The effect of PbI2 on electrical conduction in Ag2O-V2O5-B2O3 superionic glass system

Solid State Ionics 186 (2011) 7–13

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Solid State Ionics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s s i

The effect of PbI2 on electrical conduction in Ag2O-V2O5-B2O3 superionic glass system Manish S. Jayswal, D.K. Kanchan ⁎, Poonam Sharma, Meenakshi Pant Department of Physics, Faculty of Science, The M.S. University of Baroda, Vadodara 390002, Gujarat, India

a r t i c l e

i n f o

Article history: Received 26 July 2010 Received in revised form 2 January 2011 Accepted 30 January 2011 Available online 1 March 2011 Keywords: Amorphous materials Quenching Electrical transport Ionic conduction Electrochemical impedance spectroscopy

a b s t r a c t Conductivity measurements and modulus formalism have been used to study the transport properties of PbI2 doped silver boro-vanadate glasses prepared by melt quenching technique. The samples are characterized by XRD and DSC measurements. A correlation between Rτ, the decoupling index and σDC has been discussed. The observed conductivity values suggest enhancement in conductivity by the introduction of PbI2 salt in the host glass matrix. AC conductivity data are analyzed by fitting the data to Jonscher's universal power law, σ′(ω)=σDC +Aωn. The power law exponent, n, is found to be independent of temperature and composition. The experimental modulus spectra are analyzed and calculated the stretched exponential constant β using the non-linear KWW decay function. Furthermore, the scaling of both ac conductivity and electric modulus at different temperatures is found to merge near perfectly on to a single master curve suggesting that all the dynamic processes possess good time temperature superposition. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Appreciably high ionic conductivity of AgI doped glass materials has led to a systematic investigation of their various physical and chemical properties. These materials possess excellent chemical durability, high ionic conductivity and along with that tuning of their properties by changing their chemical composition is possible, which make them useful as solid electrolytes in “all solid state batteries”, electro chromic devices, gas sensors, etc. [1–3]. As it is well known that AgI in its α-phase, after 147 °C till just before its melting point, is a prototype superionic conductor and it has been a center of attraction to stabilize such a highly conducting phase at the room temperature in many host glass systems including binary, ternary and quaternary glass systems [4–6]. Many interesting results have been obtained regarding the nature of electrical conductivity of these glasses. Instead of directly doping pure AgI in a host glass, some different routes have also been attempted, like using a stoichiometric composition instead of pure AgI in the host glass [7], or doping with a suitable MIn type salt in an Ag2O containing glass and thereby forming AgI as a result of exchange reaction between the two, based on Lewis HSAB (Hard and Soft Acids and Bases) principle [8], where a hard acid ion prefers to co-ordinate to a hard base ion and vice-versa. This approach has led to the usage of metal halide salts e.g., CuI, CsI, BiI3 and CdI2 as dopant, which form AgI in the host glass by an exchange reaction with Ag2O/AgPO3. According to the HSAB theory, Pb+ 2 ion is a borderline acid and I− is a soft base while Ag+ is a soft acid and O− 2

⁎ Corresponding author. Tel.: + 91 265 2795339. E-mail address: [email protected] (D.K. Kanchan). 0167-2738/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2011.01.016

is a borderline base, hence an exchange reaction between PbI2 and Ag2O takes place as per the following equation [9] +2

Pb½I

þ

þ

+2

+ 2Ag½o →2Ag½I + Pb½O

ð1Þ

From the above reaction we see that for one molecule of PbI2 and one molecule of Ag2O, as a result of the exchange reaction, two AgI and one PbO molecules are formed in the glass network. Addition of a network modifier such as Ag2O introduces ionic bonds, usually associating NBOs (non-bridging oxygen) along with modifying cations. Ag2O leaves its oxygen and negative charges to the glass network, which becomes rich in charge carriers (Ag+) and gains the capability to act as a solvent for the metal halide salts. Hence the mobility associated with an iodide environment is considered to be higher and based on the fact that increase in the percentage of AgI in the glass gives rise to higher conductivities. Incorporation of metal halides in the mixed glass formers is considered to be a predominant factor playing the role of enhancing the conductivity of conventional glasses to achieve the values of super ionic conductors. Many reports suggest that the conductivities have been enhanced by mixing of two different glass formers with different coordination polyhedrons [10,11]. However, such a mixture of glass-formers has a tendency of phase separation at low modifier molar ratio; therefore the complete substitution of one network former by another is always possible. More recently, the trend of replacing Ag+ ions with other feasible cations in dopants like CuI, CdI2 etc. has been followed to realize new materials exhibiting comparable electrical conductivities and exploiting the favorable character of silver ion to electrical conduction [12,13]. Moreover, this new route adopted in developing such materials has paved the way for the “mixed cation effect” [14] wherein a second cation is

M.S. Jayswal et al. / Solid State Ionics 186 (2011) 7–13

involved in the process of conduction actively or by influencing conductivity via structural alterations. As PbO acts as a glass modifier, it expands the glass network by creating more open and channel type structures, which are helpful for easy movement of Ag+ ions [15]. The effect on conductivity by influencing the network by addition of PbI2 in the host glass network has been observed in many chalcogenide and chalcohalide glasses, too [16,17]. In view of this, the present study aims to study the effect due to varying concentrations of a new dopant salt, PbI2, on ac conductivity and modulus formalism in the case of the glass system x [PbI2:2Ag2O]−(100-x) [0.7 V2O5 −0.3 B2O3], where 30≤x≤55 in steps of 5.

207 oC

Heat FLow (mW) Endo Exo

8

215 oC 93 oC

35% 30%

103 oC

40

2. Experimental

80

120

160

200

240

280

320

360

400

t (oC)

Analytical Reagent grade starting chemicals: PbI2, Ag2O, V2O5 and H3BO3 were used to prepare the samples. All the compositions were weighed according to their mole%, crushed and then mixed thoroughly using an agate mortar pestle for 2 h to ensure proper mixing and homogeneity of the compositions to be formed. The glass mixture, kept in a porcelain crucible, was maintained at 400 °C for half an hour to completely convert H3BO3 into B2O3. After that, the samples were melted at 800 °C in a muffle furnace for 4 h. The melt was poured on a thick metallic copper plate and quenched with another copper plate kept at room temperature. X-ray diffraction was carried by X-ray diffraction analyzer (Shimadzu) at 2θ = 2°/min scan rate. The glass transition temperature of the amorphous samples was measured by Differential Scanning Calorimeter (Sieko instruments (model 6200)) at a heating rate of 5 °C/min. The impedance studies in the present work were carried out using Agilent e4980A LCR meter in the frequency range 20 Hz–2 MHz and the temperature range 303 K–423 K. For electrical measurements, the as quenched glass pieces were polished on both faces with a silicon carbide lapping paper to ensure uniform surface and thickness across the sample. Silver paint was applied on the opposite faces of the polished glass pieces to make contact electrodes. 3. Result and discussion 3.1. Characterization The amorphous nature of the samples was characterized by XRD and DSC measurements. In the XRD measurements, as shown in Fig. 1, only a broad peak in the low angle region, free from any sharp peaks is observed which confirms the amorphous nature of the samples. Fig. 2 depicts Differential Scanning Calorimeter (DSC) scans recorded for samples under study. It reveals an endothermic baseline shift corresponding to the glass transition followed by an exothermic

Intensity (arb. units)

x = 55%

Fig. 2. DSC scans for x=30% and 35% glass compositions. (Y-axis data is in arbitrary units).

peak due to crystallization of glassy phase. The observation of glass transition temperature, Tg, by DSC further confirmed the glassy nature of the samples. The glass transition, Tg, values for all the compositions are given in Table 1. One may also observe that at least two exothermic peaks are present which correspond to different crystalline phases occurring at these temperatures, which we intend to study as a separate work in future. 3.2. Impedance spectroscopy Fig. 3 depicts the complex impedance plot of the x = 30 mol% sample at room temperature. Two semicircular arcs are distinguishably visible, one in the high frequency region with a small radius, and the other being in the lower frequency side with a comparatively larger radius. According to impedance spectroscopy, this kind of behavior can best be understood (represented) by a series combination of two parallel lumped RC circuits as shown in the inset of Fig. 3. The first semicircle (R1C1 couple) arises due to the bulk resistance of the sample, it is extrapolated and its intersection with the real axis is taken as the resistance of the sample, while the other semicircle (R2C2 couple) arises due to polarization of mobile Ag+ ions at the electrode– electrolyte interface [18]. The obtained semicircle is found to be depressed, i.e., its center lying below the real axis means that the relaxations of ions are non-Debye in nature. Each sample shows similar behavior at all temperatures. The obtained impedance plots were analyzed using the non-linear least square (NLLS) fitting. The first semicircle is extrapolated and its intersection with the real axis is taken as the bulk resistance of the sample. 3.3. Conductivity studies DC conductivity of the samples is calculated from their bulk resistance (obtained from the complex impedance plots) and the known geometrical dimensions of glass sample. Fig. 4 shows the logarithm of DC conductivity against 1000/T. It is a well known fact that the Lewis acid–base exchange reactions based on the HSAB

x = 50% x = 45% x = 40%

0

10

20

30

40

2θ Fig. 1. XRD scans for all glass compositions.

Table 1 Values of the DC conductivity σDC, glass transition temperature Tg, activation energies Eσ and Eτ, KWW stretched exponential parameter β, frequency exponent, n and hopping frequency ωp at 303 K.

x = 35%

x mol%

σDC (S/cm)

Tg (°C)

Eσ (eV)

Eτ (eV)

β

n

ωp (Hz)

x = 30%

30 35 40 45 50 55

1.08 × 10− 3 9.07 × 10− 5 5.24 × 10− 5 2.62 × 10− 4 3.23 × 10− 3 1.94 × 10− 2

102 93 90 100 109 96

0.45 0.47 0.60 0.56 0.50 0.49

0.46 0.48 0.60 0.59 0.47 0.35

0.63 0.65 0.57 0.52 0.52 0.56

0.71 0.84 0.89 0.65 0.74 0.70

4.10 × 105 5.28 × 104 2.81 × 104 4.06 × 104 8.05 × 105 1.92 × 106

50

M.S. Jayswal et al. / Solid State Ionics 186 (2011) 7–13

30

(a) Original Data fit result

300000

9

35

0.60

Ea

0.58

σDC

40

45

50

55

-1

-2

100000

Eσ (eV)

Low frequency region High frequency region CPE1

CPE2

ω

0.54 -3 0.52

σDC (S/cm)

-Z’’ (Ω )

200000

log

0.56

0.50 -4 0.48

R1

0 0

100000

R2

200000

0.46 300000

-5

Z’ ( Ω)

30

35

40

45

50

55

x mol% (PbI2 : 2 Ag2O) Fig. 3. Complex impedance plot and its equivalent circuit for x=30 mol% sample at 303 K.

(b)

ð2Þ

where, σo = conductivity pre-exponential factor, Eσ = conductivity activation energy, k = Boltzmann's constant, T = absolute temperature. Fig. 5(a) shows the variation of DC conductivity and activation energy with the compositions at 303 K. The σDC curve clearly exhibits two different regions with a minimum at 40 mol%. The conductivity decreases up to 40 mol% of PbI2, then starts increasing for x N 40 mol%. According to the Anderson–Stuart formalism [19], the total activation energy Ea, required for an ionic jump to occur may be divided into two fractions: Es, the elastic strain energy associated with the distortion of the glass network as the Ag+ ion jumps from one equilibrium position to the next and Eb, the electrostatic binding energy which is the energy required to overcome the electrostatic forces between Ag+ ions and the neighboring oxygen and iodide ions and is related to the average local environment (i.e. bond length and coordination numbers) of the mobile cations. Hence, Eb must relatively be affected by the cation concentration in the undoped network glasses.

0

log σ (S/cm)

-1

-2

30 % 35 % 40 % 45 %

-5 2.4

50 % 55 % 2.7

3.0

1000 / T

3.3

(K-1)

Fig. 4. Arrhenius plots of DC conductivity for different compositions of (PbI2:2Ag2O).

log σDC -2

σDC (S/cm)

σDC = σo expð−Eσ = kT Þ

-4

10

log Rτ

9

-3 8

log Rτ

principle of ion exchange reactions between Ag and Pb resulting in the formation of AgI have most likely taken place within the rapidly quenched systems as can be seen from the Arrhenius plots in Fig. 4 obtained for all the six compositions in the present mixed system. All the samples exhibit a good approximation to the Arrhenius relation with activation energy in the range of 0.46–0.59 eV as follows,

-3

-1

+2

log

+

-4 7 -5 30

35

40

45

50

55

x mol% (PbI2 : 2 Ag2O) Fig. 5. (a) Variation of activation energy and DC conductivity with (PbI2:2Ag2O) content at T = 303 K. (b) Variation of DC conductivity and decoupling index Rτ with (PbI2:2Ag2O) content at T = 303 K.

In the present case, PbO along with Ag2O which are formed by the ion exchange reaction between Ag+ and Pb+ 2 by the Hard and Soft Acids and Bases (HSAB) principle are not able to encourage the formation of apparently more non-bridging oxygen groups in the structural network below 40 mol%. This development might be reducing the pathways for the migration of mobile cationic species and reduces the conductivity up to 40 mol%. Beyond 40 mol% of PbI2:2Ag2O, Pb+ 2 ions start changing their local coordination from exclusively I− to entirely non-bridging oxygen, and the local environment of the Ag+ ions change to induce an enhancement in the conductivity or a decrease in activation energy, Eb. The variation in conductivity with composition is also confirmed by the decoupling index Rτ values. Decoupling index, Rτ, in an ionically conducting glass system, is a measure of how strongly the mobile ions are decoupled from the glass matrix [20]. It is defined as the ratio of the average structural relaxation time τs (Tg) to the average conductivity relaxation time τc (Tg) at the glass transition temperature. Generally τs = 200 s at Tg (as it is difficult to determine its value at other temperatures) [20–23], while the τc (Tg) values were determined by extrapolating the logτc → 1000/T graph (Fig. 10) to Tg. Fig. 5(b) shows the variation of Rτ and σDC versus the x mol% (PbI2:2Ag2O). It may be noted that the values of Rτ (Tg) decrease with the increase of modifier content (PbI2 and Ag2O) and show a minimum at x = 40 mol% sample. This observation is in good agreement with the variation of the conductivity with PbI2:2Ag2O content. The decrease in the calculated value of Rτ (Tg) with increase in (PbI2:2Ag2O) content up to 40 mol%

M.S. Jayswal et al. / Solid State Ionics 186 (2011) 7–13

-3

45 mol%

σ’ (S/cm)

suggests that the motion of Ag+ ions is coupled more and more with the viscous motion of the glass network suggesting a decrease in the conductivity. After that, as the concentration further increases, coupling of Ag+ with viscous motion reverts and consequently, both decoupling index and conductivity start increasing. Similar correlation between Rτ and σDC has been discussed by Bhattacharya et al. also [24]. Many workers observed that a glass doped even at a lower concentration of PbI2 results into higher conductivities when compared to the AgI doped glasses [9,14,25,26]. It is a fact that the concentration of the iodine content originating from dopant salt PbI2 is double than in the case of AgI. Hence, a small variation in the concentration of PbI2 would rapidly increase in the number of I− ions causing structural deformation and expanding the network further and hence increasing the mobility of the conducting ions.

-4

log

10

-5

423 K 413 K 403 K 393 K 383 K 373 K 363 K 353 K 343 K 333 K 323 K 313 K

3.4. AC conductivity

303 K

Fig. 6 shows the graph of log σ′ → log f for different compositions of PbI2. There are generally two crossover regions present, the one appearing in the lower frequency region occurs due to polarization effects at the electrodes, while the bulk behavior appears in higher frequency region only. The plateau region in the higher frequency region is extrapolated to find out the σDC value. The frequency dependent conductivity data were analyzed using Jonscher's universal power law [27], 0

n

σ ðωÞ = σDC + Aω

ð3Þ

where, σDC is the DC conductivity, A is a constant, ω is the radial frequency and n is the frequency exponent (usually 0 b n b 1). The frequency exponent n was found to be in the range of 0.6–0.9 and was found to be independent of temperature and composition as well. The hopping frequency ωp is the frequency, at which relaxation effects begin to appear and it was found to shift towards higher frequencies with increase in temperature and can be calculated as ωp = [σDC/A]1/n [9], where (σ′ (ω) is equal to 2σDC) and A, n, and σDC are different parameters obtained from Eq. (4) and is given in Table 1. Fig. 7 shows the frequency dependence of conductivity at different temperatures for the composition x = 45 mol%. The conductivity exhibits a typical frequency independent plateau at lower frequencies and a crossover or a dispersive region at higher frequencies. Similar behavior is observed for other compositions also. The frequency response of conductivity in glasses may be entirely due to the translational and localized hopping of ions [28]. The translational hopping gives rise to long range electrical transport at very low -3.0 -3.5

log

σ’ (S/cm)

-4.0 -4.5 -5.0 -5.5

2

3

4

5

6

log f (Hz) Fig. 7. Frequency dependent conductivity at different temperatures for x = 45 mol%.

frequencies, while the high frequency dispersion may be correlated to the forward–backward hopping of the ions at high frequencies which requires only a fraction of energy that is involved in the long-range diffusion of ions. The frequency independent plateau at low frequency region arises due to contribution of DC conductivity and the switch over of the frequency independent region to frequency dependent region at higher frequencies implies the onset of conductivity relaxation [29]. The onset frequency of conductivity relaxation shifts towards higher values with increasing temperature, as shown in Fig. 7. Scaling is an important tool to understand the AC conductivity behavior of ionically conducting glasses. It allows collapsing of different data sets to a single master curve, indicating that the processes can be separated into a common physical mechanism modified by thermodynamic scales [30]. Different scaling approaches have been used by many workers, e.g.; ac conductivity data scaled by DC conductivity σDC , and the frequency axis scaled by different parameters, e.g. σDCT [30] or ωp [31] etc., where ωp is hopping frequency and T is absolute temperature in Kelvin. In the present study, we have used Roling's scaling model [30] for scaling of the conductivity versus frequency curves. The scaled conductivity spectra (conductivity master curve) for the x=30 mol% glass at different temperatures is shown in Fig. 8(a). The conductivity spectra for different temperatures merge near perfectly into a single curve (conductivity master curve) which indicates the existence of a time temperature superposition and a temperature independent relaxation mechanism, but the scaling at different compositions does not result into a single master curve, as can be seen from Fig. 8(b). The scaling approach used here suggests that the conductivity relaxation is a temperature independent process in these glasses, however it is independent of the composition, i.e. it depends on the mobile ion concentration [30].

50 mol% 55 mol%

3.5. Modulus studies

30 mol% 45 mol%

-6.0

-6

35 mol% 40 mol%

-6.5 2

3

4

5

6

log f (Hz) Fig. 6. Variation of conductivity with frequency for different compositions of (PbI2:2Ag2O) at room temperature (303 K).

As we have discussed in Section 3.2, the transition from frequency independent to frequency dependent conductivity marks the onset of a relaxation phenomenon, which we are going to analyze here in terms of the modulus function. The advantage of the modulus formalism is that the polarization effects occurring at the electrode–electrolyte interface are suppressed. Pioneered by Macedo et. al. [32], the modulus formalism is now a well established tool to analyze the relaxation processes occurring due to the motion of ions in superionic glasses, crystals and melts. Fig. 9(a) shows the frequency dependent real part of the modulus for x=50 mol%

M.S. Jayswal et al. / Solid State Ionics 186 (2011) 7–13

(a)

(a)

11

6

1.5 303 K 313 K 323 K 333 K 343 K 353 K 363 K 373 K 383 K 393 K 403 K 413 K 423 K

0.5

4

373 K 363 K

M’

log (σ’/σDC)

1.0

303 K 413 K 403 K 393 K 383 K

353 K 343 K 333 K

2

323 K 313 K 303 K

0

0.0

2 5

6

7

8

log (f/σDCT)

6

7

303 K 313 K 323 K 333 K 343 K 353 K 363 K 373 K 383 K 393 K 403 K 413 K 423 K

2.0 30 % 35 % 40 % 45 % 50 % 55 %

0.010

M’’

log (σ’/σDC)

5

(b) 0.015

1.0

4

log f (Hz)

(b)

1.5

3

9

0.005 0.5

0.0 0.000 1

2

-0.5 5

6

7

8

9

log (f/σDCT) Fig. 8. (a) Conductivity scaling spectrum at different temperatures for x = 30 mol%. (b) Conductivity scaling spectrum for different compositions at 303 K.

at all temperatures. It is clear from the figure that M′ shows dispersion as frequency rises, and reaches to a maximum value at high frequencies while it tends to zero at lower frequencies indicating negligible polarization at the electrodes [33]. Fig. 9(b) shows the frequency dependent M″ curve. It is observed that the modulus spectrum has a similar shape at all temperatures with a long and flat tail extending from the low-frequency region up to the intermediate frequency region. This type of behavior may be attributed to the large capacitance associated with the electrodes while that part of the peaking curve observed at higher frequencies may be due to the bulk effect. The non-perturbed shape of the modulus spectra obtained at various temperatures has indicated the temperature independence of the distribution of relaxation times. It is also clear from these modulus spectra that it is possible effectively to suppress the electrode–electrolyte interface effects in the modulus formalism. Also to be noted that the M″ peak shifts towards the higher frequencies with temperature, without any significant variation in peak height or spectral shape. The shapes of M″ curves look alike and differ only in peak position and FWHM (Full Width at Half Maximum) value. The conductivity relaxation frequency ωc corresponding to M″max gives the average or characteristic relaxation time by the condition that ωcτc =1 [34]. The frequency range below M″max determines the range where charge carriers are mobile over long distances while the frequency range above M″max is the frequency range where the charge carriers are confined to potential wells and are mobile over short ranges only.

3

4

5

6

log f (Hz)

10

Fig. 9. (a) Real part of electric modulus versus log f at different temperatures for x=50 mol%. (b) Imaginary part of electric modulus versus log f at different temperatures for x=30 mol%.

The obtained M″ data were fitted to stretched exponential KWW function,   β ϕðt Þ = exp ð−t =τm Þ ;

ð4Þ

using the procedure of Moynihan et al. [35]. Here β is an exponent denoting deviation from the ideal Debye behavior. A lower value of β is an indication of higher ionic conductivity. The β values, which are obtained in the range of 0.5–0.6 at room temperature, are almost independent of composition, which indicates that the ion–ion interactions are independent of composition. τm in the above equation is the relaxation time pertaining to the M″max (corresponding frequency is called fmax). Fig. 10 shows the reciprocal temperature dependence of the relaxation time for all the glass compositions and it closely fits to the following Arrhenius relation [24] τc = τo expðEτ = kT Þ

ð5Þ

where, τc is the characteristic relaxation time, τo is the pre-exponential factor and Eτ is the activation energy for τc. The activation energy Eσ, obtained from the DC conductivity processes, which is the activation energy for long range charge transport and Eτ from the relaxation processes, which corresponds to the short distance transport, are found to be nearly same. The comparable values of Eσ and Eτ (Table 1) suggest that the DC conduction process and the conductivity relaxation processes, both are activated by the same mechanisms [24,36]. The consistent shift in the fmax position with rise of temperature may be explained on the basis of the

12

M.S. Jayswal et al. / Solid State Ionics 186 (2011) 7–13

log τc (sec.)

-4.0

-4.8

(a)

30 % 35 % 40 % 45 % 50 % 55 %

303 K 313 K 323 K 333 K 343 K 353 K 363 K 373 K 383 K 393 K 403 K 413 K 423 K

1.0

0.8

M’’/’’max

-3.2

-5.6

0.6

0.4

-6.4 0.2 -7.2 0.0 -8.0 2.6

2.8

3.0

3.2

3.4

-5

-4

-3

-2

1000/T (K-1) Fig. 10. Arrhenius plot of relaxation time for different compositions of (PbI2:2Ag2O).

-1

0

1

2

3

4

log (f/fmax)

(b) 1.0

4. Conclusion The DC conductivity is found to decrease with PbI2 and show a minimum at 40 mol% and rises afterwards with the PbI2 salt concentration. The observed change in decoupling index also supports the variation of the conductivity as a function of composition. The relaxation dynamics of the glasses from conductivity formalisms and electric modulus analysis and the activation energy obtained from conductivity and characteristic relaxation time obtained from modulus have been compared. Modulus analysis reveals the non-Debye nature indicating the distribution of relaxation times. The scaling approach for frequency dependent conductivity as well as the modulus function suggests that the relaxation of ions is a temperature independent phenomenon but is influenced by the varying composition.

Acknowledgement One of the authors DKK thankfully acknowledge the financial support by the DST, New Delhi, India via grant no. SR/S2/CMP-40/ 2004.

30 mol% 35 mol% 40 mol% 45 mol% 50 mol% 55 mol%

0.8

M’’/’’max

distribution of attempt frequencies for the barrier cross-over or a distribution of jumps or flight distances following the cross-over. The broadness of the M″ versus log f curves is interpreted in terms of the distribution of relaxation times for distinguishable processes. According to Hasz et al. [37] the distribution of relaxation time is connected with a distribution of free energy barriers for ionic jumps, in which distribution is increased with increasing disorder whereas Grant et al. [38] attributed the distribution of relaxation times as not due to the disordered structure of glasses but is assumed to be the consequence of the cooperative nature of the conduction process. To warrant a better insight of the relaxation processes, we have used the scaling approach for the imaginary part of modulus, M″. Figs. 11 (a) and (b) present, the scaling of the M″ curves (M″/M″max →log (f/fmax)) for x=45 mol% at different temperatures and for all the compositions respectively. The data for different temperatures are found to merge near perfectly into a single master curve, which suggests that all the dynamic processes occurring at different time scales exhibit the same activation energy and the distribution of relaxation times is independent of temperature. However, it can be seen from Fig. 11(a) that the scaling of M″ curve at any particular temperature for all the samples does not result into a single master curve at all, which implies that the conductivity relaxation may be independent of temperature but it surely depends on the composition of the glass.

0.6

0.4

0.2

0.0 -4

-3

-2

-1

0

1

2

3

log (f/fmax) Fig. 11. (a) The plot of the scaled M″ against scaled frequency for x = 45 mol%. (b) The plot of the scaled M″ versus scaled frequency for all the compositions at 303 K.

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