Supplementary Information: Anharmonic lattice dynamics of superionic lithium nitride Gabriel Krenzer 1 , Chang-Eun Kim 2 , Kasper Tolborg 1 , Benjamin J. Morgan 3 , and Aron Walsh No diffraction data showing uncertainties on the Li positions could be found. β-Li 3 N is usually synthesised at high pressure, which might be the reason why the reported P 6 3 cm phase was not reported in the literature. It is important to note, however, that the P 6 3 /mmc phase could also be stabilized by phonon-phonon interactions meaning that the P 6 3 cm is never stable. The direct conversion between energy barrier and temperature alone is not enough to confirm that the P 6 3 cm phase really exists over the stability range of β-Li 3 N, hence the above discussion should be taken lightly. Further experimental investigations, or temperature-dependent lattice dynamics calculations including phonon-phonon interactions are necessary.