Hydrogen diffusion in TiCr$_2$H$_x$ Laves phases: A combined ab initio and machine-learning-potential study

TL;DR

The paper addresses how hydrogen diffuses in TiCr2 Laves-phase alloys across C15 and C14 structures and varying hydrogen content. It combines DFT calculations of migration barriers with machine-learning interatomic potentials to perform large-scale MD and extract diffusion coefficients over wide temperature and concentration ranges. The key findings include a strong asymmetry between Ti–H and Cr–H breaking during jumps, a non-monotonic diffusion coefficient with hydrogen content, and Arrhenius diffusion with barriers around 0.21–0.25 eV that agree with many experiments; discrepancies in absolute diffusion values are attributed to defect trapping in non-stoichiometric samples and potential DFT functional limitations. This work demonstrates the utility of MLIPs for diffusion studies in complex Laves phases and provides atomistic insights to guide tuning of hydrogen kinetics in multi-component storage materials.

Abstract

The kinetics of hydrogen diffusion in C15 cubic and C14 hexagonal TiCr$_2$H$_x$ (0 < $x$ <= 4) Laves-phase hydrogen storage alloys is investigated with density functional theory (DFT) and machine learning interatomic potentials (MLIPs). Generalized solid-state nudged elastic band calculations are conducted based on DFT for all symmetrically inequivalent paths between the first-nearest-neighbor face-sharing interstitial sites. The hydrogen migration barriers are substantially higher for the paths that require breaking a Ti-H bond than for those that require breaking a Cr-H bond. Molecular dynamics (MD) simulations with the MLIPs also demonstrate that hydrogen migration occurs more frequently within the hexagonal rings made of the A$_2$B$_2$ interstitial paths, each requiring the breaking of Cr-H bonds, than along the inter-ring paths. The diffusion coefficients of hydrogen obtained from the MD simulations reveal a non-monotonic dependence on hydrogen concentration, which is more pronounced at lower temperatures. Time-averaged radial distribution functions of hydrogen further show that hydrogen avoids face-sharing positions during diffusion and that the hydrogen occupancy at the second-nearest-neighbor edge-sharing positions increases with increasing hydrogen concentration. The diffusion coefficients of hydrogen within 400-1000 K follow an Arrhenius relationship, with activation barriers consistent with most experimental values. One-order of magnitude overestimation of diffusion coefficients compared with some experiments suggests a substantial impact of hydrogen trapping by defects such as Cr vacancies and Ti anti-sites in non-stoichiometric TiCr$_2$ in experiments.

Figures (10)

• Figure 1: 48-metal-atom cells of the C15 cubic and the C14 hexagonal Laves phases together with symmetrically distinct interstitial sites. Ti--H bonds are depicted thicker than Cr--H bonds to indicate that the former requires higher energies to break during hydrogen migration (cf. Sec. \ref{['sec:results:migration_energies']}). The gray-colored cell for C15 represents a cubic supercell surrounding the 48-metal-atom cell.
• Figure 1: Diffusion coefficient of C15 TiCr$_2$H$_{3.0}$ as a function of supercell size. Error bars represent the standard deviations obtained from five independent MD simulations.
• Figure 2: All symmetrically distinct migration paths between face-sharing interstitial sites in the dilute limit (single hydrogen atom in the simulation cell). Arrows correspond to the available paths for hydrogen to migrate between two sites, along with their multiplicities and hydrogen migration barriers (meV) in Table \ref{['tab:migration']}. Loops indicate migration between the sites of the same type.
• Figure 2: Ratio of MSDs of hydrogen atoms parallel and perpendicular to the [0001] direction in C14 TiCr2H_1.0 from five independent MD simulations at different temperatures.
• Figure 3: Cages of A2B2 and AB3 interstitial sites surrounding A atoms in the AB2 Laves phases, which correspond to the diffusion pathways of hydrogen. Colored spheres represent interstitial sites, where the A2B2 sites are shown as larger spheres compared to the AB3 sites. Bonds between the interstitial-site spheres represent possible migration paths for hydrogen atoms, where thicker bonds show low-migration-energy paths within hexagonal rings associated with B–H bond breaking, and thinner bonds denote high-migration-energy paths requiring A–H bond breaking when jumping from the A2B2 sites. In the C15 Laves phase, the 96g sites form low-migration-energy hexagonal rings. In the C14 Laves phase, the 6h1–6h2 and the 12k2-24l sites form symmetrically distinct low-migration-energy hexagonal rings. (a) Part of the super-network of the cages in each Laves phase. (b) Expansion of a single cage in each Laves phase.