Nuclear and charge density distributions in ferroelectric PbTiO3: maximum entropy method analysis of neutron and X-ray diffraction data

Abstract

We conducted in-situ high-temperature neutron and X-ray diffraction studies on tetragonal PbTiO3. Using a combination of Rietveld analysis and Maximum Entropy Method, the nuclear and charge density distributions were determined as a function of temperature up to 460 °C. The ionic states obtained from charge density distributions reveal that the covalency of Pb–O2 bonds gradually weakens with increasing temperature. The spontaneous polarizations calculated from the contributions of ionic state, ionic displacement, and nuclear polarization, are in good agreement with the experimental measurements. This method provides an effective approach to determine spontaneous polarizations in multiferroics with high-current leakage and low resistance.