It has been recently evidenced from transmission electronic microscopy [1] the capability of the oxygen atoms to order in titanium alloys. These ordered structures correspond to the Ti6O-type precipitates having the same crystalline structure as the matrix (namely α-hcp lattice) but with the oxygen atoms ordered in the interstitial sites instead of being randomly distributed. X-ray diffraction experiments also point out a slight variation of the lattice parameters [1] related to these ordered precipitates compared to the ones of the matrix. In addition, these studies [1] show that the oxygen ordering is observed even for a low oxygen content (~ 0.15 wt. %), raising the question of the solubility limit of oxygen in α -Ti. The latter is poorly known since no consensual value of the oxygen solubility limit (for a given temperature) emerges from studies reported in the literature.  Our work shows, by evaluating the formation enthalpies of different ordered and disordered compounds in the Ti - Ti6O composition range, that, for a given composition, the ordered structures are always more stable than disordered ones,  in agreement with experiments [1]. No intermediate stable structure at 0 K is found below the convex hull linking Ti and Ti6O. According to thermodynamics, a supersaturated Ti-O solid solution should decompose in Ti and Ti6O phases. Furthermore, by considering the contribution of the vibrational free energy within the quasi-harmonic approximation, we show in agreement with experiments [2] that the lattice parameters of these ordered and disordered compounds increase with oxygen content and that this increase is more important for c than for a parameter. At a given temperature and oxygen content, the oxygen ordering lead to an increase in the c parameter and a decrease in the a parameter. In order words, oxygen ordering in Ti-O alloys is associated to a slight variation of the lattice parameter in agreement with experiments [1]. Moreover, we set up a thermodynamic model relying on ab initio free energies and taking into account the contribution of vibrational energies to evaluate the solubility limit of oxygen in α-Ti as a function of temperature.

[1] Poulain et al.   “First experimental evidence of oxygen ordering in pure and commercially pure titanium”, submitted (2022).
[2] Wiedemann et al. “Micro hardness and lattice parameter calibrations of the oxygen solid solutions of unalloyed -titanium and Ti-6Al-2Sn-4Zr-2Mo”, Metall. Trans. 18, 1503-1510 (1987).