FORCED TRANSLATIONAL VIBRATIONS OF 90-DEGREES DOMAIN-WALLS AND THE DIELECTRIC-DISPERSION IN FERROELECTRIC CERAMICS

A theory of collective translational vibrations of 90-degrees domain w alls (DWs) in ferroelectric ceramics is presented. Vibrational motions of DWs forming a regular domain structure of a representative grain a re assumed to be completely correlated but independent of DW oscillati ons in other grains. A dynamic mechanical stress field appearing in a ceramic because of DW vibrations is calculated. In contrast to former studies, this calculation takes into account effects due to the laggin g of sound waves emitted by oscillating DWs and gives a general expres sion for the dynamic mechanical restoring force acting on DWs. From th is expression we derive the equation of sustained forced DW vibrations in an oscillating external electric field that is valid for a wide fr equency range including microwave frequencies. A general solution of t his equation is found, which enables us to compute numerically the dep endencies of amplitude and phase of DW vibrations on the frequency ome ga of the applied electric field. It is shown that in the low-frequenc y range omega < omega=c(t)/g (c(t)=velocity of transverse sound wave, g=grain size) the general equation of DW vibrations can be reduced to a simplified equation that includes the static restoring force, the i nertial reaction, and the radiation reaction self-force of the DWs emi tting sound waves. Analytic expressions are derived for the DW effecti ve mass and for the factors characterizing the static restoring force and the radiation reaction. The contribution of DW vibrations to the c omplex dielectric constants of ferroelectric ceramics is calculated. I t is predicted that at very high frequencies omega much greater than o mega the DW contribution to the real part of permittivity strongly de creases due to clamping of DWs. In this frequency range a peak of diel ectric losses should also arise being caused by the emission of sound waves from oscillating DWs. It is emphasized that the above effects ca n be correctly described on the base of the general equation of DW vib rations only.