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Study of dielectric and impedance properties of Mn ferrites
Physica B 406 (2011) 382–387
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Study of dielectric and impedance properties of Mn ferrites Khalid Mujasam Batoo n King Abdullah Institute for nanotechnology, King Saud University, Riyadh-11451, Saudi Arabia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 25 March 2010 Received in revised form 27 October 2010 Accepted 28 October 2010
The paper reports on the effect of Al substitution on the structural and electrical properties of bulk ferrite series of basic composition MnFe2 2xAl2xO4 (0.0 r x r 0.5) synthesized using solid state reaction method. XRD analysis confirms that all the samples exhibit single phase cubic spinel structure excluding presence of any secondary phase. The dielectric constant shows a normal behaviour with frequency, whereas the loss tangent exhibits an anomalous behaviour with frequency for all compositions. Variation of dielectric properties and ac conductivity with frequency reveals that the dispersion is due to Maxwell–Wagner type of interfacial polarization in general and hopping of charge between Fe + 2 and Fe + 3 as well as between Mn + 2 and Mn + 3 ions at octahedral sites. The complex impedance plane spectra shows the presence of two semicircles up to x ¼ 0.2, and only one semicircle for the higher values of x. The analysis of the data shows that the resistive and capacitive properties of the Mn ferrite are mainly due to processes associated with grain and grain boundaries. & 2010 Elsevier B.V. All rights reserved.
Keywords: Ferrites Dielectric constant Impedance spectroscopy
1. Introduction Ferrite materials have always attracted lots of attention of the scientific community due to their wide range of the technological applications. Various physical properties of ferrites are highly influenced by the distribution of cations among the sublattices, nature of grain (shape, size and orientation), grain boundaries, voids, inhomogeneities, surface layers and contacts, etc. The information about the associated physical parameters of the microstructural components is important since the overall property of the materials is determined by these components. Progresses in the use and development of new ferrites have been rapid as compared to other areas of research [1–3]. One important characteristic of ferrites are their high values of resistivity and low eddy current losses [4], which make them ideal for high frequency applications. Owing to the dielectric behavior, they are sometimes called multiferroics. They are important commercially because they can be applied in many devices such as phase shifter, high frequency transformer cores, switches, resonators, computers, TVs and mobile phone [5,6]. One way of reducing the dielectric loss in power electronic application is to reduce the intensity of polarization inside the ferrite ceramics. Effect of such process in macro view is to reduce the complex permittivity, specially its imaginary part in order to better the techniques it is necessary to understand the chemical mechanism and crystal structure of the ferrites [7]. MnFe2O4 has attracted considerable attention due to its broad applications in n
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several technological fields, including electronic devices, ferro fluids, magnetic drug delivery, microwave devices and high density information storage [8–10]. The objective of the present work is to study the effect of Al doping on the dielectric properties of these ferrites over the wide range of frequencies at room temperature. It is interesting to see that various physical parameters and characteristic properties that influence the performance of the materials can be known and interpreted from the complex plane impedance spectra. In this article, we report the influence of Al substitution on the structural, dielectric and impedance properties of MnFe2 2xAl2xO4 ferrite as a function of frequency and composition at room temperature.
2. Experimental Polycrystalline spinel ferrite series of basic composition, MnFe2 2xAl2xO4 (0 rxr0.5) has been synthesized using conventional solid state reaction method. Stoichiometric amounts of AR grade oxides of iron, aluminum and manganese were mixed together. The mixture of each composition was ground for 1 h using motor and agate, and pre-sintered at 1000 1C for 13 h. The pre-sintered mixture was ground again and pressed into discshaped pellets. The pellets were finally sintered at 1300 1C for 5 h and slowly cooled to room temperature at a rate of 1 1C/min. X-ray powder diffraction (XRD) patterns were recorded on a D8 Bruker Advanced diffractometer (Bruker AXE) with CuKa radiation at a sweep rate of 21/min. The dielectric and impedance spectroscopy measurements, as a function of frequency at room temperature,
K. Mujasam Batoo, Alimuddin / Physica B 406 (2011) 382–387
were performed using LCR HI-Tester (HIOKI 3532-50) in the frequency range 42 Hz–5 MHz.
3. Results and discussion
333
422
400
440
311 220
422
400
333
440
311
The mean radius of the ions at tetrahedral site rtetr and octahedral site roct has been calculated according to the following equations [13]: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rtetr ¼ a 3ðm-0:25Þ-R0 ð2Þ ð3Þ
where R0 is the radius of the oxygen ion (R0 ¼1.26 A˚ [14]) and m the oxygen parameter (m ¼ 0.375 for MnFe2O4). Fig. 3 shows the variation of rtetr and roct as a function of composition. It has been found that both rtetr and roct decrease with increase in Al content, which shows that Al ions are distributed over both the sites (A and B). Fig. 4(a) and (b) shows the SEM micrographs of the samples with 0.1 and 0.2 wt% MnFe2O4. It is seen that the surface of the samples shows formation of some plane rocky structures deteriorated by the discontinuous grain growth. Also, the porosity in the samples increases with increase in doping concentration. The microstructure shows the presence of only one type of grains, excluding the presence of any other secondary phases.
x = 0.2
220
spinel cubic ferrites [11,12]. The lattice parameter has been found to decrease with increase in Al concentration, which can be explained on the basis of the mismatch of ionic radii of replacer ˚ is smaller and replacent. Since, the ionic radius of Al3 + ion (0.51 A) ˚ the value of lattice parameter than that of Fe3 + ion (0.67 A), decreases with increase in the value of x. The cationic distribution of Mn ferrite system is written as Mnd Alg Fe½1ðd þ gÞ Mn1d Alxg Fe1x þ d þ g O4 ð1Þ
roct ¼ að5=8-mÞ-R0
x = 0.4
3.1. Dielectric constant
x = 0.0
20
30
40
50
440
333
422
400
311
400 350 300 250 200 150 100 50 0 -50 400 350 300 250 200 150 100 50 0 -50 700 600 500 400 300 200 100 0 -100
220
Intensity (a.u.)
X-ray diffraction patterns of MnFe2 2xAl2xO4 (Fig. 1) ferrites analyzed using Powder-X software confirmed that all the samples exhibit single phase cubic spinel structure excluding the presence of any undesirable secondary structures. Fig. 2 shows the variation of lattice parameter (a) with composition. The values of the lattice constant have been found in the range of lattice parameters of
383
60
70
2θ Fig. 1. XRD pattern of the MnFe2 xAlxO4 ferrite.
The effect of frequency on the dielectric constant has been studied for all the samples. Figs. 5 and 6 depict the variation of real and imaginary parts of the dielectric constant with frequency. The value of e0 is much higher at lower frequencies. It decreases with the increase in frequency from 42 Hz–5 MHz. At very high frequencies, its value becomes so small that it becomes independent of frequency as described in Ref. [15]. The variation in dielectric constant may be explained on the basis of space–charge polarization produced due to the presence of higher conductivity phases (grains) in the insulating matrix (grain boundaries) of a dielectric, which produces localized accumulation of charge under the
8.54
0.95
8.52
0.90
8.50
0.85
8.48
rtetra & rocta
Lattice constant 'a' (A°)
1.00
8.46 8.44
0.80 0.75 0.70
8.42
0.65
8.40
0.60
8.38
0.55 0.0
0.1
0.2 0.3 composition ( x )
0.4
Fig. 2. Variation of lattice parameter ‘a’ with Al doping.
0.5
rtetra roct
0.0
0.1
0.2 0.3 composition (x)
0.4
0.5
Fig. 3. Variation of ionic radii of tetrahedral and octahedral sites with Al doping.
384
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Fig. 4. SEM micrographs of the Mn ferrite for compositions x¼ 0.1 and 0.2.
110000
0.0 0.1 0.2 0.3 0.4 0.5
100000 90000 80000 70000 ε'
60000 50000 40000 30000 20000 10000 0 -10000
2
1
3
4 5 log (f ) Hz
6
7
Fig. 5. Variation of dielectric constant with frequency.
14 0.0 0.1 0.2 0.3 0.4 0.5
12 10
tan δ
8 6 4 2 0 -2
1
2
3
4
5
6
log (f ) Hz Fig. 6. Shows the variation of loss tangent (tan d) with frequency.
7
influence of an electric field as demonstrated [16]. The assembly of space charge carriers in a dielectric takes a finite time to line up their axes parallel to an alternating electric field. If the frequency of the field reversal increases, a point is reached where the space charge carriers cannot keep up with the field and, the alternation of their direction lags behind that of the field as discussed in Ref. [16]. This results in a reduction in the dielectric constant of the material. Shaikh et al. [17] have quoted a similar kind of trend for dielectric constant with the change in frequency. According to Maxwell and Wagner [18,19] two-layer model, space–charge polarization is because of the inhomogeneous dielectric structure of the material. It is formed by large well conducting grains separated by thin poorly conducting intermediate grain boundaries. Rabinkin and Novikova [20] pointed out that polarization in ferrites is similar to that of conduction. The electron exchange between Fe2 + 2Fe3 + results in local displacement of electrons in the direction of applied field that determines polarization. Polarization decreases with increasing value of frequency, and then reaches a constant value. It is due to the fact that beyond a certain frequency of external field, the electron exchange Fe2 + 2Fe3 + cannot follow the alternating field. The high value of the dielectric constant at lower frequency is due to the predominance of the species like Fe2 + ions, oxygen vacancies, grain boundary defects, etc [19,21], while the decrease in dielectric constant with frequency is natural, i.e., any species contributing to the polarizability is found to show the applied field lagging behind at higher frequencies [22].
3.2. Loss tangent (tan d) The variation of tan d as a function of frequency at room temperature for all compositions is shown in Fig. 7. The loss tangent (tan d) represents the energy dissipation in a dielectric. The loss tangent peaks are found to shift towards the lower frequency region with increasing value of Al content. Also, the height of the peak has been found to decrease with increase in doping concentration. The peaking behaviour of tan d is clearly explained in the light of Rezlescuu model [23]. According to this model, the peaking behaviour appears when the frequency of charge hopping between the two valence states of the same element matches with the frequency of the applied field, i.e.,
ot ¼ 1
ð5Þ
where t is the relaxation time of hopping process and o the angular frequency of the field (o ¼2pfmax). The relxation time t is inversely proportional to the jumping probability per unit time, P, according
-3.5 -4.0 -4.5 -5.0 -5.5 -6.0 -6.5 -7.0 -7.5 -8.0 -8.5 -9.0 -9.5 -10.0 -10.5 -11.0 -11.5
0.0 0.1 0.2 0.3 0.4 0.5
385
0.5
0.4
0.3 n
lnσac (ohm.m)−1
K. Mujasam Batoo, Alimuddin / Physica B 406 (2011) 382–387
0.2
0.1
0.0 2
4
6
8
10 ln (ω) Hz
12
14
Fig. 7. Plots of ln sAC (ohm cm) 1 with respect to ln o (Hz) for all the samples at room temperature.
0.1
0.2 0.3 composition ( x )
0.4
0.008
From Eqs. (5) and (6), it is clear that fmax is proportional to P. The shift in the peak position of tan d towards the lower frequency region with increasing Al concentration indicates that the jumping probability decreases as doping content increases. This decrease in the jumping probability may be attributed to the decrease in Fe3 + ion number at B-sites, which are responsible for the polarization in ferrites. The decrease in peak height with the composition may also be explained on the basis of increasing value of resistivity/ decreasing number of Fe3 + ions at octahderal site.
σac
0.004 0.002 0.000 8 4 0 15000
ε"
3.3. AC conductivity
5KHz 10KHz 100KHz 1MHz
0.006
tan δ
ð6Þ
0.5
Fig. 8. Variation of exponent n with respect to the composition at room temperature.
to the relation:
t ¼ 1=P
0.0
16
10000 5000
Frequency dependence of ac conductivity is expressed as
where the first term is dc conductivity due to band conduction and is a frequency independent function. The second term is pure AC conductivity due to hopping processes at the octahedral site and is a frequency dependent function. The first term is predominant in low frequencies and at high temperatures, while the second term is predominant in high frequencies and at low temperatures. The frequency dependence of the second term sac can be written as
sAC ¼ Aon
0 6000
ð7Þ
ð8Þ
where A is a constant having the units of conductivity and the exponent ‘n’ a temperature dependent constant, s is the real part of the conductivity and o the angular frequency (o ¼2pf). Fig. 8 shows the variation ln s versus ln o with slopes equal to the exponent n in the frequency range 42 Hz–5 MHz,at room temperature. The ac conductivity shows an increasing trend with the frequency for all compositions. Its value first increases linearly according to the power law Equation (8). It is seen that the values of ac conductivity increases gradually with increase in frequency, which is the normal behaviour of ferrites. The increase in ac conductivity with applied field can be explained on the basis of the pumping force of the applied field that promotes the tranferring of charge carriers between the two Fe ion states, and liberation of charges from different trapping centers. These charge carriers
4000 ε'
sutot ¼ so ðTÞ þ sðo,TÞ
2000 0 0.0
0.1
0.2 0.3 composition ( x )
0.4
Fig. 9. Variation of ac conductivity with composition at selected frequencies.
participate in conduction process along with electrons produced from the valence exchange bewteen different metal ions. Fig. 9 shows the variation of exponent n with a composition at room temperature. The values of exponent ‘n’ are found in the range 0.52–0.79 and are found to be composition dependent. 3.4. Compostional depandence of (e0 , e00 , tan d and sAC) Fig. 10 presents the variation of dielectric parameters (e0 , e00 , tan d and sAC) as a function of composition at selected frequencies. It can be seen that all the dielectric parameters (e0 , e00 , tan d) and conductivity sAC increase up to 10% of Al doping, thereafter, these parameters decrease with a further doping of Al. The behaviour can
386
K. Mujasam Batoo, Alimuddin / Physica B 406 (2011) 382–387
3500 3000 2500 2000
0
10
0.4 0
1500 1000 500 0 -500
0.5
6 4 2 0
Z" ( x 103 K . Ω)
Z' (x 103 K . Ω)
2 1 0
0.0 0.1 0.2 0.3 0.4 0.5
8 4 0
2
3
4 5 log (f ) Hz
6
7
0
0.5
Fig. 10. Shows the variation of Z0 with respect to the frequency.
be explained on the basis that in Al containing ferrites, Al ions prefer to occupy the octahedral coordination until the ratio of Al substitution becomes greater than 60%, where after, Al ions may increase in tetrahedral sites causing migration of equal number of ions to the octahedral sites [24]. When the Al is doped in the system, it occupies the octahedral site in the ferrite system, decreasing the Fe ion number responsible for polarization in the ferrite system. Hence the value of dielectric constant decreases with increasing Al content in the present system.
0.2 0.0
20
0.3 10
20
30
40
0.2
0.0 1
10
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.1
0.2
0.3
0.4
0.5
0.6
0.1 0.0
2 1 0
0.0 0
1
2
3
Z' ( x 103 K . Ω) Fig. 11. Shows Cole–Cole plot for all Mn ferrite compositions.
3.5. Impedance Impedance spectroscopy is an important method to study the electrical properties of ferrites as the impedance of grains can be separated from the other impedance sources, such as impedance of electrodes and grain boundaries. One of the important factors, which influences the impedance properties of ferrites is the microstructural effect. The impedance measurement gives us information about the resistive (real part) and reactive (imaginary part) components of a material. Fig. 11 shows the variation of real part of Z with frequency. The values of Z0 are found to decrease with increase in the value of frequency. There are three generic relaxation dispersion situations that may occur for solids while discussing Z00 as a function of frequency: conductive system associated charge carriers, dielectric-system dispersion usually arising from dipole rotation of lattice entities and the presence of both types of dispersions within measured frequency range. A ferrite material is assumed to be consisting of piled up crystalline plates. From the microstructural point of view, a sample is assumed as a microstructure made up of parallel conducting plates (grains) separated by resistive plates (grain boundaries). Generally, two semicircles are observed in the Cole–Cole plot; first semicircle at low frequency represents the resistance of the grain boundary and second semicircle obtained at high frequency corresponds to the resistance of grain or bulk properties. The phenomenon is typically related to the existence of a distribution of relaxation time, which is according to the Cole–Cole type of distribution based on two-layer model, in which the resulting complex impedance is composed of two overlapping semicircles. Fig. 12 shows the complex impedance or Cole–Cole plot for all the compositions as a function of frequency at room temperature. Two semicircles are found up to 20% of Al doping, indicating a Cole– Cole type of distribution, while only one semicircle has been found
Fig. 12. (a) and (b) Fitted plot for the compositions x¼ 0.0 and 0.4 by non-linear least square fitting routine (NLLS).
for higher compositions (x Z0.3). Decentralization in the semicircles has been observed in compositions of Mn ferrite. The electrical response of polycrystalline series of MnFe2O4 ferrite doped by Al can be represented by two parallel RC equivalent circuits in series configuration [25,26], and can be visually observed when there is a significant difference between the two resonant frequencies. Such an interpretation is indeed very helpful to represent the sample by an electrical circuit as a combination of resistors and capacitors. The representation of sample through an electrical circuit analog is very helpful in representing the electrical features of the sample. Fig. 12 shows the proposed model for the analysis of the impedance spectroscopy data, where, the parameters Rgb, Cgb and ogb correspond to the resistance, capacitance and the relaxation frequency ( ¼1/t) of the grain boundary volume, respectively, and Rg, Cg and og are the corresponding quantities for the grain. The above mentioned parameters were calculated at room temperature by analyzing the data using the non-linear leastsquare (NLLS) fitting routine and are tabulated in Table 1. The resistance of the circuit represents a conductive path and a given resistor in a circuit account for the bulk conductivity of the sample. Also the capacitances will be generally associated with spacecharge polarization regions. A parallel arrangement of the phases
K. Mujasam Batoo, Alimuddin / Physica B 406 (2011) 382–387
Table 1 Impedance parameters obtained experimentally for MnFe2 2xAlxO4 ferrite. Chemical formula
Rg (kO)
Cg (F)
tg (s)
Rgb (kO)
Cgb (F)
tgb (s)
MnFe2O4 MnFe1.8Al0.2O4 MnFe1.6Al0.4O4 MnFe1.4Al0.6O4 MnFe1.2Al0.8O4 MnFe1Al1O4
74.65 45.36 77.21 – – ––
1.224E 7 0.001E 6 3.677E 7 – – ––
0.009 0.055 0.028 – – ––
61.93 6.76 25.64 3299.5 1590.7 804.53
5.92E 7 5.54E 5 4.79E 6 3.81E 10 1.14E 9 3.17E 9
0.036 0.055 0.123 0.001 0.002 0.003
correspond to only one semicircle, which has been observed for the compositions x¼0.3, 0.4 and 0.5. The area of the semicircle represents the grain boundary resistance (Rgb), and is found to increase continuously with increasing value of x and overlaps with the semicircle representing the grain resistance (Rg), and it becomes impossible to separate the two semicircles. It is seen that there are two effects pertaining to the microstructural inhomogeneity –grain and grain boundary. No other relaxation mechanism, such as electrode effect and ionic species diffusion is identified for the analyzed frequency range. Since the relaxation time of grain and grain boundary are different, the impedance spectroscopy allows separation of two, thus resulting in separate semicircles. This clearly indicates that the resistance values for the grain boundary increase with acceptor addition, which may be attributed to contribution from the physical loci, such as grain boundary or grain interior. Also, close to grain boundaries, the transport properties of a materials are controlled by imperfections, expected to be present in higher concentrations than in grains, leading to an additional contribution to the intergrain (grain boundary) impedance. The internal space–charge created at grain boundaries may lead to a significant increase in the concentration of mobile effects [27–29,]. Alternatively, this can represent an additional relaxation process associated with point defects, such as trapping and detrapping of electrons in deep traps within the grain interiors or in depletion layer regions adjoining the grain boundaries. It is seen that among all the compositions MnFe1.8Al0.2O4 exhibits lowest values of resistance (Rg and Rgb) but highest values of the capacitances (Cg and Cgb). The capacitance of grain boundary is larger than that of capacitance of grain, which can be explained on the basis that capacitance is inversely proportional to the thickness of the media. The higher values of capacitance for both grain and grain boundary for the composition MnFe1.8Al0.2O4 means this composition exhibits greater polarizability. The impedance results obtained are found consistent with the conductivity data for all compositions.
technique. The dispersion in dielectric properties have been explained in the light of space charge polarization discussed in Maxwell–Wagner model. The AC conductivity of the samples has been discussed in the light of the hopping model. The complex impedance plane spectra the show presence of two semicircles up to x¼0.2, and only one semicircle for the higher value of x, i.e., impedance of MnFe2O4 is composition dependent property, which is in good agreement with the Cole–Cole type of distribution. The analysis of the complex impedance data shows that the capacitive and the reactive properties of the materials are mainly attributed to the processes that are associated with the grain and grain boundary.
Acknowledgement One of the authors (K.M. Batoo) is thankful to I.U.A.C., New Delhi for financial support through UFUP project. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
4. Conclusion We have successfully synthesized single phase polycrystalline MnFe2 2xAl2xO4 with spinel structure through solid state reaction
387
[27] [28] [29]
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Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Study of dielectric and impedance properties of Mn ferrites Khalid Mujasam Batoo n King Abdullah Institute for nanotechnology, King Saud University, Riyadh-11451, Saudi Arabia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 25 March 2010 Received in revised form 27 October 2010 Accepted 28 October 2010
The paper reports on the effect of Al substitution on the structural and electrical properties of bulk ferrite series of basic composition MnFe2 2xAl2xO4 (0.0 r x r 0.5) synthesized using solid state reaction method. XRD analysis confirms that all the samples exhibit single phase cubic spinel structure excluding presence of any secondary phase. The dielectric constant shows a normal behaviour with frequency, whereas the loss tangent exhibits an anomalous behaviour with frequency for all compositions. Variation of dielectric properties and ac conductivity with frequency reveals that the dispersion is due to Maxwell–Wagner type of interfacial polarization in general and hopping of charge between Fe + 2 and Fe + 3 as well as between Mn + 2 and Mn + 3 ions at octahedral sites. The complex impedance plane spectra shows the presence of two semicircles up to x ¼ 0.2, and only one semicircle for the higher values of x. The analysis of the data shows that the resistive and capacitive properties of the Mn ferrite are mainly due to processes associated with grain and grain boundaries. & 2010 Elsevier B.V. All rights reserved.
Keywords: Ferrites Dielectric constant Impedance spectroscopy
1. Introduction Ferrite materials have always attracted lots of attention of the scientific community due to their wide range of the technological applications. Various physical properties of ferrites are highly influenced by the distribution of cations among the sublattices, nature of grain (shape, size and orientation), grain boundaries, voids, inhomogeneities, surface layers and contacts, etc. The information about the associated physical parameters of the microstructural components is important since the overall property of the materials is determined by these components. Progresses in the use and development of new ferrites have been rapid as compared to other areas of research [1–3]. One important characteristic of ferrites are their high values of resistivity and low eddy current losses [4], which make them ideal for high frequency applications. Owing to the dielectric behavior, they are sometimes called multiferroics. They are important commercially because they can be applied in many devices such as phase shifter, high frequency transformer cores, switches, resonators, computers, TVs and mobile phone [5,6]. One way of reducing the dielectric loss in power electronic application is to reduce the intensity of polarization inside the ferrite ceramics. Effect of such process in macro view is to reduce the complex permittivity, specially its imaginary part in order to better the techniques it is necessary to understand the chemical mechanism and crystal structure of the ferrites [7]. MnFe2O4 has attracted considerable attention due to its broad applications in n
Tel.: + 91 9897810509; fax: + 966 1 4670662. E-mail address: [email protected]
0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.10.075
several technological fields, including electronic devices, ferro fluids, magnetic drug delivery, microwave devices and high density information storage [8–10]. The objective of the present work is to study the effect of Al doping on the dielectric properties of these ferrites over the wide range of frequencies at room temperature. It is interesting to see that various physical parameters and characteristic properties that influence the performance of the materials can be known and interpreted from the complex plane impedance spectra. In this article, we report the influence of Al substitution on the structural, dielectric and impedance properties of MnFe2 2xAl2xO4 ferrite as a function of frequency and composition at room temperature.
2. Experimental Polycrystalline spinel ferrite series of basic composition, MnFe2 2xAl2xO4 (0 rxr0.5) has been synthesized using conventional solid state reaction method. Stoichiometric amounts of AR grade oxides of iron, aluminum and manganese were mixed together. The mixture of each composition was ground for 1 h using motor and agate, and pre-sintered at 1000 1C for 13 h. The pre-sintered mixture was ground again and pressed into discshaped pellets. The pellets were finally sintered at 1300 1C for 5 h and slowly cooled to room temperature at a rate of 1 1C/min. X-ray powder diffraction (XRD) patterns were recorded on a D8 Bruker Advanced diffractometer (Bruker AXE) with CuKa radiation at a sweep rate of 21/min. The dielectric and impedance spectroscopy measurements, as a function of frequency at room temperature,
K. Mujasam Batoo, Alimuddin / Physica B 406 (2011) 382–387
were performed using LCR HI-Tester (HIOKI 3532-50) in the frequency range 42 Hz–5 MHz.
3. Results and discussion
333
422
400
440
311 220
422
400
333
440
311
The mean radius of the ions at tetrahedral site rtetr and octahedral site roct has been calculated according to the following equations [13]: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rtetr ¼ a 3ðm-0:25Þ-R0 ð2Þ ð3Þ
where R0 is the radius of the oxygen ion (R0 ¼1.26 A˚ [14]) and m the oxygen parameter (m ¼ 0.375 for MnFe2O4). Fig. 3 shows the variation of rtetr and roct as a function of composition. It has been found that both rtetr and roct decrease with increase in Al content, which shows that Al ions are distributed over both the sites (A and B). Fig. 4(a) and (b) shows the SEM micrographs of the samples with 0.1 and 0.2 wt% MnFe2O4. It is seen that the surface of the samples shows formation of some plane rocky structures deteriorated by the discontinuous grain growth. Also, the porosity in the samples increases with increase in doping concentration. The microstructure shows the presence of only one type of grains, excluding the presence of any other secondary phases.
x = 0.2
220
spinel cubic ferrites [11,12]. The lattice parameter has been found to decrease with increase in Al concentration, which can be explained on the basis of the mismatch of ionic radii of replacer ˚ is smaller and replacent. Since, the ionic radius of Al3 + ion (0.51 A) ˚ the value of lattice parameter than that of Fe3 + ion (0.67 A), decreases with increase in the value of x. The cationic distribution of Mn ferrite system is written as Mnd Alg Fe½1ðd þ gÞ Mn1d Alxg Fe1x þ d þ g O4 ð1Þ
roct ¼ að5=8-mÞ-R0
x = 0.4
3.1. Dielectric constant
x = 0.0
20
30
40
50
440
333
422
400
311
400 350 300 250 200 150 100 50 0 -50 400 350 300 250 200 150 100 50 0 -50 700 600 500 400 300 200 100 0 -100
220
Intensity (a.u.)
X-ray diffraction patterns of MnFe2 2xAl2xO4 (Fig. 1) ferrites analyzed using Powder-X software confirmed that all the samples exhibit single phase cubic spinel structure excluding the presence of any undesirable secondary structures. Fig. 2 shows the variation of lattice parameter (a) with composition. The values of the lattice constant have been found in the range of lattice parameters of
383
60
70
2θ Fig. 1. XRD pattern of the MnFe2 xAlxO4 ferrite.
The effect of frequency on the dielectric constant has been studied for all the samples. Figs. 5 and 6 depict the variation of real and imaginary parts of the dielectric constant with frequency. The value of e0 is much higher at lower frequencies. It decreases with the increase in frequency from 42 Hz–5 MHz. At very high frequencies, its value becomes so small that it becomes independent of frequency as described in Ref. [15]. The variation in dielectric constant may be explained on the basis of space–charge polarization produced due to the presence of higher conductivity phases (grains) in the insulating matrix (grain boundaries) of a dielectric, which produces localized accumulation of charge under the
8.54
0.95
8.52
0.90
8.50
0.85
8.48
rtetra & rocta
Lattice constant 'a' (A°)
1.00
8.46 8.44
0.80 0.75 0.70
8.42
0.65
8.40
0.60
8.38
0.55 0.0
0.1
0.2 0.3 composition ( x )
0.4
Fig. 2. Variation of lattice parameter ‘a’ with Al doping.
0.5
rtetra roct
0.0
0.1
0.2 0.3 composition (x)
0.4
0.5
Fig. 3. Variation of ionic radii of tetrahedral and octahedral sites with Al doping.
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Fig. 4. SEM micrographs of the Mn ferrite for compositions x¼ 0.1 and 0.2.
110000
0.0 0.1 0.2 0.3 0.4 0.5
100000 90000 80000 70000 ε'
60000 50000 40000 30000 20000 10000 0 -10000
2
1
3
4 5 log (f ) Hz
6
7
Fig. 5. Variation of dielectric constant with frequency.
14 0.0 0.1 0.2 0.3 0.4 0.5
12 10
tan δ
8 6 4 2 0 -2
1
2
3
4
5
6
log (f ) Hz Fig. 6. Shows the variation of loss tangent (tan d) with frequency.
7
influence of an electric field as demonstrated [16]. The assembly of space charge carriers in a dielectric takes a finite time to line up their axes parallel to an alternating electric field. If the frequency of the field reversal increases, a point is reached where the space charge carriers cannot keep up with the field and, the alternation of their direction lags behind that of the field as discussed in Ref. [16]. This results in a reduction in the dielectric constant of the material. Shaikh et al. [17] have quoted a similar kind of trend for dielectric constant with the change in frequency. According to Maxwell and Wagner [18,19] two-layer model, space–charge polarization is because of the inhomogeneous dielectric structure of the material. It is formed by large well conducting grains separated by thin poorly conducting intermediate grain boundaries. Rabinkin and Novikova [20] pointed out that polarization in ferrites is similar to that of conduction. The electron exchange between Fe2 + 2Fe3 + results in local displacement of electrons in the direction of applied field that determines polarization. Polarization decreases with increasing value of frequency, and then reaches a constant value. It is due to the fact that beyond a certain frequency of external field, the electron exchange Fe2 + 2Fe3 + cannot follow the alternating field. The high value of the dielectric constant at lower frequency is due to the predominance of the species like Fe2 + ions, oxygen vacancies, grain boundary defects, etc [19,21], while the decrease in dielectric constant with frequency is natural, i.e., any species contributing to the polarizability is found to show the applied field lagging behind at higher frequencies [22].
3.2. Loss tangent (tan d) The variation of tan d as a function of frequency at room temperature for all compositions is shown in Fig. 7. The loss tangent (tan d) represents the energy dissipation in a dielectric. The loss tangent peaks are found to shift towards the lower frequency region with increasing value of Al content. Also, the height of the peak has been found to decrease with increase in doping concentration. The peaking behaviour of tan d is clearly explained in the light of Rezlescuu model [23]. According to this model, the peaking behaviour appears when the frequency of charge hopping between the two valence states of the same element matches with the frequency of the applied field, i.e.,
ot ¼ 1
ð5Þ
where t is the relaxation time of hopping process and o the angular frequency of the field (o ¼2pfmax). The relxation time t is inversely proportional to the jumping probability per unit time, P, according
-3.5 -4.0 -4.5 -5.0 -5.5 -6.0 -6.5 -7.0 -7.5 -8.0 -8.5 -9.0 -9.5 -10.0 -10.5 -11.0 -11.5
0.0 0.1 0.2 0.3 0.4 0.5
385
0.5
0.4
0.3 n
lnσac (ohm.m)−1
K. Mujasam Batoo, Alimuddin / Physica B 406 (2011) 382–387
0.2
0.1
0.0 2
4
6
8
10 ln (ω) Hz
12
14
Fig. 7. Plots of ln sAC (ohm cm) 1 with respect to ln o (Hz) for all the samples at room temperature.
0.1
0.2 0.3 composition ( x )
0.4
0.008
From Eqs. (5) and (6), it is clear that fmax is proportional to P. The shift in the peak position of tan d towards the lower frequency region with increasing Al concentration indicates that the jumping probability decreases as doping content increases. This decrease in the jumping probability may be attributed to the decrease in Fe3 + ion number at B-sites, which are responsible for the polarization in ferrites. The decrease in peak height with the composition may also be explained on the basis of increasing value of resistivity/ decreasing number of Fe3 + ions at octahderal site.
σac
0.004 0.002 0.000 8 4 0 15000
ε"
3.3. AC conductivity
5KHz 10KHz 100KHz 1MHz
0.006
tan δ
ð6Þ
0.5
Fig. 8. Variation of exponent n with respect to the composition at room temperature.
to the relation:
t ¼ 1=P
0.0
16
10000 5000
Frequency dependence of ac conductivity is expressed as
where the first term is dc conductivity due to band conduction and is a frequency independent function. The second term is pure AC conductivity due to hopping processes at the octahedral site and is a frequency dependent function. The first term is predominant in low frequencies and at high temperatures, while the second term is predominant in high frequencies and at low temperatures. The frequency dependence of the second term sac can be written as
sAC ¼ Aon
0 6000
ð7Þ
ð8Þ
where A is a constant having the units of conductivity and the exponent ‘n’ a temperature dependent constant, s is the real part of the conductivity and o the angular frequency (o ¼2pf). Fig. 8 shows the variation ln s versus ln o with slopes equal to the exponent n in the frequency range 42 Hz–5 MHz,at room temperature. The ac conductivity shows an increasing trend with the frequency for all compositions. Its value first increases linearly according to the power law Equation (8). It is seen that the values of ac conductivity increases gradually with increase in frequency, which is the normal behaviour of ferrites. The increase in ac conductivity with applied field can be explained on the basis of the pumping force of the applied field that promotes the tranferring of charge carriers between the two Fe ion states, and liberation of charges from different trapping centers. These charge carriers
4000 ε'
sutot ¼ so ðTÞ þ sðo,TÞ
2000 0 0.0
0.1
0.2 0.3 composition ( x )
0.4
Fig. 9. Variation of ac conductivity with composition at selected frequencies.
participate in conduction process along with electrons produced from the valence exchange bewteen different metal ions. Fig. 9 shows the variation of exponent n with a composition at room temperature. The values of exponent ‘n’ are found in the range 0.52–0.79 and are found to be composition dependent. 3.4. Compostional depandence of (e0 , e00 , tan d and sAC) Fig. 10 presents the variation of dielectric parameters (e0 , e00 , tan d and sAC) as a function of composition at selected frequencies. It can be seen that all the dielectric parameters (e0 , e00 , tan d) and conductivity sAC increase up to 10% of Al doping, thereafter, these parameters decrease with a further doping of Al. The behaviour can
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3500 3000 2500 2000
0
10
0.4 0
1500 1000 500 0 -500
0.5
6 4 2 0
Z" ( x 103 K . Ω)
Z' (x 103 K . Ω)
2 1 0
0.0 0.1 0.2 0.3 0.4 0.5
8 4 0
2
3
4 5 log (f ) Hz
6
7
0
0.5
Fig. 10. Shows the variation of Z0 with respect to the frequency.
be explained on the basis that in Al containing ferrites, Al ions prefer to occupy the octahedral coordination until the ratio of Al substitution becomes greater than 60%, where after, Al ions may increase in tetrahedral sites causing migration of equal number of ions to the octahedral sites [24]. When the Al is doped in the system, it occupies the octahedral site in the ferrite system, decreasing the Fe ion number responsible for polarization in the ferrite system. Hence the value of dielectric constant decreases with increasing Al content in the present system.
0.2 0.0
20
0.3 10
20
30
40
0.2
0.0 1
10
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.1
0.2
0.3
0.4
0.5
0.6
0.1 0.0
2 1 0
0.0 0
1
2
3
Z' ( x 103 K . Ω) Fig. 11. Shows Cole–Cole plot for all Mn ferrite compositions.
3.5. Impedance Impedance spectroscopy is an important method to study the electrical properties of ferrites as the impedance of grains can be separated from the other impedance sources, such as impedance of electrodes and grain boundaries. One of the important factors, which influences the impedance properties of ferrites is the microstructural effect. The impedance measurement gives us information about the resistive (real part) and reactive (imaginary part) components of a material. Fig. 11 shows the variation of real part of Z with frequency. The values of Z0 are found to decrease with increase in the value of frequency. There are three generic relaxation dispersion situations that may occur for solids while discussing Z00 as a function of frequency: conductive system associated charge carriers, dielectric-system dispersion usually arising from dipole rotation of lattice entities and the presence of both types of dispersions within measured frequency range. A ferrite material is assumed to be consisting of piled up crystalline plates. From the microstructural point of view, a sample is assumed as a microstructure made up of parallel conducting plates (grains) separated by resistive plates (grain boundaries). Generally, two semicircles are observed in the Cole–Cole plot; first semicircle at low frequency represents the resistance of the grain boundary and second semicircle obtained at high frequency corresponds to the resistance of grain or bulk properties. The phenomenon is typically related to the existence of a distribution of relaxation time, which is according to the Cole–Cole type of distribution based on two-layer model, in which the resulting complex impedance is composed of two overlapping semicircles. Fig. 12 shows the complex impedance or Cole–Cole plot for all the compositions as a function of frequency at room temperature. Two semicircles are found up to 20% of Al doping, indicating a Cole– Cole type of distribution, while only one semicircle has been found
Fig. 12. (a) and (b) Fitted plot for the compositions x¼ 0.0 and 0.4 by non-linear least square fitting routine (NLLS).
for higher compositions (x Z0.3). Decentralization in the semicircles has been observed in compositions of Mn ferrite. The electrical response of polycrystalline series of MnFe2O4 ferrite doped by Al can be represented by two parallel RC equivalent circuits in series configuration [25,26], and can be visually observed when there is a significant difference between the two resonant frequencies. Such an interpretation is indeed very helpful to represent the sample by an electrical circuit as a combination of resistors and capacitors. The representation of sample through an electrical circuit analog is very helpful in representing the electrical features of the sample. Fig. 12 shows the proposed model for the analysis of the impedance spectroscopy data, where, the parameters Rgb, Cgb and ogb correspond to the resistance, capacitance and the relaxation frequency ( ¼1/t) of the grain boundary volume, respectively, and Rg, Cg and og are the corresponding quantities for the grain. The above mentioned parameters were calculated at room temperature by analyzing the data using the non-linear leastsquare (NLLS) fitting routine and are tabulated in Table 1. The resistance of the circuit represents a conductive path and a given resistor in a circuit account for the bulk conductivity of the sample. Also the capacitances will be generally associated with spacecharge polarization regions. A parallel arrangement of the phases
K. Mujasam Batoo, Alimuddin / Physica B 406 (2011) 382–387
Table 1 Impedance parameters obtained experimentally for MnFe2 2xAlxO4 ferrite. Chemical formula
Rg (kO)
Cg (F)
tg (s)
Rgb (kO)
Cgb (F)
tgb (s)
MnFe2O4 MnFe1.8Al0.2O4 MnFe1.6Al0.4O4 MnFe1.4Al0.6O4 MnFe1.2Al0.8O4 MnFe1Al1O4
74.65 45.36 77.21 – – ––
1.224E 7 0.001E 6 3.677E 7 – – ––
0.009 0.055 0.028 – – ––
61.93 6.76 25.64 3299.5 1590.7 804.53
5.92E 7 5.54E 5 4.79E 6 3.81E 10 1.14E 9 3.17E 9
0.036 0.055 0.123 0.001 0.002 0.003
correspond to only one semicircle, which has been observed for the compositions x¼0.3, 0.4 and 0.5. The area of the semicircle represents the grain boundary resistance (Rgb), and is found to increase continuously with increasing value of x and overlaps with the semicircle representing the grain resistance (Rg), and it becomes impossible to separate the two semicircles. It is seen that there are two effects pertaining to the microstructural inhomogeneity –grain and grain boundary. No other relaxation mechanism, such as electrode effect and ionic species diffusion is identified for the analyzed frequency range. Since the relaxation time of grain and grain boundary are different, the impedance spectroscopy allows separation of two, thus resulting in separate semicircles. This clearly indicates that the resistance values for the grain boundary increase with acceptor addition, which may be attributed to contribution from the physical loci, such as grain boundary or grain interior. Also, close to grain boundaries, the transport properties of a materials are controlled by imperfections, expected to be present in higher concentrations than in grains, leading to an additional contribution to the intergrain (grain boundary) impedance. The internal space–charge created at grain boundaries may lead to a significant increase in the concentration of mobile effects [27–29,]. Alternatively, this can represent an additional relaxation process associated with point defects, such as trapping and detrapping of electrons in deep traps within the grain interiors or in depletion layer regions adjoining the grain boundaries. It is seen that among all the compositions MnFe1.8Al0.2O4 exhibits lowest values of resistance (Rg and Rgb) but highest values of the capacitances (Cg and Cgb). The capacitance of grain boundary is larger than that of capacitance of grain, which can be explained on the basis that capacitance is inversely proportional to the thickness of the media. The higher values of capacitance for both grain and grain boundary for the composition MnFe1.8Al0.2O4 means this composition exhibits greater polarizability. The impedance results obtained are found consistent with the conductivity data for all compositions.
technique. The dispersion in dielectric properties have been explained in the light of space charge polarization discussed in Maxwell–Wagner model. The AC conductivity of the samples has been discussed in the light of the hopping model. The complex impedance plane spectra the show presence of two semicircles up to x¼0.2, and only one semicircle for the higher value of x, i.e., impedance of MnFe2O4 is composition dependent property, which is in good agreement with the Cole–Cole type of distribution. The analysis of the complex impedance data shows that the capacitive and the reactive properties of the materials are mainly attributed to the processes that are associated with the grain and grain boundary.
Acknowledgement One of the authors (K.M. Batoo) is thankful to I.U.A.C., New Delhi for financial support through UFUP project. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
4. Conclusion We have successfully synthesized single phase polycrystalline MnFe2 2xAl2xO4 with spinel structure through solid state reaction
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[27] [28] [29]
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