The correlations between mean phonon frequencies and migration barriers observed in Muy et al. and Krauskopf et al. motivated calculation of the mean frequency of the 10% of modes with the greatest alignment in each material. This metric is more significantly correlated with vacancy migration barriers (R 2 = 0.40, Figure ), but the correlation is negative. This trend primarily arises from the fact that all Zn spinels exhibit lower mean frequencies and greater migration barriers in comparison to Mg spinels. In both classes of materials, well-aligned modes correspond primarily to metal cation motion (Figures and). (For this reason, the cation-projected band center for each material is similar to the mean frequency of the 10 % most-aligned modes; see Figure .) Because Zn is heavier than Mg, well-aligned modes in Zn spinels exhibit lower frequencies, contributing to the negative correlation in Figure . Accounting for this mass difference by weighting the mean frequency for each material by m 1/2 , where m represents the mass of the respective cation, does not yield a stronger trend (R 2 = 0.24). The frequency of the single mode with the greatest alignment exhibits a similar trend with respect to vacancy migration barriers (R 2 = 0.28, Figure ). The modes considered in the above analyses are selected only based on their alignment relative to other modes within the same material. The associated metrics therefore do not account for the possibility that most modes in some materials may exhibit poor alignment in an absolute sense or relative to those in other materials (as is observed for the Zn spinels; see Figure ). We therefore developed a new, more general metric that captures variations in alignment across different materials. This metric is derived from the equipartition theorem, which states that the root mean square displacement |Q qν | of phonon mode qν associated with thermal excitation is inversely proportional to its frequency at a fixed temperature. The displacement amplitudes of individual atoms associated with this excitation are therefore |Q qν u qνκα | (eq 3). Combining this observation with eq 4 implies that the extent to which thermal excitation of a single phonon mode displaces atoms in directions aligned with a given displacement field is |Q qν |a qν . If large atomic displacements are associated with low migration barriers, according to the argument in Muy et al., inverse displacements should correlate directly with migration barriers. This motivates the introduction of the following quantity, which can be understood as the average inverse displacement of all modes in directions aligned with a given displacement field upon thermal excitation: