Impurity dependence of the Curie temperature and microwave absorption in ferroelectric crystals

Abstract

Using the method of double-time temperature-dependent Green's functions and Kubo formalism, a general expression is derived for the complex dielectric constant of a defect ferroelectric crystal in the paraelectric phase taking into account the change of mass as well as harmonic force constant between impurity atom and host-lattice atoms. The results are used to obtain an expression for the frequency and temperature dependence of the dielectric loss at microwave frequencies due to impurity and anharmonic scattering. Neglecting the polarization of ions it is shown that the influence of defects on the dielectric constant at low frequencies can be expressed by a change only in the Curie temperature, as is known experimentally. To a first-order approximation of the defect parameters, the Curie-temperature shift is found to depend only on the harmonic-force-constant changes between the impurity and host-lattice atoms, and is proportional to the concentration of defects, as has been experimentally established.