The perovskite to post-perovskite transition in CaIrO 3: Clapeyron slope and changes in bulk and shear moduli by density functional theory

Abstract

The thermodynamic properties of perovskite (pv) and post-perovskite (ppv) of CaIrO 3 are derived from total energy calculations using density functional theory. Negative molar volume and enthalpy changes of 0.40 cm 3 mol −1 and 11.8 kJ mol −1 for the pv to ppv transition at 0 K stabilize ppv at low temperatures and high-pressures. Vibrational entropies calculated in the harmonic approximation, using the direct method, favour pv with increasing temperatures (105.5 J K −1 mol −1 for pv versus 99.2 J K −1 mol −1 for ppv at 298 K). A main reason for the lower entropy of post-perovskite compared to perovskite is probably related to constraints on certain vibrational modes imposed by edge-sharing of octahedra in post-perovskite. The Clapeyron slope of the pv–ppv phase boundary is deduced from the calculated enthalpy and volume of transition in conjunction with an experimental transition temperature. The resulting d p/d T of 18 MPa K −1 is in good agreement with experimental determinations reported in literature. The high-pressure properties were calculated from the variation of the total energy with volume using the Murnaghan (M) and the Birch–Murnaghan (B–M) equations-of-state. The two methods give the same values for the bulk modulus but somewhat different values for the pressure derivative of the bulk modulus: K 0 = 178 GPa and K ′ 0 = 2.8 ( M ) and 3.3 (B–M) for pv compared to K 0 = 164 GPa and K ′ 0 = 3.9 ( M ) and 4.0 (B–M) for ppv. By holding K ′ 0 for pv fixed at 4.0, K 0 is reduced to 172 GPa. The bulk moduli at zero pressure were also derived through calculation of the elastic constants giving K 0 = 172 GPa for pv compared to K 0 = 157 GPa for ppv. In order to compare the changes in the bulk and shear moduli across the pv–ppv phase transition, also the shear moduli were derived from the elastic constants. Whereas the bulk modulus decreases by about 9% from perovskite to post-perovskite, the shear modulus increases by about 15% across the transition. The elastic parameters obtained for the CaIrO 3 polymorphs are consistent with those of MgSiO 3 and with seismic velocity variations in the lowermost mantle. Our DFT-results demonstrate that CaIrO 3 may be a useful low-pressure analogue for studies of the general properties of the pv–ppv-transition relevant to the D″ layer since the negative and positive changes in bulk and shear moduli, respectively, across the pv- to ppv-transition boundary appear to be strongly linked to the nature of the two crystal structures.