Surface relaxation in ferroelectric perovskites

Abstract

Lattice relaxation on the surface of ${\mathrm{PbTiO}}_3$ and ${\mathrm{BaTiO}}_3$ is investigated under the assumption that the spurious lattice expansion in perovskite nanocrystals is caused by the surface relaxation. By comparing the observed peak position and full width at half maximum with those of the calculated x-ray diffraction patterns from a cubic lattice containing surface relaxation, the maximum relaxation on the surface of ${\mathrm{PbTiO}}_3$ is found to be 0.035 nm, and 0.015 nm for ${\mathrm{BaTiO}}_3.$ The relaxation is decreased to $1/e$ at 1.5 layers in ${\mathrm{PbTiO}}_3$ and 8 layers in ${\mathrm{BaTiO}}_3.$ These values are consistent with the extrapolation lengths predicted by a modified Landau theory explaining the size effect on the phase transition temperature.