Figure 4

Molecular dynamics simulation of diffusion in Na _x CoO₂ in the square and disordered phases. The left-hand panels show the trace of sodium positions over the duration of the simulations (the boxes show the cells used in the MD simulations), and the right-hand panels show the root-mean-square displacement of sodium ions as a function of time. The different colours give trajectories for different ions, with the same colour for a given ion in successive panels from left to right. (a) For the square phase the tri-vacancy clusters are well separated, and there are very few hops compared to the stripe phase. (b) For isolated 2d vacancies there is negligible hopping of ions. (c) In the disordered phase the introduction of a vacancy next to a tri-vacancy cluster results in multiple hops. For interconnected pathways of the type shown in Fig. 2(c) bulk translational diffusion is predicted by consideration of the available pathways, though the timescale of these simulations is insufficiently long to demonstrate this directly.