Nearly metastable rhombohedral phases of bcc metals

摘要

The energy E(cla) for a bcc element stretched along its [001] axis (the Bain path) has a minimum at c/a=1, a maximum at c/a=2~(1/2), and an elastically unstable local minimum at c/a=2~(1/2). An alternative path connecting the bcc and fcc structures is the rhombohedral lattice. The primitive lattice has R3m symmetry, with the angle α changing from 109.4° (bcc), to 90° (simple cubic), to 60° (fcc). We study this path for the non-magnetic bcc transition metals (V, Nb, Mo, Ta, and W) using both all-electron linearized augmented plane wave and projector augmented wave vasp codes. Except for Ta, the energy E(α) has a local maximum at α=60°, with local minima near 55° and 70°, the latter having lower energy, suggesting the possibility of a metastable rhombohedral state for these materials. We first examine the elastic stability of the 70° minimum structure, and determine that only W is elastically stable in this structure, with the smallest eigenvalue of the elastic tensor at 4 GPa. We then consider the possibility that tungsten is actually metastable in this structure by looking at its vibrational and third-order elastic stability.