Structure constraints and instability leading to the post-perovskite phase transition of MgSiO3

Recent experience with Rietveld refinement of structural analogues and literature surveys, suggests anion-anion repulsion limits the stability of the perovskite phase, including in the MgSiO3 perovskite to post-perovskite transition. Assuming rigid octahedral coordination, still to be tested experimentally, the critical point where intra- and inter-octahedral anion-anion distances are equal provides a useful metric for predicting the pressure of the perovskite/post-perovskite transition and the Clapeyron slope of the phase boundary, once pressure and temperature derivatives of relevant structure parameters are known. The inter-octahedral anion-anion distances and the polyhedral volume ratio are rigorously formulated as a function of octahedral rotation in this work, assuming the orthorhombic (Pbnm) perovskite structure, where regular octahedra share each corner and conform to the in- and anti-phase rotation schemes designated by space group symmetry. These mathematical expressions are consistent with structure data from 70 perovskite-structured materials surveyed in the literature at ambient as well as extreme conditions and define structure constraints, such as the minimum polyhedral volume ratio, which must be reached before the phase transition to the post-perovskite structure-type can proceed. The formalism we present is general for perovskite (Pbnm) and dependent on the accuracy with which structures can be determined from, sometimes compromised, high pressure diffraction data.