Abstract
A continuum model for the behavior of elastic ferroelectrics is proposed in this work. The electric field and the electric field gradient together with spontaneous dipole and quadrupole polarization are taken as independent variables of the stored energy function. Thus, a theory with reversible and spontaneous polarization is created. The main focus is on the role of the reversible and spontaneous quadrupoles. It is proved, both analytically and numerically, that spontaneous quadrupole polarization is responsible for the geometry of domain walls in the bulk of elastic ferroelectrics. On the other hand, reversible quadrupoles play a prominent role in the size effect of a thin ferroelectric film.
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