The phase diagrams of KCaF3 and NaMgF3 by ab initio simulations

ABF 3 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, KCaF 3 and NaMgF 3 , have been investigated in detail by static ab initio computer simulations based on density functional theory. Six ABF 3 polymorphs were considered, as follows: the orthorhombic perovskite structure (GdFeO 3 -type; space group Pbnm ); the orthorhombic CaIrO 3 structure ( Cmcm ; commonly referred to as the “post-perovskite” structure); the orthorhombic Sb 2 S 3 and La 2 S 3 structures (both Pmcn ); the hexagonal structure previously suggested in computer simulations of NaMgF 3 ( P 6 3 / mmc ); the monoclinic structure found to be intermediate between the perovskite and CaIrO 3 structures in CaRhO 3 ( P 2 1 / m ). Volumetric and axial equations of state of all phases considered are presented. For KCaF 3 , as expected, the perovskite phase is shown to be the most thermodynamically stable at atmospheric pressure. With increasing pressure, the relative stability of the KCaF 3 phases then follows the sequence: perovskite → La 2 S 3 structure → Sb 2 S 3 structure → P 6 3 / mmc structure; the CaIrO 3 structure is never the most stable form. Above about 2.6 GPa, however, none of the KCaF 3 polymorphs are stable with respect to dissociation into KF and CaF 2 . The possibility that high-pressure KCaF 3 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 NaMgF 3 , 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 NaMgF 3 phases follows the sequence: perovskite → CaIrO 3 structure → Sb 2 S 3 structure → P 6 3 / mmc structure. However, only the perovskite and CaIrO 3 structures are stable with respect to dissociation into NaF and MgF 2 .