First-principles lattice dynamics and thermodynamic properties of pre-perovskite PbTiO ₃

It was recently found that nanowires of PbTiO ₃ synthesized through an intermediate pre-perovskite phase exhibit enhanced spontaneous polarization. Here we investigated the pre-perovskite PbTiO ₃ (PP-PTO) nanowire phase at finite temperatures employing first-principles quasiharmonic calculations. We calculated its band gap, phonon dispersions, phonon density of states, Debye temperature, and thermodynamic properties. The corresponding calculations for cubic and tetragonal PbTiO ₃ were also carried out for comparison. In the current calculations, the amount of imaginary frequencies associated with the ideal cubic PTO structure, i.e., a cubic cell shape with ion positions at the ideal cubic perovskite lattice sites, was decreased to a negligible level by employing a constrained cubic structure, a structure with the same cubic cell shape as the ideal cubic PTO structure but allowing the ion positions to relax to thermodynamically more stable tetragonal positions at 0 K. In contrast to the general observation that a higher volume phase would have relatively higher entropy, it is found that the PP-PTO phase possesses the lowest entropy while having the largest volume compared to cubic and tetragonal PbTiO ₃ phases. Furthermore, the temperature-pressure phase diagram for the three PbTiO ₃ phases was obtained, which demonstrates that PP-PTO could be stabilized under a large volume or a negative pressure. This study provides insights to experimentally synthesizing the PP-PTO phase and to better understanding its phase transition into the converted tetragonal PbTiO ₃ nanowires with enhanced piezoelectric and ferroelectric properties.