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

TL;DR

This study combines ab initio calculations and machine learning to analyze hydrogen diffusion mechanisms and barriers in TiCr2H_x Laves phases, revealing concentration-dependent diffusion behavior and the influence of defects.

Contribution

It provides a comprehensive computational analysis of hydrogen diffusion pathways, barriers, and dynamics in TiCr2H_x alloys using DFT and MLIPs, highlighting the effects of concentration and defects.

Findings

Hydrogen diffusion barriers are higher for paths breaking Ti-H bonds.

Hydrogen prefers interstitial paths involving Cr-H bonds.

Diffusion coefficients show non-monotonic concentration dependence.

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.