AC conductivity and dielectric properties of SiO2–Na2O–B2O3–Gd2O3 glasses

Journal of Alloys and Compounds 579 (2013) 394–400

Contents lists available at SciVerse ScienceDirect

Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom

AC conductivity and dielectric properties of SiO2–Na2O–B2O3–Gd2O3 glasses Ragab M. Mahani a,⇑, Samir Y. Marzouk b a b

Microwave Physics and Dielectrics Department, National Research Centre, 12311 Dokki, Cairo, Egypt Arab Academy of Science and Technology, Faculty of Engineering, P.O. Box 2033, Al Horria, Heliopolis, Cairo, Egypt

a r t i c l e

i n f o

Article history: Received 17 September 2012 Received in revised form 19 May 2013 Accepted 24 May 2013 Available online 14 June 2013 Keywords: Borosilicate glass Gadolinium oxide Permittivity Conductivity

a b s t r a c t The present paper studies the dielectric properties and ac conductivity of sodium borosilicate glasses doped with varying concentrations of Gd2O3, while maintaining the SiO2:Na2O:B2O3 ratios constant for all compositions. The samples were prepared using rapid quenching method. Their dielectric and electrical properties were measured in the frequency range (102–106 Hz) and temperature range (298–523 K). Experimental results showed that all dielectric and electrical properties are dominated by mole% of Gd2O3. The decrease and increase in these properties were found to be due to formation of short range ordered structure and non-bridging oxygen, respectively. Different models were suggested to describe the conduction mechanism of the investigated compositions based on mole% of Gd2O3. Correlated barrier hopping model (CBH) was suggested to describe the conduction mechanism of 0–2.52 mole% Gd2O3 doped – samples. While, overlapping large polaron tunneling (OLPT) model was applied to describe conductivity of 2.83 mole% Gd2O3 doped sample. Interestingly, an inverse – OLPT model was suggested to describe the conduction mechanism of composition doped with 3.13 mole% of Gd2O3. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction Borosilicate glasses are of great importance because of their technological and scientifically applications. Glasses of this type are widely used in many applications ranging from chemically resistant laboratory glassware, host materials for encapsulation of radioactive waste to optical components and sealing materials [1]. Existing of B2O3 in the present glasses, forms a network structure and produces a glass with a higher melting point in addition a greater ability to withstand temperature changes [2]. In addition, borosilicate glasses have been known the excellent host matrices for the rare earth oxides because of their good glass forming nature compared to several other conventional systems. So, borosilicate glasses containing rare earths are found to have unique optical, thermal, mechanical, electrical and magnetic properties [3–6]. Nevertheless, most studies concerning rare earth doped borate glasses were mainly explored for optical applications [7–9]. Understanding the conduction mechanisms in these disordered materials provides a more comprehensive image of the system dynamics and transport mechanisms. Electrical properties of borosilicate glasses doped with rare earth have been extensively stud-

⇑ Corresponding author. Tel.: +20 1227821431; fax: +20 233371362. E-mail address: [email protected] (R.M. Mahani). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.05.173

ied [10–17]. However, no attempt was done to study the electrical properties of these glasses when doped with gadolinium oxide. In order to extend the available information concerning the rare earth doped glasses, an attempt is made to study how the electrical conductivity as well as dielectric properties are changed with varying Gd+3 ions content in the SiO2–Na2O–B2O3 glass network by means of dielectric spectroscopy. Gadolinium oxide (Gd2O3) is chosen as a doping of this study because of its high permittivity and a wide energy band gap (5.4 eV), good thermal stability that make it as a promising material [18,19]. The role of Gd2O3 in oxide glasses is of particular interest because it may serve as a network modifier. The samples under investigation were prepared by rapidquenching method. Their electrical and dielectric properties were measured over a frequency range (102–106 Hz) and temperature range (298–523 K).

2. Experimental work 2.1. Preparation of glasses Sodium borosilicate glasses doped with different mole% Gd2O3 are prepared by rapid-quenching method. Batches of each glass composition are listed in Table 1. The analytical-grade materials of purity more than 99.9% of SiO2, Na2CO3, H3BO3, and Gd2O3 chemicals were used to prepare the glass samples. Required amounts in wt% of chemicals in powder form are weighted using a digital balance (HR200) having an accuracy of ±0.0001 g. The homogeneity of the chemicals mixture

395

R.M. Mahani, S.Y. Marzouk / Journal of Alloys and Compounds 579 (2013) 394–400 Table 1 Compositions and Na2O/B2O3 ratio (R) of borosilicate glasses doped with Gd2O3 from 0 to 3.13 mole%. Glass compositions (mole%)

Na2O/B2O3 (R)

SiO2

Na2O

B2O3

Gd2O3

76.40 75.91 75.42 74.47 74.24 74.00

14.80 14.70 14.60 14.44 14.39 14.35

8.80 8.73 8.68 8.57 8.54 8.52

0.00 0.64 1.28 2.52 2.83 3.13

3. Results and discussion 1.68 1.68 1.68 1.68 1.68 1.68

3.1. The frequency and temperature dependence

is achieved by repeated grinding using an agate mortar. The mixture is preheated at 673 K for 60 min (in platinum crucible) to remove H2O and CO2. The preheated mixture is then melted in a muffle furnace whose temperature is controlled at 1873 K for 60 min, and bubble-free liquid was obtained. The mixture is stirred intermediately in order to obtain homogeneous mixture. The molten mixture is then poured in a cubic-shaped split mold made of mild steel which had been preheated at about 675 K. Annealing is carried out for a period of 60 min at 723 K. Bulk glass samples of about 1  1  1 cm3 are thus obtained. For dielectric measurements, each glass sample is first ground on a glass plate using SiC abrasives by setting it in a holder to maintain the two opposite faces parallel and then polished with fine alumina abrasive and machine oil on a glass plate. Samples in the form of discs having thicknesses between 0.3 and 0.7 cm and constant diameters (0.8 cm) are coated with silver paste to ensure a good contact between the sample surfaces and the stainless steel electrodes of the cell capacitor. The variation in the sample thickness is found to be ±7 lm. The amorphous nature in all glass samples is confirmed using X-ray diffraction (XRD). 2.2. Dielectric measurements The electrical conductivity and dielectric properties are measured using a computerized LRC meter (Hioki model 3531 Z Hi Tester). The present experiments are carried out by applying an electromagnetic field in the frequency range 102– 106 Hz through glass within temperature range of 298–523 K at intervals of 25 K. One of the most important dielectric properties is the permittivity (e0 ) which is calculated using the following relation:

e0 ¼

Cd

ð1Þ

eo A

e00 ¼ e0 tan d

ð2Þ

where C is the capacitance of the measured sample in Farad, d is the thickness of the sample in meter, A is the cross sectional area of the sample and eo is the permittivity of free space (8.854  1012 Fm1) while e0 0 represents the dielectric loss i.e. the energy absorbed by the medium. Measuring the properties at different temperatures are carried out by inserting the sample between two cell electrodes and then is inserted into non-inductive furnace, used for heating the samples with constant rate. Temperature of samples is measured by thermometer placed in contact with it. The ac conductivity (rac) of the samples is estimated from the dielectric parameters. As long as the pure charge transport mechanism is the major contributor to the loss mechanism, rac as a function of dielectric loss can be estimated using the following relation:

rac ¼ xeo e00

where qb is the density of the buoyant, wa and wb are the sample weights in air and the buoyant, respectively. The experiment was repeated three times and the error in density measurement in all glass samples is ±5 kg/m3.

3.1.1. Dielectric properties The permittivity (e0 ) and the dielectric loss (e00 ) of Gd2O3 – doped samples are measured over a wide range of frequency and at various temperatures. Sample doped with 3.13 mole% of Gd2O3 is chosen as a representative example in this study, see Fig. 1. Both e0 and e0 0 show a decrease with increasing frequency. The decrease e0 may be due to dipolar polarization and interfacial polarization. The dipolar or molecular polarization arises from orientation of permanent dipoles in the direction of the electric field. While, interfacial polarization occurs due to impedance of mobile charge carriers by interfaces. Dielectric loss (e00 ) arises from two contributions: one from dielectric polarization process and the other from dc conduction. The large values seen in e0 and e00 at low frequency reflecting the effect of space charge polarization and/or the conducting charge carriers motion [22,23]. However, no distinct relaxation processes can be recognized in the dielectric relaxation spectra represented by e0 0 . This may be due to the ionic dc conductivity (rdc) effect that masks the possible relaxation processes. The real (M0 ) and imaginary (M00 ) part of electric modulus provide information about the ionic conduction mechanism in the absence of a well-defined dielectric loss peak [24]. Therefore, both properties of the investigated samples are investigated as a function of frequency as shown in Fig. 2. At lower frequencies, M0 exhibits very small values and tends to be zero indicating the absence of electrode polarization effect [25,26], see Fig. 2a. With increasing frequency, M0 shows an increase due to distribution of relaxation processes over a range of frequencies [27]. The region noticed between the low and high frequency plateau indicates the frequency range within which the ions (Gd3+, O2 and Na+) can move. In this region, a corresponding peak in M00 spectra is shown in Fig. 2b. The well-defined peak is noticed for compositions doped with 0–2.52 mole% of Gd2O3. This peak corresponds to the movement of charge carriers leading to dc conductivity (rdc). In contrast, the peak becomes much broader for sample doped with higher concentrations. Such behavior may be attributed to superposition of different relaxation processes that are associated to formation of non-bridging oxygen and different structural units. This result is discussed in more details in Section 3.2.3.1.

ð3Þ

where x = 2pt, is the angular frequency and t is the frequency of the applied electric field in Hertz. An alternative approach to investigate the electrical response of the glasses is to analysis the results using the real (M0 ) and imaginary parts (M0 0 ) of electrical modulus [20,21] as following:

M0 ¼

e0 e02 þ e002

ð4Þ

M 00 ¼

e00 e02 þ e002

ð5Þ

a

b

2.3. Density measurements Density of all glass samples was measured by Archimedes method and calculated by using the following relation:

q ¼ qb 

Wa Wa  Wb

ð6Þ

Fig. 1. Frequency dependence of the real (e0 ) and imaginary part (e0 0 ) of sodium borosilicate glasses doped with 3.13 mole% of Gd2O3, measured at different temperatures.

396

R.M. Mahani, S.Y. Marzouk / Journal of Alloys and Compounds 579 (2013) 394–400

0.4

a

At 473 K

At 473 K

b

0.20

0.15

0.3

0.10 M''

M' 0.2

0.05

0.1

0.0

0.00 10

2

10

3

10

4

10

5

10

6

10

2

10

3

υ / Hz 0.00 mole % Gd 2 O 3 0.64 mole % Gd 2 O3

10

4

10

5

10

6

υ / Hz 2.83 mole % Gd2 O3 3.13 mole % Gd2 O3

1.28 mole % Gd 2 O3 2.52 mole % Gd 2 O3

Fig. 2. Frequency dependence of the real (M0 ) and imaginary part (M0 0 ) of electrical modulus at 473 K for sodium borosilicate glasses containing different mole% of Gd2O3.

-6.0 -7

0.64 mole % of Gd2 O3

0.00 mole % 0.64 mole % 1.28 mole % 2.53 mole % 2.83 mole % 3.13 mole %

-8 298K 323K 348K 373K 398K 423K 448K 473K 498K 523K

-9

-10

2

3

4

5

6

log σdc [S / cm]

log σac (S/cm)

II -7.5

I

-9.0

-10.5

log (υ / Hz) Fig. 3. The frequency dependence of rac of borosilicate glasses containing 0.64 mole% of Gd2O3. rac is measured in the temperature range from 298 to 523 K.

2.0

2.4

1000/T K 3.1.2. Electrical conductivity 3.1.2.1. ac conductivity. It is pointed out that the frequency dependence electrical conductivity r(x) in solids arises from the flow of current occurs by hopping of localized carriers whether electrons or ions. For the investigated samples, the frequency and temperature dependence of conductivity (r) of each glass composition is studied. Sample doped with 0.64 mole% Gd2O3 is taken as a representative example, see Fig. 3. At low frequencies and high temperature, r shows frequency independent nature (plateau nature) which gives rise to dc – conductivity (rdc) arising from the random diffusion of the ionic charge carriers via activated hopping process [28]. This process is discussed above in terms of real and imaginary parts of electrical modulus. Values of rdc are obtained by extrapolating r to zero frequency using Jonsher equation [29]. At higher frequencies, r shows frequency dependence which gives rise to ac – conductivity (rac). In this case, rac increases roughly in a power law fashion; rac(x) = Axs and eventually becomes almost linear at even higher temperatures [30]. Where, A is temperature-dependent constant and s is a frequency exponent that depends on temperature. According to hopping theory, if hopping takes place between localized states with random distribution, rac directly proportional to xs, where 0.5 < s < 1. It is known that the low values of s indicate multi hopping process while high values of s indicate single hopping process [31]. This leads one to conclude that the conduction mechanism is single hopping for all compositions at the different temperatures except that for 0, 0.64 and 2.52 mole% of Gd2O3 which are multi hopping at temperatures higher than 498 K. The observed increase in rac of borosilicate glasses at high frequencies is due to the local motion of Na+ cations [32] envisaged by

2.8

3.2

-1

Fig. 4. The temperature dependence of rdc of the borosilicate glasses doped with 0– 3.13 mole% of Gd2O3. The symbols represent the measured data while thin lines represent fitting the data with linear equation. The vertical dashed line separates regions I and regions II where rdc changes with temperature at different rates.

single ionic jump diffusion mechanism as proposed by several authors [33,34]. 3.1.2.2. dc conductivity. The dc electrical conductivity (rdc) of borosilicate doped with different mole% of Gd2O3 is measured in a temperature range of 298–523 K as shown in Fig. 4. rdc shows an Arrhenius behavior in the temperature ranges from 298 to 423 K and from 448 to 523 K in regions I and II, respectively. The conductivity data may be fitted to straight lines, where conductivity can be analyzed by an Arrhenius equation of the form [35–37]:



rdc ¼ ro exp 

DE KT

 ð7Þ

where ro is the pre-exponential factor and DE is the activation energy for conduction. ro and DE are determined for each conduction region as listed in Table 2. Fitting the data by the above equation, four parameters can be given namely; rI, DEI for the first conduction region (I) in addition rII and DEII are given for the second conduction region (II). The activation energy noticed at higher temperature (DEII) shows higher values comparing with that noticed at lower temperatures (DEI). The lower and higher values of activation energies could be attributed to the intermolecular and intramolecular conduction process, respectively. Accordingly, there are two stages of carrier motion within the studied compositions, which are the intramolecular and intermolecular transfer of the

397

R.M. Mahani, S.Y. Marzouk / Journal of Alloys and Compounds 579 (2013) 394–400 Table 2 Values of rI, rII, DEI and DEII obtained from analyzing (rdc) are listed for borosilicate glasses containing from 0 to 3.13 mole% of Gd2O3. Gd2O3 (mole%)

rI (S/cm)

rII (S/cm)

DEI (eV)

DEII (eV)

0.0 0.64 1.28 2.52 2.83 3.13

9.6  109 3.16  109 5.42  108 1.41  105 4.47  107 4.26  105

0.0042 0.02917 0.32063 0.43662 0.45709 1.26343

0.026 0.018 0.038 0.067 0.043 0.063

0.108 0.126 0.138 0.136 0.132 0.121

current carrier. In the intramolecular transfer of electrons, electrons can hop from one atomic site to another if orbitals exist at these sites with the same energy levels. While, in intermolecular orbital overlap, electrons or holes can travel from one kind of macromolecule to another. If we assume excited carriers within the molecules, the carriers are retarded by the barrier macromolecules. The activation energy of the intramolecular conduction process is higher. Therefore, the first step of conduction starts between molecules since the lower activation energy corresponds to intermolecular transfer, while the higher activation energy corresponds to intramolecular transfer [36,37]. It also noticed from Table 2 that values of rI are smaller than that compared to rII which attributes partially to the smaller density of states and mainly because the charge carriers have a much lower mobility. On the other hand, the decrease in activation energies with increasing Gd2O3 could be attributed to formation of nonbridging oxygen whereas the increase activation energy is due to short range ordered structure formed in the glass network. Effect of Gd2O3 is discussed in detalis below (see Section 3.2). 3.1.3. Density of states The relationship between rac and the density of states at Fermi level N(EF) is determined by the following relation:

h m i4 p rac ðxÞ ¼ e2 KT½NðEF Þ2 a5 x ln ph 3 x

ð8Þ

where a is the exponential decay parameter of localized state wave function, and tph is the phonon frequency, e is the electronic charge, K is the Boltzmann’s constant (8.617  105 eV K1). N(EF) of all compositions can be calculated from this relation by assuming tph = 1013 Hz and a1 = 10 Å [38]. The calculated values are plotted as a function of temperature over different frequencies. Samples doped with 0 and 3.13 mole% of Gd2O3 are chosen as representative examples in this study, see Fig. 5. It is clear that N(EF) increases with increasing temperature and frequency. Similar behavior is found for all compositions studied. This is may be attributed to changes

a

3.2. The composition dependence Before going on discuss the effect of Gd2O3 on properties of borosilicate glasses, it is important to specify of Na2O/B2O3 ratio (R) in these glasses. It is noted that the alkali ion prefers to associate with the boron as long as R < 0.5. So that boron presumably converts BO3 units to BO4 units and creating no NBO in the glass network structure [39]. But for the investigated compositions, it is noticed that R > 0.5 (1.68) as shown in Table 1. In this case, most of Na+ together with Gd3+ ions have combined effects to transfer the SiO4 tetrahedral units (Q4) with four bridging oxygen to SiO4 (Q3) with three bridging oxygen and one non-bridging oxygen in addition the change in BO4 to BO3 units. Consequently, increase in the number of NBOs [40]. This means that Gd2O3 acts as a modifier oxide that becomes part of the glass by modifying the three dimensional network and modifier cations reside in the interstitial space of the network as positive ions. 3.2.1. Density and molar volume The compositional dependence of both density (q) and molar volume (VM) of borosilicate glasses modified by Gd2O3 are shown in Fig. 6. It is clear that as Gd2O3 content increases, q increases with two different rates indicating non-linear behavior. So, q slightly increases with increasing Gd2O3 from 0 to 2.52 mole% and then remarkably increases for doped compositions at higher concentrations. The increase in density with Gd2O3 indicates that replacing SiO2 by addition of small amount of Gd2O3 results in an increase of molecular weight of the oxide ions in the glass. Consequently, an increase in density of the glasses containing Gd3+ comparing to that obtained for SiO2. This is due to the density of Gd2O3 (7.90 g cm3) is more than that indicated for SiO2 (2.648 g cm3). Also, VM shows an increase for samples doped from 0 to 2.52 mole% of Gd2O3; confirming incorporation of Gd2O3 does not fill the network structure, leading to the expansion of the net work structure and consequently the formation of more open structure. In addition to this, the increase in VM is attributed to the increase in NBOs. While, VM shows a decrease for samples containing Gd2O3 from 2.52 to 3.13 mole% that may reflect compaction of these glasses. In this case, incorporation of Gd2O3 will act to fill the interstices of the net work structure and consequently the formation of close packed structure increases. Similar behaviors reported [41,42] that the incorporation of Gd2O3 and Er2O3 in the net works of telluride and borosilicate glasses, respectively, showed a decrease in their molar volumes confirming the filling action of the

b

0 mole % Gd 2 O3

6

3.13 mole % Gd 2O3

2

4

10 Hz

4

3

10 Hz 5

10 Hz 5

2

5X10 Hz

2

6

10 Hz

0

N (E) eV-1cm*10 23

N (E) eV -1cm*10 23

6

occurring in width of the localized states of the band structure and consequently an increase in rac.

0 300

400

T/K

500

300

400

500

T/K

Fig. 5. The temperature dependence of density of states N (EF) of Gd2O3 – free sample (a) and that doped with 3.13 mole% (b). The measurements are carried out at different frequencies.

398

R.M. Mahani, S.Y. Marzouk / Journal of Alloys and Compounds 579 (2013) 394–400

27

2900 ρ

298 K 373 K 473 K

VM

ρ [kg / m3 ]

26

2700 25

VM [m 3 / mole]

2800

ε' 10

2600 0

1

2

3

24

1 0

mole % of Gd 2O3

2

4

6

8

10

Gd2O3 / wt %

Fig. 6. Mole% of Gd2O3 dependence of density (q) and molar volume (VM) of borosilicate glasses.

Fig. 8. The permittivity (e0 ) of sodium borosilicate glasses as a function of Gd2O3 contents. The measurements are carried out at 1 kHz and different temperatures namely; 298, 373 and 473 K.

ε'

2

10

ε'' 2

10

N(Ef )

4

σ -6

2

3

N (Ef )*10 23

10

1

10

σ [kg / m ]

1

ε''

ε'

10

0 -7

0

10 0

1

2

10

3

mole % of Gd 2O3 Fig. 7. Mole% of Gd2O3 dependence of permittivity (e0 ) and dielectric loss (e0 0 ) of borosilicate glasses measured at 500 Hz and 473 K.

-2

0

1

2

3

mole % of Gd2O3 Fig. 9. Mole% of Gd2O3 dependence of density of states N(Ef) and conductivity (r) of borosilicate glasses measured at 5  105 Hz and 523 K.

interstices of their network structures. These features indicate a more complicated mechanism that must be used to explain the molar volume composition relation. 3.2.2. Dielectric properties The permittivity (e0 ) and dielectric loss (e00 ) dependence of Gd2O3 content is investigated at constant frequency (500 Hz) and constant temperature (473 K) as presented in Fig. 7. It is evident that both e0 and e00 gradually increase with increasing Gd2O3 content till 2.52 mole% then they remarkably increase at higher concentrations. The decrease in e0 at low concentrations of Gd2O3 may be due to short range ordered structure formed in the glass network. This ordered structure increases density and thus a decrease in charge carriers mobility and dipole polarization and consequently a decrease in e0 . The noticeable increase in e0 at higher concentrations arises from increasing of NBOs [41,42]. This can be explained as NBOs increases, connectivity of the glass network structure decreases as the main bonds of the network Si–O–Si changes to Si–O–Gd with different average bond length and consequently an increase in e0 is obtained. In order to clarify the effect of Gd2O3, e0 of all compositions is studied at constant frequency (1 kHz) and different temperatures namely; 298, 373 and 473 K as shown in Fig. 8. At all temperatures, a gradual increase of e0 with increasing Gd2O3 content up to 2.52 mole% that followed by a remarkable increase at higher concentrations. The rate of change at higher temperatures seems to be higher than those observed at low temperatures. This is due to the expected contribution of the ionic conductivity. Greater nobilities of Gd3+, O2 and Na+ ions are bind to different localized

states and when they acquire thermal energy they move freely through the glass network structure. So, the increase in temperature induced an expansion of molecules causing an increase in the polarization of charge carriers and hence an increase in e0 [43–45]. The increase in temperature may result in weakens of the intermolecular forces and hence enhances the orientational vibration, (ii) it increases the thermal agitation and hence strongly disturbs the orientational vibrations. Consequently, an increase in e0 is expected. This result seems to be in good agreement with that reported in oxide glasses [46]. 3.2.3. Density of states and ac conductivity In this part of work, the composition dependence of density of states, N(EF) and ac conductivity (rac) is studied at 5  105 Hz and 523 K as shown in Fig. 9. It is evident that both parameters nearly have the same behavior. N(EF) shows at first decrease upon adding 0.64 mole% of Gd2O3 and then followed by an increase with different rates at higher concentrations. So, the rate of increase becomes higher for doped samples at concentrations higher than 2.52 mole% of Gd2O3. While, rac shows a decrease with increasing Gd2O3 up to 1.28 mole% and then it remarkably increases at higher concentrations. The increase in both N(EF) and rac with increasing Gd2O3 is also attributed to the increase in NBOs. So, NBOs causes a band tailing into the gap (alteration in structure) and thus a decrease in the bond strength. Consequently, Na+ and Gd3+ ions become more freely to jump from site to the next in the glass network structure causing an increase in rac. On the other hand,

R.M. Mahani, S.Y. Marzouk / Journal of Alloys and Compounds 579 (2013) 394–400 0.00 mole % 0.64 mole %

Gd 2O3 Content

a 1.0

4. Conclusion

2.83 mole % 3.13 mole %

1.28 mole % 2.52 mole %

Inverse OLPT

b

1.1

1.0

0.8

S

S 0.9

0.6

0.4

0.8 OLPT

300

400

T/K

500

300

400

399

500

T/K

Fig. 10. The temperature dependence of frequency exponent (s) of borosilicate glasses containing different mole% of Gd2O3. The vertical dashed line indicates the temperature at which s changes with different rates.

the observed decrease in both properties at low concentrations of Gd2O3 may be attributed to short range ordered formed in the glass structure that disappears at higher concentrations. So, ordered structure even is small affects mobility of the charge carriers whether electrons or ions so that it hindrances the motion of carriers and thus a decrease in conductivity. From above one can be concluded that the investigated properties of borosilicate glasses are dominated by short rang order structure and non-bridging oxygen respectively, at low and high mole% of Gd2O3. 3.2.3.1. Conduction mechanism. It is known that the frequency exponent (s) is used to indicate the modification of network structure [47]. Therefore, its dependence on compositions is investigated at different temperatures as shown in Fig. 10. Fig. 9a shows that s decreases with increasing temperature for glasses doped with 0, 0.64, 1.28 and 2.52 mole% of Gd2O3. This behavior is common interpreted by correlated barrier hopping model (CBH) [48], where electrons in charged defect states hope over a Columbic at the Fermi level. In case of doped samples from 2.83 to 3.13 mole% of Gd2O3, the situation becomes different. For glasses doped with 2.83 mole% of Gd2O3, s shows a decrease with increasing temperature to a minimum value that followed by an increase at higher temperatures as shown in Fig. 10b. Such mechanism can be interpreted by the overlapping large polaron tunneling (OLPT) model [49]. In this model, the polaron energy is derived from the polarization variations in the lattice [50]. Coulomb interaction takes place in long range; potentials of neighboring sites are in a state of overlapping on one another. This leads on to suggest that the superposition of relaxation processes associated to interaction of Gd3+ and Na+ ions with both SiO4 and BO4 may responsible for such overlapping. This assumption may be confirmed by the broadness seen in imaginary part of the electrical modulus (M00 ), see Fig. 2. Interestingly, an opposite behavior is noticed for glasses doped with 3.13 mole% of Gd2O3. So that s shows an increase with increasing temperature to a maximum value (indicated by the vertical dashed line at a particular temperature; 400 K) that followed by a decrease at higher temperatures. According to our knowledge, there is no any available model or theory considering this behavior. This leads one to suggest a new model called an Inverse – OLPT model. In this model, the relaxation processes associated to interaction of Gd3+ and Na+ ions with both SiO4 and BO4 are separated due to formation of different structural units. Consequently, the suggested overlapping process mentioned above may be disappeared.

In conclusion, the electrical and dielectric properties of sodium borosilicate doped with gadolinium oxide have been studied at various temperatures and frequency. Formation of short range ordered structure and non-bridging oxygen are suggest to be responsible respectively for the decrease and increase of all electrical properties measured. In this study, different models are used to describe the conduction mechanism based on Gd2O3 content. So that for samples doped with 0, 0.64, 1.28 and 2.52 mole% of Gd2O3, correlated barrier hopping (CBH) model is applied to describe their conduction mechanisms. While, overlapping large polaron tunneling (OLPT) model is applied to describe the conduction mechanism of 2.83 mole% Gd2O3 – doped sample. In this model we suggest that the superposition of relaxation processes associated to interaction of Gd3+ and Na+ ions with both SiO4 and BO4 may responsible for such overlapping. Interestingly, a new model called an Inverse – OLPT model is suggested to describe the conduction mechanism of 3.13 mole% Gd2O3 – doped sample. In this model, the relaxation processes associated to interaction of Gd3+ and Na+ ions with both SiO4 and BO4 are separated due to formation of different structural units.

References [1] D. Manara, A. Grandjean, D.R. Neuville, J. Non-Cryst. Solids 355 (50–51) (2009) 2528–2531. [2] S. Gopi, S. Kulwant, Manupriya, M. Shaweta, S. Harvinder, B. Sukhleen, Radiat. Phys. Chem. 75 (9) (2006) 59–966. [3] D. Maumita, K. Annapurna, P. Kundu, R.N. Dwivedi, S. Buddhudu, Mater. Letter. 60 (2006) 222. [4] B. Frank, V. Stephan, W. Arpad, Imre, Helmut Mehrer, J. Non-Cryst. Solids 351 (2005) 3816–3825. [5] C.K. Jayasankar, P. Babu, J. Alloy Comp. (1998). [6] Y.M. Samir, Physica B 405 (2010) 3395–3400. [7] G.S. Murugan, T. Suzuki, Y. Ohishi, Appl. Phys. Lett. 86 (16) (2005) 1109. [8] D. Xun, J. Yang, S. Xu, N. Dai, L. Wen, L. Hu, Z. Jiang, Chin. Phys. Lett. 20 (01) (2003) 130. [9] M.F. Churbanov, G.E. Snopatin, E.V. Zorin, S.V. Smetanin, E.M. Dianova, V.G. Plotnichenkoa, V.V. Koltasheva, E.B. Kryukovaa, I.A. Grishinb, G.G. Butsinb, J. Optoelectron. Adv. Mater. 07 (04) (2005) 1765. [10] A. Grandjean, M. Malki, C. Simonnet, J. Non-Cryst. Solids 352 (2006) 2731. [11] N. Nagaraga, T. Sankarappa, M. Prashant Kumar, Santosh Kumar, P.J. Sadashivaiahalah, Optoelectron. Adv. Mater. Rapid Commun. 2 (1) (2008) 22–25. [12] M. Prashant Kumar, T. Sankarappa, Optoelectron. Adv. Mater. Rapid Commun. 2 (4) (2008) 237–241. [13] R.K. Mishra, R. Mishrab, C.P. Kaushik, A.K. Tyagi, B.S. Tomar, D. Das, Kanwar Raj, J. Hazard. Mater. 161 (2009) 1450–1453. [14] V.K. Deshpande, Ramesh N. Taikar, Mater. Sci. Eng. B 172 (2010) 6–8. [15] Parvinder Kaur, Gurinder Pal Singh, Simranpreet Kaur, D.P. Singh, J. Mol. Struct. 1020 (2012) 83–87. [16] C.R. Gautam, Devendra Kumar, Om Parkash, O.P. Thakur, J. Ceram. (2013) 9. Article ID 879758. [17] Y. Xiong, K. Yamaji, N. Sakai, H. Negishi, T. Horita, H. Yokokawa, J. Electrochem. Soc. 148 (2001) E489. [18] B.A. Orlowski, E. Guziewicz, N.E. Orlowska, A. Bukowski, R.L. Johnson, Surf. Sci. 507–510 (2002) 218. [19] J.C. Chen, G.H. Shen, L.J. Chen, Surf. Sci. 142 (1999) 291. [20] C.R. Mariappan, G. Govindaraj, J. Non-Cryst. Solids 352 (2006) 2737. [21] P.B. Macedo, C.T. Moynihan, R. Bose, Phys. Chem. Glasses 13 (1972) 171. [22] R.W. Wagner, Arch. Electrotech. 2 (1914) 371. [23] R.W. Sillars, Inst. Elect. Eng. 80 (1937) 378. [24] S. Hazra, A. Ghosh, Phys. Rev. B 55 (10) (1997) 6278–6284. [25] F. Yakuphanoglu, Physica B 393 (2007) 139–142. [26] A. Dutta, T.P. Sinha, P. Jena, S. Adak, J. Non-Cryst. Solids 354 (2008) 3952–3957. [27] L.N. Patro, K. Hariharan, Mater. Chem. Phys. 116 (2009) 81–87. [28] Jeppe.C. Dyre, J. Appl. Phys. 64 (1988) 2456. [29] A.K. Jonscher, Nature 267 (1977) 673. [30] K. Otto, Phys. Chem. Glasses 7 (1966) 29. [31] M. Pollak, Philos. Mag. 23 (1971) 519. [32] K. Funke, Jump relaxation in solid electrolytes, Prog. Solid State Chem. 22 (1993) 111–195. [33] J.L. Souquet, M. Duclot, M. Levy, Solid State Ion. 105 (1998) 237–242. [34] Arpad W. Imre, Stephan Voss, Helmut Mehrer, J. Non-Cryst. Solids 333 (2004) 231. [35] F. Yakuphanoglu, Ph.D. thesis, Firat University, Elazig, Turkey, 2002.

400

R.M. Mahani, S.Y. Marzouk / Journal of Alloys and Compounds 579 (2013) 394–400

[36] Y. Aydogdu, F. Yakuphanoglu, A. Aydogdu, M. Sekerci, Y. Balci, I. Akosy, Synth. Metals 107 (1999) 191. [37] Y. Aydogdu, F. Yakuphanoglu, A. Aydogdu, E. Tas, A. Cukurovali, Solid State Sci. 4 (2002) 879. [38] V.K. Bhatnagar, K.L. Bhatia, J. Non-Cryst. Solids. 119 (1990) 214. [39] A.K. Varshneya, In: Fundamentals of Inorganic Glasses, Academic Press, NewYork, 1994. [40] M.S. Gaafar, S.Y. Marzouk, Physica B 388 (2007) 294. [41] Yasser.B. Saddeek, Mater. Chem. Phys. 91 (2005) 146.

[42] [43] [44] [45] [46] [47] [48] [49] [50]

S.Y. Marzouk, M.S. Gaafar, Solid State Commun. 144 (10–11) (2007) 478. D. Maurya, J. Kumar, Shripal, J. Phys. Chem. Solids 66 (2005) 1614. Dökme, S ß . Altindal, Physica B: Condensed Matter 391 (2007) 59. Dökme, S ß . Altindal, Physica B: Condens. Matter 393 (1–2) (2007) 328. A.A. Bahgat, Y.M. Abou-Zeid, Phys. Chem. Glasses 42 (2001) 01. M.M. El-Desoky, K. Tahoon, M.Y. Hassaan, Mater. Chem. Phys. (2001) 180. S.R. Elliott, Phil. Mag. B 36 (1977) 1291. A.R. Long, Adv. Phys. 31 (1982) 553. A. Ghosh, Phys. Rev. B 341 (1990) 1479.