Spatially-varying inversion near grain boundaries in MgAl₂O₄ spinel

Complex materials, containing multiple chemical species, often exhibit chemical disorder or inversion. Typically, this disorder is viewed as spatially homogeneous throughout the material. Here, we show, using a simple grain boundary in MgAl₂O₄ spinel, that this is not the case and that the level of inversion at the grain boundary plane is different than in the bulk. This has ramifications for the energetics of the boundary and how defects interact with it, as exemplified by the relative formation energy of vacancies. Using these results as motivation, we construct a simple model of inversion versus grain size that captures the salient behavior observed in experiments and allows us to extract inversion-relevant properties from those same experiments, suggesting that grain boundaries in the experimentally prepared material are essentially fully inverse. Together, these results highlight the role that microstructure plays on the inversion in the material.