Transport properties of super ionic AgI-Ag2O-V2O5-TeO2 ... - NOPR

Indian Journal of Pure & Applied Physics Vol. 48, January 2010, pp. 39-46

Transport properties of super ionic AgI-Ag2O-V2O5-TeO2 glasses Poonam Sharma, D K Kanchan*, Meenakshi Pant & K Padmasree1 Department of Physics, Faculty of Science, M S University of Baroda, Vadodara (Gujarat) 390 015 1

Cinvetav-Satillo, Carretera Saltillo-Monterrey km 13, 25900 Ramos arizpe, Coahuilla, MAXICO *E-mail: [email protected] Received 29 June 2009; revised 23 September 2009; accepted 7 October 2009

The conductivity of super ionic conducting glass system xAgI : ( 95-x) [Ag2O:2V2O5]: 5TeO2, where 40 ≤×≤65 has been studied by impedance spectroscopy. The spectrum has been recorded in temperature range 296-353 K with frequency range 10 Hz to 32 MHz. The glass samples have been characterized by X-ray, FTIR and DSC studies. The FTIR spectra reveal that the network structure remains essentially the same with AgI concentration. The temperature dependent conductivity satisfies the Arrhenius relationship. The measurements show that the conductivity increases from σ = 7.62×10−7 to 1.15×10−4 S/cm with increasing AgI content, while the activation energy decreases from 0.49 to 0.30 eV. The frequency dependence of the ac conductivity follows the Jonscher’s universal power law σ(ω) = σdc + Aωs. The dielectric properties are calculated using impedance data for all the glass samples. Keywords: Super ionic conductivity, Glass transition temperature, Impedance, Dielectric

1 Introduction The AgI-doped silver oxysalt systems have been studied since a long time because of their high ionic conductivity and good stability towards temperature and moisture1-3. Silver iodide is a prototype super ionic conductor, which undergoes a phase transition from wurtzite β-AgI to bcc α-AgI with 104 increase in the ionic conductivity. In β-AgI, the ionicconductivity is due to thermally activated Ag+ interstitials, while in α-AgI the cations diffuse between preferred sites in a very open structure. Glasses of silver based pseudo-binary and ternary compounds have been synthesized to improve the ionic conductivity of these electrolytes4. It was also found that the introduction of two network formers enhanced the ionic conductivity, as binary and ternary glasses have less glass forming region and low ionic conductivity as compared to quaternary super ionic glasses5. The AgI-Ag2O-V2O5, Ag2O-TeO2, AgI-Ag2O-TeO2 and V2O5-TeO2 based glass systems have been studied4,6-11, but very limited studies have been done on silver-based vanado-tellurite glasses11,12. High ionic conduction had been studied in AgI-Ag2O-V2O5 system due to the presence of the dopant AgI1,2. However, an increase in ionic conductivity in Ag2OP2O5 glass system is also observed due to introduction of Te ions13. In Ag2O-V2O5-TeO2 glass system, Ag2O causes the splitting of V-O-V and O-Te-O bonds, which are, converted into non-bridging oxygens

(NBOs) and bridging oxygens (BOs). Since, glassforming properties of V2O5 are moderate and it is difficult to obtain glasses with high V2O5 contents by classical techniques, hence to use another glass former TeO2 along with V2O5 is worth investigation. The glasses mixed with TeO2 possess the properties like low melting point, high refractive index and high dielectric constant. It has been observed that these glasses with low modifier content consist of a continuous random network constructed by sharing corners of TeO4 trigonal and TeO3 with NBO, which permeates the whole network. The XPS studies in Ag2O-V2O5-TeO2 glasses14 showed that various structural units of tellurium oxide groups restrict the intervalence transfer and thus, reduce the electron mobility. In this paper, the conductivity and relaxation mechanism in the system xAgI-(95-x)[Ag2O:2V2O5]5TeO2, where 40 ≤ x≤ 65 in steps of 5 has been studied. The effect of the addition of AgI in the glass with V2O5 and TeO2 as glass former on its transportmechanism and relaxation dynamics, and the influence of AgI on conductivity via structural alterations due to the presence of another former TeO2 have also been studied. 2 Experimental Details The glass samples were prepared by using the reagent grade chemicals. Appropriate amounts of AgI, Ag2O, V2O5 and TeO2 were weighed and then ground

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INDIAN J PURE & APPL PHYS, VOL 48, JANUARY 2010

in an agate mortar and pestle by wet grinding method. The mixture was kept in an alumina crucible in a controlled electric furnace at 673 K. Subsequently, the furnace was heated to 1073 K at a rate of 100 K/h and the melt was kept for 4 h at that temperature. After 4 hours, the melt was immediately poured on a heavy copper block kept at room temperature and pressed by another copper block to quench it. X-ray diffraction was carried by X-ray diffraction analyzer (Shimadzu) at 2°/min scan rate. The glass transition temperature of the amorphous samples was measured by differential scanning calorimeter at a heating rate of 10 K/min, by TA instruments (Model MBSE-2910). Fourier transform infrared (FTIR) spectra were measured in the range of 400-1100 cm−1 using an FTIR spectrophotometer (Bruker Model Vertex 70). Density of all the samples at room temperature was determined by the Archimedes method using methanol as the immersion fluid. Electrical properties were measured using an Impedance analyzer (Solartron 1260) in the frequency range of 10 Hz to 32 MHz from 296 to 353 K. The measurements were made by two-probe method in which quenched glass samples of about 1mm thickness were coated with silver paint to serve as electrodes. The samples were kept in contact with two polished, cleaned and spring-loaded copper electrodes. The ionic transference number was determined using the Wagner’s polarization technique.

characteristic bands. The IR spectra reveal absorption bands at 497 cm−1, a broad band in the range 650-740, 850, 900, 920 and 970 cm−1 and a small kink at 1020 cm−1. It is observed that there is no change in the position of any vibrational bands except a slight shift of the broad band in the range 650-740cm−1 towards higher frequency side. The band at 497 cm−1 is due to υsym stretching vibrations of V-O-V bridge of V2O7−4 groups15. This band is clearly observed for x=50 mol% while it is weak for other compositions. The broad band in the range of 650-740 cm−1 may be arising due to the presence of different bands of V-O-V and Te-O groups of varying lengths in this region. This broad band may be due to the stretching vibrations of the Te-Oax (axial) and Te-Oeq (equatorial) bonds in

3 Results and Discussion 3.1 XRD and DSC

X-ray diffraction (XRD) patterns of the powdered samples consisted of a wide halo without any diffraction lines of crystalline phases (Fig. 1), indicating the amorphous character of the samples. Differential scanning calorimetery is used to study the glass transition and crystallization process in quenched glasses. The glass transition temperature is indicative of the stability of a glass with most stable glass having the higher Tg. It has been observed that all the samples have nearly same glass transition temperature in the range of 362-365 K and crystallization temperature in the range of 433-442 K.

Fig. 1 — X-ray diffraction patterns of the glass samples

3.2 Infrared spectra

The presence of different structural groups in different compositions of the present super ionic glasses can be established from the infrared (IR) spectra (Fig. 2). All the spectra have the same

Fig. 2 — FTIR Spectra recorded for the different glasses

SHARMA et al.: TRANSPORT PROPERTIES OF SUPER IONIC GLASSES

deformed TeO4 groups at 665 cm−1, stretching vibrations of TeO3 of Te2O5 units at 680 cm−1 and symmetric V-O-V stretching vibrations16-18. The band at the position of 850 cm−1 is attributed to the asymmetric vibrations of the V-O-V bonds involved in the corner sharing of VO5 polyhedra18. The absorption bands at 895 and 917 cm−1 are assigned to VO3 terminal stretching of the pyrovanadate ions. The band at 966 cm−1 is assigned to symmetric stretching vibrations of the VO2 groups of the VO4 polyhedral. The similar band positions in the IR spectrum for AgI-Ag2O-V2O5 system are also reported by Arof and Radhakrishna2. A small kink observed at 1020 cm−1 is assigned to the vibrations of the non-bridging V=O of the VO5 groups19. In the present IR spectra study, no change in the positions of V2O5 bands (in the range of 850-1020 cm−1) has been observed, which is expected, because the ratio of Ag2O/V2O5 is fixed as 0.5 for all compositions. Although the amount of TeO2 is kept 5 mole%, its value with respect to Ag2O varies hence, it is the modifier, Ag2O, which may be responsible for causing any change in the vibration bands of TeO2 in the frequency range 650-740 cm−1. Several studies on AgI based systems revealed that the addition of AgI shows a little or no change in IR spectra, which implies that the network structure is not strongly affected by the addition of AgI2.

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3.3.1 Conductivity

Logarithmic conductivity as a function of inverse temperature for glass samples with different silveriodide compositions is plotted in Fig. 4. The figure shows that the dc conductivity (σdc) increases with temperature as well as with the concentration of AgI. The plots are straight lines indicating that the dc conductivity obeys the Arrhenius relation. The activation energy of conduction are measured from the slope of logσdc against 1000/T. Fig. 5 shows the dc conductivity and activation energy for all the samples of the present study. The dc conductivity is found to increase with the increase of AgI concentration and activation energy decreases with the same. The ac conductivity of the present glass samples has been measured in the frequency range 10 Hz to 32 MHz with the temperature range 296 to 353 K.

3.3 Impedance analysis

Complex plane plots of electrical impedance are usually used as a means of estimating dc conductivity. Impedance analysis (cole-cole plots) are shown in Fig. 3 for x= 50 mol% at various temperatures. It is seen that as the temperature is increased, all depressed semicircles shifted to higher frequency side i.e., the bulk resistance of the sample decreases with the increase of temperature, which is an indication of a thermally activated conduction mechanism. The depressed semicircles arise from ionic migration in the glassy matrix and are due to distribution of relaxation times20. The high frequency impedance plot is characteristics of the parallel combination of a capacitor and a resistor respectively, which are the bulk capacitance Cb and the bulk resistance Rb of the material21. Semicircle fits are used to determine the zero frequency impedance i.e., resistance and by using the known geometrical dimensions of the glass sample, the dc conductivity was determined.

Fig. 3 — Impedance plot for x= 50 mol% at different temperatures

Fig. 4 — Arrhenius plots of dc conductivity for different compositions


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The conductivity is determined from the data of complex impedance values and calculated by using the relation12: σ′ = (t/a) (Z′/(Z′2+ Z′′2))

... (1)

where Z′ and Z′′ are real and imaginary parts of impedance respectively, t is the sample thickness and a is the area of the sample. The frequency dependent behaviour of conductivity is analyzed on the basis of Jonscher universal power law22 : σ (ω) = σdc + Aωs

… (2)

where σdc is the dc conductivity of the sample, A is a constant for a particular temperature, ω (= 2πf) is the angular frequency of the applied field and s is the power law exponent in the range 0 < s < 1. The observed values of dc conductivity σdc, constant A, frequency exponent s and other parameters at room temperature for the investigated series are given in Table 1. The power law has been applied to many materials to analyze the ac conductivity behaviour in glasses and amorphous semiconductors1,10,19-23. The

Fig. 5 — Variation of dc conductivity and activation energy with AgI content

frequency dependence of conductivity is a sum of dc conductivity due to movements of free charges and polarization conductivity due to movements of bound charges. The frequency dependence of the conductivity at various temperatures for the glass sample containing x= 60 mol% is shown in Fig. 6. It is observed from the figure that the conductivity increases gradually as frequency increases. The electrode polarization effects are found to cover-up the dc conductivity plateau region and are absent in the dispersive region at high frequencies. The lowconductivity value at low frequencies is related to the accumulation of ions due to the slow periodic reversal of the electric field. In the high frequency or in midfrequency region, the power law nature (σ(ω)∝ωn ) is observed and the conductivity sharply increases with the frequency. Fig. 7 shows the ac conductivity of all compositions at different frequencies. In higher frequency range, ac conductivity is observed to increase with AgI content.

Fig. 6 — Frequency dependent conductivity at different temperatures for glass with x = 60 mol%

Table 1 — Some physical parameters of the present system at room temperature x (mol%) 40 45 50 55 60 65 40

log10σdc (Ω−1 cm−1)

7.62×10−7 2.93×10−6 9.92×10−6 2.91×10−5 4.78×10−5 1.15×10−4 1.9×10−4 (without TeO2)

A (Ω cm−1rad−s)

s

Ag+ ion Concentration (×10−2 mol cm−3)

ρ (gm cm−3)

2.85×10−10 3.55×10−10 5.52×10−11 1.59×10−11 2.72×10−12 6.15×10−10 —

0.56 0.58 0.72 0.81 0.92 0.70 —

1.70 1.76 1.80 1.93 2.01 2.13 —

4.69 4.78 4.83 5.13 5.25 5.52 —

−1


Fig. 7 — Variation of conductivity with AgI contents at different frequencies (T≈303 K)

The studies on silver-based super ionic conducting glasses agree with the conclusion that the insertion of metallic oxide (Ag2O as modifier) disrupts the glassy network leading to the different structural arrangements of V2O5-TeO2 glass chains. This change results in the formation of NBO and O-Ag partial covalent bonding24. The Ag+ ions bonded to the NBOs have less freedom to move and are expected to be less mobile compared to Ag+ ions in an iodine environment. As it is known from the structural studies that the glass network is not strongly modified by the addition of halide salt (AgI) to the glass2; hence, in the present system, the increase in conductivity is explained by diffusion path model given by Minami24. The diffusion path model requires that the different anion potentials are formed by the interaction of a mobile cations, Ag+, with anions I− and O−. The potential with I− ions by Ag+ are smaller than those made with O− ions. The Ag+ ions in the shallow iodide potential are more mobile than Ag+ ions in the deep oxide potentials. When these potentials are connected for a long period, they form a favourable path for ion transport known as diffusion path with minimum activation energy. Thus, the increase in AgI amount creates more and more diffusion paths, in the present system, thereby increasing the conductivity and a decrease in activation energy with AgI content as shown in Fig. 4. It is also reported that there is only a weak interaction between the telluride network and the silver iodide, hence silver and iodide remain preferentially linked together and contribute to ionic conductivity25. In AgI-Ag2O-V2O5 glasses, at low AgI concentration, AgI would disperse homogenously in

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the network structure while at high AgI concentration (above 40 mol% of AgI), I-I sub-structure formed the new ionic conduction channel for Ag+ ions26. In addition to it, in the present glasses, the total silver ion concentration in the glass system increases (Table 1), this should be responsible for consistent increase of conductivity. In AgI-Ag2O-V2O5 super ionic system1,2, conductivity is reported of the order of 10−3 S/cm whereas in Ag2O-V2O5-TeO2 system13, conductivity is reported in the range of 10−6-10−9 S/cm. In present system, although conductivity is observed to increase with AgI content which is generally observed in AgI-based glasses, it is still lower (in the range of 10−4-10−7 S/cm), as compared to AgI-Ag2O-V2O5 glass system. Hence, a sample of 40 AgI-60(Ag2O: 2V2O5) without TeO2 was also prepared whose conductivity was observed in the order of 10−4 S/cm (Table 1). It implies that the addition of TeO2 in xAgI(Ag2O-2V2O5) system is responsible for lower value of the conductivity even though a small amount of TeO2 (5 mol%) is used. It is known that the glass with TeO2 has the continuous network by sharing corners of TeO4 trigonal bipyramids and TeO3+1 polyhedra having one NBO atom and make different isolated units like TeO52− and TeO32− ions with the change in the composition27. Glasses with TeO2 have different structural units and connecting style from the conventional glass formers such as V2O5, P2O5 and B2O3. Therefore, the continuous structural transition in TeO2 through continuous creation of NBOs in TeO2 might be affecting the path ways for the transportation of the silver ion carriers in the glass system. To understand the relaxation dynamics in terms of conductivity spectra at different temperatures, the conductivity is scaled using Ghosh’s scaling model28. In this scaling process, the ac conductivity is scaled by dc conductivity σdc, while the frequency axis is scaled by the hopping frequency ωp at different temperatures. It can be seen from Fig. 8 that the conductivity spectra for different temperatures merge on a single master curve for a glass composition (x=40 mol%) indicating the temperature-independent relaxation dynamics. Other glass samples have shown the similar conductivity spectra at different temperatures and superimposed. It is observed that the spectra for different compositions do not superimpose on a single curve which implies that the relaxation dynamic process is composition dependent. It is also reported that the conductivity spectra for telluride mixed glasses do not superimpose due to change in structure28.


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Fig. 8 — Plot of the scaled conductivity vs normalized frequency for x= 40 mol% 3.3.2 Dielectric

In the present work, the complex permittivity of the system is calculated using the impedance data: ε* = 1/(jωC0 Z*) = ε′ – j ε′′

… (3)

where Z* is the complex impedance, C0= ε a/t, ε is the permittivity of free space (8.854×10−12 F/m), ε′ and ε′′ represent the dielectric constant and dielectric loss respectively. In the Debye approximation, assuming a single relaxation time, the equation for complex permittivity can be given as: ε* = ε∞ + (ε0 – jε∞)/(jωτ)

… (4)

where ε0 and ε∞ are the low and high frequency dielectric constants, respectively. Substitution and separation of real and imaginary parts give the equally familiar expressions for the dielectric constant, ε′ and dielectric loss ε′′, ε′= ε∞ (ε0 – ε∞)/(1 + ω2τ2) 2 2

ε′′= (ωτ) (ε0 – ε∞)/(1 + ω τ )

… (5) … (6)

In Debye like material, the moving charges are localized and the ε′′ versus ε′ representation gives a semicircle centered on the real axis and one relaxation time is considered. However, in presently investigated system, there is a different case where many relaxations are present. Figure 9[(a) and (b)] show the change in the dielectric constant (ε′) and dielectric loss (ε′′), respectively, with temperature at different fixed frequencies, for the sample that contains 40 mol% as silver iodide. It appeared that both ε′ and ε′′ are

Fig. 9 — (a)Dielectric constant, ε′ and (b) dielectric loss, ε′′, as a function of temperature for sample, x=40 mol%

almost independent of temperature at high frequencies and show weak frequency dispersion. At low frequencies, the ions align themselves along the field direction and fully contribute to the total polarization and dielectric constant and so they show strong temperature dependence. As the frequency rises, the ions are not able to follow the electric field direction and as a result their contribution to the polarization is less. Therefore, the dielectric constant decreases with the increase in frequency at all the temperatures under study. A similar behaviour is observed for other compositions. The variation of logarithm of real part of dielectric constant (ε′) with frequency at different temperatures for x= 45 mol% system is shown in Fig. 10(a). It is noticed that the dielectric constant, ε’ increases with increasing temperature in low frequency region Fig. 9(a) and starts decreasing with increasing


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Fig. 11 — Relaxation time, τσ vs 1000/T for x= 60 mol% Table 2 — Activation energies for the dc conductivity (Eσ) and the conductivity relaxation time (Eτ)

Fig. 10 — (a) Frequency dependence of the dielectric constant, for x=45 mol% glass sample at different temperatures and (b) Dielectric constant, ε’ vs AgI content at 303 K

frequency and becomes constant at very high frequencies for all compositions and temperatures. In low frequency region, the contribution of charge accumulation at the interface leads to net polarization of the ionic medium results in the formation of space charge region at electrode-electrolyte interface29. The dielectric constant is observed to increase with temperature due to the orientation of dipoles which facilitate the increase in permittivity at higher temperature. It is also observed that the frequency of dispersion shifts towards high frequency side with temperature and the AgI content. Fig. 10(b) shows the real part of dielectric constant at different frequencies with AgI content at 303 5K. The dielectric constant is observed to increase with AgI content except for x= 65 mol% sample which has a low value only at

AgI content (mol%)

Eσ (eV)

Eτ (eV)

40 45 50 55 60 65

0.49 0.46 0.40 0.33 0.31 0.30

0.46 0.42 0.35 0.27 0.24 0.16

10 kHz. It shows that at high frequencies, the value of dielectric constant is almost composition independent due to the very less contribution of the ionic polarization while at low frequencies; it has higher values due to the long range ionic motion of Ag+ ions in the system. The frequency and temperature dependence of the dielectric study give useful information about the relaxation dynamics of the mobile ions. The conductivity relaxation time is found out as suggested by Macedo et al. for a conducting dielectric30 as follows: τσ = ε∞ ε0/σdc

... (7)

Logarithmic dielectric relaxation time (τσ) as a function of inverse temperature for x= 60 mol% is shown in Fig. 11. Relaxation time is observed to satisfy the Arrhenius dependence for all the compositions. The activation energy Eσ from the dc conduction process, which is the activation energy for long distance charge transport and Eτ from the relaxation process, which corresponds to shortdistance transport are given in Table 2. The activation

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energy Eσ is comparable with Eτ up to 50 mol% and after that some difference between the two is observed. Generally, the dielectric constant results due to the contributions of electronic, ionic and dipole orientation contributions to the polarizability. However, the electronic contributions are very small in presently investigated system, because the transport number of Ag+ ions observed by Wagner’s polarization method is in the range of 0.97-0.9931. The ionic polarization arises from the displacement of ions of opposite sign from their regular lattice sites resulting from the applied electric field as well as deformation of the electronic shells from the relative displacement of the Ag+ ions. When the frequency of the applied field is further increased, the dielectric constant decreases. The reason for this may be that the dipoles are no longer able to rotate sufficiently rapidly so that their oscillations begin to lag behind those of the applied field. As the frequency becomes higher and higher, ionic and orientation source of polarizability decrease and finally disappear due to inertia of Ag+ ions and a constant value is observed as shown in Fig. 10. 4 Conclusions Frequency dependent conductivity of silver oxysalt glasses mixed with V2O5 and TeO2 as glass formers and varying AgI salt is found to obey the Jonscher’s Universal law. The FTIR studies revealed almost no change in the structure with the addition of AgI. The enhancement in conductivity is observed with the addition of AgI. The presence of TeO2 in AgI-Ag2OV2O5 system has reduced. The scaling approach for frequency dependent conductivity suggests that conduction mechanism is independent of temperature but it is composition dependent. Dielectric studies show ionic migration and polarization with frequency and temperature. The dielectric loss, which is due to the persistence of Ag+ ion mobility and dipolar relaxation loss, is temperature and frequency dependent. The distribution of relaxation times is evident from the conductivity and dielectric constant which are frequency dependent. The activation energy Eσ from the dc conduction process and Eτ from the relaxation process are found to be comparable up to 50 mol%.

Acknowledgement Authors (DKK and PS) thankfully acknowledge the financial support by the DST, New Delhi, India via Grant No. SR/S2/CMP-40/2004 and UGC, New Delhi, India for RFSMS fellowship. References 1 Bhattacharya S & Ghosh A, J Chem Phys, 123 (2005) 124514. 2 Arof A K & Radhakrishna S, J Alloys Compounds, 200 (1993) 129. 3 Arof A K, J Power Sources, 52 (1994) 129. 4 Dutta D & Ghosh A, Phys Rev B, 72 (2005) 024203. 5 Padmasree K P & Kanchan D K, J Non-Cryst Solids, 352 (2006) 3841. 6 Kumar R S, Hariharan K, Dhanabalan M & Reddy K V, Solid State Ionics, (86-88) (1996) 441. 7 Bhattacharya S & Ghosh A, Phys Rev B 68 (2003) 224202. 8 Bhattacharya S & Ghosh A, Solid State Ionics, 161 (2003) 61. 9 Dutta D & Ghosh A, J Phys: Condens Matter, 16 (2004) 2617. 10 Pant M, Kanchan D K & Gondaliya N, Mater Chem Phys, 115 (2009) 98. 11 Dutta D & Ghosh A, J Chem Phys, 128 (2008) 044511. 12 Pant M, Kanchan D K, Sharma P, Jayswal M S, Mater Sci & Engg B 149 (2008) 18. 13 Chowdari B V R & Kumari P P, J Non-Cryst Solids, 197 (1996) 31. 14 Moawad H M M, Jain H, El-Mallawany R, Ramadan T & ElSharbiny M, J Am Ceram Soc, 85 (2002) 2655. 15 Murugesan S, Wijayasinghe A & Bergman B, Solid State Ionics, 178 (2007) 779. 16 Yahia I S, Saddeek Y B, Sakr G B, et al., J Magnetism & Magnetic Materials, In Press, 2009. 17 Dimitriev Y & Chim Chronica, New Ser, 23 (1994) 361. 18 Gandhi Y, Venkatramaiah N, Ravi Kumar V & Veeraiah N, Physica B: Condens Matter, 404 (2009) 1450. 19 Padmsree K P, Kanchan D K, Panchal H R, Awasthi A M & Bharadwaj S, Solid State Commun 136 (2005) 102. 20 Padmasree K P, Kanchan D K & Kulkarni A R, Solid State Ionics, 177 (2006) 475. 21 Jonscher A K, J Mater Sci, 13 (1978) 553. 22 Jonscher A K, Nature, 267 (1977) 673. 23 Schroder T B & Dyre J C, Phys Rev Lett 84 (2000) 2188. 24 Minami T, J Non-Cryst Solids, 73 (1985)273. 25 Dexpert-Ghys J, Piriou B, Rossignol S, et al, J Non-Cryst Solids, 170 (1994)167. 26 Takahashi H, Rikitake N, Sakuma T & Ishii Y, Solid State Ionics, 175 (2004) 671. 27 Sekiya T, Mochida N, Ohtsuka A & Tonokwa M, J NonCryst Solids, 144 (1992) 128. 28 Ghosh A & Pan A, Phys Rev Lett, 84 (2000) 2188. 29 Ingram M D, Phys Chem Glasses, 28 (1987) 215. 30 Macedo P B, Moynihan C T & Bose R, Phys Chem Glass, 13 (1972) 171. 31 Sharma P, Kanchan D K, Pant M, et al., Proc 11th Asian Conf Solid State Ionics (Macmillan India Ltd , India), 2008, pp 371-378.