Effective Medium Theories

Predicting macroscopic properties of materials involves two tasks:

• 1. Projection of macroscopic loading conditions onto the microstructural level with sufficient and adjusted details (resulting in fluctuating internal fields)

• 2. Averaging the local reaction of material to obtain the macroscopic response to the loadings

For piezoelectric/ferroelectric polycrystalline materials, the relevant micro-structural level is presented by special domain configurations within grains which have different orientations. The local material response comprises the elastic, dielectric, and intrinsic piezoelectric effect as well as the restructuring of domain configuration by movement of domain walls or complete reorientation of the spontaneous polarization, i.e., domain switching. Other processes as moving free charges and/or defect dipoles are normally not considered in present micro-macro models. They appear in the form of already averaged local properties, e.g., as an effective frictional force or activation energy for domain wall movement.