The phase diagrams of KCaF₃ and NaMgF₃ by ab initio simulations

ABF₃ compounds have been found to make valuable low-pressure analogues for high-pressure silicate phases that are present in the Earth's deep interior and that may also occur in the interiors of exoplanets. The phase diagrams of two of these materials, KCaF₃ and NaMgF₃, have been investigated in detail by static ab initio computer simulations based on density functional theory. Six ABF₃ polymorphs were considered, as follows: the orthorhombic perovskite structure (GdFeO₃-type; space group Pbnm); the orthorhombic CaIrO₃ structure (Cmcm; commonly referred to as the "post-perovskite" structure); the orthorhombic Sb₂S₃ and La₂S₃ structures (both Pmcn); the hexagonal structure previously suggested in computer simulations of NaMgF₃ (P6₃/mmc); the monoclinic structure found to be intermediate between the perovskite and CaIrO₃ structures in CaRhO₃ (P2₁/m). Volumetric and axial equations of state of all phases considered are presented. For KCaF₃, as expected, the perovskite phase is shown to be the most thermodynamically stable at atmospheric pressure. With increasing pressure, the relative stability of the KCaF₃ phases then follows the sequence: perovskite → La₂S₃ structure → Sb₂S₃ structure → P6₃/mmc structure; the CaIrO₃ structure is never the most stable form. Above about 2.6 GPa, however, none of the KCaF₃ polymorphs are stable with respect to dissociation into KF and CaF₂. The possibility that high-pressure KCaF₃ polymorphs might exist metastably at 300 K, or might be stabilised by chemical substitution so as to occur within the standard operating range of a multi-anvil press, is briefly discussed. For NaMgF₃, the transitions to the high-pressure phases occur at pressures outside the normal range of a multi-anvil press. Two different sequences of transitions had previously been suggested from computer simulations. With increasing pressure, we find that the relative stability of the NaMgF₃ phases follows the sequence: perovskite → CaIrO₃ structure → Sb₂S₃ structure → P6₃/mmc structure. However, only the perovskite and CaIrO₃ structures are stable with respect to dissociation into NaF and MgF₂.