Nature of ferroelectric-paraelectric phase transition and origin of negative thermal expansion inPbTiO3

Ferroelectric-paraelectric (FE-PE) phase transitions have been primarily explained by the phenomenological Landau-Devonshire theory and a soft-zone-center mode of vibration in the literature. In this work, we study the atomic structure and polarization evolution of $\mathrm{PbTi}{\mathrm{O}}_{3}$ as a function of temperature using ab initio molecular dynamics simulations. In contrast to conventional molecular dynamics analyses where results are averaged over time, we categorize the atomic configurations as a function of time in terms of Ti-O bond lengths in the nearest-neighboring shell. We show that an appreciable amount of cubic configuration exists at temperatures about 300 K below its FE-PE phase transition temperature of 763 K, even though the time-averaged overall atomic configuration is tetragonal. The quantitative results depict that as the temperature increases the population of the cubic configuration increases and that of the tetragonal configuration decreases, signifying that the FE-PE phase transition is intrinsically second order. It reveals that the thermal fluctuation of the cubic configurations in the tetragonal matrix makes a significant contribution to the negative thermal expansion in the FE phase region because the cubic configuration has smaller volume and higher entropy than the tetragonal matrix.