**Polymorphism and melt in high-pressure tantalum. II. Orthorhombic phases**

JB Haskins and JA Moriarty, PHYSICAL REVIEW B, 98, 144107 (2018).

DOI: 10.1103/PhysRevB.98.144107

Continuing uncertainty in the high-pressure melt curves of bcc
transition metals has spawned renewed research interest in the phase
diagrams of these materials, with tantalum becoming an important
prototype. The present paper extends the quantum-based investigation of
high-T, P polymorphism and melt in Ta that was begun in Paper I **Haskins
et al., Phys. Rev. B 86, 224104 (2012)** on five candidate cubic and
hexagonal structures (bcc, A15, fcc, hcp, and hex-omega) to here treat
four promising orthorhombic structures (Pnma, Fddd, Pmma, and alpha-U).
Using DFT-based MGPT multi-ion potentials that allow accurate MD
simulations of large systems, we showed in Paper I that the mechanically
unstable fcc, hcp, and hex-omega structures can only be stabilized at
high-T, P by large anharmonic vibrational effects, requiring systems of
similar to 500 atoms to produce size-independent melt curves and
reliable calculations of thermodynamic stability. This reversed a
previous small-cell quantum-simulation prediction of a high-T, P hex-
omega phase. Subsequent DFT calculations have now suggested a more
energetically favorable and mechanically stable Pnma structure, which
again small-cell quantum simulations predict could be a high-T, P phase.
Our present MGPT total-energy and phonon calculations show that not only
Pnma, but all four orthorhombic structures considered here, are
similarly energetically favorable, and that Fddd in addition to Pnma is
mechanically stable at T = 0 up to 420 GPa. MGPT-MD simulations further
reveal spontaneous temperature-induced Pnma. bcc and Fddd. bcc
transformations at modest temperatures, peaking at similar to 1450 K
near 100 GPa. At high temperatures near melt, we find T-dependent c/a
and b/a axial ratios and large stabilizing anharmonicity present in all
four orthorhombic structures. The anharmonicity drives significantly
larger melt size effects, requiring systems of similar to 1000-4000
atoms to produce converged melt curves for reliable predictions of
relative thermodynamic stability. In the large-cell limit, with similar
to 40000 solid-phase atoms and accurate two-phase MGPT-MD melt
simulation, we find that Pnma, Fddd and alpha-U have melt temperatures
that are equal to bcc over small pressure ranges in the vicinity of 100
GPa, but that the orthorhombic melt temperatures never exceed bcc up to
420 GPa. This finding suggests that Pnma, Fddd, and alpha-U remain
highly competitive metastable phases that could coexist with bcc and
possibly be observed experimentally. Finally, to add additional insight
into our results we have constructed global Helmholtz free energies for
the A15, Pnma, and Fddd phases of Ta, complementing previous free
energies obtained for the bcc, fcc, and liquid phases.

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