Chapter 6 ELECTRICAL CONDUCTIVITY ANALYSIS

Transcription

1 Chapter 6 ELECTRICAL CONDUCTIVITY ANALYSIS

2 CHAPTER Introduction The suitability and potentiality of a material for device applications can be determined from the frequency and temperature response of its electrical conductivity. Thus electrical characterization of a material is an essential part of ceramic technology. In dielectric materials, the electrical conduction takes place by the transportation of weakly bounded charge carriers under the influence of an applied ac electric field. The study of electrical conductivity is useful to determine the kind of conduction (i.e electronic, ionic, and orientational) active inside the material at different frequency domains of applied field. Depending on the type of charge carriers like free electrons / holes or cations / anions, that dominates the conduction process, the solids may be classified as an electronic or ionic conductor. In dielectrics lattice defects and oxygen ion vacancies in oxygen-octahedral plays an important role towards the conduction mechanism. The nature of conduction mechanism influences the activation of energy of the charge carriers. In the present study the complex impedance spectroscopy method is used to evaluate and interpret the electrical conduction process in the materials under study. 6.2 ac Conductivity (σ ac ) The ac conductivity is an intrinsic characteristic of the material which depends on the composition, structural symmetry, grain size, distribution of grains and purity of the material. In the bulk polycrystalline materials the ac conductivity mechanism is classified as(i) ac conductivity due to long range hopping of charge carriers and (ii) localized transportation due to oxygen vacancies. In polar dielectrics (eg: ferroelectrics), the conduction may be due to ions or electrons. The ratio of ionic and electronic conduction in dielectric materials varies with temperature and frequency. The ac conductivity of the ceramic compounds under study was calculated by using following equation: σ = ωε ε tanδ (6.1)

3 Where, ε ε = permittivity of the material, tanδ = dielectric loss [285].The variation of ac conductivity with temperature explains the type ( single relaxation or multiple relaxation ) and strength of relaxation in the material. The conductivity increases steadily with increase in temperature in most of the polar dielectrics but significant changes can be observed in ferroelectric materials near the transition temperature. 6.3 Temperature response of ac conductivity (a) Effect of temperature on σ ac of BFPTO compounds Figure 6.1(a-f) shows the Arrhenius plot of ac conductivity i.e. logσ ~ for PT modified BFO compounds (BFPTO) at frequencies 10kHz, 100kHz, 500kHz and 1MHz in the temperature range (25 o C 500 o C). In all the compounds of BFPTO, at lower temperature the ac conductivity increases with rise in frequency indicating the dispersive nature of conductivity. This fact may be attributed to possible release of space charge at higher frequencies even at lower temperature. It is clearly observed from the Arrhenius plots that the dispersion of ac conductivity at low temperature region increases gradually with increase in PT concentration i.e as x value increases from 0.1 to 0.5. The increase in conductivity with increase in temperature confirms the NTCR behavior of the materials. As discussed in chapter- 4, first dielectric anomaly is noticed in the BFPTO compounds at temperature about 220 o C 250 o C, this fact is also reflected in the Arrhenius plots When the temperature increases beyond the temperature related to the dielectric anomaly, all the curves tends to merge into a single curve. This fact indicates that at higher temperature the space charge releases and also recombines almost at the same rate, thus the ac conductivity of the material becomes independent of frequency. Hence the temperature response of ac conductivity indicates that the conduction process in the material is due to space charge conduction. The activation energy (E ) for each compound of BFPTO at different frequencies was calculated by the following empirical relation; ( ) σ = σ exp E KT (6.2) 166

4 (a) Figure 6.1(a-f) :Arrhenius plot of ac conductivity for Bi 1-x Pb x Fe 1-x Ti x O 3 (BFPTO) compounds in temperature range 25 o C 500 o C 167

5 Where K= Boltzmann constant and σ = represents the value of ac conductivity at very high temperature when E KT 0. The value of activation energy was found to increase when temperature increased i.e more energy is required to counter the thermal fluctuations of excited chargecarriers at high temperatures. The comparison of activation energy for different BFPTO compounds at selected frequencies in high temperature range is presented in the Table 6.1. It is noticed that larger the frequency smaller the activation energy. Table 6.1 Comparison of activation energy E a (ev) of BFPTO (Bi 1-x Pb x Fe 1-x Ti x O 3 ) compounds at selected frequencies in high temperature range. x 10kHz 100kHz 500kHz 1MHz (b) Effect of temperature on σ ac of BFPZTO compounds Figure 6.2(a-e) shows the variation of ac conductivity of the samples of the BPFZTO (Bi 1-x Pb x Fe 1-x (Zr 0.5 Ti 0.5 ) x O 3 ), with x =0.0,0.2,0.3,0.4,0.5) materials with inverse of absolute temperature at selected frequencies 10 khz, 100 khz, 500 khz and 1 MHz. It is noticed that the value of σ increases with increase in frequency in the low temperature region in all the samples, indicating the dispersive nature of conductivity with frequency. This dispersive nature of conductivity is sensitive to the composition and observed to increase with increase in the PZT concentration in the material, because (as discussed in chapter-3) the unit cell volume of the crystals increases due to larger ionic sizes of Pb 2+,Zr 4+ and Ti 4+ ions as compared to that of Bi 3+ and Fe 3+ ions, when the concentration of PZT increases. As a result the space charge release phenomena is enhanced, which causes the conductivity to increase. Also the offvalence substitution results an increase in the oxygen vacancies, as a consequence the probability of long range ordering hopping of the charge carriers at high frequencies increases, hence the ac conductivity of the compounds increases. It is also noticed from the plots that 168

6 curves tends to merg as the concentration of PZT in the compounds of BPFZTO increases, which confirms that the conduction mechanism is dominated by charge carriers such as oxygen vacancies. The dispersion in ac conductivity at lower temperature region decreases significantly due to PZT doping in BFO. The increase of conductivity with increase in temperature for all frequencies shows that the temperature coefficient of resistivity of the materials is negative i.e the material exhibit NTCR behavior [286]. The order of conductivity of the materials at high temperature range (above 100 o C) becomes equal to that of semiconductors. At high temperature the dispersion in conductivity decreases and all the curves tends to merge at some temperature (around 350 o C), corresponding to the dielectric anomaly observed in the compounds, with further increase in temperature the conductivity decreases suddenly and almost attains a constant value at all frequencies. The dielectric anomaly is a characteristic compositional effect occurring at some definite temperature (this temperature is different for different samples under study), therefore at dielectric anomaly region of temperature the conductivity of the materials becomes independent of frequency. The values of activation energies at different frequencies at higher temperature range were found by using the empirical formula given in equation (6.2). The data given in the Table-6.2 indicates that in each compound higher frequency smaller the ac activation energy. This is because, overall conductivity in the material is due to the hopping/ long range mobility of charge carriers at low frequencies while at higher frequencies the hopping is localized near the neighboring defect site because the charge carriers have smaller response time to external excitations [287]. Table 6.2 Comparison of activation energy E a (ev) of BFPZTO (Bi 1-x Pb x Fe 1- x(zr 0.5 Ti 0.5 ) x O 3 ) compounds at selected frequencies in high temperature range. x 10kHz 100kHz 500kHz 1MHz

7 (a) Figure 6.2(a-e) Arrhenius plot for Bi 1-x Pb x Fe 1-x (Zr 0.5 Ti 0.5 )xo 3 (BFPZTO) compounds in temperature range 25 o C 500 o C 170

8 6.3.1(c) Effect of temperature on σ ac of BFPZLTO compounds Figure 6.3(a-e) shows the Arrhenius plot of ac conductivity i.e. logσ ~ for PZLT modified BFO compounds (BFPZLTO) at selected frequencies in a wide temperature range (25 o C 500 o C). The plots of each compound shows that the conductivity increases with rise in temperature for all the selected frequencies and all the curves tends to merge at higher temperature irrespective of frequency. The larger value of σ at the higher temperatures suggests the importance of ionic charge carriers like oxygen vacancies. It was noticed that with increase in the La concentration in BFPZLTO compounds, the ac conductivity decreases. This may be due to decrease in the grain size and increase in the grain boundary area with increase in the La concentration as the ionic radius of La 3+ is very large as compared to the ionic radius of Fe 3+. Due to the increase in grain boundary areas the charge carriers may trapped within the inter-grain boundaries causing the increase in grain boundary capacitive effect and consequently decrease in conductivity. The conductivity peak appearing at temperature around 180 o C to 200 o C in the BFPZLTO sample with x= 0.3 may be assigned to a transient interaction between oxygen ion vacancies and Fe3 + / Fe 2+ redox coupling. The activation energy E for the BFPZLTO compounds at high temperature were calculated from the slope of the Arrhenius plots at different frequencies. The variation of activation energy with frequency in each sample is presented in Table6.3. The activation energy in each compound decreases with increase in frequency, indicating that smaller energy can overcome the fluctuations caused by the thermal excitation at higher frequencies. Table 6.3 Comparison of activation energy E a (ev) of (Bi 0.5 Pb 0.5 [Fe (0.5-X) La X (Zr 0.25 Ti 0.25 )]O 3 ) BFPZLTO compounds at selected frequencies in high temperature range. x 10kHz 100kHz 500kHz 1MHz ( )

9 (a) (e) Figure 6.3(a-e): Arrhenius plot for Bi 0.5 Pb 0.5 [Fe (0.5-X) La X (Zr 0.25 Ti 0.25 )]O 3 (BFPZLTO) compounds in temperature range 25 o C 500 o C 172

10 6.4 Frequency response of ac conductivity As discussed, the conduction in polar dielectric materials depends on the type and extent of polarization and behavior of different components of polarization to the applied ac perturbation. Usually the polarization effect is strong at low frequency range of applied field and decreases gradually as frequency of perturbed source increases because of the dipole relaxation, consequently the ac conductivity of the materials depends on the frequency of the perturbed field. Figure 6.4 shows the frequency response of ac conductivity for an ideal dielectric material. The conductivity spectrum has three distinguished regions showing low frequency dispersion, an intermediate plateau region and high frequency ac conductivity dispersion. At very low frequency the conductivity of the material is very small due to larger extent of charge accumulation. The variation of polarization at electrode-electrolyte interface with the frequency controls the ac conductivity of the material. At intermediate frequencies conductivity is almost frequency independent but at frequency range conductivity increases due to the possible release of space charge. log σ ac Polarization region Plateau region Dispersion region Frequency Figure 6.4: Variation of ac conductivity with frequency of ideal dielectrics The frequency dependent total conductivity of the materials can be explained by the well known augmented Jonscher s power law; σ (ω) = σ + σ (ω) (6.3) = σ +Aω = Kω + Kω ω = Kω 1 + ω ω = σ ω ω (6.4) 173

11 where σ is frequency independent conductivity, σ (ω) is the frequency dependent component of ac conductivity, A and K is temperature dependent proportionality constant, ω characteristic threshold frequency for hopping and n lies between 0 to 1. In the above equation the first and second term refers to the universal dielectric response (UDR) and nearly constant loss (NCL) respectively (a) Frequency effect on ac conductivity of BFPTO compounds The variation of ac conductivity (σ ) with frequency for Bi 1-x Pb x Fe 1- xti x O 3 (BFPTO) compounds are shown in Figure 6.5 (a-f) in the frequency range (1kHz- 1MHz) at different selected high temperatures. In the selected frequency range for observation, the conductivity spectra of each sample of BFPTO exhibits two distinct regions corresponding to (i) frequency independent conduction (plateau region) and (ii) frequency dependent ac conduction (dispersive region). The graphs gives a clear signature of the compositional effect on the ac conductivity of the materials. At each temperature, in the observed frequency range the conductivity of the BFPTO compound with x=0.1 is significantly larger than that in pure BFO, but with increase in the value of x i.e. PT concentration the conductivity of the materials decreases gradually. The effect of frequency on the conductivity of the studied materials were analyzed by using universal Jonscher s power law (represented in equation 6.3). The well fit of the above equation to the experimentally calculated data (in Figure 6.5(a-f) solid line represents the fitted curve using non-linear regression method and symbols represents the experimental values) confirms that the conduction process obeys universal power law in the material. According to Jonscher s power law the dispersive nature of ac conductivity is due to the relaxation of the mobile charge carriers at high frequencies. The frequency threshold beyond which the dispersion region starts is a characteristic frequency of the material, where the relaxation effects of ions starts. This frequency is temperature dependent (in the present compounds the value of this frequency shifts towards the higher side with increase in temperature) i.e dispersion region decreases with increase in temperature in the frequency range of experiment. This fact indicates that the ion hopping rate is less at lower temperature than that at higher temperature. 174

12 x Figure 6.5(a-f) frequency effect on ac conductivity of Bi 1-x Pb x Fe 1-x Ti x O 3 (BFPTO) compounds 175

13 With increase in the PT content in BFPTO, the dispersive region increases, this indicates that PT acts as a good relaxer in the fabricated compounds. This dispersion of the ac conductivity at high frequencies may be attributed to the disordering of cations between neighboring sites and presence of space charge polarization [288]. From the non-linear fitting data it was observed that, n < 1 for all materials of BFPTO, which indicates that charge carriers execute translational motion with a sudden hopping (b) Frequency effect on ac conductivity of BFPZTO compounds The comparative study of frequency response of the ac conductivity (σ ac ) of the samples of BPFZTO in the frequency range (1kHz-1MHz) is shown in the logσ ac vs frequency plot. Figure-6.6(a-e). In the low frequency region ac conductivity of the samples is almost independent of frequency suggesting the d.c conduction behavior dominates the ac conduction.. At high frequency the capacitive reactance of the sample decreases, hence the impedance is reduced, which causes an increase in the ac conductivity of the sample. The large slope in the conductivity spectrum may be interpreted as the conductivity due to the hopping of the mobile species, which increases with increase in frequency (ω) and proportional to ω n according to Jonscher law : σ (ω) = σ dc + Aω n. Which indicates that the electrical network RC response is qualitatively similar to the universal dielectric response(udr)[289]. In the experimental frequency range, the dispersive region of the conductivity plots are mostly observed, which suggests that relaxation occurs in the materials at lower frequencies as compared to that in BFPTO compounds. The linear behavior of some of the plots may be attributed to a probable release of space charge in the bulk of the samples. The slope of ac conductivity ~ frequency plot changes at the temperature, at which the grain resistance dominates the grain boundary resistance. The frequency at which the slope changes corresponds to the polaron hopping of charged species. At this frequency the charge carriers gains sufficient energy to tunnel through the barrier, which causes an increase in conductivity. 176

14 (b) (c) (d) (e) Figure 6.6(a-e) frequency response of ac conductivity of Bi 1-x Pb x Fe 1-x (Zr 0.5 Ti 0.5 )xo 3 (BFPZTO) compounds 177

15 As discussed before dielectric anomalies are observed in the BFPZTO compounds at temperature about 350 o C. The effects of dielectric anomaly on the conductivity of the material is clearly observed from the Figure 6.7(a-e) showing the frequency response of ac conductivity of the materials in the temperature range 300 o C 400 o C ( ±50 o C of the temperature corresponding to the dielectric anomaly point).the value of ac conductivity increases when temperature increases up to 350 o C and then decreases with further increase in temperature in the compounds with x=0.2 and 0.4. In these compounds the characteristic frequency from which ion relaxation starts decreases above the temperature 350 o C(i.e the dispersive region width of the conductivity spectrum increases after the dielectric anomaly. But this trend is not observed in the compounds with x value 0.3 and

16 Figure 6.7(a-e) Frequency response of ac conductivity of Bi 1-x Pb x Fe 1- x(zr 0.5 Ti 0.5 )xo 3 ( BFPZTO) compounds below and above dielectric anomaly temperature 179

17 6.4.1(c) Frequency response of ac conductivity of BFPZLTO compounds: Figure 6.8(a-d) represents the changes of ac conductivity with frequency of Bi 0.5 Pb 0.5 [Fe (0.5-x) La x (Zr 0.25 Ti 0.25 )]O 3 (BFPZLTO) and BFO samples at some selected high temperatures in the frequency range 1kHz -1MHz. The ac conductivity of the BFPZLTO compounds is observed to increase with increase in frequency at all temperatures. But with increase in the La concentration in BFPZLTO compounds, the ac conductivity decreases. The comparison of the graphs indicates that at all frequencies and at all temperatures (not shown here) the conductivity of the BFPZLTO compound with x=0.3 is less than that in pure BFO, which indicates that the capacitive effect of the grain and grain boundary increase with increase in La concentration thus the lossy effect decreases. In the frequency range of experiment the conductivity plot exhibits some portion of the frequency independent conductivity plateau region and dispersive region. The backward extrapolation of the graphs give the value of σ of the material at the given temperature. The dispersion is observed at high frequencies and the dispersive region in the conductivity spectra increases in the observed frequency range as the La concentration increases. The best fit of the above equation with the experimental data confirms that conduction process in the BFPZLTO and BFO samples obeys Jonscher s power law [290]. 180

18 (e) Figure 6.8(a-e) Frequency response of ac conductivity of Bi 0.5 Pb 0.5 [Fe (0.5-x) La x (Zr 0.25 Ti 0.25 )]O 3 (BFPZLTO) compounds 181

19 6.5 Conclusions: The above discussion indicates that: The conduction mechanism in the material is governed by polaron transportation, oxygen ion vacancies and space charge transportation. Larger the frequency of the applied alternating field smaller the activation energy of each compound. Jonscher s universal power law holds good to explain the frequency dependence of ac conductivity of all the studied materials. 182