Origin of the tetragonal-to-hexagonal phase transitions in Fe-doped BaTiO$_3$

TL;DR

This study uses first-principles calculations to understand the phase transition from tetragonal to hexagonal in Fe-doped BaTiO₃, identifying key mechanisms and the effects of defects and doping levels.

Contribution

It provides a detailed theoretical analysis of the phase transition mechanisms in Fe-doped BaTiO₃, including the effects of oxygen vacancies and Jahn-Teller distortions, which were not previously quantified.

Findings

Crossover from tetragonal to hexagonal phases occurs around 4% Fe doping.

Oxygen vacancies lower the crossover concentration to about 2%.

Jahn-Teller distortions and charge redistribution influence phase stability.

Abstract

Based on detailed first-principles calculations, we investigate the tetragonal-to-hexagonal phase transition in Fe-doped BaTiO$_3$. Total energy calculations confirm a crossover from the tetragonal to hexagonal phases around 4\% Fe, in agreement with experimental observations, where comparative calculations show that neither CaTiO$_3$ nor SrTiO$_3$ exhibits similar behavior under equivalent substitution. Furthermore, three possible mechanisms are quantified: oxygen vacancies shift the crossover concentration from $\sim$4\% to $\sim$2\% through charge compensation, Jahn-Teller distortions impose a larger elastic penalty, both favoring tetragonal-to-hexagonal phase transitions; whereas the tolerance factor is reduced in comparison with that of pristine BaTiO$_3$ for reasonable Fe valence states, disfavoring the occurrence of the hexagonal phases. Detailed analysis on the electronic structure reveals that the charge redistribution induced by oxygen vacancy is strongly orbital dependent due to the local crystal structure distortions.