Stacking fault energetics of α − and γ -cerium investigated with ab initio calculations

At ambient pressure the element cerium shows a metastable (${t}_{1/2}\ensuremath{\sim}40$ years) double-hexagonal close-packed $\ensuremath{\beta}$ phase that is positioned between two cubic phases, $\ensuremath{\gamma}$ and $\ensuremath{\alpha}$. With modest pressure the $\ensuremath{\beta}$ phase can be suppressed, and a volume contraction (17%) occurs between the $\ensuremath{\gamma}$ and the $\ensuremath{\alpha}$ phases as the temperature is varied. This phenomenon has been linked to subtle alterations in the $4f$ band. In order to rationalize the presence of the metastable $\ensuremath{\beta}$ phase, and its position in the phase diagram, we have computed the stacking fault formation energies of the cubic phases of cerium using an axial interaction model. This model links the total energy differences between hexagonal closed-packed stacking sequences and stacking fault energetics. Total energies are calculated by density functional theory and by dynamical mean-field theory merged with density functional theory. It is found that there is a large difference in the stacking fault energies between the $\ensuremath{\alpha}$ and the $\ensuremath{\gamma}$ phase. The $\ensuremath{\beta}\text{-phase}$ energy is nearly degenerate with the $\ensuremath{\gamma}$ phase, consistent with previous third-law calorimetry results, and dislocation dynamics explain the pressure and temperature hysteretic effects.