Study of dielectric and resonance and anti-resonance property of dielectric relaxor ceramic: [Ba(Nd_0.1Ti_0.8Nb_0.1)O₃]_0.50[Na_0.5Bi_0.5TiO₃]_0.40[CaTiO₃]_0.10

Simulation of dielectric and resonance and anti-resonance data using modified Lorentz equation (T and $$\omega $$ ω simultaneously) of relaxor ferroelectric and piezoelectric ceramics

“…This equation does not give much information except for area under the curve, width and peak positions. Hence, in our earlier studies, we have proposed modified Lorentz equation (equation (5)) [12][13][14] and were successful in fitting the dielectric resonance and anti-resonance data. Here, ε s is the static dielectric constant, ε ∞ is the infinite dielectric constant, N A is the Avogadro number, ρ is the experimental density, α is the polarizability, M is the molecular weight, d 33 is the piezoelectric charge constant, g 33 is the piezoelectric voltage constant, ω is the angular frequency, ω c1 is the angular resonance frequency, ω c2 is the angular anti-resonance frequency and τ , τ c1 and τ c2 are the relaxation times.…”

“…Since the dielectric constant is frequency-and temperaturedependent, it is better to modify equation (5) to describe the dielectric dependence on ω and T simultaneously. Hence, in the present study, the terms ((T * K B /E act_R ) 2 ) + 1) and ((T * K B /E act_AR ) 2 ) + 1) are incorporated into equation (5) and is shown as equation (6). The incorporation of these terms in equation (5) allow us to determine the activation energy for resonance (E act_R ) and activation energy for anti-resonance (E act_AR ) along with the previously obtained parameters like d 33 and g 33 .…”

“…It would be better if one can describe the temperature dependence of dielectric constant at different constant frequencies directly. This has prompted us to propose a modified Lorentz equation to describe the temperature dependence of dielectric constant of normal [4] and relaxor [5,6] ferroelectrics in our previous studies. The proposed modified Lorentz equation describes the dielectric constant as a function of temperature only and not with frequency.…”

“…From the resonance and antiresonance frequency values and capacitance at 1 kHz, the piezoelectric charge constant is also estimated using the standard piezoelectric formula [11], but this formula is arbitrary, even though piezoelectric standards are followed. In view of the above, in our previous studies, we have proposed a modified Lorentz equation to simulate the dielectric resonance and anti-resonance data to obtain the polarizability, piezoelectric charge constant and piezoelectric voltage constant and were successful in fitting the experimental data using the modified Lorentz equation very well and obtained the above parameters indirectly from the fitting [12][13][14]. But, this modified Lorentz equation describes the variation of dielectric constant with frequency only, but not with temperature.…”

“…Hence, in the present study, the Lorentz equation was re-modified to describe the variation of dielectric constant with frequency and temperature simultaneously and was successful in fitting the experimental resonance and anti-resonance data. Inclusion of T in equation (6) has made it possible to obtain the activation energy for resonance and anti-resonance.…”