Figure and f shows the number of Fe 3+ ions in tetrahedral sites and serves as a direct measure of the total degree of inversion for each structure. The structures sampled tend to have low levels of tetrahedral Fe 3+ with no structure sampled with more than half the tetrahedral sites occupied by Fe 3+ . There is an obvious trend of structures with higher degrees of inversion having high energies relative to the end members. When looking at the structures in the context of octahedral Mn and Zn, there is a preference for having octahedral Zn over octahedral Mn as structures tend to have lower energies (Supplementary Figures ).