Machine Learning Potentials for Hydrogen Absorption in TiCr$_2$ Laves Phases

TL;DR

The paper tackles how hydrogen atoms occupy and order within TiCr2 Laves phases (C15 and C14) across a wide concentration range by combining first-principles DFT with active-learning–driven moment tensor potentials. It develops phase-specific MLIPs, uses BHMC to locate minimum-energy H configurations, and validates predictions against DFT, revealing solubility limits, two-phase regions, and novel ordered hydrides such as C15 with Cc symmetry at x ≈ 1 and C14 with Ama2 at x ≈ 1.5. The approach yields formation enthalpies and occupancy trends across 0 < x ≤ 6, reproducing experimental phase behavior at low temperatures and offering a robust framework for exploring PCT diagrams in hydrogen storage Laves-phase alloys. The work demonstrates that MLIPs can reliably extend first-principles insights to high-concentration regimes and complex ordering, enabling accelerated design of hydrogen storage materials.

Abstract

The energetics of hydrogen absorption in C15 cubic and C14 hexagonal TiCr$_2$H$_x$ 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 $α$ 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 TiCr$_2$H shows the $Cc$ monoclinic symmetry, while C14 TiCr$_2$H$_{1.5}$ shows the $Ama2$ orthorhombic symmetry, both of which have not been reported for this system. The first and the second hydride phases, i.e., $β$ and $β'$, at 0 K are found around $x = 3$ and $x = 4$, respectively, for both the C15 and the C14 phases. In the second-hydride $β'$ phases, C15 TiCr$_2$H$_4$ shows the $I4_1/a$ tetragonal symmetry, while C14 TiCr$_2$H$_4$ shows the $R\bar3c$ rhombohedral symmetry. Hydrogen repulsion are found to extend to edge-sharing interstices, affecting the hydrogen ordering. Furthermore, the $6h_2$ A$_2$B$_2$ interstices are found to be energetically substantially more preferable for C14 TiCr$_2$H$_x$ than the other A$_2$B$_2$ interstices at low hydrogen concentrations, influencing the hydrogen-occupation trend.

Figures (12)

• Figure 1: Crystal structures of (a) the C15 cubic and (b) the C14 hexagonal Laves phases. Elements A (Ti) and B (Cr) are shown as gray and blue spheres, respectively. The conventional unit cell of the C15 cubic phase is emphasized by the black lines, and the primitive unit cell is indicated by the purple lines. Visualization is performed using OVITO stukowski_visualization_2009.
• Figure 1: Mean numbers of neighboring hydrogen atoms sharing vertices, edges, and faces in TrCr2H_x in the simulations using the 48-metal-atom cells.
• Figure 1: Volume expansion of TiCr2H_x as a function of hydrogen concentration predicted by MTPs. Computational data are provided for $x$ in increments of 0.5. Experimental data are derived from Johnson and Reilly johnson_reaction_1978 for the C15 TiCr_1.8H_x at room temperature and from Klyamkin klyamkin_effect_1999 for C14 TiCr_1.8H_3.40 at 293K and 200MPa.
• Figure 2: Flowcharts depicting the methods to generate various types of configurations used for the training datasets of the MTPs. The technique also includes active-learning parts employing the already trained MTPs to look for additional configurations that further enhance the transferability of the MTPs.
• Figure 3: All symmetrically distinct face-sharing configurations together with their multiplicities and their hydrogen repulsion energies (meV/pair) in Table \ref{['tab:repulsion_faces']}.