Constraints on the phase diagram of molybdenum from first-principles free-energy calculations

Abstract

We use first-principles techniques to reexamine the suggestion that transitions seen in high-$P$ experiments on Mo are solid-solid transitions from the bcc structure to either the fcc or hcp structures. We confirm that in the quasiharmonic approximation the free energies of fcc and hcp structures become lower than that of bcc at $P>325$ GPa and $T$ below the melting curve, as reported recently. However, we show that if anharmonic effects are fully included this is no longer true. We calculate fully anharmonic free energies of high-$T$ crystal phases by integration of the thermal average stress with respect to strain as structures are deformed into each other, and also by thermodynamic integration from harmonic reference systems to the fully anharmonic system. Our finding that fcc is thermodynamically less stable than bcc in the relevant high-$P$/high-$T$ region is supported by comparing the melting curves of the two structures calculated using the first-principles reference-coexistence technique. We present first-principles simulations based on the recently proposed Z method, which also support the stability of bcc over fcc.