Exploring Cation Selection and Disorder within Entropy-Driven $A_{6}B_{2}$O$_{17}$ ($A$=Zr/Hf, $B$=Nb/Ta) Oxides

We investigate the local atomic and electronic structure, thermodynamic stability, and defect chemistry of $A_{6}B_{2}$O$_{17}$ ($A$ = Zr/Hf, $B$ = Nb/Ta) oxides using first-principles density functional theory (DFT) calculations. We examine both ordered unit cells as well as fully disordered special quasirandom structures to clearly discern the effects of cation disorder. Structural predictions align closely with previous experimental results and follow established ionic radii trends. The electronic structure is strongly dependent on $B$-cation species: $A_{6}$Ta$_{2}$O$_{17}$ compositions have ~30% larger band gaps than their $A_{6}$Nb$_{2}$O$_{17}$ counterparts. Defect chemistry is similar for all compositions, with anion vacancies being more energetically favorable than corresponding cation defects. All explored $A_{6}B_{2}$O$_{17}$ compositions are enthalpically unstable with respect to their $A$O$_{2}$ and $B_{2}$O$_{5}$ competing oxides and are therefore classified as entropy-stabilized materials, supporting prior experimental results. The pronounced agreement between our disordered supercell predictions with experimental measurements indicates all explored $A_{6}B_{2}$O$_{17}$ compositions contain substantial cation disorder across all 6-, 7-, and 8-coordinated sites. Our findings collectively provide a fundamental understanding of the $A_{6}B_{2}$O$_{17}$ material family through DFT calculations, establishing a framework for future compositional tuning to engineer targeted material properties.