X-ray investigation, high-resolution electron holography, and density functional calculations of single-crystallineBaTiO3

Abstract

Single crystal x-ray diffraction (XRD), high-resolution electron holography and density functional calculations (DFT) are employed to investigate single-crystalline ${\mathrm{BaTiO}}_{3}$ in the noncentrosymmetric tetragonal phase. From XRD and DFT the structure parameters, the electron density and corresponding properties, such as atomic charges and the dipole moment are determined. For this purpose the maximum-entropy method was utilized to get accurate electron densities in the case of XRD, whereas all-electron calculations were performed in the framework of DFT. A comparison of experimental results and density functional calculations yield a rather good agreement. The electron density distributions are used to determine the ``natural'' unit cell corresponding to the neutral boundary cells of the whole crystal and its dipole moment, providing the boundary conditions necessary for calculating the electrostatic potential within the unit cell through the Poisson equation. The electrostatic potential was then utilized to perform electron scattering simulations within the framework of the Multislice formalism, resembling unique features of experimentally recorded electron holograms. It is shown that the phase wedge in the scattered wave, which is due to the polarization field within the specimen, is essential for the image reconstruction. This essential feature has not been included in simulations before.