] K.V.P.M. Shafi, Y. Koltypin, A. Gedanken, R. Prozorov, J. Balogh, J. Lendvai, I. Felner, J. Phys. Chem. 101B (1997) 6409. [4] M. Elbschutz, S. Shtrikman, J. Appl. Phys. 39 (1968) 997. [5] I. Anton, I.D. Dabata, L. Vekas, J. Magn. Magn. Mater. 85 (1990) 219. [6] R.D. McMickael, R.D. Shull, L.J. Swartzendruber, L.H. Bennett, R.E. Watson, J. Magn. Magn. Mater. 111 (1992) 29. [7] D.L. Leslie-Pelecky, R.D. Rieke, Chem. Mater. 8 (1996) 1770. [8] Y. Tamaura, Y. Ueda, J. Matsunami, N. Hasegawa, M. Nezuka, T. Sano, M. Tsusi, Sol. Energy 65 (1999) 55. [9] S.F. Mansour, Egypt. J. Solids 21 (2005). [10] D.C. Bharti, K. Mukherjee, S.B. Majumdar, Mater. Chem. Phys 120 (2010) 509. [11] S. Bid, S.K. Pradhan, Mater. Chem. Phys. 82 (2003) 27. [12] S.K. Pradhan, S. Bid, M. Gateshki, V. Petkov, Mater. Chem. Phys. 93 (2005) 224. [13] W.I. Archer, R.D. Armstrong, Electrochemistry 7 (1979) 157. [14] T. Straton, A. MacHale, D. Button, H.L. Turner, N.B. Hannay, U. Colombo (Eds.), Electronic Materials, Plenum, New York, 1979, pp. 71–81. [15] Y.C. Yeh, T.Y. Tseng, J. Mater. Sci. 24 (1989) 2739. [16] M.H. Abdullah, A.N. Yusoff, J. Alloys Compd. 233 (1996) 129. [17] S.A. Mazen, H.M. Zaki, S.F. Mansour, Int. J. Pure Appl. Phys. 3 (2007) 40. [18] D. Niznansky, N. Viart, J.L. Renspinger, IEEE Trans. Magn. 30 (1994) 821. [19] J.M. Yang, W.J. Tsuo, F.S. Yen, J. Solid State Chem. 145 (1999) 50. [20] Y. Shi, J. Ding, X. Liu, J.J. Wang, J. Magn. Magn. Mater. 205 (1999) 249. [21] P. Druska, U. Steinike, V. Sepelak, J. Solid State Chem. 146 (1999) 13. [22] V. Sepelak, K. Tkacova, V.V. Boldyrev, U. Steinike, Mater. Sci. Forum 783 (1996) 228. [23] V. Sepelak, A. Yu, U. Rogachev, D. Steinike, C. Uecker, S. Wibmann, K.D. Becker, Acta Crystallogr. Suppl. Issue A 52 (1996) C-367. [24] V. Sepelak, A. Yu, U. Rogachev, D. Steinike, C. Uecker, F. Krumcich, S. Wibmann, K.D. Becker, Mater. Sci. Forum 139 (1997) 235.
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