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

Abstract

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 quantumbased investigation of high-T,P polymorphism and melt in Ta that was begun in Paper I [Phys. Rev. B 86, 224104 (2012)] on five candidate cubic and hexagonal structures (bcc, A15, fcc, hcp and hex-w) to here treat four promising orthorhombic structures (Pnma, Fddd, Pmma and a-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-w structures can only be stabilized at high-T,P by large anharmonic vibrational effects, requiring systems of ~ 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-w 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 up to 420 GPa. MGPT-MD simulations further reveal spontaneous temperature-induced Pnma bcc and Fddd bcc transformations at modest temperatures, peaking at ~ 1450 K near 100 GPa. At high temperatures near melt, we find T-dependent and axial ratios and large stabilizing anharmonicity present in all four orthorhombic structures. The → → c / a b / a anharmonicity drives significantly larger melt size effects, requiring systems of ~ 1000-4000 atoms to produce converged melt curves for reliable predictions of relative thermodynamic stability. In the large-cell limit, with ~ 40,000 solid-phase atoms and accurate two-phase MGPT-MD melt simulation, we find that Pnma, Fddd and a-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 a-U remain highly competitive metastable phases that could co-exist 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.