Polymorphism and melt in high-pressure tantalum. II. Orthorhombic phases
JB Haskins and JA Moriarty, PHYSICAL REVIEW B, 98, 144107 (2018).
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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