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Impedance spectroscopy and dielectric relaxation in alkali tungsten borate glasses
Journal of Alloys and Compounds 475 (2009) 804–809
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Impedance spectroscopy and dielectric relaxation in alkali tungsten borate glasses A. Sheoran a , S. Sanghi a,∗ , S. Rani a , A. Agarwal a , V.P. Seth b a b
Department of Applied Physics, Guru Jambheshwar University of Science and Technology, Hisar 125001, Haryana, India Department of Applied Sciences, Prabhu Dayal Memorial College of Engineering, Bahadurgarh 124507, Haryana, India
a r t i c l e
i n f o
Article history: Received 4 June 2008 Received in revised form 30 July 2008 Accepted 7 August 2008 Available online 28 October 2008 Keywords: Amorphous material Dielectric response Electrical transport Electromechanical impedance spectroscopy
a b s t r a c t Glasses with composition xWO3 ·(30 − x)M2 O·70B2 O3 (M = Li, Na, 0 ≤ x ≤ 15 mol%) have been prepared using normal melt-quench technique. Variation of density, molar volume and theoretical optical basicity with glass composition has been studied. The complex impedance of these glasses has been measured in the temperature range from 523 to 623 K and in frequency range from 100 Hz to 1 MHz. The complex impedance data have been analyzed using the conductivity and electric modulus formalism. The effects of composition and temperature on conductivity are discussed. The frequency dependence of the ac conductivity is found to obey Jonscher’s relation. The dc conductivity is dominated by alkali ions and increases with rise of temperature. The correlation between the conductivity and conductivity relaxation is analyzed. Scaling of the conductivity data has been carried out. The stretching exponent ˇ is found to be temperature independent. The overlapping of the normalized peaks corresponding to impedance and electric modulus and the same thermal activation energy for conduction and relaxation suggest the single mechanism for the dynamic processes in the present glasses. © 2008 Published by Elsevier B.V.
1. Introduction The studies on transport properties of glasses have been carried out for a long time because of their potential applications in technology like solid-state batteries, chemical sensors and fuel cells [1–5]. These glasses have several advantages over crystalline counterparts, such as easy formability over wide ranges of composition, isotropicity, absence of grain boundaries and ease of fabrication in complex shapes, which make them particularly attractive in practical applications. The nature of electrical conductivity in a multicomponent system depends on the type, number and mobility of charge carriers. Various attempts have also been made to enhance the conductivity and chemical durability of glasses, e.g., incorporation of another glass former or modifier oxide or alkali halides, etc. [6,7]. The ability of boron to exist in both three and four coordinated environments and high strength of the covalent B–O bonds imparts borates to form stable glasses. A large number of binary and ternary borate glassy systems have been synthesized using alkali oxides as network modifiers which show ionic conductivity by alkali cations [8,9]. In view of favorable properties of tungsten ions, such as high electronegativity and polarizability, large ion radius and change-
∗ Corresponding author. Tel.: +91 1662 263384; fax: +91 1662 276240. E-mail address: [email protected] (S. Sanghi). 0925-8388/$ – see front matter © 2008 Published by Elsevier B.V. doi:10.1016/j.jallcom.2008.08.006
able valence, the conductivity of alkali tungsten borate glasses have been studied in the present work. It has been reported that a permanent blue color centre appears in (Li2 B4 O7 )1−x (WO3 )x glasses for high content of WO3 (x > 0.47). The formation of this blue color centre also depends on the temperature of melt, reaction times and the melting atmosphere [10–14]. For x < 0.33 these glasses are colorless [13] and W5+ :W6+ ratio is zero for x < 0.20 [12]. The study on the electronic and ionic conductivities in Li2 O·B2 O3 ·WO3 glasses show that the electronic conduction results from the electron-charge transfer between two neighboring W5+ O6 and W6+ O6 octahedra and ionic conductivity increases with increase in WO3 :B2 O3 ratio for constant Li2 O content [15]. It is well known that impedance spectroscopy (IS) is a powerful method for characterization of many electrical properties of various kinds of solid and liquid materials [16]. The aim of the present work is to study the conduction mechanism in M2 O·WO3 ·B2 O3 (M = Li, Na) glasses over a wide temperature and frequency range. The complex impedance spectra have been analyzed in conductivity as well as electric modulus formalism to understand conduction characteristics. Scaling of the conductivity data has also been carried out. 2. Experimental The glasses with composition xWO3 ·(30 − x)M2 O·70B2 O3 (where M = Li, Na; 0 ≤ x ≤ 15 mol%) were prepared using the normal melt-quenching method using AR grade chemicals Li2 CO3 , Na2 CO3 , WO3 and H3 BO3 . Approximately 15 g of chemicals were thoroughly mixed in porcelain crucible and then melted at 1473 K by using
A. Sheoran et al. / Journal of Alloys and Compounds 475 (2009) 804–809 Table 1 Composition, density (D), molar volume (VM ) and theoretical optical basicity (th ) of tungsten alkali borate glasses Sample code
WN1 WN2 WN3 WN4 WN5 WN6 WN7 WL1 WL2 WL3
D (g/cm3 )
Composition (mol%) WO3
Na2 O
Li2 O
B2 O3
0.0 2.5 5.0 7.5 10.0 12.5 15.0 0.0 2.5 12.5
30.0 27.5 25.0 22.5 20.0 17.5 15.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 30.0 27.5 17.5
70.0 70.0 70.0 70.0 70.0 70.0 70.0 70.0 70.0 70.0
2.40 2.48 2.62 2.62 2.71 2.80 2.87 2.35 2.48 2.85
VM (cm3 /mol)
29.58 30.36 30.31 31.90 32.49 32.91 33.55 26.04 26.79 30.38
th
0.516 0.525 0.535 0.543 0.551 0.561 0.568 0.481 0.494 0.542
805
increases with increase in WO3 :M2 O ratio (Table 1). This may be easily understood by the relation:
th = 1.67 1 −
1
˛2− o
(2)
where ˛2− o is the oxide ion polarizability. This equation shows that with increase in polarizability, basicity increases. It is well known that W6+ ions are highly polarizable due to their large ionic radius and small cation unit field strength. Optical basicity can also be used to classify the covalent/ionic character of the glass samples, i.e., as the basicity increases, covalent character in glass samples decreases. Therefore in the present glasses, the covalent character decreases with increase in WO3 :M2 O ratio. 3.3. Electrical conductivity
electric muffle furnace for about half an hour. The melt was swirled occasionally to ensure homogeneity. The colorless glass samples were obtained by pouring the melt onto a stainless steel plate and pressed with another plate. Compositions of glasses studied with their corresponding codes are listed in Table 1. The density (D) of all the samples was measured by Archimedes’ method with xylene as a buoyant liquid. The molar volume of the samples was calculated using the relation, VM = MT /D where MT is the total molecular weight and D is the density. The theoretical optical basicity of (th ) has been also determined [17] using the reported values of oxides constituents in the literature. For electrical measurements the samples were cut in rectangular/square shapes and were polished on both sides to a thickness of about 1 mm. Colloidal silver paint was used as an electrode material. The samples were annealed at 473 K for 2 h to ensure the contact between the electrode and the sample surfaces. A constant voltage of 1 V was applied across the sample to measure the real and imaginary parts of complex impedance using an inductance analyzer (QuadTech 1910) in the frequency range 100 Hz to 1 MHz. These ac measurements were recorded in the temperature range 523–623 K. The complex impedance data Z* (ω) were plotted (Nyquist diagram) in the complex plane (Z (ω) vs. Z (ω)) for different temperatures. Electrical conductivity and dielectric parameters were evaluated using the experimental data and the sample dimensions.
3. Results and discussion 3.1. Density and molar volume The values of density (D) and molar volume (VM ) for all the samples are displayed in Table 1. It is observed from this table that the density increases with increase in WO3 content. Since WO3 has higher molecular mass than M2 O, therefore it is an expected result. The molar volume of these glasses also increases with WO3 concentration. It can be understood that a more open structure results with increase in WO3 :M2 O ratio. Alkali borate glasses are composed of both triangular and tetrahedral units. The observed variation in molar volume is due to the fact that when M2 O is replaced by WO3 then more oxygens are introduced into the network, allowing the formation of additional BO4 units and simultaneously formation of bulky WO6 octahedra occurs.
The Nyquist diagrams of experimental IS data of glasses at each temperature consist of a single depressed semicircle related to bulk effects. A typical Nyquist plot for WN2 glass sample at different temperatures is shown in Fig. 1. The barely visible beginning of residual semicircle at low frequencies is attributed to electrode effects and this part of spectrum can be reduced with finely polished samples with sputtered electrodes. The centre of each semicircle is found to be depressed below the real axis. This suggests that associated relaxation of ions is non-Debye in nature. As temperature increases, the radius of semicircular arc, corresponding to the bulk resistance of the samples, decreases indicating that the conduction is thermally activated. Similar results have been obtained for all other glass samples. The dc resistance of the samples was obtained from the intersection of the semicircle with the real axis at low frequency and the dc conductivity, dc , was calculated using sample dimensions. The complex impedance data have been analyzed in conductivity as well as electric modulus formalism to shed light on conduction characteristics. Fig. 2 shows the Arrehenius plots of dc conductivity for the present glasses. This figure shows that the dc increases with increase in temperature for all glass samples, which is a characteristic of thermally stimulated process. Further dc conductivity decreases with increase in WO3 :M2 O ratio and this may be due to the decrease in the concentration of
3.2. Theoretical optical basicity Theoretical optical basicity, th , serves in the first approximation as a measure of the ability of oxygen to donate a negative charge in the glasses. In other words, the optical basicity reflects the Lewis basicity of oxide glasses. th for the glass systems under study has been calculated using the relation: th = XWO3 WO3 + XM2 O M2 O + XB2 O3 B2 O3
(1)
where WO3 , M2 O and B2 O3 are optical basicity values assigned to the constituent oxides; and XWO3 , XM2 O and XB2 O3 are the equivalent fractions of the different oxides, i.e., the proportion of oxide atoms they contribute to the glass system. The values of WO3 , M2 O and B2 O3 have been taken from the literature [18]. th
Fig. 1. Nyquist plots for WN2 glass sample at various temperatures.
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Fig. 2. Temperature dependence of dc xWO3 ·(30 − x)M2 O·70B2 O3 (M = Li, Na) glasses.
conductivity
( dc )
for
alkali ions and increase in the concentration of tetrahedral borons which increases network dimensionality blocking the motion of cations [19]. This decrease in dc conductivity is in agreement with increase in th . The values of dc at 623 K and activation energy for dc conduction (Edc ) calculated from the Arrehenius plots for the present glass samples are listed in Table 2. Haung et al. prepared Li2 O·B2 O3 ·WO3 glasses at temperature of 1073–1323 K for 1 h obtaining colored glasses for Li2 O < 35 mol% and colorless glasses for Li2 O > 35 mol% [15]. For glasses with Li2 O < 35 mol% the electrical conduction is mixed in nature and the electronic conduction results from the electron-charge transfer between two neighboring W5+ O6 and W6+ O6 octahedra. Glasses with Li2 O > 35 mol% are ionic conductors and ionic conductivity increases with increase in WO3 :B2 O3 ratio for constant Li2 O content. It has been reported that the formation of blue color centre in (Li2 B4 O7 )1−x (WO3 )x glasses depends on the amount of WO3 , the temperature of the melt, the reaction time and the melting atmosphere [10–14]. This formation of the blue color centre has been explained in terms of intervalence electron transfer W5+ (A) + W6+ (B) ⇔ W6+ (A) + W5+ (B) between sites A and B for x > 0.40 whereas for x < 0.33, these glasses are colorless [11,13–14]. von Dirke et al. observed blue coloration in these glasses for short reaction times (10–15 min) with large WO3 content [10]. Staske et al. have reported that in these glasses W5+ :W6+ ratio increases slightly from zero for x > 0.20 [12]. Goldstein et al. have reported that in binary sodium borate and sodium
Fig. 3. Plot for conductivity scaling: log(/ dc ) vs. log(f/ dc T) for WL2 glass sample. Inset shows the frequency dependence of total conductivity, (ω), for WL2 glass sample at different temperatures.
silicate glasses, the presence of W6+ is predominant [20]. In the present study, the sample preparation has been carried out at 1473 K (30 min) and therefore it is assumed that only W6+ ions are present and conductivity is ionic in nature. Thus, there is no electronic contribution towards conductivity in the present glasses. Such behaviour suggests that the conductivity depends strongly on alkali content and its mobility. The complex impedance plots consisting of single semicircles also strengthen the presence of ionic conductivity. Fig. 3 (inset) shows the frequency dependence of total conductivity for WL2 glass sample at different temperatures. Other glass samples also show similar behaviour. The electrical conductivity described by Jonscher [21] exhibits a power law at higher frequencies and terminates by constant dc conductivity at low frequencies. This leads to the empirical form of the total conductivity (ω) for
Table 2 The dc conductivity ( dc ), ac conductivity ( ac ), activation energies for dc and ac conductivities (Edc and Eac ), s parameter, dielectric loss (tan ı) and relaxation times ( M and Z ) for tungsten alkali borate glasses Sample code
dc at 623 K ( m)−1
Edc (eV)
ac at 623 K, 10 kHz ( m)−1
Eac at 623 K, 10 kHz (eV)
WN1 WN2 WN3 WN4 WN5 WN6 WN7 WL1 WL2 WL3
1.52 × 10−3 7.61 × 10−4 4.16 × 10−4 1.45 × 10−4 9.80 × 10−5 4.98 × 10−5 7.92 × 10−6 2.29 × 10−3 1.82 × 10−3 8.24 × 10−5
0.94 0.98 1.13 0.75 0.77 – – 0.93 1.02 0.79
1.57 × 10−3 8.43 × 10−4 4.41 × 10−4 1.58 × 10−4 1.05 × 10−4 4.77 × 10−5 1.78 × 10−5 2.33 × 10−3 1.83 × 10−3 8.97 × 10−5
0.87 0.94 0.97 0.98 0.85 0.77 0.84 0.91 0.97 0.88
s at 543 K
at 623 K
0.64 0.79 0.88 0.91 0.93 0.95 0.96 0.68 0.80 0.96
0.21 0.23 0.38 0.65 0.70 0.89 0.91 0.23 0.25 0.88
tan ı at 623 K, 1 kHz
M at 623 K (s)
Z at 623 K (s)
19.31 8.79 6.32 2.27 2.08 0.60 0.26 27.78 30.31 2.41
7.24 15.90 31.80 79.60 79.60 318.00 318.00 3.18 3.06 75.80
7.96 15.90 15.90 79.60 79.60 318.00 318.00 3.18 3.18 79.60
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different temperatures, i.e., expressed as
(ω) = dc 1 +
ω s ω0
(3)
where ‘s’ is a material and temperature dependent parameter. From Fig. 3 (inset), it is also evident that frequency dependence of conductivity shows two distinct regimes within the measured frequency window: (i) the low frequency plateau region corresponding to frequency independent conductivity dc and (ii) high frequency dispersion region. Eq. (3) results from the relaxation of dissociated ions in the glass matrix. Diffusion of these ions results in the frequency independent dc conductivity dc at low frequencies. With increasing frequency, the conductivity increases as a power law with exponent ‘s’. The values of ‘s’ are evaluated from the slope of frequency dependent ac conductivity ( ac ) at high frequencies and are included in Table 2 at two different temperatures (543 and 623 K). It is evident from Table 2 that the values of ‘s’ are temperature dependent and are higher for lower temperatures. Further, the ‘s’ values are material dependent (Table 2) and the glasses with higher alkali content have lower ‘s’ values. The values of ac and activation energy for ac conduction (Eac ) at 10 kHz (623 K) are presented in Table 2. Scaling of conductivity is an important concept as it reduces the conduction process to simpler parts so that a deeper understanding might be achieved. Recently, studies have been made on large number of amorphous materials suggesting the temperature independent ionic conductivity relaxation mechanism based on time–temperature superposition principle. The frequency dependent conductivity has been normalized with respect to dc conductivity and temperature by plotting (ω)/ dc vs. f/ dc T, according to the Summerfield scaling law [22]: (ω) =F dc
f dc T
(4)
From Fig. 3, it is seen that the normalized conductivity data corresponding to different temperatures are superimposable into a single ‘master curve’, indicating temperature independent relaxations and validity of Summerfield scaling function. However, the deviation observed in low frequency dispersion region is found to be negligible. Similar scaling has been observed for other glass samples under study.
Fig. 4. Frequency dependence of real part of dielectric permittivity (ε ) for WN1 glass sample. Inset shows the frequency dependence of imaginary part of dielectric permittivity (ε ) for WN1 glass sample.
quite smaller than those occurring at low frequencies. This may be attributed to the migration of ions in the glass or losses by conduction. Consequently, tan ı for glasses with higher conductivity are higher (Table 2). Tangent loss increases gradually with rise in temperature (Fig. 5) and does not exhibit any relaxation peak. The absence of loss peaks restricts to use the conventional methods for
3.4. Dielectric properties The complex permittivity ε*(ω) = 1/(jωC0 Z* ) can be expressed as a complex number: ε∗ (ω) = ε (ω) − ε (ω) ε (ω)
(5)
ε (ω)
and are real and imaginary parts of the complex where permittivity. The variation of ε and ε with frequency for WN1 glass sample at different temperatures is shown in Fig. 4. All the other glasses in the present study show the similar behaviour. Starting from the high frequency end, with decrease in frequency, ε monotonically increases from ε∞ and shows tendency off to a plateau before the appearance of a final rapid rise. This is associated with electrode polarization arising usually from space charge accumulation at the glass-electrode interface. The constant value of ε (∞) at high frequency results from the rapid polarization processes occurring in the glass samples [23]. The factor which measures the phase difference due to the loss of energy within the sample at a particular frequency is the tangent loss factor given by tan ı = ε /ε . Temperature dependence of tan ı at different frequencies for WN3 glass sample is shown in Fig. 5 which shows that the dielectric losses at high frequencies are
Fig. 5. Temperature dependence of dielectric loss (tan ı) at different frequencies for WN3 glass sample.
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ization to the electric modulus. Two apparent relaxation regions appear above and below fM . The low frequency region (fM ) the charge carriers are confined to potential wells and are mobile over short distances. The relaxation time, M , can be extracted from fM (=1/2 M ). The values of M (at 623 K) for the present glasses are displayed in Table 2. The activation energy values for electrical relaxation (EM ) are determined from the slopes of log fM vs. 1000/T plots and these are found to be comparable to those of activation energy values for dc conduction, Edc . The asymmetric M peak originates from the nature of relaxation behaviour. This non-Debye behaviour of the M spectra can be associated to the distribution of relaxation times. The amorphous nature of glasses and hence a distribution of mobile ion sites having different environments is thought to be the cause for the non-Debye conductivity relaxation [25]. An ideal dielectric or a glass having very low concentration of mobile ions exhibits Debye relaxation where (t) is a simple exponential. However, for the glasses such as studied here, we have taken the relaxation function (t) as Kohlrausch–Williams–Watts (KWW) function also known as stretched exponential function [26] given by
ˇ t
Fig. 6. Frequency dependence of the real (M ) and imaginary (M ) parts of the electric modulus for WN3 glass sample at various temperatures.
estimating the relaxation frequency and the nature of dispersion characterized by a distribution of relaxation times. It is well known that electronic, ionic, dipolar and space charge polarization contribute to the dielectric constant. In ionically conducting glasses, the dielectric properties mainly arise from the ionic motions. The free-energy barriers impeding the ionic diffusion, however, can be expected to vary from site to site, so there are different ionic motions in glasses. The first is the rotation of ions around their negative sites. The second is short distance transport, i.e., ions hop out of sites with low free-energy barriers and tend to pile up at sites with high free-energy barriers in the electric field direction in dc or low frequency electric field or oscillate between the sites with high free-energy barriers in an ac electric field. Both the first and second motions make a contribution to dielectric constant ε of glasses. In the third ionic motion, ions with higher energy can penetrate the glasses, i.e., conduct electricity and cause the dielectric loss ε . The dielectric modulus model is useful for analyzing electrical relaxation processes whose measurement is compromised by high capacitance effects, such as those due to electrode polarization [24]. The dielectric modulus (M* ) is defined as M ∗ = 1/ε∗ (ω) =
ε − ε = M + M |ε∗ |2
= M∞ 1 −
∞
exp(−ωt) 0
∂
− ∂t
dt
(6)
where M∞ is the reciprocal of high frequency dielectric constant ε∞ and (t) is the relaxation function which describes the decay of electrical field in the material. Fig. 6 shows the real and imaginary part of the electric modulus, M* as a function of frequency for WN3 glass sample at different temperatures. The maximum in the imaginary part of electric modulus M peak shifts to higher frequency with increasing temperature. The M curves show a maximum at a characteristic frequency, which is known as relaxation frequency, fM . The low values of M at low frequencies indicate negligible contribution of electrode polar-
(t) = exp −
M
(7)
where ˇ is the Kohlrausch stretched exponent, and is a measure of non-exponentiality which tend to unity in case of an ideal Debye-type relaxation. It was considered that the stretched exponential is a manifestation of distribution of relaxation times [27,28]. Alternatively, an approach pioneered by Ngai and Jain [29] attempts to attribute this phenomenon to the stretching of a single primitive relaxation time by interaction with other relaxing species. The ˇ parameter has been evaluated using the full width at half-maxima value of M peak [30]. It varies from 0.71 to 0.80 for different glass samples and is temperature independent. This temperature independent nature of the ˇ is substantiated from the superimposed plots between M /Mmax and log(f/fmax ) as shown in Fig. 7. This suggests that the conductivity relaxations occurring at different frequencies exhibit temperature independent dynamical processes. This time–temperature superposition shows that conduction mechanism remains unchanged. It indicates a common ion transport mechanism, which operates in the entire range of composition and temperature studied. Comparison of the impedance and electrical modulus data allow the determination of bulk response in terms of localized, i.e., defect relaxation or non-localized conduction, i.e., ionic or electronic conductivity [31]. Fig. 8 shows the variation of normalized parameters M /Mmax and Z /Zmax as a function of frequency for WN1 glass sample at 623 K. It is possible to determine the type of dielectric response by inspection of magnitude of overlapping between the peaks of both parameters Z (ω) and M (ω). The observed overlap ping peak position of M /Mmax and Z /Zmax curves is evidence of delocalized or long-range relaxation. The plots of relaxation frequency maximum (i.e., log fZ and log fM ) as a function of reciprocal of temperature for WN1 glass sample are shown in inset of Fig. 8. Almost identical values are observed for the activation energy (EZ ) for conduction derived from Z (ω) and activation energy of dielectric relaxation (EM ). The relaxation times for the two peaks describing the same relaxation process are in good agreement [31]. Values of relaxation time corresponding to complex function Z* (ω), i.e., Z are also displayed in Table 2. This table shows that the values of Z and M are nearly equal. Also, both the and Z /Zmax peaks describe the same relaxation proM /Mmax
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cesses (Fig. 8). Therefore, the overlapping of peaks (Fig. 8) and same thermal activation energy of the dynamic processes occurring at different frequencies exhibit the existence of single conduction mechanism and measured response is due to long-range conduction. 4. Conclusion Increase in density and molar volume in theses glasses with increase in WO3 :M2 O ratio indicates the formation of bulky WO6 octahedra. The theoretical optical basicity increases with increase in WO3 content which indicating the weakening of the covalent character in these glasses. The dc conductivity decreases with increase in WO3 :M2 O ratio and is ionic in nature. This ionic conduction depends on the concentration of mobile alkali ions and their mobility. There are no W5+ ions present in these colorless glasses and tungsten ions primarily exist in their highest oxidization state, W6+ . The dielectric loss for these glasses is due to electrical conduction of alkali ions within the glass matrix. The normalized conductivity data corresponding to different temperatures are superimposable into a single ‘master curve’, indicating temperature independent relaxations. The stretched exponent factor ‘ˇ’ is temperature independent and it varies from 0.71 to 0.80 for different glass samples. The overlapping of M (ω) and Z (ω) peaks and same thermal activation energy of the dynamic processes occurring at different frequencies exhibit the existence of single conduction mechanism and measured response is due to long-range conduction. Fig. 7. Normalized plots of dielectric modulus against normalized frequency for WN2 glass sample.
Acknowledgements Authors are thankful to AICTE and UGC New Delhi for providing financial support. References
Fig. 8. Frequency dependence of normalized peaks (M /Mmax and Z /Zmax ) for WN1 glass at 623 K. Inset shows the temperature dependence of relaxation frequencies fM and fZ for WN1 glass sample.
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Impedance spectroscopy and dielectric relaxation in alkali tungsten borate glasses A. Sheoran a , S. Sanghi a,∗ , S. Rani a , A. Agarwal a , V.P. Seth b a b
Department of Applied Physics, Guru Jambheshwar University of Science and Technology, Hisar 125001, Haryana, India Department of Applied Sciences, Prabhu Dayal Memorial College of Engineering, Bahadurgarh 124507, Haryana, India
a r t i c l e
i n f o
Article history: Received 4 June 2008 Received in revised form 30 July 2008 Accepted 7 August 2008 Available online 28 October 2008 Keywords: Amorphous material Dielectric response Electrical transport Electromechanical impedance spectroscopy
a b s t r a c t Glasses with composition xWO3 ·(30 − x)M2 O·70B2 O3 (M = Li, Na, 0 ≤ x ≤ 15 mol%) have been prepared using normal melt-quench technique. Variation of density, molar volume and theoretical optical basicity with glass composition has been studied. The complex impedance of these glasses has been measured in the temperature range from 523 to 623 K and in frequency range from 100 Hz to 1 MHz. The complex impedance data have been analyzed using the conductivity and electric modulus formalism. The effects of composition and temperature on conductivity are discussed. The frequency dependence of the ac conductivity is found to obey Jonscher’s relation. The dc conductivity is dominated by alkali ions and increases with rise of temperature. The correlation between the conductivity and conductivity relaxation is analyzed. Scaling of the conductivity data has been carried out. The stretching exponent ˇ is found to be temperature independent. The overlapping of the normalized peaks corresponding to impedance and electric modulus and the same thermal activation energy for conduction and relaxation suggest the single mechanism for the dynamic processes in the present glasses. © 2008 Published by Elsevier B.V.
1. Introduction The studies on transport properties of glasses have been carried out for a long time because of their potential applications in technology like solid-state batteries, chemical sensors and fuel cells [1–5]. These glasses have several advantages over crystalline counterparts, such as easy formability over wide ranges of composition, isotropicity, absence of grain boundaries and ease of fabrication in complex shapes, which make them particularly attractive in practical applications. The nature of electrical conductivity in a multicomponent system depends on the type, number and mobility of charge carriers. Various attempts have also been made to enhance the conductivity and chemical durability of glasses, e.g., incorporation of another glass former or modifier oxide or alkali halides, etc. [6,7]. The ability of boron to exist in both three and four coordinated environments and high strength of the covalent B–O bonds imparts borates to form stable glasses. A large number of binary and ternary borate glassy systems have been synthesized using alkali oxides as network modifiers which show ionic conductivity by alkali cations [8,9]. In view of favorable properties of tungsten ions, such as high electronegativity and polarizability, large ion radius and change-
∗ Corresponding author. Tel.: +91 1662 263384; fax: +91 1662 276240. E-mail address: [email protected] (S. Sanghi). 0925-8388/$ – see front matter © 2008 Published by Elsevier B.V. doi:10.1016/j.jallcom.2008.08.006
able valence, the conductivity of alkali tungsten borate glasses have been studied in the present work. It has been reported that a permanent blue color centre appears in (Li2 B4 O7 )1−x (WO3 )x glasses for high content of WO3 (x > 0.47). The formation of this blue color centre also depends on the temperature of melt, reaction times and the melting atmosphere [10–14]. For x < 0.33 these glasses are colorless [13] and W5+ :W6+ ratio is zero for x < 0.20 [12]. The study on the electronic and ionic conductivities in Li2 O·B2 O3 ·WO3 glasses show that the electronic conduction results from the electron-charge transfer between two neighboring W5+ O6 and W6+ O6 octahedra and ionic conductivity increases with increase in WO3 :B2 O3 ratio for constant Li2 O content [15]. It is well known that impedance spectroscopy (IS) is a powerful method for characterization of many electrical properties of various kinds of solid and liquid materials [16]. The aim of the present work is to study the conduction mechanism in M2 O·WO3 ·B2 O3 (M = Li, Na) glasses over a wide temperature and frequency range. The complex impedance spectra have been analyzed in conductivity as well as electric modulus formalism to understand conduction characteristics. Scaling of the conductivity data has also been carried out. 2. Experimental The glasses with composition xWO3 ·(30 − x)M2 O·70B2 O3 (where M = Li, Na; 0 ≤ x ≤ 15 mol%) were prepared using the normal melt-quenching method using AR grade chemicals Li2 CO3 , Na2 CO3 , WO3 and H3 BO3 . Approximately 15 g of chemicals were thoroughly mixed in porcelain crucible and then melted at 1473 K by using
A. Sheoran et al. / Journal of Alloys and Compounds 475 (2009) 804–809 Table 1 Composition, density (D), molar volume (VM ) and theoretical optical basicity (th ) of tungsten alkali borate glasses Sample code
WN1 WN2 WN3 WN4 WN5 WN6 WN7 WL1 WL2 WL3
D (g/cm3 )
Composition (mol%) WO3
Na2 O
Li2 O
B2 O3
0.0 2.5 5.0 7.5 10.0 12.5 15.0 0.0 2.5 12.5
30.0 27.5 25.0 22.5 20.0 17.5 15.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 30.0 27.5 17.5
70.0 70.0 70.0 70.0 70.0 70.0 70.0 70.0 70.0 70.0
2.40 2.48 2.62 2.62 2.71 2.80 2.87 2.35 2.48 2.85
VM (cm3 /mol)
29.58 30.36 30.31 31.90 32.49 32.91 33.55 26.04 26.79 30.38
th
0.516 0.525 0.535 0.543 0.551 0.561 0.568 0.481 0.494 0.542
805
increases with increase in WO3 :M2 O ratio (Table 1). This may be easily understood by the relation:
th = 1.67 1 −
1
˛2− o
(2)
where ˛2− o is the oxide ion polarizability. This equation shows that with increase in polarizability, basicity increases. It is well known that W6+ ions are highly polarizable due to their large ionic radius and small cation unit field strength. Optical basicity can also be used to classify the covalent/ionic character of the glass samples, i.e., as the basicity increases, covalent character in glass samples decreases. Therefore in the present glasses, the covalent character decreases with increase in WO3 :M2 O ratio. 3.3. Electrical conductivity
electric muffle furnace for about half an hour. The melt was swirled occasionally to ensure homogeneity. The colorless glass samples were obtained by pouring the melt onto a stainless steel plate and pressed with another plate. Compositions of glasses studied with their corresponding codes are listed in Table 1. The density (D) of all the samples was measured by Archimedes’ method with xylene as a buoyant liquid. The molar volume of the samples was calculated using the relation, VM = MT /D where MT is the total molecular weight and D is the density. The theoretical optical basicity of (th ) has been also determined [17] using the reported values of oxides constituents in the literature. For electrical measurements the samples were cut in rectangular/square shapes and were polished on both sides to a thickness of about 1 mm. Colloidal silver paint was used as an electrode material. The samples were annealed at 473 K for 2 h to ensure the contact between the electrode and the sample surfaces. A constant voltage of 1 V was applied across the sample to measure the real and imaginary parts of complex impedance using an inductance analyzer (QuadTech 1910) in the frequency range 100 Hz to 1 MHz. These ac measurements were recorded in the temperature range 523–623 K. The complex impedance data Z* (ω) were plotted (Nyquist diagram) in the complex plane (Z (ω) vs. Z (ω)) for different temperatures. Electrical conductivity and dielectric parameters were evaluated using the experimental data and the sample dimensions.
3. Results and discussion 3.1. Density and molar volume The values of density (D) and molar volume (VM ) for all the samples are displayed in Table 1. It is observed from this table that the density increases with increase in WO3 content. Since WO3 has higher molecular mass than M2 O, therefore it is an expected result. The molar volume of these glasses also increases with WO3 concentration. It can be understood that a more open structure results with increase in WO3 :M2 O ratio. Alkali borate glasses are composed of both triangular and tetrahedral units. The observed variation in molar volume is due to the fact that when M2 O is replaced by WO3 then more oxygens are introduced into the network, allowing the formation of additional BO4 units and simultaneously formation of bulky WO6 octahedra occurs.
The Nyquist diagrams of experimental IS data of glasses at each temperature consist of a single depressed semicircle related to bulk effects. A typical Nyquist plot for WN2 glass sample at different temperatures is shown in Fig. 1. The barely visible beginning of residual semicircle at low frequencies is attributed to electrode effects and this part of spectrum can be reduced with finely polished samples with sputtered electrodes. The centre of each semicircle is found to be depressed below the real axis. This suggests that associated relaxation of ions is non-Debye in nature. As temperature increases, the radius of semicircular arc, corresponding to the bulk resistance of the samples, decreases indicating that the conduction is thermally activated. Similar results have been obtained for all other glass samples. The dc resistance of the samples was obtained from the intersection of the semicircle with the real axis at low frequency and the dc conductivity, dc , was calculated using sample dimensions. The complex impedance data have been analyzed in conductivity as well as electric modulus formalism to shed light on conduction characteristics. Fig. 2 shows the Arrehenius plots of dc conductivity for the present glasses. This figure shows that the dc increases with increase in temperature for all glass samples, which is a characteristic of thermally stimulated process. Further dc conductivity decreases with increase in WO3 :M2 O ratio and this may be due to the decrease in the concentration of
3.2. Theoretical optical basicity Theoretical optical basicity, th , serves in the first approximation as a measure of the ability of oxygen to donate a negative charge in the glasses. In other words, the optical basicity reflects the Lewis basicity of oxide glasses. th for the glass systems under study has been calculated using the relation: th = XWO3 WO3 + XM2 O M2 O + XB2 O3 B2 O3
(1)
where WO3 , M2 O and B2 O3 are optical basicity values assigned to the constituent oxides; and XWO3 , XM2 O and XB2 O3 are the equivalent fractions of the different oxides, i.e., the proportion of oxide atoms they contribute to the glass system. The values of WO3 , M2 O and B2 O3 have been taken from the literature [18]. th
Fig. 1. Nyquist plots for WN2 glass sample at various temperatures.
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Fig. 2. Temperature dependence of dc xWO3 ·(30 − x)M2 O·70B2 O3 (M = Li, Na) glasses.
conductivity
( dc )
for
alkali ions and increase in the concentration of tetrahedral borons which increases network dimensionality blocking the motion of cations [19]. This decrease in dc conductivity is in agreement with increase in th . The values of dc at 623 K and activation energy for dc conduction (Edc ) calculated from the Arrehenius plots for the present glass samples are listed in Table 2. Haung et al. prepared Li2 O·B2 O3 ·WO3 glasses at temperature of 1073–1323 K for 1 h obtaining colored glasses for Li2 O < 35 mol% and colorless glasses for Li2 O > 35 mol% [15]. For glasses with Li2 O < 35 mol% the electrical conduction is mixed in nature and the electronic conduction results from the electron-charge transfer between two neighboring W5+ O6 and W6+ O6 octahedra. Glasses with Li2 O > 35 mol% are ionic conductors and ionic conductivity increases with increase in WO3 :B2 O3 ratio for constant Li2 O content. It has been reported that the formation of blue color centre in (Li2 B4 O7 )1−x (WO3 )x glasses depends on the amount of WO3 , the temperature of the melt, the reaction time and the melting atmosphere [10–14]. This formation of the blue color centre has been explained in terms of intervalence electron transfer W5+ (A) + W6+ (B) ⇔ W6+ (A) + W5+ (B) between sites A and B for x > 0.40 whereas for x < 0.33, these glasses are colorless [11,13–14]. von Dirke et al. observed blue coloration in these glasses for short reaction times (10–15 min) with large WO3 content [10]. Staske et al. have reported that in these glasses W5+ :W6+ ratio increases slightly from zero for x > 0.20 [12]. Goldstein et al. have reported that in binary sodium borate and sodium
Fig. 3. Plot for conductivity scaling: log(/ dc ) vs. log(f/ dc T) for WL2 glass sample. Inset shows the frequency dependence of total conductivity, (ω), for WL2 glass sample at different temperatures.
silicate glasses, the presence of W6+ is predominant [20]. In the present study, the sample preparation has been carried out at 1473 K (30 min) and therefore it is assumed that only W6+ ions are present and conductivity is ionic in nature. Thus, there is no electronic contribution towards conductivity in the present glasses. Such behaviour suggests that the conductivity depends strongly on alkali content and its mobility. The complex impedance plots consisting of single semicircles also strengthen the presence of ionic conductivity. Fig. 3 (inset) shows the frequency dependence of total conductivity for WL2 glass sample at different temperatures. Other glass samples also show similar behaviour. The electrical conductivity described by Jonscher [21] exhibits a power law at higher frequencies and terminates by constant dc conductivity at low frequencies. This leads to the empirical form of the total conductivity (ω) for
Table 2 The dc conductivity ( dc ), ac conductivity ( ac ), activation energies for dc and ac conductivities (Edc and Eac ), s parameter, dielectric loss (tan ı) and relaxation times ( M and Z ) for tungsten alkali borate glasses Sample code
dc at 623 K ( m)−1
Edc (eV)
ac at 623 K, 10 kHz ( m)−1
Eac at 623 K, 10 kHz (eV)
WN1 WN2 WN3 WN4 WN5 WN6 WN7 WL1 WL2 WL3
1.52 × 10−3 7.61 × 10−4 4.16 × 10−4 1.45 × 10−4 9.80 × 10−5 4.98 × 10−5 7.92 × 10−6 2.29 × 10−3 1.82 × 10−3 8.24 × 10−5
0.94 0.98 1.13 0.75 0.77 – – 0.93 1.02 0.79
1.57 × 10−3 8.43 × 10−4 4.41 × 10−4 1.58 × 10−4 1.05 × 10−4 4.77 × 10−5 1.78 × 10−5 2.33 × 10−3 1.83 × 10−3 8.97 × 10−5
0.87 0.94 0.97 0.98 0.85 0.77 0.84 0.91 0.97 0.88
s at 543 K
at 623 K
0.64 0.79 0.88 0.91 0.93 0.95 0.96 0.68 0.80 0.96
0.21 0.23 0.38 0.65 0.70 0.89 0.91 0.23 0.25 0.88
tan ı at 623 K, 1 kHz
M at 623 K (s)
Z at 623 K (s)
19.31 8.79 6.32 2.27 2.08 0.60 0.26 27.78 30.31 2.41
7.24 15.90 31.80 79.60 79.60 318.00 318.00 3.18 3.06 75.80
7.96 15.90 15.90 79.60 79.60 318.00 318.00 3.18 3.18 79.60
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different temperatures, i.e., expressed as
(ω) = dc 1 +
ω s ω0
(3)
where ‘s’ is a material and temperature dependent parameter. From Fig. 3 (inset), it is also evident that frequency dependence of conductivity shows two distinct regimes within the measured frequency window: (i) the low frequency plateau region corresponding to frequency independent conductivity dc and (ii) high frequency dispersion region. Eq. (3) results from the relaxation of dissociated ions in the glass matrix. Diffusion of these ions results in the frequency independent dc conductivity dc at low frequencies. With increasing frequency, the conductivity increases as a power law with exponent ‘s’. The values of ‘s’ are evaluated from the slope of frequency dependent ac conductivity ( ac ) at high frequencies and are included in Table 2 at two different temperatures (543 and 623 K). It is evident from Table 2 that the values of ‘s’ are temperature dependent and are higher for lower temperatures. Further, the ‘s’ values are material dependent (Table 2) and the glasses with higher alkali content have lower ‘s’ values. The values of ac and activation energy for ac conduction (Eac ) at 10 kHz (623 K) are presented in Table 2. Scaling of conductivity is an important concept as it reduces the conduction process to simpler parts so that a deeper understanding might be achieved. Recently, studies have been made on large number of amorphous materials suggesting the temperature independent ionic conductivity relaxation mechanism based on time–temperature superposition principle. The frequency dependent conductivity has been normalized with respect to dc conductivity and temperature by plotting (ω)/ dc vs. f/ dc T, according to the Summerfield scaling law [22]: (ω) =F dc
f dc T
(4)
From Fig. 3, it is seen that the normalized conductivity data corresponding to different temperatures are superimposable into a single ‘master curve’, indicating temperature independent relaxations and validity of Summerfield scaling function. However, the deviation observed in low frequency dispersion region is found to be negligible. Similar scaling has been observed for other glass samples under study.
Fig. 4. Frequency dependence of real part of dielectric permittivity (ε ) for WN1 glass sample. Inset shows the frequency dependence of imaginary part of dielectric permittivity (ε ) for WN1 glass sample.
quite smaller than those occurring at low frequencies. This may be attributed to the migration of ions in the glass or losses by conduction. Consequently, tan ı for glasses with higher conductivity are higher (Table 2). Tangent loss increases gradually with rise in temperature (Fig. 5) and does not exhibit any relaxation peak. The absence of loss peaks restricts to use the conventional methods for
3.4. Dielectric properties The complex permittivity ε*(ω) = 1/(jωC0 Z* ) can be expressed as a complex number: ε∗ (ω) = ε (ω) − ε (ω) ε (ω)
(5)
ε (ω)
and are real and imaginary parts of the complex where permittivity. The variation of ε and ε with frequency for WN1 glass sample at different temperatures is shown in Fig. 4. All the other glasses in the present study show the similar behaviour. Starting from the high frequency end, with decrease in frequency, ε monotonically increases from ε∞ and shows tendency off to a plateau before the appearance of a final rapid rise. This is associated with electrode polarization arising usually from space charge accumulation at the glass-electrode interface. The constant value of ε (∞) at high frequency results from the rapid polarization processes occurring in the glass samples [23]. The factor which measures the phase difference due to the loss of energy within the sample at a particular frequency is the tangent loss factor given by tan ı = ε /ε . Temperature dependence of tan ı at different frequencies for WN3 glass sample is shown in Fig. 5 which shows that the dielectric losses at high frequencies are
Fig. 5. Temperature dependence of dielectric loss (tan ı) at different frequencies for WN3 glass sample.
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ization to the electric modulus. Two apparent relaxation regions appear above and below fM . The low frequency region (
ˇ t
Fig. 6. Frequency dependence of the real (M ) and imaginary (M ) parts of the electric modulus for WN3 glass sample at various temperatures.
estimating the relaxation frequency and the nature of dispersion characterized by a distribution of relaxation times. It is well known that electronic, ionic, dipolar and space charge polarization contribute to the dielectric constant. In ionically conducting glasses, the dielectric properties mainly arise from the ionic motions. The free-energy barriers impeding the ionic diffusion, however, can be expected to vary from site to site, so there are different ionic motions in glasses. The first is the rotation of ions around their negative sites. The second is short distance transport, i.e., ions hop out of sites with low free-energy barriers and tend to pile up at sites with high free-energy barriers in the electric field direction in dc or low frequency electric field or oscillate between the sites with high free-energy barriers in an ac electric field. Both the first and second motions make a contribution to dielectric constant ε of glasses. In the third ionic motion, ions with higher energy can penetrate the glasses, i.e., conduct electricity and cause the dielectric loss ε . The dielectric modulus model is useful for analyzing electrical relaxation processes whose measurement is compromised by high capacitance effects, such as those due to electrode polarization [24]. The dielectric modulus (M* ) is defined as M ∗ = 1/ε∗ (ω) =
ε − ε = M + M |ε∗ |2
= M∞ 1 −
∞
exp(−ωt) 0
∂
− ∂t
dt
(6)
where M∞ is the reciprocal of high frequency dielectric constant ε∞ and (t) is the relaxation function which describes the decay of electrical field in the material. Fig. 6 shows the real and imaginary part of the electric modulus, M* as a function of frequency for WN3 glass sample at different temperatures. The maximum in the imaginary part of electric modulus M peak shifts to higher frequency with increasing temperature. The M curves show a maximum at a characteristic frequency, which is known as relaxation frequency, fM . The low values of M at low frequencies indicate negligible contribution of electrode polar-
(t) = exp −
M
(7)
where ˇ is the Kohlrausch stretched exponent, and is a measure of non-exponentiality which tend to unity in case of an ideal Debye-type relaxation. It was considered that the stretched exponential is a manifestation of distribution of relaxation times [27,28]. Alternatively, an approach pioneered by Ngai and Jain [29] attempts to attribute this phenomenon to the stretching of a single primitive relaxation time by interaction with other relaxing species. The ˇ parameter has been evaluated using the full width at half-maxima value of M peak [30]. It varies from 0.71 to 0.80 for different glass samples and is temperature independent. This temperature independent nature of the ˇ is substantiated from the superimposed plots between M /Mmax and log(f/fmax ) as shown in Fig. 7. This suggests that the conductivity relaxations occurring at different frequencies exhibit temperature independent dynamical processes. This time–temperature superposition shows that conduction mechanism remains unchanged. It indicates a common ion transport mechanism, which operates in the entire range of composition and temperature studied. Comparison of the impedance and electrical modulus data allow the determination of bulk response in terms of localized, i.e., defect relaxation or non-localized conduction, i.e., ionic or electronic conductivity [31]. Fig. 8 shows the variation of normalized parameters M /Mmax and Z /Zmax as a function of frequency for WN1 glass sample at 623 K. It is possible to determine the type of dielectric response by inspection of magnitude of overlapping between the peaks of both parameters Z (ω) and M (ω). The observed overlap ping peak position of M /Mmax and Z /Zmax curves is evidence of delocalized or long-range relaxation. The plots of relaxation frequency maximum (i.e., log fZ and log fM ) as a function of reciprocal of temperature for WN1 glass sample are shown in inset of Fig. 8. Almost identical values are observed for the activation energy (EZ ) for conduction derived from Z (ω) and activation energy of dielectric relaxation (EM ). The relaxation times for the two peaks describing the same relaxation process are in good agreement [31]. Values of relaxation time corresponding to complex function Z* (ω), i.e., Z are also displayed in Table 2. This table shows that the values of Z and M are nearly equal. Also, both the and Z /Zmax peaks describe the same relaxation proM /Mmax
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cesses (Fig. 8). Therefore, the overlapping of peaks (Fig. 8) and same thermal activation energy of the dynamic processes occurring at different frequencies exhibit the existence of single conduction mechanism and measured response is due to long-range conduction. 4. Conclusion Increase in density and molar volume in theses glasses with increase in WO3 :M2 O ratio indicates the formation of bulky WO6 octahedra. The theoretical optical basicity increases with increase in WO3 content which indicating the weakening of the covalent character in these glasses. The dc conductivity decreases with increase in WO3 :M2 O ratio and is ionic in nature. This ionic conduction depends on the concentration of mobile alkali ions and their mobility. There are no W5+ ions present in these colorless glasses and tungsten ions primarily exist in their highest oxidization state, W6+ . The dielectric loss for these glasses is due to electrical conduction of alkali ions within the glass matrix. The normalized conductivity data corresponding to different temperatures are superimposable into a single ‘master curve’, indicating temperature independent relaxations. The stretched exponent factor ‘ˇ’ is temperature independent and it varies from 0.71 to 0.80 for different glass samples. The overlapping of M (ω) and Z (ω) peaks and same thermal activation energy of the dynamic processes occurring at different frequencies exhibit the existence of single conduction mechanism and measured response is due to long-range conduction. Fig. 7. Normalized plots of dielectric modulus against normalized frequency for WN2 glass sample.
Acknowledgements Authors are thankful to AICTE and UGC New Delhi for providing financial support. References
Fig. 8. Frequency dependence of normalized peaks (M /Mmax and Z /Zmax ) for WN1 glass at 623 K. Inset shows the temperature dependence of relaxation frequencies fM and fZ for WN1 glass sample.
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