Dielectric properties of Ti x Li 1 x La 0.1 Fe 1.9 O 4 ferrite thin films

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1 Indian Journal of Pure & Applied Physics Vol. 48, August 2010, pp Dielectric properties of Ti x Li 1 x La 0.1 Fe 1.9 O 4 ferrite thin films H M Abdelmoneim Physics Department, Faculty of Science, Cairo University, Giza, Egypt abdelmoneimhussein@gmail.com Received 30 September 2009; accepted 3 March 2010 The variation of dielectric constant (ε'), dielectric loss factor (ε") and the ac conductivity (σ ac ) of mixed Ti x Li 1 x La 0.1 Fe 1.9 O 4 (where x = 0.1, 0.3, 0.5, 0.7 and 0.9) ferrite thin films has been studied as a function of both frequency and temperature. The variation of dielectric constant with different temperature in all films gives a broad peak. The maximum peak is almost fixed at 500 K independent of lithium content. The ε'(f) and ε"( f ) curves at different temperatures for all samples show a higher dispersion in the low frequency region. The conduction phenomenon is explained on the basis of a correlated barrier hopping (CBH) model. According to the CBH model, the maximum barrier height at infinite separation (U M ) is determined. Keywords: Dielectric constant, Loss factor, ac Conductivity, CBH model 1 Introduction The technology of ferrite materials have reached a very advanced stage now-a-days in which the design engineers control the properties to a large extent, to suit the particular purpose of the device. They play a very important role in various technological applications from microwave to radio wave frequencies 1,2. The selection of a ferrite material for specific applications depends mainly on the preparation condition (sintering temperature, sintering time and rate of heating/cooling) and on the substitution of different valence cations 3-5. The dielectric properties of ferrites are dependent upon the several factors including the method of preparation, chemical composition and grain structure or size. When a ferrite is sintered under slightly reducing condition, the valence state of the ions changes and the individual cations so formed in the sample lead to high conductivity. On the other hand, when the material is cooled in an oxygen atmosphere, it is possible to form films of high resistivity over the constituent grains 1-6. Ferrite in which the individual high conducting grains behave as inhomogeneous, dielectric constants as high as 10 5 are found in the case of ferrite at low frequencies 1-7. The physical properties of Ti-Li-La ferrite thin films including compound of lithium-titanium ferrite, has not been investigated properly. The addition of lanthanum enhances and improves electrical properties where La 3+ ions substitute the Fe 3+ ions in the composition. In addition, Li 1+ improves the magnetic properties of the compound and the combination of Ti 4+ and Li +1 ions stabilizes the material electrically. Therefore, a systematic investigation of electrical properties would be essential. The study would also elucidate the conduction mechanism in these materials. The dielectric constant, dielectric loss factor and ac electrical conductivity as a function of frequency and temperature and the titanium and lithium contents have been studied in the present paper. 2 Experimental Details Polycrystalline samples of Ti x Li 1 x La 0.1 Fe 1.9 O 4 : x = 0.1, 0.3, 0.5, 0.7, 0.9 were prepared by the conventional ceramic technique 8 from high-purity oxides TiO, Fe 2 O 3 and La 2 O 3 with LiOH (which was changed to Li-oxide by heating) in stoichiometric proportions. The powders were grounded together for 2 h using an agate mortar. The mixture was transferred to an agate ball mill for 2 h and calcined for 5 h with a heating rate of 2 C/min followed by cooling to room temperature in air with the same rate as that of heating. The pre-sintered samples were crushed again and mixed for another 2 h with acetone, to be reduced into small crystallites of uniform size. The mixture was dried and a few drops of isopropyl alcohol were added as a binder. The powder was compressed uniaxially under a pressure of N/m 2 into pellet form of diameter 10 mm and thickness about 1.5 mm. The pellets 9 were sintered at 1200 C for 10 h and cooled to room temperature at

2 ABDELMONEIM: DIELECTRIC PROPERTIES OF FERRITE THIN FILMS 563 the above mentioned rate. The pre- and final-sintering were carried out using a Lenton furnace of type UAF 16/5 (UK). The pellets were grounded again to a powder. X-ray diffraction pattern was carried out by Diano X-ray diffractometer with Cu K α radiation to ensure the formation of the sample structure. X-ray patterns for the samples Ti x Li 1 x La 0.1 Fe 1.9 O 4 (x = 0.1, 0.3, 0.5, 0.7, 0.9) as shown in Fig. 1, indicate the crystalline phase of the face center cubic (fcc) system. The films of different compositions were deposited on a cleaned glass substrate (having two evaporated Al electrodes) holded and maintained at approximately 25 C under a vacuum 10 6 Torr, at a rate of 1 o As 1 by thermal evaporation using an Edwards coating unit model E-306A. The thickness of the films as well as the deposition rate was controlled using a quartzcrystal thickness monitor (Edward FTM5). Films of thickness (d = 100±1 nm.), area (1 cm 0.5 cm) were stored in a dry, non-oxidizing atmosphere. The dielectric constant was studied as a function of frequency (100 Hz-20 khz) and temperature at test frequencies using RLC Meter Bridge (model PM6304). The electrodes of sample were painted with silver paste to ensure good electric contacts. The dielectric constant (ε') was calculated by using the formula: ε' = Cd/ε o a (1) where C is the capacitance of the film, ε o the permittivity of the free space and a is the crosssectional area. The dielectric loss factor has been calculated from the relation: ε" = ε' tan δ (2) where tanδ is the loss tangent. The ac conductivity of the samples (σ ac ) was determined from dielectric parameters using the relation 10 : σ ac = ω ε o ε" (3) where ω is the angular frequency. The accuracy of both ε' and ε" was about ± 0.1%. Fig. 1 X-ray diffractograms for the ferrite samples Ti x Li 1 x La 0.1 Fe 1.9 O 4 ; for (A) x = 0.1, (B) x = 0.3, (C) x = 0.5, (D) x = 0.7 and (E) x = 0.9

3 564 INDIAN J PURE & APPL PHYS, VOL 48, AUGUST Results and Discussion 3.1 Dielectric constant The variation of dielectric constant with temperature at 1 khz for different Ti and Li concentrations thin film samples is shown in Fig. 2. For all composites, the dielectric constant is found to increase with this increase in temperature, reaching a maximum value at a particular temperature followed by decreasing trend. It was observed that the dielectric constant at both room and peak maximum temperatures changed irregularly with the lithium content in composites [Fig. 2]. Among these samples, the film with x = 0.5 has the highest value of dielectric constant within the temperature range K. In addition, the peaks are broad and their position of peak maximum is nearly constant at about 500 K for all samples. In case of ferrites, electron hopping between Fe 2+ and Fe 3+ ions on the octahedral sites is responsible for the conduction that is thermally activated by increasing temperature. It was expected that the valence Fe 3+ /Fe 2+ ions is the predominant one. The electron hopping causes local displacement of electrons in the direction of the externally applied field, causing dielectric polarization in the ferrite The huge increase in the ε' at maximum peak can be explained by the temperature dependent characteristics of domain wall motion and/or the increase in the drift mobility of electrons 14. At low temperature, it is difficult for the domain to move so that the extrinsic contribution of domain walls to the dielectric response is small. At temperature above maximum peak, the decrease in the dielectric constant with temperature is attributed to the increase in chaotic thermal oscillation of the ferrite composite molecules and the diminishing degree of order of the orientation of the dipoles. Also, it may be due to random vibrational motion of ions and electrons as they become less susceptible in the direction of applied field 15. The variation of dielectric constant as a function of frequency at different temperatures for all films under investigation has a similar behaviour. We, therefore, chose the sample with x = 0.5 as a representative for the sake of brevity [Fig. 3]. The dielectric constant decreases rapidly at lower frequencies and slightly at relatively higher frequencies showing dispersion in dielectric constant [Fig. 3]. It is worthnoting that the magnitude of frequency dispersion depends on the Fig. 2 Variation of dielectric constant with temperature at 1 khz for different Li content thin film samples. The inset of Fig. is the dielectric constant at both room and peak maximum temperatures with lithium content (1 x)

4 ABDELMONEIM: DIELECTRIC PROPERTIES OF FERRITE THIN FILMS 565 temperature showing that the dielectric decrement is larger at the peak temperature. This dielectric dispersion is attributed to the Maxwell 16 and Wagner 17 type of interfacial polarization in agreement with Koop's theory 18. As the frequency increases ionic and orientation sources of polarizability decrease and finally disappear due to inertia of the molecules and ions. In practice, there is relaxation time for charge transport and therefore, the dielectric constant depends upon the applied frequency. The high value of the dielectric constant in the present composite is not usually intrinsic but may be rather associated with space charge polarization and inhomogeneous dielectric structure. These inhomogenities are impurities, grain structure and pores Dielectric loss factor All dielectric materials have two types of losses. One is a conduction loss, representing the flow of actual charges through the dielectric material. The other dielectric loss is due to the movement or rotation of the atoms in an alternating field. Fig. 4 shows the temperature dependence of the dielectric loss factor ε" for all composites at 1 khz. It can be seen that ε"(t) curves exhibit one pronounced relaxation peak at lower lithium concentrations x = 0.7 and 0.9 while it disappears at higher contents of lithium. The relaxation peak maximum can be observed when jumping or hopping frequency of electrons between different valance cations becomes approximately equal to the frequency of the applied field and the phenomenon is termed as ferrimagnetic resonance 16,19. The disappearance of the relaxation peak may be due to the short time of relaxation, i.e. the process takes place so quickly, and/or smallness of its relaxation peak value. Since the replacement of small ionic radius of monovalent Li 1+ ions at the expense of relatively larger Ti 4+ ions may cause the ions to move freely shifting the relaxation peak to shorter time range not allowed in experimental conditions. The variation of the dielectric loss factor ε" with frequency for the sample of x = 0.5 (as a representative for all films) at different temperatures is shown in Fig. 5. The variation in ε" shows a similar dispersion behaviour as seen for ε' versus frequency. The decrement of ε"(f ) curve is very fast at higher temperature (572 K) while it decays with slow rate reaching a constant value at a lower temperature (478 K). This dielectric loss factor curve is attributed to domain wall resonance 20. At higher frequencies, losses are found to be low if domain wall motion is inhibited and magnetization is forced to change by rotation 21. Fig. 3 Variation of dielectric constant as a function of frequency at different temperatures for x = 0.5

5 566 INDIAN J PURE & APPL PHYS, VOL 48, AUGUST 2010 Fig. 4 Temperature dependence of dielectric loss factor (ε") for all composites at 1 khz Fig. 5 Variation of dielectric loss factor (ε") with frequency for the sample of x = 0.5 at different temperature

6 ABDELMONEIM: DIELECTRIC PROPERTIES OF FERRITE THIN FILMS ac Conductivity (σ ac ) To determine the most dominant ac conduction mechanism of the present ferrite composites, the dependence of σ ac on frequency at different temperature points is considered. The ac conductivity is usually expressed as: σ ac = A ω s (4) where A and s are constants. Figure 6 shows the frequency dependent ac conductivity plots for the sample with x = 0.5 (as a representative for all samples). Similar behaviour is also observed for other composites. The conductivity is observed to increase monotonically with increase in frequency and becomes weakly dependent at both high frequency and temperature. This type of behaviour reveals that the mechanism responsible for conduction could be the hopping one. In addition, Fig. 6 shows that the ac conductivity increases as the temperature increases. This increase may be due to the increasing liberation of more trapped charge carriers from the vacancies that were found at different depths 22,23. According to the quantum mechanical tunneling (QMT) model 24, the power s of Eq. (3) is either temperature independent or an increasing function of temperature. On the other hand, the correlated barrier hopping (CBH) model 25 predicts that the power s is a decreasing function of temperature. Values of s were derived by calculating the slope of the frequency dependence σ ac (ω) from Fig. 6. The variation of s with temperature for all composite ferrites is shown in Fig. 7. It is observed that the exponent s decreases with increasing temperature and its value is less than unity, i.e., 0 < s < 1 for all samples except the sample of lower concentration of Li (x = 0.9) which shows an increase of s in the relatively lower temperature region ( K) then decreases, thereafter, the result leads to the prediction that the CBH model is the most suitable mechanism to explain the ac conduction behaviour in the composites of x = 0.1, 0.3, 0.5 and 0.7 throughout the whole temperature range. However, in case of the composite sample x = 0.9, the behaviour in the temperature region ( K) is well accounted for by the CBH model, whereas the lower temperature region ( K), the behaviour is probably due to small-prolaron quantum tunneling. In the CBH model 26, the exponent s was found to obey the equation: s = [1 6 k T]/[U M k ln (1/ωτ o )] (5) Fig. 6 Frequency dependent ac conductivity plots of the sample at x = 0.5

7 568 INDIAN J PURE & APPL PHYS, VOL 48, AUGUST 2010 Fig. 7 Variation of s with temperature for all composite ferrites where k is the Boltzmann constant, U M is the maximum barrier height at infinite separation, which is called the polaron binding energy, the binding energy of the carrier in its localized sites, τ o is a characteristic relaxation time which is of the order of an atomic vibrational period ( s). Using the above calculated value of s, the maximum barrier height at infinite separation U M could be calculated according to Eq. (4); this is presented in Table 1. The values of U M change irregularly with both temperature and Ti/Li concentration ratio. This reflects that the thermal agitation varies the value of the degree of overlap of Coulomb potential wells of the considered sites. Among these samples, U M value of composite sample of x = 0.7 is the lower one. The variation of ac conductivity with temperature for all films at 1 khz is shown in Fig. 8. Figure 8 shows a semiconductor behaviour in the full range of temperature for all samples except the samples of lower Li content, namely for x = 0.7 and 0.9 in the temperature range K, which revealed a metallic behaviour. The region of reduction conductivity is considered to be associated with impurity conduction besides the contribution of carrier-phonon interaction 26. The increase in conductivity with rise of temperature is due to the increase in the thermally activated electron drift Table 1 Maximum barrier height at infinite separation U M x 450 K 500 K 550 K U M (ev) U M (ev) U M (ev) mobility of charge carriers according to the hopping conduction mechanism. The electron conduction in ferrites can be explained by the Verwey model of electron hopping 27 which involves exchange of electrons between ions of the same elements present in different valence states, and distributed randomly over crystallographically equivalent lattice sites. The behaviour of ε' and σ ac are explained qualitatively by the assumption that the conduction processes are of the same origin. Figure 8 shows that there are three straight lines in each plot with different slopes obeying Arrhenius equation: σ ac = σ aco exp( E o /kt)...(6) where σ aco is constant and E o is the activation energy. The activation energy values are presented in Table 2.

8 ABDELMONEIM: DIELECTRIC PROPERTIES OF FERRITE THIN FILMS 569 Fig. 8 Variation of ac conductivity with temperature for all films at 1 khz Table 2 Activation energy values x E(I) ev E(II) ev E(III) ev It is obvious that the values of activation energy vary according to Li/Ti composition ratio. The data in Table 2 indicate that the electronic conduction can be assumed to be effective in all regions. 4 Conclusions It is observed that the Ti and Li substituted in Laferrite thin films show a concentration dependence of ε', ε" and σ ac at various frequency and temperature points. The decreasing dielectric constant and dielectric loss with frequency show dispersion in the low frequency range. The dielectric constant dispersion is explained on the basis of interfacial and space polarization while the dispersion in the dielectric loss factor is attributed to domain wall resonance. The samples show the positive temperature coefficient of conductivity, which is most desirable for developing highly sensitive thermal detectors, sensors, etc. The character of dependence of the exponent s on temperature may reveal that the CBH model is the most dominant mechanism contributing to the ac conduction in the investigated samples. Acknowledgement The author thanks Prof Dr M A Ahmed for kindly helping in the preparation of ferrite material. References 1 Visnanathan B & Muthy V R K, Ferrite materials science and technology, Nerosa, Publishing House, New Delhi (1990). 2 Patil S A, Soudagar M K, Podil B L & Sawart S R, Solid State Commun, 78 (1991) Rezlescu N & Rezlescu E, Phys Status Solidi a, 23 (1974) Below K P, Antoshina L A & Markosyan A S, Sos Phys Solid State(USA), 25 (1983) Kulkarni V R, Todkaar M M & Vaingenkar A S, Indian J Pure & Appl Phys, 24 (1986) 294.

9 570 INDIAN J PURE & APPL PHYS, VOL 48, AUGUST Bellod S S & Chougule B K, Materials Chemistry & Physics, 66 (2000) Kumar B K & Srivastava G P, Proc Int Conf Ferrites, India, 5 (1989) Lakshman A, Rao K H & Mendiratta R G, J Magn Matter, 250 (2002) Ahmed M A & Bishay Samiha T, J Magn Matter, 279 (2004) Hanumaion A, Bhimosankaram T, Suryanarayan S V & Kumar G, Bull Mater Sci, 17 (1994) Bellod S S & Chougule B K, Material Chemisty & Physics, 66 (2000) Potil D S, Chougule S S, Lokare S A & Chougule R K, J Alloys & Compounds, 452 (2008) Chougule S S & Chougule B K, Materials Chemistry & Physics, 108 (2008) Koop C G, Phys Rev, 83 (1951) Agarwal D C, Asian J Phys, 6 (1997) Maxwell J C, Electricity & Magnetism, Oxford University Press, London, (1993) Wagner K W, Ann Phys, 40 (1993) Koop's C G, Phys Rev, B83 (1951) Rabinkin L I & Norikova L I, Ferrites (Minsk), (1960) Deven R S & Chougule B K, Physica B, 393 (2007) Deven R S, Kolekar Y D & Chougule B K, J Alloys & Compounds, 461 (2008) Viswanathan B & Murthy V R K, Ferrite Materials, Narosa, New Delhi, (1990). 23 Song J M & Koh J G, IEEE Trans Mag, (1996) Austin I G & Mott N F, Advances in Phys, 18 (1969) Elliot S R, Philos Mag, 36 (1977) 1291; Ibid, 37 (1978) Mazen S A, El Falaky A & Mansour S F, Phys Status Solidi, (b) 201 (1997) Verwey E J, Haayman P W & Romeyn F C, J Chem Phys, 4 (1947) 181.

Dielectric behaviour and a.c. conductivity in Cu x Fe 3 x O 4 ferrite

Bull. Mater. Sci., Vol. 23, No. 5, October 2000, pp. 447 452. Indian Academy of Sciences. Dielectric behaviour and a.c. conductivity in Cu x Fe 3 x O 4 ferrite A N PATIL, M G PATIL, K K PATANKAR, V L MATHE,