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

Dielectric data of new [\(\hbox {Ba}(\hbox {Nd}_{x}\hbox {Ti}_{1-2x}\hbox {Nb}_{x})\hbox {O}_{3}\)]\(_{0.30}\)[\(\hbox {Na}_{0.5}\hbox {Bi}_{0.5}\hbox {TiO}_{3}\)]\(_{0.70}\) (\(x = 0.075\)) relaxor ceramic was modelled using a new modified Lorentz equation (T and \(\omega \) simultaneously) as proposed by us. The activation energy for thermally activated orientation of dipoles and relaxation times were estimated. Dielectric resonance and anti-resonance data as a function of temperature and angular frequency of other piezoelectric compound [\(\hbox {Ba}(\hbox {Nd}_{0.1}\hbox {Ti}_{0.8}\hbox {Nb}_{0.1})\hbox {O}_{3}\)]\(_{0.35}\) \([(\hbox {Na}_{0.5}\hbox {Bi}_{0.5})\hbox {TiO}_{3}\)]\(_{0.65}\) was also modelled using the modified Lorentz equation as proposed by us. It is shown that using this equation, it is possible to obtain the polarizability, piezoelectric charge constant, piezoelectric voltage constant and activation energy for resonance and anti-resonance.