Mechanical and Dielectric Response of PZT and Tetragonal to Monoclinic Phase Transition: I. Theory

The PZT material near the morphotropic phase boundary where a monoclinic phase was observed is studied in this paper. A theory of the tetragonal to monoclinic phase transition was developed within the Landau free energy approach. The order parameter is the electric polarization vector. The phase transition from the tetragonal to the monoclinic phase is of the first order near the second order. The tetragonal and monoclinic phases are described as equilibrium states within this theory. Dielectric response near the phase transition from the tetragonal to the monoclinic phase was studied for the crystal and for the ceramic and polycrystalline material taking into account the diagonal 33 and the off diagonal 31 components of susceptibility. The later diverges at temperature of stability boundary for the monoclinic phase, and it is zero in the tetragonal phase. Such a behavior is not observed in the effective dielectric static constant temperature dependence for ceramics and polycrystalline materials. We explain absence of a large contribution of the off diagonal susceptibility by a grain structure of the material and by percolation properties of this microcomposite. Above the percolation transition the off diagonal contribution to the effective susceptibility is not present. Observed temperature behavior of the effective dielectric susceptibility is thus qualitatively explained. Effective susceptibility which is decreasing in tetragonal phase is in the monoclinic phase also decreasing, however below phase transition temperature the decrease is slower. A quantitative theoretical behavior of dielectric susceptibility for both phases is found. Mechanical response of PZT material to a uniaxial stress is studied theoreticaly for both phases. Observed temperature behavior of it, a well around the transition temperature from the tetragonal to monoclinic phase transition, is qualitatively explained.