AC conductivity and dielectric studies in V2O5–TeO2 and V2O5–CoO–TeO2 glasses

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Journal of Molecular Structure 889 (2008) 308–315 www.elsevier.com/locate/molstruc

AC conductivity and dielectric studies in V2O5–TeO2 and V2O5–CoO–TeO2 glasses T. Sankarappa a,*, M. Prashant Kumar a, G.B. Devidas a, N. Nagaraja a, R. Ramakrishnareddy b a

Department of Physics, Gulbarga University, Gulbarga, Karnataka 585 106, India Department of Physics, Sri Krishnadevaraya University, Ananthapur, AP, India

b

Received 15 October 2007; received in revised form 17 January 2008; accepted 11 February 2008 Available online 19 February 2008

Abstract Single and mixed transition metal ions doped tellurite glasses were investigated for dielectric properties in the frequency range 50 Hz to 5 MHz and temperature range 300–500 K. From the total conductivity derived from the dielectric spectrum the frequency exponent, s, and dc and ac components of the conductivity were determined. The temperature dependence of dc and ac conductivities at different frequencies was analyzed using Mott’s small polaron hopping model and, the high temperature activation energies have been estimated and discussed. The frequency exponent, s, was compared with theoretical models. The ac conductivity variation with frequency has been fit to Hunt’s expression given for x > xm and the fit was found to be good which reveal that Hunt’s model explains the measured data satisfactorily in the experimental frequency domain. Ó 2008 Elsevier B.V. All rights reserved. PACS: 72.80.Ng; 72.20.-i; 77.22Gm Keywords: Tellurite glasses; Transition metal ions; Ac conductivities; Activation energies

1. Introduction Transition metal oxide glasses have always been studied to better understand the transport mechanisms in these electronic semiconductors [1–4]. Among various types of glasses, the tellurite based glasses exhibit high dielectric constant and electrical conductivity compared to other glass systems, which has been argued to be due to the unshared pair of electrons of the TeO4 group that do not take part in the bonding [5]. The dc conductivity studies in various different types of glasses doped with transition metal ions (TMI) revealed that the conduction mechanism in them can be explained by Mott’s small polaron hopping model [3,4]. Hunt’s model has been used to describe ac con*

Corresponding author. Tel.: +91 8472 263298; fax: +91 8472 263206. E-mail address: sankarappa@rediffmail.com (T. Sankarappa).

0022-2860/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2008.02.009

ductivity behavior in V2O5–B2O3 glasses and showed that the relaxation process has a local character [2]. The frequency dependent conductivity and dielectric properties studied in the frequency range 0.1–100 kHz and temperature range 77–400 K in V2O5–TeO2 glasses revealed that neither quantum mechanical tunneling nor hopping over the barrier models were suitable to explain the frequency dependent conductivity [3]. Impedance spectroscopy over a wide frequency scale has been traditionally applied to understand the frequency dependence of complex conductivity in various glassy materials [6–9]. At low frequencies, a random diffusion of the ionic charge carriers via activated hopping has been observed to be resulting in a frequency-independent conductivity in different ion conducting materials [10,11]. However, r0 (x) exhibits dispersion at higher frequencies, which increases roughly in a power-law trend

T. Sankarappa et al. / Journal of Molecular Structure 889 (2008) 308–315

Since no data for ac electrical conductivity in V2O5– TeO2 glasses is available in the literature for temperatures above 400 K and frequency above 100 kHz, we have embarked on investigating ac conductivity in these glasses in the temperature range 300–500 K and frequency 50 Hz to 5 MHz. There are no reports in the literature on ac conductivity of MT glasses considered here. 2. Experimental The glasses were prepared by melt-quenching technique using the analytical grade V2O5, Co3O4 and TeO2 (Sigma–Aldrich). The relevant chemicals in appropriate weight ratios were taken in a porcelain crucible and melted for more than an hour in a muffle furnace at 1200 K. The melt was quickly quenched to room temperature by pouring on a stainless steel plate and covering with another stainless steel plate. The random pieces of the glass samples thus formed were collected. In order to relieve mechanical stresses the samples were annealed at 500 K. The amorphous nature of glass samples was confirmed by XRD studies. The DSC studies were carried out on the present samples and the glass transition temperatures thus obtained have been presented and discussed elsewhere [15]. The frequency dependent measurements of capacitance, C, and dissipation factor, tan d, were obtained using a computer controlled LCR HiTester (HIOKI, 3532-50) for different frequencies in the range 50 Hz to 5 MHz and temperature from 300 to 500 K. The dielectric constant (e0 ), dielectric loss factor (e00 ) and ac conductivity (rac) were determined as per the following expressions, Cd eo A e00 ¼ e0 tan d rac ¼ xeo e00 e0 ¼

3.1. Dielectric properties Figs. 1 and 2 depict the variation of dielectric constant, e0 , and dielectric loss, e00 (as insets) with frequency, respectively, for glasses ST1 and MT1 at various temperatures. It can be noticed that in both the series of glasses, the e0 and e00 decreases with increase in frequency and increases with increase in temperature. Similar results were observed in the case of other ST and MT samples. These measured e0 values of the present glasses are in agreement with the reported e’ values for similar glass systems [16,17]. These figures clearly display that both e0 and e00 decrease abruptly with increase in frequency below about 10 kHz. It may be due to interfacial effects such as space charge polarization, etc. To analyze and understand the bulk dielectric properties as a function of composition of the present glasses, only the high frequency data has been considered. The increase in dielectric constant of the sample with increase in temperature is usually associated with the decrease in bond energies [18]. That is, as the temperature increases two effects on the dipolar polarization may occur; (i) it weakens the intermolecular forces and hence enhances the orientational vibration, (ii) it increases the thermal agitation and hence strongly disturbs the orientational vibrations. The dielectric constant becomes larger at lower frequencies and at higher temperatures which is normal in oxide glasses and, is not an indication for spontaneous polarization [18]. This may be due to the fact that as the frequency increases, the polarizability contribution from ionic and orientation sources decreases and finally disappear due to the inertia of the ions. In Figs. 1 and 2, it is seen that the e0 increases with increase in temperature and at high temperatures it

313K 353K 393K 433K 473K 503K

2.8

2.6

4.0

313K 353K 393K 433K 473K 503K

3.5 3.0

log (e'')

(i) (V2O5)x–(TeO2)1x, x = 0.10, 0.20, 0.30 and 0.40, labeled as ST1, ST2, ST3 and ST4. (ii) (V2O5)0.4 (CoO)x (TeO2)0.6x, x = 0.3, 0.4 and 0.5, labeled as MT1, MT2 and MT3.

3. Results and discussion

2.5 2.0 1.5 1.0 0.5

log (ε')

and eventually becoming almost linear at even higher frequencies. Interestingly, polaronic conductors also exhibit a behavior similar to the ionic ones. Nevertheless, the dispersion clearly reflects a correlated kind of motion of the ions occurring on relatively short time scales [12–14]. In the present paper, we report a detailed study on ac electrical conductivity in single and mixed TMI doped tellurite glasses in the following mentioned compositions,

309

0.0 -0.5

1

2

3

4

5

6

7

log (F) (Hz)

2.4

ð1Þ 2.2

ð2Þ ð3Þ

where eo is the permittivity of free space, x is the frequency of the input signal, d is thickness of the glass sample and A is cross sectional area of the sample.

1

2

3

4

5

6

7

log (F) (Hz)

Fig. 1. Plots of log(e0 ) versus log(F) for the glass ST1 at different temperatures. Inset shows the frequency dependence of e0 0 for the same sample.

T. Sankarappa et al. / Journal of Molecular Structure 889 (2008) 308–315

3.4 log (ε'')

3.2 3.0

log (ε')

2.8 2.6

5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0

a 1.2x10

1.0x10 313K 353K 393K 433K 473K 503K 1

2

3

4

5

log (F) (Hz)

2.4 2.2 2.0 1.8

6

7

313K 353K 393K 433K 473K 503K

8.0x10

6.0x10

3

3

2

2

8x102

Dielectric constant, ε'

3.6

Dielectric loss, ε''

310

7x102 6x102 5x102 4x102 3x102 2x102 1x102 0.1

4.0x10

2.0x10

2

0.2

0.3

0.4

Mole fraction of V2O5

2

0.0

1.6 1

2

3

4

5

6

0.2

0.1

7

b

80

180

70

3.2. Conductivity The frequency dependence of conductivity in ST1 and MT1 glasses has been depicted in Fig. 4(a) and (b), respectively. It can be observed from these figures that the conductivity increases with increase in frequency. Similar kind of observation has been made for remaining ST and MT glasses. The ac conductivity is generally expressed as [20], ð4Þ

where rdc(=r0) is the frequency-independent component, A is a temperature dependent constant, s is the frequency

160 140 120

60

Dielectric loss, ε''

increases more rapidly. This behavior is typical to the polar dielectrics in which the orientation of dipoles is facilitated with rising temperature and thereby the dielectric constant is increased. At low temperatures, the contribution of electronic and ionic components to the total polarizability will be small. As the temperature is increased the electronic and ionic polarizability sources start to increase. From Fig. 3(a) and (b) (insets), it can be noted that the dielectric constant, e0 increases with increase in TMI concentration in both the glass systems. It may be attributed to the decrease in electronic contribution to the total polarizability [19]. The compositional dependence of dielectric constant is very much similar to that of ac conductivity. Fig. 3(a) and (b) shows the compositional dependence of dielectric loss, e00 at 500 kHz and at 470 K in both ST and MT glass samples, respectively. The e00 is found to increase with increase in V2O5 content in ST glasses and CoO content in MT glasses. The compositional dependence of dielectric loss is very much similar to that of ac conductivity and dielectric constant.

¼ r0 þ Axs

0.4

200

Dielectric constant, ε'

Fig. 2. Plots of log(e0 ) versus log(F) for the glass MT1 at different temperatures. Inset shows the frequency dependence of e00 for the same sample.

rTotal ¼ rdc þ rac

0.3

Mole fraction of V2O5

log (F) (Hz)

50

100 80 60 40

40

0.3

0.4

0.5

Mole fraction of CoO

30 20 10 0.3

0.4

0.5

Mole fraction of CoO

Fig. 3. Compositional dependence of dielectric loss, e00 at 500 kHz and temperature, 473 K for (a) ST and (b) MT glasses. Insets represent the variation of dielectric constant, e0 with mole fractions of (a) V2O5 and (b) CoO at frequency 500 kHz and temperature, 473 K. Solid lines are the guides to the eye.

exponent and rac(=Axs) represents the dissipative contribution to the total conductivity, which depends both on temperature and composition of the sample [2]. Eq. (4) was fit to the data and shown in Fig. 4(a) and (b) for ST1 and MT1 samples. It may be noted that in order to highlight the quality of fit the data has been exhibited on log–log scale in these figures. The best fits gave dc component, r0, temperature dependent constant, A, and frequency exponent, s. Similar regressional analysis has been performed on ac conductivity of the remaining ST and MT samples. The temperature dependence of dc conductivity, r0, for both ST and MT glasses is presented in Fig. 5(a) and (b). It can be seen that the dc conductivity, r0 increases with increase in temperature, which reveals the semiconducting nature of the present glass samples. Within the studied range of temperature, the r0 varied in the range from 102 ohm1 m1 to 107 ohm1 m1 for ST glasses and

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a

a

-4

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-2

ST1 ST2 ST3 ST4

-3

x

-4

-6

ln(σ0T) (ohm m K)

-1

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-1

ln(σ) (ohm-1m-1)

-5

-10

313K 353K 393K 433K 473K 503K

-12

Slope=1 -14

-6 -7 -8 -9 -10 -11 -12 -13 -14

4

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16

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ln(F) (Hz)

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103/T(K-1)

b

x

-5

-7

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MT1 MT2 MT3

-1

-1

ln(σ0T) (ohm m K)

ln(σTotal) (ohm-1m-1)

b

2.4

-10

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Slope=1

-14

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-15 4

6

8

10

12

14

16

ln(F) (Hz)

Fig. 4. The plots of total conductivity, ln(rTotal), versus ln(F) for (a) ST1 and (b) MT1 glasses. Solid lines are the best fits to Eq. (4). The linear line, x with slope unity connects the cross over frequency, F0 of each isotherm.

in the range 103 ohm1 m1 to 106 ohm1 m1 for MT glasses. From these figures it can also be noted that the conductivity increases with increase in TMI concentration in both ST and MT glasses. The increase in conductivity with TMI content in both the systems can be attributed to decrease in polaron hopping distance with increase in TMI content [9,21]. Further, the observed trend of increase in conductivity with increase in second TMI content in MT glasses is in agreement with Hirashima et al. [22] and contrary to [23,24] where the addition of second transition metal ions hindered the electronic motion and hence the conductivity was found to be decreasing. The r0 values were subtracted from the total conductivity and obtained the pure ac conductivities, as per the expression given in Eq. (4). Fig. 6(a) and (b) demonstrates the temperature variation of ac conductivity at different frequencies for ST1 and MT1 glasses, respectively. The ac conductivity was observed to be increasing with increase

-14 1.8

2.0

2.2

2.4

2.6 3

2.8

3.0

3.2

-1

10 /T (K )

Fig. 5. The plots of ln(r0T) versus (1/T) for (a) ST and (b) MT glasses. Solid lines are the least square linear fits to the data in the high temperature region.

in frequency. The similar kind of variation was observed for the other ST and MT glasses. The variation of conductivity was observed to be a thermally activated process and is due to the hopping of polarons between the multivalent states of transition metal ions in the glass matrix [25]. The temperature dependence of both pure dc and ac conductivities have been considered in the light of Mott’s small polaron hopping model. According to Mott’s SPH model [26], the electrical conductivity in non-adiabatic regime is expressed as, r ¼ ðr0 =T Þ expðW =k B T Þ

ð5Þ

where W is the activation energy and r0 is the pre-exponential factor. The plots of ln(rT) versus (1/T) shown in Figs. 5 and 6 for ST and MT glasses, respectively, were made as per

312

a

T. Sankarappa et al. / Journal of Molecular Structure 889 (2008) 308–315 Table 1 Variation of dc activation energy, Wdc and ac activation energy Wac at different frequencies for ST and MT glasses

-8

1 MHz

ln(σacT) (ohm-1m-1K)

-9

Glass 500 kHz

-10

-11

ST1 ST2 ST3 ST4 MT1 MT2 MT3

100 kHz

-12

Wdc (eV)

σ0

Wac (eV)

0.428 0.416 0.402 0.385 0.523 0.506 0.486

100 kHz

500 kHz

1 MHz

0.401 0.395 0.383 0.366 0.499 0.431 0.392

0.368 0.362 0.323 0.311 0.476 0.430 0.377

0.321 0.326 0.313 0.292 0.433 0.409 0.373

-13

a

-14 2.0

2.2

2.4

2.6 3

2.8

3.0

3.2

ST1 ST2 ST3 ST4

1.0

-1

10 /T(K ) Frequency exponent, s

b -2

1 MHz

ln(σacT) (ohm-1m-1K)

-4

500 kHz -6

0.9

CBH Fit line

0.8

100 kHz -8 0.7 300

σ0

-10

350

400

450

500

Temperature (K) -12

)

b -14 1.8

2.0

2.2

2.4

2.6 3

2.8

3.0

1.3

MT1 MT2 MT3

3.2

-1

1.2

Fig. 6. The plots of ln(racT) versus (1/T) for (a) ST1 and (b) MT1 glasses. Solid lines are the least square linear fits to the data in the high temperature region.

Eq. (5). It can be noted from these figures that the curves are linear at high temperature and non-linear at low temperature. The least square linear lines were fit to the data at high temperatures. From the slopes of the linear lines the activation energy, Wdc, associated with r0 were determined. Similarly, the ac activation energies, Wac, were estimated from the slopes of the least square linear fits. The best fits of ln(rT) versus (1/T) gave r2 = 0.992–0.996 (r = correlation coefficient). These Wdc and Wac values are tabulated in Table 1. The activation energies in both ST and MT glasses were found to decrease with increase in mole fraction of V2O5 and CoO, respectively. The ac activation energies of all studied ST and MT glasses were observed to be decreasing with increase in frequency, which is consistent with the conductivity variation with the frequency. Fig. 7(a) and (b) display the temperature dependence of frequency exponent, s, obtained from the non-linear fits made to the Eq. (4) (Fig. 4), respectively, for ST and MT

Frequency exponent, s

10 /T (K )

1.1 1.0 0.9 0.8

CBH Fit line

0.7 0.6 300

350

400

450

500

Temperature (K)

Fig. 7. Temperature dependence of frequency exponent, s, for (a) ST and (b) MT glasses. A line due to CBH model fit is also shown for ST1 and MT1 in the plots (a) and (b), respectively.

glasses. For the present glasses, the frequency exponent, s, values were determined to be lying between 1.31 and 0.64 in the studied range of temperature. Fig. 7 clearly indicates the frequency exponent, s, does not show a systematic variation with temperature and composition in both the systems. This kind of variation in s with temperature may

T. Sankarappa et al. / Journal of Molecular Structure 889 (2008) 308–315

s¼1

6k B T W M þ k B T lnðxs0 Þ

313K 353K 393K 433K 473K 503K

6 5 4 3 2 1 0 -1 -8

-6

-4

-2

0

2

4

6

2

4

8

ln (F/F0)

b 5

313K 353K 393K 433K 473K 503K

4

ð6Þ

where WM is the maximum height of the energy band and e0 is the permittivity of free space. The frequency exponent, s is given as [30]

8 7

3

ln(σac/σ0)

W ¼ WM

2e2  0 pe eo R

a

ln(σac/σ0)

be due to the different contributions from conducting and dielectric losses at different temperatures [31,32]. Owen [27] reported the electrical properties of glasses in an alternating field depend not only on the mobile ions but also on the relatively immobile ions, which also take part in network forming. Several authors [28,29] have computed ac conductivity for single electron motion undergoing quantum mechanical tunneling (QMT). In QMT model, the prediction was made to the effect that the conductivity is linearly dependent on temperature and the frequency exponent, s, is independent of temperature but frequency dependent. However, it can be clearly seen from the Fig. 7(a) and (b) that the frequency exponent, s, decreases with increase in temperature, thereby conflicting with the prediction of QMT model. Elliott’s [30] Correlated Barrier Hopping (CBH) model relates the potential barrier to the inter site separation. At a site separation R, the Columb well overlaps between the neighboring hopping sites and that results in lowering of the effective barrier from WM to W, which for two-electrons case is given by,

313

2

1

ð7Þ

where so is the characteristic relaxation time. The Eq. (7) has been fit to the experimental frequency exponent values. Fits to the data for ST1 and MT1 are shown in Fig. 7(a) and (b). It can be observed from these figures that experimental s values disagree with CBH model fit. This observation is in agreement with the literature, wherein the temperature dependence of frequency exponent has been reported to be disagreeing with QMT and CBH models [31–34]. The cross over frequency (F0) from dc to dispersive like behavior has been found to be increasing with temperature. This frequency F0 is defined through r0 (F0) = 2rdc [35]. It has been observed that the frequency F0 is a thermally activated one with the same energy as the dc conductivity. Therefore, it is obvious to note that by connecting the cross over frequencies one obtains a straight line with a slope equal to unity as shown in Fig. 4(a) and (b). By shifting or scaling the conductivity isotherms along the straight line with slope one, the conductivity master curves are drawn and shown in Fig. 8(a) and (b) for ST1 and MT1, respectively. From these plots it is clear that the time– temperature superposition principle is fulfilled which in turn suggest the occurrence of a temperature independent relaxation mechanism [35]. The validity of the scaling law has been found to be valid for TMI doped glasses also [36].

0

-1 -10

-8

-6

-4

-2

0

6

ln (F/F0)

Fig. 8. The ac conductivity master curves for the glasses (a) ST1 and (b) MT1.

3.3. Relaxation processes Hunt’s model considers two distinct charge migration processes depending on the frequency domains i.e., x < xm and x > xm where xm is the frequency corresponding to the peak in dielectric loss. The term xm is generally taken as equivalent to the cross over frequency F0, which is nothing but the characteristic frequency for the onset of ac conduction [14]. For present glass systems, the Hunt’s model has been used to study the dielectric relaxation processes, which is well adapted to the oxide glasses [37–39]. In these two domains, the total conductivity can be expressed as,   s  x rt ðxÞ ¼ rdc 1 þ A for x > xm xm   r  x rt ðxÞ ¼ rdc 1 þ KðdÞ for x < xm xm

ð8Þ ð9Þ

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a

dc and ac components of the conductivity were extracted using dielectric data. The analyses of these three quantities lead to the following mentioned conclusions.

-8.0 -8.5

(i) Temperature dependence of ac conductivity at different frequencies and dc conductivity exhibit the behavior at high temperatures similar to that predicted by the Mott’s small polaron hopping model. Activation energies were determined. (ii) The measured temperature dependence of the frequency exponent does not agree with QMT and CBH models. (iii) The ac conductivity appeared to be behaving as per the Hunt’s expression given for x > xm where xm (=F0) correspond to dielectric peak.

-9.5

-1

-1

ln(σ) (ohm m )

-9.0

-10.0 -10.5

313K 353K 393K 433K

-11.0 -11.5 -12.0 -1

0

1

2

3

4

5

6

ln(ω/ωm)

-8

-9

Acknowledgements

-7

-1

-1

ln(σ) (ohm m )

b

It is for the first time that the dielectric studies on vanado-tellurite glasses for temperatures above 400 K and frequencies above 100 kHz are reported. Also it is for the first time that vanado-cobalt tellurite glasses have been investigated.

One of the authors, T. Sankarappa acknowledges the rigorous research training that he received from Professor M. Springford and Dr. P.J. Meeson at University of Bristol.

-1 0

-1 1

313K 353K 393K 433K

-1 2

References

-1 3 -5

-4

-3

-2

-1

0

1

2

3

4

5

6

ln(ω/ωm)

Fig. 9. The plots of ac conductivity, ln(rac) versus ln(x/xm) for samples (a) ST1 and (b) MT1. The solid lines are the best fits to Hunt’s Eq. (8).

where r ¼ 1 þ d  d f , d being the dimensionality and df = 2.66 [40], A and K(d) are the constants [2–5]. Considering xm to be equivalent to F0, the Eq. (8) has been fit to conductivity data for the samples ST1 and MT1 and are shown in Fig. 9(a) and (b), respectively, on log–log scale. The best fits gave rdc, A and exponent, s, which are same as that obtained from the fits made to Eq. (4) (Fig. 3). Therefore, it can be said that the ac conductivity in present glasses is very well explained by Hunt’s model in the frequency domain x > xm. Here, it is assumed that the experimental frequencies are lying above xm and therefore Eq. (9) has not been used. 4. Conclusion Single and mixed transition metal ions doped tellurite glasses were investigated for dielectric properties. The dielectric spectra in terms of frequency, temperature and composition have been discussed. The frequency exponent,

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