Nearly metastable rhombohedral phases of bcc metals
The energy E(c/a) 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, and an elastically unstable local minimum at c/a>2. An alternative path connecting the bcc and fcc structures is the rhombohedral lattice. The primitive lattice has R 3̄ m 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. © 2008 U.S. Government.
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- Fluids & Plasmas
- 09 Engineering
- 03 Chemical Sciences
- 02 Physical Sciences
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Published In
DOI
EISSN
ISSN
Publication Date
Volume
Issue
Related Subject Headings
- Fluids & Plasmas
- 09 Engineering
- 03 Chemical Sciences
- 02 Physical Sciences