  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.
