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AC conductivity and dielectric behavior of CoAlxFe2−xO4
Solid State Sciences 6 (2004) 61–69 www.elsevier.com/locate/ssscie
AC conductivity and dielectric behavior of CoAlx Fe2−x O4 A.M. Abo El Ata a , S.M. Attia b , T.M. Meaz a,∗ a Physics Department, Faculty of Science, Tanta University, Tanta, Egypt b Physics and Chemistry Department, Faculty of Education, Tanta University, Kafer El-Shiekh, Egypt
Received 20 May 2003; received in revised form 29 September 2003; accepted 16 October 2003
Abstract AC conductivity and dielectric properties have been studied for a series of polycrystalline spinel ferrite with composition CoAlx Fe2−x O4 , as a function of frequency and temperature. The results of AC conductivity were discussed in terms of the quantum mechanical tunneling and small polaron tunneling models. The dispersion of the dielectric constant was discussed in the light of Koops model and hopping conduction mechanism. The dielectric loss tangent tan δ curves exhibits a dielectric relaxation peaks which are attributed to the coincidence of the hopping frequency of the charge carriers with that of the external fields. The AC conductivity, dielectric constant, and dielectric loss tangent were found to increase with increasing the temperature due to the increase of the hopping frequency, while they decrease with increasing Al ion content due to the reduction of iron ions available for the conduction process at the octahedral sites. 2003 Elsevier SAS. All rights reserved. Keywords: Spinel ferrite; AC conductivity; Dielectric constant; Dielectric loss tangent; Conduction mechanism
1. Introduction
2. Experimental details
Low cost, easily manufacturing and interesting electric and magnetic properties lead the polycrystalline ferrite to be one of the most important material that has attracted a considerable attention in the field of technological application in a wide range of frequency extended from microwave to radio frequency. These materials are in the category of magnetic semiconductors. Their electrical and dielectric properties depends on the preparation conditions, such as sintering temperature, sintering atmosphere and soaking time as well as the type of the substituted ions. It was proposed that the air-sintered ferrites are characterized by microstructure consisting of relatively high conductive grains separated by high resistive thin layers (grain boundaries) [1,2]. Most of the external applied electric field to the specimen is concentrated on the grain boundary regions, therefore the electrical properties of the grain boundary phase control the electric and dielectric properties of this materials. The aim of this work is to study the effect of Al ion substitution on the behavior of AC conductivity and dielectric properties of CoFe2 O4 at different frequencies and temperatures.
2.1. Preparation of the samples
* Corresponding author.
E-mail address: [email protected] (T.M. Meaz). 1293-2558/$ – see front matter 2003 Elsevier SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2003.10.006
High pure cobalt, aluminum and ferric oxides, were mixed together in molar ratio to prepare a series of polycrystalline spinel ferrites with chemical composition CoAlx Fe2−x O4 , with x = 0.0, 0.4, 0.8, 1.2 and 1.6, using the conventional ceramic method. After mixing the gradients for 3 h using electrical grinding machine, the final products were presintered at 900 ◦ C for 5 h and slowly cooled to room temperature. The mixtures were reground again for 3 h, and the final fine powders were pressed in disk-shaped samples with thickness ranges from 0.25 to 0.3 cm and diameter ∼ 1.4 cm. Then, the disks were sintered at 1200 ◦ C for 5 h. The samples were slowly cooled to room temperature. Finally, the surfaces of the disks were polished and coated by sliver paste that acts as a good contact for measuring the electric and dielectric properties. X-ray diffraction analysis confirms the existence of a single-phase spinel ferrite. 2.2. Measurements The AC conductivity and the dielectric properties were measured at different temperatures using a complex impedance technique with low frequency lock-in-amplifier in
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the frequency range 102 –105 Hz. The details of the circuit and measurements were reported elsewhere [3,4].
3. Results and discussion 3.1. X-ray analysis and estimation of cation distribution Fig. 1 shows the X-ray diffraction patterns for the samples under investigation. The X-ray chart shows the existence of a single phase spinel ferrites without any extra lines corresponding to any other phases. The lattice parameter was calculated for each sample according to the equation a = dhkl h2 + k 2 + l 2 , (1) where dhkl is the interplaner distance for a given plan with Miller indices (hkl). Fig. 2 shows the variation of the lattice parameter a with Al ion content. It is found that the lattice parameter decreases with increasing Al ion substitution. The decrease of the value of the lattice parameter with increasing Al ion substitution can be explained on the basis of ionic radius, where the ionic radius of Al3+ ion is smaller than that of Fe3+ ion. The mean radius of the ions at tetrahedral site rtetr and octahedral site roct were calculated according to Eqs. (2) and (3) [5]. √ rtetr = a 3(µ − 0.25) − Ro , (2)
5 − µ − Ro , roct = a 8
(3)
where Ro is the radius of the oxygen ion (Ro = 1.26 Å [6]), and µ is the oxygen parameter (µ = 0.381 for CoFe2 O4 [6]). The behavior of rtetr and roct as a function of composition is shown in Fig. 2. It is shown that both rtetr and roct decrease with increasing Al ion content indicating that Al ions are distributed over A and B sites. The cation distribution for CoFe2 O4 was estimated according to Eqs. (2) and (3), and on the basis that the cation distribution for a given ferrite system can be expressed as [5] Meδ Fe1−δ [Me1−δ Fe1+δ ]O4 ,
(4)
where Me is the divalent ion and δ determine the cation distribution. The mean radius of the ion at tetrahedral site ban be expressed as rtetr = δrMe2+ + (1 − δ)rFe3+ .
(5)
From Eqs. (2) and (5), δ can be determined. For Al substituted samples, the cation distribution can be expressed as Coδ Alγ Fe1−(δ+γ )[Co1−δ Alx−γ Fe1−x+δ+γ ]O4 .
(6)
Taking into consideration that the Co ion content is unchanged for the system CoAlx Fe2−x O4 , then the cation distribution for Al-substituted samples can be estimated assuming that the distribution of Co ion over A- and B-site is the same for all samples, i.e., δ is assumed to be constant. The estimated cation distribution for CoAlx Fe2−x O4 is given in Table 1.
Fig. 2. The composition dependence of the lattice parameter, rtetr and roct . Table 1 The estimated cation distribution
Fig. 1. X-ray diffraction patterns for the system CoAlx Fe2−x O4 .
Composition
Tetrahedral site
Octahedral site
CoFe2 O4 CoAl0.4 Fe1.6 O4 CoAl0.8 Fe1.2 O4 CoAl1.2 Fe0.8 O4 CoAl1.6 Fe0.4 O4
Co0.275 Fe0.725 Co0.275 Fe0.602 Al0.123 Co0.275 Fe0.452 Al0.273 Co0.275 Fe0.321 Al0.404 Co0.275 Fe0.184 Al0.541
Co0.725 Fe1.275 Co0.725 Fe0.998 Al0.277 Co0.725 Fe0.748 Al0.527 Co0.725 Fe0.479 Al0.796 Co0.725 Fe0.216 Al1.059
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3.2. The AC conductivity behavior Fig. 3 illustrates the variation of the real part of AC conductivity σ with the temperature at different selected frequencies for all samples. It is shown that σ exhibits a semiconductive behavior with the temperature, where the AC conductivity increases with increasing the temperature. Fig. 4 depicts the frequency dependence of the real part of AC conductivity σ for all samples at different temperatures. It is shown that, for CoFe2 O4 sample (where x = 0.0), the dispersion of AC conductivity appears at low temperature and relatively high frequency region. With replacement of Fe3+ ions by Al3+ ions, the dispersion region is shifted towards relatively lower frequencies. Generally, the dispersion of AC conductivity decreases with increasing the temperature for all samples. At relatively high temperatures, the
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AC conductivity seems to be frequency independent. The results of AC conductivity σ can be explained on the basis of the assumption that σ can be expressed as [7] σ = σDC + σAC ,
(7)
where the first term is a temperature dependent term represent the DC electric conductivity which is related to the drift mobility of the free charge carriers, and the second term is a frequency and temperature dependent term which is related to the dielectric relaxation of the bound charger carriers. The first term is predominant at low frequencies and high temperature, while the second term is predominant at high frequencies and low temperatures. The frequency dependence of the second term σAC can be written as [7,8] σAC = Aωn ,
Fig. 3. The variation of σ with the temperature as 103 /T , at different selected frequencies for all studied samples.
(8)
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Fig. 4. The variation of electrical conductivity σ with the frequency at different selected temperatures for all studied samples.
where A is a constant having the units of the conductivity, and the exponent n is a temperature dependent constant. By subtracting the value of σDC from σ at different frequencies and temperatures, the exponent n can be calculated as a function of temperature for each sample by plotting ln σAC versus ln ω according to Eq. (8). Fig. 5 shows the variation of the exponent n with the temperature for all the studied samples. It is shown that, for CoFe2 O4 (where x = 0.0), the exponent n is approximately temperature independent, while for Al substituted Co ferrites, n decreases with increasing the temperature. In order to explain the behavior of σ with both frequency and temperature, different theoretical models have been proposed to correlate the conduction mechanism of AC conductivity with n(T ) behavior [9].
According to quantum-mechanical tunneling model [10– 12], the exponent n is temperature independent. The large overlapping polaron model [11] predicted that n decreases with increasing temperature up to certain temperature after which it begin to increase with further increase of temperature. The small polaron tunneling model and the classical hopping model over a barrier separating two sites [13] predicted that n decreases with increasing the temperature. Comparing our results of n(T ) Fig. 5, with the above mentioned models, it can be concluded that the quantummechanical tunneling mechanism is the most probable conduction mechanism for the CoFe2 O4 (where x = 0.0). For Al substituted samples, the behavior of n with the temperature may be discussed in the light of both small polaron tunneling mechanism or classical barrier hopping mechanism. But in the case of low mobility semiconductor-like ferrite hav-
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Fig. 5. The variation of the parameter n with the temperature for all samples.
Fig. 6. The composition dependence of the AC conductivity at room temperature.
ing exceedingly narrow band or localized levels, the charge carriers are considered to be localized at ions or vacant sits, so in such cases the most probable conduction mechanism is the small polaron tunneling mechanism rather than the classical barrier hopping mechanism [14]. Fig. 6 shows the dependence of σ on the composition at room temperature and at three different selected frequencies 1, 10 and 100 kHz. For CoFe2 O4 (x = 0.0), the value of σ is high (∼ 10−3 −1 cm−1 ). Addition of Al ions reduces the value of σ (∼ 10−9 −1 cm−1 at frequency 1 kHz for x = 1.6). It is known that some of Fe3+ ions are usually reduced to Fe2+ ions in most ferrites during sintering process at elevated firing temperature [15,16]. Fe2+ ions preferred to occupy the octahedral B-site [16–19]. In this case the electric conduction occurs as a result of electron hopping between Fe2+ and Fe3+ ions at the octahedral sites. According to the estimated cation distribution (Table 1), the population of Al ions over B-site is higher than that at A-site. Therefore, the introduction of Al+3 ions to the lattice of CoFe2 O4 , will reduce the number of iron ions available for the conduction process at the octahedral site which in turn reduce the value of AC conductivity. 3.3. Dielectric constant behavior Fig. 7 illustrate the variation of the real part of the dielectric constant ε with frequency at different selected
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temperatures. For CoFe2 O4 (where x = 0.0), the values of the dielectric constant are abnormally high with respect to that of the other samples. Generally the dielectric constant, ε , decreases with increasing frequency but the dispersion feature is nearly temperature independent for CoFe2 O4 . The high values of ε can be explained on the basis of the Maxwell–Wagner model and Koops’ phenomenological theory [1,20,21]. According to these models, the dielectric material with a heterogeneous structure can be imagined as a structure consists of well conducting grains separated by highly resistive thin layers (grain boundaries). In this case, the applied voltage on the sample drops mainly across the grain boundaries and a space charge polarization is built up at the grain boundaries. The space charge polarization is governed by the available free charges on the grain boundary and the conductivity of the sample. Koops proposed that the effect of grain boundaries is predominant at low frequencies. The thinner the grain boundary, the higher the dielectric constant value is. The observed decrease of ε with increasing the frequency can be attributed to the fact that the electron exchange between Fe2+ and Fe3+ ions can not follow the change of the external applied filed beyond a certain frequency [22]. Introduction of Al ions to CoFe2 O4 ferrite reduces the values of the dielectric constant ε and enhance the effect of the temperature on the dispersion of ε at low frequencies. The effect of the temperature on the dielectric constant at high frequencies is negligible. The results of the dielectric relaxation intensity ε
(i.e., the difference between the values of the dielectric constant at low and high frequencies) are displayed as a function of temperature for each sample in Fig. 8. It is shown that ε increases with increasing the temperature for all composition, while it decreases with increasing Al ion substitution. Fig. 9 illustrates the variation of ε with the temperature at different selected frequencies for all samples. It is shown that, for Al ion substituted samples, the effect of temperature on the dispersion of ε is week at low temperature region. With increasing the temperature, ε increases slowly at high frequencies, while it increases sharply at relatively low frequency region. The behavior of ε with the temperature can be explained as follows: at relatively low temperature, the charge carriers on most cases cannot orient themselves with respect to the direction of the applied field, therefore, they posses a week contribution to the polarization and the dielectric constant ε . As the temperature increases, the bound charge carriers get enough excitation thermal energy to be able to obey the change in the external field more easily. This in turn enhances their contribution to the polarization leading to an increase of the dielectric constant ε of the sample [23]. Fig. 10 shows the composition dependence of ε at three different frequencies 1, 10 and 100 kHz at room temperature. It is shown that ε is relatively high (∼ 107 ) for the sample with x = 0.0, then it drops up to ∼ 30 with introduction of
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Fig. 7. The variation of ε with the frequency at different temperatures for all samples.
Fig. 8. The variation of the dielectric relaxation intensity, ε , with the temperature for all samples.
small amount of Al ions at x = 0.4, then it decrease slowly with further increase of Al ion substitution. The decrease of the dielectric constant ε with increasing of Al ions substitution can be explained with the aid of the interpretation of the behavior of ε with the composition for Cux Mn1−x Fe2 O4 , Cux Zn1−x Fe2 O4 as reported by Rezlescu [24], and MgAl2−x Fe2 O4 as reported by Radhakrishna [25], and Zn0.25Ni0.75 Tit Fe2−2t O4 as reported by Prakash [16]. Basically, the whole polarization in ferrites is mainly contributed by the space charge polarization which is governed by the number of space charge carriers and the conductivity of the material [16,26], and the hopping exchange of the charges between two localized states which is governed by the density of the localized state and the resultant displacement of these charges with respect to the external field. It
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Fig. 9. The variation of ε with the temperature at different frequencies for all samples.
is mainly responsible for both space charge polarization and the hopping exchange of the charges between the localized states. Therefore, increasing of Al ions content causes a decrease in the polarization, which is accompanied by a decrease in the dielectric constant ε of the composition. 3.4. The dielectric loss tangent behavior
Fig. 10. The composition dependence of the dielectric constant at room temperature.
has been shown in Section 3.2, that the addition of Al ions to CoFe2 O4 implies a reduction of iron ions on B-sites, which
Fig. 11 displays the variation of dielectric loss tangent tan δ with the frequency at different temperatures for all samples. It is shown that tan δ(F ) curves exhibits a peaking behavior for all compositions. The observed peaks are a function of both temperature and composition. As the temperature increases, the peaks are shifted towards higher frequency, while, they are shifted towards lower frequencies with increasing Al ion substitution. It can be noted also
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Fig. 11. The variation of tan δ with the frequency at different temperatures for all samples.
that the height of the peak decreases with increasing Al ion substitution, while it increases as the temperature increases. The observed peaks of tan δ(F ) curves can be explained according to the fact that a strong correlation between the conduction mechanism and the dielectric behavior exist in ferrites [24,27]. In this case, the peak is expected when the hopping frequency of the electron between Fe2+ and Fe3+ ions is approximately equal to that of the external applied electric field. In this case ωτ = 1,
(9)
where τ is the relaxation time of the hopping process and ω is the angular frequency of the external field (ω = 2πfmax ) [28]. It is also known that the relaxation time τ is inversely proportional to the jumping probability per unit
time, P , according to the relation [28] 1 τ = P. 2
(10)
So, from Eqs. (9) and (10), it is expected that fmax is proportional to P . The shift of the peak of tan δ towards high frequency with increasing temperature indicates that the jumping probability per unit time P increases with increasing the temperature. On the other hand, the shift of the peak of tan δ towards lower frequencies with increasing Al ion substitution indicates that the jumping probability decreases as Al ion content increases. This reduction of jumping probability may be ascribed to the decrease of iron ions in B-site, which is responsible for the polarization in theses ferrites.
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tion mechanism for CoFe2 O4 , while the small polaron tunneling model may be the probable conduction mechanism model for Al substituted CoFe2 O4 . The decreases of σ with the x were attributed to the reduction of the iron ions available for conduction process over octahedral site. Also the decrease of ε with x, were attributed to the strong correlation between the conduction process and dielectric polarization in ferrites. References
Fig. 12. The variation of ln τ with the temperature for all samples.
The decrease of the height of the peak of tan δ with increasing Al ion substitution may be attributed to the increase of resistivity of the sample arising due to the reduction of the iron ions available for the conduction process. The relaxation time τ can be written as [29] τ = τo eED /(kT) ,
(11)
where τo is the relaxation time at infinity high temperature, ED is the activation energy for dielectric relaxation, and k is Boltzmann constant. Fig. 12 shows the logarithmic representation of the relaxation time τ versus 103 /T for all samples. Each sample exhibits a straight line with slope equal to ED /k. The activation energy of the dielectric relaxation ED lies between 0.116 to 0.225 eV for the studied samples. The low values of ED confirm that the hopping conduction mechanism is the predominant mechanism in these samples.
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
4. Conclusion The results of the AC electric conductivity with frequency were explained on the basis of the hopping conduction mechanism and the space charge polarization discussed by Maxwell–Wagner and Koops’ models. The conduction mechanism of AC conductivity were discussed by comparing the behavior of the frequency exponent n(T ) with many theoretical models. It was found that the quantum mechanical tunneling model is the most probable model for conduc-
[21] [22] [23] [24] [25] [26] [27] [28] [29]
C. Koops, Phys. Rev. 83 (1951) 121. A. Dias, R. Luiz Moreire, J. Mater. Res. 12 (8) (1998) 2190. A.M. Abo El Ata, M. El Hiti, J. Phys. III (France) 7 (1997) 883. M.A. Ahmed, M. El Hiti, M. Mossad, S.M. Attia, J. Magn. Magn. Mater. 146 (1995) 84. J. Smith, H.P. Wijn, Ferrites, Cleaver-Hume, London, 1959, Chapter 8. E.P. Wohlfarth, Ferromagnetic Materials, vol. 3, North-Holland, Amsterdam, 1982, Chapter 4. Y. Yamazaki, M. Satou, Jpn. J. Appl. Phys. 12 (7) (1973) 998. A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectric Press, London, 1983, p. 223. S. Hazara, A. Chosh, Philosophical B 74 (3) (1996) 235. H. Botthger, V.V. Bryksin, Phys. Status Solidi B 78 (1976) 415. A.R. Long, Adv. Phys. 31 (1982) 553. N.F. Mott, A.E.A. Davis, Electronic Processed in Non-Crystalline Materials, second ed., Clarendon Press, Oxford, 1979, p. 225. S.R. Elliott, Adv. Phys. 36 (1987) 135. P.V. Reddy, V.D. Reddy, D. Ravinder, Phys. Status Solidi A 127 (1991) 439. S.S. Surgavanshi, C.N. Jadhav, S.A. Patil, S.R. Sawant, J. LessCommon Met. 168 (1991) 169. C. Prakash, J.S. Baijal, J. Less-Common Met. 107 (1985) 51. R.B. Jotania, R.V. Updahyay, R. Klkarni, IEEE Trans. Magn. 28 (1992) 1889. B.V. Bhise, M.B. Dononr, S.A. Patil, S.R. Sawant, J. Mater. Sci. Lett. 10 (1991) 922. A. Ahmad, J. Mater. Sci. 27 (1992) 4120. J. Maxwell, Electricity and Magnetism, vol. 1, Oxford Univ. Press, 1873, Section 328. K. Wagner, Ann. Phys. 40 (1913) 817. V.R.K. Murthy, J. Sobhamadri, Phys. Status Solidi A 36 (1976) 133. M.R. Anantharaman, S. Sindhu, S. Jagatheesan, K.A. Molini, P. Kurian, J. Phys. D: Appl. Phys. 32 (1999) 1801. N. Rezlescu, E. Rezlescu, Phys. Status Solidi A 59 (1980) 323. S. Rahakrishna, K.V.S. Badarinath, J. Mater. Sci. Lett. 3 (1984) 867. B.K. Kuanr, G.P. Srivastava, J. Appl. Phys. 75 (10) (1994) 6115. K. Iwauchi, J. Appl. Phys. 10 (1971) 1520. M.B. Reddy, P.V. Reddy, Phys. D: Appl. Phys. 24 (1991) 975. K. Standly, Oxide Magnetic Materials, Clarendon Press, Oxford, 1974, p. 114.
AC conductivity and dielectric behavior of CoAlx Fe2−x O4 A.M. Abo El Ata a , S.M. Attia b , T.M. Meaz a,∗ a Physics Department, Faculty of Science, Tanta University, Tanta, Egypt b Physics and Chemistry Department, Faculty of Education, Tanta University, Kafer El-Shiekh, Egypt
Received 20 May 2003; received in revised form 29 September 2003; accepted 16 October 2003
Abstract AC conductivity and dielectric properties have been studied for a series of polycrystalline spinel ferrite with composition CoAlx Fe2−x O4 , as a function of frequency and temperature. The results of AC conductivity were discussed in terms of the quantum mechanical tunneling and small polaron tunneling models. The dispersion of the dielectric constant was discussed in the light of Koops model and hopping conduction mechanism. The dielectric loss tangent tan δ curves exhibits a dielectric relaxation peaks which are attributed to the coincidence of the hopping frequency of the charge carriers with that of the external fields. The AC conductivity, dielectric constant, and dielectric loss tangent were found to increase with increasing the temperature due to the increase of the hopping frequency, while they decrease with increasing Al ion content due to the reduction of iron ions available for the conduction process at the octahedral sites. 2003 Elsevier SAS. All rights reserved. Keywords: Spinel ferrite; AC conductivity; Dielectric constant; Dielectric loss tangent; Conduction mechanism
1. Introduction
2. Experimental details
Low cost, easily manufacturing and interesting electric and magnetic properties lead the polycrystalline ferrite to be one of the most important material that has attracted a considerable attention in the field of technological application in a wide range of frequency extended from microwave to radio frequency. These materials are in the category of magnetic semiconductors. Their electrical and dielectric properties depends on the preparation conditions, such as sintering temperature, sintering atmosphere and soaking time as well as the type of the substituted ions. It was proposed that the air-sintered ferrites are characterized by microstructure consisting of relatively high conductive grains separated by high resistive thin layers (grain boundaries) [1,2]. Most of the external applied electric field to the specimen is concentrated on the grain boundary regions, therefore the electrical properties of the grain boundary phase control the electric and dielectric properties of this materials. The aim of this work is to study the effect of Al ion substitution on the behavior of AC conductivity and dielectric properties of CoFe2 O4 at different frequencies and temperatures.
2.1. Preparation of the samples
* Corresponding author.
E-mail address: [email protected] (T.M. Meaz). 1293-2558/$ – see front matter 2003 Elsevier SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2003.10.006
High pure cobalt, aluminum and ferric oxides, were mixed together in molar ratio to prepare a series of polycrystalline spinel ferrites with chemical composition CoAlx Fe2−x O4 , with x = 0.0, 0.4, 0.8, 1.2 and 1.6, using the conventional ceramic method. After mixing the gradients for 3 h using electrical grinding machine, the final products were presintered at 900 ◦ C for 5 h and slowly cooled to room temperature. The mixtures were reground again for 3 h, and the final fine powders were pressed in disk-shaped samples with thickness ranges from 0.25 to 0.3 cm and diameter ∼ 1.4 cm. Then, the disks were sintered at 1200 ◦ C for 5 h. The samples were slowly cooled to room temperature. Finally, the surfaces of the disks were polished and coated by sliver paste that acts as a good contact for measuring the electric and dielectric properties. X-ray diffraction analysis confirms the existence of a single-phase spinel ferrite. 2.2. Measurements The AC conductivity and the dielectric properties were measured at different temperatures using a complex impedance technique with low frequency lock-in-amplifier in
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the frequency range 102 –105 Hz. The details of the circuit and measurements were reported elsewhere [3,4].
3. Results and discussion 3.1. X-ray analysis and estimation of cation distribution Fig. 1 shows the X-ray diffraction patterns for the samples under investigation. The X-ray chart shows the existence of a single phase spinel ferrites without any extra lines corresponding to any other phases. The lattice parameter was calculated for each sample according to the equation a = dhkl h2 + k 2 + l 2 , (1) where dhkl is the interplaner distance for a given plan with Miller indices (hkl). Fig. 2 shows the variation of the lattice parameter a with Al ion content. It is found that the lattice parameter decreases with increasing Al ion substitution. The decrease of the value of the lattice parameter with increasing Al ion substitution can be explained on the basis of ionic radius, where the ionic radius of Al3+ ion is smaller than that of Fe3+ ion. The mean radius of the ions at tetrahedral site rtetr and octahedral site roct were calculated according to Eqs. (2) and (3) [5]. √ rtetr = a 3(µ − 0.25) − Ro , (2)
5 − µ − Ro , roct = a 8
(3)
where Ro is the radius of the oxygen ion (Ro = 1.26 Å [6]), and µ is the oxygen parameter (µ = 0.381 for CoFe2 O4 [6]). The behavior of rtetr and roct as a function of composition is shown in Fig. 2. It is shown that both rtetr and roct decrease with increasing Al ion content indicating that Al ions are distributed over A and B sites. The cation distribution for CoFe2 O4 was estimated according to Eqs. (2) and (3), and on the basis that the cation distribution for a given ferrite system can be expressed as [5] Meδ Fe1−δ [Me1−δ Fe1+δ ]O4 ,
(4)
where Me is the divalent ion and δ determine the cation distribution. The mean radius of the ion at tetrahedral site ban be expressed as rtetr = δrMe2+ + (1 − δ)rFe3+ .
(5)
From Eqs. (2) and (5), δ can be determined. For Al substituted samples, the cation distribution can be expressed as Coδ Alγ Fe1−(δ+γ )[Co1−δ Alx−γ Fe1−x+δ+γ ]O4 .
(6)
Taking into consideration that the Co ion content is unchanged for the system CoAlx Fe2−x O4 , then the cation distribution for Al-substituted samples can be estimated assuming that the distribution of Co ion over A- and B-site is the same for all samples, i.e., δ is assumed to be constant. The estimated cation distribution for CoAlx Fe2−x O4 is given in Table 1.
Fig. 2. The composition dependence of the lattice parameter, rtetr and roct . Table 1 The estimated cation distribution
Fig. 1. X-ray diffraction patterns for the system CoAlx Fe2−x O4 .
Composition
Tetrahedral site
Octahedral site
CoFe2 O4 CoAl0.4 Fe1.6 O4 CoAl0.8 Fe1.2 O4 CoAl1.2 Fe0.8 O4 CoAl1.6 Fe0.4 O4
Co0.275 Fe0.725 Co0.275 Fe0.602 Al0.123 Co0.275 Fe0.452 Al0.273 Co0.275 Fe0.321 Al0.404 Co0.275 Fe0.184 Al0.541
Co0.725 Fe1.275 Co0.725 Fe0.998 Al0.277 Co0.725 Fe0.748 Al0.527 Co0.725 Fe0.479 Al0.796 Co0.725 Fe0.216 Al1.059
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3.2. The AC conductivity behavior Fig. 3 illustrates the variation of the real part of AC conductivity σ with the temperature at different selected frequencies for all samples. It is shown that σ exhibits a semiconductive behavior with the temperature, where the AC conductivity increases with increasing the temperature. Fig. 4 depicts the frequency dependence of the real part of AC conductivity σ for all samples at different temperatures. It is shown that, for CoFe2 O4 sample (where x = 0.0), the dispersion of AC conductivity appears at low temperature and relatively high frequency region. With replacement of Fe3+ ions by Al3+ ions, the dispersion region is shifted towards relatively lower frequencies. Generally, the dispersion of AC conductivity decreases with increasing the temperature for all samples. At relatively high temperatures, the
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AC conductivity seems to be frequency independent. The results of AC conductivity σ can be explained on the basis of the assumption that σ can be expressed as [7] σ = σDC + σAC ,
(7)
where the first term is a temperature dependent term represent the DC electric conductivity which is related to the drift mobility of the free charge carriers, and the second term is a frequency and temperature dependent term which is related to the dielectric relaxation of the bound charger carriers. The first term is predominant at low frequencies and high temperature, while the second term is predominant at high frequencies and low temperatures. The frequency dependence of the second term σAC can be written as [7,8] σAC = Aωn ,
Fig. 3. The variation of σ with the temperature as 103 /T , at different selected frequencies for all studied samples.
(8)
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Fig. 4. The variation of electrical conductivity σ with the frequency at different selected temperatures for all studied samples.
where A is a constant having the units of the conductivity, and the exponent n is a temperature dependent constant. By subtracting the value of σDC from σ at different frequencies and temperatures, the exponent n can be calculated as a function of temperature for each sample by plotting ln σAC versus ln ω according to Eq. (8). Fig. 5 shows the variation of the exponent n with the temperature for all the studied samples. It is shown that, for CoFe2 O4 (where x = 0.0), the exponent n is approximately temperature independent, while for Al substituted Co ferrites, n decreases with increasing the temperature. In order to explain the behavior of σ with both frequency and temperature, different theoretical models have been proposed to correlate the conduction mechanism of AC conductivity with n(T ) behavior [9].
According to quantum-mechanical tunneling model [10– 12], the exponent n is temperature independent. The large overlapping polaron model [11] predicted that n decreases with increasing temperature up to certain temperature after which it begin to increase with further increase of temperature. The small polaron tunneling model and the classical hopping model over a barrier separating two sites [13] predicted that n decreases with increasing the temperature. Comparing our results of n(T ) Fig. 5, with the above mentioned models, it can be concluded that the quantummechanical tunneling mechanism is the most probable conduction mechanism for the CoFe2 O4 (where x = 0.0). For Al substituted samples, the behavior of n with the temperature may be discussed in the light of both small polaron tunneling mechanism or classical barrier hopping mechanism. But in the case of low mobility semiconductor-like ferrite hav-
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Fig. 5. The variation of the parameter n with the temperature for all samples.
Fig. 6. The composition dependence of the AC conductivity at room temperature.
ing exceedingly narrow band or localized levels, the charge carriers are considered to be localized at ions or vacant sits, so in such cases the most probable conduction mechanism is the small polaron tunneling mechanism rather than the classical barrier hopping mechanism [14]. Fig. 6 shows the dependence of σ on the composition at room temperature and at three different selected frequencies 1, 10 and 100 kHz. For CoFe2 O4 (x = 0.0), the value of σ is high (∼ 10−3 −1 cm−1 ). Addition of Al ions reduces the value of σ (∼ 10−9 −1 cm−1 at frequency 1 kHz for x = 1.6). It is known that some of Fe3+ ions are usually reduced to Fe2+ ions in most ferrites during sintering process at elevated firing temperature [15,16]. Fe2+ ions preferred to occupy the octahedral B-site [16–19]. In this case the electric conduction occurs as a result of electron hopping between Fe2+ and Fe3+ ions at the octahedral sites. According to the estimated cation distribution (Table 1), the population of Al ions over B-site is higher than that at A-site. Therefore, the introduction of Al+3 ions to the lattice of CoFe2 O4 , will reduce the number of iron ions available for the conduction process at the octahedral site which in turn reduce the value of AC conductivity. 3.3. Dielectric constant behavior Fig. 7 illustrate the variation of the real part of the dielectric constant ε with frequency at different selected
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temperatures. For CoFe2 O4 (where x = 0.0), the values of the dielectric constant are abnormally high with respect to that of the other samples. Generally the dielectric constant, ε , decreases with increasing frequency but the dispersion feature is nearly temperature independent for CoFe2 O4 . The high values of ε can be explained on the basis of the Maxwell–Wagner model and Koops’ phenomenological theory [1,20,21]. According to these models, the dielectric material with a heterogeneous structure can be imagined as a structure consists of well conducting grains separated by highly resistive thin layers (grain boundaries). In this case, the applied voltage on the sample drops mainly across the grain boundaries and a space charge polarization is built up at the grain boundaries. The space charge polarization is governed by the available free charges on the grain boundary and the conductivity of the sample. Koops proposed that the effect of grain boundaries is predominant at low frequencies. The thinner the grain boundary, the higher the dielectric constant value is. The observed decrease of ε with increasing the frequency can be attributed to the fact that the electron exchange between Fe2+ and Fe3+ ions can not follow the change of the external applied filed beyond a certain frequency [22]. Introduction of Al ions to CoFe2 O4 ferrite reduces the values of the dielectric constant ε and enhance the effect of the temperature on the dispersion of ε at low frequencies. The effect of the temperature on the dielectric constant at high frequencies is negligible. The results of the dielectric relaxation intensity ε
(i.e., the difference between the values of the dielectric constant at low and high frequencies) are displayed as a function of temperature for each sample in Fig. 8. It is shown that ε increases with increasing the temperature for all composition, while it decreases with increasing Al ion substitution. Fig. 9 illustrates the variation of ε with the temperature at different selected frequencies for all samples. It is shown that, for Al ion substituted samples, the effect of temperature on the dispersion of ε is week at low temperature region. With increasing the temperature, ε increases slowly at high frequencies, while it increases sharply at relatively low frequency region. The behavior of ε with the temperature can be explained as follows: at relatively low temperature, the charge carriers on most cases cannot orient themselves with respect to the direction of the applied field, therefore, they posses a week contribution to the polarization and the dielectric constant ε . As the temperature increases, the bound charge carriers get enough excitation thermal energy to be able to obey the change in the external field more easily. This in turn enhances their contribution to the polarization leading to an increase of the dielectric constant ε of the sample [23]. Fig. 10 shows the composition dependence of ε at three different frequencies 1, 10 and 100 kHz at room temperature. It is shown that ε is relatively high (∼ 107 ) for the sample with x = 0.0, then it drops up to ∼ 30 with introduction of
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Fig. 7. The variation of ε with the frequency at different temperatures for all samples.
Fig. 8. The variation of the dielectric relaxation intensity, ε , with the temperature for all samples.
small amount of Al ions at x = 0.4, then it decrease slowly with further increase of Al ion substitution. The decrease of the dielectric constant ε with increasing of Al ions substitution can be explained with the aid of the interpretation of the behavior of ε with the composition for Cux Mn1−x Fe2 O4 , Cux Zn1−x Fe2 O4 as reported by Rezlescu [24], and MgAl2−x Fe2 O4 as reported by Radhakrishna [25], and Zn0.25Ni0.75 Tit Fe2−2t O4 as reported by Prakash [16]. Basically, the whole polarization in ferrites is mainly contributed by the space charge polarization which is governed by the number of space charge carriers and the conductivity of the material [16,26], and the hopping exchange of the charges between two localized states which is governed by the density of the localized state and the resultant displacement of these charges with respect to the external field. It
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Fig. 9. The variation of ε with the temperature at different frequencies for all samples.
is mainly responsible for both space charge polarization and the hopping exchange of the charges between the localized states. Therefore, increasing of Al ions content causes a decrease in the polarization, which is accompanied by a decrease in the dielectric constant ε of the composition. 3.4. The dielectric loss tangent behavior
Fig. 10. The composition dependence of the dielectric constant at room temperature.
has been shown in Section 3.2, that the addition of Al ions to CoFe2 O4 implies a reduction of iron ions on B-sites, which
Fig. 11 displays the variation of dielectric loss tangent tan δ with the frequency at different temperatures for all samples. It is shown that tan δ(F ) curves exhibits a peaking behavior for all compositions. The observed peaks are a function of both temperature and composition. As the temperature increases, the peaks are shifted towards higher frequency, while, they are shifted towards lower frequencies with increasing Al ion substitution. It can be noted also
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Fig. 11. The variation of tan δ with the frequency at different temperatures for all samples.
that the height of the peak decreases with increasing Al ion substitution, while it increases as the temperature increases. The observed peaks of tan δ(F ) curves can be explained according to the fact that a strong correlation between the conduction mechanism and the dielectric behavior exist in ferrites [24,27]. In this case, the peak is expected when the hopping frequency of the electron between Fe2+ and Fe3+ ions is approximately equal to that of the external applied electric field. In this case ωτ = 1,
(9)
where τ is the relaxation time of the hopping process and ω is the angular frequency of the external field (ω = 2πfmax ) [28]. It is also known that the relaxation time τ is inversely proportional to the jumping probability per unit
time, P , according to the relation [28] 1 τ = P. 2
(10)
So, from Eqs. (9) and (10), it is expected that fmax is proportional to P . The shift of the peak of tan δ towards high frequency with increasing temperature indicates that the jumping probability per unit time P increases with increasing the temperature. On the other hand, the shift of the peak of tan δ towards lower frequencies with increasing Al ion substitution indicates that the jumping probability decreases as Al ion content increases. This reduction of jumping probability may be ascribed to the decrease of iron ions in B-site, which is responsible for the polarization in theses ferrites.
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tion mechanism for CoFe2 O4 , while the small polaron tunneling model may be the probable conduction mechanism model for Al substituted CoFe2 O4 . The decreases of σ with the x were attributed to the reduction of the iron ions available for conduction process over octahedral site. Also the decrease of ε with x, were attributed to the strong correlation between the conduction process and dielectric polarization in ferrites. References
Fig. 12. The variation of ln τ with the temperature for all samples.
The decrease of the height of the peak of tan δ with increasing Al ion substitution may be attributed to the increase of resistivity of the sample arising due to the reduction of the iron ions available for the conduction process. The relaxation time τ can be written as [29] τ = τo eED /(kT) ,
(11)
where τo is the relaxation time at infinity high temperature, ED is the activation energy for dielectric relaxation, and k is Boltzmann constant. Fig. 12 shows the logarithmic representation of the relaxation time τ versus 103 /T for all samples. Each sample exhibits a straight line with slope equal to ED /k. The activation energy of the dielectric relaxation ED lies between 0.116 to 0.225 eV for the studied samples. The low values of ED confirm that the hopping conduction mechanism is the predominant mechanism in these samples.
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
4. Conclusion The results of the AC electric conductivity with frequency were explained on the basis of the hopping conduction mechanism and the space charge polarization discussed by Maxwell–Wagner and Koops’ models. The conduction mechanism of AC conductivity were discussed by comparing the behavior of the frequency exponent n(T ) with many theoretical models. It was found that the quantum mechanical tunneling model is the most probable model for conduc-
[21] [22] [23] [24] [25] [26] [27] [28] [29]
C. Koops, Phys. Rev. 83 (1951) 121. A. Dias, R. Luiz Moreire, J. Mater. Res. 12 (8) (1998) 2190. A.M. Abo El Ata, M. El Hiti, J. Phys. III (France) 7 (1997) 883. M.A. Ahmed, M. El Hiti, M. Mossad, S.M. Attia, J. Magn. Magn. Mater. 146 (1995) 84. J. Smith, H.P. Wijn, Ferrites, Cleaver-Hume, London, 1959, Chapter 8. E.P. Wohlfarth, Ferromagnetic Materials, vol. 3, North-Holland, Amsterdam, 1982, Chapter 4. Y. Yamazaki, M. Satou, Jpn. J. Appl. Phys. 12 (7) (1973) 998. A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectric Press, London, 1983, p. 223. S. Hazara, A. Chosh, Philosophical B 74 (3) (1996) 235. H. Botthger, V.V. Bryksin, Phys. Status Solidi B 78 (1976) 415. A.R. Long, Adv. Phys. 31 (1982) 553. N.F. Mott, A.E.A. Davis, Electronic Processed in Non-Crystalline Materials, second ed., Clarendon Press, Oxford, 1979, p. 225. S.R. Elliott, Adv. Phys. 36 (1987) 135. P.V. Reddy, V.D. Reddy, D. Ravinder, Phys. Status Solidi A 127 (1991) 439. S.S. Surgavanshi, C.N. Jadhav, S.A. Patil, S.R. Sawant, J. LessCommon Met. 168 (1991) 169. C. Prakash, J.S. Baijal, J. Less-Common Met. 107 (1985) 51. R.B. Jotania, R.V. Updahyay, R. Klkarni, IEEE Trans. Magn. 28 (1992) 1889. B.V. Bhise, M.B. Dononr, S.A. Patil, S.R. Sawant, J. Mater. Sci. Lett. 10 (1991) 922. A. Ahmad, J. Mater. Sci. 27 (1992) 4120. J. Maxwell, Electricity and Magnetism, vol. 1, Oxford Univ. Press, 1873, Section 328. K. Wagner, Ann. Phys. 40 (1913) 817. V.R.K. Murthy, J. Sobhamadri, Phys. Status Solidi A 36 (1976) 133. M.R. Anantharaman, S. Sindhu, S. Jagatheesan, K.A. Molini, P. Kurian, J. Phys. D: Appl. Phys. 32 (1999) 1801. N. Rezlescu, E. Rezlescu, Phys. Status Solidi A 59 (1980) 323. S. Rahakrishna, K.V.S. Badarinath, J. Mater. Sci. Lett. 3 (1984) 867. B.K. Kuanr, G.P. Srivastava, J. Appl. Phys. 75 (10) (1994) 6115. K. Iwauchi, J. Appl. Phys. 10 (1971) 1520. M.B. Reddy, P.V. Reddy, Phys. D: Appl. Phys. 24 (1991) 975. K. Standly, Oxide Magnetic Materials, Clarendon Press, Oxford, 1974, p. 114.