Potassium Ordering and Structural Phase Stability in Layered K_<i>x</i>CoO₂

The recent surge of interest in K-ion batteries necessitates a fundamental understanding of phase stability and K ordering tendencies in common electrode materials. We report on a first-principles study of phase stability in layered KxCoO2 (0 ≤ x ≤ 1) in the O1/P3/O3 family of host structures and identify K ordering preferences within each host. We find that the P3 host is stable at intermediate K concentrations and exhibits a multitude of hierarchical orderings characterized by well-ordered domains separated by antiphase boundaries. We also predict the stability of a new family of layered structures at high K concentrations that are highly distorted and host both octahedrally and prismatically coordinated K within each intercalation layer.