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Influence of structural ordering on electrical conductivity of nanostructured manganese zinc ferrite
Materials Chemistry and Physics 138 (2013) 102e107
Contents lists available at SciVerse ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Influence of structural ordering on electrical conductivity of nanostructured manganese zinc ferrite N. Sivakumar 1 Materials Science Centre, Department of Nuclear Physics, University of Madras, Guindy Campus, Chennai 600 025, India
h i g h l i g h t s < Nanostructured MneZn has been successfully prepared by using co-precipitation method. < Increase in structural improvement was proven by FESEM and BET techniques. < Cation distribution change on annealing is the reason for decrease in conductivity. < Short-range type of hopping mechanism exhibited in the MneZn sample.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 October 2011 Received in revised form 30 October 2012 Accepted 11 November 2012
In the present study, nanostructured manganese zinc ferrite of 11 nm grain size was synthesized by coprecipitation technique and subsequently suitably heat treated to obtain higher grain sizes. The plot of temperature dependence of dc conductivity shows the semiconducting nature of samples. The observed changes in the electrical conductivity have been attributed with the influence of structural ordering upon annealing. The observed decrease in conductivity when the grain size is increased from 11 to 69 nm upon annealing is clearly due to the structural ordering which is evident from FESEM. Ó 2012 Elsevier B.V. All rights reserved.
Keywords: A. Nanostructures B. Chemical synthesis C. Electrical characterization D. Electrical properties
1. Introduction ManganeseeZinc (MneZn) ferrite has been used in high frequency components such as transformers, choke coils, noise filters or magnetic recording heads because of their high magnetic permeability and low magnetic losses. Moreover, these have been used in shielding components for electromagnetic interference (EMI) and switch mode power supplies (SMPS) due to their specific electrical resistivity and initial permeability being much higher than those of the existing metallic alternatives at high frequencies (up to 1 MHz) [1]. In recent decades spinel ferrites have been shown to exhibit interesting electrical properties in the nanocrystalline form compared with those of the micrometer sized grains [2,3]. Both magnetic and electrical properties of the polycrystalline materials are generally determined by the combination of the
E-mail address: [email protected]. Present address: Nano Solar Division, Amrita Centre for Nanosciences, Kochi 682 041, India. 1
0254-0584/$ e see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matchemphys.2012.11.019
following factors: method of preparation, grain size, sintering time, oxygen parameter, cation distribution, cooling conditions and the ratio of Fe3þ to Fe2þ ions. The dependence on the latter is usually ascribed to the variation in the Fe2þ ions with oxygen partial pressure and temperature [4]. Klinger and Samokhvalov [4] have observed that the thermoelectric power of the MneZn ferrites originates from Fe2þ and Fe3þ ion pairs. Ravinder [5] has measured both the electrical conductivity and thermoelectric power of the bulk MneZn ferrites as a function of temperature and composition. He has reported that the electrical conductivity decreased and thermoelectric power increased as the ratio of manganese to zinc decreased. But, the author has not studied the effect of grain size on the electrical properties in the nanostructured form. Earlier studies have shown that MneZn ferrite with the composition Mn0.82Zn0.36Fe1.64O3.64 exhibit the maximum magnetization required for ferrofluid applications [6]. Knowledge of the electrical properties of this composition will be useful for widening its range of applications [7]. This is the motivation behind study the effect of grain size on the electrical conductivity properties of manganeseezinc ferrite in the nano regime.
N. Sivakumar / Materials Chemistry and Physics 138 (2013) 102e107
2. Experimental MneZn ferrite was synthesized by using the co-precipitation technique from the solutions of Fe, Mn and Zn with the molar concentrations 1.64, 0.82 and 0.36 M, respectively as reported earlier [6,8]. To achieve various grain sizes, the as-prepared sample (sample A) was heat treated at different temperatures, such as 1273 K (sample B) and 1373 K (sample C) for duration of 2 h. The phase analysis for the as-prepared and the heat treated samples was carried out using X-ray diffraction (XRD) with a Rigaku-make high precision Guinier X-ray diffractometer and Cu Ka radiation. The electrical conductivity measurements were carried out using an impedance analyzer (Solartron 1260 Impedance/Gain e Phase Analyzer) in the temperature range from 298 to 650 K and in the frequency range from 1 Hz to 10 MHz. Before starting the measurements, the sample was preheated to 450 K for 15 min to remove the moisture content. The temperature was measured with an accuracy of 1 K using an Eurotherm (818 P) PID temperature controller. Surface morphological features of the samples were observed using a field emission scanning microscope (FE-SEM, S4700, Hitachi, Japan). Image J software was used to determine the particle size distribution in the samples. The specific surface area (SBET, m2 g1) of the samples was measured using Brunauere EmmetteTeller (BET) surface area analyzer (ASAP 2010 Micromeritics, USA). 3. Results and discussion 3.1. Structural analysis and surface morphology The XRD patterns confirmed the presence of spinel phase without any impurity phase for the as-prepared and sintered samples, as reported in our earlier article [8]. The average grain size of the samples has been determined from the full-width at half-maximum of the (311) peak in the X-ray diffraction pattern using the Scherrer’s formula [9] and the values obtained for the samples A, B, and C are 11,
103
59 and 69 nm respectively. The microstructure of samples for A, B, and C are shown in Fig. 1(a), (b) and (c) respectively. Moreover, the corresponding particle size distribution graph for A, B, and C are shown in Fig. 2(a), (b) and (c) respectively The particle size distribution for sample A is found to be 15e25 nm. In the case of sample B and C are around 30e50 nm and 300e500 nm respectively. Moreover, the FESEM micrographs show an improvement in the structural homogeneity with heat treatment. In order to find the structural improvement as a supportive evident, BET analysis was carried out for all the samples. The BET surface area of sample A, B and sample C was determined as 3.46, 2.74 and 0.54 m2 g1 respectively, which is clearly indicates that the structural improvement exhibits in sintered samples (B and C). The reason is that, during sintering, the surface area and pore volume would be reduced which indicated that the porosity is very low. Also, in the higher temperature range (1273 and 1373 K) the pore coalescence caused by the collapse of porous structure results in the progressive reduction in specific area, as well as pore volume, leading to particle coarsening [10]. 3.2. d.c. Conductivity Fig. 3 shows the ColeeCole [11] plot or complex impedance spectra for sample A, measured at various temperatures. Similar measurements have been made for other samples also. The plot exhibits only one semicircle which indicates that the contribution to electrical conductivity arises mainly from the grain boundary [8]. The equivalent circuit based on the impedance data for sample A is shown in Fig. 4. The parameters Rgb, Cgb and (up)gb correspond to the resistance, capacitance and the relaxation frequency (up)gb (¼1/ s) of the grain boundary. The grain boundary resistance was obtained by analyzing the impedance data using the non-linear leastsquares (NLLS) fitting routine. From the grain boundary resistance (Rgb) value, the dc conductivity was calculated by using geometrical dimensions of the sample. The Arrhenius plots for the electrical conductivity of samples AeC in the temperature range between 415 and 590 K, are shown in Fig. 5. For all samples, the conductivity
Fig. 1. The SEM images of Mn0.82Zn0.36Fe1.64O3.64 spinel samples: (a) as-prepared, annealed at (b) 1273 K and (c) 1373 K for 2 h each.
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(b)
(a)
Particle Distribution (%)
Particle Distribution (%)
35 30 25 20 15 10 5 0
10
20
30
40
50
60
40 35 30 25 20 15 10 5 0
70
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60
70
80
90
Particle Size (nm)
Particle Size (nm)
Particle Distribution (%)
(c) 35 30 25 20 15 10 5 0 100 200 300 400 500 600 700 800 900
Particle Size (nm) Fig. 2. The particle size distribution of Mn0.82Zn0.36Fe1.64O3.64 spinel samples: (a) as-prepared, annealed at (b) 1273 K and (c) 1373 K for 2 h each.
increases with temperature as expected from the semiconducting behavior of spinel ferrites. The activation energy for the thermally activated hopping process was obtained by fitting the dc conductivity data with the Arrhenius relation,
sT ¼ s0 exp
Ea kB T
(1)
where s0 is the pre-exponential factor with the dimensions of (Ucm)1K, Ea is the activation energy for dc conductivity and kB is the Boltzmann constant. Fig. 5 shows that the temperature dependence of the conductivity could be fitted only with two straight lines of different slopes for sample A which occurs at temperature 500 K, which is attributed to change in the conduction mechanism [12]. The change in the slope at higher temperature for the sample A may be due to the oxygen vacancies [13] and these
-1.6
5
Zim (x 10 ) Ω
-1.2
448 K 473 K 493 K 503 K
anion vacancies may be responsible for the conductivity with higher activation energy of 0.73 eV in the high temperature region. Oxygen vacancy conduction in spinel ferrites has been reported in literature [3]. But, the sintered samples B and C with the grain sizes 59 and 69 nm do not exhibit any change in the slope of the sT versus 1/T plot, may be due to the number of oxygen vacancies becoming negligible because of the sintering at high temperatures in air. From Fig. 5, the conductivity is observed to decrease with annealing. Conductivity is, in fact, due to the result of the combined influence of several factors such as Fe2þ ion concentration, crystal structure perfection, microstructural homogeneity and grain size. The conductivity of polycrystalline materials in general decreases with the reduction of grain size. Smaller grains imply a larger number of insulating grain boundaries which act as a barrier to the flow of electrons. Also, smaller grains imply smaller grain-to-grain surface contact area and therefore a reduced electron flow. But, in the present studies, we have observed a reverse trend. The decrease in conductivity with annealing temperature can be explained in terms of increasing structural improvement (reduced imperfections) which is also evident from the FE-SEM studies (Fig. 1). Thermal annealing might have decreased the defect concentration,
-0.8
C gb
(ωp)gb=1/R gbCgb
-0.4
0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
5
Zre (x 10 ) Ω Fig. 3. The complex impedance spectra for Mn0.82Zn0.36Fe1.64O3.64 measured at various temperatures for sample A.
R gb Fig. 4. The proposed model for the impedance behavior shown in the Fig. 3. Cgb is the grain boundary capacitance and Rgb is the grain boundary resistance.
N. Sivakumar / Materials Chemistry and Physics 138 (2013) 102e107
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The conductivity spectra at different temperatures are fitted by Eq. (2), using NLLS fitting routine and the parameters sdc, up, and n are extracted from the analysis. The frequency exponent, n takes values near or just below unity and the parameter A is frequency independent, but may be temperature dependent. The characteristic frequency is the hopping frequency up which is obtained from the experimental data by using the relation [16],
sac up ¼ 2sdc
(3)
According to Almond and West [16], the Eq. (2) can be written as
sac ¼ sdc 1 þ ðusÞn
Fig. 5. The Arrhenius plots for the electrical conductivity of nanocrystalline Mn0.82Zn0.36Fe1.64O3.64 spinel samples. The solid lines are the linear fit to the experimental data (Eq. (1)).
which decreases the conductivity. Verma et al. [14] and Van Uitert [15] have also explained the decrease in conductivity in terms of increased homogeneity and structural perfection with increase in annealing temperature in nickel zinc ferrite. 3.3. The a.c. conductivity studies The a.c. conductivity for the as-prepared sample (A) of manganeseezinc spinel at various temperatures is shown in Fig. 6. The conductivity (sac) is found to be frequency independent in the low frequency region (u < up). When the frequency exceeds the hopping frequency up, conductivity (sac) increases with frequency following the power law dispersion sac f un (where n < 1). The a.c. conductivity behavior is analyzed using the conductivity formalism (universal power law) [16],
sac ¼ sdc þ Aun ¼ sdc 1 þ u=u p
n :
(2)
383 K 398 K 423 K 448 K 473 K Fit by Eqn (5)
-1
σ ac(Scm )
1E-4
1E-5
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
Frequency (Hz) Fig. 6. The frequency dependent conductivity of the sample A (11 nm) Mn0.82Zn0.36Fe1.64O3.64. The continuous lines result from the fitting with Eq. (4).
(4)
where, s is the average relaxation time. Fig. 6 shows the plot of a.c. conductivity for sample A (11 nm) of manganeseezinc spinel for various temperatures and the data were fitted using Eq. (4). The measured data are well fitted to Eq. (4). In general, a frequency independent conductivity, equal to the d.c. conductivity, should be obtained at lower frequencies where also the electrode and the grain boundary phenomena are significant. But, in practice, such a frequency independent plateau is observed, often over several decades of frequency, but is limited to higher frequencies by an additional bulk or grain interior phenomenon [17]. This takes the form of a power law increase in conductivity with the frequency. From Fig. 6, we can observe that the plateau region is extended to higher frequencies as the temperature is increased. The increase in electrical conductivity with temperature is attributed to the increase in the drift mobility of the thermally activated charge carriers according to the hopping mechanism [13,15]. Increasing temperature thermally activates the electron exchange between Fe2þ and Fe3þ ions on octahedral sites. Moreover, in the high frequency range, the increase of bulk conductivity is due to the high frequency dispersion [17]. The inverse power law time dependence of the transient current proved Curie-von Schweideler theory [18], and showed an interaction dipole/charge carrier system. Though, it has been observed only in the transient regime, and that is the reason the power law has more prominence at the high frequency range. The frequency independent conductivity region was also extended toward higher frequencies because of the exponential increase in the dc leakage current with the temperature. Also, the value of n was decreased at high temperatures, signifying an increasing in the randomness in the system, which made the dipoles react independently of each other to the external field. Fig. 7(a) and (b) show the plot of a.c. conductivity and permittivity for all the three grain sizes respectively at selected frequencies. The grain size, grain boundaries, and sintering temperature are the important factors that influence the conductivity. Both the a.c. conductivity and permittivity are found to decrease as the grain size increases. The higher value of conductivity and the higher value of permittivity in sample A (11 nm) are possibly due to large surface polarization owing to the large surface area of individual grains and the presence of a localized state in the forbidden energy gap which arises due to lattice imperfections [17]. According to the correlated barrier hopping model [19], ac conductivity
ωp
1E-6
sac ¼
p3 24
N 2 3 R2u u
(5)
where N is the concentration of defect sites contributing to the hopping mechanism, 3 is the dielectric permittivity, and Ru is the hopping distance. Thermal annealing (for sample, B, and C) gives
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N. Sivakumar / Materials Chemistry and Physics 138 (2013) 102e107
(a)
(b)
1E-4
1 MHz 500 kHz 100 kHz
Dielectric permittivity
1 MHz 500 kHz 100 kHz
σac (Scm-1)
1E-5
1E-6
10
20
30
40
50
60
10
2
10
70
20
30
40
50
60
70
Grain size (nm)
Grain size (nm)
Fig. 7. Grain size dependence of (a) a.c. conductivity (b) dielectric permittivity for Mn0.82Zn0.36Fe1.64O3.64 spinel ferrite for three different frequencies. The continuous line is guide to eye.
(a)
(b) 423 K 448 K 483 K 493 K 503 K 513 K 523 K 533 K
M''/M''max
0.8 0.6
1.0
0.4
0.6 0.4
0.2
0.2
0.0
0.0
1E-3
A (11 nm) B (59 nm) C (69 nm)
0.8
M''/M''max
1.0
0.01
0.1
1
10
100
0.01
0.1
log (f/fmax)
1 log (f/fmax )
10
100
Fig. 8. The plots of M0 0 /M0 0 max versus log (f/fmax) for (a) sample A (11 nm) for various temperatures and (b) for all the four grain sizes of Mn0.82Zn0.36Fe1.64O3.64 spinel ferrite measured at 423 K.
rise to more uniform crystal structures (as evidenced by FE-SEM studies and BET analysis) with reduced imperfections, thereby, decreasing the value of N, which ultimately reduces the value of a.c. conductivity as the annealing temperature increases. George et al. [20] have observed a similar behavior in conductivity and permittivity in the case of cobalt ferrite prepared by solegel method, who also explained it in terms of increased structural perfection with the sintering temperature. Therefore, the above results suggest that the structural ordering has a great influence on conductivity, which is more significant than that of the grain size effect in these samples.
(a)
3.4. Electrical modulus studies Fig. 8 shows a master plot for the imaginary part of the electric modulus in which each frequency is scaled by the peak frequency, fmax, and M00 is scaled by M00 max. From Fig. 8(a) we note that all the curves for different temperatures overlap on a single master curve for sample A (11 nm) indicating that the relaxation mechanism is temperature independent. Similarly, the same kind of behavior follows for all other grain sizes also. Moreover, Fig. 8(b) shows that the curves for all the grain sizes overlap on a single master curve, but in the high frequency region there are some deviations due to
(b) M''/M''max(316 kHz) Z''/Z''max (251 kHz)
1.0
0.8
Normalized peak
0.8
Normalized peak
M''/M''max(199 kHz) Z''/Z''max (199 kHz)
1.0
0.6 0.4 0.2 0.0
0.6 0.4 0.2 0.0
1
10
100 1000 Frequency (kHz)
10000
1
10
100
1000
10000
Frequency (kHz)
Fig. 9. The logarithmic plot of normalized parameters (M0 0 , Z0 0 ) for (a) sample A (11 nm) and (b) sample C (69 nm) of Mn0.82Zn0.36Fe1.64O3.64 spinel ferrite measured at 523 K.
N. Sivakumar / Materials Chemistry and Physics 138 (2013) 102e107
grain interior or grain effect. The value of full-width at halfmaximum (FWHM) is found to be > 1.14 decades [21] as evaluated from the normalized modulus spectrum which suggests the presence of non-Debye type of relaxation phenomena in good agreement with the observations from complex modulus spectrum. The variation of normalized parameters M00 /M00 max and Z00 /Z00 max as a function of logarithmic frequency measured at 523 K for sample A (11 nm) is shown in Fig. 9(a). From the figure we note that the peak frequency shifts towards higher frequency region as it moves from Z00 to M00 . The mismatch between the peaks of both these parameters gives an evidence for the existence of two polarization phenomena [22,23].The very distinct curves of M00 /M00 max and Z00 /Z00 max illustrates clearly that polarization process is an evidence of short-range conductivity. Moreover, the polarization process is due to a localized conduction of multiple carriers that describes the presence of multiple relaxation processes in the material. But, in the case of sample C, it has been observed that both Z00 and M00 peaks overlap better which supports the argument that there is only one relaxation process (Fig. 9(b)). Also, M00 /M00 max exhibits peaks at high frequency and it reduces to zero at low frequencies. This suggests that electrode polarization phenomenon is negligible or absent. 4. Conclusion
of temperature dependence on dc conductivity shows the semiconducting nature of samples and the conductivity is of short-range type such as a hopping -type mechanism. The important finding of the present study is that the structural ordering has a great influence on conductivity, which is more significant than that of the grain size effect in these samples. References [1] [2] [3] [4] [5] [6] [7] [8] [9]
[10] [11] [12] [13] [14]
Nanostructured manganese zinc ferrite spinel ferrite has been studied by the complex impedance spectroscopy technique. In this study, the electrical conductivity of the heat-treated materials is studied by impedance spectroscopy which showed reduction in conductivity with increasing temperature due to improvement in structural ordering (reduced imperfections and increase in grain sizes) and possible change in the cation distribution. Moreover, the possible change in cation distribution on annealing might have contributed to the observed decrease in the conductivity. The plot
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[15] [16] [17] [18] [19] [20] [21] [22] [23]
J.-H. Lee, M. Martin, H.-I. Yoo, J. Phys. Chem. Solids 61 (2000) 1597. A. Dias, R.L. Moreira, Mater. Lett. 39 (1999) 69. N. Ponpandian, A. Narayanasamy, J. Appl. Phys. 92 (2002) 2770. M.I. Klinger, A.A. Samokhvalov, Phys. Stat. Sol. (b) 79 (1977) 9. D. Ravinder, J. Appl. Phys. 75 (1994) 6118. B. Jeyadevan, C.N. Chinnasamy, K. Shinoda, K. Tohji, H. Oka, J. Appl. Phys. 93 (2003) 8450. P.C. Fannin, S.W. Charles, T. Relihan, J. Magn. Magn. Mater. 167 (1997) 274. N. Sivakumar, A. Narayanasamy, B. Jeyadevan, R. Justin Joseyphus, C. Venkateswaran, J.Phy.D: Appl. Phys. 41 (2008) 245001. B.D. Cullity, Elements of X-ray Diffraction, Addison Wesley, London, 1978; A. Verma, T.C. Goel, R.G. Mendiratta, R.G. Gupta, J. Magn. Magn. Mater. 192 (1999) 271. T.V. Mani, P.K. Pillai, A.D. Damodaran, K.G.K. Warrier, Mater. Lett. 19 (1994) 237. K.S. Cole, R.H. Cole, J. Chem. Phys. 9 (1941) 341. G.F. Goya, H.R. Rechenberg, J. Magn. Magn. Mater. 203 (1999) 141. N. Ponpandian, P. Balaya, A. Narayanasamy, J. Phys. Condens. Matter 14 (2002) 3221. A. Verma, T.C. Goel, R.G. Mendiratta, R.G. Gupta, J. Magn. Magn. Mater. 192 (1999) 271. L.G. Van Uitert, J. Chem. Phys. 23 (1995) 1883. D.P. Almond, A.R. West, Solid State Ionics 9-10 (1983) 277. D.P. Almond, G.K. Duncan, A.R. West, Solid State Ionics 8 (1983) 159. E. Von Schweidler, Ann. Phys. (Leipzig) 24 (1907) 711. G. Williams, D.C. Watts, Trans. Faraday Soc. 66 (1970) 80. M. George, S.S. Nair, K.A. Malini, P.A. Joy, M.R. Anantharaman, J. Phys. D: Appl. Phys. 40 (2007) 1593. C.T. Moynihan, L.P. Boesch, N.L. Laberge, Phys. Chem. Glasses 14 (1973) 122. K. Prasad, Lily, K. Kumari, K.L. Yadav, J. Phys. Chem. Solids 68 (2007) 1508. M.A.L. Nobre, S. Lanfredi, J. Phys. Chem. Solids 64 (2003) 2457.
Contents lists available at SciVerse ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Influence of structural ordering on electrical conductivity of nanostructured manganese zinc ferrite N. Sivakumar 1 Materials Science Centre, Department of Nuclear Physics, University of Madras, Guindy Campus, Chennai 600 025, India
h i g h l i g h t s < Nanostructured MneZn has been successfully prepared by using co-precipitation method. < Increase in structural improvement was proven by FESEM and BET techniques. < Cation distribution change on annealing is the reason for decrease in conductivity. < Short-range type of hopping mechanism exhibited in the MneZn sample.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 October 2011 Received in revised form 30 October 2012 Accepted 11 November 2012
In the present study, nanostructured manganese zinc ferrite of 11 nm grain size was synthesized by coprecipitation technique and subsequently suitably heat treated to obtain higher grain sizes. The plot of temperature dependence of dc conductivity shows the semiconducting nature of samples. The observed changes in the electrical conductivity have been attributed with the influence of structural ordering upon annealing. The observed decrease in conductivity when the grain size is increased from 11 to 69 nm upon annealing is clearly due to the structural ordering which is evident from FESEM. Ó 2012 Elsevier B.V. All rights reserved.
Keywords: A. Nanostructures B. Chemical synthesis C. Electrical characterization D. Electrical properties
1. Introduction ManganeseeZinc (MneZn) ferrite has been used in high frequency components such as transformers, choke coils, noise filters or magnetic recording heads because of their high magnetic permeability and low magnetic losses. Moreover, these have been used in shielding components for electromagnetic interference (EMI) and switch mode power supplies (SMPS) due to their specific electrical resistivity and initial permeability being much higher than those of the existing metallic alternatives at high frequencies (up to 1 MHz) [1]. In recent decades spinel ferrites have been shown to exhibit interesting electrical properties in the nanocrystalline form compared with those of the micrometer sized grains [2,3]. Both magnetic and electrical properties of the polycrystalline materials are generally determined by the combination of the
E-mail address: [email protected]. Present address: Nano Solar Division, Amrita Centre for Nanosciences, Kochi 682 041, India. 1
0254-0584/$ e see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matchemphys.2012.11.019
following factors: method of preparation, grain size, sintering time, oxygen parameter, cation distribution, cooling conditions and the ratio of Fe3þ to Fe2þ ions. The dependence on the latter is usually ascribed to the variation in the Fe2þ ions with oxygen partial pressure and temperature [4]. Klinger and Samokhvalov [4] have observed that the thermoelectric power of the MneZn ferrites originates from Fe2þ and Fe3þ ion pairs. Ravinder [5] has measured both the electrical conductivity and thermoelectric power of the bulk MneZn ferrites as a function of temperature and composition. He has reported that the electrical conductivity decreased and thermoelectric power increased as the ratio of manganese to zinc decreased. But, the author has not studied the effect of grain size on the electrical properties in the nanostructured form. Earlier studies have shown that MneZn ferrite with the composition Mn0.82Zn0.36Fe1.64O3.64 exhibit the maximum magnetization required for ferrofluid applications [6]. Knowledge of the electrical properties of this composition will be useful for widening its range of applications [7]. This is the motivation behind study the effect of grain size on the electrical conductivity properties of manganeseezinc ferrite in the nano regime.
N. Sivakumar / Materials Chemistry and Physics 138 (2013) 102e107
2. Experimental MneZn ferrite was synthesized by using the co-precipitation technique from the solutions of Fe, Mn and Zn with the molar concentrations 1.64, 0.82 and 0.36 M, respectively as reported earlier [6,8]. To achieve various grain sizes, the as-prepared sample (sample A) was heat treated at different temperatures, such as 1273 K (sample B) and 1373 K (sample C) for duration of 2 h. The phase analysis for the as-prepared and the heat treated samples was carried out using X-ray diffraction (XRD) with a Rigaku-make high precision Guinier X-ray diffractometer and Cu Ka radiation. The electrical conductivity measurements were carried out using an impedance analyzer (Solartron 1260 Impedance/Gain e Phase Analyzer) in the temperature range from 298 to 650 K and in the frequency range from 1 Hz to 10 MHz. Before starting the measurements, the sample was preheated to 450 K for 15 min to remove the moisture content. The temperature was measured with an accuracy of 1 K using an Eurotherm (818 P) PID temperature controller. Surface morphological features of the samples were observed using a field emission scanning microscope (FE-SEM, S4700, Hitachi, Japan). Image J software was used to determine the particle size distribution in the samples. The specific surface area (SBET, m2 g1) of the samples was measured using Brunauere EmmetteTeller (BET) surface area analyzer (ASAP 2010 Micromeritics, USA). 3. Results and discussion 3.1. Structural analysis and surface morphology The XRD patterns confirmed the presence of spinel phase without any impurity phase for the as-prepared and sintered samples, as reported in our earlier article [8]. The average grain size of the samples has been determined from the full-width at half-maximum of the (311) peak in the X-ray diffraction pattern using the Scherrer’s formula [9] and the values obtained for the samples A, B, and C are 11,
103
59 and 69 nm respectively. The microstructure of samples for A, B, and C are shown in Fig. 1(a), (b) and (c) respectively. Moreover, the corresponding particle size distribution graph for A, B, and C are shown in Fig. 2(a), (b) and (c) respectively The particle size distribution for sample A is found to be 15e25 nm. In the case of sample B and C are around 30e50 nm and 300e500 nm respectively. Moreover, the FESEM micrographs show an improvement in the structural homogeneity with heat treatment. In order to find the structural improvement as a supportive evident, BET analysis was carried out for all the samples. The BET surface area of sample A, B and sample C was determined as 3.46, 2.74 and 0.54 m2 g1 respectively, which is clearly indicates that the structural improvement exhibits in sintered samples (B and C). The reason is that, during sintering, the surface area and pore volume would be reduced which indicated that the porosity is very low. Also, in the higher temperature range (1273 and 1373 K) the pore coalescence caused by the collapse of porous structure results in the progressive reduction in specific area, as well as pore volume, leading to particle coarsening [10]. 3.2. d.c. Conductivity Fig. 3 shows the ColeeCole [11] plot or complex impedance spectra for sample A, measured at various temperatures. Similar measurements have been made for other samples also. The plot exhibits only one semicircle which indicates that the contribution to electrical conductivity arises mainly from the grain boundary [8]. The equivalent circuit based on the impedance data for sample A is shown in Fig. 4. The parameters Rgb, Cgb and (up)gb correspond to the resistance, capacitance and the relaxation frequency (up)gb (¼1/ s) of the grain boundary. The grain boundary resistance was obtained by analyzing the impedance data using the non-linear leastsquares (NLLS) fitting routine. From the grain boundary resistance (Rgb) value, the dc conductivity was calculated by using geometrical dimensions of the sample. The Arrhenius plots for the electrical conductivity of samples AeC in the temperature range between 415 and 590 K, are shown in Fig. 5. For all samples, the conductivity
Fig. 1. The SEM images of Mn0.82Zn0.36Fe1.64O3.64 spinel samples: (a) as-prepared, annealed at (b) 1273 K and (c) 1373 K for 2 h each.
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N. Sivakumar / Materials Chemistry and Physics 138 (2013) 102e107
(b)
(a)
Particle Distribution (%)
Particle Distribution (%)
35 30 25 20 15 10 5 0
10
20
30
40
50
60
40 35 30 25 20 15 10 5 0
70
10
20
30
40
50
60
70
80
90
Particle Size (nm)
Particle Size (nm)
Particle Distribution (%)
(c) 35 30 25 20 15 10 5 0 100 200 300 400 500 600 700 800 900
Particle Size (nm) Fig. 2. The particle size distribution of Mn0.82Zn0.36Fe1.64O3.64 spinel samples: (a) as-prepared, annealed at (b) 1273 K and (c) 1373 K for 2 h each.
increases with temperature as expected from the semiconducting behavior of spinel ferrites. The activation energy for the thermally activated hopping process was obtained by fitting the dc conductivity data with the Arrhenius relation,
sT ¼ s0 exp
Ea kB T
(1)
where s0 is the pre-exponential factor with the dimensions of (Ucm)1K, Ea is the activation energy for dc conductivity and kB is the Boltzmann constant. Fig. 5 shows that the temperature dependence of the conductivity could be fitted only with two straight lines of different slopes for sample A which occurs at temperature 500 K, which is attributed to change in the conduction mechanism [12]. The change in the slope at higher temperature for the sample A may be due to the oxygen vacancies [13] and these
-1.6
5
Zim (x 10 ) Ω
-1.2
448 K 473 K 493 K 503 K
anion vacancies may be responsible for the conductivity with higher activation energy of 0.73 eV in the high temperature region. Oxygen vacancy conduction in spinel ferrites has been reported in literature [3]. But, the sintered samples B and C with the grain sizes 59 and 69 nm do not exhibit any change in the slope of the sT versus 1/T plot, may be due to the number of oxygen vacancies becoming negligible because of the sintering at high temperatures in air. From Fig. 5, the conductivity is observed to decrease with annealing. Conductivity is, in fact, due to the result of the combined influence of several factors such as Fe2þ ion concentration, crystal structure perfection, microstructural homogeneity and grain size. The conductivity of polycrystalline materials in general decreases with the reduction of grain size. Smaller grains imply a larger number of insulating grain boundaries which act as a barrier to the flow of electrons. Also, smaller grains imply smaller grain-to-grain surface contact area and therefore a reduced electron flow. But, in the present studies, we have observed a reverse trend. The decrease in conductivity with annealing temperature can be explained in terms of increasing structural improvement (reduced imperfections) which is also evident from the FE-SEM studies (Fig. 1). Thermal annealing might have decreased the defect concentration,
-0.8
C gb
(ωp)gb=1/R gbCgb
-0.4
0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
5
Zre (x 10 ) Ω Fig. 3. The complex impedance spectra for Mn0.82Zn0.36Fe1.64O3.64 measured at various temperatures for sample A.
R gb Fig. 4. The proposed model for the impedance behavior shown in the Fig. 3. Cgb is the grain boundary capacitance and Rgb is the grain boundary resistance.
N. Sivakumar / Materials Chemistry and Physics 138 (2013) 102e107
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The conductivity spectra at different temperatures are fitted by Eq. (2), using NLLS fitting routine and the parameters sdc, up, and n are extracted from the analysis. The frequency exponent, n takes values near or just below unity and the parameter A is frequency independent, but may be temperature dependent. The characteristic frequency is the hopping frequency up which is obtained from the experimental data by using the relation [16],
sac up ¼ 2sdc
(3)
According to Almond and West [16], the Eq. (2) can be written as
sac ¼ sdc 1 þ ðusÞn
Fig. 5. The Arrhenius plots for the electrical conductivity of nanocrystalline Mn0.82Zn0.36Fe1.64O3.64 spinel samples. The solid lines are the linear fit to the experimental data (Eq. (1)).
which decreases the conductivity. Verma et al. [14] and Van Uitert [15] have also explained the decrease in conductivity in terms of increased homogeneity and structural perfection with increase in annealing temperature in nickel zinc ferrite. 3.3. The a.c. conductivity studies The a.c. conductivity for the as-prepared sample (A) of manganeseezinc spinel at various temperatures is shown in Fig. 6. The conductivity (sac) is found to be frequency independent in the low frequency region (u < up). When the frequency exceeds the hopping frequency up, conductivity (sac) increases with frequency following the power law dispersion sac f un (where n < 1). The a.c. conductivity behavior is analyzed using the conductivity formalism (universal power law) [16],
sac ¼ sdc þ Aun ¼ sdc 1 þ u=u p
n :
(2)
383 K 398 K 423 K 448 K 473 K Fit by Eqn (5)
-1
σ ac(Scm )
1E-4
1E-5
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
Frequency (Hz) Fig. 6. The frequency dependent conductivity of the sample A (11 nm) Mn0.82Zn0.36Fe1.64O3.64. The continuous lines result from the fitting with Eq. (4).
(4)
where, s is the average relaxation time. Fig. 6 shows the plot of a.c. conductivity for sample A (11 nm) of manganeseezinc spinel for various temperatures and the data were fitted using Eq. (4). The measured data are well fitted to Eq. (4). In general, a frequency independent conductivity, equal to the d.c. conductivity, should be obtained at lower frequencies where also the electrode and the grain boundary phenomena are significant. But, in practice, such a frequency independent plateau is observed, often over several decades of frequency, but is limited to higher frequencies by an additional bulk or grain interior phenomenon [17]. This takes the form of a power law increase in conductivity with the frequency. From Fig. 6, we can observe that the plateau region is extended to higher frequencies as the temperature is increased. The increase in electrical conductivity with temperature is attributed to the increase in the drift mobility of the thermally activated charge carriers according to the hopping mechanism [13,15]. Increasing temperature thermally activates the electron exchange between Fe2þ and Fe3þ ions on octahedral sites. Moreover, in the high frequency range, the increase of bulk conductivity is due to the high frequency dispersion [17]. The inverse power law time dependence of the transient current proved Curie-von Schweideler theory [18], and showed an interaction dipole/charge carrier system. Though, it has been observed only in the transient regime, and that is the reason the power law has more prominence at the high frequency range. The frequency independent conductivity region was also extended toward higher frequencies because of the exponential increase in the dc leakage current with the temperature. Also, the value of n was decreased at high temperatures, signifying an increasing in the randomness in the system, which made the dipoles react independently of each other to the external field. Fig. 7(a) and (b) show the plot of a.c. conductivity and permittivity for all the three grain sizes respectively at selected frequencies. The grain size, grain boundaries, and sintering temperature are the important factors that influence the conductivity. Both the a.c. conductivity and permittivity are found to decrease as the grain size increases. The higher value of conductivity and the higher value of permittivity in sample A (11 nm) are possibly due to large surface polarization owing to the large surface area of individual grains and the presence of a localized state in the forbidden energy gap which arises due to lattice imperfections [17]. According to the correlated barrier hopping model [19], ac conductivity
ωp
1E-6
sac ¼
p3 24
N 2 3 R2u u
(5)
where N is the concentration of defect sites contributing to the hopping mechanism, 3 is the dielectric permittivity, and Ru is the hopping distance. Thermal annealing (for sample, B, and C) gives
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N. Sivakumar / Materials Chemistry and Physics 138 (2013) 102e107
(a)
(b)
1E-4
1 MHz 500 kHz 100 kHz
Dielectric permittivity
1 MHz 500 kHz 100 kHz
σac (Scm-1)
1E-5
1E-6
10
20
30
40
50
60
10
2
10
70
20
30
40
50
60
70
Grain size (nm)
Grain size (nm)
Fig. 7. Grain size dependence of (a) a.c. conductivity (b) dielectric permittivity for Mn0.82Zn0.36Fe1.64O3.64 spinel ferrite for three different frequencies. The continuous line is guide to eye.
(a)
(b) 423 K 448 K 483 K 493 K 503 K 513 K 523 K 533 K
M''/M''max
0.8 0.6
1.0
0.4
0.6 0.4
0.2
0.2
0.0
0.0
1E-3
A (11 nm) B (59 nm) C (69 nm)
0.8
M''/M''max
1.0
0.01
0.1
1
10
100
0.01
0.1
log (f/fmax)
1 log (f/fmax )
10
100
Fig. 8. The plots of M0 0 /M0 0 max versus log (f/fmax) for (a) sample A (11 nm) for various temperatures and (b) for all the four grain sizes of Mn0.82Zn0.36Fe1.64O3.64 spinel ferrite measured at 423 K.
rise to more uniform crystal structures (as evidenced by FE-SEM studies and BET analysis) with reduced imperfections, thereby, decreasing the value of N, which ultimately reduces the value of a.c. conductivity as the annealing temperature increases. George et al. [20] have observed a similar behavior in conductivity and permittivity in the case of cobalt ferrite prepared by solegel method, who also explained it in terms of increased structural perfection with the sintering temperature. Therefore, the above results suggest that the structural ordering has a great influence on conductivity, which is more significant than that of the grain size effect in these samples.
(a)
3.4. Electrical modulus studies Fig. 8 shows a master plot for the imaginary part of the electric modulus in which each frequency is scaled by the peak frequency, fmax, and M00 is scaled by M00 max. From Fig. 8(a) we note that all the curves for different temperatures overlap on a single master curve for sample A (11 nm) indicating that the relaxation mechanism is temperature independent. Similarly, the same kind of behavior follows for all other grain sizes also. Moreover, Fig. 8(b) shows that the curves for all the grain sizes overlap on a single master curve, but in the high frequency region there are some deviations due to
(b) M''/M''max(316 kHz) Z''/Z''max (251 kHz)
1.0
0.8
Normalized peak
0.8
Normalized peak
M''/M''max(199 kHz) Z''/Z''max (199 kHz)
1.0
0.6 0.4 0.2 0.0
0.6 0.4 0.2 0.0
1
10
100 1000 Frequency (kHz)
10000
1
10
100
1000
10000
Frequency (kHz)
Fig. 9. The logarithmic plot of normalized parameters (M0 0 , Z0 0 ) for (a) sample A (11 nm) and (b) sample C (69 nm) of Mn0.82Zn0.36Fe1.64O3.64 spinel ferrite measured at 523 K.
N. Sivakumar / Materials Chemistry and Physics 138 (2013) 102e107
grain interior or grain effect. The value of full-width at halfmaximum (FWHM) is found to be > 1.14 decades [21] as evaluated from the normalized modulus spectrum which suggests the presence of non-Debye type of relaxation phenomena in good agreement with the observations from complex modulus spectrum. The variation of normalized parameters M00 /M00 max and Z00 /Z00 max as a function of logarithmic frequency measured at 523 K for sample A (11 nm) is shown in Fig. 9(a). From the figure we note that the peak frequency shifts towards higher frequency region as it moves from Z00 to M00 . The mismatch between the peaks of both these parameters gives an evidence for the existence of two polarization phenomena [22,23].The very distinct curves of M00 /M00 max and Z00 /Z00 max illustrates clearly that polarization process is an evidence of short-range conductivity. Moreover, the polarization process is due to a localized conduction of multiple carriers that describes the presence of multiple relaxation processes in the material. But, in the case of sample C, it has been observed that both Z00 and M00 peaks overlap better which supports the argument that there is only one relaxation process (Fig. 9(b)). Also, M00 /M00 max exhibits peaks at high frequency and it reduces to zero at low frequencies. This suggests that electrode polarization phenomenon is negligible or absent. 4. Conclusion
of temperature dependence on dc conductivity shows the semiconducting nature of samples and the conductivity is of short-range type such as a hopping -type mechanism. The important finding of the present study is that the structural ordering has a great influence on conductivity, which is more significant than that of the grain size effect in these samples. References [1] [2] [3] [4] [5] [6] [7] [8] [9]
[10] [11] [12] [13] [14]
Nanostructured manganese zinc ferrite spinel ferrite has been studied by the complex impedance spectroscopy technique. In this study, the electrical conductivity of the heat-treated materials is studied by impedance spectroscopy which showed reduction in conductivity with increasing temperature due to improvement in structural ordering (reduced imperfections and increase in grain sizes) and possible change in the cation distribution. Moreover, the possible change in cation distribution on annealing might have contributed to the observed decrease in the conductivity. The plot
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[15] [16] [17] [18] [19] [20] [21] [22] [23]
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