Microwave dielectric properties
5.7 Low frequency dielectric properties
The frequency dependence of imaginary part of impedance (-Zʺ) of (Mg0.95Co0.05)TiO3 ceramics measured at different temperatures is shown in Figure 5.10.
Figure 5.10: Frequency dependent imaginary part of impedance (-Zʺ) for (Mg0.95Co0.05)TiO3
The value of Zʺ exhibits
monotonically with increase in frequency ( However at 773 K, a broad peak in
single curve for frequencies > 400 kHz for all th
process may be due to the presence of immobile species at low temperature and formation of defects at high temperatures.
Figure 5.11(a) and (b) shows the (Mg0.95Co0.05)TiO3 sample measured 300 - 673 K the plots of Zʹ vs.
of the sample. But at 773 K, these curve almost semi circular arc with non frequency intercept has been observed.
Figure 5.11: (a, b) The Nyquist plots (Cole measured at different temperature (300 model for the Cole - Cole configuration.
Generally, the semicircle behavior of complex impedance plots can be explained on the basis of an equivalent circuit model (Cole
this model, the high frequency intercept provides the value of the series resistance and the magnitude of semi circle diameter gives the electrical dc
specified temperature. The maximum value corresponds to the relaxation frequency
= 1/RC. The present -Z''
exhibits a very high value at low frequencies and decrease monotonically with increase in frequency (f) in the temperature range of
peak in Zʺ ( f ) is observed at 110 kHz. All the curves merge into single curve for frequencies > 400 kHz for all the investigated temperatures. This
process may be due to the presence of immobile species at low temperature and formation of tures.
Figure 5.11(a) and (b) shows the Nyquist plots of the complex impedance spectrum of sample measured at different temperatures. In the temperature range
ʹ vs. -Zʺ linearly lineup towards Zʺ axis indicating high resistivity of the sample. But at 773 K, these curve almost semi circular arc with non
frequency intercept has been observed.
(a, b) The Nyquist plots (Cole - Cole graphs) of (Mg0.95Co0.05
measured at different temperature (300 - 773 K). The inset of 11(b) shows equivalent circuit Cole configuration.
Generally, the semicircle behavior of complex impedance plots can be explained on the cuit model (Cole- Cole) as shown in the inset of Figure 5.11(b). In this model, the high frequency intercept provides the value of the series resistance and the magnitude of semi circle diameter gives the electrical dc - resistivity of the sample at
ified temperature. The maximum value corresponds to the relaxation frequency
and Z' Cole-Cole configuration represents two parallel RC very high value at low frequencies and decrease in the temperature range of 300 - 673 K.
observed at 110 kHz. All the curves merge into e investigated temperatures. This relaxation process may be due to the presence of immobile species at low temperature and formation of
yquist plots of the complex impedance spectrum of at different temperatures. In the temperature range of ting high resistivity of the sample. But at 773 K, these curve almost semi circular arc with non - zero high
0.05)TiO3 ceramics equivalent circuit
Generally, the semicircle behavior of complex impedance plots can be explained on the Cole) as shown in the inset of Figure 5.11(b). In this model, the high frequency intercept provides the value of the series resistance and the resistivity of the sample at a ified temperature. The maximum value corresponds to the relaxation frequency ω = 2πf two parallel RC
circuit. The semi circle arc at low frequency circuit corresponds to grain boundary resistance (Rgb) and the high frequency arc indicates the contribution from grains (Rg). The data at 773 K is well match with the single RC circuit and the relaxation time (τ) is calculated by substituting ω in the equation: τ = 1/ω as 1.4×10-6 sec. Similar results of high temperature Cole - Cole plots measured at 800oC was reported by Kuang et al. [34] for MgTiO3 ceramics.
Figure 5.12: The Variation in ac-conductivity (σac) of (Mg0.95Co0.05)TiO3 sample as a function of frequency (f) measured at different temperatures.
The ac-conductivity (σac) of (Mg0.95Co0.05)TiO3 sample as a function of frequency measured at various temperatures is shown in Figure 5.12. For T < 673 K, the conductivity is almost varies linearly with the frequency and no dc-plateau region has been observed within the frequency range of 103 - 106 Hz. On the otherhand, at 773 K, frequency independent conductivity (plateau) is observed at low frequencies (f < 30 kHz), due to the contribution of dc conduction mechanism. Beyond a critical frequency the conductivity follows linearly with frequency which is expected due to the contribution of grains [35]. The dependence of ac - conductivity on the frequency is generally described using Jonscher power law [36]
Aωs
σ ω
σ( )= (0)+ (4) where σ(ω) is the total conductivity of the system, σ(0) is the contribution from dc conductivity (frequency independent part), ω is the angular frequency of the ac signal (ω = 2πf ) and “s” and “A” are the temperature dependent characteristic parameters. The term Aωs
contains the ac dependence and characterizes all dispersion calculated “s” and “A” are found
value of “s” should lie between 0 and 1. In the present case slightly higher values noticed. The similar results were
Figure 5.13(a) and (b) shows the frequency dependent dielectric constant tangent (tanδ) of (Mg0.95Co
dielectric constant and tanδ
decrease in dielectric constant with increase in frequency is a typical characteristic of the linear dielectric. The obtained dielectric constant and loss tangent values are in the range between 6454 -15.35 and 0.93
between 300 K - 773 K. The obtained dielectric constant at 10 measured at microwave frequencies (
dielectric constant with frequency can be explained on the basis of Maxwell layer and koop’s phenomenological theory [
frequency increases, the electrons reverse their direction of motion more often which decreases the probability of electrons reaching the grain boundary which results the reduction in polarization therefore decreasing the dielectric constant.
frequencies may be due to the contributions from metal electrode and the electrode interfaces.
Figure 5.13: The frequency dependent (a) dielectric constant ( of (Mg Co )TiO sample, measured at different temperatures.
contains the ac dependence and characterizes all dispersion phenomenons
found to be 1.16 and 0.74, respectively at 773 K. Usually, the
” should lie between 0 and 1. In the present case slightly higher values results were reported for chalcogenide materials [38].
Figure 5.13(a) and (b) shows the frequency dependent dielectric constant
Co0.05)TiO3 sample measured at different temperatures. Both the are found to decrease with increase in applied frequency. The decrease in dielectric constant with increase in frequency is a typical characteristic of the The obtained dielectric constant and loss tangent values are in the range 15.35 and 0.93 - 0.0011 respectively for the measured temperatures
773 K. The obtained dielectric constant at 106 Hz is identical to the value red at microwave frequencies (εr ~ 17.3) for the same sample. The dispersion in dielectric constant with frequency can be explained on the basis of Maxwell
layer and koop’s phenomenological theory [39]. These models demonstrates that as the equency increases, the electrons reverse their direction of motion more often which decreases the probability of electrons reaching the grain boundary which results the reduction in polarization therefore decreasing the dielectric constant. This variation
frequencies may be due to the contributions from metal electrode and the electrode
The frequency dependent (a) dielectric constant (εr) and (b) loss tangent (tan sample, measured at different temperatures.
phenomenons [37]. The respectively at 773 K. Usually, the
” should lie between 0 and 1. In the present case slightly higher values of “s” is
Figure 5.13(a) and (b) shows the frequency dependent dielectric constant (εr) and loss sample measured at different temperatures. Both the with increase in applied frequency. The decrease in dielectric constant with increase in frequency is a typical characteristic of the The obtained dielectric constant and loss tangent values are in the range 0.0011 respectively for the measured temperatures in Hz is identical to the value
~ 17.3) for the same sample. The dispersion in dielectric constant with frequency can be explained on the basis of Maxwell - Wagner two These models demonstrates that as the equency increases, the electrons reverse their direction of motion more often which decreases the probability of electrons reaching the grain boundary which results the reduction This variation in loss at lower frequencies may be due to the contributions from metal electrode and the electrode
) and (b) loss tangent (tanδ)
Figure 5.14 shows the variation in dielectric constant (εr) and loss tangent (tanδ) of (Mg0.95Co0.05)TiO3 sample as a function of temperature measured at 106 Hz. Both the dielectric constant εr andtanδ increases linearly with temperature. This can be explained as, at low temperatures the molecules cannot orient themselves in polar dielectrics. When the temperature rises, the orientation of dipoles is facilitated and this increases dielectric constant. At high temperatures, the dielectric losses caused by the dipole mechanism reach their maximum value and the degree of dipole orientation increases. Apart from dipole losses electrical conduction also increases with increase in temperature. These factors would cause the increase in both dielectric constant and dielectric loss of (Mg0.95Co0.05)TiO3 ceramics with increase in temperature [40].
Figure 5.14: Variation in dielectric constant (εr) and loss tangent (tanδ) of (Mg0.95Co0.05)TiO3 sample as a function of temperature measured at 106 Hz.