Figure 3

Potential energy second derivatives for cations in layers adjacent to CoO₂ layers. Mean potential energy second derivatives (proportional to force constants) and associated standard deviations (shaded regions) for (a) Na ions in NaCoO₂, (b) Na ions in Na_0.5CoO₂, and (c) Ca ions in Ca₃Co₄O₉ in in-plane (X and Y) and out-of-plane (Z) directions.