Effect of elastic boundary conditions on morphotropic Pb(Zr,Ti)O3piezoelectrics

Abstract

Most of the technologically important transducers are made of poled-polycrystalline lead zirconate–lead titanate Pb(Zr,Ti)${\mathrm{O}}_3$ compositions near the morphotropic phase boundary where the [Zr]:[Ti] ratio is approximately 1:1. The effect of elastic boundary conditions on single-domain stability and properties of compositions near the morphotropic phase boundary in the ${\mathrm{PbZrO}}_3$-${\mathrm{PbTiO}}_3$ phase diagram is of considerable interest, since in a polycrystalline ensemble, the elastic and electric boundary conditions are uncertain. In this work, a phenomenological free-energy function which we developed earlier is used to determine the influence of elastic boundary conditions upon the relative stability points and the rhombohedral (R3m)–tetragonal (P4mm) degeneracy required for the morphotropy at [Zr]:[Ti] ratio near 1:1.