Charge transfer behavior of erbium substituted Mg–Ti ferrites

Materials Chemistry and Physics 81 (2003) 63–77

Charge transfer behavior of erbium substituted Mg–Ti ferrites M.A. Ahmed∗ , E. Ateia, G. Abdelatif, F.M. Salem Department of Physics, Faculty of Science, Cairo University, Giza, Egypt Received 9 July 2002; received in revised form 6 January 2003; accepted 17 February 2003

Abstract The dielectric constant ε and the electrical conductivity (σ) for Mg1+x Tix Ery Fe2−2x−y O4 ; 0.1 ≤ x ≤ 0.9 doped with a constant rare earth ions, y = 0.025 were measured in the temperature range, 350–750 K. The measurements were carried out as a function of frequency, 50–1000 kHz. X-ray diffractograms show that, the investigated samples reveal spinel structure. From the obtained data, it was found that the effective number of ferrous ions on octahedral sites which was available for the electric polarization as well as electrical conductivity decreases with increasing Ti concentration. The effect of ␥-irradiation on both structural and electrical properties was also studied. The ratio Fe2+ /Fe3+ plays a dominant role in the decrease of the crystal size due to irradiation damage with ␥-rays. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Mg–Ti ferrites, dielectric behaviour; ␥-Irradiation

1. Introduction Polycrystalline ferrites have high dielectric constants which makes them very useful for microwave applications. Ferrites remain the best magnetic materials because they are inexpensive, more stable and have a wide range of technological applications like high quality filters, radio wave circuits and operating devices [1]. The electrical conductivity and dielectric behavior of ferrites markedly depend on the preparation conditions such as sintering temperature, chemical composition, the quantity and type of additives. Study of the effect of these factors on the electrical properties offers much valuable informations on the behavior of the localized electric charge carriers which can lead to a good explanation and understanding of the mechanism of the electric conduction and the dielectric in ferrite systems. Elementary charged particles and electromagnetic radiation with high energy interact with electronic shells or the atomic nuclei of substances passing through them. These interactions result in an elastic and inelastic scattering of particles attended by the excitation and ionization of the atoms, as well as the nuclear reactions and also disturbances in the structure of the matter, so called radiation damage [2]. In some compounds such as ferrites, the ␥-irradiation will vary the valence of cations to higher values, resulting in the initiation of electrons which increases the conductivity [3]. ∗ Corresponding author. E-mail address: [email protected] (M.A. Ahmed).

Ahmed and Bishay [4] studied the effect of ␥-irradiation on the electrical properties of Li–Co ferrites doped with rare earth ions. The results showed that, irradiation doses have high effect on the electrical properties of the samples. These cause inflection in the dielectric properties from decreasing the polarization at 1 Mrad to increasing it at 3 Mrad while the activation energy decreases with increasing dose due to the increase in electron exchange interaction. The present investigation is carried out in an attempt to study the effect of Ti substitution on the structural and electrical properties of Mg–Ti ferrites doped with a constant concentration of rare earth element (Er). Another purpose of this work is to throw light on the mechanism of interaction of ionizing radiation with the investigated samples. 2. Experimental Magnesium titanium ferrites doped with a constant concentration of rare earth ion (Er) and different titanium concentrations were prepared using the standard ceramic technique [5]. Analar grade form oxides (BDH) were mixed in stoichiometric ratios using agate mortar for 4 h. The mixture was transferred to an electric shaker and ball mill for another 4 h. The samples were pressed into pellets form of diameter 0.9 cm and 1.5 mm thickness, using hydraulic press with pressure of 5 × 108 N m−2 . Presintering was carried out at 900 ◦ C for 15 h using Lenton furnace type UAF 16/5 (England) with rate of heating 4 ◦ C min−1 , then cooled

0254-0584/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0254-0584(03)00143-3

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M.A. Ahmed et al. / Materials Chemistry and Physics 81 (2003) 63–77

to room temperature with the same rate as that of heating. The final sintering (firing) was performed at 1200 ◦ C for 100 h with the same rate. For the electrical measurements, the pellets were good polished to remove any roughness. The two surfaces of each pellet were coated with silver paste (BDH) and checked for good conduction. The real part of the dielectric constant ε and ac conductivity were measured using HIOKI bridge model 3530 (Japan) at frequencies from 50 to 1000 kHz as a function of temperature from 295 to 750 K. The temperature of the sample was measured using T-type thermocouple connected to a temperature controller where the junction of the thermocouple was contacted with the sample to prevent any temperature gradient. The accuracy of measuring temperature was better than ±1 ◦ C. The experimental data was reproducible with the same accuracy of ±1%. The X-ray diffraction patterns were obtained using Diano corporation of target Co K␣ (λ = 1.79026 Å). The indexing of the X-ray data is carried out using the computer program Treor [6]. The samples were irradiated with ␥-rays (10, 20, and 30 Mrad). The irradiation was carried out at the National Center of Radiation Technology, Cairo Egypt by using a gamma cell 4000 A irradiation facility (manufactured at Bhabha Atomic Research Center, India). The

gamma chamber 4000 A is a compact and self-contained irradiation unit offering an irradiation volume of approximately 4000 cm3 . This irradiation facility can hold up to 10,000 Ci of Co60 . The source cage holds the radiation source pencils vertically and symmetrically along its periphery.

3. Results and discussion X-ray diffractogram for MgFe2 O4 is shown in Fig. 1. Table 1 reports the d-values, relative intensities (I/I0 ), Miller indices (h k l) for MgFe2 O4 as compared with the JCPDS cards. From the reported X-ray data, it is clear that the sample with x = y = 0 exhibits a cubic spinel structure with average unit cell parameter a = 8.387 Å. The effect of Ti4+ ion concentration on the structure of Mg1+x Tix Ery Fe2−2x−y O4 ; y = 0.025 and 0.3 ≤ x ≤ 0.9 is shown in Fig. 2 and Table 2. The diffraction patterns show that, all samples exhibit a cubic spinel structure. The observed interplaner distance “d” of the corresponding planes increases evidently at the initial substitution of Ti from x = 0.3 to 0.9 which is an indication to the increase of the unit dimensions.

Fig. 1. X-ray diffractogram for MgFe2 O4 .

M.A. Ahmed et al. / Materials Chemistry and Physics 81 (2003) 63–77 Table 1 Values of d spacing, relative intensity I/I0 and Miller indices (h k l) for the prepared sample MgFe2 O4 as compared with those of the JCPDS cards JCPDS card

Prepared sample

d (Å)

I/I0

hkl

d (Å)

I/I0

hkl

4.850 2.969 2.532 2.099 1.713 1.616 1.485 1.328 1.281 1.212 1.122

8 35 100 25 12 30 40 2 8 4 4

111 220 311 400 422 511, 333 440 620 533 444 642

4.842 2.965 2.527 2.096 1.712 1.614 1.482 1.326 1.279 1.210 1.120

5 39 100 23 9 23 36 3 6 3 2

111 220 311 400 422 511 440 620 533 444 642

Fig. 3(a) and (b) correlates the variation of both the lattice parameter (a, Å) and the porosity as a function of Ti concentration (x). The porosity of the samples is calculated using the relation P = 1−D/Dx [7] where D and Dx are the experimental and theoretical densities, respectively. The theoretical density is determined using the formula Dx = ZM/NV [8], where M is the molecular weight, N is Avogadro’s number, Z is the number of nearest neighbors, and V is the unit cell volume as determined from X-ray analysis. From Fig. 3, it is clear that, the porosity increases with increasing Ti content. This can be attributed to the Ti4+ ions those replaces

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the Fe3+ ions on octahedral site. In other words, the Ti4+ ion with radius 0.68 Å which is relatively larger than that of Fe3+ ion (r = 0.64 Å) initiate some vacancies with the result of increasing porosity of the sample [9]. Fig. 4(a–f) is a set of typical curves indicating the variation of the real part of the dielectric constant with the absolute temperature for Mg1+x Tix Ery Fe2−2x−y O4 ; y = 0.025 and 0.1 ≤ x ≤ 0.9, as a function of frequency ranging from 50 kHz to 1 MHz with sintering temperature of 1200 ◦ C and heating rate 4 ◦ C min−1 , respectively. The general trend of the obtained data is the slight increase in ε (up to ≈500 K) followed by a large increase passing by the transition temperature for each sample. This may be due to the following: the small thermal energy given to the system is not sufficient enough to free more of the localized dipoles and the field oriented them in its direction. From a closer look to this region, one can find that, ε is nearly temperature independent. This means that the electronic polarization is the most predominant one. In the second region of temperature, ε increases for all samples but with different rates depending on Ti concentration. This increase in ε is due to electron hopping between the ferrous and ferric ions on the octahedral sites. This electron hopping causes local displacement in the external field direction, producing change in polarization as well as ε [10]. The decrease in ε with increasing frequency is due to the fast alternation of the field accompanied with the applied frequency, where the alternation of the dipoles increases as

Fig. 2. X-ray diffractograms for Mg1+x Tix Ery Fe2−2x−y at different Ti concentration.

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Table 2 Effect of Ti concentration on the structural parameters of Mg1+x Tix Ery Fe2−2x−y O4 ; 0.3 ≤ x ≤ 0.9; y = 0.025; sintered at 1200 ◦ C with rate of heating 4 ◦ C min−1 x = 0.3a

x = 0.5b

x = 0.7c

x = 0.9d

d (Å)

I/I0

hkl

d (Å)

I/I0

hkl

d (Å)

I/I0

hkl

d (Å)

I/I0

hkl

4.865 2.976 2.537 2.106 1.718 1.619 1.488 1.214

14 32 100 56 7 21 43 5

111 220 311 400 422 511 440 444

4.873 2.983 2.543 2.108 1.720 1.623 1.490 1.217

15 33 100 65 7 23 51 7

111 220 311 400 422 511 440 444

4.874 2.984 2.543 2.108 1.722 1.624 1.491 1.217

24 26 100 85 8 27 57 8

111 220 311 400 422 511 440 444

4.879 2.984 2.432 1.725 1.625 1.491 1.287 1.217

25 18 69 100 6 19 54 11

111 220 311 400 422 511 440 444

a

System: System: c System: d System: b

spinel, spinel, spinel, spinel,

a a a a

= 8.417 Å; = 8.432 Å; = 8.435 Å; = 8.440 Å;

V V V V

= 596.309 Å3 . = 599.592 Å3 . = 600.143 Å3 . = 601.201 Å3 .

well as the friction between them, the quantity of heat dissipated in the entire volume of the sample increases and the aligned dipoles will be disturbed with the result of decreasing ε . From Fig. 4(f) it can be seen, that the dispersion of the dielectric constant with frequency is maximum for the sample with x = 0.1. A comparison of the dispersion curves for the samples with increasing titanium concentration shows that the change in the value of ε at lower frequencies of the applied field is larger than that at higher frequencies. The variation of the dielectric relaxation intensity decreases with increasing titanium concentration which is in good agreement with the results of Iwauchi [11]. This observed variation in the dielectric relaxation intensity which is governed by the number of space charge carriers and resistivity of the sample due to the inhomogeneous dielectric structure as discussed by Maxwell [12] and Wagner [13]. The effective number of ferrous ions on octahedral sites available for electric polarization decreases with increasing titanium concentration implies that the flow of space charge carriers is obstructed and thus the build-up of space charge polarization is impeded. So one can expect a decrease in dielectric intensity with increasing Ti concentration. In the investigated samples, the main source of polarization and charge carriers is the valance exchange between the metal ions of different valences in the same equivalent lattice site. The iron ions are the most effective ones, where Fe2+ ↔ Fe3+ + e− . In other words, a composite ion consisting of Ti4+ , Mg2+ and Er3+ (ionic radii 0.68, 0.84 and 0.88 Å, respectively) replaces an Fe3+ ion whose ionic radius is 0.64 Å, thereby they are incorporated continuously into the spinel lattice. The interionic distances such as A–O, B–O or A–A, B–B or A–B increases continuously [14]. This is a reason for a comparatively high value of ε at x = 0.1 as shown in Fig. 4(e). Fig. 5 is a typical curve, correlates the ac conductivity (ln σ) and the reciprocal of absolute temperature at different frequencies for the sample with x = 0.1, y = 0.025 and rate 4 ◦ C min−1 at 1200 ◦ C. From the figure, it is clear that the data obeys the well-known Arrhenius relation [15]

σ = σ0 exp(−E/kT), where σ 0 is constant; k, E and T are the Boltzmann’s constant, activation energy and the absolute temperature, respectively. Increasing temperature leads to an increase in σ, which is the normal behavior of semiconducting material. In the paramagnetic region of disordered state, the increase in frequency has no effect on the conductivity corresponding to thermally activated charge carriers (band conduction mechanism) [16]. While in the ferrimagnetic region the activation energy for electric conduction decreases as the frequency increases corresponding to the thermally activated mobility (hopping conduction model) [4] and not to thermally creation of charge carriers. As it was mentioned before the valence exchange Fe2+ ↔ Fe3+ + e− is the main source of electron hopping in this process. On passing through the transition temperature, a change in the gradient of the straight line takes place [15]. The magnitude of this gradient depends on the exchange interaction between the outer and inner electrons of the metal ions, which is changed at the transition temperature due to transfer of the system from the ferrimagnetic to the paramagnetic state. Table 3 shows the activation energies of low (EI ) and high (EII ) temperature regions at different Ti concentration (x) for the investigated samples. The reported data of low (EI ) and high (EII ) temperature regions shows that, the activation energy for electric conduction in the paramagnetic region EII is higher than that in the ferrimagnetic region EI . This could be related to the disordered state in the paramagnetic Table 3 The activation energy in eV for the low (EI ) and high (EII ) temperature ranges at different Ti concentration Ti concentration

0.1 0.3 0.5 0.7

100 kHz

1000 kHz

EI (eV)

EII (eV)

EI (eV)

EII (eV)

0.137 0.215 0.489 0.622

0.737 0.455 0.573 0.622

0.149 0.340 0.799 –

0.425 0.860 0.799 0.179

M.A. Ahmed et al. / Materials Chemistry and Physics 81 (2003) 63–77

Fig. 3. The variation of both the lattice parameter (a, Å) and the porosity as a function of Ti concentration.

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68 M.A. Ahmed et al. / Materials Chemistry and Physics 81 (2003) 63–77 Fig. 4. (a–f) The variation of the real part of the dielectric constant ε with the absolute temperature for Mg1+x Tix Ery Fe2−2x−y O4 , y = 0.025 and 0.1 ≤ x ≤ 0.9. (a) x = 0.1, (b) x = 0.3, (c) x = 0.5, (d) x = 0.9, (e) the variation of ε with Ti concentration, (f) the variation of the real part of the dielectric constant ε with frequency (kHz).

M.A. Ahmed et al. / Materials Chemistry and Physics 81 (2003) 63–77

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Fig. 5. The variation of ac conductivity (ln σ) with the reciprocal of absolute temperature. x = 0.1, y = 0.025, rate 4 ◦ C min−1 and sintering temperature 1200 ◦ C.

Fig. 6. X-ray diffractograms for Mg1.5 Ti0.5 Er0.025 Fe0.975 O4 , sintered at 1200 ◦ C at different heating rates.

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Table 4 Effect of heating rates on the structural parameters of Mg1+x Tix Ery Fe2−2x−y O4 (x = 0.5) 2 ◦ C min−1a

4 ◦ C min−1b

6 ◦ C min−1c

8 ◦ C min−1d

d (Å)a

I/I0

hkl

d (Å)

I/I0

hkl

d (Å)

I/I0

hkl

d (Å)

I/I0

hkl

4.8871 2.9845 2.5442 2.1090 1.7226 1.6237 1.4909 1.2170

24 35 100 63 8 29 43 8

111 220 311 400 422 511 440 444

4.8737 2.9834 2.5433 2.1087 1.7208 1.6234 1.4907 1.2172

15 33 100 65 7 23 51 7

111 220 311 400 422 511 440 444

4.8791 2.9834 2.5432 2.1088 1.7207 1.6235 1.4907 1.2170

20 30 100 56 6 24 45 6

111 220 311 400 422 511 440 444

4.8035 2.9532 2.5219 2.0960 1.7114 1.6142 1.4845 1.2131

12 39 100 61 8 32 55 8

111 220 311 400 422 511 440 444

a

System: System: c System: d System: b

spinel, spinel, spinel, spinel,

a a a a

= 8.438 Å; = 8.432 Å; = 8.434 Å; = 8.372 Å;

V V V V

= 600.802 Å3 . = 599.592 Å3 . = 600.001 Å3 . = 586.884 Å3 .

region with respect to the ordered one in the ferrimagnetic region. This result is in agreement with the theory developed by Irkhin and Turov [17]. Fig. 6(a–d) and Table 4 illustrate the effect of heating rates on the structural properties of Mg1+x Tix Ery Fe2−2x−y O4 , x = 0.5, and sintered at 1200 ◦ C. The data illustrates that, all the samples with different heating rates are spinel. The inset of Fig. 6 shows the variation of the unit cell volume with heating rate (2, 4, 6 and 8 ◦ C min−1 ). Form the figure, it is clear that, the volume of the unit cell is nearly constant with heating rate up to 6 ◦ C min−1 and then decreases. This means that, expansion of the spinel lattice reaches its maximum at this rate due to initiation of cluster vacancy pairs. The dependence of the ac conductivity on the reciprocal of absolute temperature for the above sample sintered at 1200 ◦ C with different heating rates (2, 4, 6 and 8 ◦ C min−1 ) is shown in Fig. 7(a–d). Same behavior as described before is obtained, where the conduction is due to thermally activated mobility. EI gives a maximum value at 6 ◦ C min−1 , Fig. (7e) which enhances the above expectation about the critical heating rate. This means that, by varying the heating rate the grain size will be increased [18] slightly up to the critical rate after which it decreases sharply as shown from interplaner distances “d” in Table 4. This sharp decrease in “d” spacing, decreases the hopping length and consequently increases the conductivity σ. Fig. 8 represents the diffraction patterns for Mg1.1 Ti0.1 Er0.025 Fe1.775 O4 ; before and after ␥-irradiation; sintered at 1200 ◦ C with heating rate 2 ◦ C min−1 . From the figure a noticeable shift for the peaks occurred. This is because the ␥-irradiation may change the ratio of Fe2+ /Fe3+ on the octahedral sites as a consequence of ␥ + Fe2+ ↔ Fe3+ + e− . The number of ferric ions of radius (0.64 Å) which are produced from this reaction is much more than the number of ferrous ions of radius (0.76 Å). This leads to a decrease in the crystal size [3]. Table 5 reports the variation of the interplaner distance, relative intensity and Miller indices for the irradiated and unirradiated sample. The observed interplaner

distance “d” of the corresponding planes decreases with radiation doses. This result agrees well with our expectation. Fig. 9(a–e) shows the variation of ε with the absolute temperature as a function of frequency for the unirradiated and irradiated sample, x = 0.1, rate 2 ◦ C min−1 , with sintering temperature 1200 ◦ C at different doses of 0.0, 10, 20 and 30 Mrad. The data in the figure gives the same trend, as described before in Fig. 4, with the appearance of small peaks in the unirradiated sample. These peaks may be due to either releasing some trapped charge carriers or participating of another type of polarization such as Maxwell–Wagner one, which acts on the surface of the conducting grains [19,20] to decrease the non-conducting layer separating them. The two factors act in cooperation with each other leading to an increase in ε . From Fig. 9(b), the vanishing of the peaks and the higher values of ε with the appearance of a small hump at ≈450 K is observed. This can be explained in view of interaction of ␥-rays with the matter, which is summarized in two steps. The first one is the increase in hopping rate caused from depressing the jump length with the result of more interaction between Fe3+ and Fe2+ . These jumping electrons oriented in the field direction and consequently give rise to ε [21]. The production of Fe2+ after irradiation was confirmed by Mousa et al. [22]. The second step is Table 5 Values of d spacing, relative intensity I/I0 and Miller indices (h k l) for irradiated and unirradiated Mg1.1 Ti0.1 Er0.025 Fe1.775 O4 Before irradiationa

After irradiation by 30 Mradb

d (Å)

I/I0

hkl

d (Å)

I/I0

hkl

4.880 2.980 2.530 2.067 1.710 1.617 1.480

6.10 10.30 100.00 47.00 11.29 29.67 59.64

111 220 311 400 422 511 440

4.866 2.950 2.520 2.090 1.700 1.610 1.480

8.10 51.00 100.00 25.50 13.21 44.10 64.86

111 220 311 400 422 511 440

a b

System: spinel, a = 8.3842 Å; V = 589.383 Å3 . System: spinel, a= 8.350 Å; V = 582.272 Å3 .

M.A. Ahmed et al. / Materials Chemistry and Physics 81 (2003) 63–77 Fig. 7. (a–e) The variation of ac conductivity (ln σ) with the reciprocal of absolute temperature for Mg1.5 Ti0.5 Er0.025 Fe0.975 O4 , at different heating rates. (a) rate 2 ◦ C min−1 , (b) rate 4 ◦ C min−1 , (c) rate 6 ◦ C min−1 , (d) rate 8 ◦ C min−1 . 71

72 M.A. Ahmed et al. / Materials Chemistry and Physics 81 (2003) 63–77

Fig. 8. X-ray diffractograms for Mg1.1 Ti0.1 Er0.025 Fe1.775 O4 , sintered at 1200 ◦ C, rate 2 ◦ C min−1 .

M.A. Ahmed et al. / Materials Chemistry and Physics 81 (2003) 63–77 Fig. 9. (a–e) The variation of the real part of the dielectric constant ε with the absolute temperature for Mg1.1 Ti0.1 Er0.025 Fe1.775 O4 , sintered at 1200 ◦ C, rate 2 ◦ C min−1 . (a) Uniradiated, (b) 10 Mrad, (c) 20 Mrad, (d) 30 Mrad, (e) the variation of the real part of the dielectric constant ε with different doses of irradiation. 73

74 M.A. Ahmed et al. / Materials Chemistry and Physics 81 (2003) 63–77 Fig. 10. (a–d) The variation of ac conductivity (ln σ) with the reciprocal of absolute temperature for Mg1.1 Ti0.1 Er0.025 Fe1.775 O4 , sintered at 1200 ◦ C, rate 2 ◦ C min−1 before and after irradiation. (a) Uniradiated, (b) 10 Mrad, (c) 20 Mrad, (d) 30 Mrad.

M.A. Ahmed et al. / Materials Chemistry and Physics 81 (2003) 63–77 Fig. 11. (a–d) The variation of ac conductivity(ln σ) with the reciprocal of absolute temperature for Mg1.1 Ti0.1 Er0.025 Fe1.775 O4 irradiated 10 Mrad dose, at different heating rates, (a) rate 2 ◦ C min−1 , (b) rate 40 ◦ C min−1 , (c) rate 6 ◦ C min−1 , (d) rate 8 ◦ C min−1 .

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Table 6 The activation energy in eV of Mg1.1 Ti0.1 Er0.025 Fe1.775 O4 , for the low (EI ) and high (EII ) temperature ranges at different ␥-irradiation doses Dose (Mrad)

0 10 20 30

EI (eV)

EII (eV)

100 kHz

1000 kHz

100 kHz

1000 kHz

0.161 0.114 0.049 0.094

0.117 0.189 0.116 0.104

0.283 0.344 0.831 0.252

0.145 0.344 0.086 0.556

the generation of some vacancies at different depths which act as trapping centers. The liberation of charge carriers from these trapping centers needs different energies. In Fig. 9(c), 20 Mrad ␥-rays was not the sufficient energy to liberate charge carriers from the trapping centers at deeper depths, leading to a decrease in ε . From the experimental data, the critical dose of irradiation is 20 Mrad as shown in Fig. 9(e). Fig. 9(d) shows a drastic increase in ε which can be explained in view of structural changes due high ␥-doses. In other words, the four oxygen anions which surround the metal ion in tetrahedral sites are displaced outwards along the body diagonal of the cube. These four oxygen anions still occupy the centers of an enlarged tetrahedron and retain the cubic symmetry [23]. Some distortion may occur to the tetrahedral sites due to such displacement and it will move the anions away from the nearest tetrahedral cations. The result of this process is an increase in the polarization as well as the rate of the electron exchange between ferrous and ferric ions in the high resistivity region. The dispersion or decrease in ε as the frequency increases takes place when the electron exchange interaction or hopping between the ferrous and ferric ions at the octahedral sites cannot follow the alternation of the applied ac electric field. Fig. 10(a–d) correlates the electrical conductivity (ln σ) and the reciprocal of absolute temperature as a function of the applied frequency before and after ␥-irradiation. From the figure, it is clear that the conductivity increases as the ␥-dose increases even in the case of 20 Mrad which still has higher conductivity values than the unirradiated samples. This increase in σ can be attributed to the increase in the ratio of Fe2+ /Fe3+ on the octahedral sites as a consequence of the hopping process [24]. By comparing the transition temperature of the sample irradiated at (0, 10, 20 and 30 Mrad) one can find that, the transition temperature increases with increasing dose as a result of increasing the ordered region. In other words, the arrangement of the magnetic dipoles takes place due to energy of ␥-radiation on the expense of paramagnetic region, though increasing Tc [25]. The values of the activation energy decrease with increasing dose (Table 6). This can be explained as mentioned before. Fig. 11(a–d) illustrates the variation of ac conductivity and the reciprocal of absolute temperature for the irradi-

ated samples as a function of frequency at different heating rates 2, 4, 6 and 8 ◦ C min−1 and sintering temperature 1200 ◦ C. From the figure, it is clear that all samples have the same trend as described before but with some important remarks that appear from comparison between Figs. 7 and 11. The first remark is that, the conductivity values for irradiated samples at all rates are higher than unirradiated ones at the same rates. Also, the gradient of the straight lines in the conductivity data of the irradiated samples is smaller than that of the unirradiated ones which means that ␥-radiation decreases the activation energy. Accordingly, one can conclude that ␥-radiation energy helps the alignment of charge carriers (hopping electrons) which are disturbed due to thermal energy and fast rate of heating especially at 8 ◦ C min−1 .

4. Conclusion The results of this study can be summarized as follows: 1. All samples reveal spinel structure in spite of the presence of rare earth ions. 2. Both electrical conductivity and dielectric constant decrease as Ti4+ ion substitution increases. 3. In both irradiated and unirradiated samples the activation energy in the paramagnetic region is higher than that in the ferrimagnetic region. 4. The interplaner distance of the investigated samples decreases with increasing ␥-doses leading to a decrease in the crystal size. 5. The rate of heating as well as the thermal energy have a noticeable effect on the structural and the electrical properties of the investigated samples. References [1] J. Kulikowski, J. Magn. Magn. Mater. 41 (1984) 56. [2] B. Tareev, Physics of Dielectric Materials, Moscow, 1979. [3] N.Z. Darwish, O.M. Hemeda, Appl. Radiat. Isot. 45 (4) (1994) 445. [4] M.A. Ahmed, S.T. Bishay, J. Phys. D: Appl. Phys. 34 (2001) 1–7. [5] Raul Valenzuela, Magnetic Ceramics, New York, 1994. [6] P.E. Werner, Treor, Trial and Error Program for Indexing Unknown Powder Patterns, Stockholm, Sweden, 1984. [7] K.J. Stanlley, Oxide Magnetic Materials, Clarendon Press, Oxford, 1972. [8] B.D. Cullity, Elements of X-Ray Diffraction, Addison-Wesley Press, Reading, MA, 1959. [9] Y. Purushotham, V.D. Reddy, Phys. Stat. Sol. (a) 140 (1993) K89. [10] P.V. Reddy, T.S. Rao, J. Less Common Met. 86 (1982) 255. [11] K. Iwauchi, Jpn. J. Appl. Phys. 10 (1971) 1520. [12] J.C. Maxwell, Electricity and Magnetism, vol. 1, Oxford University Press, Oxford (Section 328). [13] K.W. Wagner, Ann. Phys. Leipzig 40 (1913) 817. [14] Y. Purushotham, N. Kumar, Phys. Stat. Sol. (a) 148 (1995) K17. [15] J. Smit, H.P. Wijn, Ferrites, Cleaver Hume Press, London, 1959.

M.A. Ahmed et al. / Materials Chemistry and Physics 81 (2003) 63–77 [16] M.A. Ahmed, M.A. El Hiti, Magn. Magn. Mater. 146 (1995) 84. [17] Y.P. Irkhin, E.A. Turov, Sov. Phys. JETP 33 (1957) 673. [18] M.A. Ahmed, K.A. Darwish, E.H. El Khawas, J. Mater. Sci. Lett. 16 (1997) 1948. [19] C.G. Koops, Phys. Rev. 38 (1951) 216. [20] G. Moltgen, Z. Angew. Phy. 4 (1952) 216.

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[21] N.Z. Darwish, Appli. Phys. Commun. 13 (2) (1994) 101. [22] M.A. Moussa, A.M. Summan, M.A. Ahmed, Thermochemica Acta 158 (1990) 177–181. [23] V.K.R. Murthy, J. Sobanadri, J. Phys. Stat. Sol. (a) 36 (1976) 133. [24] M.A. Ahmed, F. Mohsen, Egypt. J. Phys. 1 (1997) 151. [25] O.M. Hemeda, N.Z. Darwish, Appl. Phys. Commun. 13 (1) (1994) 29.