Using the ab initio calculations, we study the lattice distortion of HfNbTaTiVC5, HfNbTaTiZrC5 and MoNbTaTiVC5 high-entropy carbide (HEC) ceramics. Results indicate that the Bader atomic radius and charge transfer in HECs is very close to those from binary carbide. The degree of lattice distortion strongly depends on the alloying element. The Bader atomic radius can excellently describe the lattice distortion in HEC. Further, the corresponding atomic radius and formation enthalpy of binary carbides may be indicators to predict the single-phase HECs.

Based on ab initio molecular dynamics simulations, we determined the melting curve of magnesium (Mg) up to ∼460 GPa using the solid–liquid coexistence method. Between ∼30 and 100 GPa, our melting curve is noticeably lower than those from static experiments but is in good agreement with recent shock experiments. Up to ∼450 GPa, our melting curve is generally consistent with the melting points from first-principles calculations using the small-cell coexistence method. We found that, at high pressures of a few hundred GPa, due to the strong softening of interatomic interactions in the liquid phase, solid–liquid coexistence simulations of Mg show some characteristics distinctively different from other metal systems, such as aluminum. For example, at a given volume, the pressure and temperature range for maintaining a stable solid–liquid coexistence state can be very small. The strong softening in the liquid phase also causes the unusual behavior of reentrant melting to occur at very high pressures. The onset of reentrant melting is predicted at ∼305 GPa, close to that at ∼300 GPa from the small-cell coexistence method. We show that the calculated melting points, considering reentrant melting, can be excellently fitted to a low-order Kechin equation, thereby making it possible for us to obtain a first-principles melting curve of Mg at pressures above 50 GPa for the first time. Similar characteristics in solid–liquid coexistence simulations, as well as reentrant melting, are also expected for other systems with strong softening in the liquid phase at high pressures.