Cerium and its technologically relevant compounds are examples of anomalous mixed valency, originating from two competing oxidation states—itinerant ${\mathrm{Ce}}^{4+}$ and localized ${\mathrm{Ce}}^{3+}$. Under applied stress, anomalous transitions are observed but not well understood. Here we treat mixed valency as an “alloy” problem involving two valences with competing and numerous site-occupancy configurations. We use density-functional theory with Hubbard U (i.e., DFT+U) to evaluate the effective valence and predict properties, including controlling the valence by pseudoternary alloying. For Ce and its compounds, such as $(\mathrm{Ce},\mathrm{La}{)}_2(\mathrm{Fe},\mathrm{Co}{)}_{14}\mathrm{B}$ 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 ${\mathrm{Ce}}^{3+}$, 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.

• Received 15 December 2013
• Revised 3 June 2014

DOI:https://doi.org/10.1103/PhysRevB.89.235126