The conduction mechanism and dielectric behavior of cadmium bismuth silicate glasses

By using the traditional melt-quench method, cadmium bismuth silicate glasses with composition; 20CdO·(80-x)Bi2O3·xSiO2 (10≤x≤50 mol%) were fabricated. Impedance spectroscopy was used to examine the conduction and relaxation mechanisms in prepared glasses over the range of frequency 10Hz–7MHz and temperature 473–703 K. Values of dc conductivity (σdc), the activation energy for dc conduction (Edc), frequency exponent parameter (s), and relaxation energy (Eτ) were extracted from the experimental impedance data. The conductivity spectra follow Jonscher’s power law and the obtained conductivity values were found to be compositional dependent ascribed to the existence of mixed former effect in understudy glasses. The frequency exponent parameter increases with frequency and approaches unity at higher frequencies. For each glass composition, almost equal values of Eτ and Edc show that the charge carriers have to cross a similar energy barrier in relaxation and conduction processes. The exact overlaying of normalized electrical modulus plots as a single master curve signifies temperature-independent dynamical processes at various frequencies.


Introduction
Bi2O3 based glasses are technologically substantial materials since they exhibit outstanding physical and chemical properties include higher density, lower melting temperatures, improved refractive indices and superior chemical stability.Due to the high refractive indices and excellent transmission in infrared region bismuth silicate glasses are widely used in tunable lasers, optical, and electronic applications [13].Because of their solid state technical uses, electrical characteristics of the Bi2O3 containing glasses have received much attention in recent years.These glasses can be employed in microwave integrated circuits, sensors, electrochemical and photovoltaic cells [46].In the past, silicate-based glasses have been widely investigated.Efforts have been made to study and understand binary and ternary bismuth silicate glasses for the last two decades.Various publications reveled that Bi2O3 can build networks of BiO3 units (serve as network former) and BiO6 units (serve as network modifer) in oxide glasses [79].The inclusion of different heavy metal oxides, such as Bi2O3, PbO were reported to improve the physical properties of silicate glasses.The strong polarizability of bismuth ion and 6s 2 electronic lone-pair in the valence shell of Bi2O3, may significantly alter the electrical characteristics of the oxide glasses [10,11].Thus, in view point of above present work if focused to study the effect of

Results and discussion
A well-known technique for analysing the movement of charge carriers in solid materials is impedance spectroscopy.Analysis of these spectra helps to identify and understand conduction mechanism.Table 1 depicts the Nyquist diagrams at 633703K for CBS4 glass sample.With the rise in temperature the radius of the semicircular arc reducing indicating that movement of charge carriers is thermally stimulated.Also, depressed semicircles below the Z axis clearly signify the non Debye type of relaxation.All other studied samples show similar results.Using the dimensions of each same and bulk resistance values from Figure 1, the dc conductivity (σdc) was computed.Figure 2 presents the plot of logarithm of dc conductivity vs. 1000/T for all the CBS glasses.The Figure display an Arrhenius type temperature dependency and the feature of thermally stimulated transport in accordance [12] with the relation: The straight line fits of the curves displayed in Figure 2 were used to extract the activation energy (Edc) values for conduction process.Persual to Table 1, with decrease in bismuth concentration σdc decreases and Edc follow the opposite trend.The decrease in dc conductivity can be explained on the basis that at high concentration of Bi2O3, the structure of glasses is made up of BiO3 structural units that serve as network formers and BiO6 structural units that serve as network modifiers, while isolated SiO4 tetrahedra are formed due to strong Si-O covalent bonds.With subsequent addition of SiO2 at the expense of Bi2O3, dimensionality of glass network increases by cross-linked SiO4 tetrahedra and hence impeding cation motion and overall ion mobility.Deviation from linear variation at x = 40 mol% (anomalous behavior) is seen which may be due to that when ratio of Bi2O3/SiO2 is one,SiO4 tetrahedra are formed at a rate that balances the formation of bismuth octahedra then the network modifying character of Cd 2+ comes into play.CdO as a modifier produces more open channels for mobile charge carriers and hence conductivity increases at this particular composition.Therefore, the partial substitution of conventional glass former by a conditional glass former keeping modifier concentration constant for the glasses containing binary network formers, conductivity values are observed to be improved owing to the mixed former effect.Influences of mixed former effect were also reported in zinc bismuth silicate and zinc bismuth lithium borate glass systems [1315].The power law [16] of the form may accurately describe almost all thermally induced hopping process es involving ions.
Figure 3 illustrates the variation of total conductivity σ(ω) with frequency for CBS4 sample.In the frequency dependent conductivity curve two separate regimes are visible in the studied frequency range: (a) The low frequency plateau regime, represents σdc for which conductivity seems to be independent of frequency, (b) The dispersion regime occur at high frequency.As the temperature rises, the changeover to frequency dependent dispersion regime from the frequency independent plateau regime shifts towards higher frequency.Table 1 lists the values of ac conductivity (σac) for each sample (at 673 K, 10 kHz).The nonlinear variation in conductivity parameters with composition (at Bi2O3/SiO2 = 1) again predicts the peculiar behavior of the CBS4 glass sample.
The slope of the plot between logarithms of σ(ω) and f in the high frequency zone provide the value of frequency exponent parameter (s).Table 1 contains the values of s shows that frequency exponent parameter drops with increasing temperature and obtained values are much less than unity.Also, these values are dependent on the dimensionality of conduction space within the material as glasses with lower SiO2 concentration have lower 's' parameter values.sample (at 633-703K).Inset: Variation of tan vs. temperature at various frequencies.
Figure 4 demonstrate the variation of tan vs. log f for the CBS4 glass sample at 633-703K and their values are included in Table 1 (at 673K, 10 kHz).When only thermal energy type relaxation is present, the primary contributor to the dielectric losses are the thermally induced relaxation of freely rotating dipoles.At higher temperatures, electrical conduction-associated ion hopping motion contributes to dielectric loss.According to Figure 4 as tan is located in the low frequency regime, thus loss magnitude rises at lower frequencies while at higher frequencies, the magnitude of the loss is considerably lower.The mobility of charge carriers within the glass, which causes conduction losses, is usually attributed due to this kind of frequency dependency of tan.As a result, samples with higher electrical conductivity associate more dielectric losses than the samples with lower electrical conductivity.The inset of Fig. 4 also displays variation of tan vs. temperature at various frequencies.It shows that dielectric losses are significantly reduced at higher frequencies in comparison to those occuring at lower frequencies.
The dielectric modulus is a complex quantity expressed as real M(ω) and imaginary parts M(ω) and is defined as 1/ε*; The relation between electric modulus and frequency is expressed as [17]: Where (t) is the relaxation function specifies the decay of electrical field within the material.This approach is especially useful for identifying bulk effects like average conductivity relaxation times and the electrode polarisation phenomena [18].The relaxation function also known as Kohlrausche Williams Watts function is expressed as [19]: Where parameter is the Kohlrausche stretched exponent.Exponent  defines the deviation and in the case of unity value it defines an ideal Debye type relaxation.Figure 5 presents the plot of M(ω) and M(ω)with log f at various temperatures.Qualitatively similar curves of dielectric modulus were obtained for other CBS glasses.Very small value of M(ω) exhibits at lower range of frequencies attributing the easy migration of charge carriers.At higher frequencies, M'(ω) tends to M, thus shows a dispersion that caused due to the large capacitance values linked with electrodes.An asymmetric maximum is observed in the imaginary part of dielectric modulus at the dispersion area of M(ω).The corresponding peak frequency is called the relaxation frequency (fM").For the frequency range lower than fM", the charge carriers remain mobile across large distances and can be linked to the hopping conduction mechanism.After relaxation frequency, the charge carriers remain localized to the potential wells, thus mobile only for short distances.This behavior can be linked to the relaxation polarization processes [20].Hence, the peak frequency shows the switchover from long range mobility of charge carriers to short range.Table 1 displays the values of relaxation time (M") derived from relation fM" (=1/2πM") at 673 K which satisfy the Arrhenius relation; M" = 0exp(E/kT).Figure 6 presents the log M" vs. 1000/T plot for CBS glasses at various temperatures.Table 1 lists the activation energy values (Eτ) for relaxation process computed by using the slope of linear fitted plot (Figure 6) and by applying the Arrhenius relation.For each glass composition, Edc and E values follow similar trend are values are nearly equal show that the charge carriers must overawed the similar energy barrier during conduction and relaxing [21].The whole width at half maximum (FWHM) value from peaks of M"(ω) curve has been used to evaluate the  parameter.From Table 1, value of has been found to be temperature independent and almost constant for studied glass series.Almost constant value of exponent  has also been reported by Majhi and Varma [22] in ZnO•Bi2O3•B2O3 glasses.Further, as frequency exponent has slight temperature dependence, hence in the present glasses relation  = 1-s does not hold.Figure 7 displays the normalised modulus isotherm plots for CBS4 glass sample with the frequency axis scaled by fM", M′ and M′′ axis are scaled by the M′ and M′′max respectively.The scaling behaviour is same for all the understudy glasses.The exact overlaying of all the scaled curves onto a single master curve shows that the conductivity relaxation that takes place at various frequencies exhibits temperature independent dynamical processes.

Conclusions
Impedance spectroscopy has been used to examine the ac and dc conductivity within a broad frequency and temperature range.The value of dc conductivity decreases with a rise in SiO2 concentration and is governed by the Arrhenius law.The replacement of the network former by SiO4 tetrahedra blocks the movement of mobile ions, causes the dc conductivity to drop with a rise in SiO2 content.An anomalous behavior is observed at x = 40 mol%, that might be caused by the network-modifying nature of the cadmium oxide.A close equivalence between the activation energies for relaxation as well as conduction processes suggests that the charge carrier cross the similar barrier during conducting and relaxing.The exact overlaying of scaled electric modulus curves onto a single master curve signifies the temperature independent dynamical processes for conductivity relaxation mechanism at different frequencies.

Figure 3 . 4 .
Figure 3.Variation of log σ (ω) vs. log f at Figure 4. Plot of tan vs. log f for CBS4 glass Various temperatures for CBS4 glass sample.sample(at 633-703K).Inset: Variation of tan vs. temperature at various frequencies.

Figure 7 .
Figure 7. Normalized plots of and M/M and M/Mmax with normalized frequency for CBS4 glass sample.