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

TL;DR

This paper develops a Landau theory for the tetragonal to monoclinic phase transition in PZT, analyzing dielectric and mechanical responses near the transition, and explains experimental observations in ceramics and polycrystalline materials.

Contribution

It provides a theoretical model describing the phase transition and dielectric response of PZT near the morphotropic boundary, including effects of grain structure and susceptibility behavior.

Findings

Dielectric susceptibility diverges at the monoclinic stability boundary.

Effective dielectric constant in ceramics does not show large off-diagonal contributions.

Mechanical response behavior around the transition temperature is qualitatively explained.

Abstract

The PZT material near the morphotropic phase boundary where a monoclinic phase was observed is studied. A theory of the tetragonal to monoclinic phase transition was developed within the Landau free energy approach. The phase transition from the tetragonal to the monoclinic phase is of the first order near the second order. 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 for ceramics and polycrystalline materials. We explain absence of a large contribution of the off diagonal susceptibility by a grain structure of the material. Above the percolation transition the off diagonal contribution to the effective susceptibility is not present. 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.