Bonding character and octahedral geometry as key determinants of solute miscibility in Ir-based oxides

The miscibility between two oxides can be estimated using the Hume-Rothery criteria, which consider crystal structure, ionic radius, and cation valence. However, rutile-based IrO₂-TiO₂ and IrO₂-SnO₂ systems show unexpectedly limited miscibility despite fully satisfying these criteria. This puzzling phenomenon has not been explained since their phase diagrams were first reported in 1967. Here we find that d⁰ and d¹⁰ M cations (such as 3d⁰ Ti⁴⁺ and 4d¹⁰ Sn⁴⁺) form primarily ionic M-O bonds due to the lack of overlap between their d states and O 2p states, while Ir-O bonds in IrO₂ exhibit highly covalent bonding characteristics. Consequently, these two distinct bonding types at a shared oxygen site in the edge-sharing rutile structure lead to geometrically frustrated electron density localization, resulting in the immiscibility of M in IrO₂. However, this frustration is significantly alleviated when the bonds meet in a corner-sharing octahedral geometry with a nearly linear Ir-O-M configuration. Complete solid solutions across the entire composition range can thus be achieved in cubic-perovskite-based Ir oxides with exclusively corner-sharing octahedral geometry. Our findings highlight the crucial role of bonding characteristics and octahedral geometries in determining oxide miscibility.