Figure shows the Li-ion-projected phonon bandcentre, calculated using the conventional temperature independent scheme (Equation , and with temperaturedependent phonon occupation weightings (Equation ). This analysis gives a temperature-independent ω av = 12.04 THz. Including the temperature-dependent phonon occupation number weightings, we obtain a lower, temperature-dependent value of ω av (298 K) = 8.08 THz, and that ω av (678 K) = 8.31 THz. The difference between the temperature-independent and temperaturedependent ω av values is due to the low occupancy of vibrational modes above 10 THz across the temperature range of interest (see Figure ). The temperatureindependent phonon band centre calculation is equivalent to computing the temperature-dependent value at T = ∞ K, i.e. all phonons are equally occupied, regardless of their frequency. The behaviour observed here, that the temperature-dependent ω av (T ) < ω av is general; the effective phonon band-centre at 298 K will always be lower than the temperature-independent value. The degree to which ω av (T ) and ω av differ, however, is likely to vary for different materials, and this may cause changes in previously observed trends with respect to room temperature ionic conductivity measurements . For α-Li 3 N above 300 K, the temperature-dependent phonon band-centre has a nearly constant value. Notably, we do not predict any change in behaviour at 678 K, as might be expected if this descriptor were describing something fundamental about the ionic conduction across the superionic transition. We further expect that using a temperature-dependent fully-anharmonic phonon DOS will not change the overall value of the phonon bandcentre across the superionic transition either . This result is perhaps not unexpected because the phonon bandcentre is an average quantity, and it has been suggested that a superionic transition is associated with the breakdown of a single phonon mode . Our finding that the phonon band-centre fails to capture any signature of the superionic transition in α-Li 3 N, even when temperature-dependent phonon occupations are incorpodata . It is therefore possible that β-Li3N takes its lower energylower symmetry structure with P 6 3 cm symmetry, instead of the accepted P 6 3 /mmc symmetry. This point is discussed further in the SI. rated, shows that this metric may not be reliable as a descriptor of ionic conductivities in solid electrolytes that exhibit a superionic phase transition. More generally, this result challenges the idea that the phonon band centre provides a useful conceptual framework for thinking about the microscopic dynamics of fast-ion conductors and how these relate to macroscopic ion-transport.