Although we calculate a large broadening for all modes, we expect this to be a limitation of the simulation approach rather than a physical behaviour. Some phonons will remain coherent, even within the superionic regime; for example, acoustic modes near the Γpoint, or optical modes with little or no contribution from the mobile lithium ions. We interpret the results as a sign that the normal-mode-decomposition-technique applied to moderately sized supercells fails in the diffusive regime. It represents an inability to project the velocity auto-correlation functions obtained from the hightemperature AIMD back onto the wave vectors, q, or the eigenvectors, e qλ that represent small harmonic displacements.