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Study of dielectric behaviour of Mn–Zn nano ferrites
ARTICLE IN PRESS
Journal of Physics and Chemistry of Solids 68 (2007) 378–381 www.elsevier.com/locate/jpcs
Study of dielectric behaviour of Mn–Zn nano ferrites A. Thakur, P. Mathur, M. Singh Department of Physics, Himachal Pradesh University, Summer Hill, Shimla 171005, India Received 19 June 2006; received in revised form 10 September 2006; accepted 22 November 2006
Abstract Dielectric properties of Mn0.4Zn0.6Fe2O4 ferrites synthesised by co-precipitation method have been investigated as a function of frequency (up to 30 MHz) at different temperatures. Dispersion in dielectric constant has been observed between temperatures 450–500 K. DC resistivity was found to increase up to 100 times greater than those for the samples prepared by the conventional ceramic methods. Resistivity variation with temperature is also reported in the present work. The particle size is calculated using Scherrer equation for Lorentzian peak, which comes out between 9 and 19 nm. Possible mechanisms contributing to these processes have been discussed. r 2006 Published by Elsevier Ltd. Keywords: A. Ceramic; A. Magnetic materials; A. Nanostructures; C. X-ray diffraction; D. Dielectric properties
1. Introduction Soft ferrites are among the most widely used magnetic materials having low cost, high performance for highfrequency applications [1–3]. Mn–Zn ferrites have many important applications in this context. The properties of ferrites are very sensitive to the processing techniques [4–7]. With the production of Mn–Zn ferrite on nanoscale, its properties have been enhanced to a greater extent. Spinel Mn–Zn ferrites have been used in various components for the application in high-frequency range. In order to get good quality ferrites with reproducible stoichiometric composition and desired microstructures, a recently reported co-precipitation method has been used to synthesise ferrite in the present work. The co-precipitation method offers a synthesis route for the production of ferrite, which is uniform and non-aggregated. Ferrites are commonly produced by a ceramic process involving hightemperature solid-state reaction between the constituents of oxides and carbonates. We have found in the coprecipitation method that if pH is controlled by using a base solution, precipitates are formed, which results in homogeneous, fine and reproducible ferrites. Though the Corresponding author.
E-mail address: [email protected] (M. Singh). 0022-3697/$ - see front matter r 2006 Published by Elsevier Ltd. doi:10.1016/j.jpcs.2006.11.028
ferrite was prepared at 200 1C, but to obtain good results, ferrite sample was sintered at 500 1C. 2. Experiment Mn–Zn ferrite of composition Mn0.4Zn0.6Fe2O4 was prepared by the co-precipitation method. The materials used were manganese chloride (98% Merck, India), zinc chloride (96% Merck, India), iron (III) chloride (98% Merck, India) and sodium hydroxide (96% Merck, India). One molar solution of these materials was made with distilled water. Sodium hydroxide (70 ml) was taken from one molar solution in approximately 1760 ml of distilled water to have the concentration of 0.37 mol/l and heated to boiling. Manganese chloride, zinc chloride and iron (III) chloride were taken from their molar solution in accurate stoichiometric proportions. These solutions were poured as quickly as possible into the boiling solution of NaOH under vigorous stirring produced by the glass mechanical stirrer (500 rpm). Mixing is very important; otherwise segregation of phases can take place. After co-precipitation, pH is set to 12.5–13. Reaction vessel was covered with a plastic cover to diminish the evaporation of the solution. Reaction was continued for 30–40 min at temperature 90–100 1C under vigorous stirring. Reaction vessel was cooled to ambient temperature and particles precipitate.
ARTICLE IN PRESS A. Thakur et al. / Journal of Physics and Chemistry of Solids 68 (2007) 378–381
Total volume was reduced to 500 ml by the aspiration of supernatant. Suspension was centrifuged in four beakers at 7000 rpm for 10 min. Precipitate was washed with distilled water (900 ml) and centrifuged once more in four beakers at 7000 rpm for 10 min. The residue was dried and was calcinated in a box-type furnace for 15 h at the rate of 200 1C/h to obtain a ferrite powder. This powder was mixed with 2% P.V.A. binder and pressed into pellets of 1.50 cm diameter and 0.20 mm thickness under pressure of 5 ton (1 ton ¼ 1.016 103 kg) and rings of 1.5 cm outer diameter, 1.0 cm inner diameter and 0.20 cm thickness under a pressure of 3 ton. These samples were sintered in air at 500 1C at a heating rate of 250 1C/h for another 15 h and were subsequently cooled. The pellets were coated with a silver paste to provide the electrical contacts and the rings were wound with about 50 turns of 30 SWG enameled copper wire to form the torroids. X-ray diffraction (XRD) measurements were taken on a Rigaku Geiger Flex 3 kW diffractometer using CuKa source. Dielectric constant and the loss factor were measured up to 30 MHz by using an Agilent Technologies 4285A Precision LCR Meter. Resistivity as a function of temperature was measured by using the two-probe method. Curie temperature was measured by using the gravity method. 3. X-ray study XRD pattern of the ferrite sample pre-sintered at 200 1C and sintered at 500 1C are shown in Figs. 1 and 2. The 311
550
450
511/333 220
422
400
400 30
40
50
60
2θ Fig. 1. XRD of Mn0.4Zn0.6Fe2O4 sintered at 200 1C.
550
Counts
d¼
0:9l , ðw w1 Þ cos y
where d is the grain diameter, w and w1 are the halfintensity width of the relevant diffraction peak and the instrumental broadening, respectively, l is the X-ray wavelength and y is the angle of diffraction. The average particle size was found to be 9 nm at 200 1C and 19 nm at 500 1C. 4. Electrical resistivity The variation of the DC resistivity, r, with temperature is shown in Fig. 3. The DC resistivity decreases from 33 106 to 4 106 O cm when temperature is increased from 300 to 500 K, which is about 10–100 times more than that of the ceramic ferrite. This observation is of significant importance as it makes these ferrites suitable for the highfrequency applications, where eddy current losses become appreciable. The higher values of DC resistivity is because of the stoichiometric compositions, better crystal structures and the improved nanostructures obtained by the coprecipitation method. Sample sintered at the low temperature possesses small grain size [4]. Sample with small grain consists of more number of grain boundaries. The grain boundaries are the region of mismatch between the energy states of adjacent grains and hence act as barrier to the flow of electrons. Another advantage of the small grain size is that it helps in reducing Fe2+ ions as oxygen moves faster in the small grains, thus keeping iron in Fe3+ state [9]. Therefore, the sample sintered at a low temperature is
311
500
35 440
511/333
450 400
observed diffraction lines were found to correspond to those of the standard pattern of the manganese ferrite with no extra lines, indicating thereby that the samples have a single-phase spinel structure and no unreacted constituents were present in these samples. The diffraction peaks are quite broad because of the nanometer size of the crystallite. Lattice constant ‘a’ for the samples sintered at 200 and 500 1C was calculated from the observed ‘d’ values and found to be 8.318 and 8.329 A˚, respectively. The peak becomes sharper with the increase in the sintering temperature. The particle size of the samples has been estimated from the broadening of the XRD peaks using the Scherrer equation [8] for Lorentzian peak
220
422
400
350
ρ (106 ohm cm.)
Counts
440 500
379
30 25 20 15 10 5
30
40
50 2θ
Fig. 2. XRD of Mn0.4Zn0.6Fe2O4 sintered at 500 1C.
60
300
350
400
450
500
Temperature (K) Fig. 3. Variation of DC resistivity with temperature.
550
ARTICLE IN PRESS A. Thakur et al. / Journal of Physics and Chemistry of Solids 68 (2007) 378–381
380
found to exhibit high resistivity as compared to the ceramic ferrite [2,6]. tanδε
The variation of the dielectric constant, e0 , with log frequency at different temperatures is shown in Fig. 4. These variations can be explained on the basis of space charge polarization model of Wagner [10] and Maxwell [11] and is in agreement with the Koop’s phenomenological theory. The slight peaks are observed at all the temperatures between the frequency range of 0.1–1 MHz. These peaks can be explained on the basis of resonance that occurs when the frequency of applied field equals the Larmor precision of electron spin. The dispersion at Curie temperature, 475 K, can be explained on the basis of available ferrous ions on the octahedral sites. As a consequence, it is possible for these ions to be polarized to a maximum extent. Further, it is seen that the dielectric constant, e0 , decreases with an increase in frequency at all the temperatures, as is expected. The dielectric constant, e0 , is in the range of 10–480 at different temperatures. The observed dispersion of the dielectric constant can be explained on the basis of hopping conduction between Fe3+ and Fe2+, Mn2+ and Mn3+, Zn2+ and Zn3+ pairs of ions. A decrease in the dielectric constant at higher frequencies is also observed. This can be explained on the basis that the solid is assumed as composed of wellconducting grains separated by the poorly conducting grain boundaries [12,13]. The electrons reach the grain boundary through hopping and if the resistance of grain boundary is high enough, electrons pile up at the grain boundaries and produce polarization. However, as the frequency of the applied field is increased, the electrons reverse their direction of motion more often. This decreases the probability of electrons reaching the grain boundary and as a result polarization decreases. Therefore, with an increasing frequency of the applied field, the dielectric constant decreases. The results obtained in the present work and the explanation given above is in agreement with those reported by Koops [13]. Fig. 5 shows the variation of dielectric loss factor, tan de, with frequency at different temperatures. This variation is similar to the variation of e0 with frequency and can be 500
300 K 350 K 400 K 450 K 475 K 500 K
400 ε'
300 200 100 0 1 log frequency (MHz)
10
Fig. 4. Variation of dielectric constant, e0 , with log frequency at different temperatures.
300K 350K 400K 450K 475K 500K
2.5 2.0 1.5 1.0 0.5 0.0 0.1
1
10
log frequency (MHz)
Fig. 5. Variation of dielectric loss factor, tan de, with log frequency at different temperatures.
ε'
5. Dielectric study
0.1
3.0
500 450 400 0.1 MHz 350 1 MHz 300 5 MHz 10 MHz 250 30 MHz 200 150 100 50 0 275 300 325 350 375 400 425 450 475 500 525 Temperature (K)
Fig. 6. Variation of dielectric constant, e0 , with temperature at different frequencies.
explained on the basis of Koops’ phenomenological model. Similar variation of the dielectric loss factor with frequency also justifies the low value of dielectric loss. Fig. 6 shows the variation of the dielectric constant, e0 , with temperature at different frequencies. From the graph, it can be seen that the dielectric constant initially increases gradually with an increase in temperature up to 475 K, which is designated as the dielectric transition temperature, Td(K). Beyond this temperature, the value of dielectric constant decreases. A similar temperature variation of dielectric constant was reported earlier [14–16]. The Curie temperature, Tc(K), was determined by the gravity method and found to be 476 K which is in good agreement with the transition temperature, Td(K). The anomaly in variation of e0 as observed at 475 K for all the frequencies is attributed to the transition of the sample from ferrimagnetic (magnetically ordered) to the paramagnetic state (disordered state). The increase in the dielectric constant with temperature suggests that the effect of temperature is more pronounced on the interfacial than on dipolar polarisation. At high frequencies, electronic and ionic polarizations are main contributors [17] and their temperature dependence is insignificant. The low value of the dielectric constant at higher frequencies is therefore understandable. It can be seen from Fig. 6 that even at 1 MHz frequency, the sample is having an appreciable value of dielectric constant, which makes it useful for the high-frequency applications.
ARTICLE IN PRESS A. Thakur et al. / Journal of Physics and Chemistry of Solids 68 (2007) 378–381
log ρ x 103 (ohm.cm.)
4.6
381
7. Conclusion
4.4 4.2 4.0 3.8 3.6 1.5
2.0
2.5
3.0
3.5
1000 (K-1) T Fig. 7. Variation of log r 103 O cm with 1000/T K1.
6. Resistivity vs. temperature Fig. 7 shows the variation of log r with 1/T. The resistivity of the sample decreases with increasing temperature according to the relation r ¼ roeEr/kT, where Er represents the activation energy [18], which is the energy needed to release an electron from an ion for a jump to the neighbouring ion, so giving rise to the electrical conductivity. Upon an electron jump, a displacement of the ions occurs in the neighbourhood of the electron in question. Activation energy, Er, was calculated from the slope of the graph given in Fig. 7. According to the relation E r ¼ 0:198 103 dðlog rÞ=dð1=TÞ. It is found that the value of activation energy in the ferrimagnetic region is lower than that of the paramagnetic region. The lower activation energy in the ferromagnetic region is attributed to the magnetic spin disordering [19] due to decrease in the concentration of current carriers [20], while the change in activation energy is attributed to the change in conduction mechanism [21,22]. Activation energy for the sample is found to be 0.3435 eV, which indicates that ferrite formed is p-type semiconductor. The increase in resistivity is also attributed to the p-type conductivity, which increases the activation energy on the basis of Verwey conduction mechanism [18].
The dielectric constant and the loss factor decrease rapidly with an increase in frequency and then reach a constant value. We can have a good quality ferrite even at low temperature if the duration of the sintering temperature is increased. Temperature dependence of the dielectric constant has an abnormal value at Curie temperature. On nanolevel, we were successful to have an appreciable value of the dielectric constant with resistivity 10–100 times more as compared to the conventional ceramic methods. References [1] S.J. Shukla, K.M. Jadhav, G.K. Bichile, J. Pure Appl. Phys. 39 (2001) 226. [2] M. Singh, S.P. Sud, Mod. Phys. Lett. 14 (2000) 531–537. [3] M.I. Rosales, E. Amano, M.P. Cuautle, R. Valenzuela, Mater. Sci. Eng. B 49 (1997) 221. [4] A. Thakur, M. Singh, Ceram. Int. 29 (2003) 505–511. [5] A. Verma, T.C. Goel, R.G. Mendiratta, in: Second International Conference on Processing Materials for Properties, The Mineral, Metal & Material Society, 2000, pp. 493–497. [6] B.S. Chauhan, R. Kumar, K.M. Jadhav, M. Singh, J. Magn. Magn. Mater. 283 (2004) 71–81. [7] A. Verma, T.C. Goel, R.G. Mendiratta, Mater. Sci. Techol. 16 (2000) 712–715. [8] B.D. Cullity, Elements of X-ray Diffraction, Addison-Wesley, Reading, MA, 1978. [9] K. Iwauche, Jpn. J. Appl. Phys. 10 (1971) 1520–1528. [10] K.W. Wagner, Ann. Phys. (Leipzig) 40 (1913) 817. [11] J. C. Maxwell, Electricity and Magnetism, vol. 1, Oxford University Press, Oxford, Section 328. [12] L. Radhapiyari, S. Phanjoubam, H.N.K. Sarma, C. Prakash, Mater. Lett. 44 (2000) 65. [13] C.G. Koops, Phys. Rev. 83 (1951) 121. [14] D. Ravinder, K. Vijaya Kumar, Bull. Mater. Sci. 24 (2001) 505–509. [15] A.K. Singh, T.C. Goel, R.G. Mendiratta, J. Appl. Phys. 91 (2002) 6626–6629. [16] S.A. Olofa, J. Magn. Magn. Mater. 131 (1994) 103. [17] L.L. Hench, J.K. West, Principles of Electronic Ceramics, Wiley, New York, 1990, p. 189. [18] E.J.W. Verwey, P.W. Haaijman, F.C. Romeyn, G.W. van Oosterhout, Philips Res. Rep. 5 (1950) 173–187. [19] K. Barerner, P. Mandal, R.V. Helmolt, Phys. Stat. Sol. (b) 223 (2001) 811–820. [20] J. Baszsynski, Acta Phys. Polym. 35 (1969) 631. [21] V.R.K. Murthy, J. Sobhandri, Phys. Stat. Sol. (A) 38 (1977) 647. [22] M. Singh, S.P. Sud, Mater. Sci. Eng. B 83 (2000) 181.
Journal of Physics and Chemistry of Solids 68 (2007) 378–381 www.elsevier.com/locate/jpcs
Study of dielectric behaviour of Mn–Zn nano ferrites A. Thakur, P. Mathur, M. Singh Department of Physics, Himachal Pradesh University, Summer Hill, Shimla 171005, India Received 19 June 2006; received in revised form 10 September 2006; accepted 22 November 2006
Abstract Dielectric properties of Mn0.4Zn0.6Fe2O4 ferrites synthesised by co-precipitation method have been investigated as a function of frequency (up to 30 MHz) at different temperatures. Dispersion in dielectric constant has been observed between temperatures 450–500 K. DC resistivity was found to increase up to 100 times greater than those for the samples prepared by the conventional ceramic methods. Resistivity variation with temperature is also reported in the present work. The particle size is calculated using Scherrer equation for Lorentzian peak, which comes out between 9 and 19 nm. Possible mechanisms contributing to these processes have been discussed. r 2006 Published by Elsevier Ltd. Keywords: A. Ceramic; A. Magnetic materials; A. Nanostructures; C. X-ray diffraction; D. Dielectric properties
1. Introduction Soft ferrites are among the most widely used magnetic materials having low cost, high performance for highfrequency applications [1–3]. Mn–Zn ferrites have many important applications in this context. The properties of ferrites are very sensitive to the processing techniques [4–7]. With the production of Mn–Zn ferrite on nanoscale, its properties have been enhanced to a greater extent. Spinel Mn–Zn ferrites have been used in various components for the application in high-frequency range. In order to get good quality ferrites with reproducible stoichiometric composition and desired microstructures, a recently reported co-precipitation method has been used to synthesise ferrite in the present work. The co-precipitation method offers a synthesis route for the production of ferrite, which is uniform and non-aggregated. Ferrites are commonly produced by a ceramic process involving hightemperature solid-state reaction between the constituents of oxides and carbonates. We have found in the coprecipitation method that if pH is controlled by using a base solution, precipitates are formed, which results in homogeneous, fine and reproducible ferrites. Though the Corresponding author.
E-mail address: [email protected] (M. Singh). 0022-3697/$ - see front matter r 2006 Published by Elsevier Ltd. doi:10.1016/j.jpcs.2006.11.028
ferrite was prepared at 200 1C, but to obtain good results, ferrite sample was sintered at 500 1C. 2. Experiment Mn–Zn ferrite of composition Mn0.4Zn0.6Fe2O4 was prepared by the co-precipitation method. The materials used were manganese chloride (98% Merck, India), zinc chloride (96% Merck, India), iron (III) chloride (98% Merck, India) and sodium hydroxide (96% Merck, India). One molar solution of these materials was made with distilled water. Sodium hydroxide (70 ml) was taken from one molar solution in approximately 1760 ml of distilled water to have the concentration of 0.37 mol/l and heated to boiling. Manganese chloride, zinc chloride and iron (III) chloride were taken from their molar solution in accurate stoichiometric proportions. These solutions were poured as quickly as possible into the boiling solution of NaOH under vigorous stirring produced by the glass mechanical stirrer (500 rpm). Mixing is very important; otherwise segregation of phases can take place. After co-precipitation, pH is set to 12.5–13. Reaction vessel was covered with a plastic cover to diminish the evaporation of the solution. Reaction was continued for 30–40 min at temperature 90–100 1C under vigorous stirring. Reaction vessel was cooled to ambient temperature and particles precipitate.
ARTICLE IN PRESS A. Thakur et al. / Journal of Physics and Chemistry of Solids 68 (2007) 378–381
Total volume was reduced to 500 ml by the aspiration of supernatant. Suspension was centrifuged in four beakers at 7000 rpm for 10 min. Precipitate was washed with distilled water (900 ml) and centrifuged once more in four beakers at 7000 rpm for 10 min. The residue was dried and was calcinated in a box-type furnace for 15 h at the rate of 200 1C/h to obtain a ferrite powder. This powder was mixed with 2% P.V.A. binder and pressed into pellets of 1.50 cm diameter and 0.20 mm thickness under pressure of 5 ton (1 ton ¼ 1.016 103 kg) and rings of 1.5 cm outer diameter, 1.0 cm inner diameter and 0.20 cm thickness under a pressure of 3 ton. These samples were sintered in air at 500 1C at a heating rate of 250 1C/h for another 15 h and were subsequently cooled. The pellets were coated with a silver paste to provide the electrical contacts and the rings were wound with about 50 turns of 30 SWG enameled copper wire to form the torroids. X-ray diffraction (XRD) measurements were taken on a Rigaku Geiger Flex 3 kW diffractometer using CuKa source. Dielectric constant and the loss factor were measured up to 30 MHz by using an Agilent Technologies 4285A Precision LCR Meter. Resistivity as a function of temperature was measured by using the two-probe method. Curie temperature was measured by using the gravity method. 3. X-ray study XRD pattern of the ferrite sample pre-sintered at 200 1C and sintered at 500 1C are shown in Figs. 1 and 2. The 311
550
450
511/333 220
422
400
400 30
40
50
60
2θ Fig. 1. XRD of Mn0.4Zn0.6Fe2O4 sintered at 200 1C.
550
Counts
d¼
0:9l , ðw w1 Þ cos y
where d is the grain diameter, w and w1 are the halfintensity width of the relevant diffraction peak and the instrumental broadening, respectively, l is the X-ray wavelength and y is the angle of diffraction. The average particle size was found to be 9 nm at 200 1C and 19 nm at 500 1C. 4. Electrical resistivity The variation of the DC resistivity, r, with temperature is shown in Fig. 3. The DC resistivity decreases from 33 106 to 4 106 O cm when temperature is increased from 300 to 500 K, which is about 10–100 times more than that of the ceramic ferrite. This observation is of significant importance as it makes these ferrites suitable for the highfrequency applications, where eddy current losses become appreciable. The higher values of DC resistivity is because of the stoichiometric compositions, better crystal structures and the improved nanostructures obtained by the coprecipitation method. Sample sintered at the low temperature possesses small grain size [4]. Sample with small grain consists of more number of grain boundaries. The grain boundaries are the region of mismatch between the energy states of adjacent grains and hence act as barrier to the flow of electrons. Another advantage of the small grain size is that it helps in reducing Fe2+ ions as oxygen moves faster in the small grains, thus keeping iron in Fe3+ state [9]. Therefore, the sample sintered at a low temperature is
311
500
35 440
511/333
450 400
observed diffraction lines were found to correspond to those of the standard pattern of the manganese ferrite with no extra lines, indicating thereby that the samples have a single-phase spinel structure and no unreacted constituents were present in these samples. The diffraction peaks are quite broad because of the nanometer size of the crystallite. Lattice constant ‘a’ for the samples sintered at 200 and 500 1C was calculated from the observed ‘d’ values and found to be 8.318 and 8.329 A˚, respectively. The peak becomes sharper with the increase in the sintering temperature. The particle size of the samples has been estimated from the broadening of the XRD peaks using the Scherrer equation [8] for Lorentzian peak
220
422
400
350
ρ (106 ohm cm.)
Counts
440 500
379
30 25 20 15 10 5
30
40
50 2θ
Fig. 2. XRD of Mn0.4Zn0.6Fe2O4 sintered at 500 1C.
60
300
350
400
450
500
Temperature (K) Fig. 3. Variation of DC resistivity with temperature.
550
ARTICLE IN PRESS A. Thakur et al. / Journal of Physics and Chemistry of Solids 68 (2007) 378–381
380
found to exhibit high resistivity as compared to the ceramic ferrite [2,6]. tanδε
The variation of the dielectric constant, e0 , with log frequency at different temperatures is shown in Fig. 4. These variations can be explained on the basis of space charge polarization model of Wagner [10] and Maxwell [11] and is in agreement with the Koop’s phenomenological theory. The slight peaks are observed at all the temperatures between the frequency range of 0.1–1 MHz. These peaks can be explained on the basis of resonance that occurs when the frequency of applied field equals the Larmor precision of electron spin. The dispersion at Curie temperature, 475 K, can be explained on the basis of available ferrous ions on the octahedral sites. As a consequence, it is possible for these ions to be polarized to a maximum extent. Further, it is seen that the dielectric constant, e0 , decreases with an increase in frequency at all the temperatures, as is expected. The dielectric constant, e0 , is in the range of 10–480 at different temperatures. The observed dispersion of the dielectric constant can be explained on the basis of hopping conduction between Fe3+ and Fe2+, Mn2+ and Mn3+, Zn2+ and Zn3+ pairs of ions. A decrease in the dielectric constant at higher frequencies is also observed. This can be explained on the basis that the solid is assumed as composed of wellconducting grains separated by the poorly conducting grain boundaries [12,13]. The electrons reach the grain boundary through hopping and if the resistance of grain boundary is high enough, electrons pile up at the grain boundaries and produce polarization. However, as the frequency of the applied field is increased, the electrons reverse their direction of motion more often. This decreases the probability of electrons reaching the grain boundary and as a result polarization decreases. Therefore, with an increasing frequency of the applied field, the dielectric constant decreases. The results obtained in the present work and the explanation given above is in agreement with those reported by Koops [13]. Fig. 5 shows the variation of dielectric loss factor, tan de, with frequency at different temperatures. This variation is similar to the variation of e0 with frequency and can be 500
300 K 350 K 400 K 450 K 475 K 500 K
400 ε'
300 200 100 0 1 log frequency (MHz)
10
Fig. 4. Variation of dielectric constant, e0 , with log frequency at different temperatures.
300K 350K 400K 450K 475K 500K
2.5 2.0 1.5 1.0 0.5 0.0 0.1
1
10
log frequency (MHz)
Fig. 5. Variation of dielectric loss factor, tan de, with log frequency at different temperatures.
ε'
5. Dielectric study
0.1
3.0
500 450 400 0.1 MHz 350 1 MHz 300 5 MHz 10 MHz 250 30 MHz 200 150 100 50 0 275 300 325 350 375 400 425 450 475 500 525 Temperature (K)
Fig. 6. Variation of dielectric constant, e0 , with temperature at different frequencies.
explained on the basis of Koops’ phenomenological model. Similar variation of the dielectric loss factor with frequency also justifies the low value of dielectric loss. Fig. 6 shows the variation of the dielectric constant, e0 , with temperature at different frequencies. From the graph, it can be seen that the dielectric constant initially increases gradually with an increase in temperature up to 475 K, which is designated as the dielectric transition temperature, Td(K). Beyond this temperature, the value of dielectric constant decreases. A similar temperature variation of dielectric constant was reported earlier [14–16]. The Curie temperature, Tc(K), was determined by the gravity method and found to be 476 K which is in good agreement with the transition temperature, Td(K). The anomaly in variation of e0 as observed at 475 K for all the frequencies is attributed to the transition of the sample from ferrimagnetic (magnetically ordered) to the paramagnetic state (disordered state). The increase in the dielectric constant with temperature suggests that the effect of temperature is more pronounced on the interfacial than on dipolar polarisation. At high frequencies, electronic and ionic polarizations are main contributors [17] and their temperature dependence is insignificant. The low value of the dielectric constant at higher frequencies is therefore understandable. It can be seen from Fig. 6 that even at 1 MHz frequency, the sample is having an appreciable value of dielectric constant, which makes it useful for the high-frequency applications.
ARTICLE IN PRESS A. Thakur et al. / Journal of Physics and Chemistry of Solids 68 (2007) 378–381
log ρ x 103 (ohm.cm.)
4.6
381
7. Conclusion
4.4 4.2 4.0 3.8 3.6 1.5
2.0
2.5
3.0
3.5
1000 (K-1) T Fig. 7. Variation of log r 103 O cm with 1000/T K1.
6. Resistivity vs. temperature Fig. 7 shows the variation of log r with 1/T. The resistivity of the sample decreases with increasing temperature according to the relation r ¼ roeEr/kT, where Er represents the activation energy [18], which is the energy needed to release an electron from an ion for a jump to the neighbouring ion, so giving rise to the electrical conductivity. Upon an electron jump, a displacement of the ions occurs in the neighbourhood of the electron in question. Activation energy, Er, was calculated from the slope of the graph given in Fig. 7. According to the relation E r ¼ 0:198 103 dðlog rÞ=dð1=TÞ. It is found that the value of activation energy in the ferrimagnetic region is lower than that of the paramagnetic region. The lower activation energy in the ferromagnetic region is attributed to the magnetic spin disordering [19] due to decrease in the concentration of current carriers [20], while the change in activation energy is attributed to the change in conduction mechanism [21,22]. Activation energy for the sample is found to be 0.3435 eV, which indicates that ferrite formed is p-type semiconductor. The increase in resistivity is also attributed to the p-type conductivity, which increases the activation energy on the basis of Verwey conduction mechanism [18].
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