Rotator and extender ferroelectrics: Importance of the shear coefficient to the piezoelectric properties of domain-engineered crystals and ceramics

TL;DR

This paper emphasizes the critical role of the shear coefficient d15 in determining the piezoelectric response of ferroelectric crystals, classifying them as rotators or extenders based on polarization rotation mechanisms.

Contribution

It introduces the concepts of rotator and extender ferroelectrics, linking shear coefficient values to polarization rotation and piezoelectric anisotropy across various crystal structures.

Findings

High shear coefficient d15 correlates with polarization rotation.

Largest piezoelectric anisotropies are in 3m crystals.

Piezoelectric anisotropy increases near phase transitions.

Abstract

The importance of a high shear coefficient d15 (or d24) to the piezoelectric properties of domain-engineered and polycrystalline ferroelectrics is discussed. The extent of polarization rotation, as a mechanism of piezoelectric response, is directly correlated to the shear coefficient. The terms "rotator" and "extender" are introduced to distinguish the contrasting behaviors of crystals such as 4mm BaTiO3 and PbTiO3. In "rotator" ferroelectrics, where d15 is high relative to the longitudinal coefficient d33, polarization rotation is the dominant mechanism of piezoelectric response; the maximum longitudinal piezoelectric response is found away from the polar axis. In "extender" ferroelectrics, d15 is low and the collinear effect dominates; the maximum piezoelectric response is found along the polar axis. A variety of 3m, mm2 and 4mm ferroelectrics, with various crystal structures based on oxygen octahedra, are classified in this way. It is shown that the largest piezoelectric anisotropies d15/d33 are always found in 3m crystals; this is a result of the intrinsic electrostrictive anisotropy of the constituent oxygen octahedra. Finally, for a given symmetry, the piezoelectric anisotropy increases close to ferroelectric-ferroelectric phase transitions; this includes morphotropic phase boundaries and temperature induced polymorphic transitions.