Compositional and Oxygen-Vacancy Effects on Phase Stability and Electronic Properties in Lanthanide High-Entropy Oxides

Cerium-based lanthanide high-entropy oxides (LN-HEOs) are promising candidates for solid-state electrolyte (mass transport) applications due to their ability to accommodate high concentrations of oxygen vacancies while retaining a fluorite-derived structure. However, synthesis often yields undesired ordered oxygen-deficient phases, such as bixbyite, depending on composition and processing conditions. We utilize first-principles density functional theory (DFT) calculations to systematically investigate phase stability in the model system $C{e}_x{\left(\mathrm{YLaPrSm}\right)}_{1-x}{O}_{2-\delta }$, with the aim of elucidating the thermodynamic factors governing fluorite–bixbyite competition and identifying structure‒property relationships to oxygen transport. By independently varying cerium concentration and oxygen vacancy content, we predict that the transition from disordered fluorite to ordered bixbyite is driven primarily by compositional and vacancy-ordering effects, rather than through changes in cation valence. Free-energy analysis reveals that at high vacancy concentrations, bixbyite is enthalpically favored due to ordered oxygen vacancies, while fluorite is stabilized at lower vacancy concentrations and higher cerium content through configurational entropy of the anion sublattice. These DFT results clarify the competing energetic contributions that control phase stability and structure–valence relationships in LN-HEOs and establishes a mechanistic framework for designing vacancy-tolerant oxide electrolytes with tunable phase behavior.