The importance of a high shear coefficient d 15 (or d 24 ) 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 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.* email: matthew.davis@epfl.ch 2

Articles you may be interested inStructure, piezoelectric, and ferroelectric properties of BaZrO3 substituted Bi(Mg1/2Ti1/2)O3-PbTiO3 perovskite The orientation dependence of the longitudinal piezoelectric coefficient, d 33 * , is investigated as a function of temperature in BaTiO 3 and PbTiO 3 crystals using the Landau-Ginsburg-Devonshire theory. We show that a presence of the ferroelectric-ferroelectric phase transitions in BaTiO 3 leads to enhanced d 33 * along nonpolar directions. The reason for this is that in the vicinity of a phase transition temperature at which a polarization vector changes its direction ͑tetragonalorthorhombic/monoclinic, orthorhombic/monoclinic-rhombohedral͒, the shear piezoelectric coefficients become high. It is shown for all ferroelectric phases of BaTiO 3 that the shear stress deforms the crystal cell and changes the polarization direction in a similar way as the corresponding temperature-induced phase transition. The influence of the piezoelectric shear effect on the anisotropy of d 33 * is particularly pronounced in the orthorhombic/monoclinic phase where the piezoelectric shear coefficients are determined by the presence of both the high-temperature tetragonal and the low-temperature rhombohedral phases. In PbTiO 3 , which does not exhibit ferroelectric-ferroelectric phase transitions, the shear piezoelectric effect is weak and d 33 * has its maximum along the polar axis at all temperatures. These results can be generalized to include phase transitions induced by electric-field and composition variations and are valid for all perovskite materials, including complex relaxor-ferroelectric perovskites that have recently attracted attention for their exceptionally large piezoelectric properties.

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The influence of the uniaxial bias stress on the piezoelectric properties of tetragonal BaTiO 3 and PbTiO 3 monodomain crystals is modeled in the framework of the phenomenological Landau-Ginzburg-Devonshire theory. It is shown that tensile and compressive stresses, both applied along the spontaneous polarization direction, reduce and enhance the piezoelectric response, respectively. The enhancement effect is due to the flattening of the free-energy profile and the corresponding dielectric softening of crystals, caused by the compressive stress. In BaTiO 3 crystals, at temperatures close to the tetragonal-orthorhombic phase transition temperature, the free-energy profile flattening and dielectric softening are the largest along axes perpendicular to the polarization direction, facilitating thus the polarization rotation away from the ͓001͔ c polar axis. The resulting enhancement of the shear piezoelectric coefficient is directly responsible for the increase of the longitudinal piezoelectric coefficient along the ͓111͔ c axis. At temperatures deep within the tetragonal phase in BaTiO 3 , and over the whole ferroelectric region of PbTiO 3 , the flattening of the free-energy profile and the dielectric softening by compressive stress are the strongest along the polar axis. The resulting enhancement of the longitudinal piezoelectric coefficient is thus the largest along the polar ͓001͔ c direction. These results, which can be applied to other perovskite crystals, have broad implications.

This paper discusses the mechanisms that can contribute to the enhanced longitudinal piezoelectric effect along nonpolar directions in perovskite crystals, such as BaTiO