Micromechanics and Some Aspects of Phase Fields in Ferroelectric Crystals
George Weng (Rutgers University)
Prager Medal Lecture
Tue 8:00:00 AM
Salomon 101
Ferroelectric crystals possess several distinct characteristics that make it a unique class of multi-functional materials. In addition to its strong electromechanical coupling, there is the existence of polarization domains which can be reoriented to produce various domain patterns under an external electric field and/or mechanical stress, and it also exhibits several types of crystal structures at different temperatures. Domain switch and phase transition thus form the two fundamental processes that control the ferroelectric characteristics. In this talk we first present a micromechanics approach that can have wide applicability for the study of bulk ferroelectrics, and then present some phase-field results calculated from the Landau theory for nanostructures. In the micromechanics approach we start out from consideration of crystal structures and Eshelby mechanics to determine the change of Gibbs free energy and the thermodynamics driving force during domain growth and phase transition. This theory is applicable to any ellipsoidal shape of the product phase including lamellar structures. With rank-1 and rank-2 laminated domain patterns, it is shown that the derived driving force turns into the jump of Eshelby's energy-momentum tensor across the domain wall, serving as the force for the wall motion. When supplemented with the kinetic equations for the growth of 180o and 90o domains and a homogenization scheme, the theory can be applied to study various ferroelectric characteristics. We in particular use it to uncover the influence of a fixed axial compression on the hysteresis behavior of a [001]-poled BaTiO3 crystal, and demonstrate how a suitable amount of axial compression can greatly enhance the butterfly-shaped strain and total actuation strain. We also show how the triple hysteresis loops of a BaTiO3 crystal can be generated at temperatures slightly below 7.02oC (the tetragonal-to-orthorhombic transition temperature), and explain why the corresponding variation of its dielectric constant exhibits the mansion-like profile. Our starting points in the phase-field study are the time-dependent Ginzburg-Landau kinetic equation and the Landau-Ginzburg-Devonshire energy density. We use it to study two specific nano problems: i) the effect of surface tension of a free-standing BaTiO3 nano-thin film, and ii) the effect of grain size of a nanocrystalline BaTiO3 polycrystal. In the first case we show that, even though surface tension tends to cover only 2-3 atomic layers, it can still lower the coercive field of the nano film and cause it to gradually lose its ferroelectricity as the film thickness decreases from 40 nm down to 4 nm. In the second case we show how the size of hysteresis loop decreases and how its shape tilts, and how the domain pattern inside the grains changes from a largely aligned one to vortex structure as the grain size decreases from 80 nm to 10 nm. We conclude this talk by drawing the distinctions between the two approaches, and pointing out their respective virtues.