Theory of the banded domain structure in coarse-grained ferroelectric ceramics

Abstract A theory of the banded domain a-structures in tetragonal ferroelectric ceramics is presented. The mechanical sources of internal stresses appearing on the grain and band boundaries at a phase transition are modelled by arrays of wedge disclinations and continuously distributed fictitious dislocations. With the aid of the disclination and dislocation models the ceramic elastic energy due to the internal stress field is evaluated. This result is used to calculate the equilibrium geometric parameters of the banded domain structure which minimize the internal energy of a coarse-grained ceramic. The dependencies of the equilibrium parameters on the grain size are discussed. The influence of external static and low-frequency electric fields on the banded domain structure is also considered on the basis of an energetic approach. The amplitudes of reversible displacements are calculated for the 90° domain walls inside bands and for the band boundaries consisting of alternating stripes of 90° and 180° walls. On this base the domain contribution to the ceramic electric permittivity is estimated.