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

TL;DR

This study uses advanced first-principles calculations to reassess phase stability of molybdenum under high pressure and temperature, revealing that anharmonic effects favor the bcc structure over fcc and hcp phases.

Contribution

It provides the first comprehensive anharmonic free energy calculations for molybdenum's high-pressure phases, challenging previous harmonic approximation results.

Findings

Anharmonic effects stabilize bcc over fcc and hcp at high P and T.

First-principles melting curves show bcc is more stable.

Z method simulations support bcc stability.

Abstract

We use first-principles techniques to re-examine 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 harmonic 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.