Visualization of spontaneous electronic polarization in Pb ion of ferroelectric PbTiO₃ by synchrotron-radiation x-ray diffraction

In this study, we accurately visualized the valence electron density distributions of ferroelectrics PbTiO₃ and BaTiO₃ by analyzing synchrotron-radiation powder x-ray diffraction (SXRD) data using the Rietveld method and the maximum entropy method. Clear SXRD evidence indicates that the Pb ion in PbTiO₃ is polarized in the ferroelectric phase, whereas the Ba ion in BaTiO₃ is not polarized and fully ionized as a Ba²⁺ ion. The large electronic polarization of the Pb ion is attributed to the anisotropic spatial distribution of the lone-pair electrons of the Pb²⁺ ion, particularly the anisotropic p-like orbital of the lone-pair electrons caused by the formation of Pb–O covalent bonds. In PbTiO₃, the contribution of the electronic polarization of the Pb ion to the spontaneous polarization is significant. We experimentally evaluate the contributions of the ionic polarization and the electronic polarization, respectively, from the valence electron density distribution map and demonstrate that the spontaneous polarization can be calculated from the SXRD data as the sum of them. One of the Ti–O covalent bonds is broken at the phase transition in PbTiO₃, whereas no change in the atomic coordination is observed in BaTiO₃. When focusing on the covalent bonding network, we propose using a layered material for PbTiO₃ in the ferroelectric phase. These results agree well with those of first-principles calculations. We expect further comprehensive valence electron density studies can be performed by combining SXRD experiments and first-principles calculations to better understand the emergence of ferroelectricity.