The nuclear-density distribution of anatase (TiO2) is obtained from neutron powder-diffraction data by the maximum-entropy method (MEM). In MEM analysis, no structural model is required. The nuclear-density distribution indicates the smearing of nuclei by thermal motions, which is not necessarily harmonic. In order to show the complementarity of neutron and X-ray diffraction experiments in structural studies, the electron density distribution of anatase is also derived by the MEM. In comparison with the nuclear densities, the MEM electron-density distribution is more broadly distributed, which must represent the more wave-like nature of electrons. In addition, strong covalent bonding between the Ti and O atoms is evident. The thermal smearing may be intuitively understood in terms of the arrangement of the covalent bonds, i.e., isotropic thermal motions for Ti atoms which are octahedrally bonded to six O atoms, and anisotropic motion for the O atom which is bonded to three Ti atoms in a planar triangular configuration. For the O atoms, thermal vibrations perpendicular to the plane of the bonds, which involve bond bending but no bond compression, have the larger amplitudes.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Electrical and Electronic Engineering