Interpretation of the diffuse scattering in Pb-based relaxor ferroelectrics in terms of three-dimensional nanodomains of the ⟨110⟩-directed relative interdomain atomic shifts

Abstract

Polar nanoregions in relaxor ferroelectrics were modeled by the Monte Carlo method. To account for correlations between atomic shifts, Potts-like models were applied with a random field used to mimic the chemical disorder impact on the polar ordering. The diffuse scattering effects for generated structures were calculated and compared with the neutron and x-ray experimental data known from the literature. An alternative explanation of diffraction effects contrary to the polar ``pancakes'' concept reported in several recent papers is given. Generated three-dimensional polar domains with the walls parallel to {110}-type crystallographic planes result in one-dimensional diffuse scattering rods fully compatible with the experimental results. Moreover, special extinction conditions for diffuse lines clearly indicate that the relative shifts of the atoms in the neighboring domains have to be parallel to ⟨110⟩-type directions. This can be achieved by various combinations of atomic shifts. Therefore, it is impossible to elucidate their actual directions based only on the analysis of the diffuse scattering effects. We show that the intensities of diffuse scattering are sensitive to the relative magnitudes of the atomic displacements and can be used as a starting point for their determination.