The Prager Medal Lecture: Micromechanics and some aspects of phase fields in ferroelectric crystals

Ferroelectric crystals represent a very unique class of multifunctional materials. In addition to strong electromechanical coupling, there exist ferroelectric domains, which can be switched through the application of an electric field or mechanical stress. In addition, these crystals possess several distinct crystal structures over a wide temperature range. As such, phase transition can take place as the crystals are cooled down or heated up, without or with the additional effect of stress or electric field. Domain switch and phase transition represent the two fundamental processes that can affect their microstructures and electromechanical characteristics. In this lecture, we highlight the applications of micromechanics to bulk ferroelectrics and phase fields to nano-structures. The starting points of micromechanics are crystal structures and the Eshelby mechanics, whereas those of the phase fields are the time-dependent Ginzburg-Landau kinetic equation and the Landau-Ginzburg- Devonshire energy density function. We explain how micromechanics can have wide applicability in the study of domain switch and phase transition, and change of dielectric constants, of bulk BaTiO₃ crystals, and how phase fields can provide the nano-scale domain patterns, influence of surface tension on free-standing BaTiO₃ nano-thin films, and grain-size dependence of ferroelectric characteristics in nano-grained BaTiO₃ polycrystals.