2. Model Development for Ferroelectric Compounds
Society for Industrial and Applied Mathematics eBooks · 2005
Ferroelectric materials are defined as those which exhibit, at temperatures below the Curie point, a domain structure and spontaneous polarization which can be reoriented by applied electric fields. As detailed in Section 2.1, the domain morphology results from the alignment of dipoles to minimize electrostatic and elastic energy, and materials with this structure will exhibit varying degrees of hysteresis at all drive levels. This definition is analogous to the designations ferromagnetic and ferroelastic for compounds exhibiting magnetic and elastic domains, and the combined class of ferroelectric, ferromagnetic and ferroelastic materials will be collectively referred to as ferroic materials. To simplify the discussion, we will focus primarily on the ferroelectric materials BaTiO3 (barium titanate), Pb(Zr,Ti)O3 (lead zirconate titanate or PZT), the film polyvinylidene fluoride (PVDF), and the electrostrictive material Pb(Mg,Nb)O3 (PMN) at temperatures below the freezing point — however, the theory and models encompass a broad range of ferroelectric compounds. BaTiO3 was the first piezoceramic material to be developed commercially and, due to its simplicity, it complements PbTiO3 in providing an ideal prototype for describing the constituent dipole and domain processes. For present applications, however, it has been largely superseded by PZT due to the enhanced performance capabilities of the latter, and we focus the model development on PZT. At low temperatures, PMN exhibits ferroelectric behavior whereas it exhibits relaxor ferroelectric behavior at temperatures between the freezing point and Curie point — model development for PMN in this latter state is addressed in Chapter 3. To achieve bidirectional strains in compounds such as PZT, it is necessary to pole the material and operate around this poled state. For low to moderate input fields, this yields approximately linear responses which motivated the original linear analysis of Voigt and the linear constitutive relations developed in Section 2.2. These are often referred to as the piezoelectric relations and materials operating in approximately linear regimes are frequently designated as piezoelectric materials. It should be emphasized that piezoelectric in this context has a linear connotation and refers to the coupled direct and converse piezoelectric effects exhibited by the materials.