  Motion of ferroelectric domain walls greatly contributes to the macroscopic
dielectric and piezoelectric response of ferroelectric materials. The domain
wall motion through the ferroelectric material is however hindered by pinning
on crystal defects which substantially reduces these contributions. Here, using
thermodynamic models based on the Landau-Ginzburg-Devonshire theory, we find a
relation between microscopic reversible motion of non-ferroelastic 180-degree
domain walls interacting with a periodic array of pinning centers and the
nonlinear macroscopic permittivity. We show, that the reversible motion of
domain walls can be split into two basic modes. First, the bending of a domain
wall between pinning centers, and, second, the uniform movement of domain wall
plane. We show that their respective contributions may change when the
distribution of pinning centers is rearranged during the material aging. We
demonstrate that it is possible to indicate which mechanism of the domain wall
motion is affected during material aging. This allows to judge whether the
defects only homogeneously accumulate at domain walls or prefer to align in
certain directions inside the domain wall plane. We suggest that this
information can be obtained using simple macroscopic dielectric measurements
and a proper analysis of the nonlinear response. Our results may therefore
serve as a simple and useful tool to obtain details on domain wall pinning in
an aging process.

Materials Science