AC conductivity and dielectric properties of Ti-doped CoCr1.2Fe0.8O4 spinel ferrite

ARTICLE IN PRESS Physica B 405 (2010) 619–624

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AC conductivity and dielectric properties of Ti-doped CoCr1.2Fe0.8O4 spinel ferrite M.A. Elkestawy a,, S. Abdel kader b, M.A. Amer b a b

Physics Department, Faculty of Science, Suez Canal University, Suez, Egypt Physics Department, Faculty of Science, Tanta University, Tanta, Egypt

a r t i c l e in fo

abstract

Article history: Received 1 March 2009 Received in revised form 7 April 2009 Accepted 16 September 2009

Dielectric properties of spinel ferrite samples Co1 + xTixCr1.2  2xFe0.8O4 (0 r xr 0.5) were investigated as a function of frequency at different temperatures using a complex impedance technique. Also Cole–Cole diagrams of both permittivity and electric modulus were investigated at different temperatures to have an insight into the electric nature of the studied solids. It has been found that the electric modulus M* is the dominating property clarifying the intrinsic picture of these polycrystalline ferrites. The low conductivity and loss factor values indicate that the studied compositions may be good candidates for practical applications. & 2009 Elsevier B.V. All rights reserved.

PACS: 72.80.Jc 75.50.Pp 77.22.Ch 77.22.Gh Keyword: Dielectric constant AC conductivity Electric modulus Ferrites

1. Introduction Ferrites are very important and widely used materials in technical designing and applications. One of the most important attributes or advantage of ferrites is their very high degree of compositional variability. In some cases, substitution of some trivalent ions such as Al3 + or Cr3 + for Fe3 + is made for special magnetic or electrical functions; these may include reducing the saturation magnetization, increasing the temperature stability, or increasing the resistivity [1]. A large increase of research interest for spinel ferrites has been seen in the last few decades, in view of their technological applications and for fundamental understanding [2]. By adding Cr to cobaltferrite some temperature stability in magnetization values has been observed although the values have been decreased in magnitude [3].Many investigations had been carried out on Co-, Ti-, Co–Mn–Ti-, Co–Ti-, and Mg–Ti- ferrites using several techniques to study their physical and structural properties [4]. The effect of substitution of Co2 + and Ti4 + ions for Fe3 + ions on the different

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E-mail address: [email protected] (M.A. Elkestawy). 0921-4526/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2009.09.076

properties of Co1 + xTixFe2(1  x)O4 ferrites has been studied [4]. Some effects have been observed at x =0.3, which was considered as the critical concentration of Co2 + and Ti4 + in that group of compositions [4]. The present work is devoted to the study of AC conductivity, dielectric constant, and dielectric loss tangent of the compositions Co1 + xTixCr1.2  2xFe0.8O4. These studies may give valuable information on the electrical properties, which are very important for practical applications of ferrites. In other words the present work completes the investigations of those ¨ compositions for which Mossbauer studies have been already done [5].

2. Experimental Details of the sample preparation have been reported in a previous work [5]. For measurements of AC conductivity (s0 AC), dielectric constant (e0 ), and dielectric loss tangent (tan d) the surfaces of the disc-shaped samples were coated with a thin layer of silver paste to provide good contact to the external electrodes. The measurements were carried out inside an evacuated silica tube using the two-probe method with a complex impedance technique [6].

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3. Results and discussion 3.1. AC conductivity and dielectric properties 3.1.1. AC conductivity Fig. 1 illustrates the frequency dependence of the real part of complex AC conductivity s0 AC for only three of the investigated compositions at different values of temperature since it can be

seen that the trend of behavior is almost similar in all samples. This trend is that s0 AC increases slightly with increasing frequency and more significantly with increasing temperature. This behavior agrees with the expected behavior of ferrites. In general, ferrites are known to be dielectrics with semiconducting nature at elevated temperatures [6]. Also,from the figure, it is obvious that the effect of variation of x (i.e. composition) on conductivity is not large except for x= 0.5, where there is an observed increase in

Ln (F (Hz)) 0.0001

100

Ln (σac (Ω-1cm-1))

0.00001 0.000001

1000 T = 657.5 K T = 611.34 K T = 572.97 K T = 518.53 K T = 454.49 K T = 388.71 K T = 325.3 K

10000

100000

x = 0.0

0.0000001 0.00000001 0.000000001 Ln (F (Hz)) 100 0.001

1000

10000

100000

x = 0.3

Ln (σac (Ω-1cm-1))

0.0001 0.00001 0.000001 0.0000001 0.00000001 0.000000001

T = 651.95 K T = 421.35 K

T = 584.31 K T = 392.95 K

T = 548.8 K T = 352.71 K

T = 494.73 K

Ln (F (Hz)) 100 0.01 0.001

1000

10000

100000

T = 576.67 K T = 542.17 K

x = 0.5

T = 491.64 K

Ln (σac (Ω-1cm-1))

T = 463.42 K

0.0001

T = 414.72 K T = 391.05 K T = 366.51 K

0.00001

T = 333.87 K T = 312.57 K

0.000001 0.0000001 0.00000001

Fig. 1. (a)–(c) Plots of log(s0 ac) versus log(F) at selected temperatures for three of the studied compositions.

ARTICLE IN PRESS M.A. Elkestawy et al. / Physica B 405 (2010) 619–624

conductivity values, which may be attributed to the well-known fact that conductivity in most cases of ferrites is mainly due to the hopping of electrons between Fe2 + ions and Fe3 + ions existing simultaneously in the B-sites, and since the existence of Fe2 + ions on the B-sites results from—in addition to hopping between Fe3 +

621

and Co2 + —the hopping between Cr3 + and Fe3 + ions, it is expected that in the x = 0.5 sample, where the number of Co ions has increased in the B-site [5], the fraction of Fe2 + ions will be the largest among the studied compositions, leading to this observed increase in conductivity. However, the very low values of

70 60 50

ε'

40 30

T = 611.34 K

x = 0.0

T = 572.97 K T = 549.3 K T = 518.53 K T = 492.49 K T = 419.48 K T = 388.71 K

20

T = 325.3 K

10 0 100

1000

10000

100000

Ln (F (Hz)) 70

T = 644.48 K T = 603.61 K T = 569.1 K T = 543.07 K

x = 0.1

60

T = 514.66 K

50

T = 483.89 K T = 415.62K T = 390.58 K

ε'

40 30 20 10 0 100

1000

10000

100000

Ln (F (Hz)) 16000

10000

T = 576.67 K T = 542.17 K T = 491.64 K T = 463.42 K T = 433.15 K T = 414.72 K T = 366.51 K

8000

T = 333.87 K T = 312.57 K

14000

ε'

12000

x = 0.5

6000 4000 2000 0 100

1000

10000

100000

Ln (F (Hz)) Fig. 2. (a)–(c) Dielectric constant e versus log(F) at selected temperatures for three of the studied compositions. 0

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increase in e0 values with increasing temperature is attributed to the semiconducting nature of the materials. To illustrate the few exceptions at high temperatures, where an initial increase of e0 occurs with increasing frequency and then the usual decrease of e0 with further increase of frequency, we can refer to Rezlescu model, which assumes a collective contribution of two types of hopping electric charge carriers to dielectric polarization at elevated temperatures to explain such a behavior [13]. The effect of the variation of x on e0 at x Z0.3 is significant. This increase in e0 values can be justified by referring to the published cation distribution [5], where Co ions significantly increase at xZ0.3, consequently increasing the probability of charge carriers hopping and accumulation at the grain boundaries. Fig. 3 displays the frequency dependence of the loss factor (tan d) at different selected temperatures. The properties of ferrites that are of prime concern to users or designers are mainly the saturation induction, permeability, temperature stability of permeability, low-level losses, and tan d or loss factor [1]. We can see that the studied compositions show desirable low loss values especially at room and reasonable application temperatures. Also, the values of tan d are in good agreement

conductivity along with the small variation with frequency may make the compositions (up to x =0.4) good candidates for some practical applications.

3.1.2. Dielectric constant (e0 ) behavior Fig. 2 illustrates the frequency dependence of the real part of dielectric constant e0 at different selected temperatures and for only three of the studied compositions as sufficient examples of the behavior. The dielectric constant increases with increasing temperature and with decreasing frequency. The same dielectric behavior has been previously reported by many others working in the field [7–11]. This is justified by considering Koop’s model of inhomogeneous structure of polycrystalline ferrites, where there are well-conducting grains separated by poorly conducting grain boundaries [12]. The variation in conductivity between these regions causes accumulation of charge carriers at grain boundaries, which contributes significantly to the dielectric constant at low frequencies. As the frequency increases these accumulated charges can no longer follow the field and their contribution to the dielectric constant ceases. Also, the general

1000

1000

T = 657.5 K T = 611.34 K

10 1

x = 0.0

T = 549.3 K

100

T = 518.53 K T = 454.49 K

Ln (tanδ)

Ln (tanδ)

100

T = 388.71 K T = 325.3 K

0.1

x = 0.1

10 1 0.1

0.01 100

1000

10000

0.01 100

100000

T = 644.48 K T = 603.61 K T = 543.07 K T = 483.89 K T = 448.75 K T = 415.62K T = 390.58 K

1000

Ln (F (Hz))

10000

100

100 x = 0.4

Ln (tanδ)

1 T = 604.61 K T = 421.35 K

T = 548.8 K T = 392.95 K

T = 517.4 K T = 456.86 K

1000

10

1

T = 494.73 K

10000

100000

0.1 100

T = 587.04 K

T = 551.54 K

T = 519.4 K

T = 407.15 K

T = 367.91 K

T = 447.39 K

1000

Ln (F (Hz))

10000 Ln (F (Hz))

100 x = 0.5

Ln (tanδ)

Ln (tanδ)

x = 0.3

10

0.1 100

100000

Ln (F (Hz))

10

1

0.1 100

T = 576.67 K T = 491.64 K T = 463.42 K

T = 414.72 K T = 391.05 K T = 366.51 K

T = 349.94 K T = 333.87 K

1000

10000

100000

Ln (F (Hz)) Fig. 3. (a)–(e) Plots of log(tan d) versus log(F) at selected temperatures for the five studied compositions.

T = 485.26 K

100000

ARTICLE IN PRESS M.A. Elkestawy et al. / Physica B 405 (2010) 619–624

0.03

0.045

0.025

0.04

x = 0.0

0.03 T = 657.5 K T = 611.34 K T = 572.97 K T = 549.3 K T = 518.53 K T = 492.49 K T = 454.49 K T = 419.48 K T = 388.71 K T = 350.34 K T = 325.3 K

0.015 0.01 0.005 0

0

M"

M"

T = 644.48 K T = 603.61 K T = 569.1 K T = 543.07 K T = 514.66 K T = 483.89 K T = 448.75 K

x = 0.1

0.035

0.02

0.025 0.02 0.015 0.01 0.005 0

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

0

M' 0.03 x = 0.3

x = 0.4

0.02

0.02

0.015 M"

0.015 T = 651.95 K T = 604.61 K T = 584.31 K T = 548.8 K T = 517.4 K T = 494.73 K T = 456.86 K T = 421.35 K T = 392.95 K

0.01 0.005 0

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 M'

0.025

0.025

M"

623

0

0.01

0.02

0.03

0.04

0.05

0.01

T = 587.04 K T = 551.54 K T = 519.4 K T = 485.26 K T = 447.39 K T = 407.15 K T = 367.91 K T = 330.04 K

0.005 0

0.06

0

0.01

0.02

0.03

0.04

0.05

0.06

M'

M' 0.03 x = 0.5

0.025

M"

0.02 0.015

T = 576.67 K T = 542.17 K T = 491.64 K T= 463.42 K T = 433.15 K T = 414.72 K T = 391.05 K T = 366.51 K T = 349.94 K T = 349.94 K T = 312.57 K

0.01 0.005 0 0

0.01

0.02

0.03

0.04

0.05

0.06

M' Fig. 4. (a)–(e) M00 (f) versus M0 (f) at selected temperatures for the five studied compositions.

with results of many other researchers, for example those of Abo El Ata et al. [10]. The peaks of tan d that appear at some temperatures (higher than 400 K) and shift to higher frequencies with increasing temperature are known to occur when the hopping frequency of electric charge carriers approximately becomes equal to that of the external applied AC electric field [14]. However, this may not prevent the use of these compositions at lower temperatures.

3.2. Electric modulus M* In the present work an almost new method [15,16] has been followed to have an insight on the electric properties of the solid under study; that is, by investigating Cole–Cole diagrams of both M00 (f) versus M0 (f) and e00 (f) versus e0 (f) at different temperatures, where, if a master plot collecting all data in a single semicircular curve is found this would show to which category the solid

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belongs; whether to a category where ‘‘electric compliance’’ is dominating or to a category where ‘‘electric stiffness’’ is dominating. ‘‘Electric compliance’’, i.e. how easily dipoles are created and/or oriented in the solid, is represented by the permittivity e*(o), whilst ‘‘electric stiffness’’, i.e. with what difficulty dipoles are created and/or oriented in the solid, is represented by the electric modulus M*(o). For the present ferrites the electric modulus M* has been found as the dominating property according to Fig. 4. To recall the significance of that finding we may revise the physical meaning of the electric modulus M  ðoÞ ¼ M 0 ðoÞ þ iM 00 ðoÞ

ð1Þ

as defined by M  ðoÞ ¼ 1=e ðoÞ

ð2Þ

The use of M*(o) has the meaning of the following relationship: EðoÞ ¼ M  ðoÞDðoÞ

ð4Þ

The physical significance of these two representations is that in Eq. (4) the electric field E is the independent variable, which determines the dielectric displacement, while the converse is true of Eq. (3), where D is the independent variable. Now, it so happens that the great majority of practical situations involve electric field as the independent variable, so that Eq. (4) is applicable, and there are only relatively few situations where the opposite is the case. One such example is the motion of space charge r in a dielectric system where the resulting D field is directly related through div D ¼ r

4. Conclusions The very low values of conductivity along with small variation with frequency may make spinel ferrite samples of these compositions (up to x= 0.4) good candidates for practical applications. The studied compositions show desirable low loss values especially at room and reasonable application temperatures. The results of AC conductivity, dielectric constant, and electric modulus investigation, are consistent, reinforce each other, and prove by an almost new method the intrinsic picture of polycrystalline ferrites as composed of well-conducting grains and poorly conducting grain boundaries.

ð3Þ

which is the converse of the more commonly used relationship DðoÞ ¼ e ðoÞEðoÞ

polarization by a large interfacial contribution, which explains both the high values of e0 and their decrease with increasing frequency, where the charges at the boundaries cannot reverse orientation as fast as the field.

ð5Þ

If it were desired to calculate the resulting electric field one would have to use Eq. (3), in which the electric modulus is the independent variable [17]. Therefore, finding that the studied compositions belong to this category gives an additional proof of the usually proposed intrinsic picture of polycrystalline ferrites as composed of well-conducting grains and poorly conducting grain boundaries leading—as previously mentioned—to the accumulation of charges at the boundaries, consequently increasing the

References [1] A. Goldman, Modern Ferrite Technology, Marcel Dekker, Inc., New York, 1993. [2] R.N. Bhowmik, R. Ranganathan, B. Ghosh, S. Kumarb, S. Chattopadhyay, Journal of Alloys and Compounds 456 (2008) 348. [3] R.N. Singh, N.K. Singh, J.P. Singh, G. Balaji, N.S. Gajbhiye, International Journal of Hydrogen Energy 31 (2006) 701. [4] M.A. Amer, Physics of Low-Dimensional Structures (2006) 96. [5] M.A. Amer, Phys. Stat. Sol. (b) 237 (2) (2003) 459. [6] M.H. Shaaban, M.K. El Nimr, A.A. Ahmed, Journal of Material Science: Materials in Electronics 4 (1993) 208. [7] M.A. Ahmed, M.K. El Nimr, M.A. El Hiti, M.A. Amer, J. Mater. Sci. Lett. 16 (1997) 1076. [8] M.A. El Hiti, M.A. Ahmed, M.M. Mosaad, S.M. Attia, J. Magn. Magn. Mater. 150 (1995) 399. [9] M.A. Ahmed, M.K. El Nimr, A. Tawfik, A.M. El Hasab, Journal of Magnetism and Magnetic Materials 98 (1991) 33. [10] A.M. Abo El Ata, M.K. El Nimr, D. El Kony, A.H. Al-Hammadi, Journal of Magnetism and Magnetic Materials 204 (1999) 36. [11] A.M. Abo El Ata, M.A. El Hiti, Journal de Physique III France 7 (1997) 883. [12] C.G. Koops, Phys. Rev. 83 (1951) 121. [13] N. RezIescu, E. Reslescu, Phys. Stat. Sol., (a) 23 (1974) 575. [14] S.S. Ata-Allah, M.K. Fayek, Phys. Stat. Sol., (a) 175 (1999) 725. [15] S.A. Safaan, A.S. Seoud, R.E. El Shater, Phys. B. 365 (2005) 27. [16] S.A. Saafan, Physica B 403 (2008) 2049. [17] A.K. Jonscher, Universal Relaxation Law, Chelsea dielectrics press, London, 1996.