Pair distribution function analysis driven by atomistic simulations: Application to microwave radiation synthesized TiO$_2$ and ZrO$_2$

TL;DR

This paper introduces a workflow combining atomistic simulations and PDF analysis to identify defect structures in microwave-synthesized TiO₂ and ZrO₂, revealing dominant defect types and analyzing atomic displacements.

Contribution

The study presents a novel integrated approach for defect analysis in disordered materials using atomistic simulations refined against experimental PDFs.

Findings

TiO₂ has titanium vacancies and interstitials as dominant defects.

ZrO₂ is dominated by oxygen vacancies.

Atomic displacement parameters are closely related to mean squared displacements.

Abstract

A workflow is presented for performing pair distribution function (PDF) analysis of defected materials using structures generated from atomistic simulations. A large collection of structures, which differ in the types and concentrations of defects present, are obtained through energy minimization with an empirical interatomic potential. Each of the structures is refined against an experimental PDF. The structures with the lowest goodness of fit $R_w$ values are taken as being representative of the experimental structure. The workflow is applied to anatase titanium dioxide ($a$-TiO$_2$) and tetragonal zirconium dioxide ($t$-ZrO$_2$) synthesized in the presence of microwave radiation, a low temperature process that generates disorder. The results suggest that titanium vacancies and interstitials are the dominant defects in $a$-TiO$_2$, while oxygen vacancies dominate in $t$-ZrO$_2$. Analysis of the atomic displacement parameters extracted from the PDF refinement and mean squared displacements calculated from molecular dynamics simulations indicate that while these two quantities are closely related, it is challenging to make quantitative comparisons between them. The workflow can be applied to other materials systems, including nanoparticles.