Bond-Strength-Based Understanding of Oxygen Vacancy Migration Barriers in Rutile Oxides

We carry out bond-strength based analysis for the migration barrier ($E_{\mathrm{B}}$) of oxygen vacancies in rutile-type 3$d$ transition-metal dioxides by combining density-functional theory (DFT) and the bond-valence model. The covalent and ionic contributions to chemical bonding are explicitly decomposed and quantified by the sum of the integrated crystal orbital Hamilton population ($S_c$) and the Madelung energy ($S_i$), respectively. Both $S_c$ and $S_i$ exhibit strong correlations with the $E_{\mathrm{B}}$ from DFT ($E_{\mathrm{B}}^{\mathrm{D}\mathrm{F}\mathrm{T}}$), and their average $\bar{S}$ provides a reasonable estimate of $E_{\mathrm{B}}^{\mathrm{D}\mathrm{F}\mathrm{T}}$ across the oxide series. Inspired by the bond-valence model, two parameters are extracted by fitting to a large dataset of 3$d$ transition-metal dioxides. Our results show that using these parameters, $E_{\mathrm{B}}$ of oxygen vacancies can be efficiently estimated.