Machine learning potentials for hydrogen absorption in TiCr2 Laves phases

The energetics of hydrogen absorption in C15 cubic and C14 hexagonal TiCr₂H_x Laves phases is investigated for 0 $<$ x $\le$ 6 with density functional theory (DFT) and machine learning interatomic potentials (MLIPs). The MLIPs are trained with configurations generated through a series of active-learning schemes. Basin-hopping Monte Carlo (BHMC) simulations based on the MLIPs predict minimum-energy hydrogen configurations, along with enthalpies of formation and hydrogen orderings. The obtained phase transformations at 0 K agree well with the experiments at low temperatures. The hydrogen solubility limits in the low-concentration $\alpha$ phases at 0 K are predicted to be x = 1.0 and x = 1.5 for the C15 and the C14 phases, respectively. At these concentrations, C15 TiCr₂H shows the $Cc$ monoclinic symmetry, while C14 TiCr₂H_1.5 shows the $Ama2$ orthorhombic symmetry, both of which have not been reported for this system. The first and the second hydride phases, i.e., $\beta$ and ${\beta }^{\prime }$, at 0 K are found around x = 3 and x = 4, respectively, for both the C15 and the C14 phases. In the second-hydride ${\beta }^{\prime }$ phases, C15 TiCr₂H₄ shows the $I{4}_1/a$ tetragonal symmetry, while C14 TiCr₂H₄ shows the $R\bar{3}c$ rhombohedral symmetry. Hydrogen repulsions are found to extend to edge-sharing interstices, affecting the hydrogen ordering. Furthermore, the 6h₂ A₂B₂ interstices are found to be energetically substantially more preferable for C14 TiCr₂H_x than the other A₂B₂ interstices at low hydrogen concentrations, influencing the hydrogen-occupation trend.