Role of the soft dielectric energy in poling ceramics, glass-like systems and in domain average engineering

In the classical approach of interpreting the process of poling ceramics, the energy F₁=-E_iP_Si is considered to be the decisive source of the procedure. However, induced polarization of anisotropic grains also contributes to the free energy. The corresponding term F₂=-(½)ε_ijE_iE_j may influence the poling process. Its possible role is discussed using a 2D model and taking into account the dielectric anisotropy and its temperature dependences. It is shown that for low applied fields (E<E*/√2, where E* is a function of material parameters) the role of F₁ prevails so that the classical approach holds while for high fields (E>E*) the energy F₂ plays the decisive role and the P_s vector needs not to acquire the orientation closest to the field E. In the intermediate region of fields the influences of both energy contributions compete. In a similar way, the piezoelectric energy -d_ijE₁T_jk can be involved in the process, where the stress T_jk is applied and influenced by mutual clamping of grains or particles in glassy systems. The energy of a soft dielectric can also influence the results when devising domain-average-engineered samples of single-crystalline ferroics: crystalline specimens divided into a very large number of domains, representing μ domain states where μ is smaller than the theoretically allowed maximum number