Molybdenum at High Pressure and Temperature: Melting from Another Solid Phase

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.

Figure 1

The difference of the Gibbs free energies of the bcc and fcc phases of Mo as a function of pressure for several temperatures. A positive difference indicates that the fcc phase is more stable.

Figure 2

Data on the phase stability of Mo. The bcc-fcc phase boundary was constructed using the results shown in Fig. 1. Circles, diamonds, triangles and squares represent melting conditions obtained from AIMD for bcc and fcc Mo; the legend indicates the number of atoms in the AIMD simulation; except one point (bcc, 2-phase method) the $Z$ method was used. Unless shown explicitly, the error bar is smaller than the size of the corresponding symbol. Our fcc and bcc melting curves obtained from AIMD simulations are shown as solid thick and thin curves, respectively. The two points with temperature error bars are the solid-solid and solid-liquid transitions as measured in shock-wave experiments [2, 4]; the corresponding phases on the Hugoniot are shown as a solid curve (bcc phase), long dashed curve (another solid phase), and short-dashed curve (liquid).