AC electrical conductivity and dielectric studies of bulk p-quaterphenyl

Synthetic Metals 205 (2015) 139–144

Contents lists available at ScienceDirect

Synthetic Metals journal homepage: www.elsevier.com/locate/synmet

AC electrical conductivity and dielectric studies of bulk p-quaterphenyl A.A. Attia a, * , H.S. Soliman a , M.M. Saadeldin b , K. Sawaby b a b

Physics Department, Faculty of Education, Ain Shams University, Roxy, Cairo 11757, Egypt Physics Department, Faculty of Science, Cairo University, Giza 12613, Egypt

A R T I C L E I N F O

A B S T R A C T

Article history: Received 1 October 2014 Received in revised form 4 April 2015 Accepted 8 April 2015 Available online xxx

The frequency and temperature dependence of AC conductivity, dielectric constant and dielectric loss of p-quaterphenyl in pellet form were investigated in the frequency range of 200 Hz–2.4 MHz and temperature range of 301–423 K. The X-ray diffraction of p-quaterphenyl at room temperature shows monoclinic structure. The unit cell parameters and the values of Miller indices hkl and lattice spacing dhkl corresponding to each diffraction line of p-quaterphenyl were investigated using some computer programs. The behavior of AC conductivity was interpreted by the correlated barrier hopping (CBH) model. Temperature dependence of AC conductivity indicates that AC conduction is a thermally activated process. AC activation energy decreases with increasing frequency which confirms the hopping conduction as the dominant mechanism. The density of localized states N(EF) near the Fermi level was found in the range of 1.33–2.44
1018 eV1 cm3 for the investigated range of frequency and temperature. Dielectric constant and dielectric loss showed a decrease with increasing frequency and an increase with increasing temperature. The calculated value of the maximum barrier height Wm (0.64 eV) according to the Guintini equation agreed with that proposed by the theory of hopping of charge carriers over a potential barrier. Dielectric relaxation studies were obtained from the dielectric modulus. The frequency dependence of real and imaginary parts of the complex dielectric modulus was investigated for various temperatures. The frequencies corresponding to the maxima of the imaginary electric modulus at various temperatures were found to obey an Arrhenius law with an activation energy of 0.02 eV. The relaxation time decreases with the increase in temperature and the relaxation time at infinite temperature was 24.5 ms. The high frequency dielectric constant was estimated for various temperatures. ã 2015 Elsevier B.V. All rights reserved.

Keywords: p-Quaterphenyl X-ray analysis AC conductivity Dielectric properties

1. Introduction The study of organic materials which have semiconducting properties particularly their electrical behavior is at present a dynamic field of research, since a number of applications can be foreseen such as photovoltaic devices, light emitting diodes, Schottky diodes, field effect transistors and gas sensing devices [1–4]. Due to their flexibility, low cost and ease of production they are capable of replacing inorganic semiconductors in a number of applications such as flat panel displays, plastic integrated circuits and solar energy conversion. Therefore, the study of these compounds is very essential to understand the behavior of their electronic physical properties under various conditions such as changes in temperature, pressure, frequency, ambient gases, etc. [5]. Measurements of AC conductivity of semiconductors have

* Corresponding author. Tel.: +20 1001655010. E-mail address: [email protected] (A.A. Attia). http://dx.doi.org/10.1016/j.synthmet.2015.04.003 0379-6779/ ã 2015 Elsevier B.V. All rights reserved.

been extensively used to understand the conduction mechanisms in these materials [6]. Various models, such as quantummechanical tunneling (QMT) model [7,8], small polaron tunneling (SPT) model [9,10], large polaron tunneling (LPT) model [9] and correlated barrier hopping (CBH) model [11,12] have been proposed to explain the AC conduction mechanism in different materials. Among the multitude of organic material available phenylene are promising candidates for optoelectronic applications. Quaterphenyl (p-4P, C24H18) is an aromatic molecule of the oligophenyls: p-quaterphenyl (p-4P), p-quinquephenyl (p-5P) and p-sexiphenyl (p-6P). These oligophenyls may be of interest because of their particularly high thermal stability and possible chemical compatibility with the processing required for integrated organic devices [13]. Some evidence of photovoltaic effect was obtained in our lab from heterojunction based on p-quaterphenyl thin film deposited by thermal evaporation on p-Si substrate (under study). Some literature exists concerning study of DC conduction mechanism in p-quaterphenyl [14,15]. To our present knowledge, the literature

140

A.A. Attia et al. / Synthetic Metals 205 (2015) 139–144

survey reveals that the AC conductivity and dielectric studies on p-quaterphenyl have not been reported so far. Therefore, in this paper, the frequency and temperature dependence of AC conductivity and dielectric properties were measured and investigated for p-quaterphenyl in bulk form. 2. Experimental technique The powder of p-quaterphenyl was obtained from Sigma–Aldrich Company. p-Quaterphenyl powder was ground finally and compressed under a suitable pressure to form a pellet of about 8 mm diameter and 1.3 mm thickness. X-ray diffraction study was performed for the powder of p-quaterphenyl at room temperature. A Philips X-ray diffractometer (model X’Pert) was used for the measurements, with monochromatic Cu (Ka), operated at 40 kV and 25 mA. For dielectric properties and AC conductivity measurements, Ohmic contacts were made by two Al electrodes on the parallel surfaces of the sample. The sample holder was inserted into an electric furnace. Dielectric and AC conductivity measurements were carried out on this sample using a programmable automatic RLC bridge, (model Hioki 3532 Hitester). The capacitance C, the impedance Z and the loss tangent (tan d) were directly measured in the frequency range 200 Hz–2.4 MHz. The temperature of the sample was measured by using a Chromel–Alumel thermocouple in the range from 301 K to 423 K. The dielectric constant (e1) of the material was calculated using the formula: e1 = Cd/eoa, where d is the thickness, a is the cross-sectional area of the pellet and eo is the permittivity of free space. Also, the dielectric loss (e2) was calculated using the relation: e2 = e1tan d, where d = 90  ’ where ’ is the phase angle. The AC conductivity of the sample (s ac) was determined from dielectric parameters using the relation: s ac = veoe2 [16,17], where v is the angular frequency. 3. Results and discussion 3.1. X- ray diffraction analysis The X-ray diffraction (XRD) pattern for the powder of p-quaterphenyl at room temperature is shown in Fig. 1. As shown in this figure the powder XRD pattern has many diffraction peaks with different intensities indicating that the p-quaterphenyl powder has a polycrystalline nature. The unit cell parameters of p-quaterphenyl were determined for the first time by using the CRYSFIRE computer program [18]. The data analysis of the structure is highly matched with a monoclinic structure with space group P21 and cell parameters a = 8.11 Å, b = 5.61 Å, c = 17.91 Å and b = 95.8 . The values of Miller indices hkl and lattice spacing dhkl corresponding to each diffraction line were indexed using CHECKCELL program [19] and tabulated in Table 1. Relative intensity and comparison between the measured and calculated values for each diffraction line were also included in Table 1. The highest preferred orientation is found along the (0 0 4) plane.

Fig. 1. XRD pattern of p-quaterphenyl in the powder form.

Table 1 X-ray indexing for the powder of p-quaterphenyl. No.

dmeas. (Å)

dcal. (Å)

2umeas. (degree)

2ucal. (degree)

Relative intensity (%)

hkl

1 2 3 4 5 6 7 8 9 10 11

8.870 6.000 4.628 4.435 3.859 3.177 2.969 2.541 2.226 2.046 1.979

8.909 5.939 4.606 4.455 3.852 3.175 2.970 2.541 2.227 2.049 1.972

9.964 14.750 19.162 20.005 23.028 28.059 30.065 35.295 40.483 44.227 45.795

9.920 14.903 19.254 19.915 23.072 28.078 30.066 35.290 40.466 44.153 45.994

72.17 38.49 31.64 100.0 24.66 15.37 3.60 3.28 9.96 7.11 9.54

002 003 11 0 004 201 2 11 006 214 008 305 403

3.2. AC conductivity Fig. 2 presents the dependence of the AC conductivity (s ac) on the frequency (200 Hz–2.4 MHz) of p-quaterphenyl pellet at different temperatures (301–423 K) on ln–ln plotting. The AC conductivity increases with the increase of frequency, where s ac(v) increases gradually for all the temperatures at low frequency then it increases rapidly with increasing frequency. The AC conductivity (s ac) is related to relaxation and polarization conductivity (frequency dependent and weakly temperature dependent). Similar behavior is observed in several semiconductor materials [20,21]. The relation between the AC conductivity and the frequency of the applied field is described by the following equation [22,23]:

s ac ðvÞ ¼ Avs

(1)

where A is a constant, v is the angular frequency and s is the frequency exponent which generally is less than or equal to one. The exponent s is a very important parameter since its value and behavior with temperature and/or frequency determines the dominant conduction mechanism. According to the quantum mechanical tunneling (QMT) model [24] for the case of non polaron forming carriers, s is predicted to be temperature independent but frequency dependent. For the case of small polaron tunneling, s is predicted to increase as temperature increases. In large polaron tunneling, s should be both temperature

Fig. 2. Frequency dependence of s ac(v) of bulk p-quaterphenyl at different temperatures; the inset figure represents the variation of frequency exponent s versus temperature.

A.A. Attia et al. / Synthetic Metals 205 (2015) 139–144

and frequency dependent, for small values of polaron radius, s exhibits a minimum at a certain temperature and subsequently increases with increasing temperature in the same way as the case of small polaron QMT. The correlated barrier hopping CBH model [25,26] predicts s to be both temperature and frequency dependent and s should decrease with increasing temperature. Among these models, the CBH model, proposed by Elliott [26], is the most appropriate model. In this model, the charge carriers hop between two sites over a barrier separating them. The frequency exponent s is a measure of the degree of correlation between AC conductivity s ac and frequency v. At low frequency, s should be zero for random hopping (i.e., s ac is frequency independent). At high frequency range, s approaches to one particularly at low temperature as correlation increases (i.e., s ac is frequency dependent). The value of s for p-quaterphenyl at various temperatures is determined from the linear slope of the curves of ln s ac(v) versus ln v in the frequency range of 1.6
105 Hz–3.3
106 Hz. It is noticed that s value decreases with the increase of temperature as shown in the inset of Fig. 2. Such a temperature dependence of s and its range of values, for p-quaterphenyl, are consistent with the correlated barrier hopping (CBH) model. According to Austin–Mott formula [24], based on CBH model, s ac(v) can be explained in terms of hopping of electrons between pairs of localized states at the Fermi level. The process of hopping of electrons is affected also by the density of localized states N(EF) near the Fermi level. Thus, the AC conductivity can be expressed as follows:

s ac ðvÞ ¼


p 3

h
v i4 p ½NðEF Þ2 kB Te2 a5 v ln

(2)

v

where kB is the Boltzmann’s constant, e is the electronic charge, a is the exponential decay parameter of localized states wave functions and np is the frequency of the phonons. By assuming vp = 1012 Hz and a1 = 10Å [27],N(EF) was calculated at different frequencies and temperatures. The values of N(EF) was found to be of the order of 1.33–2.44
1018 eV1 cm-3 for the investigated range of temperature and frequency. The variation of AC conductivity with temperature for p-quaterphenyl at different frequencies is shown in Fig. 3. The figure shows a semiconductor behavior in the full range of temperature with a linear relationship between ln s ac and the inverse of temperature at different frequencies. The increase in conductivity with the rise in temperature is due to the increase in

141

the thermally activated electron drift velocity of charge carriers according to the hopping conduction mechanism. The activation energy DEac of the AC conduction is calculated at different frequencies using the well-known Arrhenius equation:   DEac s ac ¼ s o exp (3) kB T where s o is the pre-exponential constant. The frequency dependence of AC activation energy for p-quaterphenyl is shown in Fig. 4. It is observed that DEac decreases with increasing frequency. The increase of the applied field frequency enhances the electronic jumps between the localized states; consequently the activation energy DEac decreases with increasing the applied frequency [28,29]. Such a decrease confirms that hopping conduction is the dominant mechanism. 3.3. Dielectric constant, e1 The real part of the complex dielectric constant is e1(v) which corresponds to the dielectric constant of the sample. Fig. 5 illustrates the frequency dependence of the dielectric constant e1 for p-quaterphenyl at different temperatures. It is clear from the figure that e1 decreases with increasing frequency. The observed decrease of e1 with frequency is greater at lower frequency, which can be attributed to the fact that the value of e1, at low frequencies, for polar materials is due to the contribution of multicomponent of polarization mechanisms (electronic, ionic, orientation and interface). In other words, when the frequency of the field is much less than the inverse of relaxation time t (i.e., «1/t ), electric dipoles follow the field and e1  es (es = low frequency value of e1 or value of dielectric constant at quasistatic fields). As the frequency is increased (v < 1/t ), dipoles cannot rotate sufficiently rapidly, so that their oscillations lag behind those of the field and dielectric constant e1 slightly decreases. When the frequency becomes the characteristic frequency (v = 1/t ), e1 drops suddenly indicating relaxation process. At very high frequency (v » 1/t ), dipoles can no longer follow the field and the orientation polarization stops and e1  e1 (e1 = high frequency value of e1). So e1 decreases approaching a constant value at high frequencies due to the interfacial polarization only, which is effective in multiphase materials [30]. This qualitative behavior may be observed in Fig. 5. The dielectric constant gradually decreases with increasing frequency and becomes almost frequency independent at higher frequency region.

-14

0.12 0.10

-16

0.08

-17

-18

-19

ΔEac(eV)

lnσac (Ω . m)

−1

-15

0.6 kHz 1.5 kHz 6.0 kHz 15.0 kHz 60.0 kHz 150 kHz

0.06 0.04 0.02

-20

0.00

2.4

2.6

2.8

3.0

3.2

3.4

-1

1000/T(K)

Fig. 3. Temperature dependence of s ac(v) of bulk p-quaterphenyl at different frequencies .

0.0

5.0x10

4

1.0x10

5

1.5x10

5

ω(Hz) Fig. 4. Variation of AC activation energy with frequency for bulk p-quaterphenyl.

142

A.A. Attia et al. / Synthetic Metals 205 (2015) 139–144

26 301 K 318 K 343 K 363 K 383 K 403 K 423 K

24 22 20

ε1

18 16 14 12 10 8 8

10

12

14

16

lnω Fig. 5. Frequency dependence of dielectric constant e1 of bulk p-quaterphenyl at different temperatures.

Fig. 6 shows the temperature dependence of the dielectric constant e1 at different frequencies for p-quaterphenyl. It is clear from the figure that e1 increases as the temperature increases over the whole investigated range of frequency. The increase of e1 with temperature can be attributed to the fact that dipoles in polar materials cannot orient themselves at low temperatures. When the temperature is raised, the orientation of the dipoles is facilitated and thus increases the orientational polarization, and in turn increases e1. 3.4. Dielectric loss, e2 The imaginary part of the complex dielectric constant is e2(v) which corresponds to the dielectric loss of the sample. Dielectric relaxation studies are important to understand the nature and the origin of dielectric losses, which in turn, may be useful in the determination of the structure and defects in solids. When an electric field acts on any matter, the latter dissipates a certain quantity of electric energy that transforms into heat energy. This phenomenon is commonly known as loss of power, meaning an

average electric power dissipated in matter during a certain interval of time. The amount of power losses in a dielectric under the action of the applied field is commonly known as dielectric losses [21]. Fig. 7shows the frequency dependence of dielectric loss e2 for p-quaterphenyl at different temperatures. At lower frequency range, dielectric loss e2 is rather high for all temperatures, and decreases with increasing frequency and it increases with increasing temperature similar to the dependence of dielectric constant on temperature. This indicates the thermally activated nature of the dielectric relaxation of the sample. The decrease of e2 with the increase in frequency can be attributed to the fact that the value of e2, at low frequencies, is due to the migration of ions in the material. At moderate frequencies, the value of e2 is due to the contribution of ions jump, conduction losses of ions migration and ions polarization losses. At high frequencies, ions vibrations may be the only source of dielectric loss and so e2 has the minimum value [28]. An analysis of the data obtained for the frequency dependence of dielectric loss shows that e2 follows a power law with angular frequency v as Ref. [31]:

e2 ¼ Bvm

(4)

where B is a constant and m is the frequency power factor. Fig. 8 represents the relation between ln e2 versus ln v for p-quaterphenyl, which is found to be straight lines in frequency range beginning from about the characteristic frequency up to the end of the investigated range for each constant temperature. The values of the power m were calculated from the slopes of the obtained straight lines in Fig. 8 as a function of temperature. It was found that m tends to decrease with increasing temperature. According to Giuntini model for dielectric relaxation [32]: m = 4kBT/Wm, where Wm is the maximum barrier height. Value of Wm was calculated from the slope of the linear variation of m versus T and was found to be 0.64 eV. Fig. 9 shows the temperature dependence of dielectric loss e2 of p-quaterphenyl at different frequencies. The increase of e2 with temperature can be explained by Stevels and Fouad et al. [33,34] who divided the relaxation phenomena into three parts, conduction loss, dipole loss and vibrational loss. At low temperatures, the conduction, dipole and vibrational losses have minimum values since they are proportional to (s /v). As the temperature increases, s increases and so the conduction loss increases. This increases the value of e2 with increasing temperature. 5

0.6 kHz 1.5 kHz 6.0 kHz 15 kHz 60 kHz 150kHz

20

18

301 K 318 K 343 K 363 K 383 K 403 K 423 K

4

16

ε1

ε2

3

14

2 12

1 10 300

320

340

360

380

400

420

T(K) Fig. 6. Temperature dependence of dielectric constant e1 of bulk p-quaterphenyl at different frequencies.

8

10

12

14

16

lnω Fig. 7. Frequency dependence of dielectric loss e2 of bulk p-quaterphenyl at different temperatures.

A.A. Attia et al. / Synthetic Metals 205 (2015) 139–144

143

0.0 301K 318K 343K 363K 383K 403K 423K

-0.2

0.10

M1

lnε2

-0.4

0.12

-0.6

0.08

-0.8

301 K 318 K 343 K 363 K 383 K 403 K 423 K

0.06 -1.0

0.04 -1.2 10

11

12

13

14

15

16

Fig. 8. Plot of ln e2 versus ln v of bulk p-quaterphenyl at different temperatures.

3.5. Electric modulus analysis Dielectric relaxation studies can be obtained from the dielectric modulus representation that in the absence of a well-defined e2(v) peak [35]. From the physical point of view, the electrical modulus corresponds to the relaxation of the electric field in the materials when the electric displacement remains constant. The complex dielectric modulus M*(v) is defined by [36–38]: 1

e  ðvÞ

¼

1 ; ½e1 ðvÞ þ ie2 ðvÞ

M  ðvÞ ¼ M1 þ iM2 and M1 ¼

e1

e2

; M2 ¼ 2 ðe21 þ e22 Þ ðe1 þ e22 Þ

3.5

10

12

14

16

lnω

lnω

M  ðvÞ ¼

8

(5)

Fig. 10. Frequency dependence of real part of electric modulus M1 of bulk pquaterphenyl at different temperatures.

where e*(v) is the complex dielectric permittivity. Based on Eq. (5) we have changed the form of presentation of the dielectric data from e1(v) and e2(v) to M1(v) and M2(v) The obtained modulus spectra M1(v) and M2(v) are depicted in Figs. 10 and 11, respectively. Data presented in this way exhibit a pronounced relaxation peak for M2(v) that moves toward higher frequencies with increasing temperature showing the thermally activated nature of the relaxation time t . The frequency region below peak maximum determines the range in which charge carriers are mobiles on long range distances and above peak maximum, the carriers are confined to potential wells being mobile on short distances. As a convenient measure of the characteristic relaxation time t , one can choose the inverse of frequency of the maximum peak position, i.e., t = vm1. Thus, we can determine the temperature dependence of the characteristic relaxation time as shown in the inset of Fig. 11, which satisfies Arrhenius law:   E t ¼ t o exp R (6) kB T

0.6 kHz 1.5 kHz 6.0 kHz 15 kHz 60 kHz 150kHz

3.0

ε2

2.5

2.0

1.5

1.0

0.5 300

320

340

360

380

400

420

T(K) Fig. 9. Temperature dependence of dielectric loss e2 of bulk p-quaterphenyl at different frequencies.

Fig. 11. Frequency dependence of imaginary part of electric modulus M2 of bulk pquaterphenyl at different temperatures; the inset figure represents the plot of ln t versus 1000/T.

144

A.A. Attia et al. / Synthetic Metals 205 (2015) 139–144

where ER is activation energy of the relaxation process and t o is the relaxation time at infinite temperature. Values of ER and t o were calculated from the slope and intercept of the linear variation of ln t versus 1000/T which equal 0.02 eV and 24.5 ms, respectively. The relaxation time is decreased due to the dipoles following the motion of the alternating field due to dissipated thermal energy. Fig. 10 shows that the values of M1(v) increase with frequency and reach a maximum at a constant value due to the relaxation process. At the lower frequencies, M1(v) approaches to zero. This suggests that the electrode polarization is removed [39,40]. The values of the real part of the modulus at limiting high frequency M1 are calculated at different temperatures from the saturation of the Fig. 10 at the maximum frequency (2.4 MHz). Accordingly, the high frequency dielectric constant e1 can be calculated according to e1 = 1/M1. The value of e1 was found to increase with increasing temperature in the range of 8.33–9.37 corresponding to the temperature range of 301–423 K.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]

4. Conclusions The frequency and temperature dependence of the AC conductivity, dielectric constant and dielectric loss of bulk p-quaterphenyl in a pellet form were investigated in the frequency range of 200 Hz–2.4 MHz and temperature range of 301–423 K. The X-ray diffraction of the sample in powder form shows monoclinic structure at room temperature. The AC conductivity increases with increasing frequency. s ac(v) was explained in terms of the correlated barrier hopping (CBH) model. The AC conductivity is thermally activated process. The activation energy DEac of AC conduction decreases with increasing frequency. The values of density of localized states N(EF) near the Fermi level were calculated for the investigated range of temperature and frequency. The dielectric constant (e1) decreases with increasing frequency while increases as the temperature increases. The frequency dependence of dielectric loss shows that e2 follows a power law as e2 = Bvm. Similar to the dependence of dielectric constant (e1) on temperature, the dielectric loss (e2) increases with increasing temperature. The temperature dependence of the dielectric loss (e2) is associated with the conduction, dipole and vibrational losses. Dielectric relaxation studies were obtained from the dielectric modulus. The dielectric relaxation of the system has a thermally activated nature. The relaxation time decreases with the increase in temperature. The high frequency dielectric constant e1 increases with increasing temperature.

[20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40]

C.W. Tang, Appl. Phys. Lett. 48 (1986) 183–185. G.D. Sharma, S.G. Sangodkar, M.S. Roy, Mater. Sci. Eng. B 41 (1996) 222–227. D.D.C. Bradley, Synth. Met. 54 (1993) 401–415. G.D. Sharma, D. Saxena, M.S. Roy, Synth. Met. 106 (1999) 97–105. N.M. Amar, A.M. Saleh, R.D. Gould, Appl. Phys. A 76 (2003) 77–82. A. Shwani, K. Sharma, K.L. Bhatia, J. Non-Cryst. Solids 109 (1989) 95–104. M. Pollak, Philos. Mag. 23 (1971) 519–542. A. Ghosh, J. Phys. Rev. B 42 (1990) 5665–5676. M. Pollak, G.E. Pike, Phys. Rev. Lett. 28 (1972) 1449–1451. X. Le Cleac’h, J. Phys. 40 (1979) 417–428. S.R. Elliott, Philos. Mag. B 36 (1977) 1291–1304. K. Shimakawa, Phil. Mag. B 46 (1982) 123–135. D.J. Gundlach, Y.Y. Lin, T.N. Jackson, D.G. Schlom, Appl. Phys. Lett. 71 (1997) 3853–3855. J. Swiatek, D.C. Larson, Acta Phys. Acad. Sci. Hung. 46 (1979) 101–112. S. Kania, A. Lipinski, W. Mycielski, Thin Solid Films 72 (1980) L11–L13. H.M. Abdelmoneim, Indian J. Pure Appl. Phys. 48 (2010) 562–570. A. Dutta, C. Bharti, T.P. Sinha, Indian J. Eng. Mater. Sci. 15 (2008) 181–186. R. Shirley, The CRYSFIRE System for Automatic Powder Indexing: User’s Manual, The Lattice Press, Guildford, Surrey GU2 7NL, England, 2000. J. Laugier, B. Bochu, LMGP-Suite of Programs for the Interpretation of X-ray Experiments, ENSP/Laboratoires des Materiaux et du Genie Physique BP 46.38042, Saint Martin d’Heres, France, 2000. M.M. El-Nahass, A.A. Attia, G.F. Salem, H.A.M. Ali, M.I. Ismail, Physica B 434 (2014) 89–94. F. Yakuphanoglu, I.S. Yahia, B.F. Senkal, G.B. Sakr, W.A. Farooq, Synth. Met. 161 (2011) 817–822. S.R. Elliott, Adv. Phys. 36 (1987) 135–218. M.A. Ahmed, U. Seddik, N.G. Imam, World J. Condens. Matter Phys. 2 (2012) 66–74. I.G. Austin, N.F. Mott, Adv. Phys. 18 (1969) 41–102. M.A. Ahmed, N. Okasha, R.M. Kershi, J. Magn. Magn. Mater. 321 (2009) 3967–3973. S.R. Elliott, Solid State Commun. 28 (1978) 939–942. V.K. Bahatnagar, K.L. Bhatiam, J. Non-Cryst. Solids 119 (1990) 214–231. A.E. Bekheet, N.A. Hegab, Vacuum 83 (2009) 391–396. F. Yakuphanoglu, E. Evin, M. Okutan, Physica B 382 (2006) 285–289. D.K. Mahato, A. Dutta, T.P. Sinha, Bull. Mater. Sci. 34 (2011) 455–462. M.A.M. Seyam, A.E. Bekheet, A. Elfalaky, Eur. Phys. J. Appl. Phys. 16 (2001) 99–104. J.C. Giuntini, J.V. Zanchetta, J. Non-Cryst. Solids 34 (1982) 419–424. J.M. Stevels, in: S. Flügge (Ed.), Handbuch der Physik, vol. 20, Springer- Verlag, Berlin, 1957, pp. p. 350. S.S. Fouad, A.E. Bekheet, A.M. Farid, Physica B 322 (2002) 163–172. R. Ayouchi, D. Leinen, F. Martin, M. Gabas, E. Dalchiele, J.R. Ramos-Barrado, Thin Solid Films 426 (2003) 68–77. R.K. Dixon, Phys. Rev. B 42 (1990) 8179–8185. A. Oueslati, F. Hlel, K. Guidara, M. Gargouri, J. Alloys Compd. 492 (2010) 508–514. H. Smaoui, L.E.L. Mir, H. Guermazi, S. Agnel, A. Toureille, J. Alloys Compd. 477 (2009) 316–321. F.S. Howell, R.A. Bose, P.B. Macedo, C.T. Moynihan, J. Phys. Chem. 78 (1974) 639–648. P.S. Anantha, K. Hariharan, Mater. Sci. Eng. 121 (2005) 12–19.