Environment Sensitive Embedding Energies of Impurities, and Grain Boundary Stability in Tantalum

Metalloid impurities have a very low solubility in Tantalum, and therefore prefer to segregate at the grain boundaries (GBs). In order to analyze the energetics of the impurities on the Tantalum GB, the LMTO calculations were performed on a simple 8-atom supercell emulating a typical (capped trigonal prism) GB environment. The so-called “environment-sensitive embedding energies” were calculated for Hydrogen, Boron, Carbon, Nitrogen, Oxygen, Phosphorus, and Sulphur, as a function of the electron charge density due to the host atoms at the impurity site. The calculations showed that, at the electron density typical of a GB, Carbon has the lowest energy (followed by Nitrogen and Boron) and thus would compete with the other impurities for the site on the GB, tending to displace them from the GB. The above energies were then used in a modified Finnis-Sinclair embedded atom approach for calculating the cohesive energies and the equilibrium interplanar distances in the vicinity of a (111) Σ3tilt GB plane, both for the clean GB and that with an impurity. These distances were found to oscillate, returning to the value corresponding to the equilibrium spacing between (111) planes in bulk BCC Tantalum by the 10th-12th plane off the GB. Carbon, Nitrogen and Boron somewhat dampen the deformation wave (making the oscillations less than in the clean GB), while Oxygen, Phosphorus and Sulphur result in an increase of the oscillations. The cohesive energies follow the same trend, the GB with Carbon being the most stable. Thus, Carbon, Nitrogen and Boron may be thought of as being cohesion enhancers, while Oxygen, Phosphorus and Sulphur result in decohesion effects.