Figure 1

Isochores of perovskite ($Pv$) and post-perovskite ($cmcm$) phases calculated by means of MD, using both pair potential [13, 18] and ab initio interaction models [23, 24] shown by different colors as indicated in the legend. The volumes are chosen as described in the text. The irregular behavior of calculated pressures is the indication of thermal instability. Thermal instability temperatures ($T_{\mathrm{inst}}$) of the $Pv$ were fitted by the Simon functional curve (magenta curve). The $T_{\mathrm{inst}}$ of the $cmcm$ phase at $P<100\mathrm{GPa}$ is lower than that of perovskite while at higher $P$ the order is reversed. The values of $T_{\mathrm{inst}}$ obtained from the AIMD and classical MD calculations are in reasonably good agreement; hence the pair potential model [13] is reliable. Some disagreement at lower $P$ is most likely due to a nearly constant shift between ab initio and experimental $P$ of about 12 GPa [23]. Somewhat higher $T_{\mathrm{inst}}$ of the classical $cmcm$ phase at $P$ above 100 GPa suggests that a proper correction has to be made for $T_m$ calculated using the classical model.Reuse & Permissions

Figure 2

$\mathrm{Si}\mathrm{\text{−}}\mathrm{O}$, $\mathrm{Mg}\mathrm{\text{−}}\mathrm{O}$, and $\mathrm{O}\mathrm{\text{−}}\mathrm{O}$ radial distribution functions (RDF) and the $Pv$ equation of state (EOS) at $T=0\mathrm{K}$ (inset). RDFs are obtained by AIMD at $P=273\mathrm{GPa}$ and $T=9576\mathrm{K}$, which is a point of thermal instability (Fig. 1), and compared to RDFs calculated using the classical model [13] at the same $P$ and $T$. The EOS in the inset was calculated using the same ab initio method with all the parameters as used in AIMD, and is compared to experimental data [28, 29, 30]. The calculated pressures are shifted uniformly upward from the experimental values by 12 GPa. This 12 GPa shift has also been seen in other recent work on $Pv$ [23]. The data support our results on the ${\mathrm{MgSiO}}_3$ melting.Reuse & Permissions

Figure 3

${\mathrm{MgSiO}}_3$ phase diagram. Melting temperatures were calculated using the 2-phase MD method [13] with the same model [18] that was used to calculate the overheating (Fig. 1). The melting curves of the $Pv$ and $cmcm$ phases overlay the thick black melting curve of ${\mathrm{MgSiO}}_3$. The $Pv-cmcm$ phase boundary is indicated by a thin black line. The phenomenological melting curve (Eq. (2)) is shown by a dashed line. Experimental melting data are shown by squares [7, 8] and solid lines [4, 5, 6].Reuse & Permissions