Temperature-dependent Multi-well Free-energy Landscape for Phase Transitions: PbTiO3 as a Prototype

TL;DR

This paper introduces a simple analytical model for the temperature-dependent free-energy landscape of phase transitions, successfully describing properties of PbTiO3 and potentially applicable to other critical phenomena.

Contribution

The model uses Boltzmann thermal mixing among multiple potentials, offering a new approach that aligns with thermodynamic data and captures various phase transition properties.

Findings

Accurately describes temperature dependence of polarization, heat capacity, permittivity, and lattice parameters in PbTiO3.

Provides a parametrization method based on 0 K thermodynamics data from DFT calculations.

Potentially applicable to other critical phenomena like superconductivity and magnetic transitions.

Abstract

It has been a long challenge to analytically construct the quantitative temperature-dependent multi-well free-energy landscape over the space of order parameters describing phase transitions and associated critical phenomena. Here we propose a simple analytical model for the free energy landscape based on a priori concept of Boltzmann thermal mixing among multiple parabolic potentials representing different energetically degenerated ground states in contrast to the popular Landau theory using the high-temperature disordered state as a reference. The model recovers both the Weiss molecular field theory and the temperature dependent behaviors of the second order Landau coefficient. It is rather remarkable that such a simple analytical expression can describe a wide variety of properties across the ferroelectric phase transition in PbTiO3, including the temperature dependences of the spontaneous polarization, the heat capacities, the permittivity tensor, and the lattice parameters. The approach also allows parametrization of the free energy function across phase transitions based directly on the 0 K thermodynamics data that can be obtained from DFT calculations. We anticipate that the approach can be equally applied to other types of critical phenomena, e.g., the superconducting phase transition, the metal-insulator transition, and the magnetic transitions.