International Journal of Applied Ceramic Technology

Dielectric Relaxation in CaO–Bi2O3–B2O3 Glasses



Glasses in the system CaO–Bi2O3–B2O3 (in molar ratio) have been prepared using melt-quenching route. Ion transport characteristics were investigated for this glass using electric modulus, ac conductivity and impedance measurements. The ac conductivity was rationalized using Almond–West power law. Dielectric relaxation has been analyzed based on the behavior of electric modulus behavior. The activation energy associated with the electrical relaxation determined from the electric modulus spectra was found to be 1.76 eV, close to that the activation energy for dc conductivity (1.71 eV) indicating that the same species took part in both the processes. The stretched exponent β (0.5–0.6) is invariant with temperature for the present glasses.


Transparent glasses engrafted with polar/nonlinear optic crystallites have great potential for myriad applications as these exhibit interesting physical properties and could be fabricated in large sizes with high degree of transparency over a wide range of wavelengths of light. Among many glasses, Bi2O3 containing glasses are of particular interest owing to their long infrared cutoff, high third-order nonlinear optical susceptibility that make them ideal candidates for use in infrared transmission components, ultrafast optical switches and photonic devices.1,2 Borate-based glass research has been an intensive topic in recent times owing to their interesting electrical, optical, and thermal properties.3–5 Recently, considerable attention has been paid to noncentrosymmetric bismuth borate-based compounds keeping their piezoelectric, ferroelectric, pyroelectric, and nonlinear optical properties in view.6–8 Various borate-based single crystals including LiB3O5, Li2B4O7, BiB3O6, and BaBiBO4 have been investigated and reported to posses promising physical properties.9–12

We have been making systematic attempts to explore the possibilities of using bismuth borate-based glass systems containing nano/microcrystals of the same composition for pyroelectric, electro-optic, and nonlinear device applications. Recently CaBi2B2O7 (CBBO) single crystals were reported to belong to polar space group Pna21.13 It is a promising compound from the pyroelectric, ferroelectric, and nonlinear optical properties view point. Dielectric properties have a direct influence on the aforementioned properties, which have been studied and the results obtained therein are reported in present article. Therefore, the present work has relevance to the development of technology related to the pyroelectric-based detectors, nonlinear optical frequency doublers, and so forth.

Keeping the potential applications of transparent glass nano/micro glass-composites in view, attempts were made to fabricate CaO-Bi2O3-B2O3 (CBBO) glasses and glass nano/microcrystal composites (glasses embedded with CaBi2B2O7 crystallites) and examine their ferroelectric, pyroelectric, and nonlinear optical properties. It is to be noted that on heat-treating the above glasses at appropriate temperatures one would obtain complete CBBO crystalline phase.

It is essential to understand the ac response of these materials as most devices in practice operate in the ac mode and the electrical conductivity has a significant influence on the pyroelectric and ferroelectric-based devices. To begin with, the conductivity and modulus behavior of the as-quenched CBBO glasses have been studied and the results obtained theirin are reported in the present article.

Experimental Procedure

Transparent glasses in the composition CaO–Bi2O3–B2O3 (in molar ratio) were fabricated via the conventional melt-quenching technique. For this, CaCO3 (99.95%, Aldrich, St. Louis, MO), Bi2O3 (99.9%, Merck, Whitehouse Station, NJ), and B2O3 (99.9%, Aldrich) were thoroughly mixed and melted in a platinum crucible at 1373 K for 1 h. Melts were quenched by pouring on a steel plate and pressed with another plate to obtain 1–1.5-mm-thick glass plates. X-ray powder diffraction (XRD) study was performed at room temperature on the as-quenched samples to confirm their amorphous nature. The differential scanning calorimetric (DSC) (model: Diamond DSC, Perkin-Elmer, Shelton, CT) run was carried out in the 550–900 K temperature range at a heating rate of 10 K/min on the as-quenched CBBO glass plate. The experiment was conducted in dry nitrogen ambience. The as-quenched glass plates weighing 15 mg were used for the experiments. Dielectric and impedance studies on the as-quenched glass samples were carried out as a function of frequency (100 Hz–10 MHz) and temperature using an impedance/gain phase analyzer (HP 4194A, Agilent Technologies, Palo Alto, CA). For this purpose the samples were sputtered with gold and silver epoxy was used to bond silver leads to the samples.

Results and Discussion

The XRD pattern that is obtained at room temperature for the as-quenched powdered sample, confirms its amorphous nature (Fig. 1). In the inset of the Fig. 1, the typical DSC curve for the as-quenched CBBO glass plate at a heating rate of 10 K/min is shown. An endotherm around 686 K followed by an exotherm at 825 K are observed, which are associated with the glass transition (Tg) and the onset of the crystallization (Tcr) temperatures of the as-quenched CBBO glass. A significant difference that exists between the glass transition (Tg=686 K) and the onset of the crystallization (Tcr=825 K) temperatures accounts for good thermal stability of the CBBO glasses. A parameter usually used to estimate the glass stability is the thermal stability (ΔT),14 which is defined by

Figure 1.

 X-ray diffraction pattern for the as-quenched CBBO glass plate: inset shows the differential scanning calorimetric trace for the as-quenched CBBO glass plate.

Larger the difference between the Tcr and Tg, higher the thermal stability of the glasses. The value obtained for ΔT using Eq. (1) is 159, for the present glasses (CBBO) reflecting the higher thermal stability than the other known Bi2O3–B2O3-based glasses.15

The frequency (100 Hz–10 MHz) dependence of the dielectric constant (ɛ′r) and loss (D) at various temperatures (300–700 K) for the as-quenched samples is depicted in Figs. 2a and b, respectively. In general, the dielectric constant and the loss decrease with increase in frequency at all the temperatures under study. The dielectric loss spectra obtained at various temperatures did not show any loss peak in the 100 Hz–10 MHz frequency range, typical of low-loss dielectric materials.16 It is also confirmed that the low-loss materials show featureless dielectric response, rather than loss peaks.

Figure 2.

 The frequency response of the (a) dielectric constant (ɛ′r) and (b) loss (D) at different temperatures for the as-quenched CBBO glasses.

When the dielectric constant and the loss of a material increases exponentially at low frequencies and high temperatures, it is difficult to distinguish the interfacial polarization and conductivity contributions from that of the intrinsic dipolar relaxation. This difficulty is overcome by representing the dielectric data in terms of the electric modulus. When the data are presented in modulus formalism, the effect of conductivity could be suppressed. The complex modulus inline imagewas introduced to describe the dielectric response of nonconducting materials. The formalism has been also applied to the materials with nonzero conductivity. The usefulness of the modulus representation in the analysis of the relaxation properties was demonstrated for both vitreous ionic conductors17 and polycrystalline ceramics.18

The definition of the dielectric modulus that could be expressed as:


where the function ϕ(t) gives the time evolution of the electric field within the dielectrics. The real and imaginary parts of the complex modulus could be expressed in terms of the imaginary and the real parts of the dielectric constant:


Any change in the spectra of the real part (M′) of the modulus is indicative of a change in the stiffness of the material under study, and the frequency region where this change occurs is emphasized by a loss peak in the imaginary part of the modulus. Variations of the real and imaginary parts of the electric modulus at different temperatures (648–698 K) are shown in the Figs. 3a and b, respectively. It is clearly seen that the value of M′ increases with increase in frequency and reaches a constant value (M=1/ɛ) at higher frequencies. On the other hand the peaks evolved in M″ spectra, indicate a relaxation process that is not evident in the dielectric loss spectra. As the temperature increases, M′ decreases in the low-frequency regime and saturates at high frequencies (Fig. 3a). The Cole–Cole modulus (M′ and M″) plot at various temperatures is depicted as an inset in Fig. 3a. The incidence of a suppressed semicircle implies a deviation from the ideal Debye behavior. The M″ spectra (at various temperatures) show an asymmetric peak approximately centered in the dispersion region of M′ (Fig. 3b). There is an upward shift in the peak position with increase in temperature. The region that is left to the peak is where the ions are mobile over long distances, and that in the right is where the ions are spatially confined to their potential wells.19 The region where the peaks occur is indicative of the transition from long-range to short-range mobility or more quantitatively defined as most probable ion relaxation times (τσ), from the condition 2πfmax=1. The inset in Fig. 3b shows the dependence of relaxation time on the reciprocal of temperature. It clearly suggests that the relaxation time follows the Arrhenius equation that could be expressed as


where τσo is the pre-exponential factor, Ea is the activation energy, kB is the Boltzmann constant and T is the absolute temperature. The activation energy Ea obtained from the linear fit is 1.73 eV. The value suggests that oxygen ion migration takes place via hopping mechanism at high temperatures.20,21Figure 4 shows the superimposed plots obtained by scaling each frequency by the frequency of the maximum loss (Mmax). The near perfect overlap of the curves at different temperatures, superimpose on the single master curve, illustrate that all the dynamic processes occurring at different frequencies exhibit the same thermal activation energy. These master plots could be analyzed in terms of nonexponential decay function or Kohlrausch–Williams–Watts (KWW) parameter (β),22 which could be expressed as


where τo is the characteristic relaxation time, the function ϕ(t) gives the time evolution of an electric field. The stretched exponential parameter decreases with an increase in the relaxation time distribution. When, β→1 indicates the ideal Debye single relaxation and β→0 corresponds to the maximum interaction between the ions.19 The shape of each spectrum for the as-quenched sample could be quantified with a β value obtained by fitting the M″ spectrum for each temperature by the method of Bergman et al.,23 which could be expressed as


where Mmax is the maximum value of the imaginary part of modulus (M″), ωmax is the maximum angular frequency and β is the KWW parameter. The solid lines in Fig. 3b are theoretical fits of the Eq. (6). Figure 5 shows the temperature dependence of β. The β values obtained in the 648–698 K temperature range are less than unity and are independent of temperature indicating that the interaction between the charge carriers is unaffected by the temperature variation.

Figure 3.

 The frequency dependence of the (a) real (M′) and (b) imaginary (M″) part of electric modulus for the as-quenched CBBO glass, solid lines are the theoretical fit of the Eq. (6); inset in (a) shows the Cole–Cole plot at different temperatures and inset in (b) shows the Arrhenius plot of the relaxation times as a function of temperature, where solid line is the linear fit.

Figure 4.

 Modulus master plots for the as-quenched CBBO glasses at different temperatures.

Figure 5.

 Variation of Kohlrausch parameter β with temperature.

The effect of conductivity on the dielectric properties could be studied by deriving the conductivity using the relation inline image, where σ′ is the real part of the conductivity, ω is the angular frequency, ɛ″r is the imaginary part of the dielectric constant. Figure 6 shows the temperature dependence of the ac conductivity at different frequencies. In the high-temperature range the conductivities at all the frequencies understudy display strong temperature-dependent behavior and there is a overlap between the spectra obtained at different frequencies. This particular behavior at high temperatures is attributed mainly to the dc conduction mechanism. The solid line that is shown in the figure is the linear fit and the slope of which gives an activation energy of about 1.76 eV, which is attributed to the oxygen ion hopping.

Figure 6.

 Temperature dependence of ac conductivity at different frequencies: solid line is the linear fit.

The ac conductivity data at various temperatures as a function of frequency are shown in Fig. 7. The ac conductivity in general increases with increase in frequency at all the temperatures under investigation. However, the conductivity in the 300–470 K temperature range at high frequencies (>1 kHz) is almost independent of temperature. The conductivity behavior of the present glass is rationalized by invoking Almond–West power law. The real part of conductivity spectra could be explained by the power law proposed by Almond and West.24,25 In this, the real part of the frequency-dependent conductivity could be expressed as


where σdc is the dc conductivity for a particular temperature, n is the power law exponent that varies from 0 to 1 depending on temperature. The exponent n represents the degree of interaction between the mobile ions with the lattice around them. ωH, is the characteristic hopping frequency of the charge carriers, obtained from the experimental data at which σ(ωH)=2σdc. The above equation (Eq. [7]) is frequently used in the analysis of ac conductivity data. The hopping frequency (ωH) is considered to be a more appropriate parameter for the scaling of the conductivity spectra for the glasses, where dielectric loss peak maxima value cannot be obtained. The CBBO glass was observed to obey the above-mentioned universal power law and a fit of Eq. (7) to the experimental data is shown as the inset in Fig. 7. ac conductivity spectra for different temperatures are fitted to Eq. (7) and the parameters σdc, and ωH are extracted.

Figure 7.

 Variation of ac conductivity as a function of frequency at different temperatures; inset shows a theoretical l fit (solid line) of Eq. (7) to the experimental data.

Figures 8a and b show the ωH and σdc of the present glass as a function of the inverse of temperature (1000/T). Increase in the ωH and σdc with temperature is due to the increase in the thermally activated mobility of ions, which could be explained based on hopping conduction mechanism. The activation energies for the thermally activated hopping process are obtained by fitting the dc conductivity and the hopping frequency data and the respective Arrhenius equations could be expressed as


where σdc is the dc conductivity pre-exponential factor, Edc the dc conductivity activation energy for mobile ions, ω0 the pre-exponential of the hopping frequency, EH is the activation energy for hopping frequency, kb is the Boltzmann constant, and T is the temperature. The solid lines in Figs. 8a and b are the linear fits. The activation energy of hopping frequency (EH) is found to be very close to that of the activation energy Edc for dc conductivity. The values of the activation energy obtained from Fig. 6 and Almond–West-type power law fit are similar in magnitude implying that the same kind of relaxation process is involved. The closeness of the activation energies suggested that the same mechanism of ion transport is dominated in the high-temperature range and above glass transition temperature the glass transition temperature is a kinetic parameter and only configurational changes occur within the system as viscosity changes around this temperature. There are no structural changes from glass to super-cooled state that can affect the overall transport mechanism of the system under study.

Figure 8.

 Arrhenius plots of (a) hopping frequency and (b) dc-conductivity for the as-quenched CBBO glasses.

Figure 9 shows the master plot of ac conductivity for the as-quenched CBBO glass, where the frequency has been normalized by the peak frequency for the temperature of the imaginary part of the electric modulus and the conductivity has been reduced by the dc conductivity (σdc). According to the temperature independent behavior of the relaxation function and the superposition principle, the curves are superimposed implying that the mechanism of ion transport is the same for the range of temperatures under study.

Figure 9.

 Master plot of the normalized σdc conductivity versus normalized frequency.

In order to have further insight into the frequency dependent conductivity behavior of the as-quenched CBBO glasses at various temperatures, the real and imaginary parts of complex impedance are plotted against the frequency, which are shown in the Figs. 10a and b. At lower temperatures, Z′ decreases with increases in frequency (Fig. 10a) up to a certain frequency (≈10 kHz), and subsequently becomes frequency independent. Figure 10b shows the variation of Z″ with frequency at various temperatures. Z″ at each temperature exhibits a relaxation peak whose peak frequency fm shifts toward higher frequencies with increase in temperature and follows the Arrhenius law. The activation energy of 1.74 eV is obtained by plotting a graph between the relaxation time and the temperature (inset in Fig. 10a). This would suggest that the relaxation is temperature dependent, and it is not a single relaxation time. Inset in Fig. 10b shows the master plots of Z″ with Zmax and f/fmax, the entire spectrum collapses into a single master curve implying that the same relaxation mechanism is active in the entire temperature range.

Figure 10.

 The frequency dependence of the real and imaginary parts of the impedance for the as-quenched CBBO glass; inset in (a) shows the Arrhenius plot of the relaxation times as a function of temperature, where solid line is the linear fit (b) impedance master plots for the as-quenched CBBO at different temperatures.

Further to the above description of experimental data the variation of normalized parameter Z″/Zmax and M″/Mmax at 698 K as a function of frequency is shown in Fig. 11 for the as-quenched CBBO glasses. Comparison of the impedance and modulus data allows one to rationalize the bulk response in terms of localized (i.e., dielectric relaxation) and nonlocalized (i.e., ionic conductivity)26 relaxation processes. The Debye model is related to an ideal frequency response of localized (dielectric) relaxation. In reality the nonlocalized process (ionic conductivity) would dominate at low frequencies. Thus, the high dielectric loss (D), is usually accompanied by raising dielectric constant (ɛ′r) at low frequencies. Such a behavior is found for the present glass (Fig. 2). However, the Z″/Zmax and M″/Mmax peaks in Fig. 11 do not completely overlap suggesting that there are contributions from both the long range and localized relaxation mechanisms to the dynamic process occurring at different frequencies.

Figure 11.

 Frequency dependence of the normalized M″/M″max and Z″/Z″max peaks for the as-quenched CBBO glass.


The ac and modulus behavior of the as-quenched CBBO glasses have been studied over a wide range of temperatures and frequencies. The scaling of the modulus (M″) and impedance (Z″) clearly indicates that the ion transport mechanism is the same over the temperature range under study. The stretched exponent β is invariant with temperature. The study of the conductivity shows that the conductivity at high temperature is ionic in nature and due to the motion of oxygen ions. The ac conductivity behavior has been fitted to Almond–West type of expression.