Phonon quarticity induced by changes in phonon-tracked hybridization during lattice expansion and its stabilization of rutile TiO$_2$

TL;DR

This study reveals that lattice expansion causes a transition from quadratic to quartic phonon potentials in rutile TiO$_2$, stabilizing its structure at high temperatures through a mechanism involving phonon-tracked hybridization.

Contribution

It uncovers the role of phonon-tracked hybridization in inducing quartic phonon potentials, explaining the high-temperature stability of rutile TiO$_2$ beyond quasiharmonic predictions.

Findings

Anomalous acoustic phonons increase in frequency with temperature.

Lattice expansion transforms phonon potentials from quadratic to quartic.

Phonon-tracked hybridization flattens the interatomic potential well.

Abstract

Although the rutile structure of TiO$_2$ is stable at high temperatures, the conventional quasiharmonic approximation predicts that several acoustic phonons decrease anomalously to zero frequency with thermal expansion, incorrectly predicting a structural collapse at temperatures well below 1000\,K. Inelastic neutron scattering was used to measure the temperature dependence of the phonon density of states (DOS) of rutile TiO$_2$ from 300 to 1373\,K. Surprisingly, these anomalous acoustic phonons were found to increase in frequency with temperature. First-principles calculations showed that with lattice expansion, the potentials for the anomalous acoustic phonons transform from quadratic to quartic, stabilizing the rutile phase at high temperatures. In these modes, the vibrational displacements of adjacent Ti and O atoms cause variations in hybridization of $3d$ electrons of Ti and $2p$ electrons of O atoms. With thermal expansion, the energy variation in this "phonon-tracked hybridization" flattens the bottom of the interatomic potential well between Ti and O atoms, and induces a quarticity in the phonon potential.