Predicting phase transitions in PbTiO$_3$ using zentropy through quasiharmonic phonon calculations

TL;DR

This paper predicts the phase transition temperature of PbTiO$_3$ using a novel zentropy approach combined with phonon calculations, achieving results close to experimental data.

Contribution

It introduces a zentropy-based method incorporating local tetragonal configurations and phonon calculations to predict phase transitions in PbTiO$_3$, surpassing traditional models.

Findings

Predicted transition temperature of 716 K closely matches experimental 763 K.

Helmholtz energies derived from DFT phonon calculations support the prediction.

Method accounts for local structures like domain walls, improving accuracy.

Abstract

According to x-ray diffraction (XRD) measurements, PbTiO$_3$ undergoes a phase transition from a tetragonal ferroelectric (FE) phase to a cubic paraelectric phase at 763 K. However, x-ray absorption fine-structure (XAFS) measurements indicate that PbTiO$_3$ is locally tetragonal even after the phase transition. The difference in these results is because XAFS measurements can probe local features of a structure, while XRD averages over such local features. For both measurements to be consistent, PbTiO$_3$ is macroscopically cubic but locally tetragonal after the phase transition. Despite this, most models, such as the Laundau-Ginsburg-Devonshire theory and effective Hamiltonians, are still unable to explain this phenomenon. Moreover, these methods involve model parameters fitted to experimental or theoretical data and do not consider other tetragonal configurations, such as domain walls, to predict the phase transition. In our previous study, we used our zentropy approach to predict the phase transition by considering the tetragonal FE ground-state configuration and the tetragonal 90{\deg} and 180{\deg} domain wall configurations with their total energies at 0 K. In this paper, the Helmholtz energies of the three configurations are obtained from density functional theory calculations through energy-volume curves and phonon calculations. The predicted phase transition temperature using the meta-GGA $r^2\text{SCAN}$ and revised multiplicities of configurations is 716 K, showing good agreement with the experimental value of 763 K.