Oxygen and nitrogen interstitial ordering in hcp Ti, Zr, and Hf: An<i>ab initio</i>study

Abstract

We investigate the ordering of oxygen and nitrogen interstitials in hcp Zr, Hf, and Ti using the corresponding oxygen-oxygen and nitrogen-nitrogen interactions obtained in the state-of-the-art first-principles calculations. Two main contributions, chemical and strain induced, to the interstitial-interstitial interactions are obtained by different techniques. We find that there is the strong repulsion between interstitial atoms at the nearest- and next-nearest-neighbor coordination shells, which is solely determined by the chemical interaction determined on a fixed ideal lattice, while both contributions are important for more distant coordination shells. The Monte Carlo simulations reveal the existence of three stoichiometric compositions, ${\text{MeI}}_{1/6}$, ${\text{MeI}}_{1/3}$, and ${\text{MeI}}_{1/2}$, for the ground-state structures of interstitials, having different ordering types. Our results for the structures of oxygen interstitials are in good agreement with existing experimental data for the Ti and Hf alloys. In the case of Zr-O interstitial alloys, we correctly predict the general type of ordering, although the detailed structure is at variance the experimental observations. The ordering transition temperatures in some cases are overestimated by a factor of 2. We also predict the ordering type of nitrogen interstitials in hcp Ti, Zr, and Hf, which are similar to those in the case of oxygen interstitials.