Ab initio based description of the unusual temperature increase of the electric field gradient at Ti sites in rutile TiO2

TL;DR

This study uses ab initio calculations combined with temperature-dependent atomic displacements to explain the unusual increase of the electric field gradient at Ti sites in rutile TiO2, matching experimental observations.

Contribution

The paper introduces a novel ab initio method that accounts for temperature effects on electric field gradients in TiO2, explaining experimental anomalies.

Findings

Reproduces the temperature increase of the electric field gradient in TiO2.

Shows the temperature dependence of the asymmetry parameter eta.

Quantifies the increase as half of the experimental value, suggesting additional effects.

Abstract

Combining a precise ab initio electron band structure calculation of the TiO2 rutile structure with the temperature evolution of the Ti mean-square displacements, we reproduce a puzzling temperature increase of the electric field gradient at Ti sites in TiO2, observed experimentally. Our method employs a procedure of averaging two quadrupole electron density components (L = 2) inside a sphere vibrating with the Ti nucleus at its center, where the key factor introducing the temperature dependence is the square root of the Debye-Waller factor. Although the Debye-Waller factor always reduces the corresponding Fourier component, in TiO2 due to the interplay between terms of opposite signs, it results in a net increase of the whole sum with temperature, leading to the growth of the electric field gradient. Quantitatively, we find that the increase of electric field gradient is only half of the experimental value, which we ascribe to anharmonic effects or a strong oxygen position influence. In addition, our method reproduces the unusual temperature dependence of the asymmetry parameter eta, which first decreases with temperature, goes to zero and then increases.