X-ray and neutron scattering

Abstract:

The phenomenon of self-organization of domains into a “square-net pattern” in single-crystal, flux-grown BaTiO3 several degrees below the ferroelectric to paraelectric phase transition was investigated using in situ synchrotron x-ray topography. The tetragonal distortion of the crystal was determined by measuring the angular separation between the diffraction images received from 90° a and c domains in the projection topographs, and shows a rapid decrease towards 110 °C, the onset temperature for self-organization. The onset of self-organization is accompanied by bending of the {100} lattice planes parallel to the crystal surface, which produces a strain that persists up to and beyond the Curie temperature, where the crystal becomes cubic and the self-organized domains disappear. At the Curie point, the bending angle α100 = 8.1(±0.3) mrad is at a maximum and corresponds to the radius of curvature of the surface being 16.3(±0.6) mm.

Abstract:

By using a symmetry motivated basis to evaluate local distortions against pair distribution function data (PDF), we show without prior bias, that the off-centre Ti displacements in the archetypal ferroelectric BaTiO3 are zone centred and rhombohedral-like across its known ferroelectric and paraelectric phases. We construct a simple Monte Carlo (MC) model which captures our main experimental findings and demonstrate how the rich crystallographic phase diagram of BaTiO3 emerges from correlations of local symmetry-breaking distortions alone. Our results strongly support the order-disorder picture for these phase transitions, but can also be reconciled with the soft-mode theory of BaTiO3 that is supported by some spectroscopic techniques.