Polymorphism and melt in high-pressure tantalum

Recent small-cell (150 atom) quantum molecular dynamics (QMD) simulations for Ta based on density functional theory (DFT) have predicted a hexagonal \ensuremath{\omega} (hex-\ensuremath{\omega}) phase more stable than the normal bcc phase at high temperature ($T$) and pressure ($P$) above 70 GPa [Burakovsky et al., Phys. Rev. Lett. 104, 255702 (2010)]. Here we examine possible high-$T,P$ polymorphism in Ta with complementary DFT-based model generalized pseudopotential theory (MGPT) multi-ion interatomic potentials, which allow accurate treatment of much larger system sizes (up to \ensuremath{\sim}80 000 atoms). We focus on candidate bcc, A15, fcc, hcp, and hex-\ensuremath{\omega} phases for the high-$T,P$ phase diagram to 420 GPa, studying the mechanical and relative thermodynamic stability of these phases for both small and large computational cells. Our MGPT potentials fully capture the $T=0$ DFT energetics of these phases, while MGPT-MD simulations demonstrate that the higher-energy fcc, hcp, and hex-\ensuremath{\omega} structures are only mechanically stabilized at high temperature by large, size-dependent, anharmonic vibrational effects, with the stability of the hex-\ensuremath{\omega} phase also being found to be a sensitive function of its $c/a$ ratio. Both two-phase and Z-method melting techniques have been used in MGPT-MD simulations to determine relative phase stability and its size dependence. In the large-cell limit, the two-phase method yields accurate equilibrium melt curves for all five phases, with bcc producing the highest melt temperatures at all pressures and hence being the most stable phase of those considered. The two-phase bcc melt curve is also in good agreement with dynamic experimental data as well as with the MGPT melt curve calculated from bcc and liquid free energies. In contrast, we find that the Z method produces only an upper bound to the equilibrium melt curve in the large-cell limit. For the bcc and hex-\ensuremath{\omega} structures, however, this is a close upper bound within 5$%$ of the two-phase results, although for the A15, fcc, and hcp structures, the Z-melt curves are 25$%$--35$%$ higher in temperature than the two-phase results. Nonetheless, the Z method has allowed us to study melt size effects in detail. We find these effects to be either small or modest for the cubic bcc, A15, and fcc structures, but to have a large impact on the hexagonal hcp and hex-\ensuremath{\omega} melt curves, which are dramatically pushed above that of bcc for simulation cells less than 150 atoms. The melt size effects are driven by and closely correlated with similar size effects on the mechanical stability and the vibrational anharmonicity. We further show that for the same simulation cell sizes and choice of $c/a$ ratio, the MGPT-MD bcc and hex-\ensuremath{\omega} melt curves are in good agreement with the QMD results, so the QMD prediction is confirmed in the small-cell limit. But in the large-cell limit, the MGPT-MD hex-\ensuremath{\omega} melt curve is always lowered below that of bcc for any choice of $c/a$, so bcc is the most stable phase. We conclude that for the non-bcc Ta phases studied, one requires simulation cells of at least 250--500 atoms to be free of size effects impacting mechanical and thermodynamic phase stability.