Abstract
Cerium and its technologically relevant compounds are examples of anomalous mixed valency, originating from two competing oxidation states -- itinerant Ce$^{3+}$ and localized Ce$^{4+}$. Under applied stress, anomalous transitions are observed but not well understood. Here we treat mixed valency as an "alloy" involving two valences with competing and numerous site-occupancy configurations, and we use density functional theory with Hubbard U ($i.e.$, DFT+U) to evaluate the effective valence and predict properties, including controlling valence by pseudo-ternary alloying. For Ce and its compounds, such as (Ce-La)$_2$(Fe-Co)$_{14}$B permanent magnets, we find a stable mixed-valent $\alpha$-state near the spectroscopic value of $\nu_s=3.53$. Ce valency in compounds depends on its steric volume and local chemistry; for La doping, Ce-valency shifts towards $\gamma$-like Ce$^{3+}$, as expected from steric volume; for Co doping, valency depends on local Ce-site chemistry and steric volume. Our approach captures the key origins of anomalous valency and site-preference chemistry in complex compounds.
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