Domain Wall Contributions to Piezoelectricity in Relaxor-Lead Titanate Single Crystals

It is demonstrated that the dielectric permittivity and piezoelectric coefficients in relaxor-PbTiO3 single crystals close to the morphotropic phase boundary (MPB) can be augmented by contributions from domain walls. Landau-Ginzburg-Devonshire models, incorporating both polarization and strain gradients through the domain walls, show that wall contributions in domain engineered single crystals originate from enhanced, field-induced polarization rotation in static domain walls, unlike ceramics, in which piezoelectricity is enhanced by domain wall translation. For 71° domain walls in 0.7 Pb(Mg1/3Nb2/3)O3 – 0.3PbTiO3 the piezoelectric charge coefficient d33 at the center of the wall ranges from 5000 to >30,000 pC N−1 depending on the wall width. Thus, a sufficiently high domain wall density can account for the experimentally observed augmentation in the measured properties compared to single domain models. The symmetry of the domain walls explains both the variety of average symmetries observed close to the MPB and the experimentally observed switching of the [001]-oriented crystals into the tetragonal phase via a symmetry-improbable MC phase. For a crystal of rhombohedral ground state, the presence of domain walls will impart monoclinic symmetry, the predominance of which increases with increasing domain wall density.