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Journal of Non-Crystalline Solids 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 / j n o n c r y s o l

AC conductivity and impedance measurements in alkali boro-tellurite glasses S. Suresh a, M. Prasad b, V. Chandra Mouli a,⁎ a b

Department of Physics, Osmania University, Hyderabad-500007, Andhra Pradesh, India Department of Physics, PG college, Secunderabad, Andhra Pradesh, India

a r t i c l e

i n f o

Article history: Received 10 July 2009 Received in revised form 23 April 2010 Available online 27 June 2010 Keywords: AC conductivity; Tellurite glasses; Impedance

a b s t r a c t AC conductivity and impedance measurements were carried out for an alkali boro-tellurite glass system having composition 60B2O3-10TeO2-5TiO2-25R2O (where R — Li, Na and K). The impedance plots (Z″ (ω) vs. Z′ (ω)) for all glass samples were recorded and found to exhibit good single well-shaped semi circles over the studied temperature range. Frequency dependence of the imaginary part of impedance Z″(ω) and the imaginary part of modulus (M″) for all glass samples at different temperatures was also investigated. The conductivity isotherms show a transition from independent DC region to dispersive region where the conductivity continuously increases with increasing frequency. For low frequency region, conductivity values (σac) at RT are relatively low in the order of 10− 8 to 10− 9 (Ohm-cm)− 1. However, there is an increase in conductivity with temperature for all glass samples showing conductivities at 300 °C (σ300) in the range 10− 6 to 10− 5.5 (Ohm-cm)− 1. In the high frequency region, conductivity is enhanced by one order of magnitude (10− 5 (Ohm-cm)− 1) as temperature is increased. Power law parameter (s) is determined for all the glass samples at various temperatures and lowest ‘s’ values are found to be for lithium-containing glasses. An excellent time-temperature superposition in the imaginary part of the dielectric modulus (M″) conﬁrms that the dynamical process is temperature independent and is also indicative of a common ion transport mechanism. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Boro-tellurite glasses have been extensively studied due to the industrial importance of tellurites in making glasses with desirable optical properties [1–5]. Since both classical glass former B2O3 and conditional glass former TeO2 are present in boro-tellurite glasses, it leads complex speciﬁcation and interesting properties in glass structure. Introduction of alkali ions in these glasses exhibits high electrical conductivity and hence can also be applied as solid electrolytes in high density batteries, electrochromic display and sensors. There have been studies on alkali ion transport in tellurite and boro-tellurite glasses [6–8]. The present work deals with the conductivity and dielectric relaxation behavior of the glass samples in the B2O3-rich area of the 60B2O3-10TeO2-5TiO2-25R2O (where R = Li, Na and K) glass system. This study involves one kind of alkali oxide gradually replaced by another at constant B2O3 and TeO2 concentrations to obtain better ionic conducting material, thus enabling its application in fabrication of various types of solid state ionic devices.

were taken in appropriate proportion. The weighed chemicals constitute to a 5 g batch and were ground thoroughly in a motor to get homogeneous mixture. The batches were then melted in a platinum crucible in a high temperature mufﬂe furnace at 900–950 °C for about 30 min and stirred frequently to ensure homogeneity. The melt is quenched on stainless steel plate maintained at 300 °C. All the samples were transferred to annealing furnace and annealed at 300 °C for 4 h to avoid cracking and shattering of the glasses. Glass samples were cooled to room temperature. Glassy nature of the samples was conﬁrmed by XRD studies. A.C conductivity and impedance measurements were carried out using Frequency Resonance Analyser (FRA) (Auto Lab, PGSTAT 30) for different frequencies in the range of 100 Hz to 1 MHz and temperature from RT to 350 °C. Compositions of the glasses studied and their corresponding codes are listed in Table 1. 3. Results and discussions 3.1. Impedance plots

2. Experimental Glasses were prepared by conventional melt quenching method. The starting materials, TeO2, H3BO3, TiO2, Li2CO3, Na2CO3 and K2CO3 ⁎ Corresponding author. Tel.: +91 9866428911. E-mail address: [email protected] (V. Chandra Mouli). 0022-3093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2010.05.052

The impedance plots (Z″ (ω) vs. Z′(ω)) for all the glass samples were recorded and found to exhibit good single well-shaped semi circles (cole–cole plots) over the studied temperature range. A typical impedance plot for BTTL glass at different temperatures is shown in Fig. 1. The semicircle plot indicates that the materials are in single phase [9]. It is clear that all the semicircles start on the real impedance axis at the lowest frequency. This starting point is found to decrease

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Table 1 Compositions of the glasses prepared, along with codes of designation. Code

Compositions (mol%)

BTTL BTTN BTTK

60B2O3-10TeO2-5TiO2-25Li2O 60B2O3-10TeO2-5TiO2-25Na2O 60B2O3-10TeO2-5TiO2-25K2O

with increase in temperature. This behavior of cole–cole plots is characteristic of the conducting nature of the glass samples. The radius of the semicircles decreases with increase in temperature indicating relaxation time of relaxing species borne out by frequency explicit plots. The intercept of the semicircle with real axis on the low frequency side is normally referred as the bulk resistance (Rb) of the glass samples [10]. The intercept of the semicircle shifts towards lower Z′ value with increase in temperature which indicates the decrease in bulk resistance. Bulk resistance (Rb) and capacitance (Cb) values are calculated from the complex impedance plots at various temperatures for all glass samples. From Table 2 it is clear that resistance values are low for lithium-containing glasses.

Table 2 Capacitance, resistance and FWHM values from impedance plots (Z″ vs. Z′ and Z″ vs. freq) for the BTTR glass series. Temperature (°C)

Capacitance (pF)

BTTL 200 225 250 275 300

Resistance (Ω)

FWHM (Hz)

39.8 39.5 38.7 34.6 30.4

8 × 105 7.7 × 105 2.5 × 105 1.1 × 104 4.9 × 103

5006 12549 34699 88800 181350

BTTN 200 250 275 300 325

48.5 40.1 40.5 39.8 34.7

5 × 106 4.1 × 105 3.8 × 104 3.6 × 104 1.6 × 104

–

BTTK 225 250 275 300

30.4 37.8 32.0 27.3

7.9 × 105 2.07 × 105 7.9 × 104 3 × 103

2108 8902 25024 66463

1363 5230 16868 41877

3.2. Complex modulus The complex modulus spectrum indicates electrical phenomenon with the smallest capacitance occurring in a dielectric medium. Frequency dependence of the imaginary part of impedance (Z″(ω)) and the imaginary part of modulus (M″) for glass sample (BTTL) at different temperatures are shown in Fig. 2. Remaining glass samples show similar behavior. In the case of Z″(ω) vs. frequency curves, a peak is observed at a certain frequency and shifted towards the high frequency side with increase in temperature, but the shape of the curve remains the same. The magnitude of this peak decreased with increasing temperature, indicating increase in ionic migration loss in the glass system. In the case of M″ vs. frequency curves (Fig. 2), a peak is observed at a certain frequency and its magnitude increased with rise in temperature, indicating that the number of charge carriers increases by thermal activation. From the ﬁgure it can be observed that all the curves seem to be overlapping over one another at the high frequency region for different temperatures. Merging of all Z″ and M″ curves at high frequency regime indicates disappearance of space charge polarization. Whereas Z″max and M″max do not occur at the same frequency region, a broadened modulus spectra is obtained which is an indication of the wide distribution of relaxation time [11]. The presence of a single peak of Z″ and M″ indicates bulk conductivity and absence of any grain boundary contribution to impedance. The full width at half maximum (FWHM) values are calculated from both Z″max and M″max peaks for all glass samples and tabulated in

Fig. 1. Complex impedance plots for the BTTL glass sample.

Tables 2 and 4. It is clear from the table that FWHM values increase with increase in temperature. The frequency ωc, where the maximum M″ occurs is the indication of transition from a short range to long-range mobility at decreasing frequency, given by the condition ωcτc = 1, where τc is the conductivity relaxation time. It is also observed that as temperature increases Z″ peaks broaden at low frequency regime whereas in the case of M″ vs. frequency curves, M″ peaks broaden at high frequency regime. This type of temperature and frequency dependence of Z″ and M″ arises due to the distribution of relaxation time that is interconnected with a distribution of free energy barrier for ionic jumps, in which distribution is increased with increasing disorder of cation in the conduction process of glassy materials. The raise in Z″ peak occurring at low frequencies is due to the electrode polarization. Similar behavior was reported by Padmasree et al. [11]. The real (M′(ω)) and imaginary (M″(ω)) parts of electric modulus as a function of temperature and frequency for BTTN glass sample are shown in Fig. 3. The variations of electric modulus are qualitatively similar for all other glass samples under study. M′ exhibits very small value at low frequencies indicating that electrode polarization makes negligible contribution to M*(ω). As the frequency is increased, M′(ω) shows a dispersion tending to M∞ at higher frequencies. M″(ω) exhibits low value at low frequencies which may be due to the large value of capacitance associated with electrodes. M″(ω) plots show asymmetric maxima at the dispersion region of M′(ω). This maxima

Fig. 2. Frequency dependence of Z″ and M″ plots for the BTTL glass sample.

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Table 3 Activation energies for the BTTR glass series. Glass code

Eτ (eV) from Z″

Eτ (eV) from M″

BTTL BTTN BTTK

0.99 1.16 1.11

0.77 1.17 1.09

at different temperatures The relaxation time τ follows Arrhenius relation τ = τo exp ðΕτ = ΚΤÞ

Fig. 3. Frequency dependence of real and imaginary parts of the modulus for the BTTN glass sample.

(=M″max) shifts to higher frequency with increase of temperature, which suggests that the effect due to electrode polarization can be avoided [12]. ωmax values are obtained from M″ vs. logω and Z″ vs. logω plots. The most probable relaxation time τ is obtained by substituting ωmax values in condition ωmτm = 1. Fig. 4a and b shows logτ vs. 1000/Τ plots for relaxation from Z″ and M″ respectively for BTTR glass series

Fig. 4. (a) Log τ vs. 1000/T plots from relaxation Z″ for the BTTR glass series. Solid lines are the least-square straight-line ﬁts to the data. (b) Log τ vs. 1000/T plots from relaxation M″ for the BTTR glass series. Solid lines are the least-square straight-line ﬁts to the data.

ð1Þ

Solid lines in Fig. 4a and b are ﬁtted to the above equation using the least-square linear ﬁt and slope gives the relaxation activation energy Ετ and its magnitude is given for all glass samples in Table 3. From the table, it is observed that the activation energies for the relaxation Ετ from Z″ are near coincidence to activation energies which are calculated from M″. 3.3. Normalized plot of dielectric modulus Fig. 5 shows the normalized plot of the modulus data for the sample BTTK at different temperatures. The approximate overlap of the modulus curves for all temperatures indicates that the dynamical processes occurring at different frequencies are independent of temperature. Remaining glass samples show similar behavior. It is found that except at very high frequencies, all such M″/M″max plots (as a function of frequency) have been seen to collapse (Fig. 5) very satisfactorily indicating that the mechanism of charge transport is independent of temperature [1]. Fig. 6 shows the M″ vs. M′ plot for the BTTK sample which traces out a semicircle. The behavior is similar to the one observed in the cole–cole plot diagram (Fig. 1) except that the area under the semicircle increases with increase in temperature. In the plot the intercept of the semicircle on the x-axis gives out the inverse of capacitance at that temperature. The capacitance of the samples at a particular temperature is calculated from the above plot according to the relation M″ = Co/2C, where Co = (εoA)/d (A and d are the area and the thickness of the sample and εo is the permittivity of the free space) and C is the capacitance of the sample. Using this relation, capacitance values are calculated for all glass samples and given in Table 4. Capacitance behavior is found to decrease with increase in temperature. Resistance values are calculated using ωRC = 1 and are tabulated in Table 4. From the table, the resistance and capacitance values do not follow a systematic trend when one alkali oxide is replaced by one another.

Fig. 5. The normalized modulus spectra for BTTK glass samples.

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Fig. 6. M″ vs. M′ plot for the BTTK glass sample.

3.4. AC conductivity behavior AC conductivity measurements were carried out for the all glass samples as a function of frequency and the plots are shown in Fig. 7. The AC conductivity behavior of all the glass samples is qualitatively similar. The AC conductivity exhibits a change of slope to higher values as the frequency is increased. From Fig. 7 it is observed that AC conductivity spectra show two distinct regimes within the measured frequency, (i) plateau and (ii) dispersion regions. The plateau region corresponds to frequency independent conductivity σ(0) that it is obtained by extrapolating the conductivity value to zero frequency. At higher frequencies conductivity exhibits dispersion. Frequency independent conductivity maybe attributed to the long-range transport of mobile alkali ions in response to the applied ﬁeld, where only successful diffusion contributes to the DC conductivity σ(0) [10]. In addition, random distribution of the ionic charge carriers via activated hopping gives rise to a frequency independent conductivity at lower frequencies whereas at higher frequencies conductivity exhibits dispersion, increasing roughly in a power law fashion and eventually becoming almost linear at even higher frequencies [13]. The characteristic frequency is taken as a frequency at which the dispersion deviated from the DC plateau is also termed as the hopping

Table 4 Capacitance, resistance and FWHM values from modulus plots (M″ vs. M′ and M″ vs. freq) for the BTTR glass series. Temperature

Capacitance (pF)

BTTL 200 225 250 275 300

163 123 82 73 47

Resistance (M Ω) 33 17 8 0.116 0.076

FWHM (Hz) 10036 25678 79307 105946 227350

BTTN 200 225 250 275 300

282 250 160 100 85

183 55 19 12 6

1020 3803 14510 44240 99693

BTTK 225 250 275 300

249 203 140 72

97 32 15 10

2187 8149 25173 77747

Fig. 7. Conductivity isotherms of (a) BTTL, (b) BTTN and (c)BTTK glass samples.

rate. From Fig. 7, it is observed that characteristic frequency or hopping rate shifts towards the high frequencies with increasing the temperature and reached closely paralleling the plateau region of DC conductivity [10]. Fig. 8 shows the crossover frequency for BTTL, BTTN and BTTK glass samples as a function of reciprocal temperature. This ﬁgure is ﬁtted to above Eq. (1) using the least-square linear ﬁt. Reciprocal temperature dependence of the crossover frequency ωH reveals that it obeys the Arrhenius relation. From the ﬁgure it was found that hopping rate in lithium is followed by potassium and sodium for borate-rich glasses (BTTR).

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Fig. 8. Crossover frequency for BTTL, BTTN and BTTK glasses shown as a function of the reciprocal of temperature. Solid lines are the least-square straight-line ﬁts to the data.

Fig. 10. Logσ vs. logω plots for BTTL, BTTN and BTTK glass samples at RT and 300 °C.

The behavior of the conductivity spectrum can be explained on the basis of Almond–West type power law with single exponent.

samples showing conductivities at 300 °C (σ300) in the range of 10− 6 to 10− 5.5 (Ohm-cm)− 1. In the high frequency region, conductivity is enhanced by one order of magnitude up to 10− 5 (Ohm-cm)− 1 as temperature is increased. When alkali oxides are replaced by one another, conductivity is almost constant at room temperature and variation was found to be pronounced at elevated temperatures. The highest conductivity value is exhibited by lithium-containing glass. Usually in alkali borate glasses ionic conductivity increases in order σLi b σNa b σK but this order of conductivity is found to be different in the present glass series BTTR (Borate rich) where, the conductivity of lithium is more followed by potassium and sodium but this amount of increase between sodium and potassium is negotiable. From the ﬁgure, it is understood that the conductivity of lithium is more due to its high mobility. Variation of conductivity in present glasses maybe attributed to the alkali effect and the highest conductivity of lithium content glasses may form highly disordered matrix with more opened channels for the easy migration of Li+ ions.

s

σ ðωÞ = σ0 + Aω

ð2Þ

where, σ0 is frequency independent and it is identiﬁed with the DC conductivity and the second term is the purely dispersive component of the AC conductivity, depending on the frequency ω (ω = 2πƒ is the angular frequency) in a characteristic power law fashion. A and s are power law ﬁt parameters. In the present study the power law exponent ‘s’ has been found to be material dependent [14]. Power law parameter s is determined for all the glass samples at various temperatures. The variation of the ‘s’ values with various temperatures for BTTR glass series is shown in Fig. 9. It is clear from the ﬁgure that all ‘s’ values are temperature dependent and some of them are more than unity at certain temperatures. And it is also observed that the s value decreases as temperature increases. Similar behavior was reported by Veeranna et al. [15]. In the present study, lowest ‘s’ values are found to be for lithiumcontaining glasses. Usually the lowest ‘s’ value indicates high degree modiﬁcation. This behavior can be attributed to the inter lithium ion interaction inﬂuencing the AC transport phenomenon. Fig. 10. shows logω vs. logσ plots at RT and at 300 °C for the BTTR glass series. Here the conductivity increases from room temperature to 300 °C. For low frequency region, conductivity values at RT (σac) are relatively low, in the order of 10− 8 to 10− 9 (Ohm-cm)− 1. However, a dramatic increase in conductivity is seen with temperature, all glass

4. Conclusions AC conductivity and relaxation behavior of alkali boro-tellurite glasses have been examined. It is found that AC conductivity is more for lithium followed by potassium and sodium but this amount of increase between sodium and potassium is negotiable. Lowest ‘s’ values are found to be for lithium-containing glasses. Scaling analysis of dielectric modulus shows excellent time-temperature superposition indicating common ion transport mechanism. References

Fig. 9. Variation of power law exponent, s,with temperature. The lines are drawn as a guide for the eye.

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