Vacancy migration barriers used for the correlation analyses in this work were obtained from previous studies, in which barriers were calculated using the nudged elastic band method with forces obtained from DFT. In anti-perovskite materials, vacancies migrate along the edges of X 6 A octahedra, where X is Ca or Mg, and A is N, P, or As (Figures and). Due to tilting and distortion of these octahedra, orthorhombic anti-perovskites exhibit 12 distinct migration pathways with different barriers. Percolation theory was used in ref 17 to calculate an effective migration barrier for each material based on the connectivity of octahedra. In spinel materials, vacancies migrate between neighboring tetrahedral sites through intermediate metastable octahedral sites (Figure ). All tetrahedral sites are equivalent.