Anisotropic systems, piezoelectric

Sintered ceramics made of lead-zirconium titanate (PZT Pb(Tii jZr,)03 x S 0.5) are usually used for phoioacoustic experiments [105, 106]. The unit cell of the lead-zirconium titanate has a perovskite structure. Below the Curie temperature (328 °C for the PZT-4 (Vemitron) used by us [24]), the cells are tetragonally deformed, i.e., positive and negative charges are shifted and electric dipole moments are produced. In analogy to ferromagnetism, domains with randomly distributed polarization direction are formed. By the application of an electric field, these can be orientated in a preferred direction, and the sintered polycrystalline ceramic is then remanently polarized. The properties of these anisotropic piezoelectric materials are described by various parameters which depend on the polarization and deformation direction. In the common terminology, the < ordinate system shown in Fig. 3 is obtained for the cylindrical piezoelectric crystals [24]. 

Realization of mechanically well-defined state is not easy. Sample is always kept in some holder (e g. between metallic jaws) in order to reach uniaxial homogeneous stress. Metallic jaws are deformed along with the sample. Normally isotropic metal is in contact with anisotropic piezoelectric material. Uniaxially acting force on metallic jaws results in shear components of the mechanical stress at the interface between metal and piezoelectric material due to the anisotropy of it. Stress components system therefore include more components in the piezoelectric sample (stress... 

Bent, A.A. Hagood, N.W. and Rodgers, J.P. Anisotropic actuation with piezoelectric fiber composites. J. Intelligent Mater. Systems and Structures, 6(3) (1995), pp. 338-349... 

The chapter begins with an overview of elastic anisotropy in crystalline materials. Anisotropy of elastic properties in materials with cubic symmetry, as well as other classes of material symmetry, are described first. Also included here are tabulated values of typical elastic properties for a variety of useful crystals. Examples of stress measurements in anisotropic thin films of different crystallographic orientation and texture by recourse to x-ray diffraction measurements are then considered. Next, the evolution of internal stress as a consequence of epitaxial mismatch in thin films and periodic multilayers is discussed. Attention is then directed to deformation of anisotropic film-substrate systems where connections among film stress, mismatch strain and substrate curvature are presented. A Stoney-type formula is derived for an anisotropic thin film on an isotropic substrate. Anisotropic curvature due to mismatch strain induced by a piezoelectric film on a substrate is also analyzed. 

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