Modeling dielectric response and losses of ferroelectrics at microwave frequencies

Displacement type ferroelectric BaxSr1-xTiO3 is characterized by the second order phase transition. In a perfect ferroelectric crystal the phase transition takes place at temperature T-C, which is called the Curie temperature. In the case of the real crystal, the temperature of the phase transition T is displaced to lower temperature and the temperature of the maximum of epsilon(T) T-m is displaced to higher value with respect to T-C. Thus, for the real ferroelectric sample (not for an incipient ferroelectric), one has T-C' < T-C < T-m. In the case of a thin film sample, the phase transition and the dielectric response of a ferroelectric sample are affected by the size of the sample, what is treated as a size effect. Experimental data obtained as a result of measurement of the dielectric constant as a function of temperature can be used for finding the parameters of the material.