Theoretical examination of stress fields in Pb(Zr_0.5Ti_0.5)O_3

TL;DR

This paper develops a rigorous theoretical framework for analyzing local stress fields in complex bonded systems, specifically applied to Pb(Zr_0.5Ti_0.5)O_3 and related materials, to understand their stress and piezoelectric responses.

Contribution

It introduces a general formulation for local stress fields compatible with first-principles methods, applied to various phases of Pb(Zr,Ti)O_3 to compare stress and piezoelectric behaviors.

Findings

Stress fields vary with material phase and deformation type.

Piezoelectric responses are correlated with stress field characteristics.

The framework enables detailed stress analysis in complex ferroelectric systems.

Abstract

In this paper, we develop a rigorous formulation of the local stress field. This approach can be used in conjuction with any first-principles method to study stress fields in complex bonded systems. In particular we investigate the induced stress fields resulting from homogeneous deformations for tetragonal PbTiO_3 and rhombohedral PbZrO_3. As an extension of these findings we also compute the induced stress fields resulting from homogeneous deformations of the (100) and (111) orderings of Pb(Zr_0.5Ti_0.5)O_3. The stress-field responses in these four materials are compared and their piezoelectric responses are discussed.