We have investigated the melting of hcp Fe at high pressure by employing molecular dynamics simulations in conjunction with the full potential linear muffin tin orbital method. Apart from being of fundamental value, the melting of iron at high pressure is also important for our understanding of the Earth. The subject of iron melting at high pressures is controversial. The experimental data for the iron melting temperature can be separated into two regions, “low” and “high.” Here we present an ab initio simulated iron melting curve which is in agreement with the low temperatures at lower pressures, but is in excellent agreement with the high—mostly shockwave—temperatures at high pressures. A comparison with available data lends support to the presented iron melting curve.

Two mechanisms of melting are known, heterogeneous, where melting starts at surfaces, and homogeneous, where the liquid nucleates in the bulk crystal. If melting occurs homogeneously, a crystal can be superheated significantly above its melting temperature $\left(T_m\right)$. At present, the physical meaning of the limit of superheating $\left(T_{\mathit{LS}}\right)$ is unknown. We demonstrate, by molecular dynamics simulations, that the total energy of a solid at $T_{\mathit{LS}}$ is equal to the total energy of its liquid at $T_m$ at the same volume. In the high pressure limit $T_{\mathit{LS}}$ and $T_m$ are connected by the constant $k_{AB}=\mathit{ln}2∕3$ via the relation $k_{AB}=T_{\mathit{LS}}∕T_m-1$.

The equation of state of KCl and KBr, compressed in a helium pressure medium in a diamond-anvil cell, has been measured by x-ray diffraction in the B1 and B2 phases up to 165~GPa at 298 K. The P-V-T of B2 KCl and B2 KBr has been calculated by ab initio molecular dynamics in a wide compression range and up to 7000 K. The thermal pressure exhibits a linear behavior with temperature and remains low under high compression. The experimental P-V points and the thermal pressure calculated by molecular dynamics have been used to set up a high-pressure\char21{}high-temperature equation of state of B2 KCl and B2 KBr. With these equations of state, B2 KCl and B2 KBr can be used as pressure markers in laser-heated diamond-anvil-cell experiments.

The Gibbs free energies of bcc and fcc Mo are calculated from first principles in the quasiharmonic approximation in the pressure range from 350 to 850 GPa at room temperatures up to 7500 K. It is found that Mo, stable in the bcc phase at low temperatures, has lower free energy in the fcc structure than in the bcc phase at elevated temperatures. Our density-functional-theory-based molecular dynamics simulations demonstrate that fcc melts at higher than bcc temperatures above 1.5 Mbar. Our calculated melting temperatures and bcc-fcc boundary are consistent with the Mo Hugoniot sound speed measurements. We find that melting occurs at temperatures significantly above the bcc-fcc boundary. This suggests an explanation of the recent diamond anvil cell experiments, which find a phase boundary in the vicinity of our extrapolated bcc-fcc boundary.