First-principles investigation of phase stability in layered NaxCrO2

Layered oxide intercalation compounds continue to attract interest as electrode materials for Na-ion batteries. However, many of these materials undergo complex phase transitions during cycling that influence battery performance but are still not completely understood. We have conducted a first-principles study of layered Na_x⁢CrO₂ (0 ≤ x ≤ 1) to assess phase stability between various Na-vacancy ordered phases in the O3 and P3 host structures. We predict that many of the low-energy phases belong to families of Na orderings that follow specific patterns. At high x, we identify families of vacancy row orderings in O3, which may also couple to magnetic orderings of the Cr spins. We predict similar orderings at intermediate x in P3 that contain antiphase boundaries between regions of the x = 1/2 ordering. In both cases, the average spacing between rows/boundaries is set by the overall composition. At x = 0, we find a strong preference for charge disproportionation and migration of Cr to tetrahedral sites in the intercalation layers. Finally, we obtain generally good agreement with experimental observations and rationalize key discrepancies.