ABSTRACT
Piezoelectricity, discovered in Rochelle salt in 1880 by Jacques and Pierre Curie, is the term used to describe the ability of certain materials to develop an electric charge that is proportional to a direct applied mechanical stress. œese materials also show the converse e¥ect; that is, they will deform (strain) proportionally to an applied electric Ÿeld. Some crystalline materials show piezoelectric behavior due to their unique crystal structure. œe lattice structure of a crystal is described by the Bravais unit cell [1]. œere are 230 microscopic symmetry types (space groups) in nature, based on the several symmetry elements such as translation, inversion center, mirror plane, or rotation axes.œe combinations of these symmetry elements yield the macroscopic symmetry known as point groups. All natural crystals can be grouped into 32 di¥erent classes (point groups) based on their symmetry elements.œe 32 point groups can be further classiŸed into two subgroups: (1) crystals with a center of symmetry and (2) crystals with no center of symmetry.œe 11 centrosymmetric subgroups do not show piezoelectricity.Of the 21 noncentrosymmetric groups, 20 show the piezoelectric e¥ect along unique directional axes. An important class of piezoelectric materials includes ferroelectrics, in which the piezoelectric e¥ect is closely related to the ferroelectric polarization that can be reversed by the application of su¬ciently high electric Ÿeld [2,3]. To induce piezoelectric properties in ferroelectric materials, a poling procedure is o£en required, which consists of the temporary application of a strong electric Ÿeld. Poling is analogous to the magnetizing of a permanent magnet.
