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Electronic transport and relaxation studies in bismuth modiﬁed zinc boro-tellurite glasses Sunil Dhankhar a, R.S. Kundu a, R. Parmar b, S. Murugavel c, R. Punia a, d, *, N. Kishore a a

Department of Applied Physics, Guru Jambheshwar University of Science & Technology, Hisar 12500, India Department of Physics, Maharishi Dayanand University, Rohtak 124001, India c Department of Physics and Astrophysics, University of Delhi, Delhi 11000, India d Department of Physics, Indira Gandhi University Meerpur, 123401 Rewari, India b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 25 June 2015 Received in revised form 19 August 2015 Accepted 20 August 2015 Available online 25 August 2015

The ac conductivity of tellurium based quaternary glasses having composition 60 TeO2 e 10 ZnO e (30 x) B2O3 e xBi2O3; x ¼ 0, 5, 10, 15 and 20 has been investigated in the frequency range 101 Hz to 105 Hz and in the temperature range 483 Ke593 K. The frequency and temperature dependent ac conductivity increase with increase in bismuth content and found to obey Jonscher's universal power law. The dc conductivity, crossover frequency and frequency exponent have been estimated from the ﬁtting of the experimental data of conductivity with Jonscher's universal power law. In the studied glasses the ac conduction may be described by overlapping of large polaron tunneling model. The activation energy is found to be decrease with increase in bismuth content and variable range hopping (VRH) proposed by Mott with some modiﬁcation suggested by Punia et al. is more or less suitable to explain dc conduction. The value of the stretched exponent (b) obtained by ﬁtting of M00 reveals the presence of non-Debye type of relaxation in the presently studied glass samples. Scaling spectra of electric modulus (M0 and M00 ) collapse into a single master curve for all the compositions and temperatures. The values of activation energy of electric modulus (ER) and conduction (W) are nearly equal for all the studied glasses, indicating that the polaron have to overcome the same energy barrier during conduction as well as relaxation processes. The conduction and relaxation process in the presently studied glass samples are composition and temperature independent. © 2015 Elsevier Masson SAS. All rights reserved.

Keywords: Jonscher's power law Overlapping of large polaron tunneling Polarons Electric modulus Relaxation

1. Introduction Heavy metal oxide glasses such as TeO2, Bi2O3 etc. have been studied extensively in the recent years [1e4] due to their wide applications in the ﬁeld of glass ceramics, layers for optical and electronic devices, thermal and mechanical sensors, reﬂecting windows, etc. [5e9]. TeO2 based glasses have low melting temperatures, high dielectric constant, and good infra red transmissions [10e13], which makes them suitable candidates for a wide range of applications such as optical materials used in laser technology [14,15] and fast-ions conducting solid electrolytes [16,17]. Glasses containing Bi2O3 and ZnO have a long infra red cut off and third order non linear optical susceptibility which make them ideal

* Corresponding author. Department of Physics, Indira Gandhi University Meerpur, 123401 Rewari, India. E-mail address: [email protected] (R. Punia). http://dx.doi.org/10.1016/j.solidstatesciences.2015.08.016 1293-2558/© 2015 Elsevier Masson SAS. All rights reserved.

candidate for application as infra red transmission components and photonic devices [18,19]. Addition of heavy metal oxides (like Bi2O3, Nb2O3) to tellurite glasses enhances both the physical and optical properties of these glasses and addition of ZnO to tellurite glass network increases the stability of glass network and glass forming ability [20,21]. The temperature dependence of conductivity of tellurite glasses has been found to show the characteristic transition between conduction in a polaron band and due to hopping [22,23]. The conductivity in these glasses depends on number of mobile charge carriers and their mobility [24]. The electronic transport properties of TeO2 e Bi2O3, TeO2 e V2O5 e Bi2O3, TeO2 e ZnO, Bi2O3 e B2O3 e ZnO and other tellurite based glass system have been studied by many researchers [25e30]. But, there is hardly any report in literature on systematically composition and frequency dependent ac conductivity, scaling behavior, electric modulus formulation and conduction mechanism of TeO2 e Bi2O3 e B2O3 e ZnO glass system. In the present study, we report the ac conductivity, dielectric

S. Dhankhar et al. / Solid State Sciences 48 (2015) 230e236

properties, electric modulus formulation and relaxation studies of the tellurium based quaternary glasses using impedance spectroscopy.

2. Experimental Glasses having compositions 60 TeO2 e 10ZnO e (30 x) B2O3 e xBi2O3; x ¼ 0, 5, 10, 15 and 20 were prepared using analar grade ZnO, Bi2O3, B2O3 and TeO2 chemicals by melt-quench technique. The detailed discussion of preparation of studied glass system is reported elsewhere [1]. X-ray diffraction studies of the samples performed using Rigaku Table-Top X-Ray Diffractometer conﬁrm the amorphous nature of these samples. The values of glass transition temperature (Tg) of different samples were measured by DSC technique using T A Instruments, Model no. Q600 SDT, at a heating rate 10 C/min in nitrogen atmosphere. The glass samples were cut and ground to get rectangular shapes with thickness about 1 mm and their surfaces were polished. For electrical measurements, both sides of the polished samples were coated with silver to serve as electrodes. Conductivity measurements were carried out by using Alpha-A high resolution dielectric, conductivity, impedance, and gain phase modular measurement system by Novocontrol Technologies GmbH & Co. KG in the frequency range of 101 Hz to 105 Hz and temperature ranging from 483 K to 593 K. The ﬁtting of experimental data was done by using linear ﬁt and non-linear curve ﬁtting modules of Origin Pro 8.6 software.

3. Results and discussion The ac conductivity of different glass compositions of 60 TeO2 e 10ZnO e (30 x) B2O3 e xBi2O3; x ¼ 0, 5, 10, 15 and 20 glass system recorded in temperature range 483 Ke593 K and frequency range 101 Hz to 105 Hz show similar frequency and temperature dependence. The frequency dependent conductivity goes on increasing with increase Bi2O3 content in studied frequency range at any particular temperature, a typical compositional variation of s0 (u) with frequency at 553 K is shown in Fig. 1. The frequency dependent conductivity is characterized by two regions: (i) plateau region and (ii) dispersion region as observed for various other oxide glasses [24e28]. The ac conductivity s0 (u) of the studied glass system is analyzed in the light of Jonscher's Universal Power Law [31,32].

Fig. 1. Compositional variation of total ac conductivity s0 (u) of 60 TeO2 e 10ZnO e (30 x) B2O3 e xBi2O3 glass system at 553 K.

s u s0 ðuÞ ¼ sdc 1 þ uH

231

(1)

where sdc is direct current (dc) conductivity, uH is crossover frequency separating dc regime (plateau region) from the dispersive conduction and s is frequency exponent that lies between 0.7 and 1 [31,33]. The values of sdc, uH and s are obtained by the ﬁtting of the experimental data of s0 (u) measured at different temperatures with Eq. (1). As shown in Fig. 2, the experimental data ﬁtted with Jonscher's universal power law (Eq. (1) gives very good ﬁtting with best parameter ﬁt, R2, in the range 0.9995e0.9998. Jonscher's universal power law is observed to be obeyed in all the presently studied glass compositions indicating that the ac conduction in the present glass system may be attributed to hopping mechanism [31]. The conduction mechanism in any material could be understood from the temperature dependent behavior of frequency exponent (s). Various models based on classical hopping of charge carriers over barrier, quantum mechanical tunneling and the overlapping large-polaron tunneling [24,34e39], have been proposed on the basis of variation of frequency exponent with temperature and frequency. (i) If s decreases with temperature then it follows correlated barrier hopping (CBH) conduction mechanism [40]. (ii) If s depends upon frequency but is in dependent of temperature then the conduction mechanism can be explained by the quantum mechanical electron tunneling theory [40]. (iii) If s increases with increase in temperature, then the conduction process can be explained with the small polaron quantum mechanical tunneling theory where as if s decreases at ﬁrst, reaching a minimum and increases thereafter with increase temperature then it can be explained by large polaron quantum mechanical tunneling model [40]. The temperature dependence of frequency exponent (s) obtained from the ﬁtting of experimental data with Eq. (1) is found to be lying between 0.7 and 1 in the studied range of temperature. For the presently studied glass system, frequency dependence of s has not been observed in the studied frequency range, so temperature dependence of frequency exponent plays a key role in estimation of conduction mechanism. In studied tellurium based quaternary glasses, s ﬁrst decreases and attains minima and then after, it

Fig. 2. Measured total ac conductivity (s0 ) for 60 TeO2 e 10ZnO e (30 x) B2O3 e xBi2O3 glass composition shown as function at twelve different temperatures. The solid lines in the ﬁgure are the best ﬁts obtained from ﬁtting of experimental data with Jonscher's power law.

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Fig. 3. The variation of frequency exponent (s) for different 60 TeO2 e 10ZnO e (30 x) B2O3 e xBi2O3 glass compositions are shown as a function of temperature (T).

increases with temperature as shown in Fig. 3. So, the conduction mechanism in the studied glass system may be attributed to Overlapping Large Polarons Tunneling (OLPT). The mechanism of charge carriers transport has also been studied using the reduced plot of frequency versus reduced conductivity. In the past few years different scaling models have been proposed. The ac conductivity of the studied glass system has been scaled by sdc, while the frequency axis is scaled with Jonscher's cross-over frequency (uH) as scaling frequency. It has been observed that both compositional and temperature dependent scaling spectra lie on a single master curve conﬁrming that uH is appropriate scaling frequency and all the studied glass compositions have similar conduction mechanism. A typical plot of scaling spectra at different temperatures for x ¼ 5 and different compositions at a particular temperature at 523 K is shown in Figs. 4 and 5 respectively. The results of ac scaling are in accordance with those obtained from study of frequency exponent i.e all the glass compositions shows similar type of conduction mechanism in the studied frequency and temperature range. DC conductivity has been obtained from ﬁtting of the experimental data of s0 (u) at different temperatures with Jonscher's equation and it is observed that it lies in the range from

Fig. 5. Compositional dependence scaling spectra for different 60 TeO2 e 10ZnO e (30 x) B2O3 e xBi2O3 glass compositions with Jonscher's cross-over frequency (uH) as scaling frequency at T ¼ 523 K.

Fig. 6. The reciprocal temperature dependence of dc conductivity for different compositions of 60 TeO2 e 10ZnO e (30 x) B2O3 e xBi2O3 glasses.

1010e106 Scm1. As shown in Fig. 6, the dc conductivity is observed to obey Arrhenius behavior, expressed by the following equation [40,41]:

sdc (T) ¼ so exp [W/kT] (2)

Fig. 4. Temperature dependence scaling spectra for different 60 TeO2 e 10ZnO e (30 x) B2O3 e xBi2O3 glass compositions with Jonscher's cross-over frequency (uH) as scaling frequency for x ¼ 5.

where so is the pre-exponential parameter which depends on the semiconductor nature, W denotes the thermal activation energy of electrical conduction and k is Boltzmann constant. The activation energy (W) values have been calculated from the slope of log sdc versus 1000/T graph obtained from linear ﬁtting of the experimental data. The values of W have been listed in Table 1. The activation energy is observed to decrease indicating thereby increase in conductivity with increase in bismuth content. It may be due to increase in the number of non-bridging oxygen (NBOs) with increase in bismuth content in the studied glass system [25,42]. The increase in NBOs facilitates the easy movement of charge carriers in the glass network. Differential Scanning Calorimetry (DSC), Fourier Transform Infrared spectroscopy (FTIR) and Raman spectroscopy also reveals the increase in NBOs on addition of Bi2O3 in the studied system [1]. The decrease in activation energy is found to be

S. Dhankhar et al. / Solid State Sciences 48 (2015) 230e236

233

Table 1 Activation energy (W), Band gap energy (Eg), Concentration of Bi-ions (N), Mean spacing between Bi-ions (R), Polaron radius (rP), Density of states at Fermi level (N(EF)), inverse localization length (a), Relaxation time of electric modulus (tM00 ) and activation energy of electric modulus (ER) of 60 TeO2. 10ZnO. (30 x) B2O3. xBi2O3 glasses with different values of x. Physical parameters

x¼0

x¼5

x ¼ 10

x ¼ 15

x ¼ 20

W (eV) Eg (eV) N(x 1021 cc) R (Ǻ) r (Ǻ) N(EF) (x 1020 eV1 cm1) a (Ǻ1) (by Mott's VRH model with Bo ¼ 6.8) tM'' (ms) at 553 K ER (eV)

0.5840 3.57 e e e e e 72.03 0.5831

0.5675 3.40 2.020 7.19 3.19 8.49 0.475 41.97 0.5668

0.5484 3.31 3.845 6.38 2.57 16.75 0.569 25.70 0.5472

0.5334 3.24 5.501 5.66 2.28 24.67 0.624 7.06 0.5332

0.5198 3.18 7.125 5.20 2.09 32.65 0.663 2.75 0.5196

consistent with decrease in the band gap energy on increasing bismuth [1]. The concentration of bismuth ions (N) has been estimated using the following relation [43].

WBi2 O3 N ¼ 2dNA MBi2 O3

(3)

where d is the density, MBi2O3 is molecular weight of Bi2O3, WBi2O3 is weight fraction of Bi2O3 and NA is the Avogadro's number. The correlation between N and mean spacing between any two Bi-ions (R) is generally described as [43,44].

R¼

1 1 3 N

(4)

Using above relations, polaron radius (rp) is given by [43,45].

rp ¼

1 hpi13 R 2 6

3 4pR3 W

B ¼ Bo

(9)

where a is the inverse localization length of s-like wave function. Bo is a constant taken as 6.8 [43]. The values of a are tabulated in Table 1 are in very good agreement with those suggested by Murawski et al. [47] for oxide glasses. The values of aR are comparable to one (3.41e3.45) in the studied glass samples. So, VRH conduction may be applicable to the present glass system. The inequality a1 < rP < R is satisﬁed in the whole temperature range, so the polaron theory is applicable in the presently studied glass compositions. In terms of complex dielectric constant (ε*), the complex electric modulus is deﬁned as [48,49]. M* ¼ (ε*)1

(10)

and

(5) 00

The density of states, N (EF) for the thermally activated electron hopping near the Fermi level is calculated by the relation [38,43]:

NðEF Þ ¼

14 a3 kNðEF Þ

(6)

The values are of the order of 1020 eV1 cm1 and the calculated values of W, N, R, rP and N (EF) are given in Table 1 shows that activation energy decrease with increase in conductivity, which is an expected result and is attributed to decrease in the polaron hopping distance, R with increase in bismuth content. A variable range hopping (VRH) conduction given by Mott in low temperature range with some modiﬁcation suggested by Punia et al. in intermediate temperature region (Bo ¼ 6.8) is used to explain three dimensional VRH in bulk disordered semiconductors. The plot log sdc versus T1/4 (shown in Fig. 7) gives better linear ﬁt with linearity ~0.9999 in comparison to the Arrhenius plots i.e. log sdc versus 1000/T which shows linearity ~0.999. So, VRH model is suitable for describing the dc conductivity in the studied glass samples. The dc conductivity for 3-D Mott VRH model with modiﬁcations described by Punia et al. [43,46].

M* ¼ M 0 þ iM ¼

ε0

00

ε þi 00 00 ðε0 Þ2 þ ðε Þ2 ðε0 Þ2 þ ðε Þ2

(11)

where M0 , M00 and ε0 , ε00 are the real and imaginary parts of the electric modulus and dielectric constants, respectively. The real part of modulus spectrum at different temperatures shows the general trend as shown by various other semiconducting glasses [25,50,51].i.e. at lower frequencies it appears to zero while at higher

sdc ¼ Ae

B 1 T4

(7)

where A and B are constants, given by relations A ¼ nph e2 N (EF) R2

(8)

Fig. 7. The plot of log sdc versus T1/4 for different compositions of 60 TeO2 e 10ZnO e (30 x) B2O3 e xBi2O3 glasses. Where symbols represent experimental data and solid lines represent the linear ﬁt.

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S. Dhankhar et al. / Solid State Sciences 48 (2015) 230e236

frequencies a plateau is obtained. A typical graph of M0 spectrum at different temperature is shown in Fig. 8. The negligible value of M0 at lower frequencies indicates that the electrode polarization have a negligible contribution to M* and the dispersion is mainly due to conductivity relaxation [52e54], while at higher frequencies, M0 reaches a maximum constant value M∞. The value of M∞ decreases with the increase in temperature, this decrease in M∞ may be due to bismuth content [25]. The imaginary part of electric modulus for x ¼ 5 sample as a function of frequency at various temperatures is shown in Fig. 9. The plot exhibit a clear relaxation peaks at characteristics frequencies and peak is found to shift to higher frequencies with increasing and temperature. The appearance of peaks in the modulus spectra is clear indication of the conductivity relaxation process. The peak represents that there is changeover in mobility of polaron from long range to short range. The polaron have the capability to move long distance below the frequency region where peak occurs but the polaron are restricted to move only within potential well above the frequency range [25,26,51]. The imaginary part of electric modulus (M00 ) could be expressed as Fourier transform of a relaxation function F(t) [51,53].

2 M* ¼ M∞ 41

Z∞

3 d4 dt 5 expð utÞ dt

Fig. 9. Imaginary part of electric modulus spectra as a function of frequency at different temperatures of 60 TeO2 e 10ZnO e (30 x) B2O3 e xBi2O3 glass samples. The solid lines are the best ﬁts of Eq. (14).

(12)

0

00

M ¼

00

Mmax b b ð1 bÞ þ 1þb b fmax þ ff f

(14)

max

where M∞ is the high-frequency asymptotic value of real part of the dielectric constant and the function 4 (t) is the time evolution of the electric ﬁeld within the material and usually taken as the KohlrauscheWilliamseWatts (KWW) function [55,56].

"

t 4ðtÞ ¼ exp tm

b # (13)

where tm is the conductivity relaxation time and the term b is the stretched exponent and is a measure of the degree of interaction between the charge carriers. The value of b varies in between 0 and 1 and for an ideal Debye-type relaxation the value of b equals to 1 [25]. The values of b can be calculated based on electric modulus studies carried out at various temperatures. The electric modulus behavior of presently studied glass system is analyzed by the modiﬁed KWW function as suggested by Bergman [57]. Accordingly, the imaginary part of electric modulus may be represented as

Fig. 8. Real part of electric modulus as a function of frequency for 60 TeO2 e 10ZnO e (30 x) B2O3 e xBi2O3 glass sample at different temperatures.

00

where Mmax is the peak value of M00 and fmax is the corresponding 00 frequency. The value of Mmax , fmax and b are determined from the linear ﬁtting of the experimental data of M00 gives very good ﬁtting with best parameter ﬁt, R2, in the range 0.9995e0.9998. It is observed that with increase in bismuth content, the value of peak frequency (fmax) increases. The values of b, obtained from ﬁtting, are presented in Fig. 10 and they are lying in between 0.73 and 0.84. Perusal of the data presented in Fig. 11, it is observed that b has a very small temperature dependency suggesting a non-Debye type relaxation mechanism [58]. The relaxation time tM00 has been calculated by the relation

tM00 ¼

1 2pfmax

(15)

Fig. 10. Variation of exponent (b) with temperature for different compositions of 60 TeO2 e 10ZnO e (30 x) B2O3 e xBi2O3 glass system.

S. Dhankhar et al. / Solid State Sciences 48 (2015) 230e236

235

00

00

Fig. 12. Plot of M0 =M0∞ and M =Mmax versus f/fmax at 553 K for different compositions. Fig. 11. Variation of log (tM00 ) versus 1/T for 60 TeO2 e 10ZnO e (30 x) B2O3 e xBi2O3 glass system. Here symbols represent experimental data and solid lines represent the linear ﬁt.

and it is found to lie in the range 1.14 mse718 ms. The relaxation time shows a decreasing trend with increase in bismuth content (relaxation times of various compositions at 553 K are presented in Table 1). This is in accordance with the results of conductivity as the conductivity of the present glass system also increases with increase in bismuth content. The activation energy involved in the relaxation process could be obtained from the temperature dependent relaxation time as [59].

E tM00 ¼ to exp R kT

(16)

where ER is the activation energy associated with the relaxation process or modulus relaxation energy, to is pre exponential factor, k is Boltzmann constant, and T is absolute temperature. The linear ﬁtting of plots between log tM00 and 1/T for different compositions of the presently studied glass system is shown in Fig. 11. The estimated values of activation energy are presented in Table 1. Perusal of the data presented in Table 1, shows that both the dc activation energy (W) and the modulus relaxation energy (ER) shows the same trend i.e. both show a decrease in their values with increase in bismuth content (x). Perusal of data presented in Table 1, it is observed that the values of ER and W are nearly equal for all the studied compositions, suggesting that the polaron have to overcome the same energy barrier during conduction as well as relaxation processes. The reduced part of the electric modulus (M0 /M0 ∞ and M00 / 00 M max) has been plotted as a function of reduced frequency (f/fmax) for different glass compositions and different temperatures shown in Figs. 12 and 13. The modulus spectra for both compositions and temperatures overlap on a single master curve indicates that relaxation process in the presently studied glass samples are composition and temperature independent [50]. 4. Conclusions The ac conductivity of tellurium based quaternary glasses has been investigated in the frequency range 101 Hz to 105 Hz in the temperature range 483 Ke593 K and is found to be increase with increase in bismuth content. The observed dispersion behavior of ac conductivity of tellurium based quaternary glasses obeys the Jonscher's universal power law and the theoretical ﬁtting of

00

00

Fig. 13. Scaled imaginary part of electric modulus spectra (M0 =M0∞ and M =Mmax versus f/fmax) for x ¼ 10 at different temperatures.

experimental data for Jonscher's power law is in good agreement for all compositions. Further it is observed that the Overlapping Large Polarons Tunneling (OLPT) Model is more or less suitable to describe the ac conduction mechanism of present glass system. The activation energy for dc conduction is found to be decrease with increase in bismuth content and dc conduction takes place via variable range hopping (VRH). The imaginary part of modulus (M00 ) spectra has been ﬁtted to modiﬁed Kohlrausch-Williams-Watts (KWW) function. The value of the stretched exponent (b) reveals the presence of non-Debye type of relaxation in the presently studied glass samples. Scaling spectra of electric modulus (M0 and M00 ) collapse into a single master curve for all the compositions and temperatures. The values of ER and W are nearly equal for all the studied glass compositions, indicating that the polaron have to overcome the same energy barrier during conduction as well as relaxation processes. The conduction and relaxation process in the presently studied glass samples are composition and temperature independent. References [1] R.S. Kundu, S. Dhankhar, R. Punia, K. Nanda, N. Kishore, J. Alloys Compd. 587 (2014) 66e73. [2] R. Punia, R.S. Kundu, J. Hooda, S. Dhankhar, S. Dahiya, N. Kishore, J. Appl. Phys. 110 (2011) 033527. [3] N. Berwal, R.S. Kundu, K. Nanda, R. Punia, N. Kishore, J. Mol. Struct. 1097

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