Micro-mechanics of multi-phase ferroelectric domain structures

TL;DR

This paper develops micro-mechanical models for ferroelectric ceramics, especially PZT near the morphotropic phase boundary, to understand phase coexistence and compatibility of domain structures.

Contribution

It introduces a method to analyze the mechanical and electrical compatibility of multiple phases within ferroelectric domains, incorporating composition-dependent strain and polarization data.

Findings

Derived relationships for phase coexistence conditions

Analytical fit of strain and polarization data for PZT

Modeling approach for multi-phase crystallite behavior

Abstract

High-strain piezoelectric materials are often ceramics with a complicated constitution. In particular, PZT is used with compositions near to a so-called morphotropic phase boundary, where not only different variants of the same phase (domains), but different phases may coexist. Micro-mechanical models for ferroelectric ceramics would be much more realistic, if these effects could be incorporated. In this paper, we consider the conditions of mechanical and electrical compatibility of ferroelectric domain structures. We are able to address the question of coexistence of different crystallographic phases within the very same crystallite. In general, the spontaneous strain and spontaneous polarization of different phases are not compatible. The numerical analysis of the derived relationships are susceptible to the crystallographic description of the phases in question. In this presentation, a simple analysis and analytical, composition dependent fit of strain and polarization of PZT at room temperature for available data are used. The outlined approach can be used to model the overall behavior of multi-variant and multi-phase crystallites with certain, simplified geometrical arrangements of the constituents.